This graph models the number of teachers assigned to a school, as determined by the number of students. What is the constant of proportionality?

1/25
1/20
1/15
1/10

The questions are:

This is best answered using a Venn diagram. If you look at the separate areas, you see there are 7 areas.

The common area is the two students who takes the three classes.

4 said they were taking both math and English 

4 – 2 = 2 only take math & English

7 said they were taking both science and math

7 – 2 = 5 only take math and science

10 said they were taking both science and English

10 – 2 = 8 only take science and English

17 said they were taking English

17 – (2 + 8 + 2) = 5 take only English

22 said they were taking math

22 – (2 + 5 + 2) = 13 take math

24 said they were taking science

24 – (2 + 8 + 5) = 9 only take science

Adding them all up:

2 + 9 + 13 + 5 + 8 + 5 + 2 = 44

So, 44 students are taking the 3 courses

53 – 44 = 9 students are not taking any of the 3 courses

5 + 13 + 9 = 27 take only 1 of these courses

The value of the equation after the division and simplification is A = 7/24 or A = 0.291667

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first fraction be p = 1/6

Let the second fraction be q = 4/7

Now , the equation is A = p/q

On dividing the terms p and q , we get

Substituting the values in the equation , we get

A = ( 1/6 ) / ( 4/7 )

On simplifying the equation , we get

A = ( 1/6 ) x ( 7/4 )

A = 7/24

So , the value of A after division is

Now , on further simplification , we get

A = 0.291667

Hence , the equation after simplification is A = 0.291667

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Erving Spencer contributes $60 to his pension every paycheck, with a biweekly pay schedule on a $24,000 yearly salary. Regarding the retirement funds, after 30 years, Alexx would have more money than Spenser because Alexx's investment grows at an unimpeded 5% annually, while Spenser's grows at 4.75% annually after fees.

Firstly, let's address the question about Erving Spencer's pension contributions per paycheck. Erving Spencer makes $24,000 a year and is paid biweekly, which means there are 26 paychecks in a year. To calculate how much goes into the pension every paycheck, we apply the percentage of the pension contribution to each paycheck:

Now, let's perform the calculations:

Contribution per paycheck = ($24,000 / 26) * 0.065

= $923.08 * 0.065

= $60

Therefore, $60 goes into Erving Spencer's pension every paycheck.

Now, for the question about the retirement fund's administrative fee:

Alexx and Spenser each invest $5,000 in the same stock. Alexx's investment grows by 5% annually without any fees, while Spenser's grows by 4.75% annually after a 0.25% fee. After 30 years:

We can calculate the final amounts and then find the difference between them, which would be how much more Alexx has than Spenser after 30 years.

The probability that the stock closed at less than the mean for that year is approximately 0.5, assuming a normal distribution.

1. In a normal distribution, the mean divides the distribution into two equal halves, with 50% of the data falling below the mean and 50% above it.

2. Therefore, the probability that a randomly chosen data point (in this case, the closing price of  stock) is below the mean is 0.5 or 50%.

Now, let's dive into the step-by-step calculation to illustrate this:

1. Identify the Mean and Standard Deviation: While you mentioned not to calculate the mean, it's important to understand that for a normal distribution, the mean is at the center and separates the distribution into equal probabilities on either side. However, we do need to know the standard deviation, which measures the spread of data points around the mean. Let's assume the mean closing price for stock over the past year is $X, and the standard deviation is $Y.

2. Use the Standard Normal Distribution: Since we're dealing with a normal distribution, we can use the standard normal distribution to find probabilities. This distribution has a mean of 0 and a standard deviation of 1.

3. Standardize the Data: To work with the standard normal distribution, we need to standardize the data point we're interested in. Let's denote the closing price of  stock on the chosen day as $Z. We standardize this value using the formula:

  [tex]\[ Z = \frac{{Z - X}}{{Y}} \][/tex]

  Here, ( Z ) is the standardized value.

4. Find the Probability: Once we have the standardized value ( Z ), we can look it up in a standard normal distribution table or use software/tools to find the probability that a randomly chosen value from a standard normal distribution is less than ( Z ). This probability will be the same as the probability that the stock closed at less than the mean for that year.

5. Conclusion: Based on the properties of a normal distribution, the probability that a randomly chosen data point (stock closing price) is below the mean is always 0.5 or 50%. This holds true regardless of the specific mean or standard deviation values for  stock.

complete question

And 1. if a person bought 1 share of  stock within the last year, what is the probability that the stock on that day closed at less than the mean for that year? hint: you do not want to calculate the mean to answer this one. the probability would be the same for any normal distribution.

Answer:

$972

Step-by-step explanation:

Ajax buys 20 shares of stock at $20.

The cost of 20 shares = 20 × $20 = $400

The shares increase in value by 20%

Now the cost of 20 shares = 400 + (20%×400)

                                            = 400 + 80

                                            = $480

Cost per share =  [tex]\frac{480}{20}[/tex] = $24

He sells 10 shares = $20 × 10 = $240

Now he has 10 share costs $240

After the shares decrease in value by 10%, he buys another 20 shares.

Cost per shares after decrease by 10% = 24 - (10%×24)

                                                                 = 24 - 2.40

                                                                 = $21.60

He buys 20 shares and his remaining 10 shares = 20 + 10 = 30 shares

Cost of 30 shares = 21.60 × 30 = $648

The shares then all increase by 50% = 648 + (50% × 648)

                                                             = 648 + (0.5 × 648)

                                                             = 648 + 324

                                                             = $972

The total value of the 30 shares that Ajax own is $972

There are 6 sides of the die, let us say that side 1 is S1, side 2 is S2 and so on.

Assigning a value of 3 to S1, so the probabilities are:

                                          Probability

S1 = 3                                    3/8

S2 = 1                                    1/8

S3 = 1                                    1/8

S4 = 1                                    1/8

S5 = 1                                    1/8

S6 = 1                                    1/8

total = 8                               

The combinations that the sum of the two rolls will be 4 are:

S1 and S3

S3 and S1

S2 and S2

So the total probability is:

P = (3/8) * (1/8) + (1/8) * (3/8) + (1/8) * (1/8)

P = 0.1094 = 10.94%

So there is about 0.1094 or 10.94% probability that the sum will be 4.

Answer: [tex]\frac{1}{4}[/tex]

Step-by-step explanation: If this is from a quiz from Buzz (Acceleration Education) Then this is the answer.

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let x = bagels

0.75x +1.29 <= 7.00

solve:

0.75x +1.29<=7.00

0.75x <= 7.00 - 1.29

0.75x <=5.71

5.71 /0.75 = 7.6

x<=7 bagels

The smaller of two consecutive integers is 9.

Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers.

For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.

Given that, three times the smaller of two consecutive integers is added to four times the larger, the result is 67, we need to find the smaller integer,

Let the two consecutive integers be, x and x+1,

Establishing the equation according to the question,

3x + 4(x + 1) = 67

7x + 4 = 67

7x = 67-4 = 63

x = 9

Hence, the asked smaller integer is 9.

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To calculate the total dividend PRH will receive, multiply the dividend per share by the number of shares PRH owns.

To calculate how much PRH will receive in dividends, we need to know the number of shares PRH owns. Let's assume PRH owns X number of shares. We can multiply the dividend of $56.25 per share by the number of shares to find the total dividend PRH will receive.

Total Dividend = $56.25 x X

For example, if PRH owns 100 shares, the total dividend will be $56.25 x 100 = $5625.

Without knowing the number of shares PRH owns, we cannot calculate the total dividend payment. With the number of shares, multiply by the dividend per share ($56.25) to get the total dividends. For present value calculations, divide the PDV of profits by the number of shares to get the price per share.

To determine how much PRH will receive in dividends from Marks Brothers, a specific number of shares owned by PRH would be needed. Without this information, we cannot calculate the exact dividend payment to PRH. However, if we had the number of shares, we would multiply that number by the dividend per share, which is $56.25, to find the total dividend payment PRH would receive.

For example, if PRH owns 10 shares, the calculation would be 10 shares × $56.25 per share = $562.50 in total dividends. To understand the calculations surrounding the present value or PDV, consider that a different PDV calculation needs to be done for amounts received at different times. Once the PDV of total profits is calculated, it can be divided by the number of shares to find the price per share. Using the provided example with a total PDV of profits being $51.3 million and 200 shares, the calculation would be $51.3 million / 200 = 0.2565 million or $256,500 per share.

Note that in the real world, expected profits are estimates rather than exact figures, and determining an accurate interest rate is part of that estimation process.

Final answer:

The stone would be 579 feet high after 3 seconds.

Explanation:

To calculate the height of the stone 3 seconds later, we can use the kinematic equation for position:

h = h0 + (v0 · t) + ((1/2) · a · t2)

where:

h is the final height

h0 = 675 feet is the initial height

v0 = 16 ft/s is the initial velocity

t = 3 seconds is the time

a = -32 ft/s2 is the acceleration due to gravity

Let's plug in the values and calculate:

h = 675 + (16 · 3) + ((1/2) · (-32) · 32)

Solving this equation, we get:

h = 675 + 48 - 144

h = 579 feet

The balloon payment is approximately $1,084,898.37.

To calculate the balloon payment, we first need to determine the remaining balance of the mortgage after the initial 22 years of payments (30 years total - 8 years).

Step 1: Calculate the monthly interest rate.

Monthly interest rate = Annual interest rate / 12

Monthly interest rate = 6.4% / 12 = 0.00533

Step 2: Calculate the number of payments made in 22 years.

Number of payments = 22 years * 12 months/year = 264 payments

Step 3: Use the formula for the remaining balance of a mortgage.

Remaining balance = [tex]P * [(1 + r)^n - (1 + r)^t] / [(1 + r)^n - 1][/tex]

Where:

P = principal amount of the loan

r = monthly interest rate

n = total number of payments

t = number of payments already made

Substitute the given values into the formula:

Remaining balance = $1,640,000 * [(1 + 0.00533)^360 - (1 + 0.00533)^264] / [(1 + 0.00533)^360 - 1]

Remaining balance = $1,084,898.37

The balloon payment is the remaining balance after 22 years. Therefore, the balloon payment is approximately $1,084,898.37.

The expected number of bad apples is [tex]\( \frac{2}{10} \times 3 = 0.6 \) bad apples.[/tex]

The expected number of bad apples when grabbing 3 apples from a pool of 10, of which 2 are bad, can be calculated using probability.

To calculate this, follow these steps:

1. Calculate the probability of picking a bad apple:

  The probability of picking a bad apple is the ratio of the number of bad apples to the total number of apples. In this case, it's [tex]\( \frac{2}{10} = 0.2 \) or 20%.[/tex]

2. Multiply the probability by the number of apples picked:  

  Multiply the probability of picking a bad apple by the number of apples you're picking.  

 [tex]\( 0.2 \times 3 = 0.6 \)[/tex]

When you pick 3 apples randomly from a pool of 10, you're essentially conducting a sampling experiment. The probability of picking a bad apple on any given pick is[tex]\( \frac{2}{10} \),[/tex]  which simplifies to 0.2 or 20%.

Since you're picking 3 apples, you multiply the probability of picking a bad apple by 3 to find the expected number of bad apples. This is because in expectation, you would expect that proportion of bad apples in your sample. So, [tex]\( 0.2 \times 3 = 0.6 \)[/tex], which means you would expect to pick approximately 0.6 bad apples when picking 3 from the pool of 10, assuming the picking is random.

So, the final answer is that you would expect about 0.6 bad apples when picking 3 apples from a pool of 10, of which 2 are bad.

complete question

There are 10 apples in the fridge and 2 of them are bad. if you grab 3 apples, what is the expected number of bad apples

Answer:

$233.75Step-by-step explanation: