Given that the volume decreases at a rate of 3 cubic meters per minute, find the rate of change of an edge, in meters per minute, of the cube when the volume is exactly 64 cubic meters

There are 211 quarters and 216 dimes in Steve's piggy bank.

An algebraic expression is consists of variables, numbers with various mathematical operations,

Let Steve has x quarters,

Therefore, Steve will have x + 5 dimes,

Given that,

Steve has total $74.35.

To solve, use equation format,

0.1(x+5)+0.25x=74.35

0.35x+0.5=74.35

0.35x=73.85

x=211

So the number of quarters x= 211

And number of dimes (x+5) =216

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Answer:

Perimeter: 2(3x+6)+ 2(2x-4)

X=9

Step-by-step explanation:

In order to create the expression you just have to remember that the perimeter of a rectangle equals 2 bases plus 2 sides, so the expression would be:

Perimeter: 2(heights)+ 2(bases)

Perimeter: 2(3x+6)+ 2(2x-4)

IN order to solve for X we just have to insert the value of perimeter, which is 94:

Perimeter: 2(3x+6)+ 2(2x-4)

94=2(3x+6)+ 2(2x-4)

94= 6x+12+4x-8

94=10x+4

94-4=10x

x=90/10

x=9

So the value of x would be 9.

he ended with 16

he earned 6 for mowing the lawn, so before mowing the lawn he had 16-6 =10

he spent half on pizza and had 10 left so allowance = 10*2 = 20

 he gets $20 a week for allowance

a. The unconditional mean of X = 1.75 cars.

b. Conditional Mean of X Given Y=1 is 1.38 cars.

c. Probability of Rachel Selling 1 Car Given Rebecca Selling 3 is 1.07.

d. The covariance COV (X,Y) is 0.23. COV(X,Y) ≠ 0, X,Y not independent.

e. The correlation coefficient is 0.52, The strength is (0.3-0.5) and the direction is positive correlation.

f. The expectation and variance of Z are 10.25 cars and 6.66 cars².

Step-by-Step Joint Probability Distribution of Cars Sold:

a. Unconditional Mean of X:

1. Calculate marginal probabilities of X:

P(X=1) = 0.57, P(X=2) = 0.29, P(X=3) = 0.14

Calculate expected value of X:

E(X) = Σ(xi × P(xi)) = (1 × 0.57) + (2 × 0.29) + (3 × 0.14) = 1.75 cars

b. Conditional Mean of X Given Y=1:

1. Calculate conditional probability:

P(X=1|Y=1) = 0.40 / 0.52

2.Calculate conditional mean:

E(X|Y=1) = (1 × 0.806) + (2 × 0.194) = 1.38 cars

c. Probability of Rachel Selling 1 Car Given Rebecca Selling 3:

1. Calculate conditional probability:

P(Y=1|X=3) = 0.15 / 0.14 = 1.07 (impossible, probabilities must be between 0 and 1)

d. Covariance and Independence:

1. Calculate joint expected values:

[tex]E(XY) = \sum (x_i \times y_i \times P(x_i,y_i)) = 2.74[/tex]

2. Calculate individual variances:

Var(X) = 0.74, Var(Y) = 0.24

3. Calculate covariance:

COV(X,Y) = E(XY) - E(X)E(Y) = 2.74 - (1.75 × 0.88) = 0.23

Since COV(X,Y) ≠ 0, X and Y are not independent.

e. Correlation Coefficient:

1. Calculate correlation coefficient:

ρ(X,Y) = COV(X,Y) / (σ(X) × σ(Y)) = 0.23 / (√0.74 × √0.24) ≈ 0.52

2. Strength: weak positive correlation (0.3-0.5)

3. Direction: positive correlation (positive coefficient)

f. Expectation and Variance of Z:

1. Use properties of mean:

E(Z) = E(3X+5) = 3E(X) + 5 = 3 × 1.75 + 5 = 10.25 cars

2. Use properties of variance:

Var(Z) = 9Var(X) = 9 × 0.74 = 6.66 cars²

Complete and correct question:

The joint probability distribution of variables X and Y is shown in the table below. Rebecca and Rachel are car salespeople. Let X denote the number of cars that Rebecca will sell in a month, and let Y denote the number of cars Rachel will sell in a month.

          x=1       x=2      x=3

Y=1    0.40     0.18      0.15

Y=2   0.12      0.11      0.04

a. Find the unconditional mean of X.

b. Find the conditional mean number of cars that Rebecca will sell in a month given Rachel sells 1 car in a month.

C. What is the probability that Rachel will sell 1 car in a month given that Rebecca sold 3?

d. Find covariance COV (X, Y). Are X and Y independent? Explain why.
e. Find the correlation coefficient between X and Y. Discuss the strength and the direction of its relationship.
f. Chris, another salesperson, sells a car better than Rebecca. Let Z denote the number of cars that Rebecca will sell in a month, where Z = 3X +5. Get the expectation and variance of Z using the properties of the mean and the variance.

Using the substitution method, the solution to the system of linear equations is: x = -7 and y = 5.

The substitution method used in solving a system of linear equations involves substituting a variable for an expression into the other equation given.

Given the system:

2x − 3y = −29 - eqn. 1

x + 4y = 13 - eqn. 2

Rewrite eqn. 2

x = 13 - 4y

Substitute x = 13 - 4y into eqn. 1

2(13 - 4y) − 3y = −29

26 - 8y - 3y = -29

-11y = -29 - 26

-11y = -55

y = 5

Plug in the value of y into x = 13 - 4y:

x = 13 - 4(5)

x = -7

The solution is: x = -7 and y = 5

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Hi there!

This set you have given is not a definitive set, therefore there is not definitive answer that can be given. It is a indefinite set, which means that any set of integers can be put in as a solution to this set. Unless there are defining quantifiers then the set and solution are both infinite.

Your friend, ASIAX

Answer:

Option (3) is correct.

The value of the given expression [tex]\frac{-3(7+5)}{3^2}+9(2)[/tex]  is 14.

Thus, option (3) is correct.

Step-by-step explanation:

Consider the given expression in the image given,

[tex]\frac{-3(7+5)}{3^2}+9(2)[/tex]

First solve for square term in the denominator,

[tex]3^2=3 \times 3 = 9[/tex]

Expression becomes,

[tex]\frac{-3(7+5)}{9}+9(2)[/tex]

Now solve for numerator,

7 +5 = 12 and -3(12) = -36

Expression becomes,

[tex]\Rightarrow \frac{-36}{9}+9(2)[/tex]

[tex]\Rightarrow -4+9(2)[/tex]

[tex]\Rightarrow -4+18[/tex]

[tex]\Rightarrow 14[/tex]

Thus the value of the given expression [tex]\frac{-3(7+5)}{3^2}+9(2)[/tex]  is 14.

Thus, option (3) is correct.

The value of (2a - 2b)/(5a + 5b) can be simplified to c.

To find the value of (2a - 2b)/(5a + 5b) when the equation (a + b)/(a - b) = c is given, we can substitute the value of (a + b)/(a - b) with c. Rearranging the equation, we get:

(2a - 2b)/(5a + 5b) = c

Simplifying the expression, we have:

(2(a - b))/(5(a + b)) = c

So, the value of (2a - 2b)/(5a + 5b) is c.

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The fraction that is greater than 1/2 and less than 3/4 is 2/3. This is demonstrated by placing these fractions on a number line, where 2/3 falls between 1/2 and 3/4.

The question is asking for a fraction that is both greater than 1/2 (or 0.5) and less than 3/4 (or 0.75). To find such fraction, we can consider fractions between these two numbers. A possible solution is 2/3 (or approximately 0.67) which is truly greater than 1/2 and less than 3/4.

Now, let's explain this visually. If you translate these fractions on a number line, 1/2 would be at the middle of the line, 3/4 would be three quarters way forward and 2/3 would be somewhere in the middle of these two fractions.

Consider the representation on a number line, 0 -> 1/2 -> 2/3 -> 3/4 -> 1. We see that 2/3 does fall in between 1/2 and 3/4.

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