The account value after forty years is approximately $489,074,140.57.
What is formula for the future value of an annuity?To calculate the account value after forty years, we need to use the formula for the future value of an annuity:
[tex]FV = P * [(1 + r)^n - 1] / r[/tex]
where FV is the future value, P is the annual payment, r is the interest rate, and n is the number of periods.
In this case, we have:
P = $3,000 in year 1, and then $3,300 in year 2, $3,600 in year 3, and so on
r = 8.35% = 0.0835 (assuming the interest rate is compounded annually)
n = 40 years
To compute the future worth of the annuity, we really want to ascertain the aggregate sum of installments over the 40 years. This should be possible involving the equation for the amount of a number-crunching series:
S = n/2 * [2a + (n-1)d]
where S is the sum, a is the first term, d is the common difference, and n is the number of terms.
In this case, we have:
a = $3,000
d = $300
n = 40
Plugging these values into the formula, we get:
S = 40/2 * [2($3,000) + (40-1)($300)] = $2,340,000
Thus, the aggregate sum of installments more than 40 years is $2,340,000.
We can now enter these figures into the formula for annuity future value:
[tex]FV = P * [(1 + r)^n - 1] / r[/tex]
[tex]FV = $2,340,000 * [(1 + 0.0835)^{40} - 1] / 0.0835[/tex]
FV = $2,340,000 * 209.251
FV = $489,074,140.57
Consequently, after forty years, the account's value is approximately $489,074,140.57.
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13 Which polynomial is twice the sum of 4x^2-x + 1 and -6x^2 + x - 4?
(3)-4x²-6
(4)-2x²+x-5
(1)-2r²-3
(2)-41²-3
Answer: is option (3) -4x²-6.
Step-by-step explanation: First, we need to add the two given polynomials:
4x^2 - x + 1 + (-6x^2 + x - 4) = -2x^2 - 3
Now, we need to multiply this sum by 2:
2(-2x^2 - 3) = -4x^2 - 6
Therefore, the polynomial that is twice the sum of 4x^2-x+1 and -6x^2+x-4
sam is a regular at joe's diner. according to the waitress, the probability that sam will order ham is 0.8 and the probability that he will order coffee is 0.65. what is the probability that he will order neither ham nor coffee?
For an event based on order by sam for ham and coffee with different probabilities, then the probability that he will order neither ham nor coffee is equals to the 0.07.
We have sam is a regular customer at joe's diner. Let us consider two events be defined as A: sam will order ham
B: sam will order coffee
Now, the probability that sam will order ham, P( A) = 0.8
The probability that sam will order coffee, P( B) = 0.65
We have to determine the probability that he will order neither ham nor coffee.
Probability is chances of occurrence of an event. It is calculated by dividing the favourable response to total possible outcomes. Probability value always lies between 0 to 1. Apply probability law P( will order ham ) + P( will not order ham) = 1
=> Probability that sam will not order ham
[tex]P( \bar A ) [/tex] = 1 - 0.8 = 0.2
Probability that sam will not order coffee,
[tex]P( \bar A ) [/tex]= 1 - 0.65 = 0.35
Now, as we see both events A and B are independent events so, there corresponding also independent. Therefore, Probability that he will order neither ham nor coffee, [tex] P( \bar A ∩ \bar B) [/tex]
[tex]= P( \bar A) P(\bar B) [/tex]
= 0.2 × 0.35 = 0.07
Hence, required probability is 0.07.
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Find all angle measures in the diagram.
The measure of ZKJL =
The measure of ZNJM =
The measure of ZMJL=
Answer: 1. 45%
2. 32%
3. 67%
5.
Alice is making a sculpture that is in the shape of a square pyramid on
top of a square prism. She wants to make it out of metal, fill it with
silicone and then paint it. Find the Surface Area and Volume for the
decomposable solid described below and then determine the cost of the
silicone, metal and the paint: [40 marks]
The Square Pyramid fits perfectly atop the Square Prism. The base of the
prism is a square with sides of 5 cm. The height of the prism is 8 cm.
The pyramid has a slant height of 3cm. There is no surface between the
pyramid and the prism.
Paint
$0.75 per 10
cm²
Pyramid
Cost of Materials
Metal
$12.25 per 100
cm²
Using a ruler, sketch the net of each of the parts of the sculpture. [4]
marks]
Silicone
$40/liter
Prism
Volume of the square prism is 200 cm³
Surface area of the square pyramid is 55 cm²
Total volume is 212.5 cm³
How to calculate the volumeThe base of the square prism is a square with sides of 5 cm. The height of the prism is 8 cm. Therefore, the surface area of the square prism is:
Surface area of one face of the square prism = (5 cm x 8 cm) = 40 cm²
There are 6 faces in a cube, therefore total surface area of the square prism = 6 x 40 cm² = 240 cm²
Volume of the square prism = (5 cm x 5 cm x 8 cm) = 200 cm³
The base of the square pyramid is also a square with sides of 5 cm. The slant height of the pyramid is 3 cm. The height of the pyramid can be found using the Pythagorean theorem:
Height² = slant height² - (1/2 base length)² = 3² - (1/2 x 5)² = 9 - 6.25 = 2.25
Height = √2.25 = 1.5 cm
Surface area of the square pyramid = (0.5 x base perimeter x slant height) + base area = (0.5 x 20 cm x 3 cm) + (5 cm x 5 cm) = 30 cm² + 25 cm² = 55 cm²
Volume of the square pyramid = (1/3 x base area x height) = (1/3 x 5 cm x 5 cm x 1.5 cm) = 12.5 cm³
The total surface area of the decomposable solid is:
Total surface area = Surface area of square prism + Surface area of square pyramid = 240 cm² + 55 cm² = 295 cm²
The total volume of the decomposable solid is:
Total volume = Volume of square prism + Volume of square pyramid = 200 cm³ + 12.5 cm³ = 212.5 cm³
The cost of materials includes the cost of metal for the sculpture, silicone for filling the sculpture, and paint for painting the sculpture.
The cost of metal for the sculpture is:
Cost of metal = (Total surface area x Cost per 100 cm²) = (295 cm² x $12.25/100 cm²) = $36.14
The cost of silicone for filling the sculpture is:
The volume of the decomposable solid is 212.5 cm³
The cost of silicone is $0.25 per cm³
Cost of silicone = (Volume of sculpture x Cost per cm³) = (212.5 cm³ x $0.25/cm³) = $53.13
The cost of paint for painting the sculpture is:
The total surface area of the decomposable solid is 295 cm²
The cost of paint is $0.75 per 10 cm²
Cost of paint = (Total surface area x Cost per 10 cm²) = (295 cm² x $0.75/10 cm²) = $22.13
Therefore, the total cost of materials for the sculpture is:
Total cost of materials = Cost of metal + Cost of silicone + Cost of paint = $36.
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when we have data with two quantitative variables, x and y. suppose the general trend changes direction (for example, increases and then decreases). suppose we would like to determine if there is a relationship between x and y, and if so, we wish to create a model that allows us to predict the expected value of y based on x. what is a good method to use?
Once you have information with two quantitative factors, x, and y, and you watch a common slant that changes heading, one good method to decide in case there's a relationship between x and y and to form a show that permits you to anticipate the anticipated esteem of y based on x is to utilize polynomial regression.
Polynomial relapse may be a sort of relapse investigation in which the relationship between the free variable (x) and the dependent variable (y) is modeled as an nth-degree polynomial. By fitting a polynomial work to the information, you'll be able to capture the common drift of the information even if it changes course and utilizes it. to foresee the anticipated esteem of y based on a given esteem of x.
polynomial relapse can be a valuable method to analyze and show information with a changing drift and give experiences into the relationship between x and y.
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a hose fills hot tub at 4.6 gallons per minute. how many hours will it take to fill a 440-gallon hot tub?
It will take approximately 1.59 hours to fill the hot tub with a hose that has a filling rate of 4.6 gallons per minute
Assuming that the filling rate of the hose is constant, we can use the formula:
time = volume / rate
where time is the time taken to fill the hot tub, volume is the volume of the hot tub (440 gallons), and rate is the filling rate of the hose (4.6 gallons per minute).
Substituting the values, we get:
time = 440 / 4.6
which simplifies to:
time = 95.65 minutes
To convert minutes to hours, we divide by 60 (since there are 60 minutes in an hour):
time = 95.65 / 60
which simplifies to:
time = 1.59 hours
Therefore, it will take approximately 1.59 hours to fill the hot tub with a hose that has a filling rate of 4.6 gallons per minute.
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It will take approximately 1.594 hours to fill a 440-gallon hot tub with a hose that fills at a rate of 4.6 gallons per minute.
To determine how many hours follow these steps:
First, we need to find out how many minutes it takes to fill the hot tub.
Divide the total volume of the hot tub (440 gallons) by the rate at which the hose fills (4.6 gallons per minute):
440 gallons ÷ 4.6 gallons/minute = 95.65 minutes
Now, we need to convert the minutes into hours.
Since there are 60 minutes in an hour, divide the minutes by 60:
95.65 minutes ÷ 60 minutes/hour = 1.594 hours
It will take approximately 1.594 hours to fill a 440-gallon hot tub with a hose that fills at a rate of 4.6 gallons per minute.
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if you repeated a hypothesis test 1,900 times (in other words, 1,900 different samples from the same population), how many times would you expect to commit a type i error, assuming the null hypothesis were true, if
Answer: Assuming a significance level of 0.05 for each hypothesis test, the probability of committing a Type I error (rejecting the null hypothesis when it is actually true) in any given test is 0.05.
Therefore, the expected number of Type I errors in 1,900 hypothesis tests is:
Expected number of Type I errors = (0.05) x (1,900) = 95
So, we would expect to commit a Type I error about 95 times in 1,900 hypothesis tests, assuming the null hypothesis were true.
Step-by-step explanation:
A clothing store has each customer spin this spinner to reveal a discount. Even numbers get 20% off and odd numbers get 15% off. The pointer lands on an even number 135 times out of 250 spins
The average discount that is obtained by spinning the spinner is 17.7%.
Let, the probability of landing on an even number is denoted by P(E) and the probability of landing on an odd number is denoted by P(O).
We have that the pointer lands on an even number 135 times out of 250 spins.
So, the probability that is of landing on an even number is:
P(E) = Number of times the pointer lands on an even number / Total number of spins
P(E) = 135 / 250
Since, we have the sum of probabilities of all possible outcomes must be 1, we can find the probability of landing on an odd number as follows:
P(O) = 1 - P(E)
P(O) = 1 - (135 / 250)
Now, we know that even numbers get 20% off, and odd numbers get 15% off.
We find the average discount considering these probabilities:
Average Discount = (P(E) * 20%) + (P(O) * 15%)
Average Discount = (135 / 250) * 20% + [1 - (135 / 250)] * 15%
Now, let's perform the calculations:
Average Discount = (135 / 250) * 0.20 + [1 - (135 / 250)] * 0.15
Average Discount = 0.108 + (1 - 0.54) * 0.15
Average Discount = 0.108 + 0.46 * 0.15
Average Discount = 0.108 + 0.069
Average Discount = 0.177
So, the average discount that is obtained by spinning the spinner is 17.7%.
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complete question:
A clothing store has each customer spin this spinner to reveal a discount. Even numbers get 20% off and odd numbers get 15% off. The pointer lands on an even number 135 times out of 250 spins. find the average discount obtained by spinning the spinner?
will give brainliest to first answer
Answer:
the answer to your question is x=3
Answer:
Option A: x = 3
Step-by-step explanation:
The lowest part of the parabola has an x-value of 3.
The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 2. There are two dots above 8. There are three dots above 6, 7, and 9.
Which of the following is the best measure of variability for the data, and what is its value?
The range is the best measure of variability, and it equals 8.
The range is the best measure of variability, and it equals 2.5.
The IQR is the best measure of variability, and it equals 8.
The answer is "The IQR is the best measure of variability, and it equals 7. because the best measure of variability for the data is the IQR, and its value is 7
What is the linear function?A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.
According to the given information:The given plot displays the distribution of the number of roses purchased per day at a grocery store. The best measure of variability for this data would be the interquartile range (IQR) since it is robust to outliers and provides a measure of the spread of the middle 50% of the data.
To calculate the IQR, we need to find the first quartile (Q1) and the third quartile (Q3). Q1 is the median of the lower half of the data, and Q3 is the median of the upper half of the data.
From the plot, we can see that there are a total of 11 data points: one at 1, two at 2, three at 6, three at 7, two at 8, and three at 9. The median (Q2) is 7 since it is the middle value when the data are arranged in order.
To find Q1, we need to find the median of the lower half of the data. Since there is one data point below 6 and three data points at 6, the lower half of the data consists of four points: 1, 2, 6, and 6. The median of this set is (1+2)/2 = 1.5.
To find Q3, we need to find the median of the upper half of the data. Since there are two data points at 8 and three data points at 9, the upper half of the data consists of five points: 8, 8, 9, 9, and 9. The median of this set is (8+9)/2 = 8.5.
Therefore, the IQR is Q3-Q1 = 8.5-1.5 = 7.
Therefore, the answer is "The IQR is the best measure of variability, and it equals 7. because the best measure of variability for the data is the IQR, and its value is 7
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In an instant lottery, your chances of winning are 0.1. If you play the lottery twice and outcomes are independent, the probability that you win at least once is
The probability of winning at least once when playing the instant lottery twice is 0.19, or 19%.
To find the probability of winning at least once in the instant lottery when playing twice, we can use the complement rule.
The complement rule states that the probability of an event occurring (in this case, winning at least once) is equal to 1 minus the probability of the event not occurring (in this case, not winning both times).
Determine the probability of not winning in a single game, which is 1 - 0.1 = 0.9.
Calculate the probability of not winning both times, since outcomes are independent, by multiplying the probabilities of not winning each time: 0.9 * 0.9 = 0.81.
Finally, find the probability of winning at least once by subtracting the probability of not winning both times from 1: 1 - 0.81 = 0.19.
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show your work 3.37 times 9
Answer:
[tex]3.37 \times 9 \\ = 30.33[/tex]
hope it helps
Prisms that have 2400cm
Answer: A Rectangular prism
Use the formula from question 12 to estimate the amount of material required to cover Firm 1's structure, not including the floor. Show your calculations
formula: 2(lw + wh + lh)
Answer:
Step-by-step explanation:
Total enclosed space of the structure 1's = 6597.35ft³Firms 1's structure is in the form of the cylinder. So the formula used for the calculation of the enclosed space or volume of the cylinder is:
Volume of the cylinder = πr²h .........(i)
where r = radius of the structure
Diameter(d) = 70ft
Given r = 70/2 = 35ft
h = Height of the structure
Given h = 60ft
By substituting the values of radius (r) and height (h) in equation (i), we get
V = π(35)²(60)ft³
V = 3.14(35)(60)ft³
V = 6597.345ft³
Total volume or enclosed space of Firm 1 is 6597.35ft³To know more about cylinder, kindly visit
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For which distributions is the median the best measure of center?
Select each correct answer.
hurry pls
The 1st and the 3rd are the distributions where the median the best measure of center
What is meant by medianThe median represents the central value in a dataset that is organized in ascending or descending order. If there are an even number of data points, the median can be calculated as the mean of the two middle values.
This method is much less prone to influence by extreme values when compared to other methods such as the mean. Hence, it is considered a more reliable measure of center particularly for datasets with outliers.
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Serena is making a model of one of the Egyptian pyramids. The square base has sides that are all 4. 8 in. Each of the triangular faces has a base of 4. 8 in and a height of 4. 2 in. How much paper would it take to cover the entire pyramid?
To cover the entire area of pyramid, Serena would need approximately 63.36 square inches of paper.
The area of the square base is
4.8 in x 4.8 in = 23.04 sq in
The area of each triangular face is
(1/2) x base x height = (1/2) x 4.8 in x 4.2 in = 10.08 sq in
Since there are four triangular faces, the total area of the triangular faces is
4 x 10.08 sq in = 40.32 sq in
Therefore, the total surface area of the pyramid is
23.04 sq in + 40.32 sq in = 63.36 sq in
So, it would take 63.36 square inches of paper to cover the entire pyramid.
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the sample size formula for estimating a proportion using a confidence interval with margin of error e involves the product p(1-p). this product is not known. a conservative approach is to use
A value of 0.25 for p(1-p) in the sample size formula when the true value of p is unknown.
This is because the value of p(1-p) is maximum when p=0.5, and since we do not have any information about the true value of p, assuming p=0.5 is the most conservative approach. Therefore, to calculate the sample size required to estimate a proportion using a confidence interval with a margin of error e, we can use the formula:
[tex]n = [z^2 * p(1-p)] / e^2[/tex]
where z is the z-score corresponding to the desired level of confidence (e.g., 1.96 for 95% confidence), and e is the desired margin of error. We can use p=0.5 and solve for n to get a conservative estimate of the sample size required for the given confidence level and margin of error.
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If prior knowledge or data suggests that the proportion is significantly different from 0.5, then a more accurate estimate of p should be used in the formula.
To calculate the sample size formula for estimating a proportion using a confidence interval with a margin of error e, we
use the following formula:
[tex]n = (Z^2 × p × (1-p)) / e^2[/tex]
where n is the required sample size, Z is the Z-score corresponding to the desired level of confidence,
p is the estimated proportion, and
e is the margin of error.
Since the product p(1-p) is not known, a conservative approach is to use p = 0.5, which is the value that maximizes the
product p(1-p) for any given proportion.
This approach ensures that the sample size will be large enough to obtain a reliable estimate of the proportion, even if
the true proportion is close to 0 or 1. However, if prior knowledge or data suggests that the proportion is significantly
different from 0.5, then a more accurate estimate of p should be used in the formula.
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Joe’s broker’s fee schedule is given in the table. Joes current portfolio is worth $50,000. He wants to purchase 50 shares of a company’s stock fir a purchase price of $15 per share.
Joe will need to pay a commission of _____.
The total amount charged by the broker will be ______.
Space 1: $7. 50, $5. 00, $1. 50
Space 2: $17. 50, $15. 50, $15. 0
Jow will need to pay a commision of $7.50. The total amount charged by the broker will be $17.50
Joes current portfolio is worth $50,000
A purchase price one share = $15
He wants to purchase 50 shares of a company's stock
Using unitary method the cost of 50 shares would be,
C = 50 × 15
C = $750
Since his portfolio is less than $100000 the amount chanrged by the broker would be equal to the 1% commision plus fees per trade.
First we find the commision.
1 percent of $750
= 1/100 × 750
= $7.5
And the fees per trade = $10
So, the total amount charged by the broker = $10 + $7.5
= $17.5
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Find the complete question below.
If I was asked to think of a number and multiply it by 2, I could
write this algebraically as 2x.
Write the following algebraically, using x as your unknown.
"I think of a number, add 3 to it and multiply the result by 7."
if your degrees of freedom is 24, your sample size when conducting a t test for dependent means must be ______. a. 26 b. 23 c. 25 d. 24
If the degree of freedom is 24, your sample size when conducting a t-test for dependent means must be 25. Option C is the correct answer.
The sample size when conducting a t-test for dependent means depends on the specific study design and the level of significance desired, and cannot be determined solely based on the degrees of freedom.
However, if we assume that the sample size is equal for both groups, then the formula to calculate the degrees of freedom for a t-test for dependent means is:
df = n - 1
Where "n" is the number of pairs of observations in the sample.
Therefore, if the degree of freedom is 24, then the number of pairs of observations in the sample would be:
n = df + 1 = 24 + 1 = 25
Hence, the answer is 25.
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ey of the
1
11. The table shows the wages of a worker in
an office. Which equation can be used to
represent how much, y, the worker earns in x
hours?
Hours
2
CIT
4
10
6
10
A. y = 20x+ 5.50
B. y = 10x + 5.50
C. y = 20.5x
Dy = 10x
Wages
$25.50
$45.50
$65.50
$105.50
12. Carlisle is going to paint his living room
Answer:
To determine which equation represents how much the worker earns in x hours, we can use the table to find the rate of pay per hour, which is the change in wages divided by the change in hours:
Change in wages = $105.50 - $25.50 = $80
Change in hours = 6 - 2 = 4
Rate of pay per hour = Change in wages / Change in hours
= $80 / 4
= $20
Therefore, the worker earns $20 per hour. To find the total earnings, we can multiply the hourly rate by the number of hours worked:
y = $20x
Therefore, the correct equation is D) y = 10x, which represents how much the worker earns in x hours.
Step-by-step explanation:
Cameron invests money in an account paying a simple interest of 7% per year. If no money will be added or removed from the investment, what should he multiply his current balance by to find his total balance in a year in one step?
The total balance in a year after the simple interest is A = P ( 1 + r )
Given data ,
Let the total balance in a year after the simple interest is A
Now , the multiply the initial balance by (1 + r), where r is the annual interest rate as a decimal.
In this case, the interest rate is 7%, or 0.07 as a decimal.
Therefore, Cameron should multiply his current balance by (1 + 0.07) = 1.07 to find his total balance in a year in one step.
For example, if Cameron's current balance is $10,000, his total balance after one year with simple interest would be:
Total balance = $10,000 x 1.07 = $10,700
Hence , the total balance is given by A = P ( 1 + r )
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In your notebook, draw a right angle and then draw a bisector of the right angle. Label all parts. What are some properties of the angles formed by the bisector? Use complete sentences for full credit.
The angles formed by the bisector are equal in measure, adjacent, supplementary, form a linear pair, and are congruent.
When a line bisects an angle, it divides the angle into two equal parts. The resulting angles have several properties
They have equal measures: The two angles formed by the bisector have the same degree measurement.
They are adjacent: The two angles share a common side and vertex.
They are supplementary: The sum of the two angles formed by the bisector is 180 degrees.
They form a linear pair: The two angles, together with the adjacent angle on the other side of the bisector, form a straight line or a linear pair.
They are congruent: The two angles formed by the bisector are congruent to each other.
These properties are useful in solving problems involving angle bisectors in geometry.
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I have solved the question in general, as the given question is incomplete.
The complete question is:
What are some properties of the angles formed by the bisector?
kelly has 3 bags whith 8 pieces of candy in each bag.lori has 8 bags whith 6 pieces candy in each . how much more candy does lori have then kelly
If Kelly has 3 bags containing 8 pieces each, and Lori has 8 bags containing 6 pieces each, then Lori have 24 candies more than Kelly.
If Kelly has 3 bags which contains 8 pieces of candy in each bag,
then Total number of candies with Kelly is = 3×8 = 24 candies,
If Lori has 8 bags which contains 6 pieces of candy in each bag,
then Total number of candies with Lori is = 8×6 = 48 candies,
So, to find how much more candy Lori has than Kelly, we need to subtract the number of pieces of candy Kelly has from the number Lori has;
The equation to find the difference in candies is written;
⇒ Difference = (total candies with Lori) - (total candies with Kelly),
⇒ Difference = 48 - 24 = 24 candies;
Therefore, Lori has 24 more pieces of candy than Kelly.
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Gaulle Company began the year with a balance of $6,000 in Accounts Receivable and ended the year with $9,000 in the account. Revenues for the period amounted to $38,000. Under the direct method, Gaulle will report cash collected from customers of:A. $44,000B. $35,000C. $41,000D. $47,000
Under the direct method, Gaulle will report cash collected from customers of $35,000.cash collected from customers is determined by adding the changes in Accounts Receivable to the revenues recognized during the period.
Beginning Accounts Receivable was $6,000 and ending Accounts Receivable was $9,000, indicating that customers owed Gaulle an additional $3,000 during the year.
Revenue for the year was $38,000, which represents the total sales generated by the company during the period. To calculate the cash collected from customers, we need to subtract the change in Accounts Receivable from the revenue recognized during the period.
Therefore, the cash collected from customers for Gaulle is calculated as follows:
Cash collected from customers = Revenue - Decrease in Accounts Receivable
= $38,000 - ($9,000 - $6,000)
= $35,000
Therefore, the answer is B. $35,000.
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Jason is a high school basketball player. In a particular game, he made some free throws (worth one point each) and some two point shots. Jason made a total of 13 shots altogether and scored a total of 20 points. Write a system of equations that could be used to determine the number of free throws Jason made and the number of two point shots he made. Define the variables that you use to write the system..
The system of equations that could be used to determine the number of free throws Jason made and the number of two point shots he made are: x + y = 13 and 1x + 2y = 20
How to answer the aforementioned questionsLet x be the number of free throws Jason made and y be the number of two-point shots he made.
Then, we can write a system of equations based on the given information:
x + y = 13 (total number of shots made)
1x + 2y = 20 (total number of points scored)
The first equation shows Jason's total number of shots, which include both free throws and two-point attempts.
The second equation indicates Jason's total amount of points, taking into account that two-point shots are worth twice as much as free throws.
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You want to estimate the proportion of individuals in your area who think the public school system needs major overhauling. If you believe the proportion will be about 35%, how many individuals will you need to sample if you want a 95% margin of error to be no more than 3%? at least 30 at least 1068 at least 972
We cannot have a fraction of a person in the sample, we need to round up to the next whole number, which is 1022.
So, you will need to sample at least 1022 individuals to achieve a 95% confidence level with a margin of error no more than 3%.
This means that the correct answer among the given options is "at least 1068".
To estimate the sample size needed for survey, you can use the formula for sample size calculation in a proportion estimation problem.
The formula is:
[tex]n = (Z^2 * p * (1-p)) / E^2[/tex]
where:
n = required sample size
Z = Z-score, which corresponds to the desired confidence level (1.96 for a 95% confidence level)
p = estimated proportion (0.35 in this case)
E = desired margin of error (0.03 in this case)
Now, let's plug the values into the formula:
[tex]n = (1.96^2 * 0.35 * (1-0.35)) / 0.03^2[/tex]
n = (3.8416 * 0.35 * 0.65) / 0.0009
n = 0.919326 / 0.0009
n ≈ 1021.473.
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Part A: Complete the square to rewrite the following equation in standard form. Show all
necessary work. (6 points)
x² - 4x + y² + 8y = -4
Part B: What are the center and radius of the circle? (4 points)
Answer:
A) (x - 2)² + (y + 4)² = 4²B) The center is (2, - 4), radius is r = 4 units-----------------------------
Standard form for the equation of a circle is:
(x − h)² + (y − k)² = r²,where the center is (h, k) and the radius is r units.
Part AComplete the square by adding missing parts of the identity:
(a ± b)² = a² ± 2ab + b²Apply this to the given equation:
x² - 4x + y² + 8x = - 4x² + 2(-2)(x) + (-2)² + y² + 2(4)(y) + 4² = - 4 + (-2)² + 4²(x - 2)² + (y + 4)² = - 4 + 4 + 4²(x - 2)² + (y + 4)² = 4²Part BAs per the standard form, the center is (h, k) = (2, - 4) and radius is r = 4 units.
Mr. and Mrs. Johnson took their three children to the movies. If adult tickets cost $7 and children's tickets cost $4, what is the ratio of the total cost of the parents' tickets to the total cost of the children's tickets? Write your answer in the form aib, where a and b are whole numbers.
Let's assume that Mr. and Mrs. Johnson bought x adult tickets and y children's tickets.
Since there are three children, we know that:
y = 3x
The total cost of the parents' tickets is 7x, and the total cost of the children's tickets is 4y. Substituting y = 3x, we get:
total cost of parents' tickets = 7x
total cost of children's tickets = 4(3x) = 12x
Therefore, the ratio of the total cost of the parents' tickets to the total cost of the children's tickets is:
(7x) / (12x) = 7/12
So the answer is 7/12, which cannot be simplified further. Therefore, the ratio is 7/12, which can be written in the form aib as 0+7/12i.
Answer: 7:6
Step-by-step explanation:
1. There are two adults (Mr. and Mrs. Jonhson) and three children. So let's make adults = y and children = x
2. Adult tickets cost $7. So we are going to multiply 7 x 2y = $14
3. Children's tickets cost $4. So we are going to multiply 4 x 3x = $12
4. The last step is to fully reduce [tex]\frac{14}{12}[/tex] = [tex]\frac{7}{6}[/tex]
5. So the answer is 7:6
Anthony has 35 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.) The area of the land is 132 square meters. List each set of possible dimensions (length and width) of the field.
The two possible sets of dimensions for the rectangular plot are:
Length = 27 meters, Width = 4 meters
Length = 4 meters, Width = 15.5 meters
Let's denote the length of the rectangular plot by L and the width by W. We know that the total length of the fencing needed is 35 m, which we can use to create an equation:
L + 2W = 35
The area of the land is 132 square meters, which we can use to create another equation:
LW = 132
We can solve the first equation for L:
L = 35 - 2W
Substituting this into the second equation, we get:
(35 - 2W)W = 132
Expanding and rearranging, we get a quadratic equation:
2W^2 - 35W + 132 = 0
We can solve for W using the quadratic formula:
W = [35 ± √(35^2 - 4(2)(132))] / (2(2))
W = [35 ± √(841)] / 4
W = [35 ± 29] / 4
Solving for W, we get two possible values:
W = 4 or W = 15.5
If W is 4 meters, then L is:
L = 35 - 2W = 27
If W is 15.5 meters, then L is:
L = 35 - 2W = 4
Therefore, the two possible sets of dimensions for the rectangular plot are:
Length = 27 meters, Width = 4 meters
Length = 4 meters, Width = 15.5 meters
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