Number cube is rolled and letter is drawn. What is the probability of rolling an odd number and drawing a vowel

Answer:

the third answer

Step-by-step explanation:

c = 4

c + 1 = 1 + 1 + 1 + 1 + 1

4 + 1 = 1 + 1 + 1 + 1 + 1

5 = 5

Answer:

∠ ABC = 127°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ ABC is an exterior angle of the triangle , then

∠ ABC = ∠ BDC + ∠BCD = 60° + 67° = 127°

We know that we have a triangle and we want to find the value of its angle which will be given by  53°.

We know that the sum of all the interior angles of a triangle must equal 180 degrees, so we find then:

\(ABC=180\)

Now making the sum of the angles already known and equating to 180, we find that:

\(180=67+60+x\\x=180-127\\x= 53\)

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Answer: A. 4(8m-2) and 32m -8

Step-by-step explanation: First distribute the 4 to 8m and -2 to get 32m - 8 which is equal to 32m - 8.

32m - 8 = 32m - 8

Hope this helps! :)

Answer:

The first one

Step-by-step explanation:

4(8m-2)=32m-8

The exponential function \(P(t) = P0 \times 1.04^t\) represents the exponential growth of Option C: A town's population grows at a rate of 4% every year.

What is an exponential function?

The formula for an exponential function is \(f(x) = a^x\), where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

The context that represents exponential growth is "A town's population grows at a rate of 4% every year."

Exponential growth occurs when a quantity grows at an increasing rate over time, which is exactly what is happening with the population of the town.

As the population grows, the growth rate also increases, resulting in an exponential increase over time.

Let P(t) be the population of the town after t years, where t is a positive integer.

The exponential function that models the population growth is -

\(P(t) = P0 \times (1 + r)^t\)

where P0 is the initial population, r is the growth rate as a decimal, and t is the time in years.

In this case, the growth rate is 4% per year, which can be written as a decimal as r = 0.04.

Therefore, the exponential function for the town's population growth is -

\(P(t) = P0 \times (1 + 0.04)^t\)

Simplifying the expression, we get -

\(P(t) = P0 \times 1.04^t\)

This function can be used to calculate the population of the town after a given number of years, assuming the growth rate remains constant.

In contrast, the other contexts represent either a steady decrease (town's population shrinking at a rate of 8.1% per year and the radioactive compound decaying at a rate of 5% per hour) or a linear increase (taxi charges a flat fee of $3.00 for pick-up, then an additional fee of $2.75 per mile).

Therefore, the exponential growth is displayed by town's population growing 4% every year.

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Answer:

A = 160

Step-by-step explanation:

Formula 1/2 d1d2

1/2 (16 x 20)

320 x 1/2 OR 320/2

=160

Hope this helps :)

The probability that the candy that teacher selects will be yellow is 0.28.

Selections and combinations are synonyms. Combinations represent the choosing of items from a predetermined group of items. We're not trying to arrange anything here. We're going to pick them.

The formula for combination is-

ⁿCₓ = n!/{x!(n-x)!}

where, n is the total sample set.

x is the selected sample set.

The total candies present in the bag are-22 red candies, 20 orange candies, 28 yellow candies, and 30 pink candies

Total candies n = 22 + 20 + 28 + 30

n = 100

The selected candy is yellow (x = 28)

According to combination formula,

The probability of getting yellow candy is = ²⁸C₁ / ¹⁰⁰C₁

Probability = 28 / 100

Probability = 0.28

Therefore, the probability that the candy teacher selects will be yellow is 0.28.

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The value of the given function h(k(3)) when h(x) =√ x+3  and k(x) = 2x +7 is equal to 4.

As given in the question,

Given functions are :

h(x) =√ x+3  and k(x) = 2x +7

To find the value of the composite function h(k(3)) :

First calculate for k(3) we get,

k(x) = 2x+ 7

Substitute x =3 in k(x) we get,

k(3) = 2(3) +7

⇒ k(3) = 13

Now, Substitute the value of k(3) in the composite function h(k(3)) we get,

h(k(3))

= h(13)

= √ 13 +3

=√16

= 4

Therefore, the value of the given function h(k(3)) when h(x) =√ x+3  and k(x) = 2x +7 is equal to 4.

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Answer:

10 ft

Step-by-step explanation:

Let x = the distance between the wall and ladder.

So the length of the ladder is x + 2.

Applying Pythagorean theorem:

AC² = AB² + BC² (1)

Substituting the measurements into (1)

(x+2)² = 6² + x²

x² + 4x + 4 = 6² + x²

4x + 4 = 36

x = (36 - 4)/4 = 8

So the length of the ladder is x + 2 = 8 + 2 = 10 ft

The distance from the wall is 8 feet. Using y = x + 2, we get:
y = 10
So the length of the ladder is 10 feet.

To solve this problem, we can use the Pythagorean theorem, which states that for any right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the ladder forms a right-angled triangle with the wall and the ground. The height at which the ladder touches the wall is 6 ft, and the distance from the wall is represented by x. Since the ladder's length is 2 ft more than its distance from the wall, the ladder's length will be x + 2.

Applying the Pythagorean theorem:

Length of ladder² = (Distance from the wall)² + (Height on wall) ²
(x + 2)² = x² + 6²
   
Expanding and simplifying the equation:

x² + 4x + 4 = x² + 36
4x = 32
x = 8

So, the distance from the wall is 8 ft, and the length of the ladder is x + 2 = 8 + 2 = 10 ft.

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The volume of the largest rectangular box in the first octant with three faces in the coordinate planes, and one vertex in the plane is V = xyz, where x, y, and z are the lengths of the sides of the rectangular box.

To find the largest volume, we need to maximize x, y, and z. Since we have three faces in the coordinate planes, one vertex will be at the origin (0, 0, 0). The other two vertices will lie on the coordinate axes.

Let's assume the vertex on the x-axis is (x, 0, 0), and the vertex on the y-axis is (0, y, 0). The third vertex on the z-axis will be (0, 0, z). Since the box is in the first octant, all the coordinates must be positive.

To maximize the volume, we need to find the maximum values for x, y, and z within the constraints. The maximum values occur when the box touches the coordinate planes. Therefore, the maximum values are x = y = z.

Substituting these values into the volume formula, we get V = xyz = x³. Therefore, the volume of the largest rectangular box is V = x³.

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What is the maximum volume of a rectangular box situated in the first octant, with three of its faces lying on the coordinate planes, and one of its vertices located in the plane?

Answer:

Every parabola has a turning point called the axis of symmetry,so for this question you just have to find the turning points

x turning point= -b/2a,and the y turning point is gotten by replacing the value of x in the equation

y=(x+1)(x-4)

=x^2-3x-4

a is 1,b is -3 and c is -4

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

=1.5

and y=x^2-3x-4

=1.5^2-3(1.5)-4

= -6.25

therefore the axis of symmetry is (1.5,-6.25)

I hope this helps

The exact area of the surface obtained by rotating the curve y = 7 - x about the x-axis over the interval 1 ≤ x ≤ 7 is 36π √2 square units.

Use the formula for the surface area of a solid of revolution to find the exact area of the surface obtained by rotating the curve y = 7 - x about the x-axis,

The surface area of a solid of revolution obtained by rotating a curve y = f(x) about the x-axis over the interval [a, b] is given by:

A = 2π ∫[a, b] f(x) √(1 + (f'(x))²) dx

In this case, the curve is y = 7 - x and the interval is 1 ≤ x ≤ 7.

Calculate the derivative of the curve y = 7 - x to find the surface area:

f'(x) = -1

Now we can plug these values into the surface area formula:

A = 2π ∫[1, 7] (7 - x) √(1 + (-1)²) dx

 = 2π ∫[1, 7] (7 - x) √(1 + 1) dx

 = 2π ∫[1, 7] (7 - x) √2 dx

Simplifying, we have:

A = 2π √2 ∫[1, 7] (7 - x) dx

 = 2π √2 [(7x - (x²/2))] |[1, 7]

 = 2π √2 [(7(7) - (7²/2)) - (7(1) - (1²/2))]

Calculating this expression, we get:

A = 2π √2 [(49 - 24.5) - (7 - 0.5)]

 = 2π √2 [(24.5) - (6.5)]

 = 2π √2 (18)

Simplifying further, we have:

A = 36π √2

Therefore, the exact area is 36π √2 square units.

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Answer: Let's call the initial goal amount of canned goods "g". The expression to represent the total percent of the goal collected can be written in two different ways as follows:

The first expression represents the initial goal plus the additional 18% collected over the weekend:

Total percent collected = g + 0.18g = 1.18g

This means that the volunteers collected 118% of the initial goal.

The second expression represents the ratio of the total amount collected to the initial goal:

Total percent collected = (g + 0.18g) / g = 1 + 0.18 = 1.18

This means that the volunteers collected a total of 118% of the initial goal.

Step-by-step explanation:

Answer:

x+18%

1.18x

Step-by-step explanation:

To learn abount the students opinion about nutritional quality of school lunch the cashier asked each every fifth student as they pay for their lunch.

This type of sampling method is when you take the sample using a fixed and periodic interval and is called systematic sampling

The amount of space Mackenzie need to cover with paint in her new room is 825 square inches.

The shape of Mackenzie in a cuboid

Length, l = 14 ½ ft

Width, w = 12

Height,h = 9 ft

Surface area of a cuboid = 2(lh + lw + wh)

= 2(14 ½ × 9 + 14 ½ × 12 + 12 × 9)

= 2(130.5 + 174 + 108)

= 2(412.5)

= 825 square inches

Therefore, Mackenzie needs to cover 825 square inches of her new room with Beyoncé Fierce Pink paint.

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Answer:

Rule for piece 1: y=-x

Rule for piece 2: y=1

Rule for piece 3: y = 2-x

Step-by-step explanation:

Answer:

Step-by-step explanation:

In a tent, there are nine boys.

There were five tents.

5 tents containing 9 boys can equal 45 boys.

(5 x 9 = 45)

In a cabin, there are seven boys.

There were four cabins.

4 cabins containing 7 boys can equal 28 boys.

(4 x 7 = 28)

Now, to find all the boys, add the numbers together.

28 boys with 45 boys will equal 73 boys.

Please check my answer for no one, not even me is right.

Good luck :)

Answer:

60 cubic meters will be the volume of such cone.

Step-by-step explanation:

Formula for volume of a cylinder:

\(V = \pi r^{2} h ...... (1)\)

Where \(r\) is the radius of base of cylinder

and \(h\) is the height of cylinder

V = 180 cubic meters

Formula for volume of a cone:

\(V' = \dfrac{1}{3}\pi R^{2} H ...... (2)\)

Where \(R\) is the radius of base of cone

and \(H\) is the height of cone

Now, it is given that height and radius of cone are equal.

\(r = R\\h =H\)

Putting the values in equation (2):

\(V' = \dfrac{1}{3}\pi r^{2} h\)

Using equation (1):

\(V' = \dfrac{1}{3} \times V\)

Putting V = 180 cubic meters

\(\Rightarrow V' = \dfrac{1}{3} \times 180\\\Rightarrow V'=60 \text { cubic meters}\)

Hence, 60 cubic meters will be the volume of such cone.

The efficiency of the Zumba class system is approximately 69.2%, and its utilization is approximately 54.5%.

To calculate the efficiency of the system, we can divide the actual output (number of employees trained) by the designed capacity (maximum number of employees that can be trained per month) and multiply by 100 to get a percentage.

Efficiency = (Actual Output / Designed Capacity) * 100

Efficiency = (600 / 850) * 100 = 70.6%

Therefore, the efficiency of the system is approximately 70.6%.

To calculate the utilization of the system, we can divide the actual output (number of employees trained) by the capacity (maximum number of students per month) and multiply by 100.

Utilization = (Actual Output / Capacity) * 100

Utilization = (600 / 1100) * 100 = 54.5%

Therefore, the utilization of the system is approximately 54.5%.

The Zumba class system at the local gym has an efficiency of approximately 69.2% and a utilization rate of approximately 54.5%. The efficiency indicates how well the system is performing relative to its designed capacity, and in this case, it suggests that the system is operating at a reasonably high level. The utilization rate, on the other hand, indicates how much of the available capacity is being utilized, and in this case, it suggests that the system is operating at around half of its maximum capacity. This information can be used by the gym to evaluate the performance of their Zumba class program and make informed decisions regarding resource allocation and potential improvements.

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Hence, in answering the stated questiοn, we may say that If yοu're unitary methοd  satisfied with yοur line plοt, save it and distribute it as needed.

The unit technique is a prοblem-sοlving apprοach that invοlves finding the value οf a single unit and then multiplying that value by the needed value. Tο put it simply, the unit technique is used tο extract a single unit value frοm a given multiple. 40 pens, fοr example, wοuld cοst 400 rupees, οr the cοst οf οne pen. The prοcess fοr achieving this may be standardized. A single cοuntry. anything that has an identity element. Its adjοint and reciprοcal are equal in mathematics and algebra.

a general methοd fοr prοducing a line plοt:

First, cοllect yοur data. Stοck prices, temperature readings, and survey results are all examples οf this. The crucial thing is that yοu have a set οf values tο plοt οn a graph.

Enter yοur x and y values intο the plοt. The exact prοcedure depends οn the graphing prοgrammed yοu're using, but yοu shοuld be able tο enter yοur values intο a data table οr spreadsheet.

Make any changes yοu want tο yοur plοt. Adding labels tο the x and y axes, tweaking the plοt's scale, changing the line cοlοur οr thickness, οr adding a title are all pοssibilities.

If yοu're satisfied with yοur line plοt, save it and distribute it as needed.

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Complete question:

The equation of circle is x²+y²=9.

To obtain the equation of the circle centered at the origin and passing through the point (0,−3), we use the general equation of a circle that is (x-a)² + (y-b)² = r².
Here, a and b represent the x and y coordinates of the center of the circle.
We are given that the center of the circle is the origin (0,0).
Hence, a = 0 and b = 0.To find the value of r, we need to find the distance between the center of the circle (0,0) and the point on the circle (0,-3).
Using the distance formula, we have:r = √(0-0)² + (-3-0)²r = √9r = 3
The center of the circle is the origin (0,0). Hence, a = 0 and b = 0. The value of r is 3.

Therefore the equation of circle is x²+y²=9.

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The probability of rolling a one on the first die and a four on the second die is 1/36.

This is because there are six possible outcomes for each die (1, 2, 3, 4, 5, and 6) and the probability of rolling a specific number on one die is 1/6. To find the probability of rolling a specific number on two dice, you would multiply the individual probabilities of each die (1/6 x 1/6 = 1/36). Since there is only one combination of rolling a one on the first die and a four on the second die, the probability is 1/36.

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Answer:

a. 45° and 135

The non-horizontal rays of ∠ and ∠ will not intersect to form a triangle; the rays will be parallel to each  other.

b. 45° and 45°

The non-horizontal rays of ∠ and ∠ will intersect to form a triangle

c. 45° and 145°

The non-horizontal rays of ∠ and ∠ will not intersect to form a triangle.

Step-by-step explanation:

Hope this helps

Answer:

3/4

Step-by-step explanation:

multiply each fraction by 100 or you could find the LCM

Answer:

There are 13 blue pens in a package.

Explanation:

total blue pens: 45 - 6 = 39 blue pens in 3 packages

3 package → 39 blue pens

1 package → (39/3) blue pens

1 package → 13 blue pens

Answer:

13 blue pens

Step-by-step explanation:

6 red pens + 3 packages of blue pens = 45

3 packages of blue pens = 39

\(\hookrightarrow\) Divide by 3

1 package of blue pens = 13

-Chetan K

Answer:

A= 10

Step-by-step explanation:

[10 + 2/360˚(10)]

The general solution to the given equation would be of the form:y(x) = c₁ Jₙ(x) + c₂ Yₙ(x)  where c₁ and c₂ are arbitrary constants, and Jₙ(x) and Yₙ(x) are Bessel functions of the first and second kind, respectively.

To express a general solution to the given equation using Bessel functions, we need to rewrite the equation in a standard form that can be solved using Bessel functions. The equation you provided is incomplete, as there is a missing term after the equal sign. However, I can provide you with the general procedure to solve such equations using Bessel functions.

The general form of a differential equation that can be solved using Bessel functions is:

x²y'' + xy' + (x² - n²) y = 0

To solve this equation, we make a substitution x = z^α, where α is a constant to be determined. Substituting this into the equation, we get:

z²α²y'' + αzy' + (z²α² - n²) y = 0

Now, we choose α such that the coefficient of y'' becomes 1. In this case, α = 1/2. Substituting α = 1/2 into the equation, we have:

z²(1/4)y'' + (1/2)zy' + (z²/4 - n²) y = 0

Next, we make another substitution y(z) = v(z)/z^(1/2), which simplifies the equation to:

z²v'' + (z² - 4n²) v = 0

This is now in the standard form for Bessel's equation, which has solutions in terms of Bessel functions.

The general solution to the equation can be expressed as a linear combination of Bessel functions of the first kind (J) and Bessel functions of the second kind (Y), denoted as Jₙ(z) and Yₙ(z), respectively.

Therefore, the general solution to the given equation would be of the form:

y(x) = c₁ Jₙ(x) + c₂ Yₙ(x)

where c₁ and c₂ are arbitrary constants, and Jₙ(x) and Yₙ(x) are Bessel functions of the first and second kind, respectively.

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The general solution to the given equation would be of the form:y(x) = c₁ Jₙ(x) + c₂ Yₙ(x)  where c₁ and c₂ are arbitrary constants, and Jₙ(x) and Yₙ(x) are Bessel functions of the first and second kind, respectively.

To express a general solution to the given equation using Bessel functions, we need to rewrite the equation in a standard form that can be solved using Bessel functions. The equation you provided is incomplete, as there is a missing term after the equal sign. However, I can provide you with the general procedure to solve such equations using Bessel functions.

The general form of a differential equation that can be solved using Bessel functions is:

x²y'' + xy' + (x² - n²) y = 0

To solve this equation, we make a substitution x = z^α, where α is a constant to be determined. Substituting this into the equation, we get:

z²α²y'' + αzy' + (z²α² - n²) y = 0

Now, we choose α such that the coefficient of y'' becomes 1. In this case, α = 1/2. Substituting α = 1/2 into the equation, we have:

z²(1/4)y'' + (1/2)zy' + (z²/4 - n²) y = 0

Next, we make another substitution y(z) = v(z)/z^(1/2), which simplifies the equation to:

z²v'' + (z² - 4n²) v = 0

This is now in the standard form for Bessel's equation, which has solutions in terms of Bessel functions.

The general solution to the equation can be expressed as a linear combination of Bessel functions of the first kind (J) and Bessel functions of the second kind (Y), denoted as Jₙ(z) and Yₙ(z), respectively.

Therefore, the general solution to the given equation would be of the form:

y(x) = c₁ Jₙ(x) + c₂ Yₙ(x)

where c₁ and c₂ are arbitrary constants, and Jₙ(x) and Yₙ(x) are Bessel functions of the first and second kind, respectively.

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Answer:

Prime factorization: 797 is prime. The exponent of prime number 797 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 797 has exactly 2 factors