Type the correct answer in each box. Use numerals instead of words.
Functions f and g are represented in the table and the graph.
Answers
The values of the functions from the graph and table are; (f ° g)(4) = 4 and x = 0 at (g ° f)(x) = 1
How to solve function inputs?1) We want to find the value of (f ° g)(4). This can also be expressed as;
f(g(4))
Now, from the given graph, g(4) = 2. Thus;
f(g(4)) = f(2)
From the table, f(2) = 4. Thus;
(f ° g)(4) = 4
2) We are given; (g ° f)(x) = 1
This is also expressed as;
g(f(x)) = 1
From the graph g(x) = 1 is at x = 1. Thus;
f(x) = 1 and from the tabe;
x = 0 at f(x) = 1
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Related Questions
The following shape is only based on squares, semicircles and quarter circles. Find the Area and Perimeter of the shaded part. Answers in terms of pi.
Answers
The perimeter of the shaded region is 8π cm and the area of the shaded region is 32(π - 2) cm² or 36.53 square cm.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have shown a square in which a one-fourth circle is shown and making an ellipse.
The perimeter of the circle = 2πr = 2π(8) = 16π cm
The perimeter of the one-fourth is circle = (16π)/4 = 4π cm
The perimeter of 2 one-fourth circle = 2(4π) = 8π cm
The area of the one-fourth circle = (1/4)πr² = (1/4)π(8)² = 16π square cm
The area of the right-angle triangle = (1/2)(8)(8) = 32 square cm
The area of the shaded region = 2(16π - 32) = 36.53 square cm
or
= 32(π - 2)cm²
Thus, the perimeter of the shaded region is 8π cm and the area of the shaded region is 32(π - 2) cm² or 36.53 square cm.
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3x9= 2x+5
Step Two: 3x = 2x + 14
Which choice justifies this step?
Answers
Answer: Addition property of equality
Step-by-step explanation:
Assuming you meant 3x-9=2x+5, it would be the addition property of equality since you are adding 9 to both sides.
In a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests,
Paul has scored 91, 88, and 93 on the first three. What range of scores on the fourth test will give Paul a C for the
semester (an average between 70 and 79, inclusive)? Assume that all test scores have a non-negative value.
Express your answer in interval notation.
Answers
Answer:
[8, 44]
Step-by-step explanation:
The average of equally-weighted values is their sum divided by their number.
SetupFor some fourth test score x, Paul wants an average between 70 and 79. This gives rise to the inequality ...
70 ≤ (91 +88 +93 +x)/4 ≤ 79
SolutionMultiplying by 4, we have ...
280 ≤ 272 +x ≤ 316
8 ≤ x ≤ 44 . . . . . . . . . . subtract 272
Paul will get a C if his fourth test score is in the interval [8, 44].
Is the function one-to-one? {(-19,9),(-2,9),(-7,-16)}
Answers
Answer:
no
Step-by-step explanation:
the y coordinate 9 repeats twice
Consider the limaçon with equation r = 3 4cos(θ). how does the quotient of a and b relate to the existence of an inner loop?
Answers
If the equation is r = 3 +4cos(θ) then because b/a>1 the curve is a limacon with an inner loop.
Given limacon with equation r=3+4cos(θ) and we have to answer how the quotient of a and b relate to the existence of an inner loop.
Equation is like a relationship between two or more variables expressed in equal to form and it is solved to find the value of variables.
formula of polar graph is similar to r= a+ b cos (θ).
Case 1. If a<b or b/a>1
then the curve is a limacon with inner loop.
Case 2. If a>b or b/a<1
Then the limacon does not have an inner loop.
Here given that [tex]r=3+4cos[/tex] (θ)
It is observed that , a<b or b/a>1
Therefore the curve is limacon with an inner loop.
Hence because b/a>1 the curve is a limacon with an inner loop.
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Answer:
The answer is B
Step-by-step explanation:
What is the range of the function f(x)=1/2√x?
A. all real numbers
B. all real numbers greater than but not equal to 0
C. all real numbers less than or equal to 0
D. all real numbers greater than or equal to 0
Answers
Answer:
D. all real numbers greater than or equal to 0
Step-by-step explanation:
The range is the set of y-values.
Mia counts on in steps of 100 she starts at 946. Write the next number she says
Answers
Answer:
100+946=1046
Ao the next no. Is 1046
Rhoda is asked to graph this system of equations:
5x-6y=4
3y+2x=7
How many times will the lines intersect?
A. The lines will not intersect
B. The lines will intersect once.
C. There is no way to tell without graphing the lines first.
D. The lines will intersect infinitely many times, because they are identical.
Answer back fast!
I will award Brainliest too!
Answers
Answer: B. The lines will intersect once.
Step-by-step explanation:
Multiplying the bottom equation by 2, we get 6y+4x=14.
Adding this to the first equation, this gives 9x=18, and thus x=2.
Therefore, since this means there will be 1 solution, the lines will intersect once.
The answer for this math problem because I don’t really understand it
Answers
Answer:
See below
Step-by-step explanation:
Start by subtracting 5.2 from both sides of the equation
so "subtraction property of equality " I suppose ......
then the next step would be divide both sides by 2.5
which would be division property of equality
Answer: Subtraction Property of Equality
Step-by-step explanation:
- the subtraction property of equality is the rule that when you subtract the same number to or from both sides of an equation and get an equivalent equation
__________________________________________________________
- for this equation you would subtract 5.2 from the left-side of the equation and subtract it from 35.2 on the right side of the equation
- this is to isolate n
- basically 2.5n = 30 since n is a variable and that number multiplied by 2.5 will equal 30
- so the new equation would be 2.5n = 30
- so then: [tex]\frac{n}{2.5}[/tex] = [tex]\frac{30}{2.5}[/tex] so n = 12
hope this helps :)
Please give an answer and solution.
Answers
Using proportions, it is found that 78 students would prefer long jump.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Out of 300 students, 26% would prefer long jump, hence the amount is given by:
n = 0.26 x 300 = 78 students.
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Leroy wants to tile the floor in his kitchen. The floor is 10 feet by 12 feet. Each tile is 6 by 8 inches. How many tiles will he need to finish the job?
a. 124 tiles
b. 360 tiles
c. 412 tiles
d. 514 tiles
Answers
Answer:
B
Step-by-step explanation:
Convert everything to inches first
The floor is 120 inches by 144 inches
The floor can be covered with (120/6) * (144/8) tiles
(120/6) * (144/8) = 20*18=360 tiles, hence b.
A certain medical test is known to detect 73% of the people who are afflicted with the disease Y. If 10 people with the disease are administered the test, what is the probability that the test will show that: All 10 have the disease, rounded to four decimal places? At least 8 have the disease, rounded to four decimal places? At most 4 have the disease, rounded to four decimal places?
Answers
The probability of an event is the measurement of the chance of that event's occurrence. The probabilities of considered events are:
P(At least 8 have the disease) ≈ 0.4378P(At most 4 have the disease) ≈ 0.0342How to find that a given condition can be modeled by binomial distribution?Binomial distributions consist of n independent Bernoulli trials. Bernoulli trials are those trials that end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as
X = B(n,p)
The probability that out of n trials, there'd be x successes is given by
P(X=x) = [tex]^nC_xp^x(1-p)^{n-x}[/tex]
Since 10 people can be either diseased or not and they be so independent of each other (assuming them to be selected randomly) , thus, we can take them being diseased or not as outputs of 10 independent Bernoulli trials.
Let we say
Success= Probability of a diseased person tagged as diseased by the clinic
Failure = Probability of a diseased person tagged as not diseased by the clinic.
Then,
P(Success) = p = 72% = 0.72 (of a single person)
P(Failure) = q = 1-p = 0.28
Let X be the number of people diagnosed diseased by the clinic out of 10 diseased people. Then we have: X ≈ B(n+10,P=0.73)
Calculating the needed probabilities, we get:
a) P(At leased 8 have disease) = P(X≥8) =P(X=8) + P(X=9) + P(X=10)
P(X≥8) = [tex]^{10}C_8(0.73)^8(0.28)^2+^{10}C_9(0.73)^9(0.27)^1+^{10}C_{10}(0.73)^{10}(0.27)^0[/tex]
P(X≥8) ≈ 0.2548 + 0.1456 + 0.0374 ≈ 0.4378
b) P(At most 4 have the disease) = P(X≤4) = P(X=0) + P(X=1)+P(X=2)+P(X=3)+P(X=4)
P (X ≤ 4) =
[tex]^{10}C_0(0.73)^0(0.27)^{10}+^{10}{C_1(0.73)^1(0.27)^9+^{10}{C_2(0.73)^2(0.27)^8+^{10}C_3(0.73)&^3(0.27)^7 \\[/tex]
[tex]+^{10}C_4(0.73)^4(0.27)^6[/tex]
P (X ≤ 4) = 0.000003 + 0.000076+0.00088+0.00604+0.02719
P (X ≤ 4) = 0.0342
Thus,
The probabilities of considered events are:
P(At leased 8 have disease) = 0.4378 approxP(At most 4 have the disease) = 0.0342 approxLearn more about binomial distribution here:
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To solve the division problem, multiply
by the reciprocal of the divisor.
1/9 divided by 3=1/9X1/? Solve the question mark.
Answers
Therefore your answer is
3
Hope this helped :)
Answer:
?=3
Step-by-step explanation:
3=3/1
Flip 3/1 and you get
1/3
Which linear inequality is represented by the graph?
Answers
Answer: 3
Step-by-step explanation:
Use a graphing calculator to find the value of the correlation coefficient r and determine if there is a strong correlation among the data.
(1, 5), (4, 8), (8, 3), (13, 10), (19, 13)
Answers
Using a calculator, the correlation coefficient is of 0.7649. Since the correlation is greater than 0.6, there is strong correlation.
What is a correlation coefficient?It is an index that measures correlation between two variables, assuming values between -1 and 1.If it is positive, the relation is positive, that is, they are direct proportional. If it is negative, they are inverse proportional.If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.Using a calculator, we insert the points (x,y) to find the coefficient. In this problem, the points are given as follows:
(1, 5), (4, 8), (8, 3), (13, 10), (19, 13)
The coefficient is of 0.7649. Since the correlation is greater than 0.6, there is strong correlation.
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(b) Solve the trigonometric equation and verify that its solutions are the x-coordinates of the maximum and minimum points of f. (Calculus is required to find the trigonometric equation. For each solution, give an exact answer and then round to four decimal places. Enter your answers from smallest to largest.)
Answers
The given trig equation is obtained by solving for the critical points of [tex]f[/tex], which is done by differentiating [tex]f[/tex] and setting the derivative equal to zero.
We have
[tex]18 \sin(x) \cos(x) - 9 \sin(x) = 0[/tex]
[tex]9 \sin(x) (2 \cos(x) - 1) = 0[/tex]
[tex]9 \sin(x) = 0 \text{ or } 2 \cos(x) - 1 = 0[/tex]
[tex]\sin(x) = 0 \text{ or } \cos(x) = \dfrac12[/tex]
In the interval [tex]0\le x< 2\pi[/tex], we have
[tex]\sin(x) = 0 \implies x = 0 \text{ or } x = \pi[/tex]
and
[tex]\cos(x) = \dfrac12 \implies x = \dfrac\pi3 \text{ or } x = \dfrac{5\pi}3[/tex]
In order from smallest to largest, that's
[tex]x = 0 \text{ or } x = \dfrac\pi3 \text{ or } x = \pi \text{ or } x = \dfrac{5\pi}3[/tex]
The solution to the Trigonometric equation is given as below.
What is a Trigonometric equation?A trigonometric equation is one that involves one or more unknown trigonometric ratios. It is represented in terms of sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec) angles.
The solution to the above problem is?The provided trigonometric equation is produced by determining the critical points of f by differentiating and setting the derivative to zero.
Thus,
18 sin (x) cos (x) - 9 sin (x) = 0
8 sin(x) = 0 or 2 cos (x) - 1 = 0
Sin (x) = 0 or Cos (x) = 1/2
Given the interval of 0 ≤ x ≤ 2π
→ Sin (x) = 0 → x = 0 or x = π
and
Cos (x) = 1/2
→ x = π/3 or x = 5π/3
Arranging the values from the smallest to the largest, we have:
x = 0 or x = π/3
x = π or x = 5π/3
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LC)A polygon is shown:
A polygon MNOPQR is shown. The top vertex on the left is labeled M, and rest of the vertices are labeled clockwise starting from the top left vertex labeled, M. The side MN is parallel to side QR. The side MR is parallel to side PQ. The side MN is labeled as 5 units. The side QR is labeled as 7 units. The side MR is labeled as 3 units, and the side NO is labeled as 2 units.
The area of polygon MNOPQR = Area of a rectangle that is 15 square units + Area of a rectangle that is ___ square units. (Input whole numbers only, such as 8.)
Answers
The area of polygon MNOPQR = (Area of a rectangle that is 15 square units + Area of a rectangle that is 2 square units)
How to determine the area of the rectangleFrom the information about the polygon MNOPQR, side MN is parallel to side RQ and also the side MR is parallel to side PQ
With a perpendicular line drawn from point O on the side RQ, which intersects with line RQ at point S.
We can then divide the polygon into two different rectangles
MNSR with A₁ as its area
OPQS with A₂ as its area
For rectangle MNSR, line MN is 5 units and line MR is 3 units
The formula for area of a rectangle is given as;
A₁ = (length)×(width)
Substitute the values
A₁ = 5 × 3
A₁ = 15 square units
For rectangle MNSR, line MN= line RS and line MR = line NS,
We have RS= 5 units and NS= 3 units
So, line SQ= RQ- RS = 7-5 = 2 units
Also, OS= NS - NO = 3- 2 = 1 unit
Let's substitute the values
A₂ = 2 × 1
A₂ = 2 square units
Therefore, the area of polygon MNOPQR = (Area of a rectangle that is 15 square units + Area of a rectangle that is 2 square units)
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Solve: 4x−1>7 or 5x−1<−6
Answers
Answer and Explanation:
First, solve for x in both inequalities:
4x − 1 > 7 5x − 1 < −6
4x > 8 5x < −5
x > 2 x < −1
Because this is an OR problem, determine if there is any overlap. (See the attached image for details.) There is not, so the answer is no solution or Ø.
Find the exact values of the trigonometric functions of theta if theta terminated in quadrant 4. Tangent of theta = -3/4
Answers
Answer:
sin=-3/5
cos=4/5
tan-3/4
csc=5/-3
sec=5/4
cot=4/-3
Step-by-step explanation:
you draw a right triangle in the fourth quadrant and then use pythagoreas theorem to find the length of the hypotenuse(2 sides are -3 and 4, hypotenuse is 5), and then just use the sides to find all 6 trigonometric functions.
A baker is making 41/8 batches of cookies. If each batch requires 3/4 of a stick of butter, how much butter will he need for all 41/8?
Answers
Answer: 123/32 or 3 27/32 sticks
Step-by-step explanation:
41/8*3/4 =
41*3/8*4 =
123/32 =
3 27/32
Pls help! Geometry
What is the perimeter of the shape above?
What is the area of the shape above?
Answers
(a) The arc length of each of the two smaller semicircles is [tex]4\pi[/tex], and the arc length of each of the two larger semicircles is [tex]15\pi[/tex]. Therefore, the perimeter is [tex]2(4\pi)+2(15\pi)=38\pi[/tex].
(b) The area of each of the smaller semicircles is [tex]\frac{1}{2}(\pi)(4^2)=8\pi[/tex], and the areaof each of the larger semicircles is [tex]\frac{1}{2}(\pi)(15^2)}=\frac{225\pi}{2}[/tex].
So, the combined areas of the four semicircles is [tex]241\pi[/tex].
The area of the rectangle is 60, so the total area is [tex]241\pi+60[/tex].
Geometry Perimeter and area
A)
B)
C)
Answers
Explanation: π(6)^2= 113.1cm^2
6cm is the radius of the big circle
B) 28.27
Explanation: π(3)^2= 28.27
C)56.56cm^2
Explanation: Subtract the area of the two yellow circles which is (28.27+28.27 =56.54)
from the area of the big circle which is 113.1.
113.1-56.54=56.56
help please. been stuck on this for the past hour!!
Answers
Answer:
A) 100 terms, B) 63 terms, C) 101 terms==========================
Given sequences:A) 1, 4, 4², ..., 4⁹⁹B) 11, 15, 19, 23, ..., 259C) 44, 45, 46, ..., 144To findThe number of terms.SolutionA) We know any number with power of zero equals 1, therefore the sequence can be expressed as powers of 4:
4⁰, 4¹, 4², 4³, ... , 4⁹⁹The number of terms from zero to 99 is:
99 + 1 = 100B) This is a AP with the first term of 11 and common difference of 4.
The nth term equation is:
aₙ = a₁ + (n - 1)dSubstitute the values and solve for n:
259 = 11 + (n - 1)*44(n - 1) = 259 - 114(n - 1) = 248n - 1 = 248/4n - 1 = 62n = 63C) Same as above, the sequence is AP, with the first term 44 and common difference 1.
Applying the nth term formula:
144 = 44 + (n - 1)*1n - 1 = 144 - 44n - 1 = 100n = 101Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each value to the correct expression.
8
5
0
27
15
22
Answers
Using PEDMAS, the value of each expressions are:
a. 1 + 5 × 2 + (1 + 3)² = 27
b. 0.25 × 4³ - 1 = 15
c. 4 + 8(1/4 + 2) = 22
How to Apply PEDMAS in Evaluating an Expression?PEDMAS implies that you solve a problem first following the order, parentheses, exponent, division, multiplication, addition, and subtraction.
Let's evaluate the expressions using PEDMAS:
a. 1 + 5 × 2 + (1 + 3)²
1 + 5 × 2 + (4)²
1 + 5 × 2 + 16
1 + 10 + 16
= 27
b. 0.25 × 4³ - 1
0.25 × 64 - 1
16 - 1
= 15
c. 4 + 8(1/4 + 2)
4 + 8(9/4)
4 + 18
= 22.
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A recent survey found that 4% of the population of the United States is unemployed. If Charlotte, North Carolina, has 26,440 unemployed, what is the population of Charlotte?
Answers
The population of Charlotte is 661,000.
What is the population of Charlotte?Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.
The population of Charlotte = number of unemployed people / percentage of unemployed
26,440 / 0.04 = 661,000
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How to solve the inequality of ...
Answers
Answer:
x<3−√11 /2 or x > 3 +√11/2
Step-by-step explanation:
Solve the inequality for x by finding a, b, and c of the quadratic then applying the quadratic formula.
A 20-foot ladder is leaning against a building. The ladder forms an angle of 55" with the ground.
Part A: How far away from the building is the bottom of the ladder? Round the answer to the nearest tenth.
Part B: How far up the building does the ladder go? Round the answer to the nearest tenth.
Part C: If the ladder is repositioned, and the base is now 9 feet from the building, what is the new angle that the ladder makes with the ground? Round the answer to the nearest tenths place.
Answers
You are one of 16 finalists on a game show.
One finalist is randomly selected to answer
a trivia question for a prize. What is the
probability that you will be selected?
Write your answer as a percent.
Answers
If one finalist is randomly selected for a prize then the probability that person will be selected is 6.25%.
Given A person is one of 16 finalists and one finalist is randomly selected for a prize.
Probability is the likeliness of happening an event among all the events possible. The formula of calculating probability is number of events possible/total outcomes.
The value of probability lies between 0 and 1. It cannot be negative because there might be chances of something and sometimes not so the value be 0.
Total finalists=16
Probability=1/16
When we convert it in percentage it will be 1*100/16
=6.25%
Hence the probability that person will be selected is 6.25%.
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Figure B is a scaled copy of Figure A.
Figure B
Figure A
What is the scale factor from Figure A to Figure B?
Answers
Answer:
The scale factor would be 1/2.
Step-by-step explanation:
2 of the sides both are 4 units.
If you go to figure B, it got smaller.
So in this case, you would divide.
On figure B, 2 of the sides are 2 units.
If you did it in reverse, you would get 2 because 2 times 2 is 4.
But we divide, so 4/2 is 2, so the scale factor would be:
1/2
Hope this helped!
And brainliest pls :)
What is the value of x in the equation three-fourths (one-fourth x 8) minus (one-half x 2) = startfraction 3 over 8 endfraction (4 minus x) minus one-fourth?
Answers
The value of x in the equation is x=-44.
The given equation is [tex]\frac{3}{4}\left(\frac{1}{4}x+8\right)-\left(\frac{1}{2}x+2\right)=\frac{3}{8}(4-x)-\frac{1}{4}[/tex].
An algebraic expression in mathematics is an expression that's made from variables and constants, together with algebraic operations (addition, subtraction, etc.). Expressions are made of terms.
Firstly, apply the distributive property as a(b+c)=ab+ac and get
[tex]\begin{aligned}\frac{3}{4}\times \frac{1}{4}x+\frac{3}{4}\times 8-\frac{1}{2}x-2&=\frac{3}{8}\times 4-\frac{3}{8}\times x-\frac{1}{4}\\ \frac{3x}{16}+6-\frac{x}{2}-2&=\frac{3}{2}-\frac{3x}{8}-\frac{1}{4} \end[/tex]
Now, rearrange the terms by taking variable terms on the left-hand side and constant terms on the right-hand side as
[tex]\frac{3x}{16}-\frac{x}{2}+\frac{3x}{8}=\frac{3}{2}-\frac{1}{4}-6+2[/tex]
Further, simplify the above expression by taking L.C.M as
[tex]\begin{aligned}\frac{3x-8x+6x}{16}&=\frac{6-1}{4}-4\\ \frac{x}{16}&=\frac{5-16}{4}\\ \frac{x}{16}&=\frac{-11}{4}\end[/tex]
Then, multiply both sides with 4 and get
[tex]\begin{aligned}4\times \frac{x}{16}&=4\times \frac{-11}{4}\\ \frac{x}{4}&=\frac{-11}{1}\end[/tex]
Furthermore, cross multiply both sides and get
[tex]x=-44[/tex]
Hence, the value of x in the equation which is given [tex]\frac{3}{4}\left(\frac{1}{4}x+8\right)-\left(\frac{1}{2}x+2\right)=\frac{3}{8}(4-x)-\frac{1}{4}[/tex] is x=-44.
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