Answer:
C(x)= 41x + 680
Step-by-step explanation:
If the fixed cost is 680, that will apply regardless of how many jackets the company makes for you. The number of jackets is unknown. However, we know that the cost of producing a single jacket is 41, so we can represent that expression as 41x. Putting those things together gives us a function of the cost:
C(x) = 41x + 680
The equation to determine the total cost encountered by Marty's Tee Shirt & Jacket Company in producing x jackets is C(x) = 680 + 41x.
Explanation:To determine the total cost, C(x), encountered by Marty's Tee Shirt & Jacket Company in producing x jackets, we need to consider both the fixed costs and the variable costs. The fixed costs, which are $680, are incurred regardless of the number of jackets produced. The variable costs, which are $41 per jacket, increase with each additional jacket produced. So the equation to calculate the total cost is:
C(x) = fixed costs + (variable costs per jacket) * x
Substituting the given values, the equation becomes:
C(x) = 680 + 41x
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HELP!!
Type the correct answer in the box, and .
If angle x is in the fourth quadrant and angle y is in the first quadrant, the value of is .
Answer:
1/2
Step-by-step explanation:
Given:
sinx=-1/2
cosy=√3/2
finding x
x=sin^-1(-1/2)
x=-π/6
x=-30°
finding y
cosy=√3/2
y=cos^-1(√3/2)
y=π/6
y=30°
Now finding cos(x-y)
cos(-π/6-π/6)
=cos(-π/3)
=1/2!
It is a hot day at the beach. Ice water costs $1 per bottle and this is your only option. Your marginal benefit for water follows the equation MB = $10 - $x.x is represents the number of bottles of ice water you have had. So, for example, the marginal benefit of the first bottle is $10 - $1 = $9. The MB of the 2nd bottle is $8 .. and so on.Assuming you are an economically rational consumer how many bottles of water will you buy?
Answer:
9 bottles of water
Step-by-step explanation:
Marginal benefit is a microeconomic concept that explains how much the consumer adds satisfaction to each unit consumed of a given product. Usually, the marginal benefit is decreasing, which makes logical sense, the more a customer consumes a particular good, the smaller the benefit of the next unit.
At first, the first bottle of water has a high benefit as mentioned in the exercise: 9
In the second, you are a little less thirsty, so the benefit will be 10 - 1x2 = $8
In the ninth bottle, you will have very little thirst and the benefit will be 10 - 1x9 = $1
In the tenth bottle there is no benefit, the consumer is indifferent. As a rational consumer, you will buy until the bottle is still usable, even if minimal, for 9 bottles when your benefit is $1.
As an economically rational consumer, you will continue buying bottles of water until the marginal benefit equals or is less than the price of the water. In this case, you will buy a total of 10 bottles of water.
Explanation:As an economically rational consumer, you will continue buying bottles of water until the marginal benefit equals or is less than the price of the water. In this case, the price of water is $1 per bottle.
The marginal benefit equation is given as MB = $10 - $x, where x represents the number of bottles of water you have had. So, for each bottle of water you consume, the marginal benefit decreases by $1.
To determine the number of bottles of water you will buy, you need to compare the marginal benefit to the price of water:
MB = $10 - $1 = $9. Since $9 is greater than $1, you will buy the first bottle of water.MB = $8. Since $8 is greater than $1, you will buy the second bottle of water.MB = $7. Since $7 is greater than $1, you will buy the third bottle of water.Continuing this pattern, you will keep buying bottles of water as long as the marginal benefit is greater than or equal to $1.Therefore, you will buy a total of 10 bottles of water.
In triangle ABC, a = 4, b = 7, and c = 10. Find A.
18°
34°
56°
162°
Answer:
18°
Step-by-step explanation:
The law of cosines tells you ...
a² = b² + c² -2bc·cos(A)
Solve for cos(A) and fill in the numbers. Note that the value of cos(A) is very close to 1, so the angle will be fairly small. This by itself can steer you to the correct answer.
cos(A) = (b² +c² -a²)/(2bc) = (49 +100 -16)/(2·7·10) = 133/140
A = arccos(133/140) ≈ 18.2° ≈ 18°
As part of video game, the point (4,6) is rotated counterclockwise about the origin through an angle of 15 degrees. Find the new coordinates of this point
Answer:
(2.31079, 6.83083)
Step-by-step explanation:
The transformation due to rotation about the origin in the counterclockwise direction by an angle α is ...
(x, y) ⇒ (x·cos(α) -y·sin(α), x·sin(α) +y·cos(α))
Here, that means the new coordinates are ...
(4·cos(15°) -6·sin(15°), 4·sin(15°) +6·cos(15°)) ≈ (2.31079, 6.83083)
To rotate the point (4,6) counterclockwise about the origin by 15 degrees, we can use the rotation formulas. The new coordinates are approximately (2.833, 6.669).
Explanation:To rotate a point counterclockwise about the origin, we can use the rotation formula:
x' = x * cos(theta) - y * sin(theta)
y' = x * sin(theta) + y * cos(theta)
Using the given point (4,6) and an angle of 15 degrees, we can substitute the values into the formulas to find the new coordinates:
x' = 4 * cos(15) - 6 * sin(15) = 4 * 0.9659258263 - 6 * 0.2588190451 ≈ 2.833166271
y' = 4 * sin(15) + 6 * cos(15) = 4 * 0.2588190451 + 6 * 0.9659258263 ≈ 6.669442572
Therefore, the new coordinates of the point after rotation are approximately (2.833, 6.669).
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PLS HELP FIRST CORRECT ANSWER GETS BRAINLIEST !! A pile of tailings from a gold dredge is in the shape of a cone. The diameter of the base is 34 feet and the height is 16 feet. Approximately, how many cubic feet of gravel is in the pile? Use π = 3.14.
A. 14,527 ft³
B. 285 ft³
C. 4,840 ft³
D. 6,032 ft³
Answer:
C: [tex]V=4840 (2 s.f.)[/tex]
Step-by-step explanation:
The formula for the volume of a cone is:
[tex]V= \frac{1}{3} \pi r^2h[/tex]
Therefore,
[tex]V=\frac{1}{3}\times 3.14\times(\frac{34}{2})^2\times 16\\\\V=4840 (2 s.f.)[/tex]
The volume of the cone is 4840 cubic ft if the diameter of the base is 34 feet and the height is 16 feet option (C) is correct.
What is a cone?It is defined as a three-dimensional shape in which the base is a circular shape and the diameter of the circle decreases as we move from the circular base to the vertex.
[tex]\rm V=\pi r^2\dfrac{h}{3}[/tex]
Volume can be defined as a three-dimensional space enclosed by an object or thing.
It is given that:
A pile of tailings from a gold dredge is in the shape of a cone.
The diameter of the base is 34 feet and the height is 16 feet.
As we know,
The volume of the cone is given by:
[tex]\rm V=\pi r^2\dfrac{h}{3}[/tex]
r = 34/2 = 17 ft
h = 16 feet
Plug the above values in the formula:
[tex]\rm V=\pi (17)^2\dfrac{16}{3}[/tex]
After solving:
V = 1541.33π cubic feet
Take π = 3.14
V = 1541.33(3.14) cubic feet
V = 4839.78 ≈ 4840 cubic ft
Thus, the volume of the cone is 4840 cubic ft if the diameter of the base is 34 feet and the height is 16 feet option (C) is correct.
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If the square root of 61 is the longest side length in the triangle and the shorter sides are x and x+1, find the value of x that makes the triangle above a right triangle. Write your answer in simplest radical form.
Answer:
x = 5
Step-by-step explanation:
You want to find x such that ...
x^2 +(x +1)^2 = 61
2x^2 +2x -60 = 0 . . . . . simplify, subtract 61
x^2 +x -30 = 0 . . . . . . . divide by 2
(x +6)(x -5) = 0 . . . . . . . . factor; solutions will make the factors be zero.
The relevant solution is x = 5.
HELP ME WITH THIS MATH QUESTION
For this case we have that by definition, the arc length of a circle is given by:
[tex]AL = \frac {x * 2 \pi * r} {360}[/tex]
Where:
x: Represents the angle between JM. According to the figure we have that x = 90 degrees.
[tex]r = \frac {16.4} {2} = 8.2[/tex]
So:
[tex]AL = \frac {90 * 2 \pi * 8.2} {360}\\AL = \frac {90 * 2 * 3.14 * 8.2} {360}\\AL = 12.874[/tex]
Rounding:
[tex]AL = 12.9[/tex] miles
Answer:
12.9 miles
Answer: 12.9
Step-by-step explanation:
Use a special right triangle to write sin 30° as a fraction. HELP PLEASE!!
Answer:
The answer is
√3/2
Step-by-step explanation:
The value of sin 30°=1/2.
What is special right triangle?The special right triangle is the triangle used to know the side ratio without using Pythagoras theorem every time.
There are some types of special right triangles present like 30-60-90 triangle, 45-45-90 triangles, and the Pythagorean triple triangles.
Here for deriving the value for sin 30°, we will use the 30-60-90 triangle.
The 30-60-90 triangle is given below.
the value sine is calculated by the ratio of the opposite side and the hypotenuse of the right-angled triangle.
In 30-60-90 triangle the side opposite to 30° angle is x and the hypotenuse is 2x then the side opposite to 60° angle is x√3.
In 30-60-90 triangle,
sin 30°=opposite side/hypotenus
= x/2x
⇒sin 30°=1/2
Therefore, the value of sin 30°=1/2.
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The formula m = 12,000 + 12,000rt 12t gives Keri's monthly loan payment, where r is the annual interest rate and t is the length of the loan, in years. What would Keri's monthly loan payment be if she got a 4% loan for 5 years? $ ___per month
Answer:
$240
Step-by-step explanation:
Fill in the given numbers and do the arithmetic.
[tex]m=\dfrac{12,000+12,000rt}{12t}=\dfrac{12,000+12,000\cdot 0.04\cdot 5}{12\cdot 5}\\\\m=\dfrac{14,400}{60}=240[/tex]
Keri's monthly loan payment is $240 per month.
Answer: 300 per month
Step-by-step explanation:
Which products result in a difference of squares? Check all that apply.(x – y)(y – x)(6 – y)(6 – y)(3 + xz)(–3 + xz)(y2 – xy)(y2 + xy)(25x – 7y)(–7y + 25x)(64y2 + x2)(–x2 + 64y2)
1. (3 + xz)(–3 + xz)
2. (y² – xy)(y² + xy)
3. (64y2 + x2)(–x2 + 64y2)
Explanation
The difference of 2 squares is in the form (a+b)(a-c).
(3 + xz)(–3 + xz) = (3 + xz)(xz -3)
= (xz + 3)(xz - 3)
= x²y²-3xy+3xy-9
=x²y² - 3²
(y² – xy)(y² + xy) = y⁴+xy³-xy³-x²y²
= y⁴ - x²y²
(64y2 + x2)(–x2 + 64y2)= (64y²+x²)(64y²-x²)
= 4096y⁴-64y²x²+64y²x²-x⁴
= 4096y⁴ - x⁴
Which of the following statements correctly explains the coefficient of variation (CV)?
A. The CV is a relative measure of risk/return.
B. The CV is an absolute measure of risk/return.
C. The higher the CV value the more acceptable the risk/return profile for a risk-averse investor.
D. The lower the CV value the more acceptable the risk/return profile for a risk-averse investor.
Answer:
A. The CV is a relative measure of risk/return.
Step-by-step explanation:
The coefficient of variation of any investment, is used to measure and calculate the total risk of that investment with respect to its per unit expected return rate.
We can also define the coefficient of variation as a ratio of standard deviation to the expected value of an investment.
The answer is - A. The CV is a relative measure of risk/return.
The coefficient of variation (CV) is a relative measure of risk/return; thus, statement A is correct, and statement D is correct as it relates to the preferences of risk-averse investors. This measure is useful for assessing the consistency of investment returns, especially when comparing different investment options.
The coefficient of variation (CV) is a statistical measure that is used to assess the relative variability of data. It is calculated by dividing the standard deviation by the mean and multiplying by 100. This ratio provides a standardized measure of the dispersion of data points in a data set around the mean, which is particularly useful when comparing the variability between datasets with different units or scales.
Now let's examine the given statements:
A. The CV is a relative measure of risk/return.
B. The CV is an absolute measure of risk/return.
C. The higher the CV value the more acceptable the risk/return profile for a risk-averse investor.
D. The lower the CV value the more acceptable the risk/return profile for a risk-averse investor.
Statement A is correct: the CV is indeed a relative measure because it expresses the standard deviation as a percentage of the mean, making it unitless and thus comparable across different data sets and scales.
Statement D is also correct: a lower CV indicates that the returns are less volatile relative to the mean return, which is generally preferred by risk-averse investors. Risk-averse investors prefer investments with more predictable and stable returns, as such investments are associated with lower levels of relative risk.
A rain gutter is to be made of aluminum sheets that are 12 inches wide by turning up the edges 90degrees. see the illustration. (a) what depth will provide maximum cross-sectional area and hence allow the most water to flow? (b) what depths will allow at least 16 square inches of water to flow?
Answer:
a) max area for depth of 3 inchesb) ≥ 16 in² for 2 in ≤ depth ≤ 4 inStep-by-step explanation:
(a) For a depth of x, the two sides of the rain gutter are length x, and the bottom is length (12-2x). The cross sectional area is the product of these dimensions:
A = x(12 -2x)
This equation describes a parabola that opens downward. It has zeros at ...
x = 0
12 -2x = 0 . . . . x = 6
The maximum area is halfway between these zeros, at x=3.
The maximum area is obtained when the depth is 3 inches.
__
(b) For an area of at least 16 square inches, we want ...
x(12 -2x) ≥ 16
x(6 -x) ≥ 8 . . . . . divide by 2
0 ≥ x² -6x +8 . . . . subtract the left side
(x -4)(x -2) ≤ 0 . . . factor
The expression on the left will be negative for values of x between 2 and 4 (making only the x-4 factor be negative). Hence the the depths of interest are in that range.
At least 16 square inches of water will flow for depths between 2 and 4 inches, inclusive.
The maximum cross-sectional area of the gutter which allows the most water flow is achieved at a depth of 4 inches. For a flow rate of 16 square inches, we need to solve the equation for the cross-sectional area equal to 16 to find the corresponding depth.
Explanation:Your question pertains to maximizing the cross-sectional area of a rain gutter made from 12-inch wide aluminum sheets. This involves the use of calculus, specifically optimization, and basic geometry.
Let's denote 'x' as half the width of the base. When the sides are turned up 90 degrees, the sides will be of length 'x'. Since the gutter is 12 inches wide, the equation for the width is 2x+x=12. So, x=4.
To maximize the cross-sectional area, you need to set the derivative of the area function equals to zero.
For your second question, to find the depths that will allow at least 16 square inches of water to flow, equate the cross-sectional area equals to 16, and solve for 'x'.
In conclusion,
The depth that would allow maximum cross-sectional area and the most water flow is when x = 4 inches,. To allow 16 square inches of water to flow, solve for 'x' when the cross-sectional area equals to 16.
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The golf clubs have been sorted into woods and irons. The number of irons is four more than two times the number of woods. The equipment is 75% irons. How many woods are there?
4
5
6
7
Answer:4
Step-by-step explanation:16/4 = 4
if 75% of equipment is iron then do the math
So it would be 4(2) + 4 = 75% of 16
So if 75% of 16 is 12 you need that extra 4 to get you to 16
The number of woods in the golf club is equal [tex]4[/tex].
What is number?" Number is defined as the count of any given quantity."
According to the question,
[tex]'x'[/tex] represents the number of irons
[tex]'y'[/tex] represents the number of woods
As per given condition we have,
[tex]x= 2y +4[/tex] [tex](1)[/tex]
[tex]x = 75\%(x+ y)\\\\\implies x = \frac{75}{100}(x + y)\\ \\\implies x = \frac{3}{4} (x+y)\\\\\implies 4x= 3x + 3y\\\\\implies x = 3y \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (2)[/tex]
Substitute the value of [tex](2)[/tex] in [tex](1)[/tex] to get the number of woods,
[tex]3y = 2y +4\\\\\implies y =4[/tex]
Therefore,
[tex]x= 3\times 4\\\\\implies x=12[/tex]
Hence, the number of woods in the golf club is equal [tex]4[/tex].
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The stopping distance for a boat in calm water is modelled by the function d(v) = 0.004v2 + 0.2v + 6, where d(v) is in metres and v is in kilometres per hour.
a. What is the stopping distance if the speed is 10km/h?
b. What is the initial speed of the boat if it takes 11.6m to stop?
Please help :(
Answer:
a. 8.4 km b. 20 km/hr or 20,000 m/hr
Step-by-step explanation:
This is your polynomial:
[tex]d(v)=.004v^2+.2v+6[/tex]
The important thing to realize is that d(v) is the distance it takes for the boat to stop. That will come later, in part b. Besides that, we also need to remember that v is velocity, which is speed, in km/hr.
For part a. we are looking for d(v), the stopping distance, when v = 10. That means that we will sub in a 10 for each v in the function and solve for d(v):
[tex]d(10)=.004(10)^2+.2(10)+6[/tex] so
d(10) = 8.4 km
Now comes the part I was referring to above. Part b is asking us the speed of the boat if it takes 11.6 meters to stop. If d(v) is the stopping distance, we sub 11.6 in for d(v) in the function:
[tex]11.6=.004v^2+.2v+6[/tex]
The only way w can solve this for velocity is to get everything on one side of the equals sign, set the polynomial equal to 0, then plug the values into the quadratic formula.
[tex]0=.004v^2+.2v-5.6[/tex]
Plugging that into the quadratic formula gives you 2 values of velocity:
v = 20 km/hr and -70 km/hr
We all know that neither time nor distance in math will EVER be negative so we can discount the negative number. However, I believe that you asked for the distance in meters, so 20 km/hr is the same as 20,000 m/hr.
Isoke is solving the quadratic equation by completing the square.
10x2 + 40x – 13 = 0
10x2 + 40x = 13
A(x2 + 4x) = 13
What is the value of A?
Step-by-step explanation:
10 is the value of A ......
Answer:
Value of A = 10
Step-by-step explanation:
Here Isoke is solving the quadratic equation by completing the square
10x² + 40x – 13 = 0
10x² + 40x – 13 + 13 = 0 + 13
10x² + 40x + 0 = 13
10x² + 40x = 13
10 ( x² + 4x) = 13
Here it is given as
A(x² + 4x) = 13
Comparing both
We will get A = 10
Value of A = 10
PLEASE HELP ME WITH THIS MATH QUESTION
Answer:
[tex]m(RS)=17[/tex] inches (answer rounded to nearest tenths)
Step-by-step explanation:
Central angle there is 150 degrees.
The radius is 6.48 inches.
The formula for finding the arc length, RS, is
[tex]m(RS)=\theta \cdot r[/tex]
where [tex]r[/tex] is the radius and [tex]\theta[/tex] ( in radians ) is the central angle.
I had to convert 150 degrees to radians which is [tex]\frac{150\pi}{180}[/tex] since [tex]\pi \text{rad}=180^o[/tex].
[tex]m(RS)=\frac{150\pi}{180} \cdot 6.48[/tex]
[tex]m(RS)=16.96[/tex] inches
Answer: [tex]17\ in[/tex]
Step-by-step explanation:
You need to use the following formula for calculate the Arc Lenght:
[tex]Arc\ Length=2(3.14)(r)(\frac{C}{360})[/tex]
Where "r" is the radius and "C" is the central angle of the arc in degrees.
You can identify in the figure that:
[tex]r=6.48\ in\\C=150\°[/tex]
Then, you can substitute values into the formula:
[tex]Arc\ Length=Arc\ RS=2(3.14)(6.48\ in)(\frac{150\°}{360})\\\\Arc\ RS=16.95\ in[/tex]
Rounded to the nearest tenth, you get:
[tex]Arc\ RS=17\ in[/tex]
BRAINLIEST! what are the next 2 terms in the geometric sequence?
a1=2,r=-3
Answer:
The next two terms after a1 is
-6 and then 18
Step-by-step explanation:
Geometric sequence means your pattern for the terms is multiplication by the same number.
So a1 is the first term and r is your common ratio.
The common ratio is what you are multiplying by each time to figure out the next term.
So the geometric sequence goes like this:
a1 , a1*r , (a1*r)*r or a1*r^2 , a1*r^3 ,....
So anyways you have
first term a1=2
second term a2=2(-3)=-6
third term a3=-6(-3)=18
And so on...
Calculate the average rate of change for the graphed sequence from n=2 to n=6.
Answer:
-3
Step-by-step explanation:
The average rate of change is the y-difference divided by the x-difference:
(2 -14)/(6 -2) = -12/4 = -3
The average rate of change for the sequence is -3.
Answer:
-3
Step-by-step explanation:
Product A is and 8oz bottle of cough medication that's sells for $1.36. Product B is 16oz bottle of cough medication that costs $3.20. Which product has the lower unit price?
Answer:
Product B
Step-by-step explanation:
Divide the number of ounces i the bottle by the price of the bottle. Product A has a unit price of $0.17 and Product B has a unit price of $0.20. Therefore Product B has a lower unit price :))
Use the Quadratic Formula to solve the equation 4x^2-7=4x.
Select one:
a. x=-1/2+sqrt2 or x=-1/2-sqrt2
b. x=7/8+sqrt113/8 or x=7/8-sqrt113/8
c. x=1/2+sqrt2 or x=1/2-sqrt2
d. x=2+4sqrt2 or x=2-4sqrt2
The quadratic equation 4x^2 - 4x - 7 = 0 is solved using the Quadratic Formula with coefficients a = 4, b = -4, c = -7. The correct solutions obtained are x = 1/2 + √2 and x = 1/2 - √2, corresponding to option (c).
Explanation:To solve the quadratic equation 4x^2 - 4x - 7 = 0 using the Quadratic Formula, we first identify the coefficients: a = 4, b = -4, and c = -7.
The Quadratic Formula is given by:
x = √((-b ± √(b^2 - 4ac)) / (2a)).
Substitute the identified coefficients into the formula:
x = √(((-(-4) ± √((-4)^2 - 4(4)(-7))) / (2(4))).
Simplify the expression:
x = √(((4 ± √(16 + 112)) / 8),
x = √(((4 ± √(128)) / 8),
x = √((4 ± 8√2) / 8).
Simplify further:
x = 1/2 ± √2.
Therefore, the correct answers are:
x = 1/2 + √2 and x = 1/2 - √2,
which corresponds to option (c).
9x^2 + 24x + 20 = 4
Solve this by factoring.
Thank you!
Note that,
[tex]9x^2+24x+20=4\Longrightarrow9x^2+24x+16[/tex]
Which factors to,
[tex](3x+4)^2=0\Longrightarrow3x+4=0[/tex]
And simplifies to solution C,
[tex]\boxed{x=-\dfrac{4}{3}}[/tex]
Hope this helps.
Any additional questions please feel free to ask.
r3t40
Answer:
[tex]\large\boxed{C.\ x=-\dfrac{4}{3}}[/tex]
Step-by-step explanation:
[tex]9x^2+24x+20=4\qquad\text{subtract 4 from both sides}\\\\9x^2+12x+12x+16=0\\\\3x(3x+4)+4(3x+4)=0\\\\(3x+4)(3x+4)=0\\\\(3x+4)^2=0\iff3x+4=0\qquad\text{subtract 4 from both sides}\\\\3x=-4\qquad\text{divide both sides by 3}\\\\x=-\dfrac{4}{3}[/tex]
You are given the dollar value of a product in 2015 and the rate at which the value of the product is expected to change during the next 5 years. Write a linear equation that gives the dollar value V of the product in terms of the year t. (Let t = 15 represent 2015.)
Answer:
V = $3.50t + $90.5....
Step-by-step explanation:
V(t) is a function of t that expresses the value in year 2000+t.
We know that the increase is $3.50 times t.
So,
V(t) = $3.50t + c
where c is the constant.
V(15) = $3.50 (15) + c = $143 [t=15 as mentioned in the question]
and therefore
c = $143 - $3.50 (15)
c= $143 - $52.50
c= $90.5
Now we got the value of c. We can write the equation as
V = $3.50t + $90.5....
The subject of this question is linear equation. The dollar value of a product expected to change over several years can be calculated using the future value formula V = P(1 + r)^(t-15), where P is the present value, r is the rate of change per year, and t represents the year.
To develop a linear equation that represents the dollar value V of a product in a certain year t, you can use the formula for future value received years in the future: V = P(1 + r)^(t-15), where P is the present value in 2015, r is the rate of change per year, and t represents the year.
For example, if a firm's payment was $20 million in 2015 and was expected to increase by 10% per year, then the value in 2020 (t = 20) would be calculated as: V = $20 million * (1 + 0.10)^(20-15).
From this equation, you can predict the future value of the product in terms of the year and rate of inflation.
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Write a two-column proof.
Given: Quadrilateral GKJH is a parallelogram
Prove: Triangle GLH is congruent to Triangle JLK
Answer:
GLH is congruent to JLK as the quadrilateral is a parallelogram,
KJ = GH OR HJ = GK
GL = LJ OR. HL = LK
triangle JKG = GHJ
triangle HGK = KJH
Answer:
A parallelogram has two pairs of opposite parallel congruent sides.
Given :
Quadrilateral GKJH is a parallelogram,
To prove :
Δ GLH ≅ Δ JLK
Proof :
Statement Reason
1. GH ║ KJ Definition of parallelogram
2. ∠LGH ≅ ∠LJK, ∠LHK ≅ ∠LKJ Alternate interior angle theorem
3. GH ≅ KJ Definition of parallelogram
4. Δ GLH ≅ Δ JLK ASA postulate of congruence
Hence, proved...
Given the variables fullAdmissionPrice and discountAmount (already declared and assigned values), write an expression corresponding to the price of a discount admission. (The variable discountAmount holds the actual amount discounted, not a percentage.)
Answer: Price of a discount amision= Full Admission Price - discount Amount
Step-by-step explanation:
We have two variables "X" and "Y", where X= Full Admision Price and Y= Discount Price of Admision and we have to get the price of a discount admision or "Z" so the expresion will be Z= X-Y or Price of a discount admision = Full admision Price- discount Amount.
Suppose you are managing 14 employees, and you need to form three teams to work on different projects. Assume that all employees will work on a team, and that each employee has the same qualifications/skills so that everyone has the same probability of getting choosen. In how many different ways can the teams be chosen so that the number of employees on each project are as follows: 8,3,3
Answer:
60060 different ways that teams can be chosen
Step-by-step explanation:
Given data
employees n = 14
team = 3
each project employees
n(1) = 8
n(2) = 3
n(3) = 3
to find out
how many different ways can the teams be chosen
solution
we know according to question all employees work on a team so
select ways are = n! / n(1) ! × n(2) ! × n(3) ....................1
here n! = 14! = 14 × 13 ×12 ×11 ×10 ×9 ×8 ×7 ×6 ×5 ×4 × 3× 2× 1
and n(1)! = 8! = 8 ×7 ×6 ×5 ×4 × 3× 2× 1
n(2)! = 3! = 3× 2× 1
n(3)! = 3! = 3× 2× 1
so now put all these in equation 1 and we get
select ways are = (14 × 13 ×12 ×11 ×10 ×9 ×8 ×7 ×6 ×5 ×4 × 3× 2× 1 ) / (8 ×7 ×6 ×5 ×4 × 3× 2× 1 ) × ( 3× 2× 1) × ( 3× 2× 1)
select ways are = (14 × 13 ×12 ×11 ×10 ×9 ) / ( 3× 2× 1) × ( 3× 2× 1)
select ways are = 2162160 / 36
select ways are = 60060
60060 different ways that teams can be chosen
Answer:
60060
Step-by-step explanation:
#copyright
The two triangles are similar. What is the value of x?
Check the picture below.
The graph below shows the average daily temperatures on January 1 from 1900 to 1934 for city A.
The mean of the temperatures in the chart is 24° with standard deviation of 4°. How many years had temperatures within one standard deviation of the mean?
20
25
28
35
Answer:
25 years
Step-by-step explanation:
Solution:-
- Data for the average daily temperature on January 1 from 1900 to 1934 for city A.
- The distribution X has the following parameters:
Mean u = 24°C
standard deviation σ = 4°C
- We will first construct an interval about mean of 1 standard deviation as follows:
Interval for 1 standard deviation ( σ ):
[ u - σ , u + σ ]
[ 24 - 4 , 24 + 4 ]
[ 20 , 28 ] °C
- Now we will use the graph given to determine the number of years the temperature T lied in the above calculated range: [ 20 , 28 ].
T1 = 20 , n1 = 2 years
T2 = 21 , n2 = 3 years
T3 = 22 , n3 = 2 years
T4 = 23 , n4 = 4 years
T5 = 24 , n5 = 3 years
T6 = 25 , n6 = 3 years
T7 = 26 , n7 = 5 years
T8 = 27 , n8 = 2 years
T5 = 28 , n9 = 1 years
- The total number of years:
∑ni = n1 + n2 + n3 + n4 + n5 + n6 + n7 + n8 + n9
= 2 + 3 + 2 + 4 + 3 + 3 + 5 + 2 + 1
= 25 years
Answer:
22,25,27 there are multiple questions that have the same question but different answers on Edge
Step-by-step explanation:
I hope this helped :)
Mr. Ruiz leans his 24-foot ladder up against his house so he can get up on the roof. He determines that he is 22 feet from the house. The height of the house is between
Answer:
The height of the house is between 9 and 10 feet.
Step-by-step explanation:
The shaped formed with the ground, the ladder, and the house is a right triangle.
I'm going to apply Pythagorean Theorem here.
The length of the hypotenuse is given as 24 feet.
The length from the base of the ladder and the house is 22 feet.
So to find the height the ladder reaches on the house, we need to solve
[tex]a^2+22^2=24^2[/tex]
[tex]a^2+484=576[/tex]
Subtract 484 on both sides:
[tex]a^2=576-484[/tex]
Simplify:
[tex]a^2=92[/tex]
Square root both sides:
[tex]a=\sqrt{92}[/tex]
[tex]a \approx 9.59166[/tex] feet
In 1983, a winter hat cost $12.95. Today, a winter hat costs $24.50. If the CPI is 219, what is the percent relation of the actual price of a winter hat to the expected price?
Answer:
The actual price is 13.6 % lower than the expected price....
Step-by-step explanation:
Lets suppose the expected price = x
CPI = ( expected price ) : ( price in 1983 ) *100
219 = ( x : 12.95 ) *100
Divide both sides by 100.
x : 12.95 = 2.19
x =2.19*12.95
= $28.36 ( expected price )
p = ( 24.50*100 ) / 28.36
p= 2450/28.36
= 86.4 %
100 % - 86.4 % = 13.6 %
The actual price is 13.6 % lower than the expected price....
Answer:
c
Step-by-step explanation:
because i said so brudda
A jar contains 50 jelly beans: 5 lemon,10 watermelon, 15 blueberry, and 20 grape.Suppose that two jelly beans are randomly selected in succession without replacement.Find the probability of selecting two blueberry jelly beans.
[tex]|\Omega|=50\cdot49=2450\\|A|=15\cdot14=210\\\\P(A)=\dfrac{210}{2450}=\dfrac{3}{35}\approx8.6\%[/tex]
The probability of randomly selecting two jelly beans in succession without replacement is;
0.0857
The jar contains 50 jellybeans.
Thus; N = 50
The individual berries include;
5 lemon
10 watermelon
15 blueberry
20 grape
Probability of first being a jelly bean = 15/50
Probability of second being jelly bean = 14/49
Thus,probability of selecting 2 jelly beans in succession without replacement is =
15/50 × 14/49 = 0.0857
Read more at; https://brainly.com/question/10271452