I NEED HELP SOLVING THIS MATH PROBLEM PLEASE.

Answer:

2553(base 7) = 969(base 10)

Step-by-step explanation:

3 in units place means 3.

5 in the 7's place means 5 × 7 = 35

5 in the 7²'s place means 5 × 7² = 5 × 49 = 245

2 in the 7³'s place means 2 × 7³ = 2 × 343 = 686

3 + 35 + 245 + 686 = 969

Answer:

32) (x+12)(2)+(y)(2)=25

Step-by-step explanation:

(x-a)(2)+(y-b)(2)=r(2)

(x-(-12)(2)+(y-0)(2)=5(2)

(x+12)+(y)=25

Answer(s):

(32) - [tex](x +12)^2 + y ^2 = 25[/tex]

(33) - [tex](x +2)^2 + (y+6 )^2 = 36[/tex]

(34) - [tex](x -8)^2 + (y+1 )^2 = 100[/tex]

(35) - [tex](x -13)^2 + (y+12 )^2 = 1[/tex]

Step-by-step explanation:

To solve these types of problems, it is only a matter of memorizing the equation of a circle and plugging in values appropriately.

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{The Equation of a Circle:}}\\\\(x - h)^2 + (y - k)^2 = r^2\\\text{Where} \ r \ \text{is the radius of the circle and} \ (h,k) \ \text{is the center of the circle.}\end{array}\right}[/tex]

For the following problems, find the equation of a circle with the given information.

(32) - [tex]\text{Center at} \ (-12,0) \ \text{and a radius,} \ r=5[/tex]

(33) - [tex]\text{Center at} \ (-2,-6) \ \text{and a radius,} \ r=6[/tex]

(34) - [tex]\text{Center at} \ (8,-1) \ \text{and a radius,} \ r=10[/tex]

(35) - [tex]\text{Center at} \ (13,-12) \ \text{and a radius,} \ r=1[/tex]

Question #32:

[tex](x - h)^2 + (y - k)^2 = r^2\\\\\Longrightarrow (x - (-12))^2 + (y - 0)^2 = (5)^2\\\\\Longrightarrow \boxed{ (x +12)^2 + y ^2 = 25}[/tex]

Question #33:

[tex](x - h)^2 + (y - k)^2 = r^2\\\\\Longrightarrow (x - (-2))^2 + (y - (-6))^2 = (6)^2\\\\\Longrightarrow \boxed{ (x +2)^2 + (y+6 )^2 = 36}[/tex]

Question #34:

[tex](x - h)^2 + (y - k)^2 = r^2\\\\\Longrightarrow (x - 8)^2 + (y - (-1))^2 = (10)^2\\\\\Longrightarrow \boxed{ (x -8)^2 + (y+1 )^2 = 100}[/tex]

Question #35:

[tex](x - h)^2 + (y - k)^2 = r^2\\\\\Longrightarrow (x - 13)^2 + (y - (-12))^2 = (1)^2\\\\\Longrightarrow \boxed{ (x -13)^2 + (y+12 )^2 = 1}[/tex]

Thus, all problems have been solved.

The coordinates for the center of the circle are (1/2, 1), and the length of the radius is 2 units. Option C is a correct choice.

To find the coordinates of the center of the circle and the length of the radius, we need to rewrite the equation of the circle in standard form, which is (x - h)² + (y - k)² = r². Here, (h, k) represents the coordinates of the center of the circle, and r represents the radius.

Given equation: x² + y² - x - 2y - 1 = 0

To convert it into standard form, we complete the square for the x and y terms separately.

Rearranging the equation:

x² - x + y² - 2y = 1

Completing the square for x:

(x² - x + 1/4) + (y² - 2y) = 1 + 1/4

Completing the square for y:

(x² - x + 1/4) + (y² - 2y + 1) = 1 + 1/4 + 1

Simplifying:

(x - 1/2)² + (y - 1)² = 9/4

Comparing it with the standard form, we can see that:

Center coordinates: (1/2, 1)

Radius: √(9/4) = 3/2 = 1.5 units

Therefore, the correct answer is C. The coordinates for the center of the circle are (1/2, 1), and the length of the radius is 2 units.
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Question -

A circle is defined by the equation given below. x² + y² - x - 2y - 1 = 0 What are the coordinates for the center of the circle and the length of the radius?

A. (-1,-1), 2 units −1),

B. (- 1/2 ,1), 4 units

C. (1/2 , 1), 2 units

D. (-1/2 ,-1), 4 units

If you have a system of two equations with two unknowns, and the graphs of the two equations do not intersect, the system must have no solution.

option C.

When we have a system of two linear equations in two variables, it can be represented graphically as two lines in a plane. The solution to the system corresponds to the point of intersection of these lines.

If the two lines do not intersect, then they are parallel. In this case, there is no point that satisfies both equations, which means that there is no solution to the system of equations.

In other words, if the two graphs do not intersect, it means that there are no values of the two unknowns that can simultaneously satisfy both equations.

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The distance between the points are matched as;

1. 10. 6

2. 7. 6

3. 7. 1

Using the Pythagorean theorem, we have that the square of the hypotenuse side is equal to the sum of the squares of the other two sides, we have that;

1. Opposite = 8

Adjacent = 7

Substitute the values

x² =8² + 7²

Find the square

x² = 64 + 49

x = √113

x = 10. 6

2. x²= 3² + 7²

Find the square value

x² = 9 + 49

x² = 58

Find the square root

x = 7. 6

3. x² = 5² + 5²

find the value

x² = 50

x = √50

x = 7. 1

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Answer:

The volume of the figure is 76ft³.

Step-by-step explanation:

Divide the figure into 2 parts to make it easier to solve for the volume.

V1 = 6ft(2ft)(3ft)

V1 = 36ft³

V2 = 4ft(2ft)(5ft)

V2 = 40ft³

V = V1 + V2

V = 36ft³ + 40ft³

V = 76ft³

Answer:

Step-by-step explanation:

Sure! Here's an example of using tomato sauce and spaghetti as a ratio in a math problem:

Problem: Jane is making spaghetti and tomato sauce for dinner. She wants to mix the tomato sauce and spaghetti in a ratio of 1:4. If she uses 2 cups of tomato sauce, how many cups of spaghetti should she use?

Solution:

To solve this problem, we can set up a proportion using the given ratio:

Tomato sauce : Spaghetti = 1 : 4

Let's assign the variable 'x' to represent the number of cups of spaghetti.

Therefore, the proportion becomes: 1/4 = 2/x

To solve for 'x', we can cross-multiply and solve for 'x':

1 * x = 4 * 2

x = 8

Therefore, Jane should use 8 cups of spaghetti to maintain a ratio of 1:4 with 2 cups of tomato sauce.

You can include these calculations and steps to show how you arrived at the answer.

Step-by-step explanation: Here's an example of using tomato sauce and spaghetti as a ratio in a math problem:

Problem: Jannay has tomato sauce and spaghetti in a ratio of 1:4. If she uses 2 cups of tomato sauce, how many cups of spaghetti should she use?

Solution:

To solve this problem,

Tomato sauce : Spaghetti = 1 : 4

Assign the variable 'x' to represent the number of cups of spaghetti.

The proportion becomes: 1/4 = 2/x

To solve for 'x',  cross-multiply and solve for 'x':

1 * x = 4 * 2

x = 8

Therefore, Jannay should use 8 cups of spaghetti to maintain a ratio of 1:4 with 2 cups of tomato sauce.

Answer:

Step-by-step explanation:

1. The figure  is a rectangular prism.

Formula: V = lwh

Given: 13 ft x 7ft x 9 ft

Substitute the values to the formula and solve.

V = lwh

V = 13ft(7ft)(9ft)

V = 819 ft³

2. The given figure is a triangular prism. Notice that the base forms a right triangle.

Formula: V = 1/2bhl

Given:

b = 9m

h = 12m

l = 16 m

Substitute the given values to the formula and solve.

V = 1/2(9m)(12m)(16m)

V = 864 m³

3. This is a cylinder

Formula: V = πr²h

Given:

r = 11 yd

h = 26 yd

Solve:

V = π (11yd)²(26yd)

V = 9883.45 yd³

4. The figure is a rectangular prism.

Formula: V = lwh

Given dimensions: 9m x 9m x 13.5m

Solve:

V = 9m(9m)(13.5m)

V = 1093.5 m³

5. The figure is a triangular prism

Formula: V = 1/2bhl

Given:

b = 15yd

h = 13 yd

l = 24 yd

Solve:

V = 1/2 (15yd)(13yd)(24yd)

V = 2340 yd³

The percent of sales tax on the food total is 6%.

We must first determine the 20% of the total amount of food that is the tip:

Tip = 0.2 * $32.50 = $6.50

The total cost of the meal before tax is:

Total cost before tax = food total + tip = $32.50 + $6.50 = $39.00

The cost of the lunch, including the sales tax of $1.95, is

Sales tax and the total cost before taxes = $39.00 + $1.95 =  $40.95.

The final price of the lunch, including tax and tip, is thus $40.95. You can compute the percentage of sales tax on the entire amount of food as follows:

Percent of sales tax on food = (sales tax / food total) * 100%

= ($1.95 / $32.50) * 100%

= 6%

So, the percent of sales tax on the food total is 6%.

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Amount of ice cream can the cone hold is, 9.8 inches³

We have to given that;

An ice cream cone has a height of 6 inches and a diameter of 2.5 inches.

Hence, We get;

Radius of cone = 2.5 / 2 = 1.25 inches

Since, We know that;

Volume of cone is,

V = πr²h/3

v = 3.14 × 1.25² × 6 / 3

V = 9.8 inches³

Hence, Amount of ice cream can the cone hold is, 9.8 inches³

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The coordinates in the solution to the systems of inequalities is (-2, 1)

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

y > -x - 4

y > 2x - 6

By imagining where the shading should be, we have

From the imagined graph, we have solution to the system to be the shaded region

The coordinates in the solution to the systems of inequalities is (-2, 1)

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The volume of a sphere can be calculated using the formula V = (4/3)πr³, where V is the volume and r is the radius.

Given that the sphere and the cylinder have the same radius and height, we can assume that the radius of both shapes is the same.

Let's denote the radius as 'r'. The volume of the cylinder is given as 50 ft³.

The volume of the cylinder is calculated using the formula V = πr²h, where h is the height.

Since the height of the cylinder is not given, we cannot determine the exact value of 'r' or calculate the volume of the sphere.

However, if we assume that the height of the cylinder is equal to its diameter (which is twice the radius), we can proceed with the calculation.

If the height of the cylinder is equal to 2r, the volume of the cylinder becomes:

50 = πr²(2r)

50 = 2πr³

Dividing both sides of the equation by 2π gives:

25 = πr³

Now, we can substitute this value of πr³ into the volume formula of the sphere:

V = (4/3)πr³

V = (4/3)(25)

V = 100/3

Therefore, if the height of the cylinder is equal to its diameter, the volume of the sphere would be 100/3 ft³. However, please note that this assumption might not necessarily be valid without further information about the relationship between the height and radius of the cylinder.

Answer: The Volume of the sphere is 100/3 cubic feet.

Step-by-step explanation:

It is clearly seen in the given figures, the height is two times the radius. Therefore, h is equal 2r.

We know that,

The volume of the sphere is π x r^2 x h. (r is radius and h is height)

So putting the values of height, h in the above formula, we get:

πxr^2x2r

= 2 * π * r^3.

= 2 * π * r^3 = 50

= π * r^3 = 25

We get, r^3 = 7.957747155

Therefore, r = 1.996472712

Now that we have the measure of the radius, we can find the volume of the sphere!

(4 / 3) * π * r^3

(4/3) * π * (1.996472712)^3

= (4/3) * π * 7.957747155

= (4/3) * π * (25 / π)

= (4/3) * 25

= 100/3 cubic feet.

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The correct statement regarding the proportional relationships is given as follows:

D. The first bucket will be completely filled 11 minutes before the second bucket.

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

For the first bucket, the equation is given as follows:

y = 0.4x.

Meaning that 0.4 gallons are inserted each minute, hence the time to insert 2 gallons is given as follows:

2/0.4 = 5 minutes.

For the second bucket, the constant is taken from the graph as follows:

k = 0.5/4

k = 0.125.

Hence the time is given as follows:

2/0.125 = 16 minutes.

Hence the difference is of:

16 - 5 = 11 minutes.

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The relative change is approximately -14.9%, indicating a decrease of approximately 14.9% in per person consumption of beef from 2000 to 2020.

To find the absolute and relative change as a percentage in the U.S. per person consumption of beef from 2000 to 2020, we can follow these steps:

Calculating the absolute change:

Absolute change = Final value - Initial value

= 57.7 pounds - 67.8 pounds

= -10.1 pounds

Step 2: Calculate the relative change:

Relative change = (Absolute change / Initial value) * 100

= (-10.1 pounds / 67.8 pounds) * 100

≈ -14.9%

The absolute change is -10.1 pounds, indicating a decrease in per person consumption of beef.

The relative change is approximately -14.9%, indicating a decrease of approximately 14.9% in per person consumption of beef from 2000 to 2020.

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A triangle with side lengths of 9, 40, and 41 is a valid right triangle.

The set of measurements 9, 40, and 41 could be the lengths of the sides of a right triangle. This is because these measurements satisfy the Pythagorean theorem,

which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, 9² + 40² = 41²,

which confirms that this set of measurements is valid for a right triangle. Additionally, 9 and 40 are both smaller than 41, which is consistent with the fact that the hypotenuse of a right triangle is always the longest side.

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To calculate the maxHP values for levels 62-70 by plugging in the appropriate level values into the formula.

One way to extend the maxHP for levels beyond 60 is to use the same formula that was used to calculate the maxXP for levels 1-60, but with the appropriate values plugged in.

The formula for the maxHP for a given level can be approximated as:

maxHP = baseHP x  (1 + level/5)²

where baseHP is the starting HP for level 1 (in this case, it's 330).

To extend the maxHP for levels 61-70, you can simply plug in the appropriate level values into the formula and calculate the corresponding maxHP values.

For example, to find the maxHP for level 61, you would plug in level = 61:

maxHP = 330 x (1 + 61/5)²

maxHP ≈ 2619.9

Similarly, you can calculate the maxHP values for levels 62-70 by plugging in the appropriate level values into the formula.

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The equation that represents the situation is a = b- 4.

Since the plant grows at a constant rate, we can assume that the height of the plant is increasing linearly with time.

Let's use the data from Week 1 and Week 2 to find the rate of growth for each plant:

For Plant A: Growth rate = (24 cm - 22 cm) / (2 weeks - 1 week) = 2 cm/week

For Plant B: Growth rate = (28 cm - 26 cm) / (2 weeks - 1 week) = 2 cm/week

Since the growth rate is constant, we can use the equation of a line to model the height of each plant over time:

For Plant A: a = 2t + b, where t is the time in weeks and b is the initial height of the plant.

For Plant B: b = 2t + c, where c is the initial height of Plant B.

We can find the values of b and c by substituting the data from Week 1 into these equations:

For Plant A: 22 = 2(1) + b, so b = 20.

For Plant B: 26 = 2(1) + c, so c = 24.

Now we can substitute these values into the equations for Plant A and Plant B:

Plant A: a = 2t + 20

Plant B: b = 2t + 24

To find an equation that gives Plant A's height in terms of Plant B's height, we can solve the equation for t in terms of b:

b = 2t + 24

2t = b - 24

t = (b - 24) / 2

Then we can substitute this expression for t into the equation for Plant A:

a = 2t + 20

a = 2[(b - 24) / 2] + 20

a = b - 24 + 20

a = b - 4

So the equation we were looking for is:

a = b - 4

Therefore, to find Plant A's height in centimeters given Plant B's height in centimeters, we simply subtract 4 from Plant B's height.

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The correct graph of the inequality ( |x| + 3 > 3) is attached accordingly.

Recall that the absolute value (or modulus) of a real number x is its non-negative value regardless of its sign. For example, 5 has an absolute value of 5, and 5 has an absolute value of 5.

A number's absolute value can be conceived of as its distance from zero along the real number line.

So, given  |x| + 3 > 3

Add minus three to both sides

|x| + 3  + (-3) > 3 + (-3)

|x|  > 0

Thus, the absolute value of x is

x > 0 or x < -0

put in the form of inequality, we have

x > 0 or x < 0

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Answer:

20 times

Step-by-step explanation:

There are 5 color options that are all the same size.

So orange = 1/5.

(1/5) * 100 = 20 times

Answer: let me explain!

Step-by-step explanation: So this might seem really confusing at first, but it’s actually suuuuuuper easy :P

So, if you think about it, every five seconds the amount of peanuts…well I don’t know how to explain it but let me show you this with numbers.
(4x2)x2x2x2 and so on. The number multiplies by two every five seconds from there. So figure out how many groups of five second there are in 100 seconds by dividing!

It’s 20!

So since 5 happens 20 times, and every time 5 happens, 2 happens, 2 also happens 20 times! (If that makes any sense)

So that answer would be 8x*twenty twos*

Which is…*drumroll please*

8,388,608
I even double checked!

And for the briefcase skeleton thing

She needs to try it 25 times because there are 5 books and each book can be switched with the other 4 times if the first one doesn’t work, therefore you need to multiply and the equation would be 5^2, or in other words, 25.
Don’t forget ur units!

Hope this helps :P

Answer:

D

Step-by-step explanation:

First, to find the length of the side FH we will use the Pythagorean theorem which states [tex]a^2+b^2=c^2[/tex]. We can say that FH = a, FG = b, and HG = c. Since we know the values of b and c, we will rearrange the formula to solve for a [tex]a = \sqrt{c^2-b^2}[/tex]. That will be [tex]\sqrt{18^2-12^2)[/tex] which gives us 13.4 for the missing side.

Now to solve for the angles we will use simple trigonometry. Since we know that [tex]sin(\theta) = \frac{opposite} {hypotenuse}[/tex], we can do inverse trigonometry for the missing angles [tex]sin^{-1}(\frac{opposite}{adjacent}) = \theta[/tex]. For angle H, we can do [tex]sin^{-1}(\frac{12}{18})[/tex] which gives us 41.8 degrees. For angle G we can do [tex]sin^{-1}(\frac{13.4}{18})[/tex] and we get 48.1 degrees. We could also use inverse cos and trig to solve it.

Looking at the answer choices, only answer choice D is correct.

Answer: 350000

Step-by-step explanation: Let the total sale of noodles by the wholesaler be x.

Given: Commission for the wholesaler is 10%

After receiving a 10% commission the company got rupees 315000.

x-10% of x =315000

x - 10\100 = 315000

x-x\10 = 315000

10x - 10\10 =315000

9x = 3150000

x= 3150000\9

x= 350000

The  Linear function is y equals negative one third times x plus 1

A linear function is a function that has a constant rate of change, meaning that as one variable (usually x) increases or decreases by a certain amount, the other variable (usually y) also changes by a constant amount.

Out of the four given equations, the only one that represents a linear function is the third one:

y equals negative one third times x plus 1

This is because the equation has a constant rate of change of -1/3 for any change in x. For example, if we increase x by 3, y will decrease by 1 (because 3*(-1/3) = -1). Similarly, if we decrease x by 3, y will increase by 1. This constant rate of change is what makes the equation represent a straight line when graphed.

The other three equations do not represent linear functions.

The first equation, x = 3, is not a function at all because there are multiple possible y values for the given x value of 3.

The second equation, y = 3x2, is a quadratic function because it contains an x2 term, which means that the rate of change of y with respect to x is not constant.

The fourth equation, 3x - 4 = 7, is a linear equation but not a function because for any given x, there is only one corresponding value of y. However, when the equation is solved for y, it becomes y = 3x - 3, which represents a linear function with a constant rate of change of 3.

The  linear function is y equals negative one third times x plus 1

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a) Value of K is Option 3. 98.83%

b) It takes Option 2. 183 bounces for the ball to bounce back to a height of less than 3 inches (1/4 of a foot).

a) To determine k, we can use the formula for the nth term of a geometric sequence:

[tex]a_n[/tex] = [tex]a_1[/tex] * [tex]r^{(n-1)}[/tex]

where a_1 is the initial term, r is the common ratio, and n is the term number.

We know that [tex]a_1[/tex] = 10 feet and [tex]a_5[/tex] = 9.04 feet, so we can set up the equation:

[tex]a_5[/tex] = [tex]a_1[/tex] * [tex]r^{(5-1)}[/tex]

9.04 = 10 * [tex]k^4[/tex]

Solving for k, we get:

k = [tex](9.04/10)^{(1/4)}[/tex] = 0.9883 or 98.83%

Therefore, the answer is (Option 3) 98.83%.

b) We can use the formula for the nth term of a geometric sequence again to find the height of the ball after the nth bounce:

[tex]a_n[/tex] = 10 * [tex]k^{(n-1)}[/tex]

We want to find the smallest n such that a_n < 1/4 foot, or 0.25 feet. Substituting k = 0.9883, we get:

10 * [tex]0.9883^{(n-1)}[/tex] < 0.25

Solving for n, we get:

n > log(0.25/10) / log(0.9883) + 1

n > 183.3

Since n must be a whole number, the smallest n that satisfies this inequality is n = 184. Therefore, it takes 183 bounces for the ball to bounce back to a height of less than 3 inches (Option 2).

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The partial fraction of the given rational expression is [tex]\frac{25}{(x+1(x+2)} =\frac{25A}{3(x-1)} -\frac{25B}{3(x+2)}[/tex]

Given the following equation below:

[tex]\frac{25}{(x+1(x+2)}[/tex]

We are expression as the sum of partial fractions

Let the numerator of both partial expressions be A and B to have:

[tex]\frac{25}{(x+1(x+2)} =\frac{A}{x-1} +\frac{B}{x+2}[/tex]

Simplifying the expression, we will have;

[tex]\frac{25}{(x+1(x+2)} =\frac{A(x+2)+B(x-1)}{x-1(x+2)}[/tex]

Cancelling the denominator:

25 = A(x+2) + B(x-1)


If x - 1 = 0, then x = 1. Substitute to have:

25 = A(1+2)

3A = 25
A = 25/3

If x + 2 = 0, x = -2

25 = B(-3)
B = -25/3

Substitute into the function to have:

[tex]\frac{25}{(x+1(x+2)} =\frac{25A}{3(x-1)} -\frac{25B}{3(x+2)}[/tex]

This gives the partial fraction of the given rational expression.

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Answer:

The total number of marbles in the bag is 4 + 12 + 8 + 2 = 26.

The probability of not picking a red marble out of the bag is equal to the number of marbles that are not red divided by the total number of marbles in the bag.

The number of marbles that are not red is 4 (blue) + 8 (green) + 2 (yellow) = 14.

Therefore, the probability of not picking a red marble out of the bag is 14/26 or 7/13.

So the probability of not picking a red marble is 7/13.

The room temperature after 8 hours after the process begins would be 10°C.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

Based on the information provided above, a linear equation that models the cooling machine is given by;

y = mx + c

y = -5x + 50

By substituting the given parameter (x = 8 hours), we have the following:

y = -5(8) + 50

y = -40 + 10

y = 10°C

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The additional interest on the loan by the rates is $2150241.13

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

Principal, P = $271,000

Time = 40 years

Rates = 7% and 5%

The interest is calculated as

I = P(1 + r)ˣ - P

So, we have

Calculate the difference in the interests

Difference = 3787078.07443 - 1636836.94099

So, we have

Difference = 2150241.13344

Approximate

Difference = 2150241.13

Hence, the additional interest is $2150241.13

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An estimated 3,042 people in attendance would prefer relish on a hot dog.

Given that;

For a recent football game of 8,450 in attendance,

And, 150 people were asked for they prefer on a hot dog.

Now, For number of people in attendance would prefer relish on a hot dog, we can use the proportion of people in the sample who preferred relish:

By proportion we get;

x = (54/150) x 8450

x = 54 * 56 1/3

x = 3042

Therefore, An estimated 3,042 people in attendance would prefer relish on a hot dog.

Learn more about the proportion visit:

https://brainly.com/question/1496357

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