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3 years ago

10

A rectangle is 8 feet long. It’s width is represented by “seven plus x feet.” Which expression represents the area, in square fe

et, of the rectangle?

1 answer:

elena-s [515]3 years ago

3 0

A=8•(7+x)'

a=area

You multiply 7+x by 8 to get the area. This is the equation you need.

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Suppose that in a random selection of 100 colored candies, 24% of them are blue. The candy company claims that the percentage

LuckyWell [14K]

Answer:

We conclude that the percentage of blue candies is equal to 23% at 0.01 significance level.

Step-by-step explanation:

We are given that in a random selection of 100 colored candies, 24% of them are blue.

The candy company claims that the percentage of blue candies is equal to 23%.

<u><em>Let p = percentage of blue candies.</em></u>

So, Null Hypothesis, $H_0$ : p = 23% {means that the percentage of blue candies is equal to 23%}

Alternate Hypothesis, $H_A$ : p $\neq$ 23% {means that the percentage of blue candies is different from 23%}

The test statistics that would be used here <u>One-sample z proportion test statistics</u>;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n}} }$ ~ N(0,1)

where, $\hat p$ = sample proportion of blue colored candies = 24%

n = sample of colored candies = 100

So, <em><u>test statistics</u></em> = $\frac{0.24-0.23}{\sqrt{\frac{0.24(1-0.24)}{100}} }$

= 0.234

The value of z test statistics is 0.234.

<u>Now, at 0.01 significance level the z table gives critical values of -2.5758 and 2.5758 for two-tailed test.</u>

<em>Since our test statistics lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which </em><u><em>we fail to reject our null hypothesis.</em></u>

<em />

Therefore, we conclude that the percentage of blue candies is equal to 23%.

6 0

3 years ago

How to find the complement of a 58 degree angle

Butoxors [25]

Answer:

32°

Step-by-step explanation:

Complementary angles sum to 90°

the complement of 58° is

90° - 58° = 32°

4 0

2 years ago

Read 2 more answers

Consider F and C below. F(x, y, z) = y2 sin(z) i + 2xy sin(z) j + xy2 cos(z) k C: r(t) = t2 i + sin(t) j + t k, 0 ≤ t ≤ π (a) Fi

Liono4ka [1.6K]

Answer:

a) $f (x,y,z)= xy^2\sin(z)$

b) $\int_C F \cdot dr =0$

Step-by-step explanation:

Recall that given a function f(x,y,z) then $\nabla f = (\frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z})$ . To find f, we will assume it exists and then we will find its form by integration.

First assume that F = $\nabla f$ . This implies that

$\frac{\partial f}{\partial x} = y^2\sin(z)$ if we integrate with respect to x we get that

$f(x,y,z) = xy^2\sin(z) + g(y,z)$ for some function g(y,z). If we take the derivative of this equation with respect to y, we get

$\frac{\partial f}{\partial y} = 2xy\sin(z) + \frac{\partial g}{\partial y}$

This must be equal to the second component of F. Then

$2xy\sin(z) + \frac{\partial g}{\partial y}=2xy\sin(z)$

This implies that $\frac{\partial g}{\partial y}=0$ , which means that g depends on z only. So $f(x,y,z) = xy^2\sin(z) + g(z)$

Taking the derivative with respect to z and making it equal to the third component of F, we get

$xy^2\cos(z)+\frac{dg}{dz} = xy^2\cos(z)$

which implies that $\frac{dg}{dz}=0$ which means that g(z) = K, where K is a constant. So

$f (x,y,z)= xy^2\sin(z)$

b) To evaluate $\int_C F \cdot dr$ we can evaluate it by using f. We can calculate the value of f at the initial and final point of C and the subtract them as follows.

$\int_C F \cdot dr = f(r(\pi))-f(r(0))$

Recall that $r(\pi) = (\pi^2, 0, \pi)$ so $f(r(\pi)) = \pi^2\cdot 0 \cdot \sin(\pi) = 0$

Also $r(0) = (0, 0, 0)$ so $f(r(0)) = 0^2\cdot 0 \cdot \sin(0) = 0$

So $\int_C F \cdot dr =0$

5 0

2 years ago

23 times 4 times 25 times 23 times(25 times 4) times 4 =

Dmitrij [34]

21160000
just multiply every number you see but make sure you multiply the numbers inside the parentheses first

3 0

3 years ago

Read 2 more answers

Find EF and FD.

vichka [17]

9514 1404 393

Answer:

EF = 13.1

FD = 35.3

Step-by-step explanation:

The distance between two points on a number line is the positive difference between their coordinates.

EF = F - E = 19 -5.9

EF = 13.1

__

FD = F - D = 19 -(-16.3) = 19 +16.3

FD = 35.3

6 0

2 years ago