What is the relationship between the foci, transverse axis, and asymptotes of a hyperbola?

Principal =P = $18,000

time = T = 10 years

(a) Simple interest

SI = P x R x T

Where:

R = simple interest in decimal form = 5/100= 0.05

SI = 18,000 x 0.05 x 10 = $9,000

Value of investment = 18,000 + 9,000 = $27,000

(b) compounded monthly

A = P (1 + r/n )^nt

Where:

A= future amount

n = number of compounding periods per unit t = 12

A= 18,000 (1 + 0.05/12)^12*10

A= $29,646.17

Answer:56000

Step-by-step explanation:

Answer:

300g for 7.49 has the best value

Step-by-step explanation:

200g for 5.69

200/5.69

35.15g for 1

300g for 7.49

300/7.49

40.05g for 1

Answer:

Yes, in a Cartesian Coordinate system each point is given by two numbers. If the question is "where" the function has a max or min value, that's "x", the first number in pair. If the question is "what" is that max or min function value, thats "y", the second number in the pair

The amount of money that is currently in the RRSP fund is approximately $117,303.70.

To know the amount of money in RRSP

Use the formula for the future value of an annuity:

\(FV = PMT * ((1 + r/n)^(n*t) - 1) / (r/n)\)

where:

FV = future value

PMT = regular payment

r = interest rate

n = number of compounding periods per year

t = number of years

For the first 5 years, we have:

PMT = $2,487.00

r = 6% per year, compounded quarterly, so r/n = 0.06/4 = 0.015

n = 4 quarters per year

t = 5 years

Plug the values into the formula

FV1 = $2,487.00 * (\((1 + 0.015)^(4*5)\) - 1) / (0.015)

= $39,947.05

For the last 9 years, we have:

PMT = $2,487.00

r = 8% per year, compounded quarterly, so r/n = 0.08/4 = 0.02

n = 4 quarters per year

t = 9 years

FV2 = $2,487.00 * (\((1 + 0.02)^(4*9)\) - 1) / (0.02) = $77,356.65

Sum up the two amounts to know the total future value in RRSP

FV_total = FV1 + FV2

= $39,947.05 + $77,356.65

= $117,303.70

Hence, the current balance in the RRSP is approximately $117,303.70.

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The question is incomplete, kindly find the complete question below

Sue has contributed $2,487.00 every three months for the last 14 years into an RRSP fund. The interest earned by these deposits was 6% compounded quarterly for the first 5 years and 8% compounded quarterly for the last 9 years. How much money is currently in the RRSP? The balance is $. (Round the final answer to the nearest cent as needed. Round intermediate values to four decimal places as needed

Answer:

58.1cm

Step-by-step explanation:

perimeter of a semi-circle = πd/2

d is the diameter

Given

diameter = 37cm

Perimeter of the semi circle =  π(37)/2

Perimeter of the semi circle = 18.5(3.14)

Perimeter of the semi circle = 58.09 cm

Hence the perimeter of the semi-circle is 58.1cm

Answer:

3

Explanation:

For every 3 cupcakes that Edgar gets, Fred gets 1. So, if Edgar gets 9, Fred gets 3.

The probability distribution for the 30 pieces of fruit, in the order listed, is:

a. 1/30, 3/30, 1/30, 4/30, 1/30, 5/30

To determine the probability distribution for the 30 pieces of fruit, we need to calculate the probability of each fruit appearing in the specified order.

Based on the given information:

Fruit: Apples, Bananas, Lemons, Oranges, Pears

Quantities: 6, 9, 2, 8, 5

To calculate the probability, divide the quantity of each fruit by the total number of pieces of fruit (which is 30 in this case).

The probability distribution for the 30 pieces of fruit, in the order listed, is as follows:

a. 1/30, 3/30, 1/30, 4/30, 1/30, 5/30

b. 1/30, 4/30, 2/30, 5/30, 10/30

c. 10/30, 15/30, 15/30

d. 1/30, 1/30, 1/30, 4/30, 2/30, 15/30, 5/30, 15/30, 15/30

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Answer:

It is the distribution of the statistic if we were to draw all possible samples of a given size from the population and calculate the statistic for each sample.

Step-by-step explanation:

The sampling distribution of a statistic refers to the range of all possible sample values of the statistic that could be drawn from the parent population under the specified sampling plan.

In other words, it is the distribution of the statistic if we were to draw all possible samples of a given size from the population and calculate the statistic for each sample.

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Answer:

To solve the equation (4x - 24) + x = 14, we can start by combining like terms on the left side of the equation:

4x - 24 + x = 14

Next we'll add the x terms together and the constants together:

5x - 24 = 14

Then we'll add 24 to both sides to get all the x terms on one side:

5x = 38

Finally we'll divide both sides by 5 to find the value of x:

x = 7.6

So the solution to the equation is x = 7.6

Answer:

Step-by-step explanation:

"or" means sum, that is all x≤-2 plus all x≥3

≤-2  mens all numbers less than -2 and the -2

≥3  mens all numbers greater than 3 and the 3

Answer:

(2, -1)

Step-by-step explanation:

The lines intersect at (2,-1), I graphed out the equations

the area of a circle with a rectangle will be [π w²2]/4.

What is the area of a circle?

The measurement of the circle's boundaries is called as the circumference or perimeter of the circle. whereas the circumference of a circle determines the space it occupies. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units like cm or unit m are typically used to measure it. The circle's radius is considered while calculating the circumference of the circle using the formula. As a result, in order to calculate the circle's perimeter, we must know the radius or diameter value.

area of the circle will be πr².

The area of a circle inscribed in a rectangle if the length of the rectangle is l and the width is w

= [π w²2]/4.

Hence the area of a circle with a rectangle will be [π w²2]/4.

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Skew lines and parallel lines do not intersect

As a general rule, skew lines are lined that are not on the same plane; they are not parallel to each other and they do not intersect

Using the above definition as a guide, the skew lines in the figure are:

Parallel lines and skew lines are different in the following ways:

Parallel lines and skew lines are alike in the following way:

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Answer:

x - 12

Step-by-step explanation:

Given

12 + ? = x ( subtract 12 from both sides )

? = x - 12

The other number is x - 12

Answer:

b = 25°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180° , that is

b + 110° + 45° = 180°

b + 155° = 180° ( subtract 155° from both sides )

b = 25°

Answer:

Step-by-step explanation: There are 8 people in the gym.

An hour later, there are double that number.

How many people are in the gym now?

Answer:

19

Step-by-step explanation:

Okay here , we are dealing with absolute values.

This means we shall be taking the positive values only of terms inside the double tube | |

So -7 absolute value is 7

and thus multiplied by 4 gives 28

and we are subtracting 9 from this;

This gives 28-9 = 19

Answer:

7.1 cm

Step-by-step explanation:

50 squared is closest to 7, which is the square root of 49.

A large population with a sample size of 30 or more has the smallest standard deviation, as the standard deviation is inversely proportional to the sample size. A smaller standard deviation indicates more consistent data. To minimize the standard deviation, the sample size depends on the population's variability, with larger sizes needed for highly variable populations.

If the population is large, a sample size of 30 or more will give the smallest standard deviation to the statistic. The reason for this is that the standard deviation of the sample mean is inversely proportional to the square root of the sample size.

Therefore, as the sample size increases, the standard deviation of the sample mean decreases.To understand this concept, we need to first understand what standard deviation is. Standard deviation is a measure of the spread of a dataset around the mean. A small standard deviation indicates that the data points are clustered closely around the mean, while a large standard deviation indicates that the data points are more spread out from the mean. In other words, a smaller standard deviation means that the data is more consistent.

when we are taking a sample from a large population, we want to minimize the standard deviation of the sample mean so that we can get a more accurate estimate of the population mean. The sample size required to achieve this depends on the variability of the population. If the population is highly variable, we will need a larger sample size to get a more accurate estimate of the population mean. However, if the population is less variable, we can get away with a smaller sample size.

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Answer:

The additive inverse is \(\frac{1}{2}\), and the multiplicative inverse is -2.

Step-by-step explanation:

Hope this helped!

The proportion of those surveyed who chose basketball as their favorite sport is 34.149 (option a)

Let's denote the proportion of adults who chose basketball as their favorite sport as P(Basketball). To calculate P(Basketball), we need to divide the total number of adults who chose basketball by the total number of surveyed adults. Mathematically, it can be represented as:

P(Basketball) = (Number of adults who chose basketball) / (Total number of surveyed adults)

To calculate the number of adults who chose basketball, we sum up the values from the age range categories:

Number of adults who chose basketball = Number of adults (18-30) who chose basketball + Number of adults (31-50) who chose basketball + Number of adults (51 and above) who chose basketball

Looking at the table, we find that the number of adults (18-30) who chose basketball is 15, the number of adults (31-50) who chose basketball is 8, and the number of adults (51 and above) who chose basketball is 11. Adding these values together, we get:

Number of adults who chose basketball = 15 + 8 + 11 = 34

Now, let's calculate the total number of surveyed adults. We can sum up the values from the age range categories:

Total number of surveyed adults = Total number of adults (18-30) + Total number of adults (31-50) + Total number of adults (51 and above)

From the table, we find that the total number of adults (18-30) is 49, the total number of adults (31-50) is 48, and the total number of adults (51 and above) is 52. Adding these values together, we get:

Total number of surveyed adults = 49 + 48 + 52 = 149

Now, we have the values we need to calculate the proportion:

P(Basketball) = (Number of adults who chose basketball) / (Total number of surveyed adults)

= 34 / 149

Hence the correct option is (a).

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The value of p is 0.18.

The value of \(\bar{p}\) (p with a hat on top) is 0.21.

The standard deviation of the sampling distribution of \(\bar{p}\) is approximately 0.024.

No, this school does not have an unusually high proportion of students that are vegetarian.

In this scenario, p represents the true population proportion of undergraduates in California colleges and universities who are vegetarians. The given information states that 18% (or 0.18) of all undergraduates are vegetarians.

\(\bar{p}\) (p with a hat on top) represents the sample proportion of vegetarians in the random sample drawn by the cafeteria management. They selected 300 students, and out of those, 63 identified as vegetarians. To calculate \(\bar{p}\) , we divide the number of vegetarians in the sample (63) by the sample size (300).

Therefore, \(\bar{p}\) = 63/300 ≈ 0.21.

The standard deviation of the sampling distribution of \(\bar{p}\), denoted as σ(\(\bar{p}\)), is calculated using the formula: σ(\(\bar{p}\)) = √[(p * (1 - p)) / n], where p is the true population proportion, and n is the sample size.

In this case, σ(\(\bar{p}\)) ≈ √[(0.18 * (1 - 0.18)) / 300] ≈ 0.024.

To determine if the school has an unusually high proportion of vegetarian students, we compare the sample proportion (\(\bar{p}\)) with the population proportion (p). Since \(\bar{p}\) (0.21) is greater than p (0.18), we can conclude that the observed proportion of vegetarians in the sample is higher than the expected population proportion.

However, without further context or a specific criterion for what constitutes "unusually high," we cannot definitively state whether the school's proportion of vegetarian students is considered unusually high.

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Answer:

y = -2x + 14

Step-by-step explanation:

OK so first u have to do y = -2x + b cuz its parallel

then u gotta just plug in the ordered pair so

6 = -2(4)+b

6 = -8 +b

14 = b

So now u have to do

y = -2x + 14

Answer:

52ft

Step-by-step explanation:

The ratio of false positives to true positives is 8 over 54.

According to the Question

Results of a strep throat test performed on a sample of 400 ill people are displayed in the table's data. People who have the flu and those who don't are separated into two categories. The patients are then separated into groups based on whether they tested positive or negative for strep throat within each of these categories.

We must first define what a true positive and a false positive are in order to calculate the ratio of false positives to true positives. A patient who tests positive for strep throat but does not actually have the illness is said to have a false positive. The 8% of patients in this instance who tested positive for strep throat but did not have the flu would fall under that category. A patient who tests positive for strep throat and truly has the illness is said to have a true positive. That would be the 54% of patients who tested positive for both the flu and strep throat in this instance.

We divide the percentage of false positives (8%) by the percentage of true positives (54%), which gives us the ratio of false positives to true positives.

As a result, the ratio becomes 8% / 54%, or 8/54.

It's critical to remember that this ratio is dependent on the sample and test performed and may not be the same for different populations or testing methodologies.

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the critical value or values of χ² based on the given information is 22.362.

To find the critical value(s) of the chi-square (χ²) distribution based on the given information, we need to follow these steps:

1. Determine the degrees of freedom (df): In this case, since the sample size (n) is 14, the degrees of freedom (df) would be n - 1, which is 13.

2. Identify the significance level (α): The given α value is 0.05.

3. Determine the critical value(s): Since the alternative hypothesis (H1) states that σ > 3.5, we are dealing with a right-tailed test. Using a chi-square table or calculator, find the critical value corresponding to df = 13 and α = 0.05.

Based on the given information, the critical value of χ² with 13 degrees of freedom and a significance level of 0.05 for a right-tailed test is approximately 22.362.
The critical value of the χ² distribution is approximately 22.362.

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