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Vesna [10]
3 years ago
8

A test is worth a total of 150 points and contains 70 questions. Some of the questions are worth 2 points and some are worth

Mathematics
1 answer:
FrozenT [24]3 years ago
4 0

Answer:

65 two-point questions, and 5 four-point questions.

Emma answered 2 four-point questions.

Step-by-step explanation:

1. Assigning variables and writing equations

We will set the number of 2 point questions as "x" and number of 4 point questions as "y"

We know that:

x+y=70 (number of 2 point questions+number of 4 point questions=total number of questions)

2x+4y=150 (number of points that a two point question is worth*number of two point questions+number of points that a four point question is worth*number of four point questions=total points on test)

2. Combining equations

x+y=70, 2x+4y=150

We will solve one of these equations.

x+y=70

x=70-y

Next, we will substitute the other equation with this solution.

2*(70-y)+4y=150

140-2y+4y=150

2y=10

y=5

Use this solution to find x.

x+y=70

x+5=70

x=65

<em>We found that there are 65 two-point questions, and 5 four-point questions. </em>

3. Finding Emma's test results

In this case, we know how many two-point questions she answered. So, we will only be using one variable in this equation, which is y.

46*2+4y=100

92+4y=100

4y=8

y=2

<em>So, she answered 2 questions correctly. </em>

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Answer:

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3 0
3 years ago
Read 2 more answers
How many different 5​-letter radio station call letters can be made a. if the first letter must be Upper C comma Upper X comma U
Lady_Fox [76]

Answer:

a) 1,518,000

b) 2,284,880

c) 60,720

Step-by-step explanation:

a) a. if the first letter must be Upper C comma Upper X comma Upper T comma or Upper M and no letter may be​ repeated?

We draw 5 boxes, and based on that we will see the total possible cases. There are 26 alphabets

The first box should have C or X or T or M .No letter may be repeated.

Any                    Any             Any                 Any                    Any

5 alphabets    of the            of the              of the                 of the

C,X , T , M      remaining     remaining       remaining          remaining

                   25 alphabets   24 alphabets   23 alphabets   22 alphabets

Therefore; total possible call letters = 5 × 25 × 24 × 23 × 22 = 1,518,000

b)

The first box should have C or X or T or M Repeats as allowed

Any                    Any             Any                 Any                    Any

5 alphabets    of the            of the              of the                 of the

C,X , T , M      remaining     remaining       remaining          remaining

                   26 alphabets   26 alphabets   26 alphabets   26 alphabets

Therefore Total possible call letters = 5 × 26 × 26 × 26 × 26 = 2,284,880

c)   The first box should have   C,X , T , M  and end with S

So the last place if fixed, and we now have 25 alphabets. The first box can go in 5 ways. The next box then will have only 24 letters to choose from, as the first box has taken a letter and the last box already has S in it. Repetition not allowed

Any                    Any             Any                 Any                       S

5 alphabets    of the            of the              of the                  is fixed

C,X , T , M      remaining     remaining       remaining           here

                   24 alphabets   23 alphabets   22 alphabets  

Therefore Total possible call letters = 5 × 24 × 23 × 22  × 1 =  60,720

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3 years ago
The given line passes through the points (0, −3) and (2, 3).
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3 years ago
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ad-work [718]
Using google translate: 
When photocopying a credential, it is first enlarged to triple and subsequently the resulting copy is halved. What is the final effect on the original credential? If the credentials is a rectangle of 10 by 6 cm. What area will you have in the first photocopy? And in the second?

Original: 10 by 6 cm  ;  Area = length * width = 10 x 6 = 60 cm²

first copy: enlarged to triple
10 x 3 = 30 
6 x 3 = 18
30 x 18 = 540 cm²

second copy: halved
30 x 1/2 = 15
18 x 1/2 = 9
15 x 9 = 135 cm²


7 0
3 years ago
Please answer this math question.
Temka [501]
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6 0
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