A real estate agent would like to develop a model for predicting sale price of homes in a suburban area. One variable that can be useful for predicting home value is home interior size, which is measured in square feet. Using 13 homes sold recently in the area, the real estate agent uses software to find a least-square line to summarize the relationship. The resulting equation is sale price hat = 0.152 (size) minus 32.84. A graph titled home price versus home size (square feet) has home size (Square feet) on the x-axis, and home price (thousands of dollars) on the y-axis. Points increase in a line with positive slope. A graph titled residuals versus home size (square feet) has home size (square feet) on the x-axis, and residual on the y-axis. Points are scattered throughout the graph. Based on the scatterplot and residual plot shown, is a linear model appropriate for summarizing the relationship? A linear model is appropriate because the residual plot shows no pattern. A linear model is appropriate because the mean of the residuals appears close to zero. A linear model is not appropriate because there are potential outliers in the residual plot. A linear model is not appropriate because of the random scatter of points in the residual plot.

Answer:

A = principal +interest

P = Principal Amount

r = rate

t = time

A = P(1 + rt)

5 000 = P[(1 + 0.05(821/364.25)]

5 000 = P(1 + 0.05(2.254)

5 000 = P(1 + 0.1127)

5 000 = 1.1127P

P = 4 493.5742

Therefore, you need to deposit an amount of $4 493.5742 to have $5 000 in 821 days.

Step-by-step explanation:

Answer:

[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} n&A \\\cline{1-2}\vphantom{\dfrac12} 1& \$4376.10\\\vphantom{\dfrac12} 2& \$4442.10\\\vphantom{\dfrac12} 4& \$4476.86\\\vphantom{\dfrac12} 12& \$4500.73\\\vphantom{\dfrac12} 365& \$4512.49\\\vphantom{\dfrac12} \sf Continuous& \$4512.89 \\\cline{1-2} \end{array}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

Substitute the given values into the formula to create an equation for A in terms of n:

[tex]\implies A=2100\left(1+\dfrac{0.085}{n}\right)^{9n}[/tex]

Substitute each value of n into the equation:

[tex]\begin{aligned}n=1 \implies A&=2100\left(1+\dfrac{0.085}{1}\right)^{9 \times 1}\\&=2100\left(1.085\right)^{9}\\&=\$4376.10\end{aligned}[/tex]

[tex]\begin{aligned}n=2 \implies A&=2100\left(1+\dfrac{0.085}{2}\right)^{9 \times 2}\\&=2100\left(1.0425\right)^{18}\\&=\$4442.10\end{aligned}[/tex]

[tex]\begin{aligned}n=4 \implies A&=2100\left(1+\dfrac{0.085}{4}\right)^{9 \times 4}\\&=2100\left(1.02125\right)^{36}\\&=\$4476.86\end{aligned}[/tex]

[tex]\begin{aligned}n=12 \implies A&=2100\left(1+\dfrac{0.085}{12}\right)^{9 \times 12}\\&=2100\left(1.00708333...\right)^{108}\\&=\$4500.73\end{aligned}[/tex]

[tex]\begin{aligned}n=365 \implies A&=2100\left(1+\dfrac{0.085}{365}\right)^{9 \times 365}\\&=2100\left(1.00023287...\right)^{3285}\\&=\$4512.49\end{aligned}[/tex]

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\\phantom{ww}$\bullet$ $P =$ principal amount \\\phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\\phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\\phantom{ww}$\bullet$ $t =$ time (in years) \\\end{minipage}}[/tex]

[tex]\implies A=2100e^{0.085 \times 9}[/tex]

[tex]\implies A=2100e^{0.765}[/tex]

[tex]\implies A=2100(2.14899437...)[/tex]

[tex]\implies A=\$4512.89[/tex]

Input the calculated values into the table:

[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} n&A \\\cline{1-2}\vphantom{\dfrac12} 1& \$4376.10\\\vphantom{\dfrac12} 2& \$4442.10\\\vphantom{\dfrac12} 4& \$4476.86\\\vphantom{\dfrac12} 12& \$4500.73\\\vphantom{\dfrac12} 365& \$4512.49\\\vphantom{\dfrac12} \sf Continuous& \$4512.89 \\\cline{1-2} \end{array}[/tex]

Answer:

2

Step-by-step explanation:

whose possible values are − 2 , 1 , 2 , 3 , and 6 .

0.95 is Pearson correlation shows the greatest strength or consistency of relationship

Pearson correlation is a statistic measuring the linear interdependence between two variables or two sets of data.

The value of correlation coefficient must be between -1.00 and +1.00 that  measures the strength and direction of the relationship between two variables.

When one variable changes, the other variable changes in the same direction.

The closer to either indicates a stronger relationship or the greatest strength or the consistency of the relationship.

The strongest must be 0.95. It is a strong positive correlation.

The correct answer is = 0.95

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Answer:

D

Step-by-step explanation:

5/3 x - 2/3 x = -4

3/3 x = -4

x = -4

Answer:

The area is in contact with the ground if A box exerts 10,000 Pa of pressure on the ground. If the box weighs 1000 N is 10 m².

( which is D/10 m²).

Step-by-step explanation:

so what is pressure?

In the physical sciences, pressure is defined as the stress at a point within a confined fluid or the perpendicular force per unit area. A 42-pound box with a bottom area of 84 square inches will impose pressure on a surface equal to the force divided by the area it is applied to, or half a pound per square inch.

Answer: 10,000 pa

Step-by-step explanation:

Pressure = Force / Area

Force = 10,000

Area = 1 m^2

Pressure = 10,000 / 1

Pressure = 10,000 pa.

uuuuuuuuuuuuuuuurrrrrrrrrrrrrrrr mom

Weekly paycheck of Catherine is $573.5 and her annual income is $29,904.01.

Unit rate is defined as the number of one quantity needed for a single other quantity.

In other words, if we know the unit rate, we can calculate any amount of one quantity corresponding to any amount of the other quantity by multiplying the unit rate with the number of other quantity.

Here unit rate of Catherine's pay = $15.50 per hour

Given that Catherine works 37 hours per week.

Weekly paycheck of Catherine = unit rate × number of hours per week

                                                    = 15.50 × 37

                                                    = $573.5

Annual Income of Catherine = Unit rate × number of hours per year

There are 52.143 weeks in a year.

Catherine works 37 hours per week.

Number of hours Catherine working in an year = 52.143 × 37 = 1929.291

Annual Income of Catherine = 15.50 × 1929.291

                                               = $29,904.01

Hence, calculation of student is wrong since the weekly paycheck is $573.5 and her annual income is $29,904.01.

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If they purchased 7 bags of popcorn and 3 drinks, the price would be $44.25; p bags of popcorn and d beverages would cost 4.50p+4.25d.

What is a formula?

Equation is the name given to two or more expressions with the equal sign.

Due to that

$4.50 worth of popcorn

beverage for $4.25.

There are 3 drinks and 7 bags of popcorn.

So let's calculate the overall cost.

7(4.50)+3(4.25)

31.5+12.75

44.25

So if they purchased 7 bags of popcorn and 3 beverages, the price would be $44.25

The price for p bags of popcorn and d drinks must now be determined.

4.50p+4.25d

Therefore, the price would be $44.25 if they purchased 7 bags of popcorn and 3 drinks, and the cost would be 4.50p+4.25d for p bags of popcorn and d beverages.

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a)There is a 4% probability that all nine trials will last at least 225 days.

b)Approximately at least 163 days, 90% of the total of 9 of these trials will last.

Given, A typical criminal trial lasts 21 days on average, with a 7-day

standard variation. There are nine trials chosen at random.

Let's look at the mean, which is 21, and the standard deviation, which is 7, respectively. Sample size is 9 people.

Assume that X is the sum of the nine trails' days and X represents the total number of days.

It is understood that X may have any distribution if it is a random variable with an unknown or known distribution. If n is increased, the probability that the random variable X, which is made up of sums, has a normal distribution increases.

a)There is a 4% probability that all nine trials will last at least 225 days.

b)Approximately at least 163 days, 90% of the total of 9 of these trials will last.

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There is a 4% probability that all nine trials will last at least 225 days.

Approximately at least 163 days, 90% of the total of 9 of these trials will last.

Answer:

a. 750 pages

b. 45 pages

Step-by-step explanation:

If you're decreasing 45 of something each day from 750, it makes sense that the 'something' is pages; instead of decreasing, it's reading.

So

a. 750 pages

b. 45 pages

Answer:

Look below

Step-by-step explanation:

Example for A

1/5 y= 3/5 x

1/5 y= 3/5 x +4

Example for B

0x=0y

0x=0y+3

Answer for C

add statement for the y not to be equal to 0

Answer:

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

Simplify considering that (n - 3) > (n - 5) and their difference is 2:

Answer:

80 degrees

Step-by-step explanation:

π=180 degrees

4π/9 =

4*180/9 =   ==> substitute 180 for π

720/9 = ==> simplify

80 degrees

a) If we select without taking the order into consideration there are  2380.

b) If we take the order into consideration, we have 57120 ways

We talk about the selection when we are talking about how a material can be chosen in the midst of many other materials that we have. In this case we are told that we want to choose 4 objects, without replacement, from 17 distinct objects.

If the order is not important then we need to do a combination and we have;

n!/r! (n - r)!

17!/4!(17 - 4)!

17 * 16 * 15 * 14 * 13!/4! * 13!

= 57120/24

= 2380

If we are looking at the order we have;

n!/(n-r)!

17!/(17 - 4)!

17 * 16 * 15 * 14 * 13!/13!

= 17 * 16 * 15 * 14

= 57120

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Answer:

c = 50°

Step-by-step explanation:

Since Triangle QRP is an isosceles triangle, the base angles of the triangle are equal.

Angle RQP = 180 - 115

= 65° (sum of angles on straight line)

Angle RPQ = Angle RQP = 65°

c = 180 - 65 - 65

= 50° (sum of angles in a triangle)

Answer:

55.5

Step-by-step explanation:

[tex]DE=\sqrt{(-9-9)^2+(8-5)^2}=\sqrt{333} \\ \\ DF=\sqrt{(-9-(-5))^2+(-9-8)^2}=\sqrt{305} \\ \\ EF=\sqrt{(-5-9)^2+(-9-5)^2}=\sqrt{392}[/tex]

The perimeter is thus [tex]\sqrt{333}+\sqrt{305}+\sqrt{392} \approx 55.5[/tex].

Quadratic function has minimum value which is -8.

correct option: 1

A variable with the largest power of two in a quadratic equation is called a variable. Quad, which signifies square, is the root of the term quadratic. The phrase must be two times its own strength, neither higher nor lower.

Given that they are the x values for which f(x) = 0, the roots of the function f(x) = ax² + bx + c correspond to the solutions of the quadratic equation ax² + bx + c = 0.

The term ax² is known as the quadratic term (hence the function's name), the word bx is known as the linear term, and the value c is known as the constant term.

Here, the given function,

f(x) = x² - 2x - 7 .......... (i)

now, differentiate with respect to x

d/dx {f(x)} = d/dx ( x²) - d/dx (2x) - d/dx (7)

or, f'(x) = 2x - 2 ............. (ii)

Now, put f'(x) = 0

so, 0 = 2x - 2

or, 2x - 2 = 0

or, 2x = 2

or, x = 1

From equation (ii)

f'(x) = 2x - 2

now, differentiate with respect to x

f''(x) = 2 > 0

So, it implies that, the function has minimum value at x = 1

Now, putting x = 1 in equation (i), we get -

f(1) = (1)² - 2×(1) - 7

f(1) = - 8

Function has minimum value is: - 8.

Thus, correct option is : (1)

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Answer:

So, a+2a=180°

Simplify.

3a=180°

To isolate a , divide both sides of the equation by 3 .

3a3=180°3    a=60°

The measure of the second angle is,

2a=2×60°       =120°

So, the measures of the two supplementary angles are 60° and 120° .

The domain and the range of the graphed function are given as follows:

The domain of a function is composed by the set that contains all possible values assumed by the input of the function. Hence, considering the graph of the function, the domain is given by the values of x of the graph.

Thus the domain of this function is given as follows:

D: (-9, -1] U (0, 4].

As there is an interval between -1 and 0 for which the function is not defined, and open circle defines that the interval is open at x = -9 and at x = 0.

The range of a function is composed by the set that contains all possible values assumed by the output of the function. Hence, considering the graph of the function, the range is given by the values of y of the graph.

Then the range of the function is given as follows:

R: (-6, 8.6].

Open interval due to the open circle at y = -6, closed at the value between 8 and 10 which is of 8.6.

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Answer:

x = 3/5

Step-by-step explanation:

[tex]125x^{3} -27=0[/tex]

[tex]125x^{3} =27[/tex]

[tex]\sqrt[3]{125x^{3} } =\sqrt[3]{27}[/tex]

[tex]5x=3[/tex]

[tex]x=\frac{3}{5}[/tex]

Hope this helps

To eliminate y from the first equation, we can multiply the entire equation by -2. This will give us:

-2x - 4y = -12

Now, if we add this equation to the second equation, the y terms will cancel out, leaving us with:

-2x - 4(2) + 5z = 26

-2x + 5z = 26

Now we have two equations in two variables, x and z. We can solve this system of equations by substituting the value of y from the second equation into the first equation. This gives us:

x + 2(2) = -6

x = -10

Substituting this value of x into the second equation, we get:

-2(-10) + 5z = 26

20 + 5z = 26

5z = 6

z = 1.2

Finally, we can substitute the values of x and z back into the second equation to find the value of y:

-2(-10) - 6(1.2) + 5(1.2) = 26

20 - 7.2 + 6 = 26

12.8 = 26

This system of equations has no solution, since we have found values of x and z that make the second equation true, but substituting these values into the first equation results in a false statement. This means that there is no set of values for x, y, and z that will make all three equations true at the same time.

A statement which best describes one of these transformations is that: A. triangle 1 is rotated to result in triangle 2.

In Mathematics, there are four (4) main types of transformation and these include the following:

In Mathematics, a rotation simply refers to a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Since triangle 2 has identical (similar) side lengths and angle measures, but is rotated and triangles 1 and 4 are identical, we can logically deduce that triangle 1 underwent a rotation to produce triangle 2.

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The values of x that can't be equal for the expression are 0 and 5

From the question, we have the following parameters that can be used in our computation:

(5x-2)/(x^2-5x)

This means that we set the denominator to 0

So, we have

x^2 - 5x = 0

Factorize

(x - 5)x = 0

So, we have

x - 5 = 0 and x = 0

Solve for x

x = 5 and x = 0

Hence, the solution is x = 5 and x = 0

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Answer:

3/2

Step-by-step explanation:

9/6

(9:3)/(6:3) = 3/2

6/4

(6:2)/(4:2) = 3/2

3/2

Answer:

[tex]\begin{array}{|c|c|}\cline{1-2}\vphantom{\dfrac12} K & t\\\cline{1-2} \vphantom{\dfrac12} 1 & 0\\\vphantom{\dfrac12} 2 & 7.3\\\vphantom{\dfrac12} 3&11.6 \\\vphantom{\dfrac12} 4& 14.6\\\vphantom{\dfrac12} 6&18.9 \\\vphantom{\dfrac12} 8& 21.9\\\vphantom{\dfrac12} 10& 24.2\\\vphantom{\dfrac12} 12&26.2\\ \cline{1-2}\end{array}[/tex]

See attachment for the graph.

Step-by-step explanation:    

Given equation for t:

[tex]t=\dfrac{\ln (K)}{0.095}[/tex]

Substitute the given values of K into the equation for t and round the answers to one decimal place:

[tex]\begin{array}{|c|c|}\cline{1-2}\vphantom{\dfrac12} K & t\\\cline{1-2} \vphantom{\dfrac12} 1 & 0\\\vphantom{\dfrac12} 2 & 7.3\\\vphantom{\dfrac12} 3&11.6 \\\vphantom{\dfrac12} 4& 14.6\\\vphantom{\dfrac12} 6&18.9 \\\vphantom{\dfrac12} 8& 21.9\\\vphantom{\dfrac12} 10& 24.2\\\vphantom{\dfrac12} 12&26.2\\ \cline{1-2}\end{array}[/tex]

To sketch the graph of the given function (see attachment):

Answer:

no

Step-by-step explanation

y=x+9

4=1+9

1+9=10

10 is not equal to 4

y=10x+7

=40+7

47 does not equal 4

The equation 3x - 6 = x + 6 - 5x has one solution, which is x = 12/7.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

The given equation is,

3x - 6 = x + 6 - 5x

To determine the solutions, solve the equation,

3x - 6 = 6 - 4x

7x = 12

x = 12/ 7

The equation has one solution, which is 12/7.

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Answer:

106*

Step-by-step explanation:

a triangle is 180*

to find angle BCA, you do 180 - (64+42)

that =74*

a straight line is also 180* so you do 180 - BCA

180-74=106

106