Question 12(Multiple Choice Worth 2 points)
(Three-Column Tables MC)

The relationship between the number of pies-to-cakes chosen by middle school students as their favorite dessert is shown in the table.


Pie 36 42 60
Cake D 7 C
Total 42 A B


What is the value of C in the table?
6
10
49
70

Answer:

1.5 miles less

Step-by-step explanation:

Step 1:  Find equation for Alexanda

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex].

If we allow (8, 345.6) to be our x1 and y1 and (12, 518.4) to be our x2 and y2, our slope is

[tex]m=\frac{(518.4-345.6)}{(12-8)}\\ m=\frac{172.8}{4}\\ m=43.2[/tex]

[tex]345.6=43.2(8)+b\\345.6=346.6+b\\0=b[/tex]

Thus, the equation for Alexandra is y = 43.2x

Step 2: Plug in 1 for x for both Fabian and Alexandra's equations and subtract

Since x is is gallons, we plug in 1 for x for each equation and subtract Fabian's miles from Alexandra's miles to find how many miles less can Fabian drive one 1 gallon of gas than Alexandra:

Fabian:  y = 41.7(1) = 41.7

Alexandra:  y = 43.2(1) = 43.2

Difference of Alexandra and Fabian's miles:  43.2 - 41.7 = 1.5

Answer:

Step 1: Write down the decimal as a fraction with the decimal number as the numerator and 1 as the denominator.

Step 2: Multiply both the numerator and denominator by 10^n, where n is the number of digits after the decimal point.

Step 3: Simplify the resulting fraction.

Using these steps, we can convert the given decimal numbers to fractions:

0.65

Step 1: 0.65 = 65/100

Step 2: Multiply numerator and denominator by 10 to get rid of the decimal point: 65/100 = 650/1000

Step 3: Simplify by dividing numerator and denominator by their greatest common factor of 50: 650/1000 = 13/20

Therefore, 0.65 expressed as a fraction in simplest form is 13/20.

2.¯5

To handle repeating decimal numbers, we can use the following method:

Step 1: Let x be the repeating decimal number.

Step 2: Multiply both sides of x by 10^n, where n is the number of digits in the repeating part of the decimal number.

Step 3: Subtract the original number from the number obtained in step 2 to eliminate the repeating part.

Step 4: Solve for x by dividing both sides of the equation obtained in step 3 by an appropriate factor.

Step 1: Let x = 2.¯5

Step 2: Multiply both sides by 10: 10x = 25.¯5

Step 3: Subtract the original equation from step 1: 10x - x = 25.¯5 - 2.¯5

Simplifying: 9x = 23

Step 4: Solve for x by dividing both sides by 9: x = 23/9

Therefore, 2.¯5 expressed as a fraction in simplest form is 23/9.

1.0¯24

Step 1: Let x = 1.0¯24

Step 2: Multiply both sides by 10^2 to eliminate the repeating part: 100x = 124.¯24

Step 3: Subtract the original equation from step 1: 100x - x = 124.¯24 - 1.0¯24

Simplifying: 99x = 123

Step 4: Solve for x by dividing both sides by 99: x = 123/99

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor of 3: 123/99 = 41/33.

Therefore, 1.0¯24 expressed as a fraction in simplest form is 41/33.

Step-by-step explanation:

0.65 expressed as a fraction in simplest form is 13/20.

2.5 expressed as a fraction in simplest form is 5/2.

1.024 expressed as a fraction in simplest form is 256/250.

0.65 expressed as a fraction in simplest form:

Write the decimal as a fraction by placing it over 1. In this case, 0.65 becomes 0.65/1.

Remove the decimal by multiplying both the numerator and the denominator by a power of 10 that will eliminate the decimal.

In this case, multiplying by 100 will do the trick, so we get (0.65 × 100)/(1 × 100) = 65/100.

Lastly, simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

The GCD of 65 and 100 is 5, so dividing both by 5 yields 13/20.

2.5 expressed as a fraction in simplest form:

Write the decimal as a fraction by placing it over 1. In this case, 2.5 becomes 2.5/1.

Remove the decimal by multiplying both the numerator and the denominator by a power of 10 that will eliminate the decimal.

In this case, multiplying by 10 will do the trick, so we get (2.5 × 10)/(1 × 10) = 25/10.

Lastly, simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

The GCD of 25 and 10 is 5, so dividing both by 5 yields 5/2.

1.024 expressed as a fraction in simplest form:

Write the decimal as a fraction by placing it over 1. In this case, 1.024 becomes 1.024/1.

Remove the decimal by multiplying both the numerator and the denominator by a power of 10 that will eliminate the decimal.

In this case, multiplying by 1000 will do the trick, so we get (1.024 × 1000)/(1 × 1000) = 1024/1000.

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

The GCD of 1024 and 1000 is 8, so dividing both by 8 yields 128/125.

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an = a1 + (n - 1)d

Substituting the values

an = 2 + (n - 1)8

We have to find the 25th term n = 25

a25 = 2 + (25 - 1)8

a25 = 2 + (24)8

a25 = 2 + 192

a25 = 194

======================================================

Explanation:

The gap between adjacent terms is 8.

The long way to get the answer would be to keep adding 8 to each term to generate the next one. You'd need to do this 20 times. There are 5 terms here already, so you need 25-5 = 20 more operations of "add 8".

I don't recommend this option. I recommend the shortcut mentioned in the next section.

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The shortcut would be to find the nth term of the arithmetic sequence

[tex]a_1 = 2 = \text{ first term}\\\\d = 8 = \text{ common difference}\\\\a_n = \text{ nth term}\\\\a_n = a_1 + d(n-1)\\\\a_n = 2 + 8(n-1)\\\\[/tex]

As a check, plug n = 1 into that formula to get [tex]a_1 = 2[/tex]. Plug n = 2 to get [tex]a_2 = 10[/tex] and so on. I'll leave this check portion for the student to do.

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The last step is to plug n = 25 into that formula to determine the 25th term.

[tex]a_n = 2 + 8(n-1)\\\\a_{25} = 2 + 8(25-1)\\\\a_{25} = 2 + 8(24)\\\\a_{25} = 2 + 192\\\\a_{25} = 194\\\\[/tex]

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Extra section (optional):

We can use a spreadsheet to generate the 25 terms. This is to help check the answer.

2, 10, 18, 26, 34, 42, 50, 58, 66, 74, 82, 90, 98, 106, 114, 122, 130, 138, 146, 154, 162, 170, 178, 186, 194

Answer:

Step-by-step explanation:

Area of a square = length²

If the area of a square is given, in order to determine the length, find the square root of the area.

√16 / 36 = 4/6 foot

Answer: I must say it's (0,3)

Step-by-step explanation: The two lines meet at (0,3) so it's (0,3).

Hope it helps! :D

Answer:

B

Step-by-step explanation:

Answer:

Part-a: The price of the share decreased by $3.25 from the start of day 1 to the end of day 4.

Part-b: The price of the share at the start of day 1 was $106.10.

Step-by-step explanation:

Part A: To calculate the change in price from the start of day 1 to the end of day 4, we need to add up all the daily changes. The daily changes given are:

Day 1: +2.75

Day 2: -4.375

Day 3: +0.875

Day 4: -2.5

Adding these values together:

Change = 2.75 - 4.375 + 0.875 - 2.5 = -3.25

The price of the share decreased by $3.25 from the start of day 1 to the end of day 4.

Part B: To find the price of the share at the start of day 1, we need to subtract the total change from the given price at the end of day 4.

Price at the end of day 4 = $102.85

Total change = -3.25

Price at the start of day 1 = Price at the end of day 4 - Total change

= $102.85 - (-3.25)

= $102.85 + 3.25

= $106.10

Therefore, the price of the share at the start of day 1 was $106.10.

Answer:

15 cm × 9.5 cm = 142.5 square cm

Answer:

The area of the given figure is 142.5 sq. cm.

Step-by-step explanation:

The area of a parallelogram is given by the base multiplied by the height. The base in the given figure is 15 cm whereas the height is 9.5 cm.

15 × 9.5 equals 142.5

Hence, the area is 142.5 sq. cm.

Domain is all real numbers. Range is

Step-by-step explanation:

The function  is a transformation of the parent function  by moving the function up by 3 units.

So, the graph of the function is shown below.

From the graph, it is clear that the  values has no limitation and hence can take any real values. Domain is the set of all possible  values.

So, domain is the set of all real numbers.

Range is the set of all possible values for  for the given domain.

From the graph, the minimum value of  is at the point (. So, the minimum value of y is 3. The  value then goes on increasing towards infinity.

Therefore, range is a real number greater than or equal to 3.

So, range is  or  

Answer:

790,000

Step-by-step explanation:

The 5 represents the number by itself so it would be

10x10x10x10x10=100,000

7.9x100,000=790,000

Step-by-step explanation:

if you multiply something by 10 = 10¹, you move the decimal point 1 position to the right (and fill up with a 0, if necessary).

if you multiply something by 100 = 10², you move the decimal point 2 positions to the right (and fill up with 0s as needed).

if you multiply something by 1000 = 10³, you move the decimal point 3 positions to the right (and fill up with 0s as needed).

...

you see the pattern ?

so, when multiplying by 10⁵ (100,000) we shift the decimal point 5 pairings to the right and fill up with 0s as needed.

therefore,

7.9 × 10⁵ = 790,000.-

Answer:

A weighs 30 because it is always on the higher side

Answer:

The answer is 78

Step-by-step explanation: Well, first thing I did was cut into two shapes so a square and a rectangle and 3 x 2 = 6    and 9 x 8 = 72 and 72 +6 = 78

Answer:

78

Step-by-step explanation:

3 x 2= 6

9 x 8 = 72

72 + 6 = 78

Answer:surface area of pyramid is 118.80

And the volume of the cube is 1000

Step-by-step explanation:explain on picture

Answer:169.92 cm^2

Step-by-step explanation:

The base is 7.2 x 7.2 (This equals 51.84)

The area of one triangle is 29.52

There are 4 triangles with the same side lengths so you multiply 29.52 x 4.

This would equal 188.08.

Then you add everything together.

This equals 169.92 cm^2.

Answer:1,000 m^3

The formula for volume is hlw.

One of the side lengths of the cube is 10.

If the height, length, and width are ten, then you multiply them all together.

This would give you 1,000.

Answer: The answer is B

Step-by-step explanation:

The statement which is true include the following: C. function 2 is the only nonlinear function.

In Mathematics and Geometry, a linear function refers to a type of function whose equation is graphically represented by a straight line on the xy-plane or cartesian coordinate.

This ultimately implies that, a linear function has the same (constant) slope and it is typically used for uniquely mapping an input variable to an output variable, which both increases simultaneously.

In this context, we can logically deduce that function 2 is a quadratic function and as such, it is the only nonlinear function.

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Answer:

3.3/11 = DF/7.6

DF = (3.3 × 7.6)/11 = 2.28

Answer:

below

Step-by-step explanation:

2.1 k and f

2.2 a and d

2.3 m = 90 - 59 = 31

2.4 d = 180 - 59 = 121

a) The predicted heating cost for a month with temperature of 25 ºF is given as follows: $65.70.

b) The predicted heating cost for a month with temperature of 0 ºF is given as follows: $96.20

c) For an increase of one degree Fahrenheit, the predicted decrease in the cost is of $1.22.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The slope and the intercept for the function in this problem are given as follows:

Hence, the predicted cost for a month with temperature of 25ºF is given as follows:

y = -1.22(25) + 96.20 = $65.70.

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Answer:

A set of ordered pairs represents a function if each input (first coordinate) corresponds to one and only one output (second coordinate). In other words, there can't be two different second coordinates for the same first coordinate.

Using this definition, we can determine which of the sets of ordered pairs represents a function:

A: {(-4, -3), (-2, -1), (-2, 0), (0, -2), (0, 2)}

The input -2 has two different outputs (-1 and 0), and the input 0 also has two different outputs (-2 and 2). Therefore, this set does not represent a function.

B: {(-5, -5), (-5, -4), (-5, -3), (-5, -2), (-3, 0)}

The input -5 has four different outputs (-5, -4, -3, and -2), but each of the other inputs has only one output. Therefore, this set does not represent a function.

C: {(-4, -5), (-4, 0), (-3, -4), (0, -3), (3, -2)}

The input -4 has two different outputs (-5 and 0), but each of the other inputs has only one output. Therefore, this set does not represent a function.

D: {(-6, -3), (-4, -3), (-3, -3), (-2, -3), (0, 0)}

Each input has only one output, so this set represents a function.

Therefore, the set of ordered pairs that represent a function is D: {(-6, -3), (-4, -3), (-3, -3), (-2, -3), (0, 0)}.

Answer:

3

Step-by-step explanation:

the formula for the area of a rectangle is length x width, and so you do 3/5 x 5, which ends up as 15/5, since 5 is also 5/1. Then you get 3 as the area of the rectangle's area.

Answer:

3 ft

Step-by-step explanation:

3/5 x 5 = 15/5

15 / 5 = 3

Answer:

2/3

Step-by-step explanation:

because 1 1/2 x 2/3 = 2 1/4

Answer:

1 1/2 = 3/2

2 1/4 = 9/4

3/2 divided by 9/4 = 3/2 multiplied by 4/9 = 2/3

EXPLANATION : when we have 2 fractions and we have to divide them , we have to reverse the fraction that we are dividing by and multiply it. sometimes we can simplify the fractions , sometimes we can't. for example , with 3/2 multiplied by 4/9 we simplified 3 and 9 and the 2 and the 4 which left us with 1/1 ( 1 ) multiplied by 2/3 , which gave us the answer 2/3 .

Hope I helped!

Answer:

C = 2π(3/8) = 3π/4 units

Step-by-step explanation: The area of the circle is given by the formula A = πr^2, where A is the area and r is the radius.Therefore, 9/64π = πr^2Simplifying, we get:r^2 = 9/64Taking the square root of both sides, we get:r = 3/8The circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius.Therefore, the circumference of the circle is:C = 2π(3/8) = 3π/4 units

Answer: It is D.  Carl had 8 pounds of ice after 2 minutes, didn't use any ice for 4 minutes, and then used one half pound each minute for 6 minutes.

Step-by-step explanation: