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3 years ago

1/2 (x - 10) = 7 what does x =

Mathematics

2 answers:

iVinArrow [24]3 years ago

7 0

Answer:

x = 24

Step-by-step explanation:

distibute: 1/2x - 5 = 7

add 5 to both sides: 1/2x = 12

multiply by 2 on both sides: x = 24

To check your work:

1/2[(24) - 10] = 7

simplify inside the parenthesis: 1/2[14] = 7

multiply: 7 = 7

the statement is true so your answer is corect

Vika [28.1K]3 years ago

6 0

X=24

Work: x-10=14 x=14+10

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Answer:

9 represents the initial height from which the ball was dropped

Step-by-step explanation:

Bouncing of a ball can be expressed by a Geometric Progression. The function for the given scenario is:

$f(n)=9(0.7)^{n}$

The general formula for the geometric progression modelling this scenario is:

$f(n)=f_{0}(r)^{n}$

Here,

$f_{0}$ represents the initial height i.e. the height from which the object was dropped.

r represents the percentage the object covers with respect to the previous bounce.

Comparing the given scenario with general equation, we can write:

$f_{0}$ = 9

r = 0.7 = 70%

i.e. the ball was dropped from the height of 9 feet initially and it bounces back to 70% of its previous height every time.

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Answer:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=12.8$

The sample deviation calculated $s=4.324 \approx 4.3$

$12.8-4.604\frac{4.324}{\sqrt{5}}=3.896$

$12.8+ 4.604\frac{4.324}{\sqrt{5}}=21.704$

So on this case the 99% confidence interval would be given by (3.896;21.704)

Step-by-step explanation:

Data: 10,9,20,13,12

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)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

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:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=12.8$

The sample deviation calculated $s=4.324$

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

$df=n-1=5-1=4$

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(0.005,4)".And we see that $t_{\alpha/2}=4.604$

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

$12.8-4.604\frac{4.324}{\sqrt{5}}=3.896$

$12.8+ 4.604\frac{4.324}{\sqrt{5}}=21.704$

So on this case the 99% confidence interval would be given by (3.896;21.704)

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