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Sidney made root beer floats for her friends when they came over. The table shows the ratio of cups of ice cream to cups of soda used to make the floats.

Ice Cream (cups) Soda (cups)
3.5 10.5
8 24
12.5 37.5
15 ?


At this rate, how much soda will Sidney use for 15 cups of ice cream?

30 cups
35 cups
40 cups
45 cups

The equation for the situation described in your problem would be y  is $10x + $2.50  .

To utilize substitution to resolve an equational system:

Divide one of the two variables in one of the equations.

Substitute the expression that the isolated variable's equivalent from Step 1 into the other equation.

Solve the linear equation for the last variable.

system of equations, simultaneous equations Algebraic equations involving two or more must be solved cooperatively (i.e., the solution must satisfy all the equations in the system). For a system to have a single solution, the number of equations must equal the number of unknowns. Even then, a solution is not guaranteed.

The following equation would apply to the scenario in your problem:

y =$10x + $2.50  

y = $2x + $4.00

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Answer:

2. sec x + c

1.1 view attached pic

1.2 view attached pic

Step-by-step explanation:

The required values of the angle ∠1 and ∠2 are  135°and 135°respectively.

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

We need to find angle 1 and 2

So, by using corresponding angle theorem,

∠1 = 135°

Similarly for ∠2

By using vertically opposite angle,

∠2 =135°

Thus, required value of the angle are ∠1 = 135°, ∠2 =135°.

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Answer:

20

Step-by-step explanation:

=12÷3[-15-5{6-8+2}]

=12÷3[-15-5{6-10}]

=12÷3[-15-5-4]

=12÷3[20-4]

=12÷3+16

=4+16

=20

The correct set of data matched to the stem and leaf plot is given as follows:

1.5, 1.5, 1.6, 2.1, 2.1, 2.1, 3.5, 3.6.

The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:

1|6 = 1.6.

(in the context of this problem).

Following the key format, the measures listed in the answer represent the correct data-set from the stem-and-leaf plot.

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Answer:

8

Step-by-step explanation:

x= 24/3 = 8

Answer:

[tex] \sf \: x = 8[/tex]

Step-by-step explanation:

Given equation,

→ 3x = 24

Now the value of x will be,

→ 3x = 24

→ x = 24 ÷ 3

→ [ x = 8 ]

Hence, the value of x is 8.

Answer:

nches. L.S.A.=2π(3)(9)=54π inches2. ≈169.64 inches2

Step-by-step explanation:

Answer: Jenna would have $37,175 in 30 years if she saves $2500 per year with an interest rate of 10% compounded annually.

Step-by-step explanation:

To calculate the total amount Jenna would have after 30 years of saving $2500 per year with an interest rate of 10% compounded annually, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the final amount (principal + interest)

P = the initial principal (the amount Jenna saves each year, $2500 in this case)

r = the interest rate (10% in this case, so 0.10)

n = the number of times interest is compounded per year (annually in this case, so 1)

t = the number of years (30 in this case)

Plugging in the values:

A = $2500(1 + 0.10/1)^(1*30) = $2500(1.10)^30 = $2500(14.87) = $37,175

So, Jenna would have $37,175 in 30 years if she saves $2500 per year with an interest rate of 10% compounded annually.

Answer:

$411,235.06

Step-by-step explanation:

The measure of angles a, b, c, d and e are 54°, 18°, 108°, 81° and 99°.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Given that, workers in an office of 40 staff were asked their favorite type of take-away.

Fraction of a person = 1 degree

Here, 360° = 40 people

So, 1 degree = 40/360 =1/9

Now, angle a =6/40 ×360

= 54°

Angle b= 2/40 ×360

= 18°

Angle c= 12/40 ×360

= 108°

Angle d = 9/40 ×360

= 81°

Angle e =11/40 ×360

= 99°

Therefore, the measure of angles a, b, c, d and e are 54°, 18°, 108°, 81° and 99°.

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Answer:

33

Step-by-step explanation:

55/100×60

= 33pink blocks

The number of center of rotations to produce the image is (d) infinite

An arrow pointing to the left is symmetric around its central axis.

This means that any point along the central axis of the arrow can serve as a center of rotation to produce an image of a left-pointing arrow.

The central axis is a straight line that runs through the middle of the arrow from the tip to the base, and also extend through the arrow's depth.

Hence, the number of possible centers of rotation that will produce an image of a left-pointing arrow is infinite.

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Answer:

Step-by-step explanation:

[tex]\sf 6(9-6)-23+4[/tex]

[tex]\sf (6)(3)-23+4[/tex]

[tex]\sf 18-23+4[/tex]

[tex]\sf -5+4[/tex]

[tex]\sf -1[/tex]

Answer:

First you are to do what is in the parenthesis first:

9 - 6 = 3

The equation is now:

6 * 3 - 23 + 4

Then you do the multiplcation:

6 * 3 = 18

18 - 23 + 4

23 + 4 = 27

27 - 18 = 9

Step-by-step explanation:

Hope it helps! =D

Answer: B is the answer

Step-by-step explanation:

Answer:

280 cubic m

Step-by-step explanation:

SA of rectangular prism = 2lh + 2lw + 2hw

w = width

l = length

h = height

SA = 2(5)(6) + 2(5)(10) + 2(6)(10)

SA = 2(30) + 2(50) + 2(60)

SA = 60 + 100 + 120

SA = 280

Dyscalculia is a learning disorder that affects a person’s ability to do the math.

A learning problem called dyscalculia diminishes a person's capacity for math. Similar to how dyslexia impairs reading-related brain regions, dyscalculia interferes with the knowledge and skills connected to math and numbers. Although dyscalculia often first manifests in childhood, it can even affect adults who are unaware of it.

The signs of this condition typically emerge in childhood, particularly as kids start to master the fundamentals of math. However, many adults who suffer from dyscalculia are unaware of it. When forced to do the math, people with dyscalculia frequently experience mental health problems like anxiety, depression, and other distressing emotions.

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The measure of angle m∠CBD is equal to 55°

We shall first find the measure of the angle m∠CDB so that we can evaluate for the measure of angle m∠CBD using the sum of interior angles of a triangle theorem as follows:

m∠ADB and m∠CDB are on a straight line and their sum is equal to 180° so;

m∠CBD + 80° = 180° {sum of angles on a straight line}

m∠CDB = 180° - 80° {subtract 80° from both sides}

m∠CDB = 100°

m∠BCD + m∠CDB + m∠CBD = 180° {sum of interior angles of a triangle}

25° + 100° + m∠CBD = 180°

125° + m∠CBD = 180°

m∠CBD = 180° - 125° {subtract 125° from both sides}

m∠CBD = 55°

In conclusion, the measure of angle m∠CBD is equal to 55°.

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The rate of petrol in this case is R9 per liter.

What is rate?

In mathematics, rate is a measure of how one quantity changes in relation to another quantity. It is often expressed as a ratio or fraction, where the numerator represents the amount of change in the first quantity and the denominator represents the amount of change in the second quantity.

The rate of petrol can be expressed as the cost per liter. To find the cost per liter of petrol in this case, we can divide the total cost by the total amount of petrol:

Cost per liter = Total cost / Total amount

For the given scenario, we have 20 litres of petrol for R180. So the rate can be calculated as:

Rate = Total cost / Total amount = R180 / 20 litres

Simplifying the expression, we get:

Rate = R9 per litre

Therefore, the rate of petrol in this case is R9 per liter.

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Answer: 180 kilometers

Step-by-step explanation:

Answer:

I think she runs 1 kilometer every 5 minutes

Step-by-step explanation:

The values of x in the one-step equation are presented as follows;

A one-step equation is one in which the solution can be found with a single step operation.
The solution of the one-step equation found using inverse operations can be presented as follows;

1. 4·x = 16

4·x/4 = 16/4 = 4

4·x/4 = x = 4

x = 4

2. x + 9 = 13

x + 9 - 9 = 13 - 9

x = 4

3. x - 8 = 14

x - 8 + 8 = 14 + 8

x = 22

4. x/5 = 13

(x/5) × 5 = 13 × 5

(x/5) × 5 = x = 13 × 5 = 65

x = 65

5. x - 6 = 11

x - 6 + 6 = 11 + 6

x = 17

6. 2·x = 88

2·x/2 = 88/2 = 44

2·x/2 = x = 44

x = 44

7. 6·x = 16

6·x/6 = 16/6

6·x/6 = x = 16/6 = 2.[tex]\overline{6}[/tex]

x = 2.[tex]\overline{6}[/tex]

8. x + 2.5 = 7.5

x + 2.5 - 2.5 = x = 7.5 - 2.5 = 5

x = 5

9. (2/3)·x = 8

(2/3)·x/(2/3) = 8/(2/3) = 8 × (3/2) = 12

(2/3)·x/(2/3) = x = 12

x = 12

10. x/3 = -7

x/3 × 3 = -7 × 3 = -21

x = -21

11. x - 1.6 = -8.2

x - 1.6 + 1.6 = -8.2 + 1.6 = -6.6

x = -6.6

12. 4·x = -2

4·x/4 = -2/4 = -1/2

4·x/4 = x = -1/2

x = -1/2

13. The number of slices into which the cake is divided = 6 Slices

The amount of calories per each slice of the cake = 280 calories

The amount of calories in the whole cake is therefore;

The sum of the calories in the cake  = 6 × 280 calories = 1,680 calories

14. Amount of coffee Pedro served to his friends = 34 ounces

Amount of coffee left over = 20 ounces

The total amount of coffee Pedro made = 20 + 34 = 54

The amount of coffee Pedro makes = 54 ounces

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Answer:

The derivative of the profit function P(x) is called marginal profit with notation: P ... Example 2: Given the average cost in dollar per unit C = 357x + 1800 , find: ... (1) the selling price to maximize the revenue is 31 − 3 = 28 dollars per unit ... Example 6: A company has established that the revenue function in dollars is R(x)=2x.

Step-by-step explanation:

Answer:

27 is 7.5% of the number 360

The asymptotes of f vertically (x)x=4, -4 are the vertical asymptotes.

An area on a graph where a function approaches infinity or negative infinity is known as a vertical asymptote. It happens when a rational function, which is a function that can be expressed as the quotient of two polynomials, has a denominator equal to zero but a numerator that is not. As a result, there is a noticeable "break" in the graph when the function becomes unbounded. For instance, when x=3, the vertical asymptote of the function 1/(x-3) exists.

As per the data given in the above question are as bellow,

The provided data are,

[tex]\mathrm{F}(\mathrm{x})=\frac{3 \mathrm{x}^2}{\mathrm{x}^2-16}[/tex]

When it comes to vertical asymptotes, the denominator is zero.

[tex]\mathrm{x}^2-16 & =0 \\\mathrm{x}^2 & =16 \\[/tex]

x= ±4

x=4,-4

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Answer: Yes it's 7

Step-by-step explanation:

10/100 x 70 = 7

Answer:The correct answer would be 7

Step-by-step explanation:

By resolving the following equation for y, you can make the work a little simpler: x + y = 6

The link between data pieces is displayed in tables of values. In science lesson, you might utilize a values table. Data is recorded in tables of values by scientists and researchers, who then examine the data to look for patterns. As a result, they can use this pattern to anticipate future events.

y = 6 - x, which means to take 6 out of both sides.

Now you can simply fill in the x-values and determine y. For instance,

y = 6 -(-2) = 8 . . . for x = -2

y = 6 - 3 = 3 . . . . for x = 3

The table and graph that are attached both display these values.

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Answer:

no solutions

Step-by-step explanation:

8(2w - 3) = 4(4w - 8)

Use distributive property.

16w - 24 = 16w - 32

subtract 16w from both sides.

-24 = -32

When the variable falls out of the equation as you are working on it, and you're left with a false statement, there is no solution.

Answer:

no solution

Step-by-step explanation:

to find the value of w, we have to isolate it on one side of the equation.

first, we distribute the numbers outside of the parentheses and multiply them to each term on the inside. this gives us:

16w - 24 = 16w - 32

next, we move 24 to the other side of the equation by adding 24 to both sides. by doing this, we get rid of 24 on the left side by making its value 0, and we add it to -32 on the right side. this gives us:

16w = 16w - 8

after this, we do the same with the 16w on the right side and subtract it from both sides. however, you might notice that there's a problem here.

when you try to move the 16w on the right side to the left side, you subtract 16w from itself, which gets rid of the variable entirely. whenever this happens, there are no values of the variable that make the equation possible- meaning that the answer is no solution.

hope this helped, good luck!

Answer:

42+25n

Step-by-step explanation:

[tex]7+5(7+5n)\\=7+35+25n\\=42+25n[/tex]

The volume of the piece is: 4489.33

To find the volume of this piece, we need to subtract the volume of the cylindrical hole from the volume of the sphere.

The volume of the sphere is given by the formula: V = (4/3) * pi * r^3

Where r is the radius of the sphere, so in this case: V = (4/3) * pi * (7cm)^3 = 1436 * 3.14 cm^3 = 4511.32 cm^3

The volume of the cylinder is given by the formula: V = pi * r^2 * h

Where r is the radius of the cylinder and h is the height of the cylinder, since the hole is drilled through the center of the sphere, the height of the cylinder is equal to the radius of the sphere, so: V = 3.14 * (1cm)^2 * 7cm = 21.99 cm^3

So the volume of the piece is: 4511.32 - 21.99 = 4489.33 cm^3

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Colin had $23 to spend on four raffle tickets after buying them had $11. So each raffle ticket cost is $3 and the equation is 4x + 11 = 23.

Colin had $23 to spend on four raffle tickets after buying them had $11

We have to determine how much each raffle ticket cost and the equation.

Let the cost of one raffle is x.

So the cost of four raffle is 4x.

Colin has total $23.

Colin has left money = $11

So the required equation should be

4x + 11 = 23

Now solving the equation

Subtract 11 on both side, we get

4x = 12

Divide by 4 on both side, we get

x = 3

The cost of one raffle is $3.

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The expressions which are having common denominator 24 are

13/24  +  7/12 , 1/8  -  5/3 and for 10 are 5 - 7/10 , 3/2 -  4/5 and for 12 are

7/6  -  5/12, -3/4 - 2/3.

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants.

Given ,

So given expressions are,

13/24  +  7/12   =  13+ 7*2 / 24  = 13+14 / 24 = 27/24

7/6  -  5/12 = 7*2 - 5 / 12  = 14-5/12 = 9/12

-3/4 - 2/3 = - (3/4 + 2/3 ) = - ( 9 + 8 / 12) = -17/12

5 - 7/10  = 5*10 - 7 / 10  =  50 - 7 / 10 = 43/10

1/8  -  5/3   = 3 - 8*5 / 24  = 3-40 / 24 = -37 / 24

3/2 -  4/5 = 3*5 - 2*4 / 10  = 15-8 / 10  = 7/10

Therefore, The expressions which are having common denominator 24 are 13/24  +  7/12 , 1/8  -  5/3 and for 10 are 5 - 7/10 , 3/2 -  4/5 and for 12 are 7/6  -  5/12, -3/4 - 2/3.

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The value of x when using addition property of equality to solve the given problem is; -44

The addition property of equality is a property of equality that states that when the same quantity is added to both sides of an equation, it will produce an equivalent equation. For example, 4 = 2 + 2 is an equation due to the fact that both the right and the left-hand sides of the equal sign represent the number 4.

The equation to solve is;

-60 = x - 16

By the use of addition property of equality, we will add 16 to both sides to get;

-60 + 16 = x - 16 + 16

x = -44

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