Answer:
The inverse is x/3 -1
Step-by-step explanation:
y = 3x+3
To find the inverse, exchange x and y
x = 3y+3
Solve for y
x-3 =3y+3-3
x-3 = 3y
Divide by 3
x/3 - 3/3 = 3y/3
x/3 -1 = y
The inverse is x/3 -1
An economics professor conducts an experiment to determine if viewing his online video reviews improve the performance of his students on exams. He uses only economics students enrolled in his classes. The treatment group will watch the videos prior to the first exam, and the control group will not watch the videos. Then the scores of the first exam will be compared.
Which of the following variables’ effects could be mitigated by the random assignments? Check all that apply.
Intelligence
Study habits
Professor
Course textbook
Work schedule
Answer:
1,2,5
A,B,E
Intelligence
Study habits
Work schedule
ED2021
Intelligence and study habits could be mitigated by random assignments.
Options A and B are the correct answer.
What is a random assignment?Random assignment refers to the process of randomly assigning participants to either the treatment or control group in an experiment.
We have,
Random assignment is done to minimize the effect of extraneous variables, such as intelligence and study habits, that could potentially affect the results of the experiment.
By randomly assigning participants to either the treatment or control group, the differences between the two groups are assumed to be due to chance alone.
Variables such as the professor, course textbook, and work schedule are not affected by random assignments.
These variables are considered to be controlled variables that are held constant across both the treatment and control groups.
Thus,
Intelligence and study habits could be mitigated by random assignments.
Learn more about random assignments here:
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What was the average speed if I drove 60 miles per hour to get to my grandmas house and 30 miles per hour to get home. Represent this in two different ways and explain your reasoning.
Answer:
40 mph.
Step-by-step explanation:
Suppose grandma's house is 30 miles away (any distance would do but 30 is convenient).
Speed = distance / time
time = distance / speed
Time to get there = 30/60 = 1/2 hour.
Time to get back = 30/30 = 1 hour
Average speed = total distance/ total time
= (30 + 30) / ( 1 + 1/2)
= 60 / 1.5
= 40 miles per hour.
You cannot take the average of the speeds directly
(60+ 30)/2 = 45 is not correct as you cannot average ratios ( speed is a ratio).
The number of bacteria in a certain culture grows exponentially at a rate of 1% per hour. Assuming that 5,000 bacteria are present initially, find the time required for the bacteria population to reach 45,000. (Round your answer to the nearest hour.)
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Answer:
221 hours
Step-by-step explanation:
The population is given by the exponential equation ...
population = (initial value) × (1 +growth rate)^t
where the units of t are the same as the units of growth rate.
This lets us write ...
p(t) = 5000×1.01^t
We want this to be 45000, so ...
45000 = 5000×1.01^t
9 = 1.01^t . . . . . . . . . . . . divide by 5000
log(9) = t×log(1.01) . . . . take logs
t = log(9)/log(1.01) ≈ 220.8
It will take about 221 hours for the population to reach 45000.
Pat bought a new anchor for her boat. She needed to buy rope for the anchor At the
Rope
-N-S store, rope it sold in 4 1/2meter segments. Pat bought 190 segment
for the anchor. Just in case she needed mere.che bought an extra 27 sements. In all,
how many meters of rope did Pat buy?
A.4342
meters
B.976 1/2meters
C.217 meters
D.868 1/2 meters
Answer:
B
Step-by-step explanation:
Total segment bought=190+27=217 segments
Total length of the whole anchor=217*9/2=1953/2=976 1/2 meters
Read image for instructions
The last part answers the first part for you, just look at the y-values.
In other words:
A' (-8, 2)
B' (-4, 3)
C' (-2, 8)
D' (-10, 6)
Explanation:
When you reflect any point over the x-axis, the y-value of the ordered pair is going to change.
This makes sense especially considering that the x-axis is horizontal, so the only way you could cross is to move up or down. If you were to move left or right, you'd only be able to cross the y-axis, since it's vertical.
Now for the last part, as I mentioned above, if you are reflecting across the y-axis, the x-values of the ordered pair is going to change.
A'' (8, 2)
B'' (4, 3)
C'' (2, 8)
D'' (10, 6)
Take note that the only thing that changes for the respective value is its sign, while the number itself stays the same.
Find f(-1) given f(x) = –2x^3 + 3x^2 – 22
[tex]\\ \sf\longmapsto f(-1)[/tex]
[tex]\\ \sf\longmapsto -2x^3+3x^2-22[/tex]
[tex]\\ \sf\longmapsto -2(-1)^3+3(-1)^2-22[/tex]
[tex]\\ \sf\longmapsto -2(-1)+3(1)-22[/tex]
[tex]\\ \sf\longmapsto 2+3-22[/tex]
[tex]\\ \sf\longmapsto 5-22[/tex]
[tex]\\ \sf\longmapsto -17[/tex]
Janet invests a sum of EUR in an account that offers 3.5% simple interest. After ten years her investment is worth 7425 EUR. How much did she invest?
We need to find the amount of money Janet invested in 10 years to yield 7425 EUR
She invested EUR 21,214.29
Simple interest = P × R × T
Where,
P = principal = ?
R = interest rate = 3.5% = 0.035
T = Time = 10 years
Simple interest = 7425 EUR
Simple interest = P × R × T
7425 = p × 0.035 × 10
7425 = p × 0.35
7425 = 0.35p
Divide both sides by 0.35
P = 7425 / 0.35
= 21,214.285714285
Approximately,
P = EUR 21,214.29
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Using the formula D = s:t where D equals distance traveled, r equals the average rate of
speed, and t equals the time traveled, choose the expression or equation that correctly
represents this information.
Mary drove 150 miles in three hours. What was her average rate of speed?
=
150 = 3
r = 3 = 150
O p + 150 · 3
Answer: r = 50 miles/h
Step-by-step explanation:
Let r be the rate of average speed.
Then
r = D/t
r = 150/3
r = 50 miles/h
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NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!
12. The coordinate grid below represents a town.
a. Curtis's house is at (-4, -6) and Jean's house is at (-4, 3). Plot the plots where Curtis's house and Jean's house are located.
b. Each unit on the grid represents 1 mile. If Curtis can ride his bike at a constant rate of 12 miles per hour, how long would it take Curtis to ride from his house to Jean's house?
THIS IS NOT MULTIPLE CHOICE!!!
We are given:
Coordinates of Curtis's house: (-4, -6)
Coordinates of Jean's house: (-4, 3)
a) Plotting these points:
in the given coordinates, the first number is called the abscissa and denotes the x-coordinate of the point.
the second number is the ordinate. it denotes the y-coordinate of the point
Plotting Curtis's house:
We will start from the origin (0,0). move 4 units to the left because that's where x = -4 is.
Then, we will move 6 units downwards and mark the point.
The point we just marked is (-4, -6), Curtis's house
Plotting Jean's house:
We will go to x = -4 like we just did when plotting curtis's house
then, we will move 3 units upwards and mark the point.
This point is (-4, 3), Jean's house
b) Time taken by Curtis:
Distance between the points:
distance = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex] (distance formula/Pythagoras' Theorem)
where (x₁, y₁) = (-4, -6) and (x₂, y₂) = (-4, 3)
replacing the values in the formula, we get:
distance = [tex]\sqrt{(-4 - (-4))^2 + (3 - (-6))^2}[/tex]
distance = [tex]\sqrt{(0)^2 + (9)^2}[/tex]
distance = [tex]\sqrt{(9)^2}[/tex] = 9 units
since each unit on the grid represents one mile,
distance = 9 miles
speed of Curtis = 12 miles/hour
we know that speed is just (distance covered)/(time taken)
speed = (distance covered)/(time taken)
replacing known values
12 = 9 / time
12 * time = 9 [multiplying both sides by time]
time = 9/12 [dividing both sides by 12]
time = 3/4 hours
time = 0.75 hours OR 45 minutes
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Answer:
a) see attached
b) 3/4 hour (45 minutes)
Step-by-step explanation:
a) The attached graph shows the points plotted.
__
b) The points lie on the same vertical line. The distance between them is the difference of their y-coordinates: 3 -(-6) = 9 (miles).
The time is related to distance and speed by ...
time = distance/speed
time = (9 mi)/(12 mi/h) = 9/12 h = 3/4 h
It would take Curtis 3/4 hour to ride from his house to Jean's house.
Which is the graph of the linear inequality 2x – 3y < 12? On a coordinate plane, a solid straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded. On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the right of the line is shaded. On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the left of the line is shaded.
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Answer:
(c) On a coordinate plane, a dashed straight line has a positive slope and goes through (0, negative 4) and (3, negative 2). Everything to the left of the line is shaded.
Step-by-step explanation:
The x-coefficient is positive, so we can determine the shading from ...
2x ... < ... (pay attention to the x-term and the inequality symbol)
That is, the solution region will have x values that are less than those on the (dashed) boundary line. Lower x-values are to the left, hence shading is on the left side of the boundary. (That's all you need to know here to make the correct choice.)
_____
Additional comment
If the choices are "above" or "below", then you will want to look at the y-term and the inequality symbol. If the coefficient of the variable of interest is negated (as it is for y here), then you need to consider the inequality symbol reversed: -y < ... ⇔ y > .... Here, that means the shading is above the line. Since the slope of the line is positive, "left" and "above" are the same thing.
Answer:
c
Step-by-step explanation:
E2021
find the surface area of the cylinder
Answer
50.24
Step-by-step explanation:
Differentiate 4x^2+y^2=36 with respect to x. Hence find the turning points of the curve.
If y = y(x), then the derivative with respect to x is dy/dx. Differentiating both sides of the given equation gives
d/dx [4x ² + y ²] = d/dx [36]
8x + 2y dy/dx = 0
2y dy/dx = -8x
dy/dx = -4x/y
The turning points of the curve, taken as a function of x, are those points where the derivative vanishes.
-4x/y = 0 ===> x = 0
This value of x corresponds to two points on the curve,
4×0² + y ² = 36 ===> y ² = 36 ===> y = ±6
So there are two turning points, (0, -6) and (0, 6).
I need help with this question
A car dealer's markup on every car they sell is 20%. For what price did the dealership buy a car that they sold for $18,600?
Answer:
buying price = $15,500
Step-by-step explanation:
selling price 20% more than the buying price
let the buying price be 100% then;
selling price = 120%
120% = $18,600
100% = ?
(100 × 18600) ÷ 120
= $15,500
What are the divisible number(s) for 430?
Answer:
The numbers that 430 is divisible by are 1, 2, 5, 10, 43, 86, 215, and 430.
if fog(x)=((2x-1)/x) and g(x)=5x+2. find f(x)
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Answer:
f(x) = (2x -9)/(x -2)
Step-by-step explanation:
We can use the fact that g(g^-1(x)) = x.
[tex](f\circ g)(x) = f(g(x))\\\\(f\circ g)(g^{-1}(x))=f(g(g^{-1}(x)))=f(x)[/tex]
So, we need to know the inverse of g(x):
x = g(y)
x = 5y +2
x -2 = 5y
y = (x -2)/5 . . . . inverse of g(x)
Then we have ...
[tex]f(x)=(f\circ g)(g^{-1}(x))=(f\circ g)\left(\dfrac{x-2}{5}\right)\\\\f(x)=\dfrac{2\left(\dfrac{x-2}{5}\right)-1}{\left(\dfrac{x-2}{5}\right)}=\dfrac{2x-4-5}{x-2}\\\\\boxed{f(x)=\dfrac{2x-9}{x-2}}[/tex]
A line contains the piont (4,5) and is perpendicular to a line with a slope of -2/3. Write an equarion of the line satisfying the given conditions. Write the answer in slope-intercept form
Answer:
[tex]y=\frac{3}{2}x-3.5[/tex] or, preferably, [tex]y=\frac{3}{2}x-\frac{7}{2}[/tex]
Step-by-step explanation:
First is to find the perpendicular slope. In this case, you swap the numerator and denominator and then multiply that fraction by -1.
In this case, -2/3's inverse slope is 3/2.
Now, the initial y=3/2 passes through 7.5,5
So, you must subtract 3.5 from that to make it pass through 4,5.
In this way, you get the answer in slope-intercept form.
Answer:
y = [tex]\frac{3}{2}[/tex] x - 1
Step-by-step explanation:
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{2}{3} }[/tex] = [tex]\frac{3}{2}[/tex] , then
y = [tex]\frac{3}{2}[/tex] + c ← partial equation in slope- intercept form
To find c substitute (4, 5) into the partial equation
5 = 6 + c ⇒ c = 5 - 6 = - 1
y = [tex]\frac{3}{2}[/tex] x - 1 ← equation of line
A student records the temperature at noon every day for 365 days and displays the results in the following bar graph. Does the bar graph depict the data fairly?
Answer: no, the vertical scale does not start at zero.
Step-by-step explanation:
Least you greatest (help please but don’t give wrong answer pls)
Answer:
84.16, 84.31, 675/8, 423/5
Step-by-step explanation:
If car eyelashes sold for $13.99. If you bud double that, how much would you have paid for them? (Hint if needed: if they had been exactly $14, how different would your answer be?)
Answer:
13.99 x 2 = 27.98 dollars
now if they were 14 dollars exactly and you doubled that it would be 28 dollars so the difference would be 0.02 cents
Step-by-step explanation:
help me plzzzzzzzzzzzzzzzzzzzzzzzzzz
The perimeter of the rectangle below is 124 units. Find the length of side cd
Answer:
CD = 38
Step-by-step explanation:
Since AB = 3x + 2, CD = 3x + 2
To solve for the length of CD, we'll need to solve for x first by using the perimeter formula
Solving for x...
[tex](3x+2)+(3x+2)+2x+2x=124[/tex]
[tex]3x + 3x + 2x + 2x = 120[/tex]
[tex]10x=120[/tex]
[tex]x=\frac{120}{10}[/tex]
[tex]x=12[/tex]
Now that we know what x equals, plug in x into the expression of side CD
CD = 3x + 2
CD = 3(12) + 2
CD = 36 + 2
CD = 38
Therefore, the length of side CD = 38
-------------------------------------------------------
Check:
AB = CD | BC = DA
38 + 38 for AB and CD
BC + DA = 2x + 2x
BC + DA = 2(12) + 2(12)
BC + DA = 24 + 24
BC + DA = 48
38 + 38 + 48 = perimeter
perimeter = 124
plzzz help me i need help picture below
A local bakery buys their flour in bulk. The relationship between the cost of the flour and its weight is shown in the graph below.
Is the relationship shown a direct variation? Explain your reasoning using complete sentences.
The point (1, 0.50) is on this graph. What does this ordered pair represent?
Approximately how much does the bakery pay for 40 pounds of flour?
Answer:
It is a direct variation...
The price of flour does not increase or decrease the
more that you purchase (no discount for large purchases)
(1,0.5) means that a pound of flour costs 50
40 pounds would cost $20
Step-by-step explanation:
Put the shapes in the venn diagram. Is this right? if wrong tell me please.
Answer:
I'm not sure if the kite outside has at least a pair of equal sides. The rest I think are right though? Correct me if I'm wrong.
The probability of winning a raffle is 2/5. What is the probability of not winning the raffle?
0
3/5
2/5
Answer:
3/5
Step-by-step explanation:
um 3/5+2/5 = 1
I need help on this math problem.
Find the area of the region.
Three petals of r = cos(9θ)
The length of a rectangle is five times the width if the area of the rectangle is 180 in.² then find the length and the width
Let breadth be x
Length=5x
ATQ
[tex]\\ \sf \longmapsto Area=Length\times breadth[/tex]
[tex]\\ \sf \longmapsto 5x(x)=180[/tex]
[tex]\\ \sf \longmapsto 5x^2=180[/tex]
[tex]\\ \sf \longmapsto x^2=\dfrac{180}{5}[/tex]
[tex]\\ \sf \longmapsto x^2=36[/tex]
[tex]\\ \sf \longmapsto x=\sqrt{36}[/tex]
[tex]\\ \sf \longmapsto x=6in[/tex]
Width=6inLength=6×5=30inA survey of 1,500 Canadians reveals that 945 believe that there is too much violence on television. In a survey of 1,500 Americans, 810 believe that there is too much television violence.
a. What would be the most appropriate test here to test the claim that Americans are less sensitive to violence on TV as Canadians?
b. My parameter of interest here would be: __________
c. The direction of test would be {Let Canadians be group 1 and Americans be group 2): __________
The test statistic is given by t and t is calculated with the help of the test statistic formula. The value of t is 4.45.
What is test statistics?The test statistic summarizes the observation data into a unique number using central tendency, the variation, sample, and size in your statistical model.
here, we have,
The given information will be shown below.
The first sample size n₁ = 36
The second sample size n₂ = 34
The mean of the first sample x₁ = 68.5
The mean of second sample x₂ = 70
Then the test statistic will be given as:
t = -4.45
The test statistic | t | = |–4.45| = 4.45
More about the test statistic link is given below.
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complete question:
g A test was conducted to determine if there is a difference between Canadian and American average heart rates. A group of 36 Canadians and 34 Americans were randomly selected and their heart rates measured in beats per minute (bpm). The mean heart rate for Canadians was 68.5 and 70 for Americans. The pooled standard deviation of 2.0 beats/minute was calculated. Estimate a plausible range of differences between the mean heart rate of Canadians and Americans. What statistical procedure should be used to answer this research question
A computer is priced at $2,000. If the sales tax rate is 7.5%, find the total cost of the
computer
please help:((
Answer:
it would just be 2000 * 1.075
Step-by-step explanation:
2150
Price = $2000
Sales tax
= 7.5% of Price
= 7.5% of $2000
= (7.5/100) × $2000
= 0.075 × $2000
= $150
Total price
= Price + Sales tax
= $2000 + $150
= $2150
which of the following is equal to the square root of 27/16
Answer:
Step-by-step explanation:
Prime factorize 27 and 16
27 = 3 * 3 * 3
16 = 2 * 2 * 2 * 2
[tex]\frac{\sqrt{27}}{\sqrt{16}}=\frac{\sqrt{3*3*3}}{\sqrt{2*2*2*2}}[/tex]
[tex]= \frac{3\sqrt{3}}{2*2}\\\\\\=\frac{3\sqrt{3}}{4}[/tex]
Answer: (3√3)/4
Explanation:
√(27/16)
=(3√3)/4
Because 27 = 3²×3
And 16 = 4²
So 4 is left and one 3 goes out and one stays in
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