Summary consider the exponent properties (a^n)^m=a^nm and a^nb^n=(ab)^n. what is the main difference in these properties? when simplifying an expression, how would you decide which one to use?

The equivalent value of the equation is n = 0.3

Given data ,

Let the equation be represented as A

Now , the value of A is

3.6 = 12n   be equation (1)

On simplifying , we get

Divide by 12 on both sides , we get

n = 3.6 / 12

On further simplification , we get

n = 0.3

Hence , the expression is n = 0.3

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The value of x is 7.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

∠TUV = 9x + 1

∠TUW = 7x - 9

∠WUV = 5x - 11

Now,

∠TUV = ∠TUW + ∠WUV

Substituting the values.

9x + 1 = 7x - 9 + 5x - 11

Adding like terms.

9x + 1 = 12x - 20

1 + 20 = 12x - 9x

21 = 3x

Dividing 3 on both sides.

x = 21/3

x = 7

Thus,

x is 7.

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Evaluating multiple companies before making an investment decision helps to make informed decisions, diversify your portfolio, and maximize returns.

It is critical to consider multiple companies before investing because:

Diversification reduces the risk of loss because the performance of one company does not determine the overall performance of your portfolio.

Opportunity Cost: Comparing and selecting the best investment options allows you to avoid missing out on potential higher returns by evaluating multiple companies.

Due Diligence: Investing in a company necessitates extensive research and due diligence. When you look at multiple companies, you can compare financial statements, management, products, and other factors that can affect stock performance.

Finally, evaluating multiple companies prior to making an investment decision allows you to make informed decisions, diversify your portfolio, and maximize returns.

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Answer:

4h^3 - 8h^2 + 17h + 3

Step-by-step explanation:

I put it into my calculator, let me know if that helped!

Answer: it's C

Step-by-step explanation:

Answer:D

Step-by-step explanation:

Answer:

12/8 = 1.5 °C per hour

Step-by-step explanation:

basically write the change over time in a formula, calculate it and find the answer, using the answer u can say that:

over the course of 8 hrs, the temperature has been reducing by a rate of 1.5°C/hr. (link it to the context as well)

a)  The sample space for this experiment:

S = { E1E2, E1W2,E2W2, E1W1, E2W1, W1W2 }

b) The probability that the expert will correctly identify (by guessing) both of the cans containing water is:  1/6

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

Now, According to the information:

Let E1 and E2 represent the empty cans and W1 and W2 be the cans filled with water.  

S = { E1E2, E1W2,E2W2, E1W1, E2W1, W1W2 }  

By merely guessing, the events are equally likely. Since there are 6 possible outcomes,  

The probability that the expert will correctly identify (by guessing) both of the cans containing water is:

Since there are 6 possible outcomes,  

probability = 1/6

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The given question is incomplete, complete question is:

According to Webster’s New Collegiate Dictionary, a divining rod is "a forked rod believed to indicate [divine] the presence of water or minerals by dipping downward when held over a vein." To test the claims of a divining rod expert, skeptics bury four cans in the ground, two empty and two filled with water. The expert is led to the four cans and told that two contain water. He uses the divining rod to test each of the four cans and decide which two contain water. a List the sample space for this experiment. b If the divining rod is completely useless for locating water, what is the probability that the expert will correctly identify (by guessing) both of the cans containing water?

The percent markup for the cost of shirt = 50%

Let us assume that the cost of each shirt be x dollars

A department store buys 300 shirts at a cost of $1,800.

Using unitary method the price of each shirt would be,

x = 1800/300

x = 6 dollars

A department store sells 300 shirts for $9 each.

So, Selling price of one shirt = $9

Price markup = Selling price - Cost price

                      = $9 - $6

                      = $3

The percent markup would be,

p = (Price markup / cost price) × 100

p = (3/6) × 100

p = 50%

Therefore, the percent markup = 50%

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The probability of drawing at least 7 clubs in 15 draws from a standard deck of 52 cards is approximately 0.496.

The number of ways to draw 7 or more clubs in 15 draws can be found by using the cumulative distribution function for the binomial distribution. This distribution models the number of successful outcomes (clubs) in n independent trials (card draws), each with the same probability of success (drawing a club). The cumulative distribution function gives the probability of getting a certain number of successful outcomes or fewer.

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Answer: (−10)=2(+1)

Step-by-step explanation:

The solution of the equations y = - 2x + 17 and y = x - 7 will be (8, 1). Then the correct option is D.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The linear equations are given below.

y = - 2x + 17           ...1

y = x - 7                 ...2

From equations 1 and 2, then we have

x - 7 = - 2x + 17

3x = 24

x = 8

Then the value of 'y' is given as,

y = 8 - 7

y = 1

The solution of the equations y = - 2x + 17 and y = x - 7 will be (8, 1). Then the correct option is D.

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Answer:y=-5/3x+26/3

Step-by-step explanation:

2-7/4-1=-5/3

(4,2)

y-2=-5/3(x-4)

y-2=-5/3x+20/3

  +2             +2

y=-5/3x+26/3

[tex]y=-\frac{5}{3}x+\frac{26}{3}[/tex]

It passes through the points

Yes, television commercials are an effective way to promote a new product.

The survey organization conducted a telephone survey in December 2008 to gauge the effectiveness of television commercials in promoting new products among a sample of 1,009 randomly selected adults in the United States.

The survey asked the respondents whether they believed that television commercials were an effective way to promote a new product at the time of the survey. The results of the survey can provide insights into the public's perception of television commercials as a tool for promoting new products, as well as how this perception may have changed over time.

The findings can also be useful for marketers and advertisers who want to understand consumer attitudes toward television commercials and use this information to guide their advertising strategies. However, it's important to note that the results of this survey are limited to the specific time and population studied and may not be generalizable to other populations or time periods.

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Answer:

Step-by-step explanation:

a. The equation of the line that describes the relationship between distance and time for Car X can be found by using the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.

To find the slope (m), we can use the formula: m = (change in y) / (change in x) = (distance traveled) / (time elapsed) = 174 miles / 3 hours = 58 miles per hour.

Since the car starts at time x = 0 and has traveled 174 miles at time x = 3, the y-intercept (b) can be found by setting x = 0 and solving for y: y = 58x + b, and y = 174 when x = 3, so b = 174 - 58(3) = -160.

Putting it all together, we get the equation: y = 58x - 160.

b. The graph that represents the relationship between distance and time for Car X is a line that passes through the point (0, -160) and has a slope of 58. This line represents the linear relationship between the distance traveled and the time elapsed for Car X.

The y-intercept of -160 represents the distance traveled when time is equal to 0. The slope of 58 represents the rate of change of the distance traveled with respect to time. This means that for every hour that passes, Car X travels 58 miles.

Answer:

14

Step-by-step explanation:

formula

SQURED A+B=C

10+b =18

100+b=324

100-100 324-100

=224

squre root of 224

is 14

Answer: I believe its 4.16 centimeters

Step-by-step explanation:

I do not have an explanation, but I hope the answer is correct.

The possible values are -

(a²,b²) = p

(a²,b) = p if p|-r and (a²,b) = p² if p|r

(a²,b³) = p² if p|-r and (a²,b³) = p³ if p|r

What is gcd?

The greatest common factor (GCF) that divides two or more numbers is known as the greatest common divisor (GCD). The highest common factor is another name for it (HCF).

Since (a, b) = p it can be written a = pr and b = ps where r and s are integers such that (r, s) = 1.

Then a² = p²r².

Then by Theorem 1.7, (a²,b) = (p²r²,ps) = p(pr²,s).

By Theorem 1.8, (r²,s) = 1 .

Thus, there are two cases to consider: if p|s then, (a²,b) = p², and if p|-s then (pr²,s) = 1 (Again by Theorem 1.8)  so that (a²,b) = p in that case.

Thus, there are two cases for (a²,b): namely p or p².

The same analysis shows that (a³,b) must be either p, p² or p³ depending on the power of p that divides b.

Analyze (a²,b³) as follows.

Using the notation already introduced, and

Theorem 1.7, it is obtained that (a²,b³) = (p²r²,p³s³) = p²(r²,ps³).

Since, (r, s) = 1, Theorem 1.8 shows that (r²,s³) = 1.

Therefore, there are two possibilities for (a²,b³) -

(a²,b³) = p² if p|-r and (a²,b³) = p³ if p|r.

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The cost to ride 5.25 miles in a taxi is, $5.63.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

The equation represents the cost y (in dollars) of riding in a taxi x miles is,

⇒ y = 0.5x + 3

Hence, The cost to ride 5.25 miles in a taxi is,

⇒ y = 0.5x + 3

Substitute x = 5.25 in above equation,

⇒ y = 0.5 × 5.25 + 3

⇒ y = 2.63 + 3

⇒ y = $5.63

Thus, The cost to ride 5.25 miles in a taxi is, $5.63.

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The simplified form of the expression is given by 4⁹/y³

Exponent is a mathematical operation, written as an. Here the expression an involves two numbers, the base 'a and the exponent or power 'n'. Exponents are used to simplify algebraic expressions.

Given here : The exponents (4³/y)³

Simplifying we get

(4³/y)³

When multiplying two bases of the same value, keep the bases the same and then add the exponents together to get the solution.

4³ ˣ ³ / y³

4⁹/y³

Thus the simplified form of the expression is given by 4⁹/y³

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The measure of angle Y, according to the stated statement, is 55 degrees.

An adverb used to describe something which goes together with something else and improves or completes it is complimentary (as in complementary colors)

The total of two complimentary angles is 90 degrees. As a result, we have:

m∠S + m∠Y = 90

Substituting the given equation m∠S = 5(m∠Y) − 240°, we get:

5(m∠Y) − 240° + m∠Y = 90

By merging like variables in the equation, we can reduce it to:

6(m∠Y) - 240° = 90

Adding 240 to both sides, we get:

6(m∠Y) = 330

Dividing both sides by 6, we get:

m∠Y = 55

Therefore, the measure of angle Y is 55 degrees.

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The answer choice that is the best measure of center for the data, and what is its value is D. The median is the best measure of center, and it equals 8.

A measure of center gives an idea of the central tendency of the data.

The median is a better choice here because it is not affected by extreme values, unlike the mean.

From the dots plotted on the line graph, it is evident that there are more data points around 8 than any other value. Hence, the median of the data would be closest to 8.

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Answer: The median is the best measure of center and it equals 8

Step-by-step explanation:have a good day!

The distance across the lake is approximately 62.5 meters, rounded to the nearest hundredth of a meter.

To find the distance across the lake (BC), we can use the following formula based on triangle similarity:

BC/AD = DB/DE

Where BC is the distance across the lake, AD is the known direct measurement made by Dominic, DB is the known measurement from point B to the landmark, and DE is the known measurement from point D to the landmark.

Let's assume that AD = 100 meters, DB = 50 meters, and DE = 80 meters. Then we can calculate BC as follows:

BC = (BC/AD) * AD = (DB/DE) * AD

BC = (50/80) * 100

BC = 62.5 meters

So, the distance across the lake is approximately 62.5 meters, rounded to the nearest hundredth of a meter.

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3 3/2 hours as a decimal= 4.5

1 1/3 hours as a decimal = 1.3

Duration of the film show = 4.5 hours

Hours spent on advertisements = 1.3 hours

Actual duration of the film = 4.5 - 1.3 hours

= 3.2 hours

3.2 hours as a fraction = 3 1/5 hours.

Therefore, the actual duration of the film was 3 1/5 hours.

Movie lasted 3 hours and 10 minutes

[tex]3\frac{3}{2} - 1 \frac{1}{3} = \frac{9}{2} - \frac{4}{3} = \frac{27 - 8}{6} = \frac{19}{6} = 3 \: \frac{1}{6} [/tex]

Answer:

Both models are exponential

A: $21,573.58

B: $21,589.58

Step-by-step explanation:

A

f(x) = 16,000[tex](1 + .03/4)^{4(10)}[/tex]

f(x) = (16000)[tex]1.0075^{40}[/tex]

f(x) = $21,573.58  Rounded to the nearest cent.

B

f(x) = 16000[tex](1+ .03/12)^{12(10)}[/tex]

f(x) = (16000)[tex]1.0025^{120}[/tex]

f(x) = $21,589.66 Rounded to the nearest cent

Answer:

∠ BCA = 75°

Step-by-step explanation:

∠ ABC = 90° ( angle in a semicircle )

then the 2 remaining angles in Δ ABC = 90° , that is

∠ BAC + ∠ BCA = 90° ( ∠ BCA = 5 × ∠ BAC )

∠ BAC + 5 ∠ BAC = 90°

6 ∠ BAC = 90° ( divide both sides by 6 )

∠ BAC = 15°

Then

∠ BCA = 90° - 15° = 75°

The required equation in a system of equations that has a solution (4, −1) is given as y = -1/4x.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
Let's assume that the equation passing through the origin and (4, -1)

The equation is given as,

(y₂ - y₁) /  (x₂ - x₁)

y - y₁ = (y₂ - y₁) /  (x₂ - x₁) (x - x₁)
y - 0 = -1 - 0 / 4 - 0 [x - 0]
y = -1/4x

Thus, the required other equation in a system of equations has a solution (4, −1) is given as y = -1/4x.

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Answer:

Step-by-step explanation: y=22.5

Step-by-step explanation:

The velocity of the particle at a given value of θ can be found by taking the derivative of the position vector with respect to time:

v(θ) = dr/dt = dr/dθ * dθ/dt = dr/dθ * ω

where ω is the angular velocity and dr/dθ is the derivative of the position vector with respect to θ.

The position vector r = a * e^(b * θ) * i + a * b * e^(b * θ) * j

Taking the derivative with respect to θ:

dr/dθ = a * b * e^(b * θ) * i + a * b^2 * e^(b * θ) * j

So the velocity of the particle is given by:

v(θ) = a * b * e^(b * θ) * ω * i + a * b^2 * e^(b * θ) * ω * j

Answer:

Step-by-step explanation:

v(θ) = a * b * e^(b * θ) * ω * i + a * b^2 * e^(b * θ) * ω * jj

The system of equations for cost of company A and B is c = 40 + 2s and c = 40 + 4s respectively.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The amount of videos streamed is = s

The cost of streaming each video is = c

The amount of money charged by company A as membership fee is = $40.

The amount of money charged by company A per video stream is = $2.

The equation for cost of company A will be -

c = 40 + 2s

The amount of money charged by company B as membership fee is = $40.

The amount of money charged by company B per video stream is = $4.

The equation for cost of company A will be -

c = 40 + 4s

Therefore, the equations are c = 40 + 2s and c = 40 + 4s.

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Video streaming company A charges a one-time $40 membership fee and $2 per video stream

Video streaming company B charges a one-time $20 membership fee and $4 per video stream.

Let the variable s represent the amount of videos streamed and let the variable c represent the cost

For how many video streams will the cost be the same for both companies?

Which system of equations can be used to solve this problem?