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2 years ago

A 15- ft tree casts an 18- ft shadow at the same time a 24- ft tree casts a shadow. How long is the shadow of the 24- ft tree

Mathematics

1 answer:

anzhelika [568]2 years ago

4 0

Answer:

28.8 ft

Step-by-step explanation:

We can use proportion in calculating this.

Let X= height of the shadow of 24- ft tree.

The proportion can be set up as

(15- ft tree) /( 18- ft shadow )=(24- ft tree) / X

15/18 = 24/X

Making X subject of the formula

15X = 18 × 24

X= (18×24)/15

X=28.8 ft

Hence, the shadow of the 24- ft tree is 28.8 feet

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Nabil is writing a science fiction novel that takes place in another galaxy. In her galaxy, all the planets travel in an ellipti

ASHA 777 [7]

The equation that models the movement of Tanus around Ini, where Ini is located at (0, 0) is x^2/75^2 + y^2/37.5^2 = 1

<h3>Write an equation that models the movement of Tanus around Ini, where Ini is located at (0, 0)</h3>

The given parameters are:

The length of Tanus’ major axis = 150 million miles

The length of its minor axis = 75 million miles

The center of the ellipse = (0, 0) --- the location of Ini

When the coordinate of the center of an ellipse is (0, 0), the standard form of the ellipse is represented as:

x^2/a^2 + y^2/b^2 = 1

Where:

Length of the major axis = 2a

Length of the minor axis = 2b

This means that:

2a = 150 and 2b = 75

Divide both sides of 2a = 150 by 2

a = 75

Divide both sides of 2b = 75 by 2

b = 37.5

Substitute b = 37.5 and a = 75 in the standard form of the ellipse represented as: x^2/a^2 + y^2/b^2 = 1

x^2/75^2 + y^2/37.5^2 = 1

Hence, the equation that models the movement of Tanus around Ini, where Ini is located at (0, 0) is x^2/75^2 + y^2/37.5^2 = 1

Read more about equation of ellipse at:

brainly.com/question/16904744

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3 0

1 year ago

Suppose that the distribution of IQ's of North Catalina State University's students can be approximated by a normal model with m

konstantin123 [22]

Answer:

The required probability is 0.6517

Step-by-step explanation:

Consider the provided information.

North Catalina State University's students can be approximated by a normal model with mean 130 and standard deviation 8 points.

μ₁ = 130 and σ₁ = 8

Chapel Mountain University's students can be approximated by a normal model with mean 120 and standard deviation 10 points.

μ₂ = 120 and σ₂ = 10

As both schools have IQ scores which is normally distributed, distribution of this difference will also be normal with a mean of μ₁-μ₂ and standard deviation will be $\sqrt{\sigma_1^2+\sigma_2^2}$

Therefore,

μ = 130-120=10

$\sigma = \sqrt{8^2+10^2}=12.806$

Now determine the probability of North Catalina State University student's IQ is at least 5 points higher than the Chapel Mountain University student's IQ:

$z=\frac{\bar x-\mu}{\sigma}$