Prove the following?

Answer:

Step-by-step explanation:

12/70 is the probability of getting a point in the triangle.

From the dimension given in the figure,

height of the triangle  = 6 cm

base of the triangle  = 4 cm

width of the rectangle = 7 cm

length of  the rectangle = 10 cm

From the general formula of the area of a triangle and a rectangle,

The area of the triangle = 1/2*base*height

in a given case,

Area of triangle = 1/2*4*6=12 cm²

The area of the rectangle = length * width

in the given case,

Area of the rectangle = 7*10=70 cm²

So the probability of randomly choosing a point in the triangle:

Probability =Area of triangle/area of the rectangle

probability = 12/70

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Answer:

16x^(7/2)

Step-by-step explanation:

When rewriting radicals as fractions, the numerator is the power the term is to and the denominator is how many times the term is “rooted”:

2^4 sqrt(x^7) —> 16x^(7/2)

Answer:

Area of circle = pi×r²

Where, pi =22/7 or 3.142

r = 8cm

Area =22/7 × 8²

=201.142

Approximately 201 to the nearest whole number

You're welcome

The area of the given kite is,

⇒ A = 26 units²

Now, In this case we have that the area of the kite is given by the area of two triangles,

And, the triangles share the same base with length,

2 + 2 = 4.

And, One of the triangles has height of 6 and the other has height of 7.

So, the total area of kite is,

A = 1/2 × 4 × 6 + 1/2 × 4 × 7

A = 12 + 14

A = 26 units²

Therefore, The area of the given kite is,

⇒ A = 26 units²

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The graph of the functions f(x) and g(x) is given below.

Given that:

Function, f(x) = x³

Translated function, g(x) = (x + 6)³

If the function is translated by 'h' units horizontally and 'k' units vertically, then x and y are replaced with (x - h) and (y - k), respectively.

The curve of the function g(x) is translated left side by 6 units.

The graph of the functions is given below.

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Note that in  Circle Q, m∠1  = 66° (Option A)

Note that inthe circle above, the angle which creates the arc 114° lies ont he same line with ∠1. Since sum of angles on a Straight line sum up to 180°.

∠1 = 180 -114 = 66°

A circle is defined as a form made up of points in a two-dimensional plane that are equidistant from a particular location. A circle is defined as a closed curve with no corners or vertices. Circles define several circular forms in our everyday lives.

Circular shapes include:

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Answer:  [tex]g^2-9g+14[/tex]

Step-by-step explanation:

(g-7)(g-2)

[tex]g^2 - 2g-7g+14[/tex]

[tex]g^2-9g+14[/tex]

Use FOIL method.

Answer: The last one is the right one

Step-by-step explanation:

So first solve for n

1/2n+3<5

1/2n<2, multiple by 2 on both sides to remove fraction

n<4

the circle will be at 4, and since n<4, n is less than 4, so your line must also be less that 4.

Answer: A h = - 2

Step-by-step explanation:

Substitute -2 for h

4(-2) + 3 < 10

-8 + 3 < 10

-5 < 10 true

The end behavior of [tex]g(x) = -3e^x[/tex] is As x approaches positive infinity, g(x) approaches negative infinity, As x approaches negative infinity, g(x) approaches 0.

To determine the end behavior of the function g(x) = -3e^x, we need to consider what happens to the output of the function as x gets very large (approaches positive infinity) or very small (approaches negative infinity).

As x approaches positive infinity, e^x also approaches positive infinity, since e is a positive number greater than 1. Therefore, -3e^x approaches negative infinity as x approaches positive infinity. We can write this as:

lim x → ∞ (-3[tex]e^x[/tex]) = -∞

This means that the function g(x) approaches negative infinity as x approaches positive infinity.

Similarly, as x approaches negative infinity, e^x approaches 0, since e to a negative power is equal to 1 divided by e raised to the absolute value of that power. Therefore, -3e^x approaches 0 as x approaches negative infinity. We can write this as:

lim x → -∞ (-3[tex]e^x[/tex]) = 0

This means that the function g(x) approaches 0 as x approaches negative infinity.

So, in summary, the end behavior of g(x) = -3[tex]e^x[/tex] is:

As x approaches positive infinity, g(x) approaches negative infinity.

As x approaches negative infinity, g(x) approaches 0.

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Answer:

  (c)  B'(3, -2); C'(7, 8); D'(-5, -1)

Step-by-step explanation:

Apparently, you want to know the coordinates of B', C', and D' after reflection of B(-2, 3), C(8, 7), and D(-1,-5) in the line y = x.

The reflection in the line y = x has the effect of swapping the x- and y-coordinates:

  (x, y) ⇒  (y, x)

No sign changes are involved.

The reflected coordinates are ...

  B'(3, -2); C'(7, 8); D'(-5, -1)

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The setting of a novel is important because it provides the reader with context on the time, place, and environment that the story takes place in.

It aids in setting the tone, showcasing personalities and tensions, and offering hints about the story's message.

One can establish an ambiance or emotional tone in a novel by means of its setting. One illustration can be seen in the book "The Great Gatsby" authored by F. Scott Fitzgerald uses the backdrop of the Jazz Age to generate a feeling of splendor and exhilaration.

The rapid tempo of the book mirrors the busy lives led by the characters, while the opulent festivities and luxurious habits of the affluent are employed to cultivate an air of indulgence and debauchery.

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The full question is:

On the importance of setting in the novel, comment on how it can be used to create a sense of realism, atmosphere, and meaning?

The measure of angle QRS in triangle QRS is 56.8 degrees.

To find the measure of angle QRS in triangle QRS, we can use the fact that the sum of the measures of the angles in a triangle is always 180 degrees.

We know that:

- The measure of angle RSQ is 48.2 degrees

- The measure of angle SQR is 75 degrees

Let x be the measure of angle QRS. Then, we can write:

RSQ + SQR + QRS = 180

Substituting the known values, we get:

48.2 + 75 + x = 180

Simplifying and solving for x, we get:

x = 180 - 48.2 - 75x = 56.8

Therefore, the measure of angle QRS in triangle QRS is 56.8 degrees.

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Answer:

In mathematics, a function is a rule that assigns one unique output value for each input value. A linear function is a function that has a constant rate of change between its input and output values. This means that if we plot the function on a graph, it will form a straight line.

For example, the function f(x) = 2x + 1 is a linear function because its graph is a straight line. As x increases by 1, the output of the function increases by 2.

On the other hand, a nonlinear function is a function that does not have a constant rate of change between its input and output values. This means that if we plot the function on a graph, it will not form a straight line.

For example, the function f(x) = x^2 is a nonlinear function because its graph is a curve. As x increases, the output of the function increases at an increasing rate.

In general, nonlinear functions can take many different forms and can have complex behaviors, whereas linear functions have a simple, predictable behavior.

Answer: The value of X is 12.

Step-by-step explanation:

K and M are parallel lines so,

6x-13 = 4x+11

Subtract 4x from both sides,

2x-13 = 11

Add the 13 to both sides,

2x = 24

Divide by 2,

x = 12

:).

Answer:

Step-by-step explanation:

6x - 13 = 4x + 11

2x = 11 + 13

2x = 24

x = 24 : 2

x = 12

The length of BC is determined as  6√31  by applying trigonometry ratio.

The length of BC is calculated by applying the following formulas for trig ratios.

The trig ratio is simplified as;

SOH CAH TOA;

SOH ----> sin θ = opposite side / hypothenuse side

CAH -----> cos θ = adjacent side / hypothenuse side

TOA ------> tan θ = opposite side / adjacent side

The hypothenuse side of the right triangle is given as 12√31 and the opposite side is length BC.

The length of BC is calculated as follows;

sin 30 = BC / 12√31

BC = 12√31 x sin (30)

BC = 12√31 x ¹/₂

BC = 6√31

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Step-by-step explanation:

First, let's find the square root of 30.6:

√30.6 ≈ 5.53 (rounded to two decimal places)

Now, let's multiply the square root by 2:

5.53 × 2 = 11.06

so first I would move -6x to the other side and -2 at the same time it would look like this

24+2=6x+7x

and simplify

26= 13x

divide both sides by 13 to find x

2= x

Answer:

-2x^2 - 2x + 5

Step-by-step explanation:

Combine like terms (same variable and degree) to simplify

3x^2-5x^2+5x-7x+3+2

-2x^2-2x+5

Answer:

Combining like terms, we get:

-2x² - 2x + 6

Answer: yes

Step-by-step explanation:

There is a 48% chance of selecting a club or a face card from a standard 52-card deck.

To find the probability of picking a club or a face card from a standard 52-card deck, we need to determine the number of favorable outcomes (cards that are either clubs or face cards) and divide it by the total number of possible outcomes (all the cards in the deck).

There are 13 clubs in a deck, as there is one club for each rank (Ace, 2, 3, ..., 10, Jack, Queen, King). Additionally, there are 12 face cards (Jack, Queen, and King) in each suit, including clubs. So, the number of favorable outcomes is 13 (clubs) + 12 (face cards in clubs) = 25.

The total number of cards in a deck is 52.

Therefore, the probability of picking a club or a face card is 25/52 ≈ 0.48 (rounded to two decimal places).

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The total area Cydney painted on the display stand is 416 square inches, excluding the bottom of the larger cube.

5. To solve the problem, we need to find the total area that Cydney painted on the display stand.

Plan for solving the problem:

6. Solving the problem:

The surface area of a cube is given by the formula: [tex]6 * (side length)^2[/tex].

For the larger cube:

Surface area of the larger cube =[tex]6 * (8 inches)^2[/tex] = 6 * 64 square inches = 384 square inches.

For the smaller cube:

Surface area of the smaller cube = [tex]6 * (4 inches)^2[/tex]= 6 * 16 square inches = 96 square inches.

Since the bottom of the display stand was not painted, we need to subtract the area of the bottom face of the larger cube:

Area of the bottom face of the larger cube = [tex](side length)^2[/tex] =[tex](8 inches)^2[/tex] = 64 square inches.

Finally, we can calculate the total area Cydney painted by adding the surface area of both cubes and subtracting the area of the bottom face of the larger cube:

Total area painted = (Surface area of the larger cube + Surface area of the smaller cube) - Area of the bottom face of the larger cube

= (384 square inches + 96 square inches) - 64 square inches

= 480 square inches - 64 square inches

= 416 square inches

Therefore, Cydney painted a total area of 416 square inches on the display stand.

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The graph of g(x) will have the same shape as f(x), but every y-coordinate will be increased by 4 units,The graph of h(x) will have the same shape as f(x), but every x-coordinate will be decreased by 1 unit,The graph of k(x) is 20 and every y-coordinate is increased by 10 units and the graph of m(x) is horizontally squeezed.

To describe the graphs of the given functions, let's first analyze the effects of the transformations applied to the original function f(x) = 5 sin(x).

1. g(x) = 5 sin(x) + 4:

The function g(x) is obtained by vertically shifting the graph of f(x) by 4 units upward. This means that the graph of g(x) will have the same shape as f(x), but every y-coordinate will be increased by 4 units.

2. h(x) = 5 sin(x + 1):

The function h(x) is obtained by horizontally shifting the graph of f(x) to the left by 1 unit. This means that the graph of h(x) will have the same shape as f(x), but every x-coordinate will be decreased by 1 unit. The period of the function remains the same.

3. k(x) = 20 sin(x) + 10:

The function k(x) is obtained by vertically stretching the graph of f(x) by a factor of 20 and then shifting it 10 units upward. This means that the amplitude of the graph of k(x) is 20 (compared to the amplitude of 5 in f(x)), and every y-coordinate is increased by 10 units.

4. m(x) = 5 sin(4x - 1):

The function m(x) is obtained by compressing the graph of f(x) horizontally by a factor of 4, reflecting it across the y-axis, and shifting it 1 unit to the right. This means that the period of m(x) is 1/4 of the period of f(x), and the graph is horizontally squeezed. The reflection across the y-axis means that the graph of m(x) will be inverted compared to f(x). The amplitude remains the same.

Remember that the graph of the original function f(x) = 5 sin(x) represents a sine wave with an amplitude of 5 and a period of 2π. Applying the transformations described above will modify the position, scale, and shape of the graph, resulting in the respective graphs for each function g(x), h(x), k(x), and m(x).

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The surface area of the cylinder is 948m²

The area occupied by a three-dimensional object by its outer surface is called the surface area. The surface of a cylinder is expressed as ;

SA = 2πr(r+h)

Where r is the radius of the base and h is the height of the cylinder.

r =8m

h = 4m

SA = 2 × 3.14 × 8 (8+4)

SA = 78.96 × 12

SA = 947.52 m²

to the nearest whole number

SA = 948 m²

therefore the surface area of the cylinder is 948 m²

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The minimum number of tickets the agent must sell to have a 95% chance of selling at least one prize-winning ticket is 368 tickets

To unravel this issue, we are able to utilize the concept of likelihood. Let's begin with discovering the likelihood of not offering any prize-winning tickets with one ticket:

- The likelihood of not winning with one ticket is 499/500 (since there's as it were one winning ticket out of 500).

- The likelihood of not winning with n tickets is (499/500)[tex]^n[/tex](since the probabilities are autonomous and we duplicate them together).

Presently, we need to discover the least number of tickets the specialist must offer to have a 95% chance of offering at the slightest one prize-winning ticket. In other words, we need to discover the least esteem of n such that:

- The likelihood of not winning with n tickets is less than or rises to 5% (or 0.05).

- This can be identical to (499/500)[tex]^n[/tex]≤ 0.05.

We will illuminate for n utilizing logarithms:

- Take the normal logarithm of both sides:

ln[(499/500)[tex]^n[/tex]] ≤ ln(0.05).

- Utilize the logarithmic property of types to bring down the example:

n ln(499/500) ≤ ln(0.05).

- Fathom for n by partitioning both sides by ln(499/500) and taking the ceiling work (since n must be an entire number):

n = ceil[tex][ln(0.05) / ln(499/500)].[/tex]

Employing a calculator, we get 

n = ceil[tex][ln(0.05) / ln(499/500)][/tex]≈ 368

In this manner, the specialist must offer at the slightest 368 tickets to have a 95% chance of offering at the slightest one prize-winning ticket. 

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For the additive opposites x+4y=28 and -x+y=12, yes, y is equal to 8.

In order to solve the given system of equations, we would apply the substitution method. Based on the information provided above, we have the following system of equations:

x + 4y = 28      .......equation 1.

-x + y = 12         .......equation 2.

By making x the subject of formula in equation 2, we have the following:

x = y - 12           .......equation 3.

By using the substitution method to substitute equation 3 into equation 1, we have the following:

y - 12 + 4y = 28

5y = 28 + 12

5y = 40

y = 40/5

y = 8

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Answer: 3 1/3

Step-by-step explanation:

if the width of the rectangle is equal to “x” then the length is equal to 3x+2

The area is 40ft^2

so: 40=(3x+2)(x)

Then we simplify and subtract 40 in both sides:

0=3x^2+2x-40

Then we will use the quadratic formula to solve for x

X=(-2-sqr(2^2-4(3)(-40)))/2*3

And

X=(-2+sqr(2^2-4(3)(-40)))/2*3

then x is either equal to 3 1/3 or -4, since the answer cannot be negative, the answer is 3 1/3