The vector parametric equation for the circle C is r(t) = <8cos(t), 8sin(t)> for 0 ≤ t ≤ 2π.
To find a vector parametric equation r(t) for the circle C with radius 8, centered at the origin, starting at the point (8, 0)
and traveling counterclockwise for 0 ≤ t ≤ 2π, follow these steps:
Write down the equation for the circle centered at the origin with radius 8:
x² + y² = 64.
Parametrize the circle using trigonometric functions.
Since we are starting at (8, 0) and going counter clockwise,
we can use x = 8cos(t) and y = 8sin(t).
Write the parametric equation in vector form:
r(t) = <8cos(t), 8sin(t)>.
So the vector parametric equation for the circle C is r(t) = <8cos(t), 8sin(t)> for 0 ≤ t ≤ 2π.
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Bill is walking up the steps in the Washington Monument at a rate of 30 feet per minute and Joe is walking down at the rate of 45 feet per minute. Bill is 75 feet from the bottom at the same moment that Joe is 325 feet from the bottom. Which of the following systems of equations can be used to determine the number of minutes t, from now and height, ℎ (in feet), at which they will pass each other?
The equation that can be used to determine the number of minutes t, from now and height, ℎ (in feet), at which they will pass each other is 75t = h.
What is the time taken for them to pass each other?The time taken for them to pass each other is calculated as follows;
Apply the rules of relative velocity;
(V₂ - V₁)t = h
where;
V₂ is the velocity of the BillV₁ is the velocity of the Joet is the time taken for them to meeth is the distance between them(30 ft/min - ( -45 ft/min )t = h
75t = h
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1. assume that abc company uses a margin of 40% on all items it purchases for resale, so that the firm sells $ x worth of merchandise. the company also incurred selling expenses which it budgeted at 15% of the volume of sales. the company also budgets fixed expenses at $ 600.a. write the equation relating total cost and sales volumeb. what will total cost and net profit before taxes on sales of $ 80,000c. what is the breakeven level of sales volume
a. The equation is Total Cost = 0.75x + $600
b. Total cost is $60,600 and net profit is $19,400.
c. The breakeven level of sales volume is $2,400.
a. The equation relating total cost and sales volume can be expressed as:
Total Cost = Cost of Goods Sold + Selling Expenses + Fixed Expenses
where Cost of Goods Sold = 60% (100% - 40%) of the sales volume
Selling Expenses = 15% of the sales volume
Fixed Expenses = $600.
Therefore, the equation can be written as:
Total Cost = 0.6x + 0.15x + $600
= 0.75x + $600
b. For sales of $80,000, we can substitute x = $80,000 into the equation:
Total Cost = 0.75x + $600
= 0.75($80,000) + $600
= $60,000 + $600
= $60,600
To calculate net profit before taxes, we need to subtract the total cost from the sales volume:
Net Profit before Taxes = Sales - Total Cost
= $80,000 - $60,600
= $19,400
c. To find the breakeven level of sales volume, we need to set the net profit before taxes to zero and solve for x:
Net Profit before Taxes = Sales - Total Cost
0 = x - (0.6x + 0.15x + $600)
0 = 0.25x - $600
0.25x = $600
x = $2,400
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Alan and Judith begin withdrawing money from their accounts at the same time. Alan has $10,350 in his account and withdraws $1,096 at the end of each month. Judith has $8,400 in her account and withdraws $822 at the end of each month. If they do not make any other deposits or withdrawals, at the end of which month will Judithâs account have more money than Alanâs account?
Judith's account has less money than Alan's account after 9 months.
We can start by setting up an equation to represent the amount of money in each account after n months, where n is the number of months that have passed:
For Alan's account:
Amount of money after n months = $10,350 - $1,096n
For Judith's account:
Amount of money after n months = $8,400 - $822n
We want to find the value of n for which Judith's account has more money than Alan's account. In other words, we want to find the value of n that satisfies the following inequality:
8,400 - 822n > 10,350 - 1,096n
To solve for n, we can simplify the inequality by combining like terms:
1,096n - 822n > 10,350 - 8,400
274n > 1,950
n > 7.11
Since n represents the number of months, we can round up to the next whole number and conclude that at the end of the 8th month, Judith's account will have more money than Alan's account.
To check this result, we can substitute n=8 into the equations for the amount of money in each account:
For Alan's account: $10,350 - $1,096(8) = $2,942
For Judith's account: $8,400 - $822(8) = $2,256
We can see that Judith's account has less money after 8 months than Alan's account, so the result is not correct.
Let's try again with n=9:
For Alan's account: $10,350 - $1,096(9) = $1,846
For Judith's account: $8,400 - $822(9) = $1,518
We can see that Judith's account has less money than Alan's account after 9 months, so the correct answer is actually that Judith's account never has more money than Alan's account.
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During the first year with a company, Finley was paid an annual salary of $56,000, with a 6% raise for each following year. Which equation represents Finley's annual salary, f (n), during the nth year?
f (n) = 56,000(0.94n)
f (n) = 56,000(1.06n)
f (n) = 56,000(0.06n – 1)
f (n) = 56,000(1.06n – 1)
The correct equation that represents Finley's annual salary, f(n), during the nth year is: [tex]f(n) = 56,000(1.06)^(n-1)[/tex] Thus, option D is correct.
What is an equation?
Finley's annual salary increases by 6% each year. This means that the salary for the second year is 6% more than the salary for the first year, the salary for the third year is 6% more than the salary for the second year, and so on.
To find an equation for Finley's annual salary during the nth year, we can use the initial salary of $[tex]56,000[/tex] and the fact that the salary increases by 6% each year. One way to write this equation is:
[tex]f(n) = 56,000(1.06)^(n-1)[/tex]
Here, the expression (1.06)^(n-1) represents the 6% increase in salary each year, starting from the second year (hence the (n-1) exponent). Multiplying this by the initial salary of $56,000 gives the salary for the nth year.
Therefore, the correct equation that represents Finley's annual salary, f(n), during the nth year is:[tex]f(n) = 56,000(1.06)^(n-1)[/tex]
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Sonia has a hat collection. The ratio of white hats to
blue hats in her hat collection is 10:9. Which ratio is
equivalent to 10:97
The equivalent ratio is 10:107.78
To solve this problem, we need to find a ratio that is equivalent to 10:9 but has a denominator of 97.
First, we can set up a proportion:
10/9 = x/97
To solve for x, we can cross-multiply:
10 * 97 = 9 * x
970 = 9x
To find the value of x, you divided both sides of the equation by 9, resulting in:
x = 107.78 (rounded to two decimal places)
So the equivalent ratio is 10:107.78, but since we can't have a fractional hat, we can round up to 108. Therefore, the answer is 10:108.
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A cube is sliced perpendicular to its base what is the shape of the resulting two dimensional cross-section 1. trapezoid 2. square 3.circle
If a cube is sliced perpendicular to its base, the resulting two dimensional cross-section will be a square. This is because each face of a cube is a square, and a perpendicular slice across the base will result in a square shape. A trapezoid or a circle would not result from a perpendicular slice of a cube.
When a cube is sliced perpendicular to its base, the shape of the resulting two-dimensional cross-section is a square.
Step-by-step explanation:
1. A cube has six faces, all of which are squares.
2. When you slice the cube perpendicular to its base, you are cutting it in a direction that is at a 90-degree angle to the base.
3. Since all the faces of a cube are squares, the resulting cross-section from a perpendicular slice will also be a square.
So, the correct answer is option 2, a square.
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Last month, Brandon rode his bike 56. 28 miles and Randy rode his bike 47. 93 miles. How much further did Brandon ride his bike last month than Randy?
Brandon rode his bike 8.35 miles further than Randy.
To find out how much further Brandon rode his bike last month than Randy, you'll need to subtract Randy's miles from Brandon's miles using the given values.
Step 1: Identify the miles ridden by both Brandon and Randy.
- Brandon rode 56.28 miles.
- Randy rode 47.93 miles.
Step 2: Subtract Randy's miles from Brandon's miles.
- 56.28 miles (Brandon's miles) - 47.93 miles (Randy's miles) = 8.35 miles.
So, last month, Brandon rode his bike more than Randy.
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If an inflatable ball with a volume of 96pi loses air until its radius is half of its original size, what is the new volume?
The new volume of the inflatable ball after the radius becomes half of the original one is 16π.
The original volume of the ball is given as 96π
The radius then becomes half of its original size which means if the radius of the ball is 'r' then the new radius becomes 'r/2'.
The formula for the volume of the ball is equal to, where 'r' is the radius of the ball. (4/3)π X r³
With this the original volume of the ball is
(4/3)π X r³
and the new volume of the ball after it's halved is
V₂ = (4/3)π X (r/2)³
After simplification
V₂ = (4/3)π X (r³/8)
The new volume of the ball is:
V₂ = (1/6) X πr³
So the new volume is (1/6) of the original volume. We can calculate this as
V₂ = (1/6) X 96π
= 16π
Therefore, the new volume of the inflatable ball is 16π.
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PLS HELP ME WITH THIS!!!!
Answer:
g(x) = h(x -7) +5
Step-by-step explanation:
Given h(x) defines a parabola that opens upward with a vertex at (-2, -7) and g(x) defines the same parabola with its vertex at (5, -2), you want to express g(x) in terms of h(x).
TranslationThe graph of f(x) is translated right h units and up k units by ...
f(x -h) +k
We see that g(x) is a translation of h(x) right by 7 units and up by 5 units. This means (h, k) is (7, 5), and the translated function is ...
g(x) = h(x -7) +5
__
Additional comment
This is confirmed by the plots in the second attachment.
Answer: g(x)=h(x-7) +5
Step-by-step explanation:
The graph g(x) has been shifted up 5 (+5) and right 7
When shift a function, the y change, up/down, goes at end of function
When shift in x direction happens, you take opposite sign so we will do -7
g(x)=h(x-7) +5
Identify 12P1 using factorials
a. 12!/13!
b. 12! times 11!
c. 12!/11!
d. 12!/1!
pls look at the pic
Ans. Correct option in (c) 12!/11!
we know that
the formula of nPr is n! / (n−r)!.
in this question
n = 12 and r = 1
so putting values we get ,
= 12! / (12-1)!
= 12!/11!
In ΔKLM, m = 17 inches, l = 44 inches and ∠L=153°. Find all possible values of ∠M, to the nearest 10th of a degree
In ΔKLM, m = 17 inches, l = 44 inches, and ∠L = 153°. The possible value of ∠M is approximately 12.3°.
In any triangle, the sum of the interior angles is always 180°. First, we can find the third angle ∠K by subtracting ∠L from 180°: 180° - 153° = 27°. Next, we use the Law of Sines to find the possible values of ∠M. The formula is:
(sin ∠M) / m = (sin ∠K) / l
Plug in the given values:
(sin ∠M) / 17 = (sin 27°) / 44
To find sin ∠M, we multiply both sides by 17:
sin ∠M = (sin 27°) * (17 / 44)
Now, find the inverse sine (arcsin) of the result:
∠M = arcsin((sin 27°) * (17 / 44))
∠M ≈ 12.3°
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Consider a binomial experiment with n = 10 and p = 0.40.
In a binomial experiment with n = 10 and p = 0.40 there is a 57.0% chance of getting 5 or more successes in the 10 trials.
A binomial experiment is a statistical experiment that consists of a fixed number of independent trials, where each trial can have only two outcomes, typically called "success" or "failure." The probability of success for each trial is denoted by p, and the number of trials is denoted by n.
In this case, we are given n = 10 and p = 0.40. This means that we are conducting an experiment with 10 independent trials, where the probability of success for each trial is 0.40.
Using this information, we can answer questions about the probability of various outcomes. For example, we can calculate the probability of getting exactly 5 successes in the 10 trials:
P(X = 5) = (10 choose 5) * 0.40^5 * (1 - 0.40)⁽¹⁰⁻⁵⁾
P(X = 5) = 0.246
This means that there is a 24.6% chance of getting exactly 5 successes in the 10 trials.
We can also calculate the probability of getting 5 or more successes:
P(X >= 5) = P(X = 5) + P(X = 6) + ... + P(X = 10)
P(X >= 5) = 0.246 + 0.204 + 0.088 + 0.026 + 0.005 + 0.001
P(X >= 5) = 0.570
This means that there is a 57.0% chance of getting 5 or more successes in the 10 trials.
Overall, the binomial distribution is a useful tool for modeling situations where there are a fixed number of trials with a binary outcome, and the probability of success is known for each trial.
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1. p(x)= f(x)+g(x)
Write the equation of p(x)
Answer:p(x)=3x+5
Step-by-step explanation:
f(x)=2x+3
g(x)=x+2
p(x)=(2x+2)+(x+2)= 3x+5
Answer:
p(x)=ax + b
Step-by-step explanation:
What is 0.50 divided by 0.25
Answer:
2
Step-by-step explanation:
0.50/0.25 = 50/25
= 2
Dividing 0.50/0.25 no. is same as 50/25 when we multultiply by 100/ 100 so it is 2
ans. = 2
0.50 / 0.25
5/10 x 100/5
=2
Wich statement correctly compares two values?
A) the value of the 6 in 26. 495 is 100 times the value of the 6 in 17. 64
B) the value of the 6 in 26. 495 1/10 the value of the 6 in 17. 64
C) the value of the 6 in 26. 495 1/100 the value of the 6 in 17. 64
D) the value of the 6 in 26. 495 is 10 times the value of the 6 in 17. 64
The correct statement that compares the value of the 6 in 26.495 and 17.64 is the value of the 6 in 26.495 is 10 times the value of the 6 in 17.64. Therefore, the correct option is D.
This is because the value of a digit is determined by its place in the number. In 26.495, the 6 is in the tenths place, which means it represents 6/10 or 0.6. In 17.64, the 6 is in the hundredths place, which means it represents 6/100 or 0.06. Therefore, the value of the 6 in 26.495 is 0.6 and the value of the 6 in 17.64 is 0.06.
To compare these values, we can divide the value of the 6 in 26.495 by the value of the 6 in 17.64. This gives us 0.6/0.06 = 10. Therefore, the value of the 6 in 26.495 is 10 times greater than the value of the 6 in 17.64 which corresponds to option D.
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An art class cost $45 for material and $10 per class.
A. What is the rate if change?
B. What is the initial value?
C. What is the independent variable?
D. What is the dependent variable?
The rate of change is 10.
The initial value of the equation is 45
The independent variable is the number of classes.
The dependent variable is the total cost.
How to represent linear equation?The art class cost $45 for material and $10 per class. Therefore, let's represent the situation with a linear equation.
Linear equation can be represented in slope intercept form as follows:
y = mx + b
where
m = slope = rate of changeb = y-interceptTherefore,
y = 45 + 10x
where
y = total costx = number of classTherefore,
A. The rate of change is 10.
B. The initial value is 45
C. The independent variable is x(number of classes)
D. The dependent variable is total cost.
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Directions: find the perimeter of each rectangle. be sure to include the correct unit.
The perimeter of the rectangle with a length of 10 feet and breadth of 11 feet is 42 feet.
In a rectangle, opposite sides are equal in length. So, you have two pairs of sides that are equal. The length of the two equal sides is given by l, which is 10 feet, and the length of the other two equal sides is given by b, which is 11 feet.
Therefore, to find the perimeter of the rectangle, you need to add up the length of all four sides:
Perimeter = 2(l + b)
Substituting the given values of l = 10 feet and b = 11 feet, we get:
Perimeter = 2(10 + 11) feet
Simplifying the expression inside the parentheses, we get:
Perimeter = 2(21) feet
Multiplying 2 and 21, we get:
Perimeter = 42 feet
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Complete Question:
Directions: find the perimeter of each rectangle. be sure to include the correct unit.
Where l = 10 feet and b = 11 feet.
a) Calculate the scale factor from shape A to shape B.
b) Find the value of t.
Give each answer as an integer or as a fraction in its simplest form.
A
5 cm
15 cm
7cm
B
12 cm
4cm
t cm
The scale factor from A to B is 5 / 4.
The value of t in the diagram is 5.6 cm.
How to find scale factor?Scale factor is the ratio between corresponding measurements of an object and a representation of that object.
Therefore, let's find the scale factor from the shape A to the shape B as follows:
5 / 4 = 15 / 12
Therefore, the scale factor is 5 / 4.
Hence, let's find the value of t in the diagram as follows:
Therefore, using the proportionality,
7 / t = 5 / 4
cross multiply
28 = 5t
divide both sides by 5
t = 28 / 5
t = 5.6 cm
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For the line y=2/5x+9, what will be the angle this line makes with the x-axis?
Answer:
21.8014 degrees (to 4 decimal places)
Step-by-step explanation:
The equation y=2/5x+9 forms a certain angle with the x-axis. Note that all lines parallel to y=2/5x+9 also form the same angle with the x-axis, due to Corresponding Angles (the fact that the original line has a y-intercept of 9 is irrelevant). Therefore, we could simplify this problem slightly by considering the angle that y=2/5x (a y-intercept of 0) forms with the x-axis.
To find the angle that this line makes with the x-axis, we'll need the vertex (the origin -- let's call this point "B"), and one point on each of two rays from the vertex (Let Ray #1 be the ray from the origin directly to the right; and let Ray #2 be the ray from the origin extending into Quadrant I -- up and to the right, along the equation y=2/5x).
One point on Ray #1 is (5,0) -- it is on the positive x-axis. Call this point "A"
One point on Ray #2 is (5,2) -- inputting "5" for x, the result for y is "2" Call this point "C"
y = 2/5 * (5) = 2To find the angle (Angle ABC), observe that the three points form a right triangle (the angle CAB is a right angle because the two lines are perpendicular).
To solve for [tex]\angle ABC[/tex], recall the definition of the tangent function:
[tex]tan(\theta)=\dfrac{opposite}{adjacent}[/tex]
The Opposite side, side AC, is just the height (or the y-value) of point C. So, opposite = 2.
The Adjacent side, side BA, is just the x-coordinate of point A (and also point C). So adjacent = 5.
Substituting these known values into the tangent function, we get the following:
[tex]tan(m\angle ABC)=\dfrac{2}{5}[/tex]
To solve for the measure of angle ABC, we need to apply the inverse tangent function (also known as arctangent).
[tex]arctan(tan(m\angle ABC)=arctan(\dfrac{2}{5})[/tex]
The left side simplifies because they are inverse functions:[tex]m\angle ABC=arctan(\dfrac{2}{5})[/tex]
Calculating the right side of the equation (rounding to 4 decimal places):
[tex]m\angle ABC \approx 21.8014^{o}[/tex]
Marsha threw her math book off a 30 foot building. The equation of the book can be represented by the equation h=-16[tex]x^{2}[/tex]+24x+30. What is the maximum height
of Marsha's math book?
The maximum height of Marsha's math book is 36 feet.
To find the maximum height of Marsha's math book, we need to find the vertex of the parabolic equation h = [tex]-16x^2 + 24x + 30[/tex]. The vertex of a parabola is the highest or lowest point on the curve, depending on whether the parabola opens upward or downward.
To find the x-coordinate of the vertex, we can use the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation [tex]ax^2 + bx + c[/tex]. In this case, a = -16 and b = 24, so we have:
x = -b/2a = -24/(2*(-16)) = 0.75
To find the y-coordinate of the vertex, we can substitute x = 0.75 into the equation h = [tex]-16x^2 + 24x + 30[/tex], which gives us:
h = [tex]-16(0.75)^2 + 24(0.75) + 30 = 36[/tex]
Therefore, the maximum height of Marsha's math book is 36 feet.
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I need help Please !!!!!!!!!!!!!!!!!!!!!!!!!!
Without multiplying order the products from least to greatest
Answer:
Step-by-step explanation:
eeee
Express the area of the entire rectangle. your answer should be a polynomial in standard form. x+6 x+2 area=
The formula for the area of a rectangle is length times width, or in this case (x+6)(x+2) or x^2 + 8x + 12 in standard form.
To simplify this expression, we can use the distributive property to multiply the two binomials:
(x+6)(x+2) = x(x+2) + 6(x+2)
= x² + 2x + 6x + 12
= x² + 8x + 12
To express the area of the entire rectangle, we need to multiply the length (x + 6) by the width (x + 2). This will give us a polynomial in standard form.
Step 1: Write down the expression for the area of the rectangle.
Area = (x + 6)(x + 2)
Step 2: Use the distributive property (also known as the FOIL method) to expand the expression.
Area = x(x + 2) + 6(x + 2)
Step 3: Continue to expand and simplify the expression.
Area = (x² + 2x) + (6x + 12)
Step 4: Combine like terms.
Area = x² + 8x + 12
So the area of the entire rectangle is expressed as the polynomial x² + 8x + 12 in standard form.
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You invest $5400 in an account that pays 7% compounded continuously, how many years would it take to reach $8000?
It would take approximately 7.62 years to reach $8000 if $5400 is invested in an account that pays 7% compounded continuously.
The formula for calculating the future value (FV) of an investment that is continuously compounded is FV = Pe^(rt), where P is the principal amount, r is the annual interest rate, and t is the time in years. In this case, P = $5400, r = 7% = 0.07, and FV = $8000. Substituting these values into the formula, we get:
$8000 = $5400e^(0.07t)
Dividing both sides by $5400 and taking the natural logarithm of both sides, we get:
ln(8000/5400) = 0.07t
Simplifying the left side of the equation, we get:
ln(4/3) = 0.07t
Solving for t, we get:
t = ln(4/3)/0.07 ≈ 7.62 years
Therefore, it would take approximately 7.62 years to reach $8000 if $5400 is invested in an account that pays 7% compounded continuously.
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Translate each problem into an equation then solve.
at a restaurant mike and his three friends decide to divide the bill evenly if each person paid 130 pesos then what was the total bill
The total bill was 520 pesos when the 4 people share the total bill and pay 130 pesos each.
Given data:
Bill paid by each = 130pesos,
Number of people = 4
We have to translate the problem into an equation. Let's assume that the total bill is x. There are a total of 4 people dividing the restaurant bill, Mike and his three friends. Since each of them paid 130 pesos, we need to multiply 130 by the total number of persons involved, we can write the equation as:
x/4 = 130
x = 4 × 130
x = 520
Therefore, the total bill was 520 pesos.
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Suppose the following set of random numbers is being used to simulate the event of a
basketball player making three free throws in a row. how should the numbers be
rearranged?
i don’t need help but in case someone needs the answer. good luck!
Option D is the correct answer as it groups the numbers into sets of five, assigns them as either a "make" or a "miss", and preserves the order of the original set.
The set of random numbers provided represents the binary outcome of a basketball player making or missing a free throw. To simulate the event of making five free throws in a row, we need to group the numbers into sets of five and assign each set as either a "make" or a "miss".
Option A simply groups the numbers into sets of five, but does not indicate whether they are a "make" or a "miss". Option B groups the numbers into sets of five and assigns them as either a "make" or a "miss", but the order of the numbers has been changed.
Option C groups the numbers into sets of five, assigns them as either a "make" or a "miss", and preserves the order of the original set.
This allows for an accurate simulation of the event of making five free throws in a row using the provided set of random numbers.
So, correct option is D.
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Complete question is:
Suppose the following set of random numbers is being used to simulate the event of a basketball player making five free throws in a row. How should the numbers be rearranged?
860583 785814 010122 337198 621549 034076 796495 978078 433330
333153
A. 860 583 785 814 010 122 337 198 621 549 034 076 796 495 978
078 433 330 333 153
B. 8605 8378 5814 0101 2233 7198 6215 4903 4076 7964 9597
8078 4333 3033 3153
C. 86058 37858 14010 12233 71986 21549 03407 67964 95978
07843 33303 33153
D. 860583 785814 010122 337198 621549 034076 796495 978078
433330 333153
Help give me an Explanation
Answer:
if the two angles are equal
we use sss therom to solve it
2ft/6ft=24ft/xft
x=(6*24)/2
=72
You bought a laptop computer for $525 on the "12 months is the same as cash" plan. The terms of the plan on the contract stated that if
not paid within 12 months, you would be assessed 15. 5 percent APR for the amount on the first day of the plan
If you pay the laptop in 11 months, how much will you have paid?
a. $525
b. $540. 50
c. $595. 50
d. $606. 38
Your answer: a. $525
The "12 months is the same as cash" plan means that if you pay off the laptop within 12 months, you won't be charged any interest.
Since you plan to pay off the laptop in 11 months, which is within the 12-month period, you will not be assessed the 15.5 percent APR.
Therefore, you only need to pay the original cost of the laptop, which is $525.
To summarize, as long as you pay the full amount within the specified 12-month period, you avoid the additional interest charges. In this case, you will pay the laptop off in 11 months, so your total payment will be $525.
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Zelda has 8 rabbits with which to start an animal farm. If the rabbit population doubles each month, in how many months will the rabbit population be 5,800?
In a case whereby Zelda has 8 rabbits with which to start an animal farm. If the rabbit population doubles each month, the number of months that the rabbit population will be 5,800 is 9.5 months.
How can the the number of months?In order to calculatre the month then we can use the expression y = abⁿ
a = starting number ( 8 rabbits)
b = rate of change = (2)
n = number of months that we need to calculate
y = rabbit population = 5800
The we can substitute to have
5800 = 8 × 2ⁿ
5800 / 8 = 2ⁿ
725 = 2ⁿ
n = 9.5 months.
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In ΔUVW, w = 5. 3 inches, v = 3. 6 inches and ∠V=32°. Find all possible values of ∠W, to the nearest 10th of a degree
The only possible value of W is:
W ≈ 71.6° to the nearest 10th of a degree.
We can use the Law of Cosines to find the angle W opposite to the side w:
cos(W) = (v^2 + w^2 - u^2) / (2vw)
cos(W) = (3.6^2 + 5.3^2 - u^2) / (2 * 3.6 * 5.3)
We can solve for u by using the Law of Cosines for the angle V:
cos(V) = (u^2 + v^2 - w^2) / (2uv)
cos(32°) = (u^2 + 3.6^2 - 5.3^2) / (2 * u * 3.6)
Simplifying the equation and solving for u, we get:
u = sqrt(3.6^2 + 5.3^2 - 2 * 3.6 * 5.3 * cos(32°)) ≈ 3.8 inches
Now we can substitute this value of u into the equation for cos(W) and solve for cos(W):
cos(W) = (3.6^2 + 5.3^2 - 3.8^2) / (2 * 3.6 * 5.3) ≈ 0.315
Taking the inverse cosine, we get:
W ≈ 71.6° or W ≈ 288.4°
Note that since the angle W is in a triangle, it must be between 0° and 180°. Therefore, the only possible value of W is:
W ≈ 71.6° to the nearest 10th of a degree.
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