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3 years ago

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I’m confused on this explain

1 answer:

romanna [79]3 years ago

6 0

Triangles BAD and BCD are congruent by the HL theorem. That is, they have identical length hypotenuses (BD) and one leg is also identical in length to that in the other triangle. (AD ≅ CD)

Since the triangles are congruent, corresponding angles are equal, so ∠CBD = ∠ABD = 28°. The angle you are interested in is the sum of these two angles,

... ∠ABC = 28°+28° = 56°

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A group of high school athletes has an average GPA of 2.7 with a standard deviation of 0.9. a)Find the percentage of athletes wh

mart [117]

Answer:

a) The percentage of athletes whose GPA more than 1.665 is 87.49%.

b) John's GPA is 3.645.

Step-by-step explanation:

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:

$\mu = 2.7, \sigma = 0.9$

a)Find the percentage of athletes whose GPA more than 1.665.

This is 1 subtracted by the pvalue of Z when X = 1.665. So

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

$Z = \frac{1.665 - 2.7}{0.9}$

$Z = -1.15$

$Z = -1.15$ has a pvalue of 0.1251

1 - 0.1251 = 0.8749

The percentage of athletes whose GPA more than 1.665 is 87.49%.

b) John's GPA is more than 85.31 percent of the athletes in the study. Compute his GPA.

His GPA is X when Z has a pvalue of 0.8531. So it is X when Z = 1.05.

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

$1.05 = \frac{X - 2.7}{0.9}$

$X - 2.7 = 1.05*0.9$

$X = 3.645$

John's GPA is 3.645.

8 0

3 years ago

Order these decimals form greatest to least 3.6; 0.36; 36; 0.036

aliina [53]

36, 3.6, 0.36, 0.036 is the order

4 0

3 years ago

Read 2 more answers

Folding a rectangle along one diagonal results in a shape whose area is 2/3 that of the original

Charra [1.4K]

Answer:

60°

Step-by-step explanation:

<em>Refer to attached picture</em>

Given rectangle ABCD. Its folded shape is given as well.

It has sides a and b and diagonal d, with the angle BCD marked as α.

We need to find the value of angle AOC or BOD.

This is going to be 2α, which is easy to find out. BOD is cut by the angle bisector, each of the angles is α.

Let the area of the rectangle is A, then the folded shape has area 2/3A.

<u>The area of rectangle ABCD:</u>

A = ab

<u>From the triangle CBD we get:</u>

a/d = sin α ⇒ a = d sin α
b/d = cos α ⇒ b = d cos α

<u>Then</u>

A = d sin α * d cos α = d²sin α cos α

Now, lets find the area of the folded shape.

It is the area of the rectangle minus the area of the triangle CMB as this part is lost as part of overlap.

<u>Area of the triangle:</u>

A = 1/2dh

<u>Since h/(d/2) = tan α ⇒ h = 1/2d tan α, the area is:</u>

A = 1/2d*1/2d tan α = 1/4d² tan α

<u>We have the difference of the areas which is 1/3 of the area of the rectangle:</u>

1/3(d²sin α cos α) = 1/4d² tan α
sin α cos α = 3/4 tan α
sin α cos α = 3/4 sin α / cos α
cos² α = 3/4
cos α = √(3/4)
cos α = √3/2
α = arccos (√3/2)
α = 30°

<u>The acute angle formed by the two diagonals of the rectangle is:</u>

2α = 2*30° = 60°

3 0

2 years ago

Round to the nearest hundred 449-162

sergiy2304 [10]

499-162=287
287 rounded to the nearest hundred is 300

the answer is 300

6 0

3 years ago

Read 2 more answers

Can i please get help with this question?

docker41 [41]

The area is 60 and the lenght is 7 times longer than the width which is (w+7) and the formula is l×w=A, and the answer is
w(w+7)=60

5 0

3 years ago