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nikdorinn [45]
3 years ago
11

A circle with radius of \greenD{1\,\text{cm}}1cmstart color #1fab54, 1, start text, c, m, end text, end color #1fab54 sits insid

e a \blueD{3\,\text{cm} \times 3\,\text{cm}}3cm×3cmstart color #11accd, 3, start text, c, m, end text, times, 3, start text, c, m, end text, end color #11accd rectangle. What is the area of the shaded region?
Mathematics
2 answers:
Natasha2012 [34]3 years ago
5 0

Answer:

5.86cm²

Step-by-step explanation:

it is correct on khan academy

iris [78.8K]3 years ago
4 0

Answer:

5.86cm²

Step-by-step explanation:

Area of the shaded region = Area of the rectangle - Area of the circle

Area of rectangle = Length * Width

Area of rectangle = 3cm * 3cm

Area of rectangle = 9cm²

Area of the circle = πr²

Given radius r = 1cm

Area of the circle = 3.14(1)²

Area of the circle = 3.14cm²

Area of the shaded region = 9 - 3.14

Area of the shaded region = 5.86cm²

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To make fruit punch for a party, we need 4 1⁄2 gallons of ginger ale, 1 gallon of strawberry juice, 2 3⁄4 gallons of frozen oran
lina2011 [118]

For this case we convert the mixed numbers to fractions:

4 \frac {1} {2} = \frac {2 * 4 + 1} {2} = \frac {9} {2}\\2 \frac {3} {4} = \frac {4 * 2 + 3} {4} = \frac {11} {4}

Now we add the fractions:

\frac{9} {2}+1+ \frac {11} {4} + \frac {1} {8} =

We find the least common multiple of the denominators. The l.c.m is 8, then we divide by each denominator and multiply the result by each numerator.

\frac {36 + 8 + 22 + 1} {8} =\\\frac {67} {8} =

8,375

Thus, the punch recipe implies 8.375 gallons. If we convert to a mixed number we have:

8 \frac {3} {8} gallons

Answer:

8 \frac {3} {8}gallons

4 0
3 years ago
Suppose the standard deviation of a normal population is known to be 3, and H0 asserts that the mean is equal to 12. A random sa
blagie [28]

Answer:

z=\frac{12.95-12}{\frac{3}{\sqrt{36}}}=1.9  

p_v =P(z>1.9)=0.0287  

If we compare the p value and the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 12 at 5% of signficance.  

Step-by-step explanation:

Data given and notation  

\bar X=12.95 represent the sample mean

\sigma=3 represent the population standard deviation for the sample  

n=36 sample size  

\mu_o =12 represent the value that we want to test  

\alpha=0.05 represent the significance level for the hypothesis test.  

z 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 is equal to 12, the system of hypothesis would be:  

Null hypothesis:\mu \leq 12  

Alternative hypothesis:\mu > 12  

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}} (1)  

z-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:  

z=\frac{12.95-12}{\frac{3}{\sqrt{36}}}=1.9  

P-value  

Since is a right tailed test the p value would be:  

p_v =P(z>1.9)=0.0287  

Conclusion  

If we compare the p value and the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is higher than 12 at 5% of signficance.  

4 0
3 years ago
Read 2 more answers
one sixth of the students in a school marching band are in the percussion section, the percussion section has 6 students, how ma
Igoryamba

Answer:

36 students

Step-by-step explanation:

because if 1/6 is 6 students then you have to multiply the 6 by 6

4 0
3 years ago
Read 2 more answers
10
MA_775_DIABLO [31]

Answer:

8

Step-by-step explanation:

how i got cause i had same answer not to long ago

7 0
3 years ago
Determine the equation of the graph.
ruslelena [56]

Answer: C

y=-5cos(x) is the graphed equation. Cos(x) starts at (0,0) and one period is 2pi or 6.28 and by cos(x) multiplied by -5 starts the cosine wave at (0,-5) and thus corresponds to the graphed equation shown.

Any questions please feel free to ask. Thanks

6 0
3 years ago
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