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3 years ago

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2 sides of a triangle measure 34 inches and 52 inches. What is the possible third side "x"? A.) 34 < x < 52 B.) 0 < x &

lt; 18 C.) 18 < x < 86 D.) 0 < x < 86

1 answer:

frozen [14]3 years ago

3 0

Answer:

C.) 18 < x < 86

Step-by-step explanation:

triangle property: sum of any 2 sides is larger than the third side

if x <= 18 18 + 34 no larger than 54

if x >= 86 34 + 52 no larger than 86

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In a 3-digit number, the hundreds digit is one more than the ones digit and the tens digit is twice the hundreds digit. If the s

MaRussiya [10]

Answer:

The mentioned number in the exercise is:

<u>362</u>

Step-by-step explanation:

To obtain the mentioned number in the exercise, first you must write the equations you can obtain with it.

If:

x = hundredths digit
y = tens digit
z = ones digit

We can write:

x = z + 1 (the hundreds digit is one more than the ones digit).
y = 2x (the tens digit is twice the hundreds digit).
x + y + z = 11 (the sum of the digits is 11).

Taking into account these data, we can use the third equation and replace it to obtain the number and the value of each digit:

x + y + z = 11
(z + 1) + y + z = 11 (remember x = z + 1)
z + 1 + y + z = 11
z + z +y + 1 = 11 (we just ordered the equation)
2z + y + 1 = 11 (z + z = 2z)
2z + y = 11 - 1 (we passed the +1 to the other side of the equality to subtract)
2z + y = 10
2z + (2x) = 10 (remember y = 2x)
2z + 2x = 10
2z + 2(z + 1) = 10 (x = z + 1 again)
2z + 2z + 2 = 10
4z + 2 = 10
4z = 10 - 2
4z = 8
z = 8/4
<u>z = 2</u>

Now, we know z (the ones digit) is 2, we can use the first equation to obtain the value of x:

x = z + 1
x = 2 + 1
<u>x = 3</u>

And we'll use the second equation to obtain the value of y (the tens digit):

y = 2x
y = 2(3)
<u>y = 6</u>

Organizing the digits, we obtain the number:

Number = xyz
<u>Number = 362</u>

As you can see, <em><u>the obtained number is 362</u></em>.

8 0

3 years ago

what is the area of the figure ? answers a. 12 units2 b. 17 units 2 c. 16 units 2 d. 24 units2 e. none

stellarik [79]

9514 1404 393

Answer:

17 square units

Step-by-step explanation:

There are several ways you can divide this figure into areas that are easily computed.

One that comes to mind is to consider the triangle that would include the missing area at lower right. That triangle would have a base of 6 and a height of 8, so an area of ...

A = (1/2)bh

A = (1/2)(6)(8) = 24 . . . . square units

The part at lower right that is cut out is a sort of reversed L-shape that is 3 squares along the bottom and 4 more up the side, for a total of 7 squares.

Then the area of the shaded part is ...

A = 24 - 7 = 17 . . . . square units

3 0

3 years ago

I need answer asap pls help

MariettaO [177]

Answer: A= (3,-3) . B(4,1). C= (1,0)

Step-by-step explanation:

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3 years ago

At a new exhibit in the Museum of Science, people are asked to choose between 94 or 220 random draws from a machine. The machine

Tresset [83]

Answer:

0.0869 = 8.69% probability of getting more than 61% green balls.

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 normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, 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 $s = \frac{\sigma}{\sqrt{n}}$ .

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

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$

The machine is known to have 99 green balls and 78 red balls.

This means that $p = \frac{99}{99+78} = 0.5593$

Mean and standard deviation:

$\mu = p = 0.5593$

$s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.5593*0.4407}{99+78}} = 0.0373$

a. Calculate the probability of getting more than 61% green balls.

This is 1 subtracted by the pvalue of Z when X = 0.61. So

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

By the Central Limit Theorem

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

$Z = \frac{0.61 - 0.5593}{0.0373}$

$Z = 1.36$

$Z = 1.36$ has a pvalue of 0.9131

1 - 0.9131 = 0.0869

0.0869 = 8.69% probability of getting more than 61% green balls.

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3 years ago

When data is displayed with a scatter plot, it is often useful to attempt to represent that data with the equation of a straight

Alexus [3.1K]

The line is often referred to as the "line of best fit", this line is drawn so that more accurate conclusions can be drawn from given data. This has numerous uses across the sciences.

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3 years ago