Rewrite the function by completing the square.
f(x) = x^2 – 10x—96

Answers

Answer 1

Answer:

Answer:

$f(x) = (x - 5)^(2) - 121$ .

Step-by-step explanation:

The goal is to rewrite $f(x)$ in the vertex form $a\, (x - h)^(2) + k$ by completing the square (where $a$ , $h$ , and $k$ are constants.)

Expand the vertex form expression:

$\begin{aligned}& a\, (x - h)^(2) + k\n &= a\, (x - h)\, (x - h) + k \n &= a\, \left(x^2 - h\, x - h\, x + h^2\right) + k \n &= a\, \left(x^2 - 2\, h\, x + h^2\right) + k\n &= a\, x^2 - 2\, a\, h\, x + \left(a\, h^2 + k\right) \end{aligned}$ .

Compare this expression to $f(x) = x^2 - 10\, x - 96$ and solve for the constants $a$ , $h$ , and $k$ . Make sure that the coefficient of each term matches:

Coefficient for the $x^2$ term: $a$ in the expanded expression and $1$ in the expression for $f(x)$ . Hence, $a = 1$ .

Coefficient for the $x$ term: $(-2\, a\, h)$ in the expanded expression and $(-10)$ in the expression for $f(x)$ . Hence, $-2\, a\, h = -10$ .

Coefficient for the constant term: $\left(a\, h^2 + k\right)$ in the expanded expression and $(-96)$ in the expression for $f(x)$ . Hence, $a\, h^(2) + k = -96$ .

Substitute $a = 1$ into the second equation, $-2\, a\, h = -10$ , and solve for $h$ .

$-2 \, h = -10$ .

$h = 5$ .

Substitute both $a = 1$ and $h = 5$ into the third equation, $a\, h^(2) + k = -96$ , and solve for $k$ .

$5^2 + k = -96$ .

$k = -121$ .

Therefore, $a\, (x - h)^(2) + k$ becomes $(x - 5)^2 + (-121)$ .

Hence, the vertex form of the parabola $f(x)$ would be:

$f(x) = (x - 5)^(2) - 121$ .

Answer 2

Answer:

Answer:

(x - 5)² -121 = 0

Step-by-step explanation:

if you need to find the roots you can take the square root of each side:

(x-5)² = 121

square root of (x-5)² is x-5

square root of 121 is ±11

first root: x-5 = 11

x = 16

second root: x-5 = -11

x = -6

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7) In 2014, the attendance at Jefferson School's School Festival was 650. In 2015, the attendance was 575. What was the percent change in attendance from 214 to 2015? Round to the nearest tenth. * A 11% B 12% decrease C 13% D 14%

Answers

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Letter B

Consider the following hypothesis test:H 0: = 17H a: 17A sample of 40 provided a sample mean of 14.12. The population standard deviation is 4.a. Compute the value of the test statistic (to 2 decimals). (If answer is negative, use minus "-" sign.)b. What is the p-value (to 4 decimals)?c. Using = .05, can it be concluded that the population mean is not equal to 17? SelectYesNoItem 3Answer the next three questions using the critical value approach.d. Using = .05, what are the critical values for the test statistic (to 2 decimals)? ±e. State the rejection rule: Reject H 0 if z is Selectgreater than or equal togreater thanless than or equal toless thanequal tonot equal toItem 5 the lower critical value and is Selectgreater than or equal togreater thanless than or equal toless thanequal tonot equal toItem 6 the upper critical value.f. Can it be concluded that the population mean is not equal to 17?

Answers

Answer:

We conclude that the population mean is not equal to 17.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 17

Sample mean, $\bar{x}$ = 14.12

Sample size, n = 40

Alpha, α = 0.05

Population standard deviation, σ = 4

First, we design the null and the alternate hypothesis

$H_(0): \mu = 17\nH_A: \mu \neq 17$

We use Two-tailed z test to perform this hypothesis.

a) Formula:

$z_(stat) = \displaystyle\frac{\bar{x} - \mu}{(\sigma)/(√(n)) }$

Putting all the values, we have

$z_(stat) = \displaystyle(14.12 - 17)/((4)/(√(40)) ) = -4.5536$

b) P-value can be calculated from the standard z-table.

P-value = 0.0000

c) Since the p-value is less than the significance level, we reject the null hypothesis and accept the alternate hypothesis. Thus, the population mean is not equal to 17

d) Now, $z_(critical) \text{ at 0.05 level of significance } = \pm 1.96$

e) Rejection Rule:

We reject the null hypothesis if it is less than lower critical value and greater than the upper critical value

If the z-statistic lies outside the acceptance region which is from -1.96 to +1.96, we reject the null hypothesis.

f) Since the calculated z-stat lies outside the acceptance region, we reject the null hypothesis and accept the alternate hypothesis. Thus, the population mean is not equal to 17.

Final answer:

The test statistic is -1.78 and the p-value is 0.0761, indicating that we fail to reject the null hypothesis. Therefore, it cannot be concluded that the population mean is not equal to 17.

Explanation:

The test statistic can be calculated using the formula:

test statistic = (sample mean - population mean) / (population standard deviation / sqrt(sample size))

Plugging in the given values, we get:

test statistic = (14.12 - 17) / (4 / sqrt(40))

Calculating this gives us a test statistic value of -1.78.

The p-value can be calculated using the test statistic. We need to find the probability that a test statistic at least as extreme as -1.78 would occur assuming the null hypothesis is true. Using a standard normal distribution table or software, we find the p-value to be approximately 0.0761.

Since the p-value is greater than the significance level (alpha = 0.05), we fail to reject the null hypothesis. Therefore, we can conclude that there is not enough evidence to suggest that the population mean is not equal to 17.

Learn more about Hypothesis testing here:

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Pls help me with this and show any work

Answers

Answer: 9.5 (D.)

Step-by-step explanation:

SOCAHTOA

the sin of an angle is equal to the opposite side over the hypotenuse.

angle: 32

opposite side: x

hypotenuse: 18 m

1. sin32 = x/18

2. 18(sin32) = x

3. 9.5 = x

if you are confused with how it went from 18(sin32) to 9.5, you can plug 18(sin32) into your calculator.

The dot plot below shows the hourly rate of some babysitters in a city:A number line is shown from 1 dollar to 7 dollars in increments of 1 dollar for each tick mark. The horizontal axis label is Dollars per hour. There are 3 dots above 4 dollars, 2 dots above 5 dollars, 4 dots above 6 dollars, and 1 dot above 7 dollars. The title of the line plot is Babysitting Rates.

Which statement best describes the shape of the data?

It is symmetric and has a peak at $7.00.
It is not symmetric and has a peak at $6.00.
It is a cluster from $1.00 to $7.00 and has gaps.
It is a cluster from $1.00 to $7.00 and has no gaps.

Answers

Answer:

It is not symmetric and has a peak at $6.00

Step-by-step explanation:

Drawn in text in a vertical fashion, we might show it as ...

4 | ooo

5 | oo

6 | oooo

7 | o

The data is clearly not symmetric, has a range from 4 to 7, and has a peak at 6. The appropriate description is ...

It is not symmetric and has a peak at $6.00

A cereal comes in three different package sizes. 8 ounce box $12, 12 ounce box $16,16 ounce box $20 what is the ratio of the coast of an 8 ounce box to a 16 ounce box of cereal

Answers

The ratio between two numbers can be written in terms of fraction by writing the first number as numerator and the second number as denominator. The ratio of the given two boxes is 0.6.

What is the application ratio and proportion?

A ratio is the relation between two numbers a and b as a / b. A proportion is the equality of two ratios as a / b = c / d.

Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.

Given that,

The cost of 8 ounce box is $12,

The cost of 12 ounce box is $16,

And, the cost of 16 ounce box is $20.

The ratio of two numbers a and b is given as a : b = a / b.

Thus the ratio of the cost of an 8 ounce box to a 16 ounce box is given as,

12 : 20

= 12 / 20

= 0.6.

Hence, the ratio between the cost of the two boxes is 0.6.

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Check and simplify ratios:

8 ounces to 12 dollars - 8:12
Simplified: 2:3

16 ounces to 20 dollars - 16:20
Simplified: 4:5

Percentages?

2 / 3 = 66.66%
4 / 5 = 80%

The 16 ounce box has a larger ratio than the 8 ounce box

amelia and 2 of her friends went out to lunch. each girl ordered exactly the same meal. the total cost 55.08, which included 8% sales tax. what was the price of each meal, not including tax?