Mary works as a tutor for $12 an hour and a waitress for $15 an hour. This month she worked a combined total of 91 hours at her two jobs let t be the number of hours Mary worked as a tutor this month write an expression for the combined total dollar amount she earned this month

The value of Sin2t is 1/4 and cos2t is (15/16)^1/2  and tan2t is 1/(15)^1/2.

According to the statement

we have given that the sint=1/8 then we have to find the exact value of

sin(2t) , cos(2t) , and tan(2t).

Here the value of Sint = 18

then sin2t becomes

sin2t = 2*1/8 then

sin2t = 1/4.

And

(Cos2t)^2 = 1 - (Sin2t)^2

(Cos2t)^2 = 1 - 1/16

(Cos2t)^2 = (16 - 1)/16

(Cos2t)^2 = 15/16

(Cos2t) = (15/16)^1/2

then

tan2t = sin2t/cos2t

tan2t = (1/4)/(15)^1/2 / 4

tan2t = 1/(15)^1/2

these are the values of given terms.

So, The value of Sin2t is 1/4 and cos2t is (15/16)^1/2  and tan2t is 1/(15)^1/2.

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The sum of the pulses allows us to find that the answer for the sum at a point x is

If the waves travel in the same direction, their sum gives resulting waves that can be maximum or minimum depending on the phase between them, un stationary patterns.

If the directions are coincident directions, they add place to the interference processes, in this case, stationary patterns are formed on a screen.

If the waves travel in the opposite direction the sum of the two waves gives rise to a wave that maximum is the sum of the amplitudes of the two pulses

In the case of a pulse that corresponds to a single wavelength, the result is an instantaneous maximum,  which after the pulse passes, returns to zero.

Consequently, there is no stationary pattern, so there is no interference between the two pulses.

In conclusion with the sum of the pulses, we can find that the answer is No interference pattern is produced as the amplitude does not remain constant.

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Answer:

153

Step-by-step explanation:

i = square root of -1

i = √-1

(3+12√-1) (3-12√-1)

√a times √b = √ab

a√b times c√d = (a times c) √ (b times d)

9 - (36√-1) + (36√-1) - (144(√-1)^2) =

9 - 0 - (144 * -1) =

9 - 0 - (-144) =

9 - (-144) =

9 + 144 =

153

*** funny thing is if you put

(3+12i) (3-12i)  

in a calculator

it works!

it gives you the answer 153

another way:

Expand the expression using

(a-b) (a+b) =

a²-b² :

3²-(12i)²

Simplify using exponent rule with same exponent

(a*b)^n =

a^n*b^n:

3²-12²* i²

Calculate the power:

9-144* i²

Rewrite by definition

i²=-1:

9–144×(−1)

Calculate the product or quotient: 9+144

Calculate the sum or difference: 153

Answer: 153

gathmath

The answers to the questions are:

1. x = 4

2.  x = 1.5

3. x = 1.875

4. x = 1

1. 4x + 3 = 19

4x = 19 - 3

4x = 16

divide by 4

x = 4

(4/3)x + 5 = 17

= 1.33x + 5 = 7

Take like terms

1.33x = 7-5

1.33x = 2

divide through by 1.33x to get 2

x = 2/1.33

x = 1.5

4x(6 - 2) - 10 = 20

Multiply and open the bracket

24x - 8x - 10 = 20

Take like terms

16x = 20+10

16x = 30

x = 30/16

= 1.875

4.3x + 0.7 = 5

4.3x = 5 - 0.7

4.3x = 4.3

x = 1

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Answer:

2x - 3

Step-by-step explanation:

10x²-23x+ 12 ÷ 5x-4

Answer:

2x - 3

Step-by-step explanation:

[tex](5x-4)(2x-3)=10x^{2} -23x+12[/tex]

Hope this helps

Evaluating the given expressions and inequalities, we have;

[tex]11) \: \frac{x}{4} \cdot \left(2 + y - x \right) = 4[/tex]

12) (8•a - 5•b) - 2•(a + b) = 4

[tex] 13) \: \frac{p \cdot (p + {a}^{2} )}{6} = 55 [/tex]

[tex] 14) \: 3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} = 12 [/tex]

[tex] 16) \: x \geq 11\frac{2}{3} [/tex]

17) k > 9

18) v > 9

20) m ≤ 16

The given expressions are;

[tex]11) \: \frac{x}{4} \cdot \left(2 + y - x \right)[/tex]

Where x = 4, and y = 6, we have;

[tex]\frac{x}{4} \cdot \left(2 + y - x \right) = \frac{4}{4} \cdot \left(2 + 6 - 4 \right) = 4[/tex]

Therefore;

[tex]\frac{x}{4} \cdot \left(2 + y - x \right) = 4[/tex]

12) (8•a - 5•b) - 2•(a + b)

Where a = 3 and b = 2, we have;

(8•a - 5•b) - 2•(a + b) = (8×3 - 5×2) - 2•(3 + 2) = 4

Therefore;

[tex]13) \: \mathbf{\frac{p \cdot (p + {a}^{2} )}{6}} [/tex]

Where a = 7, and p = 6, we have;

[tex] \frac{p \cdot (p + {a}^{2} )}{6} = \mathbf{ \frac{6 \times (6 + {7}^{2} )}{6}} = 55 [/tex]

Therefore;

[tex] \frac{p \cdot (p + {a}^{2} )}{6} = 55 [/tex]

[tex]14) \: \mathbf{3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} } [/tex]

Where m = 5, and n = 6, we have;

[tex] 3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} = \mathbf{3\times 5 - \frac{2\times 5}{2} +\frac{6}{3} }= 12 [/tex]

Therefore;

[tex] 3\cdot m - \frac{2\cdot m}{2} +\frac{n}{3} = 12 [/tex]

[tex]16) \: \mathbf{1 \frac{1}{6} }\leq \frac{x}{10} [/tex]

Which gives;

[tex] \frac{7}{6} \times 10 \leq x [/tex]

[tex] \mathbf{ \frac{35}{3} }\leq x [/tex]

[tex] x \geq 11\frac{2}{3} [/tex]

17) 20 < k + 11

Therefore;

k > 20 - 11 = 9

18) 6•v > 54

v > 54 ÷ 6 = 9

Therefore;

[tex]20) \: 8 \geq \mathbf{ \frac{m}{2}} [/tex]

Therefore;

2 × 8 = 16 ≥ m

Which gives;

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This enables us to conclude that Sarita's solution is accurate, but her verification was flawed. ( 5 - 3 [tex]\neq[/tex] 2 ).

What is linear equation?

When the greatest power of the variable is consistently 1, an equation is considered to be linear. A one-degree equation is another name for it.

Given the following equation:

5(x-3) + 7(x+4) = 73

The steps to solve it are:

Apply the Distributive property:

5x - 15 + 7x + 28 = 73

12x + 13 = 73

Subtract 13 from both side

12x + 13 - 13 = 73 -13

12x = 60

Divide both side by 12

12x/12 = 60/12

x = 5.

To verify it, put the x = 5 in to the equation:

5(5 - 3) + 7(5 + 4) = 73

After solving it, we get

5(2) + 7(9)  = 73

10 + 63 = 73

73 = 73  

This enables us to conclude that Sarita's solution is accurate, but her verification was flawed. ( 5 - 3 [tex]\neq[/tex] 2 ).

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5 minutes per bracelet.

because 15/3 = 5 mins.

To find the constant of proportionality in minutes per bracelet, divide the total time by the number of bracelets:

constant of proportionality =15/3= 5 minutes.

Now, we're going to consider an example of a proportional relationship in our everyday life: When we put gas in our car, there is a relationship between the number of gallons of fuel that we put in the tank and the amount of money we will have to pay. In other words, the more gas we put in, the more money we'll pay.

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Answer:

The answer to your question is P=56

Step-by-step explanation:

P=7a=7·8=56

I hope this helps and have a good day!

The equation of the parallel line is y = -5x - 1

The equation is given as:

5x + y = 4

Make y the subject

y = -5x + 4

The slope of the above equation is

m = -5

Parallel lines have equal slope.

This means that the slope of the new line is 5

The equation is then calculated as:

y = m(x - x1) + y1

So, we have:

y = -5(x + 1) + 4

Expand

y = -5x - 5 + 4

Evaluate

y = -5x - 1

Hence, the equation of the parallel line is y = -5x - 1

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Using the monthly payment formula, it is found that her down payment should be of $1,419.

It is given by:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which:

For this problem, the parameters are:

A = 250, r = 0.072, n = 72.

Hence:

r/12 = 0.072/12 = 0.006.

We solve for P to find the total amount of the monthly payments, hence:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]P\frac{0.006(1.006)^{72}}{(1.006)^{72}-1} = 250[/tex]

0.0171452057P = 250

P = 250/0.0171452057

P = $14,581.

The total payment is of $16,000, hence her down payment should be of:

16000 - 14581 = $1,419.

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Answer:

Step-by-step explanation:

I would use the law of sins.

13/sin90 = 5/sin s

sin s  = (5 sin 90)/13

sin s = .3846.  

Now put in your calculator sin-1 .3846 and you will get the angle of 22.6 degrees rounded to the tenths place.

Answer:

22.6 = 113/5

Step-by-step explanation:

Answer:

y = 120

x = 10.6

Step-by-step explanation:

Given polygons are parallelograms.

In parallelograms, consecutive angles are supplementary which means their sum is equal to 180.

Since two parallelograms are similar:

60 + y = 180 subtract 60 from both sides

y = 120

To find the value of x:

side lengths are proportional because these are similar polygons

[tex]\frac{x+4}{22} = \frac{12}{18}[/tex] cross multiply fractions

18x + 72 = 264 subtract 72 from both sides

18x = 192 divide both sides by 18

x = 10.6 approximately

The widgets should be sold for $22.08 for the company to make the maximum profit.

To maximize a function, y = f(x), we differentiate it with respect to x, to get y' = f'(x). Equate it to zero to get the points on inflections.

Differentiate y' = f'(x) again with respect to x, to get y'' = f''(x), and put in the points of inflections to check whether y'' is greater than or less than zero. If it is greater than zero, then we have a minimum, and if it is less than zero, then we have a maximum.

In the question, we are given a profit function y, with respect to the sale price of each widget x. We are asked to find the sale price that maximizes the profit.

The function given is:

y = -30x² + 1325x - 8569.

Differentiating this with respect to x, we get:

y' = -60x + 1325.

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

0 = -60x+ 1325,

or, x = 1325/60 = 22.0833

Now, we differentiate, y' = -60x + 1325, with respect to x, to get:

y'' = -60 < 0, thus we have a maximum at x = 22.0833.

Thus, the widgets should be sold for $22.08 for the company to make the maximum profit.

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Step-by-step explanation:

The answer is 8 2 / 5 because ...

[tex]8 \frac{2}{5} = \frac{8 \times 5 + 2}{5} = \frac{42}{5} \\ [/tex]

Answer:

Here your ans and dont forget to say dhanwyad ok.

El número decimal que no es un decimal periódico es dado por:

B. [tex]\frac{11}{400}[/tex].

Un decimal periódico es un número decimal en el que la misma secuencia de dígitos se repite indefinidamente.

La conversión de las fracciones para decimales són:

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The map scale to use would be: 1 in. = 5 miles.

The scale of a map relates the actual distance of two places to the distance on paper on a scale drawing. It is a ratio between length on the map and distance in real life.

Given that, 6 inches would equal actual distance of 30 miles, let x be the actual distance on ground. We would have:

6/30 = 1/x

Solve for x

x = (30 × 1)/6

x = 5.

Therefore, the scale of the map is: 1 in = 5 miles.

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The derivative of the natural logarithm function is given by:

[tex]f^{\prime\prime}(x) = \cotg{x}[/tex]

Suppose we have a composite natural logarithm function given as follows:

[tex]f(x) = \ln{g(x)}[/tex]

The derivative of the function is given as follows:

[tex]f^{\prime}(x) = \frac{g^{\prime}(x)}{g(x)}[/tex]

In this problem, the function, which is already a first derivative, it given by:

[tex]f^{\prime}(x) = \ln{|\sin{x}|} + 3[/tex]

The derivative of a constant is of zero, and the derivative of sin(x) is cos(x), hence the derivative of the entire function is given as follows:

[tex]f^{\prime\prime}(x) = \frac{\cos{x}}{\sin{x}} = \cotg{x}[/tex]

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Using it's concept, there is a 0.0308 = 3.08% probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen. Since the letter is not replaced, the number of outcomes change, hence they are dependent.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

For the first ticket, since 5 out of 26 letters are vogal, the probability is:

5/26.

For the second ticket, since there is no replacement, the probability is:

4/25.

The probability of both tickets is:

[tex]p = \frac{5}{26} \times \frac{4}{25} = 0.0308[/tex]

0.0308 = 3.08% probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen. Since the letter is not replaced, the number of outcomes change, hence they are dependent.

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The functions f(x) = -4x + 11 and f(x) = 2/3x - 8 are having the range of {y ∈ R | -∞ < y < ∞}.

Step 1: Finding the range for the function f(x) = -(x + 1)² - 4

The given function is quadratic in the form of a(x - h)² + k,

So, the range of the function is y ≤ k if a < 0 or y ≥ k if a > 0

For the given function, a = -1 so, a < 0. thus, the range of the given function is y ≤ k, where k = -4

∴ Range of f(x) = -(x + 1)² - 4 is: (-∞ -4], {y | y ≤ -4}

Step 2: Finding the range for the function f(x) = -4x + 11

This is a linear function. So, the range is R.

∴ Range of f(x) = -4x + 11: (-∞, ∞), { y | y ∈ R}

Step 3: Finding the range for the function f(x) = 2/3x - 8

This is also a linear function. So, the range is R.

∴ Range of f(x) = 2/3x - 8: (-∞, ∞), { y | y ∈ R}

Step 4: Finding the range for the function f(x) = 2^x + 3

This is an exponential function. So, the range is y > k

Here k = 3.

∴ Range of f(x) = 2^x+3: (3, ∞), {y | y > 3}

Step 5: Finding the range for the function f(x) = x² + 7x - 9

This is a quadratic function.

we can write it as,

f(x) = x² + 2 × x × (7/2) + (7/2)² - (7/2)² - 9

     = (x + 7/2)² - 85/4

This is in the form of a(x - h)² - k. where a = 1 > 0 and k = -85/4

Since a > 0, the range of the function is y ≥ -85/4

∴ Range of f(x) = x² + 7x - 9: [-85/4, ∞), {y | y ≥ -85/4}

Therefore, the functions f(x) = -4x + 11 and f(x) = 2/3x - 8 are having the given range {y ∈ R, -∞ < y < ∞}

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Answer:

Domain:[-4,∞)

Range:[0, ∞)

Thus, choice C is the exact answer

(D) 200 DVD players were repaired in the first year.

Given:

The DVD player shipped 960 players last month

There is a record that out of every 24 players, the 5 would be repaired.

So we need to find the number of DVD players that were repaired in these 960 players.

So,

[tex]\frac{960*5}{24} \\=200[/tex]

Therefore, (D) 200 DVD players were repaired in the first year.

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The question you are looking for is here:

A DVD player manufacturer shipped 960 DVD players last month. According to the manufacturer's records, 5 out of every 24 players were repaired during the first year of ownership. How many of the 960 DVD players were repaired in the first year?

A: 40

B: 120

C: 192

D: 200

Answer:

[tex]\frac{9\pi }{4}[/tex] inches

Step-by-step explanation:

I suppose they are asking you for the length of the red part.

18[tex]\pi \\[/tex] * [tex]\frac{45}{360}[/tex] = [tex]\frac{9\pi }{4}[/tex] inches

Answer:

L = 7.07 in

Step-by-step explanation:

L = arc lenght

[tex]L=\frac{\pi (45)(9)}{180} =2.25\pi =7.07in.[/tex]

Hope this helps

Answer:

Obtuse, scalene.

Step-by-step explanation:

In ΔSVU, one angle is 120° which is obtuse angle.

So, ΔSVU is a obtuse triangle.

All the sides  have different measurements. So, It is a Scalene triangle.

The probability that a male is selected, then a female is 0.26

The probability that a female is selected, then a male is 0.26

The probability that two males are selected is 0.18

The probability that two females are selected is 0.30.

The probability that no males are selected is 0.30.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that a male is selected, then a female = (11/25) x (14 / 24) = 0.26

The probability that a female is selected, then a male = (14/25) x (11 / 24) = 0.26

The probability that two males are selected = (11/25) x (10/24) = 0.18

The probability that two females are selected = (14/25) x (13 / 24) = 0.30

The probability that no males are selected =  (14/25) x (13 / 24) = 0.30

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Throwing a coin until it lands tails is an example of a discrete random variable which does not have a finite expectation.

For the given question,

A discrete random variable is a type of variable whose value depends upon the numerical outcomes of a certain random phenomenon. Discrete random variables are always whole numbers, which are easily countable.

It is a variable that can take on a finite number of distinct values and takes numerous values. It is also known as a stochastic variable. When you consider probabilistic experiments with infinite outcomes, it is easy to find random variables with an infinite expected value.

Let X be a random variable that is equal to 2ⁿ with probability 2⁻ⁿ (for positive integer n). Then,

[tex]E(X)=\sum_{n:1}^{\infty} |2^{-n}2^{n}|[/tex]

⇒ [tex]E(X)=\sum_{n:1}^{\infty} (1)[/tex]

⇒ [tex]E(X)=\infty[/tex]

Consider the following example,

You throw a coin until it lands tails.

Let n be the number of heads

Then number of heads can be found by, 2ⁿ

Now, the expected value function is

[tex]E(X)=\frac{1}{2}(2^{0} )+ \frac{1}{4}(2^{1} )+....[/tex]

⇒ [tex]E(X)=\sum_{n:1}^{\infty} |2^{-n}2^{n-1}|[/tex]

⇒ [tex]E(X)=\sum_{n:1}^{\infty} \frac{1}{2}[/tex]

⇒ [tex]E(X)=\infty[/tex]

Since the number of outcomes is infinite. The probability of each outcome decreases exponentially.

Hence we can conclude that throwing a coin until it lands tails is an example of a discrete random variable which does not have a finite expectation.

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The projection discussed are the isometric and the orthographic projection.

The isometric projection is how the object look to the eyes when seen from a distance. It should be noted that orthographic projection give the actual measurements of the object.

The isometric drawing is through 100% true measurement of the height, width, and the depth.

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The simplification of the polynomial expression will give 3x² - 20x + 8.

The polynomial expression is given as:

(5x² + 13x4) (17x² + 7x - 19) + (5x-7)(3x + 1)

= 5x² + 13x - 4 - 17x² - 7x + 19 + 15x² + 5x - 21x - 7

Then collect like terms

= 5x² + 15x² - 17x² + (13x - 7x + 5x - 21x) - 4 - 7 + 19

= 3x² - 20x + 8.

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Answer:

OA

Step-by-step explanation:

because it only got a y parameter for each x

Answer:

Option A. (2,4),(3,9),(4,16),(5,25)

Using the hypergeometric distribution, it is found that there is a 0.0232 = 2.32% probability of getting exactly two winning numbers with one ticket.

The formula is:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

For this problem, the parameters are given as follows:

N =A + B = 54, k = 4, n = 4.

The probability of getting exactly two winning numbers with one ticket is P(X = 2), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,54,4,4) = \frac{C_{4,2}C_{50,2}}{C_{54,4}} = 0.0232[/tex]

There is a 0.0232 = 2.32% probability of getting exactly two winning numbers with one ticket.

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