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3 years ago

The attachment is there

Mathematics

1 answer:

scZoUnD [109]3 years ago

3 0

Answer:

Option D: 10.7 is the correct answer.

Step-by-step explanation:

Given that:

Hypotenuse of right triangle = 14

Height of right triangle = 9

Length of missing side = b

We can solve for missing side length by using Pythagorean theorem;

$a^2+b^2=c^2$

Here,

a = 9 , c = 14

$(9)^2+(b)^2=(14)^2\\81+b^2=196\\$

Subtracting 81 from both sides

$81-81+b^2=196-81\\b^2=115$

Taking square root on both sides

$\sqrt{b^2}=\sqrt{115}\\b=10.7$

The length of missing side is 10.7

Hence,

Option D: 10.7 is the correct answer.

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I need to find the answer to this question and please explain how.

deff fn [24]

Among the given statements, the true statements are:

If a number is divisible by 3 and 4, then it is divisible by 12.
The number 119 is a composite number.

In the question, we are asked for the true statements among the given options:

1. All even numbers are composite numbers.

Answer - False

Reason - 2 is an even number, which is not a composite number.

2. If a number is divisible by 3 and 4, then it is divisible by 12.

Answer - True

Reason - If any number, n, is divisible by any two numbers, x and y, then it is also divisible by their LCM, and the LCM of 3 and 4 is 12.

3. All prime numbers are odd numbers.

Answer - False

Reason - 2 is a prime number, which is not odd.

4. The number 119 is a composite number.

Answer - True

Reason - The number 119 is a composite number, as it is not a prime number, as it is divisible by 7 and 17 too, other than 1 and itself.

5. 12 is a factor of 6.

Answer - False.

Reason - When 6 is divided by 12, the integral quotient that we get is 0, and the remainder is 6, but for any number x, to be a factor of y, on dividing y by x, the remainder should be 0.

6. If a number is divisible by 6 and 4, then it is also divisible by 4.

Answer - False

Reason - If any number, n, is divisible by any two numbers, x and y, then it is also divisible by their LCM, and the LCM of 6 and 4 is 12.

Thus, a number divisible by 6 and 4 is divisible by 12 but not necessarily by 24. Example 12 is divisible by both 6 and 4 but not divisible by 24.

Thus, among the given statements, the true statements are:

If a number is divisible by 3 and 4, then it is divisible by 12.
The number 119 is a composite number.

Learn more about divisibility at

brainly.com/question/26789053

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2 years ago

A cliff Diver jumps from 50 feet into a lake. After hitting the water he travelled 22 feet below the surface. How far did he tra

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Add both distances together:

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3 years ago

The American Management Association is studying the income of store managers in the retail industry. A random sample of 49 manag

VashaNatasha [74]

Answer:

a) The 95% confidence interval for the income of store managers in the retail industry is ($44,846, $45,994), having a margin of error of $574.

b) The interval mean that we are 95% sure that the true mean income of all store managers in the retail industry is between $44,846 and $45,994.

Step-by-step explanation:

Question a:

We have to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.95}{2} = 0.025$

Now, we have to find z in the Z-table as such z has a p-value of $1 - \alpha$ .

That is z with a p-value of $1 - 0.025 = 0.975$ , so Z = 1.96.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.96\frac{2050}{\sqrt{49}} = 574$

The lower end of the interval is the sample mean subtracted by M. So it is 45420 - 574 = $44,846.

The upper end of the interval is the sample mean added to M. So it is 45420 + 574 = $45,994.

The 95% confidence interval for the income of store managers in the retail industry is ($44,846, $45,994), having a margin of error of $574.

Question b:

The interval mean that we are 95% sure that the true mean income of all store managers in the retail industry is between $44,846 and $45,994.

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Answer:

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