The equation of the new function after the transformations is given as follows:
f(x) = -4(x - 3)²
How to obtain the equation after the transformations?The parent function in this problem is defined as follows:
f(x) = x².
The translation of 3 units right means that we must obtain f(x - 3), that is:
f(x) = (x - 3)².
The vertical stretch by a factor of 4 means that the function must be multiplied by 4, hence:
f(x) = 4(x - 3)².
The reflection over the x-axis means that the function must be multiplied by -1, hence:
f(x) = -4(x - 3)².
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What is 5/6 −2/4 ? Please i dont know help
Answer:
ok. its 8/24. but if you got to simplify its 1/3
Step-by-step explanatin
you do 5*4 (the numerator) and 6*4(the denomerator).
this is the lcd(least comon )denominator.
repaet the steps for 2/4 but multiply by 6 on each number
once
thats
done
its
your
answer
Answer:
5/6 – 2/4
= (10–6)/12
= 4/12
= 1/3
Help me please :( thank you
Answer:
A
Step-by-step explanation:
Which is the next step in the following construction of an equilateral triangle?
circle with center P and point A along circles edge, arcs along the circle at points B, C, D, E, and F in alphabetical order, and a line segment connecting points A and C
Connect C and E with a straightedge is the next step in order to complete the construction of an equilateral triangle.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)
We have:
Circle with centre P and point A along the circle's edge, arcs along the circle at points B, C, D, E, and F in alphabetical order, and a line segment connecting points A and C.
A triangle with three sides that are all the same length and three angles that are all the same size (60°) is called an equilateral triangle.
Connect C and E with a straightedge is the next step in order to complete the construction of an equilateral triangle.
Thus, connect C and E with a straightedge is the next step in order to complete the construction of an equilateral triangle.
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5x + y = 27
- 10x + 7y = -36 what is the x-coordinate
Answer:
For 5x + y = 27; \(x=\frac{-1}{5}y+\frac{27}{5}\)
For -10x + 7y = -36; \(x=\frac{7}{10}y+\frac{18}{5}\)
Step-by-step explanation:
None because it will be in the screenshots.
Mark me brainliest if you can when someone else answers, if not then it's alright. Have a good day! :D
9514 1404 393
Answer:
x = 5
Step-by-step explanation:
The x-coordinate of the solution can be found by subtracting the second equation from 7 times the first.
7(5x +7) -(-10x +7y) = 7(27) -(-36)
45x = 225 . . . . . simplify
x = 5 . . . . . . . . . . divide by 45
The x-coordinate of the solution is 5.
_____
The y-coordinate is 2.
what do mathematicians do after a snowstorm
Omg y’all pls help me with this I’m so stuck
Answer:
E
Step-by-step explanation:
Answer:
A, C, D
Step-by-step explanation:
if you substitute x with the given value, you'll see that their answers are all less than 4 (<4)
A = -1-1 = -2
C = 4-1 = 3
D = 0-1 = -1
i dont know how to do this please help
Answer:
4
Step-by-step explanation:
Answer:3
Step-by-step explanation:
Define units for the time that Marshall has the beans and the amount of coffee beans that Marshall has left.
After 4 weeks the amount of coffee that Marshall will have left would be = 20 ounces.
How to calculate the amount of coffee left?The amount of ground coffee that Marshall bought for his office machine = 40 ounces
The quantity of coffee he uses per week in his office = 5 ounces.
Therefore for 4 weeks would be= ?
But, 1 week = 5 ounces
4 weeks = X
make X the subject of formula;
X = 5×4 = 20 ounces
The amount of ground coffee that will remain = 40-20 = 20 ounces.
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What degree measure is equivalent to 7x/11?
Enter your answer, rounded to the nearest hundredth of a degree, in the box.
The degree measure is which is equivalent to \(\frac{7 \pi}{11}\) is 114.54°.
What is meant by degree measure?The size of an angle is measured in terms of a unit of measurement. 1 degree is equivalent in magnitude to 1/360 of a whole rotation.
A rotational angle is said to have a measure of one degree, denoted by the symbol 1°, if it is (1/360)th of a revolution from the initial side to the terminal side. Radian scale. A unit circle's unit arc's centrally subtended angle is said to have a measure of 1 radian.
The radius of an arc divided by its length is known as the radian measure (r). Radian measure is a pure number that doesn't require a unit symbol because it is the ratio of one length to another.
Convert radians to degrees, multiply by 180/π, since a full circle is 360° or 2π radians.
= \($ \frac{7 \pi}{11} \times \frac{180}{\pi}\)
= \($ \frac{7 }{11} \times 180\)
=\($ \frac{1260}{11}\)
= 114.54°
Therefore, the correct answer is 114.54°.
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Full question:
Dima asked her seventh-period class how many times they attended a summer camp since first grade. She put her data in the table and used the shaded rows to find three sample means. Summer Camp Attendance 3 1 0 4 1 4 2 3 0 5 0 1 1 2 0 4 1 4 4 2 3 2 0 1 4 What is the range of the values for the sample means? 1 1. 2 1. 8 2.
The range is (0-5) and the mean is 2.1.
MeanMean is simply defined as the average of the given set of numbers. The mean is considered as one of the measures of central tendencies in statistics. The mean is said to be an arithmetic mean. It is the ratio of the sum of the observation to the total number of observations.
Given
Summer Camp Attendance 3, 1 ,0 ,4 ,1 ,4, 2, 3, 0, 5, 0, 1, 1, 2 , 0, 4, 1, 4, 4, 2, 3, 2, 0, 1, 4.
To findThe range of the values for the sample means.
How to find the range of the values for the sample means?Range = Minimum to Maximum
Range = [0 and 5]
Mean is given by
\(\rm Mean = \dfrac{sum\ of\ the\ observation}{number\ of\ the\ observation}\)
Then the mean will be
\(\rm Mean = \dfrac{ 3+1+4+1+4+2+3+5+1+1+2+4+1+4+4+2+3+1+4 }{25}\\\\Mean = \dfrac{52}{25}\\\\Mean = 2.08 \approx 2.1\)
Thus the range is (0-5) and the mean is 2.1.
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Answer:
Step-by-step explanation:
2 on edge
At a bowling alley, 46 people are waiting to bowl. Each bowling lane can hold 8 people. How many lanes will be completely filled? How many people will be left to go on the last lane?
Answer:
5 lanes will be completely full and 6 people will be left on the last lane
Step-by-step explanation:
I need help plsss help
Answer: Circle = 5 Triangle = 2 Square = 6
Step-by-step explanation: 5 + 2 = 7 2 + 6 = 8 6+2 =8, 8 + 5 =13
Help meeeeeeeeeeeeeeeeeeeeeee
Answer:
\(39.8 + ( - 49.5)\)
Step-by-step explanation:
\(39.8 + ( - 49.5) \\ 39.8 - 49.5\)
I hope I helped you^_^
Answer:- => 39.8 + (−49.5)
= (+) (-) = (-)
=> 39.8 − 49.5
Option CSolution for 1/3p+8=11
Answer:
p = 9
Step-by-step explanation:
suppose you are given a triangle with hypotenuse of length 5.5 and legs of length x−1 and x 1.
The length of legs of right triangle is 4.758 and 2.758.
Right triangle with legs of length x - 1 and x + 1, and a hypotenuse of length 5.5, we can use the Pythagorean theorem to solve for the value of x.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
So, in this case, we have:
(x - 1)² + (x + 1)² = 5.5²
Expanding the equation:
(x² - 2x + 1) + (x² + 2x + 1) = 30.25
Combining like terms:
2x² + 2 = 30.25
Subtracting 2 from both sides:
2x² = 28.25
Dividing both sides by 2:
x² = 14.125
Taking the square root of both sides:
x ≈ ±3.758
Since the lengths of the triangle's legs cannot be negative, we discard the negative value:
x ≈ 3.758
Therefore, the approximate value of x is 3.758.
The length of legs is 4.758 and 2.758.
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1. let x and y be integers. we will assume that it is not true that x or y is even and will show that 3xy + 4 is odd.
Therefore, we have shown that \(3xy + 4 \)is odd when x and y are both odd integers.
To show that 3xy + 4 is odd, we will consider the fact that x and y are both odd integers since they are not even.
Let x = 2a + 1 and y = 2b + 1, where a and b are integers.
Now, we can substitute these expressions into the given equation:
\(3xy + 4 = 3(2a + 1)(2b + 1) + 4 \)
= \( 3(4ab + 2a + 2b + 1) + 4 \)
= \( 12ab + 6a + 6b + 3 + 4 \)
= \(2(6ab + 3a + 3b) + 7 \)
The term (6ab + 3a + 3b) is an integer, let's call it c. Thus, our equation becomes:
2c + 7
Since 2c is even, and 7 is odd, the sum (2c + 7) is odd.
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44 friends evenly divided up an
�
n-slice pizza. One of the friends, Harris, ate
1
11 fewer slices than he received.
how many slices did he eat
The expression for the number of slices Harris ate is \((n/44) - 11.\)
What is the expression for slices eaten?Let s be the number of slices each friend received.
Then the total number of slices on the pizza is n and we have: 44s = n because pizza was evenly divided among the 44 friends). Harris ate 11 fewer slices than he received, so he ate s - 11 slices.
The no of slices he received is s and we have:
s = (s - 11) + Harris's slices eaten
Substituting 44s = n, we will solve for s:
44s = n
s = n/44
So, the expression for the number of slices Harris ate is \((n/44) - 11.\)
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If+you+invest+$100+at+an+interest+rate+of+15%,+how+much+will+you+have+at+the+end+of+eight+years?
Answer:
$305.9022863 or $305.90 (rounded to 2 decimal places)
Step-by-step explanation:
It is a compound interest, meaning an interest accumulates on an initial amount every period. The formula
A= P(1+R)^n
A= the total amount P=Initial amount R= rate n=time period
P=$100 R=15% or 0.15(decimal) n=8 (years)
A= 100 (1.15)^8
A= 100(3.059022863)
A=305.9022863
The amount you will have after 8 years is $220
Calculating simple interestThe formula for calculating simple interest is expressed as:
SI =PRT
P is the principal = $100
T is the time = 8 years
R is the rate. = 15%
SI = 100 * 8 * 0.15
SI = $120
Amount after 8years = $100 + $120
Amount after 8years = $220
Hence the amount you will have after 8 years is $220
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A ladder rests with one end on the ground and the other on a vertical wall 1.8m high. If a vertical support beam 0.6m long is placed under the ladder 3m away. From the wall, find the horizontal distance of the support beam from the bottom of the ladder.
Answer:
Let's denote the horizontal distance of the support beam from the bottom of the ladder as "x" meters.
According to the given information, the ladder is resting against a vertical wall that is 1.8m high, and the support beam is placed 0.6m away from the wall. The length of the support beam is 0.6m.
We can use similar triangles to solve for "x". The triangles formed by the ladder, the support beam, and the vertical wall are similar triangles.
The height of the vertical wall (1.8m) corresponds to the length of the ladder along the wall, and the horizontal distance from the wall to the support beam (0.6m) corresponds to "x" meters on the ladder.
Using the concept of similar triangles, we can set up the following proportion:
(Height of wall) / (Horizontal distance from wall to support beam) = (Length of ladder) / (Distance from bottom of ladder to support beam)
Plugging in the given values:
1.8 / 0.6 = (Length of ladder) / x
Simplifying the proportion:
3 = (Length of ladder) / x
To find the length of the ladder, we can use the Pythagorean theorem, which states that the square of the hypotenuse (ladder) is equal to the sum of the squares of the other two sides (height of wall and horizontal distance from wall to support beam).
Length of ladder = √(height of wall)^2 + (horizontal distance from wall to support beam)^2
Length of ladder = √(1.8)^2 + (0.6)^2
Length of ladder = √3.24 + 0.36
Length of ladder = √3.6
Length of ladder ≈ 1.897 m (rounded to three decimal places)
Plugging this value back into the proportion:
3 = 1.897 / x
Solving for "x":
x = 1.897 / 3
x ≈ 0.632 m (rounded to three decimal places)
So, the horizontal distance of the support beam from the bottom of the ladder is approximately 0.632 meters.
A family on a trip budgets $1,338 for meals and gasoline. If the price of a meal for the family is $90 and if gasoline costs $2.80 per gallon, then how many gallons of gasoline can the family buy if they buy 13 meals
’creating a system linear equation, the number of possible gallons of gasoline that can be purchased is 60 gallons
Given the Parameters :
Total budget = 1338Meal cost = $90Gasoline cost = $2.80 per gallon Number of meals = 13 Number of gallons of gasoline = gHence, we have :
90(13) + 2.80g = 13381170 + 2.80g = 1338
2.80g = 1338 - 1170
2.80g = 168
g = 168/2.80
g = 60
Therefore, only 60 gallons of gasoline can be purchased.
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Seaquoia River Cruises offers a 7-day travel package. The prices vary based on the room class booked, as indicated in the following spreadsheet:
The spreadsheet formulas for the indicated cells are:
C9 =sum(C2:C8)D3 =C3/100D7 = C7/100E4 = sum(C2:C4)F5 =sum(D2:D5)What are the spreadsheet formulas?The value in C9 can be found by the formula =sum(C:C8) because the values from C2 to C8 were added up.
The formula in D3 converts the value in C3 to percentages. D7 does that for C7.
E4 takes the sum of the number of rooms from C2 to C4 while F5 takes the sum of D2 to D5.
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prove the average degree in a tree is always less than 2. more specifically express this average as a function of the number of vertices in tree.
we have proven that the average degree in a tree is always less than 2.
To prove that the average degree in a tree is always less than 2, we need to first understand what a tree is. A tree is an undirected graph that is connected and acyclic, meaning it does not contain any cycles. Each node in a tree has exactly one parent, except for the root node, which has no parent. The degree of a node in a tree is the number of edges that are connected to it. For the root node, its degree is equal to the number of edges that are connected to its children.
Now, let's consider a tree with n vertices. The total number of edges in a tree is always n-1, since each node except the root node has exactly one incoming edge, and the root node has no incoming edges. Therefore, the sum of the degrees of all the nodes in a tree with n vertices is equal to 2(n-1), since each edge is counted twice, once for each of the nodes it connects.
If we let d_i denote the degree of the i-th node in the tree, then the average degree of the tree can be expressed as:
(1/n) * sum(d_i) = (1/n) * 2(n-1)
Simplifying the right-hand side, we get:
(1/n) * 2(n-1) = 2 - (2/n)
As n approaches infinity, the average degree approaches 2, but for any finite value of n, the average degree is always less than 2. Therefore, we have proven that the average degree in a tree is always less than 2.
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Bablu has three sticks of lengths 3, 4 and 5 cm. Ramesh has three sticks of lengths 3, 5 and 9 cm. How many triangles can Bablu and Ramesh make with their sticks?
Answer: They can make 4 diferent triangles if they share their sticks, one triangle as a time. If they don't share, Babu can make only one triangle. Ramesh can not make any.
Step-by-step explanation:
Combinations that work:
3,4,5
3,3,4
3,3,5
5,5,9
The lengths of two shorter sides added together have to be greater than the longest side.
How do you find the sum of the infinite geometric series given 16+12+9+...?
The sum of the infinite geometric series 16 + 12 + 9 + ... is 64.
To find the sum of an infinite geometric series, you can use the formula:
sum =\(\frac a{(1 - r)}\)
where "a" is the first term in the series and "r" is the common ratio between terms.
In this case, the first term is 16 and the common ratio is 3/4, so the sum is:
sum \(= \frac{16}{(1 - \frac{3}4)} =\frac{16}{(\frac{1}4)} = 64\)
Therefore, the sum of the infinite geometric series 16 + 12 + 9 + ... is 64.
Note that this formula is only valid if the absolute value of the common ratio is less than 1. If the absolute value of the common ratio is 1 or greater, the series will either converge to a finite value or diverge to infinity, and the sum cannot be calculated using this formula.
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Ms. Rekha spends 165.31 , inclusive of a sales tax of 15 percent ,on oranges . Calculate the original price of oranges
The original value of the oranges is 143.75.
What is Percentage?A percentage is a number or a ratio that is expressed as a fraction of 100 i.e. out of 100.
In formula, x% of amount y = y*(x/100)
Given :
Tax paid by Rekha : 15%
Final Price paid by Rekha : 165.31
Let the original price of the oranges = x
The additional tax amount on oranges
= 15% of original price of x
= 15 * x / 100
= 0.15 x
Total price paid by Rekha = Original price of orange + Tax amount
165.31 = x + 0.15x
165.31 = (1 + 0.15)x
165.31 = 1.15x
x = 165.31/1.15
x = 143.75
Thus, the original value of the oranges is 143.75.
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in the past, the number of customers using a drive-through window at aardvark bank has averaged 20 per hour, with a standard deviation of 3 per hour. this year, another bank opened up nearby. aardvark's manager believes this will result in a decrease in the number of customers. he recorded the number of customers who arrived during 36 randomly selected hours and found that the average number of customers per hour in the sample was 19.39. what is the p-value associated with this result?
The p-value corresponding to this outcome is 0.1112.
Given data;
Aardvark Bank's drive-through window has historically seen an average of 20 customers every hour, with a standard deviation of 3 per hour. Another bank in the area opened this year. The manager of Aardvark predicts a drop in clientele as a result of this. He counted the consumers who came in throughout the 36 randomly chosen hours and discovered that the sample's mean client count per hour was 19.39.
What is the p-value corresponding to this outcome?
H₀ : μ = 20
H₁ : μ < 20
Here,
n = 36, X = 19.39, σ = 3
The test statistic Z;
Z = ( X - μ ) / (σ/√n)
Z = ( 19.39 - 20 ) / ( 3/√36 )
Z = -1.22
P - value = P(Z < -1.22)
P - value = 0.1112
Therefore, this result's related p-value is 0.1112.
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An administrator of a TANF program is concerned about the length of time hard-to-place clients were able to gain employment. He wants to contrast the average length of time at a job for his clients with the national average. What statistic should he use
The administrator should use the mean duration of employment for his clients to compare it with the national average. This will help determine if his hard-to-place clients have shorter or longer job durations than the average.
What statistic should be used to compare the job duration of TANF program clients with the national average?To contrast the average length of time at a job for his clients with the national average, the administrator of the TANF program should use the mean duration of employment for his clients and compare it to the national average.
This would provide a measure of the central tendency of employment durations for his clients and allow him to compare this measure to the corresponding national statistic.
However, it is important to note that this measure alone may not provide a complete picture of employment outcomes for hard-to-place clients in the TANF program.
The administrator may also want to consider other statistical measures such as the median duration of employment or the standard deviation to get a better understanding of the distribution of employment durations among his clients.
The median duration of employment would provide a measure of the middle value of employment durations, which may be a more representative statistic if there are outliers or extreme values in the data.
The standard deviation would provide a measure of the variability in employment durations among his clients, which would be useful in determining whether there is a wide range of outcomes or if most clients have similar employment durations.
In addition to statistical measures, the administrator may also want to consider qualitative factors such as the types of jobs his clients are able to secure and whether they are able to advance in their careers over time.
This would provide a more nuanced understanding of employment outcomes and allow for a more comprehensive evaluation of the effectiveness of the TANF program in supporting hard-to-place clients in gaining and maintaining employment.
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PLEASE HELP THIS IS DUE IN THIRTY MINUTES
I FINNA GIVE YOU 30 POINTS, THAS A SCORE
You have $4800 to spend on fencing to enclose a rectangular area. You also want to make TWO pens as shown below. The cost of the vertical sides is $2.00 per foot and the horizontal sides cost $5.00 per foot. You desire to enclose the largest possible area you can.
a) Given x is the dimension of one side of the rectangle, enter an expression for the other dimension of the rectangle. Your answer should have an "x" in it. Also select appropriate units.
b) Find an expression for the area of the rectangle only in terms of x. Check the appropriate units.
c) What are the dimensions of the rectangle with the largest enclosed area? Enter your dimensions as a list of numbers separated by a comma. Start with the value of side labeled x FIRST.
d) What is the largest area you can enclose in a rectangle using feet of fencing?
Answer:
D
Step-by-step explanation:
If a bag contains 18 red, 6 yellow, 24 blue, and 8 white balloons, what is the part-lo-whole ratio of white balloons to
all balloons?
A)
1:5
B)
1:6
C)
1:7
D)
1:8
Answer:
1:6
Step-by-step explanation:
1:6
I hope this answer is correct
Drag the costs to the table to classify them as direct operational costs or costs
covered by business insurance.
Costs Covered by
Business Insurance
Direct Operational Costs
Rent, insurance, commissions, and other expenses could be added to the operating costs of a service-based business. Most of these expenses are regular daily expenses.
What are operating expenses?A continuing cost for maintaining a system, a business, or a product is known as an operating expense, operating expenditure, operational expenditure, operational expenditure, or OPEX.
The expense of creating or providing non-consumable pieces for the system or product is known as capital expenditure (capex).
For instance, the annual costs of paper, toner, power, and maintenance for a photocopier are opex, while the cost of the photocopier itself is capex.
Additional running costs for a service-based business could include rent, insurance, commissions, and other costs.
The majority of these costs are routine daily spending.
Costs that weren't directement necessary for those activities are referred to be non-operating expenses.
Therefore, rent, insurance, commissions, and other expenses could be added to the operating costs of a service-based business. Most of these expenses are regular daily expenses.
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Correct question:
A service business may have some additional operating expenses like rent, insurance, commissions, and so on. Most of these expenses are incurred on a ___ basis.