Lee wanted to compute the monthly payment on a 2 year, $8400 loan at an APR of 3. 7%. She entered the keystrokes at the right on her calculator. The display gives an answer of 48, which Lee knows is incorrect. Explain what her error was

yes, because the midpoints (a+c) = b

Given that the line's equation is y=x.

B and C are the two points on this line.

( a+ c, b) is the midpoint of B and C.

We can see from this that using the midpoint formula

a + c = \(\frac{x1+x2}{2}\)

b=\(\frac{y1+y2}{2}\)

Because both points are on y=x, we get

x1=y1, x2=y2.

As a result, x1 = a+c and 2y1 = 2b or y1 =b.

Because x1=y1, we have a+c =b.

In other words, the coordinates of the midpoint satisfy the equation y=x.

Thus, the answer is

because (a+c) = b

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The given relationships is that Necklace B is the shortest of the 3

necklaces and Necklace C would be the longest.

Reasons:

The number of necklaces = 3

Sum of the lengths of the necklaces = 445 mm

Length of Necklace A = 45 mm + Length of Necklace B

\(\displaystyle Length \ of \ Necklace \ B = \mathbf{\frac{Length \ of \ Necklace \ C}{2}}\)

Required:

The length of Necklace A

Solution:

Let A represent Necklace A, B represent Necklace B, and C represent

Necklace C, we have;

A + B + C = 445

A = B + 45

\(\displaystyle B = \frac{C}{2}\)

Therefore;

B = A - 45

2×B = C

2 × (A - 45) = C

Which gives;

A + A - 45 + 2 × (A - 45) = 445

4·A - 135 = 445

\(\displaystyle A = \frac{445 + 135}{4} = \mathbf{145}\)

The length of Necklace A = 145 mm

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Answer:

y- intercept = - 5, slope = 8

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + b ( m is the slope and b the y- intercept )

y = 8x - 5 ← is in slope- intercept form

with slope m = 8 and y- intercept b = - 5

Answer: slope: 8, intercept: (0, −5)

Step-by-step explanation:

Find the Slope and y-intercept

y = 8x − 5

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

y = mx + b

Find the values of m and b using the form y = mx + b.

m = 8

b = −5

The slope of the line is the value of m, and the y-intercept is the value of b.

Slope: 8

intercept: (0, −5)

To find the values of the piecewise-defined function f(x) at various points, we need to evaluate the function based on the given conditions. Let's calculate the following values:

f(0):

Since 0 is greater than -1 and less than 1, we use the first piece of the function:

f(0) = 5 - 2(0) = 5f(-2):

Since -2 is less than -1, we use the second piece of the function:

f(-2) = 2(-2) = -4f(2):

Since 2 is greater than 1, we use the first piece of the function:

f(2) = 5 - 2(2) = 5 - 4 = 1f(1)Since 1 is equal to 1, we need to consider both pieces of the function. However, in this case, both pieces have the same value of 2x, so we can use either one:

f(1) = 2(1) = 2

Therefore, the values of the piecewise-defined function f(x) at various points are:

f(0) = 5

f(-2) = -4

f(2) = 1

f(1) = 2

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An equilibrium phase diagram can be used to determine phase transitions, phase presence, and phase compositions at different conditions.

An equilibrium phase diagram can be used to determine the below mentioned parameters:

A) It can determine where phase transitions will occur. Phase transitions refer to changes in the state or phase of a substance, such as solid to liquid (melting) or liquid to gas (vaporization). The phase diagram provides information about the conditions at which these transitions take place, such as temperature and pressure.

B) It can determine what phases will be present for each condition of chemistry and temperature. The phase diagram shows the different phases or states of a substance (such as solid, liquid, or gas) under different combinations of temperature and pressure. It provides a visual representation of the stability regions for each phase, indicating which phase(s) will be present at a given temperature and pressure.

C) It can determine the chemistry and amount of each phase present at any condition. The phase diagram gives information about the composition (chemistry) and proportions (amount) of different phases present under specific conditions. It helps identify the coexistence regions of multiple phases and provides insight into the equilibrium compositions of each phase at various temperature and pressure conditions.

In summary, an equilibrium phase diagram is a valuable tool in understanding the behavior of substances and can provide information about phase transitions, phase stability, and the chemistry and amounts of phases present at different conditions.

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Answer: See explanation

Step-by-step explanation:

1. Complementary (adds up to 90°)

2. Neither

3. Supplementary (ads up to 180°)

4. Adds up to 90° since its complementary

22 + 4x = 90

Subtract 22 from both sides

4x = 68

Divide both sides by 4

x = 17

5. Adds up to 90° since its complementary

65 + x + 2 = 90

x + 67 = 90

Subtract both sides 67

x = 23

6. Adds up to 90° since its complementary

43 + x - 7 = 90

x + 36 = 90

Subtract both sides by 36

x = 54

7. Adds up to 180° since its supplementary

29 + x - 5 = 180

x + 24 = 180

Subtract both sides by 24

x = 156

8. Adds up to 180° since its supplementary

110 + 7x = 180

Subtract both sides by 110

7x = 70

Divide both sides by 7

x = 10

9. Adds up to 180° since its supplementary

72 + x + 4 = 180

x + 76 = 180

Subtract both sides by 76

x = 104

10. Adds up to 90° since its complementary

49 + x + 3 = 90

x + 52 = 90

Subtract both sides by 52

x = 38

11. Adds up to 180° since its supplementary

92 + x + 78 = 180

x + 170 = 180

Subtract both sides by 170

x = 10

12. Adds up to 180° since its supplementary

19 + x - 50 = 180

x - 31 = 180

Add 31 to both sides

x = 211

13. Supplementary angles add up to 180°

∠C + ∠D = 180

∠C + 45 = 180

Subtract both sides by 45

∠C = 135°

Hope I helped!

Answer:

2

Step-by-step explanation:

12 ÷ 2 = 42

father= 42

she was 10 he was as 40

10 is 4 times 40 that age

we need.so 42 min 40 is 2 =2

The ordered pairs of the function is (-2, 7), (-1, 1), (0, -1), (1, 1), and (2, 7) and the point form a  curve and the graph of the function is attached below.

Ordered pair:

Ordered pair means a composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses.

Given,

Here we have the function y = 2x² - 1

Now, we need to find the ordered pair values for the following x values and the we have to plot the graph for the function and find the shape it forms.

Here we have the value of x as -2, -1, 0, 1, 2.

Now, we have to apply these values on the function in order to find the ordered pairs,

x = -2 => y = 2(-2)² - 1 => y = 2(4) - 1 => y = 8 - 1 => y = 7

x = -1 => y = 2(-1)² - 1 => y = 2(1) - 1 => y = 2 - 1 => y = 1

x = 0 => y = 2(0)² - 1 => y = 0 - 1 =>  y = -1

x = 1 => y = 2(1)² - 1 => y = 2(1) - 1 => y = 2 - 1 => y = 1

x = 2 => y = 2(2)² - 1 => y = 2(4) - 1 => y = 8 - 1 => y = 7

Therefore, the ordered pairs of the function is

(-2, 7), (-1, 1), (0, -1), (1, 1), and (2, 7)

Now, we have to use these point to plot a graph.

And while we looking into the graph we have identified that the point form the curve.

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The optimal allocation is x = -1/2, y = 3/2, with a shadow price of 1.50.

To maximize profit, the firm needs to determine the optimal allocation of inputs x and y within the budget constraint of $100.

Let's assume the firm uses 'a' units of input x and 'b' units of input y. Since each unit of x costs $2 and each unit of y costs $3, the total cost constraint can be expressed as:

2a + 3b ≤ 100

To maximize profit, we need to differentiate the profit function P(x, y) with respect to both inputs and set the derivatives equal to zero:

∂P/∂x = 2y - 3 = 0 ---> y = 3/2

∂P/∂y = 2x + 1 = 0 ---> x = -1/2

However, x and y cannot have negative values, so these values are not feasible. To find the feasible values, we can substitute the values of x and y into the cost constraint:

2(-1/2) + 3(3/2) = 0 + 9/2 = 9/2 ≤ 100

This constraint is satisfied, so the feasible allocation is x = -1/2 and y = 3/2.

To find the shadow price, we need to determine the rate at which the maximum profit would change with respect to a one-unit increase in the budget constraint. We can do this by finding the derivative of the profit function with respect to the cost constraint:

∂P/∂(2a + 3b) = λ

Where λ represents the shadow price or the marginal value of an additional dollar in the budget. In this case, λ is the shadow price.

Taking the derivative of the profit function with respect to the cost constraint:

∂P/∂(2a + 3b) = ∂(2xy - 3x + y)/∂(2a + 3b) = 0

2y - 3 = 0 ---> y = 3/2

Thus, the shadow price (λ) is 3/2 or 1.50 when rounded to two decimal places.

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Answer:

124 amigo dame corona no e tenido

7x-5=6x+4

first take like terms,

7x-6x=4+5

from the above, when a term moves to the other side, the sign automatically changes. therefore, we +6x becomes -6x and -5 becomes +5

7x-6x=4+5

1x= 9

x= 9/1

x=9

answer is 9.

The x value is 3.99 by logarithm when the expression is 0.3=log(x-2).

Given that,

The expression is 0.3=log(x-2)

We have to find the x value

Just another approach to write exponents is with a logarithm. When exponents are not an option, we turn to logarithms to address the issue. The rules of exponents can be used to derive various logarithm formulas.

The use of a logarithm can be utilized to solve issues that cannot be resolved using the concept of exponents alone. A logarithm is simply another way to describe exponents.

Take the expression,

0.3=log(x-2)

x=3.99

Therefore, the x value is 3.99 by logarithm when the expression is 0.3=log(x-2).

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f(x) and g(x) are not closed under subtraction because when subtracted, the result will be a polynomial, the correct option is B.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics. Majorly used polynomials are binomial and trinomial.

Given f(x) and  g(x) two polynomial functions in the standard form of the polynomial,

According to Closure Property, when something is closed, the output will be the same as the input.

The polynomials f(x) and g(x) can be seen in the image.

On subtracting the two polynomials, the output will be a polynomial and so it is closed under subtraction.

Therefore, The reason why f(x) and g(x) are not closed under subtraction is that the outcome of subtraction will be a polynomial, making option B the best choice.

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Complete question:

The monthly payment for a car loan amount of $10,000, with a term of 3 years and an interest rate of 6% compounded monthly, is approximately $304.22. The total amount paid for the loan over the 3-year term is approximately $10,956.12, and the total amount of interest paid is approximately $956.12.

To find the monthly payment, we can use the formula for the monthly payment on a loan:

PMT = (P * r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

PMT = Monthly payment

P = Loan amount ($10,000)

r = Monthly interest rate (6% divided by 12 months, or 0.06/12)

n = Number of monthly payments (3 years multiplied by 12 months, or 3*12)

By plugging in the values into the formula, we find that the monthly payment is approximately $304.22.

To determine the total amount paid for the loan, we multiply the monthly payment by the total number of payments (36 months): $304.22 * 36 = $10,956.12.

The total amount of interest paid can be found by subtracting the original loan amount from the total amount paid: $10,956.12 - $10,000 = $956.12.

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The maximum value of P is 24 subject to the given constraints. Answer:Thus, the solution of the given problem is P = 24 subject to the given constraints.

To maximize the objective function P = 6x + 4y, given the constraints:x + 3y ≥ 6-x + y ≤ 4 2x + y ≤ 8 x ≥ 0, y ≥ 0We can use the graphical method to solve this Linear Programming problem.Step 1: Graph the given equations and inequalitiesGraph the equations and inequalities to determine the feasible region, i.e., the shaded area that satisfies all the constraints. The shaded area is shown in the figure below:Figure: The feasible region for the given constraintsStep 2: Find the corner points of the feasible regionThe feasible region has four corner points, i.e., A(0,2), B(2,1), C(4,0), and D(6/5,8/5). The corner points are the intersection of the two lines that form each boundary of the feasible region. These corner points are shown in the figure below:Figure: The feasible region with its corner pointsStep 3: Evaluate the objective function at each corner pointEvaluate the objective function at each corner point as follows:Corner Point  Objective Function (P = 6x + 4y)A(0,2)  P = 6(0) + 4(2) = 8B(2,1)  P = 6(2) + 4(1) = 16C(4,0)  P = 6(4) + 4(0) = 24D(6/5,8/5)  P = 6(6/5) + 4(8/5) = 14.4.

Step 4: Determine the maximum value of the objective function The maximum value of the objective function is P = 24, which occurs at point C(4,0). Therefore, the maximum value of P is 24 subject to the given constraints. Thus, the solution of the given problem is P = 24 subject to the given constraints.

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The amount of sales tax is $87.79.

Given a total purchase price of a sofa as $1,254.07 and state taxes of 7%.

We are required to calculate the amount of sales tax.

The amount of sales tax can be calculated by multiplying the purchase price by the sales tax rate.

Let's represent the sales tax rate by `r`.

Therefore, the sales tax formula is expressed as:

Sales tax = r * purchase price

In this case, the rate of the sales tax `r` is 7%.

Therefore, we have:r = 7% = 0.07

Now we substitute the values given into the formula:

Sales tax = 0.07 * $1,254.07= $87.79

Therefore, the amount of sales tax is $87.79.

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Answer:

u = 3

Step-by-step explanation:

Subtract 2 on both sides.

8 - 2 = 2u

Add like terms.

6 = 2u

Divide by 2 on both sides.

u = 3

the interval of time between when a vector takes an infectious meal, and when it begins to transmit the pathogen, is referred to as the extrinsic incubation period.

The incubation period refers to the duration of time between the invasion by an infectious pathogen and the start (first appearance) of symptoms of the disease in question. The host enters the symptomatic phase after the incubation period is over. Additionally, after infection, the host develops the ability to spread infections to other people, or they become infectious or communicable. The host person may or may not be contagious throughout the incubation phase, depending on the disease. The dynamics of disease transmission depend on the incubation period since it establishes the timing of case detection in relation to infection. This aids in assessing the success of symptomatic surveillance-based control methods.

the interval of time between when a vector takes an infectious meal, and when it begins to transmit the pathogen, is referred to as the extrinsic incubation period.

The complete question is-

The interval of time between when a vector takes an infectious meal, and when it begins to transmit the pathogen, is referred to as the: (a) vectorial capacity; (b) intrinsic incubation period; (c) vectorial competence; (d) extrinsic incubation period.

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Answer:

\(10 \sqrt{5} \ x^2y^3\sqrt{y}\)

Step-by-step explanation:

simplify \(2\sqrt{125x^4y^7}\)

Apply radical rule \(\sqrt{ab} =\sqrt{a} \sqrt{b}\):

\(\implies 2\sqrt{125}\sqrt{x^4}\sqrt{y^7}\)

\(\implies 2 \cdot 5 \sqrt{5}\sqrt{x^4}\sqrt{y^7}\)

\(\implies 10 \sqrt{5}\sqrt{x^4}\sqrt{y^7}\)

Apply radical rule \(\sqrt[n]{a^m} =a^{\frac{m}{n}}\):

\(\implies 10 \sqrt{5} \ x^{\frac42}y^{\frac72}\)

\(\implies 10 \sqrt{5} \ x^2y^3\sqrt{y}\)

Answer:

\(7x^{2}\sqrt{5y^{7} }\)

Step-by-step explanation:

First, we'll start by simplifying \(\sqrt{125}\).  2 factors of 125 are 5 and 25, and since 25 is a perfect square, that can be taken out of the radicand and added to the 2 that's already outside of it, creating \(7\sqrt{5x^{4}y^{7}}\).

x to the power of 4 can be simplified to x squared and taken out of the radicand along with that 7, so:

\(7x^{2}\sqrt{5y^{7} }\)

y to the power of 7 is a bit trickier to solve, so I left it like this, because I think it's the simplest version, but if this isn't an option then simplify further by working on the y.  

I hope this helps :)  

Answer:

y = 11

Step-by-step explanation:

being equilateral triangle

Answer:

A. X = -4

Step-by-step explanation:

\(-6x-24=3x+12\\-9x=36\\x=-4\)

Answer:

8/10 or 4/5 (simplified)

Answer:

\(\frac{4}{5}\) if simplified but the real answer would be \(\frac{8}{10}\)

Step-by-step explanation:

Step 1: Convert decimal to fraction.

0.8 = \(\frac{8}{10}\)

Step 2: simplify

\(\frac{8}{10}\) = \(\frac{8 divided by 2}{10 divided by 2}\) = \(\frac{4}{5}\)

Hope this helps =) Have a great day!

\(8700\) cubic feet of airflow are required for the entire home. Jackson may utilize this information to determine the best furnace size for the customer's requirements.

Volume is the quantity of space an object occupies, whereas capacity is a measurement of the substance—such as a solid, liquid, or gas—that an object can hold. While capacity may be measured in virtually any other unit, such as liters, gallons, pounds, etc., volume was determined in cubic units.

Volume, which is measured in cubic units, is the three dimensional space inhabited by material or surrounded by a surface. The cubic centimeter (m3), a derived unit, is the SI unit for volume.

Volume of the first section with height \(H1=10\) ft:

\(V1 = WLH1 = (20 ft)(30 ft)(10 ft) = 6000\) cubic feet

Volume of the second section with height \(H2=9\) ft:

\(V2 = (1/2)WLH2 = (1/2)(20 ft)(30 ft)(9 ft) = 2700\)cubic feet

Total volume of house,

\(V total = V1 + V2 = 6000\) cubic feet + \(2700\) cubic feet \(= 8700\) cubic feet

Therefore, the volume of airflow needed for the house is \(8700\) cubic feet.

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6 raised to the second power is 6*6 which is 32.

The standard form of 32 is 3.2*10²

The equation which is used to model this function is y = 25x.

An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra.

Given:

x=2 , y=50

x=4, y=100

As, corresponding to x =2 , y =50

For x=1 , y=25

Hence, the equation which is used to model this function is y = 25x.

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Answer:

x=366 Y=330

Step-by-step explanation:

Answer:

x=366 Y=330

Step-by-step explanation:

Hope this helped have an amazing day!

Answer:

I think it's the fourth option?

Step-by-step explanation:

Hope this is the right answer and helps!

The confidence interval is 0.039. This means that the value lies between the range of -0.039 and 0.039. Therefore, we can express the confidence interval as the mean plus or minus the margin of error.

This will give us a range in which the true population mean lies.Let's assume that the mean is 0.259. Then the lower limit of the range is given by:Lower limit = 0.259 - 0.039 = 0.22 And the upper limit of the range is given by:Upper limit = 0.259 + 0.039 = 0.298Therefore, the confidence interval is: 0.22 to 0.298Now we can see that option A is the correct answer: 0.259+0.22.

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\(\\ \sf\Rrightarrow \lim_{n\to \infty}\left(\dfrac{1}{1-n^2}+\dfrac{2}{2-n^2}\dots \dfrac{n}{1-n^2}\right)\)

\(\\ \sf\Rrightarrow \lim_{n\to \infty}\left(\dfrac{1+2+3\dots n}{1-n^2}\right)\)

\(\\ \sf\Rrightarrow \lim_{n\to \infty}\left(\dfrac{\dfrac{n(n+1)}{2}}{1-n^2}\right)\)

\(\\ \sf\Rrightarrow \lim_{n\to \infty}\dfrac{n(n+1)}{2(1-n^2)}\)

\(\\ \sf\Rrightarrow \lim_{n\to infty}\dfrac{n(1+n)}{2(1-n)(1+n)}\)

\(\\ \sf\Rrightarrow \lim_{n\to \infty}\dfrac{n}{2(1-n)}\)

\(\\ \sf\Rrightarrow \dfrac{\infty}{2-\infty}\)

\(\\ \sf\Rrightarrow \dfrac{-1}{2}\)

\({\sf \lim_{n \to \infty} (\frac{1}{1-n^2}+\frac{2}{1-n^2} +...\: \frac{n}{1-n^2}) } \\ = {\sf \lim_{n \to \infty} (\frac{1 + 2 + ..n}{1-n^2})} \\ = {\sf \lim_{n \to \infty} ( \frac{n(n + 1)}{2} \div 1 - {n}^{2} )} \\ = {\sf \lim_{n \to \infty} ( \frac{n(n + 1)}{2} \times \frac{1}{ 1 - {n}^{2}} )} \\ ={\sf \lim_{n \to \infty} ( \frac{n(n + 1)}{2(1 - {n}^{2} )} )} \\ = {\sf \lim_{n \to \infty} ( \frac{n(n + 1)}{2 (1 - n )(1 + n) } )} \\ = {\sf \lim_{n \to \infty} ( \frac{n(1 + n)}{2 (1 - n )(1 + n) } )} \\ = {\sf \lim_{n \to \infty} ( \frac{n}{2 (1 - n )} )} \\ = {\sf \lim_{n \to \infty} ( \frac{n}{2 - 2 n } )} \\ = \sf \frac{ \infty }{2 - \infty } \\ = \frac{ - 1}{2}

\)

Answer:

\( \frac{ - 1}{2} \)

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

12.75

Step-by-step explanation:

The first number, 51, is called the dividend.

The second number, 4 is called the divisor.