Select all the examples of categorical data.

colors
number of siblings
favorite pet
profits
genre of music

Answer:

a. The railing is transversal to the posts

b. In order to make the posts parallel, the angle between the posts and the transversal should be = 78°

c. The angle between the post and the ramp is 102° as we reach the post from the bottom and 102°  and 78° immediately after the post

d. 1) Alternate interior angles = 78° and 102°

2) Alternate exterior angles = 102°

3) Corresponding angles = 78° and 102° depending on the side of from which we approach the post

4) Consecutive interior = 78° and 102° depending on the side of from which we approach the post

e. The interior angles are supplementary

f. Horizontal spacing between posts =  2.93 ft.

Spacing between posts along the length of the railing =  3 ft. spacing

Step-by-step explanation:

a. A transversal is a line crossing two or more parallel lines which are in a plane at different points

Therefore, the railing is transversal to the posts

b. Whereby the ramp rises at an angle of 12°, the railing, which is the transversal is therefore inclined at 12° to the horizontal and the posts which will be vertical erect will be at 90° to the horizontal

Therefore, in order to make the posts parallel, the angle between the posts and the transversal should be 90° - 12° = 78° for each post to railing.

c. The angle between the post and the ramp before the post as we ascend the ramp is therefore, 180 - 78 = 102°  and 78° after the post

d. The alternate interior angles lie on the opposite sides of the transversal = 78° on one side and 102° on the other (Sum of angles on a straight line) which are the angles on the transversal

The alternate exterior angles lie on the exterior opposite sides of the transversal = 102°

Corresponding angles are the angles located in the corresponding positions on the transversal = 78° on one side and 102°as we cross the post (Sum of angles on a straight line)

Consecutive interior angles are the angles that are located on the same part of the transversal = 78° and 102° (Sum of consecutive interior angles of parallelogram = 180°

e. For the posts to be parallel, the consecutive interior angles should be supplementary or equal to 180°

f. Whereby we have a 12-ft rail inclined at 12°, we have;

Horizontal distance covered by the rail = 12 × cos(12) = 11.74 ft

Since we have 5 posts, there 4 equal spaces between them which gives

Spaces between posts = 11.74/4 = 2.93 ft. horizontally and 3 ft. spacing between each post along the railing.

Answer:

461.02

Step-by-step explanation:

2 × ( (12.3 × 4.3) + (12.3 × 10.7) + (4.3 × 10.7)) = 461.02 m^2

Answer:

461.02 M^2

Step-by-step explanation:

A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.

SA = 2lw+2lh+2hw

2LW = 105.78 M^2        (  52.89* 2 )

L= 12.3 M^2 , W = 4.3 M^2

LW = 52.89 M^2

2LH =  263.22       ( 131.61 * 2 )

L = 12.3 M^2 , H = 10.7 M^2

LH = 131.61 M^2

2HW = 92.02       ( 46.01 * 2 )

H = 10.7 M^2 , W = 4.3 M^2

HW = 46.01 M^2

SA = 2lw+2lh+2hw

SA = 105.78 M^2+ 263.22 M^2  + 92.02 M^2

SA = 461.02 M^2

Answer

(1-1/2 2)= 3/4 <Exact Form>  0.75<Decimal Form>

1-(1)/(100^(2) = 9999/10000 <Exact Form> 0.9999 <Decimal Form>

Step-by-step explanation:

Hope this Helps! The Crystaline Gamerz on YT! Bye! please sub

==================================================

Explanation:

Each term multiplied out is of the form 1 - 1/(k^2) which we can write as 1^2 - (1/k)^2

Note we have something in the form a^2 - b^2 with a = 1 and b = 1/k

So  

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

1^2 - (1/k)^2 = (1 - 1/k)(1 + 1/k)

1^2 - (1/k)^2 = [ (k - 1)/k ] * [ (k + 1)/k ]

----------------

Let P = [ (k - 1)/k ] * [ (k + 1)/k ]  represent the kth term we are dealing with

Then let Q be the term just after term P, so it's the (k+1) term

To form term Q, replace every k with k+1

Q =  [ (k+1 - 1)/(k+1) ] * [ (k+1 + 1)/(k+1) ]

Q = [ k/(k+1) ] * [ (k+2)/(k+1) ]

----------------

Let's multiply P and Q to find out what happens . See figure 1 in the attached images below.

As figure 1 shows, we see that the middle terms cancel out. This will happen when we multiply P*Q*R, where R is the term just after Q. Extend this idea out as far as you want and each time the middle terms will pair up and cancel.

All that's left are the first and last terms, which are

1 - 1/2 = 1/2

and

1 + 1/100 = 101/100

They multiply to 101/200

----------------

Figure 2 (also attached as an image) shows a longer way to do the problem. Basically I expanded out a bunch of terms to multiply, and then show how we have various terms pair up and cancel, in basically the same way as explained above. What's left are the first and last terms 1/2 and 101/100 which multiply to 101/200.

Answer:

Answer- 3/4 divided by 1/8 = 6/8

25 + t = 57

t = 57 - 25

t = 32

so stacy made 32 necklaces

Answer:

Opens down

Has a maximum value

Answer:

4

Step-by-step explanation:

2 2 3 5 7 7 (order from least to greatest)

3+5=8(find the most middle number,if there are two numbers you add both and then divide by 2)

8÷2

4

Hi there!! (✿◕‿◕)

⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐

First, you have to put the numbers from least to greatest.

2, 2, 3, 5, 7, 7

Then, you have to find the middle number.

2, 2, 3, 5, 7, 7

3 and 5 and both in the middle so, you add them both and divide them by 2.

3+5 = 8

8/2 = 4

4 is the median.

Hope this helped!!  ٩(◕‿◕｡)۶

Answer:

the third one is the correct answer

Answer:

6 ft

Step-by-step explanation:

Since the red line is 9 feet long, and we know that [tex]3\cdot3 = 9[/tex], we can note that 3 inches goes into 9 inches 3 times.

Now that we are making the red line increase by 2 feet for every 3 inches, we can multiply the values.

2 feet × 3 times = 6 feet

So Carver should make the red line 6 feet long.

Hope this helped!

Answer:

6ft

Step-by-step explanation:

If the scale is 3in:2ft then every 3 inches is equal to 2 feet. 9in can be divided into 3 3in sections and after the sections are scaled 3 2t sections which in all are equal to 6ft.

Answer:

[tex]12(3 + 4 + 5 + ...... + 12 + 13) = 1056[/tex]

Step-by-step explanation:

Given:

The attached

Required

Find the value of the expression

The interpretation of is to add the sequence: 12n

where n = from 3 to 13

Solving the for each term of the sequence

[tex]When\ n = 3, 12n = 12(3)[/tex]

[tex]When\ n = 4, 12n = 12(4)[/tex]

[tex]When\ n = 5, 12n = 12(5)[/tex]

....................

...........

...

.

[tex]When\ n = 12, 12n = 12(12)[/tex]

[tex]When\ n = 13, 12n = 12(13)[/tex]

The sum is then calculated as follows;

[tex]Sum = 12(3) + 12(4) + 12(4) + ...... + 12(12) + 12(13)[/tex]

12 is a common factor;

Hence;

[tex]Sum = 12(3 + 4 + 5 + ...... + 12 + 13)[/tex]

Replace ....... with actual numbers

[tex]Sum = 12(3 + 4 + 5 +6 + 7 + 8 + 9 + 10 + 11 + 12 + 13)[/tex]

[tex]Sum = 12(88)[/tex]

[tex]Sum = 1056[/tex]

Hence;

[tex]12(3 + 4 + 5 + ...... + 12 + 13) = 1056[/tex]

From the list of given options;

Option B is correct

[tex]12(3 + 4 + 5 + ...... + 12 + 13) = 1056[/tex]

Answer:

756

Step-by-step explanation:

In the last question the volume of the tank was 168 m³

so to find the cost multiply 168 and 4.5

it will cost 756

Answer:

756

Step-by-step explanation:

168 x 4.5 = 756

Answer:

30 degrees

Step-by-step explanation:

100+50=150

180-150=30

All triangles equal 180 degrees, so if the other angles equal 150 than the third angle equals 30 degrees.

Answer:

√58 or 7.62

Step-by-step explanation:

x-intercept = (7, 0)

y-intercept = (0, -3)

distance = √(-3 - 0)² + (0 - 7)² = √58 or 7.62

Answer:

ab² - a²b

Step-by-step explanation:

a²b⁴ - b²a⁴ can be factored as a²b²(b² - a²) which becomes a²b²(b + a)(b - a). Since the numerator and denominator both have (a + b) and ab the final answer is ab(b - a) = ab² - a²b.

Answer:

6x^2 - 14x + 4.

Step-by-step explanation:

5x^2 - 3x + 8 + 4x^2 - 7x - 3 - (3x^2 + 4x + 1)

=  5x^2 - 3x + 8 + 4x^2 - 7x - 3 - 3x^2 - 4x - 1

= 6x^2 - 14x + 4.

Answer:

d. y= 5x+18

Step-by-step explanation:

y=mx+b is slope intercept form

Now we plug in the information given to us which is slope(m) is 5 and a point (x,y) which is (2,28).

So by substituting we get 28=5(2)+b

simplify to 28=10+b and when we subtract 10 from both sides to isolate 'b', we get that b = 18.

So now we use the values of slope(m) and the y-intercept(b) to write the equation:

y=5x+18

Hey there! I'm happy to help!

Slope-intercept form is a way to write the equation of a line, and it is very useful. It is y=mx+b. This equation shows how y is related to x on a line. The m represents the slope, which is the incline of the line. The b represents the y-intercept, or where the line hits the y-axis.

If you find any value for x and plug it into the equation, you will figure out what y-value it matches on the line. If you had the equation you could draw the line by plugging in x-values and plotting points and connecting the dots!

Anyways, we have a slope of 5. This means that so far our equation looks like y=5x+b. It does not tell us what the y-intercept is, so we need to figure it out!

If we have the values for m, x, and b, we can solve for y. Well, we don't have b, but we do have values for y, x, and m, so we should be able to solve for b!

We will plug in our point (2,28) and solve for b!

28=5(2)+b

28=10+b

b=18

Our y-intercept is 18.

So, we can write this equation in slope-intercept form for the line that follows the condition of slope 5 and passing through (2,28) below.

y=5x+18

Therefore, our answer is d. 5x+18.

Now you can find the equation of a line given the slope and a point! Have a wonderful day! :D

Answer:

Amplitude = 3

Step-by-step explanation:

Given

The sine curve above

Required

Determine the amplitude

To determine the amplitude of a sine curve, we have to calculate the distance between the horizontal line of the curve and the top or bottom of the function

Using the top of the curve as a point of reference;

Amplitude = Top of curve - Horizontal Line.

The horizontal line is always at point 0

From the graph above, the top of the curve is at point 3

Hence,

Amplitude = 3 - 0

Amplitude = 3

Answer:

120

Step-by-step explanation:

expand and calculate

10x9x8x7!/(10-3)!x3!

10x9x8x7!/7!x3!

reduce

10x9x8x7!/7!x3!

10x9x8/3!

Calculate the product

10x9x8/3!

Now Cacluate the factorial

720/3!

720/6

reduce

120

Answer: 120

Step-by-step explanation:

Answer:

6p+19

Step-by-step explanation:

combine like terms:

8p+10+-2p+-1+10

(8p+-2p)+(10+-1+10)

6p+19

HOPE THIS HELPS!!!!!!:)

Answer:

A and C

Step-by-step explanation:

Part A

150+30x, x being the amount of visits she takes

Part C

150+30(3)

150+90

240

$240

Answer:

The x-axis.

Step-by-step explanation:

This is an ellipse.

In standard form it s  x^2/36 + y^2/9 = 0.

When y = 0, x = +/- 6 and when x = 0, y = +/- 3  so the minor axis has length 6 and the major axis has length 12 and runs along the x-axis.

Answer:

B.) f(x) = 3(4)x − 1

Step-by-step explanation:

A) f(x) = 12(4)x

B.) f(x) = 3(4)x − 1

C.) f(x) = 4(12)x

D.) f(x) = 4(3)x − 1

Given:

f(x+1) = 4f(x)

f(2)=12

f(2) = 12

f(3) = 4f(2) = 4 * 12 = 48

f(3)=48 and f(2)=12

From f(3)=48 and f(2)=12

r=48/12

=4

r=common ratio

Recall,

f(2)=12=ar

r=4

f(2)=ar=12

a*4=12

a=12/4

a=3

an=ar^(n-1)

For x term

an=3*4(x-1)

B.) f(x) = 3(4)x − 1

Answer:

B.) f(x) = 3(4)x − 1

Step-by-step explanation:

Answer:

520°

Step-by-step explanation:

A way to find the coterminal of an angle is to add or subtract mutiples of 360°

The angle which is not coterminal with 120° is 520°

"Any two angles that have the same starting and ending points regardless of the measurement are coterminal angles."

"In order to find a coterminal angle, simply add or subtract 360 degrees of the terminal angle as many times as possible."

For given example,

Given angle: 120°

First we find the coterminal angles with 120°

The coterminal angles with 120° are:

120° + 360° = 480°

120° + 720° = 840°

120° - 360° = -240°  (here, -360° means angle measured in clockwise direction)

So, the coterminal angles with 120° are 840°, 480°, -240°

Therefore, the angle which is not coterminal with 120° is 520°

Learn more about the coterminal angles here:

https://brainly.com/question/23093580

#SPJ2

Answer:

asDawas

Step-by-step explanation:

sadasda

Answer: -28, -17, 22.4, 27

hope this helps

Given:

Mean of 52 minutes and a standard deviation of 5 minutes.

Solution:

According to the empirical rule: For the normal distribution, all of the data will fall within three standard deviations of the mean.

1: 68% of the data will fall within the first standard deviation from the mean.

2: 95% of the data fall within two standard deviations.

3: 99.7% of the data fall within three standard deviations.

[tex]3SD =99.7\%=\mu\pm3\sigma\\[/tex]

Therefore, the 7 intervals and their probabilities are:

1. [tex]1SD=0.68=P(47<x<57)[/tex]

2. [tex]0.95=P(42<x<62)[/tex]

3. [tex]0.997=P(37<x<67)[/tex]

4.[tex]13.5\%=P(42<x<47)[/tex]

5.[tex]13.5\%=P(57<x<62)[/tex]

6. [tex]2.35\%=P(37<x<42)[/tex]

7.[tex]2.35\%=P(62<x<67)[/tex]

Answer:

I belive the answer should be B

Answer:

x = 65

Step-by-step explanation:

50 + 2x = 180

2x = 130

x = 65

Hope this helps)))

Answer:

65 degrees

Step-by-step explanation:

break apart the image into 2 sets of 2 lines and a transversal. Doing that you can see that 2x and 50 degrees are supplementary due to corresponding angles. 50 degrees+2x=180 degrees. Using ALgebra you can solve to find that x equals 65 degrees, which brings you to your answer

Answer:

Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication, and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

Step-by-step explanation:

Answer:

length: 5 yd

width: 4 yd

area: 20 yd^2

Step-by-step explanation:

1 yd = 3 ft

15 ft * (1 yd)/(3 ft) = 5 yd

12 ft * (1 yd)/(3 ft) = 4 yd

A = LW

A = 5 yd * 4 yd = 20 yd^2

Answer:

20 yd²

Step-by-step explanation:

1 yd = 3 ft =>

=>w = 12ft×yd/3ft = 4 yd

=> l = 15ft×yd/3ft = 5 yd

A = l × w

= 5yd × 4yd

= 20 yd²

Answer:

[tex]120\º \text{ and } 240\º[/tex]

or in radians:

[tex]$\frac{2\pi }{3} \text{ and } \frac{4\pi }{3}$[/tex]

Step-by-step explanation:

From the way you wrote, you want to solve the equation

[tex]\sqrt {2 \cos(x)+1}=0[/tex] for [tex]0 \leq x < 360\º[/tex], or in radians [tex][0, 2\pi)[/tex]

[tex]\sqrt {2 \cos(x)+1}=0[/tex]

Square both sides

[tex]2 \cos(x) +1= 0[/tex]

[tex]2\cos(x)=-1[/tex]

[tex]$\cos(x)=-\frac{1}{2} $[/tex]

In the Unit Circle, considering one revolution (interval [tex][0, 2\pi)[/tex]),

the values where [tex]$\cos(x)=-\frac{1}{2} $[/tex]  are in Quadrant II and III.

Once

[tex]$\cos(x)= \frac{1}{2} \text{ for } x = 60\º \text{ in the Quadrant I}$[/tex]

The values where

[tex]$\cos(x)=-\frac{1}{2} $[/tex]   are 120º and 240º.

Answer:

C on edge

Step-by-step explanation: