Answer:
The probability that he drove the small car is 0.318.
Step-by-step explanation:
We are given that a friend who works in a big city owns two cars, one small and one large. One-quarter of the time he drives the small car to work, and three-quarters of the time he takes the large car.
If he takes the small car, he usually has little trouble parking and so is at work on time with probability 0.7. If he takes the large car, he is on time to work with probability 0.5.
Let the Probability that he drives the small car = P(S) = [tex]\frac{1}{4}[/tex] = 0.25
Probability that he drives the large car = P(L) = [tex]\frac{3}{4}[/tex] = 0.75
Also, let WT = event that he is at work on time
So, Probability that he is at work on time given that he takes the small car = P(WT / S) = 0.7
Probability that he is at work on time given that he takes the large car = P(WT / L) = 0.5
Now, given that he was at work on time on a particular morning, the probability that he drove the small car is given by = P(S / WT)
We will use the concept of Bayes' Theorem for calculating above probability;
So, P(S / WT) = [tex]\frac{P(S) \times P(WT/S)}{P(S) \times P(WT/S)+P(L) \times P(WT/L)}[/tex]
= [tex]\frac{0.25 \times 0.7}{0.25 \times 0.7+0.75 \times 0.5}[/tex]
= [tex]\frac{0.175}{0.55}[/tex]
= 0.318
Hence, the required probability is 0.318.
Felicia is buying a Crockpot that retails for $125. She has a coupon for $40 off of any item over $100. Calculate her percent savings if she uses the coupon
Answer:
32%
Step-by-step explanation:
Given
Cost of Crockpot = $125
Coupon = $40
Coupon applies on items greater than $100
Required
Percent saved if coupon is applied.
If she applies coupon on the Crockpot, then she'll be saving $40.
Percent Savings = Amount Saved / Total Amount
Percent Savings = $40/$125
Percent Savings = 0.32
Convert to Percentage
Percent Savings = 0.32 * 100%
Percent Savings = 32%.
Hence, she'd save 32% if she applies the coupon of $40 on the Crockpot
Answer:
percentage savings = 32%
Step-by-step explanation:
She is buying a Crock-pot that retails for $125 . She has a coupon for $40 off any time she bought over $100 item.
Her percentage saving can be calculated below.
The price of the crock-pot is $125 but the amount she bought it base on coupon she has will be $125 - $40 = $85.
The normal price of the crock-pot is $125 and she bought it base on her coupon for $85, then the percentage change is
percentage saving = amount saved/normal price × 100
percentage savings = 40/125 × 100
percentage savings = 4000/125
percentage savings = 32%
The amount you bought the crock-pot was less than the original price hence Felicia saved 32% of the original price.
Two different samples will be taken from the same population of test scores where the population mean and standard deviation are unknown. The first sample will have 25 data values, and the second sample will have 64 data values. A 95% confidence interval will be constructed for each sample to estimate the population mean. Which number of data values would you expect to give a greater precision (a smaller width) for estimating the population mean? The answer is the sample with data values.
Answer:
The sample consisting of 64 data values would give a greater precision.
Step-by-step explanation:
The width of a (1 - α)% confidence interval for population mean μ is:
[tex]\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{n}}[/tex]
So, from the formula of the width of the interval it is clear that the width is inversely proportion to the sample size (n).
That is, as the sample size increases the interval width would decrease and as the sample size decreases the interval width would increase.
Here it is provided that two different samples will be taken from the same population of test scores and a 95% confidence interval will be constructed for each sample to estimate the population mean.
The two sample sizes are:
n₁ = 25
n₂ = 64
The 95% confidence interval constructed using the sample of 64 values will have a smaller width than the the one constructed using the sample of 25 values.
Width for n = 25:[tex]\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{25}}=\frac{1}{5}\ [2\cdot z_{\alpha/2}\cdot \sigma][/tex]
Width for n = 64:[tex]\text{Width}=2\cdot z_{\alpha/2}\cdot \frac{\sigma}{\sqrt{64}}=\frac{1}{8}\ [2\cdot z_{\alpha/2}\cdot \sigma][/tex]
Thus, the sample consisting of 64 data values would give a greater precision.
The number of data values would you expect to give a greater precision (a smaller width) for estimating the population mean is 64 and this can be determined by using the formula of width.
Given :
The first sample will have 25 data values.The second sample will have 64 data values. 95% confidence interval.The following steps can be used in order to determine the number of data values would you expect to give a greater precision for estimating the population mean:
Step 1 - The below formula of width is used in order to determine the number of data values.
Step 2 - The formula of width is given below:
[tex]w = 2\times z_{\alpha /2}\times \dfrac{\sigma}{\sqrt{n} }[/tex]
where [tex]z_{\alpha /2}[/tex] is the z-score, [tex]\sigma[/tex] is the standard deviation, and 'n' is the sample size.
Step 3 - Now, at n = 25 the formula of 'w' becomes:
[tex]w = 2\times z_{\alpha /2}\times \dfrac{\sigma}{\sqrt{25} }[/tex]
[tex]w = \dfrac{1}{5}\left(2\times z_{\alpha /2}\times\sigma }\right)[/tex]
Step 4 - Now, at n = 64 the formula of 'w' becomes:
[tex]w = 2\times z_{\alpha /2}\times \dfrac{\sigma}{\sqrt{64} }[/tex]
[tex]w = \dfrac{1}{8}\left(2\times z_{\alpha /2}\times\sigma }\right)[/tex]
The number of data values would you expect to give a greater precision (a smaller width) for estimating the population mean is 64.
For more information, refer to the link given below:
https://brainly.com/question/12402189
The line that passes through the point (2,-8) and
has a slope of -1 is given by the equation y +
J(x-1
Answer:
y = -x - 6
Step-by-step explanation:
I graphed the coordinate point on the graph and found an equation of the line that goes through the point with a slope of -1.
Answer:
y = -x - 6
Step-by-step explanation:
What’s the correct answer for this?
Answer:
C.
Step-by-step explanation:
Lines with equal slopes are parallel since their slopes are equal so they are parallel.
What is the simplified form of the following expression? Assume x greater-than 0
RootIndex 4 StartRoot StartFraction 3 Over 2 x EndRoot EndFraction
StartFraction RootIndex 4 StartRoot 6 x EndRoot Over 2 x EndFraction
StartFraction RootIndex 4 StartRoot 24 x cubed EndRoot Over 2 x EndFraction
StartFraction RootIndex 4 StartRoot 24 x cubed EndRoot Over 16 x Superscript 4 Baseline EndFraction
RootIndex 4 StartRoot 12 x squared EndRoot
Answer:
b
Step-by-step explanation:
i took the test myself
Answer:
B
Step-by-step explanation:
Edge 2022
Imagine that you are an engineer for a soda company, and you are tasked with finding the most economical shape for its aluminum cans You are given a set of constraints: the can must hold a volume of liquid and be a cylindrical shape of height hand radius r, and you need to minimize the cost of the metal required to make the can
Look at a variety of aluminum cans of different sizes from the supermarket. Which models from problems a–c best approximate the shapes of the cans? Are the cans actually perfect cylinders? Are there other assumptions about the manufacture of the cans that we should take into account? Do a little bit of research, and write a one-page response to answer some of these questions by comparing our models to the actual dimensions used.
Answer:
The answer to that depends on the company
Step-by-step explanation:
Solve for x in terms of b and K:
bx - 2 = K
Answer:
x=1b(k+2)=1b(k+2.0)
= k+2/x
Step-by-step explanation:
Step 1: Add 2 to both sides.
Step 2: Divide both sides by x
Answer: x=1b(k+2)=1b(k+2.0)
Hope this helps.
Find if there was a mistake in the students work.
Answer:
b
Step-by-step explanation:
Taylor is playing a board game with two friends. Using a single dice, one friend rolled a one, and the other friend rolled a three. Taylor needs to roll a number higher than both friends in order to win the game, and she wants to calculate her probability of winning. Is the probability of Taylor winning an independent even or dependent even? Why?
A. Her probability of winning is a dependent event because it doesn’t depend on the results of her friends roll
B. Her probability of winning is an independent event because it doesn’t depend on the results of her friends rolls
C. Her probability of winning is dependent event because it depends on the results of her friends rolls
D. Her probability of winning is an independent event because it depends on the results of her friends roll
Answer: C. Her probability of winning is dependent event because it depends on the results of her friends rolls.
Step-by-step explanation: In probability, dependent event is an event that is affected by the outcome of another event.
In a dice there are 6 possibilities: numbers 1, 2, 3, 4, 5 and 6. To win the game, Taylor has to roll a number higher than 1 or 3, i.e. she has to roll the numbers 4, 5 or 6.
The probability of that happening is: P(a) = 3/6 = 1/2 = 50%.
Therefore, the events are dependents, because it depended on the outcome of the friends playing the game.
Suppose A is n x n and the equation Ax = 0 has only the trivial solution. Explain why A has n pivot columns and A is row equivalent to In.
A. Suppose A is n x n and the equation Ax = 0 has only the trivial solution. Then there are no free variables in this equation, thus A has n pivot columns. Since A is square and the n pivot positions must be in different rows, the pivots in an echelon form of A must be on the main diagonal. Hence A is row equivalent to the nxn identity matrix, In
B. Suppose A is n x n and the equation Ax = 0 has only the trivial solution. Then there are no free variables in this equation, thus A has n pivot columns. Since A is square and the n pivot positions must be in different rows, the pivots in A must be on the main diagonal. Hence A is the nxn identity matrix, In.
C. Suppose A is n x n and the equation Ax=0 has only the trivial solution. Then there are n free variables in this equation, thus A has n pivot columns. Since A is square and then pivot positions must be in different rows, the pivots in an echelon form of A must be on the main diagonal. Hence A is row equivalent to the nxn identity matrix, In.
Answer:
i think that the answer is like hhhhhhhhhhhhhhhhhhhhhh
Step-by-step explanation:
Which is the equation of a parabola with vertex (0,0) and focus (0,2)?
Answer:
The equation of the parabola is y=(1/8)x^2
[tex]y=\dfrac{1}{8}x^2[/tex]
Step-by-step explanation:
We know the vertex (0,0) and the focus (0,2) of the parabola.
The equation in vertex form is written as:
[tex]y=a(x-h)^2+k\\\\\text{vertex}=(h,k)[/tex]
Then, in this case, we have the equation:
[tex]y=a(x-0)^2+0=ax^2[/tex]
As the focus is (0,2), it is at a distance of 2 units from the vertex (0,0).
For the focus, we have the following equation:
[tex]4p(y-k)=(x-h)^2[/tex]
where p is the distance from the focus to the vertex (in this case, p=2).
h and k are the vertex coordinates, both 0.
So we have:
[tex]4p(y-k)=(x-h)^2\\\\4(2)(y-0)=(x-0)^2\\\\8y=x^2\\\\y=\dfrac{1}{8}x^2[/tex]
What’s the area of this figure?
Answer:
C. 155.5 cm2
Step-by-step explanation:
area = 5*15 + (15+8)*7/2 = 75 + 80.5 = 155.5 cm2
What is the volume of an ice cream cone if the radius is 2 cm and the height is 7 cm
Hello!
Answer:[tex]\boxed{ \bf The~volume~is~29.32~cm^3.}[/tex]
___________________________________________________
Explanation:To find the volume of the cone, we must use a certain formula:
V = [tex]\frac{1}{3}[/tex]πr²h
Let's plug in our values:
V = [tex]\frac{1}{3}[/tex]π(2)²(7)
V = [tex]\frac{1}{3}[/tex]π(4)(7)
V = [tex]\frac{1}{3}[/tex]π(28)
V = 29.32
The CPI for "personal computers and peripheral equipment" in June 2006 was 10.7 (1982-1984 = 100). Interpret this index.
A. There was no significant increase in the price of "personal computers and peripheral equipment"
B. The price of "personal computers and peripheral equipment" increased 10.7%.
C. The price of "personal computers and peripheral equipment" decreased 89.3%.
D. If the average price of a computer in 1982-1984 was $3000.00, the CPI for "personal computers and peripheral equipment" would predict that the price of a computer in June 2006 would be $893.
Answer:
C. The price of "personal computers and peripheral equipment" decreased 89.3%.
Step-by-step explanation:
Consumer Price Index (CPI) measures change in price level, of weighted average market basket of consumer goods & services produced by households.
CPI calculated change in current year price level with regards to base year price level, base year price = 100. CPI > 100 implies that inflation (price rise) has occurred in current year from base year. CPI < 100 implies that deflation (price fall) has occurred in current year from base year.
CPI for 'personal computers & equipment' = 10.7 implies that prices of 'personal computers & equipment' have fallen or deflated. As per base year price = 100, prices have fallen by 100 - 10.7 = 89.3%
Answer:
The answer is "Option B"
Step-by-step explanation:
[tex]CPI = 10.7 \ in \ (\ june, \ 2006) \\\\CPI_{2006}= \frac{\ cost \ of \ basket \ of \ year \ 2006}{\ cost \ of \ basket \ of \ year \ 1982 \ to \ 84} \times 100\\\\\frac{10.7}{100} =\frac{\ cost \ of \ basket \ of \ year \ 2006}{\ cost \ of \ basket \ of \ year \ 1982 \ to \ 84}\\\\[/tex]
The cost of basket [tex]_{1982 \ to 1984} \times 0.107= \ cost \ of \ basket_{2006} \\\\[/tex]
[tex]\ cost \ of \ basket_{1982 \ to 1984} \ is \ given \ as \ 100\\\therefore \ \ cost \ of \ basket_{2006} = 100 \times 0.107\\\\[/tex]
[tex]\ = 10.7\\\\[/tex]
So, the answer is 10.7 % .
Find X such that f(x)=0 for f(x)= -2x^2-x
Answer:
[tex]x=\{-\frac{1}{2} ,\:0\}[/tex]
Step-by-step explanation:
[tex]f(x) =-2x^2 -x\\plug \: f(x) =0\\0= -2x^2 -x\\2x^2 + x = 0\\x(2x+1) = 0\\\therefore x =0 \: or \: 2x+1 = 0\\\therefore x =0 \: or \: 2x = -1\\\\\therefore x =0 \: or \: x = -\frac{1}{2} \\\\x=\{-\frac{1}{2} ,\:0\}[/tex]
If the function m(x) has the point (5, 2) on its graph name a point that would be on the function m(5x).
(1, 2)
(10, 2)
(5, 10)
(25, 2)
Answer:
21
Step-by-step explanation:
The radius of a circle is 11 in. Find its area in terms of \piπ.
Answer:
A = 121 pi in^2
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
A = pi * 11^2
A = 121 pi in^2
Answer:
121 pi in^2
Step-by-step explanation:
Area = pi *. R^2
= pi x 11^2= 121pi. in^2
Give step by step answer
Answer:
2 1/2 cups of vegetables
Step-by-step explanation:
This is an averages question, so add all numbers and divide by amount of numbers
2+1+2+1+3+6=15
15/6=2 1/2
Answer:
Nancy put 3 cups of vegetables in each container.
Step-by-step explanation:
1. Add the amount of vegetables together
2. Divided the number of vegetables by 5, since they are put into 5 separate containers.
____________________________________________________________2+1+2+1+3+6 = 15
15 divided by 5 or 5 x ? = 15
What’s the correct answer for this?
Answer:
c) √137
Step-by-step explanation:
Explanation:-
The distance between two points formula
[tex]\sqrt{(x_{2}-x_{1} )^{2} + (y_{2} -y_{1} )^{2} }[/tex]
Given points are R (3,7) and S(-1,-4)
[tex]RS = \sqrt{(-1- (3 )^{2} + (-4 -7 )^{2} }[/tex]
[tex]RS = \sqrt{(-4 )^{2} + (-11 )^{2} }[/tex]
[tex]RS = \sqrt{16 + 121 }[/tex]
RS = √137
The distance between the two points are RS = √137
Please help !!!!ASAP!!!!
Please answer the Picture below.
Answer:
Part A) shorter base = 6 yd longer base = 8 yd
Part B) C. 42 yds²
Step-by-step explanation:
Part A) The width and the length of the shorter side are the same, at 6 yds each. The longer base is 8 yds because there is a spot of 1 yd on both sides of the shorter side, making the longer side.
Part B) Find the area of the square first.
A = L x W
A = 6 x 6
A = 36 yds²
Next, find the area of a triangle and multiply the answer by 2 because there are two triangles.
A = 1/2bh
A = 1/2(1)(6)
A = 1/2(6)
A = 3(2)
A = 6 yds²
Add together all of the area measurements to find the area of the entire figure
36 + 6 = 42 yds²
Matthew has 3.5 pounds of clay to make ceramic objects.
he needs 1/2 of a pond of clay to make one bowl.
A.how many bowls can Matthew make with his clay
B. Matthew can make two mugs with the same amount of clay he uses to make one ceramic bowl. How much clay does he need to make with all of his clay
Step-by-step explanation:
Step 1: Answer part a
He has 3.5 pounds of clay and each bowl is 0.5 pounds of clay. Therefore, 3.5 / 0.5 will give us the amount of bowls he can make.
3.5 / 0.5
7
Answer: He can make 7 bowls
Step 2: Answer part b
I don't really understand what the questions asking about how much clay does he need to make with all of his clay. If you explain what that means I can answer it.
If you meant how much mugs he is able to make → 14
If you meant how much clay he needs to have for each mug → 0.25
Answer & Explanation:
Part A
It gives us 2 numbers to determined how much bowls he can make.
He need 0.5 of clay to make 1 bowl and he has 3.5 pounds of clay.
[tex]3.5[/tex] ÷ [tex]0.5[/tex]
= [tex]7[/tex]
He can make 7 bowls out of the 3.5 pounds of clay that he has.
Part B
This question is very confusing...
He can make 1 mug with 0.25 pounds of clay.
[tex]3.5[/tex] ÷ [tex]0.25[/tex]
= [tex]14[/tex]
He can make 14 mugs if he uses all of his clay.
hope this helps
give brainliest if you please
a sector with a area of 11 over 2 pi cm squared has a radius of 3 cm
Answer:
Step-by-step explanation:
Step-by-step explanation:
Area of sector = angle/360 * pi * r^2
5.5pi = angle/360 * pi * 9
5.5 = angle/360 * 9
angle = (5.5 * 360)/9 = 40 * 5.5 = 220
help plz I need big help someone plz help me with this question!
Answer:
Step-by-step explanation to be honest probably 12 if not i’m so sorry
Which table represents the statement “A giraffe runs at a rate of 32 miles per hour”? A 2-column table with 3 rows. Column 1 is labeled hours with entries 1, 2, 3. Column 2 is labeled Distance with entries 32, 64, 96. A 2-column table with 3 rows. Column 1 is labeled hours with entries 1, 2, 3. Column 2 is labeled Distance with entries 16, 32, 48. A 2-column table with 3 rows. Column 1 is labeled hours with entries 1, 2, 3. Column 2 is labeled Distance with entries 8, 16, 24. A 2-column table with 3 rows. Column 1 is labeled hours with entries 1, 2, 3. Column 2 is labeled Distance with entries 32, 33, 34.
Answer:
The answer is A.
Step-by-step explanation:
Answer:
Step-by-step explanation:
A
30 POINTS!!!!! URGENT!
Step-by-step explanation:
Average daily balance: Add all balances up and divide by the number of days.
157.63*9+239.98*1+239.98*4+180.38*1+180.38*9+190.57*1+190.57*6 gives us our total of 5756.36, and there were 9+1+4+1+9+1+6=31 days, so 5756.36/31 gives us our average of 185.69, or the fourth option
Daily interest rate: 24.99/365, as a percent, which is the first option
Finance charge: This is the cost of borrowing, and does not seem to be given, so we can take it to be the lowest amount, or the third value
New account balance: Again, this does not seem to be given, but the only option remaining is the second one
Answer:
Average daily balance: Add all balances up and divide by the number of days.
157.63*9+239.98*1+239.98*4+180.38*1+180.38*9+190.57*1+190.57*6 gives us our total of 5756.36, and there were 9+1+4+1+9+1+6=31 days, so 5756.36/31 gives us our average of 185.69, or the fourth option
Daily interest rate: 24.99/365, as a percent, which is the first option
Finance charge: This is the cost of borrowing, and does not seem to be given, so we can take it to be the lowest amount, or the third value
New account balance: Again, this does not seem to be given, but the only option remaining is the second one
m
Step-by-step explanation:
The tape diagram represents an equation.
Answer:
20
Step-by-step explanation:
6p = 120
p = 120/6
p = 20
Using the following data, calculate the mean absolute deviation:
10 7 1 6 7 9 8 10 2 5
What is the mean absolute deviation for these data? (60 points)
a) 2
b) 2.4
c) 6.5
d) 7
Answer:
2.4
Step-by-step explanation:
First we need to find the mean
Add up all the number
(10+ 7+ 1+ 6+ 7+ 9+ 8+ 10+ 2+ 5)/10
65/10 = 6.5
Then find the absolute difference from each point and the mean and sum them together and divide by the number of points
((10-6.5) + (7-6.5) +(6.5- 1) +(6.5-6) + (7-6.5)+( 9-6.5)+( 8-6.5)+ (10-6.5)+(6.5- 2)+(6.5- 5)) /10
24/10
2.4
Answer:
b) 2.4
Step-by-step explanation:
Mean = (10+7+1+6+7+9+8+10+2+5)/10
= 65/10 = 6.5
Sum|x-mean| = 3.5+0.5+5.5+0.5+0.5+2.5+1.5+3.5+4.5+1.5 = 24
MAD = 24/10 = 2.4
calculate the missing length on the right triangle solve for c using the z y t h a g o r e a n t h e o r e m a2 plus B2 equals C2
Answer:
Step-by-step explanation:
Since the diagram to this question is not given ; we will just explain the concept of the right angled triangle and a means by which we can use the Pythagoras theorem in solving such related question.
A right angled triangle has to legs which serves as the base line in which the height of the right angle is 90°.
Now; If we have a base line AB; let say , we chose any convenient radius at a and bisect an arc. at the arc we make another arc to the right ; we will have an angle at A which is 60°, So B will form a straight line up serving the role of the right angle which is 90° and where both met will be C which is 30°
So now we have a triangle ABC, if the line facing ∠ A = a ; the line facing ∠ B = b and the line facing ∠ C = c
Then; we can solve for side c if ; side a and side b are known by using the Pythagoras theorem.
Using Pythagoras theorem.
a² = b² + c²
-c² = b² - a²
Multiplying through with -
c² = - b² + a²
[tex]\mathbf{ c = \sqrt{-b^2 + a^2}}[/tex]
Since ; we already make c the subject of the formula; from the missing diagram, we can easily slot the values of a and b given to solve for the value of c using the above derived equation.
I hope that helps!.
Five friends plan to share the cost of a meal at a restaurant. Each friend’s share is at most $13. How much could the total meal cost?
Answer:
65
Step-by-step explanation:
Use the dimensions of the rectangular prism to label the indicated dimensions of its net.
Answer:
what do u mean
Step-by-step explanation: