if sinx=1/2, find cos4x​

Answer:

17.2°

Explanations

To find angle A, use the cosine rule.

a^2 = b^2 + c^2 - 2 × a × c cos A

4^2 = 7^2 + 10^2 - 2 × 7 × 10 cos A

16 = 49+ 100 - 140 × cosA

16 = 149 - 140cosA

16- 149 = - 140cosA

-133 = - 140cosA

cosA = 133/140

cosA = 0.95

A = 17.2°

Answer: [tex]\cos 34^{\circ}[/tex] and [tex]\sin 56^{\circ}[/tex]

Answer:

⅓ ×½ which will give you ⅙

Step-by-step explanation:

because

The probability that Manu will win the coin flip amongst others is 4/7

To determine the probability that Manu will win, we need to consider the possible outcomes of the coin flips.

Let's break down the scenarios:

Scenario 1: Manu wins on the first flip

- The probability of Manu winning on the first flip is 1/2, as he needs to flip heads right away.

Scenario 2: Manu wins on the second flip

- Juan flips tails (1/2 probability)

- Carlos flips tails (1/2 probability)

- Manu flips heads (1/2 probability)

- The probability of Manu winning on the second flip is (1/2) * (1/2) * (1/2) = 1/8.

Scenario 3: Manu wins on the third flip

- Juan flips tails (1/2 probability)

- Carlos flips tails (1/2 probability)

- Manu flips tails (1/2 probability)

- Juan flips heads (1/2 probability)

- Carlos flips heads (1/2 probability)

- Manu flips heads (1/2 probability)

- The probability of Manu winning on the third flip is (1/2) * (1/2) * (1/2) * (1/2) * (1/2) * (1/2) = 1/64.

The pattern continues, and we can see that Manu's probability of winning decreases exponentially with each subsequent flip.

Therefore, the total probability of Manu winning is the sum of the probabilities from each scenario:

1/2 + 1/8 + 1/64 + ...

This is an infinite geometric series with a first term (a) of 1/2 and a common ratio (r) of 1/8.

Using the formula for the sum of an infinite geometric series:

Sum = a / (1 - r)

Sum = (1/2) / (1 - 1/8)

Sum = (1/2) / (7/8)

Sum = (1/2) * (8/7)

Sum = 4/7

Therefore, the probability that Manu will win is 4/7.

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The assumptions in each case of this statistics problem is given as follows:

ts < tc Do not reject H0

P value > α Do not reject H0

There is insufficient data to determine that the mean scores of the two groups of pupils differ.

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The congruency statement that describes the figure is: D. ΔRST ≅ ΔBAC.

A congruency statement is a statement that states that two triangles are congruent to each other.

180 degrees rotation around the origin will give us the rule: (x, y) → (-x, -y)

Therefore, applying this rule to triangle RST that was rotated, we would have:

R'(-1, -1)

S'(-3, -4)

T'(-5, 0)

Translating R'S'T' 3 units up, using the rule, (x, y + 3) will give us:

B(-1, 2)

A(-3, -1)

C(-5, 3)

Therefore, we can conclude that, D. ΔRST ≅ ΔBAC.

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Answer:its D just took test:)

Step-by-step explanation:

Step-by-step explanation:

Radius = 14 cm

π = 22/7 (Because the value of the circle's radius is the multiples of 7).

• Perimeter :

= 2 . π . r

= 2 . 22/7 . 14

= 28 . 22/7 (Divide 28 and 7 with 7)

= 4 . 22/1

= 4 . 22

= 88 cm is the answer

Answer:

None

Step-by-step explanation:

We can eliminate the x's by add the 2 equations :

2y = 18

Divide both sides by 2 :

y = 9

Substitute this value into equation 1 to solve for x :

-3x + (9) = 6

Subtract 9 from both sides :

-3x = -3

Divide both sides by -3 :

x = 1

Substitute these values into equation 2 to check :

-3(1) + 6 = 12 ❌❌

So it has no solution

Answer:

i'm not realy sure what you mean by a table

8x=2x+2

subtract 2x from each side

6x=2

divide by 6

x=1/3

Hope This Helps!!!

Step-by-step explanation:

So if you want to make a table to find the solution, you'll need 3 columns, one will be the value of x, the other two will be the value of the equation (left and right) and then you'll need to look where the two equations are equal, and the solution is whatever the x-value is. It'll look something like this:

[tex]x\ \ \ \ |\ 2x+2\ |8x\\-3\ \| -4\ \ \ \ \ | -24\\-2\ \| -2\ \ \ \ \ |-16\\-1\ \| 0\ \ \ \ \ \ \ \ \ | -8\\0\ \ \ \ \|2\ \ \ \ \ \ \ \ \ | 0 \\1\ \ \ \ \| 4\ \ \ \ \ \ \ \ \ | 8\\2\ \ \ \ \|6\ \ \ \ \ \ \ \ \ | 16\\3\ \ \ \ \|8\ \ \ \ \ \ \ \ \ | 24[/tex]  

As you can see, none of rows (the two right most columns with the equations) are ever equal, on the same row. This is because the solution is not an integer. If you solve it algebraically. You'll get this:

Original equation

8x = 2x+2

Subtract 2x from both sieds

6x = 2

Divide both sides by 6

x = 2/6

Simplify the fraction

x=1/6

Answer:

Step-by-step explanation:

Comment

Start with the right hand side.

1/2(3 - x)

This reads as The difference between 3 and a number. You put it the way you read it difference between 3 and a number = 3 - x The 1/2 affects both terms. So that makes b and d incorrect.

The left side is a bit harder. You want the sum of 6 + something. Read the rest of the given

6 + 2(x +4)

Now that is all equal to

6 + 2(x + 4) = 1/2 (x - x)

The answer is A

Combining the like terms, the equivalent expression is given as follows:

-x + 25.

To add polynomials, we combine the like terms, that is, those with the same variable and exponent.

In this problem, the expression is:

(2x + 10) + (-3x + 15).

2x + 10 - 3x + 15

Combining the like terms:

2x - 3x + 10 + 15 = -x + 25.

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Answer:

A brush: $4.50

A tube of paint: $2

Step-by-step explanation:

Let b = brushes

Let p = paint

1) Set up equations.

4b + 7p = 32

6b + 8p = 43

2) Solve the system of equations using elimination.

(4b + 7p = 32)3

(6b + 8p = 43)2

-----------------------

12b + 21p = 96

12b + 16p = 86

----------------------

5p = 10

p = 10/5

p = 2

Substitute 2 into p of any of the two equations.

4b + 7(2) = 32

4b + 14 = 32

4b = 32 - 14

4b = 18

b = 18/4

b = 4.50

Therefore, a brush costs $4.50, while a tube of paint costs $2.

The linear equality y < 3x + 2 is represented by the graph attached.

An equation is an expression that shows the relationship between two or more numbers and variables.

An inequality is the non equal comparison of two or more numbers and variables.

The linear equality y < 3x + 2 is represented by the graph attached.

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Answer:

(0,-0)

Step-by-step explanation:

P(0,0)=P(0,-0)

The man paid $ 25.5 for the use of money.

The amount repaid to the bank on the due date is $3425.5

Calculating the amount of simple interest that will be charged on a loan can be done quickly and easily using the simple interest formula. To compute simple interest, multiply the principle, the number of days between payments, and the daily interest rate.

Principal(P)=$3400

Time(T)=3 months=1/4 yrs

Rate(R)=3%

The simple interest and final amount are calculated as follows:

Simple Interest(SI)=P*R*T/100

                               [tex]=\frac{3400*3*\frac{1}{4} }{100}[/tex]

                               =25.5

Net amount repaid=P+SI

                               =3400+25.5

                               =3425.5

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Answer:

Holocene

Step-by-step explanation:

The Holocene began 11,700 years ago after the last major ice age.

Answer:

obtuse because 62 + 102 < 122

S

its c, obtuse, becuase 6^2+10^2<12^2

Answer: Quadratic

Step-by-step explanation:

I'm too lazy to explain. Trust me

Using Trigonometry, the approximate distance from the observatory to the island is evaluated to be 322 feet.

Given Information

It is given that,

The height of the observatory = 150 feet

The angle of depression from the top of the observatory = 25°

We can calculate the horizontal distance of the observatory from the island using Trigonometry

What is Trigonometry?

The area of mathematics known as Trigonometry is concerned with certain functions of angles and how to use them in computations. There are six popular Trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc) are their respective names and acronyms.

Calculating the Horizontal Distance Using Trigonometry

As per the rules of the Trigonometry,

[tex]tan \alpha = \frac{Perpendicular/ Opposite Side}{Base}[/tex]

Here,

[tex]\alpha[/tex] = 25°

Perpendicular = 150 ft.

Base = Horizontal Distance

Thus, [tex]tan 25 =\frac{150}{Horizontal Distance}[/tex]

∴ x ≈ 322 ft.

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The height and the radius that minimize the material needed to manufacture the can is 4.18336 cm and 4.18337 cm respectively.

Computed using differentiation.

We assume the radius of the can be r cm, and its height to be h cm.

We are given that the can is to hold 230 cm³ of liquid, thus the volume of the can is:

V = 230,

or, πr²h = 230 {Since, the volume of a cylinder is πr²h, where r is the radius, and h is the height},

or, h = 230/(πr²) ... (i) .

We are asked to find the height and radius that minimize the amount of the material.

To calculate the amount of the material, we calculate the surface area of the can (A).

The surface area of the can = area of the base + area of the side,

or, A = πr² + 2πrh = πr(r + 2h).

Substituting h = 230/(πr²), we get:

A = πr(r + 2{230/(πr²)}),

or, A = {πr(πr³ + 460)}/πr² = πr² + 460/r.

Differentiating both sides with respect to the radius r, we get:

dA/dr = 2πr - 460/r² ...(ii)

To find the point of inflection, we equate this to zero, to get:

2πr - 460/r² = 0,

or, 2πr = 460/r²,

or, r³ = 460/2π = 73.2113,

or, r = 4.18337 cm.

To check whether the point of inflection shows the point of maximum or minimum, we differentiate (ii) with respect to the radius r, to get:

d²A/dr² = 2π + 920/r³, which is always positive when the radius r is positive.

Thus, the area is minimum when the radius r = 4.18337 cm.

Height, h = 230/(πr²) = 4.18336 cm.

Thus, the height and the radius that minimize the material needed to manufacture the can is 4.18336 cm and 4.18337 cm respectively.

Computed using differentiation.

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The blank space in the task content should be filled with; a 270° rotation about point P.

It follows from the transformation described in the task content that; Triangle KLM from which triangle K'L'M' is rotated 270 degrees about point P and then translated down and to the right.

It therefore follows from observation. that the first transformation is; a 270° rotation about point P.

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The correct option is:

As the x-values go to positive infinity, the function's values go to positive infinity.

By the description, We know that the function has the points:

(-1.25, -3.25), (0.25, -1.75) (-2.25, 0), (0, -2), (-2.75, 6), (1.5, 6)

Notice that from x = 0.25 to x = 1.5 the function goes upwards, then in the right side, the function goes up, so as x goes to positive infinity, also does f(x).

On the left side, we can see  that from x = -2.75 to x = -2.25 the function goes downwards.

So, as x goes to the left (negative infinity) f(x) goes upwards.

Then as x tends to negative infinity, f(x) tends to infinity.

The correct option is:

As the x-values go to positive infinity, the function's values go to positive infinity.

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Answer:

D

Step-by-step explanation:

edge 23

Answer:

a

Step-by-step explanation:

[tex]\Large\maltese\underline{\textsf{A. \space What is Asked}}[/tex]

Find the gradient of the line segment between the points [tex]\bf{(4,3)\:and\:(5,6)}[/tex]

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

The formula used, here is

[tex]\bf{m=\dfrac{y2-y1}{x2-x1}[/tex]

[tex]\cline{1-2}[/tex]

Now let's put in the co-ordinates from these two points.

[tex]\bf{m=\dfrac{6-3}{5-4}}[/tex] | subtract on top & bottom

[tex]\bf{m=\dfrac{3}{1}}[/tex] | divide

[tex]\bf{m=3}[/tex]

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

                      [tex]\bf{=m=3}[/tex]

[tex]\boxed{\bf{ aesthetic\not101}}[/tex]

Answer:

g=3

Step-by-step explanation:

gradient=change ofY/change of X

3-6/4-5

-3/-1 simply

gradient =3

Kenyan formula easy

The domain of the function is (-∞, 1) U(1, ∞) while the domains are values greater than or equal to 1 that is y ≥1

The domain are independent variable for which the equation exist while the range are dependent variable for which the equation exist

Given the following functions

f(x) =2/x-1

g(x) = x+1

Determine  (g ○ f)(x)

(g ○ f)(x) = g(f(x))

(g ○ f)(x) = g(2/x-1)

(g ○ f)(x) = (2/x-1) + 1

(g ○ f)(x) = 2+(x-1)/x-1

(g ○ f)(x) = x+1/x-1

Hence the domain of the function is (-∞, 1) U(1, ∞) while the domains are values greater than or equal to 1 that is y ≥1

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For Ms. Cho's class, the formula is =randBetween(1,21). The result of interest is 14 or less.

12/20 reduces to 4/5 --> 4/5 of 15 is 12.

So using the spinner to model Mr. Skinner's class, an outcome of the select 12 sections of interest represent, symbolize, and model a student bringing lunch from home.

LIkewise, 14/21 reduces to 2/3 --> 2/3 of 15 is 10.

So using the spinner to model Ms. CHo's class, an outcome of only 10 of the 15 sections of interest represent, model, and symbolize a student who brings lunch from home.

The same can be done in Excel: The function is =randBEtween( minVal, maxVal)

For example =randBetween(1,20) will model Mr. Skinner's class. A result of 12 or less represents, model, simulates, and symbolizes a student who packed their lunch.

For Ms. Cho's class, the formula is =randBetween(1,21). The result of interest is 14 or less.

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StartFraction 4 x + 40 Over (x + 2) (x + 7) EndFraction = StartFraction 8 Over x + 2 EndFraction + StartFraction negative 4 Over x + 6 EndFraction

What is partial fraction?

Partial fractions are the fractions used for the decomposition of a rational expression.

Given:

(4x + 40)/ (x + 2)(x + 6) = A/(x + 2) + B/(x + 6)

4x + 40 = A(x + 6) + B(x + 2)

4x + 40 = x(A+B) + 6A +2B

On comparing

4= A+B

A= 4-B

and, 6A +2B =40

3A + B =20

3(4-B) + B =20

12  - 3B + B =20

-2B = 8

B= -4

and, A= 8

Hence, StartFraction 4 x + 40 Over (x + 2) (x + 7) EndFraction = StartFraction 8 Over x + 2 EndFraction + StartFraction negative 4 Over x + 6 EndFraction

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Answer:

C.

Step-by-step explanation:

photo below

Answer:

spider : 5

beetle : 6

Step-by-step explanation:

Total number of legs --> 8 + 6 = 14 ( 1 set )

Number of sets that can fit --> 76 ÷ 14 = 5 R 6

Since each set has a beetle and a spider,

Number of spider -->5 × 1 = 5

Since there are additional 6 legs:

Number of beetles --> ( 5 × 1 )+ 1 = 6

Abby, Bernardo, Carl, and Debra play a game in which each of them starts with four coins. The game consists of four rounds. In each round, four balls are placed in an urn - one green, one red, and two white. The players each draw a ball at random without replacement. Whoever gets the green ball gives one coin to whoever gets the red ball. What is the probability that, at the end of the fourth round, each of the players has four coins

The probability that, at the tip of the fourth round, each of the players has four coins is 5/192.

Given that game consists of 4 rounds and every round, four balls are placed in an urn one green, one red, and two white.

It amounts to filling in an exceedingly 4×4 matrix. Columns C₁-C₄ are random draws each round; row of every player.

Also, let [tex]\%R_{A}[/tex] be the quantity of nonzero elements in [tex]R_{A}.[/tex]

Let [tex]C_{1}=\left(\begin{array}{l}1\\ -1\\ 0\\ 0\end{array}\right)[/tex].

Parity demands that [tex]\%R_{A}[/tex] and[tex]\%R_{B}[/tex] must equal 2 or 4.

Case 1: [tex]\%R_{A}[/tex]=4 and [tex]\%R_B[/tex]=4. There are [tex]\left(\begin{array}{l}3\\ 2\end{array}\right)[/tex]=3 ways to put 2-1's in [tex]R_A[/tex], so there are 3 ways.

Case 2: [tex]\%R_{A}[/tex]=2 and [tex]\%R_B[/tex]=4. There are 3 ways to position the -1 in [tex]R_A[/tex], 2 ways to put the remaining -1 in [tex]R_B[/tex] (just don't put it under the -1 on top of it!), and a pair of ways for one among the opposite two players to draw the green ball. (We know it's green because Bernardo drew the red one.) we are able to just double to hide the case of [tex]\%R_{A}=4,\%R_{B}=2[/tex] for a complete of 24 ways.

Case 3: [tex]\%R_A=\%R_B=2[/tex]. There are 3 ways to put the -1 in [tex]R_{A}[/tex]. Now, there are two cases on what happens next.

Hence, there are 3(2+2×2)=18 ways for this case. There's a grand total of 45 ways for this to happen, together with 12³ total cases. The probability we're soliciting for is thus 45/(12³)=5/192

Hence, at the top of the fourth round, each of the players has four coins probability is 5/192.

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[tex]\Large\maltese\underline{\textsf{Our problem:}}[/tex]

Which equation represents a line with slope: [tex]\bf{\dfrac{1}{2}[/tex] and y-intercept: [tex]\bf 3[/tex]?

[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]

[tex]\bf{Equation: y=mx+b[/tex]

[tex]\bf{Equation\:with\:the\:given\:information: y=\dfrac{1}{2}x+3}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Result:}[/tex]

                      [tex]\bf{y=\dfrac{1}{2}x+3}[/tex]

[tex]\boxed{\bf{aesthetic \not101}}[/tex]