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3 years ago

6

Write the expressions "Four times the difference of a number and 1 is equal to six times the sum of the number and three. Find t

he number

1 answer:

DochEvi [55]3 years ago

8 0

Answer:

4(x - 1) = 6(x + 3)

x = -11

Step-by-step explanation:

x represents “the number” so we would substitute this with a variable.

(I hope this helps! Have a great day AND STAN BTS)

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The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airp

motikmotik

Answer:

The 95% confidence interval for the population mean rating is (5.73, 6.95).

Step-by-step explanation:

We start by calculating the mean and standard deviation of the sample:

$M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{50}(6+4+6+. . .+6)\\\\\\M=\dfrac{317}{50}\\\\\\M=6.34\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{49}((6-6.34)^2+(4-6.34)^2+(6-6.34)^2+. . . +(6-6.34)^2)}\\\\\\s=\sqrt{\dfrac{229.22}{49}}\\\\\\s=\sqrt{4.68}=2.16\\\\\\$

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=6.34.

The sample size is N=50.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

$s_M=\dfrac{s}{\sqrt{N}}=\dfrac{2.16}{\sqrt{50}}=\dfrac{2.16}{7.071}=0.305$

The degrees of freedom for this sample size are:

$df=n-1=50-1=49$

The t-value for a 95% confidence interval and 49 degrees of freedom is t=2.01.

The margin of error (MOE) can be calculated as:

$MOE=t\cdot s_M=2.01 \cdot 0.305=0.61$

Then, the lower and upper bounds of the confidence interval are:

$LL=M-t \cdot s_M = 6.34-0.61=5.73\\\\UL=M+t \cdot s_M = 6.34+0.61=6.95$

The 95% confidence interval for the mean is (5.73, 6.95).

4 0

3 years ago

Tammy has a job that has a weekly salary of $1,200 but wants to switch a job that has a monthly salary of $11,700. How much more

iogann1982 [59]

Answer:

$1529.8

Step-by-step explanation:

Given:

Tammy has a job that has a weekly salary of $1,200.

But wants to switch a job that has a monthly salary of $11,700

Question asked:

How much more will she make per week if she switch to the new job?

Solution:

Monthly salary of a new job, she wants to switch = $11,700

Weekly salary of a new job, she wants to switch = ?

As we know : 1 month = 4.286 Weeks

Salary of 1 month for a new job, she wants to switch = $11,700

Salary of 4.286 Weeks for a new job, she wants to switch = $11,700

Salary of 1 Week for a new job, she wants to switch = $11700\div4.286=\$2729.81$

Now, we have to find that How much more she will make per week, if she switch to the new job.

More money she will make for a new job she wants o switch = Weekly salary for a new job, she wants to switch - Weekly salary of current job

More money she will make, for a new job = $2729.8 - $1200 = $1529.8

Therefore, she will make $1529.8 more per week if she switch to the new job.

3 0

3 years ago

Select TWO values of x that are roots

Sauron [17]

$x_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a};\ x_2=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\\\y=x^2+3x+5\\\\a=1;\ b=3;\ c=5\\\\b^2-4ac=3^2-4(1)(5)=9-20=-11\\\\x_1=\dfrac{-3-\sqrt{-11}}{2\cdot1}=\dfrac{-3-\sqrt{-11}}{2}\\\\x_2=\dfrac{-3+\sqrt{-11}}{2}$

Answer: A and B.

3 0

3 years ago

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Two twin sisters are away at college. They both called home today. Tara calls home every 4 days. Sara calls home every 3 days. H

frozen [14]

Answer:

12

Step-by-step explanation:

4*3

7 0

3 years ago