You have $12 to spend at a vending machine. A pack of Starbursts cost $1 and a pack of M&M chocolates cost $2. You want to buy at least three packs of Starbursts.

a. Write a system of linear inequalities that represents this situation.
b. How many packs of each type of candy can you possibly purchase?

Answer:

Product: 96

GCF: 4

LCM: 24

Product of the GCF and LCM: 96

Step-by-step explanation:

Now that we know what definitions are, we can solve this word problem.

12 × 8 = 96.

96 is the product.

To find the greatest common factor, we can list all of the factors for each number.

12: 1, 2, 3, 4, 6, 12

8: 1, 2, 4, 8

The largest factor both numbers have in common is 4.

Therefore, 4 is the greatest common factor.

To find the least common multiple, we can list the multiples of both numbers.

12: 12, 24, 36, 48, 60, 72, 84, 96

8: 8, 16, 24, 32, 40, 48, 56, 64

The smallest multiple both numbers have in common is 24.

Therefore, 24 is the least common multiple.

Lastly, we have to find the product of the GCF and the LCM.

The GCF is 4 and the LCM is 24.

4 × 24 = 96.

96 is the product.

Therefore, 96 is the product of the greatest common factor and the least common factor of 12 and 8.

Depending on whether a and b are real numbers, they can factor as (a + b) (a + b) or (a - b)(a - b). Forms like (a + b)(a - b) are unique products also known as the difference of squares.

When you square an integer, you get perfect squares. The number 81, for example, is a perfect square since it can be derived by squaring 9: 99=81. Because 12 can be squared to make 144, 144 is a perfect square. 13 may be squared to make 169, which is a perfect square. Mathematics-related language. Informally: When an integer (a "whole") number is multiplied by itself, whether the result is positive, negative, or zero, the result is referred to as a square number, a perfect square, or simply "a square." All square numbers are therefore 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on.

given

Perfect square trinomials, also referred to as trinomial squares, are the squares of binomial expressions.

Depending on whether a and b are real numbers, they can factor as (a + b)(a + b) or (a - b)(a - b). Forms like (a + b)(a - b) are unique products also known as the difference of squares.

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Answer:

The height of the triangle = 6 inches

The base of the triangle = 10 inches

Step-by-step explanation:

The formula for the Area of a Triangle = 1/2 × Base × Height

Area = 30 in²

h = b - 4

Hence

30 = 1/2 × b × b - 4

Cross Multiply

30 × 2 = b² - 4b

60. = b² - 4b

b² - 4b - 60

We factorise the Algebraic expression to find b

b² - 4b - 60 = 0

b² - 10b + 6b - 60 = 0

b(b - 10) + 6(b - 10) = 0

(b - 10) + (b + 6 ) = 0

b - 10 = 0 , b = 10

b + 6 = 0, b = -6

We are going to take the positive answer of b as the value of b

b = 10 inches

Solving for h

h = b - 4

h = 10 - 4

h = 6 inches

Therefore, the height of the triangle = 6 inches

base of the triangle = 10 inches

The height of the Building is 110.01 feet.

The square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides, according to Pythagoras' Theorem.

Given, Finn leaned a 100-foot ladder against the side of a building. The base of the ladder is 14 feet from the base of the building. The top of the ladder is 11 feet from the top of the building.

For the triangle made by ladder

hypotenuse = 100

base = 14

thus, from the Pythagorean theorem

hypotenuse² = base² + height²

100² = 14² + height²

height² = 10000 - 196

height = √9804

height = 99.01

total height of the wall = height of triangle + remaining height of the wall

Thus the total height of the wall  = 99.01 + 11

the total height of the wall  = 110.01

therefore, the building is 110.01 feet tall.

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Answer:42.875 feet3

Step-by-step explanation:

Answer:

Step-by-step explanation:

V=a³

=[tex](3\frac{1}{2})^3=42\frac{7}{8}[/tex]in³

Answer: [tex]35x+9\leq 310,\ 8[/tex]

Step-by-step explanation:

Given

A group of friends has $310 to spend

Parking costs $9 and ticket cost $35 per person

Suppose  there are x friends who go to amusement park

So, the cost of tickets and parking must be less than or equal to $310

[tex]\Rightarrow 35x+9\leq 310\\\text{Subtract 9 from both sides}\\\Rightarrow 35x\leq 301\\\text{Divide both sides by 35}\\\Rightarrow x\leq 8.6[/tex]

This indicates that there sholud be maximum 8 persons who can go to amusement park with this much money.

It will cost $10.00 to waterproof a canvas truck cover that is 15' x 24'.

To find this, we need to first convert the dimensions of the canvas truck cover from feet to yards, since the cost is given per square yard. 15' x 24' = 180 sq ft. 1 sq yard is equal to 9 sq ft, so 180 sq ft/9 sq ft/yard = 20 sq yard. Then we multiply the square yards by the cost per square yard to find the total cost:

It's important to note that the measurements of the canvas truck cover are given in feet and the cost is given per square yard. It's important to convert it to square yards to match the unit of measurement and calculate the cost.

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Answer:

g= 92°

h= 88°

k= 91°

m= 89°

Step-by-step explanation:

Answer:

g = 92°

h = 88°

k = 91°

m = 89°

Step-by-step explanation:

Have a nice day!

Answer:

[tex]-\sqrt{7/4}[/tex]

Step-by-step explanation:

[tex] \sin( \theta) = \frac{ \sqrt{3} }{2} [/tex]

Answer:

A, y = x

Step-by-step explanation:

Slope is equal to one

Y-intercept is origin

Answer:

A.) Y=X

Step-by-step explanation:

It intercepts with origin

Eight 1/2s are in 4. This can be visualized with pattern blocks, as four triangles (each triangle is 1/2) would be needed to make up a square (4).

Visualization is the process of creating graphical representations of data and information. It can take the form of charts, graphs, diagrams, maps, and other visual representations of data and patterns. Visualization can be used to explore, analyze, and communicate data in an effective and meaningful way, helping to make complex data more accessible and easier to understand. Visualization can also help to uncover trends and relationships that might otherwise be difficult to detect.

b. Three 2/3s are in 2. This can be visualized with pattern blocks, as three hexagons (each hexagon is 2/3) would be needed to make up a rectangle (2).
c. Six 1/6s are in 1. This can be visualized with pattern blocks, as six rhombuses (each rhombus is 1/6) would be needed to make up a hexagon (1).

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The greatest number of classrooms is 4, Joanne can distribute materials

5 flyers and 4 buttons.

The greatest number that can divide the numbers in equal parts.

It is called as greatest common factor or GCF.

Given:

Joanne is campaigning for class president and plans to distribute some campaign materials.

20 flyers and 16 buttons.

She wants each classroom to receive an identical set of campaign materials, without having any materials left over.

In order to find the greatest number of classrooms, Joanne can distribute materials:

We have,

the number of flyers = 20.

Number of buttons = 16

We need to find the GCF.

GCF of 16 - 1,2,4,8,16

GCF of 20-1,2,4,5,10,20

Clearly, 4 is the GCF.

Therefore, total number of classrooms = 4

Number of flyers distributed to each classroom

= Total number of flyers / Total number of classroom

= 20/4

= 5

Number of buttons distributed to each classroom

= Total number of buttons/ Total number of classrooms

= 16/4

= 4

Therefore, the Joanne can distribute 5 flyers and 4 buttons to each classroom.

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If $10,000 is invested at x percent simple annual interest for n years, the total amount of interest would be F = 10,000n(x/100)

Simple interest is calculated based on the principle of a loan or the initial deposit into a savings account. Simple interest doesn't compound, so a creditor will only charge interest on the principal sum, and a borrower will never be required to pay interest on interest that has already accrued.

F = P(1+rt), formula for simple rate of interest

Here,

=> Future value is F

Present value is P

=> Rate is R

=> Time is t

Substituting x for r

And, n for t

Also, 10,000 in for P

F = 10,000(1+xn)

The formula tells us principal + interest,

F = 10,000(xn)

Now, to get the x into terms of a percentage,

F = 10,000(n * x/100)

F = 10,000n(x/100)

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Answer:

C. xy²

Step-by-step explanation:

You have to add the exponents:

(xy) exponent is 1

(x) exponent is 1

Combine the (x):

xy²

Consequently, there is a 0.89736 percent chance or probability that he weighs fewer than 258 kilograms.

Probability fundamentals. A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

Here,

we use the z-score algorithm to answer this query.

Score Z = x - μ/σ

x = the raw score

 population mean= μ 

Population standard deviation is σ

Hence,

x = 258, μ = 220, σ = 30

Z = 258 - 220/30

=1.26667

Probability based on the Z-Table:

P(x<258) = 0.89736

Consequently, there is a 0.89736 percent chance that he weighs fewer than 258 kilograms.

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Answer:

B: weather occurs because the climate is constantly changing

Step-by-step explanation:

Answer:

Step-by-step explanation:

The system of linear equations has no solution when the lines are parallel. It means the lines have same slope but different y-intercepts.

The y-intercepts are different:

For the given system to have no solution we need n = -4.

1. The quotients of the following division operations are as follows:

a) 126 ÷ 12 is 10.5.

b) 217 ÷ 4 is 54.25.

c) 75 ÷ 6 is 12.5.

d) 11 ÷ 9 is 1.2222.

e) 200 ÷ 35 is 5.7143.

2a) The quotient of 7 ÷ 2.2 is a nonterminating or repeating decimal.

2b) The quotient of 0.5 ÷ 0.12 is a nonterminating or repeating decimal.

2c) The division operation with a quotient that is nonterminating or repeating decimal is 2 ÷ 2.7.

3) The identification of each resulting quotient as a terminating or nonterminating, repeating decimal is as follows:

4) The quantity of meat in one piece of hamburger, if they are evenly shared or divided, is 41.67 g.

The quotient is the result of the division operation.

Every division operation involves the dividend (the numerator), the divisor (the denominator), the division operand (÷), and the equal sign (=).

2)

a) 7 ÷ 2.2 = 3.181818

b) 0.5 ÷ 0.12 = 4.16667

c) 3 ÷ 0.8 = 3.75

9 ÷ 0.16 = 56.25

2 ÷ 2.7 = 0.740740

3)

a. 2 ÷ 3 = 0.6667

b. 5 ÷ 1.2 = 4.16667

c. 0.3 ÷ 0.9 = 0.3333

d. 2.4 ÷ 1.8 = 1.3333

4) Total weight of ground pork = 1.25 kilograms

1 kg = 1,000 g

1.25 kg = 1,250 g

The pieces of patties = 30

The weight of each piece = 41.67 g (1,250/30)

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Answer:

y = -1

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

To find slope we look for the rise/run or (y2 - y1) / (x2 - x1)

The slope here is 0, and the y-intercept is located at (0,-1), so the equation is

y = -1

Answer:

y = -1

Step-by-step explanation:

A 95% confidence interval has a critical value of 1.96, where (1-0.95)/2 = 0.025. The unknown mean's 95% confidence interval is (101.82 - 0.96, 101.82 + 0.96), which translates to (101.82 - 0.96, 101.82 + 0.96) = (100.86, 102.78).

The t-critical value marks the threshold at which the null hypothesis is accepted or disregarded. The null hypothesis is rejected if the t-statistic is closer to 0 than the t-critical value; otherwise, it is retained.

Using a standard t-test and the following formula, you can determine a t-value: t is equal to (X - ц0) / (s / √n), where X is the sample mean, 0 is the population mean, s is the sample standard deviation, and n is the sample size.

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A 95% confidence interval has a critical value of 1.96, where (1-0.95)/2 = 0.025. The unknown mean's 95% confidence interval is (101.82 - 0.96, 101.82 + 0.96), which translates to (101.82 - 0.96, 101.82 + 0.96) = (100.86, 102.78).

The t-critical value marks the threshold at which the null hypothesis is accepted or disregarded. The null hypothesis is rejected if the t-statistic is closer to 0 than the t-critical value; otherwise, it is retained.

Using a standard t-test and the following formula, you can determine a t-value: t is equal to [tex](X - ц0) / (s / √n)[/tex], where X is the sample mean, 0 is the population mean, s is the sample standard deviation, and n is the sample size.

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Answer:

x = 29

y = 119

Step-by-step explanation:

51 + x = 90

x = 90 - 51

x = 29

y = 90 + x

= 90 + 29

y = 119

Answer:

1/6

Step-by-step explanation:

if one kid shared 1/3 of cookies then each kid would have 1/3 of cookies

Answer:

Step-by-step explanation:

Answer:

10 walnuts..

Step-by-step explanation:

12 - 2 = 10

Answer:

10?

Step-by-step explanation:

12-2=10

Answer:

$21,200

Step-by-step explanation:

Given the best fit equation:

y= 34,000 - 1,600x

Where ;

y = value of vehicle in $

x = Age of vehicle in years

The predicted value of vehicle aged 8 years ;x = 8

y = 34000 - 1600(8)

y = 34000 - 12800

y = 21,200

Hence, the predicted value of car aged 8 years is $21,200

Answer: o.7619

Step-by-step explanation: i used the standard algorithm i am sorry i cant do a more in depth just hard to do with words ;)

Answer: 0.7619

:)

Step-by-step explanation:

Answer:

Los jugadores dan 36 palmadas en total.

Step-by-step explanation:

Dado que 9 jugadores de un equipo de baloncesto chocan palmadas unos con otros, para determinar cuántas palmadas dan en total, sabiendo que 2 jugadores dan una palmada, 3 jugadores, tres palmadas, 4 jugadores, seis palmadas, y 5 jugadores, diez palmadas, se debe realizar el siguiente cálculo:

Cada jugador da un número de palmadas igual al número de jugadores en el campo, menos 1. A su vez, esa palmada es recíproca con el otro jugador que la recibe, con lo cual el número de jugadores a contar va disminuyendo.

8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = X

15 + 6 + 5 + 4 + 3 + 2 + 1 = X

21 + 5 + 4 + 3 + 2 + 1 = X

26 + 4 + 3 + 2 + 1 = X

30 + 3 + 2 + 1 = X

33 + 2 + 1 = X

35 + 1 = X

36 = X

Por lo tanto, dan 36 palmadas en total.