Given function to us is : ⅚ x + 1 .
Here is step by step explanation :
Step 1 : Replace h(x) with y .
The equation becomes ,
⇒ y = ⅚x + 1 .
Step 2 : Interchange the variables .
⇒ x = ⅚y + 1.
Step 3 : Solve for y .
⇒x = ⅚ y + 1.
⇒ x - 1 = ⅚y .
⇒ y = 6/5 ( x - 1 )
⇒ y = 6/5x - 6/5 .
Step 4 : Replace y again with \(\underline{\sf h^{-1}(x)}\)
⇒ \(\bf h^{-1}(x)=\dfrac{6}{5}x-\dfrac{6}{5}\)
\(\large\boxed{\red{\bf \purple{\longmapsto}\:h^{-1}(x)\:\:=\:\:\dfrac{6}{5}x-\dfrac{6}{5}}}\)
The photo below is being enlarged to form a 24- by 30-inch print. What is the scale factor being used to enlarge it? 5 ia
Answer: 6
Step-by-step explanation:
The the scale factor being used to enlarge the photo is 6. Therefore, option B is the correct answer.
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
Given that, the photo below is being enlarged to form a 24- by 30-inch print.
In the figure, the dimensions are 4 inches and 5 inches.
Scale factor = 24/4 = 6
and 30/5 = 6
Therefore, option B is the correct answer.
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10 Students were surveyed.
How many hours do you study a week?
8 2 2 6 14 10 3 5 4
Determine the following:
A) Mean
B) Mode
C) Median
Show work please
Will mark brainlisted
Answer:mode
Step-by-step explanation:5+4+9+9+3+75+1=mode
Choose the set that is the possible side lengths of a right triangle.
a)1,1,2 b)3,5,9 c)3,4,7 d)1,1,square root2
Answer:
D
Step-by-step explanation:
Mathematically, for us to have a right triangle, Pythagoras’ theorem must be obeyed
From the theorem, the square of the hypotenuse (longest side) equals the sum of the squares of the two other sides
Let us take a look at the given set of numbers:
2 square is not same as 1 squared + 1 squared
9 squared is not equal to 3 squares + 5 squared
7 squared is not equal to 4 squared + 3 squared
But;
root 2 squared equals 1 squared plus 1 squared and that is our answer
a) Geeta buys x apples, ( ) x+7 oranges and ( ) 2 1 x- bananas. The total number of pieces of fruit Geeta buys is 30. (i) Find the number of apples Geeta buys. ................................................. [3] (ii) The cost of one apple is 15 cents. The cost of one orange is 18 cents. The total cost of all the fruit is $5.55 . Find the cost, in cents, of one banana.
The cost of one banana is 3 cents.Given that Geeta buys x apples, x+7 oranges, and 2 1 x- bananas.The total number of pieces of fruit Geeta buys is 30.
(i) To find the number of apples Geeta buys, we need to form an equation based on the given information.x + x + 7 + 2(1 x-) = 30.Simplify and solve for xx + x + 7 + 2 - 2x = 30-x + 9 = 30x = 30 - 9x = 21.Therefore, the number of apples Geeta buys is 21.
(ii) Cost of 1 apple is 15 cents.Cost of 1 orange is 18 cents.The total cost of all the fruit is $5.55.Cost of 21 apples = 21 × 15 = 315 cents.Cost of (x + 7) oranges = (x + 7) × 18.Cost of 2 1 x- bananas = (2 1 x-) × y cents, where y is the cost of one banana.
Total cost = 315 + (x + 7) × 18 + (2 1 x-) × y= 555 cents.Equating the above equation, we get;315 + (x + 7) × 18 + (2 1 x-) × y= 555315 + 18x + 126 + 2y - 2x - y = 555.
Simplify the equation.16x + y = 114.Now, we need to find the value of y, which is the cost of 1 banana. Given that 21 bananas were already bought, and we need to find the cost of one banana only.
Therefore we need to subtract the cost of 21 bananas from the total cost of all fruit and then divide by the remaining number of bananas.114 - 2 1 x- × y = cost of bananas = (555 - 315 - 18x - 126) cents = 114 cents.Therefore, 2 1 x- × y = 114 - 21 × y y = 3.Hence, the cost of one banana is 3 cents.
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HELP ASAP PLSSSSS
(picture of graph is below)
Below are the data collected from two random samples of 500 American adults on the number of hours they spend doing leisure and sports activities per day (rounded to the nearest hour):
Number of hours spent doing leisure and sports activities per day 1 2 3 4 5
Sample A: Number of adults 70 90 135 140 65
Sample B: Number of adults 80 80 130 135 75
Dan concludes that adults spend a mean of 3 hours each day doing leisure and sports activities. Bret thinks the mean is 4 hours. Who is correct—Dan or Bret? Explain your answer in two or three sentences. Make sure to use facts to support your answer.
Answer:
Dan is correct
Step-by-step explanation:
Mean = the sum of all data values divided by the total number of data values
Number of adults in Sample A:
= 70 + 90 + 135 + 140 + 65 = 500
Mean of Sample A:
= [ (1 × 70) + (2 × 90) + (3 × 135) + (4 × 140) + (5 × 65) ] ÷ 500
= 1540 ÷ 500
= 3.08
Number of adults in Sample B:
= 80 + 80 + 130 + 135 + 75 = 500
Mean of Sample A:
= [ (1 × 80) + (2 × 80) + (3 × 130) + (4 × 135) + (5 × 75) ] ÷ 500
= 1545 ÷ 500
= 3.09
Mean of the two samples:
= (3.08 + 3.09) ÷ 2
= 3.085 hours
= 3 hours (nearest hour)
The mean of Sample A is 3.08 hours and the mean of Sample B is 3.09 hours, so the mean of the entire sample is 3.085 hours. If we round this to the nearest hour, then the mean is 3 hours. Therefore, Dan is correct in concluding that the adults spend a mean of 3 hours each day doing leisure and sports activities.
Which expression represents the number -2i(5- i) + (17- 8i) rewritten in a + bi
form?
O 15-18i
O 15-2i
O 19 - 18i
O 11 + 8i
Answer:
(a) 15 -18i
Step-by-step explanation:
You want the simplified form of the expression -2i(5- i) + (17- 8i).
Complex numbersFor many purposes, the value i in a complex number can be treated in the same way a variable would be treated. When simplifying an expression involving i, any instances of i² can be replaced with the real value -1.
-2i(5- i) + (17- 8i) = -10i +2i² +17 -8i
= -2 +17 +(-10 -8)i
= 15 -18i
__
Additional comment
Your scientific or graphing calculator can probably help you evaluate such expressions.
Please help and show work only do the left side
Writing linear equations given two points can be a useful skill when graphing linear equations.
Write a linear equation that passes through the given two points?To write a linear equation given two points, you need to first find the slope of the line. You can do this by finding the change in the y-value and dividing it by the change in the x-value. From there, you can use the slope to solve for the y-intercept and write the equation.For example, if the two points are (3, 4) and (0,5), you would find the slope by calculating the change in the y-value (5-4 = 1) and dividing it by the change in the x-value (0-3 = -3).The slope would then be 1/-3, which can be simplified to -1/3. To solve for the y-intercept, you can plug in one of the points and solve for b. In this case, you would plug in (3, 4) and solve for b, giving you b = 5. Now that you have the slope and y-intercept, you can write the equation as y = -1/3x + 5.y = -1/2xy = 5/3x + 5/3y = 3/5x + 1y = -1/2x - 2y = 6/5x + 5y = -4/4x - 8y = -3/5x - 7/5y = -2x - 4y = 5/6x + 7y = -1/2x + 4To learn more about linear equation refer to:
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Plz help fast will mark brainliest!!!
I think it is 457.333333 π m3
Hope this helped :T
Answer:
1436.76
Step-by-step explanation.
\(\frac{4}{3}\pi r^{3}\)
that is the formula, with r being the radius.
then if you replace r with 7 that would be the answer.
pi, also equals 3.14159265359, or shortened 3.14.
so it would look like:
\(\frac{4}{3}*3.14*7^{3}\)
During a camping trip, Ana ate 39 grapes and Xan ate 22 grapes. There were 14
grapes left in the bag. How many grapes were in the bag before the trip?
Answer: 75 Grapes
Step-by-step explanation:
14 grapes left + 39 grapes Ana ate + 22 grapes Xan ate = Original 75 grapes in the bag
Answer:
There were 75 grapes in the bag before the trip
Step-by-step explanation:
First, you will need to add up all the grapes that they ate.
39+22=61
Then, you need to add the left over grapes and the grapes that both of them ate all together.
61+14=75
So, they had 75 grapes in the bag before the trip.
Find the value of y picture *****
I will Brainlist Who can Answer this 4 Question Math
Match the situation with the corresponding linear system. Write the letter of your answer.
Answer:
6) B
7) D
8) C
9) A
Step by step explanation:
6) Brand A sold 12 notebooks
Brand B sold 28 notebooks
7)
8) 30 pieces of 100-peso bills
10 pieces of 50-peso bills
9) 4 packages have 2 pieces
6 packages have 3 pieces.
The following system of equations is graphed below.
Find the solution to the system.
-2x+3y=-3
2x + 5y = 27
Answer:
(6,3)
Step-by-step explanation:
Which of the following are true about regression with one predictor variable (often called "simple regression")? Check all that apply. The standardized regression coefficient, beta, has the same value as r, the estimated correlation. The total squared error divided by its degrees of freedom is the square of the standard error of estimate. The slope, b, of the regression equation has the same value as r, the estimated correlation.
Regression with one predictor variable, also known as simple regression, is a statistical method that aims to establish a relationship between a dependent variable and one independent variable.True statement about regression with one predictor variable is that the standardized regression coefficient, beta, has the same value as r.
In this type of regression, the standardized regression coefficient, beta, is equivalent to the estimated correlation coefficient, r.
Therefore, the statement that the standardized regression coefficient, beta, has the same value as r is true.
The total squared error divided by its degrees of freedom gives the mean squared error, which is the average amount of error in the regression model. The square root of the mean squared error is the standard error of estimate. The statement that the total squared error divided by its degrees of freedom is the square of the standard error of estimate is false. Rather, it is the mean squared error that is the square of the standard error of estimate.
The slope, b, of the regression equation is the change in the dependent variable associated with a unit change in the independent variable. The estimated correlation coefficient, r, is the degree to which the two variables are linearly related. The statement that the slope, b, of the regression equation has the same value as r, the estimated correlation is false. Therefore, the only true statement about regression with one predictor variable is that the standardized regression coefficient, beta, has the same value as r, the estimated correlation.
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select Rational or irrational for each number
Answer:
??????.
Step-by-step explanation:
????????????????
please answer my question
100+10% =
Answer:
110
Step-by-step explanation:
10% of 100 is 10
100+10=110
Factor this trinomial completely.
2x2 + 10x + 8
A. 2(x+4)(x + 1)
B. 2(x + 4)(x - 1)
C. 2(x - 4)(x - 1)
D. 2(x 7,4)(x + 1)
Answer:
\({ \tt{2 {x}^{2} + 10x + 8 }} \\ { \tt{ = (x + 1)(x + 4)}}\)
Answer:
A. 2 ( x + 4 )( x + 1 )
Step-by-step explanation:
2x² + 10x + 8
factor out 2 from the equation
2 ( x² + 5 x + 4 )
write 5x as a sum and rewrite the expression
2 ( x² + 4x + x + 4 )
factor out x from the equation
2 ( x ( x + 4 ) + x + 4 )
factor out x + 4 from the equation
2 ( x + 4 ) ( x + 1 )
Please help please now help ASAP
Answer:
2
Step-by-step explanation:
Write an equation that represents the graph
Answer:3:40 ratio
Step-by-step explanation:
Use the information to evaluate and compare Δy and dy. (Round your answers to four decimal places.)
y = x4 + 7 x = −2 Δx = dx = 0.01
Δy =?
dy =?
Δy=v-0.32 and dy = -0.32 .Δy and dy are both used to represent changes in the dependent variable y based on changes in the independent variable x.
Δy represents the change in y (the dependent variable) resulting from a specific change in x (the independent variable). In this case, y = x^4 + 7, x = -2, and Δx = dx = 0.01. Therefore, we need to calculate Δy and dy based on these values.
To calculate Δy, we substitute the given values into the derivative of the function and multiply it by Δx. The derivative of y = x^4 + 7 is dy/dx = 4x^3. Plugging in x = -2, we have dy/dx = 4(-2)^3 = -32. Now, we can calculate Δy by multiplying dy/dx with Δx: Δy = dy/dx * Δx = -32 * 0.01 = -0.32.
On the other hand, dy represents an infinitesimally small change in y due to an infinitesimally small change in x. It is calculated using the derivative of the function with respect to x. In this case, dy = dy/dx * dx = 4x^3 * dx = 4(-2)^3 * 0.01 = -0.32.
Therefore, both Δy and dy in this context have the same value of -0.32. They represent the change in y corresponding to the change in x, but Δy considers a specific change (Δx), while dy represents an infinitesimally small change (dx) based on the derivative of the function.
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What is 5x-2+7x-5 simplified?
Answer:
12x -7
Step-by-step explanation:
how to find the rate of change
Answer:
Step-by-step explanation:
rate of change is essentially slope
\(Rate Of Change = \frac{rise}{run}\) or
\(Rate Of Change = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }\) or
\(Rate Of Change = \frac{f(x_{2})- f(x_{1}) }{x_{2} -x_{1} }\)
TRUE/FALSE. Indicate whether the statement is true or false.1. The local extrema of a curve always have a slope of zero.2. A function is increasing on an interval if the slope of the tangent is positive over the interval.3. The first derivative test is used to find points of inflection.4. To find intervals where a function is decreasing, solve f'(x) <0.5. A point of inflection occurs where the slope of the tangent to the function is at a maximum or minimum.6. A rational function always has a vertical asymptote.7. Optimization problems require solving a derivative equal to zero.8. The zeros of the graph of f'(x) indicate the locations of the maximum and minimum points on the graph of f(x).
Answer:
1 False
2 True
3 False
4 True
5 False (statement is missing)
6 False
7 True
8 True
Find the remainder term Rn in the nth order Taylor polynomial centered at a for the given function. Express the result for a general value of n. f(x)=e-2x, a-2 Choose the correct answer below. (-2)" e -2c (x- 2)" for some c between x and 2. (-2)1+1 e -2c (n+ 1)! O B. Rn(x)- -(x-2)"+1 for some c between x and 2. (-2)1+1e 2c Rn(x)=?(n+1)!-(x-2)n + 1 for some c between x and 2. n -2c OD. (x-2)"+1 for some c between x and 2.
Here is the correct answer in LaTeX code:
The correct answer is \($B\). \(R_n(x) = (-2)^{n+1} e^{-2c} (n+1)!$.\) The remainder term, \($R_n(x)$\) , in the \($n$th\) order Taylor polynomial for the function \($f(x) = e^{-2x}$\) centered at \($a = -2$\) is given by the formula:
\(\[R_n(x) = \frac{f^{(n+1)}(c) \cdot (x-a)^{n+1}}{(n+1)!}\]\)
where \($c$\) is a value between \($x$\) and \($a$\). In this case, \($a = -2$.\)
Taking the derivative of \($f(x) = e^{-2x}$\) , we have
\($f'(x) = -2e^{-2x}$, $f''(x) = 4e^{-2x}$, $f'''(x) = -8e^{-2x}$\) , and so on.
Substituting these derivatives into the remainder term formula, we get:
\(\[R_n(x) = (-2)^{n+1} e^{-2c} (n+1)! \cdot (x-(-2))^{n+1} / (n+1)!\]\)
Simplifying, we have:
\(\[R_n(x) = (-2)^{n+1} e^{-2c} \cdot (x+2)^{n+1}\]\)
So, the correct answer is \($B\). \(R_n(x) = (-2)^{n+1} e^{-2c} (n+1)!$.\)
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What is the slope of the line on the graph?
1
1/2
2
3
Answer:
2
Step-by-step explanation:
The line goes up 2 units and to the right 1 unit.
I need help how to do it and give me the answers show your work please no links and I will make you brainily person and give you points.
Answer:
Could you post the question in the comments?
Step-by-step explanation:
The difference between 3 1/2 and 1 4/5 is _____.
2 4/5
2 7/10
1 4/5
1 7/10
Hey there!☺
\(Answer:\boxed{1\frac{7}{10}}\)
\(Explanation:\)
\(3\frac{1}{2}-1\frac{4}{5}\)
Subtract the two fractions:
\(3\frac{1}{2}-1\frac{4}{5}=\frac{17}{10}\)
To get the final answer, you will have to simplify 17/10:
\(\frac{17}{10}=1\frac{7}{10}\)
1 7/10 is your answer.
Hope this helps!☺
PLEASE HELP ILL GIVE BRAINLIEST!!
180 deg rotation about the origin and a translation 2 units left
Let f be the function defined by f(x)=lnx/x. What is the absolute maximum value of f ?
A. 1
B. 1/e
C. 0
D. -e
E. if does not have an absolute maxima value
The answer is (B) 1/e.
To find the absolute maximum value of f(x) = ln(x)/x, we need to find the critical points and endpoints of the function and then evaluate f(x) at these points to determine the maximum value.
First, we find the derivative of f(x):
f'(x) = (1/\(x^2\)) * (xln(x) - 1)
Setting f'(x) = 0, we get:
xln(x) - 1 = 0
Solving for x, we get:
x = 1/e
Since f(x) is only defined for x > 0, the only critical point is x = 1/e.
Next, we evaluate f(x) at the critical point and at the endpoints of the domain of the function:
f(1/e) = ln(1/e)/(1/e) = -1/e
f(0+) = lim(x→0+) ln(x)/x = lim(x→0+) (1/x) / 1 = ∞
f(∞) = lim(x→∞) ln(x)/x = lim(x→∞) (1/x) / (1/x) = 1
Since f(x) approaches infinity as x approaches 0+, and f(x) approaches 1 as x approaches infinity, the absolute maximum value of f(x) occurs at x = 1/e, and the maximum value is f(1/e) = -1/e.
Therefore, the answer is (B) 1/e.
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-
7.5 ft
Find the perimeter of the semicircular region
17.0938 in decimal expanded form