Roberto buys a car. Because he buys the car from his cousin, he does not have to pay interest. He makes a down payment of $3,000 and pays the rest with monthly payments. The equation that represents the amount owed on the car can be represented by the equation y=−150x+2,500, where x is the number of months that Roberto pays off the loan, and y is the amount he still owes. What does 2,500 represent in this equation? A) The original cost of the car. B) The amount Roberto pays per month. C) The down payment that Roberto makes. D) The amount Roberto has to pay after the $3,000 down payment.

The value of A is 31.5.

The square root of any number is the factor that we can be multiplied by itself to get that given number. The symbol for square root is √.

Here, we are given an equation as follows-

A=√[15.5(15.5-14) (15.5-11) (15.5-6)]

Let us simplify it step by step. Firstly, we will perform the operations inside the brackets as follows-

A = √[15.5(1.5) (4.5) (9.5)]

Now, multiplying the terms we get-

A = √[15.5(1.5) (4.5) (9.5)]

A = √[(23.25) (42.75)]

A = √[(993.9375)]

Now, we calculate the square root of the number obtained above-

A = 31.5

Thus, the value of A in the equation A=√15.5(15.5-14) (15.5-11) (15.5-6) comes out to be 31.5.

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Answer:

Step-by-step explanation:

To check for 6 - Number should be Divisible by 2 and 3

4186650 is divisible by 2 % 3

To check for 8 - Las Three digits should be taken as a number and be checked if its divisible my 8

4186650 / 4 = 165.5

So the number is not divisible by 8

To check for 11 - we need to add the odd places and the even places and then subtract them both. if the answer is 11 or 0 then its divisible

4 + 8 + 6 + 0 = 19

1 + 6 + 5 = 12

19 - 12 = 7

So the number is not divisible by 11

Hope you are clear

If the first two spaces are for letters and the remaining five are for numbers, then 67,600,000 distinct seven-plate license plates are possible.

Putting things or numbers in order is known as a permutation. Combinations are a way to choose items or numbers from a collection of items or groups of items without regard to their order.

We can count the number of ways an item set can be rearranged using permutations. When counting combinations, we look at how many options we have from a larger pool of available items. Important statistical concepts include combinations and permutations.

We know that :

It consists of 10 digits and 26 letters.

Due to the repetition of letters and numbers. Since the first two positions are letters, first can be filled in.

26 * 26 = 676 ways.

Five more spots may then be filled.

10 * 10 * 10 * 10 * 10 = 100000ways

If the first two spaces are really for letters and the remaining five spaces are for numbers, then there are a variety of 7-place license plates that can be made.

26 * 26 * 10 * 10 * 10 * 10 * 10 = 67,600,000ways.

If the first two spaces are for letters and the remaining five are for numbers, then 67,600,000 distinct seven-plate license plates are possible.

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To one decimal place, round. points A(-4, 6), B(3, -7), E(-6, -5) and F (2, 0).

The distance between AB is [tex]\sqrt{185}[/tex]=13.601 and EF is [tex]\sqrt{89}[/tex]=9.433.

Given that,

To one decimal place, round.

Points A(-4, 6), B(3, -7), E(-6, -5) and F (2, 0).

We have to find the distance between two points that are AB and EF.

1. The distance between 2 points A and B.

A(-4, 6) and B(3, -7).

Distance formula is [tex]\sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

Here, x₁=-1,x₂=3 and y₁=6,y₂=-7

After substituting we get,

[tex]\sqrt{{(3 -(-1)} )^{2} +(-7 -6 )^{2} }\\[/tex]

[tex]\sqrt{{(3 +1} )^{2} +(-7 -6 )^{2} }\\[/tex]

[tex]\sqrt{{(4} )^{2} +(-13 )^{2} }\\[/tex]

[tex]\sqrt{16 +163}\\[/tex]

[tex]\sqrt{185}[/tex]

13.601

Therefore, the distance between AB is [tex]\sqrt{185}[/tex]=13.601.

2.The distance between 2 points E and F.

E(-6, -5) and F (2, 0).

Distance formula is [tex]\sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

Here, x₁=-6,x₂=2 and y₁=-5,y₂=0

After substituting we get,

[tex]\sqrt{{(2 -(-6)} )^{2} +(0 -(-5) )^{2} }\\[/tex]

[tex]\sqrt{{(2 +6} )^{2} +(0 +5 )^{2} }\\[/tex]

[tex]\sqrt{{(8} )^{2} +(5 )^{2} }\\[/tex]

[tex]\sqrt{64 +25}\\[/tex]

[tex]\sqrt{89}[/tex]

9.433

Therefore, the distance between EF is [tex]\sqrt{89}[/tex]=9.433.

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After 8 chairs have been bought in there are now 216 chairs in the theater.

A unitary method is a mathematical technique for first finding the value of a single unit and then deriving the required units by multiplying with it.

According to the given question, a small theater had 8 rows of 26 chairs each.

∴ The total number of chairs in the theater is (8×26) chairs = 208 chairs.

Later an extra 8 chairs have bought in.

∴ The total no. of chairs in the theater now is (208+8) = 216 chairs.

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y = 30x

Calculate  the number of gallos of water used to water trees i'd 30 times the number of trees.

Let's take,

Number of gallons = y

Number of trees = x

Then, according to the problem,

Number of gallons = 30*(Number of trees)

So….. y = 30*x

y = 30x

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The cost of the guitar after expansion will be $144.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

The price of guitars from universal guitar company increased by 60% when the business expanded. If a guitar cost $90 before the expansion.

Then the cost of the guitar after expansion will be

Cost = (1 + 0.60) x $90

Cost = 1.60 x $90

Cost = $144

The cost of the guitar after expansion will be $144.

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The subway car passes through 48 stations in 2hours

It is given that a subway car passes 4 stations every 10 mins.

Subway car is being referred to the metro system of New York city

It is known to us that an hour has 60 mins

We are given that subway car passes 4 stations every 10 mins

Therefore number of stations passed by subway car in 1 hour

= 60/10 x 4 = 24 stations

We are required to find the number of stations crossed by subway car in 2 hours

Therefore, number of stations crossed by subway car in 2 hours= 24 x 2

= 48  stations

Therefore, the subway car passes 48 stations in 2 hours

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If a road repair crew spread 13 1/4 tons of gravel evenly over 4.5 feet of road then 2.39 tons of gravel is spread by them on each foot of road.

This is solved by using unitary method

4.5 feet of road is getting covered by 13 1/4 tons of gravel

Then 1 foot of road will be covered by (13 1/4) /4.5 tons of gravel

= (43/4) / 4.5 tons of gravel

= 2.388 tons of gravel

2.39 tons of gravel is required to cover 1 foot

If a road repair crew spread 13 1/4 tons of gravel evenly over 4.5 feet of road then it requires 2.39 tons of gravel is spread by them on each foot of road.

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Answer:

2+x/6=w

step by step

From the given Alex and Joey  hats equation we got Alex has 24 hats Joey has 11 hats.

Given that,

Joey only has 2 times more hats than Alex, who has 2 more. The difference between the amount of hats Alex has and the 5 that Joey has is also 4 times the number of hats Alex has.

We have to discover how many hats each one of them has.

Let Alex has x hats Joey has y hats.

From the given

We get

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

x=4(y-5) --------> equation (2)

Equating equation (1) and equation (2)

2y+2=4(y-5)

2y+2=4y-20

2y-4y=-20-2

-2y=-22

y=-22/-2

y=11

Take y=11 in equation (1)

x=2(11)+2

x=22+2

x=24

Therefore,  Alex has 24 hats Joey has 11 hats.

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She will need 1.34 pounds of salt for a full of bucket of water.

It is given that, Kayke mixes 1/6 pound of salt with 1/8 bucket of water to make a saline solution.

With 1/8 bucket of water she mixes 1/6 pound of salt.

1/8 bucket of water = 1/6 pounds of salt

Now, using unitary method to find salt needed to use for a full bucket of water.

So,

1 bucket of water = 8/6 pounds of salt

= 1.34 pounds of salt.  

She will need 1.34 pounds of salt for a full of bucket of water.

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The minimum perimeter is 23.24m and dimensions of the fenced area is 15.5m x 3.8m.​

Let us assume the length of the fenced area to be L and breadth of the fenced area to be W. As we know, only three sides are to be fenced,

So, the perimeter  P of the fenced would be,

P = L + 2W

Also, it is given that, area of the fence is 60m²,

So, the are should be,

60m² = LW

60m²/L = W

Now, to minimize the perimeter,

P = L + 2W

P = L + 120/L

Differentiating both sides with respect to "L",

d(p)/dL = 1 - 240/L²

To find the value of "L", putting dp/dL equal to 0,

d(P)/dL = 0

1 - 240/L² = 0

L = √240m

Now, from the first derivative test, we know that, the perimeter will be maximum or minimum if value of L>√240 or L<√240 respectively,

For minimum, L should be,

L = √240m

L = 15.5m

Now we know from area,

area = LW

60 = 15.5 x W

W = 60/15.5

W = 3.8m

Hence, the minimum perimeter will be,

L + 2W = 23.24m

The dimensions are,

L = 15.5m

W = 3.8m

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The simplest form of product is, 28c¹³.

⇒ -7c⁷ * (-4c⁶) = 28 c¹³

The given expression can be simplified as;

The given product is;

-7c⁷ * (-4c⁶)

We have to simplify the given product.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Now, The given expression can be simplified as;

The product is given as;

-7c⁷ * (-4c⁶)

We can simplify by the rule of exponent as;

-7c⁷ * (-4c⁶)

= 28 c⁷⁺⁶

= 28 c¹³

So, -7c⁷ * (-4c⁶) = 28 c¹³

Hence, The simplest form of product is find as 28c¹³.

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Answer:

Step-by-step explanation:

Discussion

Note: I think the length is supposed to be the height of 1 cookie.

The volume of the 12 cookies (1 dozen=12) is 176,715 in^3

The area of 1 cookie is 5 in

Area = pi * r^2

Area  of one cookie = 3.14 * 5^2

Area of one cookie = 78.5 in ^2 Note this is also the area of the base of the container.

Height of the 12 cookies = Volume / Area of one cookie

Height of the 12 cookies = 176.715/78,5

Height of the 12 cookies = 2.25 inches.

Answer

Thickness (height) of one cookie = 2.25/12

Thickness (height) of one cookie = .188 inches.

Answer: 2.2 miles per hour

Step-by-step explanation:

Since we are given his speed in one third of an hour, we can simply triple his speed to get his miles per hour.

[tex]\frac{11}{15} * 3\\= \frac{33}{15}\\\\= 2 \frac{1}{5}[/tex]

or, 2.2 miles per hour

Answer:

2.2mph!

Step-by-step explanation:

Answer:

multiply input number by 2

Step-by-step explanation:

So, this is our function

y=2x===>

(3, 6), (4, 8), (5, 10), (6, 12), (7, 14)

so according to this functionality the output part is equal to input part multiplied by 2

According to the given statements:

a. If the integers x and y are, respectively, even and odd, then xy is even.

b. When x is odd, x2 is also odd.

c. If p is a prime number, p2 is not a prime number.

d. If the integers a and b are negative, then ab is also a negative number.

e. If AC and BD are diagonally arranged in a rhombus, then AC is perpendicular to BD.

A numeral system, also known as a mathematical notation, is a way of writing numbers that uses digits or even other symbols to represent the numbers in a given set in a standardized way. The same set of symbols can represent various numbers in various numeral systems.

A. if a, then b the product of an odd integer and an even integer is even.

If the integers x and y are, respectively, even and odd, then xy is even.

B. if a, then b  the square of an odd integer is odd.

When x is odd, x2 is also odd.

C.  if a, then b  the square of a prime number is not prime.

 If p is a prime number, p2 is not a prime number.

D. the product of two negative integers is negative. (this, of course, is false.)

If the integers a and b are negative, then ab is also a negative number.

E.  the diagonals of a rhombus are perpendicular.

If AC and BD are diagonally arranged in a rhombus, then AC is perpendicular to BD.

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I understand that the question you are looking for is:

Each of the following statements can be recast in the if-then form. please rewrite each of the following sentences in the form "if a, then b."

a. the product of an odd integer and an even integer is even.

b. the square of an odd integer is odd.

c. the square of a prime number is not prime.

d. the product of two negative integers is negative. (this, of course, is false.)

e. the diagonals of a rhombus are perpendicular

The measure m<D is 26

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

Given:

m<ABE = 52

<EBD = <CBD

Now,

<ABE + <EBD + <DBC = 180 (linear pair)

52 + 2<EBD = 180

2<EBD = 128

<EBD = 128/2

<EBD = 64

Now, In ΔDEB using angle sum property

<DEB + <EDB + <DBE = 180

90+ <EDB + 64=180

<EDB = 26

Hence, the measure of <D is 26 degree.

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Answer:

0.522

0.063

Step-by-step explanation:

6 x 8.7 = 52.2

6 x 1.05 = 6.3

If we move them both two decimal places then...

0.522

0.063

59265 divided by a number raised to the 8th power × 596 × 427 is presented as follows;

[tex]15082468380 \times {x}^{ - 8} [/tex]

The given number to be divided is 59265

Let x represent the number that is raised to the 8th power, we have;

The number by which 59265 is divided = x⁸

The number by which the result is multiplied = 596 × 427

Therefore, we have;

[tex] \frac{59265}{x^8} \times 596 \times 427 = \frac{59265}{ {x}^{8} } \times 254492 [/tex]

The above expression can be expressed using the rules of indices as follows;

[tex]\frac{59265 \times 254492}{ {x}^{8} } =15082468380 \times {x}^{ - 8} [/tex]

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Using relations in a right triangle, we have that the height of the tree is of 91.6 meters.

The relations in a right triangle are given as follows:

The graph for this problem is given at the end of the answer, and using it and the relations, we can build two equations involving x and the height h, and solve the system of equations for h.

From the triangle involving point G(angle of 43º), we can build the following relation:

tan(43º) = h/x

0.9325 = h/x

x = (1/0.9325)h.

x = 1.0724h (because we want to find h, hence we write x as a function of h).

From the larger triangle, that has the angle of 38º, we have the following relation.

tan(38º) = h/(x + 19).

tan(38º) = h/(1.0724h + 19). (considering that x is a function of h, as we found above).

0.7813 = h/(1.0724h + 19).

Hence, we apply cross multiplication to solve for h, as follows:

h = 0.7813(1.0724h + 19).

h = 0.8379h + 14.8447.

0.1621h = 14.8447

h = 14.8447/0.1621

h = 91.6 meters.

Hence:

The height of the tree is of 91.6 meters.

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The required solutions are,
1) point A on the triangle is the center of dilation.
2) Triangle ABC is the original triangle.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

Here,
1) As shown in the figure, after dilation the only initial point that does not change points A. So it could be concluded that point A is the center of dilation.
2) since the scale factor is of 1/2 implies that the dilated figure is lower than the size of the original figure hence, triangle ABC is the original triangle.

Thus, the required solutions are,
1) point A on the triangle is the center of dilation.
2) Triangle ABC is the original triangle.

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The inequality that shows the possible distances of house A from house C is x ≥ 5

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

An inequality is a mathematical statement that compares two values or expressions using a relational operator, such as less than (<), greater than (>), less than or equal to (≤), greater than or equal to (≥), or not equal to (≠). Inequalities are used to describe relationships between quantities or to express constraints or conditions.

We are given that;

Distance= 4miles

Let x be the distance of house A from house C. Since house B is 4 miles from house A, and house C is at least 1 mile from house B, we can write an inequality that relates x, 4, and 1:

x ≥ 4 + 1

This inequality means that the distance of house A from house C is greater than or equal to the sum of the distances of house A from house B and house B from house C.

To solve this inequality, we need to simplify it by adding 4 and 1:

x ≥ 5

Therefore, by inequality the answer will be x ≥ 5.

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Answer:

A.2

explanation:

the equation to find circumference is [tex]2\pi (radius)[/tex]

the circumference of A is [tex]2\pi 8 = 50.27[/tex]

the circumference of B is [tex]2\pi 4 = 25.13[/tex]

50.27/25.13 = 2/1

The two dependent variables will be:

1. The women who gained weight during the pregnancy.

2. The women who smoked during the pregnancy.

We are given that a study of a very large number of pregnant women in Arkansas reports that the women gained, on average, 14 pounds during their pregnancy and that 18% of the women smoked.

Now, we need to tell the two variables of the study.

Now, we can see that the independent variable is pregnant women.

Also, the two dependent variables will be:

1. The women who gained weight during the pregnancy.

2. The women who smoked during the pregnancy.

Therefore, the two dependent variables will be:

1. The women who gained weight during the pregnancy.

2. The women who smoked during the pregnancy.

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Answer:

24

Step-by-step explanation:

140/6 = 23.3333333333333

You can’t have .3 of a car, so you would need to round up.

23.333333333333333 rounds up to 24

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