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Rainbow [258]
3 years ago
6

The owner of a video game store creates the expression −2x2 + 28x + 20 to represent the store's weekly profit in dollars, where

x represents the price of a new video game.
Choose the equivalent expression that reveals the video game price that produces the highest weekly profit, and use it to determine that price.

A. −2(x − 7)2 + 118; x = $7
B. −2(x − 7)2 + 118; x = $118
C. −2(x2 − 14x) + 20; x = $14
D. −2(x2 − 14x − 10); x = $10
Mathematics
1 answer:
romanna [79]3 years ago
6 0

Answer:

A. −2(x − 7)2 + 118; x = $7

Step-by-step explanation:

The expression −2x² + 28x + 20 represent the store weekly profit in dollars, where x represents the price of a new video game.

let f(x) = −2x² + 28x + 20  

We need to rewrite this quadratic function in the vertex form.  

f(x) = −2(x² - 14x) + 20  

f(x) = −2(x² - 14x +49) - {-2(49) + 20}

f(x) = −2(x² - 14x +49) + 98 + 20

f(x) = −2(x² - 7)² + 118  

The equivalent expression that reveals the video game price that produces the highest weekly profit is -2(x-7)^2+118 and the price is $7

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Because of the commutative property of multiplication, it is true that
rewona [7]

Answer:

It is Commutative

Step-by-step explanation:

An operation ∆ is said to be Commutative if a∆b=b∆a ∀ a,b ∈ ℝ.

Given the operation ∆ defined by:

a∆b=a X b

a=\frac{3}{4}, b=4

a∆b=\frac{3}{4}X4

=\frac{3X4}{4}=3

Similarly, for the right hand side.

(\frac{4}{3})^{-1}=\frac{3}{4}

Therefore:

b∆a=4X \frac{3}{4}

=\frac{4X3}{4}=3

These are the two ways of solving this problem and we have in fact shown that the operation is commutative as:

a∆b=b∆a=3

3 0
3 years ago
Flying against the wind, a jet travels 5760 miles in nine hours flying with the wind, the same jet travels 5000 miles in five ho
aalyn [17]

Answer:

Step-by-step explanation:

9h+5h(5h-5760)-2+12=y

7 0
2 years ago
A university knows from historical data that 25% of students in an introductory statistics class withdraw before completing the
Vikki [24]

Answer:

13.4%

Step-by-step explanation:

Use binomial probability:

P = nCr p^r q^(n-r)

where n is the number of trials,

r is the number of successes,

p is the probability of success,

and q is the probability of failure (1-p).

Here, n = 16, r = 2, p = 0.25, and q = 0.75.

P = ₁₆C₂ (0.25)² (0.75)¹⁶⁻²

P = 120 (0.25)² (0.75)¹⁴

P = 0.134

There is a 13.4% probability that exactly 2 students will withdraw.

8 0
3 years ago
An air transport association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maxim
Flura [38]

Answer:

The 95% confidence interval estimate of the population mean rating for Miami is (6.0, 7.5).

Step-by-step explanation:

The (1 - <em>α</em>)% confidence interval for the population mean, when the population standard deviation is not provided is:

CI=\bar x \pm t_{\alpha/2, (n-1)}\cdot \frac{s}{\sqrt{n}}

The sample selected is of size, <em>n</em> = 50.

The critical value of <em>t</em> for 95% confidence level and (<em>n</em> - 1) = 49 degrees of freedom is:

t_{\alpha/2, (n-1)}=t_{0.05/2, 49}\approx t_{0.025, 60}=2.000

*Use a <em>t</em>-table.

Compute the sample mean and sample standard deviation as follows:

\bar x=\frac{1}{n}\sum X=\frac{1}{50}\times [1+5+6+...+10]=6.76\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}=\sqrt{\frac{1}{49}\times 31.12}=2.552

Compute the 95% confidence interval estimate of the population mean rating for Miami as follows:

CI=\bar x \pm t_{\alpha/2, (n-1)}\cdot \frac{s}{\sqrt{n}}

     =6.76\pm 2.000\times \frac{2.552}{\sqrt{50}}\\\\=6.76\pm 0.722\\\\=(6.038, 7.482)\\\\\approx (6.0, 7.5)

Thus, the 95% confidence interval estimate of the population mean rating for Miami is (6.0, 7.5).

7 0
3 years ago
How to do this problem
insens350 [35]

Answer:

multiply 2 with the parenthesis

19-2m<7+8m-8

then you put a dot between -2 amd 3

Step-by-step explanation:

5 0
3 years ago
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