Max found a car he wants to buy that costs $16,000. He can
afford to pay $250 a month for the car. His bank offers him a car
loan of 7.3%. How will the length of his loan be for this payment
amount?

Given dimensions of the room:

Length: \(\displaystyle\sf 12.5 \,m\)

Width: \(\displaystyle\sf 9 \,m\)

Height: \(\displaystyle\sf 7 \,m\)

Area of each wall:

\(\displaystyle\sf Area_1 = 12.5 \times 7 = 87.5 \,m^2\)

\(\displaystyle\sf Area_2 = 12.5 \times 7 = 87.5 \,m^2\)

\(\displaystyle\sf Area_3 = 9 \times 7 = 63 \,m^2\)

\(\displaystyle\sf Area_4 = 9 \times 7 = 63 \,m^2\)

Area of each door:

\(\displaystyle\sf Area_{\text{door}} = 2.5 \times 1.2 = 3 \,m^2\)

Area of each window:

\(\displaystyle\sf Area_{\text{window}} = 1.5 \times 1 = 1.5 \,m^2\)

Total area occupied by doors:

\(\displaystyle\sf Total_{\text{doors}} = 2 \times Area_{\text{door}} = 2 \times 3 = 6 \,m^2\)

Total area occupied by windows:

\(\displaystyle\sf Total_{\text{windows}} = 4 \times Area_{\text{window}} = 4 \times 1.5 = 6 \,m^2\)

Total wall area excluding doors and windows:

\(\displaystyle\sf Total_{\text{wall\,area}} = (Area_1 + Area_2 + Area_3 + Area_4) - Total_{\text{doors}} - Total_{\text{windows}}\)

\(\displaystyle\sf = (87.5 + 87.5 + 63 + 63) - 6 - 6\)

\(\displaystyle\sf = 275 - 6 - 6\)

\(\displaystyle\sf = 263 \,m^2\)

Cost of painting the walls:

\(\displaystyle\sf Cost_{\text{painting}} = Total_{\text{wall\,area}} \times 3.50\)

\(\displaystyle\sf = 263 \times 3.50\)

\(\displaystyle\sf = 920.50 \,Rs\)

Therefore, the cost of painting the walls of the room at Rs. 3.50 per square meter is Rs. 920.50.

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Each friend had originally 13 action figures before buying 11 more.

Given that there are 5 friends and each of them has x action figures in his or her collection. When they buy 11 more action figures, the total number of action figures they will have is 120.

a) We need to find an equation that models the problem. Let x be the original number of action figures that each friend had.

Therefore, the total number of action figures that each friend will have after purchasing 11 more is x + 11.

The total number of action figures will be 5(x + 11) = 5x + 55.

Now, according to the problem,5x + 55 = 120

This is our equation that models the problem.

b) We have to solve the equation 5x + 55 = 120 to find the original number of action figures, x, that each friend had before buying 11 more action figures.

5x + 55 = 120

5x = 120 - 55 (subtract 55 from both sides)

5x = 65x = 13

Therefore, each friend had originally 13 action figures before buying 11 more.

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The interest to pay at the end of the first month C. $18.71.

To calculate the monthly interest rate, divide the annual percentage rate by 12. For excellent credit, the monthly rate is 4.75% / 12 = 0.3958%, and for good credit, the monthly rate is 5.00% / 12 = 0.4167%.

The total cost of the mobile home including sales tax is $92,738 ($89,000 x 4.2% sales tax). With a $3,000 down payment, the amount financed is $89,738.

For excellent credit, the monthly interest rate :

= 4.75% / 12

So, the interest charged in the first month is $89,738 x  4.75% / 12 = $355.21

For good credit, the monthly interest rate is 0.4167%. So, the interest charged in the first month is $89,738 x 0.004167 = $33.91.

The difference in interest charged between good and excellent credit is $373.91 - $355.21 = $18.71.

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The complete question is:

Your parents are purchasing a mobile home for $89,000. The sales tax is 4.2%, they make a $3,000 down payment. How much more interest do your parents have to pay at the end of the first month because their rating is good rather than excellent?

Secured Unsecured

Credit APR (%) APR (%)

Excellent 4.75 5.50

Good 5.00 5.90

Average 5.85 6.75

Fair 6.40 7.25

Poor 7.50 8.40

Options:

$29.39

$21.10

$18.71

$19.02

Answer:

The 2 is 200

The 3 is 3000

The 1 is 1

And if needed

The 6 is 60

Step-by-step explanation:

2 is in hundredths place

3 is in thousand place

6 is in tens place

1 is in ones place

hope this helps

Answer:

Step-by-step explanation:

Let's start by assigning variables to the length and width of the frame. Let's call the width "w" and the length "l".

From the problem statement, we know that the perimeter of the frame is 80 inches. The formula for the perimeter of a rectangle is:

P = 2l + 2w

We can substitute the values we have:

80 = 2l + 2w

Simplifying the equation, we get:

40 = l + w

We also know that the length is five less than twice the width. Using our variables, we can write this as:

l = 2w - 5

Now we can substitute this expression for "l" into our equation for the perimeter:

40 = (2w - 5) + w

Simplifying this equation, we get:

40 = 3w - 5

Adding 5 to both sides, we get:

45 = 3w

Dividing both sides by 3, we get:

w = 15

Now that we know the width of the frame is 15 inches, we can use the equation we derived earlier to find the length:

l = 2w - 5

l = 2(15) - 5

l = 25

So the length of the frame is 25 inches.

Therefore, the width of the frame is 15 inches and the length of the frame is 25 inches.

Answer:

x = 6

Step-by-step explanation:

As stated, the scale factor from two figures is 1/4

To find the value of x we can simply use the following equation

\( \frac{(1.5)}{x} = \frac{1}{4} \)

cross multiply expressions

x = 6

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\(AB = \sqrt{ ({9 - 2})^{2} + ({5 - 3})^{2} } \)

\(AB = \sqrt{ {7}^{2} + {2}^{2} } \)

\(AB = \sqrt{49 + 4} \)

\(AB = \sqrt{53} \)

\(AB = 7.28\)

\(AB = 7.3\)

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The solution to the differential equation \(2^{\sqrt{x}}\frac{dy}{dx} = cosce(ln(y))\) is,

\(\frac{y sin(ln(y))}{2} - \frac{y cos(ln(y))}{2} = C - \frac{2 ln(2) \sqrt{x} + 2}{ln^2(2)2^{\sqrt{x}}}\).

Any equation with at least one ordinary or partial derivative of an unknown function is referred to as a differential equation.

The given differential equation is \(2^{\sqrt{x}}\frac{dy}{dx} = cosce(ln(y))\).

Now, multiplying both sides by dx we,

\(2^{\sqrt{x}}dy = cosce(ln(y))dx\).

Dividing both sides by \(2^{\sqrt{x}}\) we have,

\(sin(ln(y))dy = \frac{dx}{2^{\sqrt{x}}}\).

\(\[ \int sin(ln(y))dy = \int \frac{dx}{2^{\sqrt{x}}}\).

\(\frac{y sin(ln(y))}{2} - \frac{y cos(ln(y))}{2} = C - \frac{2 ln(2) \sqrt{x} + 2}{ln^2(2)2^{\sqrt{x}}}\).

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By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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Answer:

20

Step-by-step explanation:

10 for each for their being in the tens place, and ten for the ones place.

Answer:

Step-by-step explanation: I have no clue

Answer:

2.2

Step-by-step explanation:

8.8 / 4

you get 2.2

hope it helps

Answer:

2.2

Step-by-step explanation:

8.8 divided by 4 = 2.2

to find the interest you simply just multiply the amount by the percentage, so:

$3000 × 3.5%

= $3000÷100×3.5

=$105

Answer:

9.8w-7x+1

Step-by-step explanation:

9.8w-(7x-1)

Distribute the minus sign to each term in the parenthesis

9.8w-7x - -1

A negative negative is a positive

9.8w-7x+1

Answer:

100% B

Step-by-step explanation:

Answer:

The first choice: x^6y^5

Step-by-step explanation:

When you multiply exponential you add the exponents.

Answer:

84in

Step-by-step explanation:

Triangle Formula: 1/2bh

16*8=48*1/2 = 24

15*8= 120*1/2= 60

24+60= 84

Answer:1/4, 25%

Step-by-step explanation:

even number: 2,4,6

odd umber 1,3,5

even number probability when 1 dice is rolled: 3/6 = 1/2

2 dice is rolled: 1/2*1.2 = 1/4 = 25%

The plot of the residuals to the area indicates that the graph that corresponds to the residuals is the second option.

Please find attached the graph of the residual plot for the data created with MS Excel

A residual plot is a tool used for assessment of statistical models, to determine how fit the model is to the data. A residual plot is a plot of the residuals to the input or x-values of the data.

The trend line for the data in the question obtained using MS Excel indicates that we get; y = 0.1128·x + 3.6158

The residuals, which is the difference between the actual values and the calculated value obtained using MS Excel are;

Area (in²)    \({}\)              Residuals

x-value

5 \({}\)                             -1.0178

10 \({}\)                           -0.2718

24 \({}\)                           0.605

46 \({}\)                           0.7874

53 \({}\)                           0.7018

78 \({}\)                           0.0758

84 \({}\)                           -0.129

100 \({}\)                         -0.7538

The above values for the areas and the residuals indicates that the residual plot is n shaped, with the first two values being below the x-axis, which corresponds to the second option

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Answer: bottom right

The equations which show the total volume of the boxes Marcus shipped are as follows:

A. (20 × 10 × 7) + [2× (20 × 4 × 4)]

C. (20 × 10 × 7) + (20 × 4 × 4) + (20 × 4 × 4)

F. (200 × 7) + [2 × (80 × 4)]

Mathematically, the volume of a rectangular prism can be calculated by using this equation:

Volume = L × W × H

Where:

For rectangular prism 1, the volume is given by:

Volume 1 = L × W × H

Volume 1 = 20 × 7 × 10

Volume 1 = 200 × 7

Volume 1 = 1,400 cubic inches.

For rectangular prism 2, the volume is given by:

Volume 2 = L × W × H

Volume 2 = 20 × 4 × 4

Volume 2 = 80 × 4

Volume 2 = 320 cubic inches.

Since Marcus shipped 1 of the larger boxes and 2 of the smaller boxes, the total volume of the boxes Marcus shipped is given by these three (3) equations:

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Then, the number of pounds of food that an adult manatee can eat in "d" days can be represented by the equation: p = r x d.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.

Here,

Let's assume that an adult manatee eats "r" pounds of food per day on average. Then, the number of pounds of food that an adult manatee can eat in "d" days can be represented by the equation: p = r x d

Here, "p" represents the number of pounds of food, "r" represents the average amount of food consumed per day, and "d" represents the number of days. So, if we know the average amount of food consumed by an adult manatee per day, we can use this equation to calculate how much food it will eat in any given number of days.

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The values under and inside the radical is 4 and 129 respectively

A quadratic equation is any equation that can be rearranged in standard form as where x represents an unknown value, and a, b, and c represent known numbers. One supposes generally that a ≠ 0; those equations with a = 0 are considered degenerate because the equation then becomes linear or even simpler.

A quadratic equation is given as ax²+ bx+ c=0

this can be solved using formula x=( -b±√b²-4ac)/2a.

in the equation 2x²-10=7x, it can be Rearranged As 2x²-7x-10= 0

a= 2, b= -7 and c= -10

x= -(-7)±√(-7)²-4×2×-10)/2×2

x= 7±√49+80)/4

x= 7/4 ± √129/4

therefore the values inside and under the radical is 129 and 4

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The probability values for the questions posed are :

A.)

Number of students Taking a public speaking class majoring in business administration.

P(PS or BA) = 55/100 = 11/20

Therefore, the probability of PS or BA is 11/20

B.)

For the survey described, P(taken a public speaking class | majoring in Business Administration) represents the probability that a selected student has taken a public speaking class given that the student is majoring in business administration.

Hence, as inferred from P(A|B) ; probability of A given B.

C.)

P(PS|BA) = n(PSnBA) / n(BA)

n(PS) = 10+20 = 30

n(PSnBA) = 10

P(PS|BA) = 10/30 = 1/3

Therefore , the probability of PS|BA is 1/3.

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Answer:

A) \(\sqrt{8x/3}\)

Step-by-step explanation:

\(\sqrt{8x^{2} } /\sqrt{3x}\)

\(\sqrt{8x^{2}/{3x}\)

\(\sqrt{8x/3}\)

Therefore, A is correct

\((\stackrel{x_1}{8}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{8}}} \implies \cfrac{ 3 }{ -3 } \implies - 1\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- 1}(x-\stackrel{x_1}{8}) \\\\\\ y-5=-x+8\implies {\Large \begin{array}{llll} y=-x+13 \end{array}}\)

Beth earns $21.25 for both the jobs by working 36 hours at one job and 12 hours at another job

Addition: Addition is a way of combining things and counting them together as one large group. Addition in math is a process of combining two or more numbers. Addends are the numbers added, and the result or the final answer we get after the process is called the sum

Given that, Beth has 2 jobs and at her first job she earns $12.25 and worked 36 hours. At her second job, she earns $9.00 per hour and worked 12 hours

Her earnings for both the jobs is addition of her salary gives the answer

on adding $12.25+$9.00 = $21.25

She earns  $21.25 for both the jobs by working 36 hours at one job and 12 hours at another job

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The linear function that relates y to x is given as follows:

y = -0.5x + 57.

The slope indicates that the height decays 0.5 feet per minute. The y-intercept indicates that the descent starts at a cruising altitude of 57 feet.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:

From the table, when x = 0, y = 57, hence the intercept b is given as follows:

b = 57.

When x increases by 10, y decays by 5, hence the slope m is given as follows:

m = -5/10

m = -0.5.

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Answer:

\( \frac{92}{15} \)

Step-by-step explanation:

change to improper

\( \frac{24}{5} + \frac{4}{3} \)

this gives us

\( \frac{92}{15} \)

final answer

plz mark as brainliest

Answer:

\(\frac{92}{15} or 6\frac{2}{15}\)

Step-by-step explanation

hope this helps have a good day :)

The 95% confidence interval for the average number of units that students in their college are enrolled in is approximately 11.66 to 12.54 units. This means that we are 95% confident that the true population mean lies within this interval.

Here,

To calculate the 95% confidence interval for the average number of units that students in their college are enrolled in, we can use the formula for a confidence interval for a population mean when the population standard deviation is unknown but can be estimated using the sample standard deviation.

The formula for the confidence interval is given by:

Confidence Interval = Sample Mean ± (Critical Value) * (Standard Error)

where:

Sample Mean (x) is the mean of the sample (12.1 units in this case).

Critical Value is the value from the t-distribution corresponding to the desired confidence level and the sample size.

For a 95% confidence level and a sample size of 45, the critical value is approximately 2.013 (you can look this up in a t-table or use a calculator).

Standard Error is the standard deviation of the sample mean, which is calculated as the sample standard deviation divided by the square root of the sample size.

Given the information in the problem:

Sample Mean (x) = 12.1 units

Sample Standard Deviation (s) = 1.5 units

Sample Size (n) = 45

Confidence Level = 95%

Critical Value ≈ 2.013

Now, let's calculate the standard error:

Standard Error = s / √n

Standard Error = 1.5 / √45 ≈ 0.2236

Now, calculate the confidence interval:

Lower bound of the confidence interval:

12.1 - (2.013 * 0.2236) ≈ 11.66

Upper bound of the confidence interval:

12.1 + (2.013 * 0.2236) ≈ 12.54

So, the 95% confidence interval for the average number of units that students in their college are enrolled in is approximately 11.66 to 12.54 units. This means that we are 95% confident that the true population mean lies within this interval.

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Answer:

The speed of the plane in the still air is 420 miles/hour

The speed of the wind 60 miles/hour

Step-by-step explanation:

Let the speed of the plane with the wind be v

Let the speed of the plane against the wind be u

Now, speed = distance/time

With the wind,

v = (1440 miles)/(3 hours) = 480 miles/hour

v = 480 miles/hour

Against the wind,

u = (1440 miles)/(4 hours) = 360 miles/hour

u = 360 miles/hour

Now, let the speed of plane be p, and speed of wind be w,

Now, with the wind, the speed is 480 mph,

so,

speed of plane + speed of wind = 480 mph

p + w = 480  (i)

and against the wind, the speed is 360 mph,

so,

speed of plane - speed of wind = 360mph

p-w = 360 (ii)

adding equations (i) and (ii), we get,

p+w + p-w = 480 + 360

2p = 840

p = 840/2

p = 420 miles/hour

Then, the speed of the wind will be,

p + w = 480,

420 + w = 480

w = 480 - 420

w = 60 miles/hour

The speed of the plane in still air is calculated to be 420 mph, and the speed of the wind is calculated to be 60 mph by solving the two simultaneous equations obtained from the time, rate, and distance relationship.

This problem is about the rate, time, and distance relationships. The rate at which the airplane travels in still air is r (unaffected by wind), and the speed of the wind is w. When the plane flies with the wind, it is 'assisted' and therefore travels faster - at a speed of (r + w); against the wind, it travels slower - at a speed of (r - w).

From the problem, we know that:

By solving these two equations, we get the following:

Adding these two gives 2r = 840 => r = 420 mph (the speed of the plane in still air), and subtracting gives 2w = 120 => w = 60 mph (the speed of the wind).

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