To find the total number of people sitting in the full rows, Mandy multiplied 142 by 10 and 142 by 2 and then added the products. Does Mandy’s method make sense? Use what you know about multiplication to explain why or why not.

The domain and the range of the function are given as follows:

The function in this problem is given as follows:

y = 600 - 75x.

The input variable x represents the number of months, which cannot be negative, hence the lower bound of the domain is given as follows:

x = 0.

Meaning that the upper bound of the range is of y = 600.

The balance remaining cannot be negative, hence:

The problem asks for the domain and the range of the function.

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The perimeter of the square with side of 5 cm is 20 cm.

The perimeter of the square with side length of 15 cm is 60 cm.

The area of each square is calculated as follows;

Let the dimension of first square = x

Let the dimension of second square = y

x² + y² = 250 ---- (1)

4(x + y) = 80 ----- (2)

x + y = 80/4

x + y = 20

x = 20 - y

Substitute x in equation (1)

(20 - y)² + y² = 250

400 - 40y + y² + y² = 250

2y² - 40y + 150 = 0

y² - 20y + 75 = 0

solve for y, using formula method;

y = 15 or 5

Solve for x;

x = 20 -15 = 5 or

x = 20 - 5 = 15

The perimeter of first = 4x = 4 x 5 = 20 cm

The perimeter of the second = 4y = 4 x 15 = 60 cm

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Answer:

A) angle 3 plus angle 6 = 90°

Step-by-step explanation:

just think about it : to the left of m at the intersection with n is 90°. so, to the right it must be 90° too.

because one side of a line represents always 180° for all angles around a single point.

The exact length of the radius of this circle is 2.69 units.

Given that, the length of AB is 2.5 units and the length of CB is 1.5 units.

Since AB is perpendicular to the circle, the triangle ABC is a right triangle. By the Pythagorean theorem, the radius of the circle can be found by solving:

r² = (2.5)² + (1.5)²

r² = 7.25

r = √7.25

r = 2.69 units

Therefore, the exact length of the radius of this circle is 2.69 units.

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Answer:

0.0

Step-by-step explanation:

To find 0.007 divided by 0.498, we can perform the following calculation:

0.007 / 0.498 ≈ 0.0141

Rounding this to the nearest tenth gives:

0.0141 ≈ 0.0

Therefore, the result, rounded to the nearest tenth, is 0.0.

The value of the expression is 0.017455065

Identities enable us to simplify complicated expressions. They are the basic tools of trigonometry used in solving trigonometric equations, just as factoring, finding common denominators, and using special formulas are the basic tools of solving algebraic equations.

The given expression is (Tan π/18 + Tan π/9) ÷ (1 - Tan π/1 Tanπ/9)

This gives [Tan (π/18 * π/9) ÷ 1/(Tan(π/18 * π/9)

Simplify further to have

Tanπ²/162 * 162/π²)

This gives Tan1 =  0.017455065

This implies that  (Tan π/18 + Tan π/9) ÷ (1 - Tan π/1 Tanπ/9) = 0.017455065

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Answer: THE PRODUCT

Step-by-step explanation:

The associative property of multiplication says that the product of three or more numbers remains the same no mater how the numbers are grouped.

example (3x5x2) is the same as ( 5x2x3) both = 30

Using distributive property, the solution to the given expression is: 50v - 40w + 20

The Distributive Property is a term which is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses.

For example:

4(3 + 5)

According to the distributive property, you first have to multiply out the bracket to get:

4*3 + 4*5 = 12 + 20

= 32

Thus:

5(10v - 8w + 4) = (5 * 10v) - (5 * 8w) + (5 * 4)

= 50v - 40w + 20

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The missing number in the ratios of numbers are 16:10     8:20 and 0:30

Ratios are quantitative relationships between two numbers that describe how many times one value can contain another

the given parameters are

Forks         16          8              ----

Spoons       10         ---            30

The numbers are written in ascending order of magnitude

Using AP,

for forks: a = 16, 2nd term = 8

common difference = 8-16 - -8

For spoons a = 10, 3rd term = a + 2d = 30

30 = 10 + 2d

30 -10 = 2d

d= 20/2 = 10

Therefore the 2nd term = 10+10=20

The table reappears as follows

Forks         16          8             0

Spoons       10        20          30

Therefore the equivalent ratios are 16:10     8:20 and 0:30

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The probability that Tom will choose a red marble from the bag is 1/9.

Given that,

Tom is choosing at random from a bag of colored marbles.

Odds in favor = number of success : number of failures

Odds of getting a red marble = 1 : 8

This means that there ratio of red marbles to other marbles = 1 : 8

Number of red marbles = 1

Total number of marbles = 1 + 8 = 9

Probability of choosing a red marble = 1/9

Hence the required probability is 1/9.

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Answer:

D

Step-by-step explanation:

The solutions to y = –8x for x = 2, 4, and 8 are (2, –16), (4, –32), (8, –64), hence, option D is correct.

We are given the equation y = -8x and asked to find the solutions for x = 2, 4, and 8. To find the solutions, we substitute the given values of x into the given linear equation and solve for y.

For x = 2, we have,

y = -8x

y = -8(2)

y = -16

Therefore, the solution for x = 2 is (2, -16).

For x = 4, we have,

y = -8x

y = -8(4)

y = -32

Therefore, the solution for x = 4 is (4, -32).

For x = 8, we have,

y = -8x

y = -8(8)

y = -64

Therefore, the solution for x = 8 is (8, -64).

Putting these solutions together, we get {(2,-16), (4,-32), (8,-64)}. Hence, the correct answer is option D.

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The equation is: (2x + 8) / 4 - 3 = x - 7

The solution is x = 12

Let x be the number you thought of at the beginning. Following the steps:

Multiply by 2: 2x

Add 8: 2x + 8

Divide by 4: (2x + 8) / 4

Subtract 3: (2x + 8) / 4 - 3

The final answer is seven less than the number you thought of at the beginning: (2x + 8) / 4 - 3 = x - 7

The equation is: (2x + 8) / 4 - 3 = x - 7

2. (2x + 8) / 4 - 3 = x - 7

(1/2)x + 2 - 3 = x - 7

(1/2)x - 1 = x - 7

Now add 1 to both sides:

(1/2)x = x - 6

Subtract (1/2)x from both sides:

-1/2x = -6

Now multiply both sides by -2:

x = 12

3. Properties used to solve the puzzle

Addition Property of Equality

Multiplication Property of Equality

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Answer:

1,2, and 4

Step-by-step explanation:

vertical angles theorem, which says that the vertical angles that are formed when two lines intersect are congruent.

Step-by-step explanation:

A linear function is a function where we have a constant rate of change.

The equation of a linear function is

[tex]y = mx + b[/tex]

where m is the slope (change in y/change in x)

and b is the y intercept.

Note: Sometimes our variables will different names, but

Slope is just change in dependent variable/change in independent variable.

A linear function has a constant slope throughout.

In this problem,

t is the independent variable

W is the dependent variable

So our point will. be

(t,W)

where t is number of weeks after planted

and W is weight

So the slope would be

Change in W/Change in t.

We know at 3 weeks, the pumpkin weighed 141

So this point is

(3,141)

We know 7 weeks, later, the pumpkin weighed 372 so

(10,372)

A. The weight the pumpkin gain each week is our slope so

[tex] \frac{372 - 141}{7} [/tex]

[tex] \frac{231}{7} = 33[/tex]

So the pumpkin gained 33 pounds each week.

Part 2: Is in slope intercept form,

and we know the slope,33,

[tex]w = 33t + b[/tex]

We don't know what b is.

Let plug in a coordinate pair, and solve for b.

Let's use (3,141)

[tex]141 = 33(3) + b[/tex]

[tex]141 = 99 + b[/tex]

[tex]42 = b[/tex]

So our equation is

[tex]w = 33t + 42[/tex]

Hope this helps

The weight that the pumpkin gained per week can be found to be 33 pounds.

The equation to show the relationship between pumpkin weight and elapsed time is W = 33 t + 42

The weight gained by the pumpkin per week can be found by the formula :

= (Weight gained after 7 more weeks - Weight after 3 weeks ) / 7 weeks

= ( 372 - 141 ) / 4

= 33 pounds

This means the original weight of the pumpkin was:
= 141 - ( 33 x 3 weeks )
= 42 pounds

The equation to show the relationship between pumpkin growth and weeks is therefore:

W = Growth per week x Number of weeks + original weight

W = 33 x + 42

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The given side lengths, 6 cm and 8 cm, satisfy the Pythagorean theorem because $6^2 + 8^2 = 100 = 10^2$, which means that the triangle is a right triangle.

To determine if there is more than one right triangle with whole-number side lengths that includes these given side lengths, we need to check if there exist other pairs of whole numbers that satisfy the Pythagorean theorem and include 6 cm and 8 cm as two of their sides.

Let's call the third side of the right triangle x. Then we have:

62+82=x26^2 + 8^2 = x^262+82=x2

which simplifies to:

36+64=x236 + 64 = x^236+64=x2

100=x2100 = x^2100=x2

x=100=10x = \sqrt{100} = 10x=100

​=10

So the only other possible triangle with whole-number side lengths that includes the given side lengths has side lengths of 6 cm, 8 cm, and 10 cm.

Therefore, there is only one other right triangle with whole-number side lengths that includes the given side lengths, and it is unique.

Step-by-step explanation:

use the formula V=1/3hπr².

V=1/3×3 π 2×2

V=1/3×12π

V=4πcm3

The amount of flour that will be needed for 38 cakes is 912 grams therefore Johan does not have enough amount of flour

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation.

360 grams is needed for 15 small cakes

therefore for 1 small cake, 369/15 = 24grams will be needed

therefore for 38 small cakes = 38× 24 = 912 grams of flour will be needed.

Johan has 0.85 kg of flours which is equivalent to 0.85 × 1000grams = 850 grams of flour.

Since 912 grams will be needed for 38 small cakes , it shows that Johan does not have enough amount of flour for 38 small cakes.

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The composition of f. g derived from the equations in the attached image is:  [tex]\frac{1}{10}(2x + 1)[/tex] and f+g as  √(4x-1))/(5x²+3)

Composition is a mathematical operation that combines two functions to form a new function. From our question, we are given two functions f(x) and g(x).

One of their composition can be represented by f(g(x)).f(g(x)) means function out of g(x) will serve as input x for function f(x). In a more simpler words, f(g(x)) is the function obtained by taking the output of g(x) and using it as the input for f(x).

Using the question given as an example,

For f.g:

Firstly, we have to compute the composition of f and g.

This can be expressed as:

f(g(x))f(g(x)) = f(√(4x-1))= 1/[5(√(4x-1))² + 3]= 1/[5(4x-1) + 3]

= 1/(20x + 10)

= [tex]\frac{1}{10}(2x + 1)[/tex]

For f+g:

To find f+g, we will just add the two functions together as below:

f+g = 1/(5x²+3) + √(4x-1)= (√(4x-1) + (5x²+3)

= √(4x-1))/(5x²+3)

So the answers are;

f.g: = [tex]\frac{1}{10}(2x + 1)[/tex]

f+g =  √(4x-1))/(5x²+3)

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The probability that a student chosen at random from Jared's class does not own a trampoline is 5/12.

The probability that the student does not own a trampoline is equal to the number of students who do not own a trampoline divided by the total number of students in the class.

The number of students who do not own a trampoline is equal to the total number of students in the class minus the number of students who own a trampoline:

24 - 14 = 10

Therefore, the probability that a student chosen at random from Jared's class does not own a trampoline is:

P(not owning a trampoline) = 10/24

Simplifying the fraction,

P(not owning a trampoline) = 5/12

Therefore, the probability that a student chosen at random from Jared's class does not own a trampoline is 5/12.

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The measures of center or variability are greater than 5 degrees

This Week's Mean: (4 + 13 + 6 + 9 + 8) / 5 = 40 / 5 = 8

Last Week's Mean: (10 + 9 + 5 + 6 + 5) / 5 = 35 / 5 = 7

Then the ranges

This Week's Range: (13 - 4) = 9

Last Week's Range: (10 - 5) = 5

The MAD for both weeks

|(4 - 8)| + |(13 - 8)| + |(6 - 8)| + |(9 - 8)| + |(8 - 8)|

= 4 + 5 + 2 + 1 + 0 = 12

This Week's MAD: 12 / 5 = 2.4

|(10 - 7)| + |(9 - 7)| + |(5 - 7)| + |(6 - 7)| + |(5 - 7)| = 3 + 2 + 2 + 1 + 2 = 10

Last Week's MAD: 10 / 5 = 2

Hence the measures of center or variability are greater than 5 degrees are:

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The 25th percentile for the math scores is 71.65.

In Mathematics and Geometry, the z-score of a given sample size or data set can be calculated by using this formula:

Z-score, z = (x - μ)/σ

Where:

Note: 25th percentile for the math scores is the same as the first quartile for the math scores.

Based on the z-score table A, 25th percentile (0.25) is equal to a z-score of -0.67;

0.2514 = -0.67

By substituting the parameters, we have:

Z-score, z = (x - μ)/σ

-0.67 = (x - 75)/5

x = 75 - 3.35

x = 71.65

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Answer:

22

Step-by-step explanation:

length is given by (3--1=4)

width is given by (2--5=7)

perimeter is given by:

P=2l + 2w

P=2(4)+2(7)

P=8+14

P=22

The number of children ticket sold is 90 while the number of adult ticket sold is 200.

Math land theatre charges $5.00 for children's tickets and $9.00 for adult tickets. One night the theatre sold 290 tickets and took in $2250.

Therefore, let's find the number of each type of ticket sold as follows:

Hence,

Let

Therefore, using equation,

c + a = 290

5c + 9a = 2250

Multiply equation(i) by 5

5c + 5a = 1450

5c + 9a = 2250

subtract the equation

4a = 800

divide both sides by 4

a = 800 / 4

a = 200

Therefore, let's find c

c = 290 - 200

c = 90

Hence,

number of children's ticket = 90

number of adult tickets = 200

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Answer:

$124 per week

Step-by-step explanation:

To fins how much she needs to save each week, divide the total cost by the amount of time. In this problem, divide $2,976 by 24 weeks to find the amount she needs to save.

$2976/24=$124 per week

The number of each type of ad that the department can run each month are:

TV Ads = 32

Radio Ads = 12

News Ads =  20

x = number of tv ads

y = number of radio ads

z = number of news ads

Two formulas are indicated.

x + y + z = 64

1000x + 200y + 600z = 46400

they want as many tv ads as radio and news ads combined.

equation for that is x = y + z

since x = y + z, replace x with y + z in both equations to get;

y + z + y + z = 64

1000 * (y + z) + 200 * y + 600 * z = 46400

combine like terms and simplify to get:

2y + 2z = 64

1000y + 1000z + 200y + 600z = 46400

combine like terms again to get:

2y + 2z = 64

1200y + 1600z = 46400

Solving simultaneously gives:

y = 12

z = 20

Thus:

x = 12 + 20

x = 32

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The cost of the utility pole with a radius of 17.8 cm and a height of 700 cm is; $3774.4

From the information given, we have the following parameters;

Density = 5.4 g/cm³

Mass = Ikg = 0.71 kg

Cost per mass = $0. 51

Let's determine the volume of this cylinder:

Volume = mass / density

Substitute the values

Volume = 0.71 /5.4

Volume = 0.131 cm³

Thus, 0.131  cm³ costs $0.71

For the utility pole;

Volume = 2 πr²h

Where:

r is 17.8cm

height is 700cm

Volume = 3. 142 × 17.8 × 17.8 × 700

Volume = 696414.32 cm³

If  0.131  cm³ costs $0.71

Then  696414.32  cm³ will cost:

= 696414.32   × 0.71/ 0.131  

= 3774.4

Thus, the cost of a utility pole is  $3774.4

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The total distance traveled by Amelia to her friend's house is d = 510 miles

Given data ,

Let the distance traveled by Amelia to her friend's house be d

Now , the speed of the final 4 hours of her journey = 60 km/hr

So , the distance traveled in the final 4 hours = 4 x 60 = 240 km

And , the initial distance traveled = 270 km

So , from the graph

The total distance d = 270 + 240

d = 510 miles

Hence , the distance traveled by Amelia = 510 miles

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The probability that the sum exceeds 5 is P ( A ) = 0.6111

Given data ,

To find the probability of getting two numbers whose sum exceeds 5 when rolling a single die twice, we need to count the number of outcomes where the sum of the two numbers is greater than 5, and then divide that by the total number of equally-likely outcomes.

The outcomes where the sum exceeds 5 are:

(2, 4), (2, 5), (2, 6)

(3, 3), (3, 4), (3, 5), (3, 6)

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

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

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

There are 22 outcomes where the sum exceeds 5 out of a total of 36 equally-likely outcomes.

So, the probability of getting two numbers whose sum exceeds 5 when rolling a single die twice is:

P(sum > 5) = 22 / 36 ≈ 0.6111 or approximately 61.11 %

Hence , the probability is P ( A ) = 0.6111

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The complete question is attached below :

A single die is rolled twice. The 36​ equally-likely outcomes are shown to the right.Find the probability of getting two numbers whose sum exceeds 5