Answers
The required individual functions are given as g(x) = x⁴- 6 and f(x) = [tex]\sqrt[7]{x}[/tex].
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Given funciton
h(x) = (f o g) (x)
Where g(x) = x⁴- 6 and h(x) = [tex]\sqrt[7]{x^4-6}[/tex]
Since, put h(x) ⇒ f(x) and g(x) = x⁴- 6
f(x) = [tex]\sqrt[7]{g(x)}[/tex]
Again put g(x) ⇒ x
f(x) = [tex]\sqrt[7]{x}[/tex]
Thus, the required individual functions are given as f(x) = x⁴- 6 and g(x) = [tex]\sqrt[7]{x}[/tex].
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Related Questions
Suppose a student's grade for a course is weighted and based on three categories homework average, quiz average, and a project average.A) lithe quiz average is 80% of grade and the homework average is 20% of grade, what percentage of Students grade is their project average?B) Ifa student has a homework average of 95, a quiz average of 80, and a project average of 88, what would be students course grade? Round to nearest whole number.
Answers
The project average is 100% of the student's grade, and if the student has the given averages, their course grade would be 89%.
The project average is the only component of the student's grade that is not weighted. The homework average accounts for 20% of the grade, while the quiz average accounts for 80%. Therefore, the project average is 100% of the student's grade. If the student has the given averages, then their course grade can be calculated by multiplying the homework and quiz averages by their respective percentages and adding the two products. In this case, the student's course grade would be (95 * 0.2) + (80 * 0.8) + 88 = 89%. The student's course grade would then be rounded to the nearest whole number, which is 89%.
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find the lengths of the legs of a right triangle if it is known that sum of the lengths is 23cm, and the area of the triangle is 60cm^2
Answers
Answer:
15 and 8
Step-by-step explanation:
Let the legs be a, b
a+b=23
ab=120
Then, 23b-b^2=120. so b^2-23b+120=0. Thus (b-8)(b-15)=0. Thus b=8,15, and if b=8, then the other length a is 15.
Factor the following expression completely. 12xy-15x-20y+25
Answers
The required, given expression is completely factored as (4y -5)(3x - 5).
What is the factors?A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.
To factor the expression 12xy - 15x - 20y + 25, we can use the distributive property to factor out a common factor from each of the first two terms and the last two terms:
12xy - 15x - 20y + 25
= (12x)(y) - (15x)(1) - (20)(y) + (5)(5)
= (3x)(4y) - (5)(3x) - (4)(5y) + (5)(5)
= 3x(4y - 5) - 5(4y - 5)
= (4y -5)(3x - 5)
So, the expression is completely factored as, (4y -5)(3x - 5).
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According to the Environmental Protection Agency (EPA), the 2018 Toyota Camry L drives an average of 420.5 miles on a full tank of gas. Assume the mileage follows a normal distribution with a standard deviation of 50 miles. Answer the following questions:
17.) Determine the number of miles that the car will travel with 90%, 30%, and 50% probability on a full tank of gas.
18.) Determine the UPPER AND LOWER value(s) for the interval of miles traveled on a full tank of gas around the mean that includes approximately 68% of miles for this car.
19.) Determine the UPPER AND LOWER value(s) for the interval of miles traveled on a full tank of gas around the mean that includes approximately 95% of miles for this car.
20.) Determine the UPPER AND LOWER value(s) for the interval of miles traveled on a full tank of gas around the mean that includes approximately 99.7% of miles for this car.
Answers
17) The number of miles that the car will travel with 90%, 30%, and 50% probability on a full tank of gas is:
90% probability: 420.5 + (1.645 x 50) = 545.25 miles
30% probability: 420.5 - (1.645 x 50) = 295.75 miles
50% probability: 420.5 miles
18) The upper and lower values for the interval of miles traveled on a full tank of gas around the mean that includes approximately 68% of miles for this car is:
Upper value: 420.5 + (1 x 50) = 470.5 miles
Lower value: 420.5 - (1 x 50) = 370.5 miles
19) The upper and lower values for the interval of miles traveled on a full tank of gas around the mean that includes approximately 95% of miles for this car is:
Upper value: 420.5 + (2 x 50) = 520.5 miles
Lower value: 420.5 - (2 x 50) = 320.5 miles
20) The upper and lower values for the interval of miles traveled on a full tank of gas around the mean that includes approximately 99.7% of miles for this car is:
Upper value: 420.5 + (3 x 50) = 570.5 miles
Lower value: 420.5 - (3 x 50) = 270.5 miles
The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
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I NEED HELP RIGHT AWAY PLS HELP
You asked amusement park visitors the question "How
many times did
left the park.
you ride the Ferris wheel today?" as they
Four people said they rode a Ferris wheel
5 times.
Explain how this would be shown on a dot plot.
Answers
On a dot plot, the statement saying that Four people said they rode a Ferris wheel five times would be represented with four dots above the input five.
What is a dot plot?
A dot plot shows the number of times that each observation was accrued in a data-set, which the number of dots representing the number of observations of each input.
The parameters for this problem are given as follows:
Input: number of times people rode the Ferris wheel.Output: number of dots.Hence the statement would be represented with four dots above the input five.
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GIVING BRAILIEST TO THOSE WHO ANSWER CORRECT AND TRY. please help! thanks
Answers
Answer:
the answer is A
Step-by-step explanation:
use the formula y=mx+b
25.95 is the slope because its a constant arte of change and 50 is the y-intercept because you gain $50 in addition to the slope
Answer:
y=25.95x+50
Step-by-step explanation:
25.95 is the dependent variable, so it is the coefficient. The starting amount, or the y-intercept, is 50. This makes the equation y=25.95x+50.
simplify fully
(x^2 +4)^2 - (x^2 - 2)^2
Answers
Answer:
12x^2 + 12
Step-by-step explanation:
1. Remove the parentheses:
x^4 + 8x^2 + 16 - x^4 + 4x^2 - 4
2. Cancel out terms:
8x^2 + 16 + 4x^2 - 4
3. Combine like terms:
12x^2 + 12
(a + b)(a - b) = a^2 - b^2
We can apply this formula twice to the expression:
((x^2 + 4) + (x^2 - 2))((x^2 + 4) - (x^2 - 2)) = (2x^2 + 2)(2) = 2(2x^2 + 2) = 4x^2 + 4.
So, the fully simplified form of the expression is:
4x^2 + 4
. ¿Qué cantidad por concepto de interés simple mensual produce un capital de $ 500,000 al 8% anual de interés simple?
Answers
Answer:
$500.000 × 0.08 = $40,000
$40,000/12 = $3.333.33
Step-by-step explanation:
El interés simple mensual se puede calcular como una fracción del interés anual. Para calcular el interés simple mensual, primero debemos calcular el interés anual y luego dividirlo entre 12 para obtener el interés mensual.
El interés anual se puede calcular multiplicando el capital por la tasa de interés:
$500,000 × 0.08 = $40,000
Luego, para obtener el interés simple mensual, dividimos el interés anual por 12:
$40,000 / 12 = $3,333.33
Por lo tanto, un capital de $500,000 al 8% de interés simple generará $3,333.33 de interés simple mensual.
The volume of a rectangular prism is (x³ − 3x² + 5x − 3), and the area of its base is (x² – 2). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism?
Answers
Answer: (x^3 - 3x^2 + 5x - 3)/(x^2 - 2)
Step-by-step explanation:
It says the volume equals the height multiplied by the base area, or base area x height = volume. Because we are given the volume and the base area, we can plug in the values to get (x^2 - 2) x height = (x^3 - 3x^2 + 5x - 3). Finally, we can divide both sides by (x^2 - 2) to get height = (x^3 - 3x^2 + 5x - 3)/(x^2 - 2).
If m∠1=95°, find the measure of ∠8
Answers
Answer:
If m∠1=95°, then m∠8 can be found by using the Exterior Angle Theorem, which states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. In this case, m∠8 = 180 - (m∠1 + m∠3) = 180 - (95° + 55°) = 30.
Find the least common multiple of (x-3)^2, x^2-9, and (x+3)^3
Answers
Answer:
[tex]\textsf{LCM}=(x+3)^3(x-3)^2[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6cm}\underline{Difference of Two Squares Formula}\\\\$a^2-b^2=\left(a+b\right)\left(a-b\right)$\\ \end{minipage}}[/tex]
Factor x² - 9 by applying the Difference of Two Squares formula:
[tex]\begin{aligned}\implies x^2-9&=x^2-3^2\\&=(x+3)(x-3)\end{aligned}[/tex]
Rewrite each of the given expressions as an expansion of their factors:
[tex]\bullet \quad (x-3)^2=(x-3)(x-3)[/tex]
[tex]\bullet \quad x^2-9=(x+3)(x-3)[/tex]
[tex]\bullet \quad (x+3)^3=(x+3)(x+3)(x+3)[/tex]
Therefore, we can see that each expression has a factor of (x - 3), (x + 3) or both (x - 3) and (x + 3).
The least common multiple (LCM) of a, b, and c is the smallest multiplier that is divisible by a, b and c.
Therefore, to find the LCM of the given expressions, multiply each factor with the highest power:
[tex]\textsf{LCM}=(x+3)^3(x-3)^2[/tex]here is an equation x+4 = 17
Answers
The tape diagram is attached in the solution.
What is tape diagram?A tape diagram is a rectangular visual model resembling a piece of tape, that is used to assist with the calculation of ratios and addition, subtraction, and commonly multiplication.
Given is an equation x+4 = 17,
We need to draw a tape diagram for the same,
So, for that, since we have x + 4 which is equal to 17, so, we will draw a box, divide into two parts one will show the x part and ine will show the 4 part, and collectively it will show 17.
The value of the x+4 and 17 is the same, because, according to the diagram, the quantity x+4 collectively showing 17, therefore, they have same values.
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Use fraction strips to find each sum
2 6/10 + 1 3/5
Answers
Answer:
4 1/5
Step-by-step explanation:
6/10 = 3/5
2+1=3
3+6/5 = 4 1/5
1. Cisco Enterprises in Ontario purchased the following in a single month all-inclusive of taxes:
• 16,000 units of network routers at $79.25 each
• 12,000 units of wireless LAN adapters at $129.95 each
• 13,500 units of computer boards at $229.15 each
Assuming all purchases are taxable, calculate the total tax amount the company paid on their purchases only. Round off to 2 decimal places only.
Answers
The total tax that the business paid on its purchases only was 769720.25.
How should tax be defined?In order to pay for general public institutions, goods, and activities, local, state, and federal governments must collect mandated payments or charges from citizens and corporations.
We must first figure out the complete cost of the goods in order to determine the total taxable income the corporation paid
The cost of the 16,000 network routers is:
16,000 units x $79.25/unit = $1,268,000
The cost of the 12,000 wireless LAN adapters is:
12,000 units x $129.95/unit = $1,559,400
The cost of the 13,500 computer boards is:
13,500 units x $229.15/unit = $3,092,025
The total cost of all purchases is:
$1,268,000 + $1,559,400 + $3,092,025 = $5,919,425
To calculate the total tax amount, we need to multiply the total cost by the tax rate. Assuming a tax rate of 13%, the total tax amount is:
$5,919,425 x 0.13 = $768,527.25
Therefore, the total tax amount that the company paid on their purchases only is $768,527.25, rounded off to 2 decimal places.
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The value of a car in 2000 was $32,000 and it is decreasing in value at a rate of 16.3% per year.
a.) Write an equation that represents the situation for any amount of time from 2000.
b.) How much will the car be worth in 2035?
Answers
Answer:
see below
Step-by-step explanation:
a. amount of time = t
Value = 32000*(1-16.3%)^t
b. in 35 years Value = 32000*(1-16.3%)^35 = 63.17
Chantal draws a polygon with seven congruent sides and angles. name Chantal Shape.Is the shape a regular polygon
Answers
A polygon with seven congruent sides and angles is called HEPTAGON. In this case
What is a polygon?A polygon is a two-dimensional closed figure with three vertices, three angles, and at least three straight sides. The words "Poly" and "gon" both mean many and angle, respectively. A triangle, for instance, has three vertices, three sides, and three angles. Therefore, it qualifies as a polygon.
Chantal "draws a polygon with seven congruent sides and angles," according to the statement. Heptagon is the name for a polygon with seven identical sides and angles. This polygon is a regular one because all of its sides and angles are equal. A regular polygon must have equal side lengths and angles by definition.
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What’s The Answer To This Question
Answers
Answer:2 one
Step-by-step explanation:
Which of the following is assumed for establishing the unbiasedness of Ordinary Least Square (OLS) estimates? A. The error term has an expected value of 1 given any value of the explanatory variable. B. The regression equation is linear in the explained and explanatory variables. C. The sample outcomes on the explanatory variable are all the same value. D. The error term has the same variance given any value of the explanatory variable.
Answers
The regression equation is linear in the explained and explanatory variables.
In order for Ordinary Least Squares (OLS) estimates to be unbiased, the regression equation must be linear in both the explained and explanatory variables. This means that the relationship between the dependent variable (what is being explained) and the independent variables (what is being used to explain the dependent variable) must be linear. This is important because it ensures that the estimated coefficients of the regression equation accurately reflect the true relationship between the variables. Additionally, the error term must have an expected value of 0, given any value of the explanatory variable, and have the same variance given any value of the explanatory variable. This ensures that the estimated coefficients do not suffer from bias and that the OLS estimates are unbiased.
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M is directly proportional to r²
When r = 2, M = 14
a) Work out the value of M when r = 12.
b) Work out the value of r when M = 224.
Answers
The value of M when r = 12 and the value of r when M = 224 are 504 and 8 respectively.
What is the value of M when r = 12 and the value of r when M = 224?Direct proportionality is expressed as;
M ∝ r²
Hence; M = kr²
Where k is the proportionality constant.
Given that;
r = 2M = 14k = ?First, we determine the proportionality constant.
M = kr²
k = M/r²
Plug in r = 2 and M = 14
k = 14 / (2)²
k = 14/4
k = 7/2
Now, a) the value of M when r = 12 will b;
M = kr²
M = (7/2) × ( 12 )²
M = (7/2) × 144
M = 504
Next, b) the value of r when M = 224
M = kr²
r = √(M/k)
r = √( 224 ÷ 7/2 )
r = 8
Therefore, the values of M and r are 504 and 8 respectively.
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Suppose that the force acting on an object can be expressed by vector (-8,14), where each
measure in the ordered pair represents the force in pounds. What is the magnitude of the force? Round
your answer to the nearest hundredth.
Answers
Answer:
Magnitude of force is [tex]||v||\approx16.12\text{ lbs}[/tex]
Step-by-step explanation:
[tex]||v||=\sqrt{x^2+y^2}\\||v||=\sqrt{(-8)^2+(14)^2}\\||v||=\sqrt{64+196}\\||v||=\sqrt{260}\\||v||\approx16.12\text{ lbs}[/tex]
I need the answer to this math problem
20pts!!
Answers
Answer:
9
Step-by-step explanation:
9 makes it so that each set becomes a whole number.
Jeff created the following shape to fill with skittles. He also wants to decorate the outside with Skittle wrappers. Find the surface area to determine the number of skittle wrappers he would need to save and volume to determine how the amount of Skittles he could fill it with
Show work please and thank you
Answers
The surface area of figure is 784 ft² and the volume of the figure is 576 ft³.
What is volume?
Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.
The shape created by Jeff is a cube + square pyramid.
The height of square pyramid is = 3 ft
The sides of cube = 8 ft
The formula for volume of cube = (side)³
Volume of cube = (8)³
Volume of cube = 512 ft³
The formula for volume of square pyramid = (base)² × height / 3
Volume of square pyramid = (8)² × 3/3
Volume of square pyramid = 64 × 1
Volume of square pyramid = 64 ft³
Total volume of the figure -
Volume of cube + Volume of square pyramid
Total volume = 512 + 64
Total volume = 576 ft³
The formula for surface area of cube = 6(side)²
Surface Area of cube = 6 × (8)²
Surface Area of cube = 6 × 64
Surface Area of cube = 384 ft²
The formula for surface area of square pyramid = 6(side)²
Surface Area of square pyramid = (side)² + 2(side) √[{(side)²/4} + (height)²]
Surface Area of square pyramid = (8)² + 2(8) √[{(8)²/4} + (3)²]
Surface Area of square pyramid = 64 + 16 √[{64/4} + 9]
Surface Area of square pyramid = 80 √[16 + 9]
Surface Area of square pyramid = 80 √25
Surface Area of square pyramid = 80 × 5
Surface Area of square pyramid = 400 ft²
Total surface area of the figure -
Surface Area of cube + Surface Area of square pyramid
Total Surface Area = 384 + 400
Total Surface Area = 784 ft²
Therefore, the volume and surface area of the figure is 576 ft³ and 784 ft² respectively.
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Find the values of x and y
Answers
Answer:
x = 22
y = 59
Step-by-step explanation:
You want the values of x and y as shown in the figure where angles (2x)° and (y-15)° are vertical angles, and (2x)° and (2x+2)° are complementary.
Complementary anglesTwo angles are complementary when their sum is 90°.
(2x)° +(2x+2)° = 90°
4x = 88 . . . . . . . . . . . divide by °, subtract 2
x = 22
Vertical anglesVertical angles have the same measure:
(2x)° = (y -15)°
2·22 = y -15 . . . . . . divide by °, substitute for x
59 = y . . . . . . . . . add 15
The value of x is 22.
The value of y is 59.
It's election day for a club. If a president and vice-president are elected, how many different combinations can be made among twelve people?
Answers
Answer:
24
Step-by-step explanation:
You multiply the number of positions (2), by the number of people (12).
(b) In a continuous series, the average marks of some students is 40 and the sum of their marks (Efm) is 2000. Then find the number of students. श्रेणीहरुको औसत प्राप्ता 40 र तिनीहरूको
Answers
Answer:
50
Step-by-step explanation:
To find the number of students, we can use the formula: average = (sum of marks) / (number of students).
Substituting the given values: 40 = 2000 / number of students
Solving for the number of students: number of students = 2000 / 40 = 50
So, there are 50 students in the series.
Suppose That \( R \) Is The Finite Region Bounded By \( Y=X, Y=X+1, X=0 \), And \( X=3 \). find the exact value of the volume of the object we obtain when rotating about the -axis.
Answers
Step-by-step explanation:
Find Object Volume Rotation
Suppose That \( R \) Is The Finite Region Bounded By \( Y=X, Y=X+1, X=0 \), And \( X=3 \). find the exact value of the volume of the object we obtain when rotating about the -axis.
The region R is a triangular region defined by the lines y = x, y = x + 1, x = 0, and x = 3. To find the volume of the object obtained by rotating this region about the x-axis, we can use the method of cylindrical shells.
The height of the cylindrical shell is given by the difference between y = x and y = x + 1, or 1 unit. The radius of the cylindrical shell is given by x. Therefore, the volume of the object is given by:
\begin{align*}
V &= \int_{x=0}^{x=3} \pi x^2 \cdot 1, dx \
&= \pi \int_{x=0}^{x=3} x^2, dx \
&= \pi \left[ \frac{x^3}{3} \right]_{x=0}^{x=3} \
&= \pi \left( \frac{27}{3} - \frac{0}{3} \right) \
&= 9\pi
\end{align*}
So the volume of the object is equal to 9π cubic units.
Answer this arithmetic progression question and get 50 points + brainliest
Answers
Answer:
The 9th term is 30
---------------------------------
Use nth term equation:
[tex]a_n=a+(n-1)d[/tex], where a- the first term, n - number of terms, d - common differenceWe have:
[tex]a_7=21\ and\ a_{11}=39[/tex]And we need to find the 9th term.
Write the given terms as below and solve for d:
a + 6d = 21 anda + 10d = 39Subtract the first equation from the second:
10d - 6d = 39 - 214d = 18d = 18/4d = 4.5The first term is:
a + 10*4.5 = 39a + 45 = 39a = - 6Find 9th term:
[tex]a_9=a+8d=-6+8*4.5=-6+36=30[/tex]Answer:
The 9th term is 30
Step-by-step explanation:
Mallory's Border Collie had 13 puppies in 2 litters. Determine the rate for a ratio of the two different quantities.
2 over 13 puppies per litter
13 over 15 puppies per litter
2 over 1 puppies per litter
13 over 2 puppies per litter
Answers
The rate for a ratio of the two different quantities would be 13 over 2 puppies per litter. That is option D.
How to calculate the rate of the puppies per litter?The total number of puppies that Mallory's Border Collie has = 13 puppies.
The number of litters that the puppies are being placed = 2 litters.
Therefore, the rate of puppies per litter is calculated as follows:
13 puppies = 2 litters
X puppies = 1 litter
Make X the subject of formula;
X = 13×1/2
X= 13/2 puppies per litter
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Answer:Alex has a collection of vehicle models. He built 8 model airplanes, 4 model trains, and 12 model cars. Write a ratio to represent the ratio of cars to trains.
Step-by-step explanation:3/1 ur welcome
Standard deviation is ________. a mean of squared differences the square root of the variance unit-free the covariance
Answers
Standard deviation is the square root of the variance. A mean of squared differences the square root of the variance unit-free the covariance.
What is standard deviation?The standard deviation is a measure of variance from the mean that includes spread, dispersion, and spread. The standard deviation displays a "typical" deviation from the mean. It is a well-liked measure of variability because it retains the original units of measurement from the data set. There is a small variation when data points are near the mean, and a large variation when they are far from the mean. The values' distance from the mean is determined by the standard deviation. The most common method of measuring dispersion is standard deviation, which is based on all values.
Hence, standard deviation is the square root of the variance.
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A trucking company determined that the distance traveled per truck per year is normally distributed, with a mean of 40 thousand miles and a standard deviation of 12 thousand miles. Complete parts (a) through (c) below.
Question content area bottom Part 1
a. What proportion of trucks can be expected to travel between 23 and 40 thousand miles in a year? The proportion of trucks that can be expected to travel between 23 and 40 thousand miles in a year is enter your response here. (Round to four decimal places as needed.)
b. What percentage of trucks can be expected to travel either less than 30 or more than 60 thousand miles in a year? The percentage of trucks that can be expected to travel either less than 30 or more than 60 thousand miles in a year is enter your response here%. (Round to two decimal places as needed.)
c. How many miles will be traveled by at least 90% of the trucks?
The number of miles that will be traveled by at least 90% of the trucks is enter your response here miles. (Round to the nearest mile as needed.)
Answers
Therefore, standard deviation problem solution is at least 90% of the trucks can be expected to travel 55,36 miles or less per year.
What is Standard deviation?Statistics uses variance as a gauge of difference. The following equation of that number is used to determine the average variance in between data and the mean. It includes all data points in with its computations, in contrast to other numeric measures of variability, by comparing the value of each data point to the mean.
Here,
a.
z1 = (23 - 40) / 12 = -1.42
z2 = (40 - 40) / 12 = 0
P(-1.42 < z < 0) = 0.4199
So, approximately 0.4199 or 41.99% of trucks can be expected to travel between 23 and 40 thousand miles in a year.
b.
z1 = (30 - 40) / 12 = -0.83
z2 = (60 - 40) / 12 = 1.67
P(z < -0.83) + P(z > 1.67) = 0.2023 + 0.0475 = 0.2498
So, approximately 24.98% of trucks can be expected to travel either less than 30 or more than 60 thousand miles in a year.
c. Thus:
x = 40 + 1.28(12) = 55.36
So, standard deviation problem solution is at least 90% of the trucks can be expected to travel 55,36 miles or less per year.
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