If x is the probability of an event happening, then which of the following represents

A sphere has a diameter os 14 ft. Which equation finds the volume of the sphere?

Nutka1998 [239]

Answer:

Step-by-step explanation:

V=4/3pie(7)^3

5 0

3 years ago

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Help me jim! geometry homework

Maksim231197 [3]

Question 1

The angles 52 degrees match up. So if the sides are in proportion, then the triangles are similar.

Notice how 8/12 = 18/27 is a true equation. So the sides are in proportion to one another.

Therefore, the triangles are similar. I used the SAS similarity theorem.

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Question 2

Let's find the missing angle of the triangle on the right. For now, make that missing angle to be x.

Rule: For any triangle, the three angles always add up to 180

x+70+32 = 180

x+102 = 180

x = 180-102

x = 78

The missing angle of the triangle on the left is 78 degrees

Repeat for the other triangle as well

y+78+32 = 180

y+110 = 180

y = 180-110

y = 70

Both triangles have the angles 32, 70, 78 in whatever order you wish.

Since the angles match up like this, the triangles are similar because of the AA Similarity theorem

Technically, we only need 2 pairs of congruent angles at minimum. But having 3 congruent pairs doesn't hurt either.

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Question 3

We have a pair of congruent 54 degree angles shown. There's another pair of angles at the very top that overlap (aka shared angles).

Since we have two pairs of congruent angles, the two triangles are similar.

This time we use the AA Similarity theorem

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Question 4

Let's divide the longest side of the bottom triangle by the longest side of the triangle on top

48/32 = 1.5

Now let's divide the shortest sides of each triangle in the same order

36/24 = 1.5

Repeat for the middle-most sides

45/30 = 1.5

We get the same linear scale factor 1.5 each time. Therefore, the triangles are similar due to the SSS Similarity theorem

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Question 5

Any angle is equal to itself due to the reflexive property. So that will go for reason number 2.

Reason 3 is SAS similarity because we have the sides in proportion (statement 1) and the angles are congruent (statement 2).

3 0

2 years ago

What number must be added to the expression below to complete the square?

stiv31 [10]

D. 1/4

Explanation:

a perfect square is written in the form

$(x+a)^2 = x^2 + 2ax +a^2$ (1)

In our problem, we have this perfect square:

$x^2 - x + C$ (2)

with C being unknown. However, by comparing (1) and (2), we know that

$2a=-1$

So, we find

$a=-\frac{1}{2}$

and therefore, the missing term must be

$a^2 = \frac{1}{4}$

so the complete square is

$x^2 -x +\frac{1}{4}$

7 0

3 years ago

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What is 9.286 as a mixed number

marshall27 [118]

9.286

[To change to mixed number, count the number of digits after the decimal point. There are 3 digits, so the denominator will be 1000]

$9.286 = 9 \frac{286}{1000}$

Then we simplify the fraction
(286 ÷ 2)/(1000÷2) = 143/500

Therefore,
$9.286 = 9 \frac{286}{1000}$
$9.286 = 9 \frac{143}{500}$

8 0

3 years ago

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The Johnson twins were born nine years after their older sister. This year, the product of the three siblings ages is exactly 18

KATRIN_1 [288]

Answer: The age of the twins is 10 years.

Step-by-step explanation:

Suppose the age of older sister be x

Let the age of twins sister be x-9, as they are born after 9 years.

Product of their ages be

$x(x-9)(x-9)\\\\=x(x^2-18x+81)\\\\=x^3-18x^2+81x$