The total of monthly payments for a three-year loan is $22,317.12. The APR is 4%. How much money was originally borrowed?

Answer:

1 inch = 41 miles

Step-by-step explanation:

205 / 5 = 41

1 inch = 41 miles

Answer:

41 miles per inch

could be answered as 41/1 or 41:1

Step-by-step explanation:

Use a ratio to find the scale.

205/5

Divide the numerator and denominator by 5 to simplify.

41/1

Answer:

The quotient is x -2

Step-by-step explanation:

1. Let's simplify and find out the quotient of the following division:

(x^3+3x^2-4x-12) / (x^2+5x+6)

(x³ + 3x² - 4x - 12)/ (x² + 5x + 6)

(x + 2) (x² + x - 6) / (x + 2) (x + 3) ⇒ Factorizing on the numerator and the denominator

(x² + x - 6) / (x + 3) ⇒ Eliminating (x + 2) on the numerator and the denominator

(x + 3) (x - 2) / (x + 3) ⇒ Factorizing on the numerator

x - 2 ⇒ Eliminating (x + 3) on the numerator and the denominator

The quotient is x -2

Answer:

The answer is x-2 on EDGE

Step-by-step explanation:

Answer:

5x² - 13x + 6

Step-by-step explanation:

8x² - 6x + 2 - (3x² +7x -4)

Simplify the expression:

8x² - 6x + 2 - 3x² -7x + 4

Combine like terms:

5x² - 13x + 6

Answer: 17 and 31

Step-by-step explanation:

first number = x

second number = y

x+y=48

-(x-y=14)

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

2y=34

y=17

x=31

Answer:

17 and 31

Step-by-step explanation:

17 + 31 = 48, I basically just plugged in random numbers until I got the answer.

Answer:

4/25 pounds of candy per person.

Step-by-step explanation:

(4/5)/5=(4/5)(1/5)=4/25

To find the unit rate, you divide the total weight of the candy (4/5 pounds) by the total number of people (5). Therefore, each person received 4/25 pound of candy.

The unit rate is found by dividing the total quantity by the total number of units. In this problem, Deon divided 4/5 pounds of candy among 5 people.

To find the amount of candy per person which is the unit rate, you divide the total weight of the candy (4/5 pounds) by the total number of people (5). So, 4/5 divided by 5 equals 4/25. Thus, each person received 4/25 pound of candy.

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Number of projects that can be presented is 15.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

Division is one of the operation in mathematics where number is divided  into equal parts as that of a definite number.

Given that

Time alloted for each team = 1/5

Total time for the presentation = 3 hours

Division equation can be written as :

Number of projects = 3 / (1/5), where 3 hours is divided into 1/5 equal parts.

Number of projects = 15

Multiplication equation can be written as :

Number of projects = 3 × 5 = 15

Hence 15 projects can be presented.

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The complete question is as follows:

Teams of students in Mr. Reed’s classroom are presenting Social Studies projects. Each team has 1/5 hour for their presentation.

Suppose Mr Reeds class has 3 hours for presentations. How many projects can be presented show your solution by writing both a division equation and a multiplication equation.

3 is the least possible number that satisfied these conditions

The solution set is: x≥3

Step-by-step explanation:

Let x be the number

Then according to given statement

If five times a number is increased by four

[tex]5x+4[/tex]

At least 19 means that the result will be equal to or greater than 19

so,

[tex]5x+4\geq 19[/tex]

subtracting 4 from both sides

[tex]5x+4-4 \geq 19-4\\5x \geq 15[/tex]

Dividing both sides by 5

[tex]\frac{5x}{5} \geq \frac{15}{5}\\x\geq 3[/tex]

3 is the least possible number that satisfied these conditions

The solution set is: x≥3

Keywords: Inequality, Variables

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Answer:22/24 or 11/12

Step-by-step explanation:

Answer:

Six books are removed from the shelves, so $24-6=18$ books remain. Of these, $10-2=8$ are math books. Therefore, $8/18=\boxed{4/9}$ of the books remaining are math books.

Step-by-step explanation:

4/9

Answer:

a) c = 65.532 cm

P = 145.532 cm

b) A = 751.754 cm²

Step-by-step explanation:

This is an isosceles triangle.  The given angle is obtuse, so it must be the vertex angle.

a) One way to find the length of the third side is law of cosine:

c² = a² + b² − 2ab cos C

c² = 40² + 40² − 2(40)(40) cos 110°

c = 65.532

Another way is to cut the triangle in half and use sine.

sin (110°/2) = (c/2) / 40

c = 80 sin 55°

c = 65.532

The perimeter is the sum of the sides:

P = 40 + 40 + 65.532

P = 145.532

b) You can find the area using the SAS equation:

A = ½ ab sin C

A = ½ (40)(40) sin 110°

A = 800 sin 110°

A = 751.754

Another way is to split the triangle in half, find the height using cosine, then use half the base times height.

cos (110°/2) = h / 40

h = 40 cos 55°

h = 22.943

A = ½ ch

A = ½ (65.532) (22.943)

A = 751.754

Answer:

one million, one hundred fourteen thousand, forty

Step-by-step explanation:

Answer:

The number of students who prefer chocolate milk is 780 .

Step-by-step explanation:

Given as :

The total number of students in the school = 1200

The percentage of students who prefer plain white milk = 35 %

Let the number of students who prefer chocolate milk = x

Now, ∵ The percentage of students who prefer plain white milk = 35 %

∴ The percentage of students who prefer chocolate milk = 100 % - 35 % = 65%

So , As The number of  students who prefer chocolate milk = x

Or, 65 % of total number of students in school = x

So, x = [tex]\frac{65}{100}[/tex] × 1200

or, x = [tex]\frac{65\times 1200 }{100}[/tex]

∴  x = 780

So, the number of students who prefer chocolate milk = x = 780

And  students who prefer plain white milk = 1200 - x = 1200 - 780 = 420

Hence, The number of students who prefer chocolate milk is 780 . Answer

Answer:

7 grams

Step-by-step explanation:

If you're asking me grams specifically, and not kilograms, subtract 68 from 75 to get your answer. If it's only kilograms subtract 324 from 405. If it's both of them added together subtract 399 from 473, you're welcome!

Answer:

7 grams

Step-by-step explanation:

Answer:

814 - 64 = 750

750 ÷ 2 = 375

375 + 64 = 439

The problem can be solved by setting up two equations based on the given information, substituting one equation into the other, and then solving for the variable. In this case, 375 adult tickets were sold.

The subject of this problem is mathematics, particularly a class of problems known as linear equations. Let's assign variables to each type of ticket: A for the number of adult tickets and S for the number of student tickets.

According to the problem, S = A + 64 (because there were 64 more student tickets sold) and S + A = 814 (because a total of 814 tickets were sold).

With these two equations, you can substitute the value of S from the first equation into the second equation. Therefore, (A + 64) + A = 814. Simplify this to get 2A + 64 = 814.

To find the number of adult tickets, solve the simplified equation for A. Subtract 64 from both sides to get 2A = 750, and then divide by 2 to find that A = 375.

So, 375 adult tickets were sold.

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Answer:

Option C is the correct choice that is [tex]y<-\frac{5}{2}x-2[/tex]

Step-by-step explanation:

As this is a multiple choice question we will reduce the options and work on it with the given points [tex](0,-2),(-2,-3)[/tex]

Note:We know that [tex]\leq ,\geq[/tex] where there is [tex]=[/tex] sign associated with it have a straight line graph there is no breaking in the line.

And when there is simply [tex]<,>[/tex] we have a dashed line when we plot it on a graph.

So option B and D are discarded.

Now one-by one we will put the values [tex](x,y)\ (-2,3)[/tex] to know which equation it satisfies.

If we put [tex]y=3[/tex] then [tex]x=-2[/tex].

So working with option A.

[tex]y<-\frac{2}{5}x-2[/tex]

Plugging the values.

[tex]3<-\frac{2}{5}x-2\ ,3<\frac{-2x-10}{5}\ ,15<-2x-10\ ,15+10< -2x\ ,x=\frac{25}{-2}=-12.5[/tex]

And we know that [tex]x[/tex] must be equal to [tex]-2[/tex] so this is not the right answer.

We are left with only one choice that is C .

So option C is the correct option of the above inequality.

Answer:

Step-by-step explanation:

The expression given here is

                         [tex]x^2+19x+2[/tex]

Now if we differentiate this expression we can find the portions in its graph where it is increasing and decreasing or neither both.

If the differentiated expression is less than zero with the constant infront of highest degree positive then in the values corresponding to that [tex]x[/tex] the graph is decreasing.

If the differentiated expression is greater than zero with the constant infront of highest degree positive then in the values corresponding to that [tex]x[/tex] the graph is increasing.

  [tex]\frac{d}{dx}(x^2+19x+2)[/tex]

⇒[tex]2x+19[/tex]

For [tex]2x+19>0[/tex] ⇔[tex]x>\frac{-19}{2}[/tex]

For [tex]2x+19<0[/tex] ⇔[tex]x<\frac{-19}{2}[/tex]

Now for us the horizontal span is asked from 0 to 10 for the expression which is from [tex]x=0[/tex] to [tex]x=10[/tex] ,in which portion the value of the expression is strictly increasing so the vlaue increases from [tex]0+0+2=2[/tex] to [tex]10^2+190+2=292[/tex].

Answer:

The length of each piece is 2.5.

Step-by-step explanation:

10/4=2.5

Answer:

2.5 ft

The drawing will help

Answer:

m ∠ AMC = 75°

Step-by-step explanation:

Given:

In Δ ABC, m ∠C=90°

m∠ B =30°

CM is angle bisector

We need to find m ∠AMC

In Δ ABC Sum of all angle is 180° so we get,

[tex]m\angle A+m\angle B+m\angle C =180\\m\angle A+90+30 =180\\m\angle A+120 =180\\m\angle A=180-120\\m\angle A=60[/tex]

Now we know that CM is angle bisector of ∠C

∴ [tex]m\angle ACM +m\angle BCM =90\\m\angle ACM +m\angle ACM =90\\2m\angle ACM =90\\m\angle ACM =\frac{90}{2}=45[/tex]

Now in Δ ACM we know that Sum of all angles is 180

[tex]m\angle ACM + m\angle AMC + m\angle A=180\\45 + m\angle AMC + 60 =180\\105 + m\angle AMC =180\\m\angle AMC =180 -105 =75[/tex]

Hence m ∠ AMC = 75°

Answer:

3x^3-18x^2+26x-8

Step-by-step explanation:

(x-4)(3x^2-6x+2)

3x^3-6x^2+2x-12x^2+24x-8

3x^3-6x^2-12x^2+2x+24x-8

3x^3-18x^2+26x-8

Answer:

y = 7 is the equation of the line that passes through the point ( -2, 7 ) and has a slope of zero.

Step-by-step explanation:

Given:

Let,

A ≡ ( x1 , y1 ) ≡ ( -2, 7 )

Slope = m = 0

To Find :

Equation of Line:

Solution:

Formula for , equation of a line passing through a point (  x1 , y1 ) and having a slope m is given by

[tex](y - y_{1})=m(x-x_{1})[/tex]

Now substituting the values of x1 = -2 and y1 = 7 and slope m = 0 we get,

[tex]y-7=0\times(x--2) \\y-7=0\times (x+2)\\y-7=0\\\therefore y=7[/tex]

Which is the required equation of a line passing through the point ( -2, 7 ) and slope zero

The equation of a line that passes through a point is an algebraic equation. It can also be referred to as the Slope-Intercept Equation.

The equation of the line that passes through the point (-2, 7) and has a slope of zero is written as: y = 7

The equation of the line through a point (x1, y1) can be represented by the algebraic equation:

y = mx + c

where:

m = slope

c = y - intercept

From the question,

(x1, y1) = (-2, 7)

m = slope = 0

Substituting these values into the algebraic equation,

7 = (0 x -2) + c

7 = 0

Hence, y = 7

The equation of the line that passes through the point (-2, 7) and has a slope of zero is y = 7

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Answer:

217

Step-by-step explanation:

868/4=217

Answer:

217

Step-by-step explanation:

Answer:

c=2

Step-by-step explanation:

7(2c-1)-3=6+6c

14c-7-3=6+6c

14c-10=6+6c

14c-6c-10=6

8c-10=6

8c=6+10

8c=16

c=16/8

c=2

Answer:

Step-by-step explanation:

[tex]7(2c-1)-3=6+6c\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\\\(7)(2c)+(7)(-1)-3=6+6c\\\\14c-7-3=6+6c\qquad\text{combine like terms}\\\\14c+(-7-3)=6+6c\\\\14c-10=6+6c\qquad\text{add 10 to both sides}\\\\14c-10+10=6+10+6c\\\\14c=16+6c\qquad\text{subtract}\ 6c\ \text{from both sides}\\\\14c-6c=16+6c-6c\\\\8c=16\qquad\text{divide both sides by 8}\\\\\dfrac{8c}{8}=\dfrac{16}{8}\\\\c=2[/tex]

The total bill is $14.64 ⇒ last answer

Step-by-step explanation:

The given is;

Sandwiches

Side Orders

Beverages

∵ You order 2 veggieburgers, one salad, one fries and 2 coffees

∵ The price of the 1 veggieburgers = $3.25

∵ The price of the 1 salad = $2.5

∵ The price of the 1 fries = $1.5

∵ The price of the 1 of one coffee = $0.9

∴ The cost of the order = 2(3.25) + 1(2.5) + 1(1.5) + 2(0.9)

∴ The cost of the order = 6.5 + 2.5 + 1.5 + 1.8 = $12.3

∵ There is a tax 4%

∴ The tax = 4% × 12.3 = [tex]\frac{4}{100}[/tex] × 12.3 = $0.492

∵ There is a tip 15%

∴ The tip = 15% × 12.3 = [tex]\frac{15}{100}[/tex] × 12.3 = $1.845

To find the total bill add the cost of the order, the tax and the tip

∵ The total bill = cost of the order + tax + bill

∴ The total bill = 12.3 + 0.492 + 1.845

∴ The total bill = $14.637 ≅ $14.64

The total bill is $14.64

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Answer:

-9 2/7 is bigger than -9.3.

Step-by-step explanation:

Imagine these two integers on a number line. On the negative side of the line, these two lie. The way I think of it is that the smaller the value is on the positive side, the bigger it is on the negative side. For example, -1 is bigger than -5. -0.5 is bigger than -1. -13.5 is bigger than -13.7.

The given fraction - 9 2/7 is bigger than the given number - 9.3.

Given the fraction is - 9 2/7

-9 2/7 = - (9 + 2/7)

Now, 2/7 is equal to approximately 0.286.

So, - 9 2/7 = - ( 9 + 2/7 ) = - ( 9 + 0.286) = - 9.286

Thus, 9.286 < 9.3

When negative quantity multiplied then inequality sign changes so,

( -1 ) ( 9.286 ) > ( -1 ) ( 9.3 )

- 9.286 > - 9.3

Therefore the given fraction - 9 2/7 is bigger than the given number - 9.3.

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Answer:

Probability that the sum of the two dice is greater than 12 is ZERO.

Step-by-step explanation:

Here, when two dices are rolled together, the sample space is given as:

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5,6)

(6, 1), (6, 2), (6, 3), (6, 4),(6,5), (6,6)  = Total 36 outcomes

Now, E :  Event of getting a  sum greater than 12.

So here, number of possible outcomes  = 0

So, the probability that the sum of the two dice is greater than 12  = 0/36  = 0

So, it is an IMPOSSIBLE EVENT.

It is impossible to roll a sum greater than 12 with two standard six-sided dice, as the maximum sum possible is 12. Therefore, the probability of rolling a sum greater than 12 is zero.

The student asked about the probability that the sum of two standard six-sided dice is greater than 12. Since the highest sum one can achieve with two six-sided dice is 12 (when both dice show a 6), it is impossible to roll a sum greater than 12. Therefore, the probability of this event is zero.

When considering every outcome of rolling a die, we must include all possible individual results, which range from 1 to 6 for each die. The sum of two dice ranges from a minimum of 2 (both dice showing 1) to a maximum of 12 (both dice showing 6). Consequently, there are no combinations of dice that can result in a sum that exceeds 12.

The highest sum achievable on two six-sided dice is 6 + 6 which equals 12. This makes sums greater than 12 unattainable, and highlights the importance of considering the specified number of sides on dice when calculating probabilities related to their sums.

Answer: 0.8660254038

Answer:

y=-2

Step-by-step explanation:

y-y1=m(x-x1)

m=slope & (x1, y1) is a point on the line

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

m=(-2-(-2))/(-3-5)

m=(-2+2)/(-8)

m=0

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

y+2=0

y=0-2

y=-2

Answer:

look at above image for answer. thank you for the question

Using the given conditions, we formed two equations: x + y = -11 and x - y = -3. We then solved these simultaneous equations to find that the two numbers are -7 and -4.

We have been given two conditions to find the values of two numbers, represented by x and y. The first condition can be expressed as the equation x + y = -11. The second condition gives us the second equation x - y = -3.

adding the first and second equation:

(x + y) + (x - y) = -11 + (-3)
2x = -14
x = -7

We can then substitute the value of x back into one of the original equations to solve for y:

-7 + y = -11
y = -11 + 7
y = -4

Thus, the two numbers are -7 and -4.

Answer: 1.4862

Step-by-step explanation: To find 6% of 24.77, first write 6% as a decimal by moving the decimal point two places to the left to get 0.06.

Next, the word "of" means multiply so we will multiply 0.06 by 24.77.

(0.06) (24.77) = 1.4682

Therefore, 6% of 24,77 is 1.4862.