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3 years ago

-11=a+7 dolce equation

Mathematics

2 answers:

Lemur [1.5K]3 years ago

5 0

In order to get the answer to this question you will have to subtract 11 on both sides.

$-11=a+7$

$-7-7$

$-11 - 7 = -18$

$-18 = a$

$a = -18$

Which will mean the answer would be "-18."

Hope this helps.

zubka84 [21]3 years ago

4 0

-11 = a + 7 Given

-7 -7 Subtract 7 on each side to cancel out +7 and isolate variable

-18 = a Answer

Prove.

-11 = -18 + 7 Plug in variable value

-11 = -11

True.

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3 years ago

Majesty Video Production Inc. wants the mean length of its advertisements to be 26 seconds. Assume the distribution of ad length

Paladinen [302]

Answer:

a) By the Central Limit Theorem, approximately normally distributed, with mean 26 and standard error 0.44.

b) s = 0.44

c) 0.84% of the sample means will be greater than 27.05 seconds

d) 98.46% of the sample means will be greater than 25.05 seconds

e) 97.62% of the sample means will be greater than 25.05 but less than 27.05 seconds

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation(also called standard error) $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 26, \sigma = 2, n = 21, s = \frac{2}{\sqrt{21}} = 0.44$

a. What can we say about the shape of the distribution of the sample mean time?

By the Central Limit Theorem, approximately normally distributed, with mean 26 and standard error 0.44.

b. What is the standard error of the mean time? (Round your answer to 2 decimal places)

$s = \frac{2}{\sqrt{21}} = 0.44$

c. What percent of the sample means will be greater than 27.05 seconds?

This is 1 subtracted by the pvalue of Z when X = 27.05. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{27.05 - 26}{0.44}$

$Z = 2.39$

$Z = 2.39$ has a pvalue of 0.9916

1 - 0.9916 = 0.0084

0.84% of the sample means will be greater than 27.05 seconds

d. What percent of the sample means will be greater than 25.05 seconds?

This is 1 subtracted by the pvalue of Z when X = 25.05. So

$Z = \frac{X - \mu}{s}$

$Z = \frac{25.05 - 26}{0.44}$

$Z = -2.16$

$Z = -2.16$ has a pvalue of 0.0154

1 - 0.0154 = 0.9846

98.46% of the sample means will be greater than 25.05 seconds

e. What percent of the sample means will be greater than 25.05 but less than 27.05 seconds?"

This is the pvalue of Z when X = 27.05 subtracted by the pvalue of Z when X = 25.05.

X = 27.05

$Z = \frac{X - \mu}{s}$

$Z = \frac{27.05 - 26}{0.44}$

$Z = 2.39$

$Z = 2.39$ has a pvalue of 0.9916

X = 25.05

$Z = \frac{X - \mu}{s}$

$Z = \frac{25.05 - 26}{0.44}$

$Z = -2.16$

$Z = -2.16$ has a pvalue of 0.0154

0.9916 - 0.0154 = 0.9762

97.62% of the sample means will be greater than 25.05 but less than 27.05 seconds

8 0

3 years ago

A rectangular plot of land is to be enclosed by a fence. One side is along a river, and does not need to be enclosed. If the tot

Bad White [126]

Answer:

Width 150 meters.

Length = 350 meters.

Step-by-step explanation:

Let us assume the width of the fence = k meters

So, both sides = k + k = 2k meters

Also, the TOTAL fencing length = 600 m

So, the one side length of the fence = (600 - 2 k) meters

AREA = LENGTH x WIDTH

⇒ A(k) = (600 - 2k) (k)

or, A = -2k² + 600 k

The above equation is of the form: ax² +bx + C

Here: a = - 2 , b = 600 and C = 0

As a< 0, the parabola opens DOWNWARDS.

Here, x value is given as: $x = \frac{-b}{2a}$

Solving for the value of k similarly, we get:

$k = \frac{-b}{2a} = \frac{600}{2(-2)} = 150$

Thus the desired width = k = 150 meters

So, the desired dimensions of the plot is width 150 meters.

And length = 650 - 2k = 650 - 300 = 350 meters.

5 0

3 years ago

Enter the equivalent distance in km in the box.

devlian [24]

100 cm = 1m

To find 60 000cm, multiply by 600 :
60 000 cm = 600m

To convert from m to km, divide by 1000 :
600m ÷ 1000 = 0.6km

3 0

3 years ago