A marketing firm is considering making up to three new hires. Given its specific needs, the management feels that there is a 60% chance of hiring at least two candidates. There is only a 7% chance that it will not make any hires and a 10% chance that it will make all three hires.


a. What is the probability that the firm will make at least one hire? (Round your answer to 2 decimal places.)



b. Find the expected value and the standard deviation of the number of hires. (Round intermediate calculations to at least 4 decimal places. Round your final answers to 2 decimal places.)

Answer:

5 + m^3 n^2

----------------------

m^2 n^2

Step-by-step explanation:

To add fractions, we need to get a common denominator:

The common denominator is m^2 n^2.

Multiply the second term by m^2n/ m^2n

m/n * m^2n / m^2 n = m^3n / m^2n^2

Now we can add the two terms

5                               m^3 n^2

------                 + ---------------------------

m^2 n^2                      m^2 n^2

5 + m^3 n^2

----------------------

m^2 n^2

Answer:

-5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Sure, I can help you with that.

The scale of the map is 300 miles / 25 inches = 12 miles / inch.

Therefore, 35 inches on the map would be 35 * 12 = 420 miles.

Here's the calculation:

Code snippet

scale = actual distance / distance on map

12 miles / inch = 300 miles / 25 inches

35 inches * 12 miles / inch = 420 miles

Use code with caution. Learn more

I hope this helps! Let me know if you have other questions.

Answer:step 4

Step-by-step explanation: I just took the test pookies

Answer:

a. The cost at 3% is $46.57 b. The cost at 4% is $49.33 c. The cost at 5% is $52.21

Step-by-step explanation:

Using the Law of Cosines with angle 103° and adjacent sides 9 and 6, the remaining side is approximately 12.26 units long.

To find the remaining sides of the triangle, we can use the Law of Cosines. Let's assume that the angle of 103 degrees is opposite side c, and the adjacent sides are a = 9 and b = 6.

The Law of Cosines states:

[tex]c^2 = a^2 + b^2[/tex] - 2ab * cos(C)

Plugging in the known values:

[tex]c^2 = 9^2 + 6^2[/tex] - 2 * 9 * 6 * cos(103°)

Simplifying the equation:

[tex]c^2[/tex] = 81 + 36 - 108 * cos(103°)

Now we need to evaluate cos(103°).

Using a scientific calculator or trigonometric table, we find that cos(103°) ≈ -0.3090.

Substituting the value of cos(103°) back into the equation:

[tex]c^2[/tex] = 81 + 36 - 108 * (-0.3090)

Simplifying further:

[tex]c^2[/tex] = 117 + 33.2724

[tex]c^2[/tex]≈ 150.2724

Taking the square root of both sides:

c ≈ √150.2724

c ≈ 12.26

Therefore, the remaining side (opposite the angle of 103 degrees) is approximately 12.26 units long.

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The discount rate is increased by 12%, the new net present value will be approximately Rs. 5514.29.

To determine the net present value (NPV) when the discount rate is increased by 12%, we need to recalculate the NPV using the new discount rate.

Given:

Current NPV = Rs. 6172

Current discount rate = 9%

Increase in discount rate = 12%

To find the new NPV, we can use the formula:

New NPV = Current NPV / (1 + Increase in discount rate)

Calculating the new NPV:

New NPV = 6172 / (1 + 0.12)

New NPV = 6172 / 1.12

New NPV ≈ Rs. 5514.29

Therefore, if the discount rate is increased by 12%, the new net present value will be approximately Rs. 5514.29.

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Answer:

Step-by-step explanation:

To find the value of an investment compounded continuously, we can use the formula:

A = P * e^(rt)

Where:

A is the final amount

P is the principal amount (initial investment)

e is the mathematical constant approximately equal to 2.71828

r is the annual interest rate (as a decimal)

t is the time period in years

In this case, P = $10,000, r = 0.0315 (3.15% expressed as a decimal), and t = 13.

Plugging in the values into the formula, we get:

A = $10,000 * e^(0.0315 * 13)

Calculating the exponential part:

A = $10,000 * e^(0.4095)

Using a calculator or a math software, we can evaluate e^(0.4095) to get approximately 1.506.

A = $10,000 * 1.506

A ≈ $15,060.

Answer:

Ok, Here is your answer

Step-by-step explanation:

To find the percentage of players who played well on the baseball team, we need to divide the number of players who played well by the total number of players and then multiply by 100.

Number of players who played well = 6

Total number of players = 11

Percentage of players who played well = (6/11) x 100%

= 54.55%

Therefore, the answer is 54.55%. Hence, option D, 54.55%, is the correct answer.

The options that apply are:

A. A list of all questions from the lessons

B. Description of what you need to know or apply

C. Concepts tested

D. Reference column.

The options that are typically included in a table for each unit are:

- A list of all questions from the lessons: This helps in organizing and categorizing the questions based on the specific unit or topic.

- Description of what you need to know or apply: This provides an overview or summary of the key concepts, knowledge, or skills that are covered in the unit.

- Concepts tested: This section highlights the specific concepts or skills that will be tested or assessed in relation to the unit. It helps students understand the focus areas and what they need to prioritize in their learning.

- Reference column: This column may include additional information such as page numbers, section titles, or references to specific resources or materials that are relevant to the unit. It serves as a guide for further exploration or reference.

A brief quiz, on the other hand, is not typically included in a table for each unit. Quizzes are usually separate assessments that are administered to evaluate understanding and mastery of the unit's content.

So, the options that apply are:

- A list of all questions from the lessons

- Description of what you need to know or apply

- Concepts tested

- Reference column

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Answer:

5.4 ft²

Step-by-step explanation:

To find the surface area of the cone-shaped megaphone, use the surface area of a cone formula.

[tex]\boxed{\begin{minipage}{7cm}\underline{Surface area of a cone}\\\\$S.A.=\pi r^2+\pi rl$\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius of the circular base.\\ \phantom{ww}$\bullet$ $l$ is the slant height of the cone.\\\end{minipage}}[/tex]

The radius of a circle is half its diameter.

Therefore, if the diameter of the cone's circular base is 1.2 ft, then its radius is r = 0.6 ft.

Given values:

Substitute the values into the formula and solve:

[tex]\begin{aligned}\textsf{Surface area}&=3.14 \cdot0.6^2+3.14 \cdot 0.6 \cdot 2.25\\&=3.14 \cdot 0.36+3.14 \cdot 0.6 \cdot 2.25\\&=1.1304+1.884 \cdot 2.25\\&=1.1304+4.239\\&=5.3694\\&=5.4\; \sf ft^2\;(nearest\;tenth)\end{aligned}[/tex]

Therefore, the surface area of the cone-shaped megaphone is 5.4 ft² (rounded to the nearest tenth).

Answer:

268.8

Step-by-step explanation:

Let the sides of the base triangle be:

a = 8.8 cm

b = 5.7 cm

c = 6.8 cm

Let h be the length

h = 10.8 cm

The surface area is given by:

[tex]SA = (a + b + c)*l + 2\sqrt{ s(s - a)(s - b)(s - c)}[/tex]

Where

[tex]s = \frac{a + b + c}{2} \\\\= \frac{8.8 + 5.7 + 6.8}{2} \\\\=\frac{21.3}{2} \\\\= 10.65[/tex]

[tex]SA = (a + b + c)*l + 2\sqrt{ s(s - a)(s - b)(s - c)}\\\\= (8.8 + 5.7 + 6.8)*10.8 + 2\sqrt{ 10.65(10.65 - 8.8)(10.65 - 5.7)(10.65 - 6.8)}\\\\= 21.3*10.8 +2\sqrt{ 10.65(10.65 - 8.8)(10.65 - 5.7)(10.65 - 6.8)}\\\\=230.04 + 2\sqrt{ 10.65(1.85)(4.95)(3.85)}\\\\=230.04 + 2\sqrt{ 375.48}\\\\= 230.04 + 2*19.38\\\\=230.04 +38.76\\\\=268.8[/tex]

The percent profit will be 15.5%.The formula used to calculate the percentage profit is:Percentage Profit = (Profit / Cost Price) x 100%.

Let's assume that the retailer has an item with a wholesale price of $100. After a 54% increase in the wholesale price, the new wholesale price is $154.Now, when the retailer provides a 25% discount off the ticket price, the new price of the item becomes: $154 x 75% = $115.5.

The cost of producing the item is $100, but the retailer sells it for $115.5. Hence, the profit made by the retailer is:$115.5 - $100 = $15.5 or 15.5% profit.The percent profit that the retailer will realize is 15.5%. Therefore, the percent profit will be 15.5%.The formula used to calculate the percentage profit is:Percentage Profit = (Profit / Cost Price) x 100%.

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Answer:

B (1, -3)

Step-by-step explanation:

Step 1:  Use the midpoint formula to find the coordinates of the endpoint:

Normally, we find the midpoint of a segment using the midpoint formula, which is given by:

M = (x1 + x2) / 2, (y1 + y2) / 2, where

Since we're solving for the coordinates of an endpoint, we can allow (-5, 7) to be our (x1, y1) point and plug in (-2, 2) for M to find (x2, y2), the coordinates of the endpoint B:

x-coordinate of B:

x-coordinate of midpoint = (x1 + x2) / 2

(-2 = (-5 + x2) / 2) * 2

(-4 = -5 + x2) + 5

1 = x2

Thus, the x-coordinate of the endpoint B is 1.

y-coordinate of B:

y-coordinate of midpoint = (y1 + y2) / 2

(2 = (7 + x2) / 2) * 2

(4 = 7 + x2) -7

-3 = y2

Thus, the y-coordinate of the endpoint B is -3.

Thus, the coordinates of the endpoint B are (1, -3).

The price of coffee in 2009 would have been approximately $5.15.

To find the price of coffee in 2009, we need to use the index number for that year. According to the table, the index number for 2009 is 103.0.

We can set up a proportion to solve for the price in 2009:

Price in 2015 / Index in 2015 = Price in 2009 / Index in 2009

Let's denote the price in 2009 as x:

$4.48 / 89.8 = x / 103.0

Now we can solve for x:

x = ($4.48 / 89.8) * 103.0

x ≈ $5.15

Therefore, the price of coffee in 2009 would have been approximately $5.15.

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This is the rectangular equation described by the parameter equation x = t1/3 and y = t – 4.

Elimination of the parameter means to rewrite the equations in terms of only x and y. To do this, substitute t from one equation into the other equation. Here, the two equations are:x = t1/3 and y = t – 4Substitute t from the first equation into the second equation:y = (x^3) – 4Now the equation is in terms of x and y only.

This is the rectangular equation described by the parameter equation x = t1/3 and y = t – 4.The rectangular equation, y = (x^3) – 4 can be plotted on a graph. It is a cubic equation. The graph will look like a curve that passes through the point (0, -4) and continues to move towards infinity. The graph will be symmetric to the origin because the equation involves an odd power of x.

If the equation involved an even power of x, the graph would be symmetric to the y-axis. The graph will never touch the x-axis or y-axis, it will only approach them.In conclusion, the rectangular equation y = (x^3) – 4 is derived from the two parameter equations, x = t1/3 and y = t – 4. The graph of this equation is a cubic curve that is symmetric to the origin. The curve passes through (0, -4) and approaches the x and y-axes but never touches them.

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Answer: There will be a total of 18 books per box.

Step-by-step explanation:

Here,

Total number of boxes = 7

Total number of books = 126

Let n be the total number of books per boxes.

Now,

n = 126 / 7 = 18

Therefore, the total number of books per boxes is 18.

The area of the triangle is 47.91 units²

When all three sides of the triangle are known we can use Heron's formula. Consider the triangle ABC with sides a, b, and c has shown in the image.

Heron’s formula is:

Area =√s(s−a)(s−b)(s−c)

where,

a, b, c are the side length of the triangle

s is the semi-perimeter. s = (a+b+c)/2

In this case:

Using the knowledge of the radius of a circle. We can say:

a = BC = 3 + 9 = 12 units

b = AC = 5 + 3 = 8 units

c = AB = 5 + 9 = 14 units

s = (a+b+c)/2

s = (12+8+14)/2

s = 34/2

s = 17 units

Area = √s(s−a)(s−b)(s−c)

Area = √17(17−12)(17−8)(17−14)

Area = √17(5)(9)(3)

Area = √2295

Area = 47.91 units²

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Answer:

A, B, E

Step-by-step explanation:

Notice that A, B, and E all maintain their common ratios, while C and D do not.

This table shows the frequency of each number obtained after throwing the die 35 times

To prepare a frequency table based on the numbers obtained from throwing a die 35 times, we can list the numbers from 1 to 6 and count the frequency of each number.

Numbers: 1, 2, 3, 4, 5, 6

Frequency: 5, 14, 6, 4, 5, 1

Based on the given numbers, the frequency table would look like this:

Number   | Frequency

1                      5

2                     14

3                      6

4                      4

5                      5

6                       1

This table shows the frequency of each number obtained after throwing the die 35 times.

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Answer:

Step-by-step explanation:

x-6y=4

To solve these equations, we can use the elimination method. We want to eliminate one of the variables, either x or y, by multiplying one of the equations by a constant so that the coefficients of one variable will be the same in both equations but with opposite signs. For example, we can multiply the first equation by 4 to get:

-20x - 24y = -128

Then we can add this equation to the second equation to eliminate y:

-20x - 24y + 4x - 6y = -128 + 4

Simplifying this equation gives:

-16x - 30y = -124

Now we can isolate one variable in terms of the other:

-16x - 30y = -124

-16x = 30y - 124

x = (30/(-16))y + (-124/(-16))

x = (-15/8)y + 31/2

We can substitute this expression for x into either of the original equations to solve for y. For example, substituting into the first equation gives:

-5((-15/8)y + 31/2) - 6y = -32

Multiplying by -8 to clear the fractions gives:

75y - 248 - 48y = 256

Simplifying and solving for y gives:

27y = 504

y = 18.67

Then we can substitute this value of y back into our expression for x to find:

x = (-15/8)(18.67) + 31/2

x = -12.25

Therefore, the solution to the system of equations is:

x = -12.25

y = 18.67

The function value for f(g(4)) include the following: f(g(4)) = 6.

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.

By critically observing the table of values of the function f and g shown in the image attached above, we can reasonably infer and logically deduce the following function values:

g(4) = 1

f(g(4)) = f(1)

f(1) = 6.

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The matrix[tex]A^(-1) is a matrix with 2 rows and 2 columns, where row 1 is -0.25 and 1, and row 2 is 0.5 and -1.[/tex]

To find the inverse of a matrix, we can use the formula:[tex]A^(-1) = (1/det(A)) * adj(A)[/tex]

Where A^(-1) represents the inverse of matrix A, det(A) is the determinant of A, and adj(A) denotes the adjugate of A.

Given the matrix A with 2 rows and 2 columns:

A = | 4  4 |

      | 2  1 |

To find A^(-1), we need to calculate the determinant of A and the adjugate of A.

The determinant of A (det(A)) is calculated as:

det(A) = 4 * 1 - 2 * 4 = -4

The adjugate of A (adj(A)) is obtained by swapping the diagonal elements and changing the sign of the off-diagonal elements:

adj(A) = |  1  -4 |

             | -2   4 |

Finally, we can find A^(-1) using the formula mentioned earlier:[tex]A^(-1) = (1/det(A)) * adj(A)A^(-1) = (1/-4) * | 1 -4 |[/tex]

                       | -2   4 |

Simplifying the expression:

A^(-1) = | -0.25  1 |

              |  0.5  -1 |

Therefore, the matrix A^(-1) is a matrix with 2 rows and 2 columns, where row 1 is -0.25 and 1, and row 2 is 0.5 and -1.

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Answer:

[tex]\frac{6}{x-5}[/tex]

Step-by-step explanation:

Helping in the name of Jesus.

The area of the circle with a radius of 5 cm is approximately 78.53975 square centimeters.

To calculate the area of a circle, we need to use the formula A = πr², where A represents the area and r represents the radius of the circle. In this case, the given radius is 5 cm.

Plugging the value of the radius into the formula, we get:

A = π(5 cm)²

Simplifying the equation further, we have:

A = π(25 cm²)

Using the value of π (pi) as approximately 3.14159, we can calculate the area:

A ≈ 3.14159 × 25 cm²

A ≈ 78.53975 cm²

It's important to note that the area of a circle is always expressed in square units, as it represents the amount of space enclosed by the circle.

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Answer:

D. 2

Step-by-step explanation:

y=mx+b

m is the slope in this case, and by your equation, we can easily see that the answer should be D, with a slope of 2.

Answer:

d.2

Step-by-step explanation:

y=mx+b

m=slope

b=y-intercept

y=2x+6

m=2

b=6

slope=2

1) 2a - 100

Substituting the value of a here,

[tex] \rm 2(32) - 100 [/tex]

[tex] \rm 64 - 100 [/tex]

[tex] \rm -36 [/tex]

2) b (-12)

Substituting the value of b here,

[tex] \rm 150 (-12) [/tex]

[tex] \rm -1800 [/tex]

3) 4a + b

Substituting the values of a and b here,

[tex] \rm 4(32) + 150 [/tex]

[tex] \rm 128 + 150 [/tex]

[tex] \rm 278 [/tex]

4) 9b - 2a

Substituting the values of a and b here,

[tex] \rm 9(150) - 2 (32) [/tex]

[tex] \rm 1350 - 64 [/tex]

[tex] \rm 1286 [/tex]

The answers are:

below in [tex]\bold{bold}[/tex]

Work/explanation:

Plug in 32 for a

[tex]\sf{2(32)-100}[/tex]

[tex]\sf{64-100}[/tex]

[tex]\bf{-36}[/tex]

____________

[tex]\sf{b(-12)}[/tex]

[tex]\sf{150\cdot(-12)}[/tex]

[tex]\bf{1,800}[/tex]

____________

[tex]\sf{4a+b}[/tex]

[tex]\sf{4(32)+150}[/tex]

[tex]\sf{128+150}[/tex]

[tex]\bf{278}[/tex]

____________

[tex]\sf{9b-2a}[/tex]

[tex]\sf{9(150)-2(32)}[/tex]

[tex]\sf{1,350-64}[/tex]

[tex]\bf{1,286}[/tex]

____________

The slope-intercept form of the equation of the line that passes through (-2, -1) and is perpendicular to y + 15 = x + 10 is y = -x - 3.

To find the slope-intercept form of the equation of a line that is perpendicular to a given line, we need to determine the slope of the given line and then find the negative reciprocal of that slope.

The given line equation is y + 15 = x + 10. To rewrite it in slope-intercept form (y = mx + b), we isolate y:

y = x + 10 - 15

y = x - 5.

From this equation, we can see that the slope of the given line is 1.

To find the slope of the line perpendicular to this, we take the negative reciprocal of 1, which is -1.

Now that we have the slope (-1) and a point (-2, -1) that the line passes through, we can use the point-slope form of a line to find the equation.

The point-slope form of a line is given by: y - y1 = m(x - x1), where (x1, y1) is a point on the line.

Plugging in the values (-2, -1) and -1 for x1, y1, and m respectively, we get:

y - (-1) = -1(x - (-2))

y + 1 = -1(x + 2)

y + 1 = -x - 2.

To rewrite this equation in slope-intercept form (y = mx + b), we isolate y:

y = -x - 2 - 1

y = -x - 3.

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