a cylinder container 12 inches tall with a radius of 6 inches is completely filled with vanilla, chocolate, and strawberry ice cream in the ratio 3:2:1. Which statement(s) are correct?
A.) The volume of vanilla ice cream is V = 216π in^3
B.) The total volume of ice cream is V = 1728π in^3
C.) The total volume of ice cream is V = 432π in^3
D.) The volume of strawberry ice cream is V = 288π in^3
E.) The volume of chocolate ice cream is V = 576π in^3

Using the details given, the area of the triangle in which the angles lies between the two sides is 90.3 units²

The area of a triangle can be calculated using the formula A = 1/2bh, where b is the base of the triangle and h is the height. Area of a triangle can be calculated using the formula: Area = (base x height) / 2, where base is the length of one side and height is the length of the side that forms the angle. In order to use this formula, you must know the length of two sides and the measure of the angle between them. However, this formula is subjective to details given

The area of a triangle can be calculated by

A = a×b×sinθ

a = 15

b = 8.1

θ = 132°

Substituting the values into the formula

A = 15 × 8.1 × sin 132

A = 90.3 units²

The area of the triangle is 90.3 units²

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3/2 does not have any factors because it is a fraction and factors are integers that can divide a number evenly. Only integers can have factors, fractions cannot.

Generally, A divisor of an integer n, also known as a factor of n, is an integer m that can be multiplied by another number to generate n. Another name for this concept is a factor of n. One may also state that n is a multiple of m in this particular scenario.

A number is considered to be a factor if the division of that number by that number results in no residue. If we get a product when we multiply two whole numbers, then the numbers we are multiplying are factors of the product since they are divisible by the product. In other words, we get a product when we multiply two whole numbers. Multiplication and division are the two techniques that may be used to discover factors.

Since 3/2 is a fraction, it does not have any factors since factors are integers that may evenly divide a number. Since 3/2 is a fraction, it does not have any factors. Only integers are capable of having factors; fractions are unable to do so.

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We are aware that P = 2(a + b) units is the perimeter of a parallelogram.Consequently, the parallelogram's sides are 50 cm, 25 cm, 50 cm, and 25 cm.

We are aware that P = 2(a + b) units is the perimeter of a parallelogram.Adding up all four sides will reveal a parallelogram's perimeter.An area of a circle of radius r is known as r2 in geometry.

The circumference-to-diameter ratio, which is always the same and is roughly equivalent to 3.14159 in this context, is denoted by the Greek letter.

Let side a and the side next to it in the parallelogram be a and b, respectively.

The parallelogram's perimeter is equal to 2(a+b)=150, where a+b=75.

Since an is 25 cm taller than b, a=b+25.

By changing it in equation 1, b+25+b=75 2b=50 b=25 is obtained.

a+b=75\sa=75=25\sa=50

Consequently, the parallelogram's sides are 50 cm, 25 cm, 50 cm, and 25 cm.

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Answer:

-34 - 24i

Step-by-step explanation:

To calculate ( – 2 – 3i)^4, we can use the property that (a + bi)^n = a^n + (n*a^(n-1)b)i + (na^(n-2)*b^2)i^2 + ...

So, ( – 2 – 3i)^4 = (-2 - 3i) * (-2 - 3i) * (-2 - 3i) * (-2 - 3i)

= -2^4 - 2^3 * 3i - 2^2 * 3^2i^2 - 2 * 3^3i^3 - 3^4i^4

= -16 - 24i + 18i^2

= -16 - 24i -18

= -34 - 24i

Answer:

  see attached 0 ⇒ 0–6

Step-by-step explanation:

Given a table of ages and weights, you want the average rate of change (per month) for consecutive pairs of table values.

The average rate of change is the change in weight divided by the change in age. For example, in the interval 0–6 months, it is ...

  (17.4 -7.8)/(6 -0) = 9.6/6 = 1.6 . . . . . pounds per month

The calculations are conveniently done for the rest of the table by a spreadsheet. The results are attached. The value on each line is the average over the interval from that age to the next.

Answer: C

Step-by-step explanation: If you solve each of them (1 x 4=4, 2x4=8, 3x4=12, 6x4=24), You can see that the are rational.

Answer:

To solve this problem, we will use the following steps:

Step 1: Let's assume that the larger number is x and the smaller number is y, we know that the difference between the two numbers is 9, so we can write the equation: x-y = 9

Step 2: We know that Four times the larger number plus one-half the smaller is 45, so we can write the equation: 4x + 0.5y = 45

Step 3: Now we have two equations with two unknowns, we can solve for one of the unknowns by isolating it in one of the equations.

x-y = 9

x = y+9

Step 4: Now we can substitute the value of x in the second equation

4(y+9) + 0.5y = 45

4y + 36 + 0.5y = 45

4.5y + 36 = 45

4.5y = 9

y=2

Step 5: We can substitute the value of y in one of the equation, to find the value of x

x-2 = 9

x = 11

Final Answer: The two numbers are 11 and 2.

The solution to the expression 5 2 (3x4) divided by 3-5 is -312

Fractions are simply described as part of a whole number or variable.

There are different types of fraction which includes;

PEMDAS is a mathematical acronym used to give the order of operations to be followed in solving expressions.

It stands for;

Given the expression;

52(3×4)/3 - 5

expand the parentheses

52(12)/-2

624/-2

Divide the values

-312

Hence, the values is -312

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Answer:

t = [tex]\frac{7}{3}[/tex]

Step-by-step explanation:

t - [tex]\frac{4}{3}[/tex] = 1 ( multiply through by 3 to clear the fraction )

3t - 4 = 3 ( add 4 to both sides )

3t = 7 ( divide both sides by 3 )

t = [tex]\frac{7}{3}[/tex]

Answer: The function f(x) = || is the absolute value function of x, which is defined as f(x) = |x|. The graph of this function is a "V" shape, with the vertex at the origin (0,0) and the lines x = 0 and y = 0 as the asymptotes. The graph of f(x) starts at the origin and increases as x increases or decreases, but never reaches x-axis.

The function g(r) = (-1)|r| is the absolute value function of r, multiplied by -1. The effect of multiplying the function by -1 is to reflect the graph of f(x) across the x-axis. So the graph of g(r) will be a "V" shape, with the vertex at the origin, and the lines x = 0 and y = 0 as the asymptotes. The graph of g(r) starts at the origin and decreases as r increases or decreases, but never reaches x-axis.

In summary, the effect of the change on the graph of f(x) = || is that it will be reflected across the x-axis.

Step-by-step explanation:

Answer:

Area =312cm²

Step-by-step explanation:

since two rectangle are joined together you will find each area of the diagram and finally you add the two rectangle.

so the value for A1

A1 × Length × width.

A1 =16 ×17

A1 =272cm²

the value for A2

A2 Length × width

A2 = 14 × 3

A2 =42cm²

The area of the diagram

=A1 + A2

=272 + 42

=312cm².

The total area of the given figure is 468 cm².

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

From the given figure,

Larger rectangle has length=30 cm and width=14 cm.

Smaller rectangle has length=16 cm and width=3 cm.

We know that, the area of a rectangle is Length×Width

Area of Larger rectangle is

30×14 = 420 cm²

Area of Smaller rectangle is

16×3 = 48 cm²

Total area = 420+48 =468 cm²

Therefore, the total area is 468 cm².

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The operation statement is given as 3*(a + 5)

3 is the value of multiplication.

Inputs are the data that are entered into a program, whether manually by the programmer or digitally. These inputs are utilized to run the program and are saved as variables. A programmer may decide to incorporate outputs to keep the user updated on what is occurring inside the program.

I/O is the exchange of information between a computer or other information processing system and the outside world, which might include people or other information processing systems. The system's inputs are the signals or data it receives, and its outputs are the signals or data it sends.

Output is simply what occurs after all the code has been completed, the final outcome. It is what is entered into the console when all calculations have been completed. Basically, it's what is released.

The given Input is :

a x 3

The output it is giving is 3a + 15

One variable is a

The operation that is done is 'x' multiplication.

The operation statement is given as 3*(a + 5)

3 is the value of multiplication.

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Answer:

--------------------------------

Consecutive exterior angles are supplementary.

It proves a and b are parallel.

Corresponding angles are congruent.

It proves a and b are parallel.

Given two vertical angles showing the relation between one line and the transversal and not a reason to state the lines are parallel.

Given two angles of same value. Since they are alternate interior angles, it proves the lines a and b are parallel.

Given two angles with the sum of 180. They are same side interior angles. It proves the lines a and b are parallel.

Given two angles of same value. They are alternate exterior angles but in relation to one of the lines and it proves the two transversals are parallel but not the lines a and b.

Answer:

To solve this problem, we will use the following steps:

Step 1: Let's assume that the number of adult tickets sold is x and the number of senior/child tickets sold is y

Step 2: We know that the number of senior/child tickets sold was 27 less than twice the number of adult tickets sold, so we can write the equation: y = 2x - 27

Step 3: We also know that the total value of tickets sold was $2,647.50. Since adult tickets sold for $10 each and senior/child tickets sold for $7.50 each, we can write the equation: 10x + 7.5y = 2,647.50

Step 4: Now we have two equations with two unknowns, we can substitute one equation into another to find the value of x and y.

y = 2x - 27

10x + 7.5(2x - 27) = 2,647.50

10x + 15x - 405 = 2,647.50

25x = 3,052.50

x = 122

Step 5: We can substitute the value of x in one of the equation, to find the value of y

y = 2(122) - 27

y = 245

Final Answer: 122 adult tickets and 245 senior/child tickets were sold.

Note: We can check our solution by multiplying the number of adult tickets by $10 and the number of senior/child tickets by $7.5 to check if the total money is $2,647.50 which is true.

The number of children and adults that swan at the public pool that day would be = 208 and 209 respectively.

The number of people that swam on the summer day = 485 people.

The price paid for children = $1.25

The price paid for adults = $2.00

The total amount of money paid for the admission = $677.50.

The amount paid only for adults;

= 2/2+1.25 × 677.50/1

= 1355/3.25

= $416.92

The number of adults that swam ;

= 416.92/2

= 208.46

= 209 (approximately).

The amount paid for children;

= 1.25/3.25 × 677.50/1

= 846.875/3.25

= $260.58

The number paid for children alone;

= 260.58/1.25

=208.464

= 208 (approximately).

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Answer:

Step-by-step explanation:

2 x 12 - (9 - 3) x 2 / 2

Answer:

  369,287 in the US

  3.69287×10⁵ in the UK

Step-by-step explanation:

Given the number (8*10)+(6*10,000)+(3*100,000)+(2*100)+(9*1,000)+(7*1), you want it written in standard form.

The "standard form" of a number is different depending on your local culture.

In the US, the standard form of this number can be had by performing the indicated addition.

  (8*10)+(6*10,000)+(3*100,000)+(2*100)+(9*1,000)+(7*1)

  = 80 +60,000 +300,000 +200 +9,000 +7

  = 300,000 +60,000 +9,000 +200 +80 +7 . . . . more useful order

  = 369,287

In the UK, "standard form" of a number refers to "scientific notation". The leading digit is shown to the left of the decimal point, and the multiplier is the power of 10 corresponding to that digit's place value.

  = 3.69287×10⁵

Answer:

you could fit 7776 people on the gym floor for an event.

Step-by-step explanation:

The Locust Grove gymnasium has an area of 54 yd x 40 yd = 2160 square yards. To find the number of people that can fit on the gym floor, we need to convert the area of the gym floor to square feet and divide it by the number of square feet each person takes up.

We know that 1 yard = 3 feet, so we have to convert the area of the gymnasium in square yards to square feet by multiplying it by (3*3) = 9.

So the area of the gymnasium in square feet is 2160*9 = 19440 square feet.

To find the number of people that can fit on the gym floor, we divide the area of the gym floor by the number of square feet each person takes up.

19440 square feet / 2.5 square feet/person = 7776 people

Answer:

8:39 is the answer.

The rest, when simplified, change to 1:5.

Answer:

30%.

Step-by-step explanation:

Ayo earns 50,000 monthly and he spends 35,000 altogether, so he saves the rest of his income. To find the percentage of his savings, we can divide his savings by his total income and multiply by 100.

His total income is 50,000

His total expenditure is 35,000

His savings = total income - total expenditure = 50,000-35,000 = 15,000

So the percentage of his savings = (savings / total income) x 100 = (15,000 / 50,000) x 100 = 0.3 x 100 = 30%

Therefore, Ayo's savings percentage is 30%.

The cyclist's average speed is

14.93

mph.

Total

distance

covered is=2+8=10

Total time =10+30=40

=40/60 min

=.0.67 hours.

Convert miles per min to miles per hour,

average speed= 10 miles/0.67 hours,

=14.93 mph.

The average speed is =4.93 mph

The total distance covered is 2 + 8 = 10 miles. The total time taken is 10 minutes + 30 minutes = 40 minutes. To convert minutes to hours, divide the time in minutes by 60. So, the total time taken in hours is 40 minutes / 60 = 0.67 hours. To convert miles per minute to miles per hour, multiply the speed in miles per minute by 60. So, the average speed in miles per hour is

10 miles / 0.67 hours = 14.93 mph

The average speed is =14.93 mph

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Using the decay constant on the exponential function, the mass of the sample that will be left in 2013 is 35g

An exponential function is a function that can be expressed in the form     f(x) = b^x, where b is a positive real number and x is a real number. The graph of an exponential function is a curve that increases or decreases rapidly as x increases or decreases.

In the exponential decay, the decay function can be given as;

y = ae⁻ⁿˣ

The disintegration constant is also know as the rate of decay and we can calculate it as;

260 = 470e⁻ⁿ⁽³⁾

n = 0.197

n = 0.2

The disintegration constant is 0.2

The amount left in 2013 will be;

y = 470e⁻⁽⁰.²⁾⁽¹³⁾

y = 34.90

The mass in 2013 is 35g

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Answer:

The interest earned is $92.40

The amount in the bank is 92.40 + 700 = $792.40

Step-by-step explanation:

I do not see a number line

Interest = principle x rate x time

Interest = 700 x .033 x 4

Interest = 92.40

The resulting image of the triangle ABC after the transformations is given by the image presented at the end of the answer.

The vertices of the original triangle ABC are given as follows:

A(0,2), B(3,2), C (2,7).

First we have the reflection across the line x = 1, which is a vertical line, meaning that:

Hence the vertices after the reflection are given as follows:

A'(2,2), B'(-1,2), C'(0,7).

For example, a coordinate of 0 is one unit left of x = 1, hence the coordinate of the image will be one unit right, at x = 2.

The dilation with a scale factor of 2 centered at the origin means that the coordinates are multiplied by 2, hence:

A''(4,4), B''(-2,4), C''(0,14).

The vertices of the original triangle ABC are given as follows:

A(0,2), B(3,2), C (2,7).

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The required quadratic equaiton is h(x) = (x + 1)² -3. Option D is correct.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

here,
From the data select 1 pair of values,
x = 0, when h(0) = -2

Now, put this pair in each quadratic equation, since the equation that satisfies this fair will be the required quadratic equation.

A,
h(x) = (x − 1)² + 1
h(0) = (0 − 1)² + 1
h(0) =  2

B.
h(x) = (x − 1)² + 3
h(0) = 4

C.
h(x) = (x + 1)² - 1
h(0) = 0

D.
h(x) = (x + 1)² - 3

h(0) = 1 - 3 = -2
h(0) = -2

Thus, the required quadratic equaiton is h(x) = (x + 1)² -3. Option D is correct.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:  112112v

112112112112112112v112112. 112112112112112112112112112112Answer:

Step-by-step explanation:  112112v

112112112112112112v112112. 112112112112112112112112112112Answer:

Step-by-step explanation:  112112v

112112112112112112v112112. 112112112112112112112112112112

The equation is solved and the values of a and b is simplified as

a) The possible values of ab = 4

b) The possible values of a + b = 4

c) The possible values of a and b = 2

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

(a)

To find all possible values of ab, we can use the identity:

a⁴ + b⁴ = (a² + b²)² - 2a²b²

Substituting the given values, we have:

16 = (a² + b²)² - 2a²b²

We also know that a + b=4, which means that b = 4 - a.

Substituting this into the equation above, we have:

16 = (a² + (4-a)²)² - 2a²(4-a)²

Simplifying, we get:

16 = (2a² - 8a + 16)² - 32a² + 64a³ - 32a⁴

Expanding, we get:

16 = 4a⁴ - 64a³ + 288a² - 512a + 272

Rearranging and factoring, we get:

4a⁴ - 64a³ + 288a² - 512a + 256 = 0

Dividing by 4, we get:

a⁴ - 16a³ + 72a² - 128a + 64 = 0

This is a quartic equation, which can be factored as:

(a-2)⁴ = 0

Therefore, the only possible value of a is 2, which means that the only possible value of b is 2 as well.

So, ab = 2 x 2 = 4

(b)

We know that a + b = 4, and since a = 2, we have b = 4 - a = 2

Therefore, the only possible value of a + b is 4

(c)

From part (b), we know that the only possible value of a + b is 4. From part (a), we know that the only possible values of a and b are both equal to 2.

Therefore, the only possible solution is a = 2 and b = 2

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