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3 years ago

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Two altitudes of a triangle have lengths 12 and 14. What is the longest possible length of the third altitude, if it is a positi

ve integer?

1 answer:

Vedmedyk [2.9K]3 years ago

8 0

GGJKBVGKVJHKJL;KJHBGV

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Suppose the mean SAT verbal score is 525 with a standard deviation of 100, while the mean SAT math score is 575 with a standard

Ipatiy [6.2K]

Answer:

The mean of the combined math and verbal scores is 1100, while the standard deviation is 141.

Step-by-step explanation:

Normal variables

Normal variables have mean $\mu$ and standard deviation $\sigma$

When we add normal variables, the combined mean is the sum of both means, and the standard deviation is the square root of the sum of both variances. The distribution is still normal.

In this question:

Verbal: $\mu_{V} = 525, \sigma_{V} = 100$ .

Math: $\mu_{M} = 575, \sigma_{M} = 100$

Combined:

$\mu = \mu_{V} + \mu_{M} = 525 + 575 = 1100$

$\sigma = \sqrt{\sigma_{V}^{2}+\sigma_{M}^{2}} = \sqrt{100^2 + 100^2} = 141$

The mean of the combined math and verbal scores is 1100, while the standard deviation is 141.

6 0

3 years ago

How do I simplify (6^-2)(3^-3)(3 x 6)^4? Not the answer, just the simplified expression.

Mazyrski [523]

The simplification form of the provided expression is 108 after applying the integer exponent properties.

<h3>What is integer exponent?</h3>

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

We have an expression:

$=\left(6^{-2}\right)\left(3^{-3}\right)\left(3\:\cdot \:6\right)^4$

$=\dfrac{1}{36}\cdot \dfrac{1}{27}\left(3\cdot \:6\right)^4$

$=\dfrac{1}{36}\cdot \dfrac{1}{27}\cdot \:81\cdot \:1296$

$=\dfrac{1}{36}\cdot \dfrac{1}{27}\cdot \dfrac{104976}{1}$

$=\dfrac{104976}{972}$

= 108

Thus, the simplification form of the provided expression is 108 after applying the integer exponent properties.

Learn more about the integer exponent here:

brainly.com/question/4533599

#SPJ1

5 0

1 year ago

The problem is Question<br> Divide.52÷(−45)

Artemon [7]

Answer:

-1.555

Step-by-step explanation:

52/(-45)= -1.555555

6 0

2 years ago

Read 2 more answers

38 divided by 8. Show ALL work for credit. NO WORK NO CREDIT<br> :((

scZoUnD [109]

Answer:

38 / 8 is 4.75

Step-by-step explanation:

Um I tried putting a photo of my work but it wouldn't let me sorry ;-;

7 0

2 years ago

Make use of structure. For rectangle ABCD, two vertices are A(-2, 3) and B(4, 6). Find the slopes of BC, CD, and DA. Explain you

MrRissso [65]

We are given a rectangle ABCD

A(-2, 3)

B(4, 6)

We are asked to find the slopes of sides BC, CD, and DA.

Let me first draw a rectangle to better understand the problem

Recall that the slope is given by

$m=\frac{y_2−y_1}{ x_2−x_1}$ $\text{where}(x_1,y_1)=(-2,3)\text{and}(x_2,y_2)=(4,6)$

So the slope of side AB is

$m_{AB}=\frac{6-3}{4-(-2)}=\frac{3}{4+2}=\frac{3}{6}=\frac{1}{2}=0.5$

The sides BC and DA are perpenducluar to the side AB.

So their slopes will be

$m_{BC}=m_{DA}=\frac{1}{-m_{AB}}$

Substituting the value of slope of AB

$m_{BC}=m_{DA}=\frac{1}{-0.5}=-2$

The side CD is parallel to the side AB.

Parallel sides have equal slopes so

$m_{CD}=m_{AB}=\frac{1}{2}$

Therefore, the slopes of the rectangle ABCD are

$\begin{gathered} m_{AB}=m_{CD}=\frac{1}{2} \\ m_{BC}=m_{DA}=-2 \end{gathered}$

3 0

1 year ago