Answers
a)
\(f(4)=\dfrac{4^3}{4}+6=4^2+6=16+6=22\)
b)
\(\begin{aligned}\\&y=\dfrac{x^3}{4}+6\\&4y=x^3+24\\&x^3=4y-24\\&x=\sqrt[3]{4y-24}\\&f^{-1}(x)=\sqrt[3]{4x-24}\end\)
c)
\(f^{-1}(8)=\sqrt[3]{4\cdot8-24}=\sqrt[3]{8}=2\)
Answer:
\(\displaystyle \large{f(4)=22}\\\\\displaystyle \large{f^{-1}(x)=\sqrt[3]{4x-24}}\\\\\displaystyle \large{f^{-1}(8) = 2}\)
Step-by-step explanation:
In this problem, we are given the linear function:
\(\displaystyle \large{f(x)=\dfrac{x^3}{4}+6}\)
( a ) Find f(4)
Simply substitute x = 4 in the function f(x).
\(\displaystyle \large{f(4)=\dfrac{4^3}{4}+6}\\\\\displaystyle \large{f(4)=4^2+6}\\\\\displaystyle \large{f(4)=16+6}\\\\\displaystyle \large{f(4)=22}\)
( b ) Find the inverse
To find \(\displaystyle \large{f^{-1}(x)}\), solve for x-term then swap x-term and y-term.
\(\displaystyle \large{4f(x)=x^3+24}\\\\\displaystyle \large{4f(x)-24=x^3}\\\\\displaystyle \large{\sqrt[3]{4f(x)-24}=\sqrt[3]{x^3}}\\\\\displaystyle \large{x=\sqrt[3]{4f(x)-24}}\)
Swap f(x) and x.
\(\displaystyle \large{f^{-1}(x)=\sqrt[3]{4x-24}}\)
( c ) Find inverse f(8)
Substitute x = 8 in inverse function.
\(\displaystyle \large{f^{-1}(8) = \sqrt[3]{4(8)-24}}\\\\\displaystyle \large{f^{-1}(8) = \sqrt[3]{32-24}}\\\\\displaystyle \large{f^{-1}(8) = \sqrt[3]{8}}\\\\\displaystyle \large{f^{-1}(8) = 2}\)
Please let me know if you have any doubts!
Related Questions
so like can someone help me with this test
Answers
(2x+1)(3x+5)
explanation:
"What set of reflections would carry hexagon ABCDEF onto itself?. . Hexagon ABCDEF on the coordinate plane with pointA at negative 1, 1, pointB at negative 3, 1, pointC at negative 4, 2, pointD at negative 3, 3, pointE at negative 1, 3, and pointF at 0, 2. . .x-axis, y=x, x-axis, y=x .. y=x, x-axis, y=x, y-axis .. y-axis, x-axis, y-axis .. x-axis, y-axis, y-axis ."
Answers
A set of reflections that would carry hexagon ABCDEF onto itself would be "x-axis, y=x, x-axis" or "y=x, x-axis, y-axis".
What is a combination of reflections?
Combination of Two Reflections. A point or object once reflected can further be reflected to form a new image. The axes of these reflections may be parallel to each other or they intersect each other at a point.
Given the coordinates of hexagon ABCDEF, it can be determined that a set of reflections that would carry the hexagon onto itself would be a combination of reflections over the x-axis and y-axis.
One possibility would be to reflect over the x-axis, then reflect over the y=x line, and finally reflect over the x-axis again.
This would take the hexagon from its original position to itself.
Another possibility would be to reflect over the y = x line, then reflect over the x-axis, and finally reflect over the y-axis.
This would also take the hexagon from its original position to itself.
Hence, a set of reflections that would carry hexagon ABCDEF onto itself would be "x-axis, y=x, x-axis" or "y=x, x-axis, y-axis".
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Martín compra en la papelería una cuadernola y un block de hojas. Gastó en total $270. Se sabe además que el block de hojas sale 120 más que la cuadernola. Pregunta 4 Si "x" representa el precio de la cuadernola, ¿cómo expresarías el precio del block de hojas? El precio del block de hojas lo expresaría como
Answers
Answer:
El precio de las hojas lo expresaría como:
y= x+120, donde
x=precio de la cuadernola
y= precio del block de hojas
Step-by-step explanation:
De acuerdo a la información del enunciado, sabes que la suma del precio de una cuadernola y un block de hojas es igual a $270, lo cual puedes expresar de la siguiente forma:
x+y=270
x=precio de la cuadernola
y= precio del block de hojas
Además, en el enunciado se indica que block de hojas sale 120 más que la cuadernola lo que significa que el precio del block de hojas es igual al precio de la cuadernola más 120, lo que puedes indicar de la siguiente forma:
y= x+120
Esta ecuación la puedes reemplazar en la primera para encontrar los precios:
x+(x+120)=270
x+x=270-120
2x= 150
x=150/2
x= 75
Después puedes reemplazar el valor de x para encontrar y:
y= 75+120
y= 195
A temperature of 3225 °F will melt platinum. Gold melts at a temperature of 1947.974 °F.
How much higher is the melting temperature of platinum than the melting temperature of gold?
Answers
Answer:
1277.026
Step-by-step explanation:
What this question is asking is the difference between 3225 and 1947.974. To do this you subtract. 3225-1947.974. You get 1277.026 Deg F.
2) The area of my best friend's pool is 121ft2. What is the width of the pool if the length is 12ft?
Answers
Answer:
10.083333...ft
Step-by-step explanation:
length = 12ft
area = 121sqft
area = length * width
121sqft = 12ft * width
width = 121sqft / 12ft
\(width = 10\frac{1}{12}\mathrm{ft}\)
width = 10.08(3)ft
2+2-2-5+5+6+4+8-2+47+28
Answers
Answer:
93
Step-by-step explanation:
So, you basically basic math it, or calculator.
A salesperson contacts eight potential customers per day. From past experience, we know that the probability of a potential customer making a purchase is 0.10. a. What is the probability the salesperson will make exactly two sales in a day? b. What is the probability the salesperson will make at least two sales in a day? c. What is the expected number of sales per day?
Answers
The probability that the salesperson will make exactly two sales in a day is 0.1489, the probability that the salesperson will make at least two sales in a day is 0.1451, and the expected number of sales per day is 0.8.
Let X be the number of sales made per day by the salesperson.
Then X follows a binomial distribution with parameters n = 8 and p = 0.10.a. To find the probability that the salesperson will make exactly two sales in a day, we need to find P(X = 2).
P(X = 2) = nCx * p^x * q^(n-x) = 8C2 * (0.10)^2 * (0.90)^6 = 28 * 0.01 * 0.5314 = 0.1489
Therefore, the probability that the salesperson will make exactly two sales in a day is 0.1489.
b. To find the probability that the salesperson will make at least two sales in a day, we need to find P(X ≥ 2).
P(X ≥ 2) = 1 - P(X < 2) = 1 - [P(X = 0) + P(X = 1)] = 1 - [(8C0 * (0.10)^0 * (0.90)^8) + (8C1 * (0.10)^1 * (0.90)^7)] = 1 - [1 * 0.90^8 + 8 * 0.10 * 0.90^7] = 0.1451
Therefore, the probability that the salesperson will make at least two sales in a day is 0.1451.
c. Expected number of sales per day = E(X) = n * p = 8 * 0.10 = 0.8
Therefore, the expected number of sales per day is 0.8.
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Which window with the following dimensions is too small to allow a 48-inch piece of glass to fit through it?
28 x 45 inches
36 x 27 inches
40 x 40 inches
40 × 42 inches
Answers
The dimensions 36 x 27 inches are too small to allow a 48-inch piece of glass to fit through it.
What is meant by dimensions?An object's dimension is a topological measure of the size of its covering properties. It is the number of coordinates required to specify a point on the object.A dimension is a measurement that includes things like length, width, and height. When you talk about an object's or place's dimensions, you're referring to its size and proportions. Dimensions are the powers to which basic units or quantities are raised in order to represent a specific physical quantity. <br> e.g., : In the gravitational constant formula, the length, mass, and time dimensions are 3, -1, and -2, respectively. The dimensional formula is defined as the physical quantity expressed in terms of its basic unit with proper dimensions. Dimensional force, for example. F = [M L T-2] It's because the Force unit is Newton, or kg*m/s2.To learn more about dimensions, refer to:
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if f(x) = 3 - x^2, find f(-2)
Answers
Based on the function f(x) = 3 - x², the value of f(-2) include the following: f(-2) = -1.
What is a function?In Mathematics and Geometry, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair in tables or relations.
What is a domain?In Mathematics and Geometry, a domain is sometimes referred to as input value and it can be defined as the set of all real numbers for which a particular function is defined.
When the domain (input value) of the given function f(x) is -2, the output value (range) is given by;
f(x) = 3 - x²
f(x) = 3 - (-2)²
f(x) = 3 - 4
f(x) = -1
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factor out using the gcf 1/5c + 4/5
Answers
The factored expression of 1/5c + 4/5 is 1/5(c + 4)
How to factor the expression?From the question, we have the following parameters that can be used in our computation:
1/5c + 4/5
From the above expression, we have the following highlights
Terms of the expressions = 1/5c and 4/5Number of terms = 2In the above terms, we can see that the denominator of the terms is 5
When this denominator is removed, we have
Expression = c + 4
This means that
GCF =1/5
So, the factored expression is 1/5(c + 4)
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NO EXPLANATION JUST ANSWER!
Answers
The volume of the given cube is 8,000 cubic units if the surface area is 2,400.
What is volume?Let's first find the length of one side of the cube using the given surface area.
The surface area of a cube is given by the formula 6s², where s is the length of one side of the cube.
We are given that the surface area of the cube is 2,400. Therefore, we can set up the following equation:
6s² = 2,400
Dividing both sides by 6, we get:
s² = 400
let's see the square root of both sides, we get:
s = 20
So, the length of one side of the cube is 20.
Now, we can find the volume of the cube using the formula V = s³:
V = 20³ = 8,000
Then, the volume of the cube is 8,000 cubic units.
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Find the area of the triangle ABC given angle A = 45°, b = 8, and c = V2.
Answers
Answer:
180
Step-by-step explanation:
triangle 1/2 base x height = area 45 x 4 = 180
The continuous random variable V has a probability density function given by: 6 f(v) = for 3 ≤ ≤7,0 otherwise. 24 What is the expected value of V? Number
Answers
The expected value of the continuous random variable V is 5. The expected value of V is 5, indicating that, on average, we expect the value of V to be around 5.
To calculate the expected value of a continuous random variable V with a given probability density function (PDF), we integrate the product of V and the PDF over its entire range.
The PDF of V is defined as:
f(v) = 6/24 = 0.25 for 3 ≤ v ≤ 7, and 0 otherwise.
The expected value of V, denoted as E(V), can be calculated as:
E(V) = ∫v * f(v) dv
To find the expected value, we integrate v * f(v) over the range where the PDF is non-zero, which is 3 to 7.
E(V) = ∫v * (0.25) dv, with the limits of integration from 3 to 7.
E(V) = (0.25) * ∫v dv, with the limits of integration from 3 to 7.
E(V) = (0.25) * [(v^2) / 2] evaluated from 3 to 7.
E(V) = (0.25) * [(7^2 / 2) - (3^2 / 2)].
E(V) = (0.25) * [(49 / 2) - (9 / 2)].
E(V) = (0.25) * (40 / 2).
E(V) = (0.25) * 20.
E(V) = 5.
Therefore, the expected value of the continuous random variable V is 5.
The expected value represents the average value or mean of the random variable V. It is the weighted average of all possible values of V, with each value weighted by its corresponding probability. In this case, the expected value of V is 5, indicating that, on average, we expect the value of V to be around 5.
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-2+-6 in absolute value minus -2- -6 in absolute value
Answers
`-2+-6` in absolute value minus `-2--6` in absolute value is equal to `4`.
To solve for `-2+(-6)` in absolute value and `-2-(-6)` in absolute value and subtract them, we first evaluate the two values of the absolute value and perform the subtraction afterwards.
Here is the solution:
Simplify `-2 + (-6) = -8`.
Evaluate the absolute value of `-8`. This gives us: `|-8| = 8`.
Therefore, `-2+(-6)` in absolute value is equal to `8`.
Next, simplify `-2 - (-6) = 4`.
Evaluate the absolute value of `4`.
This gives us: `|4| = 4`.
Therefore, `-2-(-6)` in absolute value is equal to `4`.
Now, we subtract `8` and `4`. This gives us: `8 - 4 = 4`.
Therefore, `-2+-6` in absolute value minus `-2--6` in absolute value is equal to `4`.
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How much water fills the prism and what’s the slant height ?
Answers
Answer:
I. 56 cubic feet of water.
II. 5 feet
Step-by-step explanation:
Do the following question 7(x + 3) < 5x + 13?
Answers
Answer:
x < - 4
Step-by-step explanation:
7(x + 3) < 5x + 13 ← distribute parenthesis on left side
7x + 21 < 5x + 13 ( subtract 5x from both sides )
2x + 21 < 13 ( subtract 21 from both sides )
2x < - 8 ( divide both sides by 2 )
x < - 4
Step-by-step explanation: so 7 times x plus 3 is equal 21x and 5x plus 13 is equal to 18 x so the grester one is 7(x+3)
Find the value of x that makes the equation true.
2[x + (2 1/2 + 2x )] = -3 (x - 1 ) + 9
Answers
Answer:
x = 7/9 or 0.78 as a decimal
Step-by-step explanation:
have a nice day!! :)
2. Given 4x² + bx + 25, select a possible b value that will make this factorable. [A] b=-50 [B] b = -29 [C] b = 10 [D] b= 100
Answers
Answer:
b = 40 and -40
General form of Perfect square trinomial is
a
2
+
2
a
b
+
b
2
Therefore from
16
x
2
−
b
x
+
25
a
2
=
√
16
x
2
,
b
2
=
25
, then
a
=
±
4
x
,
b
=
±
5
take consideration a=4x and b=-5 (different sign), then
−
b
x
=
2
(
4
x
)
(
−
5
)
−
b
x
=
−
40
x
b
=
40
The perfect square is
(
4
x
−
5
)
2
=
16
x
2
−
40
x
+
25
.
if we consider a=4x and b=5 (same sign), then
−
b
x
=
2
(
4
x
)
(
5
)
−
b
x
=
40
x
b
=
−
40
The perfect square is
(
4
x
+
5
)
2
=
16
x
2
+
40
x
+
25
.
The first solution
(
4
x
−
5
)
2
is the best solution after comparing the expression given.
Here is a rectangle with length 5 units and width 2 units.
1. What is the area of the rectangle?
2. Dilate rectangle ABCD from point A by a scale factor of 2. Calculate the area of the image.
3. Dilate rectangle ABCD from point A by a scale factor of 3. Calculate the area of the image.
Answers
This refers to the ratio between the scale of a given original object and a new object. It is its representation but of a different size (bigger or smaller). For example, if we have a rectangle of sides 2 cm and 4 cm, we can enlarge it by multiplying each side by a number, say 2.
Solving for the area and scale factor we have:
L= 5 units
W = 2 units
The area of the rectangle =L * WA = (5 x 2)
A = 10 square units.
If the rectangle is dilated from point A by a scale factor of 2, the area of the image:A= (Scale factor of L * W)* L * W
= (2 x 2 x 5 x 2)
A = 40 square units.
If the rectangle is dilated from point A by a scale factor of 3, the area of the image is:A= (Scale factor of L * W)* L * W
= (3 x 3 x 5 x 2)
A= 90 square units
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english has 26 different letters. how many consecutive words have to be selected in a book to have at least 5 that start with the same letter?
Answers
The words need not be English language words 142506
What is permutation and combination?
A set of elements can be divided into subsets in two different ways: combination and permutation.
The components of the subset may be arranged in any order when combined. The components of the subset are listed in a permutation in a certain order.
If the word has 5 different letters then it is just 26-choose-5 or (26/5).
If the word has 4 different letters then it is just 26-choose-4 or (26/4)
have 4 options to choose which letter to duplicate twice.
This gives = 4*(26/4)
If the word has 3 different letters then it is just 26-choose-3 or (26/3).
you duplicate one of the three letters 3 times - 3 options for that, or you choose 2 letters and duplicate each one twice - again 3 options. In total this gives = 6*(26/3).
If the word has 2 different letters then it is just 26-choose-2 or (26/2).
The sets of 2 different letters and duplicate either one of the letters 4 times - 2 options; or duplicate one letter 2 times, and the other 3 times - again 2 options. In total this is = 4*(26/2).
The word has just 1 distinct letter you have = (26/1).
we get :
N = (26/5)+ 4*(26/4) + 6*(26/3) + 4*(26/2) + (26/1)
= 142506
The words need not be English language words = 142506
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What is the value of A when we rewrite 4^x+3-4^x as A times 4^x
Answers
This looks simple I belive the answer would be 35 because 4^x + 31^x = 35^x
Is 1+7/x=y a Linear equation
Answers
Answer:
No
Step-by-step explanation:
1+7/x=y cannot be a linear equation because x is the denominator. A variable in the denominator means it has restrictions to what it can or cannot be. For example it can never be 0.
The Freeman family is barbecuing veggie burgers, corn cobs, and mushroom caps in their local park. If 3/8 of the items barbecued or veggie burgers, and 1/3 of the items barbecued or corn cobs, what fraction of barbecued items are mushroom caps?
Answers
Answer:
7/24
Step-by-step explanation:
Let
total items barbequed = 1
Veggie burgers = 3/8
Corn cobs =1/3
Mushroom caps = x
Veggie burgers + corn cobs + x = 1
3/8 + 1/3 + x = 1
9+8 /24 + x = 1
17/24 + x = 1
x= 1 - 17/24
=24-17 /24
= 7/24
x = 7/24
Fraction of barbequed items that are mushroom's is 7/24
Answer:7/24
Step-by-step explanation:
Pentagon ABCDE is reflected across the line shown and then rotated
72 clockwise about its center to create congruent pentagon FGHIJ.
Label the vertices of FGHU in the correct positions on the image.
Answers
Answer:
rotate it once to the right and you will get the vertices
Step-by-step explanation:
Justin conducted a survey to find out people's favorite sport and recorded the results below. If Justin were to survey a total of 250 people, how many would you predict would name basketball?
Answers
Answer:
100 people
Step-by-step explanation:
In the attached image below we can see that the original survey was done on a total of 50 individuals (12 + 3 + 20 + 15 = 50). Out of these 50, 20 of them answered basketball.
20 / 50 = 0.40 ... multiply by 100 to get percentage
0.40 * 100 = 40%
We can see that this is 40% of the original survey sample population. If we use this same percentage, we can predict how many individuals out of 250 would answer basketball. We calculate this by multiplying 250 by 40% in decimal form, like so...
250 * 0.40 = 100
Finally, we can predict that 100 people would most likely answer basketball.
A jewelry store is selling a set of 4 pairs of gemstone earrings for $58, including tax. Neva and three of her friends want to buy the set so each could have one pair of earrings. Write a multiplication equation to find how much each person should pay.
Answers
Answer:
183
Step-by-step explanation:
tax would bring it up about 2/3 dollars
Brainliest pls
What’s the answer to this? Find 1/8 of 88
Answers
Answer:
11
Step-by-step explanation:
\(\frac{1}{8}\) of 88
= \(\frac{88}{8}\)
= 11
5/64 as a percentage, round your answer to the nearest tenth of a percent
Answers
Answer: 7.8%
Step-by-step explanation:
Because it is.
The volume of a cylinder is 156 pi centimeters cubed. What is the volume of a cone with the same base and height as the cylinder?
39 pi centimeters cubed
52 pi centimeters cubed
78 pi centimeters cubed
156 pi centimeters cubed
Answers
Answer:
the answer is 52 pi cm cubed
Answer:
(B)Step-by-step explanation:
52π cm³
or 52 pi centimeters cubed
Two large high schools in a city (3000 students in each school) claim they have a higher rate of students who go on to graduate from a 4-year university. 57% of students from school A go on to graduate from a 4 year university and 61% from school B. A random sample of 75 students from school A and 80 from school B are selected and followed to determine if they graduate from a 4-year university.
a. Find the probability that difference in sample proportions is more than 6.
b. What is the probability that School A sample proportion is more than 5% higher than School B?
Answers
a. The probability that difference in sample proportions is more than 6% is 0.1056.
b. There is a 0.2677 probability that the sample proportion from School A is greater than 5% than that from School B.
a. We must first determine the standard error of variation between the two sample proportions in order to determine the probability that the difference in sample proportions is greater than 6:
SEp1-p2 = sqrt{ [p1(1-p1)/n1] + [p2(1-p2)/n2] }
where,
P1 = 57% of students are from school A.
p2 = 61% of students are from school B.
Sample sizes from schools A and B were 75 and 80, respectively.
SEp1-p2 = sqrt{ [(0.57)(0.43)/75] + [(0.61)(0.39)/80] }
= sqrt{ 0.00233 + 0.00240 }
= 0.0803
Now, we can find the Z-score as:
Z = (p1 - p2 - D) / SEp1-p2
where,
D = 6% = 0.06
Z = (0.57 - 0.61 - 0.06) / 0.0803
= -1.248
Using a standard normal distribution table, we can find the probability that Z < -1.248 is 0.1056.
Therefore, the probability that difference in sample proportions is more than 6% is 0.1056.
b. To find the probability that School A sample proportion is more than 5% higher than School B, we need to find the standard error of the difference between the two sample proportions:
SEp1-p2 = sqrt{ [p1(1-p1)/n1] + [p2(1-p2)/n2] }
where,
57% of the population in p1 is from school A.
61% of those in p2 are from school B.
75 were included in the sample from school A, while 80 were included in the sample from school B.
SEp1-p2 = sqrt{ [(0.57)(0.43)/75] + [(0.61)(0.39)/80] }
= sqrt{ 0.00233 + 0.00240 }
= 0.0803
Now, we can find the Z-score as:
Z = (p1 - p2 - D) / SEp1-p2
where,
D = 5% = 0.05
Z = (0.57 - 0.61 - 0.05) / 0.0803
= -0.621
We can get the probability that Z -0.621 is 0.2677 by using a standard normal distribution table.
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