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Alex17521 [72]
3 years ago
14

The length of the base of a triangle is twice it’s height. If the area of the triangle is 441 square kilometers, find the height

Mathematics
1 answer:
Sonja [21]3 years ago
5 0

Answer:

21 kilometers

Step-by-step explanation:

Let the height be x. Then, the length of the base is 2x. The formula for the area is of the triangle is given by base*height/2. Therefore, the area of the triangle is equal to \frac{x \cdot 2x}{2} = x^2, which is in turn equal to 441. Since x must be positive, then 21^2=441, meaning that the height is 21 kilometers.

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A machine that produces ball bearings has initially been set so that the true average diameter of the bearings it produces is .5
lara [203]

Answer:

7.3% of the bearings produced will not be acceptable

Step-by-step explanation:

Problems of normally distributed samples can be 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 = 0.499, \sigma = 0.002

Target value of .500 in. A bearing is acceptable if its diameter is within .004 in. of this target value.

So bearing larger than 0.504 in or smaller than 0.496 in are not acceptable.

Larger than 0.504

1 subtracted by the pvalue of Z when X = 0.504.

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

Z = \frac{0.504 - 0.494}{0.002}

Z = 2.5

Z = 2.5 has a pvalue of 0.9938

1 - 0.9938= 0.0062

Smaller than 0.496

pvalue of Z when X = -1.5

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

Z = \frac{0.496 - 0.494}{0.002}

Z = -1.5

Z = -1.5 has a pvalue of 0.0668

0.0668 + 0.0062 = 0.073

7.3% of the bearings produced will not be acceptable

4 0
3 years ago
PLSS HELP
dsp73

Answer:

B,C, and D

Give thanks and brainliest!! :P

4 0
3 years ago
Read 2 more answers
Which number sentence is not true?
Nonamiya [84]

Answer:

a

Step-by-step explanation:

6 0
2 years ago
if each dimension of a unit cube is increased by 1. what is the ratio between the surface area of the new cube to that of the or
nexus9112 [7]

Answer:

4:1 or 4/1

Step-by-step explanation:

Original surface area: Each side is 1 * 1 = 1 and there are 6 sides, so 1 * 6 = 6.

New surface area: Each side is 2*2 = 4, and there are 6 sides, so 4 * 6 = 24

The ratio would be 24:6, or 4:1. As a fraction, this would be 4/1

4 0
3 years ago
Read 2 more answers
6.1.3 quiz pythagorean theorem question 9
Olegator [25]

Answer: 14.73

Step-by-step explanation:

The given triangle is a right angle triangle.

EF^2 + DF^2 = ED^2

The hypotenuse is |ED| while the two shorter legs are |EF| and |DF|.

We can then apply the Pythagoras Theorem to find the length of EF.

(EF)^2 + (DF)^2 = (ED)^2

(EF)^2 + (12)^2 = (19)^2

(EF)^2 + 144 = 361

(EF)^2 = 361 - 144

(EF)^2 = 217

EF = 14.73

6 0
3 years ago
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