The radius of a circle is 10 meters. What is the area of a sector bounded by a 45° arc?
45°
r=10 m
Give the exact answer in simplest form.

Answer: 1/8

Step-by-step explanation:

^ = Power of

/ = Fraction

(6m^-1n^0)^-3

= 6^-3(m^-1)

Formula: ( (^ab)^m =a^m b^m

6^-3 m^3

= m^3/216

Since m = 3 we evaluate.

= 27/216

= 1/8

The solution of the given system of equations is x = -4, y = 5 and z = 2 is the answer.

The system of equations given below:x + 2y + 3z = 11;2x + 4y + 5z = 21;3x + 5y + 6z = 27.

Here, we will solve this system of equations using inverse of the matrix method as follows:

We can write the given system of equations in matrix form as AX = B where, A = [1 2 3; 2 4 5; 3 5 6], X = [x; y; z] and B = [11; 21; 27].

The inverse of matrix A is given by the formula: A-1 = (1/ det(A)) [d11 d12 d13; d21 d22 d23; d31 d32 d33]  where,

d11 = A22A33 – A23A32 = (4 × 6) – (5 × 5) = -1,

d12 = -(A21A33 – A23A31) = -[ (2 × 6) – (5 × 3)] = 3,

d13 = A21A32 – A22A31 = (2 × 5) – (4 × 3) = -2,

d21 = -(A12A33 – A13A32) = -[(2 × 6) – (5 × 3)] = 3,

d22 = A11A33 – A13A31 = (1 × 6) – (3 × 3) = 0,

d23 = -(A11A32 – A12A31) = -[(1 × 5) – (2 × 3)] = 1,

d31 = A12A23 – A13A22 = (2 × 5) – (3 × 4) = -2,

d32 = -(A11A23 – A13A21) = -[(1 × 5) – (3 × 3)] = 4,

d33 = A11A22 – A12A21 = (1 × 4) – (2 × 2) = 0.

We have A-1 = (-1/1) [0 3 -2; 3 0 1; -2 1 0] = [0 -3 2; -3 0 -1; 2 -1 0]

Now, X = A-1 B = [0 -3 2; -3 0 -1; 2 -1 0] [11; 21; 27] = [-4; 5; 2]

Therefore, the solution of the given system of equations is x = -4, y = 5 and z = 2.

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Answer:

21

Step-by-step explanation:

3x7=21 possible combinations

Answer:

ygftyhhhhgffyujhhgyjjjhhguj

The probability that the gambler has strictly more than $32 after playing the game five times is 68.75%.

Probability is a branch of mathematics that deals with the likelihood of an event occurring. In this problem, we are dealing with a gambler who is playing a game with equal probability of doubling or reducing their stake to half.

The gambler's initial stake is $32. Let us consider the possible outcomes after one play of the game. The stake can either double to $64 or reduce to $16, each with equal probability. If the stake doubles, the gambler has more than their initial stake. If the stake is reduced to half, the gambler has less than their initial stake.

Now, let us consider the possible outcomes after two plays of the game. There are four possible outcomes:

(1) the stake doubles twice and the gambler has

=> $64 * 2 = $128,

(2) the stake doubles then reduces to half and the gambler has

=> $32 * 2 * 0.5 = $32,

(3) the stake reduces to half then doubles and the gambler has

=> $32 * 0.5 * 2 = $32,

(4) the stake reduces to half twice and the gambler has

=> $32 * 0.5 * 0.5 = $8.

We can represent these outcomes using a tree diagram. Each branch represents a possible outcome, and the probability of that outcome is written next to the branch.

After five plays of the game, there are 32 possible outcomes.

We can calculate the probability of the gambler having more than their initial stake by adding up the probabilities of all the outcomes where the gambler has more than $32. This turns out to be 0.6875 or 68.75%.

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Answer:

C.

\({ \tt{f(x) = \frac{12}{x} - 18}} \: and \: { \tt{g(x) = \frac{12}{x + 18} }}\)

Step-by-step explanation:

\({ \tt{f(x) = \frac{12}{x} - 18}}\)

Let inverse be m:

\({ \tt{m = \frac{12}{x} - 18 }} \\ { \tt{x(m + 18) = 12}} \\ { \tt{x = \frac{12}{m + 18} }} \\ \\ { \boxed{ \sf{f {}^{ - 1} (x) = g(x) = \frac{12}{x + 18} }}}\)

Using 2/5 will mean there is 3/5 left.

Mutiply the total length by the fraction left:

3 x 3/5 = (3 x 3) /5 = 9/5 - 1 and 4/5 meters left

Answer: 1 and 4/5 meters

The value of the voltage of the electricity is 6 + j + 2j²

From the question, we have the following parameters that can be used in our computation:

C = 2 - j

I = 3 + 2j

The formula of voltage is given as

V = CI

Substitute the known values in the above equation, so, we have the following representation

V = (2 - j) * (3 + 2j)

Open the brackets

So, we have

V = 6 + 4j - 3j + 2j²

Evaluate the like terms

V = 6 + j + 2j²

Hence, the voltage is 6 + j + 2j²

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Using the basic mathematical operations, the temperature at 6 p.m. was -5.5°F.

The basic mathematical operations are addition, subtraction, multiplication, and division.

The symbols of the basic mathematical operations are +, -, ×, and ÷.

In our daily life, these basic mathematical operations are the foundation of mathematical expressions or equations.

Temperature and Time

Time              Temperature

9 a.m.            -1.3°F

12 noon         9°F (-1.3°F + 10.3°F)

3 p.m.            -0.6°F (9°F - 9.6°F)

6 p.m.            -5.5°F (-0.6°F - 4.9°F)

Thus, using mathematical operations, the temperature at 6 p.m. was -5.5°F.

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Answer:

the temperature at 6 p.m. was -5.5°F.

Step-by-step explanation:

The area of the larger figure that is similar to the smaller one is: 28.2 m².

Where A and B represent the areas of two similar figures, and a and b are their corresponding side lengths, respectively, the formula that relates their areas and side lengths is:

Area of figure A / Area of figure B = a²/b².

Given that the two figures are similar as shown in the image above, find each of their respective side lengths if we are given the following:

Perimeter of smaller figure = 20 m

Area of smaller figure = 19.6 m²

Perimeter of larger figure = 34m

Area of larger figure = x

Therefore:

20/34 = a/b

Simplify:

10/17 = a/b.

Find the area (x) of the larger figure using the formula given above:

10²/12² = 19.6/x

100/144 = 19.6/x

100x = 2,822.4

x = 2,822.4/100

x ≈ 28.2 m²

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Answer:

The pen is $52.50 and the cost of the pencil is $2.50.

Step-by-step explanation:

What is the answer if a pen and a pencil cost 55 dollars and the pen cost 50 more dollars than the pencil​?

—

Step 1: Let Statements

Let a be the cost of the pen

Let b be the cost of the pencil

Step 2: Write Equations

a + b = 55

a = 50 + b

Step 3: Find POI

Using substitution to find the POI of both equations:

50 + b + b = 55

50 + 2b = 55

2b = 55 - 50

2b = 5

b = 5/2 or 2.5

Substitute b = 5/2 to solve for a

a = 50 + b

a = 50 + 2.5

a = 52.5

Therefore, a = 52.5 and b = 2.5

Step 4: Concluding Sentence

The cost of the pen is $52.50 and the cost of the pencil is $2.50.

Answer:

3 3/4

Step-by-step explanation:

Answer:

Three and three fourths or 15/4

Step-by-step explanation:

Answer:

Kos kosa para wlang hasol wlang kos kos sa balongosa

Answer:

X = -1.54 repeating

Step-by-step explanation:

Answer:

It's the chemical because they have to work with dangerous stuff.

Answer:

I suggest it's Ryan

Step-by-step explanation:

If John hits the center once in every 3 row, it means that he hit it 6-7 times but Ryan hits the center for about 12 times. It's definitely Ryan!

Answer:

The way I would tackle these types of problems would be to make a table, then graph the points using the results I get.

Step-by-step explanation:

So explaining the table is kinda hard since I suck at explaining, so I've attached a file showing the table I've made for number 1.

First Step:

Make the table. Make it a 3x4 table. For the top row, put y, the equation (I put 'y=2x' as shown in number 1), then x. Then for the left column, go down by one box, then put: -1, 0, 1. Really, you can put any numbers, but to make it easy for yourself, just write the numbers I've listed. These will be your y-values you'll be substituting.

Second Step:

a.) Plugging in the numbers. For the middle column, I've put down y=2x in each box, as shown in my table. Then for each of those boxes, plug in the numbers to the left of them and substitute them for the y-value. For example, look at the second row. The left box has '-1', so I replaced the 'y' in the equation and got '(-1)=2x'.

b.) After substituting the y-values, solve for x. For this case, you'll need to divide both sides by 2. If it doesn't make much sense, think about a seesaw. If you have 5 pounds on both sides, the seesaw will stay balanced. Add an additional 5 pounds to one side, then the seesaw will start tipping towards the heavier sides. So in order to keep an equation balanced, you must do any action to both sides of the equation. After diving both sides by 2, you'll get the value for x.

Final Step:

After finding the x-values for each of the y-values, it's time to graph the equations. Remember, x is left to right and y is down to up. To graph them, let's use the second row for example. y=-1 and x=-0.5. So all you need to do is to start from the origin (0,0), then go half a unit to the left, as x is negative, then go a unit down, as y is negative, then make a point. The rest should be pretty straight forward.

After making all three points, just get a ruler or any straight edge, then align it along those three points, then just make a line, and boom! You've solved number 1! For the purpose of saving my time, I'm pretty sure you can solve the rest using what I've just told you. Good luck!

We have the next function

And we must find f(-2) and f(0.3)

To find f(-2) and f(0.3) we need to know that

We can see that we have a constant function because it has the next form

That means, for any value of x the function will always be equal to 4.

Using that, we obtain

ANSWER:

f(-2) = 4

f(0.3) = 4

Answer:

1464.84375

Step-by-step explanation:

The n th term of a geometric sequence is

\(a_{n}\) = a₁ \((r)^{n-1}\)

where a₁ is the first term and r the common ratio

Here a₁ = 6 and r = 15 ÷ 6 = 2.5, thus

\(a_{7}\) = 6 × \((2.5)^{6}\) = 6 × 244.140625 = 1464.84375

The seventh term of the geometric progression will be 1464.84375

When there is a constant between the two successive numbers in the series then it is called a geometric series.

The nth term of a geometric sequence is

\(a_n =a_1(r)^{n-1}\)

where a₁ is the first term and r is the common ratio

Here a₁ = 6 and r = 15 ÷ 6 = 2.5, thus

\(a_7=6\times (2.5)^{6}\)  = 6 × 244.140625 = 1464.84375

Therefore the seventh term of the geometric progression will be 1464.84375

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The distance traveled by the tip of the second hand during a period of t minutes is πt centimeters.

To find the distance traveled by the tip of the second hand during a period of t minutes, we need to calculate the circumference of the circle formed by the tip of the second hand.

The circumference of a circle is given by the formula: C = 2πr, where r is the radius of the circle.

In this case, the radius of the circle formed by the second hand is cm. So, the circumference is:

C = 2π × r = 2π ×

Now, to find the distance traveled during t minutes, we multiply the circumference by the fraction of a full circle covered in t minutes, which is t/60 (since there are 60 minutes in an hour):

Distance traveled = C × (t/60) = (2π × ) × (t/60)

Simplifying the expression, we get:

Distance traveled = πt

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The values on the relative frequency table indicates;

Part A; 55%

Part B; 20%

Part C; There is an association between passing the exam and completing the exam review

The relative frequency table shows the mode of a dataset, from the sample obtained from a population.

The data in the table can be expressed as follows;

\({}\)                                           Passed exam Did not pass exam Row totals

Completed exam review \({}\)            55%        10%                         65%

Did not completed exam review\({}\) 20%       15%                          35%

Column Total \({}\)                               75%        25%                         100%

Part A; The above table indicates that the percentage who passed the exam given that they completed the exam review is 55%

Part B; The percentage that passed the exam given that they did not complete exam review is 20%

Part C; The conditional percentages of passing the exam and completing the exam review are very different indicating that there is an association between passing the exam and completing exam review

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The expression x to the power of 3 times x to the power of 3 times x to the power of 3 is not equivalent to an expression x to the power of 3 times 3 times 3.

For given question,

We have been given a statement 'x to the power of 3 times x to the power of 3 times x to the power of 3 '

We can write above statement in expression form as,

x³ × x³ × x³

Now, we simplify above expression.

We know that the product rule of exponents states that, 'To multiply expressions with the same base, add the exponents while keeping the base the same.'

So, x³ × x³ × x³ = \(x^{3+3+3}\)

⇒  x³ × x³ × x³ = \(x^{9}\)                    ....................................(1)

Also, we have been given a statement that 'x to the power of 3 times 3 times 3'

We can write above statement in expression form as,

\(x^{3\times 3\times 3}\)

Now we simplify above expression.

By power of a product rule of exponents,

\(x^{3\times 3\times 3}=x^{27}\)                           .....................................(2)

From (1) and (2),

x³ × x³ × x³ ≠ \(x^{3\times 3\times 3}\)

Therefore, the expression x to the power of 3 times x to the power of 3 times x to the power of 3 is not equivalent to an expression x to the power of 3 times 3 times 3.

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Answer:

See attached.  Line for x<5.

Step-by-step explanation:

Solve the equation for x.  Remember that the "<" and ">" signs are reversed when dividing or multiplying by a negative value.

The true statement of the right triangle are as follows;

sin ∅ = 4 / √97

tan β = 9 / 4

cos β = 4 / √97

4² + 9² = √97

A right angle triangle is a triangle that has one of its angles as 90 degrees.

The side and angles of the right angle triangle can be found using trigonometric ratios as follows:

sin ∅ = opposite / hypotenuse

cos ∅ = adjacent / hypotenuse

tan ∅ = opposite / adjacent

Therefore, using Pythagoras's theorem,

c² = a² + b²

where

Therefore,

4² + 9² = (√97)²

4² + 9² = √97

Using trigonometry,

sin ∅ = 4 / √97

tan β = 9 / 4

cos β = 4 / √97

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