using trig to find sides

Answer:

  (c)  five raised to the fourth power divided by three raised to the tenth power

Step-by-step explanation:

You want the simplified version of the quantity five raised to the negative second power times three raised to the fifth power end quantity all raised to the negative second power.

The relevant rules of exponents are ...

  (ab)^c = (a^c)(b^c)

  a^-b = 1/a^b

  (a^b)^c = a^(bc)

The given expression can be simplified as follows:

  [tex](5^{-2}3^5)^{-2}=5^{(-2)(-2)}3^{(5)(-2)}=5^43^{-10}=\boxed{\dfrac{5^4}{3^{10}}}[/tex]

__

Additional comment

We find math expressions easier to understand when they are written using math notation, instead of words.

Answer:

A

Step-by-step explanation:

y =  35 + 15x

A

:]

the volume of a cilinder is:

So we can replace the radius and the high so:

Now we can replace pi by 3.14 so:

Answer:

Choice A. 0.7

Explanation:

The place value of the numbers is given below

T

The most appropriate choice for population and sample will be given by-

Second option is correct

44% is the percentage of non response

What is population and sample?

Population is the entire set of items from where the data is drawn for statistical study

A random selection of members of the population is known as sample.

Here

Number of business chosen at random = 50

Number of questionnaire returned by mail = 28

Number of non responses = 50 - 28

                                            = 22

Since the committee plans to survey local businesses about the importance of students as customers, the population is all about local business.

Since the specific group from the population are 50 local businesses chosen by the committee, sample is the 50 to whom the questionnaire was sent

Percentage of non response = [tex]\frac{22}{50} \times 100[/tex]

                                                = [tex]44[/tex] %

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Complete Question

A committee on community relations in a college town plans to survey local businesses about the importance of students as customers. From telephone book listings, the committee chooses 50 businesses at random. Of these, 28 return the questionnaire mailed by the committee.

Identify the population and the sample for this study.

a)The population is all students in the college town and the sample is the 50 local businesses to whom the questionnaire was sent.

b)The population is all local businesses and the sample is the 50 to whom the questionnaire was sent.

c) The population is the 28 businesses who responded to the questionnaire and the sample is all local businesses.

d)The population is the 50 local businesses to whom the questionnaire was sent and the sample is the 28 who responded.

What is the rate (percent) of nonresponse?

(Use decimal notation. Give your answer as an exact number.)

Formula for arc length when the angle is in degrees:

r = radius = 6 in

θ= 60 degrees

We are asked to find the equation of a circle on the xy-plane, with center (3/4 , 1/2) and a radius of 3/5 units. For doing so, we remember the general equation of a circle

Where (h,k) represents the center of the circunference, and r its radius.

In our example, we obtain that,

And so,

Applying the above formula, we get that the equation of the circle will be:

This is:

SOLUTION:

Case: Spreadsheet calculations

Method:

Some common signs

'+' does sum

'-' does difference

'*' does the product

'/' does division

Hence

C7-B6 does the difference for cells C7 and B6

Final answer: Option (D)

C7-B6

An isosceles triangle is a triangle which has two of its sides with the same length

The functions and its domain are a representation of their dependance on one another.

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). In the given question, we have two functions and we are required to find the composite of which ever form of the functions as well as the domain of the said function.

[tex]f(x) = \frac{3}{x}, g(x) = 2x + 8;\\(f.g)(x) = \frac{3}{2x + 8}[/tex]

The domain of the function is given as

[tex]domain = (-\infty , -4) U (-4, \infty)\\[/tex]

In the second composition of the function,

[tex](g.f) = \frac{6}{x} + 8\\domain = (-\infty, 0) U (0, \infty)[/tex]

The third composition of function

[tex](f.f) = x\\domain = (-\infty, \infty)[/tex]

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The property use to solve the equation is as follows:

The equation can be solved as follows:

−2a = 10 − 3(2a + 6)

Using distributive property,

−2a = 10 − 3(2a + 6)

- 2a = 10 - 6a - 18

According to distributive law, multiplying the sum of two or more addends by a number produces the same result as when each addend is multiplied individually by the number and the products are added together.

Combine like terms

- 2a = 10 - 6a - 18

- 2a = -6a - 8

Using additive property of equality, we will add 6a to both sides of the equation.

The additive property of equality states that if we add or subtract the same number to both sides of an equation, the sides remain equal.

- 2a = -6a - 8

- 2a + 6a = -6a + 6a - 8

4a = - 8

using division property of equality, we will divide both sides of the equation by 4.

The division property of equality states that if both sides of an equation are divided by a common real number that is not equal to 0, the quotients remain equal.

4a = - 8

4a / 4 = -8 / 4

a = - 2

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Step 1

Given;

Step 2

Match each of the following expressions to its meaning in the context of this situation.



Answer: 7

Step-by-step explanation:

1) Set up an equation. Let x be the number of hours he works.

[tex]400\leq 64x[/tex]

2) Solve the equation

(<= mean less or equal to)

400/64 <= x

6.25 <= x

3) Solve the problem

We need to round up 6.25 as 6.25 is not on the list. Since the number has to be greater than 6.25, the next option is 7.

The sum of exterior angles of a regular polygon is 360 degree.

Determine the measure of last exterior angle of a regular pentagon.

So measure of last angle of a regular pentagon is 88 degree.

Please, give me some minutes to take over your question

_________________________________

I'm working on it

__________________________

a probability model has some features

Events (This part is ok, the probabilities are between 0 - 1 )

1) p1 = 0.2

2) p2 = 0.5

3) p3 = 0.1

____________________

The sample space is not 1 because p1+p2+p3 = 0.8

______________________________________

Answer

FALSE. No, this is not a valid probability model

In order to find the value of x, we need to remember that the sum of the interior angles of a triangle is 180°

the equation to find x is

we need to isolate the x

the answer is c x=90°

Answer:

Graphing the points we have;

Above is the graph of the given equation showing the derived points.

Explanation:

Given the equation;

To plot the graph we need to calculate the corresponding values of x and y at each point.

Let us calculate the values of y for x = -4,-2,0,2, and 4;

Therefore, Graphing the points we have;

Above is the graph of the given equation showing the derived points.

Mathematical objects other than numbers can be used in operations. Here, t can be expressed as  [tex]\frac{Q-M}{r}[/tex].

Binary and unary operations are the two most popular forms of operations. Trigonometric functions and negation are examples of unary operations that use only one value. Contrarily, binary operations, which include addition, subtraction, multiplication, division, and exponentiation, only accept two values.

Mathematical objects other than numbers can be used in operations. Logic operations like and, or, and not can be used to combine the logical values true and false. It is possible to add and subtract vectors. Utilizing the function composition operation, it is possible to combine rotations by first performing the first rotation and then the second. The binary operations union and intersection as well as the unary operation of complementation are operations on sets. Composition and convolution are two operations on functions.

Solving for t,

Q = M + Mrt

t = [tex]\frac{Q-M}{r}[/tex]

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So , the percentage of time spent on messenger work by the clerk during the week was most nearly is 16%.

From the Latin word "per centum," which meaning "by the hundred," the word "percentage" was borrowed. The denominator of percent's is 100, making them fractions. In other words, it is the relationship between a component and a whole in which the value of the entire is consistently set to 100. The value of the entire is always 100 in a percentage, which is a ratio or fraction. Sam, for instance, would have received a score of 30 out of 100 on his arithmetic test if he received a 30%. When expressed as a ratio, it is written as 030:10 and as a fraction, 30/100. An quantity or part that is contained in each hundred is known as a percentage. The symbol "%" signifies that it is a fraction with 100 as the denominator.

35 h * 1 / 5 = 7 h

35 h * 1 / 2 = 17.5 h

35 h * 1 / 7 = 5 h

7 h + 17.5 h + 5 h

= 29.5 h

The rest of his time = 35 - 29.5

= 5.5 h

5.5 / 35 = 0.15714

= 15 .714 %

Approx. 16 %

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Answer:

we can now graph the function as;

Explanation:

Given the equation;

Firstly, to derive the period, Amphitude and midline, let us compare to the general form;

From the given equation;

With the above characteristics we can now graph the function as;

Given:Three dice are tossed.

To find: Probability of rolling 3 different numbers.

Let E be the event of getting same number on three dice.

So,the favorable cases for E will be

(1,1,1) , (2,2,2) , (3,3,3), (4,4,4), (5,5,5) , (6,6,6).

So, the number of favorable cases=6

Now,the total number of cases for E will be

Since each dice has 6 numbers so three dice will have these number of cases.

Now, the probability to have a same number on 3 dice will be

Now, probability of rolling 3 different numbers is

Hence, the probability of rolling three different numbers is

We are given a function and we are asked the following questions:

Part 1. Evaluate G(-1). The value of G(-1) is the value of the independent variable, that is the vertical axis when the dependent variable is -1, that is the horizontal axis. To find the value we draw a vertical line perpendicular to the horizontal at the value -1, until we intercept the graph, from there we draw a vertical line until we intercept the vertical axis. From the graph we see that:

Part 2. Evaluate G(2). This is the value of the independent variable when the dependent variable is 2. From the graph we see:

Part 3. Determine:

Replacing the known values:

Solving the operations:

Given:

KM=12 cm.

KO=1+KL

Since KM=12 cm, we can write

Therefore, KL can be calculated as,

Now, KO can be calculated as,

Now, using geometric property,

Putting the values in the above equation, KN can be calculated as,

Now, ON can be calculated as,

Since LM=9 is a chord longer than MN in the given circle, the length of MN is less than 9.

Therefore, the segments with length 9 are LM and KN.

Using system of equations:

Length of each Plan A workout is: 0.5 hour

Length of each Plan B workout is: 1.25 hours

The number of hours that each of the workout plans last can be represented as a system of linear equations. The explanation below shows how to solve this problem using the elimination method.

Let,

x = number of hours for each plan A workout.

y = number of hours for each plan B workout.

Create the system of equations below:

Equation for Friday would be:

3x + 2y = 4 --> equation 1

Equation for Saturday would be:

8x + 4y = 9 --> equation 2

Multiply equation 1 by 4 and equation 2 by 2:

12x + 8y = 16 --> eqn. 3

16x + 8y = 18 --> eqn. 4

Substract eqn. 4 from eqn. 3:

-4x = -2

x = 1/2 = 0.5 [0.5 hours or 1/2 an hour for Plan A]

Substitute x = 0.5 into eqn.1:

3(0.5) + 2y = 4

1.5 + 2y = 4

2y = 4 - 1.5

2y = 2.5

y = 2.5/2

y = 1.25 [1.25 hours for Plan B]

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If the two line segments are parallel to each other, we can establish the following proportion and reach the result.

Therefore, our answer is [tex]p=13[/tex].

Answer: t =  4

Isolating a variable: rearranging an equation so that the variable is on its own

Calculations:

[tex]\frac{\frac{t}{4} }{16} = \frac{1}{16}[/tex]

[tex]\frac{t}{4}= 16/16[/tex]   - calculated by multiplying 1/16 by 16

[tex]t= 16/16[/tex] × [tex]4[/tex]  

[tex]t= \frac{64}{16}[/tex]

[tex]t=4[/tex] - simplified answer

The values of the function given by the graph are:

f(-2 ) = 2

f(0) = 3

f(4) = -1

Furthermore, the function terminates at x=0.

(Because there is a gap in the graph and the function's left and right-hand limits are not equal at x=0)

So from the graph, we can determine the values of the functions as,

f(-2 ) =2

f(0) = 3

f(4) = -1

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Answer:

f(–2 ) = 2

f(0) = 3

f(4) = -1

Step-by-step explanation: i hope this helps :)

Answer:

The side length, s, of the square is 18

Step-by-step explanation:

The sides can be found by taking the square root of the area.

(Area)^1/2=s, where s = side.

(324)^1/2=18