X and Y are independent random variables. X has mean 100 and standard deviation 12. Y has mean 30 and standard deviation 9. What are the mean and standard deviation of (X–Y)?

Answer:

3/8

Step-by-step explanation:

the total number of possible results is 4×4=16.

out of these 16 only the results

1 2

1 3

1 4

2 2

2 3

3 2

are desired results. these are 6.

so the probability of a desired result is 6/16 = 3/8

Answer:

[tex]\begin{array}{cc}{Class}& {Frequency} & 138 - 202 & 14 & 203 - 267 & 5 & 268 - 332 & 3 & 333 - 397 & 1 & 398 - 462 & 3 \ \end{array}[/tex]

The class with the greatest is 138- 202 and the class with the least relative frequency is 333 - 397

Step-by-step explanation:

Solving (a): The frequency distribution

Given that:

[tex]Lowest = 138[/tex] --- i.e. the lowest class value

[tex]Class = 5[/tex] --- Number of classes

From the given dataset is:

[tex]Highest = 459[/tex]

So, the range is:

[tex]Range = Highest - Lowest[/tex]

[tex]Range = 459 - 138[/tex]

[tex]Range = 321[/tex]

Divide by the number of class (5) to get the class width

[tex]Width = 321 \div 5[/tex]

[tex]Width = 64.2[/tex]

Approximate

[tex]Width = 64[/tex]

So, we have a class width of 64 in each class;

The frequency table is as follows:

[tex]\begin{array}{cc}{Class}& {Frequency} & 138 - 202 & 14 & 203 - 267 & 5 & 268 - 332 & 3 & 333 - 397 & 1 & 398 - 462 & 3 \ \end{array}[/tex]

Solving (b) The relative frequency histogram

First, we calculate the relative frequency by dividing the frequency of each class by the total frequency

So, we have:

[tex]\begin{array}{ccc}{Class}& {Frequency} & {Relative\ Frequency} & 138 - 202 & 14 & 0.53 & 203 - 267 & 5 & 0.19 & 268 - 332 & 3 & 0.12 & 333 - 397 & 1 & 0.04 & 398 - 462 & 3 & 0.12 \ \end{array}[/tex]

See attachment for histogram

The class with the greatest is 138- 202 and the class with the least relative frequency is 333 - 397

Answer:

The slope of the line is -6.

Answer:

30 gallons of each brand

Step-by-step explanation:

1 gallon of 60% + 1 gallon of 80% = 2 gallons 70% (60/2 = 30)

9514 1404 393

Answer:

  133 1/3 km/hour

Step-by-step explanation:

Average speed is computed as ...

  average speed = (total distance)/(total time)

  = (80 km +120 km +200 km)/(2/3 + 1 + 1 1/3 hour) = 400 km/(3 hour)

  = 133 1/3 km/hour

Answer:

G(x)=1/x+15

Step-by-step explanation:

.

Given:

The triangle ABC is reflected over the x-axis.

The distance between point A and A’ is 14.

To find:

The distance between the x-axis and A’.

Solution:

If a figure is reflected across the x-axis then the corresponding parts are mirror image of each other about the x-axis.

It means the distance between A and x-axis is same as the distance between x-axis and A'.

The distance between point A and A’ is 14.

Let d be the distance between the x-axis and A’. Then,

[tex]d+d=14[/tex]

[tex]2d=14[/tex]

[tex]d=\dfrac{14}{2}[/tex]

[tex]d=7[/tex]

Therefore, the correct option is 1.

Answer:

See explanation

Step-by-step explanation:

The question is incomplete, as the vertices of the triangle are not given.

A general explanation is as follows;

To calculate distance between two points, we use:

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

Take for instance;

[tex]A = (1,4)[/tex]

[tex]B = (3,-2)[/tex]

Distance AB is:

[tex]AB = \sqrt{(1 - 3)^2 + (4 - -2)^2}[/tex]

[tex]AB = \sqrt{(- 2)^2 + (4 +2)^2}[/tex]

[tex]AB = \sqrt{(- 2)^2 + (6)^2}[/tex]

Evaluate the exponents

[tex]AB = \sqrt{4 + 36}[/tex]

[tex]AB = \sqrt{40}[/tex]

[tex]AB = 6.32[/tex]

Answer:

for edmentum

Step-by-step explanation:

Answer:

B = 25

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

4(9y - 5) = 10(3y + 17) - 40

Step 2: Solve for y

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\large\textsf{4(9y - 5) = 10(3y + 17) - 40}\\\\\large\textsf{4(9y) + 4(-5) = 10(3y) + 10(17) - 10(40)}\\\\\large\textsf{36y - 20 = 30y + 170 - 40}\\\\\large\textsf{COMBINE the LIKE TERMS}\\\\\large\textsf{36y - 20 = (30 y)+ (170 - 40)}\\\\\large\textsf{36y - 20 = 30y + 130}\\\\\large\textsf{SUBTRACT 30y to BOTH SIDES}\\\\\large\textsf{36y - 20 - 30y = 30y + 130 - 30}}\\\\\large\textsf{Cancel out: 30y - 30y because that gives you 0}\\\\\large\textsf{Keep: 20 - 30y because helps solve for the y-value}[/tex]

[tex]\large\textsf{NEW EQUATION: 6y - 20 = 130}\\\\\large\textsf{ADD 20 to BOTH SIDES}\\\\\large\textsf{6y - 20 + 20 = 130 + 20}\\\\\large\textsf{Cancel out: -20 + 20 because that gives you 0}\\\\\large\textsf{Keep: 130 + 20 because that helps solve for the y-value}\\\\\large\textsf{130 + 20 = \bf 150}\\\\\large\textsf{NEW EQUATION: 6y = 150}\\\\\large\textsf{DIVIDE 6 to BOTH SIDES}\\\\\mathsf{\dfrac{6y}{6}= \dfrac{150}{6}}\\\\\large\textsf{Cancel: }\mathsf{\dfrac{6}{6}\large\textsf{ because that gives you 1}}[/tex]

[tex]\large\textsf{Keep: }\mathsf{\dfrac{150}{6}}\large\textsf{ because it helps solve for the y-value}\\\\\large\textsf{\bf y = }\mathsf{\dfrac{150}{6}}\\\\\large\textsf{OR }\\\\\mathsf{\dfrac{150}{6} }\large\textsf{ = \bf y}\\\\\\\large\textsf{SIMPLIFY ABOVE AND TOU YOU HAVE YOUR Y-VALUE}\uparrow\\\\\\\\\boxed{\boxed{\large\textsf{\huge\textsf{Answer: \bf y = 25} (Option B.)}}}\huge\checkmark\\\\\\\\\large\text{Good luck on your assignment and enjoy your day!}\\\\\\\\\\\frak{Amphitrite1040:)}[/tex]

9514 1404 393

Answer:

Step-by-step explanation:

One way to write the relationship between time, speed, and distance is ...

  time = distance/speed

For the first part of the trip, the time is ...

  t1 = 240/r

For the second part of the trip, the time is ...

  t2 = 72/(r+10)

The total time is 6 hours, so we have ...

  t1 +t2 = 6

  240/r +72/(r+10) = 6

We can simplify this a bit by multiplying by (r)(r+10)/6 to get ...

   40(r+10) +12(r) = r(r+10)

  r² -42r -400 = 0 . . . . . . . . subtract the left side and collect terms

  (r -50)(r +8) = 0 . . . . . . . . factor

  r = 50 . . . . . the positive solution of interest.

The two average speeds were 50 mph and 60 mph.

Answer: D. 38x + 1,450 > 4,000

Step-by-step explanation:

It has to be greater than 4,000 so A makes no sense

The parentheses are in the wrong place completely changing the meaning for B

C disregards the info we have about how she's already typed 1,450 words

The answer has to be D

Answer:

(-7, -1) =(x1,y1)

(8, 5)=(x2,y2)

now

[tex]slope (m) = \frac{y2 - y1}{x2 - x1} [/tex]

[tex]or = \frac{5 - ( - 1)}{8 - ( - 7)} [/tex]

[tex]or = \frac{5 + 1} {8 + 7} [/tex]

[tex]or = \frac{6}{15} [/tex]

[tex]or = \frac{2}{5} [/tex]

Step-by-step explanation:

hope it is helpful to you ☺️

Answer:

The first mechanic charged $ 85 an hour, and the second mechanic charged $ 55 an hour.

Step-by-step explanation:

Given that two mechanics worked on a car, and the first mechanic worked for 10 hours, and the second mechanic worked for 5 hours, and together they charged a total of $ 1125, to determine what was the rate charged per hour by each mechanic if the sum of the two rates was $ 140 per hour, the following calculation must be performed:

1125/15 = X

75 = X

80 x 10 + 60 x 5 = 800 + 300 = 1100

85 x 10 + 55 x 5 = 850 + 275 = 1125

Therefore, the first mechanic charged $ 85 an hour, and the second mechanic charged $ 55 an hour.

Answer:

0.0668 = 6.68% probability that an individual man’s step length is less than 1.9 feet.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Normally distributed with a mean of 2.5 feet and a standard deviation of 0.4 feet.

This means that [tex]\mu = 2.5, \sigma = 0.4[/tex]

Find the probability that an individual man’s step length is less than 1.9 feet.

This is the p-value of Z when X = 1.9. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1.9 - 2.5}{0.4}[/tex]

[tex]Z = -1.5[/tex]

[tex]Z = -1.5[/tex] has a p-value of 0.0668

0.0668 = 6.68% probability that an individual man’s step length is less than 1.9 feet.

Step-by-step explanation:

true

Answer:

C) 20

Step-by-step explanation:

The absolute value of a number represents the positive distance between the number and zero. Absolute value is therefore always positive.

The distance between -20 and 0 is 20 and therefore the answer is C) 20.

Answer:

20

Step-by-step explanation:

Absolute value = | -20 |

= 20

Option C is correct .

Answer:

please provide an image.

Step-by-step explanation:

x=-6 y= 0

x0 y= -1

y=mx+b

b= -1

0= -6m -1

-6m= 1

m= -1/6

parallel lines have the same slope

slope = -1/6

9514 1404 393

Answer:

  (f-g)(x) = 4x^3 +7x^2 -6x +1

Step-by-step explanation:

(f -g)(x) = f(x) -g(x)

  = (4x^3 +7x^2 -2x -1) -(4x -2)

  = 4x^3 +7x^2 +(-2-4)x +(-1+2)

(f -g)(x) = 4x^3 +7x^2 -6x +1

Answer:

19.634954085

Step-by-step explanation:

Pipe Diameter = Height of the trench

Pipe Height = Width of the trench

V = Pi*r^2*L/ Pi*r^2*h

= 22/7 x (2.5/2)^2 x 4

= 19.634954085

Answer:

the answers are on the picture but the numbers may be rounded

Answer:

Step-by-step explanation:

correct me if I am wrong

Answer:

68

Step-by-step explanation:

I did it on my test

The missing value in the table is 68. The correct answer would be option (B).

A linear relationship is a connection that takes the shape of a straight line on a graph between two distinct variables - x and y. When displaying a linear connection using an equation, the value of y is derived from the value of x, indicating their relationship.

The table shows the relationship between the number of faculty members and the number of students at a local school.

Faculty     Students

1                     17

2                   34

3                   51

4                    ?

The relationship between the number of faculty members and the number of students at the local school is that for every faculty member, there are 17 students.

Therefore, if there are 4 faculty members, we can find the number of students by multiplying 4 by 17, which gives us 68.

Thus, the missing value in the table is B. 68.

Learn about the linear relationship here :

https://brainly.com/question/11663530

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Answer:

200 kids and 500 adults

Step-by-step explanation:

x+y=700

7x+10y=6,400

(200,500)

kids=200

adults=500

Answer:

First term=1

Second term=-x

Third term=[tex]2x^2[/tex]

Fourth term =[tex]-\frac{28}{3!}x^3[/tex]

Step-by-step explanation:

We are given that function

[tex]f(x)=(1+3x)^{-1/3}[/tex]

We have to find the  first four non zero terms of the Maclaurin series for the binomial.

Maclaurin series of function f(x) is given by

[tex]f(x)=f(0)+f'(0)x+\frac{1}{2!}f''(0)x^2+\frac{1}{3!}f'''(0)x^3+....[/tex]

[tex]f(0)=(1+3x)^{\frac{-1}{3}}=1[/tex]

[tex]f'(x)=-\frac{1}{3}(1+3x)^{-\frac{4}{3}}(3)=-(1+3x)^{-\frac{4}{3}}[/tex]

[tex]f'(0)=-1[/tex]

[tex]f''(x)=\frac{4}{3}\times 3 (1+3x)^{-\frac{7}{3}}[/tex]

[tex]f''(0)=4[/tex]

[tex]f'''(x)=-4\times \frac{7}{3}\times 3(1+3x)^{-\frac{10}{3}}[/tex]

[tex]f'''(0)=-28[/tex]

Substitute the values we get

[tex](1+3x)^{-\frac{1}{3}}=1-x+\frac{4}{2!}x^2+\frac{-28}{3!}x^3+...[/tex]

[tex](1+3x)^{-\frac{1}{3}}=1-x+2x^2+\frac{-28}{3!}x^3+...[/tex]

First term=1

Second term=-x

Third term=[tex]2x^2[/tex]

Fourth term =[tex]-\frac{28}{3!}x^3[/tex]

Simon will pay £18 in VAT for using 3000 units of electricity in one year.

The VAT rate for gas and electric is 5%.

Therefore, Simon will pay VAT on his electricity usage.

Let's calculate Simon's annual electricity cost without VAT:

Cost per unit of electricity = 12p

= £0.12

Number of units used in one year = 3000

Electricity cost without VAT = Cost per unit × Number of units

= £0.12 × 3000

= £360

Now, let's calculate the VAT amount:

VAT rate = 5% = 0.05

VAT amount = Electricity cost without VAT × VAT rate

= £360 × 0.05

= £18

Therefore, Simon will pay £18 in VAT for using 3000 units of electricity in one year.

To learn more on VAT amount click:

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Answer:

125 boxes

Step-by-step explanation:

5*5*5

Answer:

19219.48

Step-by-step explanation:

16540x0.162+16540

The original price would be 100%

It was marked down 16.2%

100 % - 16.2% = 83.8%

The price you paid was 83.8% of the original price.

To find the original price divide the amount you paid by the percentage of the original price:

16,540 / 0.838 = 19.737.47

Original price: $19,737.47

Answer: 49 cherry tomatoes.

Step-by-step explanation:

7 x

— = — cross multiply and done.

15 105

Answer:

So 912$ is 58% of 1584 $

Step-by-step explanation: