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3 years ago

Find two consecutive odd integers such that seven times the first equals five times the second.

Mathematics

1 answer:

fredd [130]3 years ago

8 0

Answer:

Odd integers are always one more that an even integer:

1st: 2n+1

2nd: 2n+3

Step-by-step explanation:

14n+7 = 10n+15

4n = 8

n = 2

------------

1st: 2n+1 = 5

2nd: 2n+3 = 7

7x=5*(x+2)

7x=5x+10

7x-5x=10

2x=10

x=5

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The average value of two positive numbers is 30% less than one of the two numbers. By which percentage is average value bigger t

Viefleur [7K]

Answer:

75% bigger

Step-by-step explanation:

Let the first number be x and the second be y.

So:

$Average = \frac{x + y}{2}$

And:

$Average = (1 - 30\%) * x$ -----30% less than x

Substitute $Average = (1 - 30\%) * x$ in $Average = \frac{x + y}{2}$

$\frac{x + y}{2} = (1 - 30\%) * x$

$\frac{x + y}{2} = (1 - 0.30) * x$

$\frac{x + y}{2} = 0.70 * x$

$\frac{x + y}{2} = 0.70x$

Cross multiply

$x + y = 0.70x * 2$

$x + y = 1.40x$

Collect like terms

$1.40x - x = y$

$0.40x = y$

Make x the subject

$x = \frac{y}{0.40}$

$x = 2.50y$

So, the average is:

$Average = (1 - 30\%) * x$

$Average = (1 - 30\%) * 2.50y$

$Average =0.70 * 2.50y$

$Average =1.75y$

Rewrite as:

$Average =(1 + 0.75)y$

Express as percentage

$Average =(1 + 75\%)y$

This means that the average is 75% bigger than the second number

6 0

3 years ago

In a teacher's math course, a linear regression line was calculated to predict

Marat540 [252]

The given equation is the best line that approximates the linear

relationship between the midterm score and the score in the final exam.

AJ's residual is 0.3, which is not among the given options, therefore, the correct option is. <u>E. None of these</u>.

Reasons:

The given linear regression line equation is; $\hat y$ = 25.5 + 0.82· $\mathbf{\hat x}$

Where;

$\hat y$ = Final exam score;

$\hat x$ = The midterm score;

AJ score in the first test, $\hat x$ = 90

AJ's actual score in the exam = 99

Required:

The value of AJ's residual

Solution:

By using the regression line equation, we have;

The predicted exam score, $\hat y$ = 25.5 + 0.82 × 90 = 99.3

The residual score = Predicted score - Actual score

∴ AJ's residual = 99.3 - 99 = 0.3

AJ's residual = 0.3

Therefore, the correct option is option E;

<u>E. None of these</u>

Learn more about regression line equation here:

brainly.com/question/9339658

brainly.com/question/7361586

brainly.com/question/14747095

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2 years ago

Mr.Joseph recently received a notice that his average gas and electric bill would increase at the beginning of the year. He went

son4ous [18]

Answer:

about 2,546

Step-by-step explanation:

4 0

3 years ago

The 24 students in Ms.Lee class each collected an average of 18 cans for recycling the 21 students in mr galvez class each colle

puteri [66]

This is a case for multiplication of #Students by#Cans and then subtract.

Ms Lee.........
24 students × 18 cans = 432
Mr Galvez...21 students × 25 cans = 525

..525
- 432
= 093

Mr Galvez' s class collected 93 more cans than

6 0

3 years ago

Read 2 more answers

I drive 5 miles to Kansas I go back 3 miles to use the bathroom. I drive another 35 miles. Then I go back to where I cam from be

aliya0001 [1]

Answer:

Hi, this riddle could have several answers, including:

-Because I had to go to the bathroom so badly

-Because my child was supposed to get himself in the car

-Because I forgot my child was home

Or another answer is possible too!

5 0

3 years ago