Answer:
(a) 36, (b) 8, (c) - 8======================
Given functionf(x) = 8 - 4xFind the indicated values(a) f(-7)
f(-7) = 8 - 4(-7) = 8 + 28 = 36(b) f(0)
f(0) = 8 - 4(0) = 8 - 0 = 8(c) f(4)
f(4) = 8 - 4(4) = 8 - 16 = - 8Answer:
a) f(-7) = 36 b) f(0) = 8 c) f(4) = -8Step-by-step explanation:
a) f(-7) = ?
→ f(x) = 8 - 4x
→ f(-7) = 8 - 4(-7)
→ f(-7) = 8 + 28
→ f(-7) = 36
Hence, f(-7) = 36.
b) f(0) = ?
→ f(x) = 8 - 4x
→ f(0) = 8 - 4(0)
→ f(0) = 8 - 0
→ f(0) = 8
Hence, f(0) = 8.
c) f(4) = ?
→ f(x) = 8 - 4x
→ f(4) = 8 - 4(4)
→ f(4) = 8 - 16
→ f(4) = -8
Hence, f(4) = -8.
9. Emily measured the depth of water in a bathtub at two-minute intervals after the tap was turned off and the
stopper released. The table shows her data.
a) Make a scatter plot for the data.
b) Describe the correlation of the scatter plot.
c) What will the approximate depth be at 15 seconds?
From the data in the table relating time and depth, we have that:
a) The scatter plot is graphed at the end of the answer.
b) The scatter plot has negative correlation.
c) The estimate for the depth at a time of 15 seconds is of 50.37 cm.
How to built the scatter plot?The scatter plot is built inserting all the points of the table in a graph, which are in the following format:
(Time in seconds, Depth in cm).
Hence the scatter plot will be composed by a set of points, without an image, as is shown at the end of the answer.
The points from the table are listed as follows:
(2, 47), (4, 41), (6, 38), (8, 37), (10, 32), (12, 24), (14, 20), (16, 19).
As the input variable time increases, the output variable depth decreases, meaning that the points in the scatter plot also follow the format of a decreasing line, hence there is negative correlation in the scatter plot.
These points are also inserted into a linear regression calculator to built the line of best fit, which is defined as follows:
y = -2.07x + 50.89.
At 15 seconds, the estimate is obtained replacing the lone instance of x in the equation by 15, hence:
y = -2.07 x 0.25 + 50.89 = 50.37 cm.
More can be learned about scatter plots at brainly.com/question/6592115
#SPJ1
a stats 10 test has 4 multiple choice questions with four choices with one correct answer each. if we just randomly guess on each of the 4 questions, what is the probability that you get exactly 1 question correct? find the nearest answer.
if we just randomly guess on each of the 4 questions, Then the probability that you get exactly 1 question correct is 1/4.
Probability formula: P(E) = favourable outcomes/Total outcomes
The number of questions is 10
The options for each question are 4.
Possible answers are 1.
Then,
favourable events = 1 × 10= 10
Total events = 4× 10= 40
Now, find the probability by putting the values as follows:
P(E) = favourable outcomes/Total outcomes
P(E) = 10/40
P(E) = 1/4
Therefore, the probability of doing all questions correct is 1/4
learn more about of probability here
https://brainly.com/question/28952876
#SPJ4
The slope of the line below is -1/7. write a point slope equation of the line using the coordinates of the labeled point.
The equation of the line with slope -1/7 is (y-3) = -1/7(x-3).
According to the question,
We have the following information:
Slope of the line = -1/7
Points through which line is passing = (3,3)
We know that the following formula is used to find the equation of the line:
(y-y') = m(x-x') where m is the slope of the line
In this case, we have x' = 3 and y' = 3.
(y-3) = -1/7(x-3)
This expression can be solved further by multiplying -1/7 into the bracket and then by moving 3 from the left hand side to the right hand side. Then this equation will be in slope-intercept form.
Hence, the correct option is B.
To know more about equation of the line here
https://brainly.com/question/21511618
#SPJ1
What is the rectangular form of 12(cos(π) + i sin(π))?
12
-12
12 + i
–12 + i
Answer:
12-12-12+i-12+i =0-i
.
.
.
,
What is the volume of the cube that has 7.5cm?
22.5 cm³
56.25 cm³
168.75 cm²
7.5 cm
421.875 cm³
[tex]{ \boxed{ \orange{ \sf{421.875 \: {cm}^{3}}}}} [/tex]
Step-by-step explanation:-
[tex]{ \red{ \sf{Volume \: of \: the \: cube }}} = { \green{ \sf{ {a}^{3}}}} [/tex]
[tex]{ \red{ \sf{Volume \: of \: the \: cube } = }} \: \: { \green{ \sf{7.5 \times 7.5 \times 7.5}}}[/tex]
[tex]{ \red{ \sf{Volume \: of \: the \: cube = { \green{ \sf{56.25 \times 7.5}}}}}}[/tex]
[tex]{ \boxed{ \sf{Volume \: of \: the \: cube = 421.875 {cm}^{3}}}} [/tex]
The velocity, V, of a specific object being dropped from a particular height, h, can be found by the radical function V equals the square root of the quantity 2 times h times a end quantity where a represents the acceleration in ft/sec2. If the acceleration due to gravity is 32.2 ft/sec2, at what height should you drop an object in order for it to have a velocity of 60 ft/sec?
0.9 feet
55.6 feet
55.9 feet
3,864 feet
The height should you drop an object in order for it to have a velocity of 60 ft/sec is 55.9 feet
How to find the heightThe equation given in the problem is written below
v = √2ha
velocity, v = 60 ft/sec
height, h = ?
acceleration due to gravity, a = 32.2ft/sec^2
The problem asks for height hence we make h the subject of the formula
v = √2ha
v^2 = 2ha
h = v^2 / 2a
substituting the values in to the equation
h = 60^2 / (2 * 32.2)
h = 3600 / 64.4
h = 55.9 feet
Learn more about velocity here:
https://brainly.com/question/25749514
#SPJ1
13)
A translation function is defined by the rule
(x, y) → (x + 2, y - 5). Which choice will be the
image of the point (3,6) under this translation?
The image of the point (3, 6) by means of the translation formula described in the statement is (5, 1).
What is the image of a point according to a translation formula?
Herein we find the coordinates of an ordered pair set on Cartesian plane, whose image has to be found by using a rigid transformation formula known as translation formula, whose definition is described and explained below:
P'(x, y) = P(x, y) + T(x, y)
Where:
P(x, y) - Original point.P'(x, y) - Resulting point.T(x, y) - Translation vector.If we know that P(x, y) = (3, 6) and T(x, y) = (2, - 5), then the image of the original point according to the translation formula is now determined:
P'(x, y) = (3, 6) + (2, - 5)
P'(x, y) = (3 + 2, 6 - 5)
P'(x, y) = (5, 1)
The image of the point by translation formula is (5, 1).
To learn more on translations: https://brainly.com/question/12463306
#SPJ1
5. Gabi will graph f(x) = x and m(x) = f(x). Mark each statement as true or false. If false,
rewrite as true in the space below.
a. The slope of m(x) will be steeper than f(x).
_b. The y-intercept of m(x) will be units up from f(x).
d. g(x) = f(x − 3)
The Slope of the first function is greater than the slope of the second function. We can say that the function f(x) =x is steeper than the second function
What is a Slope?
A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.
A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, m = y/x, where m is the slope, can be used to express the change in the y coordinate with regard to the change in the x coordinate.
Take notice that tan = y/x.
In the given question, we have: two functions:
So, finding the slope of each of the functions;
The slope of the first function; f(x) =x is 1;
The slope of the second function: m(x) =[tex]\frac{3}{5} f(x)[/tex];
Since the Slope of the first function is greater than the slope of the second function. We can say that the function f(x) =x is steeper than the second function because the graph depends on the slope.
Hence,
the Slope of the first function is greater than the slope of the second function. We can say that the function f(x) =x is steeper than the second function.
To learn more about slope, visit;
https://brainly.com/question/3493733
#SPJ1
Other than itself, which angle is congruent to ∠DEA?
Please help!!!
Answer:
Angle CEB
Step-by-step explanation:
They are vertical angles
:]
Write 8128 as the sum of consecutive odd cubes.
The sum of consecutive odd cubes of 8128 is 1³+3³+5³+7³+9³+11³+13³+15³
Therefore, 1+27+125+343+729+1331+2197+3375=8128
What are consecutive numbers?Consecutive numbers are those that come after each other in descending order from the smallest to the largest. The difference between consecutive numbers is always fixed and follows a predictable pattern. For example, the first three consecutive natural numbers are 1, 2, 3. The simplest way to find consecutive numbers is to look at the number set and find the number that is either before or after the term of interest.
We know that consecutive odd numbers are 1,3,5,7,9,11,13,15,17..
Here 8128 is a perfect square
And it can be written as the sum of consecutive odd cubes as follows:
1³=1
3³=27
5³=125
7³=343
9³=729
11³=1331
13³=2197
15³=3375
The sum of consecutive odd cubes of 8128 is
=1³+3³+5³+7³+9³+11³+13³+15³
=1+27+125+343+729+1331+2197+3375
=8128
To know more about consecutive numbers, visit:
https://brainly.com/question/2493629
#SPJ1
the waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 0 and 8 minutes. find the probability that a randomly selected passenger has a waiting time greater than 4.25 minutes.
The probability that a randomly selected passenger has a waiting time greater than 4.25 minutes is 0.5278
The uniform distributed between a and b minutes.
The probability of finding a value above x is:
P(X > x) = [tex]\frac{b-x}{b-a}[/tex]
The time is evenly distributed between 0 and 9 minutes.
This implies that a=0 , b=9
Determine the likelihood that a randomly selected passenger will have to wait longer than 4.25 minutes.
p(X > 4.25) = [tex]\frac{9-4.25}{9-0}[/tex]
= 0.5278
There is a 52.78% chance that a randomly selected passenger will have to wait longer than 4.25 minutes.
To learn more about Probability:
https://brainly.com/question/11234923
#SPJ4
Can someone please help
After solving the value of x is 2.
From the figure:
Let ABCDE be the figure such that:
AB = 6x , BC = 6 , CD = 4,and DE = CE - CD = 12 - 4 = 8.
BD and AE are parallel lines such that:
AB/BC = ED/CD
6x/6 = 8/4
x = 8/4
x = 2.
Therefore After solving the value of x is 2.
Learn more about the value here:
https://brainly.com/question/14316282
#SPJ1
Write 36 a product of it' prime factor. Write the factor in order, from mallet to larget
The factor of 36 in order from smallest to largest is 2 × 2× 3× 3.
Prime factor:
Factors are the numbers you multiply together to get another number. In simple words, a prime factor is finding which prime numbers multiply together to make the original number.
Here we have to find the prime factor 36.
That is we have to find the smallest multiplication of digits to get the value.
36 = 2 × 2 × 3 × 3
Therefore the prime factor is 2 × 2×3×3.
To know more about the prime factor refer to the link given below:
https://brainly.com/question/18187355
#SPJ4
21. A basket holds n apples. You pick (2n - 3) apples, and your friend picks
(n+4) apples. How many apples do you and your friend pick together?
How many baskets do you need to carry all the apples? Justify your answer.
Answer:
21. A basket holds n apples. You pick (2n - 3) apples, and your friend picks
(n+4) apples. How many apples do you and your friend pick together?
How many baskets do you need to carry all the apples? Justify your answer.
Step-by-step explanation:
(2n - 3)(n + 4) binomial times a binomial equals
2n^2 + 5n - 12
Find the LCM of 2 and 3 using lists of multiples.
Answer:
Multiples of 2 = 2, 4, 6, 8, 10, 12
Multiples of 3 = 3, 6, 9, 12, 15,18
The LCM is 6.
Step-by-step explanation:
Which of the following are two-dimensional shapes? Select three options.
circle
cube
cylinder
hexagon
oval
pyramid
Answer:
Circle, hexagon, and oval
Step-by-step explanation:
They are all 2d.
13. At Greenville High School 1/3 of the students
are involved in sports. Of the students
involved in sports 20% play football. If there
are 3,000 students at the school, how
many play football? (Example 5)
Out of 3000 students at the school , 200 student plays foot ball .
In the question ,
it is given that ,
fraction of students that are involved in sports at Greenville High School = 1/3 of total students ,
percent of students that plays football = 20% of sports students .
given that the total number of students present at the school = 3000
So , the number of students involved in sports = (1/3) × 3000
= 1000
number of students who plays football = 20% of 1000
= 0.20 × 1000 ....because 20% = 0.20
= 200
Therefore , Out of 3000 students at the school , 200 student plays foot ball .
Learn more about Percent here
https://brainly.com/question/14605238
#SPJ1
Correct answer get's free 50 points
The correct statement regarding the solution of the inequality 8x - 6 < 3x + 19 is given as follows:
D. She knows that the solution must be either all the values less than 5 or all the values greater than 5.
What is the solution to the inequality?The inequality is presented as follows:
8x - 6 < 3x + 19.
Lin finds the value of x = 5 for which the two sides of the inequality are equal. Then, there are only two cases for the solution, which are listed as follows:
All values that are less than 5.All values that are greater than 5.Thus option D gives the correct option regarding how to find the solution.
The justifications for the other options being wrong are given as follows:
Options A, C and D: an inequality gives a range of values as a solution, not a single value, hence substituting the value on the inequality you verify if the value is a solution, but you do not solve, that is, you do not find all the values that are solutions to the inequality.Option E: The inequality is an open inequality, meaning that x = 5 is not a solution to the inequality.More can be learned about inequalities at https://brainly.com/question/25275758
#SPJ1
Answer:
I think its D.... id/k I think it is.
Step-by-step explanation:
a dog breeder is planning to buy more dog food. he makes a table showing how many pounds of food he will have after shopping the table is based on.how much he spends and how much food he already has which equation generates the table
The linear function that models the data-set is given as follows:
v = 4 + 0.4x.
What is a linear function?The slope-intercept representation of a linear function is presented as follows:
y = mx + b
The coefficients of the function and their meaning are obtained as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x increases by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the output y of the function when the input variable x assumes a value of 0.For this problem, the values of these parameters are given as follows:
Slope of m = 0.4, as when the input increases by 20, the output increases by 8, hence m = 8/20 = 0.4.Intercept of b = 4, as when the input is of zero, the output is of 4.Hence the equation is given as follows:
v = 4 + 0.4x.
Missing InformationThe table is given by:
Money Spent (x) $0 $20 $40 $60
Pounds of Food (v) 4 12 20 28
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
Name two points collinear to point D.
The two points that are collinear with the point D are points A and B which are on the same plane, K, as the point D
What is collinearity?Collinearity of a set of points in geometry is the property of their being on a single line. A set of points with this property is known as a collinear set. In a broader sense, the term has been applied to aligned objects, that is, things that are "in a line" or "in a row."
If two or more points lie on the same line, they are said to be collinear in geometry. As a result, collinear points are the points that lie on a single straight line.
Therefore, the points are A and B.
Learn more about collinearity on:
https://brainly.com/question/17688908
#SPJ1
Keilantra has a toy car collection of 400 toy cars. She keeps 268 of the toy cars on her wall. What percentage of Keilantra's toy car collection does she keep on her wall?
Answer:
67%
Step-by-step explanation:
[tex]\frac{268}{400}[/tex] X 100
Answer:
67%
Step-by-step explanation:
268 ÷ 400 = 0.67 = 67%
2.025 as a mixed number
Nolan has five more quarters and dimes and seven fewer nickels and dimes. He has 25 coins. How many of each coin does he have? How much money in dollars and cents is it worth?
Answer:
9 dimes, 4 nickels, 12 quarters
90 cents + 20 cents + 300 cents = 410 cents = $6.83
Step-by-step explanation:
q=5+d
n=d-7
q+n+d=25
5 + d + d - 7 + d = 25
3d-2=25
3d=27
d=9
25 - 9 = 16 nickels and quarters
q + n = 16 ---> q=16-n
n=d-7 ---> d=n+7
q=5 + n + 7
q=n+12
n+12 = 16-n
2n=4
n=4
25-(9+4)= 12 quarters
He has 2 nickels, 9 dimes, and 14 quarters, with a total value of $4.50
Step-by-step explanation:I am going to assume that the "and" in "five more quarters and dimes" and the "and" in "seven fewer nickels and dimes" is actually "than" because otherwise, there is no context in this question. If my answer is incorrect, please tell me how to correctly interpret this question.
In this scenario, the "and" in "five more quarters and dimes" and the "and" in "seven fewer nickels and dimes" is actually "than."
Amount of nickels - x
If there are seven fewer nickels than dimes, the amount of dimes is x + 7. There are five more quarters than dimes, so the amount of quarters is x + 7 + 5, which equals x + 12.
x + x + 7 + x + 12 = 253x + 19 = 253x = 6x = 2
Therefore, there are 2 nickels. Now we must figure out the number of quarters and dimes.
x + 7 = 9
x + 12 = 14
There are 9 dimes and 14 quarters.
Nickels are each worth 5 cents. 2 times 5 is 10 cents.
Dimes are each worth 10 cents. 9 times 10 is 90 cents.
Quarters are each worth 25 cents. 14 times 25 is 350 cents.
Now, we add. 10 + 90 + 350 = 100 + 350 = 450.
REMEMBER, THIS IS IN CENTS. WE MUST STILL CONVERT IT INTO DOLLARS.
450 divided by 100 is $4.50
2 7 of the pupils in year 9 say their favourite colour is red. There are 119 pupils in year 9. How many students said red is their favourite colour?.
34 students red is their favorite color
2 out of 7 of the pupils in year 9 say their favourite colour is red
Fraction of pupil that say red is their favorite colour is 7/9
There are 119 pupils in year 9
We need to calculate the number of students out of 119 that would say that their favourite colour is red
To find that,
we multiply the fraction of students that like red with the total number of students
2/7 * 119
= 34
Therefore, if 2 out of 7 of the pupils in year 9 say their favourite colour is red. Then 34 out of 119 pupil will say that their favourite colour is red.
To learn more about fraction refer here
https://brainly.com/question/1622425
#SPJ4
Lines J and k are perpendicular. The slope of line k is 3. Which equation is true?
If Lines J and k are perpendicular. The slope of line k is 3, the slope of line j is -1/3
When two lines are perpendicular to each other, the product of their slope results in -1
slope of line j x slope of line k = -1
slope of line j x 3 = -1
slope of line j is 1/3
Therefore, if Lines J and k are perpendicular. The slope of line k is 3, the slope of line j is -1/3
To learn more about equation of a line refer here
https://brainly.com/question/18831322
#SPJ1
Piper invested $4,700 in an account paying an interest rate of 4. 8% compounded continuously. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 19 years?.
Assuming no deposits or withdrawals are made, the amount in the account after 19 years is: 11,454. 133.
How to find the amount in the account?Using this formula
A = P(1+r/100)ⁿ
Where:
A = Amount =?
P = Principal = $4700
r = Interest rate =4.8%
n = the number of periods =19 years
Let plug in the formula
A = 4,700 (1 + 4.8/100)¹⁹
A = 4,700 (1 + 0.048)¹⁹
A = 4,700 (1.048)¹⁹
A = $11,454. 133
Therefore the amount is $11,454. 133.
Learn more about amount in the account here:https://brainly.com/question/14541900
#SPJ1
There are 5 player on a baketball team. In a game 4 player cored 6 point each. The team cored a Tell how to make ene of the problem total of 34 point. How many point did the other player core?
Points scored by the last player is 10 points. this can be calculated by using BODMAS rule by forming equation.
What is an equation ?
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
Main body:
Points scored by 4 players = 6 each
Total points scored by 4 players = 4*6
= 24
Total points scored by team = 34
Points scored by last player or 5th player = total points - points scored by 4 players
Points scored by 5th player = 34-24
= 10
Hence point scored by last player is 10.
To learn more about equation click on he link below
https://brainly.com/question/25896797
#SPJ4
what is the value of x in the equation 0.5x+3=4.5?
Answer:
x = 3
Step-by-step explanation:
Collect like terms
0.5x = 4.5 - 3
0.5x = 1.5
Divide both sides by 0.5
0.5x/0.5 = 1.5/0.5
x = 3
Using fractions,
1/2x = 9/2 - 3
1/2x = 3/2
Divide both sides by 1/2
x = 3/2÷1/2
Reciprocate
x = 3/2 × 2/1
x = 6/2
x = 3
On November 1st, Halloween costumes
were off their original price. If a bat
costume usually costs $28, how much
will it cost on November 1st?
$21.00
25% off 28= 7
28-7=21
2. which of these best describes a residual? a) it must be a number between 0 and 1 b) it must be positive c) it must be negative d) it must have both positive and negative values e) it represents a distance between observed and predicted values
it represents a distance between observed and predicted values
What is residual?
A residual in statistics is the discrepancy between an observed value and a value that was predicted.
Typically, the anticipated value is based on a model, like a linear regression model. The prediction error is represented by a residual, which can be either positive or negative. A positive residual indicates a difference between the observed and expected values, whereas a negative residual indicates the opposite. Specifically, the residual's absolute value is the distance between the observed value and the predicted value.
For evaluating a model's correctness, residuals are crucial. The residuals should be randomly distributed in the vicinity of zero if the model is valid. The residuals will be biased either in favor of or against the null hypothesis if the model is not accurate. A model's goodness of fit can also be evaluated using the residual. Relatively small residuals characterize a model with a high goodness of fit. Remainders that are far from zero will be present in a model with a low goodness of fit.
To Learn more about the residual from the link:
https://brainly.com/question/9329287
#SPJ4