3. A model of a building is made using a scale of 1 in to 50 feet.
What is the height of the actual building if the height of the model is 25 inches?

Answer:$31,500

Step-by-step explanation:

To calculate the total amount Mario will pay, including the loan amount and interest, for the loan from First Bank of Trust, we need to calculate the interest and add it to the loan amount.

The formula to calculate simple interest is:

Interest = (Loan Amount) x (Interest Rate) x (Loan Length)

Let's plug in the values given:

Loan Amount = $25,000

Interest Rate = 6.5% (or 0.065 as a decimal)

Loan Length = 4 years

Interest = $25,000 x 0.065 x 4 = $6,500

Now, let's calculate the total amount Mario will pay:

Total Amount = Loan Amount + Interest = $25,000 + $6,500 = $31,500

Therefore, the total amount Mario will pay, including the loan amount and interest, for the First Bank of Trust loan is $31,500.

Answer:

Step-by-step explanation:

If you remove the brackets you get

4x^2*x^2 + 4x*4x + 3*4x

4x^4 + 16x^2 + 12x

That definitely is a polynomial

In its factored form, one of the factors is a polynomial so the answer is true.

Answer:

Step-by-step explanation:

Use a simple Equation

Price = Number x Price

So Price = 536.

Since it was 67% off we multiple the price of the original by .67.

So

536 = .67x

Solve for x = 536/.67 = 800

The original Price is $800.

check by multiplying by the sale %.

Answer:

-8255

Step-by-step explanation:

Answer:

x = 1

Step-by-step explanation:

I'm going to convert this to decimal to make it easier to type

Since x = 1, there is no need to include it in the equation

1/4 - 8 = -7.75 + 12 = 4.25

-0.75 + 5 = 4.25

Answer:

By simplifying both sides of the equation, then isolating the variable.

X=1

Step-by-step explanation:

1/4*1-8+12=-3/4*1+5

The distance between two points in three-dimensional space is a measure of the separation between the two points. In this case, the two points are the center of a sphere and a point that the sphere passes through.

To find the distance, we can use the distance formula in three dimensions, which is an extension of the distance formula in two dimensions. The distance formula is:

d = √((x1 - x2)^2 + (y1 - y2)^2 + (z1 - z2)^2)

where (x1, y1, z1) is the center of the sphere and (x2, y2, z2) is the point that the sphere passes through. The square root of the sum of the squares of the differences between the corresponding coordinates gives the distance between the two points.

In this problem, the center of the sphere is not given, so it is not possible to calculate the distance between the sphere and the point. The center of the sphere is a crucial piece of information needed to solve this problem.

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Answer:

that's easy she ran 4 every day

Step-by-step explanation:

4x5 equals 20 for the first day she ran 4 second day 8 third 12 fourth 16 fifth 20

Answer:

\(x = 3\)

Step-by-step explanation:

\(5x-1=3x+5\)

Get the x's on one side.

Add 1:

\(5x-1=3x+5\\\box \ \ +1) \ \ (\ \ \ \ +1)\)

\(5x=3x+6\)

Subtract 3x from both sides.

\(\ \ \ 5x=\ \: 3x+6\\\underline{-3x} \ \ \ \ \underline{-3x}\\\)

\(2x = 6\)

Finally, divide both sides by 2.

\(2x / 2 = 6/2\)

\(x = 3\)

The worker's utility function can be represented as a combination of consumption and leisure. Let x be the number of hours worked per day, and c be the amount of consumption. Then, the worker's utility can be represented as:

U(c, 24-x) = f(c) + g(24-x)

where f(c) represents the utility from consumption, and g(24-x) represents the utility from leisure. The worker faces a budget constraint that states the amount of income they earn from work must equal their spending on consumption:

wx = pc

This constraint can be used to solve for the optimal combination of leisure and consumption that maximizes the worker's utility. By combining the utility function and the budget constraint, the worker's problem can be formulated as a maximization problem:

Maximize U(c, 24-x) subject to wx = pc

This problem can be solved using techniques such as Lagrangian optimization or constraint optimization to find the optimal values of c and x that maximize the worker's utility. The solution will depend on the specific forms of the functions f and g, as well as the values of w and p.

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Answer:

I guess the answer is 13.5

Answer:

x=6

Step-by-step explanation:

8x+2+70+60=180

8x+132=180

8x=48

x=6

8(6)+2

48+2

=50°

hope this helps :D

Answer:

x=6√3

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

The statement that is the best interpretation of the mean is that the long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week.

The data of the number of days members visited a certain fitness center varied from 0 to 7.

The mean of the random variable x = 3.12

The mean of the random variable is also known as the long-run average value of a random variable.  

Hence, we conclude that the best interpretation of the mean in the given question is that the long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week.

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Answer:

34

Step-by-step explanation:

The triangle similarity can be proven by three methods, and the AA similarity postulate states that two triangles are similar if and only if their corresponding angles are congruent.

If they have the same shape but different sizes. This is what is known as similarity. In mathematics, there are three ways to prove that two triangles are similar: AA, SAS, and SSS.

In the case of AA similarity postulate, two triangles are similar if and only if two corresponding angles are congruent, meaning they have the same degree measure.

Similarly, if triangle ABC is similar to triangle JKL by AA similarity postulate, it means that the corresponding angles of both triangles are congruent.

Therefore, it is possible that triangle ABC is similar to one or more of the triangles given, but it is not possible to say without further information such as the angles and lengths of the sides.

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Complete Question:

Define triangle is ​△ABC​ similar to Similarity property and why?

Which triangle is ​△abc​ similar to and why? responses △abc is similar to △ghi by ​aa similarity postulate. triangle a b c, is similar to , triangle g h i, by , ​, a a similarity postulate, ., △abc is similar to △jkl by ​aa similarity postulate​. triangle a b c, is similar to , triangle j k l, by , ​, a a similarity postulate, ​, . △abc is similar to △def by ​aa similarity postulate​. triangle a b c, is similar to , triangle d e f, by , ​, a a similarity postulate, ​, . ​△abc​ is not similar to any of the triangles given.

Answer:

the answer is the second choice

Step-by-step explanation:

The marginal distribution of girls based on the percentages will be 58.3%.

The number for boys is given as:

= 50 + 30 + 45

= 125

The number of females is given as:

= 50 + 80 + 45

= 175

The percentage of females will be:

= 175/(125 + 175) × 100

= 175/300 × 100

= 58.3%

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The triangle formed by the flagpole and its shadow is similar to the triangle formed by the building and its shadow. In similar triangles the ratio between corresponding sides is the same.

Use the given lengths and in the equation above and find the height of the building:

Answer: the greast common factor between the two is 160

Step-by-step explanation: Find the prime factorization of 160

160 = 2 × 2 × 2 × 2 × 2 × 5

Find the prime factorization of 4800

4800 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 5 × 5

To find the GCF, multiply all the prime factors common to both numbers:

Therefore, GCF = 2 × 2 × 2 × 2 × 2 × 5

Hope this helps and thanks again for helping me :)

Answer:

\(2\frac{13}{120}\)

Step-by-step explanation:

**Fractions for addition and/or subtraction need equal denominators

Alike denominators in parentheses

\(4\frac{2}{5} -(1\frac{2}{3}+\frac{5}{8})\\4\frac{2}{5} -(1\frac{2}{3}(\frac{8}{8}) +\frac{5}{8}(\frac{3}{3} ))\\4\frac{2}{5}-(1\frac{16}{24}+\frac{15}{24})\\4\frac{3}{5} -(1\frac{31}{24} )\\4\frac{3}{5} -(2\frac{7}{24} )\)

\(4\frac{2}{5}-2\frac{7}{24}\)

Solve

\(4\frac{2}{5}-2\frac{7}{24} \\4\frac{2}{5}(\frac{24}{24}) -2\frac{7}{24}(\frac{5}{5})\\4\frac{48}{120}-2\frac{35}{120}\\2\frac{13}{120}\)

Answer:

A) Null Hypothesis; H0: μ = 13.65

Alternative hypothesis; Ha: μ > 13.65

B) t = 1.42

C) The p-value is greater than the significance level of 0.05. Thus, we fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim that the mean transaction value is greater than $13.65.

D) type II error will be to conclude the average transaction value is equal to $13.65, in reality the average transaction value is greater than $13.65.

Step-by-step explanation:

We are given;

Population mean; μ = $13.65

Sample mean; x¯ = $14.92

Sample standard deviation; s = $5.51

Sample size; n = 38

DF = n - 1 = 38 - 1 = 37

Significance level; α = 0.05

A) The hypotheses is defined below;

Null Hypothesis; H0: μ = 13.65

Alternative hypothesis; Ha: μ > 13.65

B) Since we are given sample standard deviation, we will use formula for t-value. Formula for the test statistic is;

t = (x¯ - μ)/(s/√n)

t = (14.92 - 13.65)/(5.51/√38)

t = 1.42

C) From online p-value from t-score calculator attached, using; t = 1.42, α = 0.05, DF = 37, one tail, we have;

P-value = 0.08199

D) The p-value is greater than the significance level of 0.05. Thus, we fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim that the mean transaction value is greater than $13.65.

E) A type II error simply means accepting a null hypothesis that is not true.

Now, in this case what it will mean is to accept the null hypothesis.

Thus, type II error will be to conclude the average transaction value is equal to $13.65, in reality the average transaction value is greater than $13.65.

The fraction of the plot of land not occupied by the flowers is 0.0625 or 1/16.

Let's calculate the fraction of the plot of land that is not occupied by the flowers.

Given that initially, 1/4 of the land is allocated for orchids, we have 1 - 1/4 = 3/4 of the land remaining.

After planting the orchids, 2/3 of the remaining land is allocated for roses. Therefore, the fraction of land allocated for roses is (2/3) * (3/4) = 2/4 = 1/2.

Subtracting the land allocated for roses from the remaining land, we have 3/4 - 1/2 = 1/4 of the land remaining.

Finally, 0.75 of the remaining land is allocated for tulips. Therefore, the fraction of land allocated for tulips is 0.75 * (1/4) = 0.1875.

To find the fraction of the plot of land not occupied by the flowers, we subtract the fractions of land allocated for flowers from 1:

1 - (1/4 + 1/2 + 0.1875) = 1 - 0.9375 = 0.0625.

Therefore, the fraction of the plot of land not occupied by the flowers is 0.0625.

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Answer:

9/16 or 0.5625

Step-by-step explanation:

Answer:

9/16

Step-By-Step:

2 1/4 = 9/4

Just multiply the denominator by 4

9/4 x 4 = 9/16

6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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Answer: 22

Step-by-step explanation: 65 divided by 3 is 22

Answer:

21or22

Step-by-step explanation:

65/3

Answer:

x \(\leq\) -4

Step-by-step explanation:

1. 3x-12 \(\geq\) 7x+4

add 12 to 12 to cancel it out, add 12 to 4.

2. 3x \(\geq\) 7x+16

subtract 7x from 7x to cancel it out, subtract 7x from 3x.

3. -4x \(\geq\) 16

divide -4 from -4x to cancel it out, divide -4 from 16.

4. x \(\geq\) -4

since division was involved, the inequality symbol needs to be reversed.

ANSWER: x \(\leq\) -4

You launch an object off a 55-foot cliff. If the object was launched at 85 feet/second,  64.23 feet/second long it will take for the object to hit the ground below. This can be solved using the concept of law of conservation of energy.

Three fundamental quantities all maintain their original values. Energy, momentum, and angular momentum are these. Energy is a conserved quantity, which could surprise you if you've read instances in previous pages, such the kinetic energy of charging elephants. The first law of thermodynamics, generally known as the law of conservation of energy, stipulates that the energy of a closed system must remain constant and cannot rise or fall on its own without external intervention.

Given that,

Height of the cliff, h= 55 Foot

Initial speed of the projectile, u = 85 m/s

Let, the projectile hit the ground with velocity "v"

Applying the law of conservation of energy,

mgh + 1/2 mu² = 1/2 mv²

or, m (gh + 1/2 u²) = 1/2 mv²

or, (gh + 1/2 u²) = 1/2 v²

or, 10 × 55 + (1/2 × (55)²) = 1/2 v²

or, 550 + 1512.5 = 1/2 v²

or, 2062.5 = 1/2 v²

or, 4125 = v²

or, v = 64.23 feet/second

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