An exponential function gives a variable raised to the power of x, where the variable is a positive real number
Yes, [tex]\underline{f(x) = 3 ^{(2 \cdot x - 3)}}[/tex] is an exponential function
Reason:
An exponential function is a function that can be written in the form;
f(x) = eˣ
Where;
e = Euler's number, which is the number approximately 2.71828
In the general form, an exponential number is a number given in the form;
f(x) = a·bˣ
Where;
b = A positive real number
The given function; [tex]f(x) = 3 ^{(2 \cdot x - 3)} = \dfrac{3^{2\cdot x}}{3^3} = \dfrac{1}{27} \times 9^x[/tex] is an exponential function
Where;
a = [tex]\dfrac{1}{27}[/tex]b = 9Therefore, the correct response is; Yes, [tex]f(x) = 3 ^{(2 \cdot x - 3)}[/tex] is an exponential function
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evaluate the expression if m = -5 and n = 7
|-m+n|
|m+n|
-|m+(-n)|
-|-m|+n
Answer:
n m
Step-by-step explanation:
mn
Find the value of x
Answer:
We know that the area of a triangle is:
1/2 * base * height
We are given:
base = x + 6
height = x
area = 108 m^2
Applying the formula:
Area = 1/2 * base * height
108 = 1/2 * x * (x + 6)
x² + 6x = 216
x² + 6x - 216 = 0
x² + 18x - 12x -216 = 0 (Splitting the middle term)
x(x + 18) - 12(x + 18) = 0
(x + 18) (x - 12) = 0
Hence, we have 2 possible values for x: -18 or 12
Since taking x as -18 will result in the length of sides of this triangle to be negative, -18 is NOT the value of x
Therefore, x = 12
I need to see how you solve this problem.
Answer:
What is the problem? Pls follow me!प्रश्न 5 समीकरण हल कीजिए- (आलेख विधि से नही)
4x-5y+16 =0
2x+y-6 =0
bicol method)
Answer:
Step-by-step explanation:
Given the simultaneous equation
4x-5y+16 =0 ....... 1
2x+y-6 =0 ...... 2
Let us solve to get the variable x and y:
The equation becomes
4x-5y =-16 ........ * 1
2x+y =6 ...... *2
Using Elimination method
Multiply eqn 1 by 1 and eqn 2 by 2
4x-5y =-16
4x+2y =12
Subtract resulting equation
-5y-2y = -16-12
-7y = -28
solve for y
-7y/-7 = -28/-7
y = 4
Substitute y = 4 into equation 2 to get x
2x+y =6
2x + 4 = 6
2x = 6-4
2x = 2
x = 2/2
x = 1
hence x is 1, y is 4
pls help jwjwkwkwwkwkwkwkwkkwwkkwkwwkkwkw
Answer:
o,-3 and 1.5,0
Step-by-step explanation:
You can find a calculator on a website called Desmos that might help answer related questions.
Yoshi needs to find the inverse of f(x) = 5x – 2. What is the first step?
Answer:
D. Replace f(x) with y
Step-by-step explanation:
apex
Yoshi needs to find the inverse of f(x) = 5x – 2. The first step is to Switch x and y. The correct answer is option C.
In mathematics, an inverse function is a function that "undoes" the actions of another function. If a function f(x) maps an input x to an output y, the inverse function, denoted as f^(-1)(x) or sometimes written as f(x)^(-1), maps the output y back to the original input x. The correct answer is option C.
To find the inverse of a function, the first step is to switch the x and y variables. In this case, the function is f(x) = 5x - 2.
To find the inverse, we need to switch x and y, so the new function becomes x = 5y - 2.
It's important to note that not all functions have an inverse. A function must be one-to-one (each input maps to a unique output) for an inverse to exist. Additionally, the domain and range of a function and its inverse are swapped.
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the complement of an angle is 40° more than four times itself.find the supplement angle
Answer:
Supplement angle: 170°
Step-by-step explanation:
Equations
Let x=the required angle. Since complementary angles sum 90°, then 90-x is the complement of x. According to the conditions of the question:
[tex]90-x=40+4x[/tex]
Simplifying:
[tex]90-40=4x+x=5x[/tex]
Solving:
[tex]x=50/5=10[/tex]
The angle is 10°. The supplement angle is 180°-10°=170°.
Supplement angle: 170°
Find the reciprocal: 5/6
A. 1/6
B. 1/5
C. 5/6
D. 6/5
Answer:
D
Step-by-step explanation:
just flip the fraction
Answer:
D
Step-by-step explanation:
The reciprocal is just the fraction flipped.
The math club is selling gift wrap for a fumdraiser. They sold all 45 rolls of solid wrapping paper at $4 each and rolls of patterned wrapping paper at $5 each. If they made $265 how many rolls of patterned wrapping paper did they sell
Answer:
17 rolls
Step-by-step explanation:
4 x 45 = 180
265-180 = 85
85 ÷ 5 = 17
hope this helps ;)
if y varies directly with X and Y=24 when x=6, find x when y = 32
Answer:
8
Step-by-step explanation:
if y varies with x, then they are directly proportional, so their ratio is constant (ie x divided by y is allways the same)
when x = 6, y = 24:
y / x = 4
when y = 32:
32 / x = 4
so x = 32 / 4 = 8
if a ferry boat covers 28 miles in 4 hours how much distance will it cover in 12 hours?
Answer:
84 miles in 12 hour
Step-by-step explanation:
12/4 = 3
3*28=84
Answer:
84 miles.
Step-by-step explanation:
First, find the rate of miles travel per hour. It is given that the boat covers 28 miles in 4 hours. Simply divide 28 with 4:
28/4 = 7
The boat covers 7 miles per hour.
Now, multiply 12 hours with 7:
12 hours x 7 miles per hour = 84 miles per 12 hours.
84 miles is your answer.
~
Method of Least Squares, Evaluation of Cost Equation Lassiter Company used the method of least squares to develop a cost equation to predict the cost of moving materials. There were 80 data points ft the regression, and the following computer output was generated: Intercept $19,050 Slope Coefficient of correlation 0.91 Standard error $220 The activity driver used was the number of moves.
Required:
1. What is the cost formula?
2. Using the cost formula, predict the cost of moving materials if 340 moves are made.
3. What percentage of the variability in moving cost is explained by the number of moves? (Round percentage to two decimal places.)
Answer:
(1) The cost formula is: y = $19,050 + $12·x.
(2) The cost of moving materials if 340 moves are made is $23,130.
(3) 82.81% of the variability in moving cost is explained by the number of moves.
Step-by-step explanation:
The computer output for the regression analysis of 80 data points is as follows:
Intercept: $19,050
Slope: 12
Coefficient of correlation: 0.91
Standard error: $220
(1)
The general formula of regression equation is:
y = a + b·x
Here,
a = intercept
b = slope
The cost formula is:
y = $19,050 + $12·x
(2)
Predict the cost of moving materials if 340 moves are made as follows:
[tex]y = 19050 + 12\cdot x\\=19050+12\times 340\\=19050+4080\\=23130[/tex]
Thus, the cost of moving materials if 340 moves are made is $23,130.
(3)
The coefficient of determination R² specifies the percentage of the variance in the dependent variable (Y) that is forecasted or explained by linear regression and the forecaster variable (X, also recognized as the independent-variable).
The coefficient of determination R² can be computed by squaring the correlation coefficient value.
[tex]R^{2}=(r)^{2}=(0.91)^{2}=0.8281[/tex]
Thus, 82.81% of the variability in moving cost is explained by the number of moves.
2 - 2x +5 -3x + 3x + 4
Answer:
-2x+11
Step-by-step explanation:
You need to combine like terms, so combine the x terms first.
You would have
-2x-3x+3x=-2x
Then combine the like terms of the normal numbers
2+5+4=11
Answer:
-2x+11
-hope this is what you were looking for:))
Step-by-step explanation:
Explain how the pattern of chairs in a movie theater can be described using translation.
Answer:
Step-by-step explanation:
reflection over the x-axis as well reflected over the Y axis and rotated 90° counterclockwise and clockwise
Answer:Since the chairs all have the same orientation, any chair in a row can be described as a horizontal translation of any other chair in that row. Likewise, any row of chairs can be described as a translation of any other row of chairs up and back or down and forward.
Step-by-step explanation: Just did it, that is the sample response.
evalute a/b for a= -6 and b=-2
Answer:
3
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Define
a/b
a = -6
b = -2
Step 2: Substitute and Evaluate
-6/-2
3
79% of what number is 181
I need help with #7 #11 #12 #13 and #14 please and ASAP
Answer:
54°
Step-by-step explanation:
Since m<2 + m<1 is equal to 180, we can set up the equation to find m<1.
plug in 126 as m<2, so we get
126 + m<1 = 180
-126 -126
m<1 = 54.
From this knowledge, we know that
7.) 54°
8.) 126°
9.) 54°
10.) 126°
11.) 54°
12.) 126°
13.) 54°
14.) 126°
3(x−2)+5x=18 what is the value of x
Answer:
x=3
Step-by-step explanation:
Problem
What is the slope of the line that contains these points?
***********
slope:
PLEASE HELP ASAP!!!
A cone has a volume of 200 in^3 and a
height of 10 in. Find the radius of this cone.
Answer:
The radius is 4.37 in approximately
Step-by-step explanation:
A floor is made up of 20 triangular tiles, each with sides 40 cm, 24 cm and 32 cm. Find the cost of polishing the floor at the rate of 2 rupees per sq.cm.
Answer:
[tex]15360\,\,rupees[/tex]
Step-by-step explanation:
Let sides of the triangle be [tex]a,b,c[/tex]
[tex]a=40\,,\,b=24\,,\,c=32[/tex]
Semi-perimeter (s) = [tex]\frac{a+b+c}{2}[/tex]
[tex]=\frac{40+24+32}{2}\\ =\frac{96}{2}\\=48[/tex]
Area of one tile [tex]=\sqrt{s(s-a)(s-b)(s-c)}[/tex]
[tex]=\sqrt{48(48-40)(48-24)(48-32)}\\ =\sqrt{48(8)(24)(16)}\\ =\sqrt{147456} \\=384\,\,cm^2[/tex]
So,
Area of 20 tiles [tex]=20(384)=7680\,\,cm^2[/tex]
Cost of polishing the floor at the rate of 2 rupees per sq.cm = [tex]7680(2)=15360\,\,rupees[/tex]
312,919,563x500➗999,527
Answer:
312 , 919 , 281 , 0. 500 , 527
Step-by-step explanation:
I'm really stupid sorryyyyyyyyyyyyyy
what is 4 x 10?
Answer:
your answer would be 40.
Answer:
4 x 10 = 40 :)
HELP ASAP this is hard
Answer:
C
Step-by-step explanation:
Answer:
D) positive association because the data on the scattergraph is decreasing (y axis) as the x axis increases.
Basically the data: theres a cluster, an outlier and has a negative association. Not a positive association.
What are two ways or more to calculate slope and what is the difference between them?
Answer:
one way.
k=y2-y1 / x2-x1
Can y’all help me pls
Answer:
Step-by-step explanation:
boiii this look are as a mf
what is the scale factor of the dilation
Answer:
Step-by-step explanation:
Jamal makes $12.00/hour and worked 9 hours today. What is his total pay? Don't forget to calculate overtime pay.
Answer:
He made $108 in 9 hours
Step-by-step explanation:
I first multiplied 12 by 9 and got 108
Answer:
$108
Step-by-step explanation:
12 x 9 = 108
$108/9 hours
Can someone help me plz
Answer:
make it so that the top side is 40 and make the sides 35
Step-by-step explanation:
16. A section of an exam contains four True-False questions. A completed exam paper is selected at random, and the four answers are recorded. a. List all outcomes in the sample space. b. Assuming the outcomes to be equally likely, find the probability that all the answers are the same. c. Assuming the outcomes to be equally likely, find the probability that exactly one of the four answers is "True." d. Assuming the outcomes to be equally likely, find the probability that at most one of the four answers is "True."
Answer:
a
[ FFFF] , [FFFT] , [FFTF] , [FFTT]
[FTFF] , [FTFT] , [FTTF], [FTTT]
[TFFF] , [TFFT] , [TFTF] , [TFTT]
[TTFF] , [TTFT],[TTTF] , [TTTT]
b
[tex]P(A) = \frac{1}{8}[/tex]
c
[tex]P(B) = \frac{1}{4}[/tex]
d
[tex]P(C) = \frac{5}{16}[/tex]
Step-by-step explanation:
From the question we are told that
The number of True - False question is n = 4
The number of answers recorded are k = 4
Generally the outcomes in the sample space are 16 and they are listed below
[ FFFF] , [FFFT] , [FFTF] , [FFTT]
[FTFF] , [FTFT] , [FTTF], [FTTT]
[TFFF] , [TFFT] , [TFTF] , [TFTT]
[TTFF] , [TTFT],[TTTF] , [TTTT]
Generally from the list of the possible outcome we see that the number of outcome where the answers are the same is 2 i.e [TTTT] and [FFFF]
So the probability that all the answers are the same is mathematically represented as
[tex]P(A) = \frac{2}{16}[/tex]
=> [tex]P(A) = \frac{1}{8}[/tex]
Generally from the list of the possible outcome we see that the number of outcome where exactly one answer is true is 4 i.e [FFTF] , [FFFT],[TFFF] , [FTFF]
So the probability that exactly one of the four answers is "True." is mathematically represented as
[tex]P(B) = \frac{4}{16}[/tex]
=> [tex]P(B) = \frac{1}{4}[/tex]
Generally from the list of the possible outcome we see that the number of outcome where at most one of the four answers is true is 5 i.e [FTFF] , [FFFF] , [FFTF] , [FFFT] ,[TFFF]
So the probability that at most one of the four answers is mathematically represented as
[tex]P(C) = \frac{5}{16}[/tex]
The probabilities of all same, exactly one true, and most one of the four are true is 0.125, 0.25, and 0.3125 respectively.
What is probability?Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
A section of an exam contains four True-False questions.
A completed exam paper is selected at random, and the four answers are recorded.
Total event = 16
A. The sample space will be shown in the table below.
[tex]\rm Sample \ space = 16 \ \begin{Bmatrix}FFFF & FFFT & FFTF & FFTT \\FTFF & FTFT & FTTF & FTTT \\TFFF & TFFT & TFTF & TFTT \\TTFF & TTFT & TTTF & TTTT\end{Bmatrix}[/tex]
B. The probability that all the answers are the same will be.
Favorable event = 2 ={(TTTT, FFFF}
Then we have the probability,
[tex]\rm P(B) =\dfrac{2}{16} =\dfrac{1}{8} = 0.125[/tex]
C. The probability that exactly one of the four answers is "True".
Favorable event = 4 {(FFFT, FFTF, FTFF, TFFF}
Then we have the probability,
[tex]\rm P(C) =\dfrac{4}{16} =\dfrac{1}{4} = 0.25[/tex]
D. The probability that at most one of the four answers is "True".
Favorable event = 5 {(FFFF, FFFT, FFTF, FTFF, TFFF}
Then we have the probability,
[tex]\rm P(D) =\dfrac{5}{16} =0.3125[/tex]
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