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3 years ago

If these two shapes are similar, what is the measure of the missing length z?

Mathematics

1 answer:

Airida [17]3 years ago

7 0

Answer:

z = 10 mm

Step-by-step explanation:

$\frac{z}{15} =\frac{40}{60\\}$

$z * 60 = 40 * 15$

$60z = 600$

$z = 10\\$

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Jack is a college athlete who has been weighing himself weekly on the same scale in the athletic center for the past few years.

Radda [10]

Answer:

a) Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=\pm 1.64$

b) $\bar X \sim N(\mu ,\frac{\sigma}{\sqrt{n}})$

And the standard error is given by:

$SE = \frac{\sigma}{\sqrt{n}}=\frac{3}{\sqrt{9}}=1$

c) $\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

And the margin of error is:

$ME= z_{\alpha/2} \frac{\sigma}{\sqrt{n}} = 1.64$

And then the confidence interval is be given by:

$200-1.64 = 198.36$

$200+1.64 = 201.64$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X= 200$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=3$ represent the population standard deviation

n=9 represent the sample size

Part a

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=\pm 1.64$

Part b

The distribution for the sample mean is given by:

$\bar X \sim N(\mu ,\frac{\sigma}{\sqrt{n}})$

And the standard error is given by:

$SE = \frac{\sigma}{\sqrt{n}}=\frac{3}{\sqrt{9}}=1$

Part c

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

And the margin of error is:

$ME= z_{\alpha/2} \frac{\sigma}{\sqrt{n}} = 1.64$

And then the confidence interval is be given by:

$200-1.64 = 198.36$

$200+1.64 = 201.64$

8 0

3 years ago

Solve for x.<br><br> x = __°

Luba_88 [7]

Total inner angles add up to 720 because its a hexagon. so,
160 + 108 + 113 + 132+ 75+ x = 720
answer should be : 132°

6 0

3 years ago

A fishing rod and reel cost a total of $110. The reel cost $100 more than the rod. What is the final cost of

KIM [24]

Answer:

Hi there!

Your answer is:

The rod is equal to $5

The reel is equal to $105

Step-by-step explanation:

Rod= R

Reel= E

Rod = R

E= 100+r

(100+R)+R= 110

100+ 2R= 110

-100

2R = 10

R= 5

E= 100+5

The rod is equal to $5

The reel is equal to $105

3 0

3 years ago

The circumference of ruby's old swimming pool is 47.1 feet. Her new swimming pool has a diameter of 21 feet. How much larger is

Alla [95]

The new pool is 18.84 feet larger in circumference than the old one.

<u>Explanation:</u>

Given:

Circumference of the pool = 47.1 feet

Diameter of the new pool, d = 21 feet

radius, r = 21/2 feet

Circumference of the new pool = ?

We know:

Circumference = 2πr

where,

r is the radius

On substituting the value:

C = $2 X 3.14 X \frac{21}{2}$

C = 65.94 feet

The difference in circumference of the two pools = 65.94 - 47.1 feet

= 18.84 feet

Therefore, the new pool is 18.84 feet larger in circumference than the old one.

6 0

3 years ago

F(x) = x2 – 2x - 8

maw [93]

Answer:

The y-intercept is the point (0,-8)

see the attached figure

Step-by-step explanation:

we have

$f(x)=x^{2}-2x-8$

we know that

The y-intercept is the value of the function f(x) when the value of x is equal to zero

For x=0

$f(x)=0^{2}-2(0)-8\\f(x)=-8$

therefore

The y-intercept is the point (0,-8)

see the attached figure to better understand the problem

5 0

3 years ago