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2 years ago

The perimeter of a square is 32 centimeters. What is the length of one side?

1 answer:

6 0

L= length of one side of the square
Ok so we know the perimeter is 32 cm. Perimeter is the sum of all the sides of a shape. Now all four sides of a square are the same length. That means 4*L=32.
Now that we have the equation 4*L=32, we need to find a number that when multiplied by four, equals 32. Since 4*8=32, we know the answer must be 8cm.

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Suppose the weights of apples are normally distributed with a mean of 85 grams and a standard deviation of 8 grams. The weights

user100 [1]

Answer:

a) 0.0304 = 3.04% probability a randomly chosen apple exceeds 100 g in weight.

b) The weight that 80% of the apples exceed is of 78.28g.

Step-by-step explanation:

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.

Weights of apples are normally distributed with a mean of 85 grams and a standard deviation of 8 grams.

This means that $\mu = 85, \sigma = 8$

a. Find the probability a randomly chosen apple exceeds 100 g in weight.

This is 1 subtracted by the p-value of Z when X = 100. So

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

$Z = \frac{100 - 85}{8}$

$Z = 1.875$

$Z = 1.875$ has a p-value of 0.9697

1 - 0.9696 = 0.0304

0.0304 = 3.04% probability a randomly chosen apple exceeds 100 g in weight.

b. What weight do 80% of the apples exceed?

This is the 100 - 80 = 20th percentile, which is X when Z has a p-value of 0.2, so X when Z = -0.84.

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

$-0.84 = \frac{X- 85}{8}$

$X - 85 = -0.84*8$

$X = 78.28$

The weight that 80% of the apples exceed is of 78.28g.

5 0

2 years ago

Is -8x + 10 = 2(5-4x) one solution

Basile [38]

The answer to this is true

3 0

3 years ago

Two poles are connected by a wire that is also connected to the ground. The first pole is 18 ft tall and the second pole is 24 f

9966 [12]

Answer:

72 feet from the shorter pole

Step-by-step explanation:

The anchor point that minimizes the total wire length is one that divides the distance between the poles in the same proportion as the pole heights. That is, the two created triangles will be similar.

The shorter pole height as a fraction of the total pole height is ...

18/(18+24) = 3/7

so the anchor distance from the shorter pole as a fraction of the total distance between poles will be the same:

d/168 = 3/7

d = 168·(3/7) = 72

The wire should be anchored 72 feet from the 18 ft pole.

_____

<em>Comment on the problem</em>

This is equivalent to asking, "where do I place a mirror on the ground so I can see the top of the other pole by looking in the mirror from the top of one pole?" Such a question is answered by reflecting one pole across the plane of the ground and drawing a straight line from its image location to the top of the other pole. Where the line intersects the plane of the ground is where the mirror (or anchor point) should be placed. The "similar triangle" description above is essentially the same approach.

Alternatively, you can write an equation for the length (L) of the wire as a function of the location of the anchor point:

L = √(18²+x²) + √(24² +(168-x)²)

and then differentiate with respect to x and find the value that makes the derivative zero. That seems much more complicated and error-prone, but it gives the same answer.

7 0

2 years ago

Which numbers are solutions of the inequality?<br><br> x > –5; –7, –5, –1

yanalaym [24]

Answer:

-1 is the only answer that is greater than -5

3 0

2 years ago

What is the sum of 1/5 + -1 3/5?

Licemer1 [7]

Answer:

-1 2/5

Hope this helped! @[email protected]

6 0

3 years ago