10. Kyle has a container in a shape of a cone. The container has a radius of 5 inches and a height
of 8 inches.
a) What is the volume of the container? (Leave in terms of pi.)

Thus, the expression [1 - 4sin²a] written in the product of its values is:

(1 + 2sina)(1 - 2sina).

We can solve mathematical equations thanks to algebra's inherent characteristics. Take note that both addition and multiplication adhere to these characteristics.

This Order of Operations is a set of rules that enables mathematicians to solve issues uniformly. In this order:

using the algebraic formula:

(a² - b²) = (a + b)(a - b)

Given expression:

= 1 - 4sin²a

This can be written as:

= 1² - (2sina)²

Now, using identity:

= (1 + 2sina)(1 - 2sina)

Thus, the expression [1 - 4sin²a] written in the product of its values is:

(1 + 2sina)(1 - 2sina).

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Complete question-

Express the given as the product of both values.

1 - 4sin²a

A system of linear equations with more equations than unknowns is called overdetermined system. This system always be consistent. Because it may result in contradictions or inconsistencies.

An overdetermined system of linear equations cannot always be consistent, due to contradictions or inconsistencies. Since there are more equations than unknowns, there are likely to be restrictions and dependencies among the equations, and not all of them may be satisfied simultaneously.

However, in certain cases, an overdetermined system can still be consistent if the equations are compatible and do not contradict each other. In such cases, the system may have a unique solution or a set of solutions that satisfy all of the equations.

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Thus, the theoretical probability that Kelvin will select a red marble is 5/12.

Probability that is established using logic is known as theoretical probability.

Experimental probability is calculated based on the outcomes of numerous iterations of an experiment.

A probability is a number that falls between (and includes) 0 and 1.

If the likelihood of a situation E is represented by P(E), then:

Given:

Total marbles in  bag = 12

theoretical probability P(E) = favourable outcome / total outcome

P(red marble) = 5/12

Thus, the theoretical probability that Kelvin will select a red marble is 5/12.

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Answer:

A

Step-by-step explanation:

Given:

r (radius) = 2 in

h (height) = 8 in

Find:

A (surface area) - ?

.

First, we have to find the lateral area of the cylinder:

[tex]a(lateral) = 2\pi \times r \times h = 2 \times π\times 2 \times 8 = 32\pi \: {in}^{2} [/tex]

Now, let's find the area of both bases (since a cylinder has 2 identical bases, we have to multiply the area of one base by 2):

[tex]a(2 \: bases) = 2 \times \pi {r}^{2} = 2 \times π\times {2}^{2} = 8\pi \: {in}^{2} [/tex]

In order to find the surface area, we have to add both lateral and bases' areas together:

[tex]a(surface) =32\pi + 8\pi = 40\pi \: {in}^{2} [/tex]

The equation of the line parallel to the line shown in the graph passing through the point (-2, 3) is y = (2/3)x + (13/3) and the equation of the line perpendicular to the line shown in the graph passing through the point (-2, 3) is y = (-3/2)x.

What is slope?

The slope of a line passing through two points [tex](x_1, y_1) \: and \: (x_2, y_2)[/tex] is given by slope = [tex]\frac{(y_2 - y_1)}{(x_2 - x_1)}[/tex]

Given line passes through (0,-6) and (9,0)

To find the equation of a line parallel to a given line, we need to use the fact that parallel lines have the same slope.

The slope of the line passing through (0,-6) and (9,0) can be found using the slope formula

slope = (change in y) / (change in x)

= (0 - (-6)) / (9 - 0)

= 6 / 9

= 2/3

Therefore, any line parallel to this line will also have a slope of 2/3.

We can now use the point-slope form of a line to find the equation of the line passing through (-2,3) with a slope of 2/3:

y - y1 = m(x - x1) (point-slope form)

where m is the slope, and (x1,y1) is a point on the line.

Substituting the values, we get:

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

y - 3 = (2/3)(x + 2)

y - 3 = (2/3)x + (4/3)

y = (2/3)x + (4/3) + 3

y = (2/3)x + (13/3)

Therefore, the equation of the line parallel to the line passing through (0,-6) and (9,0) shown in the graph passing through the point (-2, 3) is y = (2/3)x + (13/3).

Using the points (0,-6) and (9,0), we can find the slope of the original line:

slope = (0 - (-6)) / (9 - 0) = 6/9 = 2/3

The slope of any line perpendicular to this line will be the negative reciprocal of this slope. So, the slope of the perpendicular line will be:

perpendicular slope = -1 / (2/3) = -3/2

Now we have the slope of the perpendicular line, and we also have a point it passes through: (-2, 3). We can use the point-slope form of a line to write the equation of the perpendicular line: y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is the point it passes through. Plugging in the values we have, we get:

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

Simplifying:

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

y = (-3/2)x + 0

So the equation of the line perpendicular to the line passing through (0,-6) and (9,0), and passing through (-2, 3), is y = (-3/2)x.

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Vertical angles are a pair of opposite angles formed by two intersecting lines. Vertical angles are congruent, meaning they have the same measure.

For example, if two lines intersect and form four angles, the two angles that are opposite each other  are vertical angles.

Adjacent angles are two angles that have a common vertex and a common side but do not overlap.

In other words, they share a ray or line segment, but they don't share any interior points.

Adjacent angles may or may not be congruent, depending on their measurement.

For example, if two angles are next to each other and share a vertex and a side, they are adjacent angles.

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The general solution of the given higher-order differential equation is y(x) = A * e^(-x/2) * cos((x/√2)) + B * e^(-x/2) * sin((x/√2)).

To find the general solution of the given higher-order differential equation, first, let's rewrite the equation in a more standard form:
16y'''' + 16y'' + 4y = 0
Now, we'll solve this fourth-order linear homogeneous differential equation using the characteristic equation method.
1. Write the characteristic equation:
16r^4 + 16r^2 + 4 = 0
2. Divide the equation by 4 to simplify:
4r^4 + 4r^2 + 1 = 0
3. Apply a substitution: let t = r^2, then the equation becomes:
4t^2 + 4t + 1 = 0
4. Solve the quadratic equation for t using the quadratic formula:
t = (-B ± √(B^2 - 4AC)) / 2A
t = (-4 ± √(4^2 - 4(4)(1))) / (2 * 4)
t = (-4 ± √(16 - 16)) / 8
t = -4/8 = -1/2
5. Substitute back r^2 for t:
r^2 = -1/2
6. Solve for r:
r = ±√(-1/2)
r = ±(1/√2)i
7. Since the roots are complex conjugates, the general solution can be written as:
y(x) = A * e^(-x/2) * cos((x/√2)) + B * e^(-x/2) * sin((x/√2))
where A and B are arbitrary constants determined by the initial conditions of the problem.

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Answer:

Step-by-step explanation:

3 divided by 3/4 can be changes to multiplication

We can solve the equation like 3*4/3

3 divided by 3/4 is 4

As per the number of gym machines, the type of data is b. quantitative discrete data.

A discrete quantitative variable has a distinct quantitative meaning but can only take particular integer values rather than any value within a period. The number of needle sticks, the number of births, and the number of hospitalisations are a few examples of discrete numeric factors.

Similarly to that, the information given in the question refers to the quantity of gym equipment, which qualifies as quantitative data because it is a numerical assessment. Furthermore, rather than representing a continuous range of values, the data is discrete, which means that it reflects a limited collection of whole integers such as 10, 12, 15, 20, and 22. These numbers are the total number of gym machines that are available.

Complete Question:

the data are the number of machines in a gym. you sample five gyms. one gym has 12 machines, one gym has 15 machines, one gym has ten machines, one gym has 22 machines, and the other gym has 20 machines. what type of data is this?

a. Qualitative data

b. Quantitative discrete data

c. Discreet data

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The area of the triangles are:

Triangle 1: 144√3 unit²

Triangle 2: 64√3 unit²

The area of a triangle is given by the formula:

A = 1/2 * b * h

where b is the base and h is height of the triangle

1st triangle:

The vertical line divides the base into two right triangles.

Considering the right triangle to the right. Let L represent the length of the base. Thus, we can say:

tan 60° = (12√3)/L

√3 = (12√3)/L

(√3)L = 12√3

L = 12

Since b = 2* L

b = 24 units

A = 1/2 * 24 * 12√3

A = 144√3 unit²

2nd triangle:

cos 60° = L/16

0.5 = L/16

L = 0.5 * 16

L = 8 units

b = 2 * 8 = 16 units

h = √(16² - 8²)    (Pythagoras)

h = 8√3 units

A = 1/2 * 16 * 8√3

A = 64√3 unit²

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Answer:

The answer to your problem is, 4.51 or in option terms A. 4

Step-by-step explanation:

A=π [tex]R^{2}[/tex]

d = 2 r

We would need to solve for D

d = 2 [tex]\sqrt{\frac{A}{tt} } = 2 x \sqrt{\frac{16}{tt} }-around- 4.51352-or-4.51[/tex]

Thus the answer to your problem is, 4.51 or A. 4

Answer:

44

Step-by-step explanation:

come on now.

the perimeter is

2×length + 2×width = 110

width = 4×length

so, we use the second equation in the first :

2×length + 2×(4×length) = 110

2×length + 8×length = 110

10×length = 110

length = 110/10 = 11

width = 4×length = 4×11 = 44

Answer:

20

Step-by-step explanation:

7 computers every 5 printers

7/5 = 28/x

Cross multiply

7x = 5*28

7x = 140

x = 20

Or in words,

7 times 4 is 28

5 times 4 is 20, which is your answer

Answer:

x=2

Step-by-step explanation:

Answer: 6x-12= -72

Step-by-step explanation: 12 is a bigger number than 6 and a negative times a positive is always a negative. 6x12 is already 72 but we have to keep the negative so it becomes -72.

Or if its another equation involving x then it's going to be 2. ;)

We know that the sum of the angles of a triangle is 180 degrees. So, we can find the value of angle LNM as follows:

m/L + m/M + m/N = 180 degrees

Substituting the given values, we get:

40 + 41 + m/N = 180

m/N = 99

Now, we can see that angle LNM is greater than both angles L and M. So, we can conclude that:

OMN > NL > LM

Then answer and explanation is in the doc below.

option (c) -No, 20 is NOT a reasonable solution because at x=-20,

an equation in which highest power of variable is always 1.

by solving the equation -6+2log(-5x)=-2 :

-6 + 2log(-5x) = -2

2log(-5x) = 4

log(-5x) = 2

-5x = 10^2

-5x = 100

x = -20

So, we found that x = -20 satisfies the equation. However, we need to check whether it is a reasonable solution or not.

Option C is correct: -20 is NOT a reasonable solution because at x = -20, the logarithm is not defined. The logarithm function is defined only for positive real numbers.

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Regenerate response

The particular solution to the differential equation dy/da = (a+1)(y+1) with the initial condition y(4) = 3 is:

[tex]y = 4e^{\frac{1}{2}a^2 + a + 10} - 1[/tex]

What is differential equation?

Differential equations are used to model a wide range of phenomena in science, engineering, and mathematics, including physics, chemistry, biology, economics, and engineering.

Integration is a mathematical concept and technique used to find the integral of a function. The integral of a function is a measure of the area under the curve of the function, between two specified points on the x-axis.

To find the particular solution to the differential equation

[tex]\frac{dy}{da} = (a+1)(y+1)[/tex]

with the initial condition y(4) = 3, we can use separation of variables:

[tex]\frac{dy}{y+1} = (a+1) da[/tex]

Integrating both sides:

[tex]\int \frac{dy}{y+1} = \int (a+1) da\ln |y+1| = \frac{1}{2}a^2 + a + C_1, \text{ where } C_1 \text{ is an arbitrary constant of integration}[/tex]

Solving for y, we get:

[tex]y+1 = Ce^{\frac{1}{2}a^2 + a}[/tex]

where C is another arbitrary constant of integration. We can solve for C using the initial condition y(4) = 3:

[tex]3+1 = Ce^{\frac{1}{2}(4^2) + 4}C = 4e^{10}[/tex]

Substituting back, we get:

[tex]y+1 = 4e^{\frac{1}{2}a^2 + a + 10}y = 4e^{\frac{1}{2}a^2 + a + 10} - 1[/tex]

Therefore, the particular solution to the differential equation dy/da = (a+1)(y+1) with the initial condition y(4) = 3 is:

[tex]y = 4e^{\frac{1}{2}a^2 + a + 10} - 1[/tex]

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Answer:

D. 20 in by 30 in by 10 in

Step-by-step explanation:

The rest of them would equal 600 in³ but answer choice D when multiplied together equaled 6,000 in³.

Answer:

(n - 3) (n + 7)

Step-by-step explanation:

n² + 4n - 21

Consider the form x² + bx + c. Find a pair of integers whose product is

c and whose sum is b. In this case, whose product is −21 and whose sum is 4.

-3, 7

Write the factored form using these integers.

(n - 3) (n + 7)

So, the answer is (n - 3) (n + 7)

Answer:

15.625 inches^3

Step-by-step explanation:

The volume of a cube is a simple calculation:

V=a^3

"a" is any edge of the cube.

Therefore, it would be (2.5^3), which would be 15.625 inches^3

Answer:

3 one

Step-by-step explanation:

Answer:

x ≈ 8.0

Step-by-step explanation:

Using the tangent of the angle is equal to the opposite over the adjacent

tan(37º) = 6/x

x = 6/tan(37º)

x=7.96226892972

Step-by-step explanation:

6.3    goes to  2.52

6.3 : 2.52   = 2.5 :1  = 5 : 2

110,664,000 possible selections for Head Girl, Deputy Head Girl, Head Boy, and Deputy Head Boy from a group of 101 girls and 105 boys.

How to calculate different possible selections could be made?​

To find the number of possible selections that can be made, we need to multiply the number of choices available for each position.

For the Head Girl position, there are 101 girls to choose from. After one girl is selected for Head Girl, there are 100 girls remaining to choose from for the Deputy Head Girl position. So there are a total of 101 x 100 = 10,100 possible combinations of girls that can be chosen for these two positions.

Similarly, there are 105 boys to choose from for Head Boy, and 104 boys remaining to choose from for Deputy Head Boy. So there are a total of 105 x 104 = 10,920 possible combinations of boys that can be chosen for these two positions.

To find the total number of possible selections, we multiply the number of combinations for the girls by the number of combinations for the boys:

10,100 x 10,920 = 110,664,000

Therefore, there are 110,664,000 different possible selections that could be made.

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The experimental probability of choosing the name Maya is [tex]23/118[/tex].

and theoretical probability is of choosing name maya is [tex]1/5[/tex]

Probability is a measure of how likely an event is to occur. Many events are impossible to forecast with absolute accuracy. We can only anticipate the possibility of an event occurring, i.e. how probable they are to occur, using it. Probability can range from 0 to 1, with 0 indicating an impossible event and 1 indicating a certain event. The probability of all events in a sample space equals one.

According to the given information:

The experimental probability = [tex]\frac{Number of times an event occur}{ Total number of trials}[/tex]

Here total trials = 118,

The number of times the name maya has been chosen =23 times.

Therefore, experimental probability = [tex]\frac{23}{118}[/tex].

Theoretical probability = [tex]\frac{Number of favourable outcome}{Number of possible otucome}[/tex]

favourable outcome = 1 (Maya)

Possibleble outcome = 5 (Total no of Names in a hat)

And the theoretical possibility of the name maya has been chosen is [tex]1/5[/tex]

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No , because 7 t shirts will cost 56 $ in linear equation.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

You have $50 to buy T-shirts.

You can buy 3 T-shirts for $24.

                 You can buy 1 T-shirts for = 24/3 = 8

then 3 + 3 = 6 = 24 + 24 = 48 + 8 =  $56

so, you don't buy 7 t - shirts because you have only $56 .

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Answer: 216

Step-by-step explanation:

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