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3 years ago

Rectangle HYGT has a perimeter of 170 inches. If the length is 10x - 7

Mathematics

1 answer:

frozen [14]3 years ago

5 0

Answer:

The wide of the rectangle = 42 inches

The length of the rectangle = 43 inches

Step-by-step explanation:

Step(i):-

Given that the length of the rectangle = 10x-7

Given that the width of the rectangle = 6x +12

The perimeter of the rectangle = 2(length + width)

Given that the perimeter of the rectangle = 170

Step(ii):-

2(length + width) = 170

length + width = 85

10x-7 +6x +12 =85

16x +5 = 85

16x = 85-5 = 80

x = $\frac{80}{16}$

x = 5

Final answer:-

The length of the rectangle = 10(5)-7 = 50-7 = 43

The wide of the rectangle = 6x +12 = 6(5) + 12 = 30+12 =42

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4 years ago

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Answer:

a) 0.0139; b) 0.1809; c) 0.4278

Step-by-step explanation:

We use a normal approximation to a binomial distribution for these problems.

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For part a,

We are asked for P(X < 20). Using continuity correction to account for the discrete variable, we find

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z = (19.5-24.24)/(2.1573) = -4.74/2.1573 = -2.20

Using a z table, we see that the area under the curve to the left of this is 0.0139.

For part b,

We are asked for P(X = 24). Using continuity correction, we find

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z = (23.5-24.24)/2.1573 = -0.74/2.1573 = -0.34

z = (24.5-24.24)/2.1573 = 0.26/2.1573 = 0.12

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We are asked to find P(25 ≤ X ≤ 28). Using continuity correction, we find

P(24.5 < X < 28.5)

z = (24.5-24.24)/2.1573 = 0.26/2.1573 = 0.12

z = (28.5-24.24)/2.1573 = 4.26/2.1573 = 1.97

Using a z table, we see that the area under the curve to the left of z = 0.12 is 0.5478. The area under the curve to the left of z = 1.97 is 0.9756. The area between them is 0.9756 - 0.5478 = 0.4278.

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3 years ago

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Alisiya [41]

The missing angles in the triangle is as follows:

∠1 = 62.5°
∠2 = 62.5°
∠3 = 55°
∠4 = 75°
∠5 = 50°

<h3>How to find the measure of angles in a triangle?</h3>

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

∠3 = 55 degrees (vertically opposite angles)

Vertically opposite angles are congruent to each other.

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

Using exterior angle theorem ,

105 = ∠5 + 55

∠5 = 105 - 55

∠5 = 50 degrees

∠4 = 180 - 50 - 55

∠4 = 75 degrees

Therefore, the other triangle is an isosceles triangle. This means the base angles are equal.

Hence,

∠1 = ∠2 = x

2x + 55 = 180

2x = 180 - 55

2x = 125

x = 125 / 2

x = 62.5 degrees.

Hence,

∠1 = ∠2 = 62.5 degrees.

learn more on angles here: brainly.com/question/28641859

#SPJ1

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