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2 years ago

10

A cosmetics company that makes small cylindrical bars of soap wraps the bars in plastic prior to shipping. Find the surface area

of a bar of soap if the diameter is 5cm and the height is 2cm.

2 answers:

ratelena [41]2 years ago

7 0

The formula you use is pi x radius ^ 2 + pi x radius x l ( l stands for lateral height)
pi x 2.5^2 + pi x 2.5(2)
3.14 x 6.25 + 3.14 x 5
19.6 + 15.7
= 35.3 cm^2

Lelu [443]2 years ago

3 0

We would have two circles of 5cm diameter each, and a rectangle of the length pi*diameter and 2cm, so lets add them:
total = 2circles + rectangle
total = 2(2*pi*(5/2)^2) + pi*diameter*heigth
= 4*pi*(2.5)^2 + pi*5*2
= 109.9
that is the surface area of a bar soap 109.9 cm^2

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The percentage of body fat of a random sample of 36 men aged 20 to 29 found a sample mean of 14.42. Find a 95% confidence interv

Rina8888 [55]

Answer:

$14.42-1.96\frac{6.95}{\sqrt{36}}=12.150$

$14.42+ 1.96\frac{6.95}{\sqrt{36}}=16.690$

So on this case the 95% confidence interval would be given by (12.150;16.690)

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".

$\bar X=14.42$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=6.95$ represent the population standard deviation

n=36 represent the sample size

Solution to the problem

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

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

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: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

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

$14.42-1.96\frac{6.95}{\sqrt{36}}=12.150$

$14.42+ 1.96\frac{6.95}{\sqrt{36}}=16.690$

So on this case the 95% confidence interval would be given by (12.150;16.690)

5 0

2 years ago

If r is the midpoint of qs rs=2x-4, st= 4x-1 and rt = 8x-43 find qs

sammy [17]

Answer:

$QS=68\ units$

Step-by-step explanation:

step 1

Find the value of x

we know that

r is the midpoint of qs

so

QR=RS

QS=QR+RS------> QS=2RS -----> equation A

RT=RS+ST ----> equation B

see the attached figure to better understand the problem

Substitute the given values in the equation B and solve for x

$8x-43=(2x-4)+(4x-1)$

$8x-43=6x-5$

$8x-6x=43-5$

$2x=38$

$x=19$

step 2

Find the value of RS

$RS=2x-4$

substitute the value of x

$RS=2(19)-4$

$RS=34\ units$

step 3

Find the value of QS

Remember equation A

QS=2RS

so

$QS=2(34)=68\ units$

6 0

2 years ago

Emily is thinking of a number, which she calls n. She finds 1/4 of the number and then subtracts 3. Write an expression to repre

Ludmilka [50]

Answer:

1/4n-3

Step-by-step explanation:

3 0

2 years ago

A cube has an edge of 2 feet. The edge is increasing at the rate of 5 feet per minute. Express the volume of the cube as a funct

Agata [3.3K]

Answer:

$V(m) = (2 + 5m)^3$

Step-by-step explanation:

Given

Solid Shape = Cube

Edge = 2 feet

Increment = 5 feet per minute

Required

Determine volume as a function of minute

From the question, we have that the edge of the cube increases in a minute by 5 feet

<em>This implies that,the edge will increase by 5m feet in m minutes;</em>

Hence,

$New\ Edge = 2 + 5m$

Volume of a cube is calculated as thus;

$Volume = Edge^3$

Substitute 2 + 5m for Edge

$Volume = (2 + 5m)^3$

Represent Volume as a function of m

$V(m) = (2 + 5m)^3$

4 0

2 years ago

When we use a confidence interval to reach a conclusion about the population mean, we are applying a type of reasoning or logic

andriy [413]

Answer:

<em>Statistical inference</em>

Step-by-step explanation:

The confidence interval is used to give a range of values for a target population while applying the law of probability. Inferential statistics makes use of data obtained from a given population to predict and make a conclusion on a study.

Statistical inference is the process of applying the tools for inferential statistics to analyze data gotten from a given fraction of the population. This process is based on probability and random sampling.

<em>When a confidence interval is used to conclude a population study, it is certainly based on probability. Therefore the correct option is statistical inference. </em>

3 0

2 years ago