Answer:
\(g^{-1}\) (x) = 8x + 48
Step-by-step explanation:
let y = g(x) and rearrange making x the subject, that is
y = \(\frac{x}{8}\) - 6 ( add 6 to both sides )
y + 6 = \(\frac{x}{8}\) ( multiply both sides by 8 )
8(y + 6) = x , distribute
8y + 48 = x
Change y back into terms of x with x = \(g^{-1}\) (x) , thus
\(g^{-1}\) (x) = 8x + 48
68x0.4 = (Type a whole number
27.2
Explanation
Step 1
eliminate the dot and count the positions
\(0.4\rightarrow4(1\text{ position)}\)Step 2
now, make
\(\begin{gathered} 68\cdot4 \\ 68\cdot4=272 \end{gathered}\)now, move the dot ( from rigth to left the numbers of positions from the previous step)
\(272.0\rightarrow(1\text{ position)}\rightarrow27.2\)Hence, the answer is 27.2
What number is missing in this equation?
(-8.7) • (-10) = ?
18.7
-18.7
87
-87
Answer:
C. 87Step-by-step explanation:
(-8.7) • (-10) = 8.7 • 10 = 87Correct option is C
Answer:
87
Step-by-step explanation:
The table shows the number of points scored by a basketball team in their first seven games.
Answer:
15
Step-by-step explanation:
the range is the largest number take away the smallest number
56-41=15
Change the following fraction to a decimal. (Carry the division for three places as indicated. Do not round your answer.)
1/64 =
1/64 fraction is equal to 0.015625 in decimal form.
To change the fraction 1/64 to a decimal, we need to perform division.
1 divided by 64 can be written as:
0.015625
----------
64 | 1.000000
0
10
0
The result of the division is 0.015625. This means that 1/64 is equal to 0.015625 in decimal form.
Note that in this case, we carried the division out to six decimal places, but the question specified that we should carry it out to three decimal places. In that case, we would round the answer to 0.016.
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the time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of
The probability of waiting longer than one hour for a taxi is approximately 0.5488
Let X be the time between arrivals of taxis at the intersection. Then, X follows an exponential distribution with a mean of 10 minutes, i.e., E(X) = 10.
We want to find the probability of waiting longer than one hour (i.e., 60 minutes) for a taxi. Let Y be the waiting time for a taxi. Then, Y = kX, where k is a constant.
We can find k as follows
E(Y) = E(kX) = kE(X) = 10k
Since the mean waiting time is one hour (i.e., 60 minutes), we have
E(Y) = 60 minutes = 1 hour
Therefore, we get
10k = 1
k = 1/10
Now we can find the probability of waiting longer than one hour for a taxi as follows
P(Y > 60) = P(kX > 60) = P(X > 6) [since k = 1/10]
where the last step follows from the fact that X follows an exponential distribution with mean 10, so P(X > x) = e^(-x/10) for any x > 0.
Therefore, we get
P(Y > 60) = P(X > 6) = e^(-6/10) = e^(-0.6) ≈ 0.5488
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The given question is incomplete, the complete question is:
The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 10 minutes. (a) What is the probability that you wait longer than one hour for a taxi?
which expression is equivalent to 15 + 3x
Answer:
A. 3(5+x)
Step-by-step explanation:
if you multiply both 5 and x by 3(outside the parentheses), 3•5 is 15, and 3•x is 3x
PLEASEEEE SOMEONE HELP I GIVE AS MUCH POINTS :’( Thank you!
The approximate area of the trapezoid is determined as 13.95 unit².
What is the approximate area of the trapezoid?The approximate area of the trapezoid is calculated as follows;
Area = ¹/₂(b₁ + b₂)h
Where;
b₁ and b₂ are the lengths of the parallel sidesh is the heightThe y-coordinates of the points on the curve at x=3/2 and x=4 is calculated as follows;
y(3/2) = - (3/2)²/2 + 3/2 + 5
y(3/2) = -9/8 + 3/2 + 5
y(3/2) = 5.375
y(4) = -4²/2 + 4 + 5
y(4) = -8 + 9
y(4) = 1
h = 5.375 - 1 = 4.375
The approximate area of the trapezoid is calculated as;
Area = ¹/₂(5.375 + 1) x 4.375
Area = 13.95 unit²
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pls solve this question step by step.
Answer:
Daughter is 14 and son is 10==========================
Let the present ages be:
Daughter - d, son - sSet equations8 years ago:
d - 8 = 3(s - 8)At present:
d = s + 4Simplify and substitute d into the first equation:
d - 8 = 3s - 24d = 3s - 16s + 4 = 3s - 163s - s = 4 + 162s = 20s = 10Find d:
d = 10 + 4 = 149. The ratio of boys to girls in Mrs. Reeves's class is 4 to 5. There are 20 girls in the
class.
What is the total number of students in Mrs. Reeves's class?
Answer:
boys : girls
4 : 5
multiply by 4
16 : 20
total = 36
Answer:
80
Step-by-step explanation:
The price of an item has been reduced by 85
%. The original price was $17
.
Answer:
The answer is 2.55
Step-by-step explanation:
As, the original price = $17
So, 85% of it have been reduced from it so
85% of 17
= 85/100 x 17 = 14.45
So it have reduced by $14.45
So, $17 - $14.45= $2.55
Instructions: Use the given information to answer the questions and interpret key features. Use any method of graphing or solving.
According to the given statement, the number of product lies on the x-coordinate axis while the the overall profit margin represents the y-coordinate axis.
The interpretation of the vertex (75,10000) shows that the maximum profit is 10,000dollars is reached when 75 items are produced. The vertex shows the maximum point on the curve.
For the x-intercepts at x = 0 and x = 150. Since the x-intercept is the point where there is no profit margin (y = 0), hence:
The x-intercept (0, 0) tells us that the profit will be 0 dollars when 0 items are produced,
The second root (150, 0) says once 150 items are made, the company is no longer making any profit.
The absolute value of (2−7)=
The absolute value is:
5Work/explanation:
First, we will evaluate 2-7.
It evaluates to -5.
Now, let's find the absolute value of -5 by using these rules:
\(\sf{\mid a\mid=a}\)
\(\sf{\mid-a \mid=a}\)
Similarly, the absolute value of -5 is:
\(\sf{\mid-5\mid=5}\)
Hence, 5 is the answer.if you were informed that it takes one year for the earth to revolve around the sun, and that the square of that period was proportional to the cube of the earth's average distance from the sun, what law would fit that description?
Answer:kepler's 3rd law
Step-by-step explanation:
paired tires researchers were interested in comparing two methods for estimating tire wear. the first method used the amount of weight lost by a tire. the second method used the amount of wear in the grooves of the tire. a random sample of 16 tires was obtained. both methods were used to estimate the total distance traveled by each tire. the table below provides the two estimates (in thousands of miles) for each tire.29 (a) construct and interpret a 95% confidence interval for the mean difference m in the estimates from these two methods in the population of tires. (b) does your interval in part (a) give convincing evidence of a difference in the two methods of estimating tire wear? justify your answer.
(a) To construct a 95% confidence interval for the mean difference in the estimates of the two methods (method 1 - method 2), we need first to find the sample mean difference and its standard error.
The sample mean difference can be calculated as follows:
mean_diff = mean(method 1 estimates) - mean(method 2 estimates)
And the standard error of the mean difference can be calculated as follows:
standard error = sqrt(variance(method 1 estimates)/n + variance(method 2 estimates)/n)
Where n is the sample size (n = 16 in this case).
Using these values, the 95% confidence interval can be calculated as follows:
mean_diff ± 1.96 * standard error
This interval gives us a range of values that we can be 95% confident contain the true population means the difference between the two methods.
(b) To determine whether our interval in part (a) gives convincing evidence of a difference in the two methods of estimating tire wear, we need to examine the confidence interval and determine whether it includes 0. If the interval includes 0, then we do not have convincing evidence of a difference between the methods, as the difference could be 0. If the interval does not include 0, then we have evidence of a difference between the methods.
Therefore, our interpretation of the interval will depend on the specific values obtained from the calculation.
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5. - (m+) =
— Чт - 1=34
Answer:
The objective of this study was to examine the chronic effects on lower-body strength in resistance trained men of performing varying training volumes over 6
Step-by-step explanation:
Please help again it’s already late so no rush but also like kinda rush?
Answer:
B) Obtuse scalene
Step-by-step explanation:
Angle of 122 > 90 so it's obtuse
7.3≠2.9≠5.3 so it's scalene
Answer:
b
Step-by-step explanation:
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z (-_-)
I just need help with this,
The correct pairs pf points and axis of symmetry are (-1,-8) & y=-8 respectively.
What is the vertex of a parabola?The vertex of a parabola is the point at the intersection of the parabola and its line of symmetry. For a parabola whose equation is given in standard form , the vertex will be the minimum (lowest point) of the graph if and the maximum (highest point) of the graph if .
Given here; A parabola with upwards curve.
Now we know, The vertex is the highest point if the parabola opens downward and the lowest point if the parabola opens upward. The axis of symmetry is the line that cuts the parabola into 2 matching halves and the vertex lies on the axis of symmetry.
Thus we can clearly observe from the graph that (-1,-8) is the vertex of the parabola and we know the parabola is symmetric around its vertex.
Therefore the axis of symmetry of the parabola is y=-8
Hence, The correct pairs pf points and axis of symmetry are (-1,-8) & y=-8 respectively.
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Complete the steps in order to write the inverse of f(x)=x+5
=x45
1.
Writing the Inverse of a Function
2.
3,
1-x-5
The equation of the inverse function of the function f(x) = x + 5 is f'1(x) = x - 5
What are inverse functions?Inverse functions are the opposite of an original equation. This means that for a function f(x), the inverse of the function f(x) is f-(x); it also represents the opposite function
How to determine the inverse functions?The function f(x) is given as
f(x) = x + 5
As a general rule, we start by writing f(x) as a variable (say f(x) = y).
So, the equation of the function becomes
y = x + 5
The next step is to switch/swap the positions of x and y in the above equation y = x + 5
The equation becomes
x = y + 5
The next step is to make y the subject of the formula in the above equation x = y + 5
The equation becomes
y = x - 5
This is done by subtracting 5 from both sides of the equation.
So, we have:
y = x - 5
Express as an inverse function
f'1(x) = x - 5
Hence, the inverse function of the function f(x) = x + 5 is f'1(x) = x - 5
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The circle graph below represents the number of students at a middle school who buy lunch. If 624 students go to the school, about how many students do not buy lunch? Students who do not buy lunch Students who buy lunch 255⁰
The federal government of the United States spent over 28.7 billion dollars on the national school lunch program for the fiscal year of 2022.
Approximately what percentage of pupils skip lunch at school?In comparison to only 4% of children aged 6 to 13 years old, nearly one in ten adolescents (aged 14 to 17) admitted to skipping lunch.The federal government of the United States spent over 28.7 billion dollars on the national school lunch program for the fiscal year of 2022. Comparatively, the cost of the national school lunch program in the prior year was about 7.9 billion dollars.The federal government of the United States spent over 28.7 billion dollars on the national school lunch program for the fiscal year of 2022.Comparatively, the cost of the national school lunch program in the prior year was about 7.9 billion dollars.To learn more about percentage refer to:
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The number of students who do not buy lunch is 624 students - 420 students = 204 students.
Approximately how many pupils skip lunch at school?The circle graph represents the proportion of students who buy lunch and those who don't. To find the number of students who don't buy lunch, we need to subtract the number of students who buy lunch from the total number of students.
Since 255° represents the proportion of students who buy lunch, we can use this to find the number of students who buy lunch. To do this, we divide the number of degrees by 360° and multiply by the total number of students, 624:
(255° / 360°) x 624 students = 420 students
Therefore, the number of students who do not buy lunch is 624 students - 420 students = 204 students.
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Are all negative numbers are integers?
Answer:
No
Step-by-step explanation:
not all negative numbers are integers.
integers are whole numbers, such as 1, 2, 3, 4, 56, 73...ect
fractions and decimans are NOT integers
NOT integers: 0.75, 1.5, 5/8, 4/9
there can be negative integers too
-1, -2, -3, -4, -34
these are some negative NOT integers:
-0.5, -1.5, -3/2, -6/7, -100/3
The point P = (-5/3 squared, y) lies on the unit circle shown below. What is the value of
y in simplest form?
The required value of y for the unit circle is: 2/3
How to find the point on the unit circle ?The circle is defined as the locus of a point whose distance from a fixed point is constant i.e center (h, k).
The equation of the circle is given by:
(x - h)² + (y - k)² = r²
where:
h, k is the coordinate of the center of the circle on coordinate plane.
r is the radius of the circle.
Here,
Equation of the unit circle is given as,
x² + y² = 1
Now substitute the given value in the equation,
5/9 + y² = 1
y² = 1 - 5/9
y² = 4/ 9
y = √(4/9)
y = 2/3
Thus, the required value of y for the unit circle is 2/3
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PLEASE ANSWER THIS QUESTION URGENT!!
The length of the required chord is approximately equal to 11.8 units.
What is the chord of a circle?In Mathematics and Geometry, the chord of a circle refers to a line segment that typically join any two (2) points on a circle.
Based on the equation of the circle, the radius can be determined as follows;
x² + y² = 36
Radius, r = √36
Radius, r = 6 units.
By applying Pythagorean's theorem, side OA can be calculated as follows;
6² - 1² = OA²
OA² = 36 - 1
OA = √35
OA = 5.9
Length of chord = 2 × OA
Length of chord = 2 × 5.9
Length of chord = 11.8 units.
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An employee earned $10.00 per hour and then received a raise that paid
him $12.50 per hour. What is the percent change in the amount of money
he makes per hour. ?
Answer:
25% pay raise
Step-by-step explanation:
12.50-10.00=2.50
2.50/10.00=1/4
1/4=25%
if 75% of all families spend more than $75 weekly for food. if the mean expenditure is $104, what is the standard deviation? you can assume the expenditures are approximately normal.
The standard deviation and the mean are 16.95 and 86.43 respectively.
Z at 75% ≈ 0.674.
Since the spending is more than $75, Z = -0.674
Z at 15% ≈ - 1.036.
Since the spending is more than $104, Z = 1.036
Now,
Z = (x-mean)/SD => Z*SD = x-mean
Therefore,
-0.674*SD = 75 - mean ------- (1)
1.036*SD = 104 -mean ------- (2)
---------------------------------------------
(1) - (2)
-1.71SD = - 29 => SD = 75/1.71 = 16.95
Substituting SD in (1) => -0.674*43.8596 = 75 -mean => mean = 75+(0.674*43.8596) = 86.43.
Then,
SD = 16.95, mean = 86.43
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who wants to play surviv.io with me ill post the code
Answer:
Sure but later
Step-by-step explanation:
Answer:
Ok then post it
Step-by-step explanation:
Which angles are adjacent to each other?
Angle 8 and Angle 4
Angle 3 and Angle 6
Angle 2 and Angle 7
Angle 4 and Angle 3
Answer:
<4 and <3
Step-by-step explanation:
Adjacent angles are two angles that have a common vertex and a common side but do not overlap.
I hope this helps.
Answer:
angles 4 and 3
Step-by-step explanation:
its the right answer
a company is placing an order for boxed lunches for a meeting of its executive board. there are 10 members of the board and each will have one lunch. the company is getting the lunches from a restaurant that has 25 varieties of boxed lunches. (a) how many different ways are there for the company to place the lunch order for the 10 lunches? note that it is not important who gets what lunch. all that matters is how many of each of the 25 possible varieties are purchased. (b) how many ways are there for the company to place the lunch order if the 10 lunches purchased are all different? (again, who gets what lunch is not important, just how many of each lunch are purchased).
a)
There are 3268760 different ways for the company to place the lunch order for the 10 lunches
b)
There are 11861676288000 ways for the company to place the lunch order if the 10 lunches purchased are all different
What is permutation and combination?
The process of placing all the components of a set into a certain sequence or order is known as permutation in mathematics. In other terms, the process of permuting is the reordering of the components of a set if the set is already ordered. Nearly all areas of mathematics include permutations in some form or another. They frequently appear when various orderings on certain finite sets are taken into account.
Contrary to permutations, the order of selection is irrelevant when choosing elements from a collection using the combination method. The number of combinations may be counted in simpler situatiThe combinationation is the taking together of n items, k at a time, without repetition. The terms k-selection or k-combination with repetition are frequently used to describe combinations where repetition is permitted.
a) total different ways are \(C^{25} _{10}\)
= 25!/(25-10)!10!
= 25!/15! * 10!
= 3268760
b) total different ways are \(P^{25} _{10}\)
= 25!/(25-10)!
= 25!/15!
= 11861676288000
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PLEASE HWLP IM ON A TIME LIMIT
Determine f(–3) for A piecewise function f of x in three pieces. The function is defined by part 1, which is x cubed for x less than negative 3, part 2, which is 2 times x squared minus 9 for negative 3 is less than or equal to x which is less than 4, and part 3 which is 5 times x plus 4, for x greater than or equal to 4..
–27
–11
9
19
A function transfers each element's value from one set to a particular element in another set. When the value of x is -3, the function's value is -11.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
As the function's value is required to be rounded when the value of x is -3, we can write the function as follows:
\(f(-3) = 5\text{x} + 4\) Because x has a value of -3,
\(f(-3) = 5(-3) + 4\)
\(\bold{f(-3) = -11}\)
Hence, when the value of x is -3, the function's value is -11.
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Quadrilateral ABCD is an isosceles trapezoid with AC=BC The base angles are
Quadrilateral ABCD is an isosceles trapezoid with AC=BC The base angles are <A and <D, as well as <B and <C
∠A and ∠D, as well as ∠B and ∠C.
In Euclidean geometry, an isosceles trapezoid is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides. It is a special case of a trapezoid. Alternatively, it can be defined as a trapezoid in which both legs and both base angles are of the same measure.
Hence, the two bases of trapezoid are:
AD and BC.
Hence, the base angles are:
∠A and ∠D, as well as ∠B and ∠C.
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Emily put $3000.00 in a 2 year CD paying 4% interest compounded monthly. After 2 years she withdrew all her money. What is the amount of the withdrawl?
Answer:
A=3244.8 dollars
Step-by-step explanation:
A=p(1+r)^t
A=3000(1+0.04)^2
A=3244.8 dollars