In calculating the factor A variation, there are two degrees of freedom. In determining the variation of factor B, there are two degrees of freedom.
What is a two-factorial design?A two-factor factorial design is an experiment that collects data for all potential values of the two factors of the study. The design is a balanced two-factor factorial design if equivalent sample sizes are used for every of the possible factor combinations.
Suppose we have two components, A and B, each of which has a high number of levels of interest. We will select a random level of component A and a random level of factor B, and n observations will be taken for each experimental combination.
From the data given:
a.
In calculating the factor A variation, there are two degrees of freedom.
In determining the variation of factor B, there are two degrees of freedom.
b.
Finding the degree of freedom using the interaction variation, there are four degrees of freedom.
c.
In finding the random variable, there are 9(4-1) = 27 degrees of freedom.
d.
In calculating the total variable, there are 9*4-1 =35 degrees of freedom.
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1. Derive the half-angle formulas from the double
angle formulas.
2. Provide the formulas to convert between polar and
rectangular forms.
3. Convert one point from rectangular to polar and
another point from polar to rectangular.
4. Convert a rectangular equation to polar (rectangular
equation must contain squared x and y variables as
well as x and y variables raised to a single power)
and a polar equation to rectangular (polar equation
must contain an rand a ¦ (theta)).
1) cos (θ / 2) = √[(1 + cos θ) / 2], sin (θ / 2) = √[(1 - cos θ) / 2], tan (θ / 2) = √[(1 - cos θ) / (1 + cos θ)]
2) (x, y) → (r · cos θ, r · sin θ), where r = √(x² + y²).
3) The point (x, y) = (2, 3) is equivalent to the point (r, θ) = (√13, 56.309°). The point (r, θ) = (4, 30°) is equivalent to the point (x, y) = (2√3, 2).
4) The linear function y = 5 · x - 8 is equivalent to the function r = - 8 / (sin θ - 5 · cos θ).
How to apply trigonometry on deriving formulas and transforming points
1) The following trigonometric formulae are used to derive the half-angle formulas:
sin² θ / 2 + cos² θ / 2 = 1 (1)
cos θ = cos² (θ / 2) - sin² (θ / 2) (2)
First, we derive the formula for the sine of a half angle:
cos θ = 2 · cos² (θ / 2) - 1
cos² (θ / 2) = (1 + cos θ) / 2
cos (θ / 2) = √[(1 + cos θ) / 2]
Second, we derive the formula for the cosine of a half angle:
cos θ = 1 - 2 · sin² (θ / 2)
2 · sin² (θ / 2) = 1 - cos θ
sin² (θ / 2) = (1 - cos θ) / 2
sin (θ / 2) = √[(1 - cos θ) / 2]
Third, we derive the formula for the tangent of a half angle:
tan (θ / 2) = sin (θ / 2) / cos (θ / 2)
tan (θ / 2) = √[(1 - cos θ) / (1 + cos θ)]
2) The formulae for the conversion of coordinates in rectangular form to polar form are obtained by trigonometric functions:
(x, y) → (r · cos θ, r · sin θ), where r = √(x² + y²).
3) Let be the point (x, y) = (2, 3), the coordinates in polar form are:
r = √(2² + 3²)
r = √13
θ = atan(3 / 2)
θ ≈ 56.309°
The point (x, y) = (2, 3) is equivalent to the point (r, θ) = (√13, 56.309°).
Let be the point (r, θ) = (4, 30°), the coordinates in rectangular form are:
(x, y) = (4 · cos 30°, 4 · sin 30°)
(x, y) = (2√3, 2)
The point (r, θ) = (4, 30°) is equivalent to the point (x, y) = (2√3, 2).
4) Let be the linear function y = 5 · x - 8, we proceed to use the following substitution formulas: x = r · cos θ, y = r · sin θ
r · sin θ = 5 · r · cos θ - 8
r · sin θ - 5 · r · cos θ = - 8
r · (sin θ - 5 · cos θ) = - 8
r = - 8 / (sin θ - 5 · cos θ)
The linear function y = 5 · x - 8 is equivalent to the function r = - 8 / (sin θ - 5 · cos θ).
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A data set contains three points, and two of the residuals are -10 and 20.
What is the third residual?
If a data set contains three points, and two of the residuals are -10 and 20, the third residual is 10 (option B).
What is a residual?A residual is the difference between the observed value and the estimated value of the quantity of interest.
The residual of a data points should normally sum up to zero (0). This means the following applies:
-10 + 20 + x = 0
x = 10
Therefore, if data set contains three points, and two of the residuals are -10 and 20, the third residual is 10.
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The equation 2x = 3y − 5 when written in slope-intercept form
Hello and Good Morning/Afternoon:
Let's take this problem step-by-step:
What does the problem want us to find:
[tex]\hookrightarrow \text {Slope-intercept form}[/tex]
What is the slope-intercept form:
[tex]\hookrightarrow \text {it is when the function has the y-variable isolated by itself to one side}\\\hookrightarrow \text{and everything else to the other side}[/tex]
Let's apply our knowledge:
[tex]2x =3y-5\\-3y=-5-2x\\y=\frac{2}{3} x+\frac{5}{3}[/tex]
Answer:[tex]y=\frac{2}{3} x+\frac{5}{3}[/tex]
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Residents in a city are charged for water usage every three months. The water bill is computed from a common fee, along with the amount of water the customers use. The last water bills for 40 residents from two different neighborhoods are displayed in the histograms. 2 histograms. A histogram titled Pine Road Neighbors has monthly water bill (dollars) on the x-axis and frequency on the y-axis. 100 to 125, 1; 125 to 150, 2; 150 to 175, 5; 175 to 200, 10; 200 to 225, 13; 225 to 250, 8. A histogram titled Front Street Neighbors has monthly water bill (dollars) on the x-axis and frequency on the y-axis. 100 to 125, 5; 125 to 150, 7; 150 to 175, 8; 175 to 200, 5; 200 to 225, 8; 225 to 250, 7. Which statement correctly compares the water bills for the two neighborhoods? Overall, water bills on Pine Road are less than those on Front Street. Overall, water bills on Pine Road are higher than those on Front Street. The range of water bills on Pine Road is lower than the range of water bills on Front Street. The range of water bills on Pine Road is higher than the range of water bills on Front Street.
The statement that correctly compares the water bills for the two neighborhoods based on the histogram given is that the range of water bills on Pine Road is higher than the range of water bills on Front Street.
What is a histogram?It should be noted that a histogram means a graph that shows the frequency of the numerical data using rectangles.
In this case, the statement that correctly compares the water bills for the two neighborhoods based on the histogram given is that the range of water bills on Pine Road is higher than the range of water bills on Front Street. This was the difference between the highest and lowest number.
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Answer: More homes on Pine Road had water bills above $200 than on Front Street.
Step-by-step explanation: edge 2023
Evaluate (f. g)(x) if f(x) = 2x² and g(x) = 3x - 2
Answer:
18x2 -24 x + 8
Step-by-step explanation:
( f o g) (x) = f ( g(x) ) = f( 3x-2) = 2( 3x-2)2 = 2( 9x2 - 12x + 4) = 18x2 -24 x + 8
Find the critical value Tc for the confidence level c=0.80 and sample size n=29
Using a calculator, the critical value for the t-distribution with a confidence level c=0.80 and sample size n=29 is of Tc = 1.3125.
How to find the critical value of the t-distribution?It is found using a calculator, with two inputs, which are given by:
The confidence level.The number of degrees of freedom, which is one less than the sample size.In this problem, the inputs are given as follows:
Confidence level of 80%.28 degrees of freedom, as there is a sample size of 29.Hence, using a calculator, the critical value for the t-distribution with a confidence level c=0.80 and sample size n=29 is of Tc = 1.3125.
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do the quantities combine?
Answer:
D
Step-by-step explanation:
Widrawal is - 30
Deposit is +30
-30+30 = 0
Evaluate this exponential expression.
OA. 19
OB. 63
OC. 66
OD. 207
6 (4+2)²-32
Answer: 184
(I am not sure if I have misunderstood the question, but the final answer I got was 184, which wasn't any one of the choices. I was wrong in understanding, please let me know and I will modify my answer)
Step-by-step explanation:
Given expression
6 (4 + 2)² - 32
Simplify values in the parenthesis
6 (6)² - 32
Simplify exponents
6 × 36 - 32
Simplify multiplication
216 - 32
Simplify subtraction
[tex]\Large\boxed{184}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
how do you compare and contrast the steps of two different constructions using a compass?
In order to compare and contrast the steps of two different constructions using a compass, we simply take a note of the different steps followed in both the constructions.
How to compare and contrast the steps?
For both the constructions, observe the corresponding steps steps that have been performed in order.
Then, note down what similarity you find while constructing the two different constructions in the first step.
Once you know the the similarities, you can further trace down the differences in the procedure of the two constructions by observing the first step. This is how you can compare and contrast the first step of two different constructions using a compass.
This process can be followed for all the steps for comparing and contrasting two different constructions.
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Carbon Company provides the following information about resources.
Unused Resources Capacity Cost Driver Volume
Resources used
Materials $ 2,300 9,000 pounds
Energy 2,210 380 machine-hours
Setups 0 87 setups
Purchasing 7,800 80 purchase orders
Customer service 9,700 70 returns
Long-term labor 4,650 330 labor-hours
Administrative 5,950 450 labor-hours
Resources supplied
Materials $ 101,300
Energy 21,590
Setups 24,360
Purchasing 26,200
Customer service 20,200
Long-term labor 29,400
Administrative 30,700
Sales revenue for Carbon Company is $600,000.
Required:
a. Prepare a traditional income statement.
b. Prepare an activity-based income statement.
a) The preparation of a traditional income statement for Carbon Company is as follows:
Carbon Company
Income Statement (Traditional)Sales revenue $600,000
Costs:
Materials $ 101,300
Energy 21,590
Setups 24,360
Purchasing 26,200
Customer service 20,200
Long-term labor 29,400
Administrative 30,700 $253,750
Operating Income $346,250
b) The preparation of an activity-based income statement for Carbon Company is as follows:
Carbon Company
Income Statement (Activity-based)Sales revenue $600,000
Resources supplied Unused Resources Used Resources
Materials $ 101,300 $ 2,300 $99,000
Energy 21,590 2,210 19,380
Setups 24,360 0 24,360
Purchasing 26,200 7,800 18,400
Customer service 20,200 9,700 10,500
Long-term labor 29,400 4,650 24,750
Administrative 30,700 5,950 24,750
Total $253,750 $32,610 $221,140
Operating Income $378,860
Data and Calculations:Unused Resources Capacity Cost Driver Volume
Resources used
Materials $ 2,300 9,000 pounds
Energy 2,210 380 machine-hours
Setups 0 87 setups
Purchasing 7,800 80 purchase orders
Customer service 9,700 70 returns
Long-term labor 4,650 330 labor-hours
Administrative 5,950 450 labor-hours
Resources suppliedMaterials $ 101,300
Energy 21,590
Setups 24,360
Purchasing 26,200
Customer service 20,200
Long-term labor 29,400
Administrative 30,700
Sales revenue $600,000
Activity-based Calculations:Resources supplied Unused Resources Used Resources
Materials $ 101,300 $ 2,300 $99,000
Energy 21,590 2,210 19,380
Setups 24,360 0 24,360
Purchasing 26,200 7,800 18,400
Customer service 20,200 9,700 10,500
Long-term labor 29,400 4,650 24,750
Administrative 30,700 5,950 24,750
Total $253,750 $32,610 $221,140
Thus, the traditional income statement for Carbon Company shows an operating income of $346,250, while the activity-based income statement shows an operating income of $378,860.
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Choose the correct graph of the given system of equations. y + 2x = −1 3y − x = 4 graph of two lines that intersect at the point negative 1, 1, with text on graph that reads One Solution negative 1, 1 graph of two lines that intersect at the point 1, 1, with text on graph that reads One Solution 1, 1 graph of two parallel lines with positive slopes with text on the graph that reads No Solution graph of two lines on top of each other with text on graph that reads Infinitely Many Solutions Question 4(Mul
The system of equations has one solution (-1, 1)
Graph of system of linear equationsFrom the question, we are to graph the given system of equations.
The given system of equation is
y + 2x = −1
3y − x = 4
The graph of the given system of equations is shown below.
From the graph, we can observe that the solution to the given system of equation is given by two lines that intersect at the point (-1, 1).
Hence, the system of equations has one solution (-1, 1)
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I think the answer is A. The first one
PLEASE HELP ASAP !!!!
Which functions have a range of {y e R-00 < y < ∞0}?
O f(x) = -4x + 11
Of(x) = x - 8
O
f(x) = 2x+3
O f(x) = -(x + 1)² - 4
O
f(x)
f(x) = x²
x² + 7x9
Answer:
Options 1 and 2
Step-by-step explanation:
Correct. The range of all linear functions without a restricted domain is the set of all real numbers.Correct. The range of all linear functions without a restricted domain is the set of all real numbers.Wrong. The exponential cannot take negative values.Wrong. Quadratics do not have a range that is the set of real numbers.Wrong. Quadratics do not have a range that is the set of real numbers.A hockey coach was taking her team out to a picnic lunch to celebrate their first win. She made 15 sandwiches, 6 of which were turkey.
If ants randomly chose to nibble on 6 of the sandwiches, what is the probability that exactly 3 of the chosen sandwiches are turkey?
The probability that exactly 3 of the chosen sandwiches are turkey is; 0.004
How to find the probability combination?We are given;
Total number of sandwiches = 15
Number of sandwiches that were turkey = 6
Now, she selects 6 of the sandwiches and we want to find the probability that exactly 3 are turkey.
Now, number of ways of selecting 6 sandwiches is; 15C6
Number of ways of selecting 3 turkey's out of the 6 chosen is; 6C3
Thus, the probability that exactly 3 of the chosen sandwiches are turkey is; 6C3/15C6 = 20/5005 = 0.004
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In parallelogram DEFG, DH equals X +3, HF equals 3Y, GH equals 2X -5 and HE equals 5Y plus to find the values of X and Y
The values of X and Y are 30 and 11 respectively
How to determine the values of X and Y?The figure that represents the complete question is added as an attachment
The given parameters are:
DH = X +3
HF = 3Y
GH = 2X -5
HE = 5Y
From the attached parallelogram, we have:
DH = HF
GH = HE
Substitute the known values in the above equation
X + 3 = 3Y
2X - 5 = 5Y
Make X the subject in X + 3 = 3Y
X = 3Y - 3
Substitute X = 3Y - 3 in 2X - 5 = 5Y
2(3Y - 3) - 5 = 5Y
Expand
6Y - 6 - 5 = 5Y
Evaluate the like terms
Y = 11
Substitute Y = 11 in X = 3Y - 3
X = 3*11 - 3
Evaluate
X = 30
Hence, the values of X and Y are 30 and 11 respectively
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find cube roots of -117 + 44i
By De Moivre's formula, the cubic roots of the complex number are 3 + i 4, - 4.96 + i 0.60 and 1.96 - i 4.60.
How to find the cube root of a complex number
Herein we have a complex number in rectangular form, from which we need its magnitude (r) and direction (θ) and the De Moivre's formula as well. The root formula is introduced below:
[tex]z^{\frac{1}{n} } = r^{\frac{1}{n} }\cdot \left[\cos \left(\frac{\theta + 2\pi\cdot k}{n}\right) +i\,\sin \left(\frac{\theta + 2\pi\cdot k}{n}\right)\right][/tex], for k ∈ {0, 1, ..., n - 1} (1)
Where n is the grade of the complex root.
The magnitude and direction of the complex number are 125 and 0.886π radians, respectively. Thus, by the De Moivre's formula we obtain the following three solutions:
k = 0
z₁ = 2.997 + i 4.002
k = 1
z₂ = - 4.964 + i 0.595
k = 2
z₃ = 1.967 - i 4.597
By De Moivre's formula, the cubic roots of the complex number are 3 + i 4, - 4.96 + i 0.60 and 1.96 - i 4.60.
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find the length of a segment in the coordinate plane with endpoints (5, -2) and (2, 2)
Answer: 5
Step-by-step explanation:
[tex]\sqrt{(5-2)^2 +(-2-2)^2}=5[/tex]
Income Statements under Absorption Costing and Variable Costing
The demand for aloe vera hand lotion, one of numerous products manufactured by Smooth Skin Care Products Inc., has dropped sharply because of recent competition from a similar product. The company's chemists are currently completing tests of various new formulas, and it is anticipated that the manufacture of a superior product can be started on December 1, one month in the future. No changes will be needed in the present production facilities to manufacture the new product because only the mixture of the various materials will be changed.
The controller has been asked by the president of the company for advice on whether to continue production during November or to suspend the manufacture of aloe vera hand lotion until December 1. The controller has assembled the following pertinent data:
Smooth Skin Care Products Inc.
Income Statement—Aloe Vera Hand Lotion
For the Month Ended October 31
Sales (400,000 units) $32,000,000
Cost of goods sold 28,330,000
Gross profit $3,670,000
Selling and administrative expenses 4,270,000
Loss from operations $(600,000)
The production costs and selling and administrative expenses, based on production of 400,000 units in October, are as follows:
Direct materials $15 per unit
Direct labor 17 per unit
Variable manufacturing cost 35 per unit
Variable selling and administrative expenses 10 per unit
Fixed manufacturing cost $1,530,000 for October
Fixed selling and administrative expenses 270,000 for October
Sales for November are expected to drop about 20% below those of the preceding month. No significant changes are anticipated in the fixed costs or variable costs per unit. No extra costs will be incurred in discontinuing operations in the portion of the plant associated with aloe vera hand lotion. The inventory of aloe vera hand lotion at the beginning and end of November is expected to be inconsequential.
Required:
Question Content Area
1. Prepare an estimated income statement in absorption costing form for November for aloe vera hand lotion, assuming that production continues during the month.
Smooth Skin Care Products Inc.
Estimated Income Statement—Absorption Costing—Aloe Vera Hand Lotion
For the Month Ending November 30
Sales
$Sales
32,000,000
Cost of goods sold:
Direct materials
$Direct materials
Direct labor
Direct labor
- Select -
- Select -
- Select -
$- Select -
Selling and administrative expenses:
$- Select -
- Select -
blank
blank - Select -
$- Select -
Question Content Area
2. Prepare an estimated income statement in variable costing form for November for aloe vera hand lotion, assuming that production continues during the month.
Smooth Skin Care Products Inc.
Estimated Income Statement—Variable Costing—Aloe Vera Hand Lotion
For the Month Ending November 30
$- Select -
Variable cost of goods sold:
$- Select -
- Select -
- Select -
blank
blank - Select -
$- Select -
- Select -
$- Select -
Fixed costs:
$- Select -
- Select -
blank
blank - Select -
$- Select -
The estimated income statement for the month shows a loss of $840000.
How to illustrate the income statement?The estimated income statement for the month will be:
Sales = $25,600,000
Less: Cost of goods sold
Direct materials (320000 × 15) = $4,800,000
Direct labor (320000 × 17) = $5,440,000
Variable costing (320000 × 15) = $11,200,000
Fixed manufacturing cost = $1,530,000
Total cost of goods sold = $22970000
Gross profit = $25,600,000 - $22970000 = $2,630,000
Gross profit = $2,630,000
Less:
Variable selling and administrative expense = $3200000
Fixed selling and administrative = $270000
Loss from operations = $840000
Therefore, the estimated income statement for the month shows a loss of $840000.
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100 POINTS Consider this piecewise function.
Plot f (x) on the graph.
NO LINKS
Answer:
The intervals represent the domain, or the values on the horizontal axis.
When x ≤ -3, the graph should form a straight line at y = 3. Because the interval includes x = -3, the rightmost part of the line should be capped with a closed dot. The line should continue for infinity to the left.
When -3 < x < 4, the graph should form a line with the equation (2x + 1). Because the interval does not include the endpoints, the endpoints should have open dots.
When x ≥ 4, the graph should form a straight line at y = -4. Because the interval includes x = 4, the leftmost endpoint should be a closed dot. The right of the line should continue for infinity.
**The included graph does not take the endpoints into account
Answer:
See attached for graph.
Step-by-step explanation:
Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.
Given piecewise function:
[tex]f(x)=\begin{cases}3 & \textsf{if }x\leq -3\\2x+1 & \textsf{if }-3 < x < 4 \\ -2 & \textsf{if } x\geq 4 \end{cases}[/tex]
Therefore, the function has three definitions:
[tex]f(x)=3 \quad \textsf{when x is less than or equal to 3}[/tex]
[tex]f(x)=2x+1 \quad \textsf{when x is more than -3 and less than 4}[/tex]
[tex]f(x)=-2 \quad \textsf{when x is more than or equal to 4}[/tex]
When graphing piecewise functions:
Use an open circle where the value of x is not included in the interval.Use a closed circle where the value of x is included in the interval.Use an arrow to show that the function continues indefinitely.First piece of function
Substitute the endpoint of the interval into the corresponding function:
[tex]\implies f(-3)=3 \implies (-3,3)[/tex]
Place a closed circle at (-3, 3).
As this piece of the function is f(x) = 3 for any value of x that is less than or equal to -3, draw a horizontal straight line to the left from the closed circle. Add an arrow at the end.
Second piece of function
Substitute the endpoints of the interval into the corresponding function:
[tex]\implies f(-3)=2(-3)+1=-5 \implies (-3,-5)[/tex]
[tex]\implies f(4)=2(4)+1=9 \implies (4,9)[/tex]
Place an open circle at (-3, -5) and (4, 9).
Join the points with a straight line.
Third piece of function
Substitute the endpoint of the interval into the corresponding function:
[tex]\implies f(4)=-2 \implies (4,-2)[/tex]
Place a closed circle at (4, -2).
As this piece of the function is f(x) = -2 for any value of x that is more than or equal to 4, draw a horizontal straight line to the right from the closed circle. Add an arrow at the end.
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Please help, due in an hour. Two sides of a triangle are 12cm and 8cm. Complete the inequality to show the possible lengths for the third side. If the third side of the triangle is x then, _
Answer:
[tex]4 < x < 20[/tex]
Step-by-step explanation:
By the triangle inequality theorem, the sum of the length of the two smaller sides must be greater than the length of the largest side. If 12 cm was the length of the largest side, notice that [tex]8+x > 12 \Rightarrow x > 4[/tex]. Similarly, if x was the length of the largest side, we'd get the inequality [tex]12+8 > x \Rightarrow 20 > x[/tex]. Combining these inequalities, we get [tex]\boxed{4 < x < 20}[/tex].
When an integer is subtracted from 2 times the next consecutive odd integer, the difference is 1. Find the value of the greater integer.
The value of the greater integer which is the next consecutive odd integer is; -1.
What is the value of the greater integer as described by the task content?By observation, it follows that the first integer can be represented by 2x+1 while the next consecutive odd integer can be represented as 2x+3.
Hence, it follows that we have;
2(2x+3) - 2x - 1 = 1
4x +6 -2x - 1 = 1
2x = -4
x = -2.
Consequently, the value of the next consecutive greater integer is; 2(-2) + 3= -1.
It consequently follows from the computations above that the value of the greater odd integer is; -1.
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A population grows according to an exponential growth model. The initial population is Po = 19 and the growth rate is r = 0.4.
Then find an explicit formula for Pn
Then use the formula to find P11
P11 equals 769.417 and general formula is 19*(1.4)^(n)
Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change of a quantity with respect to time is proportional to the quantity itself
The growth rate is .4 per time period.
the exponential growth model is f = p * (1 + .4) ^ n
f is the future value.
p is the present value.
r is the growth rate per time period.
n is the number of time periods.
in p0, n = 0
in p11, n = 11
you are given that p0 = 19
in the formula, that becomes f = 19 * (1 + .4) ^ 0 = 19 * (1.4) ^ 0 = 19.
the formula for p1 becomes f = 19 * (1 + .4) ^ 1 = 19 * (1.4) ^ 1 = 26.6
the formula for p11 becomes f = 19 * (1 + .4) ^ 11 = 19 * (1.4) ^ 11 = 769.417
the formula for pn becomes = 19*(1.4)^(n)
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On the grid draw y = 4x - 5 for values of c from -2 to 2
Step-by-step explanation:
shown above but I need words so
How many lines can you draw using 3 non-collinear points A, B and C on a plane?
Answer:3 lines could be used
Step-by-step explanation:
You need 2 points to draw a line. The order doesn't really matter. Line AB is the same as line BA. The problem is to select 2 points out of 3 to draw different lines. If we do the same to the others, we get the following pairs of points to draw lines.
AB , AC
BA , BC
CA , CB
which is only 3 lines
Circle P is centered at the origin. Which of the following statements can be used to
construct an algebraic proof the point A lies on circle P?
-6
The distance from the origin to point A is equal to the radius of circle P. Therefore, point A lies
on circle P.
O The distance from the origin to point A is less than the radius of circle P. Therefore, point A lies
on circle P.
O The distance from the origin to point A is greater than the radius of circle P. Therefore, point A
lies on circle P.
Based on visual inspection, point A lies on circle P. Therefore, point A lies on circle P.
the correct option is:
"The distance from the origin to point A is equal to the radius of circle P. Therefore, point A lies on circle P."
Which of the following statements can be used to construct an algebraic proof the point A lies on circle P?
A circle is defined as the set of equidistant points to a given point which is the center of the circle.
That distance to the center is called the radius.
Here, the center is at the point (0, 0), also called the origin, so if the distance between the point A and the origin, then point A lies on top of the circle P.
From that, we conclude that the correct option is:
"The distance from the origin to point A is equal to the radius of circle P. Therefore, point A lies on circle P."
That is the only proof that we can (and should) use to prove that a point lies on a circle.
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Answer:
The distance from the origin to point A is equal to the radius of circle P. Therefore, point A lies on circle P."
Step-by-step explanation:
I did the test
Drag each pair of coordinates to the correct location on the image. Match each pair of pilar coordinates to the equivalent polar coordinates on the image.
Answer:
(2, -60) = (-2, 120°) = (2, 300°) = (-2, -240°)(-2, 240°) = (-2, -120°) = (2, 60°) = (2, -300°)Step-by-step explanation:
Equivalent polar coordinates will have the same modulus and some multiple of 360° added to the argument, or the opposite modulus and some odd multiple of 180° added to the argument.
a∠b° = a∠(b+360n)° = -a∠(b +180 +360n)°
(2, -60°)Equivalents will be ...
(2, (-60 +360n)°) = (2, 300°)
(-2, (-60 +180 +360n)°) = (-2, -240°) = (-2, 120°)
(-2, 240°)Equivalents will be ...
(-2, (240 +360n)°) = (-2, -120°)
(2, (240 +180 +360n)°) = (2, -300°) = (2, 60°)
There are values of t so that the equation cos t = 5/3.
A. True
B. False
the statement is false, as there no exist a value of t such that cos(t) > 1.
Is the statement true or false?
Here we have the statement:
"There are values of t so that the equation cos(t) = 5/3"
Now, remember that the range of the sine and cosine equations is given by:
R: -1 ≤ y ≤ 1
And 5/3, the value in the statement, is larger than 1, which is the maximum in the range.
Then the statement is false, as there no exist a value of t such that cos(t) > 1.
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Please help it would be much appreciated
Answer:
calcium =1x40=40
chlorine=2x35=70
40+70=110
ca=40/110×100=36.36
when we approximate it become 36.4
thanks
If one wanted to solve the equation below using the quadratic formula, what would be the b value used to substitute into the quadratic equation.
3x 2 − 2 = - 5x
Answer:
b = 5
Step-by-step explanation:
All quadratic equations are formed in the format of [tex]a^{2}[/tex] + bx + c = 0
Using this formula, we can re-arrange the equation to fit the given format.
[tex]3x^{2}[/tex] - 2 = -5x
[tex]3x^{2}[/tex] + 5x - 2 = 0
5 is plugged in for "b" in this equation, therefore b = 5.
A 2-liter bottle of juice costs $2.80. A box containing six 1/2 liter bottles sells for $3.90. Which option has a higher cost per liter? What is that cost?
A. 2-liter bottle; $1.40
B. Box of six 2-liter bottles; $1.30
C. 2-liter bottle; $2.80
D. Box of six-liter bottles; $3.90
Answer:
A. 2-liter bottle;$1.40
Step-by-step explanation:
We have to find out which option has the higher cost per liter. To do this we must find out how much each option would be if it was a liter.
1st set up each equation
2-liter = $2.80 we can divide by 2 on both sides of the equal sign and we get 1 liter = $1.40.
6(1/2) liter bottles = $3.90 this becomes 3 liters = $3.90 then we divide by 3 on both sides of the equal sign and we get $1.30
2nd we compare
$1.40(2 liter bottle) > $1.30 (6 1/2 liter bottles)
Two companies working together can clear a parcel of land in 8 hours. Working alone, it would take Company A 4 hours longer to clear the land than it would Company B. How long would it take Company B to clear the parcel of land alone?
The time taken for Company B to clear the parcel of land alone is 14.25 hours
Rate of workTime for Company B to clear the parcel of land alone = xCompany B work rate = 1/xTime for Company A to clear the parcel of land alone = x + 4Company A work rate = 1/x+4Time for both Company to clear the parcel of land alone = 8 hoursBoth Company work rate = 1/81/8 = 1/x + 1/(x + 4)
1/8 = (x+4)+ (x) / (x)(x+4)
1/8 = (x+4+x) / (x² + 4x)
1/8 = 2x+4 / (x² + 4x)
cross product
1(x² + 4x) = 8(2x + 4)
x² + 4x = 16x + 32
x² + 4x - 16x - 32 = 0
x² - 12x - 32 = 0
Using quadratic formula
x = 14.25 or -2.25
The time taken for Company B to clear the parcel of land alone can only be positive,
Therefore, it is 14.25 hours
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