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Ksivusya [100]
3 years ago
15

The difference between two numbers is 15. If 8 is added to twice the greater number, the result is 4 less than 3 times the lesse

r number. Find the two numbers.
Mathematics
1 answer:
yuradex [85]3 years ago
8 0

Answer:


Step-by-step explanation:

Let x be the greater number and y be the smaller number. We know that their difference is 15, so we have

x-y=15

Then, we have the following information: if we add twice the greater (2x) and 8 (2x+8), the result is 3 times the lesser (3y) minus four (3y-4). So, we have

2x+8 = 3y-4 \iff 2x-3y = -12

So, we have the follwing system:

\begin{cases} x-y=15\\2x-3y = -12\end{cases}

From the first equation, we can derive x = y+15, and substitute this expression in the second equation to get

2(y+15)-3y = -12 \iff 2y + 30 -3y = -12 \iff -y = -42 \iff y = 42

Substitute this value for y in the first equation to get

x-42=15 \iff x=15+42 \iff x = 57

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Given a mean of 150 and a standard deviation of 25:
pishuonlain [190]
We have to define an interval about the mean that contains 75% of the values. This means half of the values will lie above the mean and half of the values lie below the mean.

So, 37.5% of the values will lie above the mean and 37.5% of the values lie below the mean.

In a Z-table, mean is located at the center of the data. So the position of the mean is at 50% of the data. So the position of point 37.5% above the mean will be located at 50 + 37.5 = 87.5% of the overall data

Similarly position of the point 37.5% below the mean will be located at 
50 - 37.5% = 12.5% of the overall data

From the z table, we can find the z value for both these points. 12.5% converted to z score is -1.15 and 87.5% converted to z score is 1.15.

Using these z scores, we can find the values which contain 75% of the values about the mean.

z score of -1.15 means 1.15 standard deviations below the mean. So this value comes out to be:

150 - 1.15(25) = 121.25

z score of 1.15 means 1.15 standard deviations above the mean. So this value comes out to be:

150 + 1.15(25) = 178.75

So, the interval from 121.25 to 178.75 contains the 75% of the data values. 
4 0
3 years ago
Pls help answer before 10:00
antiseptic1488 [7]

Answer:

1. 14

2. 2.75

3. 7.25

4. 6.5

Step-by-step explanation:

1. You just make a dot plot and count the amount of dots there are.

2. You go to your dot plot and see the smallest amount and you get your answer.

3. Same thing as the smallest amount, except you just have to find the greatest amount.

4. You just find which number appears the most on the dot plot, and bam you got your answer.

6 0
3 years ago
(1+i)^2(x+yi)=4+5i<br> Solve for x and y
faust18 [17]

Answer:

x = 5/2

y = -2

Step-by-step explanation:

(1+i)² (x+yi) = 4+5i

(1+2i+i²)(x+yi) = 4+5i

(1+2i-1)(x+yi) = 4+5i

2i(x+yi) = 4+5i

2i²y + 2xi = 4+5i

-2y + 2xi = 4 + 5i

By comparing both sides,

-2y = 4

y = -2,

2x = 5

x = 5/2

7 0
2 years ago
a parallelogram has an area of 108 square inches . the base of the parallelogram is 18 inches . explain how you could find the h
Paraphin [41]
The formula for perimeter is

Side a x2 + side b x2

So just multiply 18 by two, and subtract it from 108
4 0
3 years ago
X³ +8x² -11x -12<br><br> Synthetically divide to find all zeros?<br><br> PLz help
Katarina [22]
You have to find what x equals i think
4 0
3 years ago
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