How do I prove this?

Explain how the areas of a triangle and a parallelogram with the same base and height are related

kaheart [24]

Triangles are the most basic type of polygon that make up all other types of polygons. In other words,you can fit a certain number of congruent triangles into any kind of polygon.

6 0

3 years ago

Is the point (2,8) a solution of the equation y = 13x + 12? O Yes O No

vovikov84 [41]

Answer:

O No

Explanation:

Given equation: y = 13x + 12

To check if (2, 8) is a solution of the given equation.

Substitute x and y value in equation and check if it is true.

$\rightarrow y = 13x+12$

(x, y) = (2, 8)

$\rightarrow 8 = 13(2)+12$

simplify

$\rightarrow 8 = 38$

This following statement is false and hence (2, 8) is not a solution.

6 0

2 years ago

Find mRS using this picture. .

Degger [83]

I don’t understand your this question

6 0

2 years ago

(1 point) Scores on a certain intelligence test for children between ages 13 and 15 years are approximately normally distributed

Fynjy0 [20]

Answer:

a) 0.719 = 71.90% of children aged 13 to 15 years old have scores on this test above 92

b) A score of 89.8 marks the lowest 25 percent of the distribution

c) A score of 145.48 marks the highest 5 percent of the distribution

Step-by-step explanation:

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.

In this problem, we have that:

$\mu = 106, \sigma = 24$

(a) What proportion of children aged 13 to 15 years old have scores on this test above 92 ?

This is 1 subtracted by the pvalue of Z when X = 92. So

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

$Z = \frac{92 - 106}{24}$

$Z = -0.58$

$Z = -0.58$ has a pvalue of 0.2810

1 - 0.2810 = 0.719

0.719 = 71.90% of children aged 13 to 15 years old have scores on this test above 92

(b) What score which marks the lowest 25 percent of the distribution?

The 25th percentile, which is X when Z has a pvalue of 0.25. So it is X when Z = -0.675.

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

$-0.675 = \frac{X - 106}{24}$

$X - 106 = -0.675*24$

$X = 89.8$

A score of 89.8 marks the lowest 25 percent of the distribution

(c) Enter the score that marks the highest 5 percent of the distribution

The 100-5 = 95th percentile, which is X when Z has a pvalue of 0.95. So it is X when Z = 1.645

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

$1.645 = \frac{X - 106}{24}$

$X - 106 = 1.645*24$

$X = 145.48$

A score of 145.48 marks the highest 5 percent of the distribution

8 0

3 years ago

PLEASE HELP ASAP NOW WILL MARK BRAINIEST LOTS OF POINTS!!!! HELP NOWWWWWWWWWWW 22. Explain why an sin^-1(sin(3pi/4))not equal 3p

NemiM [27]

22. The range of the arcsine function (sin⁻¹(x)) is [-π/2, π/2]. The function will return π/4 for arcsin(sin(3π/4)) = arcsin(1/√2).

The sine function does not pass the horizontal line test, so it has no inverse over its entire domain. The arcsine function is only the inverse of the sine function over a limited domain/range.

25. sin(cos(π/2)) = sin(0) = 0.

As with any nested function evaluation, you evaluate the inner function first.

... cos(π/2) = 0

Then you evaluate the outer function.

... sin(0) = 0

7 0

3 years ago