The correct transformation of f(x) to get 4f(x+2) is by a vertical shift by 4 and 2 units in the x direction.
Given a function f(x) and other function 4f(x+2).
We are required to choose a transformation that will give 4f(x+2) from a function f(x).
Function is like a relationship between two or more variables that are expressed in equal to form. The values which we enter in a function is known as domain and the value that we get as a result are known as range.
So, we have to reach 4f(x+2) from f(x).
The value of function is usually expressed on y axis and variable x on x axis.
To increase the value of x by 2 we have to stretch it in x direction.To find the 4 times value of function we have to stretch the y axis to 4 units.
Hence the correct transformation of f(x) to get 4f(x+2) is by a vertical shift by 4 and 2 units in the x direction.
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If two 6-sided dice are rolled what is the probability that both numbers will be even?
xy =8 inches wy =24 and xz=48 inches height from the ground to the base of the window is?
The height of the ground from the base of the window is 144 inches.
How to find the side of a right angle triangle?One angle of a right angle triangle is equals to 90 degrees.
Therefore, the sides and angles of the right triangle can be found using trigonometric ratios.
tan x = WY / XY
tan x = opposite / adjacent
tan x = 24 / 8
x = tan⁻¹ 3
x = tan⁻¹ 3
x = 71.5650511771
x = 71.60°
tan 71.60 = h / 48
cross multiply
h = 48 tan 71.60
h = 48 × 3
h = 144 inches
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A bucket contains exactly 3 marbles, one red, one blue and one green. a person arbitrarily pulls out each marble one at a time. What is the probability that the last marble removed is non-red?
The probability that the last marble removed is non-red is 2/3.
According to the given question.
Total number of marbles in a bucket = 3
And, a person arbitary pulls out each marble one at a time.
So, there are 6 possible sequences of removing 3 marbles.
Let R be the red marble, B be the blue marble and G be the green marble.
The possible sequences or sample space for removing marbles are: {RBG, RGB, BGR, BRG, GRB and GBR}.
Let A denotes the event of removing the non-red marbles at the last.
The favorable cases for event A are: RBG, RGB, BRG and GRB.
As, we know that probability of any event is calculated as by taking the ratio of total number of favorable outcomes to the total number of outcomes.
Thereofre,
The probability that the last marble removed is non-red
= 4/6
= 2/3
The probability that the last marble removed is non-red is 2/3.
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Urgent!!!!!!!!!!!!!!!!!!
.Which statement is true about two ordered pairs
that are the same except for the signs of the
numbers?
A. Their points are reflections.
B. Their points are on the horizontal axis.
C. Their points are on the vertical axis.
D. Their points are in different quadrants.
Answer
The statement that is true about two ordered pairs that are the same except for the signs of the numbers is their points are in different quadrants. Option D
What are ordered pairs?Ordered pairs are known to be pairs of numbers that are used locate a point in the rectangular coordinate plane
They are written as (x ,y)
where
x is the x-coordinate y is the y-coordinateIt is important to note that the location of the ordered pair in the quadrants determines the sign of the x and y coordinates.
The signs of the ordered pairs are given as;
When (x , y) is in Quadrant I then both x and y are positive
(x , y) is in Quadrant II then x is negative and y is positive (x , y) is in Quadrant III then both x and y are negative (x , y) is in Quadrant IV then x is positive and y is negativeTherefore, the statement that is true about two ordered pairs that are the same except for the signs of the numbers is their points are in different quadrants. Option D
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HEY PLEASE HELP ASAP
Answer:
[tex]\dfrac{8y-43}{(y-1)(y-8)}[/tex]
Explanation:
[tex]\rightarrow \dfrac{5}{y-1} +\dfrac{3}{y-8}[/tex]
make the denominators similar
[tex]\rightarrow \dfrac{5(y-8)}{(y-1)(y-8)} +\dfrac{3(y-1)}{(y-8)(y-1)}[/tex]
Join both the fraction
[tex]\rightarrow \dfrac{5(y-8)+3(y-1)}{(y-1)(y-8)}[/tex]
simplify the expression
[tex]\rightarrow \dfrac{5y-40+3y-3}{(y-1)(y-8)}[/tex]
[tex]\rightarrow \dfrac{8y-43}{(y-1)(y-8)}[/tex]
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's simplify ~
[tex]\qquad \sf \dashrightarrow \: \cfrac{5}{y - 1} + \cfrac{3}{y - 8} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{5(y - 8) + 3(y - 1)}{(y - 1)(y - 8)} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{5y -40 + 3y - 3}{y {}^{2} - y - 8y + 8} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{8y -43}{y {}^{2} - 9y + 8} [/tex]
la+xl/2 - la-xl/2, if a= -2, x= -6
HELP!!!
Answer: 2
Step-by-step explanation:
1) substitute
2) calculate the difference before the absolute value
3) calculate the absolute value
4) convert into whole numbers/reduce
5) subtract the whole numbers
this is what i think might be wrong
Can someone help me please?
A.1/5
B.7/10
C.3/10
D.1/2
Using it's concept, the probability that a student plays basketball or soccer is given as follows:
B. 7/10.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
P(A or B) is the probability that a student plays basketball or soccer, hence, from the Venn diagram:
7 students play at least one of the sports, which are: Fran, Juan, Ian, Ella, Mickey, Mai and Marcus.There is a total of 10 students, which are the 7 that plays at least one of the sports, plus Karl, Jada and Gabby.Hence the probability P(A or B), that is, the probability that a student plays basketball or soccer, is given as follows:
p = 7/10.
Which means that option B is correct.
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–4.9(–7.3 + 3.6n) =
Simplify the expression please :)
Hich number is not in scientific notation? (5 points) group of answer choices 9 ⋅ 1019 7.8 ⋅ 106 1.45 ⋅ 10−7 0.33 ⋅ 10−15
Answer:
0.33 ⋅ 10^−15
Step-by-step explanation:
Scientific notation requires exactly one non-zero digit to the left of the decimal point.
The number ...
0.33 ⋅ 10^−15
has no non-zero digits to the left of the decimal point. It is not in "scientific notation."
__
Additional comment
Expressed in scientific notation, it would be ...
3.3 ⋅ 10^−16
14) Adelina is comparing prices for two brands of health and energy bars at the local grocery store.
She wants to get the best price for each bar. Feel Great energy bars are $18 for 12 bars. Super
Power bars cost $21.75 for 15 bars.
a) Write an equation to find the price for each bar of the Feel Great brand.
b) Write an equation to find the price of each bar for the Super Power brand.
c) Which bar should Adelina buy? Explain your reasoning.
The bar which Adelina should buy is super power brand because it cost less than feel great energy bar at $1.45 per bar
Unit priceFeel great energy bars = Total cost / number of bars
= $18 / 12
= $1.5 per bar
Super power brand = Total cost / number of bars
= $21.75 / 15
= $1.45 per bar
Therefore, the bar which Adelina should buy is super power brand because it cost less than feel great energy bar at $1.45 per bar
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Can you please help me with this question
When you have negative exponents, you flip it around. Let me give you two examples below.
[tex]x^{-5} = \frac{1}{x^{5} }[/tex]
[tex]10^{-2} = \frac{1}{10^{2} }[/tex]
Therefore you will be doing: [tex]\frac{4}{1} * \frac{1}{10^{2} } = \frac{4}{1} * \frac{1}{100} } = \frac{4}{100} = \frac{1}{25}[/tex]
Your final answer is 1/25.
Brainliest would make my day :)
PLEASE ANSWER QUICKLY!!!! THE FIRST ONE GETS BRAINLIEST OR 5 STARS!!! For consecutive weeks, the manager of a local restaurant collected data on the number of cheese pizzas sold each week. The data is shown in the scatterplot below.
Can the given line be used to make reasonable predictions of the number of cheese pizzas that Will be sold in upcoming weeks? Explain. (graph is below)
Answer:
Yes
Step-by-step explanation:
The given line is an average of the data points.
A team plays 93 games in a season. The team won 15
more than twice as many games as they lost.
How many wins and losses did the team have?
PLS HELPPPP THE WORDING IS CONFUSING
Answer:67 wins, 26 losses
Step-by-step explanation: They played 93 games. Let L = their losses and w = their wins. They won 15 more than twice as many games they lost so w = 2L + 15. So, 93 = 3L + 15. 93 - 15 = 78. 78 divided by 3 is 26 so they lost 26 games and won the rest of them or 93-26 = 67 wins and 26 losses.
What is the mean absolute percentage error of the forecast for march found by the exponential smoothing method with a smoothing constant of 0. 3?
The value of the mean absolute percentage error of the forecast for march found by the exponential smoothing method with a smoothing constant of 0. 3 is 16.94%
How to solve for the mean absolute percentage errorThe equation is given as
∝At + (1-∝) Ft
The value for Alpha = 0.7
1 - ∝ = 1 - 0.7
= 0.3
Forecast in match = 62
Ft = 51. 5
the difference = 62 - 51.5
= 10.5
The error = 10.5/62 * 100
= 16.94%
Hence the value of the mean absolute percentage error of the forecast for march found by the exponential smoothing method with a smoothing constant of 0. 3 is 16.94%
Complete question
The past demand data shown below can be regarded as stationary.
Month Demand
January
50
February
55
March
62
April
45
What is the mean absolute percentage error of the forecast for March found by the exponential smoothing method with a smoothing constant of 0.3?
O a. 14.68%
Ob. 16.94%
O c. 12.57%
Od. 11.33%
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G(x)=2x-8, f(x)=5-g(x) what is the value of f(10)
Answer:
-7
Step-by-step explanation:
[tex]f(10) = 5-g(10)\\=5-(2(10)-8)\\=5-(20-8)\\=5-(12)\\=-7[/tex]
A portion of the Quadratic Formula proof is shown. Fill in the missing statement.
x²+x+
X+
a
X+
2a
b
2a
Statements
2a
2a
= ±₁
==
4ac b²
+
4a² 4a²
b²-4ac
4a²
b²-4ac
4a²
b²-4ac
4a²
?
Reasons
Find a common denominator on the right side of the equation
Add the fractions together on the right side of the equation
Rewrite the perfect square trinomial on the left side of the equation as a binomial squared
Take the square root of both sides of the equation
Simplify the right side of the equation
[tex]x+\frac{b}{2a}=\pm \frac{\sqrt{b^2 -4ac}}{2a}[/tex]
The following are the distances (in miles) to the nearest airport for 11 families. 9, 11, 11, 16, 16, 24, 28, 30, 34, 42, 45 Notice that the numbers are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:
The summary of the given data is are as follows :-
Minimum: 11
Lower quartile:11
Median:24
Upper quartile:34
Maximum:45
Interquartile range:23
Given :- 9, 11, 11, 16, 16, 24, 28, 30, 34, 42, 45
Minimum = The smallest number of data
Thus Minimum = 11
Maximum = The largest number of data
Thus Maximum = 45
Median = The middle number of the data if data consists of odd number of elements
Thus Median = 45
Lower quartile = The median of the lower half of data
Thus Lower quartile = 11
Upper quartile = The median of the upper half of data
Thus Upper Quartile = 34
Interquartile range = The difference of upper and lower quartiles,
Thus Interquartile range = 34 -11 = 23
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2. Select true or false for each statement about the data above.
A. The most common length of ribbon is 11/
B. The sum of the longest and shortest lengths is 20¹
C. The difference between the longest and shortest
lengths is 2.
X
+
11
-
215
Part Two
A group of children picked oranges and made orange juice. The line plot below shows
the amount of juice each child made. Use the line plot below to answer questions 3-7.
X
x x
X
+
N
X
+
+ +
2²/12 2²/ 2/²/
Quarts of Orange Juice Made
3. What is the greatest amount of juice?
True False
416
True False
True False
XX
+
N
516
4. What is the least amount of juice?
5. What is the sum of the least and greatest amount of juice? Show your work.
X
+
M
6. What is the difference between the greatest and least amount of juice? Show your
work.
7. If the children were to share the juice equally, how much would each child get?
Show your work.
A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.
What is a line plot?A line plot can be defined as a type of graph that is used to graphically represent a data set above a number line, while using crosses, dots, or any other mathematical symbol.
Based on the data provided in the complete question, we can logically deduce the following points:
Length of ribbon (11 1/4) = 3.Length of ribbon (10 3/4) = 1.Length of ribbon (10 1/2) = 1.Length of ribbon (10 7/8) = 1.Length of ribbon (10 5/8) = 1.Length of ribbon (9 7/8) = 1.In conclusion, graph C shown in the image attached below is a line plot which correctly shows the data from the table above.
The most common length of ribbon is 11 1/4: True.
The sum of the longest and shortest lengths is 20 1/8: False.
Sum = 11 1/4 + 9 7/8
Sum = 21 9/8 ≠ 20 1/8.
The difference between the longest and shortest lengths is 2 1/8: False.
Difference = 11 1/4 - 9 7/8
Difference = 1 3/8 ≠ 2 1/8 .
Part Two.The greatest amount of juice is equal to 3.
The least amount of juice is equal to 1 4/6.
The sum of the least and greatest amount of juice is:
Sum = 1 4/6 + 3
Sum = 4 4/6 = 4 2/3.
The difference between the greatest and least amount of juice is:
Difference = 3 - 1 4/6
Difference = 8/6 = 4/3.
How much would each child get?If the children were to share the juice equally, the amount of juice each would get should be calculated by determining the mean:
Mean = [F(x)]/n
Mean = (1 4/6 + 2 + 2 + 2 + 2 2/6 + 2 5/6 + 2 5/6 + 3)/8
Mean = 18.7/8
Mean = 2.3375 = 2 27/80.
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Complete Question:
Katie recorded the length, in inches, of the ribbon pieces she was going to use for a project. Use this information for questions 1 and 2.
11 1/4, 11 1/4, 10 3/4, 10 1/2, 10 7/8, 10 5/8, 9 7/8, 11 1/4,
1. Which line plot correctly shows the data?
PLEASE ITS MY LAST QUESTION
Answer:
[tex]y = - \frac{1}{4} x - 10[/tex]
Step-by-step explanation:
The negative reciprocal of 4 is -1/4.
Let's substitute in our values, to find the y-intercept:
[tex]y = - \frac{1}{4} x + c[/tex]
[tex] - 11 = - 1 + c[/tex]
[tex]c = - 10[/tex]
Finally, our full equation is:
[tex]y = - \frac{1}{4} x - 10[/tex]
Fifteen students were divided into two classrooms in a ratio of 1:2.
How many students were in each classroom?
HELP PLEASE. Hector built a tent shaped like a rectangular pyramid. The volume of the tent is 56 cubic ft. The area of the base of the tent is 24 square ft. What is the hieght of Hectors tent in feet?
The height of the rectangular pyramid is 7 ft.
How to get the height of the rectangular pyramid?
First, we know that the volume of a rectangular pyramid is given by:
[tex]V = B*H/3[/tex]
Where B is the base, H is the height.
First, we know that the volume is 56 ft³, and the base is 24ft², then we can replace these two in the volume equation to get:
[tex]56 ft^3 = 24ft^2*H/3[/tex]
Solving that for H, we get:
[tex]H = 3*(56ft^3/24ft^2) = 7ft[/tex]
The height of the rectangular pyramid is 7 ft.
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What is the slope of the line that passes through the points (10, 3) and
(7,0)? Write your answer in simplest form.
Answer:
slope = 1
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (10, 3 ) and (x₂, y₂ ) = (7, 0 )
m = [tex]\frac{0-3}{7-10}[/tex] = [tex]\frac{-3}{-3}[/tex] = 1
The two rectangles are similar. which is the correct proportion for corresponding sides?
Option D is correct, the proportion for corresponding sides is 12/4 = 24/8.
According to the statement
we have given that the two rectangle which are similar to each other and we have to find the correct proportion for corresponding sides of rectangles.
So, we know that the
For the two rectangles to be similar, it means the ratio of their corresponding sides must be the same.
Looking at the two rectangles, the corresponding sides are pf the rectangles are:
4 m side corresponds to 8 m side in rectangle A
12m side corresponds to the 24 m side in rectangle B.
Then
The ratios of the both rectangles are:
In rectangle A is 8/4 = 2
In rectangle B is 24/12 = 2
From this it is clear that the ratios are equal.
Thus, the scale factor is 2
Since 8/4 = 24/12, we can rearrange to get;
12/4 = 24/8.
So, Option D is correct, the proportion for corresponding sides is 12/4 = 24/8.
Disclaimer: This question was incomplete. Please find the full content below.
Question:
The two rectangles are similar with sides 4 m side corresponds to 8 m side in rectangle A and 12m side corresponds to the 24 m side in rectangle B.which is the correct proportion for corresponding sides?
A. 12/3 = 24/12.
B. 12/2 = 27/8.
C. 11/4 = 23/8.
D. 12/4 = 24/8.
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What are the y-intercept and the asymptote of g(x) = 3x – 5? (0, –5); y = 3 (0, –2); y = 5 (0, –4); y = –5 (0, 5); y = –3
The y-intercept of the equation g(x) = 3^x - 5 is (0, -4) and the asymptote of the equation g(x) = 3^x - 5 is y = -5
How to determine the y-intercept?The equation of the function g(x) is given as:
g(x) = 3^x - 5
The y-intercept is a point on the graph where the value of x is 0
This is represented by x= 0 or (0, y)
This means that we substitute 0 for x in the above equation
So, we have:
g(0) = 3^0 - 5
Evaluate the exponent 3^0
g(0) = 1 - 5
Evaluate the difference of 1 and 5
g(0) = -4
Rewrite this point as
(0, -4)
This means that the y-intercept of the equation g(x) = 3^x - 5 is (0, -4)
How to determine the asymptote?The equation of the function g(x) is given as:
g(x) = 3^x - 5
The asymptote is a point on the graph where that is parallel to the graph
In the above equation, we have:
g(x) = 3^x - 5
Express the radical as 0
y = 0 - 5
Evaluate the difference of 0 and 5
y = -5
This means that the asymptote of the equation g(x) = 3^x - 5 is y = -5
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Which expression represents the following statement? Multiply 6 by 3, and then subtract the quotient of 18 and 9.
A) 6 x (3 ÷ 18) + 9
B) 6 + 3 + (18 ÷ 9)
C) (6 x 3) − 18 ÷ 9
D) 6 x (3 + 18) + 9
Answer:
C) (6 x 3) - 18 ÷ 9
Step-by-step explanation:
I'll solve this question by writing down every step and doing it one by one.
1. Multiply 6 by 3
--> This will be represented as 6 x 3.
2. Subtract the quotient of 18 and 9
--> The quotient is a number resulting in a division of another number. In this case, 18 is bigger than 9, so the quotient will be: 18 ÷ 9.
--> Since we are subtracting this from the equation we got earlier, it can be expressed as (6 x 3) - (18 ÷ 9)
This equation is the same as C) (6 x 3) - 18 ÷ 9, so C is our final answer.
Select the correct answer from each drop-down menu.
Since AC, MN, and DB intersect at O,
( A. Transitive property of congruence.)
( B. Linear pair postulate.)
( C. Congruent supplements theorem.)
( D. Vertical angles theorem.)
It is given that
( A. Linear pair postulate.)
( B. Vertical angles theorem.)
( C. Transitive property of congruence.)
( D. Congruent supplements theorem.).
The paragraph looks like:
Since AC, MN, and DB intersect at O, ∠AOM ≅ ∠NOC and ∠MOD ≅ ∠BON by the vertical angles theorem. It is given that ∠BON ≅ ∠NOC, so by the transitive property of congruence, ∠AOM ≅ ∠MOD.
In the question, we are asked to convert the given proof to the paragraph format, where the proof is already given to us.
The proof given to us is:
Statements________________________Reasons
1. AC, MN, and DB intersect at O.______1. given
2. ∠AOM ≅ ∠NOC__________________2. vertical angles theorem.
3. ∠MOD ≅ ∠BON__________________3. vertical angles theorem.
4. ∠BON ≅ ∠NOC__________________4. given.
5. ∠AOM ≅ ∠MOD_________________5. transitive property of congruence.
To convert this proof to the paragraph format, we need to translate each statement along with its reason in the paragraph.
Thus, the paragraph looks like:
Since AC, MN, and DB intersect at O, ∠AOM ≅ ∠NOC and ∠MOD ≅ ∠BON by the vertical angles theorem. It is given that ∠BON ≅ ∠NOC, so by the transitive property of congruence, ∠AOM ≅ ∠MOD.
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When rolling two dice what is the probability of rolling a sum of six or two even numbers.
The probability of rolling a sum of six or two even numbers.
is P = 1/3
How to find the probability?
Here we are rolling two dice, and each dice has 6 possible outcomes, then the total number of outcomes is:
6*6 = 36
Now, the outcomes that given a sum of 6 are:
dice 1 dice 2.
1 5
5 1
2 4
4 2
3 3
We have 5 outcomes there.
The outcomes where both numbers are even are:
dice 1 dice 2.
2 2
2 4
4 2
4 4
4 6
6 2
6 4
6 6
We have 8 outcomes here (such that 2 are in the ones we counted before).
Then the total number of outcomes that either add to 6 or have both even numbers are:
5 + 8 - 2 = 12
Then 12 out of 36 outcomes either add to 6 or have both even numbers, this means that the probability is:
P = 12/36 = 1/3
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15 The tennis team is selling tickets to a car wash for $6. When they do not
sell very many tickets, the team decreases the price 25%. What is the
new cost of a ticket?
Show your work.
Answer: $4.50
Step-by-step explanation:
Original Price: $6
Discount: 25%
Discounted Price: 6*25%= $1.5
$6-$1.5= $4.5
A sales team estimates that the number of new phones it will sell is a function of the price that it sets. It estimates that if it
sets the price at.x dollars, it will sell f(x) = 2,712 - 3x phones. Therefore, the company's revenue is x (2,712 - 3x). Find
the price x that will maximize the company's revenue.
The price x which will maximize the company's revenue is 904
How to determine the priceThe price x which will maximize the company's revenue is 240
Let
Price of the good = x
Number of goods sold = 2712- 3x
The formula for revenue is given as;
Revenue = Price × Quantity
= x( 2712 - 3x)
Expand the bracket
2712x - 3x^2
Therefore, the price x which will maximize the company's revenue will be:
2712x - 3x^2 =0
Collect like terms
3x² = 2712x
3x = 2712
Divide both side by 3
3x/3 = 2712/3
x = 904
Hence, the price x which will maximize the company's revenue is 904
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