To study the effect of neighborhood on academic performance, 1000 families were given federal housing vouchers to move out of their low-income neighborhoods. No improvement in the academic performance of the children in the families was found one year after the move.Requried:a. What are the explanatory and response variables?b. What are the subjects, factor(s), and treatment?c. What does no significant difference mean in describing the outcome of this study?d. Explain clearly why the lack of improvement in academic performance after one year does not necessarily mean that neighborhood does not affect academic performance.e. In particular, identify some lurking variables whose effect on academic performance may be confounded with the effect of the neighborhood

Answers

Answer 1

Answer:

Check below for the answers and explanations to the questions.

Step-by-step explanation:

a) The explanatory variable is "the neighborhood" because it is the one that can be controlled/varied by the experimenter and also determines the outcome of the experiment.

The response variable is the "academic performance of the children" since it is the outcome of the experiment.

b) The subjects of the study are the children of the 1000 families that were given federal housing vouchers to relocate.

The factors of the study are:

1. the low income neighborhood

2. the federal housing estate

Treatment is the combination of various levels of the factor. In this case, it is the neighborhood of the families.

c) No significant difference means that the mean of the academic performance of the children while living the low-income neighborhood equals the mean of their academic performance while living in the federal housing estate. Which means that the null hypothesis is accepted.

d) The period of evaluation after relocation is very small compared to the time that has been spent in the low-income neighborhood. The observation has to take a longer time to discover the effect of the new neighbourhood on the academic performance of the children. Therefore the lack of improvement in academic performance after one year does not necessarily mean that neighborhood does not have effect on academic performance.

e) some other variables that are not considered in this study are:

The average Intelligence Quotient of the children

The parental training

The schools attended by the children

Average number of hours spent on study


Related Questions

Scores on a recent national statistics exam were normally distributed with a mean of 82.2 and a standard deviation of 5.If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award

Answers

Answer:

The lowest score eligible for an award is 92.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

[tex]\mu = 82.2, \sigma = 5[/tex]

If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award

The lowest score is the 100 - 2.5 = 97.5th percentile, which is X when Z has a pvalue of 0.975. So X when Z = 1.96. Then

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.96 = \frac{X - 82.2}{5}[/tex]

[tex]X - 82.2 = 5*1.96[/tex]

[tex]X = 92[/tex]

The lowest score eligible for an award is 92.

Find the scale ratio for the map described below.
1 mm ​(map)equals500 m ​(actual)
The scale ratio is 1 to
nothing.

Answers

Answer:

The answer is nothing duh

Step-by-step explanation:

Which expression is equivalent to negative 4 times 4 times 4 times 4 times 4 times 4 times 4 times 4?

Answers

Answer:

-4*4^7

Step-by-step explanation:

Answer:

-65536

Step-by-step explanation:

I do not think I understand the question but -4*4*4*4*4*4*4*4=-65536

I think there may be missing information like if the question is multiple choice.

Hope that helps

What is the solution to this equation? 4x+x-15+3-8x=13

Answers

Answer:

x = -25/3

Step-by-step explanation:

The equation simplifies to -3x - 25 = 0, so

-3x = 25 =>

x = -25/3

please very soon I offer the crown !!! + 10 points urgently !!!

Answers

a- 3 o clock
b- 11
c- 7
d- 4
e- 10
f- 1

A is 3:00, Cis 7:00, E is 10:00, B is 11:00,D is 4:00, F is 1:00 for number two A : big hand at 12 little hand at 2 C: both hands at 12, E: big hand at 12 little hand at 6, B: big hand at 12 little hand at 6, D: big hand at 12 little hand at 5, F:big hand at 12 little hand at 8

Health insurers are beginning to offer telemedicine services online that replace the common office visit. Wellpoint provides a video service that allows subscribers to connect with a physician online and receive prescribed treatments. Wellpoint claims that users of its LiveHealth Online service saved a significant amount of money on a typical visit. The data shown below ($), for a sample of 20 online doctor visits, are consistent with the savings per visit reported by Wellpoint.

90 34 41106 84 5355 48 4175 49 9792 73 7480 94 10256 83

Required:
Assuming the population is roughly symmetric, construct a 95% confidence interval for the mean savings for a televisit to the doctor as opposed to an office visit (to 2 decimals).

Answers

Answer:

[tex]71.35-2.093\frac{22.48}{\sqrt{20}}=60.83[/tex]    

[tex]71.35+2.093\frac{22.48}{\sqrt{20}}=81.87[/tex]    

Step-by-step explanation:

Information given

90 34 41 106 84 53 55 48 41 75 49 97 92 73 74 80 94 102 56 83

In order to calculate the mean and the sample deviation we can use the following formulas:  

[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex] (2)  

[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}[/tex] (3)  

[tex]\bar X=71.35[/tex] represent the sample mean for the sample  

[tex]\mu[/tex] population mean (variable of interest)

s=22.48 represent the sample standard deviation

n=20 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom are given by:

[tex]df=n-1=20-1=19[/tex]

Since the Confidence is 0.95 or 95%, the significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value would be [tex]t_{\alpha/2}=2.093[/tex]

And replacing we got:

[tex]71.35-2.093\frac{22.48}{\sqrt{20}}=60.83[/tex]    

[tex]71.35+2.093\frac{22.48}{\sqrt{20}}=81.87[/tex]    

Assume that you plan to use a significance level of α = 0.05 to test the claim that p1 = p2. Use the given sample sizes and numbers of successes to find the pooled estimate. Round your answer to the nearest thousandth.
n1 = 677 n2 = 3377
x1 = 172 x2 = 654

Answers

Answer:

The calculated  value Z = 3.775 > 1.96 at 0.05 level of significance

Null hypothesis is rejected

The Two Population proportion are not equal

Step-by-step explanation:

Given first sample size n₁ = 677

First sample proportion

                             [tex]p^{-} _{1} = \frac{x_{1} }{n_{1} } = \frac{172}{677} = 0.254[/tex]

Given second sample size n₂ = 3377

second sample proportion

                             [tex]p^{-} _{2} = \frac{x_{2} }{n_{2} } = \frac{654}{3377} = 0.1936[/tex]

Null Hypothesis : H₀ :  p₁ = p₂.

Alternative Hypothesis : H₁ :  p₁ ≠ p₂.

      Test statistic

                [tex]Z = \frac{p_{1} ^{-}-p^{-} _{2} }{\sqrt{P Q(\frac{1}{n_{1} } +\frac{1}{n_{2} }) } }[/tex]

where

        [tex]P = \frac{n_{1} p_{1} + n_{2} p_{2} }{n_{1}+n_{2} } = \frac{677 X 0.254+3377 X 0.1936}{677+3377}[/tex]

       P =  0.2036

      Q = 1 - P = 1 - 0.2036 = 0.7964

       

         [tex]Z = \frac{0.254- 0.1936 }{\sqrt{0.2036 X 0.7964(\frac{1}{677 } +\frac{1}{3377 }) } }[/tex]

        Z =  3.775

Critical value ∝=0.05

Z- value = 1.96

The calculated  value Z = 3.775 > 1.96 at 0.05 level of significance

Null hypothesis is rejected

The Two Population proportion are not equal

find the quotient of (5+4i)/(6+8i) ans express in simplest forms

Answers

Answer:

Your correct answer is 31/50 + -4/25 i

Step-by-step explanation:

5+4i/6+8i = 31/50 + -4/25 i

How many parallel and perpendicular lines, are there in a trapezium?

Answers

Answer:

US

0 parallel linesoptionally, one or two (opposite) angles may be 90°

World

2 parallel linesoptionally, one line perpendicular to the two parallel lines

Step-by-step explanation:

It depends on where you are. A "trapezium" outside the US is the same as a "trapezoid" in the US, and vice versa.

A trapezium (World; trapezoid in the US) is characterized by exactly one pair of parallel lines. One of the lines that are not parallel may be perpendicular to the parallel lines, but that will only be true for the specific case of a "right" trapezium.

__

A trapezium (US; trapezoid in the World) is characterized by no parallel lines. It may have one angle or opposite angles that are right angles (one or two sets of perpendicular lines), but neither diagonal may bisect the other.

In the US, "trapezium" is rarely used. The term "quadrilateral" is generally applied to a 4-sided figure with no sides parallel.

An urn contains 25 red marbles, 27 blue marbles, and 36 yellow marbles. One marble is to be chosen from the urn without looking. What is the probability of choosing a red marble?

Answers

Answer:

25/88

Step-by-step explanation:

25 red marbles, 27 blue marbles, and 36 yellow marbles. = 88 marbles

P(red) = number of red/total

          = 25/88

Answer:

Dear user,

Answer to your query is provided below

Probability of choosing a red marble is 0.28 or (25/88)

Step-by-step explanation:

Total number of marbles = 88

Number of red marbles = 25

Probability = 25/88

A residential complex has left for the recreation area a circular-shaped extension of 40 m radius. In this space, a basketball court 30 m long by 15 m wide will be built. Also, a trapezoid-shaped park will be left in the sand, 6 m with a larger base, 4 m with a lower base and 3.5 m in height. What is the area left in the circular zone, after building the basketball court and the sand park? NOTE: remember the value of π = 3.14

Answers

Answer:

Step-by-step explanation:

Area of the circular zone = [tex]\pi[/tex]r^2

= 3.14 × 40^2 = 3.14 × 1600 = 5024 m^2

Area of the basketball court = l × b

= 30 × 15 = 450 m^2

Area of the trapezium shaped park =  ( 6 + 4 ) 3.5 / 2

= 35/2 = 17.5 m^2

∴ Area left in the circular zone = Area of the circular zone - ( Area of the basketball court + Area of the trapezium shaped park )

= 5024 - ( 450 + 17.5 )

= 5024 - 467.5

= 4556.5 m^2

hope this helps

plz mark it as brainliest!!!!!!!

Sekkrit help!!!!! If (x+1) is the factor of polynomial p(x) = ax²+x+1, then find a.

Answers

Answer:

The value of a is 0.

Step-by-step explanation:

Given that (x+1) is a factor to a function, it means that when x = -1 is substitute into the function, you will get a 0 value. So you have to substitute the value of x into the function and make it 0, to find a :

[tex]p(x) = a {x}^{2} + x + 1[/tex]

[tex]let \: p( - 1) = 0 \\ let \: x = -1[/tex]

[tex]p( - 1) = a {( - 1)}^{2} + ( - 1) + 1[/tex]

[tex]0 = a - 1 + 1[/tex]

[tex]a = 0[/tex]

Answer:

a=0

Solution,

To find a,

We should know that,

Factor of polynomial gives root of polynomial like:x-a if a factor of p(X) then p(a)=0 at X=a

So,

X+1=0

X=0-1

X=-1

put x=-1 into p(X) it gives zero.

[tex]p( - 1) = 0 \\ a {( - 1)}^{2} + ( - 1) + 1 = 0 \\ a(1) - 1 + 1 = 0 \\ a = 0[/tex]

hope this helps....

Good luck on your assignment....

A random sample of 110 lightning flashes in a certain region resulted in a sample average radar echo duration of 0.81 second and a sample standard deviation of 0.34 second. This sample data is used as a pilot study, and now the investigator would like to design a new study to construct a 99% confidence interval with width 0.1. What is the necessary sample size

Answers

Answer:

[tex]n=(\frac{2.58(0.34)}{0.05})^2 =307.79 \approx 308[/tex]

So the answer for this case would be n=308 rounded up to the nearest integer

Step-by-step explanation:

The margin of error is given by this formula:

[tex] ME=z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]    (a)

And on this case we have that ME =0.1/2 =0.05 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

[tex]n=(\frac{z_{\alpha/2} s}{ME})^2[/tex]   (b)

The critical value for 99% of confidence interval now can be founded using the normal distribution since the sample size is large enough to assume the estimation of the standard deviation as the population deviation. The critical value for this case is [tex]z_{\alpha/2}=2.58[/tex], replacing into formula (b) we got:

[tex]n=(\frac{2.58(0.34)}{0.05})^2 =307.79 \approx 308[/tex]

So the answer for this case would be n=308 rounded up to the nearest integer

the number 312 lies between the perfect cubes what are they

Answers

Answer:

216-343

Step-by-step explanation:

the number 312 lies between 125 and 330

Find the future value (FV) of the annuity due. (Round your answer to the nearest cent.) $180 monthly payment, 6.25% interest, 11 years

Answers

Answer:

The future value of the annuity due to the nearest cent is $2956.

Step-by-step explanation:

Consider the provided information:

It is provided that monthly payment is $175, interest is 7% and time is 11 years.

The formula for the future value of the annuity due is:

Now, substitute P = 175, r = 0.07 and t = 11 in above formula.

Hence, the future value of the annuity due to the nearest cent is $2956.

Step-by-step explanation:

answer part two please

Answers

Answer:

a.) 8x + 6y

b.) 4x + 2y

Step-by-step explanation:

Simply add like terms together (x with x and y with y).

A man starts walking from home and walks 3 miles at north of west, then 5 miles at west of south, then 4 miles at north of east. If he walked straight home, how far would he have to the walk, and in what direction

Answers

Answer:

Step-by-step explanation:

We shall find the solution of this problem with the help of vector notation of i , j , which show east and  north direction .

The first displacement can be represented by the following

D₁ = - 3 cos 45 i + 3 sin45 j = - 3 / √2 i + 3 / √2 j

The second  displacement can be represented by the following

D₂ = - 5 cos 45 i - 5 sin45 j = - 5 /√2 i - 5 /√2 j

The third  displacement can be represented by the following

D₃ =  4 cos 45 i + 4 sin45 j =  4 /√2 i + 4 /√2 j

Total displacement D =

D₁ +D₂ + D₃

= i ( -3 -5 + 4 ) / √2 + j ( 3 - 5 + 4 ) / √2 j

= - 4  / √2 i + 2 / √2 j

D = - 2.8288 i + 1.414 j

Magnitude of D

= √ ( 2.8288² + 1.414² )

= 3.16 miles

For direction we calculate angle with X axis

Tanθ = 1.414 / 2.8288

θ = 26 °

As x is negative and Y is positive ,

the direction will be north of west .

Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial.
n=55​,
x=33​,
p=0.55
p(3)=_________

Answers

Answer:

P(33) = 0.0826

Step-by-step explanation:

The binomial distribution in this case has parameters n=55 and p=0.55.

The probability that k successes happen with these parameters can be calculated as:

[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{55}{k} 0.55^{k} 0.45^{55-k}\\\\\\[/tex]

We have to calculate the probability fo X=33 succesess.

This can be calculated using the formula above as:

[tex]P(x=33) = \dbinom{55}{33} p^{33}(1-p)^{22}\\\\\\P(x=33) =1300853625660220*0.0000000027*0.0000000235\\\\\\P(x=33) =0.0826\\\\\\[/tex]

An airport limousine can accommodate up to four passengers on any one trip. The company will accept a maximum of six reservations for a trip, and a passenger must have a reservation. From previous records, 30% of all those making reservations do not appear for the trip. Answer the following questions, assuming independence wherever appropriate. (Round your answers to three decimal places.)
(a) If six reservations are made, what is the probability that at least one individual with a reservation cannot be accommodated on the trip?
(b) If six reservations are made, what is the expected number of available places when the limousine departs?

Answers

Answer:

(a) The probability that at least one individual with a reservation cannot be accommodated on the trip is 0.4202.

(b) The expected number of available places when the limousine departs is 0.338.

Step-by-step explanation:

Let the random variable Y represent the number of passenger reserving the trip shows up.

The probability of the random variable Y is, p = 0.70.

The success in this case an be defined as the number of passengers who show up for the trip.

The random variable Y follows a Binomial distribution with probability of success as 0.70.

(a)

It is provided that n = 6 reservations are made.

Compute the probability that at least one individual with a reservation cannot be accommodated on the trip as follows:

P (At least one individual cannot be accommodated) = P (X = 5) + P (X = 6)

[tex]={6 \choose 5}\ (0.70)^{5}\ (1-0.70)^{6-5}+{6 \choose 6}\ (0.70)^{6}\ (1-0.70)^{6-6}\\\\=0.302526+0.117649\\\\=0.420175\\\\\approx 0.4202[/tex]

Thus, the probability that at least one individual with a reservation cannot be accommodated on the trip is 0.4202.

(b)

The formula to compute the expected value is:

[tex]E(Y) = \sum X\cdot P(X)[/tex]

[tex]P (X=0)={6 \choose 0}\ (0.70)^{0}\ (1-0.70)^{6-0}=0.000729\\\\P (X=1)={6 \choose 1}\ (0.70)^{1}\ (1-0.70)^{6-1}=0.010206\\\\P (X=2)={6 \choose 2}\ (0.70)^{2}\ (1-0.70)^{6-2}=0.059535\\\\P (X=3)={6 \choose 3}\ (0.70)^{3}\ (1-0.70)^{6-3}=0.18522\\\\P (X=4)={6 \choose 4}\ (0.70)^{4}\ (1-0.70)^{6-4}=0.324135[/tex]

Compute the expected number of available places when the limousine departs as follows:

[tex]E(Y) = \sum X\cdot P(X)[/tex]

         [tex]=(4\cdot 0.000729)+(3\cdot 0.010206)+(2\cdot 0.059535)+(1\cdot 0.18522)\\+(0\cdot 0.324135)\\\\=0.002916+0.030618+0.11907+0.18522+0\\\\=0.337824\\\\\approx 0.338[/tex]

Thus, the expected number of available places when the limousine departs is 0.338.

PLEASE ANSWER!!!!!!!! Which system of equations does this graph represent? Linear graph and parabola. They intersect at 2, negative 1 and negative 3, 4 (1 point)
A. y = x2 − 5 y = −x + 1
B. y = x2 − 5 y = −x − 1
C. y = x2 + 5 y = −x + 1
D. y = x2 + 5 y = −x − 1

Answers

Answer:

Option (A)

Step-by-step explanation:

For equation of the line,

Let the equation is, y = mx + b

Slope 'm' of the line passing through two points (-3, 4) and (2, -1),

m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

   = [tex]\frac{4+1}{-3-2}[/tex]

   = -1

y-intercept of this line, b = 1

Now we substitute these values in the equation,

y = -x + 1

Let the equation of the parabola is,

y = a(x - h)² + k

Here, (h, k) is the vertex of the parabola,

Since vertex of the given parabola is (0, -5),

then the equation will be,

y = a(x - 0)²- 5

y = ax² - 5

Since a point (2, -1) lies on this parabola,

-1 = a(2)² - 5

5 - 1 = 4a

a = 1

Equation of the parabola will be,

y = x² - 5

Therefore, Option (A) will be the answer.

Surface area of a cylinder: S = 2ar+2arh , solve for h.

Answers

Answer:

[tex]h = \frac{s - 2ar}{2ar} \\ [/tex]

Step-by-step explanation:

[tex]s = 2ar + 2arh \\ s - 2ar = 2arh \\ \frac{s - 2ar}{2ar} = \frac{2arh}{2ar} \\ h = \frac{s - 2ar}{2ar} [/tex]

hope this helps you

brainliest appreciated

good luck! have a nice day!

Renee is making a scale diagram of her MP3 player. The length of her scale drawing is 8 inches, and the width is 14 inches. The actual length of the MP3 player is 4 centimeters, and the width is 7 centimeters. This is , and the scale factor is .

Answers

Answer:

2

Step-by-step explanation:

Scale Factor = [tex]\frac{AnySideOfDiagram}{AnySideOfMP3Player}[/tex]

So,

Scale Factor = [tex]\frac{8}{4} = \frac{14}{7}[/tex] = 2

So,

The scale factor is 2

A plane flies 240 miles due north, then 320 miles due west. How
many miles must it fly to return to its starting point by the shortest
route? (Enter your answer without units.)

Answers

Answer: The distance of the shortest route of return is 400

Step-by-step explanation:

The direction of travel of the plane forms a right angle triangle ABC as shown in the attached photo. C represents the starting point of the plane. To determine the distance of the shortest by which the plane can return to its starting point, BC, we would apply the Pythagorean theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

BC² = 320² + 240²

BC² = 160000

BC = √160000

BC = 400

18 + 5k / 3
I need help asap please cuz my mom asked me to solve this in 2min
#aisanmoms #SOS​

Answers

Answer:

Nothing can be further done to this equation. It has been simplified all the way.

A baseball player swings and hits a pop fly straight up in the air to the catcher. The height of the baseball in meters t seconds after it is hit is given by the quadratic function h(t)= -4.9t^2 + 9.8t + 1. How long does it take for the baseball to reach its maximum​ height? What is the maximum height obtained by the​ baseball?

Answers

Answer:

Step-by-step explanation:

max can be found by the formula:

t=-b/2a

t=-9.8/2*(-4.9)

t=-9.8/-9.8

t=1

1 sec

to find maximum height obtained we find the vertex:

plug in 1 for t and simply solve:

h(t)= -4.9t^2 + 9.8t + 1

h(t)= -4.9*1^2 + 9.8*1 + 1

h(t)= -4.9*1 + 9.8 + 1

h(t)= -4.9 + 10.8

h(t)= 5.9

height is 5.9

Fill out the tables for each scenario and answer the question that follows. Use $7.25 as the minimum wage and remember that employees in the United States must be paid time-and-a-half (1.5 times the normal hourly rate) for each hour worked over 40 hours per week

Answers

Answer:

see below for the table valuesUS labor cost: $115275 per year

Step-by-step explanation:

The labor charge is for (6 days/week). In Mongolia, the charge per laborer is then ...

  (6 days/week)($1.10/day) = $6.60/week

The three laborers working 50 weeks/year will have a labor cost of ...

  (3 laborers)($6.60/week/laborer)(50 weeks/year) = $990/year

__

In the US, the labor charge per person per week is ...

  (14 hr/day)(6 day/week) = 84 hr/week

That's 40 hours of straight pay and 44 hours of overtime pay, or ...

  7.25(40 +1.5(44)) = 7.25(106) = 768.50

For 150 person-weeks per year, the total US labor charge is ...

  ($768.50/person/week)(3 persons)(50 weeks/year) = $115,275/year

__

The materials cost for a year is ...

  ($50/rug)(12 rugs/year) = $600/year

__

The revenue is ...

  ($2000/rug)(12 rugs/year) = $24,000/year

Profit is the difference between revenue and the total of costs:

  profit = $24,000 -($990 +600 +10000) = $12410 . . . made in Mongolia

__

So, the table gets filled as follows:

  (labor, material, fixed cost, revenue, profit)

Mongolian-made

  ($990, $600, $10000, $24000, $12410)

US-made

  ($115275, $600, $10000, $24000, -$101,875)

The US labor cost would be $115,275.

_____

Comment

For the given selling price, the break-even labor cost is about $1.06 per hour (on average). At US labor rates, the break-even selling price is about $10,490 per rug.

(Geometry) PLEASE HELP ASAP

Answers

Answer:

CD=72x=7

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

Which equation is the inverse of y = x2 + 16? y = x2 – 16 y = plus-or-minus StartRoot x EndRoot minus 16 y = plus-or-minus StartRoot x minus 16 EndRoot y = x2 – 4

Answers

Answer:

[tex]\pm \sqrt{x-16}[/tex] is the inverse of [tex]y = x^2 + 16[/tex]

Step-by-step explanation:

Given that:

[tex]y = x^2 + 16[/tex]

Let us proceed step by step to calculate the inverse:

Step 1: Put [tex]y = f(x)[/tex]

[tex]f(x) = y=x^2 + 16[/tex]

Step 2: Interchange [tex]x[/tex] and [tex]y[/tex]:

[tex]x = y^2 + 16[/tex]

Step 3: Solve the equation to find the value of [tex]y[/tex]:

[tex]y^2 =x- 16\\\Rightarrow y =\pm \sqrt{x- 16}[/tex]

Step 4: Replace [tex]y[/tex] with [tex]f^{-1}(x)[/tex]:

[tex]\Rightarrow y =f^{-1}(x)=\pm \sqrt{x- 16}[/tex]

So, the inverse of [tex]y = x^2 + 16[/tex] is [tex]\pm \sqrt{x- 16}[/tex].

The equation which is the inverse of y = x2 + 16 is; f-¹ = y = ±√(x -16)

To evaluate the inverse of the function, y = x2 + 16.

We must first make x the subject of the formula and swap x and y as follows;

x = ±√(y - 16)

y = ±√(x - 16)

Therefore, the inverse function is;

f-¹ = y = ±√(x -16)

Read more on inverse function:

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Need help please guysssssss

Answers

Answer:

C

Step-by-step explanation:

3x+2-x>8

2x+2>8

2x>8-2

2x>6

x>3

Answer:

C

Step-by-step explanation:

what set of Reflections and rotations could carry ABCD onto itself?​

Answers

Reflect over y-axis,reflect over the X axis ,rotate 180°

Option D is the correct option.

Explanation:

Let's take point A which is (4,-1)

Reflection over y- axis will make this point (4,1)

Then, reflection over X axis will make this point (4,-1)

After rotation of 180 degree we will get (-4,1) .

Please see the attached picture....

Hope it helps...

Good luck on your assignment...

Answer:  d) reflect over the x-axis, reflect over y-axis, rotate 180°

Step-by-step explanation:

A reflection over the x-axis and a reflection over the y-axis is the SAME as a rotation of 180°. Together they make a rotation of 360°, which results in the image staying at the same place.

Reflection over the x-axis changes the sign of the y-coordinate

Z = (x, y)    →    Z' = (x, -y)

Reflection over the y-axis changes the sign of the x-coordinate

Z' = (x, -y)    →    Z'' = (-x, -y)

Rotation of 180° changes the signs of both the x- and y-coordinates

Z'' = (-x, -y)   →     Z''' = (x, y)

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