Item 14 Question 1 You have at most $60 to spend on trophies and medals to give as prizes for a contest. A drawing of a trophy and some medals are shown. The trophy is labeled 12 dollars each and the medals are labeled 3 dollars each. a. Write an inequality that represents the numbers of trophies x and medals y you can buy. The inequality is:

Let x = the number of songs you can buy.

If you use company A at 0.79 dollars per song, your variable is 0.79x. If you use company B at 0.99 dollars per song, your variable is 0.99x. You are going to set both equal to 30.

Company A: 0.79x = 30

Company B: 0.99x = 30

When solving (though I know you didn't ask), do note that you cannot buy part of a song so you would need to round down to the nearest whole number.

So if you use company A, you divide both sides by 0.79 to isolate the variable x and satisfy the division principle of equality:

x = 30/0.79.

Simplify and your answer is 37.97, round down to 37 songs; you'd have 37 songs with company A and 77 cents left over in your account just sitting there because what really can you do with 77 cents on the App Store?

To model the song downloading situation with a budget of $30, we use the equations 0.79x <= 30 for Company A and 0.99x <= 30 for Company B, where x is the number of songs.

To model the situation where a student has $30 to spend on downloading songs, we can write two separate linear equations, one for each company. For Company A, which charges $0.79 per song, the equation will be:

0.79x ≤ 30

Where x represents the number of songs the student can download from Company A. For Company B, which charges $0.99 per song, the equation will be:

0.99x ≤ 30

Again, x represents the number of songs the student can download from Company B, but the cost per song is different, hence a different equation.

These equations are used to determine the maximum number of songs the student can download from each company without exceeding the $30 budget.

Answer:

C) -1/4

Step-by-step explanation:

slope=rise/run

The slope of the line between the points (-4, -3) and (4, 3) is 3/4. Therefore, the correct answer is C.

The slope of a line is the ratio of the change in the y-coordinate to the change in the x-coordinate between any two points on the line. A simple formula to find the slope is:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are any two points on the line.

In this case, we can use the points (-4, -3) and (4, 3) that are given on the graph. Plugging them into the formula, we get:

m = (3 - (-3)) / (4 - (-4))

Simplifying, we get:

m = 6 / 8

Reducing to the lowest terms, we get:

m = 3 / 4

Therefore, the slope of the line is 3/4. The correct answer is C).

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Answer:

The points each have scored are Susie 45.5 points and jack 40.5 points.

Step-by-step explanation:

Given:

Susie and jack are on a basketball team.

The total amount of points scored was 86.

Susie has 5 more than as many points as jack.

Now, to find the points they each have:

Let the points of jack be [tex]x[/tex].

Then the points of Susie be [tex]5+x[/tex].

There total points scored =  86.

According to question:

[tex]x+(x+5)=86.[/tex]

⇒ [tex]x+x+5=86.[/tex]

⇒ [tex]2x+5=86.[/tex]

Subtracting both sides by 5 we get:

⇒ [tex]2x=81.[/tex]

Dividing both sides by 2 we get:

⇒ [tex]x=40.5.[/tex]

Jack scored = 40.5 points.

Putting the value of [tex]x[/tex] to get the points of Susie:

[tex]x+5[/tex]

⇒ [tex]40.5+5 = 45.5[/tex]

Susie scored = 45.5 points.

Therefore, the points each have scored are Susie 45.5 points and jack 40.5 points.

There are 21 nickels in carol bank

Solution:

Given that Carol's piggy bank consists of quarters and nickels

There are $ 4.55 in total

Let "a" be the number of nickels in bank

Let "b" be the number of quarters in bank

We know that,

1 quarter = $ 0.25

1 nickel = $ 0.05

Given that there are seven more nickels than quarters

Number of nickels = number of quarters + 7

a = b + 7 ---- eqn 1

From given question,

number of nickels in bank x value of 1 nickel + number of quarters in bank x value of 1 quarter = $ 4.55

[tex]a \times 0.05 + b \times 0.25 = 4.55\\\\(b + 7) \times 0.05 + b \times 0.25 = 4.55\\\\0.05b + 0.35 + 0.25b = 4.55\\\\0.3b = 4.55 - 0.35\\\\0.3b = 4.2\\\\b = 14[/tex]

Therefore from eqn 1

a = b + 7 = 14 + 7 = 21

a = 21

Thus there are 21 nickels in carol bank

Answer:

y = -2x - 3

Step-by-step explanation:

The line has a slope of -2

The line passes through point (-1, -1)

Lets take another point (x, y) on the line,

Slope = change in y ÷ change in x

i.e slope = [tex]\frac{y - -1}{x - -1}[/tex] = -2

[tex]\frac{y + 1}{x + 1}[/tex] = -2

y + 1 = -2x - 2

y = -2x - 2 - 1

y = -2x - 3 (this is the equation of the line).

Answer:

217

Step-by-step explanation:

124%=x

36%=63

=>[tex]x=\dfrac{63\times 124}{36}=217[/tex]

Final answer:

To find 124% of the original number, we first determine that the number is 175 by dividing 63 by 0.36 (the equivalent of 36%). We then multiply 175 by 1.24 to arrive at 217, which is 124% of the original number.

Explanation:

To solve the student's question, we'll need to find the original number that 36% represents, and then calculate 124% of that number. If 36% of a number is 63, we would set up an equation to find 100% of that number (the whole number).

Let's call the unknown number 'x'. The equation would be 0.36x = 63. To solve for 'x', we would divide both sides of the equation by 0.36:

x = 63 ÷ 0.36

Once we've found the value for 'x', we then find 124% of that number by multiplying 'x' by 1.24 (since percent means 'per hundred' and 124% is equivalent to 1.24 when expressed as a decimal).

Now, calculating the values:

x = 63 ÷ 0.36 = 175

To find 124% of 175, we do the following calculation:

1.24 × 175 = 217

Therefore, 124% of the number is 217.

To divide 6 by 2 2/3, convert 2 2/3 to the improper fraction 8/3, then multiply 6 by the reciprocal of 8/3 (which is 3/8) to get 18/8. Simplifying this by dividing both numerator and denominator by 2 gives the result 9/4 or 2 1/4.

To divide and simplify 6 divided by 2 2/3, you first need to convert the mixed number to an improper fraction. The mixed number 2 2/3 can be converted to an improper fraction by multiplying the whole number by the denominator of the fraction, then adding the numerator of the fraction to that product. This gives you:

2 x 3 + 2 = 6 + 2 = 8

So, 2 2/3 as an improper fraction is 8/3. Now, to divide the number 6 by 8/3, you will multiply 6 by the reciprocal of 8/3, which is 3/8.

6 x (3/8) = 18/8

To simplify 18/8, you divide the numerator and the denominator by their greatest common divisor, which is 2. Therefore, you get:

18 / 2 = 9 and 8 / 2 = 4

So, the simplified result of 6 divided by 2 2/3 is 9/4 or 2 1/4.

The given line has a slope of -1.

The slope of a perpendicular line is the negative reciprocal.

The slope of the new line would be positive 1.

Now using the point slope form, use the given pint to find the equation:

y -y1 = m(x -x1)

Replace x1 and y1 with the given point:

y - (-2) = 1(x -3)

Simplify:

y +2 = x -3

Subtract 2 from both sides:

y = x-5

Answer:

y = x-5

Step-by-step explanation:

Answer:

THX

Step-by-step explanation:

now i know your student id number yes

Answer:

57

Step-by-step explanation:

How I did this was 513 divided by 9 so the equation that I did was 513/9.

Answer:

57

Step-by-step explanation:  

you just need to divide=

513 divided by 9 = 57

Answer:

Vouch^ D on Edge

Step-by-step explanation:

If planet Y is twice the mean distance from the sun as planet X, the orbital period  is increased by the factor 2^3/2.

The Kepler's third law underscore the relationship between the orbital period T and the mean distance from the sun, A, in astronomical units, AU.

Mathematically, we can write; T^2 =A^3

Where;

T = orbital period

A =  mean distance from the sun

If planet Y is twice the mean distance from the sun as planet X, the orbital period  is increased by the factor 2^3/2.

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The true statements are : A, E & F

Step-by-step explanation:

In geometry symbols, ≅ means congruent to, equivalence of geometric shapes and size thus ∠B≅∠X

The symbol ~ means similarity, same shape not same size. Line segment AB~WX and line segment ZW ~ DA

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Answer:

the first one and the last 2 are correct 8D

Step-by-step explanation:

The length of one edge of a cube with a volume of 1331 cm³ is 11 cm, derived by taking the cube root of the volume.

To calculate the length of one edge of a cube when the volume is given, we use the formula for the volume of a cube: Volume = side³, where 'side' is the length of one edge of the cube.

The cube in question has a volume of 1331 cm³. To find the length of one edge of the cube, we need to take the cube root of the volume. The cube root of 1331 cm³ is 11 cm, meaning each side of the cube measures 11 cm.

The cube root is calculated because raising a number to the third power cubes it, and taking the cube root is the inverse operation. This process allows us to determine the original value that was cubed to get the volume.

Answer:

Both answer shown

IF it is

[tex]e^{ln 7x}= 7x[/tex]

OR

IF it is

[tex]e^{ln 7}\times 1}=7 [/tex]

Step-by-step explanation:

Given: Little confusion is in the question

e^ln7 x1

i.e [tex]e^{ln 7x}[/tex]

To Find:

[tex]e^{ln 7x}= ?[/tex]

Solution:

We know Logarithmic identity as

1. [tex]\ln e = 1[/tex]

2. [tex]\ln e^{x} = x[/tex]

Similarly,

3. [tex]e^{\ln x}=x[/tex]

IF it is

[tex]e^{ln 7x}= 7x[/tex]

OR

IF it is

[tex]e^{ln 7}\times 1}=7\times 1=7 [/tex]

Answer:

7x

Step-by-step explanation:

Answer:

420cal = 2 cups

Step-by-step explanation:

140cal = 2/3 cup

xcal= 2 cups

Divide 2/(2/3) = 3

Multiply both sides by 3 (answer)

140cal= 2/3 cups (3)

420cal = 2 cups

The 2 cups Contain 420 Cal.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

2/3 Cup contain = 140 Cal

So, 1 cup contain = 140 ÷ ( 2/3)

                             = 140 x 3/2

                             = 70 x 3

                             = 210

Then, In 2 cups = 210 x 2

                          = 420 Cal

Hence, 2 cups Contain 420 Cal.

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Answer:

16

Step-by-step explanation:

Quotient means the answer to a division problem.

80 ÷ 5 = 16

In long division:

   16 R0

5∫80

   5  

   30

Answer:

w = 1.25[tex]\times[/tex] t

The constant 1.25 denotes the rate of water flowing in the tub per minute.

Step-by-step explanation:

Water is running into a bathtub at a constant rate.

In 2 minutes , 2.5 gallons of water is filled in the tub. We are supposed to find the relation between the amount of water and the time taken and we also have to find the definition of the constant of proportionality.

Let w be the amount of water and t be the time taken in minutes.

The rate at which water is filled in the tub = [tex]\frac{2.5}{2}[/tex]

                                                                      = 1.25 gallons/minute

The water filled , w = 1.25[tex]\times[/tex] t

The constant 1.25 denotes the rate of water flowing in the tub per minute.

Final answer:

The question asks for two equations representing the proportional relationship between water in a bathtub (w) and time (t), given a constant fill rate. We derived that water fills the tub at a rate of 1.25 gallons per minute, leading to two equations: w = 1.25t and t = w / 1.25, explaining both the fill rate and how to calculate time based on a certain water amount.

Explanation:

The question involves finding two equations for a proportional relationship between the amount of water (w, in gallons) in a bathtub and the time (t, in minutes) it takes for the water to fill up at a constant rate, given that 2.5 gallons of water fill the tub in 2 minutes. To build these equations, we will use the information provided to determine the constant of proportionality (k), which represents the rate at which the tub fills.

First, we find the constant of proportionality (k) by dividing the amount of water by the time:

k = w / t = 2.5 gallons / 2 minutes = 1.25 gallons per minute

This gives us two equations based on this scenario:

w = 1.25t (Equation 1)

t = w / 1.25 (Equation 2)

Equation 1 tells us the amount of water (w) in the bathtub after t minutes, showing that the bathtub fills at a rate of 1.25 gallons per minute. Equation 2 allows us to find the time (t) it takes to reach a certain amount of water (w) in the bathtub, by dividing the amount of water by the rate of 1.25 gallons per minute.

The constant of proportionality (1.25 gallons per minute) in both equations indicates the rate at which the tub fills with water. It tells us that for every minute that passes, an additional 1.25 gallons of water are added to the tub.

Answer:

I think I know this one. H is the answer. H is a reflection of A over the x-axis.

Answer:

The answer is EF

Step-by-step explanation:

Im smart

Answer:

D

Step-by-step explanation:

Because B can be simplified to 3-4 ( which is the ratio needed)

therefor we know that Dis the answer

Answer:D.It is greater than the ratio of trumpets to clarinets.

First, you have to find the ratio flutes to violins. That is 9:12. Simplified, it is 3:4. Now, lets go down the list of options we have to pick

First option is A.It is the same ratio of violas to oboes. The ratio violas to oboes is 4:3. That is not the same as 3:4, so eliminate that option.

Second option is B.It is greater than the ratio of oboes to violas. The ratio oboes to violas is 3:4. This is the same as 3:4, so eliminate that option.

Third option is C.It is the same as the ratio of clarinets to trumpets. The ratio clarinets to trumpets is 6:2. That simplified is 3:1. This is not the same as 3:4. So lets eliminate that option. The only option left is option D, but how to check is down below.

Finally, the last option is D. It is greater than the ratio of trumpets to clarinets. The ratio trumpets to clarinets is 2:6. That simplified is 1:3. 3:4 is greater than 1:3, so D is the correct answer.

Answer:

Step-by-step explanation:

Supplementary angles add up to 180°.

m∠VST = m∠VSW + m∠TSW

m∠VST = 180° → m∠VSW + m∠TSW = 180°

Answer:

supplementary

Step-by-step explanation:

acute= less then 90 degrees

straight=180 degrees

complementary= 2 angles that equal 90 degrees

supplementary=2 angles that equal 180 degrees

Answer:

30 jars of nuts worth $4 per jar must be mixed with 20 jars of nuts worth $6 per jar

Step-by-step explanation:

Let

x ----> the number of jars of nuts worth $4

y ----> the number of jars of nuts worth $6

we know that

[tex]x+y=50[/tex] ----> equation A

[tex]4x+6y=4.80(50)[/tex]

[tex]4x+6y=240[/tex] ----> equation B

Solve the system by graphing

The solution of the system of equations is the intersection point both graphs

using a graphing tool

The solution is the point (30,20)

see the attached figure

therefore

30 jars of nuts worth $4 per jar must be mixed with 20 jars of nuts worth $6 per jar

The student has to mix 20 jars of $4 nuts with 30 jars of $6 nuts to end up with 50 jars of nuts each worth $4.80.

This question falls under a mathematical concept known as linear equations. Let's denote the number of $4 jars as X and the number of $6 jars as Y. According to the question, X + Y = 50 because the total number of jars is 50. We can also write another equation, which is 4X + 6Y = 50 * 4.8 ($4.80 is the average price of a jar, and there are 50 jars). Solving this system of linear equations gives us X = 20 and Y = 30. So, the student has to mix 20 jars of nuts worth $4 per jar with 30 jars of nuts worth $6 per jar to get 50 jars of nuts worth $4.80 per jar.

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Answer: The inequality symbol is reversed

Step-by-step explanation:

Given : 3 > -6

If we we multiply both side by -3 , we will have

-3(3) < -6(-3)

-9 < 18

the inequality symbol  changes because , in the rule of inequalities , anytime we multiply or divide through by negative , the inequality symbol must change

Answer:

$25.5 per hour.

Step-by-step explanation:

The function C(x) = 25.50x + 50 ........ (1)  models the total cost for a cleaning company to clean a house, where x is the number of hours it takes to clean the house.

Now, from the linear equation it is clear that the change in cost of cleaning from 3 hours and 9 hours are respectively  {From equation (1)}

C(3) = 25.5 × 3 + 50 = $126.5 and

C(9) = 25.5 × 9 + 50 = $279.5

Therefore, the average rate of change of the function between 3 hours and 9 hours will be = [tex]\frac{\textrm {Change in price of cleaning}}{\textrm {Change in hours}}[/tex]

= [tex]\frac{279.5 - 126.5}{9 - 3}[/tex]

= $25.5 per hour. (Answer)

Weight of wire of 8.7 meters is 24.36 ounces

Solution:

Given that cable repair person has 8.7 meters of wire

Each meter of the wire weighs 2.8 ounces

To find: Weight of wire

From given information,

weight of 1 meter of wire = 2.8 ounces

Therefore weight of 8.7 meters of wire is found by multiplying weight of 1 meter of wire by 8.7

weight of 8.7 meter of wire = weight of 1 meter of wire x 8.7

weight of 8.7 meter of wire = 2.8 x 8.7 = 24.36

Therefore weight of wire of 8.7 meters is 24.36 ounces

The weight of the 8.7 meters of wire is 24.36 ounces.

To find the weight of the wire, we need to multiply the length of the wire by its weight per unit length. The student has 8.7 meters of wire, and each meter weighs 2.8 ounces.

Multiply the length of the wire in meters (8.7) by the weight per meter in ounces (2.8).

8.7 meters * 2.8 ounces/meter = 24.36 ounces.

Therefore, the total weight of the wire is 24.36 ounces.

Answer:

The estimated taken to drive downtown using App is 38.4 minutes

Step-by-step explanation:

Given as :

The initial time taken to drive downtown = i = 48 minutes

The percentage error of time = r = 20%

Let The estimated time using app = t min

Let the time = 1 min

Now, according to question

The estimated time using app = The initial time taken to drive downtown × [tex](1-\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

Or, t minutes = i minutes × [tex](1-\dfrac{\textrm r}{100})^{\textrm 1}[/tex]

Or, t = 48 minutes × [tex](1-\dfrac{\textrm 20}{100})^{\textrm 1}[/tex]

Or,  t = 48 minutes × [tex]\dfrac{100-20}{100}[/tex]

Or,  t = 48 minutes × [tex]\dfrac{80}{100}[/tex]

∴ t = [tex]\dfrac{48\times 80}{100}[/tex] minutes

I.e t = 38.4 minutes

Or, The estimated time using app = t = 38.4 min

Hence, The estimated taken to drive downtown using App is 38.4 minutes Answer

Answer:

38.3

Step-by-step explanation:

38.3

5(x - 3) +6 = 5x - 9​ has infinitely many solutions

Given equation is 5(x - 3) +6 = 5x - 9​

We have to find whether the given equation has one, zero, or infinitely many solutions

Let us solve the given equation

5(x - 3) + 6 = 5x - 9​

Let us use BODMAS rule to solve the given equation

According to Bodmas rule, if an expression contains brackets ((), {}, []) we have to first solve or simplify the bracket followed by of (powers and roots etc.), then division, multiplication, addition and subtraction from left to right

So let us first solve for brackets in given equation

5x - 15 + 6 = 5x - 9

5x - 9 = 5x - 9

0 = 0

Since the statement is true, there are infinitely many solutions

Answer:

View image

Step-by-step explanation:

You treat inequality questions just like normal equation with an equal sign. You only have to worry about the inequality when you do the shading part.

Your first goal is to solve for y, which I did at the top.

And remember that when you divide/multiply by a negative number you have to flip the inequality sign.

So the first equation is already in term of y. (y < 2x + 4)

So you only have to solve for y for -3x - 2y ≥ 6.

I solved that and got y ≤ -3/2x - 3.

Now you have 2 equations. y < 2x + 4 and y ≤ -3/2x - 3

First you gotta treat it like a normal equation and graph them.

So i graphed y = 2x + 4 and y = -3/2x - 3. I assume you already know how do do that.

btw. < and > have dotted lines, while ≤ and ≥ have solid lines.

Now for the shading, you gotta look at the inequality sign.

y < 2x + 4 has a less than sign, so you have to shade everything underneath the line you graphed.

y ≤ -3/2x - 3 is also less than, so you have to shade everything underneath that line as well.

So in the future, you you get a > or ≥ then you have to shade above the graph.

1.0  0.91  0.3  0.07

descending

largest to smallest

Answer:

1.0, 0.91, 0.3, 0.07

Step-by-step explanation:

first take the decimal number(s) in front and put then first.

then take the ones closest to one

then thanks the ones closer to half

then, finally take the ones closer to zero