Given the regression line Ŷ = –6 + 0.41(X), make predictions for each of the following:
a. X = 25
b. X = 50
c. X = 75

Answers

Answer 1

For the "regression-line",  Ŷ = -6 + 0.41(X), the predicted value,

(a) when X=25 is 4.25,

(b) when X=50 is 14.50,

(c) when X=75 is 24.75.

The "Regression-Line", is Ŷ = -6 + 0.41(X), we can make predictions for the value of Y (the dependent variable) for different values of X (the independent variable).

(a) To predict the value of "Y" when X = 25, we substitute 25 into the regression line equation:

Ŷ = -6 + 0.41(25)

Ŷ = -6 + 10.25

Ŷ = 4.25

So, the predicted value of Y when X = 25 is 4.25.

(b) To predict the value of Y when X = 50, we substitute 50 into the regression line equation:

Ŷ = -6 + 0.41(50)

Ŷ = -6 + 20.50

Ŷ = 14.50

So, the predicted value of Y when X = 50 is 14.50.

(c) To predict the value of Y when X = 75, we substitute 75 into the regression line equation:

Ŷ = -6 + 0.41(75)

Ŷ = -6 + 30.75

Ŷ = 24.75

So, the "predicted-value" of Y when X = 75 is 24.75.

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Related Questions

Which choice is a term in this expression -3x - 7(x+4)

Answers

-3x is a term in the expression -3x - 7(x+4)

How to determine the term?

The expression is given as:

-3x - 7(x+4)

Considering the following expression

Ax + B(x  - b)

The terms in the expressions are Ax and B(x  - b)

This means that -3x is a term in the expression -3x - 7(x+4)

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HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! pls <3

Answers

Answer:

[tex]y=\frac{2}{3}x+\frac{4}{3}[/tex]

Step-by-step explanation:

Let's write the equation of the line in the slope-intercept form. That is, y= mx +c, where m is the slope and c is the y-intercept.

Identify 2 coordinates on the line to calculate the slope.

The 2 points are (1, 2) and (4, 4).

Slope

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

= [tex]\frac{4-2}{4-1}[/tex]

= [tex]\frac{2}{3}[/tex]

Substitute the value of the slope into m:

[tex]y=\frac{2}{3}x+c[/tex]

Substitute any point into the equation to find c:

When x= 1, y= 2,

[tex]2= \frac{2}{3}(1)+c[/tex]

Solve for c:

[tex]c= 2-\frac{2}{3}[/tex]

c= [tex]\frac{4}{3}[/tex]

Thus, the equation that represents the line is [tex]y=\frac{2}{3}x+\frac{4}{3}[/tex].

Additional:

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Find the remainder when f(x) = 8x^3+4x^2-13x+3 is divided by 2x+5

Answers

Answer:

-129

Step-by-step explanation:

good luck

Name the figure below in two different ways!
Need help fast!

Answers

Answer:

IM  and  YM

Step-by-step explanation:

not sure about the symbol part, but it's a ray !!

Answer: IM and YM

Step-by-step explanation:

It can be broken down into to different rays

ped
Complete question :

Juan is rewriting the expression 12 d minus 26 c as a product. Which statements about the expression are accurate and relevant to his rewriting the expression? Select two options. The GCF of the numbers in each term in the expression is 2. The GCF of the numbers in each term in th

Answers

So the correct statement is:

" The GCF of the numbers in each term in the expression is 2"

How to rewrite the expression as a product?

Here we have the expression:

12d - 26c

To rewrite ti as a product, we need to find the greatest common factor between 12 and 26.

The decomposition of these two numbers is:

12 = 2*2*3

26 = 2*13

The greatest common factor between the two numbers is 2, then we can rewrite:

12d - 26c = 2*(6d - 13c)

So the correct statement is:

" The GCF of the numbers in each term in the expression is 2"

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The bearing from the Pine Knob fire tower to the Colt Station fire tower is N 65° E, and the two towers are 31 kilometers apart. A fire spotted by rangers in each tower has a bearing of N 80° E from the Pine Knob and S 70° E from Colt Station (see figure). Find the distance of the fire from each tower. (Round your answers to two decimal places.)
From Pine Knob:

Answers

The distance are

a. 42.42

b. 15. 52

How to solve for the distance

80 = 65 + <ABC

<ABC = 80 - 65

= 15

Through the use of sine rule we would have

By using sine rule,

Sine 15/a = sine 135/b =

sin 30/30.

Next we have to solve b by cross multiplying

b = (30× sin135) / sin 30

= 21.21/0.5

b = 42.42 km

Also, the value of a will be:

= (42.42 × sin 15) / sin 135

= 10.98/0.7071

= 15.52

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An administer of a college believes that 40% students of the college work in part time. He
randomly surveyed of 2,512 students and finds that 1,298 of them work in part time, that is, about 51.7% of
the student being surveyed work in part time.
1.
Is the study observational or experimental?
2.
What is the population of interest?
3.
What is the parameter of interest?
4.
What is the sample in the study?
5.
What is the statistic involved?

Answers

See below for the response to each question

Is the study observational or experimental?

The study is experimental.

This is so because, the administer surveyed random college students

The population of interest

This is the total number of students in the college

Hence, the population of interest is the students in the college

The parameter of interest

This is the value that gives the required information.

Hence, the parameter of interest is the proportion of college students that work part-time

The sample in the study

This is the students that were randomly surveyed

Hence, the sample in the study is the  2,512  students that were randomly surveyed

What is the statistic involved

The statistic is the sample mean

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Question 1 1.1 Given the quadratic number pattern: 5; 10; 17; 26;.. 1.1.1 Write down the next TWO terms of the pattern. 1.1.2 D Determine the formula for the nth term of the patter 1.1.3 Which term of the pattern will have a value of 1765? 1.2 Given the quadratic pattern:x; 6; 9; y; 24; Calculate the sum of x and y. Question 2 COFF 8(1:2)​

Answers

The next two terms of the sequence based on the information given is 37 and 50.

How to illustrate the sequence?

It should be noted that from the information given, the numbers illustrated are 5, 10, 17, and 26.

In this case, there is an addition of 2 to the previous difference.

Therefore, 26 - 17 = 9.

The next number will be:

= 26 + 9 + 2 =37

The following number will be:

= 37 + 11 + 2

= 50

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what is the volume of the following rectangular prism

Answers

Answer:

[tex] \large{ \boxed{ \tt{336 \: units ^{3} }}}[/tex]

- Please see the attached picture for full solution!:)

------------ HappY LearninG <3 ----------

Petsmart's marketing team finds in their most recent report that they sell 45 guinea pigs a
year. Their sales team wanted to increase their sales and grabbed a sample of 8 types of
rodents to put on a flash sale. They sold an average of 34 rodents with a standard
deviation of 21 rodents.

Answers

Answer:

p(x)=x3-3x2+4x+50 and g(x)=x-3

Need help with defining this question.

Answers

Answer:

B.) 19

Step-by-step explanation:

According to F(5), the question wants you to plug x = 5 into the equation. Then, you need to simplify to find the output.

F(x) = x² - 2x + 4                             <----- Original equation

F(5) = (5)² - 2(5) + 4                        <----- Plug 5 into "x"

F(5) = 25 - 10 + 4                            <----- Solve 5² and -2 x 5

F(5) = 19                                         <----- Combine like terms

A=(-3,-2) B=x,3 C=(4,5) if AB = BC what is the value of X

Answers

Answer:

x=1

Step-by-step explanation:

[tex] \sqrt{( - 3 - x) ^{2} + {( - 2 - 3)}^{2} } = \\ \sqrt{ {(4 - x)}^{2} + {(5 - 3)}^{2} } \\ \\ 9 + 6x + {x}^{2} + 25 = \\ 16 - 8x + {x}^{2} + 4 = = = > \\ 34 + 6x = 20 - 8x = > \\ 14 = 14x = = = > x = 1[/tex]

Done

The value of x that makes up the coordinate of B is -1

How to find the value of x

To find the value of x, we need to determine the coordinates of point B.

Since A to (B) = B to (C), the distance from point A to point B is equal to the distance from point B to point C. The distance between two points in a coordinate plane can be calculated using the distance formula:

Distance = √((x₂ - x₁)² + (y₂ - y₁)²)

Let's calculate the distances:

Distance A to (B):

x₁ = -3 (x-coordinate of point A)

y₁ = -2 (y-coordinate of point A)

x₂ = x (x-coordinate of point B)

y₂ = 3 (y-coordinate of point B)

Distance A to (B) = √((x - (-3))² + (3 - (-2))²)

Distance A to (B) =√((x + 3)² + 5²)

Distance A to (B) = √(x² + 6x + 9 + 25)

Distance A to (B) = √(x² + 6x + 34)

Distance B to (C):

x₁ = x (x-coordinate of point B)

y₁ = 3 (y-coordinate of point B)

x₂ = 4 (x-coordinate of point C)

y₂ = 5 (y-coordinate of point C)

Distance B to (C) = √((4 - x)² + (5 - 3)²)

Distance B to (C) = √((4 - x)² + 2²)

Distance B to (C) = √((4 - x)² + 4)

Distance B to (C) = √(x² - 8x + 20)

Since A to (B) = B to (C):

√(x² + 6x + 34) = √(x² - 8x + 20)

Now, we can square both sides to get rid of the square root:

x² + 6x + 34 = x² - 8x + 20

Next, move all the x terms to one side of the equation:

x² - x² + 6x + 8x = 20 - 34

Combine like terms:

14x = -14

Finally, solve for x:

x = -14 / 14

x = -1

So the value of x is -1. Point B is located at (-1, 3).

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Write the number in words 203681 ​

Answers

Answer:

203681

203,681

Two hundred and three thousand, six hundred eighty-one

Step-by-step explanation:

The number 203681 in words can be written as two hundred and three thousands, six hundred and eighty-one.

In the question, we are asked to write the number 203681 in words.

In the given number, we have:

1 at the units place,8 at the tens place,6 at the hundreds place,3 at the thousands place,0 at the ten thousand places, and2 and the hundred thousand place.

Keeping the thousands as different section, we have 203 in thousands section, and 681 in the remaining.

203 can be named as two hundred and three.

681 can be named as six hundred and eighty-one.

Since, 203 is in the thousands section, we add thousand in its name.

Thus, the name we get is two hundred and three thousands, six hundred and eighty-one.

Thus, the number 203681 in words can be written as two hundred and three thousands, six hundred and eighty-one.

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i need this solved asap please do so

Answers

The simplified expression for h(x) = f(x)/g(x) is [tex]h(x) = \frac{1}{3}\cdot \frac{x-4}{x-\frac{2}{3} }[/tex] and the domain of the function is all real numbers except x = 2/3.

How to determine the domain of a rational function

In this problem we have a rational function, the domain of rational functions is the set of all real numbers except the values such that the denominator becomes zero. First, we need to simplify the division of two rational functions:

[tex]h(x) = \frac{\frac{3\cdot x^{2} + 17\cdot x + 20}{3\cdot x^{2} + 10\cdot x - 8} }{\frac{3 \cdot x^{2} + 8\cdot x + 5}{x^{2}-3\cdot x - 4} }[/tex]

[tex]h(x) = \frac{(3\cdot x^{2}+17\cdot x + 20)\cdot (x^{2}-3\cdot x - 4)}{(3\cdot x^{2}+10\cdot x - 8)\cdot (3\cdot x^{2}+8\cdot x + 5)}[/tex]

[tex]h(x) = \frac{1}{3}\cdot \frac{\left(x^{2}+\frac{17}{3}\cdot x + \frac{20}{3} \right)\cdot (x^{2}-3\cdot x - 4)}{\left(x^{2}+\frac{10}{3}\cdot x -\frac{8}{3}\right)\cdot \left(x^{2}+\frac{8}{3}\cdot x +\frac{5}{3} \right)}[/tex]

[tex]h(x) = \frac{1}{3}\cdot \frac{\left(x + \frac{5}{3} \right)\cdot (x+4)\cdot (x - 4)\cdot (x+ 1)}{\left(x-\frac{2}{3} \right)\cdot (x + 4)\cdot (x + 1)\cdot \left(x + \frac{5}{3} \right)}[/tex]

[tex]h(x) = \frac{1}{3}\cdot \frac{x-4}{x-\frac{2}{3} }[/tex]

The simplified expression for h(x) = f(x)/g(x) is [tex]h(x) = \frac{1}{3}\cdot \frac{x-4}{x-\frac{2}{3} }[/tex] and the domain of the function is all real numbers except x = 2/3.

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What is the value of p

Answers

Answer:

2

Step-by-step explanation:

You have the correct answer selected: 2.

The reason for this is that when there are exponents inside and outside of the parenthesis like this, they are multiplied.

2 times 2 is 4. That's why (8^2)^2 = 8^4

Answer:

p = 2

Step-by-step explanation:

[tex](8^{2}) ^{p}[/tex] = [tex]8^{4}[/tex]

  [tex]8^{2p}[/tex] =    [tex]8^{4}[/tex]

   [tex]8^{p}[/tex] = [tex]8^{\frac{4}{2}[/tex]

    p = 2

in how many ways can the letters in the word payment be arranged if the letters are taken 6 at a time

Answers

Considering the definition of permutation, in 5040 ways can the letters in the word ''PAYMENT'' be arranged if the letters are taken 6 at a time.

What is Permutation

Permutation is placing elements in different positions. So, permutations of m elements in n positions are called the different ways in which the m elements can be arranged occupying only the n positions.

That is, permutations refer to the action of arranging all the members of a set in some sort of order or sequence.

In other words, permutations (or Permutations without repetition) are ways of grouping elements of a set in which:

take all the elements of a set.the elements of the set are not repeated.order matters.

To obtain the total of ways in which m elements can be placed in n positions, the following expression is used:

[tex]mPn=\frac{m!}{(m-n)!}[/tex]

where "!" indicates the factorial of a positive integer, which is defined as the product of all natural numbers before or equal to it.

This case

In this case, you have:

the letter word "PAYMENT", where the number of letters is 7.the letters are taken 6 at a time.

Then, you know that:

m= 7n=6

Replacing in the definition of permutation:

[tex]7P6=\frac{7!}{(7-6)!}[/tex]

Solving:

[tex]7P6=\frac{7!}{1!}[/tex]

7P6= 5040

Finally, in 5040 ways can the letters in the word ''PAYMENT'' be arranged if the letters are taken 6 at a time.

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You have a job earning $12.50 per hour, and you receive a raise so that you earn $13.25 per hour. What is the percent change in your salary?

Answers

Answer: 6 %

Step-by-step explanation: 6 % of 12.5 = 0.75. 12.5 plus 0.75 = 13.25

Geometry Question!! PLEASE HELp

Answers

The difference between the distance travelled by any point on the record and it's label is; 27.57cm.

What is the difference between the distance travelled in each case?

According to the task content, it follows from observation that the quantity required is the difference between the circumference in each case and can be evaluated as follows;

Difference = π(17.78 - 9)

Difference = (22/7) × 8.78

Difference = 27.57cm.

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Enter the letter of the graphed
function.
-
-
a.y = (x + 2)(x − 1)(x − 3)
b.y = (x + 2)(x - 1)(x - 3)²
-
c. y = (x + 2)(x − 3)(x - 1)²
d.y= (x - 1)(x − 3)(x + 2)²
e.y = (x - 1)(x - 3)(x + 2)³

Answers

The graphed function is: y = (x + 2)(x − 1)(x − 3).

Option (a) is correct.

From the graph given in the question, it can be seen that the graph has 3 critical points, namely, x= -2, x = 1 and x = 3.

From all the five options given, the first option, that is, y = (x + 2)(x − 1)(x − 3), has the critical points x= -2, x = 1 and x = 3.

The critical points for a function are obtained by substituting the function to be equal to zero.

So, (x + 2)(x − 1)(x − 3) = 0

That is, x= -2, x = 1 and x = 3.

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5.5(x+6 1/2)-(x+9 1/3) - (19-x)

Answers

The simplest form of the expression given in the task content is; 5.5x +7.42.

What is the simplest form of the expression?

The expression given in the task content is;

5.5(x+6 1/2)-(x+9 1/3) - (19-x)

Hence, the expression can be written in its simplest form as follows;

5.5x + 35.75 -x -9.33 -19 +x

= 5.5x +7.42.

Remarks: The complete task requires that the expression be written in its simplest form.

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What is the solution to the equation below? (Round your answer to two
decimal places.)
5 Inx= 3.5
A. x = 4.17
B. x = 3.98
C. x = 42.40
D. x=201

Answers

Answer: 2.01

Step-by-step explanation:

[tex]5\ln x=3.5\\\\x=\frac{3.5}{5}\\\\x=e^{3.5/5}\\\\x \approx 2.01[/tex]

What is the sum of the
HCF and
LCM of the
number
2³ x 3² x 5x7 and
2² x 5² x 11

Answers

Step-by-step explanation:

. Find the factors of 330.

(a)2 x 4 x 5 x 11

(b)2 x 3 x 7 x 13

(c)2 x 3 x 5 x 13

(d)2 x 3 x 5 x 11

Show Answer

2. Find the factors of 1122.

(a)3 x 9 x 17 x 2

(b)3 x 11 x 17 x 2

(c)9 x 9 x 17 x 2

(d)3 x 11 x 17 x 3

Show Answer

3. 252 can be expressed as a product of primes as

(a)2 x 2 x 3 x 3 x 7

(b)2 x 2 x 2 x 3 x 7

(c)3 x 3 x 3 x 3 x 7

(d)2 x 3 x 3 x 3 x 7

Show Answer

4. Which of the following has most number of divisors?

(a)99

(b)101

(c)176

(d)182

Show Answer

5. A number n is said to be perfect if the sum of all its divisors (excluding n itself) is equal to n. An example of perfect number is

(a)6

(b)9

(c)15

(d)21

Show Answer

6. 1095/1168 when expressed in simplest form is

(a)13 / 16

(b)15 / 16

(c)17 / 26

(d)25 / 26

Show Answer

7. Reduce 128352 / 238368 to its lowest terms

(a)3/4

(b)5/13

(c)7/13

(d)9/13

Show Answer

8. The simplest reduction to the lowest terms of 116,690,151 / 427,863,887 is

(a)3/11

(b)7/11

(c)11/3

(d)None of these

Show Answer

9. The highest common factor of 0 and 6 is

(a)0

(b)3

(c)6

(d)Undefined

Show Answer

10. The H.C.F. of 2² x 3³ x 5⁵, 2³ x 3² x 5² x 7 and 2⁴ x 3⁴ x 5 x 7² x 11 is

(a)2² x 3² x 5

(b)2² x 3² x 5 x 7 x 11

(c)2⁴ x 3⁴ x 5⁵

(d)2⁴ x 3⁴ x 5⁵ x 7 x 11

Show Answer

11. The H.C.F. of 2⁴ x 3² x 5³ x 7, 2³ x 3³ x 5² x 7² and 3 x 5 x 7 x 11 is

(a)105

(b)1155

(c)2310

(d)27720

Show Answer

12. H.C.F. of 4 x 27 x 3125, 8 x 9 x 25 x 7 & 16 x 81 x 5 x 11 x 49 is

(a)180

(b)360

(c)540

(d)1260

Show Answer

13. Find the highest common factor of 36 and 84.

(a)4

(b)6

(c)12

(d)18

Show Answer

14. Even numbers are formed by taking at least two at a time from the numbers 0, 4, 8, 9. Their H.C.F. is

(a)2

(b)4

(c)10

(d)None of these

Show Answer

The Florida VPK assessment is considered a progress monitoring tool when administered at two assessments periods across the school year.

a. True
b. False

Answers

The given statement about the Florida VPK assessment administered at two assessments periods across the school year is; B: False

What is the Progress Monitoring Tool?

Progress monitoring or CBM is a term used in the education field to describe the process whereby the progress of students in areas like mathematics, reading, and writing are monitored on a daily and weekly basis.

Now, in Florida in the United States, This progress monitoring is called Florida Voluntary Prekindergarten (VPK) Assessment. There is usually a different version of each assessment measure that will be administered at three different times during the school-year VPK Program.

Thus, the given statement is false.

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Answer:

Step-by-step explanation:

false

The following statements are all incorrect. Explain the statements and the errors fully using the probability rules discussed in topic two. 1.The number 7 is a lucky number so you are more likely to win raffles with ticket number 7 than with a different number. 2.I roll two dice and add the results. The probability of getting a total of 8 is 1/12 because there are 12 different possibilities and 8 is one of them. 3.Mr. Verde has to have a major operation. Ninety-three percent of the people who have this operation make a complete recovery. There is a 93% chance that Mr. Verde will make a complete recovery if he has this operation.4.The Ramblers play the Chargers. The Ramblers can win, loose, or draw, so the probability that they win is 1/3. 5.I have flipped an unbiased coin four times and got heads. It is more likely to get tails the next time I flip it.6.Thirty random college students are asked if they study during the week. Since 60% said yes, a statement can be made that 40% of students only study on the weekend.

Answers

The probability is illustrated below.

How to illustrate the probability?

1) Raffles game is a gambling competition in which people get numbered tickets and each number has an equal chance of winning.

2) When two dice are rolled then there will be totally 36 outcomes. Of those the outcomes with sum 8 are (2,6),(3,5),(4,4),(5,3),(6,2).

These are 5 in number.

So,P( sum =8)= 5/36.

3)This is a true statement.

4) Here win, lose, or tie is just the outcomes where their probabilities are different from each other and those values depend upon different situations.

5) Tossing a coin is a random experiment which means that the result of the experiment (ie head or tail) cannot be predicted.

6) If 60% said yes to " study during the week" then 40% will say yes to "either won't study or study at weekend".

7) When two coins are tossed, the outcomes are as follows

H,H

H,T

T,H

T,T.

So, P( head, tail ) =2/4 =1/2

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The reasons for each incorrect statement are as follows;

The error in the statement is that, there might be other luckier numbers compared to number 7 and hence, the statement does not hold true for all numbers.The statement is incorrect because, there are 36 different possibilities and there are 5 possibilities of getting an 8.The statement is incorrect because, 93% does not necessarily represent a 93% chance of complete recovery as this is subject to other variables.The probability that they win is not 1/3 as it is subject to what the results have been over the years and not just the possible results.Since, the coin is unbiased, it follows that upon flipping the coin for the fifth time, it is not likely to have tails the next time it is flipped.The statement is incorrect because some students study during the week and weekends, hence, the conclusion is not correct.

What is Probability?

The term probability put simply is the ratio of the desired outcome to the possible outcomes. It therefore follows that probability as the name implies is used to predict the chance of an occurrence.

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Josh had to make 2,000 cookies for his bakery. 2 pieces of wheat make 8 cookies. How much wheat does he need?

Answers

Answer: 500 pieces of wheat

Explanation:

First: set up the proportion
Cookies:wheat = 8:2
Simplify = 4:1
We need to find how much wheat he needs for 2,000 cookies.
We need to assign a variable for wheat
Wheat = W
If Josh needs to make 2,000 cookies he would need W amount of wheat
Original proportion = 4:1
For 2,000 cookies = 2,000:W
To get from 4 to 2,000
2,000/4 = 500
So W/1 = 500
Isolate the variable:
w/1 (1) = 500/1
W = 500


Find the area of the trapezoid. 15ft 10ft 20ft

Answers

Answer: 175 ft squared

Step-by-step explanation: A= a + b / 2h= 20 + 152 · 10 = 175

A tree is 14 meters tall. What is its height in feet? Use the following conversion: 1 meter is 3.3 feet

Answers

The answer is 46.2ft tall

Billy eats 28 apples and he had 40 apples at the start a kid asks for an apple how many apples are there left?

Answers

Answer: 11

Step-by-step explanation: 40-28= 12-1=11

Answer:

11 apples are left.

Step-by-step explanation:

Since Billy ate 28 apples from the 40 apples he had at the start, you have to subtract 40-28, which equals 12. Lastly, you subtract 12-1, since a kid asks Billy for an apple.

I forgot how to find the range of values of x and I will be very much appreciated if I could get a step by step clear solution to get the answers!

Answers

The quadratic equation has the following results: (p, q) = (8, 15), minimum point: (h, k) = (1, 4), range of values: - 4 < x < - 3

How to analyze quadratic equations

In this question we have a quadratic equation of the form y = x² + p · x + q , whose missing coefficients can be found by solving on the following system of linear equations:

- 5 · p + q = - 25

- 3 · p + q = - 9

(p, q) = (8, 15)

The vertex represents the minimum point, which is found by changing the form of the equation from standard form into vertex form:

y = x² + 8 · x + 15

y + 1 = x² + 8 · x + 16

y + 1 = (x + 4)²

(h, k) = (1, 4)

And lastly we must solve for x in the following inequality:

x² + 8 · x + 15 < x + 3

x² + 7 · x + 12 < 0

(x + 3) · (x + 4) < 0

- 4 < x < - 3

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The height "h" of a ball thrown straight up with a velocity of 88 ft/s is given by h = -16t^2 + 88t where "t" is the time it is in the air. For how many seconds the ball is in the air before it hits the ground?

Answers

By definition of the zeros of ta quadratic function,  for 5.5 seconds the ball is in the air before it hits the ground.

Zeros of a function

The points where a polynomial function crosses the axis of the independent term (x) represent the so-called zeros of the function.

That is, the zeros represent the roots of the polynomial equation that is obtained by making f(x)=0.

In summary, the roots or zeros of the quadratic function are those values ​​of x for which the expression is equal to 0. Graphically, the roots correspond to the abscissa of the points where the parabola intersects the x-axis.

Time the ball is in the air before it hits the ground

In this case, the height "h" of a ball thrown straight up with a velocity of 88 ft/s is given by h = -16t² + 88t, where "t" is the time it is in the air.

When the ball hits he ground, he height h has a value of zero. This is h=0. Replacing in the previous expression for the height you get:

0= -16t² + 88t

It can be solved by extracting the term "t" as a common factor:

0= t×(-16t + 88)

The Zero Product Principle says that if the product of two numbers is 0, then at least one of the factors is 0. Then:

t= 0

or

0= -16t + 88

Solving: -88= -16t

(-88)÷ (-16)=t

5.5= t

Finally, this means that for 5.5 seconds the ball is in the air before it hits the ground.

Learn more about the zeros of a quadratic function:

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