A truck driver drove 120 miles in 1 3/4 hours. What is the speed of the truck in miles per hour

Bones Brothers & Associates prepare individual tax returns. Over prior years, Bones Brothers have maintained careful records

madreJ [45]

Answer:

For this case we have the following info related to the time to prepare a return

$\mu =90 , \sigma =14$

And we select a sample size =49>30 and we are interested in determine the standard deviation for the sample mean. From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And the standard deviation would be:

$\sigma_{\bar X} =\frac{14}{\sqrt{49}}= 2$

And the best answer would be

b. 2 minutes

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Solution to the problem

For this case we have the following info related to the time to prepare a return

$\mu =90 , \sigma =14$

And we select a sample size =49>30 and we are interested in determine the standard deviation for the sample mean. From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And the standard deviation would be:

$\sigma_{\bar X} =\frac{14}{\sqrt{49}}= 2$

And the best answer would be

b. 2 minutes

3 0

2 years ago

<img src="https://tex.z-dn.net/?f=simplify%20%5Csqrt%7B21%20-%2020i%7D%20" id="TexFormula1" title="simplify \sqrt{21 - 20i} " al

Valentin [98]

Answer:

o. k this is a required answere

6 0

3 years ago

Suppose a three-seat city council election. For each seat, one progressive and one conservative is running, and voters must choo

Kitty [74]

Answer:

The probability that conservative party wins all 3 seats is 0.216

The probability that conservative party wins exactly two seats is 0.432

Step-by-step explanation:

Consider the provided information.

The probability of a conservative candidate winning is p=0.6.

The probability of one progressive candidate will win is: 1-0.6=0.4

Part (a) What is the probability that the conservative party wins all three seats?

According to binomial distribution: $b(x; n, p) =^nC_xp^x(1- p)^{n-x}$

$P(x=3) =^3C_3(0.6)^3 (0.4)^{3-3}$

$P(x=3) =(0.6)^3$

$P(x=3)=0.216$

P(conservative party wins all 3 seats) = 0.216

Hence, the probability that conservative party wins all 3 seats is 0.216

Part (a) What is the probability that the conservative party wins exactly two seats?

$P(x=2) =^3C_2(0.6)^2 (0.4)^{3-2}$

$P(x=2) =3(0.36)(0.4)$

$P(x=2) =0.432$

Hence, the probability that conservative party wins exactly two seats is 0.432

5 0

3 years ago

HELP PLZZ will give brainliest <3

melisa1 [442]

Answer:

0

1

Step-by-step explanation:

First question:

You are given a side, a, and its opposite angle, A. You are also given side b. Use that in the law of sines and solve for the other angle, B.

$\dfrac{a}{\sin A} = \dfrac{b}{\sin B}$

$\dfrac{10}{\sin 30^\circ} = \dfrac{40}{\sin B}$

$\dfrac{1}{0.5} = \dfrac{4}{\sin B}$

$\sin B = 2$

The sine function can never equal 2, so there is no triangle in this case.

Answer: no triangle

Second question:

You are given a side, b, and its opposite angle, B. You are also given side c. Use that in the law of sines and solve for the other angle, C.

$\dfrac{b}{\sin B} = \dfrac{c}{\sin C}$

$\dfrac{10}{\sin 63^\circ} = \dfrac{}{\sin C}$

$\sin C = \dfrac{8.9\sin 63^\circ}{10}$

$C = \sin^{-1} \dfrac{8.9\sin 63^\circ}{10}$

$C \approx 52.5^\circ$

One triangle exists for sure. Now we see if there is a second one.

Now we look at the supplement of angle C.

m<C = 52.5°

supplement of angle C: m<C' = 180° - 52.5° = 127.5°

We add the measures of angles B and the supplement of angle C:

m<B + m<C' = 63° + 127.5° = 190.5°

Since the sum of the measures of these two angles is already more than 180°, the supplement of angle C cannot be an angle of the triangle.

Answer: one triangle

3 0

3 years ago

Are 9 and 1/9 reciprocals?

Harlamova29_29 [7]

Answer:

yes

Step-by-step explanation:

9 can be represented as 9/1, which is the reciprocal of 1/9.

5 0

2 years ago

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