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3 years ago

8

Caitlyn is going away to college and will need to rent a truck to help move. The cost of the truck is 35 plus 0.79 per mile. If

her college is 85 miles away and she budgeted 100 for rental, she will have enough money?

1 answer:

Basile [38]3 years ago

7 0

Answer:

She will not have enough money. She is $2.15 short.

Step-by-step explanation:

Giving the following information:

The cost of the truck is 35 plus 0.79 per mile.

<u>First, we need to structure the total cost formula:</u>

Total cost= 35 + 0.79x

x= number of miles

<u>Now, we calculate the total cost for 85 miles:</u>

Total cost= 35 + 0.79*85

Total cost= $102.15

She will not have enough money. She is $2.15 short.

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Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. (If an answer d

andrey2020 [161]

Answer:

The maximum value is 1/27 and the minimum value is 0.

Step-by-step explanation:

Note that the given function is equal to $(xyz)^2$ then it means that it is positive i.e $f(x,y,z)\geq 0$ .

Consider the function $F(x,y,z,\lambda)=x^2y^2z^2-\lambda (x^2+y^2+z^2-1)$

We want that the gradient of this function is equal to zero. That is (the calculations in between are omitted)

$\frac{\partial F}{\partial x} = 2x(y^2z^2 - \lambda)=0$

$\frac{\partial F}{\partial y} = 2y(x^2z^2 - \lambda)=0$

$\frac{\partial F}{\partial z} = 2z(x^2y^2 - \lambda)=0$

$\frac{\partial F}{\partial \lambda} = (x^2+y^2+z^2-1)=0$

Note that the last equation is our restriction. The restriction guarantees us that at least one of the variables is non-zero. We've got 3 options, either 1, 2 or none of them are zero.

If any of them is zero, we have that the value of the original function is 0. We just need to check that there exists a value for lambda.

Suppose that x is zero. Then, from the second and third equation we have that

$-2y\lambda = -2z\lambda$ . If lambda is not zero, then y =z. But, since $-2y\lambda=0$ and lambda is not zero, this implies that x=y=z=0 which is not possible. This proofs that if one of the variables is 0, then lambda is zero. So, having one or two variables equal to zero are feasible solutions for the problem.

Suppose that only x is zero, then we have the solution set $y^2+z^2=1$ .

If both x,y are zero, then we have the solution set $z^2=1$ . We can find the different solution sets by choosing the variables that are set to zero.

NOw, suppose that none of the variables are zero.

From the first and second equation we have that

$\lambda = y^2z^2 = x^2z^2$ which implies $x^2=y^2$

Also, from the first and third equation we have that

$\lambda = y^2z^2 = x^2y^2$ which implies $x^2=z^2$

So, in this case, replacing this in the restriction we have $3z^2=1$ , which gives as another solution set. On this set, we have $x^2=y^2=z^2=\frac{1}{3}$ . Over this solution set, we have that the value of our function is $\frac{1}{3^3}= \frac{1}{27}$

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3 years ago

what is the surface area of a rectangular prism that has a height of 5cm a width of 10cm and a depth of 4cm

Kamila [148]

2(5*10)+2(10*4)+2(5*4)=

2(50)+2(40)+2(20)=100+80+40=

220 cm^2

I found the answer by finding the areas of the 3 different sides, multiplying each area by 2 since each side has another side that is equal on a rectangular prism, then adding all of them together.

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3 years ago

A college statistics class at a nearby university has 1,000 students enrolled in it. On a recent exam, the mean score was 75% wi

IceJOKER [234]

Answer:

38.11%

Step-by-step explanation:

Given that:

Mean (μ) = 75, standard deviation (σ) = 5

Z score is a measure in statistics to determine the variation of a raw score from the mean. It is given by the equation:

$z=\frac{x-\mu}{\sigma}$

To calculate the percentage of students scored between a 73 and 78 (C grade), we need to find the z score for 73 and then for 78.

For x = 73, the z score is:

$z=\frac{x-\mu}{\sigma}=\frac{73-75}{5} =-0.4$

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$z=\frac{x-\mu}{\sigma}=\frac{78-75}{5} =0.6$

From the probability distribution table:

P(73 < x < 78) = P(-0.4 < z < 0.6) = P(z < 0.6) - P(z < -0.4) = 0.7257 - 0.3446 = 0.3811 = 38.11%

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3 years ago

What is 10 times as many as

Talja [164]

Answer:

To answer this question, more information needs to be disclosed.

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2 years ago

Which inequality represents all values of X for which the product below is defined

balandron [24]

The domain for which the function is defined is given by:

D. $x \geq 4$ .

<h3>What is the domain of a function?</h3>

The domain of a function is the set that contains all possible input values for the function.

A square root is only defined for non-negative values, hence:

$x - 4 \geq 0 \rightarrow x \geq 4$ .

$x + 1 \geq 0 \rightarrow x \geq -1$ .

The intersection of these two domains is $x \geq 4$ , hence option D is correct.

More can be learned about the domain of a function at brainly.com/question/10891721

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2 years ago