A serial killer is stalking the residents of Gloomy Falls, Mass. Where the population is 937. Every year the population decreases by 4.5%. How many residents will be left after the killer's three-year rampage? How would you stop him?

Answer:

There was 150 hamburgers sold on Saturday

Step-by-step explanation:

Step 1:  Make an equation

2x + x = 450

Step 2:  Solve for x

2x + x = 450

3x / 3 = 450 / 3

x = 150

Answer:  There was 150 hamburgers sold on Saturday

Final answer:

The local hamburger shop sold 150 hamburgers on Saturday. This was found by setting up a system of equations where H represents hamburgers and C represents cheeseburgers, and solving for H.

Explanation:

To determine how many hamburgers were sold on Saturday, we can set up a system of equations based on the information given:

Let H represent the number of hamburgers sold.

Let C represent the number of cheeseburgers sold.

We are told that the total number of hamburgers and cheeseburgers sold is 450, so:

H + C = 450

We also know that the number of cheeseburgers sold was two times the number of hamburgers sold, so:

C = 2H

Now we substitute the second equation into the first one to solve for H:

H + 2H = 450

3H = 450

H = 450 / 3

H = 150

Therefore, on Saturday, the local hamburger shop sold 150 hamburgers.

Answer:

22 1/2 cakes

Step-by-step explanation:

1 cake = 1 1/3 hours

Number of cakes in 30-hour week

= 30 ÷ 1 1/3

= 30 ÷ 4/3

= 30 x 3/4

= 90/4

= 45/2

= 22 1/2

Answer: 22 1/2 cakes

The range of the data set is 67 pounds.

The range of a data set is the difference between the maximum and minimum values. In this case, the weights of the 7 dogs are 66, 8, 12, 74, 36, 66, and 7 pounds. To find the range, we subtract the smallest value (7) from the largest value (74):

Range = 74 - 7 = 67

So, the range of the data set is 67 pounds.

Answer: 24 cups.

Step-by-step explanation:

Let be "x" the amount of cups of peaches  that Fred will need to make 60 cups of  fruit salad.

According to the information given in the exercise, you know that the ratio of cups of peaches to cups of cherries is the one shown below:

[tex]2:3[/tex]

Which can also be written as a fraction:

[tex]\frac{2}{3}[/tex]

Then, if he uses 2 cups of peaches and 3 cups of cherries, he will get 5 cups of fruit salad.

Knowing the above, you can set up the following proportion:

[tex]\frac{2}{5}=\frac{x}{60}[/tex]

Now you must solve for "x" in order to find its value. This is:

[tex](60)(\frac{2}{5})=x\\\\x=24[/tex]

Answer:

7

Step-by-step explanation:

to edge a lawn =10.he edged 4 lawn =10multiplied by 4=40

2nd. total -40=180-40=140

3rd. when he mows 1 lawn he is paid 20 what about when he is paid 140=140 divided by 20 =7

Makoto mowed 7 lawns to earn $180.

Let's denote the number of lawns Makoto mowed as m. Since he edged 4 lawns, that part of the income is 4 times $10, which sums up to $40. The total income from mowing is then $20 times the number of lawns he mowed, which is m. The equation representing Makoto's earnings is:

20m + 40 = 180

Subtracting 40 from both sides gives us:

20m = 140

Dividing both sides by 20 to solve for m gives us:

m = 7

Answer:

745.12

Step-by-step explanation:

30 x 30 = 900 which is the sign if it were a square

then you subtract the four corner pieces

900 - 4([tex]\frac{1}{2}[/tex](8.8 x 8.8))

900 - 2(77.44)

900 - 154.88

= 745.12

Answer:

5x + 22y = 21

        or

5x + 22y - 21 = 0

Step-by-step explanation:

evaluate    7 = 5x+y÷3-3y​

7 = [5x + y]/[3-3y]

Don't forget 7 can also be expressed in form 7/1,

so the step to follow is using a cross multiplication technique.

we have ;

5x + y = 7(3 - 3y)

5x + y = 21 - 21y

Collect the like terms (note when the negative sign crosses over the equal to sign it changes to positive and the same thing applies to positive sign it changes to negative respectively.)

5x + y  + 21y = 21

5x + 22y = 21

5x + 22y - 21 = 0

Answer:

Answer:

Step-by-step explanation:

Let x represent the cost of one package of tulip bulbs.

Let y represent the cost of one bag of daffodil bulbs.

Ava bought 6 packages of tulip bulbs and 12 bags of daffodil bulbs for a total of $198. This means that

6x + 12y = 198- - - - - - - - - - - - -1

Grace spent $254 buying 14 packages of tulip bulbs and 12 bags of daffodil bulbs. This means that

14x + 12y = 254- - - - - - - - - - - - 2

Subtracting equation 2 from equation 1, it becomes

- 8x = - 56

x = - 56/-8

x = 7

Substituting x = 7 into equation 1, it becomes

6 × 7 + 12y = 198

42 + 12y = 198

12y = 198 - 42

12y = 156

y = 156/12

y = 13

4

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Step-by-step explanation:

Answer:

Step-by-step explanation:

Let x represent the cost of one package of tulip bulbs.

Let y represent the cost of one bag of daffodil bulbs.

Ava bought 6 packages of tulip bulbs and 12 bags of daffodil bulbs for a total of $198. This means that

6x + 12y = 198- - - - - - - - - - - - -1

Grace spent $254 buying 14 packages of tulip bulbs and 12 bags of daffodil bulbs. This means that

14x + 12y = 254- - - - - - - - - - - - 2

Subtracting equation 2 from equation 1, it becomes

- 8x = - 56

x = - 56/-8

x = 7

Substituting x = 7 into equation 1, it becomes

6 × 7 + 12y = 198

42 + 12y = 198

12y = 198 - 42

12y = 156

y = 156/12

y = 13

4

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Answer:

1200 cm is bigger. There are 100 cm in a meter. In 10 meters, there are 1000 cm. 1200 cm is longer than 1000 cm (10 meters)

Step-by-step explanation:

Answer: 5.8 ft

Step-by-step explanation:

We can use the Pithagorean Theorem in this problem, in order to find the length of the rope:

[tex]h^{2}=a^{2}+b^{2}[/tex]

Where:

[tex]h[/tex] is the length of the rope (the hypotenuse of the right triangle formed by the height of the tent, the rope and the ground)

[tex]a=5 ft[/tex] is the height of the tent (one of the legs of the right triangle)

[tex]b=3 ft[/tex] is the other leg of the right triangle

Solving the equation with the given data:

[tex]h^{2}=5^{2}+3^{2}[/tex]

Finding [tex]h[/tex]:

[tex]h=\sqrt{(5 ft)^{2}+(3 ft)^{2}}[/tex]

[tex]h=\sqrt{25 ft+9 ft}[/tex]

[tex]h=5.83 ft \approx 5.8 ft[/tex] This is the total length of nylon rope

Answer

3

Step-by-step explanation:

the formulas say it

Answer: [tex]x=12, -2[/tex]

Step-by-step explanation:

[tex](x-5)^{2}=49[/tex]

F.O.I.L the binomial

[tex]x^2-10x+25=49[/tex]

Set to 0

[tex]x^2-10x+25_{-49} =49_{-49}[/tex]

[tex]x^2-10x-24=0[/tex]

Factor the polynomial

[tex](x-12)(x+2)[/tex]

Set to 0 and Inverse operations

[tex](x-12)=0\\x=12[/tex]

Set to 0 and Inverse operations

[tex](x+2)=0\\x=-2[/tex]

Answer:

[tex]x=12, -2[/tex]

Answer:

24 stations

Step-by-step explanation:

we know that

six stations represent 25% of the stations offered

so

using a proportion

Find out how many stations represent a percentage of 100%

[tex]\frac{6}{25\%}=\frac{x}{100\%}\\\\x=6(100)/25\\\\x=24\ stations[/tex]

Option C:

The value of m is 4.

Solution:

Given data:

AB = 4m – 15

BC = 5m –6

AC = 15

To find the value of m:

Using segment addition postulate,

AB + BC = AC

4m – 15 + 5m –6 = 15

Arrange the like terms together.

4m + 5m – 15 – 6 = 15

9m – 21 = 15

Add 21 on both sides of the equation,

9m = 36

Divide by 9 on both sides of the equation.

m = 4

The value of m is 4.

Option C is the correct answer.

Answer:

is 4

Step-by-step explanation:

i got it right on the test

Answer: 122.5 Miles.

Step-by-step explanation: This is because if you multiply 35 miles by 3.5 inches, you get 122.5 miles.

Hope this helps!

Given:

The equation of the line passes through the point (6,9) and is perpendicular to the line whose equation is [tex]4 x-6 y=15[/tex]

We need to determine the equation of the line.

Slope:

Let us convert the equation to slope - intercept form.

[tex]-6 y=15-4x[/tex]

   [tex]y=\frac{2}{3}x-\frac{5}{2}[/tex]

From the above equation, the slope is [tex]m_1=\frac{2}{3}[/tex]

Since, the lines  are perpendicular, the slope of the line can be determined using the formula,

[tex]m_1 \cdot m_2=-1[/tex]

  [tex]\frac{2}{3} \cdot m_2=-1[/tex]

      [tex]m_2=-\frac{3}{2}[/tex]

Therefore, the slope of the equation is [tex]m=-\frac{3}{2}[/tex]

Equation of the line:

The equation of the line can be determined using the formula,

[tex]y-y_1=m(x-x_1)[/tex]

Substituting the point (6,9) and the slope [tex]m=-\frac{3}{2}[/tex] in the above formula, we get;

[tex]y-9=-\frac{3}{2}(x-6)[/tex]

Simplifying the terms, we get;

[tex]2(y-9)=-3(x-6)[/tex]

[tex]2y-18=-3x+18[/tex]

[tex]3x+2y=36[/tex]

Thus, the equation of the line is [tex]3x+2y=36[/tex]

The equation of a line that is perpendicular to the line 4x - 6y = 15 and passes through the point (6,9) is 3x + 2y = 36. This is because the slope of the new line is the negative reciprocal of the slope of the given line, and the line passes through the given point (6,9).

The subject of this question is mathematics, specifically in the topic of linear equations. To find the equation of a line that is perpendicular to a given line and passes through a certain point, we first need to find the slope of the given line. The standard form of the equation of a line is Ax + By = C. The given line is 4x - 6y = 15. We can find its slope by taking the negative reciprocal of the coefficient of x (A) over the coefficient of y (B), so the slope of the given line is -4/-6 = 2/3. Since we want a line that is perpendicular to the given line, the slope of the line we are looking for would be the negative reciprocal of the slope of the given line, which would be -3/2, because perpendicular lines have slopes that are negative reciprocals of each other. Using the point-slope form of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point, the equation of the line we are looking for is y - 9 = -3/2(x - 6), which simplifies to 2y - 18 = -3x + 18 and further simplifies to 3x + 2y = 36. So the answer is none of the given options.

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Answer: b

Step-by-step explanation:

Answer:

[tex]IG=28.9\ ft[/tex]

Step-by-step explanation:

we know that

In the right triangle GHI

[tex]cos(G)=\frac{IG}{GH}[/tex] ----> by CAH )adjacent side divided by the hypotenuse)

substitute the given values

[tex]cos(21^o)=\frac{IG}{31}[/tex]

solve for IG

[tex]IG=cos(21^o)(31)=28.9\ ft[/tex]

see the attached figure to better understand the problem

Answer:

24.6

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

6 : 1

66 : X

X/66 = 1/6

X = 11

Answer:

8x^3 + 4x^2 + 4x -7

Step-by-step explanation:

Add like terms.

Answer: everything is explained in the picture

Step-by-step explanation:

Answer:

V=lwh/3

Step-by-step explanation:

Answer:

C Both relation and function.

Step-by-step explanation:

This would pass the vertical line test so it is both a relation and a function

Answer:

B) associative

Step-by-step explanation:

The associative property of multiplication says you can choose which pair of numbers to multiply first, so when every operation is multiplication, you can move parentheses without changing the answer.

The given equation 4×7×3 = 7×4×3 demonstrates the Commutative Property. This is the property which states that the order in which numbers are multiplied or added does not affect the result.

The equation 4×7×3 = 7×4×3 demonstrates the Commutative Property. In mathematics, the Commutative Property refers to the fact that the order in which numbers are multiplied does not change the result of the multiplication. This is why we can rearrange the factors 4, 7, and 3 in any order and still get the same product.

For instance, we can express the commutative property of multiplication as a×b = b×a. So, in your example, the equation 4×7×3 = 7×4×3, is an application of this principle as you are simply rearranging the order of numbers being multiplied.

Please remember that this rule applies only to addition and multiplication, not subtraction or division.

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Answer:

v > -1

Step-by-step explanation:

1/3(v-2) < v

Multiply both sides by 3(from 1/3) to equalize both sides.

This is equal to:

v-2 < 3v

Simplify equation:

v-2 < 3v =

-2 < 3v - v =

-2 < 2v

-1 < v

Swap sides:

v > -1

Therefore v is greater than -1.

Answer:

v > -1

Step-by-step explanation:

Simplify the left side.

Apply the distributive property.

13v+13⋅−2<v

Combine 13 and v

v3+13⋅−2<v

Combine 13 and −2

v3+−23<v

Move the negative in front of the fraction.

v3−23<v

Move all terms containing v to the left side of the inequality.

Subtract v from both sides of the inequality.

v3−23−v<0

Simplify the left side of the inequality.

−2(v+1)3<0

Multiply each term in −2(v+1)3<0 by −1

2(v+1)3>0

Multiply both sides of the equation by 3

2(v+1)>0⋅(3)

and again Simplify the left side.

Apply the distributive property.

2v+2⋅1>0⋅(3)

Multiply 2 by 1

2v+2>0⋅(3)

Multiply 0 by 3

2v+2>0

Subtract 2 from both sides of the inequality.

2v>−2

Divide each term by 2 and simplify.

Getting the conclusion where V is greater than 1

v>−1

Hope this helps

Final answer:

To find the width of a rectangle when the length is 2 units more than the width and the area is known to be 48 units, you can use algebraic equations to determine the width. In this case, the width of the rectangle is 6 units.

Explanation:

To find the width of the rectangle:

Let x be the width of the rectangle.

Since the length is 2 units more than the width, the length is x + 2.

Given that the area is 48 units, use the formula for the area of a rectangle: width x length = area. Therefore, x(x + 2) = 48.

Solve for x by setting up the equation: x^2 + 2x - 48 = 0.

Factor the quadratic equation: (x + 8)(x - 6) = 0.

Since the width cannot be negative, the width of the rectangle is 6 units.

The width of the rectangle is 6 units.

According to the question, the length is 2 units more than the width, so we can express the length as ( w + 2 ) units.

The area of a rectangle is given by the product of its length and width. Therefore, we can set up the following equation to represent the area of the rectangle:

[tex]\[ \text{Area} = \text{length} \times \text{width} \] \[ 48 = (w + 2) \times w \][/tex]

Expanding the right side of the equation, we get:

[tex]\[ 48 = w^2 + 2w \][/tex]

To find the value of w, we need to solve the quadratic equation. Let's rearrange the equation to set it equal to zero:

[tex]\[ w^2 + 2w - 48 = 0 \][/tex]

Now, we can factor this quadratic equation:

[tex]\[ (w + 8)(w - 6) = 0 \][/tex]

Setting each factor equal to zero gives us two possible solutions for w:

[tex]\[ w + 8 = 0 \quad \text{or} \quad w - 6 = 0 \][/tex]

Solving for w, we get:

[tex]\[ w = -8 \quad \text{or} \quad w = 6 \][/tex]

Since the width of a rectangle cannot be negative, we discard the negative solution. Therefore, the width of the rectangle is:

[tex]\[ w = 6 \text{ units} \][/tex]

Answer:

5x=-15

Step-by-step explanation:

8x-6x=4-10

2x=-6

x=-3

5x=-15

Answer: A/5+30*5

Step-by-step explanation:

Answer: 2 tons.

Step-by-step explanation:

1 pound = 0.0005 tons.

4,000*0.0005=2

Jasmine's rhino weighs 2 tons

Answer:

2 tons

Step-by-step explanation:

Since 1 ton is 2000 pounds, we can make a proportion:

2000lbs/1ton=4000lbs/xtons

4000lbs=2000lbs*xtons

2=tons

So Jasmine's pet rhino weighs 2 tons

Answer:

2x ÷ 4 = 8

Step-by-step explanation:

2x ÷ 4 = 8

2x/4 = 8

2x = 32

x = 16