Oliver's Flavored Popcorn comes in cylindrical tins divided into three equal sections of caramel, cheese, and buttered flavors. If the tin is 10 inches in diameter and 15 inches tall, what is the volume to the nearest tenth of only the cheese popcorn?

Step-by-step explanation:

_______________________________________

\(2 {x}^{2} + x - 3\)

Write the equation

_______________________________________

\( = 2 {x}^{2} + 3x - 2x - 3\)

expand x into 3x and -2x

_______________________________________

\( = x(2x + 3) - (2x + 3)\)

take x out and 2x+3 in bracket and take - out and 2x+3 in brackets

_______________________________________

\( = (2x + 3)(x - 1)\)

_______________________________________

hope it helped you:)

In the given diagram of circle O, we need to find various measurements. Let's consider the following measurements:

Diameter (d): The diameter of a circle is the distance across it, passing through the center. To find the diameter, we can measure the distance between any two points on the circle that pass through the center. Let's say we measure it as 12 units.

Radius (r): The radius of a circle is the distance from the center to any point on the circumference. It is half the length of the diameter. In this case, the radius would be 6 units (12 divided by 2).

Circumference (C): The circumference of a circle is the distance around it. It can be found using the formula C = 2πr, where π is approximately 3.14 and r is the radius. Using the radius of 6 units, we can calculate the circumference as C = 2 * 3.14 * 6 = 37.68 units. Rounding to the nearest whole number, the circumference is approximately 38 units.

Area (A): The area of a circle is the measure of the surface enclosed by it. It can be calculated using the formula A = πr^2. Substituting the radius of 6 units, we can find the area as A = 3.14 * 6^2 = 113.04 square units. Rounding to the nearest whole number, the area is approximately 113 square units.

In summary, for circle O, the diameter is 12 units, the radius is 6 units, the circumference is approximately 38 units, and the area is approximately 113 square units.

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Answer:

answer is below

Step-by-step explanation:

Answer: I worked it all out and attached an image, hope this helps!

Answer:

Having soup and salad for lunch are independent events because P(A/B)=P(A) and P(B/A) = P(B)

Step-by-step explanation:

The probability of guessing the correct answer for each question is 1/4, while the probability of guessing incorrectly is 3/4.

To calculate the probability of answering at most one correct answer, we need to consider two cases: answering zero correct answers and answering one correct answer.

For the case of answering zero correct answers, the probability can be calculated as (3/4)^5, as there are five independent attempts to answer incorrectly.

For the case of answering one correct answer, we have to consider the probability of guessing the correct answer on one question and incorrectly guessing the rest. Since there are five questions, the probability for this case is 5 * (1/4) * (3/4)^4.

To obtain the probability of answering at most one correct answer, we sum up the probabilities of the two cases:

Probability = (3/4)^5 + 5 * (1/4) * (3/4)^4.

Therefore, by calculating this expression, you can determine the probability of answering at most one correct answer among five questions when guessing randomly.

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If last week Salazar played 13 more tennis games than Perry and they played a combined total of 53 games, then Salazar played a total of 33 games.

Let the total number of games played by Perry be x.

It is given that, Salazar played 13 more tennis games than Perry.

⇒ Total games played by Salazar = x + 13

Also, Salazar and Perry played a combined of 53 games.

Hence, total number of tennis games played by Salazar and Perry = 53

⇒ Games played by Salazar + Games played by Perry = 53

⇒  x + (x + 13) = 53

2x + 13 = 53

2x = 53 - 13

2x = 40

x = 40 / 2

x = 20

Therefore, total number of games played by Salazar = x+13

= 20 + 13

= 33

Thus, Salazar played total 33 games.

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The sum of the NPV and false omission rate for any test will always be 100%.

The NPV (Negative Predictive Value) is the proportion of people who test negative for a condition and actually do not have it, while the false omission rate is the proportion of people who have the condition but test negative for it.

When we add together the NPV and the false omission rate for any test, we are essentially considering all the cases where the test result is negative.

The NPV represents the proportion of people who truly do not have the condition and test negative for it, while the false omission rate represents the proportion of people who actually have the condition but test negative for it.

Together, these two values cover all possible cases where the test result is negative, which means that they represent the entirety of the negative results for the test.

Since the sum of all probabilities for an event must always equal 100%, the sum of the NPV and false omission rate must also equal 100%.

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Let the first of the two consecutive integers be n. Then the next consecutive integer is n+1.

From the given information, we can form an inequality, which is:2n + (n+1) ≥ 25

The above inequality is formed from the statement "Twice the smaller of two consecutive integers increased by the larger integer is at least 25". Now, let's solve this inequality and find the values of n that satisfy it.2n + (n+1) ≥ 25Simplifying the above inequality, we get:3n + 1 ≥ 25

Subtracting 1 from both sides, we get:3n ≥ 24

Dividing both sides by 3, we get:n ≥ 8

Hence, the first of the two consecutive integers is greater than or equal to 8.

Therefore, the two consecutive integers that satisfy the given information are 8 and 9.

Now, we need to check which of the given values, 7, 8, or 9, satisfy the above inequality. Let's check for

n=7.2n + (n+1) = 2(7) + (7+1) = 15 < 25

Therefore, n=7 is not a solution.

Let's check for n=8.2n + (n+1) = 2(8) + (8+1) = 25 ≥ 25

Therefore, n=8 is a solution. Let's check for n=9.2n + (n+1) = 2(9) + (9+1) = 28 ≥ 25

Therefore, n=9 is also a solution.

Thus, we have found that the solutions to the given problem are n=8 and n=9.

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Answer:

4.95 x 10^-1

Step-by-step explanation:

4.95 x 10^-1

A quadratic equation can be solved by factoring if its coefficients are rational numbers and its discriminant, which is the expression under the square root in the quadratic formula, is a perfect square.

To determine if a quadratic equation can be solved by factoring, you must first ensure that its coefficients are rational numbers, meaning that they can be expressed as a ratio of two integers. Once you have confirmed this, you can calculate the discriminant of the quadratic equation, which is the expression b²-4ac, where a, b, and c are the coefficients of the quadratic equation in standard form.

If the discriminant is a perfect square, then the quadratic equation can be solved by factoring. If the discriminant is not a perfect square, then the quadratic equation cannot be solved by factoring using rational numbers, but may still be solvable using other methods, such as completing the square or the quadratic formula.

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Answer:???

Step-by-step explanation:

Answer:

(1,15)

Step-by-step explanation:

Answer:

(21, 3 )

Step-by-step explanation:

9x = 177 + 4y ( subtract 4y from both sides )

9x - 4y = 177 → (1)

6x - 5y = 111 → (2)

multiplying (1) by 5 and (2) by - 4 and adding will eliminate y

45x - 20y = 885 → (3)

- 24x + 20y = - 444 → (4)

add (3) and (4) term by term to eliminate y

(45x - 24x) + (- 20y + 20y) = 885 - 444

21x + 0 = 441

21x = 441 ( divide both sides by 21 )

x = 21

substitute x = 21 into either of the 2 equations and solve for y

substituting into (1)

9(21) - 4y = 177

189 - 4y = 177 ( subtract 189 from both sides )

- 4y = - 12 ( divide both sides by - 4 )

y = 3

solution is (21, 3 )

Answer:

X+2=2x

x+8=8x

(2x).(8x)=16x

In all, add 43 more times 5 and divide by 12 to get 58. Hence, the final response is 87.

We can employ the order of operations, which is a set of guidelines for carrying out computations in a mathematical problem. The sequence of events is:

Any calculations should be done first inside the parentheses.

Exponents (ie powers and square roots, etc) (ie powers and square roots, etc.)

Division and Exponentiation (from left to right)

Subtraction and Addition (from left to right)

These guidelines allow us to piecemeal the solution to the issue. 43 is first multiplied by 5 for a total of 215. The result of 215 divided by 12 is 17.91666667. We can round it to 18 since we don't want to utilize this large figure. 11 is then added to give us 29.

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Simplify 43 + 5/12+11+43 5/12+11

Answer:

(1, 2)

(2,2)

Step-by-step explanation:

The inequality Given :

y < 5x + 2

y ≥ One-halfx + 1

We can use the values in the options to see which satisfies the inequality :

(-1, 3) ; X = - 1, y = 3

3 < 5(-1) + 2 ; 3 < - 4 (not true)

(0, 2) ; X = 0 ; y = 2

2 < 5(0) + 2 ; 2 < 2 (nor true)

2 > 1/2(0) + 1

2 > 1 (true)

Using (1, 2).; x = 1 ; y = 2

2 < 5(1) + 2 ; 2 < 7 (true)

2 > 1/2(1) + 1 ; 2 > 1.5 (true)

Using (2, 2)

y < 5x + 2

2 < 10 + 2 ; 2 < 12 (true)

y > 1/2x + 1

2 > 1/2(2) + 1 ; 2

Answer:

Yes

Step-by-step explanation:

The expression for the power delivered to a resistance in terms of csc^2 2 pi ft is P = I^2_0 R (csc^2 2 pi ft).

According to the given information, the power delivered to a resistance R when an alternating current of frequency f and peak current I_0 passes through it is represented by the equation P = I^2_0 R sin^2 2 pi ft.

To express this equation in terms of csc^2 2 pi ft, we can use the trigonometric identity csc^2 x = 1/sin^2 x. Substituting this identity into the equation, we get P = I^2_0 R (1/sin^2 2 pi ft).

Since csc^2 x is the reciprocal of sin^2 x, we can rewrite the equation as P = I^2_0 R (csc^2 2 pi ft). This expression represents the power delivered to the resistance in terms of csc^2 2 pi ft.

Therefore, the correct expression for the power delivered to the resistance in terms of csc^2 2 pi ft is P = I^2_0 R (csc^2 2 pi ft).

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The student's final average, based on the given weights and grades, is 90.2.

To calculate the student's final average using the weighted mean, we need to multiply each grade by its corresponding weight (percentage), and then sum up these weighted values.

Given:

Exam grade: 75 (weight: 30%)

Term paper grade: 89 (weight: 10%)

Final exam grade: 98 (weight: 60%)

Calculating the weighted values:

Exam weighted value = 75 * 0.30 = 22.5

Term paper weighted value = 89 * 0.10 = 8.9

Final exam weighted value = 98 * 0.60 = 58.8

Summing up the weighted values:

Final average = Exam weighted value + Term paper weighted value + Final exam weighted value

Final average = 22.5 + 8.9 + 58.8

Final average = 90.2

Therefore, the student's final average, based on the given weights and grades, is 90.2.

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Answer:

The answer is in the 4th quadrant

Step-by-step explanation:

I really hope this helped!!! have a great day. :)

Answer: y = -1*x^2 - 4

Step-by-step explanation:

A generic quadratic equation is written as:

y = a*x^2 + b*x + c

we need to find the values of a, b, and c

We have the table:

x     y = f(x)

-4     -20

-3       -13

-2        -8

-1         -5

0         -4

1          -5

In the table we can see two things:

y(0) = a*0^2 + b*0 + c = c = -4

Then we know that:

y(x) = a*x^2 + b*x - 4

Now we only need to find a and b.

We also can see that we have symmetry around the point x = 0, this means that x = 0 is the vertex of the quadratic equation, and for a general case the vertex is at:

x = -b/2a

and this is equal to zero:

-b/2a = 0

then we must have b = 0.

So for now, the equation is:

y = a*x^2 -4

Now we can just replace the values of any of the points to find the value of a, for example we can use the point (1, -5)

this means that:

y = -5 = a*1^2 - 4

    -5 = a - 4

    -5 + 4 = a

        -1 = a

Then the quadratic equation is:

y = -1*x^2 - 4

Answer:

40-5x

Step-by-step explanation:

Sahai starts with 40 and loses 5 times the entrance fee, which is represented by x. So, 40-5x is the expression

Answer:

8.5 inches

Step-by-step explanation:

To find the height of Aba's dog -

Subtract 5 1/2 from 14 to find the amount she grew:

The result should be 8.5 or 8 1/2.

So Aba's dog grew 8.5 inches.

The radian measure of Angle E should be labeled π/3 or 60 degrees, and F should be labeled 2(π/3) or 120 degrees.

A full circle in radian measures is 2π and half π

If we divide π into 3 equal parts it should be π/3 radian.

Angle EAP would be π/3 radians because E is one-third of the way from A to P.

In degrees, π/3 radians is equal to (180/π) × π/3 = 60°

Angle FAP would be 2×(π/3) radians givn that F is 2/3 of the way from A to P.

In degrees, 2×(π/3) radians is equal to (180/π) × 2(π/3) = 120°.

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Answer:

B

Step-by-step explanation:

Expand (x+5)^2 through binomial expansion and you get x^2+10x+25.

Break up the problem into little pieces like (x-5)(x+5) and 10(x+5)

Solve the first piece (x-5)(x+5) by doing something like FOIL.

x^2-25

Do the second piece

10x+50

When you add them together, it becomes x^2+10x+25, and (x+5)^2=(x-5)(x+5)+10(x+5).

Answer: D.

Step-by-step explanation:

You can start out with the form AX = B and solve for matrix X that would yield the answer

Then X = (A^-1)(B)

A = [1    -1]

      [1     1]

A^-1 = (1/(1 - (1)(-1)))*[1    1]

                             [-1   1]

which can be written as (1/2) * [1    1]

                                                  [-1   1]

B = [26]

     [6]

(A^-1)(B) = (1/2)*[1    1] [6]

                        [-1   1] [26]

= (1/2)*[32]

          [20]

= [16]

  [10]

Answer: B

Step-by-step explanation: See picture

Rational

OPTION A is the correct answer

Answer:

A is the correct answer! :)

Step-by-step explanation:

have a nice day!~

Line Intergral value is 2/3 (5√5-2).

In this problem, we have to evaluate the line integral C xy ds, where C is the given curve C:

x = t2, y = 2t, 0 ≤ t ≤ 1.

We have to find the values of the given line integral. A line integral is a type of integral that involves integrating over a curve. The value of line integral is calculated as follows:

∫Cf(x, y) ds=∫ba f(x(t), y(t))|r'(t)| dtHere, f(x, y) = xy and the curve is given by C:

x = t2, y = 2t, 0 ≤ t ≤ 1. So, we have to find the value of the line integral as follows:

∫Cf(x, y) ds=∫ba f(x(t), y(t))|r'(t)| dt∫01 (t2)(2t)√[4t2+4] dt=∫01 2t3√[4t2+4] dtLet 4(t2+1) = u, then 8t dt = du.

Substituting the values we get,

∫01 2t3√[4t2+4] dt=∫05√(u)du=2/3 u3/2|05= 2/3 (5√5-2)

Thus, the value of the line integral is 2/3 (5√5-2).

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Mr.johns invested money in each business is first business = $26909

and second business = $27909.

Given:

Last year he gained 10% on the first investment and 12% on the second if he invested $1000 more in the first business and gained a total of $6040.

Let x be the money invested in first business

From given statements:

10x/100 + (x + 1000)12/100 = 6040

multiply by 100 on both sides

10x + 12(x + 1000) = 6040*100

10x + 12x + 12000 = 604000

22x = 604000 - 12000

22x = 59200

x = 26909 invested in first business.

second business investment = 26909 + 1000 ⇒ 27909.

Therefore Mr.johns invested money in each business is first business = $26909 and second business = $27909.

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