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Natali [406]
3 years ago
10

A three-digit number ends in number 7. If you put the number 7 in the first position, the number will increase by 324. Find the

original three-digit number.
Mathematics
1 answer:
liq [111]3 years ago
5 0

Answer:

<u>The original three-digit number is 417</u>

Step-by-step explanation:

Let's find out the solution to this problem, this way:

x = the two digits that are not 7

Original number = 10x+7

The value of the shifted number = 700 + x

Difference between the shifted number and the original number = 324

Therefore, we have:

324 = (700 + x) - (10x + 7)

324 = 700 + x - 10x - 7

9x = 693 - 324 (Like terms)

9x = 369

x = 369/9

x = 41

<u>The original three-digit number is 417</u>

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Answer:

<em>The first step is to determine the average </em>

x= \frac{0,6+0,7+ 0,7+0,3+0,4+ 0,5+ 0,4 +0,2}{8}\\\ x= 0,475

<em>The exercise says it’s a normal distribution: (n=8)</em>

s^{2}= \frac{1}{n-1} ((0,6.x)^2+2(0,7-x)^2+(0.3-x)^2+2(0.4-x)^2+(0.5-x)^2+(0.2-x)^2)\\\ \frac{1}{7}*0,235 = 0,0336 \\\\ s= 0183

<em>According to the exercise, the mean is equal to 0,5 then the value of t of the distribution can be obtained </em>

<em />

t= \frac{x-u}{\frac{s}{\sqrt{n} }}\\\ t= \frac{0,475 - 0,5}{0,183}\\\  t= -0,3860

<em>The variable t has 7 grade to liberty, we calculate the p-value as: </em>

2* P(t < - 0,3860)= \\\ 2* 0,3554 = 0,7108

This value is very high, therefore the hypothesis is not rejected

7 0
3 years ago
Colleen plans to start a small business by making and selling skirts. A sewing machine costs $250, and she estimates that she wi
Dmitrij [34]
Let C(x) be the function which calculates the total cost of making x skirts.

There is going to be a fixed constant, 250, to which we will add 15$ per x skirts.


So C(x)=250+15x

Answer: 250+15x
7 0
3 years ago
Read 2 more answers
Alexander purchased a computer on sale. The original price was $1,200. The sale price was 5/6 of the original price. How much di
Alexxx [7]

Answer:

1000

Step-by-step explanation:

1200*5/6=1000

3 0
2 years ago
The length of one base of a trapezoid is 19 less than five times the length of the other base. If the trapezoid has a height of
ycow [4]

The length of the longer base is 41 ft.

<u><em>Explanation</em></u>

Lets assume, length of one base is x ft.

As, another base is 19 less than five times the length of this base, so the length of another base = (5x- 19) ft.

The trapezoid has a height of 18 ft and area of 477 ft²

Formula for Area of trapezoid, A=\frac{1}{2} (a+b)*h , where a, b = Two bases of trapezoid and h = height of the trapezoid.

Given in the question: A= 477 and h= 18

We have also two bases as: a= x and b= 5x-19

So, according to the above formula...

A= \frac{1}{2}(a+b)h\\\\ 477=\frac{1}{2}(x+5x-19)*18\\\\ 477=9(6x-19)\\\\477= 54x-171\\\\477+171=54x\\\\648=54x\\\\x=\frac{648}{54} = 12

So, length of one base is 12 ft  and another base =(5*12-19)ft =(60-19)ft = 41 ft

That means, the length of the longer base is 41 ft.



8 0
3 years ago
Which number line represents the solutions to |-2x|=4?
Ahat [919]

Answer:

B

Step-by-step explanation:

!

3 0
3 years ago
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