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3 years ago

A circle has a radius of 8cm. An angle of 1.4 radians is subtended at the center by an arc. Calculate the length of the arc

Mathematics

1 answer:

AURORKA [14]3 years ago

5 0

Answer:

11.2 cm

Step-by-step explanation:

Given that;

Arc Length Formula (if θ is in radians): l = ϴ × r

ϴ = angle subtended in radians

r= radius of the circle

l = 8cm × 1.4 radians

l= 11.2 cm

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The weights of soy patties sold by Veggie Burgers Delight are normally distributed. A random sample of 15 patties yields a mean

Elden [556K]

Answer:

$t=\frac{3.8-4}{\frac{0.5}{\sqrt{15}}}=-1.549$

Step-by-step explanation:

Data given and notation

$\bar X=3.8$ represent the sample mean

$s=0.5$ represent the sample standard deviation for the sample

$n=15$ sample size

$\mu_o =4$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean weight is less than 4 ounces, the system of hypothesis would be:

Null hypothesis: $\mu \geq 68$

Alternative hypothesis: $\mu < 4$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{3.8-4}{\frac{0.5}{\sqrt{15}}}=-1.549$

3 0

3 years ago

a survey asked 72 randomly chosen students if they were going to attend the school play. twelve said yes. if there are 210 ticke

Ugo [173]

We can solve this by setting up a proportion:

12 seeing the play/ 72 students = 210 seeing the play/ x students

We can cross multiply to solve for x:

(12)x=(72)(210)
12x=15,120
x=1,260 students who attend the school

4 0

3 years ago

Samantha has $24 but she wants a pair of Jordan's that are $112. She does chores and she gets paid $5 for each chore. If she doe

natita [175]

Answer:

Check step-by-step.

Step-by-step explanation:

Okay, so. She gets 5 dollars and she does 15 chores. You would multiply it.

5 * 15 = $75

Then you would subtract 112 and 75.

112 - 75 = 37.

She will get $75. Then, she will need to gather $37

6 0

3 years ago

Can someone help me out with number 2?

Norma-Jean [14]

$\sin255^o=\sin(300^o-45^o)=\sin300^o\cos45^o-\cos300^o\sin45^o= \\\\=- \frac{ \sqrt{3} }{2}\cdot \frac{ \sqrt{2} }{2}- \frac{1}{2} \cdot \frac{ \sqrt{2} }{2}=- \frac{ \sqrt{6} }{4} - \frac{ \sqrt{2} }{4}= -\frac{ \sqrt{6}+\sqrt{2} }{4}$

5 0

4 years ago

The speeds of vehicles traveling on a highway are normally distributed with an unkown population mean and standard deviation. A

Maksim231197 [3]

Answer:

The 90% confidence interval would be given by (60.09;69.91)

We are 90% confident that the true mean for the speeds of vehicles traveling on a highway is between 60.09 and 69.91 miles per hour.

Step-by-step explanation:

1) 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".

$\bar X =65$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s=9 represent the sample standard deviation

n=11 represent the sample size

2) Confidence interval

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

$df=n-1=11-1=10$

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: "=-T.INV(0.05,10)".And we see that $t_{\alpha/2}=1.81$

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

$65-1.81\frac{9}{\sqrt{11}}=60.09$

$65+1.81\frac{9}{\sqrt{11}}=69.91$

So on this case the 90% confidence interval would be given by (60.09;69.91)

We are 90% confident that the true mean for the speeds of vehicles traveling on a highway is between 60.09 and 69.91 miles per hour.

3 0

3 years ago