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svet-max [94.6K]
2 years ago
8

In a survey of 1,600 people who owned a certain type of car, 720 said they would buy

Mathematics
1 answer:
bazaltina [42]2 years ago
3 0

The percentage of the people surveyed that were satisfied with the car is 45%.

<u>Given the following data:</u>

  • Total population = 1,600 people
  • Number of car owner = 720 people.

To determine the percentage of the people surveyed that were satisfied with the car:

<h3>How to solve for a percentage.</h3>

In this exercise, you're required to calculate the percentage of the total population in this survey that would by a particular type of car again because they were satisfied with it. Thus, we would solve for the percentage as follows;

Percent = \frac{Satisfied\;persons}{Total\; population} \times 100

Substituting the given parameters into the formula, we have;

Percent = \frac{720}{1600} \times 100\\\\Percent = 0.45 \times 100

Percent = 45%

Read more on percentage here: brainly.com/question/14432715

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Given:

Radius of the circle = 10 in

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To find:

The area of the sector.

Solution:

Area of a sector is

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Where, \theta is the central angle in degrees.

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A=\dfrac{45^\circ}{360^\circ}\pi (10)^2

A=\dfrac{1}{8}\pi (100)

A=12.5\pi

Therefore, the area of the sector is 12.5π sq. inches.

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Do you hypotenuse of a triangle is 1 foot more than twice the length of the shorter leg the longer leg is 7 feet longer than the
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Answer:

Shorter leg: 8 units

Longer leg: 15 units

Hypotenuse: 17 units

Step-by-step explanation:

We are given h=1+2s where h is the hypotenuse and s is the length of the shorter leg.

We got this equation from reading that the "hypotenuse of a triangle is 1 foot more than twice the length of the shorter leg". I replaced the "hypotenuse of a triangle" with h, "is" with =, "1 foot more than" with 1+ and finally "twice the length of the shorter leg" with 2s.

We also have "longer leg is 7 feet longer than the shorter leg".

I'm going to replace "longer leg" with L.

I'm going to replace "is" with =.

I'm going to replace "7 feet longer than the shorter leg" with 7+s.

So we have the equation L=7+s.

So we have a right triangle since something there is a side being referred to as the hypotenuse. We can use Pythagorean Theorem to find a relation between all these sides.

So by Pythagorean Theorem, we have: s^2+L^2=h^2.

Let's make some substitutions from above:

s^2+(7+s)^2=(1+2s)^2

Let's expand the powers using:

(a+b)^2=a^2+2ab+b^2

Applying this now:

s^2+(49+2(7)s+s^2)=(1+2(1)(2s)+(2s)^2)

s^2+49+14s+s^2=1+4s+4s^2

Combine like terms on right hand side:

2s^2+49+14s=1+4s+4s^2

Subtract everything on left hand side to get 0 on that side:

0=(1-49)+(4s-14s)+(4s^2-2s^2)

Simplify:

0=(-48)+(-10s)+(2s^2)

Reorder into standard form for a quadratic:

0=2s^2-10s-48

Every term is even and therefore divisible by 2. I will divide both sides by 2:

0=s^2-5s-24

I'm going to see if this is factoroable.

We need to see if we can come up with two numbers that multiply -24 and add up to be -5.

Those numbers are -8 and 3.

So the factored form is:

0=(s-8)(s+3)

This implies that either s-8=0 os s+3=0.

The first equation can be solved by adding 8 on both sides: s=8.

The second equation can be solved by subtracting 3 on both sides: s=-3.

The only solution that makes sense for s is 8 since it can't the shorter length cannot be a negative number.

s=8

L=7+s=7+8=15

h=1+2s=1+2(8)=1+16=17

So the dimensions of the right triangle are:

Shorter leg: 8 units

Longer leg: 15 units

Hypotenuse: 17 units

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