Consider the functions f(x) = 12^x and g(x)= -2(12)^x. Which transformations must be applied to function F to produce the graph of function g?
SELECT ALL CORRECT ANSWERS
Vertical stretch
Vertical Shift
Vertical Compression
Reflection over the x-axis
Horizontal Shift
Answers
Answer:
Step-by-step explanation:
g(x) = -2f(x)
Vertical stretch by virtue of the factor 2
Reflection over the x-axis by virtue of the factor -1
The transformations which must be applied to function F to produce the graph of function g are vertical stretch and reflection over the x-axis.
To transform the function f(x)=12ˣ into the function g(x)=−2(12)ˣ
Since g(x) is multiplied by -2 compared to f(x), this represents a vertical compression.
The absolute value of the multiplier indicates the degree of compression/stretch.
The negative sign in front of 2(12)ˣ in g(x) reflects the graph over the x-axis. This means that the graph of g(x) is reflected below the x-axis compared to f(x).
Hence, vertical stretch and reflection over the x-axis are the transformations which must be applied to function F to produce the graph of function g.
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Related Questions
Women comprise 83.3% of all elementary school teachers. In a random sample of 300 elementary school teachers, what is the probability that fewer than 260 are women?
Answers
Using the normal approximation to the binomial, it is found that there is a 0.9319 = 93.19% probability that fewer than 260 are women.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X. The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].In this problem:
Women comprise 83.3% of all elementary school teachers, hence [tex]p = 0.833[/tex]A sample of 300 teachers is taken, hence [tex]n = 300[/tex]The mean and the standard deviation for the approximation are given by:
[tex]\mu = np = 300(0.833) = 249.9[/tex]
[tex]\sigma = \sqrt{np(1 - p)} = \sqrt{300(0.833)(0.167)} = 6.46[/tex]
Using continuity correction, as the binomial distribution is discrete and the normal distribution is continuous, the probability that fewer than 260 are women is P(X < 260 - 0.5) = P(X < 259.5), which is the p-value of Z when X = 259.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{259.5 - 249.9}{6.46}[/tex]
[tex]Z = 1.49[/tex]
[tex]Z = 1.49[/tex] has a p-value of 0.9319.
0.9319 = 93.19% probability that fewer than 260 are women.
A similar problem is given at https://brainly.com/question/25347055
Caleb sketched the following diagram on graph paper. He dilated points B and C from center o. B a. What is the scale factor r? Show your work. b. Verify the scale factor with a different set of segments. C.) Which segments are parallel? How do you know? d. Which angles are equal in measure? How do you know?
Answers
A total of 180 students and 35 chaperones are going on a field trip to the Smithsonian Institution in Washington, D. C.
Write the ratio in simplest form.
the ratio of students to people on the trip
Answers
Answer:
36 : 43
Step-by-step explanation:
So, we have 180 : 35 + 180 in the students to people on the trip180 : 21536 : 43Therefore, the ratio of students to people is 36 : 43The low temperature on a certain day is 56°F. The low temperature is 14°F lower than the high temperature, h.
Which equation can be used to find the high temperature for that day?
56=h−14
56 = 14h
56 = h + 14
h + 56 = 14
Answers
Answer:10.9
Step-by-step explanation:
a plumber receives $72 an hour. how much is she paid for 20 hours of work?
Answers
Answer:
$1440
Step-by-step explanation:
$72/hour
For 20 hours, she receives
20 hours × $72/hour = $1440
Solve the equation.
2
What is the first step to isolate the variable term on one side of the equation?
What is the second step to solve for x?
Please help and be fast
Answers
Answer:
Add 1/2x, Divide by 7/6
Step-by-step explanation:
Add 1/2x to both sides
Divide both sides by 7/6
pls help. Have tried this problem a couple times but my answers didnt work
Answers
Answer:
infinite solutions...
Step-by-step explanation:
Is there more information to this problem? It can be pretty much anything.
N=3M
Nina can be 30 and Maryna 10, Nina can be 3 and Maryna 1, Nina can be 15 and Maryna 5...
Answer:
N - 4 = 3(M - 4). Simplified further, N - 4 = 3(M - 4)
Given,
Nina is N years old now and;
Maryna is M years old now
If four years ago, Nina was three times as old as Maryna was, then
Four years ago, Nina's age was N - 4
Four years ago, Maryna's age was M - 4
Given that Nina was three times as old as Maryna was four years ago, it means that
N - 4 = 3(M - 4)
To solve further
N = 3m - 12 + 4
N = 3M - 8
Step-by-step explanation:
help please asappppppppp
Answers
Answer:
First Equation: 6a-23
Second Equation: 5a-20
Step-by-step explanation:
So, I think you want me to answer part 2...
For the first equation, we can see that the denominator stays the exact same, meaning the numerator will also not change.
For the second equation, we can see the denominator changed from a-3 to 5a-15. The denominator was simply multiplied by 5. Since the denominator was multiplied by five we must multiply the numerator by five as well.
5(a-4)
5a-20
Hope this helps :)
Which is true? A 0.9919 > 0.999 B 1.4359 < 1.446 C 2.6953 = 2.75 D 4. 9395 > 5.0
Answers
Option B. is true.
A isn't true because 0.9919 is lesser than 0.999.C is false because 2.6953 is lesser than 2.75. They are not equal.D is also false because 4.9395 is not greater than 5.0.Answer:
B. 1.4359 < 1.446
Hope you could get an idea from here.
Doubt clarification - use comment section.
Solve the following system of equations:
Answers
Answer:
The correct answer is option B: (-1, -1).
Step-by-step explanation:
The easiest way to solve this system is using elimination, or by adding the two equations together. We don't have to modify the equations at all, since the x's will already cancel out as written.
Upon addition, we get:
9y = -9
If we solve the equation by dividing both sides by 9, we get:
y = -1
To find the x value, we can substitute this value back into either of our original equations.
6x + 4y = -10
6x - 4 = -10
To solve for x, we should isolate the variable, or get it alone on one side of the equation.
6x = -6
x = -1
Therefore, the solution to the system of equations is x = -1 and y = -1, or (-1, -1), which is option B.
Together, Mike and Bill have $50 more than Joe has. Mike has $26 more than Bill. The three boys have a total $506. How much money does each boy have.
Answers
i wish i had that much money
Answer:
Step-by-step explanation:
1. 84
2. 96
Answer: Divisible by 2, 3, 6
3. 896
4. 942
Answer: Divisible by 2, 3, 6
5. 22,335
6. 39,075
Answer: Divisible by 3, 5
Find Prime Factorizations and Least Common Multiples In the following exercises, find the
prime factorization.
7. 86
8. 78
Answer: 2 3 13 ⋅ ⋅
9. 455
10. 400
Answer: 222255 ⋅⋅⋅⋅⋅
11. 432
12. 627
Answer: 3 11 19 ⋅ ⋅
In the following exercises, find the least common multiple of each pair of numbers using the
prime factors method.
13. 8, 12
hope that help mark me brinliylist
1) write the measurement 4009 mm into the place value table below
a) what is 4009 mm in cm
b) what is 4009 mm in m
2) how many millimeters is 6 liters
Answers
Answer:
a)400.9 cm
b)4.009 m
c) 181.71 mm
Step-by-step explanation:
a) First know that when you move from cm to mm you multiply by 10 and when you move from mm to cm you divide by 10 because 1mm= 0.1 cm
so 4009mm/10 = 400.9cm
b) when you move from m to mm you multiply by 1000 but when you move from mm to m you divide by 1000 ,so 4009/1000 = 4.009
c) 1litre= 1000000mm³
6litre= x
xlitre= 6000000 litre mm³
divide by litre
x= 6000000 mm³
but according to the question we are not looking for cubic mm but mm the fore remove cubic by insterting cube root
x= 181.71 mm
: . c)181.71 mm
Distributive property to remove parentheses 4(3+w)
Answers
Answer:
12+4w
Step-by-step explanation:
Multiply 4 by both sides
6. (5 points) Graph using two intercepts; show your work in finding the intercepts. 6x - 3y = 18
х
Answers
Answer:
Divide both sides by 18. The new coefficients will be the reciprocals of the intercepts:
[tex]6x-3y=18 \rightarrow \frac6{18}x - \frac3{18}y = 1 \rightarrow \frac x3-\frac y6 =1[/tex] The two intercepts are then 3 and -6.
(I know, dividing by 3 both sides of the equations would have made the whole process way easier).
Alternatively, plug x = 0 to find the y intercept and y=0 to find the x intercept. Either way the graph will look something like the one I'm sketching on paint.
Of 92 adults selected randomly from one town, 61 have health insurance. Find a 90% confidence interval for the true proportion of all adults in the town who have health insurance. Group of answer choices 0.582 < p < 0.744 0.548 < p < 0.778 0.536 < p < 0.790 0.566 < p < 0.760
Answers
A 90% confidence interval for the true proportion of all adults in the town who have health insurance is 0.582 < p < 0.744
The formula for calculating the confidence interval is expressed as;
[tex]CI=p \pm z \cdot\sqrt{\frac{P(1-p)}{n} }[/tex]
p is the proportion = 61/92 = 0.66n is the sample size = 92z is the z-score at 90% = 1.645Substitute the given parameters into the formula to have:
[tex]CI=0.66 \pm 1.645 \cdot\sqrt{\frac{0.66(1-0.66)}{92} }\\CI=0.66 \pm 1.645 \cdot\sqrt{\frac{0.66(0.34)}{92} }\\CI =0.66\pm 1.645(0.0495)\\CI=0.66 \pm 0.0814\\CI = (0.582, 0.744)[/tex]
Hence a 90% confidence interval for the true proportion of all adults in the town who have health insurance is 0.582 < p < 0.744
Learn more on confidence interval here: https://brainly.com/question/15712887
Jamie is x years old. His friend Ana is the same age.
Enter an expression in the box to represent the sum of Jamie's and Ana's ages.
Answers
Explanation:
Each person is x years old. Adding those unknown ages gets us x+x = 2x
We can think of it like x being one box, so x+x represents having two boxes which shortens to 2x.
3x+5y−7x+6=12
Calculate.Solve for x.
Answers
The value of x from the equation is x = (5y - 6)/4
Given the equation 3x+5y−7x+6=12
collect the like terms;
3x-7x + 5y + 6=12
-4x + 5y = 12 - 6
-4x + 5y = 6
Subtract 6 from both sides
-4x + 5y - 5y = 6 - 5y
-4x = 6 - 5y
4x = 5y - 6
x = (5y - 6)/4
Hnce the value of x from the equation is x = (5y - 6)/4
learn more on subject of formula here: https://brainly.com/question/657646
please help!!!!
check for understanding:
Answers
a^2+b^2=c^2
But we rearrange this formula to make it
c^2-a^2=b^2
So 25^2-15^2=b^2
625-225= b^2 = 400
You now need to find the square root of 400 to find the square root of b
sqrt of 400 is 20
So 20 is the missing length in this triangle
what number I am if I am a factor of 90 but not a multiple of 6 and 9 i am greater than 10 but smaller than 20
Answers
Answer:
15
Step-by-step explanation:
15 can go into 90, 6 times. It is neither a multiple of 6 or 9. It is larger than 10 and smaller than 20.
Can someone help please
Answers
=========================================================
Explanation:
If you know the cost function C(x), to find the marginal cost, we apply the derivative.
Marginal cost = derivative of cost function
Marginal cost = C ' (x)
Since we're given the marginal cost, we'll apply the antiderivative (aka integral) to figure out what C(x) is. This reverses the process described above.
[tex]\text{Cost} = \text{antiderivative of marginal cost}\\\\\displaystyle C(x) = \int \left(35x^{4/3} - 14x^{3/4} + 1\right)dx\\\\[/tex]
[tex]C(x) = \frac{1}{1+4/3}*35x^{4/3+1} - \frac{1}{1+3/4}*14x^{3/4+1} + x + D\\\\C(x) = \frac{1}{7/3}*35x^{7/3} - \frac{1}{7/4}*14x^{7/4} + x + D\\\\C(x) = \frac{3}{7}*35x^{7/3} - \frac{4}{7}*14x^{7/4} + x + D\\\\C(x) = 15x^{7/3} - 8x^{7/4} + x + D\\\\[/tex]
D represents a fixed constant. I would have used C as the constant of integration, but it's already taken by the cost function C(x).
To determine the value of D, we plug in x = 0 and C(x) = 9000. This is because we're told the fixed costs are $9000. This means that when x = 0 units are made, you still have $9000 in costs to pay. This is the initial value. You'll find that all of this leads to D = 9000 because everything else zeros out.
Therefore, we go from this
[tex]C(x) = 15x^{7/3} - 8x^{7/4} + x + D\\\\[/tex]
to this
[tex]C(x) = 15x^{7/3} - 8x^{7/4} + x + 9000\\\\[/tex]
which is the final answer.
Which graph represents the function?
Answers
Answer:
I believe it's the middle graph. since their is a closed dot on the first line and the other 2 inequality symbols indicate that their are 2 open dots, I think the middle is correct
The line passes through point Q, located at (-1, 2), and point R, located at (1, -2). Which two points determine a line parallel to line Q R ?
Answers
Answer:
i need a picture to see sorry
Please help me will give brainliest
Answers
Answer:
f(x) = 8.917x³ + 2x² + 0.083x - 7
Step-by-step explanation:
f(x)= y
Let the coefficients of x³, x², x be a, b, c and the constant be d
y= ax³ + bx² + cx + d
When y = -65, x = -2
-65= a(-2)³ + b(-2)² + c(-2) + d
-65= -8a + 4b - 2c + d ...eq. 1
When y = -14, x = -1
-14= a(-1)³ + b(-1)² + c(-1) + d
-14= -a + b - c + d ...eq. 2
When y = -7, x = 0
-7= a(0)³ + b(0)² + c(0) + d
-7 = d ...eq.3
When y = 4, x = 1
4= a(1)³ + b(1)² + c(1) + d
4= a + b + c + d ...eq. 4
when y = 78, x = 2
78 = a(2)³ + b(2)² + c(2) + d
78= 8a + 4b + 2c + d ...eq. 5
From eq. 3, d is - 7
putting d as - 7 in equations 1, 2, 4 and 5
In eq. 1,
-65= -8a + 4b - 2c - 7
-58= -8a + 4b - 2c ...eq. 6
In eq. 2
-14= -a + b - c - 7
-7= -a + b - c ...eq. 7
In eq. 4,
4= a + b + c - 7
11= a + b + c ...eq. 8
In eq. 5
78= 8a + 4b + 2c - 7
85= 8a + 4b + 2c ...eq.9
Subtracting eq. 9 from eq. 6
-143 = -16a - 4c... eq 10
subtracting eq. 8 from eq 7
-18= -2a - 2c
9= a + c
a = 9 - c ...eq 11
putting a as 9 - c in eq. 10
-143 = -16(9 - c) - 4c
-143 = -144 + 16c - 4c
1= 12c
c = 1/12 or 0.083
putting c as 1/12 in eq. 11
a = 9 - 1/12
a = 107/12 or 8.917
Putting a as 107/12 and c as 1/12 in eq. 8
11= 107/12 + b + 1/12
multiplying through by 13
132 = 107 + 12b + 1
132 - 108 = 12b
24= 12b
b = 24/12
= 2
Therefore, a= 8.917, b= 2, c= 0.083 and d = -7
f(x) = 8.917x³ + 2x² + 0.083x - 7
state whether each of the following equations represent growth or decay.
Answers
Answer:
ehhh Pfouto math ni
dali raka AA yooo
How do you use observed data to predict unobserved
Answers
Find the future value of $124,357 deposited at 8% compounded quarterly for 4 years
Answers
Answer:
Future value, $63,398.79; Interest, $16,798.79
Step-by-step explanation:
A boat travels upstream a distance of 24 miles on a
river whose current is a constant rate of 3 mph. The boat returns downstream. The trip up the
river and back down the river takes a total time of 6 hours. What would the speed of the boat
be in still water?
Answers
Answer:the answer will be 48
Step-by-step explanation: 24 divided by 3 =8 x 6 =48
I REALLY HOPE THIS HELPS
In the multiplication sentence below, which number is the product?
9x 10 = 90
A. 9
B. 10
C. 90
SUBMIT
Answers
Answer:
C. 90
Step-by-step explanation:
The numbers being multiplied are "factors." The result of multiplication is a "product." In this problem, the product is 90.
Simplify the product.
(16+13)(12-2)
Answers
Answer:
290
Step-by-step explanation:
(16+13)(12-2)= 29 * 10 = 290
Answer:
290
Step-by-step explanation:
(16+13)(12-2)
29*10
290
LESSON 3
WHATS MORE
Translate each English phrase/sentance into Mathematical phrase/sentance
1. The sum of 4 and number________
2. Six less than a number_________
3. The product of 8 and a number______
4. The quotient of x and 7 ______
5. Five more than a number is equal to 15_____
Answers
Answer:
1. 4+x
2. x-6
3. 8x
4. x/7
5. x+5=15
Step-by-step explanation: