Solve please it is for homework

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.

Answer:

9

Step-by-step explanation:

Factor for 18 are:

1,2,3,6,9,18

Factors for 27 are:

1,3,9,27

Hope I helped <3

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:

1.  17.5 units²

2.  16 units²

Step-by-step explanation:

Given vertices of ΔABC:

Plot the vertices on the given graph paper and join with line segments to create the triangle.

As point B and C share the same x-coordinate, and points A and B share the same y-coordinate, ΔABC is a right triangle with base AB and height BC.

[tex]\begin{aligned}\textsf{Area of a triangle} & = \sf \dfrac{1}{2} \times base \times height\\\implies \textsf{Area of $\triangle$ ABC} & = \sf \dfrac{1}{2} \times AB \times BC\\& = \sf \dfrac{1}{2} \times 7 \times 5\\& = \sf \dfrac{35}{2}\\& = \sf 17.5 \:\:units^2\end{aligned}[/tex]

Given vertices of rectangle WXYZ:

Plot the vertices on the given graph paper and join with line segments to create the rectangle.

The area of a rectangle is found by multiplying the length by the width. To find the area of rectangle WXYZ, find the length (WZ or XY) and the width (WX or ZY) using the distance formula, then multiply them.

Distance between two points

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\textsf{where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points}.[/tex]

[tex]\begin{aligned}WZ & =\sqrt{(x_Z-x_W)^2+(y_Z-y_W)^2}\\& =\sqrt{(4-0)^2+(-4-0)^2}\\& =\sqrt{(4)^2+(-4)^2}\\& =\sqrt{16+16}\\& =\sqrt{32}\sf \:\:units\\\end{aligned}[/tex]

[tex]\begin{aligned}WX & =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\& =\sqrt{(x_X-x_W)^2+(y_X-y_W)^2}\\& =\sqrt{(2-0)^2+(2-0)^2}\\& =\sqrt{(2)^2+(2)^2}\\& =\sqrt{4+4}\\& =\sqrt{8}\sf \:\:units\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Area $WXYZ$} & = WZ \times WX\\& = \sqrt{32} \times \sqrt{8}\\& = \sqrt{32 \cdot 8}\\& = \sqrt{256}\\& = 16\sf \:\:units^2\end{aligned}[/tex]

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

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:

$42.38

Step-by-step explanation:

$39.99 x 0.06= 2.39

39.99 + 2.39= $42.38 (total with tax)

Answer:

Step-by-step explanation:

39.99 * 0.06 = 2.4

The total tax equals = 2.4

6% in decimal form is 0.06 multiplied by the total cost of shoes to get the total tax. 2.4

add that to the total to get the total cost with tax = $42.39

Im guessing it is Base x Height ÷ 2? My answer is 12, i aplogise if i am incorrect.

Step-by-step explanation:

Just subtract the y coordinate of B with the y coordinate of A (or C).

so since B has a y of 9 and A has a y of 5 the height is

9 - 5 =

4

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?

Answer:

1/(2 – 4i)

Explanation:

Use geeksforgeeks.org or another website

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: 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]

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

Answer:

Step-by-step explanation:NIDIHNG S,AST3RE TIRWACRE

I THINK THAT UR

Answer:

4/3 (x) = 28/3

*divide both sides by 4/3

4/3 (x) ÷ 4/3 = 28/3 ÷ 4/3

x = 7

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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The solution for variables x, y, and z are -

The given linear equation are-

x - 6y - 2z = -8   .......equation 1.

-x + 5y + 3z = 2 ......equation 2.

3x - 3y - 4z = 15 .......equation 3.

Add equation 1 and 2; gives

-y + z = -6   .....equation 4

multiply equation 2 and subtract it with equation 3;

12y + 5z = 21 ......equation 5

multiply equation 4 with 5 and subtract it from equation 5.

17 y = 51

y = 3.

Put y = 3 in equation 4 and find z.

z = -6 + 3

z = -3

Put the value of y and z in equation 1 and find x.

x = -8 + 18 + 6

x = 100

Therefore, the solution for variables x, y, and z are -

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The number is 30.

Step-by-step explanation:

n=number.

2/3n+1/6n=25

Make a common denominator for 2/3 and 1/6 and then combine like terms.

4/6n+1/6n=25

5/6n=25

divide 5/6 on both sides to isolate n.

n=25/(5/6)

oreja.

n=25/1/5/6

nu(25×6)/(5×1)

n=150/5

n=30

OR

multiply the reciprocal instead of dividing.

n=25×(6/5)

n=150/5

n=30

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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To reflect a graph, f(x) over the x-axis, you take -f(x). So if f(x)=x^2, then -f(x) is -x^2. Then g(x)=-x^2 is the reflection of your function f(x) over the x-axis.

A mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.

Four broad categories can be used to classify different types of functions. dependent upon element Function is a one-to-one relationship, a many-to-one relationship, onto function, one-to-one and into function.

An output variable and one or more input variables are the minimum number of variables in a function. An equation can have any number of variables and declares that two expressions are equal (none, one, or more).

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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/

I can't tell if the entire question is here or not, it appears to be missing something.

If you did put all of the information here, h(2) = 5 because there is no x input.

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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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 commitment adherence percentage for the week will be 53%.

How to compute the percentage?

It was stated that Amy was scheduled to service 17 intervals this week. She picked up 4 more intervals during the week.

The following can be deduced based on the information that are given:

Total intervals = 17

Taken intervals = 4+ 3 + 2 = 9

Therefore, the commitment adherence percentage for the week will be:

= 9/17 × 100

= 53%

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Complete question :

Amy was scheduled to service 17 intervals this week. She picked up 4 more intervals during the week. On Friday, she put 3 intervals up for swap. One of them was picked up by someone else. The other two were not so she released them both during the lockdown period. Amy also had technical issues but never did get a waiver, which resulted in her missing an additional 2 intervals. What was her Commitment Adherence percentage for the week? Enter whole numbers (no decimals)

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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Answer:

Before Christ

Step-by-step explanation:

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

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