the radius of a circle is 1 what is the length of an arc that subtends an angle of 10pi/9 radians

Given:

The expression given is,

Required:

To find the value of b.

Explanation:

We have the given expression as:

Let us find the value of b.

Final Answer:

The value of b is,

First, we have to use the interior angles theorem

Then, we solve for x

Then, we use this value to find each angle

1) We must solve for x the following equation:

To solve this equation, we take the natural logarithm to both sides of the equation:

Now, we use the following results:

Replacing these results in the equation above, we have:

Solving for x, we get:

2) We must solve for x the following equation:

To solve this problem, we isolate the part that involves the x:

Now, using the following property:

with:

we have:

Solving the last equation for x, we get:

Answers

1) The value of x that solves the first equation is 0.64 to two decimal places.

2) The value of x that solves the second equation is 3.90 to two decimal places.

Review of the base of a logarithm

We can define the logarithm in base a through the following equations:

When we use as a base the Euler number e ≅ 2.718, the logarithm is called "natural" and we use the following notation for it:

With this notation, we have the following properties:

One of the most important trigonometric identities is the one below

Then,

Use this result in the equation given by the problem

Furthermore,

Set y=sinx

Thus,

Finally,

Then, the answer is

The answer is x=-pi/6+2n*pi

Answer:

6/5 x 5/3 is 2

if that's what you need help with

step-by-step explanation

Answer:

Explanation:

Given a sample with the following:

• Mean,M = 90

• Standard deviation, s = 20

To find the z-score for each of the given X values, we use the formula below:

The z-scores are calculated below:

The expression 5m³ - 10m² + 8m + 2 cannot be factorized

From the question, the polynomial is given as

5m^3-10m^2+8m+2

Rewrite the polynomial properly

So, we have

5m³ - 10m² + 8m + 2

Next, we represent the above expression on a graph

From the attached graph, we can see that the polynomial expression only cross the x-axis at x = -0.197

This implies that the expression cannot be factored

So, we cannot further rewrite the given expression

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Given the equation :

solve for w, so:

subtract 182 from both sides:

multiply both sides by -1

So, the value of w = -70

Given angle FGH is a right angle. This means angle FGH is 90 degrees

But

ANSWER

-72 ft

EXPLANATION

We can draw a number line:

If the 0 of the number line is sea level, we would normally say that all positive numbers are those that are above sea level and negative numbers those that are below sea level.

Therefore, to represent an elevation that is below sea level, we'd write it as a negative number: -72 ft

To find the general solution to y we need take the sine function in both sides of the equation given:

Now, we have to find the value of y for which the sine function is equal to the right side. From the properties of the sine function and its definition we conclude that y has to be:

Therefore the general solution is:

Vertex C (4, 6 ) Rotation 180º about the origin CCW c' (-4, -6)

C (x, y ) C ' (-x, -y )

________________

Answer

Option D

From the frequency distribution, the measures are given as follows:

a) Total number of observations: 27.

b) The width of each class is of 5.

c) The midpoint of the second class if of 20.5.

d) The modal class is Class 12 - 17.

e) If another class was added, the limits would be 48 - 53.

The frequency distribution gives the number of observations that is located in each class.

Hence the total number of observations is given by the sum of the frequencies, as follows:

Total = 9 + 1 + 3 + 8 + 6 = 27.

The modal class is class with the highest number of observations, hence it is of:

Class 12-17.

The width of a class is given by the subtraction of the limits, hence:

Width = 47 - 42 = ... = 23 - 18 = 17 - 12 = 5.

For an added class, the lower bound would be one more than the last class, while the upper bound would be five added to the lower bound, hence the limits are:

48 - 53.

The midpoint of each class is given by the mean of the coordinates, hence, for the second class, it is of:

Midpoint = (18 + 23)/2 = 41/2 = 20.5.

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$ 119.607

Explanation

we can easily solve this by using a rule of three

Step 1

Let

actual price(2020)=price of 2019 + 2%

so

actual price(2020)= 102 % and

price ( 2019)=100 %

let x represents the cost for 2019, so

the proportion would be

therefore, the cost in January of 2019 is

$ 119.607

I hope this helps you

In order to calculate the total surface area we just need to sum the area of the different faces.

From the picture we see that we have the following faces.

- 2 x A (two triangles)

- S (a rectangle)

- T (a rectangle)

- B (the base rectangle)

Now me calculate the area of each one:

Now that we have the area of each face, we sum all the areas, taking in account the ones that appears twice:

And, because the lenghts are measured in ft, the final answer is:

Note:

Let's begin by identifying key information given to us:

One angle = 128 degrees, Second angle = 62 degrees

Complementary angle are angles that sum up to 90 degrees

Supplementary angles are angles that sum up to 180 degrees

We will proceed to sum these two angles together. We have:

Therefore, these angles are supplementary angles since they sum up to 180 degrees

The line of best fit could be used as a prediction tool showing a trend in the data and the line of best fit should minimize the distance between itself and the data points thus options (C) and (E) will be correct.

The graph is a geometrical representation of a function and can be plotted by taking x's and y's corresponding values within the interval.

For example plot of y = x³ ,y = sinx.

A scatter point represents the relation or function.

If a line is used to predict the function then the distance between the points to the line must be minimized.

The line is useful for the representation of the data point.

Hence "The line of best fit could be used as a prediction tool showing a trend in the data and the line of best fit should minimize the distance between itself and the data points".

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We know that

• Sean runs 6 miles per hour (rate).

• Sean's initial condition is 0.25 miles.

• Darryl runs 0.7 miles per hour faster than Sean (we have to sum).

Sean's expression would be 6x + 0.25.

Darryl's expression would be 6x + 0.7x = 6.7x.

Now, we make them equal

Given:

n = 8, p = 0.4

To find:

P(X ≤ 4)

To determine the given probability, we will apply the binomial probability formula:

3x + 5y ≥ -15 (1)

3x - y > 3 (2)

From (1) let's solve for x:

3x + 5y ≥ -15

Subtract 5y from both sides:

3x ≥ -15 - 5y

Divide both sides by 3:

x ≥ -5 - 5y/3 (3)

Replace (3) into (2)

3(-5 - 5y/3) - y > 3

Using distributive property:

-15 - 5y - y > 3

-15 - 6y > 3

Solving for x:

Add 15 to both sides:

-6y > 18

Divide both sides by -6:

y < -3

Replacing y into (3)

x ≥ 0

3x - y > 3

if x = 4 and y =9

3*4 - 9 >3

12 - 9 > 3

3 > 3

this is false because 3 = 3

Since it is given that the population grows by 5% each year, it follows that the Exponential Growth Function is the appropriate function that can be used to model the problem.

The Exponential Growth Function is given by:

Where

• a is the initial amount.

• r is the percent of increase in decimal.

• t is the time.

• y is the amount after time t.

Since we want when the initial population will triple, substitute y=3a into the equation:

Substitute r=5%=0.05 into the equation:

Solve the resulting equation for t:

The population will triple after about 22.52 years.

6y=3x-127

Replace the values of x , y in the equation by the coordinates values given on each option, and check if the equality remains.

A. (x,y) = (-2,0)

6y=3x-127

6(0) =3(-2)-127

0 = -6-127

0= -133

zero is not equal to -133.

A. is not

B. (0,-2)

6(-2) = 3(0)-127

-12 = -127

B is not

C, (6,-3)

6(-3) = 3(6)-127

-18 = 18-127

-18 = -109

C is not

D (8,2)

6(2) = 3(8)-127

12 = 24-127

12=-103

D is not

None of the points are in the graph

Question:

Solution:

Remember the following definition :

thus, if:

then, according to the given triangles in the problem, the only angle that fulfills this, is:

so that, the correct answer is:

We have the following:

To calculate the proportion, we must calculate the quotient between sugar cookies and chocolate chip cookies, as follows

Which means that for every 3 chocolate chip cookies there are 16 sugar cookies.

Solution:

Given the rectangular prism;

Where;

Thus, the lateral area, L is;

ANSWER:

Also, the single base area, B, is;

ANSWER:

Then, the surface area, S, is;

ANSWER:

Notice that, since we are rolling two dices, we are dealing with 2 independent events

Let's suppose that the numbers on each dice are 1,2,3,4.

Then, if we roll two dices, there are 16 possible pairs (in principle)

(1,1)

(1,2)

...

(1,4)

(2,1)

...

(4,4)

Each of those pairs is equally probably than the others

Know, we need to identify the pairs that add up 3:

(1,2) and (2,1) are the only possibilities

Finally, we obtain the probability:

Which is none of the options.

Another possibility is that the dices are cubes:

So, the possible combinations that can be obtained by throwing 2 cubes are:

(1,1)...(1,6),(2,1),...(6,6) Which are 36 possible combinations

And there are only 2 combinations that add up to 3: (2,1),(1,2)

So, the probability of adding up 3 is:

a. The domain of the function is the set of values of the independent variable (x) on which the function acts, in this case, the independent variable is time, since the time can only take positive values, the domain would be [0,∞) or x≥0.

The range is all the possible values that the dependent variable can take, in this case, the dependent variable is the population of fish, then it can't be a negative number, since you can't have for example -1 fish, then, again, the interval would be [0,∞) or y≥0

A graph of the function looks like this:

b. We can find the y-intercept by making x equals 0 in the formula of the function, like this:

y= 3*(2)^x

y= 3*(2)^0

y= 3*1, since any number raised to zero equals 1

y=3

Since x equals zero represents the initial time, the y-intercept represents the initial population of fish, then at the beginning, there were 3 fish.

c. We just have to replace 1 for x, and then calculate y, like this:

y= 3*(2)^x

y= 3*(2)^1

y= 3*(2)

y=6

At the end of the first week, there will be 6 fish.

d. Now, we just have to replace 4 for x, like this:

y= 3*(2)^4

y= 3*16

y=48

Then, after 4 weeks, there will be 48 fish

EXPLANATION

Given the points (x_1,y_1) = (-9,2) and (x_2,y_2) = (-4,2)

We can apply the distance formula in order to get the distance between them as shown as follows:

Replacing terms:

Adding numbers:

Computing the powers:

Hence, the distance is equal to 5 units.

1. Ratio of 10 feet to 5 yards

A yard is equvalent to 3 feet

So we can say that ratio of 10 feet to 5 yards is the same as ratio of 10 feet to 5x3 feet, which is:

ratio of 10 feet to 15 feet = 10/15

10/15 simplified by dividing both numerator and denominator by 5:

2/3

Answer:

2/3

A parallelogram with two consecutive congruent sides.

1) Since a rhombus is a quadrilateral with 4 congruent sides. Then we can examine the options and state that

2) Given that a rhombus has congruent opposite angles, with four congruent sides.

3) The answer is

A parallelogram with two consecutive congruent sides.

With two consecutive sides, the whole polygon will have congruent sides.