Given that cosine of theta equals 8 over 17 and that θ lies in Quadrant IV, what is the exact value of sin 2θ?

Answer:

$4.35

Step-by-step explanation:

8 weeks = $34.80

1 week = x

Cross-multiply

$34.80/8

=$4.35

So, for each week, Paige will pay $4.35

$(4.35 × 8 = 34.8)

The proportion equivalent with Two-thirds would be 6/9.

Since we know that the proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

We are given that the  proportion with Two-thirds

If you actually divide it’ll make since , so first  we want to divide the 2 , then you want to multiply the third of the two

2/3 x 3/3

6/9

thus, the answer will be 6/9.

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Rounding up to the nearest cent, the present value that must be invested in the CD now is approximately $3333.34.

To calculate the present value required to have $4500 after 5 years with a simple interest rate of 7.0%, you can use the formula for simple interest:

Present Value = Future Value / (1 + (Interest Rate × Time))

In this case:

Future Value = $4500

Interest Rate = 7.0%

= 0.07

Time = 5 years

Substituting these values into the formula:

Present Value = $4500 / (1 + (0.07 × 5))

Present Value = $4500 / (1 + 0.35)

Present Value = $4500 / 1.35

Present Value ≈ $3333.33

You may use the simple interest calculation to get the present value necessary to have $4500 after five years with a simple interest rate of 7.0%:

Future Value / (1 + (Interest Rate Time)) = Present Value

In this instance

$4500 is the future value.

Rate of Interest = 7.0% = 0.07

t = 5 years

Substituting these values into the formula:

$4500 / (1 + (0.07 5)) = Present Value

$4500 / (1 + 0.35) equals the present value.

Present Value = $4500 / 1.35

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The present value that must be invested now in order to have $4500 for a home-entertainment center in 5 years at an interest rate of 7.0% is approximately $3333.33

Using the formula for calculating the future value of a single sum:

Future Value (FV) = Present Value (PV) + (PV * Interest Rate * Time)

We rearrange the formula to solve for the present value (PV):

PV = FV / (1 + Interest Rate * Time)

Plugging in the given values:

FV = $4500

Interest Rate = 7.0% = 0.07

Time = 5 years

PV = $4500 / (1 + 0.07 * 5)

PV = $4500 / (1 + 0.35)

PV = $4500 / 1.35

PV ≈ $3333.33

Therefore, the present value that must be invested now in order to have $4500 for a home-entertainment center in 5 years at an interest rate of 7.0% is approximately $3333.33 (rounded up to the nearest cent).

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Step-by-step explanation:

He,smixing x and y values and averaging them. You add x of one point and add to the x value of the second point. Then divide by 2. Do the same with the y values.

Answer:

Step-by-step explanation:

To calculate your bi-weekly paycheck, follow these steps:

Step 1: Calculate the gross earnings:

Multiply the number of hours worked per week by the hourly rate.

20 hours/week * $9.00/hour = $180.00/week

Step 2: Calculate the total earnings for two weeks:

Multiply the weekly earnings by the number of weeks in a bi-weekly pay period.

$180.00/week * 2 weeks = $360.00

Step 3: Calculate the deductions:

Calculate each deduction separately and subtract them from the gross earnings.

Federal Income Tax: $360.00 * 11.9% = $42.84

State Income Tax: $360.00 * 3.6% = $12.96

F.I.C.A: $360.00 * 7.65% = $27.54

Professional Dues: Amount varies depending on the specific dues.

Total Deductions: $42.84 + $12.96 + $27.54 + Professional Dues

Step 4: Calculate the net earnings:

Subtract the total deductions from the gross earnings.

Net Earnings = Gross Earnings - Total Deductions

Once you have the net earnings, you can determine if it is sufficient to cover your monthly car insurance bill of $200. If your bi-weekly net earnings are greater than or equal to $200, you will be able to pay your car insurance bill.

It is important to note that these calculations are based on the information provided, and actual tax rates and deductions may vary depending on your specific circumstances and location.

Additionally, professional dues may differ depending on your profession. It is recommended to consult with a tax professional or payroll department for precise calculations.

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Using the concept of the word problem and utilizing the provided conditions and values, The answer is 18, 20, and 22.

A word problem in mathematics is a problem or exercise that is expressed in a natural language, rather than in mathematical notation. These types of problems often present a real-world situation that involves mathematical concepts, such as numbers, operations, or measurements. They typically require the use of mathematical reasoning and problem-solving skills to understand the problem and find a solution. Examples of word problems include: "If a train travels 60 miles per hour and you want to know how far it will travel in 4 hours", "If a rectangle is 6 meters long and 4 meters wide, what is its area?", "If a bag contains 3 red balls and 4 blue balls, what is the probability of picking a blue ball?"

In a mathematical problem, the conditions refer to the specific information or constraints provided in the problem statement that must be taken into account in order to find a solution. These conditions can include information about the quantities involved in the problem, the operations that need to be performed, or the specific requirements that the solution must meet.

Let x be the smallest of the three consecutive even integers. Then the next two integers are x+2 and x+4. We know that:

x + (x+4) * 3 = 84

Expanding and solving for x:

x + 3x + 12 = 84

4x = 72

x = 18

So the three consecutive even integers are 18, 20, and 22.

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Answer:

938 adults

268 teenagers

469 children 12 and under

Step-by-step explanation:

1675 x .56 = 938 adults

1675 x .16 = 268 teenagers

1675 x .28 = 469 children 12 and under

Answer:

7 hours

Step-by-step explanation:

here,

270/18=105/x

x=(105*18)/270

x=7

Chau made $270 for 18 hours of work. At the same rate,  Therefore Chau would have to work 7 hours at the same rate to make $105.

To find out how many hours Chau would have to work to make $105 at the same rate, we can set up a proportion using the given information:

Let x be the number of hours Chau needs to work to make $105.

We know that Chau made $270 for 18 hours of work, so the rate of earnings per hour is:

Rate = Total earnings / Number of hours

Rate = $270 / 18 hours

Rate = $15 per hour

Now, we can set up the proportion:

$15 per hour = $105 / x hours

To find x, we can cross-multiply:

$15 × x = $105

Now, solve for x:

x = $105 / $15

x = 7 hours

So, Chau would have to work 7 hours at the same rate to make $105.

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Answer:

a. Yes, the lines are parallel. The rectangles create an optical illusion that makes the lines appear to be crooked.

b. Yes, the lines (3rd and 4th in diagram) are parallel. To show this is true, place two rulers or straightedges along the lines. You’ll then see that they’re parallel.

Step-by-step explanation:

PENN

Answer:

1.

a. 12° + 68° = 80 neither

b. 95°+ 85° = 180°  Supplementary angles

c.  43° + 48° = 91° neither

d.  70°+ 20° = 90°  Complimentary angles

2.

angle a = 140

angle b = 105

angle c = 60

3.

a. ∠1 = ∠AEB

b. ∠2 = ∠BEC

c. ∠3 = ∠CED

d. ∠4 = ∠DEA

4.

a. right

b. straight

c. obtuse

d. acute

5.

a. adjacent

b. adjacent

c. vertical

d. vertical

6.

a. perpendicular

b. parallel

c. neither

d. perpendicular

7.

a. Yes

b. Yes

Step-by-step explanation:

Answer:

\(\boxed {\boxed {\sf 682}}\)

Step-by-step explanation:

The nth term of an arithmetic sequence can be found using the following formula.

\(a_n=a+d(n-1)\)

where a is the first term, d is the common difference, and n is the term.

First, we should find the common difference.

We can do this by subtracting each term from the term following it. Basically, subtract the first term from the second term, the second from the third, and so on.

\(d= a_2-a_1\)

The second term is 25 and the first is 16.

\(d= 25-16\)

\(d=9\)

Now we know the common difference is 9. We also know the first term is 16 and we are looking for the 75th term.

\(d=9 \\a=16 \\n= 75\)

Substitute the values into the formula.

\(a_{75}=16+9(75-1)\)

Solve according the PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction).

Solve the parentheses first.

\(a_{75}=16+9(74)\)

Multiply next.

\(a_{75}=16+666\)

Finally, add.

\(a_{75}=682\)

The 75th term in the sequence is 682.

Answer:

To find the percent of 125 that 375 is, we need to divide 375 by 125 and then multiply by 100.

375 / 125 = 3

So 375 is 3 times 125. Multiplying 3 by 100, we get:

3 * 100 = 300%

So the correct answer is C) 300%.

Succes!

Answer:

C) 300%

Step-by-step explanation:

Percent of 125 means the value of x/125.

Where x is the value 375.

375/125 = 3

3 * 1 =

3 * 100% = 300%

It can be mistaken as 33.33% since 125 is 33.33% of 375.

^^ This question is asking 125 is what percent of 375.

But remember, the question, 'What percent of 125 is 375?', is asking 375 is what percent of 125, not the other way around.

The calculated  of the integral expression \(\int\limits^3_1 {xf''(x)dx\) is 4

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

Also, we have

\(\int\limits^3_1 {xf''(x)dx\)

This means that we integrate the above expression twice

The first integration gives

\(\int\limits^3_1 {xf''(x)dx} = xf'(x)\right]^3_1 - \int^3_1 f'(x)dx\)

Next, we have

\(\int\limits^3_1 {xf''(x)dx} = xf'(x)\right]^3_1 - \left[f(x)\right]^3_1\)

When the equation is expanded, we have

\(\int\limits^3_1 {xf''(x)dx} = 3f'(3) - f(3) - (f'(1) - f(1))\)

Recall that f(1) = 8 and f(3) = −4 ;  '(1) = 5, and f '(3) = 1

When these values are substituted in the above equation, we have the following:

\(\int\limits^3_1 {xf''(x)dx} = 3(1) - (-4) - (5 - 8)\)

Evaluate the expressions in bracket

\(\int\limits^3_1 {xf''(x)dx} = 3 + 4 - 3\)

So, we have

\(\int\limits^3_1 {xf''(x)dx} = 4\)

Hence, the value of the derivative is 4

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Answer:

10

Step-by-step explanation:

\(\displaystyle \int^3_1xf''(x)\;\text{d}x\)

To evaluate the given definite integral, use integration by parts.

\(\boxed{\begin{minipage}{4.6 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}\)

Begin by working out which part should be u and which part should be dv/dx. As it is easier to differentiate x, and integrate f''(x), then:

\(\textsf{Let}\;u=x\)

\(\textsf{Let}\;\dfrac{\text{d}v}{\text{d}x}=f''(x)\)

Differentiate u with respect to x:

\(\dfrac{\text{d}u}{\text{d}x}=1\)

Integrate dv/dx to find v:

\(\displaystyle v=\int_a^b f''(x)\; \text{d}x=\left[\vphantom{\dfrac12}f'(x)\right]^b_a\)

Substitute the values into the integration by parts formula and evaluate the definite integral:

\(\begin{aligned}\displaystyle \int^3_1 x f''(x)\:\text{d}x &=\left[\vphantom{\dfrac12}xf'(x)\right]^3_1-\int^3_1 f'(x)\:\text{d}x\\\\&=\left[\vphantom{\dfrac12}xf'(x)\right]^3_1-\left[\vphantom{\dfrac12}f(x)\right]^3_1\\\\&=\left(3\cdot f'(3)-1\cdot f'(1)\right)-\left(f(3)-f(1)\right)\\\\&=3f'(3)-f'(1)-f(3)+f(1)\end{aligned}\)

Substitute the given values of f(1) = 8, f(3) = -4, f'(1) = 5 and f'(3) = 1:

                      \(\begin{aligned}&=3f'(3)-f'(1)-f(3)+f(1)\\\\&=3\cdot 1-5-(-4)+8\\\\&=3-5+4+8\\\\&=10\end{aligned}\)

Therefore, the evaluation of the given integral is 10.

Answer: The two lines intersect at (-4,3)

Step-by-step explanation:

So our first step would be to turn both of these into standard slope-intercept form.

1.)

4y + 3x = 0

4y = -3x

y = -3/4x

2.)

4y - x = 16

4y = x + 16

y = 1/4x + 4

Now that we have our 2 equations, y = -3/4x and y = 1/4x + 4 we can graph them to get an intersection at (-4,3)

Answer:

The photo is not clear post a clear photo then i will see that

Answer:

per = 28 units

area 32 sq units

Step-by-step explanation:

Answer:

No, a, h, and k behave differently in the square root function than they did in the quadratic function and/or cubic functions from the previous course. There is no variable (a) in front of the square root word in the square root function, and the shifts of the function are represented by h and k, respectively. Unlike in quadratic or cubic functions, where h stands for the vertex's horizontal shift and k for its vertical shift. The square root function's scope and range also vary from those of cubic and quadratic functions.

Answer:

P=0.11

Step-by-step explanation:

Answer:

\(\boxed{\sf x\le \cfrac{15}{2}}\)

\(\boxed{\sf x\le \:7.5}\)

Step-by-step explanation:

\(\sf 6x-18\le \:27\)

Add 18 to both sides.

\(\sf 6x\le \:45\)

Divide  both sides by 6:-

\(\sf \cfrac{6x}{6}\le \cfrac{45}{6}\)

\(\sf x\le \cfrac{15}{2}\)

or

\(\sf x\le \:7.5\)

__________________

-Hope this helps!

15+2.5x <55

1.15

Answer:

1.6

Step-by-step explanation:

35/22 = 1.59

round the decimal to the tens place, or the number right after the decimal

The amount of water that is needed to be added to the 12% concentration solution to make it 11% concentrated is 2 ml.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given that the alcohol solution of 22 ml has a 12% of concentration. Therefore, the amount of alcohol in the solution is,

12% of 22ml = 2.64ml

Since the amount of alcohol should be the same while the concentration should be diluted, therefore, the amount of alcohol in the final solution can be written as,

\(11\%\ of\ x = 2.64{\rm\ ml}\\\\\dfrac{11}{100} \times x = 2.64\\\\x = 24\rm\ ml\)

As the total solution with 12% concentration was 22 ml, while the total solution with 11% concentration was 24 ml.

Hence, the amount of water that is needed to be added to the 12% concentration solution to make it 11% concentrated is 2 ml.

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Answer:

B. 16.5

Step-by-step explanation:

Here we can use the opposite and the adjacent from the angle with measurement 20, or tan.

tan theta = opposite / adjacent

Substitute values.

tan 20 = 6 / x

Multiply by x.

x * tan 20 = 6

Divide by tan 20.

x = 6 / tan 20

Evaluate tan 20.

x = 6 / 0.36397023

Divide.

x = 16.48486451

Rounded to the nearest tenth, that makes your answer

B, 16.5

Answer:

D

Step-by-step explanation:

D is already in the factored form which shows that 9 and -1 are zeros of the function

The function represented by the zeroes is f ( x ) = 4 ( x - 9 ) ( x + 1 )

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given data ,

Let the function be represented as A

Now , the value of A is

f ( x ) = 4 ( x - 9 ) ( x + 1 )

Now , the zeroes of the function is given by

when f ( x ) = 0

( x - 9 ) ( x + 1 ) = 0

So , x = 9 and x = -1

Hence , the function is f ( x ) = 4 ( x - 9 ) ( x + 1 )

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Answer:

\(Company: 43 + 24.75h\)

Step-by-step explanation:

Given

Hamda:

\(Project\ Fee = 25\)

\(Hourly\ Rate = 10.50\)

Layla:

\(Project\ Fee = 18\)

\(Hourly\ Rate = 14.25\)

Required

Derive an expression for total pay

Represent the number of hours with h.

For Hamda and Layla, their pay for h hours is:

\(Pay = Project\ Fee + Hourly\ Rate * h\)

For Hamda, we have:

\(Hamda : 25 + 10.50 * h\)

\(Hamda : 25 + 10.50 h\)

For Layla, we have:

\(Layla: 18 + 14.25 * h\)

\(Layla: 18 + 14.25 h\)

For h hours, the company will pay:

\(Company: Hamda + Layla\)

\(Company: 25 + 10.50h + 18 + 14.25h\)

Collect like terms

\(Company: 25 + 18 + 10.50h + 14.25h\)

\(Company: 43 + 24.75h\)

Answer:

2 days

Step-by-step explanation:

Understanding :

Solving :

Answer:

No

Step-by-step explanation:

The line y=2x+3 has a slope of 2 and a y intercept of (0,3). Plugging in x=1, we get y=2(1)+3=5, meaning that when x=1 the line is at (1,5). Since the line cannot be at (1,5) and (1,4) at the same time, (1,4) is not on the line.

Answers:

=====================================================

Explanation:

A conditional statement is of the form "if..., then..."

For example, "If it rains, then the grass gets wet" is a conditional statement.

We can have a basic template of "If P, then Q" to represent any conditional. The P and Q are placeholders for logical statements.

The converse of that conditional is "If Q, then P". We swap P and Q.

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

So let's say we had this original conditional:

The converse would be:

Similar ideas apply for the other converses as well.

Answer:

If alternate interior angles are congruent, then lines are parallel.

If alternate exterior angles are congruent, then lines are parallel.

If corresponding angles are congruent, then lines are parallel.

If consecutive interior angles are supplementary, then lines are parallel.

If consecutive interior angles are supplementary, then lines are parallel.

Step-by-step explanation:

Converse

The converse of a statement is formed by switching the hypothesis and the conclusion.

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

Given statement:  If lines are parallel, then alternate interior angles are congruent.

Converse statement:  If alternate interior angles are congruent, then lines are parallel.

Given statement:  If lines are parallel, then alternate exterior angles are congruent.

Converse statement:  If alternate exterior angles are congruent, then lines are parallel.

Given statement:  If lines are parallel, then corresponding angles are congruent.

Converse statement:  If corresponding angles are congruent, then lines are parallel.

Given statement:  If lines are parallel, then consecutive interior angles are supplementary.

Converse statement:  If consecutive interior angles are supplementary, then lines are parallel.

Given statement:  If lines are parallel, then consecutive exterior angles are supplementary.

Converse statement:  If consecutive exterior angles are supplementary, then lines are parallel.

The given function y = 4(3/8)^x represents exponential decay.

As x increases, the value of y decreases at an increasingly rapid rate, reflecting the decay behavior of the function.

The given function is y = 4(3/8)^x. To determine if the function represents growth, decay, or neither, we need to examine the base of the exponent, which is (3/8).

When the base of an exponential function is between 0 and 1, such as (3/8) in this case, it represents exponential decay. This is because as the exponent (x) increases, the value of the function decreases.

In the given function, the coefficient 4 multiplied by the decaying exponential term (3/8)^x indicates that the function starts with an initial value of 4 and then exponentially decreases. The term (3/8)^x represents the decay factor, where x determines the extent of decay.

Therefore, we can conclude that the given function, y = 4(3/8)^x, represents exponential decay. As x increases, the value of y decreases at an increasingly rapid rate, reflecting the decay behavior of the function.

In summary, the given function y = 4(3/8)^x represents exponential decay.

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