which number is irratonal
a. _/100
b. 1/8
c. -2.2675
d. 3/16

The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

To find the values of Z, we can start by expressing 2 + i√3 in polar form. Let's denote it as re^(iθ), where r is the modulus and θ is the argument.

Given: 2 + i√3

To find r, we can use the modulus formula:

r = sqrt(a^2 + b^2)

= sqrt(2^2 + (√3)^2)

= sqrt(4 + 3)

= sqrt(7)

To find θ, we can use the argument formula:

θ = arctan(b/a)

= arctan(√3/2)

= π/3

So, we can express 2 + i√3 as sqrt(7)e^(iπ/3).

Now, we can find the values of Z by taking the natural logarithm (ln) of sqrt(7)e^(iπ/3) and adding 2πik, where k is an integer. This is due to the periodicity of the logarithmic function.

ln(sqrt(7)e^(iπ/3)) = ln(sqrt(7)) + i(π/3) + 2πik

Therefore, the values of Z are:

Z = ln(2 + i√3) + 2πik, where k is an integer.

The values of Z such that e² = 2 + i√3 are Z = ln(2 + i√3) + 2πik, where k is an integer.

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Step-by-step explanation:

EDHA I DONT LTHINK SOANSWER IT PROBLEM EASY

(–3, 5) satisfies both the equation 6x+ 5y = 7 and the equation x +4y = 17.

Betty correctly determined that the ordered pair (–3, 5) is a solution to the system of linear equations 6 x + 5 y = 7 and x + 4y = 17.

Based on this information, which statement is correct?

If a system of equations of two variables has a single solution (x, y), then both equations must be satisfied for x and y.

6 x + 5 y = 7

x + 4y = 17

The ordered pair (–3, 5) is a solution to the system of linear equations.

\(=\rm 6x +5y=17\\\\6\times (-3) + 5 \times 5 \\\\ =-18 + 25 = 7\\\\ And\\\\ x+4y = 7 \ -3 + 4\times 5\\\\ -3+20 \\\\ = 17\)

Hence, (–3, 5) satisfies both the equation 6x+ 5y = 7 and the equation x +4y = 17.

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Answer:

I believe the answer is D

Step-by-step explanation:

Given: X-3(x+2)=4X-3(x+2)=4

Find: the solution of the given equation

Explanation:

on solving equation (1) and (2) , we get

Answer:

x = -5

Step-by-step explanation:

    x - 3(x + 2)= 4

    x - 3x - 3*2 = 4     {Distributive property}

   x - 3x  - 6    = 4

Combine like terms in LHS,

         -2x - 6  = 4

Add 6 to both sides,

               -2x = 4 + 6

               -2x = 10

Divide both sides by (-2)

                   x = 10 ÷ (-2)

                   \(\sf \boxed{x= -5}\)

Answer:

a.) since he already has 40 in his savings account, start the line at (0,40) on the y-axis and then go up 15 every hour

b.) 15 or 15/1

c.) for each hour Donny spends working, the amount of money he has go up by 15

d.) (0,40)

e.) the vertical intercept or (y-intercept) is (0,40) because this is how much money Donny already has in savings

The correct answer is likelihood that a foreman would earn more than $1100 is approximately 0.8413 or 84.13%.

To determine the likelihood that a foreman would earn more than $1100, we need to calculate the probability that a normally distributed variable exceeds that threshold.

Given that the weekly incomes of shift foremen in the glass industry are normally distributed with a mean of $1000 and a standard deviation of $100, we can use the properties of the normal distribution to find the desired probability.

We can convert the problem into a standard normal distribution by applying the z-score formula:

z = (x - μ) / σ

where:

x is the value we are interested in ($1100 in this case),

μ is the mean of the distribution ($1000), and

σ is the standard deviation of the distribution ($100).

Plugging in the values:

z = (1100 - 1000) / 100

z = 1

Next, we need to find the probability associated with a z-score of 1. We can refer to a standard normal distribution table or use statistical software to find this value.

Looking up the probability corresponding to a z-score of 1, we find that it is approximately 0.8413.

Thus, the likelihood that a foreman would earn more than $1100 is approximately 0.8413 or 84.13%.

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If you select a marble without looking and then put it back if you do this 90 times, the probability of selecting an orange or a pink marble on any given trial is 1/2 or 0.5.

If you select a marble without looking and then put it back, the probability of selecting any particular marble on any given trial is the same for all marbles. Assuming there are only two possible outcomes - selecting an orange marble or a pink marble - the probability of selecting an orange or a pink marble on any given trial is 1/2 or 0.5.

Since the probability of selecting an orange or a pink marble on each trial is the same, the best prediction for the number of times you will select an orange or a pink marble out of 90 trials is an equal number of times for each color. Therefore, the best prediction for the number of times you will select an orange or a pink marble is 45 times each.

This is only a prediction based on probability, and the actual number of times you select an orange or a pink marble may differ from the prediction due to chance. However, over a large number of trials, the actual outcomes should approach the predicted probabilities.

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For a one-tailed hypothesis test (upper tail), the p-value is computed to be .034. If the test is being conducted at the 5% level of significance, the null hypothesis C. is rejected

A one-tailed hypothesis test refers to a statistical test in which the alternative hypothesis is either greater than or less than the null hypothesis, but not both. Since the problem states that it is a one-tailed hypothesis test (upper tail), the alternative hypothesis, H1, will be a greater than or > sign. Hypothesis testing is the method of determining whether or not an assertion about a population parameter is consistent with sample data. A hypothesis test is conducted to assist in deciding between two competing hypotheses. One hypothesis is the null hypothesis (H0), which is a statement of the population parameter that is being tested.

In a hypothesis test, the null hypothesis is rejected if the test statistic falls in the rejection region. The test statistic, which measures the distance between a sample estimate and the null hypothesis, is used to assess whether or not the null hypothesis should be rejected. Reject the null hypothesis if the p-value is less than or equal to α. Since the p-value of 0.034 is less than the level of significance, α, of 0.05, the null hypothesis will be rejected, according to the question above. Therefore, option C is correct.

The Question was Incomplete, Find the full content below :

For a one-tailed hypothesis test (upper tail), the p-value is computed to be .034. If the test is being conducted at the 5% level of significance, the null hypothesis

a. could be rejected or not rejected depending on the sample size.

b. could be rejected or not rejected depending on the sample mean.

c. is rejected.

d. is not rejected.

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Answer: 130=5x

Step-by-step explanation: If the cost is proportional to the number of days, the cost is the same per day. Therefore, an equation to find how much per day it would cost would be represented with the given information. She brought the kid to daycare for 5 days and paid 130$.

Therefore, the equation to figure out cost per day is-----

130$ = 5x

Hope this helped.

Sincerely,

A nerd <3

To sketch the vector, use the x and y coordinates given and draw an arrow from the origin to the indicated point. To find vectors by inspection, look for x and y components in equations or diagrams and add them together to get the resulting vector.

To sketch a vector, you should first draw a set of coordinate axes. Then, draw an arrow from the origin to the point that the vector represents. The length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector. To find vectors by inspection, you should look at the coordinates of the vector and use them to determine the magnitude and direction of the vector.

For example, if a vector has coordinates (3, 4), you can determine that its magnitude is 5 (using the Pythagorean theorem) and that its direction is northeast (since it has positive x and y coordinates). Here is an example of how to sketch a vector and find vectors by inspection:

By inspection, determine that the magnitude of v is 5 and its direction is northeast.

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Yes, line is used to define an angle.

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

When two straight lines or rays intersect at a single endpoint, an angle is created.

The vertex of an angle is the location where two points come together.

The common point is referred to as the vertex.

The length of the angle formed when two rays or arms intersect at a common vertex is known as an angle measure in geometry.

A straight line is a straight angle.

Therefore, two lines are used to define an angle.

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The function f(x).g(x) = 4x³ - 17x² + 15x + 18 and the domain of this function is (-∞, +∞).

The domain of a function is the set of all possible input values (also known as the independent variable) for which the function is defined.

In other words, it is the set of values of x for which the function has a corresponding output value (also known as the dependent variable).

Here we have

f(x) = 4x + 3

g(x) = x² - 5x + 6  

Then f(x) · g(x) can be calculated as follows

=> (4x + 3) [ x² - 5x + 6 ]

Using distributive property, we get:

=> 4x (x² - 5x + 6) + 3(x² - 5x + 6)

=> 4x³ - 20x² + 30x + 3x² - 15x + 18

=> 4x³ - 17x² + 15x + 18  

Hence, f(x).g(x) = 4x³ - 17x² + 15x + 18    

The domain of the function f(x) = 4x³ - 17x² + 15x + 18 is all real numbers since there are no restrictions or conditions that would make the function undefined for any value of x.

Therefore,

The function f(x).g(x) = 4x³ - 17x² + 15x + 18 and the domain of this function is (-∞, +∞).

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The volume of the solid obtained by rotating the region bounded by y = x^2 and y = 6 about the line x = -3 is approximately 481.39 cubic units.


To find the volume of the solid, we can use the method of cylindrical shells. The region bounded by y = x^2 and y = 6 in the first quadrant is a parabolic shape above the x-axis.
To set up the integral for the volume, we consider an infinitesimally small vertical strip of thickness Δx at a distance x from the line x = -3. The height of the strip is given by the difference between the two curves: h = 6 – x^2. The circumference of the cylindrical shell is given by the formula 2πr, where r is the distance between x and the line x = -3, which is r = x + 3.

The volume of the infinitesimal shell is then given by dV = 2π(x + 3)(6 – x^2)Δx. Integrating this expression from x = 0 to x = 3, we obtain the volume V = ∫[0,3] 2π(x + 3)(6 – x^2)dx. Evaluating this integral, we find V ≈ 481.39 cubic units.
In summary, the volume of the solid obtained by rotating the region bounded by y = x^2 and y = 6 about the line x = -3 is approximately 481.39 cubic units.

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Answer:

$1.85

Step-by-step explanation:

Answer:

14x4 so the answer would be 56 laps

Step-by-step explanation:

The function to find the inverse of is not provided in the question, therefore the steps to find the inverse cannot be shown.

In order to find the inverse of a function, the function must be provided. Once the function is given, the steps to find the inverse typically involve switching the x and y variables and solving for y. However, without the original function, it is impossible to provide an answer with steps.
find the inverse of the given function. Please provide the function that you need the inverse for, as it was not included in your question. Once you provide the function, I can give you the main answer along with a step-by-step explanation.

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Answer:

105 in each pile of cards .5 types of card in his collection

The probability that at least one of them is a girl is 0.9781

From the question, we have the following parameters that can be used in our computation:

P(Boy) = 0.529

Number of selection, n = 6

Using the above as a guide, we have the following:

P(At least 1 girl) = 1 - P(No girl)

Substitute the known values in the above equation, so, we have the following representation

P(At least 1 girl) = 1 - (0.529)^6

Evaluate

P(At least 1 girl) = 0.9781

Hence, the probability is 0.9781

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The result of the logarithmic functions by logarithm tables are listed below:

This question can be resolved by means of logarithm properties and logarithm tables or numerical methods. Now we proceed to evaluate each logarithmic functions:

Case 1:

㏒₁₀ 0.1

By using rational numbers:

㏒₁₀ (1 / 100)

By logarithm properties:

㏒₁₀ 1 - ㏒₁₀ 100

By logarithm tables:

0 - 2

- 2

Case 2:

㏒₅ 125

By logarithm tables:

3

Case 3:

㏒₈ 64

By logarithm tables:

2

Case 4:

\(\log_{\frac{1}{3} } 9\)

By logarithm tables:

- 2

Case 5:

\(\log_{\frac{1}{2}} \frac{1}{2}\)

By logarithm tables:

1

Case 6:

㏒₄₉ 7

By logarithm tables:

1 / 2

Case 7:

㏒₉ 3

By logarithm tables:

1 / 2

Case 8:

㏒₃ 81

By logarithm tables:

4

Case 9:

㏒₄ 8

By logarithm tables:

3 / 2

Case 10:

㏒₁₀₀ 10,000

By logarithm tables:

2

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Explication étape par étape:

Étant donné la fonction polynomiale f (x) = -2x² + 4x + 6. Pour vérifier si f (-1) est un facteur de l'expression, nous devons montrer que f (-1) est équivalent à zéro. S'il est nul, donc x + 1 est un facteur du polynôme.

Preuve

f (x) = -2x² + 4x + 6

f (-1) = -2 (-1) ² + 4 (-1) +6

f (-1) = -2 (1) -4 + 6

f (-1) = -2-4 + 6

f (-1) = -6 + 6

f (-1) = 0

Puisque f (-1) = 0, donc x + 1 est un facteur du polynôme.

Ensuite, il faut obtenir l'autre racine du polynôme. Pour obtenir cela, nous devons factoriser la fonction polynomiale donnée.

Soit f (x) = 0

-2x² + 4x + 6 = 0

multiplier par -1

2x²-4x-6 = 0

diviser par 2

x²-2x-3 = 0

x²-3x + x-3 = 0

x (x-3) +1 (x-3) = 0

(x + 1) (x-3) = 0

x + 1 = 0 et x-3 = 0

x = 1 et x = 3

Par conséquent, l'autre racine du polynôme en dehors de 1 est x = 3

Answer:

\( \huge \frac{2}{3} \\ \)

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

\(m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\\)

From the question we have

\(m = \frac{14 - - 4}{12 - - 15} = \frac{14 + 4}{12 + 15} = \frac{18}{27} = \frac{2}{3} \\ \)

We have the final answer as

\( \frac{2}{3} \\ \)

Hope this helps you

Answer:

(2,0) is an ordered pair

Step-by-step explanation:

y=1/2x-2 hope this helps :)

Answer:

x^2 +3x- 18=0

x^2 +6x -3x - 18 =0

x( x+6) - 3(x +6) =0

(x-3) + ( x+6) =0

therefore, x= -6,3

Answer:

He swam 1/2 mile more and biked 1  1/4 mile more in July

Step-by-step explanation:

June -- Bike    4 * ( 3  1/4)  = 13 miles

            Swim 4 * (2  1/2) = 10 miles

July -- Bike   3 * (4  3/4) = 14 1/4 miles

         Swim   3 * (3  1/2) = 10 1/2 miles

14  1/4 - 13 =   1  1/4

10  1/2 - 10 =  1/2

Yes each side and each angle has a congruent corresponding part

The sum of all repetitions performed multiplied by the resistances used during a strength-training session is the workload.

To find the sum of all repetitions performed multiplied by the resistances used during a strength-training session, you would need to calculate the total workload.

This can be done by multiplying the number of repetitions for each exercise by the resistance used for that exercise, and then adding up the results for all exercises performed during the session.

For example, if you did 10 reps of bench press with 100 pounds, 8 reps of bicep curls with 50 pounds, and 12 reps of squats with 150 pounds, the total workload would be (10 x 100) + (8 x 50) + (12 x 150) = 2,600 pounds. This number represents the total amount of weight lifted during the session and can be used to track progress and adjust future workouts.

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Answer:

To receive 1 foot of snow it will take about 18 hours.

Step-by-step explanation:

Given that a city receives 2 inches of snowfall every 3 hours, to write and graph a function that describes the relationship and determine how long does it take to receive 1 foot of snow, the following calculation must be performed:

1 foot = 12 inches

(12/2) x 3 = X

6 x 3 = X

18 = X

Thus, to receive 1 foot of snow it will take about 18 hours.

Answer:

g(x) = e^(x + 2) + 2

Step-by-step explanation:

First, let's describe the shifts.

Vertical shift.

For a function f(x), a vertical shift of N units is written as:

g(x) = f(x) + N

If N is positive, then the shift is upwards.

If N is negative, then the shift is downwards.

Horizontal shift.

For a function f(x), a horizontal shift of N units is written as:

g(x) = f(x - N)

If N is positive, the translation is to the right

If N is negative, the translation is to the left.

Now let's solve the question.

f(x) = e^x

First, we have a vertical shift up of 2 units, then:

g(x) = f(x) + 2

Now we have a shift to the left of 2 units:

g(x) = f(x - (-2)) + 2

g(x) = f(x + 2) + 2

Then:

g(x) = e^(x + 2) + 2

The given function is f(x, y) = 7xy, and the region R is defined by \(R = {(x, y): -1 ≤ x ≤ 1, 0 ≤ y ≤ √(1 - x²)}.\)

We need to find the absolute maximum and minimum values of the given function on the region R.

Absolute maximum value: For this, we need to check the values of the function at the boundary of the region R, and also at the critical points (points where the partial derivatives are 0 or undefined).

The function is continuous and differentiable everywhere, so we can use the method of Lagrange multipliers to find the critical points.

\(Let g(x, y) = x² + y² - 1 = 0\)be the equation of the boundary of the region R, and let λ be the Lagrange multiplier. Then \(we need to solve the following equations:∇f(x, y) = λ∇g(x, y)7y = 2λx7x = 2λy x² + y² - 1 = 0\)

Multiplying the first equation by x and the second equation by y, and then subtracting the resulting equations, we get:\(7xy = 2λxy² + x² - xy + y² = 1\)

Dividing the first equation by y, we get:7x = 2λ

Using this value of λ in the second equation, we get:4x² - 2xy + 4y² = 1Substituting 7x/2 for λ in the first equation, we get:y = 7x²/4Substituting this value of y in the equation of the boundary, we get:x² + (7x²/4) = 1

Solving for x, we get:x = ±√(4/11)Substituting this value of x in y = 7x²/4, we get:y = 7/11

\(Therefore, the critical points are (√(4/11), 7/11) and (-√(4/11), 7/11).\)

Now we need to check the values of the function at these points and at the boundary of the regio\(n R.f(1, 0) = 0f(-1, 0) = 0f(√(4/11), 7/11) = 7(√(4/11))(7/11) = 2√(44)/11f(-√(4/11), 7/11) = 7(-√(4/11))(7/11) = -2√(44)/11f(x, y)\) is negative for all other points on the boundary of R. Therefore, the absolute maximum value of f(x, y) on R occurs at the point \((√(4/11), 7/11), where f(x, y) = 2√(44)/11.\)

Absolute minimum value:For this, we need to check the values of the function at the critical points (excluding the boundary of R), and also at the points where the partial derivatives are 0 or undefined.

Since there are no critical points (excluding the boundary of R), we only need to check the values of the function at the points \(where x = -1, 0, or 1.f(-1, 0) = 0f(0, 0) = 0f(1, 0) = 0f(x, y) is positive for all other points in R.\)

Therefore, the absolute minimum value of f(x, y) on R occurs at any of the \(points (±1, √(3)/2), where f(x, y) = ±7√(3)/4.\)Answer:The absolute maximum value of f(x, y) on R occurs at the \(point (√(4/11), 7/11), where f(x, y) = 2√(44)/11.\)

\(The absolute minimum value of f(x, y) on R occurs at any of the points (±1, √(3)/2), where f(x, y) = ±7√(3)/4.\)

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The absolute maximum value is f(√(1/2), 1/2) = 7(√(1/2))(1/2) = (7√2)/4, and the absolute minimum value is

f(-1, 0) = 7(-1)(0) = 0.

To find the absolute maximum and minimum values of the function f(x, y) = 7xy on the region R, we need to evaluate the function at its critical points and on the boundary of the region.

First, let's find the critical points of f(x, y) by taking the partial derivatives with respect to x and y and setting them equal to zero:

∂f/∂x = 7y = 0

∂f/∂y = 7x = 0

From these equations, we find that the only critical point is (x, y) = (0, 0).

Next, we need to evaluate the function on the boundary of the region R. The boundary consists of the semicircular disk described by -1 ≤ x ≤ 1 and 0 ≤ y ≤ √(1 - x²).

1. At y = 0:

  f(x, 0) = 7x(0) = 0

2. At y = √(1 - x²):

  f(x, √(1 - x²)) = 7x√(1 - x²)

To find the absolute maximum and minimum values, we compare the values of f(x, y) at the critical point and on the boundary.

At the critical point (0, 0), f(0, 0) = 7(0)(0) = 0.

Next, we evaluate f(x, √(1 - x²)) along the boundary:

f(x, √(1 - x²)) = 7x√(1 - x²)

To find the extreme values on the boundary, we can consider the function g(x) = 7x√(1 - x²). Since y = √(1 - x²), we eliminate y from the equation and work with g(x) instead.

Now, let's find the extreme values of g(x) on the interval -1 ≤ x ≤ 1. We can find these values by taking the derivative of g(x) and setting it equal to zero:

g'(x) = 7√(1 - x²) + 7x(-x / √(1 - x²)) = 7√(1 - x²) - 7x² / √(1 - x²)

Setting g'(x) equal to zero:

7√(1 - x²) - 7x² / √(1 - x²) = 0

Multiplying through by √(1 - x²) to clear the denominator:

7(1 - x²) - 7x² = 0

7 - 7x² - 7x² = 0

14x² = 7

x² = 7/14

x² = 1/2

x = ±√(1/2)

Since we are only interested in the interval -1 ≤ x ≤ 1, we consider the solution x = √(1/2).

Now, let's evaluate g(x) at the critical points and endpoints:

g(-1) = 7(-1)√(1 - (-1)²) = -7√(1 - 1) = -7(0) = 0

g(1) = 7(1)√(1 - 1) = 7(0) = 0

g(√(1/2)) = 7(√(1/2))√(1 - (√(1/2))²) = 7(√(1/2))

√(1 - 1/2) = 7(√(1/2))√(1/2) = 7(√(1/4)) = 7(1/2) = 7/2

From these evaluations, we can see that the absolute maximum value of f(x, y) on the region R occurs at (x, y) = (√(1/2), √(1 - (√(1/2))²)) = (√(1/2), 1/2), and the absolute minimum value occurs at (x, y) = (-1, 0).

Therefore, the absolute maximum value is f(√(1/2), 1/2) = 7(√(1/2))(1/2) = (7√2)/4, and the absolute minimum value is f(-1, 0) = 7(-1)(0) = 0.

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Answer:

(mn+3m)(n+p)

Step-by-step explanation:

Answer:

(mn + 3m)(n + p)

Step-by-step explanation:

Factorize by grouping:

\(mn^2+mnp\\mn(n+p)\\\\3mn+3mp\\3m(n+p)\\\\(mn+3m)(n+p)\)