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Verizon [17]
3 years ago
14

In a circle, an arc length of 6.6 is intercepted by central angle of 2/3 radians. Determine the length of the radius.

Mathematics
1 answer:
Harlamova29_29 [7]3 years ago
3 0

Answer:

9.9

Step-by-step explanation:

To solve this problem, we first need to know that the whole length of the circunference is related to a central angle of 2pi radians. Then, we can solve using a rule of three to find the radius:

arc of 6.6 -> central angle of 2/3

arc of 2*pi*r -> central angle of 2pi

2*pi*r * (2/3) = 6.6 * 2*pi

r * (2/3) = 6.6

r = 6.6 / (2/3) = 9.9

So the length of the radius is 9.9

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Hardest thing like an object is metal.
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A coffee company wants to make sure that their coffee is being served at the right temperature. If it is too hot, the customers
Cerrena [4.2K]

Answer:

Null hypothesis:\mu = 65  

Alternative hypothesis:\mu \neq 65

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".  

For this case the value of \mu represent the parameter associated to the population (True average of cofee temperature)

Step-by-step explanation:

Data given and notation  

\bar X=70.2 represent the mean height for the sample  

s represent the sample standard deviation for the sample  

n=20 sample size  

\mu_o =765 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 true mean i equal to 70.2, the system of hypothesis would be:  

Null hypothesis:\mu = 65  

Alternative hypothesis:\mu \neq 65  

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".  

For this case the value of \mu represent the parameter associated to the population (True average of cofee temperature)

3 0
3 years ago
A tent rental company charges a mandatory $125 setup fee and a $90 hourly rental fee. Which of the following equations can be us
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B. c = 125 + 90(9) is the answer

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In a recent snail race, a snail traveled a distance of 1 1/6 inches in 2 minutes. Find the number if inches traveled per minute
Alecsey [184]

Answer:

For inch/min =0.9167 inch/min

For min/inch = 1.0908 min/inch

Step-by-step explanation:

The snail in the race traveled 11/6 inches in 2 minutes.

The number of inches per minute is equal to = (11/6)/(2)

= 11/12

=0.9167 inch/min

The number of minutes per inch is equal to = 1/(inch per min)

= 1/0.9167

= 1.0908 min/inch

Minutes per inch is gotten by taking the inverse of inch/min or dividing the number of minutes by number of inches

6 0
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Use the discriminant to determine the number of solutions to the quadratic equation 3x^2+5x=-1
kari74 [83]

Answer:

Two real distinct solutions

Step-by-step explanation:

Hi there!

<u>Background of the Discriminant</u>

The discriminant b^2-4ac applies to quadratic equations when they are organised in standard form: ax^2+bx+c=0.

All quadratic equations can be solved with the quadratic formula: x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}}.

When b^2-4ac is positive, it is possible to take its square root and end up with two real, distinct values of x.

When it is zero, we won't be taking the square root at all and we will end up with two real solutions that are equal, or just one solution.

When it is negative, it is impossible to take the square root and we will end up with two non-real solutions.

<u>Solving the Problem</u>

<u />3x^2+5x=-1<u />

We're given the above equation. It hasn't been organised completely in ax^2+bx+c=0, but we can change that by adding 1 to both sides to make the right side equal to 0:

3x^2+5x+1=0<u />

Now that we can identify the values of a, b and c, we can plug them into the discriminant:

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Therefore, because the discriminant is positive, the equation has two real, distinct solutions.

I hope this helps!

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