Evaluate the value of the expression 4(x+2-5x) when x=2

According to a report released by CIBC entitled "Women Entrepreneurs: Leading the Charge," the average age for Canadian business

SOVA2 [1]

Answer:

We conclude that the mean age of Canadian businesswomen has increased.

Step-by-step explanation:

We are given that according to a report released by CIBC entitled "Women Entrepreneurs: Leading the Charge," the average age for Canadian businesswomen in 2008 was 41.

The researchers randomly sample 97 Canadian businesswomen and ascertain that the sample mean age is 43.4. From past experience, it is known that the population standard deviation is 8.95.

Let $\mu$ = mean age of Canadian businesswomen.

So, Null Hypothesis, $H_0$ : $\mu$ $\leq$ 41 {means that the mean age of Canadian businesswomen has decreased or remained same}

Alternate Hypothesis, $H_A$ : $\mu$ > 41 {means that the mean age of Canadian businesswomen has increased}

The test statistics that would be used here One-sample z-test statistics because we know about population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean age of Canadian businesswomen = 43.4

$\sigma$ = population standard deviation = 8.95

n = sample of Canadian businesswomen = 97

So, the test statistics = $\frac{43.4-41}{\frac{8.95}{\sqrt{97} } }$

= 2.64

The value of z test statistic is 2.64.

Also, P-value of the test statistics is given by;

P-value = P(Z > 2.64) = 1 - P(Z < 2.64)

= 1 - 0.99585 = 0.00415

Now, at 1% significance level the z table gives critical value of 2.33 for right-tailed test.

Since our test statistic is more than the critical value of z as 2.64 > 2.33, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the mean age of Canadian businesswomen has increased.

4 0

3 years ago

the price of family dinner was $48.00 . A sales tax of 5% to the final bill. The family left a $10.08 tip. If the family include

tia_tia [17]

Answer:

20% tip

Step-by-step explanation:

Dinner: $48.00

Tax: 0.05($48.00) = $2.40

Total (final) bill before tip: $50.40

Tip: $10.08

Percentage tip was then $10.08 (100%) / $50.40 = 20%

The family left a 20% tip.

5 0

3 years ago

What numbers are perfect numbers

alekssr [168]

A perfect number is a number where the sum of its divisors is equal to the number.

For example 6: 1 + 2 + 3 = 6

Another example is 28: 1 + 2 + 4 + 7 + 14 = 28

Here is a short list of perfect numbers: 6, 28, 496, 8128, 33550336, and the numbers get way bigger as we go on.

5 0

3 years ago

Using complete sentences, describe how you would check the quotient of two rational expressions. Create and demonstrate your own

Kamila [148]

To check the quotient of a division problem, I would multiply the quotient by the divisor and add the remainder. If the quotient is correct, the result will be the dividend.
example is below
x2−x−6/x−3=(x−3)(x+2)/x−3=x+2

6 0

2 years ago

What is slope between the points (-5,7) and (4,-8)?

WINSTONCH [101]

The slope can sometimes be called the gradient, and the equation for the gradient is (y2 - y1)/(x2 - x1). So therefore, you'd do: (-8 - 7)/(4 - -5) which is (-15)/9) which is -1 2/3 or -1.6 (recurring), which is your answer. I hope this helps! Let me know if I've confused you :)

3 0

3 years ago

Evaluate the value of the expression4(x+2-5x) when x=2​

Evaluate the value of the expression4(x+2-5x) when x=2