If an object is dropped from a height of 150 ft, giving the equation,
h=-16x^2 + 150, what is the maximum height of the object? *

Answer: y = 1/2x - 4.5

Step-by-step explanation:

\(\displaystyle\\Answer:\ y=\frac{1}{2}x-4.5\)

Step-by-step explanation:

\(\displaystyle\\The\ slope\ =m=\frac{1}{2} \ \ \ \ \ (5,-2)\\y=mx+b\\-2=\frac{1}{2}*5+b\\\\ -2=\frac{5}{2}+b\\\\ -2=2.5+b\\\\-2-2.5=2.5+b-2.5\\\\-4.5=b\\\\Hence,\\\\y=\frac{1}{2} x-4.5\)

The number of women working for the company is 161 if the ratio of men to women working for a company is 5:7.

The ratio of men to women working for a company is 5:7

Let 5x be the total men and 7x be the total women working for the company:

Total employees  = 276

5x + 7x = 276

12x = 276

x =276/12

x = 23

Total men = 5x = 5(23) = 115

Total women = 7x = 7(23) = 161

Thus, the number of women working for the company is 161 if the ratio of men to women working for a company is 5:7.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value.

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Answer:

12:45 pm

Step-by-step explanation:

She started at 8:15 we can add the 15 minutes to 30 minutes and get 45 minutes  then we add the 4 hours to 8 am  and get 12 pm. add the 45 minutes and you get 12:45 pm

Answer:

Option (D)

Step-by-step explanation:

Rate of emptying the fuel tank = 7.5 liters per minute

Fuel emptied in x minute = 7.5x liters

Volume of the fuel in the fuel tank initially = 175 liters

Therefore, amount of fuel left in the tank after x minutes = (175 - 7.5x) liters

Function representing the emptying of the fuel tank will be,

f(x) = 175 - 7.5x

Option (D) will be the answer.

Answer:

\(\frac{1}{2}(4.5 + x) = 13.5\)

Step-by-step explanation:

To find - What is the equation that corresponds to the following expression ? : The half of the sum of 4.5 and another number is equal 13.5

Solution -

Let the another number be x

Given that ,Half of the sum of 4.5 and x  is equals to 13.5

So,

The expression becomes

\(\frac{1}{2}(4.5 + x) = 13.5\)

Answer:

30

Step-by-step explanation:

18+21= 41

71-41=30

m=30

SSS congruence rules states that if three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.

The SSS (Side-Side-Side) congruence rule states that if three sides of one triangle are equal to the three sides of another triangle, equal, and the two triangles share the same dimensions then the two triangles are congruent. This means that all of the angles and sides of the two triangles are In order for two triangles to be congruent according to the SSS congruence rule, the lengths of the three corresponding sides of the two triangles must be equal. If all three of these conditions are met, then the two triangles are congruent and can be used to solve a variety of geometric problems.

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The SSS congruence rule is rule that is used to prove two triangles congruent . Its full form is Side-Side-Side Congruence .

The Two Triangles can be called as  Congruent Triangles if their sides have same length and the angles also have the same measure.

One of the 4 rules in proving the triangles congruent is SSS .

The SSS Congruence Rules also called as (Side-Side-Side) Rule means that if all the three sides of one triangle are equal to the corresponding three sides in the other triangle ,

then we can say that the two triangles are congruent by SSS (Side-Side-Side) Rule .

Therefore , The SSS Congruence rule means Side-Side-Side Congruence .

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The theater will receive approximately $1789.62 when it cashes in the CD after 30 months by using compound interest

To calculate the amount the theater will receive when cashing in the CD after 30 months, we can use the formula for compound interest:

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

Where:

A is the final amount,

P is the principal amount (initial investment),

r is the annual interest rate (expressed as a decimal),

n is the number of times the interest is compounded per year, and

t is the number of years.

In this case, the principal amount is $1600, the annual interest rate is 4.244% (or 0.04244 as a decimal), the interest is compounded monthly (n = 12), and the investment period is 30 months (t = 30/12 = 2.5 years).

Plugging in the values into the formula, we get:

A = 1600(1 + 0.04244/12)^(12*2.5) ≈ $1789.62

Therefore, the theater will receive approximately $1789.62 when it cashes in the CD after 30 months.

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Answer:

8

Step-by-step explanation:

if you take 20 divided by 2.50 it'll give you 8. So she can buy 8 fish at 2.50 a piece with 20 dollars.

Answer:

Step-by-step explanation:

The answer is just 5

f(5)=5

The translational angular momentum of the space junk about location D just before the collision can be found by plugging the values of r_perp and p.

To calculate the translational angular momentum of the space junk about location D, we need to consider its linear momentum and the perpendicular distance from location D to the line of motion.

Step 1: Identify the linear momentum of the space junk
Linear momentum (p) is the product of mass (m) and velocity (v). Assuming we know the mass and velocity of the space junk, we can find its linear momentum:

p = m * v

Step 2: Determine the perpendicular distance (r_perp) from location D to the line of motion
As mentioned, r_perp remains the same at locations A, B, and just before reaching C.

Step 3: Calculate the translational angular momentum (L) about location D
Translational angular momentum is given by the formula:

L = r_perp * p

Since r_perp and p remain constant at locations A, B, and just before reaching C, the translational angular momentum of the space junk about location D will be the same at all these locations.

So, the translational angular momentum of the space junk about location D just before the collision can be found by plugging the values of r_perp and p into the formula above.

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Answer:

T=4

l=11.60

Step-by-step explanation:

T is for time,and time given is 4.

so t=4 years

and Interest given is 11.60 bucks

so I=11.60

keep in mind that PRINCIPAL IS NEVER A PERFENTAGE!

RATE IS ALWAYS A PERCENTAGE!

Here, principal is 100 bucks and rate is 2.9%

also keep in mind that principal isnalways greater than interest.

thank you

On average, Peter owes $127.50 on his credit card each day. His credit card has an annual interest rate of 14.99%. His finance charge for the month is $1.59.

Simple interest is calculated using the following formula: Simple Interest (SI) is calculated as P R T / 100. P stands for the principal sum, R for the interest rate, and T for the interest period. The total amount due is the sum of the principal plus the simple interest, or P + SI.

Most frequently, interest is shown as a yearly percentage of the loan amount. The interest rate on the loan is this particular percentage. For instance, if you put money in a high-yield savings account, a bank will provide you interest.

Simple (regular) interest, accumulated interest, and compound interest are the three different types of interest.

Average daily balance times  x monthly interest = the monthly finance fee.

14.99% / 12 = 1.249% per month for interest

1.249% x $127.50 = $1.59

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Answer:

b = 12.5 ft

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = \(\frac{1}{2}\) bh ( b is the base and h the perpendicular height )

Here A = 25 and h = 4 , then

\(\frac{1}{2}\) × 4 × b = 25 , that is

2b = 25 ( divide both sides by 2 )

b = 12.5 ft

The following is true about the study: e. It has one factor (medication) blocked by age.

In statistics, when a factor (independent variable) is blocked by another factor, it means that the effect of the first factor is controlled or eliminated by the second factor.

In this case, the factor that is blocked is the medication, which means that the effect of medication on the outcome variable is controlled by age.

Blocking a factor is often done in experimental design to remove the effects of extraneous variables or to control the influence of certain factors on the outcome variable.

In this case, age is considered a blocking variable because it is not of interest in the study, but it may have an effect on the outcome variable. By blocking the effect of medication by age, the study can better isolate the effect of medication on the outcome variable.

In summary, the statement e. "It has one factor (medication) blocked by age" is correct which means that the study controlled for the effect of age on the outcome variable by blocking the effect of medication by age.

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Answer:

20km/h

Step-by-step explanation:

use the speed distance time formula

it takes 45mins to get to the park which is 0.75 of an hour

20/0.75 = 20km/h

Answer:

7.5

Step-by-step explanation:

The rate of change in the given graph is 21/4.

The rate of change defines the speed of a variable changes over another variable. On the given graph, we can calculate the rate of change using the formula:

Rate of change = Δy / Δx

To calculate the rate of change of the given graph, we need to identify 2 points first. We take:

(0, 0)

(4, 21)

Rate of change = Δy / Δx

Rate of change = y₂ - y₁

                             x₂ - x₁

Rate of change = 21 - 0

                               4 - 0

Rate of change = 21/4

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Answer:

4.25

Step-by-step explanation:

she has a total of 20 dollars and she wats to buy ice cream each at 3.15 for a total of 5 people including her self.

so 3.15(5) is 15.75

then subtract 15.75 from 20

20 - 15.75 = 4.25

The monthly payment during the second year of the mortgage, when the interest rate increases to 5%, is approximately $1,654.58. To compute the monthly payment during the second year of a variable rate mortgage, we need to consider the loan amount, the interest rate, and the loan term.

Loan amount: $325,000

First-year teaser rate: 3.11%

Rate for the second year: 5%

To calculate the monthly payment during the second year, we can use the formula for calculating the fixed monthly payment on a mortgage:

Monthly payment = (Loan amount * Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-n))

Where:

Loan amount = $325,000

Monthly interest rate = Annual interest rate / 12

Annual interest rate for the second year = 5%

n = Total number of monthly payments (12 payments in a year)

First, we calculate the monthly interest rate for the second year:

Monthly interest rate = 5% / 12 = 0.4167%

Next, we substitute the values into the formula:

Monthly payment = ($325,000 * 0.4167%) / (1 - (1 + 0.4167%)^(-12))

Using a calculator, we can evaluate this expression:

Monthly payment ≈ ($325,000 * 0.4167%) / (1 - (1 + 0.4167%)^(-12)) ≈ $1,654.58

Therefore, the monthly payment during the second year of the mortgage, when the interest rate increases to 5%, is approximately $1,654.58.

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Michael needs to analyze the population data, demographics of the city, and the competition in the area to determine whether or not to open a new store.

Michael is trying to determine where to open two new store locations. He has population data to determine the amount of revenue he will receive for each location.

He is charged a $1000 fee for opening a new store at a certain location. However, he is unsure whether the population of the city would be large enough to warrant opening a new store at that location.

The first step that Michael needs to take is to analyze the population data that he has.

Based on the population data, he needs to make an informed decision about whether or not to open a new store at that location. This would require him to take into consideration the average income of the population as well as the demographics of the city.

Another important factor that Michael needs to take into consideration is the competition in the area. If there are already several stores in the area, then opening a new store might not be a good idea.

This is because the competition would be too high and he would not be able to generate enough revenue to make up for the cost of opening a new store.

However, if there are no stores in the area, then Michael might consider opening a new store. This would require him to invest a significant amount of money, but he could also generate a significant amount of revenue in return.

Additionally, he needs to take into consideration the cost of opening a new store and whether or not he can generate enough revenue to make up for that cost.

Overall, Michael needs to carefully analyze all the data that he has before making an informed decision about where to open new store locations.

In conclusion, Michael needs to analyze the population data, demographics of the city, and the competition in the area to determine whether or not to open a new store. If the population is large enough and there is no competition in the area, then he should consider opening a new store. However, if there is already a significant amount of competition in the area, then he should avoid opening a new store.

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Answer:

5 feet each

Step-by-step explanation:

So we know that 4 pieces of rope out of 5 are equal. So, we simply subtract 10 from 30 for that 10-foot piece of rope, which leaves us with 20. Divide 20 by 4 (since there is 4 pieces of rope of equal value) and it leaves us with 5 feet.

Hope I helped! :)

Interest earned on the cash balance in the bank is recorded by the bank as an increase in the depositor’s bank account.

A savings account is a type of account that can be opened with a bank. Savings account earn interest based on the amount of money in their account at the end of the month.

here. we have.

The interest that is earned depends on the number of withdraws, interest rate paid on deposits and the amount deposited in the account.  Deposits are recorded as a liability in the balance sheet of a bank. A liability is an obligation that has to be paid at sometime in the future.

This means that at the end of the month, the value of the money in the depositor's saving account increases by the value of interest paid.

For example, if the interest paid by a bank on deposits in a savings account is 10%. If an account has $1000 in the account, the value of the amount at the end of the month is 1,100 (1000 x 1.1).

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Answer:

-------------------------------

Substitute the coordinates of each point and solve the formed system:

So the value of coefficients is a = 2, b = 3.

The Median of the data shown on the line plot is 6.5.

The median of a line plot The median is the central value in a data set that is arranged in numerical order from least to greatest. In other words, the median is the middle number of a set of data. To find the median of a set of data on a line plot, follow the steps below:

Step 1: Arrange the data in numerical order from least to greatest. In the line plot provided above, the data is already arranged in order from least to greatest. It ranges from 4 to 12.

Step 2: Determine the total number of data points. In this case, there are 8 data points.

Step 3: Identify the middle value in the data set. This is done by dividing the total number of data points by 2 (the middle point). If the number of data points is even, the median is the average of the two middle values. If the number of data points is odd, the median is the middle value itself. Since there are 8 data points in the line plot above, we have an even number of data points. The two middle values are 6 and 7, so the median is the average of these two values.

Step 4: Calculate the median. Add the two middle values (6 and 7) together and divide by 2:6 + 7 = 13 13/2 = 6.5

Therefore, the median of the data shown on the line plot is 6.5.

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Answer:

y= 2 and x= -4

Step-by-step explanation:

From the given linear functions, the ordered pairs that represents a function is A= {(-6, 6),(-3, 2),(0, -1) (3, 5})

A set of ordered equation represents a linear function if the domain of the coordinates are not repeated.

For instance, the ordered pairs that is a function are the coordinates that do not have any repeated x-coordinates.

From the given linear functions, the ordered pairs that represents a function is A= {(-6, 6),(-3, 2),(0, -1) (3, 5})

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If the p-value is greater than 0.01, then there is insufficient evidence to reject the null hypothesis and the publisher's claim cannot be substantiated.

The null hypothesis for this scenario would be that the proportion of newsletter readers who own a Rolls Royce is equal to or greater than 58%. The alternative hypothesis would be that the proportion of newsletter readers who own a Rolls Royce is less than 58%. To determine whether there is sufficient evidence to substantiate the publisher's claim, a hypothesis test would need to be conducted using a significance level of 0.01. The test would involve collecting a random sample of newsletter readers and calculating the proportion who own a Rolls Royce. If the p-value (probability value) associated with the test is less than 0.01, then there is sufficient evidence to reject the null hypothesis and conclude that the proportion of newsletter readers who own a Rolls Royce is indeed less than 58%.

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