Answers
The values of the compound probabilities are
P(Blue then Red) = 4/105 = 3.81%P(Red then Green) = 2/35 = 5.71%P(Green then Green) = 1/35 = 2.85%P(Yellow then Yellow) = 1/7 = 14.29%P(Red then Red then Red) = 4/455 = 0.88%How to calculate the compound probabilitiesFrom the question, we have the following parameters that can be used in our computation:
The cubes
Where we have
Blue = 2
Green = 3
Red = 4
Yellow = 6
Givn the the cubes are not replaced after they are chosen, we have
P(Blue then Red) = 2/15 * 4/14
P(Blue then Red) = 4/105 = 3.81%
Next, we have
P(Red then Green) = 4/15 * 3/14
P(Red then Green) = 2/35 = 5.71%
P(Green then Green) = 3/15 * 2/14
P(Green then Green) = 1/35 = 2.85%
P(Yellow then Yellow) = 6/15 * 5/14
P(Yellow then Yellow) = 1/7 = 14.29%
P(Red then Red then Red) = 4/15 * 3/14 * 2/13
P(Red then Red then Red) = 4/455 = 0.88%
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Related Questions
what is 11/2 times 1/3 as a fraction
Answers
Answer:
11/2 times 1/3 is 11/6
Step-by-step explanation:
11/2 times 1/3,
We have to multiply the numerators and denominators,
[tex](11/2)(1/3) = (11*1)/(2*3) = 11/6\\11/6[/tex]
hence we get 11/6
Suppose that the functions fand g are defined as follows.
f(x)=(4+x)(6+x)
g(x) = 1+x
Find (f/g)(-5)
Find all values that are NOT in the domain of f/g
Answers
(f/g)(-5) is equal to 1/4, and the value -1 is not in the domain of f/g.
To find (f/g)(-5), we need to substitute -5 into the functions f(x) and g(x) and then divide f(-5) by g(-5).
Given:
f(x) = (4+x)(6+x)
g(x) = 1+x
Substituting -5 into the functions:
f(-5) = (4+(-5))(6+(-5)) = (-1)(1) = -1
g(-5) = 1+(-5) = -4
Now, we can calculate (f/g)(-5):
(f/g)(-5) = f(-5) / g(-5) = -1 / -4 = 1/4
Therefore, (f/g)(-5) equals 1/4.
Now let's determine the values that are not in the domain of f/g. The values that are not in the domain of f/g are the values that make the denominator g(x) equal to zero. In this case, the denominator is g(x) = 1+x.
To find the values that make the denominator zero, we solve the equation:
1 + x = 0
Subtracting 1 from both sides, we get:
x = -1
So, the value x = -1 is not in the domain of f/g because it would make the denominator equal to zero.
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Segment Line segment X Y is dilated using a scale factor of Two-thirds through P. Which segment shows the correct result of the dilation? Point P is the center of dilation. Line a is 4 units from point P, line B is 2 units from line a, line c is 2 units from line b, line d is 2 units from line c, line X Y is 2 units from line d. line a line b line c line d Mark this and return
Answers
Line d shows the correct result of the dilation, with line XY being 2 units long.
We are given that segment XY is dilated using a scale factor of two-thirds through point P, which is the center of dilation.
To determine the correct result of the dilation, we need to find the segment that satisfies the given conditions.
Starting from point P, we have line a located 4 units away from point P.
From line a, we have line b located 2 units away.
Similarly, from line b, we have line c located 2 units away.
Continuing this pattern, from line c, we have line d located 2 units away.
Finally, from line d, we have line XY located 2 units away.
Considering the dilation scale factor of two-thirds, we need to find the segment that is two-thirds the length of the previous segment.
Calculating the lengths, we find that line a is 4 units, line b is 2 units, line c is 2 units, line d is 2 units, and line XY is 2 units.
The length of line XY is already two-thirds the length of line d, satisfying the given conditions.
Therefore, line d shows the correct result of the dilation, with line XY being 2 units long.
Marking line d as the correct segment, we can now return our answer.
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in the inequalitty -2 <2, witch number appears farther right on a number line
Answers
Answer:
2
as it is a positive integer
After watching baking shows on T.V., Angie signs up for a cake-decorating class. To practice her new skills, she decorates a batch of cupcakes with sugar flowers. Angie puts 4 sugar flowers on each cupcake. In all, Angie puts 32 sugar flowers on the cupcakes.
Which equation can you use to find the number of cupcakes c Angie decorates?
Solve this equation for c to find the number of cupcakes Angie decorates.
Answers
Angie decorates 8 cupcakes after putting 4 sugar flowers on each cupcake.
To find the number of cupcakes c Angie decorates, we can use the equation:4c = 32where 'c' is the number of cupcakes Angie decorates.
4 represents the number of sugar flowers Angie puts on each cupcake, and 32 is the total number of sugar flowers Angie puts on the cupcakes.
To solve this equation for c, we need to isolate c on one side of the equation. We can do this by dividing both sides of the equation by 4. This gives us:c = 8
Therefore, Angie decorates 8 cupcakes.Here's how we get to this answer:4c = 32Divide both sides by 4 to isolate c:c/4 = 32/4c = 8
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List the sides of ∆ from shortest to longest. ∠ = 64°, ∠ = 31°
Answers
Answer:
To list the sides of triangle ∆ from shortest to longest, we need the lengths of the sides. However, the given information only provides the measures of the angles (∠). Without the side lengths, we cannot determine the order of the sides from shortest to longest.
Write the equation of a line perpendicular to y = -5x + 1 that goes through (10, 4). Show all work.
Answers
The equation of the perpendicular line is y = 1/5x + 2
How to determine the equation of the perpendicular lineFrom the question, we have the following parameters that can be used in our computation:
Line; y = -5x + 1
The slope of the above line is
m = -5
The slopes of perpendicular lines are opposite reciporcals
So, the new slope is 1/5
New = 1/5
The line passes through (10, 4)
So, we have
y = mx + c
Where
m = 1/5
This gives
1/5 * 10 + c = 4
Evaluate
c = 4 - 1/5 * 10
c = 2
So, we have
y = 1/5x + 2
Hence, the equation of the perpendicular line is y = 1/5x + 2
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Given f(x) = x − 7 and g(x) = x2 .
Find f(g(4)).
Answers
Which function has the same range as f (x) = negative 2 StartRoot x minus 3 EndRoot + 8?
Answers
g(x) = -2√x + 8 is the function that has the same range as f(x) = -2√(x - 3) + 8. Both functions have the range of y ≤ 8
The function that has the same range as f(x) = -2√(x - 3) + 8 is g(x) = -2√x + 8. Both functions have the range of y ≤ 8.There are a few steps involved in determining which function has the same range as f(x) = -2√(x - 3) + 8. The range of a function refers to all the possible output values that the function can produce.Let's begin by examining the original function:f(x) = -2√(x - 3) + 8The square root symbol (√) implies that x-3 must be greater than or equal to 0. If x-3 is negative, then the function would produce an imaginary result.
Let's solve for x when f(x) = 0:0 = -2√(x - 3) + 8-8 = -2√(x - 3)4 = √(x - 3)16 = x - 3x = 19This tells us that the x-value that produces an output of 0 is x = 19. To determine the range, we need to find the maximum and minimum output values. We can use a graphing calculator or sketch a graph to determine the shape of the function and the range.The shape of the function suggests that the range is y ≤ 8, which means that the maximum value of the function is 8. This tells us that any function with the same maximum output value of 8 will have the same range as f(x).
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Two quantities are related, as shown in the table: x y 2 10 4 9 6 8 8 7 Which equation best represents the relationship? (4 points) Group of answer choices y = 1 over 2x + 11 y = negative 1 over 2x + 11 y = 2x + 10 y = 2x + 11
Answers
The equation that best represents the relationship between x and y is:
y = -1/2x + 11
To determine the equation that best represents the relationship between the quantities x and y, we can examine the pattern in the table.
Looking at the x-values and their corresponding y-values, we can observe that as x increases by 2 units, y decreases by 1 unit.
Using this pattern, we can find the equation that represents the relationship.
When x = 2, y = 10
When x = 4, y = 9
When x = 6, y = 8
When x = 8, y = 7
Based on the pattern, we can see that y decreases by 1 unit for every 2 units increase in x.
Therefore, the equation that best represents the relationship is:
y = -1/2x + b
To find the value of b (the y-intercept), we can substitute the values of x and y from any point in the table. Let's use the first point (x = 2, y = 10):
10 = -1/2(2) + b
10 = -1 + b
b = 11
So the equation that best represents the relationship between x and y is:
y = -1/2x + 11
Therefore, the correct answer is: y = -1/2x + 11.
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A seat in Section A of the stadium is chosen at random. The fan sitting in that seat receives two free tickets to next week's game. Find the probability that a person in each color seat would receive the free tickets. 1. P(yellow) = 2. P(red) = 3. P(blue) = 4. P(blue or yellow) = 5. P(red or blue) = Red Blue Blue Blue Seats in Section A Red Red Blue Blue Red Red Blue Blue Red Blue Blue Blue Yellow Yellow Yellow Yellow Yellow Yellow Yellow Yellow
Answers
The probabilities are:
1. P(yellow) = 2/5
2. P(red) = 3/10
3. P(blue) = 3/10
4. P(blue or yellow) = 7/10
5. P(red or blue) = 3/5
To find the probability that a person in each color seat would receive the free tickets, we need to calculate the probabilities of each event.
1. P(yellow): There are 8 yellow seats out of a total of 20 seats in Section A. Therefore, the probability of selecting a yellow seat at random is P(yellow) = 8/20 = 2/5.
2. P(red): There are 6 red seats out of a total of 20 seats in Section A. Therefore, the probability of selecting a red seat at random is P(red) = 6/20 = 3/10.
3. P(blue): There are 6 blue seats out of a total of 20 seats in Section A. Therefore, the probability of selecting a blue seat at random is P(blue) = 6/20 = 3/10.
4. P(blue or yellow): To calculate the probability of selecting a blue or yellow seat, we add the individual probabilities of selecting a blue seat and a yellow seat: P(blue or yellow) = P(blue) + P(yellow) = 3/10 + 2/5 = 7/10.
5. P(red or blue): To calculate the probability of selecting a red or blue seat, we add the individual probabilities of selecting a red seat and a blue seat: P(red or blue) = P(red) + P(blue) = 3/10 + 3/10 = 6/10 = 3/5.
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FLUENCY
1. In the diagram below point C is the midpoint of AB. If the length of AB is 32 and the length
of AC is given by +10 then which of the following is the value of
(1) 11
(2) 12
(3) 3
(4) 44
Answers
The value of AC is 10.Hence, the correct option is (1) 11.
From the diagram, C is the midpoint of AB.
Now,
AC = CB (As C is the midpoint of AB)
Assuming the length of AB is 32 and the length of AC is +10, we can find the length of CB by subtracting the length of AC from the length of AB.
CB = AB - AC
CB = 32 - 10
CB = 22
Therefore the length of CB is 22.
Let's look at the following possible answers:
(1) 11 - This is not the length. CB
(2) 12 - This is not the length of the CB.
(3) 3 - This is not the CB length.
(4) 44 - not CB length.
None of the given answer options correspond to CB length (22).
Therefore, none of the specified options are valid values.
Therefore, AC + CB = AB+10 + CB = 32CB = 32 - 10 = 22
Thus, the length of CB is 22.
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A student needs to be select 3 books from 3 different mathematics, 3 different physics and I history book. What is the probability that one of them is mathematics and the other two is either physics or history books?
Answers
The probability is 5/9 or approximately 0.5555.
The probability that one of the books selected is a mathematics book and the other two are either physics or history books can be calculated as follows:
1. Calculate the total number of possible combinations of selecting 3 books out of the given options. Since there are 3 mathematics books, 3 physics books, and 1 history book, the total number of combinations is:
Total Combinations = C(3,1) * C(3,2) = 3 * 3 = 9, where C(n,r) represents the number of combinations of selecting r items from a set of n items.
2. Calculate the number of favorable combinations where one book is mathematics and the other two are either physics or history books. There are 3 ways to select one mathematics book and 3 ways to select two books from the remaining 6 (3 physics + 1 history) books. Therefore, the number of favorable combinations is:
Favorable Combinations = C(3,1) * C(6,2) = 3 * 15 = 45.
3. Calculate the probability by dividing the number of favorable combinations by the total number of combinations:
Probability = Favorable Combinations / Total Combinations = 45 / 9 = 5/1 = 5.
Therefore, the probability that one of the books selected is a mathematics book and the other two are either physics or history books is 5/9 or approximately 0.5555.
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Find x
(x+100)/(x-100) = (a+b+100)/(a+b-100)
Answers
Given the mathematical expression, it must be solved with the result [tex](\text{a} + \text{b})[/tex]
What are mathematical expressions?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division.
We are given the expression:
[tex]\dfrac{(\text{x} + 100)}{(\text{x} - 100)} = \dfrac{(\text{a} + \text{b} + 100)}{(\text{a} + \text{b} - 100)}[/tex]
The Denominators go to the other side of the equality by multiplying, so that we now have:
[tex](\text{x} + 100)(\text{a} + \text{b} - 100) = (\text{a} + \text{b} + 100)(\text{x} - 100)[/tex]
The products of the binomials are developed by the trinomials.
[tex]\text{ax} + \text{bx} - 100\text{x} + 100\text{a} + 100\text{b} - 10000 = \text{ax} + \text{bx} + 100\text{x} - 100\text{a} - 100\text{b} - 10000[/tex]
Like terms are removed.
[tex]100\text{a} + 100\text{b} - 100\text{x} = 100\text{x} - 100\text{a} - 100\text{b}[/tex]
[tex]100\text{a} + 100\text{b} - 100\text{x} - 100\text{x} + 100\text{a} + 100\text{b}[/tex]
[tex]200\text{a} + 200\text{b} - 200\text{x} =[/tex]
Grouping.
[tex]200(\text{a} + \text{b})[/tex]
Result.
[tex](\text{a} + \text{b})[/tex]
Hence, the solution to the mathematical expression is [tex](\text{a} + \text{b})[/tex]
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anne travels for 1.5 hours at an average speed of 40km/h
how far does she travel
Answers
Hello!
1. Formuladistance = speed * time
2. Applicationdistance
= 40km/h * 1.5h
= 60km
3. ConclusionShe travel 60km.
Answer:
60 km
Step-by-step explanation:
In order to find the distance that Anna has travelled, we can derive the formula from the speed formula which is:
[tex]\displaystyle{v=\dfrac{s}{t}}[/tex]
where v is speed, s is distance and t is time. So by solving for distance (s), we have:
[tex]\displaystyle{s=vt}[/tex]
Apply the distance travelled formula, we know that speed (v) = 40 km/h and time (t) = 1.5 hours. Thus,
[tex]\displaystyle{s=40 \ \text{km/h} \cdot 1.5 \text{h}}\\\\\displaystyle{s=60\ \text{km}}[/tex]
Therefore, Anna travels 60 kilometers.
An interviewer officer selects a person not suitable for the job is:
Select one:
a. Two Directional Bias
b. None of these
c. Three Directional Bias
d. Unbaised Error
e. one direction Bias
Note: Answer B is NOT the correct answer. Please find the correct answer. Any answer without justification will be rejected automatically.
Answers
The interviewer should provide clear and concise feedback on the candidate's performance in the interview, and ensure that the feedback is related to the job requirements.
In addition, the interviewer should ask relevant questions to get an idea about the interviewee's knowledge, skills, and abilities.Overall, the interviewer should strive to be fair and objective throughout the interview process, to minimize the risk of Unbiased Errors.
An interviewer officer selects a person not suitable for the job, this error is known as Unbaised Error.What is an Unbiased Error?An Unbiased error happens when you make an incorrect judgment regarding the interviewee, which may occur when the interviewer is unable to assess the interviewee objectively.
There are many factors that could contribute to an Unbiased Error, such as the interviewer's opinions and preconceptions, their biases or prejudices, the interviewer's inadequate understanding of the job requirements, or the applicant's inadequate preparation for the interview.In an unbiased interview, the interviewer does not have any preconceived ideas or predetermined judgments about the interviewee's knowledge, skills, or abilities.
The interviewer should be able to provide equal chances for all applicants, regardless of their gender, ethnicity, or any other factors that are not related to the job requirements.The interviewer should also assess the interviewee objectively, with no favoritism or bias.
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HELPPPPPPPP ASAPP
Heather and Joel bought a house for $157,200 and know that the house appreciates every year. They keep track of their house value for 5 years and model their data with the exponential equation
y = 150000(1.004)12
t
How much will their house be worth in 8 years?
A $240,000$240,000
B $220,000$220,000
C $1,258,884$1,258,884
D $14,457,600
Answers
Their house will be worth approximately $240,154.57 in 8 years.
Non of the options is correct.
To determine how much their house will be worth in 8 years, we can substitute the value of t = 8 into the exponential equation:
y = 150,000(1.004)^(12t)
y = 150,000(1.004)^(12*8)
y = 150,000(1.004)^96
Using a calculator or computer software to evaluate the exponential expression, we find:
y ≈ 150,000 * 1.601030475
y ≈ 240,154.57
None of the provided answer choices match the calculated value. However, we can examine the available options and make an estimation:
A) $240,000: This option is very close to the calculated value of $240,154.57 and is a reasonable estimate.
B) $220,000: This option is significantly lower than the calculated value and is not a close estimate.
C) $1,258,884: This option is significantly higher than the calculated value and is not a close estimate.
D) $14,457,600: This option is extremely higher than the calculated value and is not a realistic estimate.
Based on the provided answer choices, option A) $240,000 is the closest estimate to the calculated value of $240,154.57. However, please note that the actual value may vary depending on the specific calculations and rounding methods used.
Non of the options is correct.
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plsss help ill give brainliest
Answers
Answer:
Step-by-step explanation:
a) 4/10 = 40%
b) 3/10 = 30%
c) 1/10 = 10%
d) 2/10 = 20%
e) 8/12 = 67%
f) 10/12 = 83%
g) 9/12 = 75%
h) 12/12 = 100%
i) 4/12 = 33%
j) 5/12 = 42%
k) 2/12 = 16%
l) 3/12 = 25%
The following table presents the temperatures measured on a heat plate:
Using linear interpolation find the temperature at x=4, y=3.2.
Answers
The temperature at x = 4, y = 3.2, estimated through linear interpolation from the given data points, is approximately 46.744.
How to Use Linear Interpolation to find the Temperature?To find the temperature at x=4, y=3.2 using linear interpolation, first of all, determine the values at the surrounding grid points and interpolate between them.
From the given table, we can identify the following surrounding points:
Point A: (x=4, y=3)
Point B: (x=4, y=4)
Point C: (x=6, y=3)
Point D: (x=6, y=4)
Next, interpolate along the x-axis at y=3 to find the temperature at x=4:
Temperature at x=4, y=3 = Interpolate(A, B)
Also, we have to interpolate along the x-axis at y=4 to find the temperature at x=4:
Temperature at x=4, y=4 = Interpolate(A, B)
Next, we'll interpolate between the temperatures obtained above along the y-axis at y=3.2:
Temperature at x=4, y=3.2 = Interpolate(Temperature at x=4, y=3, Temperature at x=4, y=4)
Let's calculate these values step by step:
Interpolate along the x-axis at y=3:
Temperature at x=4, y=3 = Interpolate(A, B)
= 80.00 + (4-4)/(4-4) * (80.00 - 80.00)
= 80.00
Interpolate along the x-axis at y=4:
Temperature at x=4, y=4 = Interpolate(A, B)
= 38.43 + (4-4)/(4-4) * (35.03 - 38.43)
= 38.43
Interpolate between temperatures along the y-axis at y=3.2:
Temperature at x=4, y=3.2 = Interpolate(Temperature at x=4, y=3, Temperature at x=4, y=4)
= 80.00 + (3.2-3)/(4-3) * (38.43 - 80.00)
= 80.00 - 0.8 * 41.57
= 80.00 - 33.256
= 46.744
Therefore, the temperature at x=4, y=3.2 is approximately 46.744.
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show that the volume of the unit cube is one
Answers
Check the picture below.
f(x) = 4x² + 5x - 3
g(x) = 4x³ - 3x² + 5
Find (f + g)(x).
A. (f+g)(x) = 4x³+4x² + 2x + 2
B. (ƒ+g)(x) = 8x³ + 2x + 2
c. (f+g)(x) = 4x³ + x² + 5x + 2
D. (ƒ + g)(x) = −4x³ + 7x² + 5x − 8
Answers
Answer:
C
Step-by-step explanation:
(f + g)(x)
= f(x) + g(x)
= 4x² + 5x - 3 + 4x³ - 3x² + 5 ← collect like terms
= 4x³ + (4x² - 3x²) + 5x + (- 3 + 5)
= 4x³ + x² + 5x + 2
4. Uncle Royce is 42. What is his target heart rate range?
O 120-180 beats per minute
O 150-200 beats per minute
O116-160 beats per minute
O170-236 beats per minute
Answers
Step-by-step explanation:
70 to 85 % of his maximum
Maximum is estimated to be 220 - age = 220 - 42 = 178
70% of this is 125
85 % is 89 151
I believe I would go with the third choice 116-160 bpm
computing decimals 25/.2=
Answers
Answer:
125
thats the answer nothing more is needed to say. plus 25/.2= 25x10/5= 125
Answer:
125
Step-by-step explanation:
25/0.2 = 25 ÷ 2/10 = 25 × 10/2 = 25 × 5 = 125
dont understand it at alll
Answers
The word sentence should be written as an inequality as follows;
all numbers that are at most 5 ⇒ x ≤ 5.all numbers that exceed 5 ⇒ x > 5.all numbers that are at least 5 ⇒ x ≥ 5.all numbers that are not greater than or equal to 5 ⇒ x < 5.What is an inequality?In Mathematics and Geometry, an inequality is a relation that compares two (2) or more numerical data, number, and variables in an algebraic equation based on any of the inequality symbols;
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).Generally speaking, "at most" simply means less than or equal to (≤), "at least" simply means greater than or equal to (≥), "exceed" simply refers to greater than (>).
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Determine the line of best fit for the data A. y=1.1x + 5. B. y=2.8x + 10.5 C. y= 0.95x + 12
Answers
The line of best fit for the given data is represented by equation C, which is y= 0.95x + 12.
To find the line of best fit, the data points are plotted on a graph, and the line is drawn so that the distance between each data point and the line is minimized.
This is done using various statistical methods, such as the least squares method, to determine the equation of the line that best represents the data.
The equation of the line of best fit can then be used to make predictions or estimations about future values of the dependent variable based on the independent variable.
In this case, the line of best fit represents the relationship between x and y, and can be used to predict the value of y for a given value of x.
In conclusion, the line of best fit for the data is represented by equation C, y= 0.95x + 12.
This line provides the closest approximation to the data points and can be used to make predictions about future values of the dependent variable based on the independent variable.
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Find f(-2) for the
piece-wise function.
f(x) =
X
|x+
x+1
if x ≤ 0
if x > 0
f(-2)=[?]
Answers
Answer:
The answer is,
f(-2) = -2
Step-by-step explanation:
Since -2 < 0, and f(x) = x for x < 0,
so we get,
f(-2) = -2
Mark has 14 baseballs. One box holds 12 baseballs. Which mixed number represents the number of boxes Mark has filled?
A) 2 12/14
B) 1 2/14
C) 1 2/12
D) 12 12/14
Answers
Total number of baseballs = 14
Number of baseballs in each box = 12
Dividing 14 by 12, we get:
14 ÷ 12 = 1 with a remainder of 2
So Mark has filled one box completely and has 2 baseballs left over.
Expressing this as a mixed number, we get:
1 2/12
However, we can simplify this mixed number by reducing the fraction to lowest terms:
1 2/12 = 1 1/6
the mixed number that represents the number of boxes Mark has filled is option C) 1 2/12, which is equivalent to 1 1/6.
What are the factors of 42 to find it’s prime numbers and how do I put it in a factor tree
Answers
To create a factor tree for 42, we start by finding a pair of factors of 42, such as 2 and 21 and factor each branch until we have prime numbers.
Answer:
See below
Step-by-step explanation:
Starting with 42, there would be two branches of 2 and 21 connected to 42. Since 2 is prime, there are no more branches. Since 21 is composite, then two more branches are drawn of 3 and 7 connected to 21. Since 3 and 7 are prime, there are no more branches.
Therefore, the prime factorization of 42 is 2*3*7, and its factors would be 1,2,3,6,7,14,21,42.
Find the circumference of the circle. Use 3.14 for the value. Round your answer to the nearest tenth
Answers
Answer:
C = 18.2 in.
Step-by-step explanation:
Step 1: Find the diameter of the circle:
The normal formula for the circumference of a formula is given by:
C = πd, where
C is the circumference, and d is the diameter of the circle.We're given the radius, r, and since the diameter is simply twice the radius, we can find the diameter by multiplying 2.9 by 2:
d = 2r
d = 2(2.9)
d = 5.8
Thus, the diameter is 5.8 in.
Step 2: Find the circumference, C (rounded to the nearest tenth), by plugging in 5.8 for d and 3.14 for π in the circumference formula:
C = 3.14(5.8)
C = 18.212
C = 18.2
Thus, the circumference of the circle is about 18.2 in.
How much would you have to deposit today to accumulate the SAME AMOUNT OF MONEY that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn?
Answers
Answer:
7606.62
Step-by-step explanation:
Start by finding how much you will have through the annuity. The question isn't that clear, so i will just assume it's an annuity due.
[tex]p(\frac{(1+i)^n-1}{i})*(1+i)\\i=.035/12= .0029166667\\n=10*12=120\\p=75 (given)\\75\frac{(1+.0029166667)^{120}-1}{.0029166667}*(1+.0029166667)= 10788.814149\\[/tex]
Now just equate this to a time 0 payment at the same rate
[tex]10788.814149=(1+.0029166667)^{120}*x\\x= 7606.6228603=7606.62[/tex]
As a quick note, if you were supposed to assume that your annuity was an annuity immediate the answer would be 7584.50.
