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SOVA2 [1]
2 years ago
10

Use the table to write a quadratic function in vertex form. Then rewrite the function in standard form.

Mathematics
1 answer:
Kisachek [45]2 years ago
8 0

Answer:

Step-by-step explanation:

The graph decreases at first, then changes direction at (2, 5).

y = a(x-2)^2 + 5

Plug in (1,11) and solve for a:

11 = a(1-2)^2 + 5

a = 6

Equation in vertex form:

y = 6(x-2)^2 + 5

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3. The average age of online consumers a few years ago was 23.3 years with a standard deviation of 5.3 years. It is believed the
Slav-nsk [51]

Answer:

We cant say, with α =0.01, that the average age changed. The p-value is 0.014

Step-by-step explanation:

As a consecuence of the Central Limit Theorem, the mean sample has a distribution approximately normal, with unknown mean and standard deviation \sigma = 5.3/\sqrt{20} = 1.1851 (the standard deviation of one single sample divided by the  sqaure root of the sample lenght).

The null hypothesis H₀ is that the average age is still 23.3 (the mean is 23.3). The alternative hypothesis is that the mean is different. We want to see if we can refute H₀ with significance level α =0.01.

Lets call X the mean of a random sample of 20 online shoppers. As we discuse above, X is approximately normal with unknown mean and standard deviation equal to 1.1851 . If we take the hypothesis H₀ as True, then the mean will be 23.3, and if we standarize X, we have that the distribution

W = \frac{X - 23.3}{1.1851}

Will have a distribution approximately normal, with mean 0 and standard deviation 1.

The values of the cummulative ditribution of the normal function can be found in the attached file. Since we want a significance level of 0.01, then we need a value Z such that

P(-Z < W < Z) = 0.99

For the symmetry of the standard Normal distribution, we have that Φ(Z) = 1-Φ(-Z), where Φ is the cummulative distribution function of the standard Normal random variable. Therefore, we want Z such that

Φ(Z) = 0.995

If we look at the table, we will found that Z = 2.57, thus,

0.99 = P(-2.57 < W < 2.57) = P(-2.57 < \frac{X-23.3}{1.1851} < 2.57)\\ = P(-2.57*1.1851 + 23.3 < X < 2.57*1.1851 + 23.3) = P(20.254 < X < 26.345)

Thus, we will refute the hypothesis if the observed value of X lies outside the interval [20.254, 26.345].

Since the observed value is 26.2, then we dont refute H₀, So we dont accept that the number average age of online consumers has changed.

For us to refute the hypothesis we need Z such that, for the observed value, |W| > Z. Replacing X by 26.2, we have that [tex] W = \frac{26.2-23.3}{1.1851} = 2.4470. We can observe that Φ(2.447) = 0.993, substracting that amount from 1 and multiplying by 2 (because it can take low values too), we obtain that the p-value is 0.014.  

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8 0
3 years ago
An elecrrician charge a $50 house call fee and $65 per hour for ghe wok. Is it expensive to have electrician work for 6 hours of
chubhunter [2.5K]
It is more expensive to call him back two times for three hours.
5 0
3 years ago
Read 2 more answers
Find the number of ways to listen to four CDs from a selection of 8 CDs. A) 1680 B) 336 C) 70 D) 50 pls aslo explain why..
777dan777 [17]

Answer:

a) 1680

<em>The number of ways to listen to four CDs from a selection of 8 CDs = 1680</em>

Step-by-step explanation:

<u><em>Explanation:-</em></u>

Given data the number of CD' s n = 8

<em>We have to selected '4' CD' s  from total '8' CD's</em>

<em>By using permutations </em>

<em>The number of ways to listen to four CDs from a selection of 8 CDs.</em>

<em>                          =     </em>8_{P_{4} }<em> </em>

<em>  we know that </em>

           n_{P_{r} } = \frac{n!}{(n-r)!}

          8_{P_{4} } = \frac{8!}{(8-4)!} = \frac{8 X 7 X 6 x 5 X 4!}{4!} = 1680

<em>The number of ways to listen to four CDs from a selection of 8 CDs = 1680</em>

7 0
3 years ago
10 1/16ft + 8 3/8ft +1/2 ft
Whitepunk [10]

Answer:

18 15/16 ft

Step-by-step explanation:

what is the request here ?

to do the additions and bring all to one summary result of ft ?

I base my answer on this assumption.

10 1/16 = 161/16

8 3/8 = 67/8

1/2 = 1/2

note let's bring everything to 16th, so that we can actually add them.

161/16

67/8 = 134/16

1/2 = 8/16

161/16 + 134/16 + 8/16 = 303/16 = 18 15/16

cross check :

add all whole numbers first, and then add the remaining fractions too (need to bring them to 16th too).

10 + 8 = 18

1/16 + 3/8 + 1/2 = 1/16 + 6/16 + 8/16 = 15/16

together, 18 15/16

yeah, it is the same.

6 0
3 years ago
Gus and Ike carried a total of 84 books to the library. If Gus carried 5 as many books as Ike, how many books did they each carr
Alexus [3.1K]

Answer:

They each carried 25 books each.

Step-by-step explanation:

You get this by doing

84/5=16.8

then you do

84/2/5= 8.4

8.4+16.8=25.2

but round to whatever 5 or higher bump up below 5 keep the same

so your answer results in 25.

3 0
3 years ago
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