WILL MARK BRAINLIEST

The speeds of vehicles traveling on a highway are normally distributed with a population standard deviation of 7 miles per hour

True [87]

Answer: $(56.03\ ,63.97)$

Step-by-step explanation:

Given : The speeds of vehicles traveling on a highway are normally distributed .

Standard deviation: $\sigma: 7$

Since , sample size : $n=20$ , which is small sample (n<30) so the test applied here is a t-test.

Degree of freedom= $n-1=20-1=19$

Sample mean : $\overline{x}=60$

Level of significance : $1-\alpha:0.98$

Then , significance level : $\alpha: 1-0.98=0.02$

Using t-distribution table , Critical value : $\text{t-score}=t_{n-1, \alpha/2}= 2.539483$

The confidence interval for population mean is given by :-

$\overline{x}\pm t_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

$60\pm( 2.539483)\dfrac{7}{\sqrt{20}}\approx60\pm3.97=(56.03\ ,63.97)$

Hence, a 98% confidence interval for the population mean= $(56.03\ ,63.97)$

4 0

3 years ago

What property is 6+4+2

oksian1 [2.3K]

Answer:

Distributive property

Step-by-step explanation: This is distributive property because 4+2 equals six. you are distributing four and 2 to equal 6

8 0

3 years ago

(20pts) Prove that the product of any two odd numbers is always odd. Make sure to explain your proof

kozerog [31]

Answer:

See below (I hope this helps!)

Step-by-step explanation:

Because odd numbers are always 1 greater than even numbers, we can call the two odd numbers x + 1 and y + 1 where x and y are even integers. Multiplying the two gives us:

(x + 1) * (y + 1)

= x * y + x * 1 + 1 * y + 1 * 1

= xy + x + y + 1

We know that x * y will be even because x and y are also even and the sum of two even numbers will be even, and we also know that x and y are even and that 1 is odd. Since the sum of even and odd numbers is always odd, the product of any two numbers is always odd.

*NOTE: I put a limitation on x and y in my proof (the limitation was that x and y must be EVEN integers) but you don't have to do that, you could make the odd integers 2x + 1 and 2y + 1 where x and y could be any integer from the set Z like mirai123 did. I simply gave this proof because it was the first thing that came to mind. While mirai123's proof and mine are different, they are still both correct.

5 0

3 years ago

Read 2 more answers

the third term and the fifth term of a geometric progression are 2 and 1/8 respectively. If all terms are positive, find the sum

loris [4]

Answer:

42 + 2/3

Step-by-step explanation:

First, to calculate the sum of an infinite geometric series, our formula is

a₁/(1-r), with a₁ being the first term of the series and r being the common ratio. Therefore, we want to find both a₁ and r.

To find r, we can first determine that 2 * r = a₄ and a₄ * r = a₅, as the ratio separates one number from the next in a geometric series. Therefore, we have

2 * r * r = a₅

2 * r² = 1/8

divide both sides by 2 to isolate the r²

r² = 1/16

square root both sides to isolate r

r =± 1/4. Note the ± because r²=1/16 regardless of whether r = 1/4 or -1/4. However, because all terms are positive, r must be positive as well, or a₄, for example, would be 2 * (-1/4) = -0.5

Therefore, r = 1/4 .

To find the first term, we know that a₁ * r = a₂, and a₂ * r = a₃. Therefore, a₁ * r² = a₃ = 2

a₁ * 1/16 = 2

divide both sides by 1/16 to isolate a₁

a₁ = 2 * 1/ (1/16)

= 2 * 16

= 32

Plugging a₁ and r into our infinite geometric series formula, we have

a₁/(1-r)

= 32 / (1-1/4)

= 32/ (3/4)

= 32/ 0.75

= 42 + 2/3

3 0

3 years ago

A) 240 cm 2<br> B) 270 cm 2<br> C) 318 cm 2 <br> D) 348 cm 2

fgiga [73]

I think the answer is D.348

7 0

3 years ago