Theodore earned ​$ in interest after 4 years on a principal of ​$440. His simple interest rate is​ 4.2%. Bella earned ​$216 in interest after 4 years on a principal of ​$1500 . Bella Her simple interest rate is​ 3.6%. Which bank would you rather​ use, Theodore's or​ Bella's? Explain your reasoning.

Answer:

54 in

Step-by-step explanation:

6 3/4= 27/4

27/4 x 8= 54

The height of this hill is given as :  51.88 feet.

How to solve for the height of the hill

We can use trigonometry to find the height of the hill. Let's call the height of the hill "h".

From the information given, we know that:

tan(27°) = h / (103/2)

h = (103/2) * tan(27°)

Using a calculator, we would have to go ahead to get the value of the variable h or height.

So  that h ≈ 51.88 feet.

So, the height of the hill is approximately 51.88 feet.

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the dimensions of the rectangular garden are 55 ft by 60 ft.

Let's assume that the width of the rectangular garden is x ft. Then, according to the problem, the length is 5 ft longer than the width, which means the length is (x+5) ft.

The area of a rectangle is given by the formula A = length × width. In this case, we know that the area is 3300 ft². So we can set up the following equation:

3300 = x(x+5)

Expanding the right-hand side, we get:

3300 = x²2 + 5x

Now, we can rearrange this equation into a standard quadratic form, by moving all the terms to one side:

x²2 + 5x - 3300 = 0

We can solve this quadratic equation using the quadratic formula:

x = (-b ± √(b²2 - 4ac)) / 2a

where a = 1, b = 5, and c = -3300.

Plugging in these values, we get:

x = (-5 ±√5²2 - 4(1)(-3300))) / 2(1)

x = (-5 ±√(13625)) / 2

x = (-5 ± 115) / 2

We can discard the negative solution, since the width of the garden cannot be negative. Therefore, we have:

x = (-5 + 115) / 2

x = 55

So the width of the garden is 55 ft. And the length is:

x + 5 = 55 + 5 = 60

Therefore, the dimensions of the rectangular garden are 55 ft by 60 ft.

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Answer:

The area of the largest square is 289 square units, because it is the sum of areas of the two smaller squares, 64 square units and 225 square units.

Step-by-step explanation: JUST PASSED IT ON STUDY ISLAND 100% CORRECT ANSWER

Distinguish between the Population Regression Function (PRF) and the Sample Regression Function (SRF) are given below.

Here, we have,

The population regression function, also known as the PRF, is a theoretical representation of the relationship that exists between a population's dependent and independent variables. The sample regression function, also known as the SRF, is an estimation of the relationship that exists between a sample's dependent and independent variables.

The Gauss-Markov assumptions that are connected to the traditional linear regression model are that the errors follow a normal distribution, that the errors have a mean of zero, and that the errors do not have any correlation with one another. These presumptions are important due to the fact that they make it possible to employ statistical techniques when estimating the values of the model's parameters. Testing a hypothesis necessitates making a number of assumptions, one of which is that the errors will be of a homoscedastic distribution.

The log-linear form is the functional form that needs to be used in order to get an accurate estimate of the Cobb-Douglas production function. You can test the hypothesis that there is a constant return to scale by testing the hypothesis that the coefficients on the inputs are equal to one. This will allow you to determine whether or not the hypothesis is true.

Population regression function (PRF), a theoretical description of the relationship between a population's dependent and independent variables, is known as the PRF One way to estimate the strength of a link between two sets of dependent and independent variables is to use a sample regression function (SRF).

Among the Gauss-Markov assumptions that are linked to the standard linear regression model are that the errors follow a normal distribution, that the errors have a mean of zero, and that the errors are not correlated with one another. Using statistical approaches to estimate the model's parameters is made possible by these presuppositions. The homoscedastic distribution of mistakes is one of many assumptions that must be made while testing a hypothesis.

To obtain an accurate estimate of the Cobb-Douglas production function, the functional form must be in log-linear form. The hypothesis that the coefficients on the inputs are all one can be tested to see if there is a continuous return to scale. This will help you determine if the hypothesis is correct.

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complete question:

17. a) Distinguish between the population Regression Function (PRF) and the Sample Regression Function (SRF) using appropriate diagrams and specifications for each function. (30 marks) b) Outline the Gauss-Markov assumptions associated with the Classical Linear Regression Model (CLRM) and discuss their significance. State any additional assumption that is required for hypotheses testing. (30 marks) c) Consider the following Cobb-Douglas production function: Qe = B.402K where, Q = output level, L = labour input, K = capital input Which functional form should you use to estimate this model? Clearly explain how you would test the hypothesis that there is constant return to scale. (40 marks)

Answer:

$19.34

Step-by-step explanation:

3%% of 55.25 is 19.3375

round to the nearest set and you get

the discounted price which is 19.34

Complete Question

Laura and martin obtain a 25 year 120,000 conventional mortgage at 8.5% on a house selling for 140,000 their monthly mortgage payment including principal and interest is 966 dollars

a) Determine the total amount they will pay for their house

b) How much of the cost will be interest?

c) How much of the first payment on the mortgage is applied to the principal?

Answer:

a)  \(X=\$289800\)

b)  \(I=\$169800\)

c)   \(Y=\$116\)

Step-by-step explanation:

From the question we are told that:

Time \(T=25years =>300 months\)

Initial Mortgage \(N=140,000\)

Mortgage  \(N'=120,000\)

Rate \(r=8.5\%=>0.085\)

Monthly Mortgage payment P=\%966

a)

The total amount Payable X is mathematically given as

 \(X=Monthly\ Mortgage\ payment*Number\ of\ months\)

 \(X=966*300\)

 \(X=\$289800\)

b)

Generally the equation for Interest I is mathematically given by

 \(Interest= Total\ amount\ Payable -Mortgage N'\)

 \(I=289800-120000\)

 \(I=\$169800\)

c)

Generally the equation for Interest I is mathematically given by

 \(I=Ptr\)

Where

 \(t= Month +.1month=>1/12\)

Therefore

 \(I=120000*1/12*0.085\)

 \(I=850\)

Therefore the first payment on the mortgage is applied to the principal is

 \(Y=\$966-850\)

 \(Y=\$116\)

P(A∩B) = 0.35 and P(A∪B) = 0.85.

If A and B are independent events, the probability of their intersection, denoted as P(A∩B), can be calculated as the product of their individual probabilities, P(A) and P(B).

P(A∩B) = P(A) * P(B) = 0.5 * 0.7 = 0.35

To calculate the probability of their union, denoted as P(A∪B), we can use the formula:

P(A∪B) = P(A) + P(B) - P(A∩B)

Substituting the given values, we have:

P(A∪B) = 0.5 + 0.7 - 0.35 = 0.85

Therefore, P(A∩B) = 0.35 and P(A∪B) = 0.85.

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Explanation:

The given quadratic is in the form y = ax^2 + bx + c

We have a = 1, b = 2, c = 2

This then leads to

h = -b/(2a)

h = -2/(2*1)

h = -1

This is the x coordinate of the vertex (h,k)

The axis of symmetry is the vertical line passing through the vertex. So it must share the x value in question.

Meaning the axis of symmetry is x = -1. Every point on this vertical line has an x coordinate of -1. This line of symmetry splits the parabola into two equal mirrored halves.

I recommend using a graphing tool like Desmos to visually confirm the answer.

The expression that represents the value, in dollars, of a certain number of dimes, d, and nickels, n, is:

0.10d + 0.05n.

To determine the expression that represents the value, in dollars, of a certain number of dimes (d) and nickels (n), we can follow these steps:

Step 1: Consider the values associated with dimes and nickels.

Each dime has a value of $0.10.

Each nickel has a value of $0.05.

Step 2: Determine how the values of dimes and nickels contribute to the overall value.

The value of dimes is calculated by multiplying the number of dimes (d) by $0.10.

The value of nickels is calculated by multiplying the number of nickels (n) by $0.05.

Step 3: Combine the values of dimes and nickels to form the expression.

The value of dimes, 0.10d, represents the total value contributed by dimes.

The value of nickels, 0.05n, represents the total value contributed by nickels.

Therefore, Combining the value of dimes, 0.10d, and the value of nickels, 0.05n, gives us the expression 0.10d + 0.05n, which represents the value, in dollars, of a certain number of dimes (d) and nickels (n).

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Answer:

x = 59/10, z = 237/70, and y = -121/70

Step-by-step explanation:

If the calculated chi-square test statistic is greater than 4.605, we would reject the null hypothesis of equal proportions at the 10% significance level.

To find the critical value for a chi-square test at the 10% significance level, we need to use a chi-square distribution table with degrees of freedom (df) equal to the number of categories minus 1.

Suppose the instructor is testing for the equality of proportions among k categories, then the degrees of freedom will be k-1.

The critical value for a chi-square test at the 10% significance level with k-1 degrees of freedom is given by the chi-square distribution table.

For example, suppose we have k=3 categories, then the degrees of freedom will be k-1 = 2. Using a chi-square distribution table with 2 degrees of freedom and a 10% significance level, we find the critical value to be 4.605.

Therefore, if the calculated chi-square test statistic is greater than 4.605, we would reject the null hypothesis of equal proportions at the 10% significance level.

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Answer:

3:50 P.M.

Step-by-step explanation: 3 * 10 = 30 minutes

4:20 - 30 = 3:50

The triangles ΔKLM and ΔEFG can be proven similar using both SSS and SAS similarity theorems.

In this question, we need to determine whether the triangles can be proven similar using the SSS or SAS similarities theorems.

For given diagrams,

the ratio of the corresponding sides is:

KM/EG = 8/24

            = 1/3

KL/EF = 6/18

          = 1/3

and ML/GF = 5/15

                  = 1/3

The sides of both triangles is proportional .

So by SSS similarity theorem, we have ΔKLM ≈ ΔEFG

Also, ML/GF = 1/3

∠L ≅ ∠F

KL/EF = 1/3

So by SAS similarity theorem, we have ΔKLM ≈ ΔEFG

Therefore, the triangles can be proven similar using both SSS and SAS

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The figure associated to given question is as shown below.

The fifth term of the given sequence is: a₅ = 63

We are told the formula for the nth term of the sequence is given as:

aₙ = aₙ₋₁ + 6(n - 1) for n ≥ 2

We are given:

a₁ = 3

a₂ = 9

a₃ = 21

a₄ = 39

Thus:

a₅ = a₅₋₁ + 6(5 - 1)

a₅ = a₄ + (6 * 4)

a₅ = 39 + 24

a₅ = 63

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Answer:

I would think 250 + 1.5t

Step-by-step explanation:

I hope this helps :)

Answer:

y=250×1.5x

Step-by-step explanation:

It depends on how many months

ex. after 6 months

y=2250

Answer:

x-19=25 or to solve for x 25+19=x

Step-by-step explanation:

The transformed function is:

g(x) =  (3*(x + 4))² +  (3*(x + 4))

Here we have the function:

f(x) = x² + x

Now we want to apply a translation of 4 units to the left, followed by a horizontal shrink by a factor of 1/3.

First, the translation is written as:

g(x) = f(x + 4)

Now the shink will give:

g(x) = f( 3*(x + 4))

Replacing the actual function we will get:

g(x) =  (3*(x + 4))² +  (3*(x + 4))

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Answer:

-6 and -10

Step-by-step explanation:

Three times negative two equal to negative six

Negative two plus negative eight equal to negative ten

Answer:14 weeks

Step-by-step explanation:288 x 14 = 4032

Answer: 24 plants

Step-by-step explanation:

1000 is not a perfect square.

31^2  < 1000 < 32^2

Required no. of trees = 32^2  − 1000

= 1024 − 1000

= 24

Number of hours spent by Monica on TV is 45 minutes , the time spent by Becky is in mixed fraction.

What is mixed fraction?

A mixed fraction is one that has each its quotient and remainder delineated.

Main Body:

Number of hours spent by Becky on TV = 1 1/2 hours

This is a mixed fraction.

Converting into decimal form,

1 1/2 can be written as 1.5 hours

Converting hours into minutes ,

⇒1.5 * 60 = 90 minutes

Time spent by Monica = (1/2)* Becky's time

⇒Time spent by Monica = (1/2)*90

⇒ 45 minutes

Hence time spent by Monica is 45 minutes.

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The area of the region enclosed by one loop of the curve r = 3cos(7θ) can be found by calculating the definite integral of the function r with respect to θ over the appropriate interval. The result of this integral will give us the area of the region enclosed by one loop of the curve.

To find the area of the region enclosed by one loop of the curve, we need to evaluate the definite integral of the function r = 3cos(7θ) with respect to θ. Since the curve completes one loop for every interval of θ from 0 to π/7, we can set up the integral as follows:

A = ∫[0, π/7] (1/2) r^2 dθ

Using the given function r = 3cos(7θ), we substitute it into the integral and simplify:

A = ∫[0, π/7] (1/2) (3cos(7θ))^2 dθ

  = (9/2) ∫[0, π/7] cos^2(7θ) dθ

To evaluate this integral, we can use trigonometric identities or integration techniques such as u-substitution. After integrating, we obtain the value of A, which represents the area of the region enclosed by one loop of the curve.

It's important to note that the given curve r = 3cos(7θ) forms multiple loops, and to find the area of one loop specifically, we need to consider the appropriate interval for θ that corresponds to one complete loop.

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Answer:

$44

Step-by-step explanation:

og $55

20% off

55 (starting number) x .20 (price off) = 11

55-11=44

==========================================================

Explanation:

Let's use the first two rows of the table to find the slope

m = slope

m = rise/run

m = (change in y)/(change in x)

m = (y2-y1)/(x2-x1)

m = (12-10)/(6-4)

m = 2/2

m = 1

The slope is 1.

Now let's use the first row of the table, along with the slope we just found, to plug into y = mx+b. The goal is to find b.

y = mx+b

10 = 1*4+b

10 = 4+b

10-4 = b

6 = b

b = 6

The y intercept is 6.

The y = mx+b equation is y = 1x+6 which is the same as y = x+6

Answer: x = 2

Step-by-step explanation:

The rule for reflecting over  x = 2 is that y remains the same and you add how many units x = 2 is from the point.

x = 2 is has the coordinate of x = 2 and y = the y coordinate of the point.

A (-1, 1) Since the y coordinate of (-1, 1) is 1, x = 2 - (2, 1)

Add 3 units to 2, the x coordinate since -1, 1 is 3 units from 2, 1

2,1 --> 5, 1

I really didn't know how to explain but Im 100% sure Im right and I hoped this helped somehow.

Answer: false

Step-by-step explanation:

True. A conditional statement consists of an antecedent (the "if" statement) and a consequent (the "then" statement). The statement is false only when the consequent is true and the antecedent is false.

In other words, for a conditional statement "if A then B," if A is false and B is true, the statement is false. If A is true and B is false or if both A and B are false, the statement is still considered true.

The given statement is incorrect. A conditional statement is false only when the antecedent is true and the consequent is false. In a conditional statement (usually written as "if P, then Q"), the antecedent (P) represents the condition, and the consequent (Q) represents the result of the condition being satisfied. The statement is considered false if the condition (antecedent) holds, but the result (consequent) does not occur.

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Answer:

Purchases= production + desired ending inventory - beginning inventory

Step-by-step explanation:

Giving the following information:

Two pounds of raw materials are needed to produce one product.

The desired ending balance of raw materials is 10% of the next month's production needs.

The beginning inventory of raw materials is 4,000 pounds.

The raw material cost per unit is $0.50 per pound.

To calculate the direct material purchase required for a given month, we need the production for each month. I will provide the formula and a small example to guide an answer.

To calculate the purchase required, we need to use the following formula:

Purchases= production + desired ending inventory - beginning inventory

For example:

Production:

January= 5,000 units

February= 4,500 units

Direct material purchases January:

Production= 5,000*2= 10,000

Desired ending inventory= (4,500*2)*0.1= 900

Beginning inventory= (4,000)

Total purchase in pounds= 6,900

Total direct material cost= 6,900*0.5= $3,450