The composite functions are evaluated as:
a. (f ∘ g)(−2) = -9
b. (g ∘ f)(−2) = - 193
How to Solve Composite Functions?Given the functions,
f(x) = 5x − 4
g(x) = 3 − x²
a. To find the composite function, (f ∘ g)(−2), we will replace g(-2) instead of x in the function f(x).
Therefore, we would have:
(f ∘ g)(−2) = f(g(-2))
f(g(-2)) = 5(3 − (-2²)) − 4
f(g(-2)) = 5(3 − 4) − 4
f(g(-2)) = 5(-1) − 4
f(g(-2)) = -5 − 4
f(g(-2)) = -9
Therefore, (f ∘ g)(−2) = -9.
b. Also, the composite function (g ∘ f)(−2) would be evaluated by replacing f(-2) instead of x in g(x).
Therefore:
(g ∘ f)(−2) = g(f(-2))
g(f(-2)) = 3 − (5(-2) − 4)²
g(f(-2)) = 3 − (-10 − 4)²
g(f(-2)) = 3 − (-14)²
g(f(-2)) = 3 − 196
g(f(-2)) = -193
Therefore, (g ∘ f)(−2) = - 193
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One letter tile is selected and the spinner is spun. What is the probability that both will be avowel?P (vowel) Tile:P (vowel) Spinner:Multiply fractions - probability that both will be a vowel
SOLUTION:
Step 1:
To find the probability of picking a vowel from G, B, E and A.
A and E are the vowels here,
[tex]P\text{ (vowel) Tile : }\frac{2}{4}\text{ = }\frac{1}{2}[/tex]Step 2:
To find the probability that the spinner showed a vowel from A, B and C.
A is the only vowel here,
[tex]P\text{ (vowel) Spinner: }\frac{1}{3}[/tex]Step 3:
To find the probability that both will be a vowel:
[tex]\begin{gathered} P\text{ (vowel) Tile X P (vowel) spinner} \\ \frac{1}{2}\text{ x }\frac{1}{3} \\ \\ \frac{1}{6} \end{gathered}[/tex]CONCLUSION:
The probability that both will be a vowel is 1/6
Use the change of base rule to find the logarithm to four decimal places
Answer:
b. -16.7410
Explanation:
The change of base rule says that:
[tex]\log _ab=\frac{\log _{}a}{\log \text{ b}}[/tex]Where log is logarithm in base 10. So, we can rewrite the initial expression as:
[tex]\log _90.877=\frac{\log 9}{\log \text{ 0.877}}[/tex]So, using the calculator, we get:
[tex]\log _90.877=\frac{0.9542}{-0.057}=-16.7410[/tex]Therefore, the answer is b. -16.7410
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The domain and the range of the relation are given as follows:
Domain:
A. Interval: (-∞, ∞).
B. Roster: {x | x = Real}
Range:
A. Interval: (-∞, -3].
B. Roster: {y | y ≤ -3}
What are the domain and the range of a function?The domain of a function is the set that contains all the values assumed by the input of the function. In a graph, the input is given by the horizontal axis, hence the values of x.
In this problem, the x-values of the graph assume all real values, hence the notations for the domain are as follows:
In interval notation, (-∞, ∞).In roster notation, {x | x = Real}.The range of a function is the set that contains all the values assumed by the output of the function. In a graph, the output is given by the vertical axis, hence the values of y.
In this problem, y assumes values of -3 and less, hence the notations for the range are as follows:
In interval notation, (-∞, -3].In roster notation, {y | y ≤ -3}.More can be learned about domain and range at https://brainly.com/question/10197594
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Consider the following parametric equations:x = V1 -2 and y = 41-2Step 2 of 2: Determine the domain and range of the equation obtained by eliminating the parameter. Please write your answer in interval notation.
Answer:
Explanation:
Translate to an equation and solve.What is 75% of 274?is 75% of 274.(Simplify your answer. Type an integer or a decimal.)
We are asked to determine the 75% of 274. When we need to get the "n" percentage of a number "r" then we use the following relationship:
[tex]P=r\times\frac{n}{100}[/tex]Where "P" is the percentage.
Now, we substitute the given values:
[tex]P=274\times\frac{75}{100}[/tex]Solving the operations:
[tex]P=205.5[/tex]Therefore, the 75% of 274 is 205.5
the sum of the first and the third term of a GP is 10 if the first term is 2 find :(a)the common ratio (b)the 6th term
(a)the common ratio = 2
(b)the 6th term = 64
How to find the common ratio and 6th term ?
A geometric progression, which is another name for a geometric sequence, is a series of non-zero numbers .In a G.P each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratioA geometric progression is given by a, ar, a[tex]r^{2}[/tex], a[tex]r^{3}[/tex],....Here, the common ratio = r
the first term = a = 2
(a)the common ratio
[tex]a +ar^{2} = 10\\\\2(1+r^{2} ) = 10\\\\(1+r^{2} ) = 5\\\\r^{2} =4\\\\r = 2[/tex]
The common ratio (r) = 2
(b)the 6th term
[tex]a_{n}=ar^{n-1} \\\\a_{6}=ar^{6-1} \\\\a_{6} =2(2^{5} )\\\\a_{6}=64[/tex]
Thus ,the 6th term = 64
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(((50 POINTSSSS))) Three points determine △ABC. The distance between A and B is 22.2 feet. The distance between B and C is 9.9 feet.
What is the range for the distance between A and C? The range of the distance from A to C is greater than feet and less than feet.
If three points determine △ABC. The distance between A and B is 22.2 feet. The distance between B and C is 9.9 feet. The range of the distance from A to C is greater than 12.3 feet and less than 32.1 feet
How to find the maximum and the minimum range of distances
given data
The distance between A and B is 22.2 feet
The distance between B and C is 9.9 feet
The range of the distance from A to C is greater than
= 22.2 feet - 9.9 feet
= 12.3 feet
The range of the distance from A to C is less than
= 22.2 feet + 9.9 feet
= 32.1 feet
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Search on the internet and write your own conclusions about calculus (Differentiation) usage in
different life applications like economy, medicine, engineering, etc...
Calculus in real life applications is highly common in the engineering industry.
Structural engineering is one of calculus' most important practical applications. Calculus is used to determine structural requirements for earthquake design, stresses in intricate structural combinations, and heat loss in buildings. Calculus is used by architects to determine the crucially critical amount of materials needed to build support systems that can endure stress for extended periods of time. Calculus was used to foresee the effects of wind resistance when building famous structures like the Eiffel Tower.
Beams, tension, and compression members are the three structural components that civil engineers must take into account while building bridges. Calculus can be used to calculate the amount of force exerted on the beam, taking into account the weight of vehicles, pedestrians, and projected traffic on the bridge. The materials, size, and capacity can be calculated based on these variables.
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a set of quiz scores is shown in the histogram below. the mean of the data set is 6.625 and the population standard deviation is 1.9 How many numbers in the data set are within 1 standard deviation of the mean? a)7 b)10 c)12 d)13
Given
Mean = 6.625
Standard Deviation = 1.9
Values within 1 standard deviation of mean, mean:
[tex]\begin{gathered} 6.625-1.9We look at the number of values at 5, 6, 7, and 8.5 = 2 people
6 = 2 people
7 = 5 people
8 = 3 people
Total = 2 + 2 + 5 + 3 = 12 people
Answer
C
Which is an equation of a direct proportion?A. [tex]y = 8 \times [/tex][tex]y = \frac{1}{2}x + 4[/tex][tex]y = \frac{12}{x} [/tex][tex]y = 4x - 4[/tex]
The general form of a equation with direct proportion is:
[tex]y=kx[/tex]k is a constant
Because y increase when x increase, and y decrease when x decrease.
Then, of the given options the direct proportion is:
[tex]y=8x[/tex]area and percent the answer are divide in to a) b) and c)
Explanation:
To find the area of the amount of waste, we need to calculate the area of the rectangle and the area of both circles.
So, the area of the rectangle is:
[tex]\text{Area}_R=\text{Base}\cdot\text{Height }=24\cdot12=288in^2[/tex]And the area of every circle is:
[tex]\text{Area}_c=\pi\cdot r^2=\pi\cdot6^2=113.097[/tex]So, the amou
There are 625 books and she can fit 25 books in one box how many boxes does she need to move all of them
Answer: 25
Step-by-step explanation: 625 divided by 25 is 25.
A total of $6000 is invested: part at 5% and the remainder at 10%. How much is invested at each rate if the annualinterest is $5902
Given:
Principal amount = $6000.
Let x be the amount invested at 5%.
So, 6000-x be the amount invested at 10%.
The annual interest is $590
The equation is written as,
[tex]\begin{gathered} 5\text{ \%x+(6000-x)10 \%=590} \\ \frac{5}{100}x+(6000-x)\frac{10}{100}=590 \\ 0.05x+(6000-x)0.1=590 \\ 0.05x+600-0.1x=590 \\ -0.05x=-10 \\ x=\frac{10}{0.05} \\ x=200 \\ 6000-x=6000-200=5800 \end{gathered}[/tex]Answer: At 5%, the amount invested is $200, and at 10%, the amount invested is $5800.
License plates in a particular state are to consist of 2 digits followed by 3 uppercase letters. a) How many different license plates can there be in this state if repetition of letters and numbers is permitted? b) How many different license plates can there be in this state if repetition of letters and numbers is not permitted? c) How many different license plates can there be in this state if the must be , and repetition of letters and numbers is not permitted? d) How many different license plates can there be in this state if the first digit cannot be , and repetition of letters and numbers is not permitted?
As per the concept of probability,
a) There are 1757600 number of possible license plates can there be in this state if repetition of letters and numbers is permitted
b) There are 1404000 number of possible license plates can there be in this state if repetition of letters and numbers is not permitted.
Probability:
Probability refer the possible way of occurring the particular event.
Given,
License plates in a particular state are to consist of 2 digits followed by 3 uppercase letters.
Here we need to determine the number of possible license plates for both repetition phase and non repetition phase.
Here we know that, license plates consist of 3 letters followed by 2 digits.
Let us consider the numbers on license plates be N
Let us consider the letters on license plates be L
Then the license plate consisting of 3 letters and 2 digits will be writen as,
=> LLLNN.
We know that the letters can be anything from A to Z.
There are 26 letter combinations for the first letter.
Again second and third letters can be anything from the 26 letters.
So, combination for letters = 26 × 26 × 26 = 17576
Similarly, the numbers can be anything from 0 to 9.
There are 10 combinations for both places.
Then the combination for numbers = 10 × 10 = 100
Therefore, the total number of combination for letters and numbers
=> 17576 × 100 = 1757600.
Therefore, there are 1757600 license plates can be made with repetition.
Similarly, for non repetition mode,
The number of letters for each place is reduced before,
So, the combination for the letter is,
=> 26 x 25 x 24 = 15600
Similarly, the combination of numbers is,
=> 10 x 9 = 90
Therefore, the total number of combination is,
=> 15600 x 90 = 1404000
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Reduce the rational expression to lowest terms. If it is already in lowest terms, enter the expression in the answer box. Also, specify any restrictions on the variable.a²-36/5a + 30Rational expression in lowest terms:Variable restrictions for the original expression: a
The expression is given to be:
[tex]\frac{a^2-36}{5a+30}[/tex]From the numerator, using the difference of two squares, we have:
[tex]a^2-36=a^2-6^2=(a-6)(a+6)[/tex]From the denominator, by factorization, we have:
[tex]5a+30=5(a+6)[/tex]Therefore, the expression becomes:
[tex]\Rightarrow\frac{(a-6)(a+6)}{5(a+6)}[/tex]Cancel out common terms in the denominator and numerator. The simplified expression will be:
[tex]\Rightarrow\frac{a-6}{5}[/tex]From the original expression, the variable restriction will be at:
[tex]\begin{gathered} 5a+30=0 \\ Solving \\ 5a=-30 \\ a=-\frac{30}{5} \\ a=-6 \end{gathered}[/tex]The restriction is:
[tex]-6[/tex]Analyze the diagram below and answer the question that follows.DGВЬ12.412.410.2F НA10.2СЕWhich two triangles are congruent by the HL theorem?
The answer is D. None of the triangles are congruent by the HL theorem.
Because even though a and b have the same hypothenuse, they don't have the same leg, so they are not congruent and in the HL theorem they have to be equal in the hypothenuse and one of the legs.
Which is the complete factor for the problem?24x² - 6xy - 63y3(4x - 7y) (2x + 3y)3xy(4x + 7y)(3y + 2)2(12r² - 3ry) - 63y²3(8x² - 2xy-21 y²)
Consider the following polynomial:
[tex]24x^2\text{ - 6xy - 63y}^2[/tex]The common factor of this polynomial is 3. Thus, we get the following equivalent polynomial:
[tex]3(8x^2\text{ - 2xy - 21y}^2)[/tex]Now, if we factor the polynomial in the parentheses, we get:
[tex]3(2x+3y)(4x\text{ - 7y})[/tex]thus, we can conclude that the correct answer is:
Answer:[tex]3\left(4x-7y\right)(2x+3y)[/tex]y=ax+dy equals ax + d
Answer:
[tex]a=\frac{y-d}{x}[/tex]Explanation:
To solve for a in the the equation
[tex]y=ax+d[/tex]we first subtract d from both sides to get
[tex]y-d=ax+d-d[/tex][tex]y-d=ax[/tex]Finally,
[tex](y-d)\div x=\frac{ax}{x}[/tex][tex]\frac{y-d}{x}=a[/tex]A bit of rearranging gives
[tex]a=\frac{y-d}{x}[/tex]Make the following conversion in the metric system by multiplying by the appropriate conversion factor. Write your answer as a whole number or decimal.380 m to kilometers km
Start by using the definition of a kilometer with its equivalent to meters
[tex]1\operatorname{km}\rightarrow1000m[/tex]Then, using the conversion factor, convert the meters to kilometers
[tex]380m\cdot\frac{1\operatorname{km}}{1000m}=0.380\operatorname{km}[/tex]
Solve the inequality and -2x – 1 < 3 and graph your solution on the number line.
Answer:
x > -2
Explanation:
Given the inequality -2x – 1 < 3
Step 1: Add 1 to both sides of the inequality
-2x – 1 + 1 < 3 + 1
-2x < 4
Step 2: Divide both sides by -2
-2x < 4
-2x/-2 < 4/-2
x > -2
Find the graph below
How do you calculate the sum of the first k terms of a geometric sequence with common ratio b?
[tex]S_{k} =\frac{a(1-b^{k}) }{1-b^{k}}[/tex] is the formula to find sum of the first k terms of a geometric sequence with common ratio b.
What is Sequence?A sequence is defined as an arrangement of numbers in a particular order.
A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.
The sum of first k terms of a geometric sequence with common ratio b is given by the formula.
[tex]S_{k} =\frac{a(1-b^{k}) }{1-b^{k}}[/tex]
where b≠0
Where k is number of terms
b is the common ratio and a is the first term.
Hence [tex]S_{k} =\frac{a(1-b^{k}) }{1-b^{k}}[/tex] is the formula to find sum of the first k terms of a geometric sequence with common ratio b.
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Two rectangular fields, both measured in yards, are modeled below.
6
Tx-41
8
X
What value of x, in yards, would cause the fields to have equal areas?
Part B) Solve the equation you selected in Part A and answer the question.
Enter your final answer in the space provided.
The value of x = 12.
What is the area of rectangle?
Area of rectangle is the region occupied by a rectangle within its four sides or boundaries.
The area of a rectangle depends on its sides.
Area of rectangle = length × breadth
Given, area of both rectangle is same
length of 1st rectangle = x+4
breadth= 6
length of second rectangle = 8
breadth = x
According to question,
6(x+4) = 8x
6x+24 = 8x
2x= 24
x = 24/2
x =12
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Are y’all able to help me out on this question pls?
Answer:
Step-by-step explanation:
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The amount of coffee that was imported in 2007 is 2.0606 million pounds.
What is a function?It should be noted that a function simply s used to illustrate the relationship between the variables given.
From the information, the function is illustrated as:
= 0.7166x² + 6.267x + 1.344
x represents 1997 which was given as 0.
Therefore, the amount in 1997 will be:
= 0.7166x² + 6.267x + 1.344
= 0.7166(0)² + 6.267(0) + 1.344
= 0.7166 + 1.344
= 2.0606 million pounds.
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BRAINLIEST (statistics) (please help fast) A brand of frozen green beans lists a weight of 32 ounces on its bag. Because of variability in the manufacturing process, the bags often contain slightly more, or less, than 32 ounces of green beans. An inspector takes a random sample of 25 bags of green beans and records their weights. The weights and their relative frequencies are summarized in the histogram.
A histogram titled Green Beans has actual weight (ounces) on the x-axis, and relative frequency on the y-axis. 31.8 to 31.9, 0.04; 31.9 to 32.0, 0.04; 32 to 32.1, 0.12; 32.1 to 32.2, 0.2; 32.2 to 32.3, 0.36; 32.3 to 32.4, 0.23.
What is the shape of the distribution of bag weight?
uniform
skewed left
skewed right
roughly symmetric
What is the shape of the distribution of bag weight?
uniform
skewed left
skewed right
roughly symmetric
From the data and graph given, the shape of distribution is skewed left. Meaning, the left side of the graph is wider than that of the side to the right of the highest value.
Answer: Skewed left
Step-by-step explanation: less data towards the left side of the histogram
Regina Aguirre deposits $2.000 into an ordinary annuity after each 6-month period for 4 years. The acco pays 6% interest compounded semiannually. Find the a) future value, and b) total interest earned.
Answer:
same question here
Step-by-step explanation:
Answer:
Step-by-step explanation:
a) Plot the graph of y = 2^x+2 for-4 ≤ x ≤ 4
b) Draw the asymptote.
c) Write the equation of the asymptote.
I need help with question c only
Answer:
y = 2
Step-by-step explanation:
A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches ±∞.
Mathematically we write this as
[tex]f(x) \rightarrow a \text{ as } x \rightarrow \infty \text{ or } x \rightarrow -\infty[/tex]
A vertical asymptote at some constant a is where the function approaches ±∞.
Mathematically
[tex]f(x) \rightarrow \infty \text { or } f(x) \rightarrow -\infty \text{ as } x \rightarrow a[/tex]
The given function y = 2ˣ + 2 is an exponential function and exponential functions do not have a vertical asymptote
The horizontal asymptote can be found by determining what the function limit is as [tex]x \rightarrow \pm \infty[/tex]
As [tex]x \rightarrow +\infty[/tex] the function [tex]\rightarrow \infty[/tex]
As [tex]x \rightarrow -\infty[/tex] , [tex]2^x \rightarrow 0\\\\\\2^x + 2 \rightarrow 2\\\\[/tex]
So the equation for the horizontal asymptote is y = 2
The graph shows that at y = 2, the function is parallel to the line but does not touch the line
On the unit circle, which of the following angles has the terminal point coordinates
In this case,
[tex]y=-\frac{\sqrt[]{2}}{2}\text{ and x=-}\frac{\sqrt[]{2}}{2}[/tex][tex]\theta=\tan ^{-1}(1)=45^o,225^o[/tex]Since x is negative, and y is negative
[tex]\theta=225^o[/tex]The polar equation r = 7 sin (2theta) graphs as a rose.What is the length of the petals of this rose?Enter your answer in the box.
This problem is about a polar equation. It's important to know that polar coordinates depend on two variables, the angle of the vector and its distance.
[tex](r,\theta)[/tex]Where r represents the distance and theta represents the angles.
In this case, the angle is 20°, according to the problem.
So, first, we need to graph this equation in the polar system, to then measure the length of the petals
[tex]r=7\sin (2\theta)[/tex]The graph of this equation is shown in the image attached below.
In the image above, you can observe the polar equation graphed, with the coordinated system behind, this will allow us to find the length of each (which are symmetrical). You can observe that the petal on the third quadrant is at (-5,-5).
Now, we use the following formula to find the distance
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Replacing the points, we have
[tex]d=\sqrt{(-5)^2+(-5)^2}=\sqrt{25+25}=\sqrt{2(25)}=5\sqrt{2}\approx7.07[/tex]Therefore, the length of each petal is 7.07 units, approximately.you are ordering a new home theater system that consists of a tv, surround sound system and dvd player. you can choose from 17 different tv’s 7 types of surround sound systems and 13 types of dvd players. how many different home theater systems can you build?
Answer:
1,547 different home theater systems.
Explanation:
Given that you can choose between the following options:
• 17 different tv’s
,• 7 types of surround sound systems
,• 13 types of dvd players
Thus, to find the number of possible home theater systems that you can build, multiply the number of each item type.
[tex]17\times7\times13=1,547[/tex]You can build 1,547 different home theater systems.
