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2 years ago

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The length of the sides of a square measure 2x-5. The length of a rectangle measures 2x, and the width measures x + 2. For what

value of x is the perimeter of the square the same as the perimeter of the rectangle?

1 answer:

vladimir1956 [14]2 years ago

3 0

Answer:

$x = 12$

Step-by-step explanation:

Perimeter of a square:

The perimeter of a square of side x is given by:

$P_s = 4x$

Perimeter of a rectangle:

The perimeter of a rectangle of length l and width w is given by:

$P_r = 2(l + w)$

The length of the sides of a square measure 2x-5.

This means that the perimeter of the square is:

$P_s = 4(2x - 5) = 8x - 20$

The length of a rectangle measures 2x, and the width measures x + 2.

This means that the perimeter of the rectangle is:

$P_r = 2(2x + x + 2) = 2(3x + 2) = 6x + 4$

For what value of x is the perimeter of the square the same as the perimeter of the rectangle?

This is x for which:

$P_s = P_r$

So

$8x - 20 = 6x + 4$

$8x - 6x = 20 + 4$

$2x = 24$

$x = \frac{24}{2}$

$x = 12$

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Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 24 students, she finds 2 w

irina1246 [14]

Answer:

A 95% confidence interval for the proportion of students who eat cauliflower on Jane's campus is [0.012, 0.270].

Step-by-step explanation:

We are given that Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 24 students, she finds 2 who eat cauliflower.

Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

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

where, $\hat p$ = sample proportion of students who eat cauliflower

n = sample of students

p = population proportion of students who eat cauliflower

<em>Here for constructing a 95% confidence interval we have used a One-sample z-test for proportions.</em>

<u>So, 95% confidence interval for the population proportion, p is ;</u>

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level

of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < ${\hat p-p}$ < $1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

P( $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

Now, in Agresti and Coull's method; the sample size and the sample proportion is calculated as;

$n = n + Z^{2}__(\frac{_\alpha}{2})$

n = $24 + 1.96^{2}$ = 27.842

$\hat p = \frac{x+\frac{Z^{2}__(\frac{\alpha}{2}_) }{2} }{n}$ = $\hat p = \frac{2+\frac{1.96^{2} }{2} }{27.842}$ = 0.141

<u>95% confidence interval for p</u> = [ $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.141 -1.96 \times {\sqrt{\frac{0.141(1-0.141)}{27.842} } }$ , $0.141 +1.96 \times {\sqrt{\frac{0.141(1-0.141)}{27.842} } }$ ]

= [0.012, 0.270]

Therefore, a 95% confidence interval for the proportion of students who eat cauliflower on Jane's campus [0.012, 0.270].

The interpretation of the above confidence interval is that we are 95% confident that the proportion of students who eat cauliflower on Jane's campus is between 0.012 and 0.270.

7 0

2 years ago

Help please 31-33 I'm very confused

Alexxandr [17]

I'm not going to dignify this question with a response. xD

5 0

3 years ago

Will mark as Brainliest.

strojnjashka [21]

B is the answer because there are 52 weeks in a year so $52,000/52 gives 1,000 and 1,000/40 gives 25. It's not A because it can't be less that $25 but more than it.

4 0

2 years ago

Read 2 more answers

Find the height of the triangle.

Ierofanga [76]

Answer:

The value of x = 3.42

Step-by-step explanation:

Formula:

Sin ∅ = Opposite side /Hypotenuse

From the figure we can see a right angled triangle.

One angle is given, hypotenuse = 10 and height = x.

To find the value of x

sin 20 = Opposite side/hypotenuse = x/10

x = 10 * sin 20

= 10 * 0.342 = 3.42

Therefore the value of x = 3.42

7 0

3 years ago

Read 2 more answers

An experiment will be conducted in which 20 pepper plants are randomly assigned to two groups. The plants in Group 1 will receiv

Studentka2010 [4]

The experimental units in this experiment are the 10 plants in group 2.

The experimental unit is a term used in science to refer to an individual or group of objects that are initially equivalent and then undergo experimental processes.

According to the above, the experimental unit of this experiment is the group 2 of plants because these are the plants that are going to be put into experimentation with a new fertilizer.

Then, the answer is D, because it refers to the experimental unit corresponding to this experiment.

Learn more in: brainly.com/question/17034824

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2 years ago