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3 years ago

How to change 78/5 into a mixed number

Mathematics

2 answers:

hammer [34]3 years ago

8 0

Answer:

$15\frac{3}{5}$

Step-by-step explanation:

to prove the answer:

$15\frac{3}{5}$

15*5+3/5

75+3/5

78/5

therefore , $15\frac{3}{5}$ = 78/5

ch4aika [34]3 years ago

6 0

Answer:

Divide the numerator by the denominator. 78 ÷ 5 = 15 with a remainder of 3.

Write down the whole number 15 and then write down the remainder as new numerator (3) above the denominator (5), As below : 15 35.

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Amy has a triangle with side lengths of 6 and 8. What is the length of the hypotenuse.

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Hello There!

The length of the hypotenuse is 10.

We know what 2 sides are 6 and 8.

To find the third side we use the formula a^2 + b^2 = c^2

So we multiply 6 by 6 which equals 36 and then multiply 8 by 8 which equals 64.

Next we add 64 and 36 together and we get 100.

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3 years ago

How can (4x⁵/2x²)³ be solved in 2 different ways

Margaret [11]

We assume that we need to simplify the expression in two different ways.

Answer:

One way: Raise both, the numerator and denominator, to the third power, and then simplify the expression.

Second way: Simplify the terms inside parentheses, and then raise the result to the third power.

The result of both ways is the same: $\\8x^{9}$

Step-by-step explanation:

One way

Raise both, the numerator and denominator, to the third power, and then simplify the expression:

$\\ (\frac{4x^{5}}{2x^{2}})^{3}$

$\\ (\frac{64x^{5*3}}{8x^{2*3}})$

$\\ (\frac{64x^{15}}{8x^{6}})$

$\\ \frac{64}{8}\frac{x^{15}}{x^{6}}$

$\\8x^{9}$

This is the first simplification.

Second way

Simplify the terms inside parentheses, and then raise the result to the third power.

$\\ (\frac{4x^{5}}{2x^{2}})^{3}$

$\\ (\frac{4}{2}*\frac{x^{5}}{x^{2}})^{3}$

$\\ (2*x^{5-2})^{3}$

$\\ (2*x^{3})^{3}$

$\\ (2^{3}*x^{3*3})$

$\\ (8*x^{9})$

or $\\ 8x^{9}$ .

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When the sample size and the sample proportion remain the same, a 90 percent confidence interval for a population proportion p w

deff fn [24]

Answer:

A 90% confidence interval for p will be narrower than the 99% confidence interval.

Step-by-step explanation:

The formula to compute the (1 - α) % confidence interval for a population proportion is:

$CI=\hat p\pm z_{\alpha /2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

Here $\hat p$ is the sample proportion.

The margin of error of the confidence interval is:

$MOE= z_{\alpha /2}\sqrt{\frac{\hat p(1-\hat p)}{n}}$

The MOE is dependent on:

Confidence level
Standard deviation
Sample size

The MOE is directly related to the confidence level and standard deviation.

So if any of the two increases then the MOE also increases, thus widening the confidence interval.

And the MOE is inversely related to the sample size.

So if the sample increases the MOE decreases and vice versa.

It is provided that the sample size and the sample proportion are not altered.

The critical value of z for 90% confidence level is:

$z_{\alpha/2}= z_{0.10/2}=z_{0.05}=1.645$

And the critical value of z for 99% confidence level is:

$z_{\alpha/2}= z_{0.05/2}=z_{0.05}=1.96$

So as the confidence level increases the critical value increases.

Thus, a 90% confidence interval for p will be narrower than the 99% confidence interval.

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3 years ago

How to change 78/5 into a mixed number​

How to change 78/5 into a mixed number