Which expression is a sum of a number and a product? O A. 2(x-9) O B. 6x- 4 O c. 4+ 2x O D.

sleet_krkn [62]

Division , timetable , adding , and subtracting

8 0

3 years ago

Tshepo needs R5 000 urgently. He goes to the bank and borrows the money at an interest rate of 28% per annum, compounded monthly

12345 [234]

Answer:

R8000.

Step-by-step explanation:

First, let's calculate the amount they are going to have to pay the bank after 1 year. It is given by the following expression:

R5 000 * 1.28= R6400

Therefore, they have to pay R6400/12 monthly.

Now, in fifteen months the total amount to pay should be (R6400/12) * 15= R8000.

8 0

1 year ago

How can the ordered triple (−3, −2, 4) be plotted in coordinate space?

kari74 [83]

3 units back, 2 units left, 4 units up

5 0

2 years ago

Read 2 more answers

A sample of 41 observations is selected from one population with a population standard deviation of 3.4. The sample mean is 100.

Marizza181 [45]

Answer:

a) If we see the alternative hypothesis we see that we are conducting a bilateral test or two tail.

b) (-1.9886, 1.9886)

c) $t=\frac{(100 -98.4)-(0)}{\sqrt{\frac{3.4^2}{41}}+\frac{5.6^2}{45}}=1.617$

d) $p_v =2*P(t_{84}>1.617) =0.1096$

So with the p value obtained and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 is NOT significantly different than the mean for the group 2.

e) $p_v =2*P(t_{84}>1.617) =0.1096$

We can use the following excel code to calculate it: "=2*(1-T.DIST(1.617;84;TRUE))"

Step-by-step explanation:

The system of hypothesis on this case are:

Null hypothesis: $\mu_1 = \mu_2$

Alternative hypothesis: $\mu_1 \neq \mu_2$

Or equivalently:

Null hypothesis: $\mu_1 - \mu_2 = 0$

Alternative hypothesis: $\mu_1 -\mu_2\neq 0$

Our notation on this case :

$n_1 =41$ represent the sample size for group 1

$n_2 =45$ represent the sample size for group 2

$\bar X_1 =100$ represent the sample mean for the group 1

$\bar X_2 =98.4$ represent the sample mean for the group 2

$s_1=3.4$ represent the sample standard deviation for group 1

$s_2=5.6$ represent the sample standard deviation for group 2

Part a

If we see the alternative hypothesis we see that we are conducting a bilateral test or two tail.

Part b

On this case since the significance level is 0.05 and we are conducting a bilateral test we have two critical values, and we need on each tail of the distribution $\alpha/2 = 0.025$ of the area.

The distribution on this cas since we don't know the population deviation for both samples is the t distribution with $df=n_1+n_2 -2= 41+45-2=84$ degrees of freedom.

We can use the following excel codes in order to find the critical values:

"=T.INV(0.025,84)", "=T.INV(1-0.025,84)"

And we got: (-1.9886, 1.9886)

Part c

The statistic is given by this formula:

$t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{\sqrt{\frac{s^2_1}{n_1}}+\frac{S^2_2}{n_2}}$

And now we can calculate the statistic:

$t=\frac{(100 -98.4)-(0)}{\sqrt{\frac{3.4^2}{41}}+\frac{5.6^2}{45}}=1.617$

The degrees of freedom are given by:

$df=41+45-2=84$

Part d

And now we can calculate the p value using the altenative hypothesis:

$p_v =2*P(t_{84}>1.617) =0.1096$

So with the p value obtained and using the significance level given $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the mean of the group 1 is NOT significantly different than the mean for the group 2.

Part e

$p_v =2*P(t_{84}>1.617) =0.1096$

We can use the following excel code to calculate it: "=2*(1-T.DIST(1.617;84;TRUE))"

8 0

3 years ago

A freight train travels 44 feet in 1 second. At this rate, how many miles will it

Vitek1552 [10]

Answer:

The freight train will travel 30 miles.

Step-by-step explanation:

3600 seconds in one hour

44 feet a second

44 * 3600

158400

5280 feet in a mile

158400 / 5280

30 miles

6 0

3 years ago

Read 2 more answers

Which expression is a sum of a number and a product? O A. 2(x-9) O B. 6x- 4 O c. 4+ 2x O D.​

Which expression is a sum of a number and a product? O A. 2(x-9) O B. 6x- 4 O c. 4+ 2x O D.