Clyde took a survey to see the favorite pizza topping of his 6th grade classmates.
Topping
pepperoni
sausage
onions
cheese
Number of Students
45
36
9
16
What is the ratio of students who prefer sausage to students who prefer pepperoni?
O 1:2
O 2:3
O 3:4
04:5

Given:

Endpoints of a line segment AB are A(2,3) and B(8,11).

To find:

(1) Slope of AB.

(2) Length of AB.

(3) Midpoint of AB.

(4) Slope of a line perpendicular to AB.

Solution:

We have, endpoints of line segment AB, A(2,3) and B(8,11).

(1)

Slope of AB is

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\dfrac{11-3}{8-2}[/tex]

[tex]m=\dfrac{8}{6}[/tex]

[tex]m=\dfrac{4}{3}[/tex]

Therefore, the slope of AB is [tex]\dfrac{4}{3}[/tex].

(2)

Length of AB is

[tex]AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]AB=\sqrt{(8-2)^2+(11-3)^2}[/tex]

[tex]AB=\sqrt{(6)^2+(8)^2}[/tex]

[tex]AB=\sqrt{36+64}[/tex]

[tex]AB=\sqrt{100}[/tex]

[tex]AB=10[/tex]

Therefore, the length of AB is 10 units.

(3) Midpoint of AB is

[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]

[tex]Midpoint=\left(\dfrac{2+8}{2},\dfrac{3+11}{2}\right)[/tex]

[tex]Midpoint=\left(\dfrac{10}{2},\dfrac{14}{2}\right)[/tex]

[tex]Midpoint=\left(5,7\right)[/tex]

Therefore, the midpoint of AB is (5,7).

(4)

Product of slopes of two perpendicular lines is -1.

Let the slope of line perpendicular to AB be m₁.

[tex]m_1\times \dfrac{4}{3}=-1[/tex]

[tex]m_1=-\dfrac{3}{4}[/tex]

So, slope of line perpendicular to AB is [tex]-\dfrac{3}{4}[/tex].

Answer:

Step-by-step explanation:

Answer: 43.2 miles/hour

Step-by-step explanation:

Answer:I believe left

Step-by-step explanation:

Answer:

11:33 or in simplified terms 1:3

Step-by-step explanation:

Hope this helps!:)

Answer:

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

32=y

5=x

5x2

Is the equivalent to 32

Answer:

5x+2y≥3x+y≤36

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

First, we have to find three numbers out of the four that add up to 84. But, it has to be in order because the question says consecutive numbers. In case you don’t know, consecutive numbers are numbers that increase at the same rate. In this problem, the numbers increase by one. I first did 26+27+28, which equaled 81. I have to get to 84 though. So, I did 27+28+29, which equaled 84. I did it correctly because 27, 28, and 29 are consecutive number, since they go inorder, and I added them up to 84. But the question is asking which of the three is the largest number. So, out of 27, 28, and 29, 29 is the largest number.

Hope this helps and answers your question! :)

Answer:

Step-by-step explanation:

i just took the test its 29

Answer:

40

Step-by-step explanation:

200/5=x/1

Answer:

40

Step-by-step explanation:

200/5 = 40

nice dumb questions

Answer:

42

Step-by-step explanation:

Hope this helps and have a great day! :)

Answer: -7(-6) is 42

hope this helps :)

Step-by-step explanation:

when You multiply two negative numbers, the answer is positive.

Step-by-step explanation: 2 1/3

Answer:

bar graph

Step-by-step explanation:

The best choice for this scenario would be a bar graph. This is because a histogram is used to represent data ranges or data in a specifically given time interval. For example, age ranges, time ranges, and income ranges are all common examples of data that is represented using histograms. Bar graphs on the other hand tend to represent the quantity of specific pieces of data in a large set of data, such as the number of specific color cars that appear out of a wide set of colors.

Answer:

- 2/3, 2/-3

Step-by-step explanation:

none of the rest work 3/2 is a completely different number and having two negatives in a fraction make it a positive

Answer: the answer is 36

Hope this helps :)

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

Answer:

2, 6

4, 12

8, 18

and so on

Step-by-step explanation:

multiply the number on the right by itself and do the same with the number on the left, this pattern could go on forever,

Answer:

8075.

Step-by-step explanation:

Volume of the prism

= 12 1/2 * 8 1/2 * 9  1/2

= 25/2 * 17 / 2 * 19/2

= 8075/8 cm^3

The volume of the small cubes = (1/2)^3 = 1/8 cm^3

So the number required = 8075 / 8   /  1/8

= 8075*8 / 8

= 8075.

Answer:

Solving the system of equations using elimination method, we get x=2, y=0

The ordered pair is: (2,0)

Step-by-step explanation:

We need to solve the system of equations using elimination method.

[tex]5x-2y = 10\\4x + 2y = 8[/tex]

Let:

[tex]5x-2y = 10--eq(1)\\4x + 2y = 8--eq(2)[/tex]

Add both equations to eliminate y and find value of x

[tex]5x-2y = 10\\4x + 2y = 8\\------\\9x=18\\x=\frac{18}{9}\\x=2[/tex]

We get value of x=2

Now, finding value of y by putting value of x in eq(1)

[tex]5x-2y=10\\Put\:x=2\\5(2)-2y=10\\10-2y=10\\-2y=10-10\\-2y=0\\y=0[/tex]

We get value of y= 0

Solving the system of equations using elimination method, we get x=2, y=0

The ordered pair is: (2,0)

Answer:

the answer is C

Step-by-step explanation:

Answer:

p = -10

Step-by-step explanation:

-30 + 20 = -10

Answer: The answer should be A.

Step-by-step explanation: When solving the first and third equations, it becomes 0=0. I'm assuming that is one solution. Then 8x-10y=5 should be the other solution. In other words, there is 2 solutions.

The correct diagram represents the type of solution to this system of equations is shown in Option A.

We have to given that,

System of equations are,

7x - 12y + z = -1   .. (i)

8x - 10y = 5        .. (ii)

21x - 36y + 3z = -3  .. (iii)

Now, From equation (i);

Multiply by 3;

3( 7x - 12y + z)  = -1 × 3

21x - 36y + 3z = - 3

Which is same as equation (iii).

Hence, Equation (i) and (ii) are parallel to each other.

And, It's a triple relationship.

Thus, Only option A has parallel planes.

So, Option A is true.

Learn more about systems of equations at:

brainly.com/question/14323743

#SPJ2

Answer:

Step-by-step explanation:

The length of this line segment is the distance between its endpoints A and B. So, a line segment is a piece or part of a line having two endpoints. Unlike a line, a line segment has a definite length.

Answer: DA = 6

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

Explanation:

The triangles are similar, allowing us to make the proportion below

DB/DA = DA/DC

Plug in the given values. Cross multiply and solve for x

DB/DA = DA/DC

9/DA = DA/4

9*4 = (DA)*(DA)

36 = (DA)^2

(DA)^2 = 36

DA = sqrt(36)

DA = 6

The length of DA is exactly the geometric mean of the lengths BD and DC

geometric mean of x and y = sqrt(x*y)

Answer:

The correct answer is B.

Step-by-step explanation:

We have the expression:

[tex]\displaystyle \lim_{n\to\infty}\sum_{i=1}^{n}f(x_i\, ^\star)\Delta x[/tex]

In this case, B is the correct answer.

B states that any sample point can be chosen without affecting the limit.

This is a true statement. Regardless of which point we choose for our sample point, since n approaches infinity, we will have infinite partitions.

Hence, this will not affect the sum of our expression.

A and C are false because we have infinite partitions, so the statements cannot be true. D is not true simply because the left-hand values do not have to be the same as the midpoint-values depending on the behavior of the function for [a, b].  

Answer:

Step-by-step explanation:

29.

2x+4+x+2x-9=180

5x-5=180

5x=180

x=36

Q=76°

P=63°

R=36°

30.

C=90°  (Given)

4x+7+8x-1+90=180

12x+96=180

12x=84

x=7

B=55°

A=35°

Answer: 2n + 1 = n + 11

Answer:

There are 220 choices

Step-by-step explanation:

Given

[tex]People = 12[/tex]

[tex]Selection =3[/tex] (President, Treasurer and Secretary)

Required

Determine number of selection (if no restriction)

This is calculated using the following combination formula:

[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]

Where

[tex]n = 12[/tex]

[tex]r= 3[/tex]

So, we have:

[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]

[tex]^{12}C_3 = \frac{12!}{(12 - 3)!3!}[/tex]

[tex]^{12}C_3 = \frac{12!}{9!3!}[/tex]

[tex]^{12}C_3 = \frac{12*11*10*9!}{9!3!}[/tex]

[tex]^{12}C_3 = \frac{12*11*10}{3!}[/tex]

[tex]^{12}C_3 = \frac{12*11*10}{3*2*1}[/tex]

[tex]^{12}C_3 = \frac{12*11*10}{6}[/tex]

[tex]^{12}C_3 = 2*11*10[/tex]

[tex]^{12}C_3 = 220\ ways[/tex]

There are 220 choices

Answer:

C. -7

Step-by-step explanation:

Answer:

50x50=1000000

Step-by-step explanation:

Answer:

535

Step-by-step explanation:

587-34-18=

535

Answer:

550

Step-by-step explanation:

just is the answer

Answer:

0.1529

Step-by-step explanation:

Given that:

Probability of changing lane ; p = 45% = 0.45

Sample size (number of trials) = n = 7

Probability that atleast 5 vehicles will change lane :

Using the binomial probability formula :

P(x = x) = nCx * p^x * (1 - p)^(n-x)

(1 - p) = 1 - 0.45 = 0.55

P(x ≥ 5) = p(x = 5) + p(x = 6) + p(x = 7)

P(x = 5) = 7C5 * 0.45^5 * 0.55^2

P(x = 5) = 21 * 0.45^5 * 0.55^2 = 0.117221

P(x = 6) = 7C6 * 0.45^6 * 0.55^1

P(x = 6) = 7 * 0.45^6 * 0.55^1 = 0.031969

P(x = 7) = 7C7 * 0.45^7 * 0.55^0

P(x = 7) = 1 * 0.45^7 * 0.55^0 = 0.003736

P(x ≥ 5) = p(x = 5) + p(x = 6) + p(x = 7)

P(x ≥ 5) = 0.117221 + 0.031969 + 0.003736

P(x ≥ 5) = 0.152926

P(x ≥ 5) = 0.1529

Using the binomial distribution, it is found that there is a 0.1529 = 15.29% probability that a least 5 vehicles will change lanes while making the turn.

For each vehicle, there are only two possible outcomes, either they change lanes while making a turn, or they do not. The probability of a vehicle changing lanes while making a turn is independent of any other vehicle, hence, the binomial distribution is used to solve this question.

Binomial probability distribution

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem:

The probability that at least 5 vehicles will change lanes while making the turn is:

[tex]P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 5) = C_{7,5}.(0.45)^{5}.(0.55)^{2} = 0.1172[/tex]

[tex]P(X = 6) = C_{7,6}.(0.45)^{6}.(0.55)^{1} = 0.0320[/tex]

[tex]P(X = 7) = C_{7,7}.(0.45)^{7}.(0.55)^{0} = 0.0037[/tex]

Then

[tex]P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) = 0.1172 + 0.0320 + 0.0037 = 0.1529[/tex]

0.1529 = 15.29% probability that a least 5 vehicles will change lanes while making the turn.

To learn more about the binomial distribution, you can take a look at https://brainly.com/question/24863377

Answer:

$31.50

Step-by-step explanation:

42 x 0.25 = 10.5

42 - 10.50 = 31.50

$31.50

Explanation:

42 × 25% = 10.5

42 - 10.5 = 31.5

Answer:

You would tell them by labeling the x and y and the titles of the graph and what corresponds to it

Step-by-step explanation: