Trig Word Problems (Level 2)

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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The probability that 5 messages are received in 1 hour is is 0.1755 ,the probability that 10 messages are received in 1.5 hours is 0.0858 and the probability that less than 2 messages are received in 1/2 hour is 0.2873

Let X shows the number of messages received per hour. The pdf of X is

\(P(X=x)=\) \(\frac{e^{-5}\cdot 5^{x}}{x!},x=0,1,2,3,....\)

Therefore, the probability that 5 messages are received in a single hour is

\(P(X=5)=\frac{e^{-5}\cdot 5^{5}}{5!}=0.1755\)

(b) Number of message received in 1 hour is 5 so number of message received in 1.5 hour is 7.5. So the probability that 10 messages are received in 1.5 hours is

\(P(X=10)=\frac{e^{-7.5}\cdot 7.5^{10}}{10!}=0.0858\)

(c) Number of message received in 1 hour is 5 so number of message received in 1/2 hour is 2.5. So the probability that less than 2 messages are received in 1/2 hour is

\(P(X < 2)=\frac{e^{-2.5}\cdot 2.5^{0}}{0!}+\frac{e^{-2.5}\cdot 2.5^{1}}{1!}=0.2873\)

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Start by adding the whole part of the numbers

then add the fractions

since the fraction also gave a mixed number it can be added to the whole part we already had

The correct answer option is the fourth one.

Answer:

6 units

Step-by-step explanation:

Let's call the length of the rectangle "L" and the width "W".

From the problem, we know that the width is 2 units less than the length, so we can write:

W = L - 2

We also know that the area of the rectangle is 48 square units, so we can write:

A = L * W

Substituting the first equation into the second equation, we get:

48 = L * (L - 2)

Expanding the brackets, we get:

48 = L^2 - 2L

Rearranging, we get:

L^2 - 2L - 48 = 0

Now we can use the quadratic formula to solve for L:

L = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 1, b = -2, and c = -48. Substituting these values into the formula, we get:

L = (2 ± sqrt(4 + 192)) / 2

L = (2 ± sqrt(196)) / 2

L = (2 ± 14) / 2

So, L = 8 or L = -6. We can ignore the negative solution, so the length of the rectangle is 8 units.

Now we can use the first equation to find the width:

W = L - 2

W = 8 - 2

W = 6

Therefore, the width of the rectangle is 6 units.

Answer:

2×-3 is the best equation for this.

Answer: y=2x-3

Step-by-step explanation:

The probability that a student scored greater than 69 is 0.943746.

Using continuity correction we would know that a score of 69 would correspond to values between 68.5 and 69.5 , a score of 70 would correspond to values between 68.5 and 69.5, etc…

Lets, the mean of the scores as  X . Since we are taking the mean of scores, to have a mean greater than 69, at minimum, we would have to have scores that are 69, and one score that is 70, the average of  values of 68.5 and 1 value of 70 , that means we want to know:

Now,

Z= m - x/ σ                          -------------------------------- (1)

where, m is the upper value

            X is the mean score

            σ is the standard deviation

Putting the values in equation (1),

Z = 70 - 69/ 7

   = 0.1428

Now,

P( 0.1428) = 0.056854

                 = 5.6855%

So, 5.6866% of students average scored 69 or less,

                P( > 69) = 1 - 0.056854

                              = 0.943746.

therefore the probability that a student scored greater than 69 is 0.943746.

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Step-by-step explanation:

please mark me as brainlest

Volume is a three-dimensional scalar quantity. The correct option is B, (4/3)π(10)³ - (4/3)π(4)³.

We have been given that a large sphere has a diameter of 20 feet. A smaller sphere with a radius of 4 feet is cut out of the center of the larger sphere. We are asked to find the volume outside smaller sphere and inside larger sphere.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

The volume, in cubic units, of the shaded part of the sphere is the difference between the volume of the larger sphere and the smaller sphere. Therefore, the volume can be written as,

The volume of the sphere = (4/3)π(10)³ - (4/3)π(4)³

Hence, the correct option is B, (4/3)π(10)³ - (4/3)π(4)³.

Complete Question:

The large sphere has a diameter of 20 feet. A large sphere has a diameter of 20 feet. A smaller sphere with a radius of 4 feet is cut out of the center of the larger sphere. Which expression represents the volume, in cubic units, of the shaded part of the sphere? Four-thirdsπ(103) + Four-thirdsπ(43) Four-thirdsπ(103) – Four-thirdsπ(43) Four-thirdsπ(203) + Four-thirdsπ(43) Four-thirdsπ(203) – Four-thirdsπ(43)

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The statistic that can be used to objectively quantify the level of agreement between different screeners appraising an article in a systematic review is the inter-rater reliability coefficient, such as Cohen's kappa or Fleiss' kappa.

In a systematic review, multiple screeners may independently appraise articles to ensure consistency and minimize bias. The inter-rater reliability coefficient, such as Cohen's kappa or Fleiss' kappa, is used to measure the agreement between these screeners. These statistics provide a quantitative measure of the extent to which the screeners' assessments align with each other beyond what would be expected by chance. Higher values of the inter-rater reliability coefficient indicate greater agreement among the screeners, suggesting more reliable and consistent evaluations of the articles in the systematic review.

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The Propositions from the given data are All Statements except Statement A.

(a) What time is dinner? This is not a proposition because it is a question and does not have a definite truth value.

(b) It is not the case that π is not a rational number. This is a proposition and its truth value is True because pi is not a rational number.

(c) x / 2 is a rational number. This is not a proposition because it is a statement about a variable, and the truth value depends on the value of x.

(d) 2x + 3y is a real number. This is not a proposition because it is a statement about variables, and the truth value depends on the values of x and y.

(e) Either π is rational and 17 is a prime, or 7 < 13 and 81 is a perfect square. This is a proposition and its truth value is False, because neither pi is rational nor 17 is prime.

(f) Either 2 is rational and π is irrational, or 2π is rational. This is a proposition and its truth value is False, 2 is rational and π is irrational.

(g) Either 5π is rational and 4.9 is rational, or there are exactly four primes less than 10. This is a proposition and its truth value is False because 5π is not rational and 4.9 is not rational and also there are four primes less than 10.

(h) −3.7 is rational, and either 3π < 10 or 3π > 15. This is a proposition and its truth value is False because −3.7 is not rational.

(i) It is not the case that 39 is prime, or that 64 is a power of 2. This is a proposition and its truth value is True because 39 is not a prime and 64 is a power of 2.

(j) There are more than three false statements in this book, and this statement is one of them. This is a proposition and its truth value is False because it is self-referential and also it's not true that there are more than three false statements in this book.

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the total way the committee formed is 3080.

What is combination?

A combination is a choice made in mathematics from a group of different elements when the order of the choices is irrelevant (unlike permutations). For instance, if three fruits, such as an apple, an orange, and a pear, are supplied, there are three possible pairings of the two: an apple and a pear. Formally speaking, a k-combination of a set S is a subset of S's k unique components. In other words, two combinations are the same if and only if they have the same members. (It is not important how the individuals in each set are arranged.) The quantity of k-combinations for a set with n components

The available candidates from a group are 8 Democrats and 11 Republicans.

Three Democrats and two Republicans must be included on the committee that we choose.

Thus, from a pool of 11 Republicans and 8 Democrats, we must select 3 each.

Both 8C3 and 11C2 approaches are viable for achieving this.

8C3 * 11C2 = 3080 are the total ways to form this committee.

Hence the total way the committee formed is 3080.

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Answer:

5.75

Step-by-step explanation:

14 - 8.25 = 5.75

The probability that the person uses exactly one of the facilities is 0.64

Probability is the likelihood of an event happening or an event not happening.

When it is certain an event would happen the probability is 1.

Probability can be independent or mutually exclusive.

Analysis:

Find analysis in the attached file.

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\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

The Correct choice is : D

\( \dfrac{i}{j} = \dfrac{h}{k} \)

You have to replace the value given (-6 and 3) for x in the function. Then, you'll have the value.

g(6) = 110

g(-3)= 32

Answer:

15

Step-by-step explanation:

Plug it in;

f(4)= 6(4)-9

24-9

15

Hopes this helps:)

Step-by-step explanation:

here,f(4)= 6x4 -9

= 24-9

= 15

If you're asking how this is possible,

Answer and explanation:

If Sandy and Allen's mother does the job in 5 hours

And Allen and Sandy's contributions completes the job in 2.5 hours

5 hours - 2.5 hours =2.5 hours

Allen and Sandy's contribution is half of the time it took only Allen and Sandy's mother= 2.5 hours

Therefore Allen and Sandy together will take 2.5×2 = 5 hours to complete the job alone without their mother

A similar example: if it takes one person 2 hours to peel 5 potatoes and it takes 1 hour to peel same number of potatoes if a second person helps, then this second person reduces the time used by 1 hour(50%) and would take 2 hours to complete the work.

The contractor needs to use the backhoe for 4132 hours in order to break even and start making a profit.

The cost function, C, for the cost of operating a backhoe for x hours includes the purchase price of $36,200 plus the costs of fuel and maintenance, which are $6.25 per hour, as well as the cost of the operator's wages, which are $14.73 per hour. This gives us the cost equation: C = 20.89x + 36200 dollars.

The revenue function, R, for the amount of revenue gained from x hours of use is calculated by multiplying the amount of money customers pay for the contractor's backhoe service, which is $29.74, by the number of hours of use, which is x. This gives us the revenue equation: R = 29.74x dollars.

The profit function, P, for the amount of profit gained from x hours of use is calculated by subtracting the cost, C, from the revenue, R. This gives us the profit equation: P = 8.76x - 36200 dollars.

The number of hours the backhoe must be used to break even (when Profit = 0) can be calculated by setting the profit equation equal to zero and solving for x. This gives us x = 4132 hours. This means that the contractor needs to use the backhoe for 4132 hours in order to break even and start making a profit.

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Answer:

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

Use the Inscribed Angle theorem, which states that:

Find the angle measure of ∠PNM, considering the intercepted arc is PLM:

If the estimates of the coefficients of interest change substantially across specifications, then this often provides evidence that the original specification had omitted variable bias. The correct option is C)

Omitted variable bias is a statistical error that arises when a regression analysis fails to account for the effects of a relevant variable that influences both the dependent variable and independent variables. This failure causes the coefficients of the independent variables to be biased, which may lead to incorrect conclusions.

In a linear regression model, the coefficients of the variables have a direct relationship with the dependent variable. If the estimates of these coefficients change significantly across different specifications of a linear regression model, then it often provides evidence that the original specification had omitted variable bias.

The Omitted variable bias can be fixed by redefining the model by adding the relevant variable to the regression analysis or using a proxy variable, which approximates the omitted variable. The proxy variable will help in analyzing the effect of the omitted variable on the dependent variable.

Therefore, if there is a significant change in the estimates of the coefficients of interest in different specifications, it may suggest that the initial specification suffered from omitted variable bias. So, option C) is the correct option.

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Answer:

( 1,-1)

Step-by-step explanation:

To find the x coordinate of the midpoint, add the x coordinates of the endpoint and divide by 2.

( 5+-3) /2 = 2/2 = 1

To find the y coordinate of the midpoint, add the y coordinates of the endpoint and divide by 2.

(4+-6)/2 = -2/2 = -1

The coordinates of the midpoint are ( 1,-1).

The researcher's reasoning is not entirely valid. There is a statistically significant difference between the treatment and control groups, it does not necessarily mean that wearing earplugs will reduce the chance of hearing loss.

A statistically significant result means that the observed difference between the treatment and control groups is unlikely to have occurred by chance alone, but it does not imply a causal relationship. There could be other factors that contributed to the difference observed, such as differences in age, exposure to noise, or other environmental factors.

To establish a causal relationship between wearing earplugs and reducing the chance of hearing loss, a randomized controlled trial (RCT) is needed.

The reasoning is not entirely valid. While a p-value less than the significance level of 5% suggests that there is a statistically significant difference between the treatment and control groups, it does not necessarily mean that wearing earplugs will reduce the chance of hearing loss.

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Responda:

270, 00

Explicação passo a passo:

Dado o seguinte:

Pagamento diário até as 18h00

Pagamento por hora trabalhada = 5,00

Em um determinado mês:

Trabalhou 25 dias: (25 * 20) = 500,00

20 horas à noite: (20 * 5) = 100,00

Ganho total = 500 + 100 = 600,00

Despesas:

Transporte = 1/10

= (1/10) × 600 = 60,00

Quantidade restante = (600 - 60) = 540,00

Renda:

1/2 de 540 = 270,00

Valor total restante após a dedução das despesas:

600 - (270 + 60)

600 - 330 = 270,00

Answer:

23 cents

Step-by-step explanation:

Answer:

0..23

Step-by-step explanation

divide 2.99 by 13

The area of the composite solid is 602.88m²

A composite solid is a solid that is composed, or made up of, two or more solids.

The solid consist of two cones. one big and one small cone

Area of a cone can be expressed as;

A = πr² + πrl

A = πr(r+l)

For the Big cone

A = πr(r+l)

A = 3.14 × 8 ( 8+10)

A = 25.12 × 18

A = 452.16m²

Area of the small cone

A = 3.14 × 4( 4 + 8)

A = 12.56 × 12

A = 150.72m²

Therefore the area of the composite solid

= 452.16 + 150.72

= 602.88 m²

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In order to achieve a margin of error of 0.5 hours, the researcher would need a sample size of 26 from each population, i.e., a total of 52 high school students To determine the required sample size for a desired margin of error in estimating the difference between the means of two populations, we can use the formula:

n = (Z * σ / E)^2

where:

- n is the required sample size,

- Z is the z-score corresponding to the desired confidence level,

- σ is the estimated standard deviation of the population, and

- E is the desired margin of error.

In this case, we are given a 95% confidence interval with a margin of error of 0.5 hours. The conservative value for the degrees of freedom is 1.01, corresponding to the t-distribution.

To calculate the required sample size, we need the estimated standard deviation of the population. Since the standard deviations are not provided for each population separately, we can use the average of the two standard deviations as an estimate. Therefore, σ = (3 + 2) / 2 = 2.5 hours.

Plugging in the values into the formula, we have:

n = (1.01 * 2.5 / 0.5)^2

n = 5.05^2

n ≈ 25.5025

Since the sample size needs to be a whole number, we should round up the result to the nearest integer. Therefore, the required sample size is 26.

Hence, in order to achieve a margin of error of 0.5 hours, the researcher would need a sample size of 26 from each population, i.e., a total of 52 high school students (26 from the suburban district and 26 from the city district).

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Answer:

Sally is 23 years old.

Step-by-step explanation:

John's age is completely unknown, so it is known as x

Meanwhile, Sally's age can be represented as 3x+2

The sum of both ages is 30.

So, x+3x+2=30

Combine like terms.

4x+2=30

Subtract 2 from both sides.

4x=28

Divide both sides by 4.

x=7

John is 7 years old.

Sally's age: 3(7)+2=23

Sally is 23 years old.

Answer: -19.35

Step-by-step explanation:

Answer:

1.5 Hours

Step-by-step explanation:

So, 90 minutes is between 1 hour and 2 hours (2 x 60 = 120 minutes). It is exactly half way between, hence 90 minutes is 1 and 1 half hours (or less formally, 1 and a half hours).

or  

90 Minutes = 1.5 Hours = 1 Hour and 30 Minutes. Minutes to hours Time Converter 90 hours to minutes. This conversion of 90 minutes to hours has been calculated by multiplying 90 minutes by 0.0166 and the result is 1.5 hours.