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IRINA_888 [86]
2 years ago
14

HELP!!!! A quarter circle is attached to the side of a square as shown.

Mathematics
1 answer:
Paul [167]2 years ago
6 0

Answer:

28.56 m²

Step-by-step explanation:

What we need to do for the quarter circle is use the following formula: 1/4(πr²)

(4 * 4) + 1/4(3.14 * 4²)

16 + 1/4(3.14 * 16)

16 + 1/4(50.24)

16 + 12.56

28.56 m²

The best approximation for the area of this figure is 28.56 m².

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A local bottler in Hawaii wishes to ensure that an average of 22 ounces of passion fruit juice is used to fill each bottle. In o
Mandarinka [93]

Answer:

(a) Null Hypothesis, H_0 : \mu = 22 ounces  

    Alternate Hypothesis, H_A : \mu\neq 22 ounces

(b) The value of the test statistic is -2.687.

(c) The critical values are -1.96 and 1.96.

(d) We conclude that Reject H_0 since the value of the test statistic is less than the negative critical value.

Step-by-step explanation:

We are given that a local bottler in Hawaii wishes to ensure that an average of 22 ounces of passion fruit juice is used to fill each bottle.

He takes a random sample of 65 bottles. The mean weight of the passion fruit juice in the sample is 21.54 ounces. Assume that the population standard deviation is 1.38 ounce.

<em>Let </em>\mu<em> = average ounces of passion fruit juice used to fill each bottle.</em>

(a) So, Null Hypothesis, H_0 : \mu = 22 ounces     {means that the average of 22 ounces of passion fruit juice is used to fill each bottle}

Alternate Hypothesis, H_A : \mu\neq 22 ounces     {means that the average different from 22 ounces of passion fruit juice is used to fill each bottle}

The test statistics that would be used here <u>One-sample z test statistics</u> as we know about the population standard deviation;

                        T.S. =  \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \bar X = sample mean weight of the passion fruit juice = 21.54 ounces

            \sigma = population standard deviation = 1.38 ounce

            n = sample of bottles = 65

So, <u><em>test statistics</em></u>  =  \frac{21.54-22}{\frac{1.38}{\sqrt{65} } }  

                               =  -2.687

(b) The value of z test statistics is -2.687.

(c) Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 5% significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

<em>Since our test statistics does not lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which </em><u><em>we reject our null hypothesis</em></u><em>.</em>

Therefore, we conclude that Reject H_0 since the value of the test statistic is less than the negative critical value which means that the average different from 22 ounces of passion fruit juice is used to fill each bottle.

6 0
3 years ago
I need help with this I put this out 3 times I need help
anzhelika [568]
Prompt
What is a row?
4 0
2 years ago
On a 15 hour trip, Rob drove 35% of the time and Mark drove the remainder of the time. How many hours did Mark drive? Explain 9.
Zigmanuir [339]

Answer:

9.75 hours

Step-by-step explanation:

If Rob drove 35% of the time and Mark drove the remainder of the time, the total is 100 %

100-35 = 65

so Mark drove 65% of the time

The total time driven was 15 hours, so we multiply the total time driven by the percentage of time that Mark drove to find the number of hours that Mark drove.

15 * 65%

15*.65

9.75 hours

7 0
3 years ago
How do I graph f(x) = -x^2 +2x -4
tangare [24]
This is how you would graph it :

8 0
2 years ago
Read 2 more answers
In a jar of ten beads, seven are red and three are blue. a bead is drawn from the jar five times with replacement. what is the p
MatroZZZ [7]
<span>In a jar of ten beads; since 3 are blue; probability of picking a blue ball, B, = p(b) = 3/10. And P (of not picking a blue ball) ; p(b') = 7/10. Since it occurs with replacement, probabilities doesn't change Probaility of picking k blue balls from on n attempts is given by P_n(k) P_n(k) = (n, k) p^(k) q^(n -k) where p and q are b and b' respectively. P_5(2) = (5 , 2) (0.3)^(2) (0.7)^(5 - 2) P_5(2) = 5C2 (0.3)^(2) (0.7)^(3) = 0.3087</span>
6 0
3 years ago
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