Step-by-step explanation:
f(x} = 3x + 1
g(x} = 2x -- 3
f(g(x)) = 3x + 1. (Calm down right?)
Let the x in the expression be (2x -- 3)
N.B x = g{x}
f(g(x)) = 3(2x --3} + 1
Open bracket
f(g(x)) = 6x -- 9 + 1
f(g(x)) = 6x -- 8...
2... Solve for g(f(x)), using the same strategy
g(f(x)) = 2x -- 3
x = f(x)
g(f(x)) = 2(3x + 1) -- 3
g(f(x)) = 6x + 2 -- 3
g(f(x)) = 6x -- 1
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Answer:
Step-by-step explanation:
f(g(x)) means substituting g(x) in f(x)
ie, 3(2x-3)+1 = 6x-9+1 = 6x - 8
g(f(x)) means substituting f(x) in g(x)
ie, 2(3x+1)-3 = 6x2-3 = 6x - 1
please help me with question 19 please i really need the answer asap!! thanks!!
Answer:
D) 116
Step-by-step explanation:
Supplementary angles add up to 180°
∠CDE + ∠FDE = 180
3x + 10 + 6x + 8 = 180
3x + 6x + 10 + 8 = 180
Combine like terms,
9x + 18 = 180
Subtract 18 from both sides,
9x = 180 - 18
9x = 162
Divide both sides by 9
x = 162 ÷ 9
[tex]\sf \boxed{\bf x = 18}[/tex]
∠FDE = 6x + 8
= 6*18 + 8
= 108 + 8
= 116°
Automated manufacturing operations are quite precise but still vary, often with distribution that are close to Normal. The width in inches of slots cut by a milling machine follows approximately the N(0.97,0.001)
N(0.97,0.001) distribution. The specifications allow slot widths between 0.9698
0.9698 and 0.9702
What proportion of slots meet these specifications?
The proportion of slots who meet these specifications is 15.86%.
We are given that the width in inches of slots cut by a milling machine follows approximately the N(0.97,0.001) distribution.
Also, the specifications allow slot widths between 0.9698 and 0.9702
Let X = width in inches of slots cut by a milling machine
The z-score probability distribution for normal distribution is given by;
Z = (X - μ) /σ ~ N(0,1)
where, μ = population mean width = 0.97
σ = standard deviation = 0.001
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
Now, Probability that the specifications allow slot widths between 0.9698 and 0.9702 is given by = P(0.9698 < X < 0.9702)
= P(0.9698 < X < 0.9702) = P(X < 0.9702) - P(X 0.9698)
P(X < 0.9702) = P [(X - μ) /σ < [tex]\frac{0.9702 - 0.97}{0.001}[/tex]] = P (Z < 0.2) =
P(X ≤0.9698) = P [(X - μ) /σ ≤ [tex]\frac{0.9698 - 0.97}{0.001}[/tex] ] = P (Z ≤ -0.2) = 1- P(Z < 0.2)
= 1 - 5793 = 0.4207
So, in the z table the P(Z x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 0.2 in the z table which has an area of 0.5793.
Therefore, P(0.9698 < X < 0.9702) = 0.5793 - 0.4207 = 0.1586
Hence, the proportion of slots who meet these specifications is 15.86%.
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is 3/10 = 15/60 a equivalent ratios?
Answer: No.
Step-by-step explanation:
3 x 5 = 15,
but 10 x 5 = 50.
In order for the ratios to be equivalent, they would have to be written like this:
3/10 = 15/50
Therefore, it is not equivalent.
Hope this helps!
Diego and Stacy can paint a doghouse in 5 hours when working together. Diego works twice as fast as Stacy. Let x be the number of hours it would take Diego to paint the doghouse and y be the number
of hours it would take Stacy to paint the doghouse. How long would it take Stacy
to paint the doghouse if she was working alone? How long would it take Diego to paint the doghouse if he was working alone?
Please show steps!
If Stacy works alone, it will take her 11 hours 40 minutes to paint the doghouse.
If Diego works alone, it will take him 5 hours 40 minutes to paint the doghouse.
How to find how long would it take Stacy and Diego to paint the doghouse while working alonegiven data
Diego and Stacy can paint a doghouse in 5 hours
Diego works twice as fast as Stacy
Let x be the number of hours it would take Diego to paint the doghouse and y be the number
Putting the given information mathematically
Diego and Stacy can paint a doghouse in 5 hours
x + y = 5hoursDiego works twice as fast as Stacy
x = 2yx + y = 5hours
Since x = 2y
2y + y = 5
3y = 5
y = 5/3
y = 1 1/3
from x = 2y
x = 2 * 5/3
x = 10/3
x = 3 1/3
1/3 hours is a fraction of hours. we convert it to minutes by multiplying by 60
= 1/3 * 60
= 20 minutes
Therefore it will take Diego 3 hours 20 minutes and Stacy 1 hour 20 minutes for them to complete a 5 hours work
If Diego works alone
Diego alone = 5 hours + Stacy's hours * 1/2
since Diego is twice faster than Stacy then Stacy's time will be halved
Diego alone = 5 hours + 80 minutes * 1/2
Diego alone = 5 hours + 40 minutes
Diego alone = 5 hours 40 minutes
if Stacy works alone
Stacy alone = 5 hours + Diego's hours * 2
Stacy alone = 5 hours + 3 hours 20 minutes * 2
Stacy alone = 5 hours + 6 hours 40 minutes
Stacy alone = 11 hours 40 minutes
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The perimeter of an equilateral triangle is 17 inches more than the perimeter of a square, and the side of the triangle is 8 inches longer than the side of the square. Find the side of the triangle ( Hint: An equilateral triangle has three sides the same length.)
The side of the triangle is 15 inches.
How to find the perimeter of a triangle and square?The perimeter of an equilateral triangle is 17 inches more than the perimeter of a square, and the side of the triangle is 8 inches longer than the side of the square.
Hence,
let
perimeter of the square = x inches
perimeter of an equilateral triangle = x + 17
Let
side of the square = y
side of the triangle = 8 + y
Therefore,
Perimeter of the square
x = y + y + y + y
x = 4y
Perimeter of the triangle
x + 17 = 8 + y + 8 + y + 8 + y
x + 17 = 24 + 3y
x - 3y = 7
Combine the equation,
x = 4y
x - 3y = 7
Therefore,
4y - 3y = 7
y = 7
x = 4(7)
x = 28
Therefore,
side of the triangle = 8 + y = 8 + 7 = 15 inches
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Which expression is equivalent to −3(b − 7)?
Answer:
- 3b + 21
Step-by-step explanation:
- 3(b - 7) ← multiply each term in the parenthesis by - 3
= - 3b + 21
Answer:
-3(b-7) = -3b + 21
Find the measure of the missing angles.
Answer:
B = 95°C = 85°
Step-by-step explanation:
the angle C is the opposite angle to that of 85 degrees, therefore congruent, we subtract 85 x 2 ° from the sum of the angles (360 °, is a round angle) and find the sum of the other two angles, always opposite and increasing, divide by two and we have the value of the angle B
C = 85°
B = [360 - (85 * 2)] : 2
B = (360 - 170) : 2
B = 190 : 2
B = 95°
-----------------
check
85 + 85 + 95 + 95 = 360°
the answer is good
The cost to rent skis is $30 per hour plus a nonrefundable $25 deposit
A) Write an expression to rent skis for H hours
B)use the expression in part a to find the cost of renting skis for four hours
Answer:
A) 30 x ? = ? + 25 = ?.
B) 30 x 4 = 120. 120 + 25 = 145.
Answer: The answer is $145 to rent the skis for four hours.
Simplify each expression. Which expression is not equivalent to the other two?
A. 15j + 30
B. 5(3j - 6)
C. 3(5j - 10)
Answer: A is not equivalent to the other 2
Step-by-step explanation:
A. 15j+30
B. 5(3j-6) = 15j-30
C 3(5j-10) = 15j-30
multiply the stuff inside paranthesis for the last 2
So a is the outsider
A. Use the cartesian plate on the right to plot all the points.
Pt. A (-4, 3) pt. D (0, -3)
Pt. B (2, 5) pt. E (-5, -2)
Pt. C (5, -1)
[tex]__________________________[/tex]
Refer to the attachment for the answer
assume that the traffic to the web site of smiley’s people, inc., which sells customized t-shirts, follows a normal distribution, with a mean of 4.56 million visitors per day and a standard deviation of 720,000 visitors per day. (a) what is the probability that the web site has fewer than 5 million visitors in a single day? if needed, round your answer to four decimal digits
The probability that the web site has fewer than 5 million visitors in a single day is 0.7293.
For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.
First, solve for the z-score using the formula below.
z-score = (x – μ) / σ
where x = individual data value = 5 million
μ = mean = 4.56 million
σ = standard deviation = 720,000
z-score = (5 million - 4.56 million) / 720,000
z-score = 440,000 / 720,000
z-score = 0.6111
Find the probability that corresponds to the z-score in the z-table. (see attached images)
z-score = 0.6111
Using interpolation of values,
probability = 0.7293
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Numbers in front of variables
4a - 8b+ C
What's the coefficient for b in the above expression?
Answer
Submit
Answer:
- 8
Step-by-step explanation:
the coefficient is the numeric value, including the sign, in front of the variable.
4a - 8b + c
the coefficient of b is - 8
What value is equivalent to 2 × 3 + 4 − 62?
Answer:
-52
Step-by-step explanation:
I hope this helps!
Answer: -52
Step-by-step explanation: Using PEMDAS
(2x3)+4-62
6+4-62
10-62
= -52
Randy planted a small pine tree in his yard. When he bought the tree it was 6 inches tall and grew at a rate of 2 inches weekly. Write a function of height, h, in terms of weeks, w.Using the equation from problem #1 What will the height of the tree be in 13 weeks?
Answer:6+2w=h
The height of the tree will be 32 inches on week 13
Step-by-step explanation:
ok
Name the property used in the given expression −33/ 57 × −7/ 28 = −7/ 28 × −33/ 57
Answer:
Communitive Property
Step-by-step explanation:
a * b = b * a
In your case,
(-a / b) * (-c / d) = (-c / d) * (-a / b)
brainly pls :)
Answer:
Answer:
Communitive Property
Step-by-step explanation:
a * b = b * a
In your case,
(-a / b) * (-c / d) = (-c / d) * (-a / b)
Step-by-step explanation:
for a certain company, a train coming from new york to washington dc takes 3 hours to travel 228 miles. a new train company is able to complete the same journey in only 2.5 hours. how much faster is the new company’s train in terms of miles per hour?
A.) 7.5
B.) 11.7
C.) 15.2
D.) 17.3
E.) 21.4
Answer:
The new company’s train is C. 15.2 miles faster.
Step-by-step explanation:
Train A: 228/3 = 76 miles per hour
Train B: 228/2.5 = 91.2 miles per hour
91.2 - 76 = 15.2
For every 3 lemons Chrissy buys at a farm stand,
the total cost increases by $1.80.
The constant of proportionality is ?
An equation that relates the total cost, y, and the
number of lemons, x, is y = ? x.
Use the equation you wrote to complete the table.
Table:
Numbers of lemons(x) | Total cost(y)
4 | _?__
_?__ | $4.20
_?__ | $9.00
18 | _?__
Answer:
The constant of proportionality is $1.80
y = 1.80x
Step-by-step explanation:
The constant of proportionality is $1.80
An equation that relates the total cost, y, and the number of lemons, x, is
y = 1.80x
where,
y =Total cost
x = number of lemon
When x = 4
y = 1.80x
y = 1.80(4)
y = 7.2
y = $7.2
When y = $4.20
y = 1.80x
4.20 = 1.80x
x = 4.20 / 1.80
x = 2 1/3
x = 2 1/3
When y = $9.00
y = 1.80x
9.00 = 1.80x
x = 9.00 / 1.80
x = 5
x = 5
When x = 18
y = 1.80x
y = 1.80 × 18
y = 32.4
y = $32.4
Please help me with this please
Answer:
Shark 4
Step-by-step explanation:
It has the lowest value
Shaniece took a taxi from her house to the airport. The taxi company charged a pick-up fee of $3.40 plus $3.50 per mile. The total fare was $80.40, not including the tip. Write and solve an equation which can be used to determine x, the number of miles in the taxi ride.
1. What is the equation of an ellipse with center, (h, k) that is elongated in the x-direction?
The equation of an ellipse with center, (h, k) that is elongated in the x-direction is: (x - h)²/a² + (y - k)²/b² = 1.
What is defined as the ellipse?In aspects of locus, an ellipse is the collection of every point on an XY-plane with whom the distance from 2 fixed points (called foci) adds up to the a constant value.
Ellipse does have two focal points, which are also known as foci.A fixed distance is referred to as a directrix.The eccentricity of an ellipse ranges from 0 to 1.The total sum of every distance from an ellipse's locus to its two focal points is constant.Ellipse contains a single major and one minor axis, as well as a center.The standard form of equation of ellipse with centres (h, k) that is elongated in the x-direction is given as;
(x - h)²/a² + (y - k)²/b² = 1
Now, when the centre of the ellipse coincides with the origin of coordinates axis, the becomes;
x²/a² + y²/b² = 1
Thus, the equation of ellipse of obtained.
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Find irrational number, which is more than 0,6(3) and less than 0,64.
An irrational number that lies between the two given ones, 0.6333.... and 0.64 is:
√7 - 2.01 =0.63575...
How to find an irrational number between the two given ones?Remember that an irrational number is a number that can't be written as the quotient between two integers.
Here we want to find two numbers between 0.6333 (where the 3 repeats infinitely) and 0.64
So we cold try to find a number like:
6.3349412490184...
Such that there is no pattern (because if there were a pattern, it would not be an irrational number).
An example of this can be, for example:
√7 = 2.64575...
This is an irrational number.
Now, if we subtract 2.01 from that we will get:
√7 - 2.01 = 2.64575... - 2.01 = 0.63575...
This is an irrational number and lies between the two given ones, then we conclude that √7 - 2.01 =0.63575... is a correct option.
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find the slope of the line that goes through the points (-4,1) and (8,-5)
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{-5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{8}-\underset{x_1}{(-4)}}} \implies \cfrac{-6}{8 +4}\implies {\Large \begin{array}{llll} -\cfrac{1}{2} \end{array}}[/tex]
which property is represented below
Answer : Transitive Property
If that's not correct, try Symmetric or substitution cause I know it's not reflexive
Expressed as a product of its prime factors in index form, a number N is
N = 3 x 5² x x³
Express 5N² as a product of prime factors in index form.
Give your answer in terms of x.
5N² is expressed as a product of prime factors in index form as [tex]5^{5} * 3^{2} * x^{10}[/tex] .
What are prime factors index form?In the expression of a number as the product of its prime factors, known as prime factor index form, each prime factor is only mentioned once, either as itself or, if necessary, to a required power.
Given:
N is a number that is expressed as a product of its prime factors in index form.
N = [tex]3x * 5x^{2} * x^{3}[/tex]
We have to express 5N² as a product of prime factors in index form.
5N² = 5([tex]3x * 5x^{2} * x^{3}[/tex])²
= [tex]5 * 9x^{2} *5^{4} x^{2} *x^{6}[/tex]
= [tex]5 * (5^{2}x)^{2}* (3x )^{2} *x^{6}[/tex]
( using exponential properties [tex]a^{m} *a^{n} = a^{m+n} and (a^{m} )^{n} = a^{mn}[/tex])
= [tex]5^{5} * 3^{2} * x^{10}[/tex]
The prime factors of 5N² are 5,3 and x respectively.
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In Exercises 1-6, describe the transformation of f(x) = x² represented by g.
Then graph each function.
1. g(x) = x² - 2
G=
h=
M=
2. g(x) = (x - 5)²
3. g(x) = (x + 1)² + 3
The graph of the function after transformation is attached below.
The connection between several systems is defined by coordinate transformations, which offer formulas for the coordinates in one system in terms of the coordinates in another system.
The coordinate transformation from polar to Cartesian coordinates is given by the formulas x = r cos and y = r sin, for example, if the polar axis is the positive x axis on the plane and the origins of the Cartesian coordinates (x, y) and polar coordinates (r) are the same.Every bijection from the space to itself can be related to two coordinate transformations.The formulas for the new coordinates of each point's image are constructed in a way that the old coordinates of the original point's image are maintained.In particular, the change of algebraic equations, it is a typical kind of algebraic problem.The graph of the transformed function is attached below. The red graph indicates the parent function f(x) = x² and the blue graph indicated the graph of transformation g(x) = x² - 2
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you are given two reports estimating the mean increase in monthly household spending on gasoline over the past six months: report 1: based on a simple random sample of 14 households, we are 98% confident that the mean increase in monthly household spending on gasoline over the past six months is between $64.35 and $83.59. report 2: based on a simple random sample of 53 households, we are 95% confident that the mean increase in monthly household spending on gasoline over the past six months is between $58.37 and $71.93 determine which report you find most convincing, and explain your reasoning why.
In my opinion, Report 1 is more persuasive than Report 2 due to the fact that the margin of error in Report 1 is narrower than in Report 2.
This is further explained below.
What is the margin of error.?Generally, we consider report one and report two
For Report
at 98% confidence interval = $64.35 to $83.59
Therefore, the Margin of error
M.E= $83.59 - $64.35
M.E = $19.24
For Report 2:
95% confidence interval = $58.37 to $71.93
Margin of error
M.E= $71.93 - $58.37
M.E= $13.56
Since Report 1 has a smaller margin of error than Report 2, I find Report 1 to be more convincing.
In conclusion, A report with a lower margin of error, in my opinion, is often more credible than one with a bigger one.
This is because more exact data indicates a report with a reduced margin of error.
To put it another way, information in a report with a lower margin of error is more likely to be correct than information in a report with a higher margin of error.
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?:12 =7:14 what is the answer
Answer:
I believe the answer is 6:12. . .
Step-by-step explanation:
I think that 7:14 equals 1:2 in its simplest form. 6:12 also is equivalent to 1:2. 1:2 = 1:2.
pls help i rlly need this
The slope of the line is 2 , the correct option is (A).
Slope of the line is defined as the change in y coordinate with respect to the change in x coordinate of the line , the slope of the line is denoted by "m" .
The slope of the line passing through the two points (a,b) and (c,d) is given by m = (d-b)/(c-a) .
In the question ,
a line is given
let us name the points as M and N ,
the named graphed is shown below,
Assuming the cube in the graph be of 1 unit each.
So , the coordinates of M and N from the graph is
M = (1,1) and N= (-1,-3),
So the slope of the line passing through the points (1,1) and (-1,-3) is
slope = (-3-1)/(-1-1)
= -4/-2
= 2.
Therefore , the slope of the line is 2 , the correct option is (A).
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A triangle is dilated by a factor of 2 and then rotated clockwise. Which statement about the triangle's image and pre-image is correct?
The correct statement about the triangle's image and pre-image is 'the image and pre-image are not congruent because one of the transformation is rigid transformation and the other is not.'
The correct answer is an option (1)
In this question, a triangle is dilated by a factor of 2 and then rotated clockwise.
We need to select the correct statement about the triangle's image and pre-image.
We know that rotation is a rigid transformation but dilation is not a rigid transformation.
Dilation does not preserve the size of the image.
Also, the image and pre-image are not congruent as the corresponding sides of triangle's image and pre-image are not equal.
Therefore, the correct statement about the triangle's image and pre-image is 'the image and pre-image are not congruent because one of the transformation is rigid transformation and the other is not.'
The correct answer is an option (1)
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Use this table to answer the following questions.If the number of gallons of gas is known, can you find the number of gallons consumed? Explain how this value would be calculated.
The table of values indicates a proportional relationship between the number of gallons of gas and the number of miles driven, therefore;
The number of miles driven, f(x) can be found from the number of gallons of gas consumed, x, using the equation; f(x) = 31•xWhat is a proportional relationship?A proportional relationship is one in which one variable, y, can be obtained from another variable, x, by multiplying x by a factor.
Please find attached a table showing the number of gallons of gas and the miles driven obtained from a similar question online
Let x represent the number of gallons of gas and let f(x) represent the number of miles driven
The difference between the consecutive terms of the first three values in the number of gallons and miles driven are each equal to 2 and 62 respectively
4 - 2 = 2 - 0 = 2
124 - 62 = 62 - 0 = 62
Therefore, given that the first difference is constant, the first three points have a linear relation, which gives;
Slope of the line = 62/2 = 31
Intercept = 0
Therefore;
f(x) = 31•x
Checking the fourth point, gives;
x = 10
f(10) = 31 × 10 = 310
The relationship between the miles driven, f(x), and the number of gallons is therefore a proportional relationship, which is presented as follows;
f(x) = 31•x
Therefore, if the number of gallons of gas, x, is known, the number of miles driven, f(x), can be found using the equation;
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