A triangle has sides 6cm, and 7cm, use Pythagorean Theorem to figure out its hypotenuse.

The equation for an ellipse with a focus at (-2, 0) and vertices at (±7, 0) is (x + 2)²/49 + y²/1 = 1.

This equation can be derived by using the fact that the distance between the focus and the vertices of an ellipse is equal to the length of the major axis. Thus, we can calculate the length of the major axis by subtracting the x-coordinate of the focus from the x-coordinate of the vertices (which is 7 - (-2) = 9). This gives us the length of the major axis, which is 9.

Now, we can use the formula for the equation of an ellipse, given by:

(x - h)²/a² + (y - k)²/b² = 1

Where (h, k) is the center of the ellipse and a and b are the lengths of the major and minor axes, respectively. In this case, the center of the ellipse is (0, 0) and the lengths of the major and minor axes are 9 and 1, respectively.

Substituting the values into the equation, we get:

(x + 2)²/49 + y²/1 = 1

Therefore, the equation for an ellipse with a focus at (-2, 0) and vertices at (±7, 0) is (x + 2)²/49 + y²/1 = 1.

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a) The relevant population is the heavy soft-drink users in the given case, and the appropriate sampling design that should be used is  stratified random sampling. The list of all heavy soft-drink users is the sampling frame.

b) Cluster sampling refers to a sampling design where population is divided into naturally occurring groups and a random sample of clusters is chosen.

The advantages are efficient, easy to perform, and used when the population is widely dispersed. The disadvantages are sampling errors, have lower level of precision, and have the standard error of the estimate.

a) The relevant population for the public relations research department to investigate the initial reactions of heavy soft-drink users to a new all-natural soft drink is heavy soft-drink users. The appropriate sampling design that can be used to investigate the issues is stratified random sampling.

Stratified random sampling is a technique of sampling in which the entire population is divided into subgroups (or strata) based on a particular characteristic that the population shares. Then, simple random sampling is done from each stratum. Stratified random sampling is appropriate because it ensures that every member of the population has an equal chance of being selected.

Moreover, it ensures that every subgroup of the population is adequately represented, and reliable estimates can be made concerning the entire population. The list of all heavy soft-drink users can be the sampling frame.

b) Cluster sampling is a type of sampling design in which the population is divided into naturally occurring groups or clusters, and a random sample of clusters is chosen. The elements within each chosen cluster are then sampled.

The advantages of cluster sampling are:

The disadvantages of cluster sampling are:

A situation where cluster sampling would be appropriate is in investigating the effects of a new medication on various groups of people. In this case, the population can be divided into different clinics, and a random sample of clinics can be selected. Then, all patients who meet the inclusion criteria from the selected clinics can be recruited for the study. This way, the study will be less expensive, and it will ensure that the sample is representative of the entire population.

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We are given v = ds/dt, v = 9.8t + 9, s(0) = 17. We need to find the position of a body moving along a coordinate line at time t.

Using the formula of velocity, we can integrate it with respect to t to find the position of the body at any time t. The formula for velocity is:v = ds/dt... (1) Integrating equation (1) with respect to t, we get's = ∫vdt + C ...(2)

Here, C is the constant of integration, and it is found using the given initial position. Given, s(0) = 17Substitute s = 17 and t = 0 in equation (2).17 = ∫(9.8t + 9)dt + C [∵ s(0) = 17]17 = 4.9t² + 9t + C

Therefore, C = 17 - 4.9t² - 9tOn substituting the value of C in equation (2), we get:s = ∫vdt + 17 - 4.9t² - 9t ...(3)Now, we can substitute the given velocity, v = 9.8t + 9, in equation (3).s = ∫(9.8t + 9)dt + 17 - 4.9t² - 9ts = 4.9t² + 9t + 17 - 4.9t² - 9ts = 9t + 17

Hence, the position of the body at time t is 9t + 17 units.

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Based on the given computer output in Exhibit 13-6, the degrees of freedom for the sum of squares explained by the regression (SSR) is 1, which is represented by the value 4 in the "Degrees of Freedom" column under "Regression" in the "Analysis of Variance" section.

In addition, it is important to note that there are three coefficients provided in the output: Constant, X, and X2. Each coefficient is associated with a standard error value that represents the variability of the estimate. The constant coefficient has a standard error of 4.425, the X coefficient has a standard error of 2.630, and the X2 coefficient has a standard error of 12.560.

Overall, the provided output suggests that a regression model has been fitted to the data with the equation: Y = 12.924 - 3.682X + 45.216X2, where Y represents the response variable and X represents the predictor variable. The F-statistic value of 485.3 with 4 and 11 degrees of freedom in the "Analysis of Variance" section suggests that the regression model is significant and can be used to make predictions.
Based on Exhibit 13-6, the answer to your question regarding the degrees of freedom for the sum of squares explained by the regression (SSR) can be found in the Analysis of Variance

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Answer: The ratio would be 73.6

Answer: 0.0000413

Step-by-step explanation:

The -5 exponent is the amount of zeros that go behind 413.

a. An exponential growth rate equation to represent the cost C₁ of this home is \(C_1 = 250000e^{0.038t}\).

b. An exponential growth rate equation to represent the cost C₂ of this home is \(C_2 = 275000e^{0.022t}\).

c. The time in which each home would reach a price of $320,000 is 6.5 and 6.8 years respectively.

d. The price of the home in the first area is lower.

In Mathematics and Financial accounting, continuous compounding interest can be determined or calculated by using this mathematical equation (formula):

\(A(t) = P_{0}e^{rt}\)

Where:

Part a.

Based on an exponential growth rate of 3.8% in the first area, the cost of this home in t years can be written as follows;

\(A(t) = P_{0}e^{rt}\\\\C_1 = 250000e^{0.038t}\)

Part b.

Based on an exponential growth rate of 2.2% in the second area, the cost of this home in t years can be written as follows;

\(A(t) = P_{0}e^{rt}\\\\C_1 = 275000e^{0.022t}\)

Part c.

At a price of $320,000 for the home, the number of years to reach this price is given by:

\(C_1 = 250000e^{0.038t}\\\\320000 = 250000e^{0.038t}\\\\1.28= e^{0.038t}\)

ln(1.28) = 0.038t

Time, t = 0.24686007793/0.038

Time, t = 6.49 ≈ 6.5 years.

\(C_2 = 275000e^{0.038t}\\\\320000 = 275000e^{0.022t}\\\\1.16= e^{0.022t}\)

ln(1.16) = 0.022t

Time, t = 0.14842000511/0.022

Time, t = 6.75 ≈ 6.8 years.

Part d.

The house with the lower price can be determined as follows;

\(C_1 = 250000e^{0.038 t}\\\\C_1 = 250000e^{0.038\times 3}\)

C₁ = 250,000 × 1.12075212488

C₁ = $280188.03122

\(C_2 = 275000e^{0.038t}\\\\C_2 = 275000e^{0.022 \times 3}\)

C₂ = $293762.347221.

In conclusion, the home in the first area is cheaper.

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Answer:

565.606, is shown step by step in the picture

Answer:

false and true p,r and q

1/7 of the animals in the zoo are male monkeys.

To find the fraction of animals in the zoo that are male monkeys, we have to calculate the product of the fractions representing the proportion of monkeys and the proportion of male monkeys among them.

Given that 1/5 of the animals in the zoo are monkeys, we will then represent this as:

= 1/5

= 5/25.

And 5/7 of the monkeys are male which is written as 5/7.

To get fraction of male monkeys, we will multiply these two fractions:

= (5/25) * (5/7)

= 25/175

= 1/7.

Full question:

1/5 of the animals in the zoo are monkeys 5/7 of the monkeys are male. What fraction of the animals in the zoo are male monkeys?

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A function's behaviour as x approaches positive or negative infinity might reveal vertical, horizontal, and oblique asymptotes. As x approaches a value, vertical asymptotes occur. As x approaches infinity, horizontal asymptotes occur. As x approaches infinity, oblique asymptotes occur.

To identify vertical asymptotes, we examine the behavior of the function as x approaches a particular value. For example, let's consider the function f(x) = 1 / (x - 2). As x approaches 2, the denominator becomes very close to zero, causing the function to approach infinity or negative infinity. Hence, x = 2 is a vertical asymptote.

Horizontal asymptotes are determined by analyzing the behavior of the function as x approaches positive or negative infinity. For instance, let's take the function f(x) = (3x^2 + 2x - 1) / (2x^2 + x + 1). As x approaches infinity or negative infinity, the highest power terms dominate the function. In this case, both the numerator and denominator have the same highest power term (x^2), so the ratio of the coefficients determines the horizontal asymptote. Therefore, the horizontal asymptote for this function is y = 3/2.

Oblique asymptotes occur when the function approaches a non-horizontal line as x approaches positive or negative infinity. Consider the function f(x) = (3x^2 + 2x + 1) / (x + 1). By performing polynomial long division or synthetic division, we can see that the quotient is 3x + 1. As x approaches infinity or negative infinity, the function approaches the line y = 3x + 1. Hence, y = 3x + 1 is an oblique asymptote for this function.

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Answer:

The present value of $225 received at the end of five years with an interest rate of 5% is $176.29.

The correct answer is: The Stafford loan will have a higher balance by $835.39 at the time of repayment.

What is compound interest ?

Compound interest is a type of interest that is calculated on the initial principal amount as well as the accumulated interest from previous periods. In other words, it is interest that is earned on both the principal amount and the interest already earned. The interest is added to the principal amount, and the new total amount then earns interest for the next period. This cycle continues until the end of the term or until the loan is paid off. The formula for compound interest takes into account the interest rate, the number of compounding periods per year, and the length of time the money is invested.

According to the question:
To solve this problem, we need to calculate the balance of each loan at the time of repayment.

For the unsubsidized Stafford Loan, the total amount borrowed will be $11,985. Interest will be charged monthly at a rate of 3.85%/12 = 0.0032083. The loan will be repaid 6 months after graduation, so the number of monthly payments will be 6*12 = 72. Using the formula for the balance of a loan with monthly compounding, we get:

\(Balance = 11985*(1+0.0032083)^{72} = $13,190.34\)

For the PLUS Loan, the total amount borrowed will be $12,491.95. Interest will be charged monthly at a rate of 4.15%/12 = 0.0034583. The loan will be repaid immediately after graduation, so the number of monthly payments will be 12. Using the formula for the balance of a loan with monthly compounding, we get:

\(Balance = 12491.95*(1+0.0034583)^{12} = $12,354.95\)

Therefore, the PLUS loan will have a lower balance at the time of repayment, by $835.39.

The correct answer is: The Stafford loan will have a higher balance by $835.39 at the time of repayment.

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Answer:

x = -11

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

4(1) + 12(x + 3) - 6(x - 5) = 4(12) + 4(x)

Step 2: Solve for x

Answer:

P/2 - s = b

Step-by-step explanation:

Step 1: Write equation

P = 2b + 2s

Step 2: Solve for b

The value of function f(1) = 1/16.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f(x).

To find f(1), we substitute x = 1 into the given expression for f(x):

f(1) = 4(1/4)⁽¹⁺²⁾ = 4(1/4)³ = 4(1/64) = 1/16

Therefore, f(1) = 1/16.

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(a) Kwan will drive approximately 1.276 miles in 2 hours at his constant speed. (b) The equation representing the distance Kwan has driven (D) in terms of time (t) is D = 0.638t. (c) Kwan will drive approximately 0.1595 miles in 15 minutes, and (d) Kwan's trip of 234 miles will take approximately 366.8 hours at his constant rate.

(a) To determine how far Kwan will drive in 2 hours at the same constant speed, we can use the concept of proportionality. We can set up a ratio between the distance and time:

Distance / Time = Constant Speed

Let's calculate the constant speed first:

Constant Speed = Distance / Time

                 = 90 miles / 141 hours

                 ≈ 0.638 miles per hour

Now we can use the constant speed to find the distance Kwan will drive in 2 hours:

Distance = Constant Speed × Time

            = 0.638 miles per hour × 2 hours

            ≈ 1.276 miles

Therefore, Kwan will drive approximately 1.276 miles in 2 hours at this rate.

(b) The equation for D (distance) in terms of t (time) can be written as follows:

D = Constant Speed × t

Using the constant speed calculated earlier (0.638 miles per hour), the equation becomes:

D = 0.638t

(c) To determine how far Kwan drives in 15 minutes (0.25 hours), we can substitute t = 0.25 into the equation from part (b):

D = 0.638 × 0.25

    = 0.1595 miles

Therefore, Kwan will drive approximately 0.1595 miles in 15 minutes at this rate.

(d) If Kwan is driving a total of 234 miles, we can rearrange the equation from part (b) to solve for t:

D = 0.638t

234 = 0.638t

Dividing both sides of the equation by 0.638:

t = 234 / 0.638

   ≈ 366.77 hours

Kwan's trip will take approximately 366.8 hours.

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Answer:answer is 1.43

Step-by-step explanation:

Answer:

33

Step-by-step explanation:

g(x) = 2x² + 1

g(-4) = 2(-4)² + 1

= 2(16) + 1

= 33

simplify aqSimplify i31

Step 1

Since a U.S quarter is a circular coin write the expression for the area of a circle

Where

Step 2

Find the area of 1 side of a quarter to the nearest square mm

Hence, to the nearest square millimeter the area of one side of the quarter = 452 square millimeter

The value is 24 square units is parallel to the face of the right rectangular prism.

We can see that the face of the given rectangular prism shows a width 4 and a height of 6. If we cut the figure at any point along the length 20, such that the cross-section is parallel to the face, the cross-section, which occurs at x length, will always have the same dimensions, which are 4 and 6.

So the area of the cross-section which is parallel to the face of the given rectangular prism is given by:

A = 6 × 4

A = 24

Thus, the value is 24 square units is parallel to the face of the right rectangular prism.

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A = 6 × 4

A = 24

Thus, the value is 24 square units is parallel to the face of the right rectangular prism.

when we flip four coins, each coin has two possible outcomes, so the total number of possible outcomes is 2 x 2 x 2 x 2 = 16. The random variable X represents the number of tails observed when these 4 coins are flipped, and can take on values from 0 to 4.

Each of these 16 outcomes has a corresponding number of tails. For example, the outcome HHHH has 0 tails, HTTT has 4 tails, and so on.

Therefore, we can define a random variable X to represent the number of tails observed when four coins are flipped. X can take on values from 0 (when all four coins are heads) to 4 (when all four coins are tails), and the probability of each value can be determined by counting the number of outcomes that correspond to that value and dividing by the total number of possible outcomes (16). This approach does not use the binomial distribution, which is a formula used to calculate the probability of a certain number of successes in a fixed number of independent trials with a constant probability of success.

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(a) The margin of error would be approximately 2.1 percent.

(b) The 99 percent confidence interval for the true proportion is 41.5 percent to 46.5 percent.

(c) It is possible that the percentage of all voters who approve of the president's performance is 50 percent, but we cannot conclude this with certainty from the given information.

(a) Assuming a 95% confidence level and a proportion of 0.5 (worst-case scenario), the margin of error can be estimated as:

Margin of error = 1.96 * sqrt[(p * (1 - p)) / n]

where p is the proportion (0.5) and n is the sample size (2,277).

Plugging in the values, we get:

Margin of error = 1.96 * sqrt[(0.5 * 0.5) / 2,277] ≈ 0.020 or 2.0%

Therefore, the approximate margin of error for the approval rating estimate is 2.0%.

(b) To construct a 99% confidence interval for the true proportion, we can use the formula:

CI = p ± z*sqrt[(p * (1 - p)) / n]

where p is the sample proportion (0.44), n is the sample size (2,277), and z is the critical value for a 99% confidence level, which can be obtained from a standard normal distribution table or calculator. The value of z is approximately 2.58.

Plugging in the values, we get:

CI = 0.44 ± 2.58*sqrt[(0.44 * 0.56) / 2,277]

CI = 0.44 ± 0.032

CI = (0.408, 0.472)

Therefore, we can say with 99% confidence that the true proportion of voters who approve the president's performance lies between 40.8% and 47.2%.

(c) Since the 99% confidence interval does not include 50%, we can say that it is unlikely that the true proportion of voters who approve of the president's performance is 50%. However, we cannot rule out the possibility completely since the confidence interval is an estimate and there is still some level of uncertainty involved.

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The given functions ψ = 2xy and φ = x^2 - y^2 satisfy the conditions for continuity and irrotational flow.

To show continuity, we need to verify that the partial derivatives of ψ and φ with respect to x and y are equal. Let's calculate these partial derivatives:

∂ψ/∂x = 2y

∂ψ/∂y = 2x

∂φ/∂x = 2x

∂φ/∂y = -2y

From the above calculations, we can see that the partial derivatives of ψ and φ with respect to x and y are equal. Therefore, the condition for continuity, which requires the equality of partial derivatives, is satisfied.

To show irrotational flow, we need to verify that the curl of the velocity vector is zero. The velocity vector can be obtained from the stream function ψ and velocity potential φ as follows:

V = ∇φ x ∇ψ

Taking the curl of V:

∇ x V = ∇ x (∇φ x ∇ψ)

Using vector calculus identities and simplifying the expression, we find:

∇ x V = 0

Since the curl of the velocity vector is zero, the condition for irrotational flow is satisfied.

Therefore, based on the calculations and verifications, we can conclude that the given functions ψ = 2xy and φ = x^2 - y^2 satisfy the conditions for continuity and irrotational flow.

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Answer:

y=mx+b

e=mc^2

and I am sure that there are more, but those two are real equations

Step-by-step explanation:

Answer:

$10 owed for lunch.

Step-by-step explanation:

"asset" means to benefit, so the question is asking which one of these is not benefiting his net worth. he has $15 and $25 in savings, these both benefit him. he also has a $50 rare baseball card this also benefits him. the only one that takes away money is the money he owes for lunch.

Answer:

B. 85

Step-by-step explanation:

I haven't taken Geometry in 2 years So I don't remember how to explain it.

Based on quantitative reasoning, Alden should take the classes from Dr. Baeno in his next semester.

Quantitative Reasoning Behind Choosing Dr. Baeno

Alden talked to 17 friends that previously took course from Dr. Alvarez.

Eight out of 17 friends recommended Dr. Alvarez.

∴ The fraction of his friends in favor of Dr. Alvarez = 8/17

Also, Alden talked to 18 friends who took course from Dr. Baeno.

Eleven out of 18 friends recommended Dr. Baeno.

∴ The fraction of his friends in favor of Dr. Baeno = 11/18

Making Comparison

Now, since we know that,

11/18 > 8/17

The capacity for using knowledge and mathematics to address problems in the real world is known as quantitative reasoning.

Hence, applying quantitative reasoning, we can infer that it is more favorable for Alden to take classes from Dr. Baeno.

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