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Alexandra [31]
3 years ago
8

Of the 50 students in the cafeteria, 7 have red hair. Suppose there are 750 students in the school. Write a proportion that coul

d be used to predict the number of students who have red hair. Use x to represent the number of students who have red hair.
Mathematics
1 answer:
gulaghasi [49]3 years ago
7 0

Given:

Of the 50 students in the cafeteria, 7 have red hair.

Total number of students = 750

To find:

The proportion that could be used to predict the number of students who have red hair.

Solution:

Let x represent the number of students who have red hair.

The ratio of student having red hair to the total number of students are

Ratio_1=\dfrac{7}{50}

Ratio_2=\dfrac{x}{750}

The number of students having red hair is proportional to the total number of students. So, the above ratios are equal.

\dfrac{x}{750}=\dfrac{7}{50}

Multiply both sides by 750.

\dfrac{x}{750}\times 750=\dfrac{7}{50}\times 750

x=7\times 15

x=105

Therefore, the required equation is \dfrac{x}{750}=\dfrac{7}{50} and the number of students who have red hair is 105.

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Plzz anyone solve all answers plzzzzzzzz​
algol13

You posted a lot of problems here. In the future please only post one problem at a time. Thank you.

I'll do the first two problems to get you started. Hopefully it will help you finish off the rest of the questions.

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

Problem 1

{18, a, b, -3} is an arithmetic sequence or arithmetic progression (AP).

This means we have some number d added on to each term to get the next term.

first term = 18

second term = first term + d = 18+d = a

third term = second term + d = (18+d)+d = 18+2d = b

fourth term = third term + d = (18+2d)+d = 18+3d = -3

----

Let's solve that last equation for d

18+3d = -3

18+3d-18 = -3-18

3d = -21

3d/3 = -21/3

d = -7

----

The value d = -7 tells us to add -7 to each term to get the next term. In other words, we subtract 7 from each term to get the next term

first term = 18

second term = first term + d = 18+d = 18+(-7) = 18-7 = 11

third term = second term + d = 11+d = 11+(-7) = 11-7 = 4

fourth term = third term + d = 4+d = 4+(-7) = 4-7 = -3

----

We see that a = 11 and b = 4 are the second and third terms respectively.

Therefore, a+b = 11+4 = 15

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

<h3>Answer: 15</h3>

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

Problem 2

A multiple of 4 is in the form 4*n for some integer n, ie n is a whole number.

We want to know which values of 4*n are between 10 and 250.

----

Divide both 10 and 250 by 4 to get the following

10/4 = 2.5

250/4 = 62.5

If n = 2, then 4*n = 4*2 = 8 is not between 10 and 250; however n = 3 will make 4*n = 4*3 = 12 to be between 10 and 250. We see that n = 3 is the smallest possible allowed value.

If n = 62, then 4*n = 4*62 = 248 is between 10 and 250; while n = 63 will make 4*n too big because 4*63 = 252. The largest n can get is n = 62

----

The question posed in question 2 is equivalent to asking the following: "How many values are in the set {3, 4, 5, ..., 60, 61, 62}?"

You could count all of the values in the set, but that exercise is very tedious busywork. There's a much faster way. First lets consider the set below

{a, a+1, a+2, ..., b-2, b-1, b}

where a,b are integers. Basically this set starts at 'a', counts up until we get to 'b'. The handy formula

c = b-a+1

will provide the exact count of values in the set {a, a+1, a+2, ..., b-2, b-1, b}

----

In this case, a = 3 and b = 62, making

c = b-a+1

c = 62-3+1

c = 60

There are 60 values in the set {3, 4, 5, ..., 60, 61, 62}

There are 60 multiples of four that are between 10 and 250.

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

<h3>Answer: 60</h3>
4 0
3 years ago
Can someone please help
Rudiy27

It is B or 2. Hope this helps


6 0
3 years ago
I need help on this question
Margaret [11]
500(.25)=125 is the answer
8 0
3 years ago
30 points plus brainliest if you get it right with step by step explanation.
Leto [7]

Answer:

a. 150

b. y=150x+1200

Step-by-step explanation:

a. 1350-1200=150

b. if he opened it in 2005 he started his tutoring fee at 1200 that makes 1200 the y intercept

8 0
3 years ago
30 Points please help!! Please explain too!
sergiy2304 [10]
Initial: 200 feet = opp. side
Angle = 17.31, adj. Side = a
So tan (17.31) = opp. Side / adj. Side
tan (17.31) = 200 / a
--> a = 200/tan17.31 = 641.73
When stopped: adj. Still = a
Opp. Side still = 200, angle = 46.41
tan46.41 = 200 / a
--> a = 200/tan46.41 = 190.39
Now subtract those two distances to get the distance traveled from initial to when it stopped:
641.73 - 190.39 = 451.34 feet
3 0
3 years ago
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