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viktelen [127]
3 years ago
10

Wats the 60% off a prize that is $20.00

Mathematics
1 answer:
Alla [95]3 years ago
5 0
x\ \rightarrow\  the\ 60\%\ of\ a\ prize\ that\ is\ \$20.00\\\\x=60\%\ \cdot \ \$20.00= \frac{60}{100} \cdot  \$20.00=\$12.00\\\\Ans.\ \$12.00
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Two trains leave Cleveland at the same time. One train travels east and the other travels west. The speed of the westbound train
Viefleur [7K]

Answer:

<u>The Eastbound train speed is 76.5 miles per hour and the Westbound train speed is 79.5 miles per hour.</u>

Step-by-step explanation:

1. Let's review all the information provided for solving this question:

Eastbound train speed = x

Westbound train speed = x + 3 miles per hour (The speed of the westbound train is 3mph greater than the speed of the eastbound train)

Duration of trip = 3 hours

Distance between trains after 3 hours = 468 miles

2. Let's find the speed of each train, using the following equation:

3x + 3(x + 3) = 468

3x + 3x + 9 = 468

6x + 9 = 468

6x = 468 - 9 (Subtracting 9 at both sides)

6x = 459

x = 459/6 (Dividing by 6 at both sides)

x = 76.5 miles per hour

<u>The Eastbound train speed is 76.5 miles per hour and the Westbound train speed is 79.5 miles per hour.</u>

3. Proof that x = 76.5 is correct

3x + 3(x + 3) = 468

3 (76.5) + 3 (76.5 + 3) = 468

229.5 + 238.5 = 468

<u>468 = 468</u>

<u>The value of x = 76. 5 is correct. And now we know that the  Eastbound train has traveled 229.5 miles since the departure from Cleveland and the Westbound train 238.5 miles.</u>

4 0
3 years ago
The vertex form of the equation of a parabola is y=(x+5)^2 + 49. What is the standard form of the equation
svet-max [94.6K]
y=(x+5)^2+49\\&#10;y=x^2+10x+25+49\\&#10;y=x^2+10x+74
8 0
3 years ago
Read 2 more answers
Which statements are true the ordered pair (1, 2) and the system of equations? y=−2x+4 7x−2y=3 Select each correct answer.
Brilliant_brown [7]
<span>When (1, 2) is substituted into the first equation, the equation is true.

</span><span>The ordered pair (1, 2) is not a solution to the system of linear equations.</span>
4 0
4 years ago
Read 2 more answers
What is the value of the 30th percentile for the data set? 6283 5700 6381 6274 5700 5896 5972 6075 5993 5581 5972 6274 6075 5896
Alex17521 [72]
<h2>Answer:</h2>

5896

<h2>Step-by-step explanation:</h2>

Given data set:

6283 5700 6381 6274 5700 5896 5972 6075 5993 5581 5972 6274 6075 5896

To calculate the 30th percentile;

<em>i. Rearrange the given data set in ascending order.</em>

5581 5700 5700 5896 5896 5972 5972 5993 6075 6075 6274 6274 6283 6381

<em>ii. Use the following formula to get the index of the value at the 30th percentile.</em>

N = p(n)

<em>Where;</em>

N = the number of data points at or below the intended percentile.

p = the intended percentile.

n = the number of points in the data.

<em>In this case;</em>

p = 30 percent = 0.3

n = 14

<em>Substitute these values into the equation;</em>

N = 0.3(14)

N = 4.2

<em>iii. From the calculated index, find the value of the 30th percentile.</em>

If the index is a whole number x, the desired percentile is the average of the values at index x and x+1.

For example if the index is 4, then the desired percentile is the average of the values at index 4 and 5. In our case, that will be;

\frac{5896+5896}{2} = 5896

If the index is a decimal number, it is rounded up to the nearest integer. The value at the rounded index is the desired percentile.

For example, in our case, the index is 4.2 which when rounded up becomes 4.

Therefore, the data point or value at index 4 is the 30th percentile. From the arrangement in (ii) above, that will be 5896. i.e

5581 5700 5700 <u>5896</u> 5896 5972 5972 5993 6075 6075 6274 6274 6283 6381

8 0
3 years ago
Is 2:4 and 42:84 equivalent?
bezimeni [28]

Answer:

Yes.

Step-by-step explanation:

They are both divisible by 21.

6 0
3 years ago
Read 2 more answers
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