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3 years ago

Solve for x. 3(x + 2) + 4(x - 5) = 10

Mathematics

2 answers:

____ [38]3 years ago

6 0

Step-by-step explanation:

3x+6+4x-20=10

7x-14=10

7x=24

x=24/7

Troyanec [42]3 years ago

3 0

Answer:

x=3.43

Step-by-step explanation:

3(x-2)+4(x-5)=10

3x+6+4x-20=10

7x-14=10

7x=24

x=24/7

24/7=3.428571428571429(round to nearest hundredths)

x=3.43

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A professor at a university wants to estimate the average number of hours of sleep students get during exam week. The professor

kotegsom [21]

Answer:

$n=(\frac{1.64(6.995)}{1.939})^2 =35.003 \approx 36$

So the answer for this case would be n=36 rounded up to the nearest integer

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma =6.995$ represent the population standard deviation

n represent the sample size

Solution to the problem

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=1.64$

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =1.939 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

If we replace we have this:

$n=(\frac{1.64(6.995)}{1.939})^2 =35.003 \approx 36$

So the answer for this case would be n=36 rounded up to the nearest integer

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4 years ago

Which choice is equivalent to 6.25% ?

Levart [38]

.625 to find the decimal of a percentage divide by 100

6 0

3 years ago

What is 74 divided by 12?plz help I need this assignment done before 3:30 and it’s 2 hours until time

bogdanovich [222]

Answer:

6.16.

Step-by-step explanation:

hope this helps.

5 0

3 years ago

Read 2 more answers

Suppose that a and b are integers, a ≡ 4 ( mod 13 ) and b ≡ 9 ( mod 13 ) . Find the integer c with 0 ≤ c ≤ 12 such that: c ≡ 9 a

g100num [7]

Answer:

A) For c ≡ 9 a ( mod 13 ) ; C is 10

B) For c ≡ 11 b ( mod 13 ) ; C is 8

C) For c ≡ a + b ( mod 13 ); C is 0

D) For c ≡ a² + b² ( mod 13 ); C is 6

E) For c ≡ a² − b² ( mod 13 ) ; C is 0

Step-by-step explanation:

This is a modular arithmetic problem where a ≡ 4 ( mod 13 ) and b ≡ 9 ( mod 13 ).

And 0 ≤ c ≤ 12.

A) c ≡ 9 a ( mod 13 )

Substituting the value of a to obtain;

c ≡ 9 x4 ( mod 13 ) = 36 mod 13

To find 36 mod 13 using the Modulo Method, we first divide the Dividend (36) by the Divisor (13).

Second, we multiply the whole part of the Quotient in the previous step by the Divisor (13).

Then finally, we subtract the answer in the second step from the Dividend (36) to get the answer. Here is the math to illustrate how to get 36 mod 13 using Modulo Method:

36 / 13 = 2.769231

2 x 13 = 26

36 - 26 = 10

Thus, the answer to "What is 36 mod 13?" is 10

So C = 10

B) c ≡ 11 b ( mod 13 ) = 11 x 9 ( mod 13 ) = 99 ( mod 13 )

Using the same method as above,

99 ( mod 13 );

99 / 13 = 7.6155

7 x 13 = 91

99 - 91 = 8

So, C = 8

C)c ≡ a + b ( mod 13 ) = 4 + 9 (mod 13) = 13 (mod 13)

Thus;

13 / 13 = 1

1 x 13 = 13

13 - 13 = 0

So, C = 0

D)c ≡ a² + b² ( mod 13 ) = 4² + 9²( mod 13 ) = 16 + 81 ( mod 13 ) = 97 ( mod 13 )

Thus;

97 / 13 = 7.46154

7 x 13 = 91

97 - 91 = 6

So, C = 6

E)c ≡ a² − b² ( mod 13 )= 4² - 9²( mod 13 ) = 16 - 81 ( mod 13 ) = - 65 ( mod 13 )

Thus;

-65 / 13 = - 5

-5 x 13 = - 65

-65 - (-65) = 0

So, C = 0

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