sin²A+sin²A.tan²A=tan²A​

The expected payback for a person who buys 1 ticket is 1.23. Yes, the game is fair.

Given that, A raffle offers a first prize of $500 and 3 second prizes of $80 each. One ticket costs $2, and 600 tickets are sold.

The probability formula defines the likelihood of the happening of an event. It is the ratio of favourable outcomes to the total favourable outcomes. The probability formula can be expressed as, P(E)=Number of favourable outcomes/Total number of outcomes.

Now,

Expected value = sum of ( amount won ) × probability of winning

= expected value of 1st place + expected value of 2nd place + expected value of losing  

= (1/600) (500) + (3/600) (80) + (596/600) × 0

= 500/600 + 240/600  

= 740/600

= 740/600

= 1.23

Therefore, the expected payback for a person who buys 1 ticket is 1.23. Yes, the game is fair.

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"Your question is incomplete, probably the complete question/missing part is:"

A raffle offers a first prize of $500 and 3 second prizes of $80 each. One ticket costs $2, and 600 tickets are sold. Find the expected payback for a person who buys 1 ticket. Is this a fair game?

The edge length of the cube is a approximately 8.

According to the statement

We have to find that the edge of the cube.

So, For this purpose, we know that the

The edge of a cube is the line segment joining the two vertices.

From the given information:

The volume of a cube is 500 m^3.

The formula for volume of the cube is a :

volume of a cube formula: V = a^3.

v = a^3

500 = a^3

Take cube root of the volume to find the edge length

a = (500)^1/3

a = 7.93

a = 8 (approx.)

The length of the edge of the cube is a approximately 8.

So, The edge length of the cube is a approximately 8.

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No, the square of a binomial does not include only positive terms.

A mathematical expression with two terms known as a binomial expression cannot be merged unless a variable-eliminating input is provided. Positive integer exponents must be unique for each of the binomial terms. Any exponents must not be negative, zero, or a fraction.

Simplify and combine any "like" terms to add binomials. Different exponents or variables cannot be used in "like" phrases. Add, for instance, the binomials (12x + 3) and (3x - 1).

The square of a binomial may contain negative terms.

For example, (a - b)² = a² + b² - 2ab

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hi

f(x) = x-5,  then  f(5) =  0

g(x)=-4x  .   g(2) = -4*2 = -8

and  

h(x)=2f(x+1)-g(x-2)

then  

h(4) =  2* 0 - (-8)   =  8

Based on the distance that Olivia has to walk to school, the total distance that Ray walks to school in miles is 3 / 8 miles

Olivia walks 1/4 of a mile to school which means that the number of miles she walks to school is:
= 1/4 x 1

= 1/4 miles

= 0.25 miles

This 0.25 miles represents 2/3 of the distance that Ray walks to school. The total distance that Ray walks to school is therefore:

= Number of miles Olivier walks to school / Proportion of distance to Ray

= 0.25 ÷ 2/3

= 0.375

= 3 / 8 miles

In conclusion, Ray walks 3/8 miles to school.

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Answer:

Ray walks to school in miles is 3 / 8 miles.

The measure of angle c is 37 degrees and the measure of angle b is 53 degrees

Angles are formed when two or more lines intersect.

This in other words means that angles is the measure of space between the intersection of rays or lines

The measure of angle c

The given triangles are similar triangles

This means that the corresponding angles of the triangles are congruent

By comparing the corresponding angles of the given triangles, we have the following congruent equation

Angle c = 37

Hence, the measure of angle c is 37 degrees

The measure of angle b

As mentioned in part (a)

This means that the corresponding angles of the triangles are congruent

By comparing the corresponding angles of the three triangles, we have the following congruent equation

Angle b = 53

Hence, the measure of angle b is 53 degrees

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Answer:

15

Step-by-step explanation:

because it's diving the 2nd role number and that equals the numbers on the 3rd role so u do the inverse and u get 15

The intervals that contains the value of 4αβ sinθ° are

(A) (0, √2)

(B) (1, 2)

Given that, PQRS be a  quadrilateral in a plane, where;

QR = 1

∠PQR =∠QRS = 70°

∠PQS = 15°

∠PRS=40°.

Further given that, ∠RPS = θ°, PQ = α and PS = β

Now, In triangle PQR

Using sine law, we have;

PQ/sin R = QR/sin P

α/sin 30 = 1/sin 80

Thus;

α = 1/2sin80

Now, In triangle PRS

Using sine law, we have;

PS/sin R = RS/sin P

∠RPS =  ∠RSQ = 55

QR = RS = 1

β/sin 40 = 1/sinθ

βsinθ = sin40

Now, Consider 4αβ sinθ° = 4 * 1/2 sin 80 * sin 40 = 2 sin 40/(2 sin 40 cos 40)

Since sin 2x = 2 sin x cos x, then;

= 1/cos 40 = sec 40

Now, we know secx is an increasing function.

Thus;

sec 40 ∈ (2/√3, √2)

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In triangle PQR, we have by the law of sines,

[tex]\dfrac{\sin(30^\circ)}\alpha = \dfrac{\sin(80^\circ)}1 \\\\ ~~~~ \implies \alpha = \dfrac{\sin(30^\circ)}{\sin(80^\circ)}[/tex]

and by the law of cosines,

[tex]PR^2 = 1 + \alpha^2 - 2\alpha \cos(70^\circ)[/tex]

In triangle PQS, the law of sines gives

[tex]\dfrac{\sin(15^\circ)}\beta = \dfrac{\sin(85^\circ-\theta)}\alpha \\\\ ~~~~ \implies \beta = \dfrac{\sin(15^\circ)\sin(30^\circ)}{\sin(85^\circ-\theta)\sin(80^\circ)}[/tex]

In triangle PRS, again with the law of sines,

[tex]\dfrac{\sin(40^\circ)}\beta = \dfrac{\sin(140^\circ - \theta)}{\sqrt{1 + \alpha^2 - 2\alpha\cos(70^\circ)}} \\\\ ~~~~ \implies \beta = \sqrt{1+\alpha^2 - 2\alpha\cos(70^\circ)} \dfrac{\sin(40^\circ)}{\sin(140^\circ-\theta)}[/tex]

Together, these give

[tex]\dfrac{\sin(15^\circ) \sin(30^\circ)}{\sin(85^\circ-\theta) \sin(80^\circ)} = \sqrt{1 + \alpha^2 - 2\alpha \cos(70^\circ)} \dfrac{\sin(40^\circ)}{\sin(140^\circ - \theta)}[/tex]

Carefully, we can rearrange terms and invoke identities (half-angle, product-to-sum) to reduce this equation to

[tex]\dfrac{\sin(140^\circ - \theta)}{\sin(85^\circ - \theta)} = \dfrac{\sqrt{2 - 3\sin(10^\circ) - \sin^2(10^\circ) + 2\sin^3(10^\circ)}}{\sin(15^\circ)}[/tex]

On the left, substitute [tex]\phi=85^\circ-\theta[/tex], and on the right, [tex]\sigma=\csc(15^\circ)\sqrt{2-3\sin(10^\circ)-\sin^2(10^\circ)+2\sin^3(10^\circ)}[/tex]. Expand the left side and rearrange terms.

[tex]\dfrac{\sin(55^\circ-\phi)}{\sin(\phi)} = \sigma \\\\ ~~~~ \implies (\sigma + \sin(35^\circ))\sin(\phi) - \cos(35^\circ) \cos(\phi) = 0[/tex]

Condense this using the identity

[tex]R\sin(\phi-\xi) = R\cos(\xi)\sin(\phi) - R\sin(\xi)\cos(\phi)[/tex]

Solve for [tex]R,\xi[/tex].

[tex]\begin{cases}R\cos(\xi) = \sigma+\sin(35^\circ) \\ R\sin(\xi) = \cos(35^\circ)\end{cases} \implies \begin{cases}R^2 = (\sigma+\sin(35^\circ))^2 + \cos^2(35^\circ) \\\\ \tan(\xi) = \dfrac{\cos(35^\circ)}{\sigma+\sin(35^\circ)} \end{cases}[/tex]

So our equation becomes

[tex]\sqrt{(\sigma+\sin(35^\circ))^2 + \cos^2(35^\circ)} \, \sin\left(\phi - \tan^{-1}\left(\dfrac{\cos(35^\circ)}{\sigma+\sin(35^\circ)}\right)\right) = 0[/tex]

Solve for [tex]\phi[/tex], bearing in mind that [tex]40^\circ<\theta<100^\circ[/tex] so [tex]-15^\circ<\phi<45^\circ[/tex], then evaluate the target expression. (Forgive the sudden switch to approximations; I do think there is a nice analytical solution.)

[tex]\phi = \tan^{-1}\left(\dfrac{\cos(35^\circ)}{\sigma+\sin(35^\circ)}\right) \approx 8.88311^\circ \\\\ ~~~~ \implies \theta \approx 76.1169^\circ \\\\ ~~~~ \implies \beta \approx 0.68309 \\\\ ~~~~ \implies 4\alpha\beta\sin(\theta) \approx 0.91334 < 1 < \sqrt2 < 2\sqrt2[/tex]

which makes (A) the correct choice.

The number of significant digits: 2

The correct answer is an option (A)

In this question, we have been given three numbers 4.5160 x 10^−3, 2.09 x 10^7, and 5.8 x 10^3

We need to find the number of significant digits of the product of above numbers.

First we find the product of given numbers.

4.5160 x 10^−3 × 2.09 x 10^7 × 5.8 x 10^3

= (4.5160 × 2.09 ×  5.8) × (10^−3 × 10^7 × 10^3)

= 54.742952 × 10^(-3 + 7 + 3)

= 54.7 × 10^7

= 5.5 × 10^8

Here, the number of significant digits: 2

The correct answer is an option (A)

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Answer:

1/(2 – 4i)

Explanation:

Use geeksforgeeks.org or another website

Answer:

linear equations option a

Answer:

C. no association?

Step-by-step explanation:

Looks like there's no association to me. Association usually are in a linear line or curves. The data points given do not form such shapes. Hope that's right.

Here's some clarification: https://open.lib.umn.edu/macroeconomics/chapter/nonlinear-relationships-and-graphs-without-numbers/

Answer:

4/3 (x) = 28/3

*divide both sides by 4/3

4/3 (x) ÷ 4/3 = 28/3 ÷ 4/3

x = 7

The coordinates of the vertex of the parabola are (-1, -9)

From the question, we are to determine the coordinates of the vertex of the parabola

The vertex of a parabola is the point where the parabola crosses its axis of symmetry.

In the given graph, the axis of symmetry is x = -1

Thus,

The vertex of the parabola in the given graph is the point where x = -1 on the curve

At this point on the parabola, x = -1 and y = -9.

Hence, the coordinates of the vertex of the parabola are (-1, -9)

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The value of 5 divided by 1319 to two places is 3.79 × [tex]10^{-3}[/tex] .

The way of find answer is the divide 5 by 1319

We have to find 5 divided by 1319 and find each quotient to two places

To find answer = 5/1319 = 0.00379075

quotient to two places = 3.79 × [tex]10^{-3}[/tex]

The main answer is 3.79 × [tex]10^{-3}[/tex].

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Answer:

If she plans to jog 4.25 miles each day then 4.25 * 7 would equal 29.75. This is the first answer.

In order to get the second answer, we need to subtract 30.5 (What she needs to jog) over 29.75 (how much she is planned to job over the next 7 days). So 30.5 - 29.75 = 0.75

Here is the math I did to get 0.75:

= 30.5 - 29.75

= 30.5 + -29.75

= 0.75 (Answer)

Hopefully this helped :D

Step-by-step explanation:

The transformations that maps Figure Y onto Figure Z are given by:

A transformation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x).

Examples are shift left, shift right, shift down, shift up, vertical stretching, horizontal stretching, vertical compression, horizontal compression, reflection over the x-axis, reflection over the y-axis, and rotations by a determined amount(in degrees). All these translations have predetermined rules that we apply to the figures.

Another example of a transformation is a dilation, when the coordinates of the function are all multiplied by a constant, called scale factor. Due to the multiplication, after a dilation, the dilated figure is not congruent to the original figure, as they will have different side lengths.

For the dashed figure, we have that the coordinates of Y were all multiplied by 1/3, hence the first transformation is:

Dilation with a scale factor of 1/3.

Then for the dashed figure into Figure Z, the following rule is applied to each vertex:

(x,y) -> (x,-y).

Hence the second transformation is:

Reflection over the x-axis.

Due to the dilation, Figures Y and Z are not congruent.

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Answer:

O commutative property of multiplication

Step-by-step explanation:

Let's solve for x.

26(4xy)=(26)(4)xy

Step 1: Add -104xy to both sides.

104xy+−104xy=104xy+−104xy

0=0

It doesn't matter what order the numbers are multiplied in (commutative property), the result of multiplying 0 by anything (or anything by 0) is 0. No matter the type of number, whether it be an integer, fraction, decimal, or even imaginary, the product of that number and 0 is 0.

Answer:

you could use a calculator but if you don't you can follow these steps

Step 1 : to avoid confusion it is easier to remove the decimal points then multiply them (i.e. 24 × 25)

Step 2: After you've gotten the answer (600), count how many decimal places both numbers are (i.e. 2.4 is one decimal place and 2.5 is also one decimal place.. making it two decimal places)

Step 3: Move your answer to 2 decimal places (i.e 600 → 6.00 or 6)

Answer is 6

Calculations

2.4 × 2.5

= 24 × 25

= 600 to 2 decimal places

= 6

+Hope this helps

Answer:

11,250

Step-by-step explanation:

In order to find the total population just divide 4500 by 40%

[tex] = \sf \: 4500 \div \frac{40}{100} [/tex]

[tex] = \sf \: 4500 \times \frac{100}{40} [/tex]

[tex] = \sf \frac{450000}{40} [/tex]

[tex] = \sf \: 11,250[/tex]

Answer:

x = 4

Step-by-step explanation:

[tex] \sqrt{11x + 5} = 7 [/tex]

Square both sides. This step may introduce extraneous solutions, but we will deal with that after we find the solution.

[tex] (\sqrt{11x + 5})^2 = (7)^2 [/tex]

[tex] 11x + 5 = 49 [/tex]

Subtract 5 from both sides.

[tex] 11x = 44 [/tex]

Divide both sides by 11.

[tex] x = 4 [/tex]

Now we check for extraneous solutions. We substitute the value of the solution into the original equation, and we see if it makes the original equation true.

[tex] x = 4 [/tex]

[tex] \sqrt{11x + 5} = 7 [/tex]

[tex] \sqrt{11(4) + 5} = 7 [/tex]

[tex] \sqrt{44 + 5} = 7 [/tex]

[tex] \sqrt{49} = 7 [/tex]

[tex] 7 = 7 [/tex]

7 = 7 is a true equation; therefore, our solution, x = 4, is not an extraneous solution and is the correct solution of the given equation.

Answer: x = 4

Answer:

[tex]r=\sqrt[3]{\frac{9V}{\pi}}[/tex]

Step-by-step explanation:

[tex]r=3h \implies h=r/3 \\ \\ V=\frac{1}{3}\pi r^2(r/3) \\ \\ =\frac{\pi}{9} r^3 \\ \\ \frac{9V}{\pi}=r^3 \\ \\ r=\sqrt[3]{\frac{9V}{\pi}}[/tex]

Answer:

-2

Step-by-step explanation:

[tex]x-3x=2(4+x) \\ \\ -2x=2(4+x) \\ \\ -x=4+x \\ \\ -2x=4 \\ \\ x=-2[/tex]

Answer: an=21-4n

Step-by-step explanation:

17, 13, 9, 5, ...

13-17=-4

9-13=-4

5-9=-4

This sequence is an arithmetic progression a₁=17    d=-4

Hence,

[tex]a_n= a_1+(n-1)d\\\\a_n=17+(n-1)(-4)\\\\a_n=17-4n+4\\\\a_n=21-4n,\ \ \ \ n=1, 2, 3, 4, ...[/tex]

If Norman invested $100,000 for 3 years at 12%, the amount of interest earned on interest is $4,492.80

What is the future value of the investment?

The future value of the investment after 3 years is its future worth at the end of year 3 which comprises of the initial investment and the interest earned over the 3-year period as captured thus:

FV=PV*(1+r)^N

FV=future value after 3  years=unknown

PV=amount invested=$100,000

r=annual interest rate=12%

N=number of years of investment=3

FV=$100,000*(1+12%)^3

FV=$ 140,492.80

compound interest=$140,492.80-$100,000

compound interest=$40,492.80

interest on principal only=$100,000*12%*3=$36,000

interest on interest=$40,492.80-$36000

interest on interest=$4,492.80

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Answer:

Before Christ

Step-by-step explanation:

While in the past it was before Christ, its been moving to Before the Common Era

Pls mark as brainliest

Answer:

Look, I can't solve these for you: but for now Y = x + 3

Step-by-step explanation:

we know that

The linear equation in slope intercept form is equal to Y=mx+b

where

m is the slope

b is the y-intercept

step 1

Find the slope

Take two points from the graph

see the attached figure

about (37,40) and (47,50)

The formula to calculate the slope between two points is equal to

m=y2-y1

Find the y-intercept

we have

substitute in the linear equation

solve for b

therefore

The linear equation is y=x+3

Answer: f-1(x) = 1/3x.

Step-by-step explanation:

The inverse of y = 3x is f-1(x) = 1/3x.


To find the inverse, interchange the variables and solve for y

f ^− 1 (x) = In(x)/In(3)