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1 year ago

If twice a number, added to 3 is divided by the number plus 5, the result is three halves. Find the number.

Mathematics

2 answers:

Lynna [10]1 year ago

7 0

Answer:2

Step-by-step explanation:

(2x+5)/3 = 3/2

Multiply both sides by 3:

2x + 5 = 9/2

Subtract 5 from both sides:

2x = 9/2 - 5 = 9/2 - 10/2 = 3/2

Divide both sides by :

x = 3/4

larisa86 [58]1 year ago

7 0

Answer:

-1/3

Step-by-step explanation:

A number x is multiplied by 2, then has 3 added to it, then is divided by x+5, and the answer is 3 halves.

Or, as an equation:

$\frac{2x + 3}{x + 5} = \frac{3}{2}$

Let's cross multiply:

$4(2x + 3) = 2(x + 5)$

Expand:

$8x + 12 = 2x + 10$

Now solve:

$6x + 12 = 10$

$6x = -2$

$x = \frac{-1}{3}$

So the answer is -1/3

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In the diagram of a quadrilateral below, the variables represent the length of the sides in inches.

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Add 11 + 16. Plug in 11 into b-2 since b equals eleven. You should now have 11+16+11-2. Do the same thing and plug in 16 for c and 11 for b for c-b. Your solution will now be 11+16+11-2+16-11.

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2 years ago

48 cookies 25% increase

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Answer:

Step-by-step explanation:

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2 years ago

A sanitation department is interested in estimating the mean amount of garbage per bin for all bins in the city. In a random sam

soldi70 [24.7K]

Answer:

a) $52.8-2.02\frac{3.9}{\sqrt{40}}=51.554$

b) $52.8+2.02\frac{3.9}{\sqrt{40}}=54.046$

c) $52.8-2.71\frac{3.9}{\sqrt{40}}=51.129$

d) $52.8+2.71\frac{3.9}{\sqrt{40}}=54.471$

e) Yes, depends of the confidence level.

At 95 % of confidence the value 54.1985 pounds is not included on the interval. At 5% of significance the statement is FALSE.

At 99 % of confidence the value 54.1985 pounds is included on the interval. So at 1% of significance the statement is TRUE.

Step-by-step explanation:

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".

$\bar X =52.8$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=3.9 represent the sample standard deviation

n=40 represent the sample size

a) What is the lower limit of the 95% interval? Give your answer to three decimal places

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the mean and the sample deviation we can use the following formulas:

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=40-1=39$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,39)".And we see that $t_{\alpha/2}=2.02$

Now we have everything in order to replace into formula (1):

$52.8-2.02\frac{3.9}{\sqrt{40}}=51.554$

b) What is the upper limit of the 95% interval? Give your answer to three decimal places

$52.8+2.02\frac{3.9}{\sqrt{40}}=54.046$

So on this case the 95% confidence interval would be given by (51.554;54.046)

c) What is the lower limit of the 99% interval? Give your answer to three decimal places

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,39)".And we see that $t_{\alpha/2}=2.71$

Now we have everything in order to replace into formula (1):

$52.8-2.71\frac{3.9}{\sqrt{40}}=51.129$

d) What is the upper limit of the 99% interval? Give your answer to three decimal places

$52.8+2.71\frac{3.9}{\sqrt{40}}=54.471$

So on this case the 99% confidence interval would be given by (51.129;54.471)

e) Consider the claim that the mean amount of garbage per bin is 54.1985 pounds. Is the following statement true or false? The decision about the claim would depend on whether we use a 95% or 99% confidence interval: True/False

Yes, depends of the confidence level.

At 95 % of confidence the value 54.1985 pounds is not included on the interval. At 5% of significance the statement is FALSE.

At 99 % of confidence the value 54.1985 pounds is included on the interval. So at 1% of significance the statement is TRUE.

3 0

3 years ago

Natalie works in a department store selling clothing. She makes a guaranteed salary of $300 per week but is paid a commission on

Luba_88 [7]

Answer: Natalie make $ 367.5 in a week in which she made $225 in sales .

Natalie make $ ( 300+x ) in a week in which she made $ x in sales .

Step-by-step explanation:

Base Salary of Natalie = $300

Also, she gets 30% of the her total sales for the week.

If total sales in a week = $225

commission = 30% of $225

= $ ( 0.30 × 225)

= $ 67.5

Natalie got = Base Salary + Commission

= $300 + $ 67.5

= $ 367.5

∴ Natalie make $ 367.5 in a week in which she made $225 in sales .

If total sales in a week = $x

commission = 30% of $x

= $ ( 0.30 × x)

= $ 0.30 x

Natalie got = Base Salary + Commission

= $ ( 300+x )

∴ Natalie make $ ( 300+x ) in a week in which she made $ x in sales .

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2 years ago

I need help with equation number 6

Leona [35]

Combine like terms
-2x-4=-2x-4

Since the equations are the same, the answer is infinitely many solutions.

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2 years ago