vertical shrink by a factor of 1/4 of the graph of g(x)=|x|
The equation of the function after translation: [tex]$y=\frac{|x|}{4}$[/tex]
The y values advance toward the x-axis as they are multiplied by a value between 0 and 1. This is known as a vertical shrink and tends to flatten the graph.
When a base graph is multiplied by a particular factor larger than 1, vertical stretch happens. As a consequence, the graph is stretched outward while keeping the input values (or x). We anticipate that the y values in a function's graph will be further away from the x-axis when it is vertically extended.
The y-values are multiplied by a value between 0 and 1, which causes them to travel in the direction of the x-axis. This is known as a vertical shrink and tends to flatten the graph. A point (a,b) on the graph of y=f(x) y = f (x) shifts to a point (a,kb) (a, k b) on the graph of y=kf(x) y = k f (x) in both scenarios.
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a car dealer claims that buying a new car sam will pay 20% less for gas than for the car he currently owns. the car sam currently drives cost 15% less to gas than dons car. don pays 800$ per year for gas car. assume all cars will be traveling the same distance. how much does he pay for his current car?
Help pls and pls give explanation!
Sam pays 680$ per year for his current car and will pay 544$ per year if he buys the new car as per dealer's claim.
According to the question statement, A car dealer claims that buying a new car Sam will have to pay 20% less for gas than for the car he currently owns. The car Sam currently drives costs 15% less to gas than Don's car. Don pays 800$ per year for gas car. It is assumed that all cars will be travelling the same distance.
We are supposed to find out how much will Sam pay for his current car.
To solve this question, we need to know about the concept of percentage of any number.
Don currently pays 800$ per year on gas.
Sam pays 15% less than what Don pays, Therefore the money Sam is paying currently will be 800$ minus 15% of 800$ i.e.,
= [tex]800 - \frac{15}{100} *800[/tex]
= [tex]800-120[/tex]
= [tex]680[/tex]$
680$ per year is the money Sam is spending currently.
If he buys the new car, according to the claim of dealer, he will pay 20% less than what he is paying currently i.e., 680$ - 20% of 680$
= [tex]680-\frac{20}{100} *680\\[/tex]
= [tex]680 - 136[/tex]
= [tex]544[/tex]$
Therefore, Sam pays 680$ per year on gas on his current car but if he buys the new car he will pay 544$ per year on gas.
Percentage: In math, a percentage is a number or ratio that can be expressed as a fraction of 100 i.e., if we are supposed to find 20% of 80 then [tex]\frac{20}{100} *80=16[/tex]If you wish to learn more about percentage, click the link given below:
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Select all the correct answers.
Grace's work is x miles from her house. She drives to work every day of a 5-day workweek. Grace also goes to the gym every day after work, which increases her daily drive by 8 miles. The following expression shows the number of miles Grace puts on her car during the workweek.
Which of the following descriptions are equivalent ways to write this problem?
-----------------------------------------------------
1, Grace's work is x miles from her house. During the workweek, she drives the x miles between her house and work 7 times. She also goes to the gym to work out which increases her driving by 13 miles per workweek.
2. Grace's work is x miles from her house. To get to work and back, she drives 2x miles. She does this 5 times during the workweek. She also goes to the gym to work out which increases her daily driving by 8 miles. She does this 5 times.
3. Grace's work is x miles from her house. To get to work and back, she drives x miles. She does this 5 times during the workweek. She also goes to the gym to work out which increases her daily driving by 8 miles. She does this 5 times.
4. Grace's work is x miles from her house. During the workweek, she drives the x miles between her house and work 10 times. She also works out which increases her driving by 40 miles per workweek.
(this problem is multiple choice btw)
Answer: 54
Step-by-step explanation:
54
Answer: The 4 one is correct, The 2 one is correct
Step-by-step explanation:
-lukelaws hope i helped if i did please make me brainliest and if im wrong i am so sorry:(
A student has 5 ninths gallons of popcorn to give away. He wants to split it evenly between his 4 friends. How much popcorn does each friend receive?
20 over 9 gallons
1 gallon
5 over 13 gallons
5 over 36 gallons
Check
Mc
Graw
Hill
RMA1FL_0101_check2
Question 2 of 3
Question 2
Select the sentence(s) that represent(s)
the equation.
7(p +23) = 102
Save and Exit
A) Seven times the sum
of p and twenty-three
is the same as one
hundred two.
B) Seven times p plus
twenty-three equals
one hundred two.
C) Seven times the quan-
tity p plus twenty-three
equals one hundred
two.
D) The quantity seven
Submit Assignment
The sentence that represents the equation (7p + 23) = 102 is Seven times the sum of p and twenty-three is the same as one hundred two.
It is given that (7p + 23) = 102
Now, we have to write this equation in a sentence or to translate it in words.
As we can see in the given equation that seven is multiplied by p and then twenty three is added in the multiplication of seven and three, after that their addition is equal to one hundred two.
So, the Option A will be the correct answer which is Seven times the sum of p and twenty-three is the same as one hundred two.
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the formula for the volume of a cylinder is v = πr2h. The cylinder to the right has an exact volule of 500π cubic meters. Find its height
The height of the cylinder is 20 meters.
What is the volume of a cylinder?The density of a cylinder is determined by its volume, which represents how much material may be immersed in it or carried inside of it. The formula r2h, where r is the radius of the circular base and h is the height of the cylinder, determines the volume of a cylinder. Any substance that can fill the cylinder consistently with liquid or another material may be used as the material. Check the shape's volume here.
Formula= V = π r² h
According to the given value,
The formula for the volume of a cylinder is V=πr²h.
The cylinder to the right has an exact value of 500π cubic meters.
Its radius is given as 5 meters in the figure.
volume of the cylinder.
V = π r² h
We have,
V = 500π cubic meters
500π cubic meters = πr²h
Find the height of the cylinder.
We have,
500π cubic meters = πr²h
Divide both sides by π
500cubic meters = r²h
We have,
r = 5
500 cubic meters = 5² square meters x h
500cubic meters = 25 square meters x h
Divide both sides by 25
20 meter = h
h = 20 meters
Thus the height of the cylinder is 20 meters.
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Solve the following:
1. even integers between 1 and 101
2. first 25 terms of the arithmetic sequence 4, 9, 14, 19, 24 ...
Answer:
1. 2550
2. 1600
Step-by-step explanation:
Question 1Even Integer: A whole number that can be positive, negative, or zero, and that can be divided exactly by 2.
Even integers between 1 and 101:
2, 4, 6, 8, 10, ... , 100This forms an arithmetic sequence with:
first term (a) = 2common difference (r) = 2Sum of the first n terms of an arithmetic series:
[tex]\boxed{S_n=\dfrac12n[2a+(n-1)d]}[/tex]
There are 50 even integers between 1 and 101.
Therefore, to find the sum of the even integers between 1 and 101, substitute n = 50 and the found values of a and r into the formula:
[tex]\begin{aligned}\implies S_{50} & =\dfrac{1}{2}(50)[2(2)+(50-1)2]\\\\& =25[4+(49)2]\\\\& =25[4+98]\\\\& =25[102]\\\\& = 2550\end{aligned}[/tex]
Therefore, the sum of the even integers between 1 and 100 is 2550.
Question 2Given arithmetic sequence:
4, 9, 14, 19, 24, ...From inspection of the given arithmetic sequence:
first term (a) = 4common difference (r) = 9 - 4 = 5Sum of the first n terms of an arithmetic series:
[tex]\boxed{S_n=\dfrac12n[2a+(n-1)d]}[/tex]
To find the sum of the first 25 terms of the given arithmetic sequence, substitute n = 25 and the found values of a and r into the formula:
[tex]\begin{aligned}\implies S_{25} & =\dfrac{1}{2}(25)[2(4)+(25-1)5]\\\\& =\dfrac{25}{2}[8+(24)5]\\\\& =\dfrac{25}{2}[8+120]\\\\& =\dfrac{25}{2}[128]\\\\& = \dfrac{3200}{2}\\\\& = 1600\end{aligned}[/tex]
Therefore, the sum of the first 25 terms of the given arithmetic sequence is 1600.
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A white tailed deer can sprint up to 30 miles per hour. American bison can run at speeds up to 3,520 feet per minute. Which animal is faster and by how many miles per hour? There are 5,280 feet in one mile.
Answer:
The American bison is 10 miles per hour faster. It can run at 40 miles per hour.
Step-by-step explanation:
See the picture for the conversion. I used unit multiplies to change feet to miles and seconds to minutes.
PLEASE HELP... Students are making necklaces of six beads for their mothers. There are
six colours available. There is no clasp, so the necklace can be rotated.
The necklace can also be turned over.
In how many different ways can the students place the beads around the
necklace if exactly two colours are used?
Answer:
Step-by-step explanation:
#1 Number of ways picking 2 from 6 = 6C2 = 15
#2 Arranging them in a circle (consider 1 pair AB)
can be done
1,5 (ABBBBB) or (5,1)
2,4 ( AABBBB) or (4,2)
3,3
1,1 (ABABAB)
all up = 7 ways
#3 = product of #1 and #2 = 15x7 = 105
There are 60 different ways the students can place the beads on the necklace using exactly two colors.
To find the number of different ways the students can place the beads on the necklace using exactly two colors, we need to consider the different arrangements that can be made.
We can first choose the two colors to be used, which can be done in C(6, 2) = 15 ways (where C(n, r) represents the combination of n items taken r at a time).
Once the colors are chosen, we can arrange the beads on the necklace in two ways: either clockwise or counterclockwise.
We can also flip the necklace to get a different arrangement.
Therefore, for each combination of colors, there are 2 x 2 = 4 different arrangements possible.
Thus, the total number of different ways the students can place the beads on the necklace is 15 x 4 = 60.
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(PLEASE HELP!) A car travels 76 km due north and then 25 km due east.
(a) What is the cars current bearing from the starting point correct to the nearest degree?
(b) How far is the car from the starting point correct to the nearest km?
Answer:
Step-by-step explanation:
Look at the File I attached. The Question says that a car travels 76 km north then 25 km east. Now think of this as the Right angled triangle I attached in the file.
a) Bearing from the staring point to the means the degrees of the part i marked with a question mark.
Now SOH CAH TOA
76 km is the ADJACENT
25 km is the OPPOSITE
and x is the HYPOTENUSE
We have the values of the ADJACENT and the OPPOSITE.
Now see which rule has both, It is TOA(tan rule) which is:
tan(y) = OPPOSITE/ADJACENT (y is the degrees we will get)
tan(y) = 25/76 ( opposite of the degree we need is 25 and adjacent is 76)
tan inverse(25/76) = y (inverse will be given as to the power -1 on the calculator)
FINAL ANSWER OF (a) = 18.21°
b) This part is asking for the length of the hypotenuse, which i denoted as x in the attached file.
For this part, you will use the Pythagoras Theorem
Which is :
a² + b² = c²
Where c is the hypotenuse and a and b are the opposite and adjacent.
So
76² + 25² = x²
6401 = x²
√6401 = x
x = 80.01
Help please I will mark you as a brainliest.
Answer:
(5² - 8) x 2 doesn't belong
Step-by-step explanation:
this is because this answer is the only one with parintisies around the 5²
Answer and how to solve this
Step-by-step explanation:
When it says x = something, that basically means to replace the x with whatever it says x equals.
x = 0. Equation /. 3 x 0 = 0 + 1 = 1. Y = 1
x = -1. Equation/. 3 x -1 = -3 + 1 = -2. Y = -2
x = 2. Equation/. 3 x 2 = 6 + 1 = 7. Y = 7
Hope this helps!! (:
The data below shows the number of people visiting a local clinic per day to be vaccinated against Measles.
5 12 19 29 35 23 15 33 37 21 26 18 23 18 13 21 18 22 20
1.1 Determine the mean of the given data. (2)
1.2 Calculate the standard deviation of the data.(2)
1.3 Determine the number of people vaccinated against Measles that lies within ONE standard deviation of the mean.(2)
1.4 Determine the interquartile range for the data.(3)
1.5 Draw a box and whiskers diagram to represent the data.(3)
1.6 Identify any outliers in the data set. Substantiate your answer.(2)
Answer:
1.3
2.5
3.7
4.95.0
5.38
6.67
Step-by-step explanation:
Answer:
Step-by-step explanation:
34
45
11
9
78
56
Use your calculator to solve the following system: x 2y = 4 y - z = 0 x 3y - 2z = 5
-20/7 is the answer for the following equation.
There are numerous ways in which one may define an equation. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
x+2y=4 ---------(1)
y-z=0 -------(2)
x+3y-2z=5 -----(3)
from eq(1)
x = 4-2y -----(4)
from eq (2)
z=y ----(5)
putting these values in eq (3)
4-2y+3y-2(y)=5
-y +4=5
-y=5-4
y = -1
putting in eq 4
x =4 -2y
x = 4-2 (-1) = 6
putting values of y in eq(3)
z = y = -1
x =6
y = -1
z = -1
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The perimeter of a rectangle is 150 meters. If the length of the rectangle is 15 meters more than the width, what are the dimensions of the rectangle
Convert 50 pounds into kilograms
Answer:
22.6796 kg
Step-by-step explanation:
for an approximate result, divide the mass value by 2.205
but the conversion is 50 pounds = 22.696 kilograms
Answer:
22.68 kilograms
Step-by-step explanation:
I found the answer on the internet
Please help with. Scale Factors
Answer:
5×8=40
x=7×8
=56
Step-by-step explanation:
5×8=40
x=7×8
=56
What does it mean for a sample to have a standar deviation of zero? describe the scores in such a sample
Given that sample standard deviation is zero. This indicates that the variance of sample is also zero as square of sample standard deviation is sample Variance. Variance is average of the squared deviations from mean. As shown in below formula
Since Variance = 0 , we substitute in formula and we get the sum of squares of deviations of all data points from mean should be zero. This is only possible if and only if all the data points in the data distribution are same as mean of the data distribution. In the case the variance and standard deviation will be zero.
Variance = Summation n to i = 1 [tex]\frac{(X_{1-X} )^2}{n-1}[/tex]
0 = Summation n to i = 1[tex]\frac{(X_{1-X} )^2}{n-1}[/tex]
Summation n to i [tex]{(X_{1-X} )^2[/tex] = 0
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Please answer this !!!!!! will give brainliest !on first down, the vultures lost 6 yd. on second down, they lost 5yd. on third down, they lost 8 yd. use an integer to express their overall change in position as a result of the three plays.
As per given condition first they lost 5yd , second lost 6yd , third lost 8 yd ,so change in position shows lost 19 yd.
As given,
Let x be the total number of yards in the beginning
First down they lost 5 yards, second 6 yd and third 8 yd.
Required equation,
x-5-6-8
= x-19
Negative sign represent the lost of 19 yads.
Therefore, as per given condition first they lost 5yd , second lost 6yd , third lost 8 yd ,so change in position shows lost 19 yd.
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Je m'échauffe
1 QUESTIONS FLASH
Déterminer la moyenne, la médiane et l'éten-
due de chacune des séries :
2
a. série 1 : 4; 5; 12;
b. série 2: 0; 1; 2; 3;
c. série 3:3; 7; 9:11; 20;
d. série 4:2; 3; 4; 5; 6; 7.
Si quelqun pourrais m’aider sur les 3 question sa serais génial ! Silvouplais
Answer:
yookiiii8bubub7bssh8ss
John runs the same number of kilometres each day.write an expression to represent the number of kilometre john ran in june last year
An algebraic expression to represent the number of kilometres John ran in June month last year is 30a.
Given that, John runs the same number of kilometres each day.
We need to find an algebraic expression to represent the number of kilometres John ran in June month last year
What is an algebraic expression?An algebraic expression (or) a variable expression is a combination of terms by the operations such as addition, subtraction, multiplication, division, etc.
Let us assume that john is running 'a' kilometres per day.
We know that June month composed of total 30 days
So the algebraic expression for the number of kilometres John ran in June last year = Number of kilometres running per day × Number of days in the month of June
=a × 30=30a
Therefore, an algebraic expression to represent the number of kilometres John ran in June month last year is 30a.
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work out the area of the shape
Answer:
88 [tex]cm^{2}[/tex]
Step-by-step explanation:
We need to find the area of the rectangle and the triangle.
Area of the rectangle:
a = length x width
a = 11 x 6 = 66
Area of the triangle:
a = [tex]\frac{ b x h}{2}[/tex] We need to find the base and height of the triangle. The base is the same length as the length of the rectangle: 11 and the height is 10 - 6 or 4
a = [tex]\frac{11 x 4}{2}[/tex]
a = [tex]\frac{44}{2}[/tex]
a = 22
Add the area of the rectangle and the triangle together. 66 + 22 = 88
2/3 of the students in class are male. If 18 of the students are male, how many students are in the class
Answer:
27 students
Step-by-step explanation:
Split 18 into 2 to find 1/3. 18/2= 9
9= 1/3
18= 2/3
27= 3/3 or 1
Answer:
There are 27 students.
Step-by-step explanation:
Given that,
→ 2/3
→ 18 ÷ 2
→ 9 = 1/3
Now the number of students are,
→ x = (2/3) + (1/3)
→ x = 18 + 9
→ [ x = 27 ]
Hence, there are 27 students.
A right triangle has side lengths 8, 15, and 17 as shown below.
Use these lengths to find sin.X, tanX, and cos.X.
Answer:
please demonstrate how tha triangle looks like
The profits shown in retained earrings can be used for_
A. Predicting future income.
B.re-investment into the company
C. Buying a house.
D. Investing into other companies.
The profit shows in retained earning can be used for reinvestment into the company
There are many measures and uses of earnings. Some analysts like to calculate earnings before taxes (EBT), also known as pre-tax income. Some analysts prefer to see earnings before interest and taxes (EBIT). Still, other analysts, mainly in industries with a high level of fixed assets, prefer to see earnings before interest, taxes, depreciation, and amortization, also known as EBITDA.
Earnings that deviate from the expectations of the analysts that follow that stock can have a great impact on the stock's price, at least in the short term. For instance, if analysts on average estimate that earnings will be $1 per share and they come in at $0.80 per share, the price of the stock is likely to fall on that "earnings miss."
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Elsa opens an account to save money for a family vacation. the account earns an annual interest rate of 4% 4 % . she earns $37 $ 37 in simple interest after 6 6 months.
Amount while opening account at rate of 4% for 6 months and earn simple interest $37 is $1850.
As given,
Simple interest amount earned by Elsa = $37
Annual interest rate R= 4%
Time T =6 months
Let P be the principal amount she put while opening account
Simple interest = (P × R × T) / 100
⇒37 ={P × 4 × (6/12)}/100
⇒P =(37 × 100) / 2
= $1850
Therefore, amount while opening account at rate of 4% for 6 months and earn simple interest $37 is $1850.
The complete question is:
Elsa opens an account to save money for a family vacation. The account earns an annual interest rate of 4%. She earns $37 in simple interest after 6 months. How much money did she put in the account when she opened it?
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You arrive in Tokyo with $320. How many yen can you buy ?
Answer:
You can buy 31788.8 with $320.
Step-by-step explanation:
To calculate this, we know that yen is 0.01007 dollars per foreign. We also know that 1 dollar = 99.34 So, therefore you will multiply 320 * 99.34 and you will get 31788.8 Yen.
I hope this helps and have a good day! :D
please help thank youuu
Answer:
f(6) = - 10 and g(- 4) = 125
Step-by-step explanation:
substitute x = 6 into f(x) , that is
f(6) = - 2(6) + 2 = - 12 + 2 = - 10
substitute x = - 4 into g(x) , that is
g(- 4) = - 2(- 4)³ - 3 = - 2(- 64) - 3 = 128 - 3 = 125
In the student council election, 217 students vote. Uma receives 4 votes for every 3 that Paloma Receives. How many more votes does Uma receive than Paloma?
In probability 31, more votes does Uma receive than Paloma .
In statistics, what does a probability mean?
The likelihood that an event will occur in a Random Experiment is measured by probability. A number between 0 and 1 is used to quantify probability, where, broadly speaking, 0 denotes impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability.let uma u and paloma p votes
Uma = 4/7 = u/217
4 × 217 / 7 = u
u = 124
paloma = 3/7 = p/217
3 × 217 /7 = p
p = 93
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Surface Areas and Volume
Answer:
3.3.1
A cylinder has a circular base.
3.3.2
As cylinders have circular bases, the formula for the area of the base of a cylinder should be the same as the formula for the area of a circle:
[tex]\boxed{\mathrm{Area = \pi r^2}}[/tex].
3.3.3
To find the volume of a cylinder, we can imagine stacking multiple circles on top of each other so that the height of the structure increases, and the shape becomes a cylinder.
This means that the volume of a cylinder is simply the area of the base circle multiplied by the height (h) of the cylinder.
∴ [tex]\boxed{\mathrm{Volume = \pi r^2h}}[/tex].
3.3.4
We can use the above formula to calculate the volume of the given cylinder, where:
• r = [tex]\mathrm{\frac{diameter}{2}}[/tex] = [tex]\frac{8}{2}[/tex] = 4 m
• h = 3 m
∴ [tex]\mathrm{Volume = \pi \times (4 \: m)^2 \times 3 \: m}[/tex]
[tex]= \mathrm{\pi \times 16 \:m^2 \times 3 \: m}[/tex]
[tex]= \mathrm{48 \pi \: m^3 }[/tex]
[tex]= \mathrm{\bf150.8 \space\ m^3}[/tex]