Help me with my geometry

hammer [34]

Answer:

The test statistic is z=2.5.

The null hypothesis is rejected.

There is enough evidence to support the claim that more than 10% of the 16 ounce cups are underfilled.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that more than 10% of the 16 ounce cups are underfilled.

Then, the null and alternative hypothesis are:

$H_0: \pi=0.1\\\\H_a:\pi>0.1$

The significance level is assumed to be 0.05.

The sample has a size n=100.

The sample proportion is p=0.18.

$p=X/n=18/100=0.18$

The standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.1*0.9}{100}}\\\\\\ \sigma_p=\sqrt{0.001}=0.03$

Then, we can calculate the z-statistic as:

$z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.18-0.1-0.5/100}{0.03}=\dfrac{0.075}{0.03}=2.5$

This test is a right-tailed test, so the P-value for this test is calculated as:

$P-value=P(z>2.5)=0.006$

As the P-value (0.006) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that more than 10% of the 16 ounce cups are underfilled.

7 0

3 years ago

The dots in the diagram are 1 unit apart. What is the longest segment that can be drawn between two of the dots without

xz_007 [3.2K]

Answer:

the correct answer is C) √5

Step-by-step explanation:

3 0

2 years ago

Find the common ratio of the geometric sequence -2, 6, -18, ...

lara [203]

Answer:

-3

Step-by-step explanation:

You multiply by negative 3 every next term

5 0

3 years ago

Find all solutions to

BARSIC [14]

Answer:

x= 0 , $\frac{1}{14}$ , $\frac{-1}{12}$

Step-by-step explanation:

Given, equation is $\sqrt[3]{15x-1}$ + $\sqrt[3]{13x+1}$ = $4\sqrt[3]{x}$ . →→→ (1)

Now, by cubing the equation on both sides, we get

( $\sqrt[3]{15x-1}$ + $\sqrt[3]{13x+1}$ )³ = ( $4\sqrt[3]{x}$ )³

⇒ (15x-1) + (13x+1) + 3× $\sqrt[3]{15x-1}$ × $\sqrt[3]{13x+1}$ ( $\sqrt[3]{15x-1}$ + $\sqrt[3]{13x+1}$ ) = 64 x.

⇒ 28x + 3× $\sqrt[3]{15x-1}$ × $\sqrt[3]{13x+1}$ ( $4\sqrt[3]{x}$ ) = 64x.

(since from (1), $\sqrt[3]{15x-1}$ + $\sqrt[3]{13x+1}$ = $4\sqrt[3]{x}$ )

⇒ 12× $\sqrt[3]{15x-1}$ × $\sqrt[3]{13x+1}$ ( $\sqrt[3]{x}$ )= 36x.

⇒ 3x = $\sqrt[3]{(15x-1)(13+1)(x)}$ .

Now, once again cubing on both sides, we get

(3x)³ = ( $\sqrt[3]{(15x-1)(13+1)(x)}$ )³.

⇒ 27x³ = (15x-1)(13x+1)(x).

⇒ 27x³ = 195x³ + 2x² - x

⇒ 168x³ + 2x² - x = 0

⇒ x(168x² + 2x -1) = 0

⇒ by, solving the equation we get ,

x = 0 ; x = $\frac{1}{14}$ ; x = $\frac{-1}{12}$

therefore, solution is x= 0 , $\frac{1}{14}$ , $\frac{-1}{12}$

7 0

3 years ago

A rectangle has side lengths of 1 3/4 feet and 2 1/3 feet. Find the perimeter of the rectangle. Write your answer as a mixed num

katovenus [111]

Answer:

8 feet

Step-by-step explanation:

Rectangles have congruent opposite side lengths. This means that if one of its longer sides were 2 1/3 feet and one of its shorter sides were 1 3/4 feet then the other longer side would also be 2 1/3 feet and the other shorter side would be 1 3/4 feet.

Therefore to find the perimeter, you would take the given side lengths and multiply them each by 2 to account for both of the congruent sides.

2(2 1/3) + 2(1 3/4) = perimeter of rectangle

To multiply these fractions they would have to be converted into improper fractions. Multiply the whole number by the denominator and add the numerator---keeping the denominator the same in the converted form.

2 1/3 ⇒ 7/3
1 3/4 ⇒ 7/4

Now you can multiply these fractions by 2. Multiply the numerators by 2 and keep the denominator the same.

2(7/3) + 2(7/4)
14/3 + 14/4

To add them they should have common denominators so multiply 14/3 by 4/4 and 14/4 by 3/3.

14/3 (4/4) = 56/12
14/4 (3/3) = 42/12

Add 54/12 and 42/12 together by combining the numerators and keeping the denominators the same.

54/12 + 42/12 = 96/12

You can simplify this improper fraction even more by dividing 96 by 12 since 12 is a factor of 96.

96/12 = 8

The perimeter of the rectangle is 8 feet.

7 0

3 years ago

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