Question 4(8 points)
Ralph receives money from his family members for his high school graduation. He
decides he wants to spend no more than $120.00 on movies to bring with him to
college. Each DVD is $10.00, and each Blu-Ray is $15.00. He wants to purchase at least
8 movies. Determine the following,
You are given this inequality to represent "he wants to purchase at least 8
movies": x+y 28
BLANK 1: Would this be the correct way to write this (yes or no)?
BLANK 2-4: Fill in the blanks for the second inequality (all three answers are whole
numbers):
ys
x+
BLANK 5 AND 6:
What label would go on the x-axis, if you graphed this?
What label would go on the y-axis, if you graphed this?
BLANK 7 AND 8:
If Ralph were to JUST purchase DVDs, what is the maximum amount he could buy?
If Ralph were to JUST purchase Blu-Rays, what is the maximum amount he could buy?

I agree that Freddy ate 1 / 8 of the brownies in the pan because two brownies represents 1 / 8 of the brownies in the pan.

The large pan is said to have been used to make 16 brownies which means that if Freddy ate 2 brownies out of this, the proportion that he would have eaten of the cookies in the pan is:

= Number of brownies Freddy ate / Number of total brownies in the large pan

= 2 / 16

= 1 / 8

This therefore shows that Freddy's friend was right in saying that Freddy ate 1 / 8 of the brownies in the pan.

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Full question is:

A large pan is used to make 16 brownies. Freddy had two of the brownies from a large pan. His friend said he ate 1/8 of the brownies in the pan. Tell why you agree or disagree.

There are 108 rabbits in the shelter.

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.

We have to given that;

An animal shelter has 1008 cats, dogs and rabbits.

And, The ratio of the number of dogs to the number of cats in the animal shelter is 3 : 7. The ratio of the number rabbits to the number of dogs is  2 : 5.

Here, The ratio of the number of dogs to the number of cats in the animal shelter is 3:7. The ratio of the number rabbits to the number of dogs is 2:5.

So, We can formulate;

Number of dogs : Number of cats = 3 : 7

Number of rabbits : Number of dogs = 2 : 5

Hence, We get;

Number of rabbits : Number of dogs : Number of cats = 6 : 15 : 35

Since, An animal shelter has 1008 cats, dogs and rabbits.

Hence, We get;

⇒ 6x + 15x + 35x = 1008

⇒ 56x = 1008

⇒ x = 18

Thus, Number of rabbits = 6x

                                      = 6 × 18

                                      = 108

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The probability of getting two spades when two cards are drawn from the deck is 1/17.

Probability branch of mathematics the deal with the likewood of an event occouring. It is the measure of how likely it is something will happen or be the case. Probabilities expressed as a number between zero and one 00 indicates impossibility and one indicus certainity. Probability can be used to calculate the chances of certain outcome based on a state condition or data. Probability can also be used to make decision and prediction about the future.

The probability of getting two spades when two cards are drawn from a shuffled deck of cards is 3/52 x 2/51, or 1/17.

This is because there is a 3/52 chance of getting the first spade and a 2/51 chance of getting the second spade (since there is one less card in the deck).

Therefore, the probability of getting two spades when two cards are drawn from the deck is 1/17.

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Answer:

280

Step-by-step explanation:

Answer:

8×35=280.

This is the best I can give to you

Answer:

Like

Step-by-step explanation:

1. Nominal

2. Discrete

3. Quantitative

4. discrete

5. discrete

6. Qualitative

Answer:

x3+4x2+x-6

Step-by-step explanation:

do it your selve

Answer:

between 10 am - 12 pm and 2-4 pm.

Answer: d

Step-by-step explanation: -5 is the intercept since x is 0 above it.

using the y2-y1 / x2-x1  we will get 2/4 (1/2 when simplified).

The discount as a percentage is 13.8%

The price of a picnic basket is marked as $31

The original price is $36

The discount percentage can be calculated as follows

36-31/36 × 100

= 5/36 × 100

= 0.138× 100

= 13.8%

Hence the percentage discount is 13.8%

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The surface area of the open top box is 127 cm².

The area of a three dimensional object on it's outer surface is called the surface area of the object.

Given that,

Surface area of the open-top box = 2LH + 2WH + LW, where L is the length, W is the width and H is the height.

L = 3 cm

W = 5 cm

H = 7 cm

Surface area = (2 × 3 × 7) + (2 × 5 × 7) + (3 × 5)

                      = 42 + 70 + 15

                      = 127 cm²

Hence the surface area of the given open top box is 127 cm².

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Therefore , the solution of the given problem of surface area comes out to be  0.2083 yard square.

A surface is a measurement of how much overall space an object's surface takes up. Surface area of a three-dimensional shape is determined by the total area of its surroundings. Surface area is the term used to describe a triangular shape's entire surface area. The particular area of each face on a cube with six square faces can be added up to determine the cube's surface area. Alternately, you can get the box's dimensions by using the following formula: Surface (SA) equals twice twice twice twice. A three-dimensional shape's surface area is calculated as the sum of all the space it occupies.

Here,

Given : width : 5/6 yard

and length = 1/4 yard

To find the area = length * width

=> area = 5/6 * 1/4

=> area = 5/24

=> 0.2083 yard square.

Therefore , the solution of the given problem of surface area comes out to be  0.2083 yard square.

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Answer:

  1

Step-by-step explanation:

[tex](\frac{2}{3} )^{0} =1[/tex]

[tex](1)^{-3} =1[/tex]

Hope this helps

The ordered pairs are solutions to the system of equations are (-2,1.6)

In order to determine which ordered pairs are solutions to the system of equations, you need to equate the two equations and solve for x:

y = -0.5x+0.6 and y= x+3 3/5

-0.5x+0.6 = x+3 3/5

-0.5x+0.6 = x+3.6

x+3.6 + 0.5x-0.6 = 0

1.5x + 3 = 0

1.5x = -3

x = -3/1.5

x = -2

y =-0.5x+0.6

y = -0.5(-2) + 0.6

y = 1.6

y = x + 3.6

y = -2 + 3.6

y = 1.6

Thus, the ordered pairs are (-2, 1.6)

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Considering the closure under property the polynomials f(x) = a 0 + a 1 x + a 2 x^ 2 ... + a n x^ n; and g(x) = b 0 + b 1 x + b 2 x^ 2 ... + b m x^ m

In mathematics, a set is considered closed if we are able to apply and complete an operation on its components while consistently receiving a component from the same set.

A set therefore either possesses closure for a given mathematical operation or it does not.

Use of real numbers is the closure property of addition. Addition of two real numbers results in areal number

In the given problem, the set considered is polynomial addition and the addition of the two polynomial will give a sum which is a polynomial hence we say it is closed under addition.

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According to the trigonometric function,  F(t) = 20 cos (2π/5)t where t represents time, in seconds. representing the pendulum ride of the sea dragon. It will take the pendulum 5 seconds to complete one full cycle.

A period on a graph function is the distance between two repeating points.

The graph repeats itself as it advances along the x-axis, as you can see.

Periods are the cycles of this predictable repetition. Every 6.28 units, or 2 pi radians, this graph repeats.

The equation is F(t) = 20 cos (2π/5)t

The amplitude of the equation is 20 and the graph makes 2π/5 oscillations at every t seconds

the period to complete an oscillation which is 2π

2π/5 * t = 2π

t = 2π * 5/2π  

t = 5 seconds

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The lines that are true in the following statements are, Parallel lines have the same slope. Parallel lines have equal slopes. Parallel lines have different y-intercepts. Parallel lines have different x-intercepts.

Two lines in the same plane that are equally spaced apart and never cross each other are said to be parallel lines in geometry. Both horizontal and vertical shapes are possible.

The following key traits and qualities make it simple to recognize parallel lines:

They are usually parallel straight lines that are spaced equally apart.

These lines are coplanar.

No matter how far you extend them in any direction, they never come together.

All the statements mentioned are true.

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19.75 meters is the rocket's height when it has 0.5 seconds after launch

A relation is a function if it has only One y-value for each x-value.

Given that The flight of Jae and Miguel's rocket t seconds after launch is modeled by

h(t) = -5t² + 40t + 1

h(t) is their rocket's height in meters.

we have to find the rocket's height in meters 0.5 seconds after launch

Put t=0.5 in the above function.

h(0.5)=-5(0.5)² + 40(0.5)+ 1

=-5(0.25)+20+1

=-1.25+20+1

=19.75

Hence, 19.75 meters is the rocket's height when it has 0.5 seconds after launch

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The number of toys is 5 in each container.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Let x be the number of toys in each container.

Weight of one toy car = 6 pounds

Weight of the container in which toy cars shipped = 5 pounds

Weight of x toy cars = 6x

Total weight of the container when toy cars are placed = 6x + 5

Weight of one toy truck = 3 pounds

Container weight = 20 pounds

Weight of x toy trucks = 3x

Total weight of the container when toy trucks are place = 3x + 20

Given that both containers have same weight.

6x + 5 = 3x + 20

6x - 3x = 20 - 5

3x = 15

x = 5

Hence the number of toys in each container is 5.

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The complete function table using the defined function rule is as shown below.

We are given the function rule as;

h(x) = 2x - 3

From the function table attached, we will need to find the value of the function h(x) at x = -3, -2, 1, 3, 5

Thus;

Plugging in the value of -3 for x in the given function rule gives us the output as;

h(-3) = 2(-3) - 3

h(-3) = -9

Plugging in the value of -2 for x in the given function rule gives us the output as;

h(-2) = 2(-2) - 3

h(-2) = -7

Plugging in the value of 1 for x in the given function rule gives us the output as;

h(1) = 2(1) - 3

h(1) = -1

Plugging in the value of 3 for x in the given function rule gives us the output as;

h(3) = 2(3) - 3

h(3) = 3

Plugging in the value of 5 for x in the given function rule gives us the output as;

h(5) = 2(5) - 3

h(5) = 7

Thus, the complete function table is;

x        h(x)

-3       -9

-2       -7

1         -1

3         3

5         7

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Answer: The phrase "5 times a number, divided by 6" can be translated into the algebraic expression:

(5/6)x

This expression represents "5 times a number, divided by 6", where x is the unknown number.

Step-by-step explanation:

On solving the exponential function 16000 = P(0.9455)^t, the original value of the car is obtained as $18,930.

What is an exponential function?

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

The value of car in amount is A(t) = $16,000.

The rate of depreciation is x = 5.45% per year.

Rewriting the rate in exponential form - (1 - 0.0545) = 0.9455

The car is t = 3 years old.

Let P be the model that depicts the original cost of the car.

Then the exponential function will be -

16000 = P(0.9455)^t

Substituting the value of t in the equation -

16000 = P(0.9455)³

16000 = 0.8452P

P = 16000/0.8452486

P = 18,929.34 ≈ 18,930

Therefore, the original value of car was $18,930.

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a) The amounts needed for 2 batches of fudge-like brownies are of:

b) The amounts needed for 3 batches of cake-like brownies are of:

The needed amounts for each case are obtained applying the proportions in the context of this problem.

Hence:

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The amounts of eggs, water, and oil needed for 2 batches of fudge-like brownies are:

The amounts of eggs, water, and oil needed for 3 batches of cake-like brownies are:

One batch of Fudge-like brownies:

2 eggs

1/4 cup of water

1/2 cup of oil

One batch of Cake-like brownie

3 eggs

1/4 cup of water

1/2 cup of oil

The amounts of eggs, water, and oil needed for 2 batches of fudge-like brownies can be determined by multiplying each ingredients by 2

eggs = 4

cup of water = 2/4

cup of oil = 1

The amounts of eggs, water, and oil needed for 3 batches of cake-like brownies can be determined by multiplying each ingredients by 3

eggs = 9

cup of water = 3/4

cup of oil = 3/2

Therefore, the ingredients needed for the other batches is determined by multiplying each ingredients by the number of required batches.

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Answer:

the slope is -2

Step-by-step explanation:

hope this helps!!

Note that in the above mathematical scenario involving two similar triangles, the option that MUST  be correct is AC < FH (Option C) This solution is arrived at using the Open Mouth Theorem.

The above-stated Theorem in Geometry asserts that if two sides of two triangles are congruent and the included angle differs, then the greater angle is opposite the longer side.

This theorem is known as the Open Mouth Theorem because it is based on the idea that the two sides of a triangle are "pivoted" at their common vertex.

Please keep in mind that this theorem only works if we know two pairs of sides are congruent like this.

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61.67 oz of the 55% acid solution and 33.33 oz of the 30% acid solution must be mixed to produce 100 ounces of a 43% acid solution.

This is a mixture problem that can be solved using algebra. We can set up a system of equations to represent the amount of each solution being used and the final acid concentration.

Let x be the amount of 55% acid solution and y be the amount of 30% acid solution used.

We can set up the following system of equations:

(55/100)x + (30/100)y = (43/100)(x + y) (Equation 1) represents the final acid concentration.

x + y = 100 (Equation 2) represents the total amount of solution mixed

We can solve for one variable in equation (1) by isolating it and substituting it into equation (2).

Solving for x in equation (1) we get: x = (100*43/100 - y30/100)/55/100

Substituting this value into equation (2) we get: (10043/100 - y30/100)/55/100 + y = 100

Solving for y we get: y = (100*100 - 100*43)/30 = 33.33 oz

And then substituting this value back into the equation x = (100*43/100 - y30/100)/55/100 we get x = 61.67 oz

So, 61.67 oz of the 55% acid solution and 33.33 oz of the 30% acid solution must be mixed to produce 100 ounces of a 43% acid solution.

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The amount in Ravi account after 6 months will be $410.

The amount in Susan account after 6 months will be $460

From the information, Ravi and Susan each opened a savings account today. Ravi opened his account with a starting amount of $650, and he is going to take out $40 dollars per month. This will be:

650 - 40m

Susan opened her account with a starting amount of $850 dollars, and she is going to take out $65 per month. This will be:

850 - 65m

The amount in Ravi account after 6 months will be;

= 650 - 40(6)

= 410

The amount in Susan account after 6 months will be:

= 850 - 65(6)

= $460

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keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{4}}x+10\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

so we're really looking for the equation of a line whose slope is 1/4 and that it passes through (4 , 3)

[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{3})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{ \cfrac{1}{4}}(x-\stackrel{x_1}{4}) \\\\\\ y-3=\cfrac{1}{4}x-1\implies {\Large \begin{array}{llll} y=\cfrac{1}{4}x+2 \end{array}}[/tex]

An equation of the line in slope-intercept form that passes through the point (1, 17) and has a slope of 1 is equal to y = x + 16.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

Given the following parameters:

Substituting the given parameters into the point-slope formula, the equation of the line in is slope-intercept form given by;

y - y₁ = m(x - x₁)

y - 17 = 1(x - 1)

y = x - 1 + 17

y = x + 16

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