64 1/2 solve in indices

An educator claims that the average salary of substitute teachers in school districts is less than $60 per day. A random sample

valentina_108 [34]

Answer:

$t=\frac{58.875-60}{\frac{5.083}{\sqrt{8}}}=-0.626$

The degrees of freedom are given by:

$df=n-1=8-1=7$

The p value would be given by:

$p_v =P(t_{(7)}$

Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60

Step-by-step explanation:

Information given

60, 56, 60, 55, 70, 55, 60, and 55.

We can calculate the mean and deviation with these formulas:

$\bar X= \frac{\sum_{i=1}^n X_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

Replacing we got:

$\bar X=58.875$ represent the mean

$s=5.083$ represent the sample standard deviation for the sample

$n=8$ sample size

$\mu_o =60$ represent the value that we want to test

$\alpha=0.1$ represent the significance level

t would represent the statistic

$p_v$ represent the p value

Hypothesis to test

We want to test if the true mean is less than 60, the system of hypothesis would be:

Null hypothesis: $\mu \geq 60$

Alternative hypothesis: $\mu < 60$

The statistic would be given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Replacing the info we got:

$t=\frac{58.875-60}{\frac{5.083}{\sqrt{8}}}=-0.626$

The degrees of freedom are given by:

$df=n-1=8-1=7$

The p value would be given by:

$p_v =P(t_{(7)}$

Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60

3 0

3 years ago

What is the leading coefficient of the polynomial? 7x + 5x2 − 9x3 − 10

expeople1 [14]

Answer:

The leading coefficient of the polynomial is -9.

Step-by-step explanation:

9 is the leading coefficient of this polynomial because if you rearrange the exponents from greatest to least, you will get this :

-9x3 + 5x2 + 7x -10

Your leading coefficient is the number included with your degree or highest exponent.

3 0

3 years ago

Question 4 (1 point)

mrs_skeptik [129]

Answer:

(C)y=0

Step-by-step explanation:

An exponential function of the form $f(x) = a (b^x) + c$ always has a horizontal asymptote at y = c.

Given our function $y=4^x$

Comparing with the form, $f(x) = a (b^x) + c$ , we observe that c=0.

Therefore, the exponential function has an <u>asymptote at y=0.</u>

The correct option is C.

7 0

3 years ago

In 1992, the countries Chad and Denmark each had population of about 5.2 million. However,

irinina [24]

9514 1404 393

Answer:

5,339,479

Step-by-step explanation:

The populations in millions of the different countries can be represented by the equations ...

c = 5.2(1.025^t)

d = 5.2(1.001^t)

We want to find d when c = 10. Solving for t when c=10, we have ...

10 = 5.2(1.025^t)

10/5.2 = 1.025^t

log(10/5.2) = t×log(1.025)

t = log(10/5.2)/log(1.025)

Then the value of d for that value of t is ...

d = 5.2(1.001^(log(10/5.2)/log(1.025)) ≈ 5.3394789

The population of Denmark is about 5,339,479 when the population of Chad is 10 million.

_____

If we round the number of years to 26.5 before computing the population of Denmark, we get 5,339,571 -- about 92 more people. Ordinarily, one would not round intermediate results.

3 0

3 years ago

Find the circumstance of a circle with the diameter of 13 meters use 3.14 as an approximation

almond37 [142]

Answer:

okay so the circumference is 40.82m

$circumference = 2\pi \: \times r \\ = 2 \times 3.14 \times 6.5 \\ = 40.82m$

the diameter will be divided by 2 to give 6.5

4 0

2 years ago

64 1/2 solve in indices ​

64 1/2 solve in indices