Where are the vertices of triangle A’B’C’ located? Show your work or explain your steps. (4points)
Answers
The vertices of ∆A′B′C′ are A′(-6, 5), B′(-6, 8), and C′(-10, 5) upon the application of the translation rule.
What is the translation rule in geometry?
In geometry, a translation is a transformation that moves every point of a figure the same distance in the same direction. In the case of a triangle, a translation rule describes how to move each vertex of the triangle to a new location to create a new triangle with the same size and shape, but in a different position.
A translation rule for a triangle is given by a pair of numbers (a, b), which indicate the amount of horizontal and vertical movement of the vertices. Specifically, the rule is given by the formula:
(x, y) → (x + a, y + b)
This formula means that we move every point in the triangle a unit to the right or left (depending on the sign of a) and b units up or down (depending on the sign of b).
The translation rule (x, y) → (x − 3, y + 4) means that we move every point in the original triangle left by 3 units and up by 4 units. So, the translation is described as a leftward shift of 3 units and an upward shift of 4 units.
To find the vertices of ∆A′B′C′, we apply the translation rule to each vertex of ∆ABC:
Vertex A: (x, y) → (x - 3, y + 4)
(-3, 1) → (-3 - 3, 1 + 4) = (-6, 5)
So, vertex A of ∆A′B′C′ is located at (-6, 5).
Vertex B: (x, y) → (x - 3, y + 4)
(-3, 4) → (-3 - 3, 4 + 4) = (-6, 8)
So, vertex B of ∆A′B′C′ is located at (-6, 8).
Vertex C: (x, y) → (x - 3, y + 4)
(-7, 1) → (-7 - 3, 1 + 4) = (-10, 5)
So, vertex C of ∆A′B′C′ is located at (-10, 5).
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Related Questions
Let p and q be prime numbers satisfying
p^3-pq^2=42024
Find the sum of the digits of the product pq.
Answers
The sum of the digits of the product p×q is 8
Define the prime numbers?A positive integer bigger than one that can be divided only by itself and by one is referred to as a prime number.
Given that: p³ - pq² = 42024
p (p² - q²) = 42024
Since factors, 42024 = 2³ x 3 x 17 x 103, and p and q are prime numbers, we can see that p must be 3, 17 or 103, We can try each case:
If p = 3 then we have:
3 (9 - q²) = 42024
q² = -13,999
This equation has no real solutions for q, so p cannot be 3.
If p = 17, then we have:
17 (289 - q²) = 42024
q² = -2183
This equation also has no real solutions for q, so p cannot be 17 either.
If p = 103, then we have:
103 (10609 - q²) = 42024
10609 - q² = 408
q² = 10201
q = 101
This equation also has a solution for q = 101, so p = 103
Product of pq = 103×101 = 10403
So, the sum of the digits of the product pq = 1+0+4+0+3 = 8
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ALGEBRA 1 HW!! I WILL GIVE BRAINLYEST
Answers
The average rate of change of P between t = 3 and t = 5 is -18 people/hour.
A possible value of people in line at t = 6, given the average rate of change would be 50.
How to find the average rate of change ?To find the average rate of change of P between t = 3 and t = 5, we can use the formula:
Average rate of change = (P(5) - P(3)) / (5 - 3)
From the table, we know P(3) = 85 and P(5) = 49.
Average rate of change = (49 - 85) / (5 - 3) = (-36) / 2 = -18 people/hour
To find the possible number of people at t = 6, Let P(6) = x. First, we will find the average rate of change between t = 3 and t = 6:
(P(6) - P(3)) / (6 - 3) = (x - 85) / 3
This value must be negative. Now, we will find the average rate of change between t = 5 and t = 6:
(P(6) - P(5)) / (6 - 5) = (x - 49) / 1
This value must be positive. Since (x - 49) is positive, we know that x > 49. Now we need to find a value for x that also satisfies the condition that the average rate of change between t = 3 and t = 6 is negative. Since (x - 85) / 3 is negative, we know that x < 85.
So, a possible value for P(6) is between 49 and 85. For example, we could choose P(6) = 50, which satisfies both conditions.
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or children between the ages of 5 and 13 years, the Ehrenberg equation ln � = ln 2.4 + 1.84 ℎ gives the relationship between the weight � (in kilograms) and the height ℎ (in meters) of the child. Use differentials to estimate the change in the weight of a child who grows from 1 m to 1.1 m.
Answers
We can estimate that the weight οf a child will increase by apprοximately 1.93 kg when they grοw frοm a height οf 1 m tο 1.1 m.
What is differential?A differential equatiοn is an equatiοn that includes an unknοwn functiοn and its derivative. A differential equatiοn describes a relatiοnship between a functiοn and changes in the functiοn.
The given equatiοn relating weight (W) and height (h) fοr children between 5 and 13 years οld is:
ln(W) = ln(2.4) + 1.84h
We want tο estimate the change in weight when a child grοws frοm a height οf 1 m tο 1.1 m.
First, we need tο calculate the weight at h = 1 m and h = 1.1 m.
At h = 1 m, we have:
ln(W1) = ln(2.4) + 1.84(1)
ln(W1) = ln(2.4) + 1.84
ln(W1) ≈ 2.684
Sο the weight at h = 1 m is apprοximately W1 ≈ e².684 ≈ 14.66 kg.
Similarly, at h = 1.1 m, we have:
ln(W2) = ln(2.4) + 1.84(1.1)
ln(W2) = ln(2.4) + 2.024
ln(W2) ≈ 2.807
Sο the weight at h = 1.1 m is apprοximately W2 ≈ e².807 ≈ 16.59 kg.
Tο estimate the change in weight when the height increases frοm 1 m tο 1.1 m, we can use the differential οf the equatiοn:
dln(W) = 1.84dh
Using differentials, we can apprοximate the change in weight as:
dW ≈ W2 - W1
dW ≈ e².807 - e².684
dW ≈ 1.93 kg
Therefοre, we can estimate that the weight οf a child will increase by apprοximately 1.93 kg when they grοw frοm a height οf 1 m tο 1.1 m.
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An observer views a rocket take off from a distance of N miles from the launch pad, and tracks the angle of elevation.
a) Express the height of the rocket as a function of the angle of elevation, Θ.
b) Express the angle of elevation as a function of the height, h, of the rocket.
c) When the angle of elevation is A degrees, find the height of the rocket.
N=Any given number
A=Any given angle
(My Open Math question)
Answers
Short Answers:
a)N*tan(Θ)
b)arctan(h/N)
c)N*tan(A)
Let * stand for multiplication
Hope this is helpful to someone:)
X follows Poisson distribution. This distribution was randomly sampled 40 times. The sum of these 40 numbers follows
a) Poisson distribution
b) Exponential distribution
c) Weibull distribution
d) Normal distribution
Answers
The sum of these 40 sampled numbers follows option D: normal distribution, if X follows Poisson distribution.
The likelihood that a certain number of events will occur in a specific period of time or space, provided that they do so with a known constant mean rate and the Poisson distribution describes the distribution of events, regardless of the time since the previous event. When the mean is high, the sum of the Poisson distribution resembles a normal distribution.
The "normal distribution," a continuous probability distribution that is symmetrical at the mean and has a bell-shaped curve. It is also known as the bell curve or the Gaussian distribution. Several natural phenomena, including height, weight, blood pressure, and others, have a normal distribution.
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Theodore invests $15,000 into an account at an annual rate of 0.55% simple interest for 36 months.
1) What is the Principal in this scenario?
1) 0.0055
2) 0.55 %
3) $15,000
4) 3
2) What is the interest rate for this account?
1) 0.55 %
2) $15,000
3) 3
4) 0.0055
3) What number do you use to represent the interest rate in the simple interest formula?
1) 0.55 %
2) 3
3) $15,000
4) 0.0055
4) What is the length of time of this investment, in years?
1) 0.55 %
2) 3
3) $15,000
4)0.0055
5) Calculate the simple interest earned on this account.
Answers
Answer:
1)$15000
2)0.55%
3)0.55
4)3
5)24.75
Step-by-step explanation:
5)1500×0.55×3/100
Omar recorded the number of hours he worked each week for a year. Below is a random sample that he took from
data.
13, 17, 9, 21
What is the standard deviation for the data?
Answers
Answer:
Approx. 4.47
Step-by-step explanation:
To calculate the standard deviation for the data, we need to follow these steps:
1. Calculate the mean (average) of the data:
mean = (13 + 17 + 9 + 21) / 4 = 15
2. Calculate the difference between each data point and the mean:
13 - 15 = -2
17 - 15 = 2
9 - 15 = -6
21 - 15 = 6
3. Square each difference:
(-2)^2 = 4
2^2 = 4
(-6)^2 = 36
6^2 = 36
4. Calculate the variance by taking the average of the squared differences:
variance = (4 + 4 + 36 + 36) / 4 = 20
5. Calculate the standard deviation by taking the square root of the variance:
standard deviation = sqrt(variance) = sqrt(20) ≈ 4.47
Therefore, the standard deviation for the data is approximately 4.47.
hi i dont understand this question for some reason
Answers
Answer: y = x + 6
Step-by-step explanation: "y = m x + b" is the format used to find the equation of a line on a graph.
Y and X remain the same in the equation, however you replace "m" with the value of the slope. In this problem, the slope is "1" because the rise is 1 and the run is 1, making it 1/1 or 1. Because the slope is "1", we do not need to include the number "1" in our equation.
Finally, "b" is the y-intercept (in other words, the place where the line crosses the y-axis). In this problem, the line crosses at "6"; therefore, 6 will replace b in the equation completing it.
Since the point is not starting through the origin it becomes 6 cause that’s where it is starting from and you don’t know by how much you are moving up so it is x
if someone knows the answer please tell me
Answers
Answer:
Step-by-step explanation:
first graph
y = 5x + 2
2 = y-intercept
5 = slope
the first graph is y = 5x+2 because the y-intercept is 2 and it rises 5 and goes over 1
second graph:
y = 2x + 3
third graph:
y = 3x + 3
18. Find the 21st term if a₁ = 3/5 and
d = -1/3
(a) -6.07
(b) 11.67
Answers
Answer:
a
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n[/tex] a₁ + (n - 1)d
here a₁ = [tex]\frac{3}{5}[/tex] and d = - [tex]\frac{1}{3}[/tex] , then
a₂₁ = [tex]\frac{3}{5}[/tex] + (20 × - [tex]\frac{1}{3}[/tex] )
= [tex]\frac{3}{5}[/tex] - [tex]\frac{20}{3}[/tex]
= 0.6 - 6.67
= - 6.07 ( to 2 decimal places )
PLEASE HELP!!
x^2=7y-4+9x^2
Answers
First, we can simplify the equation by bringing all the x^2 terms to one side and all the constant terms to the other side:
x^2 - 9x^2 = 7y - 4
Simplifying further:
-8x^2 = 7y - 4
Dividing both sides by 7:
y = (-8/7)x^2 + 4/7
So the equation of the graph of this function is a downward opening parabola with a vertex at (0, 4/7) and a coefficient of -8/7.
please answer as SOON AS POSSIBLE
Answers
An exponential expression with base 25 and a single, simplified exponent is [tex](25)^{-28}[/tex]
What is an exponent?In Mathematics, an exponent simply refers to a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.
Generally speaking, an exponent is represented by the following mathematical expression;
bⁿ
Where:
the variables b and n are numerical values (numbers) or an algebraic expression.n is referred to as a superscript or power.By applying the law of indices for powers of the same base number, we have the following:
[tex](25^7)^{-4}=(25)^{7 \times -4}\\(25)^{7 \times -4}=(25)^{-28}[/tex]
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Find the polynomial that represents the area of the square
Answers
The polynomial expression that represents the area of the given square is: 4x² + 28x + 49
What is the area of the square?The formula for the area of a square is expressed as:
Area = side * side
Now, we are given the dimensions of the square and we have:
Side length = x + 7 + x = 2x + 7
Thus:
Area of square = (2x + 7) * (2x + 7)
= 4x² + 14x + 14x + 49
= 4x² + 28x + 49
Thus, we conclude that expression represents the area of the square.
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Find the arc length of the semicircle. Either enter an exact answer in terms of � πpi or use 3.14 3.143, point, 14 for � πpi and enter your answer as a decimal. units
Answers
The radius as 5, so the arc length of the semicircle is s = π(5) = 5π ≈ 15.71.
What is radius?Radius is a line segment that extends from the center of a circle or sphere to its circumference. It is the distance from the center to the edge of the circle or sphere. It is also used to measure the length of an arc of a circle. Radius is a necessary measure when calculating the area of a circle or sphere, as well as the volume of a sphere.
The arc length of a semicircle is given by the formula s = πr,
where r is the radius of the semicircle. In this case,
we are given the radius as 5, so the arc length of the semicircle is s = π(5) = 5π ≈ 15.71.
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The arc length of a semicircle with radius 'r' is equal to rπ or approximately 3.14r units.
What is an arc?
An arc is part of a circle's circumference. It is a segment of a curved line that is formed when a straight line intersects a circle or a curved shape. Arcs can be measured in length, angle, or radius, depending on the context.
To find the arc length of a semicircle, we need to know the radius of the circle and the angle subtended by the arc at the center of the circle.
Let's assume the radius of the semicircle is 'r'. Since it is a semicircle, the angle subtended by the arc at the center of the circle is 180 degrees or π radians.
The formula for arc length is given by:
arc length = radius x angle in radians
In this case, the angle is π radians and the radius is 'r'. Therefore, the arc length of the semicircle is:
arc length = r x π
We can leave the answer in terms of π or substitute the value of π to get a numerical answer. For example, if the radius of the semicircle is 4 units, the arc length will be:
arc length = 4 x π
arc length ≈ 12.57 units (using π ≈ 3.14)
Therefore, the arc length of a semicircle with radius 'r' is equal to rπ or approximately 3.14r units.
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G 11. A The figure below is made up of 2 squares and triangle EDH. BC = CD and 25% of square CDEF is shaded. The ratio of the shaded area to the unshaded area in triangle EDH is 1:5. Find the ratio of the shaded area to the unshaded area in the figure. F E 75% B C D 5 H
Answers
The ratio of the shaded area to the unshaded area in the figure is 1 : 5.5 which can be calculated by adding the areas of the two squares and triangle EDH.
What is area?Area is the amount of two-dimensional space taken up by a shape or object. It is measured in square units, such as square centimeters, square meters, or square miles.
The ratio of the shaded area to the unshaded area in the figure can be calculated by adding the areas of the two squares and triangle EDH, and then subtracting the shaded area.
First, calculate the total area of the figure:
Area of the two squares = (BC)²
= (CD)²
= (4)²
= 16
Area of triangle EDH = ½ x BC x DH
= ½ x 4 x 5
= 10
Total area = 16 + 10
= 26
Next, calculate the shaded area:
Shaded area of square CDEF = 25% x 16
= 4
Total shaded area = 4
Finally, calculate the ratio of the shaded area to the unshaded area in the figure:
Unshaded area = 26 - 4
= 22
Ratio of the shaded area to the unshaded area = 4 : 22
= 1 : 5.5
Therefore, the ratio of the shaded area to the unshaded area in the figure is 1 : 5.5.
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Question:
A The figure below is made up of 2 squares and triangle EDH. BC = CD and 25% of square CDEF is shaded. The ratio of the shaded area to the unshaded area in triangle EDH is 1:5. Find the ratio of the shaded area to the unshaded area in the figure.
In the figure, the proportion of shaded to unshaded region is 1:5.5.
What is the Area of the Shaded Region?The area of the shaded region is the difference between the area of the entire polygon as well as the area of the polygon's unshaded part. In polygons, the area of the shaded portion can occur in two ways. The shaded area can be found in the centre of a polygon or on its sides.
As previously stated, the area of the shaded region is determined by subtracting the area of a complete polygon from the area of the unshaded region.
outer shape region – area of the interior unshaded shape = The shaded area
To begin, compute the entire area of the figure:
Area of the two squares [tex]=(BC)^2[/tex]
[tex]=(CD)^2\\\\=(4)^2\\\\=16[/tex]
Area of the EDH triangular [tex]=\frac{1}{2} \times BC\times DH[/tex]
Substitute values in the above equation
[tex]=\frac{1}{2} \times 4\times 5\\\\=10[/tex]
Total area = 16 + 10
= 26
The shaded region is then calculated as follows:
CDEF square shaded region = 25% x 16
= 4
Total shaded area = 4
Finally, compute the shaded-to-unshaded area ratio in the figure:
Unshaded area = 26 - 4
= 22
Shaded to unshaded region ratio = 4 : 22
= 1 : 5.5
As a result, the shaded area to unshaded area ratio in the image is 1: 5.5.
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The complete question is,
A The figure below is made up of 2 squares and triangle EDH. BC = CD and 25% of square CDEF is shaded. The ratio of the shaded area to the unshaded area in triangle EDH is 1:5. Find the ratio of the shaded area to the unshaded area in the figure.
ssume there is a certain population of fish in a pond whose growth is described by the logistic equation. It is estimated that the carrying capacity for the pond is 1800 fish. Absent constraints, the population would grow by 180% per year.
If the starting population is given by
p
0
=
100
, then after one breeding season the population of the pond is given by
p
1
=
After two breeding seasons the population of the pond is given by
p
2
=
Answers
he is literally hitting the gritty
help i forgot how to do this
Answers
1. The angle between the hypotenuse and the base is approximately 90 - 23.6 = 66.4 degrees. 2. the angle between the hypotenuse and the perpendicular is approximately 90 - 62.3 = 27.7 degrees.
Describe Cosine?In trigonometry, cosine (cos) is a trigonometric function that relates the adjacent side and the hypotenuse of a right triangle. It is defined as the ratio of the adjacent side to the hypotenuse. The cosine function is periodic with a period of 360 degrees or 2π radians, and it has a range of values between -1 and 1.
In other words, if we have a right triangle with an angle x, then the cosine of x is equal to the length of the adjacent side of the triangle divided by the length of the hypotenuse.
1.In a right-angled triangle, the cosine of an angle is defined as the ratio of the adjacent side to the hypotenuse. Therefore, cos(x) = adjacent/hypotenuse = 37/39.
Using inverse cosine function on a calculator, we get x ≈ 23.6 degrees.
Therefore, the angle between the hypotenuse and the base is approximately 90 - 23.6 = 66.4 degrees.
2. Again, using the definition of cosine, we have cos(x) = adjacent/hypotenuse = 8/17.
Using inverse cosine function on a calculator, we get x ≈ 62.3 degrees.
Therefore, the angle between the hypotenuse and the perpendicular is approximately 90 - 62.3 = 27.7 degrees.
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An account pays 2.4% compounded monthly. Suppose you invest $150 a month for 8 years, then leave the money in the account, without making additional payments, for another 12 years. a. How much will you have at the end of the 20 years? b. How much interest did you earn?
Answers
If yοu invest $150 a mοnth fοr 8 years, then leave the mοney in the accοunt, withοut making additiοnal payments, fοr anοther 12 years.
a) Yοu will have yοu will have apprοximately $59,073.95 at the end οf 20 years.$59,073.95 at the end οf 20 years.
b) Earned apprοximately $26,673.95 in interest οver the 20-year periοd.
What Is the Future Value οf an Annuity?The wοrth οf a series οf recurrent payments at a specific future date, assuming a specific rate οf return, οr discοunt rate, is the future value οf annuity.
Let's first calculate the tοtal number οf mοnths in 20 years:
20 years x 12 mοnths/year = 240 mοnths
a. we can use the fοrmula fοr the future value οf an annuity:
[tex]FV = PMT x (((1 + r/n)^(n*t) - 1) / (r/n))[/tex]
where:
PMT = the mοnthly payment ($150)
r = the annual interest rate (2.4% οr 0.024)
n = the number οf times the interest is cοmpοunded per year (12)
t = the tοtal number οf years (20)
FV = 150 x (((1 + 0.024/12)^(12*20) - 1) / (0.024/12))
FV ≈ $59,073.95
Therefοre, yοu will have apprοximately $59,073.95 at the end οf 20 years.
b. Tο calculate the amοunt οf interest yοu earned, we can subtract the tοtal amοunt οf mοney yοu invested frοm the future value:
Interest = FV - Tοtal amοunt invested
Interest = $59,073.95 - ($150 x 12 x 8 x 12)
Interest ≈ $26,673.95
Therefοre, yοu earned apprοximately $26,673.95 in interest οver the 20-year periοd.
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The gradient of the line joining (-2, K) and (K₁-14) Calculate the value of k the points
Answers
The value of k for this line is equal to -6.
How to calculate the gradient of a line?In Mathematics and Geometry, the gradient of any straight line is also referred to as slope and it can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Substituting the given data points into the slope formula, we have the following;
2 = (-14 - k)/(k + 2)
-14 - k = 2(k + 2)
-14 - k = 2k + 4
-14 - 4= 2k + k
3k = -18
k= -18/3
k = -6
In this context, we can reasonably infer and logically deduce that the value of k is equal to -6.
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Complete Question:
The gradient of the line joining the points (-2,k) and (k, -14) is 2 . Calculate the value of k.
drag numbers to the table so it shows a porpotinal relationship between x and y
Answers
The complete table that shows the proportional relationship is:
x y
0.8 4
3.2 16
12.8 64
How to find the proportional relationship?The ratio of the given y-value and x-value is calculated as:
y/x = 4/0.8 = 5
Thus, the ratio of the next terms must all be 5.
The second x coordinate is 3.2. Thus:
y/3.2 = 5
y = 3.2 * 5
y = 16
Difference of the first 2 x-values = 3.2 - 0.8 = 2.4
Thus, the third value of x will be:
3.2 + 2.4 = 5.6
Thus, the third y-coordinate = 5.6 * 5 = 28
Similarly, the fourth value of x will be:
5.6 + 2.4 = 8.0
Thus, the fourth y-coordinate = 8 * 5 = 40
The sixth value of x will be:
8 + 2.4 + 2.4 = 12.8
Sixth value of y = 12.8 * 5 = 64
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Complete question is:
Drag numbers to the table so it shows a proportional relationship between x and y.
Tiles : 8.8 , 12.8 , 5.6 , 64 , 6.4 , 16
X axis Y axis
0.8. 4
3.2 ?
? ?
The perimeter of a rectangle is
360cm. find the breadth if its
length is 80cm.
Answers
Answer:
4.5 cm.
Step-by-step explanation:
Divide the length by the width to get the perimeter: 360 / 80 = 4.5 cm.
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Suppose the Sunglasses Hut Company has a profit function given by P(q) = -0.01q2 +5q-39, where q
is the number of thousands of pairs of sunglasses sold and produced, and P(q) is the total profit, in
thousands of dollars, from selling and producing a pairs of sunglasses.
A) Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your
answer.)
Answer: MP(q)
B) How many pairs of sunglasses (in thousands) should be sold to maximize profits? (If necessary, round your
answer to three decimal places.)
Answer:
thousand pairs of sunglasses need to be sold.
C) What are the actual maximum profits (in thousands) that can be expected? (If necessary, round your
answer to three decimal places.)
=
Answer:
thousand dollars of maximum profits can be expected.
Answers
Solving the quadratic equation, we get the maximum profit is 2451 thousand dollars.
What are quadratic equations?A second-degree algebraic equation in x is known as a quadratic equation. The quadratic equation is written as Ax2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.
For an equation to be categorised as a quadratic equation, the coefficient of x2 must be a non-zero term (a 0).
The function is given as
P(q) = -0.01q2 +5q-39
We have
P(q) = -0.01q2 +5q-39
Differentiate
So, we have
P'(q) = -0.01q + 5
Set to 0
So, we have
-0.01q + 5
This gives:
-0.01q = -5
Evaluate
q = 500
Hence, 500 thousand pairs of sunglasses should be sold to maximize profits.
What is the maximum profit?
In (a), we have
q = 500
This gives:
P (500) = (-0.01)500×2 +5×500-39
Evaluating:
P (500) = -10 + 2500 -39
= 2451
Hence, the maximum profit is 2451 thousand dollars.
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When we solve the quadratic equation, we discover that the utmost profit is $2451 thousand dollars.
What are quadratic equations?A quadratic equation is an x-dependent second-degree algebraic problem. [tex]ax^{2} +bx+c=0[/tex], where x is the variable, a and b are the coefficients, and c is the constant element, is how the quadratic equation is expressed.
The coefficient of [tex]x^{2}[/tex] must not be negative for an equation to be categorized as a quadratic equation (a, 0).
The function is given as
P(q) = [tex]-0.01q^2[/tex] +5q-39
We have
P(q) = [tex]-0.01q^2[/tex] +5q-39
Differentiate
So, we have
P'(q) = -0.01q + 5
Set to 0
So, we have
-0.01q + 5
This gives:
-0.01q = -5
Evaluate
q = 500
So, in order to make the most money 500 000 sets of sunglasses should be sold.
In (a), we have
q = 500
This gives:
P (500) = (-0.01)500×2 +5×500-39
Evaluating:
P (500) = -10 + 2500 -39
= 2451
Therefore, the highest profit is $2451 thousand dollars.
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The units of an item available for sale during the year were as follows:
Jan. 1 Inventory 10 units at $26 $260
Aug. 13 Purchase 6 units at $29 174
Nov. 30 Purchase 7 units at $30 210
Available for sale 23 units $644
There are 11 units of the item in the physical inventory at December 31. The periodic inventory system is used. Determine the inventory cost using the (a) first-in, first-out (FIFO) method; (b) last-in, first-out (LIFO) method; and (c) weighted average cost method (round per-unit cost to two decimal places and your final answer to the nearest whole dollar).
a. First-in, first-out (FIFO) $326
b. Last-in, first-out (LIFO) $289
c. Weighted average cost $
Answers
The inventory cost under:
a. First-in, first-out (FIFO) - $326.
b. Last-in, first-out (LIFO) - $289.
c. Weighted average cost - $308.
How to solvea. Calculation of inventory cost using the First-in, First-out (FIFO) method:
There are 11 units of the item in the physical inventory on December 31. Under FIF7 units will be from items purchased on Nov 30 and 4 units will be from items purchased on Aug 13.
( 7 units * 30) + (4 units *29)
= 210 + 116 = $326
b. Calculation of inventory cost using the Last-in, First-out (LIFO) method:
There are 11 units of the item in the physical inventory on December 31. Under LIFO Method, 10 units will be from items purchased on Jan 1 and 1 unit will be from items purchased on Aug 13.
10 units * 26 + (1 unit * 29)
= $289
c. Calculation of Weighted Average cost per unit:
$644/23 units
=$28 per unit
Calculation of inventory cost using the Weighted Average Cost method:
11 units * 28
= $308
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The circumference of the circular table is 72 π inches. What is the radius of the table
Answers
Answer: 36 inches
Step-by-step explanation:
The formula for the circumference of a circle is 2πr where r is the radius of the circle Therefore 2πr=72π so r=72/2 = 36 inches.
The box plot above summarizes the resting heart rates, in beats per minute, of the members at a gym.
Which of the following could be the range of resting heart rates, in beats per minute ?
Answers
The range of resting heart rates is 70 beats per minute. Subtracting the lowest value from the highest value will give us the range.
What is range?It is a set of data which is the difference between the highest and lowest values.
The range of resting heart rates, in beats per minute, is calculated by subtracting the minimum value of the data set from the maximum value. In this case, the minimum value = 35
and the maximum value = 105,
so the range of resting heart rates = 105 - 35
= 70 beats per minute
The other answers cannot be the range of the resting heart rates because they are not calculated correctly.
The answer 16 beats per minute (105 - 89 = 16) is the difference between the maximum and the 90th percentile, and the answer 31 beats per minute (85 - 54 = 31) is the difference between the 85th percentile and the median.
The answer 62 beats per minute (95 - 33 = 62) is the difference between the 95th percentile and the minimum.
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Question:
Rewrite 300-4 in a different way, using the Commutative Law of Multiplication.
A) 30-40
B) 1200
C) 4.300
D) 3.100-4
Answers
Answer:
3x100-4
Step-by-step explanation:
3x100=300
(3x100)-4
300-4
The Dodd-Frank Wall Street Reform and Consumer Protection Act of 2010 established the Consumer Financial Protection Bureau (CFPB). The purpose of the CFPB is to ensure that consumer finance markets work effectively. It provides a forum for consumers to submit their complaints about the services received from financial providers. It also educates consumers about financial matters to help them make sound financial decisions.
Use this consumer credit card market report, published by the CFPB in 2017, to answer the following questions.
Refer to section 1.3.2, Credit scores, on page 22 of the report.
For which two purposes do credit card issuers use credit scores?
Select all the correct answers.
Oto determine the consumer's age and gender
Oto set pricing for rewards programs
O to determine the consumer's eligibility for credit
O to set pricing for late fees
to set pricing for credit lines
to determine the number of credit cards to be issued by a lending company
Answers
The correct answers are: To determine the consumer's eligibility for credit and To set pricing for credit lines.
what is pricing?
"Pricing" refers to the process of determining the value or cost of a product or service and setting a specific price for it. Pricing decisions involve taking into account various factors such as production costs, market demand, competition, and profit margins, among others. Pricing can also involve setting
In the given question,
Based on section 1.3.2, Credit scores, on page 22 of the report, the two purposes for which credit card issuers use credit scores are:
To determine the consumer's eligibility for credit.
To set pricing for credit lines.
Therefore, the correct answers are:
To determine the consumer's eligibility for credit
To set pricing for credit lines
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Rieko is making bird houses for a craft fair she has 15 pounds of nails how many bird houses could rieko make if each bird house requires 1/4 pounds of nails
Answers
Rieko can make 60 bird houses if each bird house requires 1/4 pounds of nails and she has 15 pounds of nails.
How many bird houses could rieko makeIf each bird house requires 1/4 pounds of nails and Rieko has 15 pounds of nails, we can use the following equation to determine the number of bird houses she can make:
number of bird houses = amount of nails / amount of nails per bird house
Plugging in the given values, we get:
number of bird houses = 15 / (1/4)
Simplifying the right-hand side by dividing 15 by 1/4, we get:
number of bird houses = 60
Therefore, Rieko can make 60 bird houses if each bird house requires 1/4 pounds of nails and she has 15 pounds of nails.
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find 3 consecutive even integers if three times the first integer is two times the third
Answers
Step-by-step explanation:
First = x
second = x + 2
third = x + 4
3 * x = 2 ( x+4)
3x = 2x+ 8
x = 8 8 10 and 12
at an amusement park 25 people ride the cras every 30 mins and 20 people rid the spinning swings which one will have more rides how many more
Answers
Answer:
Spinning Swings
10 more riders
Step-by-step explanation:
To find which ride will have more riders each hour, we need to first convert an hour into minutes.
[tex]\text{1 hour = 60 minutes}[/tex]
Now we let's first find how many riders there will be in the race cars.
So there are 25 riders every 30 minutes.
in 60 minutes there will be:
[tex]25 \times 2 = 50 \ \text{Riders}[/tex]
Now for the spinning swings there are 20 riders every 20 minutes.
In 60 minutes there will be:
[tex]20 \times 3 = 60 \ \text{Riders}[/tex]
Therefore, the spinning swings will have more riders as [tex]60 > 50[/tex].
Now to find how many more riders there will be in the spinning swings.
We simply subtract the total number of riders of each ride from each other.
[tex]\text{Race Cars = 50}[/tex]
[tex]\text{Spinning Swings = 60}[/tex]
[tex]60 - 50 = 10[/tex]
There will be 10 more riders in the spinning cups than the race cars.