Answers
Answer:
1) They are not inverses
2) They are inverses
Step-by-step explanation:
We need to find the composition function between these functions to verify if these functions are inverses. If f[g(x)] and g[f(x)] are equal to x they are inverses.
1)
Let's find f[g(x)] and simplify.
[tex]f[g(x)]=\frac{1}{2}g(x)+\frac{3}{2}[/tex]
[tex]f[g(x)]=\frac{1}{2}(4-\frac{3}{2}x)+\frac{3}{2}[/tex]
[tex]f[g(x)]=\frac{7}{2}-\frac{3}{4}x[/tex]
As f[g(x)] is not equal to x, these functions are not inverses.
2)
Let's find f[g(x)] and simplify.
[tex]f[g(n)]=\frac{-16+(4n+16)}{4}[/tex]
[tex]f[g(n)]=\frac{-16+4n+16}{4}[/tex]
[tex]f[g(n)]=\frac{4n}{4}[/tex]
[tex]f[g(n)]=n[/tex]
Now, we need to find the other composition function g[f(x)]
Let's find g[f(x)] and simplify.
[tex]g[f(x)]=4(\frac{-16+n}{4})+16[/tex]
[tex]g[f(x)]=-16+n+16[/tex]
[tex]g[f(x)]=n[/tex]
Therefore, as f[g(n)] = g[f(n)] = n, both functions are inverses.
I hope it helps you!
Related Questions
The price of one gallon of milk has increased from $3.24 to $4.05. What is the percentage increase?
Answers
Answer:
the price of one gallon of milk has increased by 25%.
Step-by-step explanation:
The price of one gallon of milk has increased from $3.24 to $4.05, which is an increase of $4.05 - $3.24 = $0.81. To find the percentage increase, we can divide the amount of the increase by the original price and multiply by 100%. This gives us:
(0.81 / 3.24) * 100% = 25%
Therefore, the price of one gallon of milk has increased by 25%.
The solution is 25 %
The percentage increase in the price of one gallon of milk is given by the equation P = 25 %
What is Percentage Error?
The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.
Percentage error is the difference between the measured value and the true value , as a percentage of the true value
Percentage Error = [ ( | Measured Value - True Value | ) / True Value ]x 100
Given data ,
Let the original price of the milk be A = $ 3.24
Let the increased price of the milk be B = $ 4.05
Let the percentage increase in the price be = P
Now , the equation will be
Percentage Error = [ ( | Measured Value - True Value | ) / True Value ]x 100
Substituting the values in the equation , we get
Percentage increase P = [ ( 4.05 - 3.24 ) / 3.24 ] x 100
On simplifying the equation , we get
Percentage increase P = ( 0.81 / 3.24 ) x 100
Percentage increase P = 0.25 x 100
Percentage increase P = 25 %
Therefore , the value of P is 25 %
Hence , the percentage increase is 25 %
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Choose the function whose graph is given by:
A. y=-3.5cos x
B. y=3.5sin x
C. y=sin(3x)
D. y=2.5sin x
Answers
The function plotted in the graph is given by - g(x) = 3.5 sin(x)
What is sine function? What is sine series? What is law of sines?In trigonometry, the sine function can be defined as the ratio of the length of the opposite side to that of the hypotenuse in a right-angled triangle.Mathematically -[tex]$\sin \theta=\frac{a}{h}[/tex]
{θ} = angle theta
{a} = length of opposite side a
{h} = length of hypotenuse h
The sine series is given as follows -[tex]${\displaystyle {\begin{aligned}\sin(x)&=x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-{\frac {x^{7}}{7!}}+\cdots \;= \sum _{n=0}^{\infty }{\frac {(-1)^{n}}{(2n+1)!}}x^{2n+1}\\[8pt]\end{aligned}}}[/tex]
The law of sines states that for an arbitrary triangle with sides [a], [b] and [c] and angles opposite the sides [A], [B] and [C] -{sin(A) / a = sin(B) / b = sin(C) / c}
Given is a graph as shown in the image.
A sine function has its maximum value of [1] and the minimum value of [-1]. The given graph g(x), is a amplitude scaled version of the function f(x) given by -
f(x) = sin(x)
and
g(x) = Asin(x)
Here, [A] is equal to 3.5. So, the function g(x) is equal to -
g(x) = 3.5 sin(x)
Therefore, the function plotted in the graph is given by -
g(x) = 3.5 sin(x)
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Sample Response: First, I wrote each ratio as a fraction. Then I found a common denominator of 20. The fraction 4/10 is 8/20. Comparing numerators, 8 is less than 12, so the ratio 4:10 is smaller.
Which did you include in your answer?
Check all that apply.
Write the ratios as fractions.
Find a common denominator.
Compare the numerators to see that 4:10 is the smaller ratio.
Answers
In the aforementioned scenario, the choice you must include in your response is to find a common denominator.
In the simplest terms, what is fraction?One can refer to a fraction as being in its lowest term or in its simple form when the numerator and denominator are known to have no common factors besides 1. In general, any number of equal pieces is represented by a fraction, which is a portion of the entire. A fraction, such as one-half, eight-fifths, or three-quarters, indicates the number of parts of a particular size when it is used in daily speech.
The common denominator will be between 10 and 20, and there is a common numerator as well. The common denominator will be 20 because both can divide it and 10 is less than 20.
Finding a common denominator is the solution you should choose in the scenario mentioned above.
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Clarks Inc., a shoe retailer, sells boots in different styles. In early November the company starts selling “SunBoots” to customers for $70 per pair. When a customer purchases a pair of SunBoots, Clarks also gives the customer a 30% discount coupon for any additional future purchases made in the next 30 days. Customers can’t obtain the discount coupon otherwise. Clarks anticipates that approximately 20% of customers will utilize the coupon, and that on average those customers will purchase additional goods that normally sell for $100. Required: 1. How many performance obligations are in a contract to buy a pair of SunBoots? 2. Assume Clarks cannot estimate the standalone selling price of a pair of SunBoots sold without a coupon. Prepare a journal entry to record revenue for the sale of 1,000 pairs of SunBoots.
Answers
The journal entry is given in answer part b
What is Discount coupon?A discount coupon is defined as a certificate that entitles the customer to avail of a reduction in the invoice price if the terms mentioned on it are met. It is a technique applied by the sellers to expand sales.
Given that, Clarks Inc., a shoe retailer, sells boots in different styles. In early November, the company starts selling “SunBoots” to customers for $70 per pair. When a customer purchases a pair of SunBoots, Clarks also gives the customer a 30% discount coupon for any additional future purchases made in the next 30 days. Customers can’t obtain the discount coupon otherwise. Clarks anticipates that approximately 20% of customers will utilize the coupon, and that on average those customers will purchase additional goods that normally sell for $100.
a) Two performance obligations are associated with contract. The first one is related to the sun boots, and the other one is associated with discount coupon provided. The discount coupon would be considered a separate obligation because it gives a certain right to the customers that they would not have received if the sale was not made to them.
b) Journal entry =
Account title and explanation Debit ($) Credit ($)
Cash (1000×$70) $70000
Sales Revenue ($70,000-$6000) $64000
Deferred Revenue $6000
Now,
Computation of the deferred revenue:
Deferred revenue = pairs sold × Average purchase price × Discount × Redemption of coupon
= 1000 × 100 × 30% × 20%
= $6000
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Review the graph. Given z = -1 - i, which letter represents z3?
Answers
Answer:
C
Step-by-step explanation:
Multiply z times itself. Then multiply z times that first answer, to get z^3.
There's a formula for cubing a binomial but even if you don't remember it (like me) you can still find z^3.
But remember that i^2 = -1
This is related to sqrt(-1)= i, a definition for the imaginary number.
On the graph, go left or right for the real part and up or down for the imaginary part.
see image.
Here are the dimensions of two designs for a sandbox for the primary playground. Each sandbox is a rectangular prism. One design is 3 m by 3 m by 30 cm.
A second design is 3.25 m by 3.25 m by 25 cm.
a) Sketcheachsandbox.Includeitsdimensions.
b) Compare the designs. For each design, calculate the area
of material needed to build it and the volume of sand
it will hold.
c) Whichsandboxshouldbebuilt?Justifyyouranswer.
Answers
The volume of the first and second designs are 2.7 m³ and 2.64 m³ so, the second design will hold more sand.
What is volume?
The capacity occupied by a three-dimensional solid shape is known as volume. It is difficult to visualize in any shape, yet it may be compared among shapes. For instance, a compass box has a larger volume than an eraser placed inside of it.
Given:
One design is 3 m by 3 m by 30 cm,
A second design is 3.25 m by 3.25 m by 25 cm,
Calculate the volume for the first design as shown below,
Volume of first design = 3 × 3 × 30/ 100 (1 m = 100 cm),
The volume of the first design = 270 / 100
The volume of the first design = 2.7 m³
Calculate the volume of the second design as shown below,
The volume of the second design = 3.25 × 3.25 × 25 / 100
The volume of the second design = 264.06 / 100
The volume of the second design = 2.64 m³
The difference in the volume of both designs = The volume of the first design - The volume of the second design
The difference in the volume of both designs = 2.7 - 2.64
The difference in the volume of both designs =0.06 m³
Thus, the first design will hold more volume of sand.
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How to set up the following question in the image below?
Answers
The expected number of students that pick soda is 80
How to determine the expected number of students that pick Soda?From the bar graph, we have the following parameters that can be used in our computation:
Ice cream = 40
Soda = 20
popsicle = 10
This means that the proportion of soda is
Soda = 20/(40 + 20 + 10)
Evaluate the sum
Soda = 20/70
So, we have
Soda = 2/7
For a group of 280 students, we have
Soda = 2/7 *280
Evaluate
Soda = 80
Hence, the number of students is 80
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I need help
How do you find x:
2^(2x) + 2^(x+2) - 12 = 0
Answers
Answer:
[tex]x=1[/tex]
Step-by-step explanation:
[tex]2^{2x}-2^2 2^x-12=0 \\ \\ (2^x)^2-4(2^x)-12=0[/tex]
Factoring the quadratic in [tex]2^x[/tex],
[tex](2^x+6)(2^x-2)=0 \\ \\ 2^x=-6,2 \\ \\ 2^x=2 \implies x=1 \\ \\ 2^x=-6 \implies x \notin \mathbb{R} \\ \\ \therefore x=\log_{2} (6)[/tex]
what does
QR=
PR=
M
Answers
We need to use Right Angled Triangle Properties.
PR≈15 and QR≈12 is the length of the sides.
What is a Right Angled Triangle?
According to the definition of a right triangle, a triangle is referred to as a right-angled triangle or simply a right triangle if one of its angles is a right angle (90o). Triangle PQR is a right triangle in the illustration, and its components are its base, height, and hypotenuse. Here, QR is the base, PQ is the height, and PR is the hypotenuse. The essential side of a right triangle is its hypotenuse, which is also its largest side and sits across from the triangle's right angle.
In a right triangle we have: (Hypotenuse)2 = (Base)2 + (Altitude)2
Area of a right triangle = (1/2 × base × height) square units.
Calculation:PR is the Hypotenuse of the Triangle.
PQ=9
Angle ∡PQR=37° and Angle ∡RPQ=53°
So Sin(theta)=opposite side/Hypotenuse
⇒Sin(37°)=9/Hypotenuse
⇒Hypotenuse=9/0.6018
⇒Hypotenuse=14.955
PR⇒14.955
We know that (Hypotenuse)2 = (Base)2 + (Altitude)2
⇒(14.955)2=(9)2+(QR)2
QR=11.9438
PR≈15 and QR≈12
We need to use Right Angled Triangle Properties.
PR≈15 and QR≈12 is the length of the sides.
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Find the remainder term Rn in the nth order Taylor polynomial centered at a for the given function. Express the result for a general value of n. f(x)=e^-2x, a=2 Choose the correct answer below. O A. Rn (x) = (-2)^n e^-2c/(n+1)! (x- 2)^n for some c between x and 2. O B. Rn (x) = (-2)^n+1 e^-2c/(n+ 1)! for some c between x and 2. O C. (-2)1+1e 2c Rn(x)=?(n+1)!-(x-2)n + 1 for some c between x and 2. O D. n -2c OD. (x-2)"+1 for some c between x and 2.
Answers
The remainder term Rn is equal to (-2) raised to the power of n multiplied by e raised to the power of -2c, divided by n+1 factorial, multiplied by (x-2) raised to the power of n, for some c between x and 2.
The remainder term Rn in the nth order Taylor polynomial centered at a for the given function f(x)=e^-2x, a=2 is equal to (-2) raised to the power of n multiplied by e raised to the power of -2c, divided by n+1 factorial, multiplied by (x-2) raised to the power of n, for some c between x and 2. This remainder term represents the difference between the approximate value of the function given by the Taylor polynomial and the actual value of the function. By taking the limit as n approaches infinity, the remainder term can be used to determine the exact value of the function. The remainder term is an important concept in calculus as it is used to determine the accuracy of a given approximation.
For n=5, R5(x) = (-2)^5 e^-2c/(5+1)! (x-2)^5 for some c between x and 2.
Substituting n=5, x=7 and c=4, we have:
R5(7) = (-2)^5 e^-8/(6)! (7-2)^5
R5(7) = (-2)^5 e^-8/(720) (25)
R5(7) = (-2)^5 e^-8/18000
R5(7) = (-2)^5 e^-8/18000
R5(7) = -1.388888888 x 10^-9
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is melissa correct that m(
Answers
Answer:
no melissa isn't correct she has made 3 mistakes
Step-by-step explanation:
Can someone help me on this question?
Answers
Answer:
see below for the chart
64 pages in 1 hour
Step-by-step explanation:
You want to fill in the chart showing the analysis of the problem statement saying HP can read 16 pages in 1/4 hour. The problem statement is requesting the number of pages he can read in 1 hour.
ChartSee below for a filled-in chart.
SolutionAnalysis of the bottom line tells you that the right column is 4 times the middle column.
1 = 4 × 1/4
?? = 4 × 16 = 64
Harry Potter can read 64 pages in one hour.
Which expression can be used to represent the volume of this prism?
Responses
3 × 9 × 9 units³
2 × 3 × 3 units³
2 × 3 × 9 units³
3 × 3 × 18 units³
Answers
The expression that represents the volume of the prism is
2 × 3 × 9 units³. That is option C.
What is a prism?Prism is defined as the type of polyhedron that has two polygonal faces lying in parallel planes and with the other faces parallelograms.
A prism can be of a regular shape or of an irregular shape. The volume of a regular shapes prism can be calculated using the formula stated below
volume of a prism = l × b × h
Length (l) = 9 units
Breath = 2 units
Height (h) = 3 units.
Therefore, the volume of the given prism can be calculated as 2 × 3 × 9 units³.
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Find the Derivative of 1/x+2
Answers
Answer: 2x+1
x
Step-by-step explanation:
Jim has to choose between two gym membership plans. Plan A: $50 monthly membership fee and $10 per visit. Plan B: $25 one time membership fee and $15 per visit. How many visits must Jim make to make Plan A the cheaper option?
How many visits for them to cost the same
If you answer the visits, I will give branliest
Answers
The number or visits that Jim must make to make Plan A the cheaper option is more than 5 visits
How to illustrate the equation?An equation is the statement that illustrates the variables given. Jim has to choose between two gym membership plans.
For Plan A: $50 monthly membership fee and $10 per visit. This will be:
50 + 10v
Plan B: $25 one time membership fee and $15 per visit. This will be:
= 25 + 15v
Let v = number of visit
This will be illustrated as:
50 + 10v = 25 + 15v
Collect like terms
15v - 10v = 50 - 25
5v = 25
Divide
v = 25 / 5
v = 5
There will be more than 5 visits for a cheaper option.
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The length of a rectangle is 3 meters less than
twice its width. The area of the rectangle is
104 m²2. Find the dimensions of the rectangle.
Answers
Therefore, the length of a rectangle is 13m and width is 8m
What is area?A region's size on a planar or curved surface is described mathematically as its area. In contrast to a plane region or plane's area, which refers to a form or planar lamina, a surface area is the size of an open surface or the edge of a three-dimensional object.
Here,
width=x
length=2x-3
Area =l x w
104=(2x-3)(x)
104=2x^2-3x
52=x^2-3/2(x)
52+9/16=x^2-3/2(x)+9/16
841/16=(x-3/4)^2
29/4=x-3/4
x=32/4
x= 8m
Thus width = 8m
length = 2(8)-3 = 13m
Therefore the length of a rectangle is 13m and width is 8m
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which statement describes the solutions of this equation? x/x+2 + 1/x = 1
Answers
Answer:
[tex]\frac{x}{x+2}+\frac1x=1\\\rightarrow \frac{x^2+(x+2)}{(x^2+2x}=1\\\rightarrowx^2+x+2=x^2+2x\\\rightarrowx+2=2x\\\rightarrow x=\boxed2[/tex]
Only one solution, which is two. The answer should be C. You could obviously see that if there is no squaring then there will be no extraneous solutions.
Alex biked a 48-mile trail in 4 hours. For the first half of the time, he biked twice as fast as he did the second half of the time. What speed did Alex bike the first half?
Answers
Alex's speed in the first half of the time is 12 miles per hour
How t find the speed of bikingInformation from the problem include:
For the first half of the time, Alex biked a 48-mile trail in 4 hours.
he biked twice as fast as he did the second half of the time.
Average speed is calculated using the ratio of distance to time spent
this is represented by the formula
= distance / time
The speed for the first half is solved as below
= 48 mile / 4 hours
= 12 mile / hours
= 12 mph
speed for the first half is 12 mph
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Find the area of a circle with radius 6 ft.
Answers
Answer:
The area of the circle is 113.04 square feet.
Step-by-step explanation:
Given;Radius (r) = 6 ftπ = 3.14Formula;A = πr²A = 3.14 × (6)² ft
A = 3.14 × 36 ft
A = 113.04 square feet.
Thus, The area of the circle is 113.04 square feet.
Answer:
28.274 square feet
Step-by-step explanation:
Multiply the radius by pi
My sister is 8 years older than I am. The sum of our ages is 28. Find our ages.
I am years old. My sister is years old.
Answers
Answer:
My sister is
18
years old.
Step-by-step explanation:
s = m + 8 Eq. 1
s + m = 28 Eq. 2
s = my sister age
m = my age
Replacing Eq. 1 in Eq. 2:
(m+8) + m = 28
2m + 8 = 28
2m = 28 - 8
2m = 20
m = 20/2
m = 10
From Eq. 1:
s = m + 8
s = 10 + 8
s = 18
Check:
from Eq. 2:
s + m = 28
18 + 10 = 28
AOB is a sector of a circle, centre O and radius 12 cm. The length of arc AB is 15 cm. Find the area of the sector.
Answers
The formula to find the arc length of a circle = θ/360 ×2××r
The formula to find the area of a sector= θ/360××r²
The only thing missing is "θ"
The arc length is given to be 15cm so basically θ/360×2×3.14×12 = 15
θ= 360×15 ÷ 2×3.14×12 = 5400÷ 75.36= 71.65
now that we found "θ" we just continue with the formula to find the area of a sector (θ/360×r²)
=71.65×3.14×12²= 90cm
(it's a bit complicated but i hope this helped i tried to simplify it as much as i could)
What is the equation of the line in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
Hope this helps
Construct a confidence interval for p₁ -P2 at the given level of confidence.
x₁ = 355, n₁ = 536, x₂ =438, n₂ = 598, 99% confidence
The researchers are confident the difference between the two population proportions, p₁ - P₂, is between
(Use ascending order. Type an integer or decimal rounded to three decimal places as needed.)
Answers
Using confidence interval concepts, it is found that the correct options are:A. With 99% confidence, the mean width of all widgets is between 14.3 and 30.4.
Find the solution ?There is a 99% chance that the mean of the population is between 14.3 and 30.4.
The interpretation of a x% confidence interval is that we are x% sure that the population mean is in the interval.
In this problem, 99% confidence interval for widget width is between 14.3 and 30.4, hence we are 99% sure that the population mean, that is, the mean width of all widgets is between 14.3 and 30.4, hence options A and C are correct.
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Write an equation to match this graph.
Answers
The equation that matches the graph is 7x-30y=-275
How to find the equation of a line?We should know that an equation is a mathematical expression in which two sides are equal.
The equation of a line is the equation formed with the slope of the straight line
The slope of the of the is determined taking the points
[tex]M=\frac{Y_{2}-Y_{1} }{X_{2}-X_{1} }[/tex]
Slope=(7-1)÷(35-5)
m=1/5
The equation of the line is
1/5 = (y-1)÷(x-35)
Cross multiplying the equation
7x-245=30y-30
Rearrange,
7x-30y=-30-245
7x-30y=-275
In conclusion the equation to match the graph is 7x-30y=-275
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Test the claim that the two samples described below come from populations with the same mean. Assume that the samples are independent simple random samples. Use a significance level of alpha = 0.1 The degree of freedom is The test statistic is Determine the rejection region for the test of The final conclusion is
Answers
Final conclusion would be that the difference between the means of the two samples is not statistically significant.
What is Null Hypothesis?
The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable.
It is not possible to test the claim that the two samples come from populations with the same mean without more information about the samples themselves. In order to test this claim, you need to have the sample data, the sample sizes, and the standard deviations of the samples. You can then use a t-test for independent samples to determine whether the difference between the means of the two samples is statistically significant.
The t-test is a statistical test that is used to compare the means of two samples. The test statistic for the t-test is the difference between the means of the two samples divided by the standard error of the difference. The degree of freedom for the t-test is the sum of the sample sizes minus 2. The significance level, alpha, is the probability of making a type I error, which is the probability of rejecting the null hypothesis when it is true. The rejection region for the t-test is the set of values of the test statistic for which the null hypothesis is rejected.
If the test statistic does not fall in the rejection region, you cannot reject the null hypothesis, and you must conclude that the difference between the means of the two samples is not statistically significant.
Final conclusion would be that the difference between the means of the two samples is not statistically significant.
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If x varies directly as y, find x when y = 8 a) x = 6 when y = 32 b) x = 14 when y = -2
Answers
a) The value of x is 42.6 when k =16/3 is directly proportional to y.
b) The value of x is -56 when k is -7 is directly proportional to y.
What kind of variation is one where x and y are directly proportional?
If x = ky for some constant k can be used to indicate the relationship between the variables y and x, then we may say that y varies directly with y or that x is directly proportional to y.x varies directly as y
x α y
x = ky
a) x=6 ; y = 32
x = ky
6 = k(32)
k = 16/3
if y = 8
then,
x = (16/3) * 8
= 128/3
x = 42.6
Hence, the value of x is 42.6 when k =16/3 is directly proportional to y.
b) x= 14 and y = -2
x = ky
14 = k(-2)
k = -7
if y = 8
then,
x = ky
x= (-7) 8
x = -56
Hence, the value of x is -56 when k is -7 is directly proportional to y.
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Find the length of BD. Use that length of BC. Round to the nearest tenth
Answers
By means of trigonometric functions, the length of side BC is approximately equal to 11.6 centimeters.
How to determine a missing length in a system of triangles by trigonometric functions
In this problem we find a geometric system formed by two right triangles, from which we need to determine the exact measure of side BC. This can be done by means of trigonometric functions, that represents relationships between two sides of a right triangle:
sin θ = y / r
cos θ = x / r
tan θ = y / x
cot θ = x / y
sec θ = r / x
csc θ = r / y
Where:
r - Hypotenusex - Leg adjacent to the angle.y - Leg opposite to the angle.First, obtain the length of side BD:
cos θ = BD / AB
BD = AB · cos θ
BD = 5 · cos 30°
BD = 5√3 / 2 cm
Second, calculate the length of side BC:
sin θ = BD / BC
BC = BD / sin θ
BC = 5√3 / 2 / sin 22°
BC ≈ 11.6 cm
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Convert the measurement. 28.4 grams ≈ ounces
Answers
Answer: 1.0017805194 ounces
Step-by-step explanation:
To change 28.4 g to oz divide the mass in grams by 28.349523125. The 28.4 grams to ounces formula is [oz] = [28.4] / 28.349523125. Thus, we get (all results rounded to 2 decimals):
28.4 g to oz = about 1 oz
28.4 g to ounces = about 1 ounces
28.4 grams to ounces = about 1 oz
Twenty-eight point four grams to ounces equal 1 international avoirdupois ounces, the unit used to measure grocery products (mass) in retail stores in the United States for example.
HOPE THIS HELPS 189328 :)!Assume that a company makes only one product, maintains no beginning or ending inventories, and uses a standard costing system. The standard cost card for that product is shown below:
Standard Quantity or Hours Standard Price or Rate Standard Cost
Direct materials 3 pounds $ 13.00 per pound $ 39.00
Direct labor 2 hours $ 16.00 per hour $ 32.00
Fixed manufacturing overhead 2 hours $ 8.00 per hour $ 16.00
The company purchased 22,000 pounds of direct materials from its supplier at a cost of $12.50 per pound. The company used 22,000 pounds of direct material to start and complete 7,800 units of finished goods during the period. Its direct laborers worked 16,000 hours and were paid a total of $248,000. Based on this information, the total increase recorded in the Work in Process account related to direct labor would be:
Garrison 17e Rechecks 2020-09-29
Multiple Choice
$241,800.
$256,000.
$248,000.
$249,600.
Group Ends
Answers
Since the company paid a total of $248,000 in direct labor costs during the period, there is no difference between the standard and actual costs of direct labor.
How to calculate labor cost ?To determine the total increase recorded in the Work in Process account related to direct labor, we need to first calculate the total standard cost of direct labor for the period and then compare it to the actual cost of direct labor.
According to the standard cost card, each unit of the product requires 2 hours of direct labor at a rate of $16.00 per hour.
This means that the total standard cost of direct labor for the period is 2 * $16.00 * 7,800 = $248,000.
Since the company paid a total of $248,000 in direct labor costs during the period, there is no difference between the standard and actual costs of direct labor. Therefore, the total increase recorded in the Work in Process account related to direct labor would be $0.
To learn more about direct labor costs refer :
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How much would you need to deposit in an account now in order to have $5,000.00 in the account in 1633 days?
Assume the account earns 42% simple interest.
You would need to deposit ___
in your account now.
Answers
You would need to deposit $2,500 in order to have $5,000.00 in the account in 1633 days.
1st method: This can be found by using the simple interest formula I=PRT. In this case, I=5000, P=2500, R=.42, and T=1633. Solving for I gives you the answer.
2nd Method: If you deposit $2,500 in an account now, you will have $5,000 in the account in 1633 days. $2,500 * 1.42 = $3,550 $3,550 + $2,500 = $6,050 $6,050 / 2 = $3,025
To know about simple interest, click here
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