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3 years ago

8

The perimeter and the area of a rectangle have the same numerical value.

1 answer:

Sophie [7]3 years ago

5 0

Formula

2*(L + W) = L * W

Given

W = 3

Solution

2*(L + 3) = 3*L

2L+ 6 = 3L Subtract 2L from both sides

2L - 2L + 6 = 3L - 2L combine

6 = L

Answer: The length is 6 units long.

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At 1600 principal earns 7% interest compound semiannually twice per year after 33 years what is the balance in the account

NARA [144]

A $1,600.00 principle earns 7% interest, compounded semiannually twice per year. After 33 years, what is the balance in the account. My answer is $112,992.00

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3 years ago

On any day, the probability of rain is 0.3. The occurrence of rain on any day is independent of the occurrence of rain on any ot

poizon [28]

<h3>Answer: 0.47178 Step-by-step explanation: Find the probability for each p(X=x) up to 5 using the equation: (x-1)C(r-1)*p^r * q^x-r, where x is number of days, p = .3 (prob of rain). q=.7 (prob of not rain), and r=2 (second day of rain). also C means choose. So p(X=1) = 0 p(X=2) = 1C1 * .3^2 * .7^0 = .09 P(X=3) = 2C1 * .3^2 * .7^1 = .126 P(X=4) = 3C1 * .3^2 * .7^2 = .1323 P(X=5) = 4C1 * .3^2 * .7^3 = .12348 Then add all of them up 0+.09+.126+.1323+.12348 = .47178</h3>

3 0

3 years ago

What is the slop and y-intercept of this line y = x - 5

raketka [301]

Answer:

The slope is

1

y -intercept is

− 5

.

Step-by-step explanation:

7 0

3 years ago

Harry solves the equation 1/3t = 15. He says the solution is 30. Is his answer correct? Fill in the blanks to explain how Harry

aksik [14]

Harry can first substitute 30 for t

He can then multiply $\frac{1}{3}$ by 30 to get a product of 10

Since, 10 is not equal to 15, Harry's solution is not correct.

<em><u>Solution:</u></em>

Given that,

Harry solves the equation:

$\frac{1}{3}t = 15$

He says the solution is 30

We have to check if his answer is correct or not

<em><u>Fill in the blanks to explain how Harry can check whether his solution is correct</u></em>

Harry can first substitute 30 for t

$\frac{1}{3} \times 30 = 15$

He can then multiply $\frac{1}{3}$ by 30 to get a product of 10

$10\neq 15$

Since, 10 is not equal to 15, Harry's solution is not correct

<em><u>Correct solution:</u></em>

$\frac{1}{3}t = 15\\\\t = 15 \times 3\\\\t = 45$

Thus correct solution is 45

5 0

3 years ago

An open box with a square base is constructed so that it has a volume of 64in^3. The base needs to be made out of a material tha

Ivahew [28]

The volume of a box is the amount of space in the box

The dimensions that minimize the cost of the box is 4 in by 4 in by 4 in

<h3>How to determine the dimensions that minimize the cost</h3>

The dimensions of the box are:

Width = x

Depth = y

So, the volume (V) is:

$V = x^2y$

The volume is given as 64 cubic inches.

So, we have:

$x^2y = 64$

Make y the subject

$y = \frac{64}{x^2}$

The surface area of the box is calculated as:

$A =x^2 + 4xy$

The cost is:

$C = 2x^2 + 4xy$ --- the base is twice as expensive as the sides

Substitute $y = \frac{64}{x^2}$

$C = 2x^2 + 4x * \frac{64}{x^2}$

$C =2x^2 + \frac{256}{x}$

Differentiate

$C' =4x - \frac{256}{x^2}$

Set to 0

$4x - \frac{256}{x^2} = 0$

Multiply through by x^2

$4x^3 - 256= 0$

Divide through by 4

$x^3 - 64= 0$

Add 64 to both sides

$x^3 = 64$

Take the cube roots of both sides

$x = 4$

Recall that:

$y = \frac{64}{x^2}$

So, we have:

$y = \frac{64}{4^2}$

$y = 4$

Hence, the dimensions that minimize the cost of the box is 4 in by 4 in by 4 in

Read more about volume at:

brainly.com/question/1972490

4 0

2 years ago