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2 years ago

Solve pls brainliest

Mathematics

1 answer:

Sphinxa [80]2 years ago

7 0

Answer:

$(\frac{2}{3})^{4}$ written in simplest form is $\frac{16}{81}$

Step-by-step explanation:

When taking a fraction to a certain power, you can rewrite the expression as the numerator taken to that power over the denominator to that power. In this case, the fraction is $\frac{2}{3}$ and the exponent is 4, so you can write the expression as $\frac{2^{4}}{3^{4}}$ . $2^{4}$ is 16, and $3^{4}$ is 81, so the fraction is $\frac{16}{81}$ .

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For a large supermarket chain in a particularâ state, aâ women's group claimed that female employees were passed over for manage

PolarNik [594]

Answer:

1) As the P-value (0.097) is greater than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the women's claim that female employees were passed over for management training in favor of their male colleagues.

2) The 95% confidence interval for the population proportion is (0.173, 0.427).

The populations proportion (π=0.4) is included in this confidence interval, so the claim has no enough evidence to be supported.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that female employees were passed over for management training in favor of their male colleagues.

We use the women's part for sample and population proportions.

Then, the null and alternative hypothesis are:

$H_0: \pi=0.4\\\\H_a:\pi$

The significance level is 0.05.

The sample has a size n=50 persons.

The sample proportion is p=0.3.

$p=X/n=15/50=0.3$

The standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.4*0.6}{50}}\\\\\\ \sigma_p=\sqrt{0.0048}=0.069$

Then, we can calculate the z-statistic as:

$z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.3-0.4+0.5/50}{0.069}=\dfrac{-0.09}{0.069}=-1.299$

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

$\text{P-value}=P(z$

As the P-value (0.097) is greater than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that female employees were passed over for management training in favor of their male colleagues.

b) We have to calculate a 95% confidence interval for the proportion.

The sample proportion is p=0.3.

The standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.3*0.7}{50}}\\\\\\ \sigma_p=\sqrt{0.0042}=0.0648$

The critical z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

$MOE=z\cdot \sigma_p=1.96 \cdot 0.0648=0.127$

Then, the lower and upper bounds of the confidence interval are:

$LL=p-z \cdot \sigma_p = 0.3-0.127=0.173\\\\UL=p+z \cdot \sigma_p = 0.3+0.127=0.427$

The 95% confidence interval for the population proportion is (0.173, 0.427).

The populations proportion (π=0.4) is included in this confidence interval, so the claim has no enough evidence to be supported.

5 0

3 years ago

11. Rocco and Biff are two koalas sitting at the

bagirrra123 [75]

Answer:

Biff's tree is 14 m off the ground and Rocco's tree is 7 m off the ground.

Step-by-step explanation:

Let the height of Biff's tree be represented by x, so that the height of Rocco's tree is $\frac{x}{2}$ .

Draw a straight line from Rocco's point of view to a point t to the middle of Biff's tree. This line divides x into two equal parts, and the angle is divided into $35^{0}$ each.

By alternate angle property,

Tan $35^{0}$ = $\frac{\frac{x}{2} }{10}$

$\frac{x}{2}$ = Tan $35^{0}$ × 10

= 7.00021

⇒ x = 2 × 7.0021

= 14. 0042

x = 14

Therefore, Biff's tree is 14 m off the ground and Rocco's tree is 7 m off the ground.

5 0

3 years ago

Read 2 more answers

30 POINTS NEED HELP

KatRina [158]

a. The expression y=5x represent the number of small marbles she has.

b. The expression z=3x+2 represents the number of large marbles she has.

c. Amy has 310 small marbles, 62 medium marbles and 188 large marbles.

Step-by-step explanation:

a. Let x represent the number of medium marbles Amy has. Write an algebraic expression to represent the number of small marbles she has.

Medium marbles = x

Let,

Small marbles = y

According to given statement;

She has five times as many small marbles as medium marbles.

y = 5x Eqn 1

The expression y=5x represent the number of small marbles she has.

b. Write an algebraic expression to represent the number of large marbles she has.

Let,

Large marbles = z

The number of large marbles is two more than three times the number of medium marbles.

z = 3x+2 Eqn 2

The expression z=3x+2 represents the number of large marbles she has.

c. If Amy has a total of 560 marbles, how many of each size does she have?

x+y+z= 560 Eqn 3

Putting value of y and z from Eqn 1 and 2 in Eqn 3

$x+(5x)+(3x+2)=560\\x+5x+3x+2=560\\9x=560-2\\9x=558$

Dividing both sides by 9

$\frac{9x}{9}=\frac{558}{9}\\x=62$

Putting x=62 in Eqn 1

$y=5(62)\\y=310$

Putting x=62 in Eqn 2

$z=3(62)+2\\z=186+2\\z=188$

Amy has 310 small marbles, 62 medium marbles and 188 large marbles.

Keywords: linear equation, substitution method

Learn more about substitution method at:

#LearnwithBrainly

5 0

3 years ago

Given f(x) = x3 – 2x2 – x + 2, <br><br> the roots of f(x)

anyanavicka [17]

f(x) = x³ – 2x² – x + 2

0 = x3 – 2x2 – x + 2

(x-2)(x-1)(x+1)=0

x1=-1

x2=1

x3=2

5 0

3 years ago

Read 2 more answers

How do I solve this?

patriot [66]

You already know that y equals -4. It says that x equals 3, so multiply the -4 by 3 and because it has a negative number and a positive number it will equal -12. Remember anytime you see a letter after a number it means multiply. The complete problem should be -10 because 2 is a whole number you subtract it from -12. Hope that helped you out some.

6 0

3 years ago