MATHEMATICS HIGH SCHOOL

Which kind of function best models the data in the table? Use differences or ratios.y X
0 1.7
1 6.8
2 27.2
3 108.8
4 435.2

a. linear
b. quadratic
c. exponential
d. none of the above

Answers

Answer 1
Answer:

Answer:

Option C exponential.

Step-by-step explanation:

To find the function best models the data in the table we will find the common ratio first. If the common ratios of the function are same then it's an exponential function.

For x = 0 and x = 1

(f(1))/(f(0))=(6.8)/(1.7)=4

For x = 1 and x = 2

(f(2))/(f(1))=(27.2)/(6.8)=4

For x = 2 and x = 3

(f(3))/(f(2))=(108.8)/(27.2)=4

Now we are sure that it's an exponential function.

For linear function common difference should be same in each term.

f(1) - f(0) = 6.8 - 1.7 = 5.1

f(2) - f(1) = 27.2 - 6.8 = 20.4

Therefore it's neither a linear function nor quadratic function.

Option C. is the correct option.
Answer 2
Answer: THE ANSWER IS LETTER C

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Solve for x.
- 3x + 8y = 5
6x - 2y =10

Answers

Let us solve this system by substitution.

-3x + 8y = 5
6x - 2y = 10

According to equation 2,

6x - 2y = 10

6x = 10 + 2y

thus, x = 10 + 2y / 6

substituting the value of x in equation 1,

-3 ( 10 + 2y / 6) + 8y = 5

-30 - 6y + 8y = 5 x 6 = 30

-30 + 2y = 30

2y = 60

Thus, y = 30.

Substituting the value of y in equation 2,

6x - 2y = 10

6x - 2(30) = 10

6x - 60 = 10

6x = 70.

Thus, x = 70/6.

Thus, x = 70 / 6     ( and y = 30)

Circle R has a radius of 6, and is tangent to circle R at point Q. Also, QP = 8. (a) What is the measure of angle RQP Explain your answer.
b) What is the length of RP Explain your answer.
(c) What is the length of RS Explain your answer.
(d) What is the length of RP Explain your answer.

Answers

I found the image that is part of this problem.

Circle R has a radius of 6. The radius is from R to Q, edge of the circle. Another radius is formed from R to S.

Radius R to Q is the short leg of a right triangle. It measures 6 cm.
a) The measure of the angle RQP is 90°. It is a right triangle.
b) The length of RP is 10 cm.
RP is the hypotenuse.
a² + b² = c²
6² + 8² = c²
36 + 64  = 100
c² = 100
√c² = √100
c = 10 cm

c.) the length of RS is 6 cm. It is also a radius. 
d) The length of RP is 10 cm. Same answer as scenario b.

Find the coordinates of m, the midpoint of gh, for g(8,-6) and h(-14,12)

Answers

Answer:

m = (- 3, 3 )

Step-by-step explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint M is

M = ( (x_(1)+x_(2) )/(2) , (y_(1)+y_(2) )/(2) ) ← midpoint formula

let (x₁, y₁ ) = g (8, - 6 ) and (x₂, y₂ ) = h (- 14, 12 ) , them midpoint m is

m = ( (8-14)/(2) , (-6+12)/(2) ) = ( (-6)/(2) , (6)/(2) ) = (- 3, 3 )

The mean weight of trucks traveling on a particular section of I-475 is not known. A state highway inspector needs an estimate of the population mean. He selects and weighs a random sample of 49 trucks and finds the mean weight is 15.8 tons. The population standard deviation is 3.8 tons. What is the 95% confidence interval for the population mean?

Answers

Answer:

(14.7 , 16.9)

Step-by-step explanation:

it is given that \bar{x}=15.8 tons

σ=3.8 tons

n=49

at 95% confidence level α=1-.95=0.05

z_(\alpha )/(2)=z_(0.05)/(2)=z_(0.025)\n

=1.96 ( from the standard table)

at 95% confidence level the coefficient interval for μ is

\bar{x}\pm z_(\alpha )/(2)* (\sigma )/(√(n))

15.8\pm 1.96* (3.8)/( √(49))

15.8\pm 1.1

(14.7, 16.9)

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(a) Draw a density curve to model the amount of air that is needed to make the balloon pop. Be sure to include scales on both axes.

(b) About what percent of the time will the balloon pop upon receiving at most 28 cubic inches of air?

(c) Find the first quartile (Q1) of this distribution.


4. The manager of the arcade wants to know how quickly players switch from one game to another. After conducting a
study, he concludes that the amount of time that people spend playing a game before switching to a different game can be modeled by a normal distribution with mean 2.1 minutes and standard deviation 0.4 minutes.
Sketch the normal density curve. Label the mean and the points that are 1, 2, and 3 standard deviations from the mean.

Answers

(a) To draw a density curve for the uniform distribution on the interval from 25 to 35 cubic inches of air, you can use a horizontal line segment that represents a constant density over that interval. The density should be 1 divided by the width of the interval, which is 35 - 25 = 10 cubic inches. Here's how you can represent it graphically

What is the measure of the missing angle?

Answers

Answer:

60 degrees

Step-by-step explanation:

Every Triangle has an angle of 180degrees

so if we add all of the written angles which is 25 + 35 + 60 = 120

we take 180 degrees and subtract it with the previous answer (120)

180 - 120 = 60

Thereforeitis60degrees

Answer:

answer is 60

Step-by-step explanation:

because if the angle is 60 degrees anywhere in the triangle means its an equilateral triangle making all the angles 60 degrees
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