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2 years ago

Help please !! i will give brainliest

Mathematics

1 answer:

grin007 [14]2 years ago

6 0

Answer:

k = $\frac{5}{6}$

Step-by-step explanation:

The scale factor is calculated as the ratio of corresponding sides, figure on right to figure on left, that is

k = $\frac{30}{36}$ = $\frac{5}{6}$ ← in simplest form

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A programmer plans to develop a new software system. In planning for the operating system that he will use, he needs to estimat

Vedmedyk [2.9K]

Using the z-distribution, we have that:

a) A sample of 601 is needed.

b) A sample of 93 is needed.

c) A. Yes, using the additional survey information from part (b) dramatically reduces the sample size.

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which z is the z-score that has a p-value of $\frac{1+\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

95% confidence level, hence $\alpha = 0.95$ , z is the value of Z that has a p-value of $\frac{1+0.95}{2} = 0.975$ , so $z = 1.96$ .

For this problem, we consider that we want it to be within 4%.

Item a:

The sample size is <u>n for which M = 0.04.</u>

There is no estimate, hence $\pi = 0.5$

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 1.96\sqrt{\frac{0.5(0.5)}{n}}$

$0.04\sqrt{n} = 1.96\sqrt{0.5(0.5)}$

$\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.04}$

$(\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.04}\right)^2$

$n = 600.25$

Rounding up:

A sample of 601 is needed.

Item b:

The estimate is $\pi = 0.96$ , hence:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 1.96\sqrt{\frac{0.96(0.04)}{n}}$

$0.04\sqrt{n} = 1.96\sqrt{0.96(0.04)}$

$\sqrt{n} = \frac{1.96\sqrt{0.96(0.04)}}{0.04}$

$(\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.96(0.04)}}{0.04}\right)^2$

$n = 92.2$

Rounding up:

A sample of 93 is needed.

Item c:

The closer the estimate is to $\pi = 0.5$ , the larger the sample size needed, hence, the correct option is A.

For more on the z-distribution, you can check brainly.com/question/25404151

8 0

2 years ago

Question 2 of 10<br> Which describes the graph of y = (x-4)2 - 1?

WITCHER [35]

$y=(x-4)^2-1:$ $y=-\frac{4}{5}$

Sure hope this helps you

y = -4/5

4 0

1 year ago

20 points help help help

mrs_skeptik [129]

The perimeter of the shape is 94 cm and the area is 462 sq cm.

Step-by-step explanation:

Given,

The radius (r) = 14 cm

To find the area and perimeter of the given shape.

The given shape is $\frac{3}{4}$ of the full circle.

Formula

The perimeter of the circle = 2πr

The perimeter of the given shape = $\frac{3}{4}$ (2πr)+r+r = $\frac{3}{4}$ (2πr)+2r

The area of the circle = πr²

Now,

The perimeter of the given shape = $\frac{3}{4}$ (2× $\frac{22}{7}$ ×14)+2×14 = 94 cm

The area of the given shape = $\frac{3}{4}$ (πr²)

= $\frac{3}{4}$ × $\frac{22}{7}$ ×14² = 462 sq cm

7 0

2 years ago

Read 2 more answers

Show work 14.7 x 11.361=

Yanka [14]

Add two 0's to 14.7 making 14.700

3 0

2 years ago

A right pyramid with a regular hexagon base has a height of 3 units If a side of the hexagon is 6 units long, then the apothem i

Setler79 [48]

Answer:

Part a) The slant height is $3\sqrt{2}\ units$

Part b) The lateral area is equal to $54\sqrt{2}\ units^{2}$

Step-by-step explanation:

we know that

The lateral area of a right pyramid with a regular hexagon base is equal to the area of its six triangular faces

$LA=6[\frac{1}{2}(b)(l)]$

where

b is the length side of the hexagon

l is the slant height of the pyramid

Part a) Find the slant height l

Applying the Pythagoras Theorem

$l^{2}=h^{2} +a^{2}$

where

h is the height of the pyramid

a is the apothem

we have

$h=3\ units$

$a=3\ units$

substitute

$l^{2}=3^{2} +3^{2}$

$l^{2}=18$

$l=3\sqrt{2}\ units$

Part b) Find the lateral area

$LA=6[\frac{1}{2}(b)(l)]$

we have

$b=6\ units$

$l=3\sqrt{2}\ units$

substitute the values

$LA=6[\frac{1}{2}(6)(3\sqrt{2})]=54\sqrt{2}\ units^{2}$

3 0

2 years ago

Read 2 more answers