May someone please help me find the domain and range thank you for the help

The Expression x^2 - 6x + 9 when x = 2 + i   is -2i

To evaluate the expression x^2 - 6x + 9 when x = 2 + i, we substitute the value of x into the expression:

(2 + i)^2 - 6(2 + i) + 9

Simplifying the first term, we get:

(2 + i)^2 = 2^2 + 2(2)(i) + i^2 = 4 + 4i + i^2

Since i^2 = -1, we can substitute that in and simplify further:

(2 + i)^2 = 4 + 4i - 1 = 3 + 4i

Now we substitute this into the original expression:

(2 + i)^2 - 6(2 + i) + 9 = (3 + 4i) - 6(2 + i) + 9

Simplifying further, we get:

= 3 + 4i - 12 - 6i + 9

= 0 - 2i

= -2i

Therefore, the value of x^2 - 6x + 9 when x = 2 + i is -2i.

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The value of P(B) is simply the conditional probability of B given A, which is 0.3.

Given that events A and B are independent with P(A) = 0.63 and P(B|A) = 0.3, we can use the formula for the probability of independent events to find P(B).

P(B|A) = P(B)

Therefore, P(B) = 0.3.

Since events A and B are independent, the probability of B occurring is not affected by whether or not A occurs. Therefore, the value of P(B) is simply the conditional probability of B given A, which is 0.3.

Rounding to the nearest thousandth, P(B) is 0.300.

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Answer:

Ian has 14 more pieces of brown fabric than green fabric. (In meters its 2 1/6 more)

Step-by-step explanation:

Answer:

1500

Step-by-step explanation:

Answer:

(a) 5.3 grams

(b) 0.2 years

Step-by-step explanation:

(a) Step 1:  Since we're already given A0, we simply plug in 0.5 for t to find A(0.5), aka the amount of Thorium-234 remaining after 0.5 years:

[tex]A(0.5)=1000e^(^-^1^0^.^4^9^8^*^0^.^5^)\\A(0.5)=1000e^(^-^5^.^2^4^9^)\\A(0.5)=5.252768542\\A(0.5)=5.3[/tex]

Thus, the amount of Thorium-234 remaining after 0.5 years is approximately 5.3 grams.

(b) We plug in 115 for A(t) and 1000 for A0.  Then, we must solve for t: Thus, our equation to solve for t, time in years, is

[tex]115=1000e^(^-^1^0^.^4^9^8^t^)[/tex]

Step 1:  Divide both sides by 1000.

115/1000 = e^(-10.498t)

0.115 = e^(-10.498t)

Step 2:  Take the natural log (ln) of both sides.

ln(0.115) = ln(e^(-10.498t))

Step 3:  According to the rules of natural logs, we can bring -10.498t down and multiply it by ln(e) on the right-hand side of the equation:

ln(0.115) = -10.498t * ln(e)

ln(0.115) = -10.498t * 1

ln(0.115) = -10.498t

Step 4:  Now, we divide both sides by -10.498 and round the result to find out after about how many years will 115 grams of thorium-234 be remaining:

(ln(0.115) = -10.498t) / -10.498

0.2060223996 = t

0.2 = t

Thus, there will be 115 grams of thorium-234 remaining after about 0.2 years

Some of the reasons why math is important include:

Mathematics teaches us the invaluable skills of critical thinking via logical and systematical reasoning for solving complicated problems. It is, however, essential to know that mathematics is omnipresent in our day-to-day lives but we may not be conscious about it.

Our math-related actions include computing tips, shopping, allocating time for daily tasks as well as cooking meals. With a strong foundation in Mathematics, several career paths such as engineering, finance, accounting or data analysis can materialize for perspective job-visors; hence enabling them towards professional success.

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From the given table, the following statements can be determined:

C. There is a y-intercept at (-12, 0).

B. In the interval from x = -4 to x = 0, F(x) is decreasing.

A y-intercept is the point where the graph of a function intersects the y-axis. In this case, the y-intercept is at (-12, 0), which means that when x = 0, the value of f(x) is 0.

A function is decreasing in an interval if the values of the function decrease as the input values increase. In this case, we can see that the values of f(x) decrease as x increases from -4 to 0.

The statement A is incorrect because there is only one x-intercept at (0, 4). The statement D is incorrect because there is no line of symmetry at x=0.5.

Therefore, the statements C and B can be determined from the given table.

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Answer:

Step-by-step explanation:

There are 96 cells

The total area of the prism is (a) 120 + 20k in terms of k

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

The pentagonal prism

The total area of the prism is calculated as

Area = 2 * Pentagon + 5 * Rectangle

Given that

P = 20 and

Apothem, a = k

We have

Pentagon = 1/2 * 20 * k

Pentagon = 10k

Next, we have

Rectangle = 6 * P/5

So, we have

Rectangle = 6 * 20/5

Rectangle = 24

Recall that

Area = 2 * Pentagon + 5 * Rectangle

So, we have

Area = 2 * 10k + 5 * 24

Evaluate

Area = 20k + 120

Hence, the total area of the prism is (a) 120 + 20k

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To find the total area of a prism, we need to add up the area of all its faces. The given prism has a rectangular base with length 20 inches and width 6 inches. The area of the base is therefore 20 x 6 = 120 square inches.

The prism also has two congruent rectangular faces, each with a length of 20 inches and a height of K inches. The area of each face is therefore 20K square inches. Since there are two such faces, their total area is 2 x 20K = 40K square inches.
Finally, the prism has two more rectangular faces, each with a length of 6 inches and a height of K inches. The area of each face is therefore 6K square inches. Since there are two such faces, their total area is 2 x 6K = 12K square inches.
Adding up all the face areas, we get:
120 + 40K + 12K = 120 + 52K
Therefore, the total area (in terms of K) of the prism is 120 + 52K square inches.

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The standard deviation of the response time is 1.53 minutes.

To get standard deviation, we will determine z-scores corresponding to the given percentiles and use them to calculate the standard deviation.

Z-score = z = (x - μ) / σ

For the lower bound of 10 minutes:

z = (10 - 13) / σ

For the upper bound of 16 minutes:

z = (16 - 13) / σ

As normal distribution is symmetric, the z-score corresponding to the lower tail of 2.5% is -1.96, and the z-score corresponding to the upper tail of 2.5% is 1.96.

Using z-scores, we set up  equations:

(10 - 13) / σ = -1.96

(16 - 13) / σ = 1.96

Solving the first equation:

-3 / σ = -1.96

σ = -3 / -1.96

Solving the second equation:

3 / σ = 1.96

σ = 3 / 1.96

Dividing both sides by 1.96:

-3 / 1.96 = σ

1.53 = σ

Full question:

The respone times for a certain ambulance company are normally distributed with a mean of 13 minutes.95% of the response times are between 10 and 16 minutes. What is S.D. of the response time.

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The value of p when q is equal to 2 is 108

Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value.

This means as x increases y reduces and vice versa.

If p is inversely proportional to q, then

p = k/q

p = 18 and q = 12

18 = k/12

k = 18 × 12 = 216

When q =2

p = 216/2

p = 108

therefore the value of p is 108

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Answer:

To find the solution to the inequality 9 - y > 12, we need to isolate the variable y.

9 - y > 12

Subtract 9 from both sides:

-y > 12 - 9

-y > 3

Since we have a negative coefficient for y, we need to flip the inequality sign when multiplying or dividing by a negative number. In this case, we can multiply both sides of the inequality by -1 to simplify it further:

y < -3

The inequality states that y is less than -3.

Now let's check which value among the given options satisfies this inequality:

A) 2: 2 is not less than -3. It is greater.

B) -6: -6 is less than -3. It satisfies the inequality.

C) 8: 8 is not less than -3. It is greater.

D) -1: -1 is less than -3. It satisfies the inequality.

Based on the given options, the values that satisfy the inequality y < -

Step-by-step explanation:

The angle between the vectors is given as follows:

θ = 60º.

The formula for the angle between the vectors in this problem is given as follows:

cos(θ) = uv/(|u||v|)

The vectors are given as follows:

The dot product between the vectors is given as follows:

uv = <-2,3><1,2> = -2 + 6 = 4.

The norms for each vector are given as follows:

Applying the arccosine function, the angle is given as follows:

[tex]\theta = \arccos{\left(\frac{4}{\sqrt{13} \times \sqrt{5}}\right)}[/tex]

θ = arccos(0.49613893835)

θ = 60º. (approximately).

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Answer:

10

Step-by-step explanation:

the side is 13 and 3 so the difference is 10 on that side

on the bottom side it's 3 and if it's the same it's 10

We can infer that the point (8, -15) was reflected over the y-axis to (-8, -15) based on the change in the x-coordinate while the y-coordinate stays the same.

The y-axis reflected the point (8, -15) over to (-8, -15).

The x-coordinate changes its sign but the y-coordinate stays the same when a point is mirrored over the y-axis.

In this instance, the y-coordinate, -15, remains constant but the x-coordinate, 8, of the original point changes to -8 in the reflected point.

This shows that the y-axis is where the reflection took place.

Imagine a coordinate plane with the x-axis running horizontally and the y-axis running vertically in order to see this.

As a vertical mirror, the y-axis reflects points on either side of it.

When a point crosses the y-axis in reflection, it effectively flips to the other side of the axis while keeping its y-coordinate.

In this case, the point (8, -15) is initially situated in the positive x-direction on the right side of the y-axis.

After reflection, it becomes (-8, -15) and appears on the left side of the y-axis in the negative x-direction.

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Answer:

The point is reflected to the Y-axis. It can be either A or B, but I mostly positive it's A.

Step-by-step explanation:

Good luck on the final module exam! I'm counting on you.

The mathematical function that is modeled in this table is C) f(x) = 1,000(0.80)ˣ⁻¹.

A mathematical function is described as an equation, expression, rule or law defining the relationship between the independent variable and dependent variable.

For instance, there are many types of functions, including:

Initial value = 1,000

Percentage of decrease = 20%

Decay factor = 0.80 (1 - 0.20)

x          f(x)       Using Option C:

1        1,000      1,000(1)

2         800       1,000(0.80)¹

3         640       1,000(0.80)²

4          512       1,000(0.80)³

Thus, the correct function is Option C.

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Answer: 9530

Step-by-step explanation: It has to be 9 in the thousands place to start of. And for it to round to 10,000, it would have to be 5 since it would round up one more thousand. And I would just say 3 because its bigger. Then 0

The number that belongs on the green box is given as follows:

g = 11.08.

Suppose we have a triangle in which:

The lengths and the sine of the angles are related as follows:

[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]

The sum of the internal angles of a triangle is of 180º, hence the missing angle is given as follows:

120 + 37 + x = 180

157 + x = 180

x = 23º.

Then the relation to obtain the number in the green box is given as follows:

sin(23º)/5 = sin(120º)/g

g = 5 x sine of 120 degrees/sine of 23 degrees

g = 11.08.

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Answer:

x = 8.8 cm

Step-by-step explanation:

This is a right-angled triangle, and we are given two sides, so we can use pythagoras Theoren

[tex]a^{2} +b^{2} =c^{2}[/tex]

Where 'c' is the hypotenuse (the longest side in right angled triangle and is always opposite to the 90 degree angle).

'a' and 'b' are the other two sides.

So now we have:

2.6^2 + x^2 = 9.2^2 (Solve for 'x')

x^2 = 9.2^2 - 2.6^2

x = [tex]\sqrt{9.2^{2} - 2.6^{2} }[/tex]

x = 8.8 cm (2 s.f. as other dimensions are also 2 s.f.)

The output levels that will maximize profits are Q1 = 52.5 and Q2 = 52.5.

To maximize profits, we need to find the output levels of the two goods that will maximize the difference between total revenue and total cost (i.e., profit).

The profit function can be expressed as:

π = TR - TC

  = 15Q1 + 18Q1^2 + 15Q2 + 18Q2^2 - 20 - 2Q1.Q2 - 393

Taking the partial derivative of the profit function with respect to Q1 and setting it equal to zero, we get:

∂π/∂Q1 = 15 + 36Q1 - 2Q2 = 0

Taking the partial derivative of the profit function with respect to Q2 and setting it equal to zero, we get:

∂π/∂Q2 = 15 + 36Q2 - 2Q1 = 0

Using Cramer's rule, we can solve for Q1 and Q2:

Q1 = (2(15) - (15)(36))/(-4) = 52.5

Q2 = (2(15) - (15)(36))/(-4) = 52.5

Therefore, the output levels that will maximize profits are Q1 = 52.5 and Q2 = 52.5.

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Yes the boa constrictor population would become a problem, since the population of beetles in this rainforest community were to disappear, the population of poison dart frogs will most likely be affected;

The populations feed on Beetles and serve as food for poison dart frogs.

Since poison dart frogs depend on beetles for food, then, a decrease in the population of the beetles in the forest community will most likely result in a decrease in the population of the poison dart frogs.

In conclusion, we can say that the beetles serve as food for poison dart frogs.

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Answer:

  (x, y) = (2, 1)

Step-by-step explanation:

You want the solution to the system of equations ...

When the coefficients are not nicely related, graphical methods or matrix methods are preferred, as elimination or substitution can result in messy arithmetic with large numbers.

The first attachment shows a calculator's solution using row-reduction of the augmented matrix of coefficients. It tells us the solution is ...

  (x, y) = (2, 1)

A solution similar to the use of Cramer's rule can be found using the cross-multiplication method. For this, we rewrite the equations to general form, and make a list of the coefficients with the x-coefficients repeated at the end of the list:

Now, we form the differences of the cross products in each pair of columns:

  ∆ = (148)(148) -(231)(231) = -31,457

  ∆x = (231)(-610) -(148)(-527) = -62,914

  ∆y = (-527)(231) -(-610)(148) = -31,457

And the solution is ...

  x = ∆x/∆ = -62,914/-31,457 = 2

  y = ∆y/∆ = -31,457/-31,457 = 1

The solution is (x, y) = (2, 1).

__

Additional comment

You might consider this to be "messy arithmetic with large numbers." Yes, it looks that way, but there are actually fewer operations required here than when using the elimination method.

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The future value of the emergency fund after 6 years will be approximately $159,321.50.

To calculate the future value of the emergency fund using annuity due tables, we need to break down the given information and apply the appropriate formulas.

Given:

Sienna health and fitness deposits $5000 at the beginning of each three months.

The deposits have been made for the last 6 years.

The interest rate is 8% compounded quarterly.

To calculate the future value of the emergency fund, we need to determine the number of compounding periods and the interest rate per period.

Number of compounding periods:

Since the deposits are made every three months for 6 years, we have:

6 years * 4 quarters/year = 24 compounding periods.

Interest rate per period:

The interest rate is 8% per year, compounded quarterly. To find the interest rate per quarter, we divide it by 4:

8% / 4 = 2% per quarter.

Now, using the annuity due tables 12-1, we can find the future value factor for 24 periods at an interest rate of 2% per quarter. Let's denote this factor as FV.

Using the annuity due table, we find that the future value factor for 24 periods at 2% per quarter is 31.8643.

To calculate the future value of the emergency fund, we multiply the quarterly deposit amount ($5000) by the future value factor (31.8643):

Future Value = $5000 * 31.8643 = $159,321.50

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Answer:

The expected count of rolls to land showing a 3 is 10.00.

Answer:

2/8, 3/8, and 4/8

Step-by-step explanation:

Answer:

- 3 , 7 , - 13 , 5x + 2

Step-by-step explanation:

A

to evaluate f(0) substitute x = 0 into f(x)

f(0) = 5(0) - 3 = 0 - 3 = - 3

B

substitute x = 2 into f(x)

f(2) = 5(2) - 3 = 10 - 3 = 7

C

substitute x = - 2 into f(x)

f(- 2) = 5(- 2) - 3 = - 10 - 3 = - 13

D

substitute x = x + 1 into f(x)

f(x + 1)

= 5(x + 1) - 3 ← distribute each term in the parenthesis by 5

= 5x + 5 - 3 ← collect like terms

= 5x + 2

Answer:

A) -3

B) 7

C) -13

D) 5x+2

Step-by-step explanation:

For A, B, and C substitute the value stated in the parenthesis.

A) f(0) means to find the value when x=0, so we substitute 0 where x is in the function.

[tex]5(0)-3[/tex]

Then use PEMDAS and multiply first and then subtract 3 from the product.

[tex]5(0)=0\\0-3=-3[/tex]

B) Take the same steps as before with a different value. Substitute 2 for x.

[tex]5(2)-3\\5(2)=10\\10-3=7[/tex]

C) Also the same thing as the previous problems. Substitute -2 for the value of x.

[tex]5(-2)-3\\5(-2)=-10\\-10-3=-3[/tex]

D) Similar to above substitute x+1 where x is.

[tex]5(x+1)-3\\[/tex]

Then distribute 5(x+1) to get

[tex]5x+1(5)\\5x+5[/tex]

Then simplify the equation

[tex]5x+5-3=5x+2[/tex]

Answer:

Yes, .023 is a rational number.

Step-by-step explanation:

A rational number is defined as any number that can be expressed as a ratio of two integers, where the denominator is not zero.

To show that .023 is a rational number, we can express it as a fraction in which the numerator and denominator are integers.

We can write:

.023 = 23/1000

Both the numerator (23) and denominator (1000) are integers, so .023 is a rational number.

Answer:

The volume of the cylinder can be calculated using the formula V = πr²h, where r is the radius and h is the height:

V= πr²h = π(4cm)²(10cm) = 160π cm³

The density of the material is given by the mass per unit volume:

density = mass/volume = 500g / 160π= π(4 cm)²(10 cm)

= 160π cm³

The mass and volume are related by density (ρ), which is defined as mass per unit volume:

ρ = m/V

where m is the mass and V is the volume.

Substituting the given values, we get:

ρ = 500 g / 160π cm³

ρ ≈ 0.988 g/cm³

Therefore, the density of the material the cylinder is made of is 0.988 g/cm³.

Answer: 82

Step-by-step explanation:

Sorry if I'm wrong but I hope this helps! :)