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3
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7
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2
x
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=
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1
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4
x

Answer:

5ln3=ln(3^5)

Step-by-step explanation:

Given: 5ln(3)

Use rule: alog(b)=log(b^a), aln(b)=ln(b^a) (doesn't matter what the log base is)

Apply rule: ln(3^5)

Therefore, the solution to the equation \((z + 1)^7 + (z + 1)^7 = 0\) in the complex number system is z = -1.

To solve the equation\((z + 1)^7 + (z + 1)^7 = 0\) in the complex number system, we can simplify the equation and then find the values of z that satisfy it.

Let's start by simplifying the equation:

\((z + 1)^7 + (z + 1)^7 = 0\)

We notice that both terms on the left side of the equation are identical, so we can rewrite it as:

2(z + 1)^7 = 0

Now, we can divide both sides of the equation by 2 to isolate the term\((z + 1)^7:\)

\((z + 1)^7 = 0\)

To find the solutions, we set each factor of \((z + 1)^7\)equal to zero. In other words, we set the exponent 7 to be a multiple of 2:

z + 1 = 0

From this equation, we find that z = -1.

It's important to note that complex numbers have a real and imaginary part.

In this case, since the equation simplifies to a real number, the solution is a real number (-1).

If the equation involved complex terms or the roots of unity, the solutions could include complex numbers as well.

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First, we need to transform the mixed number into a fraction using the following expression:

So, 6 1/4 mile is equivalent to:

Then, we need to remember how to divide two fractions, so:

Now, to calculate the number of miles that Jonathn will run, we need to divide the total number of miles (25/4 miles) by 5 friends, then:

Therefore, Jonathan will run 5/4 miles

Answer: 5/4 miles

Answer:

x = 62.1

Step-by-step explanation:

Note the equal sign in this equation, what you do to one side, you do to the other. Isolate the variable, x, by dividing 10 from both sides of the equation:

\(621 = 10x\\\\\frac{621}{10} = \frac{10x}{10} \\\\x = \frac{621}{10} \\x = 62.1\)

Answer:

x = 62.1

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

16x + 19x + 5 = 180   {co-interior angles are supplementary}

Combine like terms;

35x + 5 = 180

Subtract 5 from both sides

35x = 180 - 5

35x = 175

Divide both sides by 35

x = 175/35

x = 5

19x + 5 = 19*5 + 5

           = 95 + 5

           = 100

Answer:

100⁰

Step-by-step explanation:

co interior angles add up to 180⁰

so l9x+5+16x=180⁰

35x+5⁰=180⁰

35x=180⁰-5⁰

35x=175⁰

Divide both side by the co-efficient of x which is 35

35x/35=175⁰/35⁰

x=5

Now to find the value of 19x+5,we have to substitute any x in it by 5

so 19x+5

19(5)+5

95+5

100⁰

Thanks. I hope it will be helpful to you

Answer:

y = -2/3 x - 13/3

Step-by-step explanation:

y = -2/3 x + 3/2

y = mx + b

m = -2/3

The slope of the given line is -2/3. Parallel lines have equal slopes, so our line also has slope -2/3.

m = -2/3

y = mx + b

y = -2/3 x + b

Substitute the given point for x and y and solve for b.

-7 = -2/3 (4) + b

-21/3 = -8/3 + b

b = -13/3

Answer: y = -2/3 x - 13/3

A. The margin of error for a 99% confidence interval is $$2,320.75.

B. The confidence interval for the mean starting salary of college graduates who have taken a statistics course is CI = $42,462.25 to $47,103.75

PART A.

The margin of error (ME) is determined using the formula:

ME= z ∗ σ/√n

where:

z is the z-score for the desired confidence level

σ is the population standard deviation

n is the sample size

For a 99% confidence level, the z-score is 2.576. The population standard deviation is $10,272, and the sample size is 130.

Substituting these values into the formula, we have:

ME =  2.576 ∗ 10272/√130

ME = $2,320.75

PART B

The confidence interval (CI) is determined using the formula:

CI = \(\bar{x}\) ± ME

where:

\(\bar{x}\) is the sample mean

ME is the margin of error

The sample mean is $44,783, and the margin of error is $2,320.75.

Substituting the values into the formula, we get:

CI= 44783 ± 2320.75

CI = $42,462.25 to $47,103.75

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The vertex of the graphed function f(x) = [x - 4] + 3 is (4, 3).

The function f(x) = [x - 4] + 3 is in the form of an absolute value function, where the expression inside the absolute value brackets represents the input value shifted horizontally by 4 units to the right.

The constant term of 3 represents a vertical shift upwards by 3 units.

To find the vertex of this function, we need to determine the x-coordinate that corresponds to the minimum value of the absolute value function.

In this case, since the absolute value function is within brackets and not being multiplied or divided by a coefficient, the minimum value occurs at the point where the expression inside the brackets equals zero.

Therefore, setting x - 4 = 0, we find x = 4.

Substituting this x-value into the function, we find f(4) = [4 - 4] + 3 = 3. So the vertex of the graphed function is located at the point (4, 3), where x = 4 and y = 3. This means that the graph is shifted 4 units to the right and 3 units upward from the origin.

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The range of the given equation is [-1, infinity).

We are given that;

Equation  y= underroot(x+5​)

Now,

The domain of this equation is the set of x values that make the expression under the square root non-negative.

That is, x+5 >= 0, or x >= -5. So the domain is [-5, infinity).

The range of this equation is the set of y values that are obtained by plugging in the domain values into the equation. Since the square root function is always non-negative, and we are subtracting 1 from it, the smallest possible value of y is -1, when x = -5. As x increases, y also increases, and there is no upper bound for y.

Therefore, by the range the answer will be [-1, infinity).

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Answer:

-9

Step-by-step explanation:

This equation is written in slope-intercept form. -9 represents the y-intercept, and x represents the slope, which is positive one over one.

The maximum height of the golf ball on Mars is about 48.8 meters.

To find how much longer it would take for the golf ball hit on Mars to reach the ground, we can use the given equation h = -1.9t² + 26t, where h is the height of the object and t is the time in seconds. First, we need to find the time it takes for the golf ball to reach the ground on Mars. Setting h = 0, we get:

0 = -1.9t² + 26t

Solving for t using the quadratic formula, we get t = 13.684 or t = 0.856. Since the golf ball is launched upward, we need the positive value of t, so it takes about 13.7 seconds for the golf ball to reach the ground on Mars. Therefore, it takes 13.7 − 5.4 = 8.3 seconds longer for the golf ball hit on Mars to reach the ground than the golf ball hit on Earth.

To find the maximum height of the golf ball on Mars, we can use the formula h = -1.9t² + 26t, where t is the time when the height is maximum. Since the formula is a quadratic equation, the maximum height occurs at the vertex of the parabola, which is at t = -b/2a.

In this case, a = -1.9 and b = 26, so the time at maximum height is t = -26 / 2(-1.9) = 6.842. Plugging this value into the equation for h, we get:

= -1.9(6.842)² + 26(6.842) ≈ 48.8 meters

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If the equation be \($\lim _{x \rightarrow 6}\left(\frac{x^2-x-30}{x^2-3 x-18}\right)$$\) then the value is 1.22222

The term "numerical evidence" describes information that is expressed in a numerical manner, such as numbers, quantities, or statistical data. It is thought to be objective and quantifiable, and it is used to support a claim or argument.

The quantity of sales made during a specific business quarter is an example of numerical data. Simply put, if the response includes a number, the data is quantitative (numerical).

Let the equation be \($\lim _{x \rightarrow 6}\left(\frac{x^2-x-30}{x^2-3 x-18}\right)$$\)

Simplifying the above equation, we get

\($\frac{x^2-x-30}{x^2-3 x-18}= \frac{x+5}{x+3}$\)

\($=\lim _{x \rightarrow 6}\left(\frac{x+5}{x+3}\right)$$\)

Plug in the value x = 6

= (6 + 5)/(6 + 3)

= 11/9 = 1.22222

Therefore, the equation of \($\lim _{x \rightarrow 6}\left(\frac{x^2-x-30}{x^2-3 x-18}\right)$$\) be 1.22222.

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Answer:

−10x+188

Step-by-step explanation:

Bruh, easy. Just simplify it.

Answer:

The answer is "Option a"

Step-by-step explanation:

In this question, the answer is "option a", which is equal to 10, and which is based on the training load base chart.

Answer:

90

58 is closer to 60 and 25 is closer to 30. So when you add them you get 90.

Answer:

5 + 5 + 5 + 5 + 2454 + 76492 + 69238120 + 65928 = 69383014

Step-by-step explanation:

69383014 is the answer, I used a calculator

Please let me know if Im incorrect

Answer:

5+5+5+5+2454+76492+69238120+65928=69383014

\(\displaystyle\frac{3}{16}\)

Probability represents the likelihood of an event occurring. Complex probability is the likelihood of a series of events occurring.

Independent Events

The question states that the marbles are replaced after being recorded. This means that the separate drawing of marbles is independent of each other. So, the probability of an event occurring does not change based on events that happened earlier.

This is important to this question because it means that probability does not change based on if the one red marble was drawn first or second.

Probability of a Red

First, we need to find the probability of drawing a red marble. Probability is represented as the number of successful outcomes (drawing a red) over the number of possible outcomes (number of marbles). Out of the total 12 marbles, 3 of them are red. So, the probability of drawing a red is \(\displaystyle\frac{3}{12}\).

The Complement

In probability, the complement is the likelihood of an event not occurring. So, in this situation, the complement is the likelihood of not drawing a red. Out of the total 12 marbles, 9 are NOT red. So, the complement is \(\displaystyle\frac{9}{12}\).

Complex Probability

To find the probability of 2 different events both occurring, multiply the probabilities together.

Then, we can simplify the fraction by dividing by 9

This means that the probability of drawing exactly one red is 3/16.

Answer: Statistic

Step-by-step explanation: The difference between a parameter and statistic lies in the set of observation from which either quantity is derived. The parameter represents numerical values which are derived by examining or considering an entire population while the statistic is used to define numerical quantities derived from subset of the population called the sample. In the scenario described above, the population of interest would be the entire population of student and hence statistical derivations made would be called parameters. However, the scenario only experimented using student from two different classes which is a subset of the entire population of student. Hence, the obtained mean values of 25.40 and 20.41 for students in the formal and informal classes are categorized as statistic.

Answer:

4x

Step-by-step explanation:

So what you wanna do is look everywhere a point is on a line perfectly. Then see how much it takes per point that's on a line perfectly

4.61 gallons is the mean number of gallons of milk consumed last month​.

The most typical or average value among a group of numbers is called the mean. It is a statistical measure of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."

The mean (also known as that of the arithmetic mean, which varies with respect to the geometric mean) of a data is calculated as the sum of all values divided by the total number of values. This indicator of the central tendency is usually referred to as the "average".

The total number of gallons of milk consumed is:

\((7 \times 3) + (9 \times 4) + (7 \times 7) \\= 21 + 36 + 49 = 106\)

The total number of families is \(7 + 9 + 7 = 23\)

Therefore, the mean number of gallons of milk consumed last month is:

\(106/23 = 4.61\) gallons

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Answer:

  f(x +h) = 4x² +4h² +8xh +5x +5h +3

  (f(x+h) -f(x))/h = 4h +8x +5

  f'(x) = 8x +5

Step-by-step explanation:

For f(x) = 4x² +5x +3, you want the simplified expression f(x+h), the difference quotient (f(x+h) -f(x))/h, and the value of that at h=0.

Put (x+h) where h is in the function, and simplify:

  f(x+h) = 4(x+h)² +5(x+h) +3

  = 4(x² +2xh +h²) +5x +5h +3

  f(x +h) = 4x² +4h² +8xh +5x +5h +3

The difference quotient is ...

  (f(x+h) -f(x))/h = ((4x² +4h² +8xh +5x +5h +3) - (4x² +5x +3))/h

  = (4h² +8xh +5h)/h

  (f(x+h) -f(x))/h = 4h +8x +5

When h=0, the value of this is ...

  f'(x) = 4·0 +8x +5

  f'(x) = 8x +5

__

Additional comment

Technically, the difference quotient is undefined at h=0, because h is in the denominator, and we cannot divide by 0. The limit as h→0 will be the value of the simplified rational expression that has h canceled from every term of the difference. This will always be the case for difference quotients for polynomial functions.

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Answer:

11. D

12. B?

13. A

14. C

15. E

Step-by-step explanation:

I'm not completely sure about 12

Answer:

C

\( \sqrt{48} = \sqrt{2 \times 2 \times 2 \times 2 \times 3} \\ = \sqrt{16 \times 3} \\ = 4 \sqrt{3} \)

The prime factorization to write \(\sqrt{48}\) in the simplest form as  

48 = V2 -2 -2 -2 - 3 = 4V3

Prime factorization of any number indicates to express that number as a product of prime numbers. A prime number exists as a number that has precisely two factors, 1 and the number itself.

We require to express 48 as the product of its prime factors as 48.

= 2 \(\times\) 3 \(\times\) 2 \(\times\) 2 \(\times\) 2.

Therefore, \($\sqrt{48}=\sqrt{ (2 \times 2 \times 2 \times 2 \times 2)}\)

\($=4 \sqrt{3}$\)

\($4 \sqrt{3}$\) exists in the lowest radical form.

Therefore, the correct answer is option C. 48 = V2 -2 -2 -2 - 3 = 4V3.

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The nearest whole number, we get x = 12. We can find the value of x by using the law of sines. The law of sines states that the ratio of the sine of an angle of a triangle to the length of the side opposite that angle is the same for all three angles of the triangle.

In this case, the angle opposite x is 24 degrees, and the side opposite x is 24 units. Therefore, we have:

sin(24°)/x = sin(C)/24

Solving for x, we get:

x = 24 x sin(24°) / sin(C)

Plugging in the values of the angles, we get:

x = 24 x sin(24°) / sin(120°) = 12.02

The nearest whole number, we get x = 12.

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Answer:-3

Step-by-step explanation: