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zhuklara [117]
3 years ago
12

A ball is launched from a sling shot. Its height, h(x), can be represented by a quadratic function in terms of time, x, in secon

ds.
After 1 second, the ball is 148 feet in the air; after 2 seconds, it is 272 feet in the air.

Find the height, in feet, of the ball after 6 seconds in the air.

I have no idea any help?
Mathematics
1 answer:
Vikki [24]3 years ago
5 0
From the data given, generate first the quadratic equation which best describe the height of the ball. The quadratic function has a general form of 
                                             f(x) = Ax^2 + Bx 

Substituting the known data,

                             (1)            148 = A(1^2) + B(1)
                             (2)             272 = A (2^2) + B (2)
solving for A and  B simultaneously, 

                                              A = -12
                                              B = 160

To answer this problem, substitute 6 to x. Thus, after 6 seconds, the height is 528 feet. 
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GreenBeam Ltd. claims that its compact fluorescent bulbs average no more than 3.50 mg of mercury. A sample of 25 bulbs shows a m
Harrizon [31]

Answer:

(a) Null Hypothesis, H_0 : \mu \leq 3.50 mg  

     Alternate Hypothesis, H_A : \mu > 3.50 mg

(b) The value of z test statistics is 2.50.

(c) We conclude that the average mg of mercury in compact fluorescent bulbs is more than 3.50 mg.

(d) The p-value is 0.0062.

Step-by-step explanation:

We are given that Green Beam Ltd. claims that its compact fluorescent bulbs average no more than 3.50 mg of mercury. A sample of 25 bulbs shows a mean of 3.59 mg of mercury. Assuming a known standard deviation of 0.18 mg.

<u><em /></u>

<u><em>Let </em></u>\mu<u><em> = average mg of mercury in compact fluorescent bulbs.</em></u>

So, Null Hypothesis, H_0 : \mu \leq 3.50 mg     {means that the average mg of mercury in compact fluorescent bulbs is no more than 3.50 mg}

Alternate Hypothesis, H_A : \mu > 3.50 mg     {means that the average mg of mercury in compact fluorescent bulbs is more than 3.50 mg}

The test statistics that would be used here <u>One-sample z test</u> <u>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 mg of mercury = 3.59

            \sigma = population standard deviation = 0.18 mg

            n = sample of bulbs = 25

So, <em><u>test statistics</u></em>  =  \frac{3.59-3.50}{\frac{0.18}{\sqrt{25} } }

                               =  2.50

The value of z test statistics is 2.50.

<u>Now, P-value of the test statistics is given by;</u>

         P-value = P(Z > 2.50) = 1 - P(Z \leq 2.50)

                                             = 1 - 0.9938 = 0.0062

<em />

<em>Now, at 0.01 significance level the z table gives critical value of 2.3263 for right-tailed test. Since our test statistics is more than the 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><em><u>we reject our null hypothesis</u></em><em>.</em>

Therefore, we conclude that the average mg of mercury in compact fluorescent bulbs is more than 3.50 mg.

6 0
2 years ago
10 points
velikii [3]
384. 25 is the correct answer.
7 0
3 years ago
Jason has already used 4/12 cans of paint while painting furniture. He is painting chairs which each use 10/6 cans of paint.
Lady bird [3.3K]

Answer:

Based off of the calculations I did, I got 32 as the answer.

Step-by-step explanation:

Jason uses 10/6 of the paint for each chair he paints and according to the question, there are 19 chairs.

So we multiply these two numbers to get the amount of paint used after painting all 19 chairs.

10/6 * 19 = 31.666...

Then we add the previous amount Jason used for painting the furniture to the total amount of paint used after painting the 19 chairs.

31.666... + 4/12 = 32.

Thus, Jason used 32 cans of paint in total.

5 0
2 years ago
Read 2 more answers
Jess is painting his car. He's created a purple color that uses red paint and blue paint in a ratio of 6:5. Jess uses 15
lilavasa [31]
B
I’m sure It’s current answer
4 0
3 years ago
Read 2 more answers
Plz I need help as soon as you see this... and I need the work so I understand it plz!​
poizon [28]

Answer:

8. Obtuse

11. Obtuse

Step-by-step explanation:

c^2 = a^2 + b^2

for 8, it's 6 squared plus 9 squared, which is 117. now, 15 squared is 225. 225 is bigger than 117, which makes it obtuse. if the two results equaled each other, it would be a right triangle. if the 2 smaller numbers when squared were bigger than the hypotenuse squared, then it would be acute

4 0
3 years ago
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