A local university has a current enrollment of 12,000 students. The enrollment is increasing continuously at a rate of 2. 5% each year. Which logarithm is equal to the number of years it will take for the population to increase to 15,000 students?

Answer:

12996

Step-by-step explanation:

The cost of the plan for the limited talk and text is $50 with an additional cost of $22.99 for each gigabyte of data.

Generally, a mathematical function means a rule that gives value of a dependent variable that corresponds to specified values of one or more independent variables. It can take an input from many variables but will  always give the same output, unique to that function.

We are given that "H(g) = 22.99g + 50", where H represents the cost, in dollars, and g represents the number of gigabytes of data. The main answer is based on the given function where the constant term of 50 represents the cost of the plan for limited talk and text, and the coefficient of 22.99 represents the additional cost for each gigabyte of data used.

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The safe distance between the supports to carry the load of 1500 pounds is found to be 8 meters.

One kind of proportionality relationship is inverse proportion. If two quantities remain inversely related, one will increase while the other will decrease.

The area of a circle is proportional to its radius, which serves as an illustration of direct proportion.

The equation for inverse proportion of the weight carried along with distance is:

P = 5400 /D

P is load in pounds (lb)

D is the safe distance.

Then, distance to carry 1500 lb of load is:

1500 lb = 1500*0.45 kg

1500 lb = 675 kg

675  = 5400 /D

D = 5400/675

D = 8 meters

Thus, safe distance between the supports to carry the safe load of 1500 pounds is found to be 8 meters.

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The estimated total percentage of the company that exercised at least 3 times a week is approximately 20.5%.

Using the Hansen-Hurwitz dropout plan (method), the estimated total percentage of the company that exercised at least 3 times a week is approximately 20.5%. This can be calculated by multiplying the response rate of the survey (4860/6480) by the response rate of the sample (7/80).

The response rate of the survey is 0.7479 and the response rate of the sample is 0.0875. To get the estimated total percentage of the company that exercised at least 3 times a week, you would multiply these two numbers together to get 0.205 (0.7479 x 0.0875 = 0.205).

So, the percentage is 20.5%.

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The height of the parallelogram is 9 cm.

To find the height of a parallelogram with a given base and area, we can use the formula:

Area = base x height

In this case, we are given that the base of the parallelogram is 12 cm and the area is 108 sq. cm. Substituting these values into the formula, we get:

height = 108/12

Simplifying this expression, we get:

height = 9cm

A parallelogram is a four-sided polygon with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length and parallel to each other. The opposite angles are also equal in measure, meaning that the adjacent angles are supplementary (their sum is 180 degrees).

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Answer:

B

Step-by-step explanation:

He was accepted to UCLA's School of Management

Answer:

The answer would be 80.

Step-by-step explanation:

First you want to add 16 and 24.

Next you want to multiply that answer by 2.

Then you have your answer and I hope this helps

Answer:

17

Step-by-step explanation:

The diameter of the wheel is approximately 1.918 meters.

We can use the formula:

distance traveled = circumference of wheel x number of rotations

The circumference of the wheel is equal to the distance traveled in one rotation, which is equal to the diameter of the wheel times pi (π). So we can rewrite the formula as:

distance traveled = (diameter of wheel x π) x number of rotations

where d is the diameter of the wheel.

We are given that the bicycle travels 30.09 meters and the wheel makes five rotations, so we can plug in these values:

30.09 = (d x π) x 5

Solving for d, we get:

d = 30.09 / (π x 5)

d ≈ 1.918 meters

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Answer:

Below

Step-by-step explanation:

The interior angles of ANY triangle add up to 180 degrees

   you want to divide this 180 into   2 + 3 + 4 = 9  parts

       180 / 9 = 20 degrees for each part

           2 parts = 2 * 20 = 40 °

          4 parts = 4 * 20 = 80 °

According to the image, we can see that 3 rectangles are half-shaded= 1.5 units²,

A square is a quadrilateral with four equal sides and four equal angles that is a regular quadrilateral. The square's angles are at a straight angle or 90 degrees. The square's diagonals are also equal and split at a 90-degree angle.

A rectangle with two opposite sides that have the same length can also be referred to as a square.

P.S: Rectangle attached in image.

According to the image, we can see that 3 rectangles are half-shaded.

This means that:

Half-shaded square + Half-shaded square + Half-shaded square

=> 0.5 + 0.5 + 0.5

=> 1.5 units²

Check:

To check our answer:

3 x 0.5 = Area of rectangle

=> 1.5 units² = Area of rectangle

Hence, our explanation is correct.

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Answer:

10

Step-by-step explanation:

We can use the distance formula to find the distance between the two points:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Plugging in the coordinates of A and B, we get:

Distance = √((-2 - 6)^2 + (-1 - 5)^2)

Distance = √((-8)^2 + (-6)^2)

Distance = √(64 + 36)

Distance = √100

Distance = 10

Therefore, the distance between A(6, 5) and B(−2, −1) is 10 units.

Answer:

The first person to answer was correct, the answer is 301 m squared.

Step-by-step explanation:

I took the quiz so you don't have to! <3

Answer: The equation for the 7th grade is y = 5x + 7, where y is the total number of items collected and x is the number of days. The initial value is 7 and the slope is 5.

The equation for the 8th grade is y = 8x + 20, where y is the total number of items collected and x is the number of days. The initial value is 20 and the slope is 8.

Therefore, the 8th grade has a greater slope (8) compared to the 7th grade (5). The 8th grade also has a greater initial value (20) compared to the 7th grade (7).

Step-by-step explanation:

Bi-weekly gross paycheck based on 40 hours a week at a rate of $18.25 per hour is $1,460.

What is multiplication ?

Multiplication is a basic arithmetic operation that involves combining two or more numbers to find their product or the total number of items when a certain number is repeated a certain number of times. In multiplication, the numbers being combined are called factors, and the result is called the product.

To calculate your bi-weekly gross paycheck, you need to multiply your hourly rate by the number of hours you work per week and then multiply that by 2 to account for two weeks in a pay period.

Hourly rate: $18.25

Weekly hours: 40

Bi-weekly hours: 40 x 2 = 80

Bi-weekly gross paycheck: Hourly rate x Bi-weekly hours

Bi-weekly gross paycheck: $18.25 x 80 = $1,460

Therefore, your bi-weekly gross paycheck based on 40 hours a week at a rate of $18.25 per hour is $1,460.

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Answer: 3 mph

Step-by-step explanation:

I did it in mah brain

The value of x in the given digram using trigonometry to the nearest tenth is 7.15.

In planar geometry, an angle is a form created by two rays or lines that terminate in the same place. The name "angle" comes from the Latin "angulus," which means "corner". The vertex and the two rays, which are referred to as the sides of an angle, are the shared termini of two rays.

Given an angle and the length of the adjacent side, we are to determine the value of the hypotenuse using cos.

Cos = adjacent / hypotenuse

cos 33 = 6 /x

x = 6 / cos 33

x = 6 / 0.83867

x = 7.15

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The algebraic expression that represents the sentence "N increased by 25%" is 0.25N.

Hence the correct option is A.

This means that N is multiplied by 0.25 or 1/4. To find the result of N increased by 25%, you simply need to multiply N by 0.25 and add the result to the original value of N. The option A, 0.25N, represents this concept in a clear and concise manner.

The other options (B, C, and D) are either incomplete or incorrect. It is important to understand the concept of percentage increase and how it is represented algebraically, as it is a common operation in many mathematical and real-life scenarios, such as calculating interest rates, growth rates, and inflation rates.

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Using the information provided, we can construct a 90% confidence interval for the mean number of hours a student studies per week as follows: (15.34, 16.66).

The given problem involves estimating the mean hours of studying per week for a population of students using a confidence interval. A simple random sample of 55 students is taken, and the sample mean is computed to be 16 hours per week. The population standard deviation is assumed to be known to be 3.1 hours per week. Using the formula for a confidence interval for the population mean with known standard deviation and a significance level of 0.10 (corresponding to a 90% confidence level), the lower and upper bounds of the interval are calculated to be 15.19 and 16.81 hours per week, respectively. This means that we can be 90% confident that the true mean hours of studying per week for the population of students lies within this interval

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Complete question:

A professor wants to estimate how many hours per week her students study. A simple random sample of 55 students had a mean of 16 hours of studying per week. Construct a 90% confidence interval for the mean number of hours a student studies per week. Assume that the population standard deviation is known to be 3.1 hours per week. Round to two decimal places.

Answer:

Step-by-step explanation:

Hi there I am able to help so when you do 8,552/16 it is best to reverse it then add the expression, what I mean by that is translating expressions. the answer would be 444.23 then you would want to add (480/16) no mental math how you would do this is the recalabric way, take 480/16 and put in an a fraction to make it work easier than the rest of your problems you would do the same things its simple, just repeat what I did to all the other problems,

regards, me

Mr. Donovan still needs to spend at least $70.15 in the restaurant this month to meet the Angler's Club requirement.The inequality that describes the situation is:250 - 179.85 ≤ x

where x represents the amount of money Mr. Donovan still needs to spend in order to meet the Angler's Club requirement.

To solve for x, we first subtract 179.85 from 250 to get:

70.15 ≤ x

Therefore, Mr. Donovan still needs to spend at least $70.15 in the restaurant this month to meet the Angler's Club requirement.

In summary, Mr. Donovan's spending so far this month is less than the minimum required by the Angler's Club, and he needs to spend at least $70.15 more to meet the requirement.

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The variance of the sample is 17.05. However, none of the given options matches with this value. The closest option is option (d) 16.5.

Variance is a measure of the spread or variability of a set of data. It is the average of the squared differences from the mean. The formula for variance is:

Variance = (sum of squared deviations from the mean) / (number of observations - 1)

where the squared deviation from the mean is the difference between each data point and the mean of the data set, squared. The variance is useful in statistical analysis and can provide information about the distribution of the data. A higher variance indicates that the data is more spread out, while a lower variance indicates that the data is clustered more closely around the mean.

In the given question,

To find the variance of the sample, we can use the formula:

Variance = [(sum of squared deviations from the mean)/ (number of observations - 1)]

First, we need to find the squared deviation of each observation from the mean, which is the difference between each observation and the mean, squared:

(3-5.4)² = 5.76

(5-5.4)² = 0.16

(12-5.4)² = 43.56

(3-5.4)²= 5.76

(2-5.4)²= 12.96

Next, we need to sum up these squared deviations:

5.76 + 0.16 + 43.56 + 5.76 + 12.96 = 68.2

Then, we divide the sum of squared deviations by the number of observations minus 1:

Variance = 68.2/(5-1) = 17.05

Therefore, the variance of the sample is 17.05. However, none of the given options matches with this value. The closest option is option (d) 16.5.

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The probability that it is new is 0.0833.

The probability that it is overdue is 0.25.

To solve this problem, use conditional probability.

Let A be the event that the account is new, and B be the event that the account is overdue.

A) To find the probability that an account is new given that it is overdue, calculate:

P(New | Overdue) = P(New and Overdue) / P(Overdue)

P(New | Overdue) = 0.05 / (0.05 + 0.55) = 0.0833 or 8.33%

So the probability that the account is new, given that it is overdue, is 8.33%.

B) To find the probability that an account is overdue given that it is new, calculate:

P(Overdue | New) = P(Overdue and New) / P(New)

P(Overdue | New) = 0.05 / (0.05 + 0.15) = 0.25 or 25%

So the probability that the account is overdue, given that it is new, is 25%.

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The complete question is:

A firm has classified its customers in two ways: according to whether the account is overdue and whether the account is new (less than 12 months) or old. An analysis of the firm's records provided the input for the following table of joint probabilities: One account is selected at random. If the account is overdue, what is the probability that it is new? If the account is new, what is the probability that it is overdue?

The percent rate of change to the nearest tenth of a percent is approximately 30.0% for both forms.

Starting with [tex]Y=5e^{-0.7}[/tex]  we can rewrite it using the property that [tex]e^{In(x)} = x[/tex]:

[tex]y=5e^{0.7t} = 5e^{ine^{in-0.7t} } =5e^{ln(5)}e^{-0.7t}[/tex]

Using the property that e^(ln(x)) = x again, we can simplify further:

[tex]y = 5e^{(ln(5)} e^{-0.7t} = 5(5^{1/In(5)}e^{-0.7t})[/tex]

Let [tex]a = 5^{1/ln(5)}[/tex]and r = 0.7, then we have:

[tex]y = 5a(1 + r)^{-t} ; y = a(1 - r)^t[/tex]

Rounding r to the nearest thousandth, we have:

r ≈ 0.700

To find the percent rate of change, we can use the formula:

percent rate of change = (1 ± r) * 100%

For the first form, we have:

percent rate of change = (1 - 0.700) * 100% ≈ 30.0%

For the second form, we have:

percent rate of change = (1 - 0.700) * 100% ≈ 30.0%

Therefore, the percent rate of change to the nearest tenth of a percent is approximately 30.0% for both forms.

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Part A: k = 8.4, to find the value of k, we must solve for k in the equation.

Part B: 193°F is the temperature of the water after 4.5 minutes.

Initial temperature is the temperature of a system before it undergoes a change. It can be calculated by subtracting the change in temperature from the final temperature.

Part A: k = 8.4

To find the value of k, we must solve for k in the equation.

We are given the temperature of the room (67°F) and the initial temperature of the water (208°F).

We are also given the temperature of the water after 3 minutes (193°F). We can plug these values into the equation and solve for k:

T-Ta = k(To-T)

193-67 = k(208-193)

126 = 15k

k = 126/15

k = 8.4

Part B: 193°F

To find the temperature of the cup of water after 4.5 minutes, we can plug the k-value we found in Part A into the equation, along with the given temperature of the room (67°F) and the initial temperature of the water (208°F).

T-Ta = k(To-T)

T = Ta + k(To-T)

T = 67 + 8.4(208-T)

T = 67 + 1747.2 - 8.4T

9.4T = 1814.2

T = 193

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Part A: k = 8.4, to find the value of k, we must solve for k in the equation.

Part B: 193°F is the temperature of the water after 4.5 minutes.

The temperature of a system at the start of a shift is called the initial temperature. You can figure it out by deducting the final temperature from the temperature difference.

Part A: k = 8.4

We must answer for k in the equation in order to determine its value.

We are informed of the room's temperature (67°F) and the water's starting temperature (208°F).

After three minutes, we are also told the water's temperature (193°F). We can solve for k by entering these numbers into the equation:

T-Ta = k(To-T)

193-67 = k(208-193)

126 = 15k

k = 126/15

k = 8.4

Part B: 193°F

We can enter the k-value we discovered in Part A, the given room temperature (67°F), and the starting temperature of the water (208°F) into the equation to determine the temperature of the cup of water after 4.5 minutes.

T-Ta = k(To-T)

T = Ta + k(To-T)

T = 67 + 8.4(208-T)

T = 67 + 1747.2 - 8.4T

9.4T = 1814.2

T = 193

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The complete question is,

EXIT TICKET

After heating up in a teapot, a cup of hot water is poured at a temperature of 208^0F . The cup sits to cool in a room at a temperature of 67^0 F. Newton's Law of Cooling explains that the temperature of the cup of water will decrease proportionally to the difference between temperature of the water and the temperature of the room, as given by the formula shown below.

Part A: If the cup of water reaches the temperature of 193^0 F after 3 minutes. Find the value of k, to the room, as given by the formula shown below. nearest thousandth.

Part B: Use the resulting equation to determine the Fahrenheit temperature of the cup of water, to the nearest degree, after 4.5 minutes.

Answer:

A. 450 trucks

Step-by-step explanation:

Given

Answer
A. 450 trucks

The number of vertical angles are 6

The number of linear angles are 6

The value of x is 20

Vertical angles are defined as a pair of non-adjacent angles that are formed by the intersection of two straight lines.

Four angles are created from this intersection.

Linear angles are defined as those angles that are formed when two lines intersect each other at a single point.

Note that supplementary angles are angles that sum up to 180 degrees.

Then, we have;

<1 + <5 = 180

substitute the angles

2x + 10 + 5x + 30 = 180

collect the like terms

7x = 180 -40

7x = 140

Make 'x' the subject

x = 20

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After addressing the issue at hand, we can state that  As a result, the square value of x to three significant figures is 5.03 cm.

According to Euclidean geometry, a square is an equilateral quadrilateral with four equal sides and four equal angles. It is also referred to as a rectangle with two neighbouring sides of equal length. A square is an equilateral quadrilateral because it has four equal sides and four equal angles. Square angles are 90-degree or straight angles. Furthermore, the diagonals of the square are evenly spaced and split at a 90-degree angle. a neighbouring rectangle with two equal sides. a quadrilateral with four equal-length sides and four right angles. A parallelogram with two adjacent, equal sides forming a right angle. A rhombus with straight sides.

The Pythagorean theorem can be used to find the square's diagonal:

2x2 = diagonal2 = x2 + x2 = 2x2[tex]x * \sqrt = diagonal = sqrt(2x2) (2)[/tex]

Because the diagonal equals the circle's diameter, the radius is half of the diagonal:

x * \sqrt(2) / 2 = radius

We can now use the formula for the area of a circle to calculate x:

[tex]\pi * radius2 = area[/tex]

[tex]\Pi * (x * sqrt(2) / 2)2 = 56[/tex]

[tex]56 = pi * (x^2 / 2)[/tex]

[tex]x^2 = 112 / pi[/tex]

x = 5.027 (rounded to 3 significant figures) (rounded to 3 significant figures)

As a result, the value of x to three significant figures is 5.03 cm.

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The volume of the cheese is approximately 135 cubic centimeters.

To calculate the volume of the cheese, we can use the formula:

Volume = Mass / Density

Given that the mass of the cheese is 216 grams and the density is 1.6 g/cm³, we can plug these values into the formula:

Volume = 216 g / 1.6 g/cm³

Now, we need to convert the units so that they are consistent. Since density is given in grams per cubic centimeter (g/cm³), we need to convert the mass from grams to cubic centimeters.

1 gram is equal to 1 cubic centimeter, so:

Volume = 216 cm³ / 1.6 cm³

Now, divide:

Volume ≈ 135 cm³

The volume of the cheese is approximately 135 cubic centimeters.

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