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3 years ago

Plssss some help me with my homework

Mathematics

2 answers:

Sergio039 [100]3 years ago

4 0

The missing side length is 8 units

Fantom [35]3 years ago

4 0

Answer:

a = 8

Step-by-step explanation:

Pythagoras

hypotenuse² = Attitude ² + Base²

10² = a² + 6²

100 = a² +36

change side ; a² = 100-36

a² = 64

a = √64

a = 8 (Positive number only. not minus number)

so a = 8

hope it helps ☺️

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The answer is (-4, -3)

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Two persons start running simultaneously from a certain point, one towards south and another towards east. After 2 hours, the di

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The Pythagorean theorem is sometimes known as Pythagoras' theorem. The speed of the faster person is 40 kmph.

<h3>What is Pythagoras' theorem?</h3>

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.

Let the speed of one person be represented by x, then the speed of the other person, if the speed of the second person is 75% of the first.

Speed of first-person = x
Speed of second-person = 75% of Speed of first-person = 0.75x

Now, the distance covered by two persons in 2 hours is,

Distance covered by the first-person = x × 2 = 2x
Distance covered by the second-person = 0.75x × 2 = 1.5x

Since one person runs towards the south and another towards the east. Therefore, will form a 90° angle between their directions.

Now, the distance between the two after two hours is 100 km, therefore, we can write,

(2x)² + (1.5x)² = 100²

4x² + 2.25x² = 10000

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x² = 10000/6.25

x² = 1600

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Hence, the speed of the faster person is 40 kmph.

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1 year ago

Find the z score that has 70.54% of the distribution area to its right

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The z score that has 70.54% of the distribution area is 9.92

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For the random variable x, the z-score is;

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therefore, 70.54% of the area under the curve lies to the right of x,

then the area to the left of x is;

100 - 70.54 = 29.46%

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Therefore, we get;

(x - 11)/2 = -0.54

x - 11 = -0.54(2)

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1 year ago

Suppose the test scores for a college entrance exam are normally distributed with a mean of 450 and a s. d. of 100. a. What is t

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Answer:

a) 68.26% probability that a student scores between 350 and 550

b) A score of 638(or higher).

c) The 60th percentile of test scores is 475.3.

d) The middle 30% of the test scores is between 411.5 and 488.5.

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:

$\mu = 450, \sigma = 100$

a. What is the probability that a student scores between 350 and 550?

This is the pvalue of Z when X = 550 subtracted by the pvalue of Z when X = 350. So

X = 550

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

$Z = \frac{550 - 450}{100}$

$Z = 1$

$Z = 1$ has a pvalue of 0.8413

X = 350

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

$Z = \frac{350 - 450}{100}$

$Z = -1$

$Z = -1$ has a pvalue of 0.1587

0.8413 - 0.1587 = 0.6826

68.26% probability that a student scores between 350 and 550

b. If the upper 3% scholarship, what score must a student receive to get a scholarship?

100 - 3 = 97th percentile, which is X when Z has a pvalue of 0.97. So it is X when Z = 1.88

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X when Z has a pvalue of 0.60. So it is X when Z = 0.253

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$0.253 = \frac{X - 450}{100}$

$X - 450 = 0.253*100$

$X = 475.3$

The 60th percentile of test scores is 475.3.

d. Find the middle 30% of the test scores.

50 - (30/2) = 35th percentile

50 + (30/2) = 65th percentile.

35th percentile:

X when Z has a pvalue of 0.35. So X when Z = -0.385.

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

$-0.385 = \frac{X - 450}{100}$

$X - 450 = -0.385*100$

$X = 411.5$

65th percentile:

X when Z has a pvalue of 0.35. So X when Z = 0.385.

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

$0.385 = \frac{X - 450}{100}$

$X - 450 = 0.385*100$

$X = 488.5$

The middle 30% of the test scores is between 411.5 and 488.5.

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3 years ago

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3 years ago

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