Answer:
(a) and (b)
[tex]f(g(x)) = g(f(x)) = x[/tex]
(c) and (d)
[tex]f(g(x)) =-x + 8[/tex]
[tex]g(f(x)) = x + 8[/tex]
Step-by-step explanation:
Given
(a) to (d)
Required
Find f(g(x)) and g(f(x)) for each pair
For (a) and (b), we have:
[tex]f(x) = \frac{3}{x}[/tex]
[tex]g(x) = \frac{3}{x}[/tex]
Calculate f(g(x))
[tex]f(x) = \frac{3}{x}[/tex]
[tex]f(g(x)) = \frac{3}{g(x)}[/tex]
Substitute 3/x for g(x)
[tex]f(g(x)) = \frac{3}{3/x}[/tex]
Rewrite as:
[tex]f(g(x)) = 3/\frac{3}{x}[/tex]
[tex]f(g(x)) = 3*\frac{x}{3}[/tex]
[tex]f(g(x)) = x[/tex]
Since f(x) = g(x), then:
[tex]f(g(x)) = g(f(x)) = x[/tex]
For (c) and (d)
[tex]f(x) =x + 4[/tex]
[tex]g(x) =-x + 4[/tex]
Solving f(g(x)), we have:
[tex]f(x) =x + 4[/tex]
[tex]f(g(x)) =g(x) + 4[/tex]
Substitute [tex]g(x) =-x + 4[/tex]
[tex]f(g(x)) =-x + 4 + 4[/tex]
[tex]f(g(x)) =-x + 8[/tex]
Calculating g(f(x))
[tex]g(x) =-x + 4[/tex]
[tex]g(f(x)) = -f(x) + 4[/tex]
Substitute: [tex]f(x) =x + 4[/tex]
[tex]g(f(x)) = x + 4 + 4[/tex]
[tex]g(f(x)) = x + 8[/tex]
What is the length of line segment FE?
Enter your answer, as a decimal rounded to the nearest tenth, in the box.
FE =
units
Answer:
(7,-1)because it is problem of vector lesson so that we have to use formula of vector
What is the domain of the square root function graphed below? On a coordinate plane, a curve open up to the right in quadrant 4. It starts at (0, negative 1) and goes through (1, negative 2) and (4, negative 3). x less-than-or-equal-to negative 1 x greater-than-or-equal-to negative 1 x less-than-or-equal-to 0 x greater-than-or-equal-to 0
Answer:
Its D
Step-by-step explanation:
Ed2021
Answer
x greater-than-or-equal-to 0
Step-by-step explanation:
yes
Joe wants his overall test average to be 85%. What score would he need on his next test if the test scores he has so far are: 70%, 105%, 75%, 90%, 90%?
Answer:
He would need a score of 0.8 = 80%.
Step-by-step explanation:
Average score:
The average score is the sum of all scores divided by the number of tests.
What score would he need on his next test if the test scores he has so far are: 70%, 105%, 75%, 90%, 90%?
Combining with the next text, there will be 6, and the sum will be: 0.7 + 1.05 + 0.75 + 0.9 + 0.9 + x = 4.3 + x.
Joe wants his overall test average to be 85%.
So
[tex]\frac{4.3 + x}{6} = 0.85[/tex]
[tex]4.3 + x = 5.1[/tex]
[tex]x = 5.1 - 4.3 = 0.8[/tex]
He would need a score of 0.8 = 80%.
A piecewise function is given.
Find f(-4)
Answer:
3
Step-by-step explanation:
For x<=0, f is constant: f(x) =3
-4<0, so f(-4)=3
What is the mean of the following data set? 6, 7, 3, 8, 6, 6, 2, 9, 7 A 8 B 9 C 6 D 7
Answer:
The mean is 6.
Step-by-step explanation:
PLEASE HELP
will mark brainliest
Answer:
Option B
[tex]A'(5,5)[/tex]
[tex]B'(5,1)[/tex]
[tex]C'(2,1)[/tex]
[tex]D'(1,5)[/tex]
[tex]----------[/tex]
hope it helps...
have a great day!!
what is the answer to 50.25 times x
Find the volume.
pls help!
Answer:
(8*6*8)÷2=192ft^3
Step-by-step explanation:
find the volume like you would a rectangular cube and then devide it in half. so L*H*W/2
WILL GIVE BRAINLIEST!! do not answer if you dont know what the answer is.
3(n + 2) = 9(6 - n)
Can someone pls help me with this
Answer:
8.5 pi
Step-by-step explanation:
C= 2 pi r
21 pi= 2pi r
r= 10.5
Arc length= 2pi r(145/360)
21 pi( 145/360)= 8.5 pi
How would I solve this?
If you help me with my last question I will help you with this one
Indicate the general rule for the arithmetic sequence with a3 = -12 and a8 = -37
Answer:
The general rule is [tex]a_n = -2 - 5(n-1)[/tex]
Step-by-step explanation:
Arithmetic sequence:
In an arithmetic sequence, the difference between consecutive terms is always the same, and this difference is called common difference.
The general rule of an arithmetic sequence is given by:
[tex]a_{n} = a_1 + (n-1)d[/tex]
In which [tex]a_1[/tex] is the first term and d is the common difference.
We can also find the nth term as a function of a term m, using:
[tex]a_n = a_m + (n-m)d[/tex]
a3 = -12 and a8 = -37
First we find the common difference. So
[tex]a_n = a_m + (n-m)d[/tex]
[tex]a_8 = a_3 + (8-3)d[/tex]
[tex]-37 = -12 + 5d[/tex]
[tex]5d = -25[/tex]
[tex]d = -\frac{25}{5}[/tex]
[tex]d = -5[/tex]
So
[tex]a_n = a_1 - 5(n-1)[/tex]
Finding the first term:
[tex]a_n = a_1 - 5(n-1)[/tex]
Since [tex]a_3 = -12[/tex]
[tex]a_n = a_1 - 5(n-1)[/tex]
[tex]a_3 = a_1 - 5(3-1)[/tex]
[tex]a_1 = a_3 + 10 = -12 + 10 = -2[/tex]
So the general rule is:
[tex]a_n = a_1 - 5(n-1)[/tex]
[tex]a_n = -2 - 5(n-1)[/tex]
Ethan purchased a new cell phone for $75.00. The costs of the phone is included in his first month's bill. His cell phone plan charges $0.06 for each minute used.
if Ethan has $90.00 to spend on his first month's bill, what is the maximum number of minutes he can use?
A. 80 minutes
B. 250 minutes
C. 1,250 minutes
D. 1,500 minutes
Answer:1,250
Step-by-step explanation:
In which quadrant does the point (-1, 24) lie?
OA.
Quadrant 1
OB. Quadrant II
OC. Quadrant IV
D. Quadrant III
PLEASEE, i’ve been struggling with this for a long time. What base and height should I use guys?! Pls dont you dare to scam me or you get a report
Ima mark brainliest ;-;
Answer:
3 height
7 Base
Pls help meeeeeeeeee
Answer:
3692.64 inches cubed.
Step-by-step explanation:
round this answer to the nearest tenth and that is your answer!
(a) For real applications, the normal distribution has two potential drawbacks: (1) it can be negative, and (2) it isn’t symmetric. Choose some continuous random numeric outcomes of interest to you. Are either potential drawbacks really drawbacks for your random outcomes? If so, which is the more serious drawbacks and why?
(b) Many basketball players and fans believe strongly in the “hot hand.” That is, they believe that players tend to shoot in streaks, either makes or misses. If this is the case, why does the binomial distribution not apply, at least not exactly, to the number of makes in a given number of shots? Which assumption of the binomial model is violated, the independence of successive shots, or the constant probability of success on each shot? Or can you tell? Explain your reasoning.
(c) Your company needs to make an important decision that involves large monetary consequences. You have listed all of the possible outcomes and the monetary payoffs and costs from all outcomes and all potential decisions. You want to use the EMV criterion, but you realize that this requires probabilities and you see no way to find the required probabilities. What can you do?
(d) If your company makes a particular decision in the face of uncertainty, you estimate that it will either gain $10,000, gain $1000, or lose $5000, with probabilities 0.40, 0.30, and 0.30, respectively. You (correctly) calculate the EMV as $2800. However, you distrust the use of this EMV for decision-making purposes. After all, you reason that you will never receive $2800, you will receive $10,000, $1000, or lose $5000. Discuss this reasoning.
(e) In the previous question, suppose you have the option of receiving a check for $2700 instead of making the risky decision described. Would you make the risky decision, where you could lose $5000, or would you take the sure $2700? What would influence your decision?
(f) A potentially huge hurricane is forming in the Caribbean, and there is some chance that it might make a direct hit on Hilton Head Island, South Carolina, where you are in charge of emergency preparedness. You have made plans for evacuating everyone from the island, but duh n evacuation is obviously costly and upsetting for all involved, so the decision to evacuate shouldn’t be made lightly. Discuss how you make such a decision. Is EMV a relevant concept in this situation? How would you evaluate the consequences of uncertain outcomes?
(g) You often hear about the trade-off between risk and reward. Is this trade-off part of the decision making under uncertainty when the decision-maker uses the EMV criterion? For example, how does this work in investment decisions?
(h) Under what conditions would you prefer a simple exponential smoothing model to the moving averages method for forecasting a time series? Explain your reasoning!
hello all today's people are in the class of all the dues and then you will be able and send your friends and family members from your side of your home and get it right
What is the area, in square centimeters of the shaded part of the rectangle shown below
The area of shaded region is 100 square centimeters.
What is an area?
An area is the amount of space taken up by a 2D shape or surface. The area of a shape is the number of unit squares required to completely cover it.
For the given situation,
The diagram shows the rectangle. In rectangle, some region is shaded and some region is left. The unshaded region is in the shape of the right triangle.
The area of shaded region = Area of rectangle - Area of triangle
The dimension for rectangle,
Length = 10 cm
Width = 14
The formula of area of rectangle = (length)(width)
The dimension for triangle,
Base = 10 cm
Height = 14 - 6
⇒ Height = 8 cm
The formula of area of triangle = 1/2 (base)(height)
On substituting the above values,
Thus area of shaded region = [tex](10)(14)-\frac{1}{2} (10)(8)[/tex]
⇒ [tex]140-40[/tex]
⇒ [tex]100[/tex]
Hence we can conclude that the area of shaded region is 100 square centimeters.
Learn more about area here
https://brainly.com/question/14853802
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6. Simone was timing John, Johnny and
James to see who could hold their breath
the longest. John held his breath for 10
seconds, Johnny held his breath for 15
seconds and James for 25 seconds. For how
much longer than John and Johnny did
James hold his breath?
Answer:
hgyjhudhehd
Step-by-step explanation:
what is:
k/5 + 2.5 = .5?
Answer:
k = -10
Step-by-step explanation:
k/5 + 2.5 = 0.5
k/5 = -2
k = -10
1. If CA = 12 cm, what is the measure of ER?
1CD
CD
Answer:
[tex]ER = 12cm[/tex]
Step-by-step explanation:
Given
See attachment for the given shape
Required
Length of ER
The given shape is a parallelogram and the opposite sides are: CA and ER
Given that:
[tex]CA= 12cm[/tex]
We have:
[tex]CA = ER[/tex] --- opposite sides of a parallelogram
So:
[tex]ER = 12cm[/tex]
find the area of this trapezoid. Include the correct unit in your answer.
I need help understanding this and how to do it :)
Answer:
[tex] \displaystyle A _{ \text{trapezoid}} = 70 {m}^{2} [/tex]
Step-by-step explanation:
we are given a trapezoid
we want to figure out the area
remember that,
[tex] \displaystyle A _{ \text{trapezoid}} = \frac{a + b}{2} h[/tex]
where a and b represent the parallel lines and h represents the height
we get from the pic that a and b are 5 and 15 respectively and h is 7
so substitute:
[tex] \displaystyle A _{ \text{trapezoid}} = \frac{5 + 15}{2} \times 7[/tex]
simplify addition:
[tex] \displaystyle A _{ \text{trapezoid}} = \frac{20}{2} \times 7[/tex]
simplify division:
[tex] \displaystyle A _{ \text{trapezoid}} = 10\times 7[/tex]
simplify multiplication:
[tex] \displaystyle A _{ \text{trapezoid}} = 70[/tex]
since we multiply two same units we of course have to use square unit
hence,
[tex] \displaystyle A _{ \text{trapezoid}} = 70 {m}^{2} [/tex]
How many odd numbers are in 10 to 50?
Answer:
20
Step-by-step explanation:
11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49
GIVING OUT BRAINLIEST ANSWER !! PLS HELP ME OUT !! (last minute)
Answer:
.7880
Step-by-step explanation:
Answer:
pretty sure it's 0.7880 !!! good luck, this stuff is super tough :(
Step-by-step explanation:
The exponential model A = 661.7 e^0.011t describes the population, A, of a country in millions, t years after 2003. Use the model to determine the population of the country in 2003
Answer:
661.7 million
Step-by-step explanation:
Given the exponential model :
A = 661.7 e^0.011t
The general form of an Exponential model is expresses as :
A = A0 * e^rt
Where A = final value ; A0 = Initial value ; r = growth rate and t = time elapsed
From the question t = time after 2003
Therefore, A0 = initial population, which is the population in 2003
Therefore, A0 = 661.7
Or we could put t = 0 in the equation and solve for A
A = 661.7 e^0.011(0)
A = 661.7 * 1
A = 661.7
Hence, population in 2003 is 661.7 million
You are rolling a pair of dice what's is the probability of getting different numbers on both dice
Answer:
[tex]Pr = 0.833[/tex]
Step-by-step explanation:
Given
A roll of a pair of dice
Required
The probability of getting different numbers
First, list out the sample space;
We have:
[tex]S = \{(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6),(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6),[/tex]
[tex](3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6),(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)[/tex]
[tex](5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6), (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)\}[/tex]
The total is:
[tex]Total = 36[/tex]
The outcomes of the different numbers are:
[tex]Different = \{(1, 2) (1, 3) (1, 4) (1, 5) (1, 6),(2, 1) (2, 3) (2, 4) (2, 5) (2, 6),[/tex]
[tex](3, 1) (3, 2)(3, 4) (3, 5) (3, 6),(4, 1) (4, 2) (4, 3) (4, 5) (4, 6)[/tex]
[tex](5, 1) (5, 2) (5, 3) (5, 4) (5, 6), (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) \}[/tex]
The total is:
[tex]Different = 30[/tex]
So, the probability of having a different outcome is:
[tex]Pr = \frac{Different}{Total}[/tex]
[tex]Pr = \frac{30}{36}[/tex]
[tex]Pr = 0.833[/tex]
The manager of a fleet of automobiles is testing two brands of radial tires and assigns one tire of each brand at random to the two rear wheels of eight cars and runs the cars until the tires wear out. The data (in kilometers) follow. Find a 99% confidence interval on the difference in the mean life.
Car Brand 1 Brand 2
1 36663 33866
2 43509 41829
3 36240 35500
4 32100 31950
5 37210 38015
6 48360 47800
7 38200 37810
8 33500 33215
a) Calculate SD =
b) Calculate a 99% two-sided confidence interval on the difference in mean life.
c) Which brand would you prefer? (brand 1/ no difference /brand 2)_____
Answer:
a) σ = 4933,64
b) CI 99% = ( - 5746 ; 7194 )
c) No difference in brands
Step-by-step explanation:
Brand 1:
n₁ = 8
x₁ = 38222
s₁ = 4974
Brand 2:
n₂ = 8
x₂ = 37498
s₂ = 4893
As n₁ = n₂ = 8 Small sample we work with t -student table
degree of freedom df = n₁ + n₂ - 2 df = 8 +8 -2 df = 14
CI = 99 % CI = 0,99
From t-student table we find t(c) = 2,624
CI = ( x₁ - x₂ ) ± t(c) * √σ²/n₁ + σ²/n₂
σ² = [( n₁ - 1 ) *s₁² + ( n₂ - 1 ) * s₂² ] / n₁ +n₂ -2
σ² = 7* (4974)² + 7*( 4893)² / 14
σ² = 24340783 σ = 4933,64
√ σ²/n₁ + σ²/n₂ = √ 24340783/8 + 24340783/8
√ σ²/n₁ + σ²/n₂ = 2466
CI 99% = ( x₁ - x₂ ) ± 2,624* 2466
CI 99% = 724 ± 6470
CI 99% = ( - 5746 ; 7194 )
As we can see CI 99% contains 0 and that means that there is not statistical difference between mean life of the two groups
what is the slope of the line.
Answer:
1 ..................or 1/1
Answer:
-1 is the slope
..................
Someone helppp pls :(((((
Answer:
y = ½x + 8
Step-by-step explanation:
✔️First, find the slope (m) using any two given pairs of values, say (0, 8) and (2, 9):
Slope (m) = change in y/change in x
Slope (m) = (9 - 8)/(2 - 0)
Slope (m) = 1/2
m = ½
✔️Find the y-intercept (b):
The y-inteeceot of the function would be the value of y when x = 0.
Form the table, when x = 0, y = 8. Therefore:
y-intercept (b) = 8
✔️To write the equation of the function, substitute m = ½ and b = 8 into y = mx + b.
Thus:
y = ½x + 8
WILL GIVE BRAINLIEST AND 40 POINTS TO CORRECT ANSWER (URGENT)
chef daniels places her favorite recipes in a bag for 4 pasta dishes, 5 casseroles, 3 types of chili, and 8 desserts. If Chef Daniel chooses two recipes at random (but replaces the first one before drawing the second), what is the probability that the first recipe she selects is a casserole and the second recipe she selects is a dessert?
Answer:
answer:
answe:
answ:
ans:
an:
as:
a:
: