Answer:
[tex]P = \frac{2}{3}[/tex]
Step-by-step explanation:
All the points in the plane that are 20 inches from P constituing a circle with center in P and with radius 20 inch
We need find the angle in this circle by which the point R is closer to P than it is to Q. The limit situation occurs when the distances from P to R and from R to Q are equals and have the value 20 inches. In this situation the points P, R y Q form a equilater triangle with angles of value 60°.
Thus, the point R is closer to P than it is to Q in 240° of the circle, except 60° above of the line PQ and 60° below the line PQ.
Then the probability is
[tex]P= \frac{240}{360} = \frac{2}{3}[/tex]
A student bought a juice pouch forn$2.50 and 3 bags of chips. The total cost was $5.05.Write and solve an equation to determine the cost of a bag of chips,c
Answer:
The cost of a bag of chips is [tex]c=\$0.85[/tex]
Step-by-step explanation:
Let
c ----> the cost of a bag of chips
we know that
The cost of a juice pouch ($2.50) plus the cost of 3 bags of chips must be equal to $5.05
The cost of 3 bags of chips is equal to multiply 3 by its cost c
so
The linear equation that represent this situation is
[tex]2.50+3c=5.05[/tex]
solve for c
Subtract 2.50 both sides
[tex]3c=5.05-2.50[/tex]
[tex]3c=2.55[/tex]
Divide by 3 both sides
[tex]c=2.55/3[/tex]
[tex]c=\$0.85[/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.
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:
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]
Hank has a board 1.75 meters long. He used 0.8 meter to build the walls of a birdhouse. He used 0.4 of what is left for the floor. He needs 0.6 meter for the roof. Dies he have enough wood for the roof? Explain
Answer:No, he doesn't have enough wood for the roof.
Step-by-step explanation:
Total length of Hank's board is 1.75 meters. He used 0.8 meter to build the walls of a birdhouse. This means that the length of the board left would be
1.75 - 0.8 = 0.95 meters
He used 0.4 of what is left for the floor. This means that the length of the board left would be
0.95 - 0.4 = 0.55 meters
He needs 0.6 meter for the roof. Since he has only 0.55 meters left, then, he doesn't have enough wood for the roof.
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
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
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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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]
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.
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
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 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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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
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:
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:
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.
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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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.
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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.
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.
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.
A triangle is formed from the points L(-3, 6), N(3, 2) and P(1, -8). Find the equation of the following lines:
the median from N
the right bisector of LP
the altitude from N
Answer:
Part A) [tex]y=\frac{3}{4}x-\frac{1}{4}[/tex]
Part B) [tex]y=\frac{2}{7}x-\frac{5}{7}[/tex]
Part C) [tex]y=\frac{2}{7}x+\frac{8}{7}[/tex]
see the attached figure to better understand the problem
Step-by-step explanation:
we have
points L(-3, 6), N(3, 2) and P(1, -8)
Part A) Find the equation of the median from N
we Know that
The median passes through point N to midpoint segment LP
step 1
Find the midpoint segment LP
The formula to calculate the midpoint between two points is equal to
[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
we have
L(-3, 6) and P(1, -8)
substitute the values
[tex]M(\frac{-3+1}{2},\frac{6-8}{2})[/tex]
[tex]M(-1,-1)[/tex]
step 2
Find the slope of the segment NM
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
N(3, 2) and M(-1,-1)
substitute the values
[tex]m=\frac{-1-2}{-1-3}[/tex]
[tex]m=\frac{-3}{-4}[/tex]
[tex]m=\frac{3}{4}[/tex]
step 3
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{3}{4}[/tex]
[tex]point\ N(3, 2)[/tex]
substitute
[tex]y-2=\frac{3}{4}(x-3)[/tex]
step 4
Convert to slope intercept form
Isolate the variable y
[tex]y-2=\frac{3}{4}x-\frac{9}{4}[/tex]
[tex]y=\frac{3}{4}x-\frac{9}{4}+2[/tex]
[tex]y=\frac{3}{4}x-\frac{1}{4}[/tex]
Part B) Find the equation of the right bisector of LP
we Know that
The right bisector is perpendicular to LP and passes through midpoint segment LP
step 1
Find the midpoint segment LP
The formula to calculate the midpoint between two points is equal to
[tex]M(\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]
we have
L(-3, 6) and P(1, -8)
substitute the values
[tex]M(\frac{-3+1}{2},\frac{6-8}{2})[/tex]
[tex]M(-1,-1)[/tex]
step 2
Find the slope of the segment LP
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
L(-3, 6) and P(1, -8)
substitute the values
[tex]m=\frac{-8-6}{1+3}[/tex]
[tex]m=\frac{-14}{4}[/tex]
[tex]m=-\frac{14}{4}[/tex]
[tex]m=-\frac{7}{2}[/tex]
step 3
Find the slope of the perpendicular line to segment LP
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
[tex]m_1*m_2=-1[/tex]
we have
[tex]m_1=-\frac{7}{2}[/tex]
so
[tex]m_2=\frac{2}{7}[/tex]
step 4
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{2}{7}[/tex]
[tex]point\ M(-1,-1)[/tex] ----> midpoint LP
substitute
[tex]y+1=\frac{2}{7}(x+1)[/tex]
step 5
Convert to slope intercept form
Isolate the variable y
[tex]y+1=\frac{2}{7}x+\frac{2}{7}[/tex]
[tex]y=\frac{2}{7}x+\frac{2}{7}-1[/tex]
[tex]y=\frac{2}{7}x-\frac{5}{7}[/tex]
Part C) Find the equation of the altitude from N
we Know that
The altitude is perpendicular to LP and passes through point N
step 1
Find the slope of the segment LP
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
we have
L(-3, 6) and P(1, -8)
substitute the values
[tex]m=\frac{-8-6}{1+3}[/tex]
[tex]m=\frac{-14}{4}[/tex]
[tex]m=-\frac{14}{4}[/tex]
[tex]m=-\frac{7}{2}[/tex]
step 2
Find the slope of the perpendicular line to segment LP
Remember that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)
[tex]m_1*m_2=-1[/tex]
we have
[tex]m_1=-\frac{7}{2}[/tex]
so
[tex]m_2=\frac{2}{7}[/tex]
step 3
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=\frac{2}{7}[/tex]
[tex]point\ N(3,2)[/tex]
substitute
[tex]y-2=\frac{2}{7}(x-3)[/tex]
step 4
Convert to slope intercept form
Isolate the variable y
[tex]y-2=\frac{2}{7}x-\frac{6}{7}[/tex]
[tex]y=\frac{2}{7}x-\frac{6}{7}+2[/tex]
[tex]y=\frac{2}{7}x+\frac{8}{7}[/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.
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.
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.
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
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)
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.
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]