A function that has been transformed by the given transformations is y = -f(x - 3) + 2
How to create a function that has been transformed?The transformation are given as:
Shifted right 3 unitsShifted up 2 unitsReflected about the x-axisLet the equation of the parent function be
y = f(x)
So, we have the following transformations
Shifted right 3 units
The transformation rule is
(x, y) = (x - 3, y)
So, we have:
y = f(x - 3)
Shifted up 2 units
The transformation rule is
(x, y) = (x, y + 2)
So, we have:
y = f(x - 3) + 2
Reflected about the x-axis
The transformation rule is
(x, y) = (x, -y)
So, we have:
y = -f(x - 3) + 2
Hence, a function that has been transformed by the given transformations is y = -f(x - 3) + 2
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the mathcounts international airport had 738,114 departures in 2001. if these were distributed uniformly throughout each 24-hour period, what is the mean number of seconds between each departure time? express your answer to the nearest whole number.
The MATHCOUNTS International airport had the mean number of seconds between departure time of 43 seconds in 2001.
For given question,
In 2001 there were 738,114 departures.
As we can see, 2001 was not a leap year.
So, the number of days in 2001 = 365
We find the number of departures per day in 2001.
738,114 / 365 = 2,022.23
So, approximately 2,022 departures per day.
Now we find the number of departures in an hour.
2,022 / 24 = 84.25
This means, approximately 84 departures per hour
We know that, 1 hour = 3,600 seconds
Now we find the mean number of seconds between departure time.
3,600 / 84 = 42.8
≈ 43 seconds
Therefore, the MATHCOUNTS International airport had the mean number of seconds between departure time of 43 seconds in 2001.
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3x + 8 = -10 I don’t know what this is and I need to solve it fast
Answer:
x = -6
Step-by-step explanation:
3x + 8 = -10
3x = -10-8
3x=-18
divide both sides by the coefficient of x which is 3
3x/3 = -18/3
x = -6.
GH has a midpoint at M(3, 6). Point G is at (2, 6). Find the coordinates of point H.
Write the coordinates as decimals or integers.
Thus coordiante of point H is(4,6)
The Midpoint Formula: The midpoint of two points,
(x1,y1) and (x2,y2) is the point
M=(x1+x2)/2 and (y1+y2)/2
(2+x2)/2=3
(6+y2)/2=6
solving above equation
x2=4
y2=6
Thus coordiante of point H is(4,6)
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Rewrite 120 + 400 using the GCF and factoring.
12(10 + 40)
20(10 + 2)
40(3 + 400)
40(3 + 10)
Pls help asap
the sequence obtained by starting with 10 and obtaining each term by subtracting 3 from the previous term
Answer:
A=10. D=_3
Step-by-step explanation:
Start from 10 and make minus 3 every time
Lawana is making cone-shaped hats 4 inches in diameter, 6.5 inches tall, with a slant height of 6.8 inches for party favors. Find each measure to the nearest tenth.
a. the volume of candy that will fill each cone
Given hats are forming a conical shape and the volume of the cone will be 27.28 inches³.
What is volume?Volume is the scalar quantity of any object that specified occupied space in 3D.
For example, the space in our room is referred to as volume.
Given that,
4 inches in diameter, 6.5 inches tall, slant height of 6.8 inches
So,
D = 4 inches
Now radius r = D/2
r = 4/2 = 2 inches.
Height h = 6.5 inches.
The volume of the conical bar is given as ;
(1/3)πr²h
So,
Volume = (1/3)π(2)²6.5
Volume = 27.28 inches³
Hence "The volume of the given conical-shaped hat will be 27.28 inches³".
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0.1-(-31/50)
it’s Math
So please help
Answer:
0.72 or 18/25
Step-by-step explanation:
Multiply -(-31/50)
0.1 + 31/50
To write 0.1 as a fraction with a common denominator, multiply by 50/50.
0.1*50/50+31/50
Combine 0.1 and 50/50.
0.1+50/50 + 31/50
Combine the numerators over the common denominator.
0.1*50+30/50
Simplify the numerator.
36/50
Cancel the common factor of 36 and 50.
Results are 18/25 and 0.72.
Hope this helps.
Cara's bi-weekly gross pay is $735.18. She sees that $13.97 was deducted for Medicare tax. What percent of Cara's
gross pay has been withheld for Medicare tax? Round to the nearest tenth.
a. 0.19%
b. 1.9%
c. 2.1%
d. 3.5%
Answer:
b
Step-by-step explanation:
To find the percent of Cara's gross pay, divide what was deducted for Medicare tax by what her bi-weekly gross pay is.
So,
13.97 ÷ 735.18 = 0.019
Which means 1.9%
a game where two players each throw two dice each. if any one die matches the other, you win a dollar. if there is no match, you lose a dollar. would you play this game or not and why?
Yes, I would play the game, because the probability of winning is 13/18.
Probability:
Probability refer the possible occurrence of any particular event.
Given,
A game where two players each throw two dice each. if any one die matches the other, you win a dollar. if there is no match, you lose a dollar.
Here we need to find whether we able to play this one or not.
To find that one, first, we have to identify the winning scenarios,
Let us consider five winning scenarios. Lets represent the dice outcomes as A, B, C, and D, where your dice are A and B and the other player's are C and D. The five scenarios are:
1) A = B
2) A = C
3) A = D
4) B = C
5) B = D
We know that the total possible outcomes is 6^4. We can go through each scenario and count the possible outcomes. We must be careful to avoid overcounting.
Based on this,
The probability that none match is
=> 6*5*4*3/6^4
=> 360 / 1296
=> 5 / 18
So, probability of winning is,
=> 1 - 5/18
=> 13/18.
So, based on the probability the chance of winning is high. So, we can play it.
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The sum of three consecutive even integers is 48. Find the value of the middle of the
three.
Answer:
16
Step-by-step explanation:
You want the middle of three consecutive even integers that have a sum of 48.
Consecutive even integersWe can let x represent the middle of the three integers. Then the other two are (x -2) and (x +2), and their sum is ...
(x -2) +x +(x +2) = 48
3x = 48 . . . . . simplify
x = 16 . . . . . . divide by 3
The middle integer of the three is 16.
__
Additional comment
As we see here, the average of the three integers is their sum divided by their number: 48/3 = 16. The middle of an odd number of consecutive integers will be equal to their average value. Hence, the middle integer must be 16.
Simplify this expression-
-6(2 + x)
Answer:
-12 -6x
Step-by-step explanation:
I did this by distributing
-6 x 2 = -12
-6 x x= -6x
-12 -6x is your final answer
Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day :)
Mary, Tonya, Imani, and Luz were each painting identical-sized rooms. No one was able to finish in 1 day. The table shows the fraction of each room the girls painted.
Amount Painted
Which girl painted the most?
Imani painted the wall most
In mathematics, numbers can be classified into different types i.e. real numbers, natural numbers, integers, rational numbers, etc. This includes decimals. t is a standard form representing integers and non-integers.In algebra, a decimal is one type of number in which the whole and fractional parts are separated by a decimal point. The point between the integer and the fractional part is called the decimal point. For example, 34.5 is a decimal number.Decimal Numbers may be of different types, Recurring Decimal Numbers Non-Recurring Decimal Numbers Decimal Fraction
Mary painted 3/4 of the wall
3/4 = 0.75
Tonya painted 5/4 of the wall
5/7 = 0.71
Imani painted 11/13 of the wall
11/13 = 0.84
Luz painted 11/17 of the wall
11/17 = 0.64
Imani painted the wall most
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PLEASE HELP!!!
We want to find the median of the following set of scores:
26, 9, 15, 5, 5, 27, 23, 12
Answer: 13.5
Step-by-step explanation:
First arrange the scores in order:
5, 5, 9, 12, 15, 23, 26, 27
**remove 1st and last number in the set of scores every time**
Median of 5, 5, 9, 12, 15, 23, 26, 27=
Median of 5, 9, 12, 15, 23, 26=
Median of 9, 12, 15, 23=
Median of 12, 15 =
**Take mean of remaining two numbers**
(12+15)/2=
27/2=13.5
Suppose that people check their coats in a checkroom. if all claim checks are lost and the coats are randomly returned, what is the probability that all the people will get their own coats back?
The probability that all the people will get their own coats back is 1/7.
What is probability?Likelihood is the part of science concerning mathematical depictions of how likely an occasion is to happen, or how likely it is that a suggestion is valid. The likelihood of an occasion is a number somewhere in the range of 0 and 1, where, generally talking, 0 shows difficulty of the occasion and 1 demonstrates sureness. The higher the likelihood of an occasion, the almost certain it is that the occasion will happen. A basic model is the throwing of a fair coin. Since the coin is fair, the two results are both similarly plausible; the likelihood of "heads" rises to the likelihood of "tails"; and since no different results are conceivable, the likelihood of all things considered "heads" or "tails" is 1/2.
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suppose that a function f has domain (-2,2) and range (-3,5). what is the domain of the function f(2x)?
The value of the domain for f(2x) is 2 * 4 to 2 * 18 or 8 to 36.
What is domain?The set of inputs that a function will accept is referred to as the domain of the function in mathematics. It is sometimes represented by the symbol dom(f), where f is the function.
The function f can be graphed in the Cartesian coordinate system in the specific case where X and Y are both subsets of R. In this instance, the graph's x-axis shows the domain as a projection of the function's graph there. It is a partial function in this instance, and the set of real numbers on which the formula may be evaluated to a real number is known as the natural domain or domain of definition of f.
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a restaurant offers three desserts, and exactly twice as many appetizers as main courses. a dinner consists of an appetizer, a main course, and a dessert. what is the least number of main courses that the restaurant should offer so that a customer could have a different dinner each night in the year 2003? (a) 4 (b) 5 (c) 6 (d) 7 (e) 8
8 is the least number of main courses that the restaurant should offer so that a customer could have a different dinner each night in the year 2003.
What are Integers in Math?
An integer is a number that includes negative and positive numbers, including zero. It does not include any decimal or fractional part. A few examples of integers are: -5, 0, 1, 5, 8, 97, and 3,043Let m be the number of main courses the restaurant serves, so 2m is the number of appetizers.
Then the number of dinner combinations is 2m * m * 3=6m².
Since the customer wants to eat a different dinner in all $365$ days of 2003, we must have
6m² ≥ 365
m² ≥ 60.83
Also, year 2003 is not a leap year, because 2003 divided by 4 does not equal an integer. The smallest integer value that satisfies this is E = 8.
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3x+5x-4y+9 pls help bro
Solution: 8x-4y+9
Step-by-step explanation:
Combine like terms
3x + 5x - 4y + 9
8x - 4y + 9
To find the x-intercept, substitute 0 for y and solve for x. To find the y-intercept, substitute 0 for x and solve for y.
x-intercept(s): (−9/8,0)
y-intercept(s): (0,9/4)
Rich is attending a 4-year college. As a freshman, he was approved for a 10-year, federal unsubsidized student loan in the amount of $7,900 at 4.29%. He knows he has the option of beginning repayment of the loan in 4.5 years. He also knows that during this non-payment time, interest will accrue at 4.29%.
How much interest will Rich accrue during the 4.5-year non-payment period?
Rich has to pay an interest of $1525.10 during the 4.5 year non payment period.
In the question
it is given that the Amount of loan taken by Rich = $7900
non payment time period = 4.5years
Interest charged during the non payment time = 4.29%
Interest charge for the first year = 4.29% of 7900
= 0.0429 * 7900 ...(as 4.29% = 0.0429)
= 338.91
So , the interest charge for first non payment year = $338.91
to find the interest for 4.5 years , multiply the first year interest by 4.5.
So the interest charge for 4.5 years = 4.5*338.91
=1525.095
≅1525.10
Therefore , Rich has to pay an interest of $1525.10 during the 4.5 year non payment period.
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measure the length of a ordinary sheet of 8x11 paper in metric units (if you do not have a metric measuring device, you can measure in us units and use a free online conversion tool to change to metric units). what is the area of the sheet of paper in correct metric units?
The area of the sheet of paper in correct metric units is 602.6c[tex]m^{2}[/tex].
What is an area?A region's size on a plane or curved surface is expressed by the term "area," which is a mathematical concept. As opposed to surface area, which refers to the area of an open surface or the boundary of a three-dimensional object, plane region or plane area refers to the area of a form or planar lamina. Area can be thought of as the volume of material, at a particular thickness, required to create a model of the shape, or as the volume of paint required to paint the surface in a single coat. It is equivalent to the volume of a solid or the length of a curve in two dimensions (a three-dimensional concept).
Calculations:
The length of a 8 X 11 paper in metric unit is 27.9 cm and width of 8 X 11 paper in metric unit is 21.6 cm.
Area of sheet of paper=length*width
=27.9*21.6
=602.6 c[tex]m^{2}[/tex]
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David requires at least $250 to hold his birthday party. If David can save $43 by the end of each month, how many months will he need to save to be able to afford his birthday party?
a. Write an inequality that describes this situation.
b. Solve the inequality. Show all your work.
c. Write your answer in a complete sentence.
Answer: 250/43
Step-by-step explanation
Answer:
he would need seven weeks, i believe.
What is the cos A?
i need help bad
According to given triangle the value of cos A = 3/5
We know that cos theta = Adjacent Side / Hypotenuse Side
According to the question given that Adjacent side = 3
And Hypotenuse Side = 5
Then cos A = 3/5
Hence, option 3 is correct
Each geometrical shape has unique side and angle characteristics that enable us to recognize it. The following is a list of a triangle's key characteristics.
Three vertices, three internal angles, and three sides make up a triangle.
According to the triangle's "angle sum property," a triangle's three inner angles can never add up to more than 180 degrees. Take note of the triangle PQR shown above, where the angles P, Q, and R all add up to 180 degrees.
A closed triangle has three vertices, three sides, and three angles. The symbol for a triangle with the three vertices P, Q, and R is PQR. Sandwiches and signboards in the shape of triangles are the most prevalent triangle-shaped objects.
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In the picture there is a triangle with ABC angles. Sides AB=5, BC=3, CA=4. The ratio of CosA=4/5.
Given that,
In the picture there is a triangle with ABC angles.
Sides AB=5, BC=3, CA=4
Trigonometric ratios, which contain the values of all trigonometric functions, are based on the ratio of sides of a right-angled triangle. The ratios of a right-angled triangle's sides with regard to a certain acute angle are known as its trigonometric ratios.
The right triangle's three sides are as follows:
Hypotenuse (the longest side)
Perpendicular (opposite side to the angle)
Base (Adjacent side to the angle)
According to the cos theta formula, the cos of an angle in a right-angled triangle is equal to the ratio of the Adjacent side to the hypotenuse.
Cos A = Adjacent side / hypotenuse
CosA=4/5
Therefore, CosA=4/5.
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At the ice cream shop there are 14 shakes so for every six months record the ratio is below.whats malts to total?
12. Classify the statement below as a descriptive or inferential statistic and explain why.
Because of the SG distance learners, Robin expects to serve 12% less meals this year than last year.
The given statement is a descriptive statistic.
What is descriptive statistics?Descriptive statistics are relatively short informational coefficients that summarize a given data set, which can be a representation of the entire population or a sample of a population. Descriptive statistics are divided into measurements of central tendency and measures of variability (spread). Descriptive statistics are used to describe or summarize the data in meaningful and useful ways. It would be useful to know, for example, that each of the participants in with us example wore blue shoes. Even so, it'd be useful to know how evenly distributed their anxiety ratings were.So, the statement "Robin expects to serve 12% fewer meals this year than last year" is a descriptive statistic.
Therefore, the given statement is a descriptive statistic.
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7.
If twenty-one more than a fifth of a number is equal to two times the quantity of
three less than that number, what is the number?
Answer:
The number is 15.
Step-by-step explanation:
Let n be the number.
[tex] \frac{1}{5} n + 21 = 2(n - 3)[/tex]
[tex]n + 105 = 10(n - 3)[/tex]
[tex]n + 105 = 10n - 30[/tex]
[tex]9n = 135[/tex]
[tex]n = 15[/tex]
What happens to you at the red circle on the graph?
the red point represents the moment when you return to your house, 8 time units after you originally left.
What happens to you at the red circle on the graph?
Let's assume that the graph represents the distance to your home as a function of time. (The x-axis represents time in time units and the y-axis represents the distance in distance units)
Then you can see how in the first 3 units of time you travel a certain distance from your home.
Then for the 3 next time units your position does not change, so you are in a fixed place.
In the next 3 time units you return to your house, here we reached the red point, which represents the moment when you return to your house, 8 time units after you originally left.
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A store bought jeans at a cost of $40 a pair. Select all the statements that are true.
The true statements are,
⇒ If the price is marked up 25%, the selling price will be $50.
⇒ If the selling price is $70, the price is marked up 75%.
What is the Cost price?
Cost price is the total amount of money that it costs a manufacturer to produce a given product or provide a service.
Given that:-
A Store bought jeans at a cost of $40 a pair.
If the price is marked up 25%, the selling price will be $50
⇒ 40 x 25 / 100 = 10
Selling Price = $50
Hence, This is true statement.
And, If the selling price is $70, the price is marked up 75%.
P = 70 - 40 = $30
40 x 75 / 100 = $30
Hence, This statement is true.
Therefore, the true statements are;
⇒ If the price is marked up 25%, the selling price will be $50.
⇒ If the selling price is $70, the price is marked up 75%.
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The complete question is this,
A store bought jeans at a cost of $40 a pair. Select all the statements that are true.
A. If the price is marked up 20%, the selling price will be $60.
B. If the price is marked up 25%, the selling price will be $50.
C. If the selling price is $65, the price is marked up 50%.
D. If the selling price is $70, the price is marked up 75%.
Find X
3x + 16
5x-10
Without computing, determine which
number is greater, [(-4)415 or -[(4¹2)³].
Explain your reasoning.
Since a negative number's exponent is always positive, [(-4)⁴]⁵ will always be greater than -[(4¹²)³].
What is number system?
The Number System covers any of the several sets of symbols and usage guidelines for indicating numbers, which are used to indicate how many items are present in a particular group. Thus, the Roman numeral I, the Greek letter alpha, the first letter used as a numeral, the Hebrew letter aleph, or the modern number 1, which is nothing more than Hindu-Arabic in origin, can all be used to express the idea of "oneness."
A mathematical representation of the numbers in a given set is called a number system.
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a rectangular persian carpet has a perimeter of 232 inches. the length of the carpet is 30 inches more than the width. what are the dimensions of the carpet?
The dimensions of the carpet are 73 x 43. = 3139.
What is dimension explained?In mathematics, a dimension is a way to quantify the size or separation of an area, an object, or a space inside one direction. In simpler terms, It is just the measurements of an object's length, width, and height.
What is a geometric figure?Geometric figures can be created using any configuration of points, lines, or planes. Depending on their dimensions, geometric figures can be categorized as either a space figure, a surface figure, a line, another line segment, a ray, or a point.
According to the given data:The perimeter of the carpets = is 232.
The length of the carpet = 30 in.
In a rectangle, the edge is P = 2W + 2L
In this case 232 = 2W + 2L
Also, the 2nd sentence says L = W + 30
This length variable can be changed in the perimeter formula:
232 = 2W + 2(W+30)
232 = 2W + 2W + 60
232 = 4W + 60
172 = 4W
43 = W
Then, since L = W+30
L = 43+30 = 73
So the dimensions of the carpet are 73 x 43. = 3139.
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State which metric unit you would probably use to measure item.
Mass of a beach ball
The basic unit of mass of the ball in the metric system is the gram.
What is mass?The base units of length (distance), capacity (volume), and weight (mass) in the metric system are the meter, liter, and gram, respectively. We utilize units that are derived from metric units to measure smaller or greater quantities.
Mass is a physical body's total amount of matter. Inertia, or the body's resistance to acceleration when a net force is applied, is also measured by this term. The strength of an object's gravitational pull to other bodies is also influenced by its mass.
Therefore, the basic unit of mass of the ball in the metric system is the gram.
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