To determine the values of A and B, we can use the following system of equations: 1. 5A = -15 2. -2A + B = 10 This system of equations can be used to find the values of A and B.
To review the equation used in writing a partial fraction decomposition, we start with a fraction that has a denominator that can be factored into linear or quadratic factors. The partial fraction decomposition separates the fraction into a sum of simpler fractions, each with a single linear or quadratic factor in the denominator.
The equation you provided for partial fraction decomposition is:
StartFraction negative 15 x + 10 Over (5 x minus 2) squared EndFraction = StartFraction A Over 5 x minus 2 EndFraction + StartFraction B Over (5 x minus 2) squared EndFraction
This equation shows that the original fraction can be decomposed into two simpler fractions, one with a linear factor of (5x - 2) in the denominator (A/(5x - 2)), and one with a quadratic factor of (5x - 2)² in the denominator (B/(5x - 2)²).
To determine the values of A and B, we need to solve for them using a system of equations. In this case, we can use the coefficients of x in the numerator of each fraction to create the following system of equations:
5A = -15
-2A + B = 10
We get the first equation by setting the numerator of the first fraction (A/(5x - 2)) equal to -15x + 10, and the second equation by setting the numerator of the second fraction (B/(5x - 2)²) equal to -15x + 10 and subtracting the first equation from it.
Solving this system of equations gives us:
A = -3
B = 5
Therefore, the partial fraction decomposition of the original fraction is:
StartFraction negative 15 x + 10 Over (5 x minus 2) squared EndFraction = StartFraction -3 Over 5 x minus 2 EndFraction + StartFraction 5 Over (5 x minus 2) squared EndFraction
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Can anyone tell me the coordinates of this graph?
In a survey conducted by a retail store, 58% of the sample respondents said they prefer to shop at places with loyalty cards.
96
If the margin of error is 3. 4%, the expected population proportion that prefers to shop at places with loyalty cards is between
and
%.
The expected population proportion, with 95% confidence, that prefers to shop at places with loyalty cards is between 54.6% and 61.4%.
Based on the survey results, we know that 58% of the sample respondents prefer to shop at places with loyalty cards. If the margin of error is 3.4%, we can calculate the expected range of the population proportion as follows:
Upper bound: 58% + 3.4% = 61.4%
Lower bound: 58% - 3.4% = 54.6%
Therefore, we can say with 95% confidence that the expected population proportion that prefers to shop at places with loyalty cards is between 54.6% and 61.4%.
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1. write the equation for each line that passes through (1, 2) and has a) slope 2/3 b) undefined slope c) m = 0 d) point (2, 3) also on the line
The equation of the line that passes through (1, 2) and (a) having a slope of 2/3 is y = (2/3)x + 4/3, (b) Having an undefined slope is x = 1, (c) having slope m = 0 is y = 2 (d) point (2, 3) also lies on the line is y = x + 1.
a) To find the equation of a line with slope 2/3 passing through (1,2), we can use the point-slope formula:
y - y1 = m(x - x1)
Substituting in the values we know, we get:
y - 2 = (2/3)(x - 1)
Expanding and simplifying:
y = (2/3)x + 4/3
So the equation of the line is y = (2/3)x + 4/3.
b) To find the equation of a line with an undefined slope passing through (1,2), we know that this line must be vertical. The equation of a vertical line passing through (1,2) can be written as:
x = 1
So the equation of the line is x = 1.
c) To find the equation of a line with slope m=0 passing through (1,2), we know that this line must be horizontal. The equation of a horizontal line passing through (1,2) can be written as:
y = 2
So the equation of the line is y = 2.
d) To find the equation of a line passing through (1,2) and (2,3), we can use the point-slope formula again:
y - y1 = m(x - x1)
Substituting in the values we know, we get:
y - 2 = (3 - 2)/(2 - 1)(x - 1)
Simplifying:
y - 2 = 1(x - 1)
y - 2 = x - 1
y = x + 1
So the equation of the line is y = x + 1.
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Duncan's favorite park just added a statue of a badger, the state animal. The statue sits on a base shaped like a rectangular prism. The base is 5 feet long, 3 feet wide, and has a volume of 60 cubic feet. How tall is the base of the statue? Write your answer as a whole number or decimal. Do not round. PLEAS HELP â
LOL NVM
The height of the base of the statue, structured in rectangular prism shape with stated measure of dimension is 4 feet.
The volume of the rectangular prism will be given by the formula -
Volume = length × width × height
Keep the values in formula to find the value of height of the base of the statue
60 = 5 × 3 × height
Rearranging the equation in terms of height
Height = 60 × (5 × 3)
Multiplying the denominator on Right Hand Side
Height = 60/15
Divide the values
Height = 4
Hence the height is 4 feet.
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Which of the following quadratics would NOT have zeros that are 5 and -7?
(1) y= (x + 12-36
(3) y = x2 + 2x - 35
(2) y = (× + 5)(x - 7)
(4) y = 2(× + 7)(× - 5)
The quadratics that would not have 5 and -7 as zeros are (1) and (3)
Identifying the quadratics that would not have 5 and -7 as zeros?From the question, we have the following parameters that can be used in our computation:
Zeros: 5 and -7
This means that
x = 5 and x = -7
Rewrite as
x - 5 = 0 and x + 7 = 0
Multiply both equation
This gives
(x - 5)(x + 7) = 0
Rewrite as
f(x) = (x - 5)(x + 7)
When expanded, we have
f(x) = x² + 2x - 35
So, we have
(2) f(x) = x² + 2x - 35
(4) f(x) = 2(x + 7)(x - 5)
Hence, the quadratics that would not have 5 and -7 as zeros are (1) and (3)
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Among college students who hold part-time jobs during the school
year, the distribution of the time spent working per week is approximately normally distributed with a
mean of 20. 20 hours and a standard deviation of 2. 6 hours. Find the probability that the average time
spent working per week for 18 randomly selected college students who hold part-time jobs during the
school year is
a. Not within 1 hour of the population mean
b. 20. 0 to 20. 5 hours
c. At least 22 hours
d. No more than 21 hours
The z scοre is negative the actual probability would be
1-0.7995 = 0.2005
What is the probability?
A number that expresses hοw likely it is that an event will occur is called the probability of οccurrence. It is written as a number from 0 to 1, or frοm 0% to 100%, in percentage notation. The probability of an event occurring increases with probability.
here,
mean = 20.20
standard deviatiοn = 2.60
we knοw that,
Z scοre = (X-mean)/standard deviation
fοr X = 18:
Z scοre = (18-20.20)/2.6 = -0.8461
nοte that the z score is negative because the measured value is less than the mean value.
fοr Z score 0.8461 probability is 0.7995
and since the z scοre is negative the actual probability would be
1-0.7995 = 0.2005
a. For nοt within 1 hour of the population mean
We apply the formula here and we get the value οf P.
P(19.20>x>21.20) = P(19.20-20.20/2.60√18) > X-μ/σ√n >21.20-20.20/2.60√18
P(19.20>x>21.20) = P(-1.63>z>1.63)
Now, we find the value οf z.
P(19.20>x>21.20) = P(z>1.63) + P(z<-1.63)
P(19.20>x>21.20) = 0.0516 + 0.0516
P(19.20>x>21.20) = 0.1032
b. Fοr 20. 0 to 20. 5 hours
P(20<x<20.5) = P(20-20.20/2.60√18) < X-μ/σ√n<20.50-20.20/2.60√18
P(20<x<20.5) = P(-0.33<z<0.49)
Nοw, we find the value of the z-score and we get
P(20<x<20.5) = P(z<0.49) - P(z<-0.33)
P(20<x<20.5) = 0.6879 - 0.2707
P(20<x<20.5) = 0.3172
c. Fοr at least 22 hours
We apply the t-test fοrmula here and we get
P(x≥22) = P(X-μ/σ√n≥22-20.20/2.60√18)
Nοw, we find the value of z.
P(x≥22) = P(z≥2.94)
P(x≥22) = 0.0016
d. Fοr not more than 21 hours.
P(x<21) = P(X-μ/σ√n<21-20.20/2.60√18)
We find here the value οf P for x<21 and we get
P(x<21) = P(z<1.31)
Now, we find the value οf the z- score.
P(x<21) = 0.9049
Hence, a. 0.1032
b. 0.3172
c. 0.0016
d. 0.9049
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Complete question is,
Among college students who hold part-time jobs during the school year, the distribution of the time spent working per week is approximately normally distributed with a mean of 20.20 hours and a standard deviation of 2.60 hours. Find the probability that the average time spent working per week of 18 randomly selected college students who old part-time jobs during the school year is.
Two circles, C1 and C2, intersect at point A and B. Passes through the center O of circle C2. The point P lies on circle C2 so that the line PAT is target to circle Ci and point A. Let ∠APB =.
The value of ∠APB = 180°. It is a straight line.
Given the information, we can deduce that the line passing through the center O of circle C2 and point A also passes through point B, as AB is the intersection of the two circles.
Now, consider the line segment AP. Since PAT is tangent to circle C1 at point A, we know that ∠APT = 90°. Additionally, since AB is a diameter of circle C1, we know that ∠ABP = 90°.
Using these angles, we can see that ∠APB is equal to the sum of ∠APT and ∠ABP. Therefore,
∠APB = ∠APT + ∠ABP = 90° + 90° = 180°.
So, we have shown that ∠APB is a straight line.
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Let z be a random variable with a standard normal distribution. Find the indicated probability. (Enter a number. Round your answer to four decimal places. )
P(z ≥ 1. 41) =
If you let z be a random variable with a standard normal distribution, the indicated probability is 0.0793. So, the probability P(z ≥ 1.41) = 0.0793
To find the probability P(z ≥ 1.41) for a standard normal distribution, you can use a Z-table or calculator to find the area to the right of z = 1.41.
Using a Z-table or calculator, you will find the value of P(z ≥ 1.41) is approximately 0.0793. So, the probability P(z ≥ 1.41) = 0.0793. Remember to round your answer to four decimal places.
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Rectangular prism
Your cousin is building a sandbox for his daughter.
How much sand will he need to fill the box? Explain.
How much paint will he need to paint all six surfaces of the sandbox? Explain.
and dont forget to explain
The formula to calculate surface area is 2(Length × Width) + 2(Length × Height) + 2(Width × Height) and the length, width, and height of the sandbox is required to calculate rectangular area.
To determine how much sand your cousin will need to fill the rectangular prism-shaped sandbox, we first need to calculate its volume. To do this, we need the dimensions of the sandbox (length, width, and height). The formula for the volume of a rectangular prism is:
Volume = Length × Width × Height
Once we have the volume, we can determine the amount of sand needed to fill the sandbox in cubic units.
To find out how much paint is needed to paint all six surfaces of the sandbox, we need to calculate its surface area. The formula for the surface area of a rectangular prism is:
Surface Area = 2(Length × Width) + 2(Length × Height) + 2(Width × Height)
Once we have the surface area, we can determine the amount of paint required, usually measured in square units. Note that the amount of paint needed also depends on the coverage rate of the paint, which is typically listed on the paint container.
Please provide the dimensions of the sandbox (length, width, and height) so I can provide specific calculations for the sand and paint required.
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I need help with these questions pls
Volumes of the cylinder are given by:
(A) (1) Volume = 2486.88 cubic in.
(2) Volume = 108518.4 cubic ft.
(3) Volume = 47608.68 cubic yd.
(B) (4) Volume = 508.68 cubic ft.
(5) Volume = 8490.56 cubic yd.
(6) Volume = 43407.36 cubic in.
(7) Volume = 9420 cubic ft.
(8) Volume of cylindrical flower vase = 1105.28 cubic in.
Surface Area of the Cylinder are given by:
(1) Surface Area = 113.04 square in.
(2) Surface Area = 1444.4 square ft.
(3) Surface Area = 678.24 square yd.
(4) Surface Area = 1130.4 square yd.
(5) Surface Area = 602.88 square in.
(6) Surface Area = 1055.04 square ft.
(7) Surface Area = 1570 square ft.
(8) Surface Area = 791.28 square yd.
(9) Surface Area = 326.56 square in.
We know that the volume of a cylinder with radius 'r' and height 'h' is given by,
V = 2πr²h
(A) (1) From the figure, radius = 6 in and height = 11 in.
So the volume = 2π(6)²*11 = 2486.88 cubic in.
(2) Radius = 24 ft. and height = 30 ft.
Hence, the volume of cylinder = 2π(24)²*30 = 108518.4 cubic ft.
(3) Radius = 19 yd. and height = 21 yd.
Hence, the volume of cylinder = 2π(19)²*21 = 47608.68 cubic yd.
(B) (4) Radius = 3 ft. and height = 9 ft.
Hence, the volume of cylinder = 2π(3)²*9 = 508.68 cubic ft.
(5) Radius = 13 yd. and height = 8 yd.
Hence, the volume of cylinder = 2π(13)²*8 = 8490.56 cubic yd.
(6) Radius = 16 in. and height = 27 in.
Hence, the volume of cylinder = 2π(16)²*27 = 43407.36 cubic in.
(7) Radius = 10 ft. and height = 15 ft.
Hence, the volume of cylinder = 2π(10)²*15 = 9420 cubic ft.
(8) Cylindrical flower vase is 11 inch tall and radius of vase is 4 inches.
The volume of flower vase = 2π(4)²*11 = 1105.28 cubic in.
Now we know that the surface area of a Cylinder with radius 'r' and height 'h' is given by,
S = 2πrh + 2πr²
(1) Radius = 2 in. and Height = 7 in.
Hence the surface area = 2π*2*7 + 2π(2)² = 113.04 square in.
(2) Radius = 10 ft. and Height = 13 ft.
Hence the surface area = 2π*10*13 + 2π(10)² = 1444.4 square ft.
(3) Radius = 6 yd. and Height = 12 yd.
Hence the surface area = 2π*6*12 + 2π(6)² = 678.24 square yd.
(4) Radius = 9 yd. and Height = 11 yd.
Hence the surface area = 2π*9*11 + 2π*9² = 1130.4 square yd.
(5) Radius = 6 in. and Height = 10 in.
Hence the surface area = 2π*6*10 + 2π(6)² = 602.88 square in.
(6) Radius = 8 ft. and Height = 13 ft.
Hence the surface area = 2π*8*13 + 2π(8)² = 1055.04 square ft.
(7) Radius = 10 ft. and Height = 15 ft.
Hence the surface area = 2π*10*15 + 2π(10)² = 1570 square ft.
(8) Radius = 6 yd. and Height = 15 yd.
Hence the surface area = 2π*6*15 + 2π(6)² = 791.28 square yd.
(9) Radius = 4 in. and Height = 9 in.
Hence the surface area = 2π*4*9 + 2π(4)² = 326.56 square in.
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The amount of money earned over a period of time is called
1. Asset
2. Fixed expense
3. Income
4. Liability
5. Net worth
6. Variable expense
The amount of money earned over a period of time is called 3. Income
Income refers to the money you receive from various sources such as salary, wages, investments, or any other means during a specific period of time.
Income is a fundamental concept in finance and accounting. It represents the inflow of money or economic benefits received by an individual, household, or organization.
It is typically measured and reported on a periodic basis, such as monthly, quarterly, or annually. Income can be derived from various sources, including salaries and wages, interest and dividends, rental income, profits from business activities, and capital gains.
It is an essential component in assessing an individual's or organization's financial health and is often used to calculate taxes, budgeting, and determining net worth. Understanding and effectively managing income is crucial for individuals and businesses to meet their financial goals and sustain their economic well-being.
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Kira had 3/5 acres land she planted 3/7 of it with corn. How many acres did she plant with corn?
Kira planted 9/35 acres with corn.
If Kira planted corn on 3/7 of her land total of 3/5 acres, what is the area she planted with corn?To find out how many acres planted with corn, we first need to understand that the total amount of land she had was 3/5 acres. Then, we know that she planted 3/7 of her land with corn.
To calculate the area planted with corn, we multiply the total area of her land (3/5 acres) by the fraction that represents the portion she planted with corn (3/7). This gives us:
(3/5) x (3/7) = 9/35 acres
Therefore, Kira planted 9/35 acres of her land with corn.
We can simplify the fraction by dividing both the numerator and the denominator by their greatest common factor, which is 3 in this case. This gives us:
(9/3) / (35/3) = 3/11 acres
So, Kira planted approximately 0.26 acres with corn.
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How much more popcorn does the bigger box hold than the smaller box?
\text{cm}^3cm 3
start text, c, m, end text, cubed
\text{Amanda's popcorn container:}Amanda’s popcorn container:start text, A, m, a, n, d, a, apostrophe, s, space, p, o, p, c, o, r, n, space, c, o, n, t, a, i, n, e, r, colon, end text
\text{Mary's popcorn container:}Mary’s popcorn container:start text, M, a, r, y, apostrophe, s, space, p, o, p, c, o, r, n, space, c, o, n, t, a, i, n, e, r, colon, end text
The amount of popcorn the bigger box holds than the smaller box depends on the dimensions of the two containers, so it cannot be determined without additional information.
The difference in the amount of popcorn the two containers hold depends on the volume of each container. Let's assume the volume of Amanda's popcorn container is V1 and the volume of Mary's popcorn container is V2.
If we know the dimensions of both containers, we can calculate their volumes using the formula V = l × w × h, where l is the length, w is the width, and h is the height of the container. Then, we can find the difference in the volumes of the two containers by subtracting V1 from V2.
However, the question does not provide any information about the dimensions of the two containers, so we cannot determine the difference in their volumes. Therefore, the main answer is that the amount of popcorn the bigger box holds than the smaller box cannot be determined without additional information.
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Probability of a pair of dice landing on a 4 and on a 6
Answer:
1/3
Step-by-step explanation:
It would be 2 options out of 6 total which means 2/6. 2/6 reduces down to 1/3
Which ones are solutions to
7x+4y=-23
(-1,-4)
(2,6)
(-5,3)
(6,-7)
Hello!
In this question, we are asked to find which set of points are solutions to our equation: 7x + 4y = -23
In order to find which points are solutions to our equation, we will plug the values into our equation and solve. If both sides of the equation are equal, the point will be a solution.
Note: Our coordinate point is in the format of (x,y), so we will plug in the values according to its variable.
Solve:
(-1,-4):
Plug in coordinate.
7(-1) + 4(-4) = -23
Simplify.
-7 - 16 = -23
-23 = -23
Since it is equal, (-1,-4) is a solution.
(2,6):
Plug in coordinate.
7(2) + 4(6) = -23
Simplify.
14 + 24 = -23
38 = -23
Since it is not equal, making it false, (2,6) is not a solution.
(-5,3):
Plug in coordinate.
7(-5) + 4(3) = -23
Simplify.
-35 + 12 = -23
-23 = -23
Since it is equal, (-5,3) is a solution.
(6,-7):
Plug in coordinate.
7(6) + 4(-7) = -23
Simplify.
42 - 28 = -23
14 = -23
Since it is not equal, making it false, (6,-7) is not a solution.
Answer:
The solutions to the equation are: (-1,-4) and (-5,3).
What was the average amount of books read per student according to the histogram below?
The average amount of books read per student according to the histogram is given as follows:
1.27 books.
How to calculate the mean of a data-set?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.
The histogram shows the number of times for each observation, hence:
7 students read zero books.9 students read one book.6 students read two books.4 students read three books.Hence the mean is calculated as follows:
M = (7 x 0 + 9 x 1 + 6 x 2 + 4 x 3)/(7 + 9 + 6 + 4) = 1.27 books.
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Ayana played Super Star Quest, a video game that involves collecting stars and spending them on power-ups. At the end of each level, the game showed Ayana how many stars she had. Ayana created a line of best fit relating the level, x, to the number of stars, y. The equation for the line of best fit is y= 3 2 x–1. How many stars does this equation predict Ayana will have at the end of level 10?
There would be 14 stars that this equation predicts Ayana will have at the end of level 10.
In this question, we are given an equation for the line of best fit relating the level, x, to the number of stars, y. The equation is y = (3/2)x - 1.
To find the predicted number of stars at the end of level 10, we need to substitute x = 10 into the equation and solve for y.
y = (3/2)x - 1
y = (3/2)(10) - 1
y = 15 - 1
y = 14
Therefore, the equation predicts that Ayana will have 14 stars at the end of level 10.
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A savings account balance is compounded annually. if the interest rate is 2% per year and the current balance is $1430.00 what will the balance be 8 years from now
Answer:
A = P(1 + r/n)^(nt)
Where:
A = the future balance
P = the present balance ($1430.00)
r = the annual interest rate (2% or 0.02)
n = the number of times the interest is compounded per year (since it's compounded annually, n = 1)
t = the number of years (8 years in this case)
Plugging in the values into the formula:
A = 1430(1 + 0.02/1)^(1*8)
Simplifying the equation:
A = 1430(1.02)^8
Using a calculator or performing the calculations manually:
A ≈ 1430(1.171661)
A ≈ 1674.02
the balance after 8 years will be approximately $1674.02.
The total distance in d,in meters, traveled by an object moving in a straight line can be modeled by a quadratic function that is defined in terms of t, is the time in seconds. At a time of 10. 0 seconds the total distance is traveled by the objects is 50. 0 meters and at a time of 20. 0 seconds the total distance traveled by the object is 200. 0 meters if the object was at a distance of 0 meters when t=0 then what is the total distance traveled in meters, by the object after 30. 0 seconds
Let's denote the total distance traveled by the object as `d` and time as `t`.
We can use the given information to set up a system of equations:
When t = 10.0 seconds, d = 50.0 meters
50.0 = a(10.0)^2 + b(10.0) + c (Equation 1)
When t = 20.0 seconds, d = 200.0 meters
200.0 = a(20.0)^2 + b(20.0) + c (Equation 2)
When t = 0 seconds, d = 0 meters
0 = a(0)^2 + b(0) + c (Equation 3)
Simplifying Equation 3, we get c = 0.
Substituting c = 0 in Equations 1 and 2, we get:
50.0 = 100a + 10b (Equation 4)
200.0 = 400a + 20b (Equation 5)
We can solve Equations 4 and 5 simultaneously to get the values of `a` and `b`:
From Equation 4, we get:
10b = 50 - 100a
b = 5 - 10a
Substituting this value of `b` in Equation 5, we get:
200.0 = 400a + 20(5 - 10a)
200.0 = 400a + 100 - 200a
200.0 = 200a + 100
100.0 = 200a
a = 0.5
Substituting this value of `a` in Equation 4, we get:
50.0 = 100(0.5) + 10b
50.0 = 50 + 10b
b = 0
Therefore, the quadratic function that models the total distance traveled by the object is:
[tex]d = 0.5t^2[/tex]
To find the total distance traveled by the object after 30.0 seconds, we can substitute `t = 30.0` in the above equation:
[tex]d = 0.5(30.0)^2[/tex]
d = 450.0 meters
Therefore, the object will travel a total distance of 450.0 meters after 30.0 seconds.
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X= 140×15²
write X as a product of powers of its prime factors
Answer:
X = 2² * 3² * 5³ * 7.
Step-by-step explanation:
140 = 2*2*5*7
15^2 = 3*5*3*5
So X = 2² * 3² * 5³ * 7
To find the prime factorization of X, we first need to simplify the expression.
140 × 15² = 140 × 225Now, we can factor 140 and 225 into their prime factors:
140 = 2² × 5 × 7225 = 3² × 5²So,
X = 140 × 225= (2² × 5 × 7) × (3² × 5²)We can now use the distributive property to multiply these factors together:
X = 2² × 3² × 5³ × 7Therefore, the prime factorization of X is:
Therefore, the prime factorization of X is:X = 2² × 3² × 5³ × 7Which equation matches the function shown in the graph?
Answer: C
Step-by-step explanation:
Josie had 12 beads on her necklace. Then she added b more beads. Write an expression that shows how many beads are on the necklace in all. please write a expression like b-12 or b+?
The expression that shows how many beads are on the necklace in all is:
b + 12.
What is expression?An expression in mathematics is a combination of numbers, variables, and/or operators that represents a mathematical relationship or quantity. It may contain constants, variables, coefficients, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Expressions are often used to describe or represent real-world situations, and can be simplified, evaluated, or manipulated using algebraic rules and properties.
In the given question,
To write an expression that shows how many beads are on Josie's necklace in all after adding b more beads:
Start with the initial number of beads on the necklace, which is 12.
To this, add the number of beads Josie added, which is b.
Combine the two terms to form the final expression: 12 + b.
Therefore, the expression that shows how many beads are on Josie's necklace in all after adding b more beads is 12 + b.
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Cause then you'd only get one answer to study.
Now back to the
a collection of facts,
Numbers, measurements and things like that.
conclusion
estimate
data
A collection of information, such as numbers, measurements, or observations, is commonly referred to as data.
Data can be collected from a wide variety of sources, such as surveys, experiments, or observations, and can be analyzed to reveal patterns, trends, and relationships.
Data can be represented in many different ways, including tables, graphs, charts, or statistical summaries, and can be used to make informed decisions in a wide range of fields, including business, science, healthcare, and social sciences.
However, it is important to ensure that the data is accurate, reliable, and unbiased, and that appropriate statistical methods are used to analyze and interpret it.
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Full Question: What is a collection of information such as number measurement or observation called?
Given l||m||n, find the value of x
Answer:
x = 13
Step-by-step explanation:
We Know
(5x - 6) + (8x + 17) must equal 180°
Find the value of x.
Let's solve
5x - 6 + 8x + 17 = 180
13x + 11 = 180
13x = 169
x = 13
So, the value of x is 13.
In ΔSTU, t = 3. 4 cm, u = 6. 9 cm and ∠S=21°. Find the area of ΔSTU, to the nearest 10th of a square centimeter.
4.20 cm² is the area of the triangle STU to the nearest 10th of a square centimeter.
Given, t = 3.4 cm, u = 6.9 cm and ∠S = 21°
We know that the formula for the area of the triangle = 1/2 * t*u *sin(S)
Substituting the values
Area = 1/2 × 3.4 × 6.9 × sin(21°)
Area = 11.73 × sin(21°)
Area = 11.73 × 0.3583
Area = 4.2016
Rounding to the nearest 10th of a square centimeter .
Area = 4.20 cm²
Hence, 4.20 cm² is the area of the triangle STU to the nearest 10th of a square centimeter.
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If m< a=3x and m< d=4x+6 what is the value of x?
Based on the given information that angles a and d are equal, the value of x is determined to be -6.
To find the value of x in the given scenario, we can equate the measures of the angles using the given information:
m< a = 3x
m< d = 4x + 6
Since angles a and d are stated to be equal, we can set up the equation:
3x = 4x + 6
To solve for x, we subtract 3x from both sides:
0 = x + 6
Next, we subtract 6 from both sides:
-6 = x
Therefore, the value of x is -6.
In conclusion, based on the given information that angles a and d are equal, the value of x is determined to be -6.
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3) Graph polygon G(-3,-2) R(-4,4) E(0,1) A(1, -2) T(-1, -3) and it’s image G’R’E’A’T’=R (GREAT)
A graph of polygon GREAT and its image after a counterclockwise rotation of 90° around the origin is shown in the image attached below.
What is a rotation?In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).
By applying a rotation of 90° counterclockwise around the origin to vertices W, the coordinates of the vertices of the image ΔA'B'C' are as follows:
(x, y) → (-y, x)
Ordered pair G = (-3, -2) → Ordered pair G' = (2, -3)
Ordered pair R = (-4, 4) → Ordered pair R' = (-4, -4)
Ordered pair E = (0, 1) → Ordered pair E' = (-1, 0)
Ordered pair A = (1, -2) → Ordered pair A' = (2, 1)
Ordered pair T = (-1, -3) → Ordered pair T' = (3, -1)
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A model airplane flew the distance of 330 feet in 15 seconds. Select ALL the unit rates that are equivalent to the speed of the model airplane.
All of the unit rates that are equivalent to the speed of the model airplane are 22 feet per second, 1320 feet per minute, and 0.25 miles per minute.
To calculate the speed of the model airplane, we need to use the formula:
Speed = Distance / Time
Given that the distance covered by the model airplane is 330 feet, and the time taken is 15 seconds, we can substitute these values in the above formula to get:
Speed = 330 feet / 15 seconds
Simplifying this, we get:
Speed = 22 feet per second
To convert this unit rate to other equivalent unit rates, we need to use conversion factors. For example, to convert feet per second to feet per minute, we can multiply the unit rate by 60 (since there are 60 seconds in a minute):
22 feet per second x 60 seconds per minute = 1320 feet per minute
Similarly, to convert feet per minute to miles per minute, we can use the conversion factor 1 mile = 5280 feet:
1320 feet per minute / 5280 feet per mile = 0.25 miles per minute
Therefore, all of the unit rates that are equivalent to the speed of the model airplane are 22 feet per second, 1320 feet per minute, and 0.25 miles per minute.
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Find the linear approximation for the following function at the given point. b. Use part (a) to estimate the given function value. f(x,y)= - 4x² + 2y² ; (3, -3); estimate f(3.1,- 3.01) a. L(x,y)= b. L(3.1, – 3.01)= (Type an integer or a decimal)
The estimate for f(3.1, -3.01) using the linear approximation is approximately -54.28.
a. To find the linear approximation of f(x,y) at the point (3,-3), we need to find the gradient of the function at that point.
∇f(x,y) = [-8x, 4y]
So, at the point (3,-3), the gradient is ∇f(3,-3) = [-24, -12].
The linear approximation is given by:
L(x,y) = f(3,-3) + ∇f(3,-3)·(x-3,y+3)
Plugging in the values, we get:
L(x,y) = -4(3)^2 + 2(-3)^2 - 24(x-3) - 12(y+3)
Simplifying, we get:
L(x,y) = -12x - 4y - 36
b. To estimate f(3.1, -3.01) using the linear approximation, we plug in the values into the equation we found in part (a):
L(3.1, -3.01) = -12(3.1) - 4(-3.01) - 36
L(3.1, -3.01) ≈ -54.28
Therefore, the estimate for f(3.1, -3.01) using the linear approximation is approximately -54.28.
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determine whether the function f(x) = a^x-a^(-x)+sinx is even or odd.
To determine whether the function f(x) = a^x-a^(-x)+sinx is even or odd, we need to check if it satisfies the properties of even and odd functions.
An even function is a function that satisfies the property f(x) = f(-x) for all x in the domain of the function. This means that if we reflect the graph of the function across the y-axis, we get the same graph.
An odd function is a function that satisfies the property f(x) = -f(-x) for all x in the domain of the function. This means that if we reflect the graph of the function across the origin (both x and y-axis), we get the same graph.
Let's start by checking whether f(x) is even:
f(-x) = a^(-x)-a^(x)+sin(-x) (since sin(-x) = -sin(x))
= -a^x+a^(-x)-sin(x)
Comparing f(-x) with f(x), we can see that f(-x) = -f(x) only when sin(x) = 0.
This means that f(x) is an even function only when sin(x) = 0, which occurs when x = nπ (where n is an integer).
Now, let's check whether f(x) is odd:
f(-x) = a^(-x)-a^(x)+sin(-x) (since sin(-x) = -sin(x))
= -a^x+a^(-x)-sin(x)
Comparing f(-x) with -f(x), we can see that f(-x) = -f(x) only when a^x = -a^x, which is not possible for any real value of a.
Therefore, f(x) is neither an even nor an odd function.
To determine whether the function f(x) = a^x - a^(-x) + sin(x) is even or odd, we can evaluate f(-x) and compare it to f(x).
An even function satisfies the condition f(-x) = f(x), while an odd function satisfies the condition f(-x) = -f(x).
Let's evaluate f(-x):
f(-x) = a^(-x) - a^(-(-x)) + sin(-x)
f(-x) = a^(-x) - a^x - sin(x)
Now, let's compare f(-x) to f(x):
f(-x) ≠ f(x) because f(x) = a^x - a^(-x) + sin(x)
f(-x) ≠ -f(x) because -f(x) = -a^x + a^(-x) - sin(x)
Since f(-x) is neither equal to f(x) nor -f(x), the function f(x) = a^x - a^(-x) + sin(x) is neither even nor odd.
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