Answers
1) From the total of 17 marbles, Jacob takes 2 out at random. There are
[tex]\dbinom{17}2=C(17,2)=C^{17}_2=\dfrac{P(17,2)}{2!}=\dfrac{P^{17}_2}{2!}=\dfrac{17!}{2!(17-2)!}=136[/tex]
possible outcomes of the draw. (Lots of different notations are used for the binomial coefficient; the first one is my preference.) The number of ways to draw exactly 2 orange marbles is
[tex]\dbinom70\dbinom{10}2=1\cdot1\cdot45=45[/tex]
That is, of the 3 red and 4 blue marbles - or the 7 non-orange marbles - we want 0; of the 10 oranges, we want 2.
So the probability of drawing exactly 2 orange marbles is [tex]\dfrac{45}{136}\approx0.33[/tex].
2) Now Jacob draws 3 marbles, for which there are
[tex]\dbinom{17}3=680[/tex]
possible combinations. The event that Jacob draws at least 1 orange marble is complementary to the event that Jacob draws 0 orange marbles. So if we find the probabilty of drawing 0 oranges, then we subtract this from 1 to find the probability of drawing at least 1.
There are
[tex]\dbinom73\dbinom{10}0=35\cdot1=35[/tex]
possible ways of doing, so the probability of drawing 0 oranges is [tex]\dfrac{35}{680}[/tex], in turn making the probability of drawing at least 1, [tex]1-\dfrac{35}{680}=\dfrac{645}{680}\approx0.95[/tex].
3) This question is kinda ambiguous. It's not clear whether Jacob draws a marble with or without replacement.
If he does return a drawn marble to the bag, then for each draw, there is a [tex]\dfrac{10}{17}[/tex] probability that he draws an orange marble, and a [tex]\dfrac7{17}[/tex] probability of not. The draws are presumably independent of one another, so that the probability of drawing the first orange marble on the fourth attempt would be
[tex]\dfrac7{17}\cdot\dfrac7{17}\cdot\dfrac7{17}\cdot\dfrac{10}{17}=\dfrac{3430}{83521}\approx0.041[/tex]
If no replacements are made, then as non-orange marbles are drawn from the bag, the number of non-oranges and the total number of marbles both decrease by 1. Then the probability of drawing orange on the fourth draw would be
[tex]\dfrac{\dbinom71\dbinom61\dbinom51\dbinom{10}1}{\dbinom{17}1\dbinom{16}1\dbinom{15}1\dbinom{14}1}=\dfrac5{136}\approx0.037[/tex]
If you're supposed to round to the nearest hundredths place, your final answer should be acceptable either way.
4) We want the probability that a boat is made of wood given that it has chrome accents:
[tex]P(\text{wood}\mid\text{chrome})=\dfrac{P(\text{wood AND chrome})}{P(\text{chrome})}=\dfrac{70\%}{75\%}\approx93\%[/tex]
5) We apply the inclusion/exclusion principle:
[tex]P(\text{wood OR chrome})=P(\text{wood})+P(\text{chrome})-P(\text{wood AND chrome})[/tex]
[tex]P(\text{wood OR chrome})=90\%+75\%-70\%=95\%[/tex]
6) The events of a boat having chrome accents and a boat being made of wood are independent if and only if
[tex]P(\text{wood AND chrome})=P(\text{wood})\cdot P(\text{chrome)}[/tex]
But [tex]90\%\cdot75\%=67.5\%\neq70\%[/tex], so these two events are not independent.
Related Questions
Which fraction is halfway between 3/7 and 10/21
A.) 7/15
B.) 19/42
C.) 15/42
D.) 4/9
Answers
Answer:
B) 19/42
Step-by-step explanation:
To find the fraction halfway between 3/7 and 10/21 we first find the difference between the fractions, half it, and then add it back on to the smaller one.
Because 10/21 > 3/7 we subtract in that order
[tex]\frac{10}{21} - \frac{3}{7} = \frac{10}{21} - \frac{9}{21} = \frac{1}{21}[/tex]
Half of 1/21 is 1/42 and so the fraction halfway between 3/7 and 10/21 is
[tex]\frac{3}{7} + \frac{1}{42} = \frac{18}{42} + \frac{1}{42} = \frac{19}{42}[/tex]
PLEASE HELP! :( this table below shows the future value of a certificate of deposit (CD), after x years.Andre states the applied interest is simple interest.True or False? and why if you can?
Answers
Answer:
Andre states that the applied interest is simple interest, this statement is true.
Step-by-step explanation:
From the given table it is noticed that the value of y increased by 17.50 as the value of x increased by 1.
The rate of change is calculated as
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
For first two years the rate of change is
[tex]m=\frac{535.00-517.50}{2-1}=17.50[/tex]
The rate of change for next two years is
[tex]m=\frac{552.50-535.00}{2-1}=17.50[/tex]
Similarly, the rate of change for all years in 17.50.
Since the rate of change is same for all years, therefore the future value is increased by a constant rate, therefore the applied interest is simple interest.
So, the statement "the applied interest is simple interest" is true.
Step-by-step explanation: (Apex) just did the quiz 9/26/19
A construction worker estimates that a kitchen remodel will take 1 person 120 hours. If 4 people work on the job for 6 hours a day, how many days will it take for them to complete the job?
Answers
it would take five days for them to complete their job if you want an explanation just ask
It will take 5 days for the 4 people working 6 hours a day to complete the kitchen remodel.
Let's calculate the total work hours required to complete the kitchen remodel and then determine how many days it will take for the 4 people working 6 hours a day to finish the job.
The estimated total work hours for one person to complete the remodel is 120 hours.
Total work hours required = 120 hours
Now, we have 4 people working on the job, and each person works 6 hours a day.
Total work hours per day with 4 people = 4 people * 6 hours/person = 24 hours
To find the number of days it will take to complete the job, we divide the total work hours required by the total work hours per day with 4 people:
Number of days = Total work hours required / Total work hours per day with 4 people
Number of days = 120 hours / 24 hours/day
Number of days = 5 days
It will take 5 days for the 4 people working 6 hours a day to complete the kitchen remodel.
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plz answer its easy math.
Answers
Answer:
B and E
Step-by-step explanation:
The rules of indicies states:
[tex]x^{a}[/tex] ÷[tex]x^{b}[/tex] = [tex]x^{a-b}[/tex]
So [tex]3^{-8}[/tex] ÷ [tex]3^{-4}[/tex] = [tex]3^{-8 - - 4}[/tex] = [tex]3^{-4}[/tex]
So that means B is one of the correct answers.
To find the other correct value, you can divide the two fractions as stated in the question:
[tex]3^{-8}[/tex] by [tex]3^{-4}[/tex] = [tex]\frac{1}{81}[/tex]
81 is equivalent to 3⁴
So that means E is also correct.
Hope this helps!
[tex]\text{Use}\\\\\dfrac{a^n}{a^m}=a^{n-m}\\\\a^{-n}=\dfrac{1}{a^n}\\-----------------------\\\\\dfrac{3^{-8}}{3^{-4}}=3^{-8-(-4)}=3^{-8+4}=\underbrace{\boxed{3^{-4}}}_{\boxed{B.}}=\underbrace{\boxed{\dfrac{1}{3^4}}}_{\boxed{E.}}\\\\Answer:\ \boxed{B.\ and\ E.}[/tex]
Find greatest common factor of the following monomials
45m. 6m
Answers
Answer:
m
Step-by-step explanation:
The greatest common factor is the greatest number that will divide two values. We have two values 45m and 6m. Each has numbers which multiply together to give the number. We need to find the highest value or most in common they share. Each has the factors:
45m: 1, 5, 9, 45, m
6m: 1, 2, 3, 6, m
Both have 1 and m as factors. Our GCF is these two factors multiplied which is 1m=m.
At a school for performance art students 25 of the girls study music, 35 of the girls study dance, and 16 of the girls study music and dance. What fraction of those who study music also study dance?
Answers
25+35=60
Out of 60 students, 16 study both dance and music.
16/60
Divide both sides by 4, the GCF.
16/4=4
60/4=15
Your answer would be 4/15. Hope this helps! :)
I need help with -5 -3w = 7w please!
Answers
Answer: W= 0.5
Step-by-step explanation:
You add 3w to both sides to get -5= 10w and then you divide everything by 10 to get w= 0.5
-5 - 3w = 7w
-5 - 3w+3w = 7w+3w <<--- add 3w to both sides
-5 + 0w = 10w
-5+0 = 10w
-5 = 10w
10w = -5
10w/10 = -5/10 <<--- divide both sides by 10 to isolate w
w = -5/10
w = -1/2 <<--- reduce; this is the answer in fraction form
w = -0.5 <<--- this is the answer in decimal form
A garden is 6 yards 24 inches wide and 6 yards long. Write the ratio of the width to the length as a fraction in simplest form.
Answers
Answer: 10/9
Step-by-step explanation:
On the width:
6 yards = 18 feet
24 inches = another 2 feet
Total width = 20 feet
On the length:
6 yards = 18 feet
Ratio of width to length = (20 feet) / (18 feet) = 10/9
The actual width of the garden is 72 inches, which is equivalent to 2 yards
To determine the actual width of the flower garden, we need to use the given scale of 1:12. This means that 1 inch on the plan represents 12 inches in reality. Given that the flower garden is 6 inches wide on the plan, we set up a proportion to find the actual width.
The proportion is:
1 inch on plan : 12 inches in reality = 6 inches on plan : x inches in reality
So we calculate:
(1 inch / 12 inches) = (6 inches / x inches)
Now we solve for x:
1/12 = 6/x
x = 6 * 12
x = 72 inches
Therefore, the actual width of the garden is 72 inches, which can be converted into yards by knowing that 1 yard equals 36 inches. Thus, 72 inches is equivalent to 2 yards (since 72 / 36 = 2).
p=2L+2W find p if L=10 and W=5
Answers
Answer:
30
Step-by-step explanation:
When l = 10, and w = 5
Plug in 5 for "w" and 10 for "l" inside the equation.
p = 2(10) + 2(5)
Solve for the variable "p". Simplify the equation. Remember to follow PEMDAS. First, solve the multiplication
p = 20 + 10
Next, add.
p = 30
30 is your answer for p in this problem
~
24 is 4/5% of what number
Answers
Answer:
The number is 3000
Step-by-step explanation:
Is means equals
24 = 4/5 % *n
Lets change the percent to a decimal. To change percent, we move the decimal to places to the left.
4/5= .8
4/5 % = .8% = .008
24 = .008 *n
Divide each side by .008
24/.008 = .008n/.008
3000 = n
Write a numerical or variable expression for the quantity: the value in cents of n nickels
Answers
The value in cents of n nickels: 5n
The value in cents of d dimes and p pennies: 10d + p
The value in cents of w dollars: 100w
The next whole number following a whole number w: w + 1
The value in cents of n nickels can be written as a numerical or variable expression as 5n, with n representing the number of nickels. This is because each nickel is worth 5 cents.
Explanation:The quantity in cents of n nickels can be written as a numerical or variable expression. Because each nickel is worth 5 cents, you multiply the number of nickels, represented by n, by 5. This can be written as 5n. For example, if you have 4 nickels, you could calculate the total value in cents by multiplying 5 by 4, giving you 20 cents.
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52.85 ROUNDED AT NEAREST ONE
Answers
Answer: 53
52.85 is closer to 53, than it is to 52
The digit after the ones digit is 8, which is 5 or larger, so that tells us to round up from 52 to 53. We drop everything after the ones digit.
i am a fraction greater than 1/2 and less than 6/8
Answers
Answer:
5/8
Step-by-step explanation:
it is 5/8 because if it is greater than1/2, which =to 4/8, and less than 6/8, it must be the number in between, which is 5/8
faith buys 3 pounds of flour. she uses 1/4 pound each day. in how many days does she use up the flour. ANWSER QUICK!!!!!
Answers
solve equation for x
Answers
Answer:
n-20
--------
3a
Step-by-step explanation:
(3ax - n)/5 = -4
The first step is to multiply each side by 5 to get rid of the fraction
(3ax - n)/5 * 5= -4* 5
3ax - n = -20
Then we need to add n to each side.
3ax -n+n = -20+n
3ax = n-20
Divide each side by 3a to isolate x
3ax/3a = (n-20)/3a
x = (n-20)/(3a)
At the newest animated movie, for every 9 9 children, there are 4 4 adults. There are a total of 3 9 39 children and adults at the movie. How many children are at the movie?
Answers
Answer:
27 children.
Step-by-step explanation:
For every 9 children there are 4 adults .
x + y = 39 where x = number of children and y = number of adults.
and x/y = 9/4
so 4x = 9y
then x = 9y/4 , so substituting for x in the first equation:-
y + 9y/4 = 39 Multiplying through by 4:-
4y + 9y = 156
y = 156/13 = 12 so there are 12 adults
and 39 - 12 = 27 children
The problem is solved by using the ratio of children to adults and setting up a proportion. After cross-multiplying and solving the equation, it is determined that there are 27 children at the movie.
Explanation:This is a problem of ratio and proportion. In this case, the ratio of children to adults at the movie is 9 to 4. This means that for every 13 people at the movie (9 children plus 4 adults), 9 are children. We can set up a proportion to determine how many out of the total 39 people at the movie are children.
The proportion is:
9 children / 13 total people = x children / 39 total people
We can solve this problem by cross multiplying: 9 * 39 = 13 * x, which gives us: 351 = 13x. Dividing both sides of the equation by 13, we get: x = 27.
Therefore, 27 children are at the movie.
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A line passes through the point (2, -4) and has a slop of 0 what is the equation of the line. A.)y=2, B.) x=2, C.)y=-4 or D.)x=-2
Answers
Find the value x that makes ABCD a parallelogram
Answers
Answer:
D.) 6
Step-by-step explanation:
A parallelogram needs supplementary consecutive sides. To make 150 supplementary, it needs to add 30 to make 180 degerees.
5 * 6 = 30.
Therefore, the value of [tex]x=6[/tex] degree i.e., option (D) is correct answer.
What is the parallelogram?
A parallelogram is a simple (non- self-intersecting) quadrilateral with two pairs of parallel sides.
The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
A parallelogram needs supplementary consecutive sides.
So, to make the supplementary angle i.e., [tex]150[/tex] degree .It requires to add [tex]30[/tex] to make [tex]180[/tex] degree.
[tex]x=6\\5(6)=30[/tex]
Hence, the value of [tex]x=6[/tex] degree i.e., option (D) is correct answer.
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Solve for y?
y/4-y+1/5=y+2/8
A)y=-4
B)y=-11/3
C)y=18/7
D)y=-6
Answers
the correct answer to this question would be: y=8
−(−y+18)+11 =1
y−18+11 =1
y−7 =1
y =8
18 out of 20 is what percentage
Answers
I used Google and got 90%...if you simplify it you will get 9/10 which is a 90%
If 18 out of 20 is given. Then the percentage will be 90%.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol 'percent' is used to symbolize it.
The given number statement is 18 out of 20.
Then the percentage will be
P = 18/20 x 100
P = 90%
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A moving walkway at an airport moves at a pace of 1.75 feet per second. If you stand on the walkway as it moves, how long will it take to transport you 280 feet? CLEAR CHECK 160 seconds 278.25 seconds 490 seconds 625 seconds
Answers
Answer:
160 Seconds
Step-by-step explanation:
acceleration * seconds = distance
1.75 * (x) = 280
1.75x=280
x= 280/1.75
x= 160
In the given case, It will take 160 seconds to transport you 280 feet on the moving walkway.
To determine how long it will take to transport you 280 feet on a moving walkway, we can use the formula:
This formula is particularly useful in various scenarios, such as calculating travel time for a journey, determining how long it will take for an object to reach a certain location, or estimating the time it will take for a process to complete at a given speed.
Time = Distance / Speed
Plugging in the given values, we have:
Time = 280 feet / 1.75 feet per second = 160 seconds
Therefore, the correct answer is 160 seconds.
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This month salesperson A made 11% of $67,530. Salesperson B made 8% of $85,740. Who made more commission this month? How much did that salesperson make?
Answers
Answer: Salesperson A made $7,428.30 in commission which is $569.10 more than Salesperson A.
Step-by-step explanation:
A: $67,530 * 0.11 = $7,428.30
B: $85,740 * 0.08 = $6,859.20
$ 569.10
What is the domain and range for the following function and its inverse? f(x) = -x + 5
Answers
Answer:
Domain: [tex]\mathbb{R}[/tex]
Inverse: [tex]f^{-1}(x) = -x + 5[/tex]
Step-by-step explanation:
Since this is a linear function, the domain and range is simply the set of real numbers.
The inverse is obtain by switching the places of x and y, then solving for y.
Here,
y = -x + 5
So switching x and y,
x = -y + 5
Solving for y again,
y = -x + 5
Thus,
[tex]f^{-1}(x) = -x + 5[/tex]
Answer:
The domain of linear function is always the set of all real numbers
Range is also the set of all real numbers
[tex]f^{-1}=-x+5[/tex]
Step-by-step explanation:
[tex]f(x) = -x + 5[/tex]
Domain is the set of x value and range is the set of y value. There is no restriction for x and y in a linear function.
The domain of linear function is always the set of all real numbers
Range is also the set of all real numbers
Now find the inverse
[tex]f(x) = -x + 5[/tex]
Replace f(x) with y
[tex]y = -x + 5[/tex]
Replace x with y and y with x
[tex]x = -y + 5[/tex]
Subtract 5 from both sides
[tex]x-5=-y[/tex]
Divide both sides by -1
[tex]y=-x+5[/tex]
Replace y by f^-1
[tex]f^{-1}=-x+5[/tex]
Luke receives an electric bill of $84.21\$84.21$84.21 for the month of April. The electric company charges $0.14\$0.14$0.14 per kilowatt-hour (kWh)(\text{kWh})(kWh) of electricity. Given that April has 303030 days, about how many kilowatt-hours did Luke use per day during the month of April?
Answers
Answer:
The answer would be 20.05 hours per day.
Answer: There are 20.05 kwh that Luke use per day during the month of April.
Step-by-step explanation:
Since we have given that
Amount of electric bill = $84.21
Charges of electric company = $ 0.14 per kWh
We need to find the number of kilowatt hours.
Number of days in the month of April = 30 days
According to question,
[tex]84.21=0.14\times 30\times x\\\\84.21=4.2\times x\\\\\dfrac{84.21}{4.2}=x\\\\x=20.05\ kwh[/tex]
Hence, there are 20.05 kwh that Luke use per day during the month of April.
a tv screen is 38.4” wide and 3.2” high. determine the size of the tv
Answers
the TV screen would have an area of 122.88 inches
to find this all you would have to do is multiply the 38.4 by 3.2
Answer:
The size of the tv is 122.88", or 122.88 in²
Step-by-step explanation:
a = w * h
w = 38.4
h = 3.2
a = (38.4) * (3.2)
a = 122.88
The Ratio of 3 numbers id 2:7:1. The sum of the numbers is 30. What are the 3 numbers?
Answers
Answer:
Three numbers are : 6 , 21 and 3
Step-by-step explanation:
Given,
Ratio of 3 numbers is 2:7:1 .
We can assume 3 numbers as : 2x ,7x and x respectively.
According to the problem :
2x + 7x + x = 30 {The sum of the 3 numbers is 30}
10x = 30
x = 3
Hence 3 numbers are, x = 3
2x = 2*3 = 6
7x = 7*3 = 21
Therefore we get three numbers as : 6 , 21 and 3
Remember , you can check their ratios to cross check the correct answer.
Answer:
6, 21, and 3
Step-by-step explanation:
In 2005, joe planted a tree that was 3 feet tall. In 2010, the tree was 13 feet tall. Assuming the growth of the tree is linear, what was the rate of the growth of the tree?
Answers
Answer:
2 feet per year
Step-by-step explanation:
First, we need to find the amount it grew:
13 - 3 = 10
So between 2005 and 2010 it grew 10 feet.
Now to find the yearly growth we need to divide the distance by time:
10 ÷ 5 = 2
So it grew 2 feet per year.
Hope this helps!
If (-6,-38) and (5,28) are two anchor points on the trend line, then find the equation of the line
Answers
Answer:
The equation of the line is y = 6x - 2 .
Step-by-step explanation:
Formula for the equation of line is.
[tex](y - y_{1}) = m (x - x_{1})[/tex]
Where m is the slope.
[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
As given
If (-6,-38) and (5,28) are two anchor points on the trend line.
Than
[tex]m = \frac{28 - (-38)}{5 - (-6)}[/tex]
[tex]m = \frac{28 + 38}{5 + 6}[/tex]
[tex]m = \frac{66}{11}[/tex]
m = 6
Put the value in the equation of a line.
[tex](y - (-38)) = 6 (x - (-6))[/tex]
[tex](y + 38) = 6 (x + 6)[/tex]
[tex](y + 38) = 6x + 6\times 6[/tex]
[tex](y + 38) = 6x + 36[/tex]
y = 6x +36 - 38
y = 6x - 2
Therefore the equation of the line is y = 6x - 2 .
David deposits $230 into a savings account that accrues 12% interest compounded quarterly each year. How much money will dave earn in interest after 3 years?
A. $97.93
B. $99.38
C. $327.93
D. $329.38
Answers
Answer:
C. $327.93
Step-by-step explanation:
The formula for interest compounded quarterly is
A = P(1 + r/n)nt where P is the principal
r is the rate
t is the time in years
n is the compoundings per year
p =230 r= .12 t= 3 n =4 since it is quarterly
Substituting these in
A = 230 (1+ .12/4)^(3*4)
= 230(1.03)^12
=327.93
Answer:
The answer is C. $327.93
Hope this helps and have a Merry Christmas.
P.S. Could you make me brainlest? It would help SO much. Thanks!
On Monday, Harry had 75\%75% as many toys as Teddy did. On Tuesday, after Harry acquired 3232 more toys and Teddy acquired 15\%15% more than he had on Monday, Harry had as many toys as Teddy did. How many toys did Harry have on Monday?
Answers
Let the number of toys Teddy has on Monday = x
On Monday Harry has = 75% of x or 0.75x
As given, On Tuesday, after Harry acquired 32 more toys and Teddy acquired 15% more than he had on Monday, Harry had as many toys as Teddy did.
Toys Teddy has = [tex]x+\frac{15x}{100}[/tex]
=[tex]\frac{100x+15x}{100} =\frac{115x}{100}[/tex] = 1.15x .... (i)
Toys Harry has = 0.75x+32 ...... (ii)
As both have equal toys now, so equation (i) equals equation (ii)
[tex]1.15x=0.75x+32[/tex]
[tex]1.15x-0.75x=32[/tex]
[tex]0.4x=32[/tex]
x=80
Hence, Teddy had 80 toys on Monday.
And Harry had 75% of 80 toys = 60 toys on Monday.