What are the 4 problem-solving methods?

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 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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The given exponential function exists [tex]f(x)=3(1/3)^x[/tex] . The growth value of the function is 1/3.

An exponential function exists a mathematical function of the following form: [tex]f ( x ) = a^ x[/tex].

where x exists a variable, and a exists a constant named the base of the function.

An exponential function exists of the form [tex]f(x)=ab^x[/tex]

where a ≠ 0, b > 0, b ≠1, and x exists any real number.

when b > 1, the graph increases.

when 0 < b < 1, the graph decreases.

a = initial value

r = growth or decay rate

x = number of time.

The given exponential function exists [tex]f(x)=3(1/3)^x[/tex]

The function exists a stretch of the function [tex]f(x)= (1/3)^x.[/tex]

Therefore, the correct answer is the growth value of the function is 1/3.

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The length of the arc made by the big hand if the tip travels from 6:00pm to 6:20pm is 0.52 feet

An equation is an expression that shows the relationship between two or more variables and numbers.

The clock reads 12 hours (720). The angle if the tip travels from 6:00pm to 6:20pm (20 minutes) is:

Ф = (20/720) * 360 = 10°

The length of the arc is given as:

Length of arc = (Ф/360) * 2π * length of hand = (10/360) * 2π(3) = 0.52 feet

The length of the arc made by the big hand if the tip travels from 6:00pm to 6:20pm is 0.52 feet

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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

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 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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[tex] {\qquad\quad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + \cfrac{1}{ {x}^{2} } = 34[/tex]

[ add 2 on both sides ]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + \cfrac{1}{ {x}^{2} } + 2 = 34 + 2[/tex]

[ form identity : a² + b² + 2ab ]

[tex]\qquad \sf  \dashrightarrow \: {(x)}^{2} + { \bigg(\cfrac{1}{ {x}^{} } \bigg) }^{2} + 2 \sdot(x) \sdot \bigg(\cfrac{1}{x} \bigg) = 36[/tex]

[ a² + b² + 2ab = (a + b)² ]

[tex]\qquad \sf  \dashrightarrow \: {\bigg (x + \cfrac{1}{x} \bigg) }^{2} = 36[/tex]

[tex]\qquad \sf  \dashrightarrow \: {\bigg (x + \cfrac{1}{x} \bigg) }^{} = \sqrt{ 36}[/tex]

[tex]\qquad \sf  \dashrightarrow \: x + \cfrac{1}{x} = \pm 6[/tex]

so, the value of required expression is 6

[usually positive value is considered, but if asked the value can be either positive or negative]

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 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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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 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:

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.

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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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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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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Answer:

3 elements

Step-by-step explanation:

Let A = solution set of x²-4

B = solution set of x²-3x+2

First, find the solution of each sets:

[tex]\displaystyle{x^2-4=0}\\\\\displaystyle{(x+2)(x-2)=0}\\\\\displaystyle{x=2,-2}[/tex]

Set B:

[tex]\displaystyle{x^2-3x+2=0}\\\\\displaystyle{(x-2)(x-1)=0}\\\\\displaystyle{x=1,2}[/tex]

Now we can write new set as:

A = {2, -2}

B = {1, 2}

The union of A and B means combine both sets together:

A ∪ B = {2, -2, 1, 2}

However, in a set, we do not write duplicate elements, so the union set will be:

A ∪ B = {2, -2, 1}

Hence, there are 3 elements in A ∪ B.

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.

Answer:

Domain:[-4,∞)

Range:[0, ∞)

Thus, choice C is the exact answer

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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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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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)

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 system of linear equations that represent the given situation is:

5x + 10y = 1750 and 1/3x + 1/2y = 100.

A linear equation is an equation with the highest degree of the variable is one. There may be one or more variables but their degree must be 1 to become a linear equation.

The general form of a linear equation is y = mx + c.

In the given situation,

Consider x as the number of short-sleeved shirts ordered and y as the number of long-sleeved shirts ordered.

It is given that,

Price for short-sleeved shirts = $5

Price long-sleeved shirts =$10

The total price for 100 shirts ordered = $1,750

So, we can write the linear equation as

5x + 10y = 1750  ...(i)

It is given that,

After the first week, they sold 1/3 of the short-sleeved shirts and 1/2 of the long-sleeved shirts. I.e.,

1/3x + 1/2y = 100  ...(ii)

Thus, from equations (i) and (ii), the system of linear equations that represent the given situation is

5x + 10y = 1750

1/3x + 1/2y = 100

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Disclaimer: The given question is incomplete. Here is the complete question.

Question:

The drama club is selling short-sleeved shirts for $5 each, and long-sleeved shirts for $10 each. They hope to sell all of the shirts they ordered, to earn a total of shirts ordered, and to earn a total of $1,750. After the first week of the fundraiser, they sold 1/3 of the short-sleeved shirts and 1/2 of the long-sleeved shirts, for a total of 100 shirts.

Let x represent the number of short-sleeved shirts ordered and let y represent the number of long-sleeved shirts ordered. which system of linear equations represents the situation?

Answer:

c

Step-by-step explanation:

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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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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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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Since the given lines a and b are neither parallel, nor do they intersect each other. Also, they lie on two different planes, P and Q respectively, and thus, are co-planar. hence, a and b can be called skew lines.

Definition of Skew Lines

Skew lines in 3D geometry, are, by definition, a pair of lines that are neither parallel nor intersect each other. Such lines are therefore not coplanar, according to the conclusion.

Skew lines tend to occur frequently in real-world circumstances. Let's say there is a line on the ceiling and a line on the wall. These lines can be skew lines because they lie in distinct planes if they are not parallel to one another and do not meet. Skew lines go on forever in both directions.

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Answer:

Step-by-step explanation:

Skew lines are noncoplanar and do not intersect. Line a lies in plane Q and line b lies in plane R, so the lines are not coplanar. No other plane can be drawn through the lines, so they are not parallel. So, a and b are skew.

The terms of the expression are ab, cd, ef and gh. This shpws that the expression contains 4 terms and 0 factor.

Expression consists of terms and factors. The terms are separated by the mathematical signs.

Given the expression below

ab+cd+ef+gh

The terms of the expression are ab, cd, ef and gh. This shpws that the expression contains 4 terms and 0 factor.

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(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