The sub-questions for this question are:
a) construct a binomial distribution using n=6 and p=0.34
b) graph the binomial distribution using a histogram and describe it's shape
c) what values of the random variable would you consider unusual? Explain your reasoning.
Answer:
a)
P(X=0) =0.0827
P(X=1) = 0.255
P(X=2) = 0.329
P(X=3) = 0.226
P(X=4) = 0.087
P(X=5) = 0.018
P(X=6) = 0.0015
b) graph D
c) x=5 and x=6
Step-by-step explanation:
a)
Formula for binomial distribution:
nCx(p^x)(q^(n-x))
Number of sample, n = 6
probability of success, p = 0.34
probability of failure, q = 1-p = 0.66
P(X=0) = 6C0(0.34^0)(0.66^6)
= 1*1*0.0827 = 0.0827
P(X=1) = 6C1(0.34^1)(0.66^5)
= 6*0.34*0.1252 = 0.255
P(X=2) = 6C2(0.34^2)(0.66^4)
= 15*0.1156*0.1897 = 0.329
P(X=3) = 6C3(0.34^3)(0.66^3)
= 20*0.0113 = 0.226
P(X=4) = 6C4(0.34^4)(0.66^2)
= 15*0.0058 = 0.087
P(X=5) = 6C5(0.34^5)(0.66^1)
= 6*0.003 = 0.018
P(X=6) = 6C6(0.34^6)(0.66^0)
= 1*0.0015 = 0.0015
b) the shape of the graph is the graph shape. Referring to the attachment, the correct graph is D
c) the unusual values would be x=6 and x=5, because those values are too small and lower than 0.05
The number 2^1993 + 3^1993 is a multiple of 5. What is the units digit of the quotient (2^1993 + 3^1993)/5?
The units digit of the quotient (2^1993 + 3^1993)/5 is 9.
Explanation:The units digit of the sum of two numbers is determined by the units digit of each number. To find the units digit of 2^1993, we can observe the pattern of its units digits: the units digit of 2 repeats every four powers. Therefore, 2^1993 has the same units digit as 2^1, which is 2. Similarly, the units digit of 3^1993 is the same as the units digit of 3^3, which is 7.
Now, we can calculate the units digit of the sum: 2 + 7 = 9. Since the sum is divisible by 5, and the units digit is 9, the quotient (2^1993 + 3^1993)/5 has a units digit of 9 as well.
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You have 100 dollars, and there is a dollar bill behind each door. You roll a 100 sided die 100 times, and you take the dollar behind the door on the die roll if the bill has not been taken already (e.g. you roll 16, then you take the dollar behind door 16 if you haven’t already taken it). What is your expected payoff?
Answer:
63.21.
Step-by-step explanation:
You have 100 dollars, and there is a dollar bill behind each door. You roll a 100 sided die 100 times, and you take the dollar behind the door on the die roll if the bill has not been taken already (e.g. you roll 16, then you take the dollar behind door 16 if you haven’t already taken it). What is your expected payoff?
X=Σ100i=1 1Ai
where Ai is the event that door i is opened at least once, and 1Ai is the indicator function for event Ai.
Thus the expected payoff is:
E[X]=Σ100 as i=1 Pr[Ai].
to calculate Pr[Ai].
Ai∁ is the probability of the event that after 100 rolls, door i is not chosen, which is:
Pr[Ai∁]=(99/100)^100
Thus:
Pr[Ai]=1−Pr[Ai∁]=1−(99/100)^100.
E[X]=Σ100i=1Pr[Ai]=100×(1−(99/100)^100).
Also based on the following approximation for large n's:
(1−1n)n≈1e
we have:
(99/100)^100=(1−1/100)^100≈1/e.
The expected pay off is
E[X]=100×(1−(99/100)^100)≈100×(1−1/e)≈63.21.
In the scenario where you roll a 100-sided die 100 times to collect a dollar behind each numbered door, the expected payoff is $100, since each number has an equal likelihood of being rolled once.
Explanation:The question you're asking involves probability and expected value, a concept from mathematics specifically relevant in understanding outcomes in scenarios involving randomness and repetition, like the one described with 100-sided dice and dollars behind doors. When rolling a 100-sided die 100 times for dollars behind 100 doors, your expected payoff is relatively straightforward to calculate. Since each roll has an equal chance to land on any number between 1 and 100 and no number will be chosen more than once, the expected outcome is that you will roll each number once.
Thus, on average, you are expected to open each door exactly once, so the expected payoff would be neatly the sum of all the dollars behind every door. As there are 100 doors, each with a dollar behind it, your expected payoff is simply $100.
A rectangle has an area of 96cm2. The width is four less than the length. What is the perimeter?
Answer:
Step-by-step explanation:
Let L represent the length of the rectangle.
Let W represent the width of the rectangle.
The formula for determining the area of a rectangle is expressed
LW^2
The rectangle has an area of 96cm2. This means that
LW = 96 - - - - - - - - - - 1
The width is four less than the length. This means that
L = W + 4
Substituting L = W + 4 into equation 1, it becomes
W(W + 4)= 96
W^2 + 4W = 96
W^2 + 4W - 96 = 0
W^2 + 12W - 8W - 96 = 0
W(W + 12) - 8(W + 12) = 0
(W + 12)(W - 8) = 0
W = 8 or W = -12
Since the width cannot be negative, the W = 8cm
L = W + 4 = 8 + 4 = 12 cm
The formula for determining the perimeter of a rectangle is
Perimeter = 2(L + W)
Perimeter = 2(8 + 12) =2×20
Perimeter of rectangle = 40 cm
.
Final answer:
Perimeter is 40cm.
Explanation:
To find the perimeter of a rectangle with an area of 96 cm2 where the width is four less than the length, we first need to set up equations for the area and the relationship between the sides.
Let the length be represented by L and the width by W.
We know:
Area (A) = Length (L) × Width (W) = 96 cm2Width (W) = Length (L) - 4 cmWe can substitute the second equation into the first to find the length:
A = L × (L - 4 cm) = 96 cm2
L^2 - 4L - 96 = 0
(L - 12)(L + 8) = 0
L = 12
The perimeter (P) of a rectangle is given by 2 × Length + 2 × Width or P = 2L + 2W.
Substituting the values of L and W into this formula will yield the perimeter of the rectangle.
For example, if L = 12 cm (which is a possible solution to the above problem), then W = L - 4 cm = 8 cm.
Therefore, the perimeter would be:
P = 2L + 2W = 2(12 cm) + 2(8 cm) = 40 cm
A gas station sells 4820 gallons of regular unleaded gasoline in a day when they charge $1.35 per gallon, whereas they sell 3902 gallons on a day that they charge $1.40 per gallon. Find a linear function that expresses gallons sold as a function of price. (Hint: express the given information as two ordered pairs, and then find the equation of the line that goes through the two points.) Use this function to predict the number of gallons sold at a price of $1.22 per gallon.
Answer:
The linear function that expresses gallons sold as a function of price is [tex]y=-18360x+29606[/tex].
The number of gallons sold at a price of $1.22 per gallon is 7206.8
Step-by-step explanation:
Consider the provided information.
A gas station sells 4820 gallons of regular unleaded gasoline in a day when they charge $1.35 per gallon,
They sell 3902 gallons on a day that they charge $1.40 per gallon.
Let x represents the price per gallon and y represents the number of gallons sold.
Thus the ordered pairs are (1.35,4820) and (1.40,3902)
Now find the slope of line using the formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{3902-4820}{1.40-1.35}[/tex]
[tex]m=\frac{-918}{0.05}[/tex]
[tex]m=-18360[/tex]
Now find the slope intercept as shown:
[tex](y-y_1)=m(x-x_1)[/tex]
[tex](y-4820)=-18360(x-1.35)[/tex]
[tex]y=-18360x+24786+4820[/tex]
[tex]y=-18360x+29606[/tex]
Hence, the linear function that expresses gallons sold as a function of price is [tex]y=-18360x+29606[/tex].
The number of gallons sold at a price of $1.22 per gallon.
Substitute x=1.22 in above equation.
[tex]y=-18360(1.22)+29606[/tex]
[tex]y=-22399.2+29606[/tex]
[tex]y=7206.8[/tex]
Hence, the number of gallons sold at a price of $1.22 per gallon is 7206.8
A graphic distribution of the frequency and value of the numbers obtained while an imaging plate is being read is called what?
Answer:
Histogram
Step-by-step explanation:
A histogram is a type that has a wide application in the field of statistics. Histograms provide a visual interpretation of numerical data, indicating the number of data points within a range of values. These values are called classes or boxes. The frequency of data per class is illustrated by the use of a bar. The higher the rod, the higher the data values in the box. The following steps are followed to create a histogram
-Data of the group is sorted from small to large.
-The data group has an opening.
-The group width is calculated using the data opening and number of groups. The number of groups may be given to the question or asked to be determined by the solver.
The odd number closest to the number found is then taken as the group width. The reason for taking an odd number is to simplify the process by obtaining whole numbers in the calculations.
-The data is grouped in a group width and a table is created with the number of data belonging to each group.
-The groups in the table are placed on the vertical axis and the data numbers are placed on the horizontal axis and a histogram graph is created.
Fatima works at a bakery. She places 5 candied flowers on top of each cupcake she decorates. She Will decorate 2 dozen cupcakes today and 2 dozen tomorrow how many candied flower will Fatima use in these two days
Answer: 240 candied flowers
Step-by-step explanation:
She places 5 candied flowers on top of each cupcake she decorates. She will decorate 2 dozen cupcakes today. A dozen cupcakes is 12. 2 dozen cupcakes would be 24. Total number of candied flowers that she will place on top of each cupcake today would be 24 × 5 = 120 candied flowers.
She will also decorate 2 dozens tomorrow. Total number of candied flowers that she will place on top of each cupcake tomorrow would be 24 × 5 = 120 candied flowers
Total number if candied flowers that Fatima will use in 2 days would be 120 + 120 = 240
A fire department's longest ladder is 110 feet, and the maximum height it can be used for is 100 feet. What is the angle that ladder makes with the ground at the maximum height?
Check the picture below.
Answer: The angle that the ladder makes with the ground at the maximum height is 65.37 degrees
Step-by-step explanation:
The triangle ABC is formed by the ladder and the wall is shown in the attached photo.
The angle that the ladder makes with the ground at the maximum height is represented as #. To determine #, we will apply trigonometric ratio
Sin # = 0pposite side / hypotenuse.
Hypotenuse = 110
Opposite side = 100
Sin# = 100/110 = 0.909
# = Sin^(-1)0.909
# = 65.37
give the equation of the circle whose center is (5 -3) and goes through (2 5)
Answer:
Step-by-step explanation:
The standard form for the equation of a circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]
From the info given, we have the center, (h, k) as (5, -3) and the x and y coordinates of (2, 5). We will use these to solve for r-squared, then plug back in what we need to write the equation.
[tex](2-5)^2+(5-(-3))^2=r^2[/tex] which simplifies to
[tex](-3)^2+(8)^2=r^2[/tex] and
[tex]9+64=r^2[/tex] so
[tex]r^2=73[/tex]
Filling in the equation:
[tex](x-5)^2+(y+3)^2=73[/tex]
Mustafa, Heloise, and Gia have written more than a combined total of 222222 articles for the school newspaper. Heloise has written \dfrac{1}{4} 4 1 start fraction, 1, divided by, 4, end fraction as many articles as Mustafa has. Gia has written \dfrac{3}{2} 2 3 start fraction, 3, divided by, 2, end fraction as many articles as Mustafa has. Write an inequality to determine the number of articles, mmm, Mustafa could have written for the school newspaper.
Answer:
The Inequality For determining number of equation written by Mustafa for school paper is [tex]x+\frac{1}{4}x+ \frac{3}{2}x\geq 22[/tex].
Mustafa has written more than 8 articles.
Step-by-step explanation:
Given:
Combined Total Number of articles = 22
Let the number of articles written by Mustafa be 'x'.
Now Given:
Heloise has written [tex]\frac{1}{4}[/tex] as many articles as Mustafa has.
Number of article written by Heloise = [tex]\frac{1}{4}x[/tex]
Gia has written [tex]\frac{3}{2}[/tex] as many articles as Mustafa has.
Number of article written by Gia = [tex]\frac{3}{2}x[/tex]
Now we know that;
The sum of number of articles written by Mustafa and Number of article written by Heloise and Number of article written by Gia is greater than or equal to Combined Total Number of articles.
framing in equation form we get;
[tex]x+\frac{1}{4}x+ \frac{3}{2}x\geq 22[/tex]
Hence the Inequality For determining number of equation written by Mustafa for school paper is [tex]x+\frac{1}{4}x+ \frac{3}{2}x\geq 22[/tex].
Now Solving the Inequality we get;
Taking LCM for making the denominator common we get:
[tex]\frac{x\times 4}{4}+\frac{1\times1}{4\times1}x+ \frac{3\times2}{2\times2}x\geq 22\\\\\frac{4x}{4}+ \frac{x}{4}+\frac{6x}{4}\geq 22\\\\\frac{4x+x+6x}{4} \geq 22\\\\11x\geq 22\times4\\\\11x\geq 88\\\\x\geq \frac{88}{11} \\\\x\geq 8[/tex]
Hence Mustafa has written more than 8 articles.
Answer:
inequality - m+ 1/4m + 3/2m > 22
solution set - m>8
Step-by-step explanation:
Breandan makes a cranberry orange drink by mixing 15 cups of orange juice. If he uses 27 cups of orange juice how many cups of orange juice how many cranberry juice should he use to make.
To keep the taste consistent, Brendan should use 18 cups of cranberry juice to mix with 27 cups of orange juice, preserving the original 3:2 juice ratio.
Brendan's original mixture was 15 cups of orange juice to 10 cups of cranberry juice. This creates a ratio of 15:10, which simplifies to 3:2 when divided by 5. To maintain the same taste, Brendan will want to keep the same ratio.
Now to calculate the amount of cranberry juice needed for 27 cups of orange juice, we set up a proportion
Set up a proportion to find the unknown value (x), representing the amount of cranberry juice:
3/2 = 27/x
Cross-multiply to solve for x:
3x = 2 x 27
3x = 54
Divide both sides by 3 to solve for x:
x = 54 / 3
x = 18
Brendan should use 18 cups of cranberry juice to mix with 27 cups of orange juice to keep the taste of the drink consistent.
The complete question is:
Brendan makes a cranberry-orange drink by mixing 15 cups of orange juice with 10 cups of cranberry juice. If he uses 27 cups of orange juice, how many cups of cranberry juice should he use in order for the drink to taste the same?
Bankruptcy is a process when a lender tries to obtain money from an individual's employer to pay an unpaid debt.
Answer:
false
Step-by-step explanation:
Answer:
False!!!!!
Step-by-step explanation:
it is Garnishment, not Bankruptcy! Hope this helps yall.
In the United Kingdom,Alzheimer's disease is said to affect one in fifty people over 65 years of age.If approximately 250,000 people over 65 are affected in the UK, how many people over 65 are there in total? Answer total people over 65
Total people over 65 are :12,500,000
Step-by-step explanation:
Given that the disease affects 1/50 people over 65 years of age and it is approximated that 250,000 people over 65 years are affected then;
Form an expression for total number of people over 65 of age;
Let x be the total number of people over 65 of age
Then 1/50 *x = 250,000
x=250,000 *50 =12,500,000 people are over 65 years of age
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The length, width, and height of a rectangular prism is a, (a-13), and (a+13) respectively, which statement best describes (a-13)a. the width of the rectangular prism is 13 units less than the lengthb. the height of the rectangular prism is 13 units more than the lenghtc. the width of the rectangular prism is 13 units less than the heightd. the length of the rectangular prism is 13 units less than the weight
Answer:
a. The width of the rectangular prism is 13 units less than the length.
Step-by-step explanation:
From the information given we know that
a = length of rectangular prism and
[tex]a - 13[/tex] = width of rectangular prism
An expression like [tex]a - 13[/tex] means that we need to subtract 13 units from the length to obtain the width of the rectangular prism.
Therefore,
The width of the rectangular prism is 13 units less than the length.
Two percent of the jazz records sold in April were from a new label. About how many records were from the new label?
Approximately, 2% of the jazz records sold in April were from the new label.To find this, multiply the percentage (2%) by the total jazz records sold, expressing the percentage as a decimal (0.02). The formula is[tex]\( N = 0.02 \times J \),[/tex] where [tex]\( N \)[/tex] is the number of records from the new label, and [tex]\( J \)[/tex]is the total number of jazz records sold.
Explanation:In order to determine the number of jazz records sold from the new label in April, you need to multiply the percentage by the total number of jazz records sold. Let's denote the total number of jazz records as J. The formula for calculating the number of records from the new label (N) is given by:
[tex]\[ N = (2/100) \times J \][/tex]
This is based on the fact that 2% is equivalent to 0.02 when expressed as a decimal. Therefore, the number of records from the new label is obtained by multiplying 0.02 by the total number of jazz records (J). This calculation provides the direct answer to the question.
Understanding percentages is essential in various fields, and in this scenario, it helps determine the specific quantity of records from the new label in relation to the total jazz records sold. This mathematical approach allows for a precise estimation, providing insights into the market share or performance of the new label within the jazz genre for the specified period, in this case, the month of April.
A store buys a video game for the wholesale price of $39.99. The markup on the game is 70%. If sales tax is 8% then how much money would you need to buy the game?
Answer:The amount of money that you would need to buy the game is $73.324
Step-by-step explanation:
The store buys a video game for the wholesale price of $39.99. There was a markup of 70% on the price of the game. The value of the markup would be
70/100× 39.99 = 0.7×39.99 = $27.993
Cost of the game plus 70% markup would be
39.99 + 27.993 = $67.893
There is sales tax of 8% on the game. This means that the value of the tax would be
8/100 × 67.893 = 0.08 × 67.893 = $5.431
The amount of money that you would need to buy the game would be
67.893 + 5.431 = $73.324
Write in simple radical form:
(1 +[tex]\frac{1}{\sqrt{3} }[/tex]) / (1 - [tex]\frac{1}{\sqrt{3} }[/tex])
show steps.
Answer:
The answer to your question is [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Here, there is a difference of squares, so just solve it and simplify
[tex]( 1 + \frac{1}{\sqrt{3} } ) (1 - \frac{1}{\sqrt{3} } )[/tex]
Multiply the binomials
= 1 - [tex]\frac{1}{3}[/tex]
Simplify
= [tex]\frac{3 - 1}{3}[/tex]
= [tex]\frac{2}{3}[/tex]
Which of the equations below represents a line parallel to the y-axis? A. x = 4 B. x = -y C. x = y D. x = 4y
Answer:
b
Step-by-step explanation:
A landscaping company charges customers for lawn care based on the area of their yards. Mr. Jones was charged $52 for his yard, which is 40 feet by 65 feet. If a neighbor's yard is 50 feet by 80 feet, what would the neighbor be charged based on how much Mr. Jones was charged?
Answer: The neighbor would be charged $80
Step-by-step explanation:
The dimensions of Mr Jones's yard are 40 feet by 65 feet. This means that the shape of Mr Jones's yard is rectangular. The formula for determining the area of a rectangle is length × width. The area of the yard would be
40 × 65 = 2600 square feet
Mr. Jones was charged $52 for his yard. This means that the amount that he was charged per square foot would be 52/2600 = $0.02
If a neighbor's yard is 50 feet by 80 feet, it means that the area of his yard would be 50 × 80 = 4000 square feet. The amount that the neighbor would be charged is
4000 × 0.02 = $80
The company charges $0.02 per square foot. With the neighbor's yard having an area of 4000 square feet, the total cost would be $80.
Explanation:To determine how much the neighbor would be charged, we need to find out the price per square foot the landscaping company charges. We start with Mr. Jones's yard. His yard area is 40 feet by 65 feet; multiplying these gives an area of 2600 square feet. Now, the cost for his yard is $52; by dividing this by the area, we get a cost of about $0.02 per square foot. For the neighbor's yard, which is 50 feet by 80 feet, we multiply these values to get an area of 4000 square feet. At a rate of $0.02 per square foot, the total cost for the neighbor's yard would be 4000 square feet * $0.02/square foot = $80.
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Two number cubes with faces numbered 1 to 6 are rolled. What is the probability that that sum of the rolls is 8.
A. 1/12
B. 1/11
C. 1/9
D. 5/36
E. 1/6
Answer:
D
Step-by-step explanation:
Firstly, we need to know the number of total possible results. We can do this by placing the first die in horizontal band and the second die in vertical band.
The total number of results would be 36 results.
Now, to get the number of 8s
The possible sums that can give 8 is 2 and 6, 2and 5 and 3 with 4 and 4.
All are possible two times asides the 4 and 4 that could only show one time.
This means as we can have 2 and 6 we can also have 6 and 2
The total number of expected results is thus: 5/36
Final answer:
The probability of rolling a sum of 8 with two number cubes is 5/36.
Explanation:
To find the probability of rolling a sum of 8 with two number cubes, we need to look at all the possible combinations that result in an 8.
The number cubes (dice) each have faces numbered from 1 to 6.
We can roll a (2,6), (6,2), (3,5), (5,3), (4,4) to get a sum of 8.
This gives us a total of 5 favorable outcomes.
Since each die has 6 faces, the number of possible outcomes when rolling two dice is 6 x 6, which equals 36.
To get the probability of the sum being 8, we divide the number of favorable outcomes (5) by the total number of possible outcomes (36).
This calculation gives us the probability 5/36.
Please help!
Which is a solution to the linear function 5x – 2y = 12?
A. (3, –1)
B. (2, 1)
C. (3, 1)
D. (2, –1)
Please help I'm stuck :(
You are going on a trip to see friends in Georgia. At 8 am, you have driven 50 miles. By noon, you have driven 300 miles. At the same rate, how far have you driven by 2 pm?
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speed = distance/ time
speed = 250/4
speed = 62.5 mph
distance = speed x time
distance = 62.5 x 2
distance = 125 miles
Your answer is 125 miles
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How do you do this question?
Answer:
D) dy/dx > 0 and d²y/dx² > 0
Step-by-step explanation:
Use implicit differentiation to find dy/dx and d²y/dx².
x²y³ = 576
x² (3y² dy/dx) + (2x) y³ = 0
3x²y² dy/dx = -2xy³
3x dy/dx = -2y
dy/dx = -2y / (3x)
d²y/dx² = [ (3x) (-2 dy/dx) − (-2y) (3) ] / (3x)²
d²y/dx² = (-6x dy/dx + 6y) / (9x²)
d²y/dx² = (-6x (-2y / (3x)) + 6y) / (9x²)
d²y/dx² = (4y + 6y) / (9x²)
d²y/dx² = 10y / (9x²)
Evaluating each at (-3, 4):
dy/dx = -2(4) / (3(-3))
dy/dx = 8/9
d²y/dx² = 10(4) / (9(-3)²)
d²y/dx² = 40/81
Both are positive.
In order to raise revenue, the federal government planned a tax amnesty program that allows tax delinquents to pay all owed tax without added financial penalty. However, economists projected that the federal government would collect a far lower percentage of total tax owed by delinquents than did state governments implementing similar programs.
Answer:
The correct option is E: "Unlike most federal tax delinquents, most state tax delinquents fail to pay state tax because of an oversight rather than a decision not to pay."
Step-by-step explanation:
Option A is not the correct answer because it is out of context
Option B is also out of context because what we are looking for is a connection between defaulters at state and federal level
Option C is also wrong because it would lead to the direct opposite of the projection by economists.
Option D is also wrong because once again it is out of context.
Option E is correct
Roberto shares a bag of almonds with 2 friends. He shares 1/8 bag with Jeremy and 2/8 bag with Emily. He eats 3/8 bag of the almonds himself. What fraction of the almonds do Roberto and his friends eat?
Answer:The fraction of the almonds that Roberto and his friends ate is 3/4
Step-by-step explanation:
Let x represent the total number of almonds in the bag initially. He shares 1/8 bag with Jeremy. This means that the amount of almonds that he gave to Jeremy is 1/8 × x = x/8
He shares 2/8 bag with Emily. This means that the amount of almonds that he gave to Emily is 2/8 × x = 2x/8
He eats 3/8 bag of the almonds himself. This means that the amount of almonds that he ate is 3/8 × x = 3x/8
Total number of almonds that Robert and his friends ate would be
x/8 + 2x/8 + 3x/8 = 6x/8 = 3x/4
The fraction of the almonds that Roberto and his friends ate would be
(3x/4)/x = 3/4
Roberto and his friends eat a total of 3/4 of a bag of almonds, calculated by adding the fractions of the bag each person consumed.
Explanation:The student is asking how to calculate the total fraction of a bag of almonds eaten by Roberto and his friends. Roberto shares 1/8 of the bag with Jeremy, 2/8 of the bag with Emily, and eats 3/8 of the bag himself. To find the total fraction consumed, we add these fractions together:
1/8 (Jeremy) + 2/8 (Emily) + 3/8 (Roberto) = 6/8
Since 2/8 can be simplified to 1/4, and 6/8 can be simplified to 3/4, the total fraction of the almonds eaten by Roberto and his friends is 3/4 of the bag.
Suppose that x is normally distributed with a mean of 30 and a standard deviation of 3.What is P?
a) 0.469b) 0.956c) 0.493d) 0.490e) 0.466f) none of the above
Answer:
If we assume that the deviation is [tex]\sigma=3[/tex] then the solution is:
[tex]P(2.55<X<64.95)=P(-9.15<z<11.65)=P(z<11.65)-P(z<-9.15)[/tex]
f) None of the above
If we assume that the deviation is [tex]\sigma=15[/tex] then the solution is:
[tex]P(2.55<X<64.95)=P(-1.83<z<2.33)=0.956[/tex]
b) 0.956
Step-by-step explanation:
1) Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
2) Solution to the problem
Let X the random variable that represent the variable of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(30,3)[/tex]
Where [tex]\mu=30[/tex] and [tex]\sigma=3[/tex]
We are interested on this probability
[tex]P(2.55<X<64.95)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
If we apply this formula to our probability we got this:
[tex]P(2.55<X<64.95)=P(\frac{2.55-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{64.95-\mu}{\sigma})=P(\frac{2.55-30}{3}<Z<\frac{64.95-30}{3})=P(-9.15<Z<11.65)[/tex]
And we can find this probability on this way:
[tex]P(-9.15<z<11.65)=P(z<11.65)-P(z<-9.15)[/tex]
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
[tex]P(-9.15<z<11.65)=0.99999[/tex]
If we assume that the deviation is [tex]\sigma=15[/tex] then the solution is:
[tex]P(2.55<X<64.95)=P(\frac{2.55-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{64.95-\mu}{\sigma})=P(\frac{2.55-30}{15}<Z<\frac{64.95-30}{15})=P(-1.83<Z<2.33)[/tex]
And we can find this probability on this way:
[tex]P(-1.83<z<2.33)=P(z<2.33)-P(z<-1.83)[/tex]
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
[tex]P(-1.83<z<2.33)=0.956[/tex]
An Internet service provider allows a certain number of free hours each month and then charges for each additional hour used. Wells, Ted, and Vino each have separate accounts. This month the total hours used by Wells and Ted was 105, and each used all of their free hours. Their total cost was $\$10$. Vino used 105 hours by himself and had to pay $\$26$. What is the number of cents charged for each extra hour
To find the cost charged for each extra hour, we can set up a system of equations using the given information. By solving these equations, we can determine the value of the number of free hours provided (A) and the cost charged for each extra hour (z).
Explanation:To find the cost charged for each extra hour, we need to set up a system of equations using the given information. Let:
A = number of free hours providedx = hours used by Wells and Ted (105 hours in total)y = number of extra hours used by Wells and Tedz = cost charged for each extra hourw = hours used by Vino (105 hours)From the given information, we can set up the following equations:
2A + zy = 10 (equation 1)
w + z(w-1) = 26 (equation 2)
Since Wells and Ted used all of their free hours (A), the number of extra hours used by them would be x-A (105-A). So, we can substitute y = 105-A in equation 1:
2A + z(105-A) = 10
Simplifying this equation, we get:
2A + 105z - zA = 10
Combining like terms:
A(2-z) + 105z = 10
Solving equation 2 for z:
z = (26-w)/(w-1)
Substituting this value of z in equation 3:
A(2 - (26-w)/(w-1)) + 105(26-w)/(w-1) = 10
Simplifying this equation will give us the value of A, and from there, we can find the value of z.
The nth harmonic number is defined non-recursively as: 1 1/2 1/3 1/4 ... 1/n. Come up with a recursive definition and use it to guide you to write a method definition for a double-valued method named harmonic that accepts an int parameters n and recursively calculates and returns the nth harmonic number.
Answer:
57
Step-by-step explanation:
Plssssssssssssssssssss Answer this is Major?
This activity will help you meet these educational goals:
You will create a quadratic function to model the area of a bean-bag toss carnival game, and then graph it and examine its key features.
Your woodworking class is going to make games for the school carnival. You are in charge of making a rectangular game board for a bean bag toss. The length and width of the board have a specific relationship that is shown by the algebraic expressions in the image, which represents a possible finished game board. The units are in inches.
Part A
Enter the correct answer in the box.
Use the expressions that represent the length and width of the game board to write an equation that models the area of the figure. Let y represent the area, and write your answer in the form y = ax2 + bx + c, where a, b, and c are real numbers.
Part B
Graph the equation you wrote in part A. Adjust the zoom of the graphing window so the vertex, x-intercepts, and y-intercept can be seen.
Part C
The graph of a quadratic equation always has an extreme location (maximum or minimum). State whether the parabola opens upward or downward, whether it has a maximum or a minimum, and what the coordinates of that point are. Use the pointer tool to approximate the coordinates of this extreme location to the nearest whole number.
Part D
According to the graph, what is the maximum possible area of the game board? Give your answer to the nearest whole number. (Assume that the maximum area is not reduced by the open hole in the game board.)
Part E
Type the correct answer in each box.
Use the original expressions for the length and width, and substitute the x-coordinate from the extreme location. What are the length and width of the game board at the extreme location?
The length is ________________inches, and the width is ____________
inches.
Part F
What type of quadrilateral will be formed when the game board covers the maximum possible area?
Part G
Suppose the carnival director asks you to create a game board that is 1,120 square inches. Find the dimensions that would meet this request by setting the area equation equal to 1,120, solving for x, and substituting x into the expressions for the length and width. As before, assume the open hole in the game board does not affect the area calculation.
Part H
When you solved the area equation for x, did any extraneous solutions result? Describe how an extraneous solution would arise in this situation.
Part I
What method of solving quadratics did you use to solve the equation set equal to 1,120? Why did you choose this method? Discuss the usefulness of other methods of solving quadratics as they pertain to this scenario. Use this resource to help refresh your memory on methods for solving quadratic equations.
Answer:
See below because there are 9 parts (A through I)
Explanation:
Part A: write an equation that models the area of the figure. Let y represent the area, and write your answer in the form y = ax2 + bx + c.
The figure shows a rectangular table with these dimensions:
Length: - x + 64Witdth: x + 4The area of a rectangle is width × length:
[tex](x + 4)\times (-x+64)[/tex]Use distributive property:
[tex]x\cdot (-x)+x\cdot(64)+4\cdot (-x)+4\cdot (64)=-x^2+64x-4x+256[/tex]Simplify:
[tex]-x^2+64x-4x+256=-x^2+60x+256[/tex]Part B. Graph the equation you wrote in part A. Adjust the zoom of the graphing window so the vertex, x-intercepts, and y-intercept can be seen.
1. Factor the equation:
Common factor - 1:[tex]-x^2+60x+256=-(x^2-60x-256)[/tex]
Find two numbers that add - 60 and whose product is -256. Theyb are -64 and + 4[tex]-(x-64)(x+4)[/tex]
2. Find the roots:
Equal the expression to zero:
[tex]-(x-64)(x+4)=0\\ \\ x-64=0\implies x=64\\ \\ x+4=0\implies x=-4[/tex]
Those are the x-intercepts: (-4,0) and (64,0)
3. Find the symmetry axis:
The simmetry axis is the line x = the middle value between the two roots:
[tex]x=(64-4)/2=60/2=30[/tex]
4. Find the vertex
The vertex has x-coordinate equal to the x axis (30 in this case).
Substitute in the equation of find the y-coordinate:
[tex]y=-(30-64)(30+4)=-(-34)(34)=1,156[/tex]
Hence, the vertex is (30, 1,156)
5. Find the y-intercept
Make x = 0
[tex]y=-(x^2-60x-256)=-(0-256)=256[/tex]
Hence, the y-intercept is (0, 256)
With the x-incercepts, the y-intercept, the axis of symmetry, and the vertex, you can sketch the graph.
You can see now the graph in the attached figure
Part C. Extreme location of the graph
The graph shows that the parabola opens downward. That is due to the fact that the coefficient of the leading term (x²) is negative.
The parabola starts in the second quadrant. starts growing, crosses the x-axis at (-4,0), crosses the y-axis at (0,256), reaches the maximum value at (30, 1156), and then decreases toward the fouth quadrant, crossing the x-axis at (64,0).
Thus the vertex is a maximun, and the coordinates of the maximum are (30, 1156).
Part D. According to the graph, what is the maximum possible area of the game board? Give your answer to the nearest whole number. (Assume that the maximum area is not reduced by the open hole in the game board.)
The maximum possible area of the game is the maximum value of the function y = -x² + 60x + 256.
This value was calculated as y = 1156.
Part E. Use the original expressions for the length and width, and substitute the x-coordinate from the extreme location. What are the length and width of the game board at the extreme location?
The length is:
length = - x + 64 inchesx = 30length = - 30 + 64 = 34 inchesThe width is:
width = x + 4x = 30width = 30 + 4 = 34 inchesPart F. What type of quadrilateral will be formed when the game board covers the maximum possible area?
Since the length and the width are equal, the quadrilateral is a square.
Part G. Suppose the carnival director asks you to create a game board that is 1,120 square inches. Find the dimensions that would meet this request by setting the area equation equal to 1,120, solving for x, and substituting x into the expressions for the length and width.
[tex]y=-x^2+60x+256\\ \\ 1,120=-x^2+60x+256\\ \\ x^2-60x-256+1120=0\\ \\ x^2-60x+864=0[/tex]
Factor:
Find two numbers whose sum is - 60 and the product os 864. They are -24 and - 34:
[tex]x^2-60x+864=(x-24)(x-36)[/tex]
Use the zero product rule:
[tex](x-24)(x-36)=0\\ \\ x-24=0\implies x=24\\ \\ x-36=0\implies x=36[/tex]
Now substitute to find the dimensions:
x = 36
length = - x + 64length = - 36 + 64 = 28width = x + 4 = 36 + 4 = 40Hence, legth = 28, width = 40
x = 24
length = - x + 64 = -24 + 64 = 40width = x + 4 = 24 + 4 = 28Part H. When you solved the area equation for x, did any extraneous solutions result? Describe how an extraneous solution would arise in this situation.
The two solutions are valid (non extraneous) because both leads to positive real dimensions for which the areas can be 1,120 in².
28×40 = 1,12040×28 = 1,120An extraneous solution could arise if you try to find areas for which x is greater than or equal to 64, because in that case - x + 64 would be zero or negative and dimensions must be positive.
For the same reason, also an extraneous solution would arise if you try to fix areas for which x is less than or equal to - 4.
So, the domain of your function has to be - 4 < x < 64.
Part I. What method of solving quadratics did you use to solve the equation set equal to 1,120? Why did you choose this method?
The method use was factoring.
Discuss the usefulness of other methods of solving quadratics as they pertain to this scenario.
The other importants methods are graphical and the quadratic equation.
For graphical method you graph your parabola and find the values of x that sitisfies the area searched (value of y).
The quadratic equation gives the y-values (areas) without factoring:
[tex]\frac{-b+/-\sqrt{b^2-4(a)(c)} }{2(a)}[/tex]
Katherine owns a food truck that sells tacos and burritos. She only has enough supplies to make 106 tacos or burritos. She sells each taco for $3.50 and each burrito for $6.50. Katherine must sell a minimum of $470 worth of tacos and burritos each day. If 79 tacos were sold, determine all possible values for the number of burritos that Katherine must sell in order to meet the requirements. Your answer should be a comma separated list of values. If there are no possible solutions, submit an empty answer.
Answer:
No possible solutionsStep-by-step explanation:
She has the option for supplying the total of 106 items. This 106 items can be either tacos or burritos or both with a total of 106 items.
If 79 tacos are sold, then it gives [tex]79 \times 3.50 = 276.5[/tex]
She needs to make $470 in total.
She needs to make $(470 - 276.5) = $193.5 more till now.
After selling 79 tacos, she has an option to sell maximum (106 - 79) = 27 burritos.
If she wants to make $193.5, she needs to sell [tex]\frac{193.5}{6.5} = 29.7[/tex] that is 30 burritos.
As she can sell 27 burritos in maximum, so there is no possible solutions.
A woman is purchasing fruit for some pies she is making for a party she wants to purchase at least 10 pounds of strawberries and blueberries.Strawberries are sold for $2 per pound and blueberries are sold for $3 per pound she does no want to spend more that $25 total for the fruit
The system of inequalities to represent the situation is x + y ≥ 10 and
2x + 3y ≤ 25.
What is inequality?The relation between two unequal expressions is defined as inequality.
Given that, Strawberries are sold for $2 per pound, and blueberries are sold for $3 per pound.
Let the woman purchase x pounds of strawberries and y pounds of blueberries.
Given that, the woman wants to purchase at least 10 pounds of strawberries and blueberries, therefore,
x + y ≥ 10
The total cost of purchasing x pounds of strawberries and y pounds of blueberries is:
2x + 3y
Since the woman doesn't want to spend more than $25, it follows:
2x + 3y ≤ 25
Hence, the system of inequalities to represent the situation is x + y ≥ 10 and 2x + 3y ≤ 25.
To learn more about inequalities, click here:
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To calculate the total cost of the fruit, use the equation 2x + 3y ≤ 25, where x represents the pounds of strawberries and y represents the pounds of blueberries. Graph the inequalities to find the feasible region and determine the affordable combinations of strawberries and blueberries.
Explanation:To calculate the total cost of the fruit, we need to consider the cost of strawberries and blueberries separately. Let's assume the woman purchases x pounds of strawberries and y pounds of blueberries. The cost of strawberries is $2 per pound, so the cost of strawberries will be 2x dollars. Similarly, the cost of blueberries is $3 per pound, so the cost of blueberries will be 3y dollars. The total cost will be the sum of the cost of strawberries and blueberries, which should not exceed $25. Therefore, the equation becomes: 2x + 3y ≤ 25.
Since the woman wants to purchase at least 10 pounds of strawberries, we have another condition x ≥ 10. We can graph these inequalities on a coordinate plane and find the feasible region where both conditions are satisfied. From the graph, we can determine the possible combinations of strawberries and blueberries that meet the woman's requirements.
Once we find the feasible region, we can choose a few points within that region and calculate the total cost for each point. By comparing the total cost to $25, we can determine which combinations of strawberries and blueberries are affordable for the woman.