The value of each function composition is
koh(3) = 3 and hok(-4b) = -4b
Given, Functions h and k are inverse functions, and both are defined for all real numbers.
The functions h and k are inverse functions
A function is said to have an inverse function when it is one-one and onto both.
Also, the composition of function f and function g is defined as fog i.e. f is defined on the range of g and vice-versa.
Then, foh(x) = x for all the real numbers and also,
hof(x) = x for all the real numbers.
Therefore, the value of each function composition foh at x = 3 and hof at x = -4b is 3 and -4b respectively.
Hence, the value of each function composition foh at x = 3 and hof at x = -4b is
foh(3) = 3 and hof(-4b) = -4b.
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Ari earned $356.74 the first week he
worked. The second week he earned
$427.19. To the nearest dollar ABOUT
how much less did he earn the first
week?
How do you say 7.793 in word
Answer:
seven and seven hundred nintey three thousandths
Step-by-step explanation:
Solve: cosine (x + pi) = one-half over the interval left-bracket startfraction pi over 2 endfraction, pi right-bracket.
The values that represent the solution to [tex]cos (\frac{\pi }{4} - x) = \frac{\sqrt{2} }{2} sin x[/tex] ,
x ∈ [0, 2·π) are:
[tex]x = (\frac{\pi }{2} , \frac{3\pi }{2} )[/tex]
Sine and Cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that of the hypotenuse. For an angle θ the sine and cosine functions are denoted simply as sinθ and cos θ.
Once such a triangle is chosen, the sine of the angle is equal to the length of the opposite side, divided by the length of the hypotenuse:
Sin (α) = [tex]\frac{opposite}{Hypotenuse}[/tex] and Cos (α) = [tex]\frac{Adjacent}{Hypotenues}[/tex]
Given in the question:
The given function is presented as follows;
[tex]cos (\frac{\pi }{4} - x) = \frac{\sqrt{2} }{2} sin x[/tex]
Where;
x ∈ [0, 2·π)
We have;
cos(A - B) = cos(A)·cos(B) - sin(A)·sin(B)
[tex]cos (\frac{\pi }{4} ) = \frac{\sqrt{2} }{2} , sin( \frac{\pi }{4)} =\frac{\sqrt{2} }{2}[/tex]
Which gives
[tex]cos(\frac{\pi }{4} - x ) = \frac{\sqrt{2} }{2} cos x +\frac{\sqrt{2} }{2} sinx[/tex]
Therefore, we get;
[tex]\frac{\sqrt{2} }{2} cos x = \frac{\sqrt{2} }{2} sinx - \frac{\sqrt{2} }{2} = 0[/tex]
cos x = 0
[tex]cos (\frac{\pi }{2} ) =0[/tex]
Therefore;
The possible solutions (x-values) to cos x = 0 are;
[tex]0\leq \frac{n.\pi }{2} \leq 2\pi[/tex]
Where;
n = 1, 3, 5, ...
x ∈ [0, 2·π)
We get; [tex]x = \frac{\pi }{2} or \frac{3\pi }{2}[/tex]
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Place the figures in order from least volume to greatest volume.
what is the proportion of 27/15 = 72/a
Answer:
a = 40
Step-by-step explanation:
I have 13 nutcrackers and 14 snowmen on my tree. How many stars are there? Let s repentant the amount of stars.
Hint there is 29 in all.
Answer:
There are 2 stars
Step-by-step explanation:
There are 29 items in total.
As we are given the number of two of the items(nutcrackers and snowmen)we can easily find the number of the last item(stars) by subtracting the number of nutcrackers and snowman by the number of total items.(29)
So the solution would be :
29 - (13 + 14) = number of stars
==> add 13 and 14
29 - 27 = number of stars
==> simplify
2 = number of stars
its making me type something here but question in the pic thanks :)
The value of the definite integral is 10 after breaking the limits of the integral.
What is integration?It is defined as the mathematical approach to calculating the smaller parts or components.
It is given that:
The piecewise function is given:
[tex]\rm \int\limits^4_0 {x} \, dx = \int\limits^2_0 {2} \, dx +\int\limits^4_2 {x} \, dx[/tex]
[tex]\rm \int\limits^4_0 {x} \, dx = x^2|^2_0+(1/2)x^2|^4_2[/tex]
= 4 + (1/2)[16 - 4)
= 4 + 6
= 10
Thus, the value of the definite integral is 10 after breaking the limits of the integral.
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Which is the best prediction for the number of fish in year 6 ? Round your answer to the nearest whole number .
The number of fish in year 6 will be;
⇒ y = 438.60
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The exponential regression equation is,
⇒ y = 14.08 × 2.08ˣ
Where, x is represent the year.
Now,
Since, The exponential regression equation is,
⇒ y = 14.08 × 2.08ˣ
Where, x is represent the year.
Hence, The number of fish in year 6 will be;
⇒ y = 14.08 × 2.08ˣ
⇒ y = 14.08 × 2.08⁶
⇒ y = 14.08 × 31.15
⇒ y = 438.60
Thus, The number of fish in year 6 will be;
⇒ y = 438.60
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Endure all, a manufacturer of batteries claims that the lifetime of their batteries is normally distributed with a mean of 500 hours and a standard deviation of 40 hours. What is the probability that an endure all battery selected at random will last more than 550 hours?.
Using the z-score a randomly selected Endure All battery has a 10.56% chance of lasting more than 550 hours.
What is the z-score?How closely a value relates to the mean of a set of values is measured using a Z-score.
Z-score is calculated using standard deviations from the mean.
When a data point's Z-score is 0, it indicates that its entire score is equal to the mean score.
So, how far the raw score deviates from the mean is determined using the Z score.
These steps are used to determine the Z score:
z = (x - μ)/σ
We know that: x > 550 and μ = 500, σ = 40
z = 550 - 500 / 40
z = 1.25
Using the normal distribution graph as a guide:
P(z > 1.25) = 1 - P(z < 1.25)
P(z > 1.25) = 1 - 0.8944
P(z > 1.25) = 0.1056
Therefore, using the z-score a randomly selected Endure All battery has a 10.56% chance of lasting more than 550 hours.
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You pick a card at random from an ordinary deck of 52 cards. If the card is a diamond, you get some points; if not, you lose 2 points. What value for the diamonds would make the game fair?12624 3.
Using the probability formula, the number of diamonds needed to make the game fair is determined by option (B) 6.
What is probability?Assume that there are a finite number of elementary events that are all equally likely to occur in the sample space of the experiment under consideration.
So let's say we want to determine the likelihood of an occurrence E.
So, the value of diamonds has to be:
The expected number of points that one can lose should equal the expected number of points that one can acquire for the game to be fair.
So, in order for the game to be fair, we need:
Expected points earned by selecting a diamond minus anticipated points lost by selecting a diamond.
If we choose a diamond, let's say we obtain P points.
Let X represent the random variable that records the player's score for each individual draw.
13/52 = 1/4 is the probability of selecting a diamond from a deck of 52 cards.
This is due to the fact that there are only 13 ways to choose a diamond out of the total 52 ways to choose a card.
So, the likelihood of receiving P points is 1/4, or 0.25.
The odds of not getting a diamond equal 1 minus the odds of getting a diamond equal 1 minus 0.25, which equals 0.75.
The points we receive when we don't acquire a diamond are -2. (negative since we actually lose it, so we can take it as a negative gain).
E(X) = expectation of X = 0 is therefore required (since the negative points of loosing would equate to positive point of winning, thus, making the expected overall score 0, thus, keeping it a fair game.)
We now have:
When choosing a non-diamond card, P(X = -2) equals 0.75; when choosing a diamond card, P(X = p) equals 0.25.
There are only possible values for X.
The result is:
E(X) = -2*p(X=-2)+p*p(X=p)
E(X) = -2*0.75+p*0.25
0=-1.5+0.25p
p = 1.5/0.25 = 6
Therefore, using the probability formula, the number of diamonds needed to make the game fair is determined by option (B) 6.
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Complete question:
You pick a card at random from an ordinary deck of 52 cards. If the card is a diamond, you get some points; if not, you lose 2 points. What value for the diamonds would make the game fair?
a) 12
b) 6
c) 24
d) 3
Answer:
B-6
Step-by-step explanation:
need help on 10,12, and 13 please
Answer:
Step-by-step explanation:
Answer:
(10) x=1, y=-3
(12) x=3, y=22
(13) x= 6, y= 7
Step-by-step explanation:
[10] 6x -9 =-3x
6x+3x=9
9x=9
x=9,
A group of engineers developed a new design for a steel cable. They need to estimate the amount of weight the cable can hold. The weight limit will be reported on cable packaging. The engineers take a random sample of 44 cables and apply weights to each of them until they break. The 44 cables have a mean breaking weight of 778. 1 lb. The standard deviation of the breaking weight for the sample is 15. 5 lb
(767.47, 777.13) is the confidence interval in the given situation.
What is the confidence interval?A confidence interval is a range of estimates for an unknown parameter in frequentist statistics.
The 95% confidence level is the most popular, but other levels, like 90% or 99%, are occasionally used when computing confidence intervals.
[tex]\begin{aligned}&\mathrm{CI}=(772.3-4.83,772.3+4.83) \\&\mathrm{CI}=(767.47,777.13)\end{aligned}[/tex]
Therefore, (767.47, 777.13) is the confidence interval in the given situation.
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Select the correct answer.
What are the solutions of this quadratic equation?
x² + 2x = -2
OA.
OB.
O C.
OD.
x = 1 ti
x= -1 ti
x = 0
x = ti
Answer:
The answer might be C.(x=0)
Step-by-step explanation:
hope this helps!
wyatt can husk at least 12 dozen ears of corn per hour and at most 18 dozen ears of corn per hour. based on this information, what is a possible amount of time, in hours, that it could take wyatt to husk 72 dozen ears of cor
Wyatt can husk anywhere from 12 to 18 dozen ears of corn per hour.
To find the possible amount we need to calculate the maximum and minimum time period in hours
Thus, if we need to find the time taken to husk 72 dozen ears of corn, the maximum time would be ,
=72 / 12 hours
=6 hours
And the minimum time would be used for the does wyatt takes to husk the 72 dozen of corn
=72/18 hours
=4 hours
Thus, depending on his speed, Wyatt takes anywhere from 4 to 6 hours to husk 72 dozen ears of corn.
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The graph shows the distance Caleb runs over time. Whats the slope of the line and the equation?
Answer:
slope = 1/8
equation: y = 1/8 x
Step-by-step explanation:
Let distance = y.
Let time = x.
y = mx + b
Look at point (1, 8).
Also, the line passes through (0, 0).
slope = m = 1/8
Since it is a direct proportion, b = 0.
Equation: y = 1/8 x
You are going to bake an oversized sheet cake. The recipe calls for 2 cups of sugar for every 3 cups of flour. How many cups of flour are needed if you use 18 cups of sugar? Which answer is correct?
(1): 27 cups
(2): 18 cups
(3): 9 cups
(4): 6 cups
Set 1 angles a and c are ? and are also ? Set 2 angles b and d are ? and are also?
2.
2.
1)
a = 62⁰
b
d
O
2)
b = 120°
a
d
6 friends are coming to a party and each friend want 5 cookies but each box has twelve cookies so how many boxes do they need
Answer: 3 boxes
Step-by-step explanation:
6 x 5 = 30
36(closest multiple of 12 to 30) divided by 12 = 3
Answer:
2.5 boxes
Step-by-step explanation:
So, if each friend wants 5 cookies then you would multiply 6*5 which =30. Then you would divide 30 by 12 boxes which = 2.5. So you need 2.5 boxes or 3 if they need to be whole.
An event manager is tracking participation in a tournament by age group. The manager created the following histogram:
Histogram with title Tournament Participants, horizontal axis labeled Age Group (year) with bins 0 to 19, 20 to 39, 40 to 59, and 60 to 79 and vertical axis labeled Number of People with values from 0 to 60 at intervals of 10. The first bin goes to 30, the second goes to 50, the third goes to 40, and the last goes to 10.
What percentage of the tournament participants are under the age of 20? Round to the nearest whole percent.
10%
23%
30%
77%
Round to the closest whole percent, 23% of the participants in the event are under the age of 20.
Define the term percentage of the number?Rather than being expressed as a fraction, a percentage is a piece of a whole presented as a number ranging from zero and 100. None of this is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the overall number by the entirety and multiply the result by 100 to get the percentage.For the stated question-
Total number of people = 30 + 50 + 40 + 10
Total number of people = 130
Number of participants are under the age of 20 = 30.
Let 'x' be the % of the participants are under the age of 20.
Thus,
x% of 130 = 30
x = 30 x 100 / 130
x = 23.07
x = 23%
Thus, round to the closest whole percent, 23% of the participants in the event are under age of 20.
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a surveyor took some measurements of a piece of land. the owner needs to know the area of the land to determine the value. what is the area of the piece of land?
The area of the piece of land is 849 ft².
The area of the piece of land
=22 x 30 x [tex]\frac{1}{2}[/tex] x 2 + (30-12) x 21 x [tex]\frac{1}{2}[/tex]
=660 + 18 × 21×[tex]\frac{1}{2}[/tex]
=660 + 189
=849 ft²
The area is the amount that expresses the volume of a place on the plane or on a curved surface. The location of an aircraft region or aircraft place refers back to the area of a shape or planar lamina, at the same time as floor region refers to the location of an open floor or the boundary of a three-dimensional object. the area may be understood as the amount of fabric with a given thickness that could be essential to style a model of the shape, or the amount of paint vital to cowl the surface with a single coat. it's miles the 2-dimensional analog of the length of a curve (a one-dimensional concept) or the extent of a strong (a three-dimensional concept).
The place of a shape can be measured by way of evaluating the form to squares of a hard and fast size. inside the global gadget of devices (SI), the usual unit of the vicinity is the rectangular meter (written as m²), that's the location of a rectangle whose sides are one meter long. A shape with a place of three rectangular meters would have the equal region as 3 such squares. In mathematics, the unit square is described to have placed one, and the location of another shape or floor is a dimensionless real variety.
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For what type of variable does it make sense to construct a confidence interval about a population proportion?.
Given that a population proportion represents the proportion of successes within a population and that there must be two outcomes (categories), success and failure, a confidence interval about a population proportion only makes sense for qualitative variables.
What is confidence interval?A confidence interval (CI) is a range of estimates for an unknown parameter in frequentist statistics.
The 95% confidence level is the most popular, however other levels, such 90% or 99%, are occasionally used when computing confidence intervals.
The percentage of related CIs over the long run that include the parameter's actual value is represented by the confidence level. For instance, 95% of all intervals calculated at the 95% confidence level should include the parameter's actual value.
The sample size, sample variability, and confidence level are all variables that have an impact on the CI's width
Assuming all other factors remained constant, a larger sample would result in a narrower confidence range. Additionally, more sample variability results in a wider range of.
Hence, a population proportion represents the proportion of successes within a population and that there must be two outcomes (categories), success and failure, a confidence interval about a population proportion only makes sense for qualitative variables.
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Aume that the average number of waking hour per day i 16. If we pend 70 percent of our waking hour for communicating, how many hour do we pend communicating each day?
The total number of hours spend on the communicating is 11.2 hours each day..
Explain the term percentage of the number?A value or ratio that may be stated as a portion of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.The proportion ultimately refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.As the stated question-
Average number of waking hour per day = 16.
Communicating hours = 70% of total hours.
Thus,
Communicating hours = 70 x 16 / 100
Communicating hours = 11.2 hours
Thus, the total number of hours spend on the communicating is 11.2 hours.
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There are 8 red marbles and 6 blue marbles in a bag.
(a) What is the ratio of blue marbles to red marbles?
(b) What is the ratio of all marbles in the bag to blue marbles?
the ratio of blue marvel is 4/3
the ratio of Al marbles to blue is 7/3
You have a bag with five different colored marbles in it; red, green, blue, orange, and purple. Each marble has an equal chance of
being drawn from the bag and a marble is replaced after each draw.
After four draws from the bag what is the probability that you have seen both the red and green marbles at least once?
The probability that you have seen both the red and green marbles at least once is 0.3104
Given,
1/5 chance of winning a marble of any color in a drawing.
Every draw is independent and has the same probability because the marbles are replaced.
Calculating = 1- the likelihood of not receiving both red and green marbles in any of the four draws yields the same result as P, the probability of receiving both red and green marbles at least once (Q).
The union of the following three examples represents ways to not receive both red and green in all four draws:
(1)
Probability of no red and no green in a draw = 3/5.
Probability of no red and no green in 4 draws,
Q1 = 3/5 * 3/5 * 3/5* 3/5 = 81/54
The probabilities are multiplied as each draw is independent and has the same probabilities.
(2)
The probability of no red and 1 green in 4 draws is given by binomial probability.
= (4 3) (1/5)(3/5)³ = (4 * 3³)/5¹ = 108/5⁴
The probability of no red and 2 green in 4 draws is given by binomial probability.
= (4 2) (1/5)²(3/5)² == (6 * 3²)/54 = 54/5⁴
The probability of no red and 3 green in 4 draws is given by binomial probability.
= (4 3) (1/5)³(3/5) == (4 * 3)/5¹ = 12/5⁴
The probability of no red and 4 green in 4 draws is given by binomial probability.
= (4 4) = 1 * 1/5¹ = 1/5⁴⁴
Q2= sum of all 4 above probabilities.
Q2 (108 +54 + 12+1)/5 = 175/5⁴
(3)
This probability is the same as in Q2. Q3 = 175/5⁴
Therefore the probability of not seeing both red and green at all,
Q = Q1 + Q2 + Q3.
= 81 +175 + 175/5⁴ = 413/5⁴
Finally, the probability of getting both red and green at least once,
P = 1 - Q
= 1-413/5⁴
= (625 431)/625
= 194/625
= 0.3104.
The answer is 0.3104.
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M is the midpoint of AC. A is (3, -9) and C is (-5, 16). Solve for the following
What is the midpoint M?
What is the length or distance of AC?
The coordinates of the midpoint are (-1, 3.5) and the distance of AC is 26.25 units.
How to find the coordinates of the midpoint?We know that for a segment whose endpoints are (x₁, y₁) and (x₂, y₂), the coordinates of the midpoint are:
( [x₁ + x₂]/2, [y₁ + y₂]/2)
In this case, the endpoints are: (3, -9) and (-5, 16), then the midpoint is:
M = ( [3 - 5]/2, [-9 + 16]/2)
M = (-1, 3.5)
The distance between two points (x₁, y₁) and (x₂, y₂) is:
d = √( (x₁ - x₂)^2 + (y₁ - y₂)^2)
So here the distance is:
d = √( (3 + 5)^2 + (-9 - 16)^2) = 26.25 units.
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Of the 465 sophomores at Eastside High School, exactly 13 are taking French II or Chemistry I or both. There are 40 sophomores taking French II but not Chemistry I, and 60 sophomores taking Chemistry I but not French II. How many sophomores are taking both French II and Chemistry I ? A.
There are 55 sophomores taking French II and Chemistry I.
What is the Multiplication operation?In mathematics, Multiplication operations perform Multiplying values on either side of the operator.
For example 4×2 = 8
According to the given information, the required solution would be as:
First, we need to find the number of sophomores taking French II, Chemistry I, or both:
⇒ 1/3 × 465
Apply the multiplication operation, and we get
⇒ 155
Of the 155 sophomores, 40 are taking only French II and 60 are taking only Chemistry I:
⇒ 155 - 40 - 60
⇒ 155 - 100
Apply the subtraction operation, and we get
⇒ 55
Thus, there are 55 sophomores taking French II and Chemistry I.
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this is due in 1 hour. please help!
What is a formula for the nth term of the given sequence?
180, -240, 320...
im lost
All Harriet wants for her 12th birthday is a pet dawef hamster, maybe even mire than one so the hamster doesnt get lonley. To prove to her parents how responsible she can be, sje bought a cage that has a 12- inch by 2 1/3 foot floor space and even did some research on the needs of dwarf hamsters. Harriet found out that each dwarf hamster requires atkeast 2/3 square foot of living soace. How mahy dwarf hamsters can live in the cage Harriet purchased?
Mathematically, three dwarf hamsters can live in the cage Harriet purchased.
How is the number determined?The number of dwarf hamsters that can live in Harriet's cage is determined using mathematical operations, including multiplication and division.
Mathematical operations involve the manipulation of numbers, variables, and mathematical operands to determine mathematical results.
The result of an addition is known as the sum while for a subtraction operation is the difference.
The result of a multiplication operation is known as the product like a dvision operation (also called the quotient).
The height of the cage = 12 inches or 1 foot
The length of the cage = 2¹/₃ feet
The area of the cage = 2¹/₃ ft² (1 x 2¹/₃)
The living space required by each dwarf hamster = ²/₃ ft²
The number of dwarf hamsters that can live in the cage = 3.499 (2¹/₃ ÷ ²/₃).
= 3
Thus, using mathematical operations, we can determine that the highest number of dwarf hamsters that can live in Harriet's cage is three.
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HELP ITS DUE TODAY!!!!!!
Answer: The second one (B)
Hope this helps! :)
Step-by-step explanation:
The times when Hayden made the bracelets in this situation don't matter. All that matters in this problem is how many he made. Since it tells you that he made them for 5 days, you would multiply the number of bracelets by the days, to get the total. (Or write the equation like so: 5*(2+4))
And of course, since they are divided into groups as the last step, we have division.
5*(2+4) /6