Answer:
f(g(2)) = 50
Step-by-step explanation:
evaluate g(2) then substitute the result obtained into f(x)
g(2) = 3(2) - 2 = 6 - 2 = 4 , then
f(4) = 2(4 + 1)² = 2(5)² = 2(25) = 50
Answer:
f[g(2)] = 50
Step-by-step explanation:
Given functions:
[tex]f(x)=2(x+1)^2[/tex]
[tex]g(x)=3x-2[/tex]
We are asked to determine f[g(2)], which is known as a composite function. When solving composite functions, you always work inside out.
Step 1: Find the value of g(2) by substituting 2 for x in function g(x).
[tex]\implies g(2)=3(2)-2[/tex]
[tex]\\\implies g(2)=6-2\Rightarrow g(2)=\boxed{4}[/tex]
Step 2: Substitute the found value into the composite function.
[tex]\\\implies f[g(2)]= 2(4+1)^2[/tex]
[tex]\implies f[g(2)] = 2(5)^2 \Rightarrow 2(25) \Rightarrow \boxed{50}[/tex]
Hence, the value of the composite function f[g(2)] is 50.
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Is 25 a prime number?
No, 25 is not a prime number. It can be divided by 5 without a remainder, so it has factors other than 1 and itself.
A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In other words, a prime number can only be divided evenly by 1 and by itself. They are considered to be the "building blocks" of the natural numbers, and are important in number theory and other branches of mathematics.
The factors of 25 are 1, 5 and 25. Prime numbers are numbers that are divisible by only 1 and themselves. So 25 is not a prime number.
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A paint store sells 4 pt of paint for $19.use a model to write a rate for this situation. What does this mean? Show your work
A model for the rate situation is written as
4x = $19
This means that a unit of paint is sold for $4.75 hence 4 units will be $19
What is unit price?The cost per unit of an item is represented by the unit price.
To determine the unit price of an item, we divide the price of a specific number of units by the number of units.
How to write a model for the rate situationIf a paint store sells 4 pt of paint for $19. the rate of the paint is solved for as follows
let a unit be x
4 = 19
1 = x
cross multiplying
4x = 19 * 1
x = 19 / 4
x = 4.75
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6.
In George's classroom, there are 6 girls for every 2 boys. What is the ratio of boys to the total number of students
A. 1:3
B. 3:1
C. 1:4
D. 4:1
On solving the provided question, we can say that there are 6 girls for every 2 boys, ratio = 3:1
what is ratio?Ratios show how often one number is contained in another in mathematics. For instance, the ratio of oranges to lemons in a fruit dish is 8 to 6 if there are 8 oranges and 6 lemons present. In a similar vein, the proportion of oranges to whole fruit is 8, while that of lemons to oranges is 6:8. A ratio is an ordered pair of numbers a and b that is expressed as a / b, with b not equal to zero. An equation equating two ratios is known as a ratio. The ratio can be expressed as 1:3, for instance, if there is 1 boy and 3 girls (for every boy she has 3 girls) 3/4 are girls, while 1/4 are boys.
there are 6 girls for every 2 boys.
ratio will be
6/2 = 3/1
ratio = 3:1
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The ratio of the measures of the three angles in a triangle is 14:5:11. Find the measures of the angles.
The smallest angle =
The medium angle =
The largest angle =
Answer:
See below
Step-by-step explanation:
All of the interior angles of a triangle sum to 180 °
Smallest is 5 out of (14 + 5 + 11) = 5/30 ths of 180° = 30°
Middle is 11/30 ths = 66°
Largest is 14/30 ths = 84°
Answer:
30° , 66° , 84°
Step-by-step explanation:
sum the parts of the ratio, 14 + 5 + 11 = 30 parts
divide the sum of the angles in a triangle 180° by 30 to find the value of one part of the ratio.
180° ÷ 30 = 6° ← value of 1 part of the ratio , then
smallest angle = 5 × 6° = 30°
medium angle = 11 × 6° = 66°
largest angle = 14 × 6° = 84°
Can you help me with this
Answer:
No function is shown
Step-by-step explanation:
What is the quotient of 15 divided by -3?
Answer:
Step-by-step explanation:
take -5 and times it by -3 and it will equal a positive 15
so its -5
Jon drank 2/3 liter of water on Monday before jogging. He drank 5/7 liter of water after hi jog. How much water did Jon drink altogether? Write your anwer a a Mixed number
Answer:
1 8/21.
Step-by-step explanation:
Total number of water Jon drink altogether
2/3 + 5/7
=LCM 21
=2/3 + 5/7
=14 + 15
21
=29/21
Mixed fraction
=1 8/21.
There are 30 students in a class. Today, 26 students are present. Choose an equation to show how many students are absent.
Responses
26+a=30, a=4; 4 students are absent.
26 plus A is equal to 30, , A is equal to 4, ; , 4 students are absent.,
26+30=a, a=56; 56 students are absent.
26 plus 30 is equal to A, , A is equal to 56, ; , 56 students are absent.,
a−26=30, a=56; 56 students are absent.
A minus 26 is equal to 30, A is equal to 56; 56 students are absent.
26−a=30, a=4; 4 students are absent.
The equation that shows how many students are absent is 26+a = 30 and 4students are absent
What is a linear equation?A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line.
Also a linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
There are 30 students in a class and 26 students are present.
Let's represent the number of student absent by a
therefore the sum of the number of student absent and the student present will give the total number of student.
26+a = 30 and
a = 30-26
a = 4
therefore 4 students are absent
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PLEASE HELP !!!!!!!! Joanne is copying angle BAC with technology. An angle is created from points B, A, and C. A circle with a center of A has a radius of AB and intersects with rays AB and AC. Another ray is created from points D and E. A circle has been created from point D that is congruent to circle A. Which of the following describes her next step? Draw a circle with a center F and a radius equal to BG. Draw the point of intersection between circle D and ray DE. Draw ray DE away from angle BAC. Draw the points of intersection between circle D and circle A.
He should do all the steps that are mentioned in the question to make sure the new angle is congruent to angle BAC and has the same properties.
What is the construction of a circle?
Circle constructions are used in many fields such as geometry, engineering, and architecture to create precise circles. It's a fundamental concept in mathematics, and it's important to understand how to construct circles to apply these concepts in different fields.
His next step would be to draw a circle with a center F and a radius equal to BG.
By creating a circle with a center F and a radius equal to BG, He is creating a congruent circle to the original circle A with the center A, and radius AB.
The point of intersection between circle D and ray DE would also be an important step as it would give the location of the new angle. The point of intersection between circle D and circle A would also be an important step as it would confirm that the two circles are congruent.
Drawing ray DE away from angle BAC is also an important step, as it would create a new angle with the same properties as angle BAC.
Hence, He should do all the steps that are mentioned in the question to make sure the new angle is congruent to angle BAC and has the same properties.
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2(5x-3)=24 what is x
Answer: x=3
Step-by-step explanation: So let’s first simplify, 2(5x-3)=24, which we can make, 10x-6=24. Now, to find the value of x, we will all 6 on both sides, so, 10x-6+6=24+6. This will simplify out into 10x=30, so now we divided 10 on each side - 10x/10=30/10. And we will get x=3
Answer:
x = 3
Step-by-step explanation:
2 (5x - 3) = 24
10x - 6 = 24
10x = 30
x = 3
a businessman bought x bags of maize at a cost of shs.960 per bag. he spend she 15 per bag on transport. he later sold the maize39 per tine making a profit of shs.515 per bag. (a) calculate the number of tins in one bag. (b) if the business man made total of sha 29,640. how many bags had he sol? (c) the businessman later used the total sales to buy more maize at shs.926.25 per bag he sold half of the bags to the maize millers the rate of shs.1,390 per bag and retailed the remaining at his stall to consumers at shs.39 per tin. which option would earn more profit and by how much? (2mk) (d) express the difference as a percentage of the sales to the consumers.
a) To calculate the number of tins in one bag, we can use the information given in the problem: "he later sold the maize39 per tine"
So we can assume that one bag of maize is divided into tins and the price per tin is 39 shs.
b) To find out how many bags the businessman sold, we can use the information that he made a total of 29,640 shs in profit.
We know from the problem that the profit per bag is 515 shs, so to find out how many bags he sold we can divide the total profit by the profit per bag: 29,640 shs / 515 shs/bag = 57.5 bags
c) To find out how much profit the businessman made by selling half of the bags to the maize millers, we can use the information that he bought the bags at 926.25 shs and sold them at 1,390 shs.
We know that he sold half of the total number of bags, so we can divide the total number of bags by 2: 57.5 bags / 2 = 28.75 bags
To find out the total profit he made, we can multiply the number of bags sold by the profit per bag: 28.75 bags * (1,390 shs - 926.25 shs) = 22,447.5 shs
d) To express the difference as a percentage of the sales to the consumers, we can use the information that the businessman sold the bags to the maize millers at 1,390 shs and to the consumers at 39 shs.
To find the difference, we can subtract the price he sold the bags to the consumers from the price he sold the bags to the maize millers: 1,390 shs - 39 shs = 1351 shs
To find the percentage of the difference, we can divide the difference by the price he sold the bags to the consumers and multiply by 100: (1351 shs / 39 shs) * 100 = 34,641.03%
Why is the exponential power 0 to 1?
Answer:The zero exponent is equal to 1 to satisfy a certain case in manipulating bases with exponents. When multiplying or dividing the same base with exponents we add or subtract the exponents: To find the value of (3^3) (3^2) [the short form of (3 X 3 X 3) X (3 X 3) or (27) (9)] we add exponents to get 3^ (3+2) or 3^5 with a value of 243.
Step-by-step explanation:
Students in Mr.Chow's class each contributed money for a gift to a visiting speaker. Each student contributed the same amount, and each gave Mr.Chow the exact same four coins: If $16.81 was collected in all, how many pennies were collected?
Answer:
So in total, 1681 pennies were collected.
Step-by-step explanation:
divide the total amount collected, $16.81, by the value of a penny, which is $0.01.
16.81 / 0.01 = 1681 pennies.
So in total, 1681 pennies were collected.
Mrs. Chauvet keeps a Mystery Box in her classroom. If students meet expectations for behavior, they are allowed to draw slip of paper without looking. The slips are all equal size, well mixed, and have the name of a prize written on them. Here is the probability model for the prizes a student can win:
The requried solutions are,
(A) The given probability model represents all the possible probabilities between 0 and 1.
(B) The probability that a student won't win extra recess time is 0.95.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
here,
(a)
The given probability model represents all the possible probabilities between 0 and 1, probabilities add up to 1.
(b)
The probability that a student won't win extra recess time is given as,
= 1 - p[student will win extra recess time]
= 1 - 0.05
= 0.95
Thus, the requried solutions are given above.
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How do you dilate a triangle with a scale factor of 2 3?
The basic formula to find the scale factor of a dilated figure is: Scale factor = Dimension of the new shape ÷ Dimension of the original shape.The dilation o a triangle with a scale factor of 2 3 represents a contraction.
How to Dilate a triangle with a scale factor ?
The scale factor is defined as the proportion of the new image's size to that of the previous image. A fixed location in the plane serves as the centre of dilatation. The scale factor and the centre of dilation are used to determine the dilation transformation.
The image stretches if the scaling factor is greater than 1.The image contracts if the scale factor is between 0 and 1.The original image and the resulting image are consistent if the scale factor is 1.Finding the dilation's centre point is the first step in determining the scale factor. Next, we measure the distances between the centre point and various points on the preimage and the image. According to Math Bits Notebook, the scale factor is equal to the ratio of these distances.
Since each angle is congruent, every segment is proportional, the slope of every segment is preserved, and the perimeter of the preimage and image have the same scale factor, we may use dilation scale factors to compress or enlarge a figure to the size we desire.
Dilate a triangle with a scale factor
Assume that the coordinate plane's centre of dilation is at (0, 0) at the origin. Every coordinate point of the original triangle is multiplied by the scale factor 2/3 if the scale factor is 2/3. multiplying by half after a scale factor of two.
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Need the answer to the problem below.
((7 * 4) ^ 8) ^ 10 =
Answer:
Here is your answer
((7 * 4) ^ 8) ^ 10 =
(28 ^ 8) ^ 10 =
377801998336 ^ 10 = 59243745466425005914454309773057597308923913133540598788947321202681255877119822027605832529210827998599338289790976
Step-by-step explanation:
Given: PR bisects ZQPS, PQ = 12 units, and PS= 12 units
Prove: QR
SR
P
S
How could you show QR SR?
OA.
OB.
O C.
R
OD.
Use AAS to show triangle PRQ is congruent to triangle PRS
Use SAS to show triangle PRQ is congruent to triangle SRP
Use SAS to show triangle PRQ is congruent to triangle PRS
Use ASA to show triangle PRQ is congruent to triangle PRS
From the AAS to triangle PRQ is congruent to triangle PRS. The correct option is A.
what is the triangle?A triangle, which is a polygon, has three sides and three vertices. One of geometry's basic shapes is it. A triangle with the vertices A, B, and C is referred to as Triangle ABC.
When the three points are not collinear, Euclidean geometry reveals a singular plane and triangle. A triangle is a type of polygon because it has three sides and three corners. The three sides' end-to-end intersections are referred to as the triangle's corners. The sum of the three triangle angles is 180 degrees.
Given
PQ = 12 units and PS = 12 units, with PR dividing ZQPS.
OA validates AAS's triangular display. The triangle is consistent with PRQ. Triangle is shown by SAS thanks to PRS OC. The triangle is consistent with PRQ. SEP
Every matching portion of one triangle is congruent to the other if two triangles are congruent.
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What are 4 ways to increase profit?
There are 4 ways to increase profit: Cost-cutting, increased turnover, productivity gains, and efficiency gains are among them.
What causes profit to increase?Businesses can raise revenues by selling more products or services, raising pricing, or some combination of these to enhance net margin. By lowering expenses, businesses may boost their net margin (e.g., finding cheaper sources for raw materials).
Developing and securing healthy revenues depends on strong customer connections. Customers should be matched to relationships, relationship migration pathways should be established to further integrate major accounts, and marketing should take the lead in all of these areas. Relationships should range from arm's length to deeply integrated.
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What is the easiest way to find the center of dilation?
The center point of the dilation is located, and the distances between this center point and various points on the preimage and the image are measured in order to determine the scale factor for the dilation. According to Math Bits Notebook, we can determine the scale factor by dividing these distances by two.
How To Find The Scale Factor Of A Dilation?The center point of the dilation is located, and the distances between this center point and various points on the preimage and the image are measured in order to determine the scale factor for the dilation. According to Math Bits Notebook, we can determine the scale factor by dividing these distances by two.Given that each angle is congruent, each segment is proportional, the slope of each segment is preserved, and the perimeter of the preimage and image have the same scale factor, using dilation scale factors allows us to enlarge or reduce a figure to the desired size.The following operations will then be covered in detail for you to perform:To transform, ascertain the scaling factor.What kind of dilatation is it?Assign a scale factor to the dilatation.Two dilated figures should have a perimeter ratio.To Learn more About dilation refer To:
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(3x³x+4) /(x − 2)
Help
Answer:
3x^4 + 4 / x - 2
Step-by-step explanation:
(3x³x+4) /(x − 2)
3(x ⋅ x^3) + 4 / x - 2
3x^4 + 4 / x - 2
We can't simplify anymore, so the answer is 3x^4 + 4 / x - 2
Joephine wrote the number 1-100 and placed them in a bag. If he elect a number without looking what i the probability that the number i greater than 78
The probability that the number is greater than 78 is 22/100 or 22%.
1. There are a total of 100 numbers in the bag.
2. Out of the 100 numbers, 78 are less than 78.
3. Therefore, there are 22 numbers that are greater than 78.
4. The probability of selecting a number greater than 78 is 22/100 or 22%.
Josephine wrote the numbers one to one hundred and placed them in a bag. If he randomly selects a number without looking, what is the probability that the number is greater than seventy-eight? The probability that the number is greater than seventy-eight is twenty-two out of one hundred, or twenty-two percent. This is because there are a total of one hundred numbers in the bag, and out of those one hundred numbers, seventy-eight are less than seventy-eight. Therefore, there are twenty-two numbers that are greater than seventy-eight. The probability of selecting a number greater than seventy-eight is twenty-two out of one hundred, or twenty-two percent.
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Dave says:
The only quadrilateral with 4 right angles is a rectangle.
Is Dave correct?
EXPLAIN YOUR ANSWER
No, Dave is not correct. The quadrilateral with 4 right angles is a rectangle as well as square.
Define the properties of rectangle and square?Square: 4 equal sides, four internal right angles, plus four vertices make up the flat, two-dimensional (2D) shape known as a square.
Specifications of a Square
The lengths of a square's four sides are all equal.A square's internal angles are all 90°.A square's diagonals are parallel to one another.A square has equal-length diagonals that cut each other in half.Rectangle: A rectangle is indeed a two-dimensional form with equal lengths on both sides. It has four vertices and four equal angles. A rectangle's four angles are all 90° in angle.
Rectangle's Qualities:
A rectangle's opposing sides are equal as well as parallel to one another.A rectangle has only 90° inside angles.A rectangle has equal-length diagonals that cut each other in half.To know more about the rectangle and square, here
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Trisha and Byron are washing and vacuuming cars to raise money for a class trip. Trisha raised $38 by washing
5 cars and vacuuming 4 cars. Byron raised $28 by washing 4 cars and vacuuming 2 cars. Find the amount they
charged to wash a car and vacuum a car.
Answer:
Step-by-step explanation:
Let x = amount charged for washing a car
y = amount charged for vacuuming a car
Solution :38 = 5x + 4y (1)
28 = 4x + 2y (2)
Can be solved by substitution or simply subtracting the (1) and (2) equation.
By Substitution:
38 = 5x + 4y ---> solve for x
38 - 4y = 5x (transposed 4y to the other side of the equation and it's sign changes from (+) to (-).
[tex]\frac{38-4y}{5} =x[/tex]
substitute the value of x to the (2) equation.
28 = 4x + 2 y
[tex]28=4(\frac{38-4y}{5})+2y[/tex]
[tex]28=\frac{152-16y}{5} +2y[/tex] , then multiply both side by 5 to eliminate the denominator 5.
140 = 152 - 16y + 10y (transposed 152 to the other side, change sign from (+) to (-)).
140 - 152 = -16y + 10 y
-12 = -6y (divide both side by (-6)
y = 2 or $2 (amount charged for vacuuming)
Using any of the 2 equation, we can solve for the value of x.
38 = 5x + 4 (2) (we substitute, the value of y)
38 - 8 = 5x
30/5 = x
x= 6 or $6 (amount charged for washing)
A 4 cylinder engine with 543 cubic centimeters has what approximate displacement.
543 cubic centimeters has 0.543 L approximate displacement
Engine displacement means the displacement of the piston inside cylinder from Bottom Dead Center into Top Dead Center in one cycle.
Basic formula to calculate engine displacement is
V = π/4 x [tex]D^{2}[/tex] x H x N
Where :
D = Bore Diameter
H = Length of Stroke
N = Number of Cylinder
Since the question has already stated cubic centimeter, it has already show the displacement. So, we can ignore above formula and the 4 cylinder engine information.
First, we state what is known. It is the displacement at cubic centimeter
Cubic centimeter = 543 cc
Next, we change the unit of cubic centimeter ( cc ) into liter ( L )
Displacement = cc / 1000 L
= 543 / 1000 L = 0.543 L
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Can you help me answer this question ?
Answer:
2
Step-by-step explanation:
Since k= -5/2 then -k is the opposite sign or 5/2
5/2 + 3/2 = 8/2
8/2 = 4
4 + (-2) is the same as 4-2
4-2 = 2
Answer: 2
Answer: 2
Step-by-step explanation:
The value of K is given as -5/2, so let's use it to solve the equation.
When you substitute -5/2 for k, you'll get
3/2+5/2-2 = 4-2=2
Therefore, the answer is 2.
In a company, 60 %
of the workers are women . If
This gives us a total of 1,333 male workers in the company.
What is data in mathematics?Data in mathematics is information that is used for analysis. It is typically presented in a structured format such as a table or graph and can be used to draw conclusions and make predictions. Data can come from a variety of sources, including surveys, experiments, observations, and simulations. Data can be quantitative or qualitative, and can be used to describe relationships between variables or to compare different sets of data. Data is an important tool in mathematics, as it allows us to draw conclusions from information and make decisions based on evidence.
The number of male workers in the company would be 1,333. To calculate this, we can first calculate the total number of workers in the company by multiplying the total number of female workers (800) by 100 and then dividing the result by 60 (the percentage of male workers).
This gives us a total of 1,333 male workers in the company.
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Complete questions as follows-
In a company, 60 % workers are males. If the number of female workers in the company is 800, what is the number of male workers in the company?
If a car lot 3600 in depreciation in the firt year. What i the original cot of thi car?
The original cost of the car would be the total depreciation plus the cost of the car after one year. So, the original cost of the car would be 3600 + (the cost of the car after one year).
1. Calculate the total depreciation for the year: 3600
2. Add the total depreciation to the cost of the car after one year: 3600 + (cost of the car after one year)
3. The answer is the original cost of the car: (3600 + (cost of the car after one year))
The original cost of the car would be the total depreciation plus the cost of the car after one year. So, the original cost of the car would be 3600 + (the cost of the car after one year).
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Find the mean of the life spans of the farm animals.
Farm Animal Life Span
chicken
duck
horse
pig
sheep
COW
goat
7 years
10 years
22 years
10 years
12 years
10 years
12 years
OA. 10 years
OB. 11.9 years
O C. 12 years
OD. 15 years
Answer:
Step-by-step explanation:
The mean would be 11.857142857143 , so basically 11.9
The mean life span of the given farm animals is approximately 11.9 years, obtained by adding up all the individual life spans and dividing the total by the number of animals.
Explanation:The question asks for the mean, or average, of the life spans of various farm animals. Here's how we calculate it:
Add up all the individual life spans: 7 (chicken) + 10 (duck) + 22 (horse) + 10 (pig) + 12 (sheep) + 10 (cow) + 12 (goat) = 83 years.Divide the total by the number of animals (7 in this case): 83 ÷ 7 = 11.857 years, rounded to the nearest tenth.Therefore, the mean life span of these farm animals is approximately 11.9 years, which corresponds to option B.
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1. Which polygon or polygons are regular? (2 points)
Answer: 1st, 2nd, and 3rd
Step-by-step explanation: the last one isn't because not all of the sides are the same length
What is the book entitled "applied regression analysis and other multivariable methods" about?
Answer:This bestseller will help you learn regression-analysis methods that you can apply to real-life problems. It highlights the role of the computer in contemporary statistics with numerous printouts and exercises that you can solve using the computer.
Step-by-step explanation: