66. The quadrilaterals below are similar.
What is the length of FG?

Answer:

The 95% confidence interval estimate of the population mean  is (7.38, 8.46).

Step-by-step explanation:

Before building the confidence interval, we need to find the mean and standard deviation of the sample.

In this sample, there are 50 values.

Mean of the sample:

Sum of all values divided by the number of values.

With the help of a calculator, the mean is of 7.92.

Standard deviation:

Square root of the division of the sum of the difference squared between each value and the mean by the number of the values.

With the help of a calculator, the standard deviation is of 1.8958.

Confidence interval:

We have the confidence interval for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 50 - 1 = 49

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 49 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.01

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.01\frac{1.8958}{\sqrt{50}} = 0.54[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 7.92 - 0.54 = 7.38

The upper end of the interval is the sample mean added to M. So it is 7.92 + 0.54 = 8.46

The 95% confidence interval estimate of the population mean  is (7.38, 8.46).

Given:

Two figures.

To find:

The area of the shaded regions for both figures.

Solution:

In first figure, the shaded area is a triangle with base 15 units and height 12 units. So, the area of the shaded region is equal to area of the triangle.

[tex]A=\dfrac{1}{2}\times base\times height[/tex]

[tex]A=\dfrac{1}{2}\times 15\times 12[/tex]

[tex]A=\dfrac{180}{2}[/tex]

[tex]A=90[/tex]

Therefore, the area of the shaded region is 90 square units.

In the seconds figure, we need to subtract the area of square from the area of triangle, to get the area of the shaded region.

Area of triangle with base 15 and height 18 is:

[tex]A_1=\dfrac{1}{2}\times 15\times 18[/tex]

[tex]A_1=\dfrac{270}{2}[/tex]

[tex]A_1=135[/tex]

Area of the square with sides 6.

[tex]A_2=(side)^2[/tex]

[tex]A_2=(6)^2[/tex]

[tex]A_2=36[/tex]

Now, the area of the shaded region is:

[tex]A=A_1-A_2[/tex]

[tex]A=135-36[/tex]

[tex]A=99[/tex]

Therefore, the area of the shaded region is 99 square units.

Answer:

13,34 , 150

Step-by-step explanation:

just proportions

Answer:

The shortest segment from the point to the line is perpendicular to the line.

Step-by-step explanation:

See the attached image.  The blue segments go from the point to the line, but they are longer than the shortest such segment (red).

Answer:

6x(x^2 - 2x + 3)

Step-by-step explanation:

By looking at these terms, we can realize that they all have a term to do with x and are divisible by 6. So, we have our GCF, which is 6x. Now, to factor out 6x, we have to divide every term by 6x; they will all divide without a remainder because we already established they were all divisible by 6x.

So, we get the division(for each term separately):

6x^3/6x - we can cancel out 6x from the numerator and denominator to get: x^2

-12x^2/6x -  we can cancel out 6x from the numerator and denominator to get: -2x

-18x/6x -  we can cancel out 6x from the numerator and denominator to get:

3

When we put this together we get:

6x(x^2 - 2x + 3)

This is the final answer

Answer: V=628cm³

Step-by-step explanation:

V=(3.14)r²h

V=(3.14)(5²)(8)

V=628cm²

Hope this helps! Have a great night!

Answer:

A. 9.8ft

Step-by-step explanation:

work out arc length using this formula

[tex]2\pi \: \times r \times \frac{\theta}{360} [/tex]

r is the radius, 7 in this case and theta(the symbol above 360) is the angle, 80 in this case

Answer:

y-step explanation:

Answer:

3.46

Step-by-step explanation:

Answer:

3.46

Step-by-step explanation:

346% = 346/100 = 3.46

Answer:

36

Step-by-step explanation:

Angle BEC is a right angle. The total degree of a right angle is 90. So if you subtract 90 by 54, then you get the value of the remaining angle, which is 36.

Answer: : = 5 : 9

Step-by-step explanation:

Answer:

i think it would be 5:9

Step-by-step explanation:

Change values to whole numbers.

Convert any decimal numbers to integers by multiplying both sides by 101 = 10 to eliminate all, 1, decimal places.

We then have:

2.5 : 4.5 = 25 : 45

Try to reduce the ratio further with the greatest common factor (GCF).

The GCF of 25 and 45 is 5

Divide both terms by the GCF, 5:

25 ÷ 5 = 5

45 ÷ 5 = 9

The ratio 25 : 45 can be reduced to lowest terms by dividing both terms by the GCF = 5 :

25 : 45 = 5 : 9

Therefore:

2.5 : 4.5 = 5 : 9

Answer:

m∡x = 95°

m∡y = 147°

m∡z = 128°

Step-by-step explanation:

m∡z = 180-52 = 128

measure of third angle in left triangle = 180-(45+50) = 85°

m∡x = 180-85 = 95°

measure of top angle in right triangle = 180-(95+52) = 33°

m∡y = 180-33 = 147°

Answer:

The image's not clear!

Step-by-step explanation:

Answer:

The answer is 30 (C)

Answer:

(EF-GH)/2=J

(73-10)/2=31.5=J

Step-by-step explanation:

Answer:

153:20

Step-by-step explanation:

765000/100000

=153/20

Answer:

80÷(4÷16) = 20

Step-by-step explanation:

4÷6=4

4x4=16

80÷4=20

4x20=80

Answer:

y = - 15.57x² + 179.32x + 0.20

510

Step-by-step explanation:

The quadratic model obtained using a quadratic regression solver with Coefficient rounded to the nearest hundredth is :

y = - 15.57x² + 179.32x + 0.20

Where, height = y

x = time

Using the model obtained ; the height, to the nearest foot, at a time, x = 6.4 seconds.

y = - 15.57x² + 179.32x + 0.20

y = - 15.57(6.4^2) + 179.32(6.4) + 0.20

y = 510.1008

y = 510

The quadratic model obtained using a quadratic regression solver with Coefficient rounded to the nearest hundredth is :

height = y

x = time

                          Using the model obtained;

The height, to the nearest foot, at a time, x = 6.4 seconds.

Thus, the correct answer is 510.

Know more :

https://brainly.com/question/23117287?referrer=searchResults

Step-by-step explanation:

I feel there is important information lost in the way you provided the problem statement.

e.g. "... also equal to ?"

equal to what ?

sin x = what ?

so, I can only guess some things.

answer C is definitely correct for any angle up to 180 degrees.

answer A is only correct for an angle of 45 or 225 degrees, where sin(x) and cos(x) are both 1/sqrt(2) or both -1/sqrt(2).

answer B is always wrong (459 degrees is no special number, this is a full circle of 360 degrees and then additional 99 degrees there is no special relationship between sine and cosine for 99 degrees, so sine and cosine cannot have the same value for any x).

answer D is always wrong, as there is always a 30 degree difference between the arguments for sine and cosine, and that can never lead to an equal value.

answer E is also always wrong, as these 45 degrees difference also block equal values.

9514 1404 393

Answer:

Step-by-step explanation:

Let s represent the FCI for soccer. The given values tell us ...

  s + (s +7.47) = 108.09

  2s = 100.62 . . . . . . . . . . subtract 7.47

  s = 50.31

  s+7.47 = 57.78

The FCI for soccer was $50.31; the FCI for hockey was $57.78.

Answer:

Relationship A

Step-by-step explanation:

We can see that when we plug the given x and y values the soloutioncomes out corrrect.    

Answer:

The answer is 32x+67

Step-by-step explanation:

Answer:

sin X=30 degree

cos X=30 degree

tan X=30 degree

cot X=30 degree

sec X=30 degree

Step-by-step explanation:

Answer:

y=-2/5x-11/5

Step-by-step explanation:

y-y1=m(x-x1)

y-(-3)=-2/5(x-2)

y+3=-2/5x+4/5

y=-2/5x+4/5-3

y=-2/5x+4/5-15/5

y=-2/5x-11/5