What is the actual distance between sauger ties and Kingston?

A circle has a diameter of 4 inches. A square has a side length of 4 inches. What is true about the areas of these two figures?

Nuetrik [128]

The area of the square is greater than the circle: the area of the circle is pi(r)^2 while the area of the square is length times width. The area of the circle is about 12.5 while the area of the square is 16.

4 0

3 years ago

Find the sum of first 20 to terms of an ap in which d is equal to 7 and 20 second term is 149

GuDViN [60]

Answer:

1370

Step-by-step explanation:

<h3>Given</h3>

AP with d= 7 and a₂₂ = 149

Sum of first 20 terms

<h3>Solution</h3>

<u>First, let's get the value of the first term:</u>

aₙ = a + (n-1)d
a₂₂ = a + 21d
149 = a + 21*7
a = 149 - 147
a= 2

<u>Next, let's find the sum of the first 20 terms</u>

Sₙ = 1/2n(2a+ (n-1)d)
S₂₀ = 1/2*20(2*2 + 19*7) = 10(4 + 133) = 10*137 = 1370

<u>Answer is</u> 1370

6 0

3 years ago

Read 2 more answers

What are the following numbers writen as powers? 243

puteri [66]

Answer:

$243=3^5$

Step-by-step explanation:

We have to write 243 as a power of some number.

So, if we factorize 243 we get,

243 = 3 × 3 × 3 × 3 × 3

Therefore, we can write 243 as a power of 3.

No other number can be written in powers of 243 because it do not contain any other factor than 3.

Hence, 243 can be written as :

$243=3^5$

6 0

4 years ago

The distance between Dania and Hollywood is shown on the map. What is the actual distance between Dania and Hollywood?

pishuonlain [190]

Answer:

15 miles

Step-by-step explanation:

If there are 2.5 inches and 1 inch is 6 miles, then just multiply 6 by 2.5 to get 15

6*2.5=15

8 0

3 years ago

Men are believed to have a slightly longer average length of short hospital stays than women; 5.2 days versus 4.5 days respectiv

Georgia [21]

Answer:

Since our calculated value is lower than our critical value, $z_{calc}=2.02$ , we have enough evidence to FAIL to reject the null hypothesis at 1% of singificance. So there is not nough evidence to conclude that mean for men it's significantly higher than the mean for female.

Step-by-step explanation:

1) Data given and notation

$\bar X_{1}=5.2$ represent the mean for group men

$\bar X_{2}=4.5$ represent the mean for group women

Assuming these values for the remaining data:

$\sigma_{1}=1.2$ represent the population standard deviation for the sample men

$\sigma_{2}=1.5$ represent the population standard deviation for the sample women

$n_{1}=32$ sample size for the group men

$n_{2}=30$ sample size for the group women

z would represent the statistic (variable of interest)

$p_v$ represent the p value

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if the mean for men it's higher than the mean for women, the system of hypothesis would be:

H0: $\mu_{1} \leq \mu_{2}$

H1: $\mu_{1} > \mu_{2}$

If we analyze the size for the samples both are higher than 30, and we know the population deviation's, so for this case is better apply a z test to compare means, and the statistic is given by:

$z=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}$ (1)

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

3) Calculate the statistic

We have all in order to replace in formula (1) like this:

$z=\frac{5.2-4.5}{\sqrt{\frac{1.2^2}{32}+\frac{1.5^2}{30}}}=2.02$

4) Find the critical value

In order to find the critical value we need to take in count that we are conducting a right tailed test, so we are looking on the normal standard distribution a value that accumulats 0.01 of the area on the right and 0.99 of the area on the left. We can us excel or a table to find it, for example the code in Excel is:

"=NORM.INV(1-0.01,0,1)", and we got $z_{critical}=2.33$

5) Statistical decision

Since our calculated value is lower than our critical value, $z_{calc}=2.02$ , we have enough evidence to FAIL to reject the null hypothesis at 1% of significance. So there is not nough evidence to conclude that mean for men it's significantly higher than the mean for female.

6 0

4 years ago