The image includes the questions

Answer:
i = [tex]\sqrt{-1}[/tex]
i^2 = -1

Step-by-step explanation:

I hope this helps you out :D

since i = square root of -1 when you square i (i^2) you get rid of the parenthesis.

The amount paid by the store is given as follows:

$111.54.

The amount paid by the store is obtained applying the proportions in the context of the problem.

The original price is symbolized as follows:

x.

The markup price was of 30%, hence the decimal multiplier is given as follows:

130% = 1.3.

The selling price is of $145, hence the original price is obtained as follows:

1.3x = 145

x = 145/1.3

x = $111.54.

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The numeric value of the expression when a = -2 and b = 14 is given as follows:

18.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The term inside the square root is given as follows:

a² + 12.

When a = -2, replacing the instance of a by -2, the term is given as follows:

(-2)² + 12 = 4 + 12  = 16.

The square root of 16 is of 4, while the absolute value of 14 is 14(number without the sign), hence the numeric value of the expression is of:

4 + 14 = 18.

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The inverse of a function is another function that "undoes" the original function. In other words, the composition of a function and its inverse results in the identity function.

To find the inverse of a function, you can follow these steps:

Replace the function with "y"

Switch the x and y variables

Solve for y (or in this case x)

So in this case, we can find the inverse of 8x^5+7 by replacing y with 8x^5+7, switching the x and y variables, and solving for x:

y = 8x^5+7

x = 8y^5+7

This is not an invertible function because it's not a one-to-one function, it's not a function of x.

Answer:

Hey there! The inverse of 8x^5+7 doesn't exist because it's not a function. Think about it like this, a function is like a machine that takes an input and gives you a unique output. But in this case, the machine isn't working correctly and it doesn't give you a unique output for a given input. So, in simple terms, it doesn't have an inverse.

________________________________________________________

To determine if an equation has an inverse, we need to check if it is a one-to-one function. A one-to-one function is a function in which every unique input corresponds to a unique output. If an equation is one-to-one function, then it has an inverse. If it's not one-to-one function, then it doesn't have an inverse.

To find the inverse of a linear equation, we can follow these steps:

1. Switch the x and y variables

2. Solve for y (or x)

3. Replace y (or x) with f^-1 (x) (or f^-1 (y))

For example, if we have the equation y = 2x+1, we can follow these steps:

1. x = 2y+1

2. x-1 = 2y

3. f^-1(x) = (x-1)/2

So, the inverse of the equation y = 2x+1 is f^-1(x) = (x-1)/2

As per the concept of algorithm, the reasonable number of steps is 2n.

The term algorithm in math is defined as the procedure for solving a mathematical problem in a finite number of steps that frequently involves repetition of an operation.

Here we have given that an algorithm has n number of steps.

Here we need to find the reasonable number of steps.

While we know the definition of algorithms, then her we need to understand the term reasonable time that is defined as  the algorithms with a polynomial efficiency or lower are said to run in a reasonable amount of time.

So, the reasonable number of steps is 2n where n refers the number of steps.

Complete Question:

If an algorithm has n number of steps, then in find out the reasonable number of steps?

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One metal switch box has a volume of 10.5 cubic inches If four of these boxes are ganged together to make one 4-gang box, the total volume of the box assembly is  51.84 in^3.

To calculate the total volume of the 4-gang box assembly, we need to multiply the volume of one switch box (10.5 in^3) by the number of boxes in the assembly (4). This gives us 10.5 in^3 x 4 = 42 in^3. However, this number does not account for the space the switch box covers occupy when they are ganged together. To account for this, we need to add the volume of the gap between the boxes.

This gap is typically in the range of 0.2 to 0.3 in^3. To be conservative, we will use 0.3 in^3. Adding this to our previous result gives us 42 in^3 + 0.3 in^3 = 42.3 in^3. This is the total volume of the 4-gang box assembly. To round this number to the nearest hundredth, we can round up to 42.3 in^3 = 51.84 in^3.

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Answer:

y = -2/5x - 1

Step-by-step explanation:

Parallel lines have the same gradient/slope.

m1=m2

So the equation must have m as -2/5

So we can sub that and we will get:

y = -2/5x + c

However, we still do not have c aka y intercept

So we can sub the point (5,-3) into the current equation and we will have:

-3 = -2/5(5) + c

Do the algebra and you'll get -1 = c

Sub that into the equation:

y = -2/5x -1

The appropriate design for the study includes; Treatment used; Chamomile oil treatment

Appropriate Design!” asks about the identity of design.

Method of treatment; Application of the chamomile oil to the cervical region of patients experiencing pain due to pinched nerves

Treatment assignment; Treatment should be assigned to patients with pinched nerves

Variables that should be measured; Reduction or relief of pain as reported by the patients

Part B; The study should be administered equally to both male and female as the Appropriate Design!” asks about the identity of design can be experienced by both male and female

Part C; The design could be double blind by replacing the chamomile administered by placebo, thereby preventing bias from both researcher and participants in the results of the research.

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Answer: The local restaurant states that its occupancy, the number of people inside the restaurant, can be at most 65. This includes both people working in the restaurant and the customers. When they open for the lunch rush, there are 8 employees inside the restaurant and customers start to come in at a steady rate of 3 customers per minute.

Given this information, we can set up the following inequality:

Occupancy = 8 + 3t (where t is the number of minutes after the restaurant opens) ≤ 65

This inequality represents the maximum occupancy of the restaurant, taking into account the initial number of employees (8) and the rate at which customers are coming in (3 per minute). To find the number of minutes after the restaurant opens until it reaches its maximum occupancy of 65, we can solve for t:

8 + 3t ≤ 65

3t ≤ 57

t ≤ 19

So, the restaurant will reach its maximum occupancy of 65 people after 19 minutes of being open for the lunch rush.

Step-by-step explanation:

The expression [tex](\sqrt[3]{x^4})^5[/tex] with a rational exponent is given as follows:

x^(20/3).

The general format of the exponential expression is given as follows:

[tex]a^{\frac{n}{m}}[/tex]

To obtain the radical form, we have that:

Hence the equivalent expression is given as follows:

[tex]a^{\frac{n}{m}} = \sqrt[m]{a^n}[/tex]

The parameters for this problem are given as follows:

m = 3, n = 4, a = x.

Hence the equivalent expression is given as follows:

(x^(4/3))^5.

Applying the power of power rule, we multiply the exponents, hence the equivalent expression is of:

x^(20/3).

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Rewriting the fractions 1/6 and 1/4 with their least common denominator will be 2/12 and 3/12.

The lowest common multiple of the denominators of a group of fractions is known as the lowest common denominator, or LCD, in mathematics. It makes adding, taking away, and comparing fractions easier.

When two or more fractions are given, the least common denominator is the smallest number among all the common multiples of the denominators.

The denominators of the given fractions are 6 and 4 and the least common multiple of 6 and 4 = 12

To rewrite 1/6 with denominator 12, we need to multiply 2 to the numerator and the denominator, we get:

1/6 =(1 × 2)/(2 × 6)

= 2/12

Also 1/4 = 3/12

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Complete question

Describe how you would rewrite the fractions 1/6 and 1/4 with their least common denominator

Answer:

Rewriting the fractions 1/6 and 1/4 with their least common denominator will be 2/12 and 3/12.

Step-by-step explanation:

The average rate of change of the function f(x) = 4 · x² - 7 for the interval [1, b] is m = - 4 · (b + 1).

Graphically speaking, the average rate of change associated to a function is represented by a secant line formula:

m = [f(b) - f(1)] / (b - 1)

If we know that f(x) = 4 · x² - 7, then the average rate of change is:

m = [4 · b² - 7 - 4 · 1² + 7] / (1 - b)

m = 4 · (b² - 1) / (1 - b)

m = - 4 · (b² - 1) / (b - 1)

m = - 4 · (b + 1)

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Answer: The formula to calculate the future value of an investment account is FV = PV(1+i)^n, where FV is the future value, PV is the present value, i is the interest rate (in decimal form), and n is the number of compound periods.

Given that PV = $50,000, i = 10%, and n = 4, we can plug these values into the formula:

FV = $50,000(1+0.1)^4

By using the formula, FV = $50,000(1.1)^4 = $50,000(1.4641) = $73,205.50

The future value of the retirement account after 4 years is $73,205.50

Step-by-step explanation:

The number of classes in the frequency table given below is; 5 classes

We are given the classes of the frequency table as;

23 - 24

25 - 26

27 - 28

29 - 30

31 - 32

Now, we see from the class intervals that there are a total of five classes because each class interval has a frequency of occurrence as seen in the given frequency table.

The frequencies for each class interval is as follows;

7, 2, 6, 4, 1

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70 km/hr is the speed he must drive to reach baguio in 6 hours.

The length along a line or line segment between two points on the line or line segment.

Given that joseph is figuring out a way to reach baguio at a shortest possible time using his car he can reach in baguio in 6 hours at an average speed of 70 km per hour

We need to find how  fast should he drive to reach baguio in 6 hours

using distance formula:

d=rt

d=70(6);

d=420km

420km is the actual distance of his travel;

if he wish to arrive as early as in 6 hours, then

he must have to drive faster than 70k/h;

s=420/6;

s=70 km/hr

Hence, 70 km/hr is the speed he must drive to reach baguio in 6 hours.

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As she have 3⅞ pounds of soil, she doesn't have enough soil to fill the flowerpot.

To create a mixed fraction, a suitable fraction and a whole number must be combined. Usually, it denotes a value between 0 and 1. A mixed fraction is one that contains both a whole number and a fraction. One example of a mixed fraction is 1(1/3), where 1 is a whole number and 1/3 is a fraction.

Denise need 4 pounds of soil

By adding the mixed fraction we will know if its enough or not

[tex]$=1\frac{3}{4} + 2 \frac{1}{8}[/tex]

[tex]$=\frac{7}{4} + \frac{17}{8}[/tex]

[tex]$=\frac{14}{8} + \frac{17}{8}[/tex]

[tex]$=\frac{14+17}{8}[/tex]

[tex]= \dfrac{31}{8}[/tex]

[tex]=3 \dfrac{7}{8}[/tex]

Thus, As she have 3⅞ pounds of soil, she doesn't have enough soil to fill the flowerpot.

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The two additional roots of a polynomial function P(x) = 0 with rational coefficients are -i and 7-8i.

We have to find the determine the two additional roots of a polynomial function P(x) = 0.

The answers to any given polynomial for which we must ascertain the value of the unknowable variable are known as the roots of polynomials. We can evaluate a polynomial's value to zero if we know its roots.

The given roots of P(x) = 0 is i and 7+8i.

So there conjugate are also the roots of P(x).

So the two additional roots of P(x) = 0 should be -i and 7-8i.

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The complete question is:

Find two additional roots of a polynomial function P(x) = 0 with rational coefficients given below where additional roots of P(x) = 0, i and 7+8i.

According to the given information in the question answer is  250.

Any decimal number is rounded down to the closest hundredth by the term "to the nearest hundredth." A hundredth is 1/100 or 0.01 in decimal form. For instance, increasing 2.167 to the closest tenth yields 2.17.

In this exercise, we must round the supplied number up to the nearest hundred, making it 10.2719. We must add two more decimal places to this number in order to round it to the nearest hundreds. Additionally, we saw that all of the numbers following the second decimal place are fewer than five, therefore they can be ignored and the result is 10.27.

Using the following formula, you can determine this:

x = (100 * 305) / 122

Where x is the original number and 122 is 100 + 22 (the 100 representing the original value and 22 representing the increase of 22%).

x = (100 * 305) / 122 = 250

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A probability tree is a visual representation of the possible outcomes of an event or series of events. In this case, the event takes a marble out of the bag.

The first step in building a probability tree is to create a starting point that represents the first state of the problem. In this case, the starting point is a bag containing 3 green marbles and 5 white marbles.

The next step is to branch from the starting point and show the possible results of the first event. This includes taking out  the marble out of the bag. The probability of getting a green marble is 3/8 and the probability of getting a white marble is 5/8.

After the first event, the issue status changes. In this case, the bag contains 2 green marbles and 4 white marbles.

The next step is to branch out from the state after the first event and show the possible outcomes of his second event involving pulling another marble out of his pocket. The probability of getting a green marble is 2/6 and the probability of getting a white marble is 4/6. The final step is to label the endpoints of the tree with the possible outcomes of the problem and the probabilities of each outcome.

The probability tree starts with an sack of 3 green marbles and 5 white marbles, as shown in the design showing the possible outcomes of selecting a marble, the new state of the sack after each selection, and the probability of each outcome

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The resulting augmented matrix is:

1 2 -6 | -5

0 1 -8 | 13

0 0 42 | -177

To perform the three-row operations on the augmented matrix A, we proceed as follows:

(a) R = 1 + 12:

Add 12 times row 1 with row 2,

1 2 -6 | -5

0 -14 -32 | 14

-3 -10 -2 | -4

(b) Rg - 3r + r:

Add 3 times row 2 to row 3, and subtract row 3 from row 1

1 2 -6 | -5

0 -14 -32 | 14

0 -16 -38 | -9

(c) Rs = 4r2 + 13:

Multiply row 2 by 4 and add 13 times row 2 to row 3

1 2 -6 | -5

0 1 -8 | 13

0 0 42 | -177

So the resulting augmented matrix is:

1 2 -6 | -5

0 1 -8 | 13

0 0 42 | -177

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If In the lab, Trey has two solutions that contain alcohol and is mixing them with each other. The many milliliters of solution b he use, if the resulting mixture has 261 mL of pure alcohol is: 213.93mL.

Let x be the amount of solution B he used in milliliters.

We know that the amount of solution A  used = 4× x, and that the resulting mixture has 261 mL of pure alcohol.

Percentage of alcohol in solution A is 18% and in solution B is 50%.

Set up the proportion:

(0.18 × 4x + 0.50x) = 261

Simplifying,

0.72x + 0.50x = 261

1.22x = 261

x = 261 / 1.22

x = 213.93 mL (Solution b)

Trey used 213.93 mL of solution B and 3( 213.93mL) = 855.72 mL of Solution A.

Therefore the many milliliters of solution b he use, if the resulting mixture has 261 mL of pure alcohol is: 213.93mL.

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Answer: 1.2 lb/gallon

Step-by-step explanation: SODIUM HYPOCHLORITE SOLUTION is a greenish-yellow liquid weighing approximately 10 lbs. per gallon with a specific gravity of 1.2 lb

You might not understand my explanation but just know the answer is 1.2 lb gallons :)

dx can be expressed in terms of dt as:

dx = 4t2sin(t2)cos(t2)dt + 2t[1 - cos(4t2)]dt + 2t[1 + cos(4t2)]dt

sin(x2) = 2sin(x)cos(x)

cos(x2) = cos2(x) - sin2(x)

Therefore, dx2 = 2sin(x)cos(x)dx + [cos2(x) - sin2(x)]dx

Using the half-angle identity, sin2(x) = 1/2[1 - cos(2x)] and cos2(x) = 1/2[1 + cos(2x)], we can rewrite dx2 as:

dx2 = sin(x)cos(x)dx + 1/2[1 - cos(2x)]dx + 1/2[1 + cos(2x)]dx

Now, we can express dx in terms of dt using the fact that x = t2:

dx = 2tdt

Therefore, dx2 = 2sin(t2)cos(t2)2tdt + 1/2[1 - cos(4t2)]2tdt + 1/2[1 + cos(4t2)]2tdt

Simplifying, we get dx2 = 4t2sin(t2)cos(t2)dt + 2t[1 - cos(4t2)]dt + 2t[1 + cos(4t2)]dt

Therefore, dx can be expressed in terms of dt as:

dx = 4t2sin(t2)cos(t2)dt + 2t[1 - cos(4t2)]dt + 2t[1 + cos(4t2)]dt

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Answer: √29.5= 5.43139

Answer:

To calculate the percent change from 36 to 99, you can use the formula:

((New Value - Original Value) / Original Value) x 100

((99 - 36) / 36) x 100 = 175%

So the percent change from 36 to 99 is 175%.

The percentage change from 36 to 99 will be 175% .

Given,

Number changes from 36 to 99 .

Here,

To calculate the percent change from 36 to 99, you can use the formula:

=((New Value - Original Value) / Original Value) x 100

=((99 - 36) / 36) x 100

= 175%

So the percent change from 36 to 99 is 175%.

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Answer:900

Step-by-step explanation:

Based on the table, a statement which is true is that: C. The table shows a linear relationship, but not a proportional relationship.

In Mathematics, a proportional relationship simply refers to a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the distance (miles) and time (hours) on this table as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 6/2 ≠ 11/4 ≠ 34/9 ≠ 81/16

In conclusion, we can reasonably infer and logically deduce that the table shows a linear relationship because as the time (in hours) increases, the distance (miles) also increases. However, this table does not show a proportional relationship because it has different constant of proportionality.

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The probability of each of the following events are given below:

What is Probability?

Probability is the measure of the likelihood that an event will occur. It is expressed as a number between 0 and 1, with 0 representing no chance of the event occurring, and 1 representing a certainty that the event will occur. Probability is widely used in mathematics, statistics, and science to calculate the probability of a given event occurring. It is also used to assess risk and uncertainty in decision-making.

Event A: 0.306 or 30.6%

Event B: 0.44 or 44%.

Event A: The sum is greater than 9.

We have already computed this, the probability of getting a sum greater than 9 is 11/36, which can be simplified as 0.306 or 30.6%

Event B: The sum is not divisible by 2 and not divisible by 5.

To find the probability of this event, we need to find the number of outcomes that have a sum that is not divisible by 2 or 5.

We can calculate this by listing out all the possible outcomes and counting the number that have a sum that is not divisible by 2 or 5: (1,3), (1,4), (1,6), (2,3), (2,5), (3,1), (3,2), (3,4), (3,6), (4,1), (4,3), (4,5), (5,2), (5,4), (6,1), (6,3), (6,4) and (6,6)

There are 16 outcomes that have a sum that is not divisible by 2 or 5, so the probability of getting a sum that is not divisible by 2 or 5 is 16/36, which can be simplified as 0.44 or 44%.

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Answer:(n+3)(n^2-3n+9)/125

Step-by-step explanation:

Answer:

(n+3)(n^2-3n+9)/125

Step-by-step explanation:

We can figure out the factored form of n^3+27/125 by adding all the brackets in the correct places. (I forgot what my math teacher called this process ;-;)

After adding the brackets it becomes:

(n + 3) (n² - 3n + 9) ÷ 125

(Our answer would be 125)