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Allisa [31]
2 years ago
13

A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is

the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation. x + y = 24 3x + 5y = 100 What does the solution of this system indicate about the questions on the test? The test contains 4 three-point questions and 20 five-point questions. The test contains 10 three-point questions and 14 five-point questions. The test contains 14 three-point questions and 10 five-point questions. The test contains 20 three-point questions and 8 five-point questions.
Mathematics
2 answers:
antoniya [11.8K]2 years ago
7 0
We can solve this system using elimination:

(x+y=24)3
3x+5y=100

3x+3y=72
-(3x+5y=100)
0x-2y=-28
y=14

We can then plug this back into one of the original equations:

x+14=24
x=10

We can check our answer by plugging this into both of the original equations:

10+14=24
24=24

3(10) + 5(14)=100
30+70=100
100=100

Therefore, there are 10 3-point questions and 14 5-point questions.

weqwewe [10]2 years ago
5 0

there are 10 3-point questions and 14 5-point questions.

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Can you show how you did it?<br> 8.31 - 3.43 =
d1i1m1o1n [39]

Answer:

4.68

Step-by-step explanation:

Remember to line up the decimal point. Subtract as ordinarily.

8.31

-3.43

--------

4.68

4.68 is your answer

~

7 0
2 years ago
Leah has The flowers shown she wants to put them in 4 vases with the same number in each case how many flowers does she need to
dsp73

Answer:

The solution is obtained by dividing the number of flowers by the number of vases.

Step-by-step explanation:

The story problem is very straightforward. Normally, you need to read the problem and understand it.

Let's look at the question again.

Although we do not have all the quantities, we can still show how to solve the problem.

Let x be the total  number of flowers.

There are 4 vases.

Therefore, the number of flowers in each vase will be:

x/4

Flow the same rule for similar problems.

5 0
3 years ago
The short sides of a rectangle are 2 inches. The long sides of the same rectangle are three less than an unknown number of inche
Amiraneli [1.4K]

<u>Answer</u>

The first student was right.

The length of the long side is at least 13 inches.

<u>Explanation</u>

The perimeter of any figure is the distance all round.

Perimeter of a rectangle = 2(l+w). Where l is length and w is the width.

2(l + w) ≥ 30

2{(x-3) + 2} ≥ 30

2(x-3+2) = 30

2(x - 1) ≥ 30

x - 1 ≥ 15

x ≥ 16

When x = 16,

l = 16-3

  = 13 inches

The length of the long side is 13 inches. The first student was right.

8 0
3 years ago
Read 2 more answers
Secant TP and tangent TR intersect at point 7. Chord SR and chord PQ intersect
prisoha [69]

Answer:

(C)x=11.6, y=23.2

Step-by-step explanation:

Using Theorem of Intersecting Secant and Tangent

Applying this theorem in the diagram, we have:

TQ$ X TP=TR^2

10(10+x+4)=16^2\\10(14+x)=256\\140+10x=256\\10x=256-140\\10x=116\\$Divide both sides by 10\\x=11.6

Next, we apply Theorem of Intersecting Chords

PV X VQ=SV X VR

4 X x= 2 X y

Recall earlier we got: x=11.6

2y=4 X 11.6

2y=46.4

Divide both sides by 2

y=46.4/2=23.2

Therefore: x=11.6, y=23.2

5 0
3 years ago
Medicare would like to test the hypothesis that the average monthly rate for one-bedroom assisted-living facility is equal to $3
aliina [53]

Answer:

C) more than the absolute value of the critical value, we can conclude that the average monthly rate for an assisted-living facility is not equal to $3,300.

Step-by-step explanation:

Hello!

Interest hypothesizes is " the average monthly rate for one-bedroom assisted-living facility is equal to $3300" symbolically: μ = 3300

The study variable is:

X: Monthly rate for a one-bedroom assisted-living facility.

Since there is no information about the distribution of the variable, to be able to study the population mean, I'll assume that the variable has a normal distribution.

The hypothesis is:

H₀: μ = 3300

H₁: μ ≠ 3300

α: 0.05

The statistic to use, considering that there is no known population information and the sample size, is a Student t:

t= <u> X[bar] - μ </u> ~t_{n-1}

       S/√n

n= 12

X[bar]= $3690

S= $530

Using the sample data, calculate the statistic value:

t= <u> 3690 - 3300 </u> = 2.549

       530/√12

The rejection region for this test is two-tailed, with critical values:

t_{n-1; \alpha /2} = t_{11; 0.025} = -2.201

t_{n-1;1-\alpha /2} = t_{11; 0.975} = 2.201

The decision rule is:

Reject the null hypothesis if t ≤ -2.201 or if t ≥ 2.201

Not reject the null hypothesis if -2.201 < t < 2.201

Since the calculated value (2.549) is greater than the right critical value (2.201) the decision is to reject the null hypothesis.

With a signification level of 5%, there is enough evidence to reject the null hypothesis. This means that the population mean of the monthly rate for a one-bedroom assisted living facility is different from $3300.

I hope it helps!

7 0
2 years ago
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