Binomial problems Basic
The workers' union at a particular university is quite strong. About 96% of all workers employed by the university belong to the workers' union. Recently, the
workers went on strike, and now a local TV station plans to interview 5 workers (chosen at random) at the university to get their opinions on the strike. What is
the probability that exactly 4 of the workers interviewed are union members?
Round your response to at least three decimal places. (If necessary, consult a list of formulas)
0

A point that best represent the location for them to put the science project is: A. (6.5, 6).

In order to determine the midpoint of a line segment with two (2) end points, we would add each point together and then divide by two (2):

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

By substituting the given end points into the formula for the midpoint of a line segment, we have the following;

Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Midpoint = [(5 + 8)/2, (8 + 4)/2]

Midpoint = [(13)/2, 12/2]

Midpoint = (6.5, 6).

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Answer: 48 cm square

Step-by-step explanation:

We can first divide this shape into two rectangles, cutting it off at the 6cm line. The rectangle below has an area of 20cm square, noted by the 10 cm base and 2 cm base thickness. For the other rectangle, we can see that the height is 9cm, but since we already have done the bottom rectangle, we can subtract 2cm away from the 9cm ad get 7 cm. So the height for the top rectangle is 7cm. Then doing the same thing for the width with 10cm and 6cm gives us 4 cm. This then gives us a total of 28cm for the top and 20cm for the bottom. This combines to get us 48 cm. THE FIGURE IS NOT TO SCALE.

The classification , symmetry , maximum r-values and the zeroes of the function are solved

Given data ,

a)

Let the function be represented as A

Now , the value of A is

r² = 25 sin( 2θ )

The equation represents a cardioid

It is symmetric about the polar axis.

The maximum values of r occur at θ = (π/4) + kπ/2, and the maximum value of r is 5.

The equation has zeroes at θ = kπ/2, and the corresponding values of r are given by r = 0

b)

The equation represents a limaçon.

It is symmetric about the polar axis.

The maximum value of r is 7.

The equation has zeroes at θ = arccos(1/3) + 2kπ or θ = -arccos(1/3) + 2kπ, and the corresponding values of r can be found by substituting into the equation r = 4 - 3cos(θ).

c)

The equation represents an Archimedean spiral.

It does not possess any symmetry.

There is no maximum r value.

The equation has a zero at θ = 1/2.

Hence , the zeroes of the function are solved

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Answer:

Step-by-step explanation:

The volume of the largest piece is given as follows:

V = 10603 cm³.

The volume of a cone of radius r and height h is given by the equation presented as follows:

V = πr²h/3.

The dimensions for the largest piece in this problem are given as follows:

Hence the volume of the largest piece is given as follows:

V = π x 15² x 45/3

V = 10603 cm³.

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1. The location of point A  and B in complex (a + bi) form is 4 + 3i, B is -6 + 4i.

2. The modulus of point A is 5.

3. The length of AB is 10.

4. B in polar form is 2√13 × (cos(146°) + i sin(146°))

5. The product of two complex numbers in rectangular form is  -36 - 2i

6. z1/z2 in polar form is z1/z2 = 4 cis (7π/6 - π/4)

1. The location of each point A and B are as follows  Arrow A is at (4, 3) and arrow B (-6, 4). therefore the location in complex (a + bi) form is 4 + 3i, B is -6 + 4i.

2. The modulus of a complex number (a + bi) is represented as √(a² + b²) ⇒ √(4² + 3²) = √(16 + 9) = √25 = 5.

3. We can calculate the length of vector AB with √(x₂-x₁)² + (y₂-y₁)²)

AB = √((-6 - 4)² + (4 - 3)²)

AB = √((-10)² + 1)

AB = √(100 + 1)

AB = √101 ⇒ 10

4. The modulus of B, r = √((-6)² + 4²) = √(36 + 16) = √52 = 2√13

θ = 180° - arctan(|4/-6|) = 180° - arctan(2/3)

θ = 180° - 33.69° = 146.31°

5. The product of the complex number can be see as follows

(4 + 3i) × (-6 + 4i) = (4×-6 - 34) + (4×4 + 3×-6)i

= (-24 - 12) + (16 - 18)i

= -36 - 2i.

6. (7π/6 - π/4) = (14π/12 - 3π/12) = 11π/12.

11π/12 × (180/π) = 165°.

In Polar form z1/z2 = 4 cis (7π/6 - π/4)

= 4 cis 165°.

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Answer:

16x^(7/2)

Step-by-step explanation:

When rewriting radicals as fractions, the numerator is the power the term is to and the denominator is how many times the term is “rooted”:

2^4 sqrt(x^7) —> 16x^(7/2)

The length of the AB in the curved road path comes out to be 98.2 feet

Given:

Radius = 88 feet

DE = 15 feet

CD is the radius of the circle

CD = CE + DE

88 = CE + 15

CE = 73 feet

Since the CD is the perpendicular bisector the AE and BE are equal in length

In triangle CBE,

It is right-angled at E,

By Pythagoras' theorem:

hyp² = height² + base²

88² = 73² + BE²

7744 = 5329 + BE²

BE² = 2415

BE = 49.1 feet

AB = BE + AE

AB = BE + BE

AB = 2BE

AB = 2 * 49.1

= 98.2 feet

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The complete question is:

The curved road at the right is part of circle C which has a radius of 88 feet. What is AB as shown in the figure? Round to the tenth

Answer:

Step-by-step explanation:

You want the amounts invested at 9% and 6% if they total $11,335 and the interest from the 9% investment exceeds the interest from the 6% investment by $865.35.

If we let x represent the amount invested at 9%, the amount invested at 6% is (11335-x). The relation between the values of interest earned is ...

  (x)·9% -(11335-x)·6% = 865.35

  0.15x -680.10 = 865.35 . . . . . simplify

  0.15x = 1545.45 . . . . . . . . add 680.10

  x = 10303 . . . . . . . . . . . divide by 0.15

  11335 -x = 1032

$10,303 was invested at 9%; $1,032 at 6%.

__

Additional comment

It is convenient to use a single variable, and to let it represent the amount invested at the higher rate. If you use a system of 2 equations, you can effectively do this by substituting for the variable representing the amount invested at the lower rate. Using this approach keeps all of the numbers positive, tending to reduce errors.

Answer:

Amount invested at 9% = $6832.15; Amount invested at 6% = $4502.85

Step-by-step explanation:

We'll need a system of equations to find the amounts invested at both 9% and 6% and we'll need to convert the percentages to decimals (i.e., 0.09 and 0.06):

First equation in system:  

We know that the interest earned from the 9% investment is $865.35 greater than the interest earned from the 6% investment.

Thus, one equation we can use is x = y + 865.35

Second equation in system:

We also know that the amount invested at 9% plus the amount invested at 6% equals $11335.00

Thus, our second equation is 0.09x + 0.06y = 11335

Step 1:  We can use substitution to solve.  We must plug in x from the first equation for x in the second equation to solve for y:

0.09(y + 865.35) + 0.06y = 11335

0.09y + 77.8815 + 0.06y = 11335

0.15y + 77.88 = 11335

0.15y = 11257.12

y = 75047.46667

y = 75047.47

Step 2:  Now we can plug in 75047.47 for y into any of the two equations in our system to solve for y.  Because the first equation is simpler, let's use this one:

x = 75047.47 + 865.35

x = 75912.82

Step 3:  We can now find the amount invested by multiplying x by 0.09 and y by 0.06:

0.09x = 0.09(75912.82) = 6832.1538 = $6832.15

0.06y = 0.06(75047.47) = 4502.8482 = $4502.85

Optional Step 4:  We can check that our numbers are correct by substituting 75912.82 for x and 75047.47 for y in the two equations in our system:

Checking solutions for first equation:

75912.82 = 75047.47 + 865.35

75912.82 = 75912.82

Checking solutions for second equation:

0.09(75912.82) + 0.06(75047.47) = 11335

6832.1538 + 4502.8482 = 11335

6832.15 + 4502.85 = 11335

11335 = 11335

The profit percentage is 20% when car cost 450000 and sold for 540000.

The formula i.e., Profit = Selling Price - Cost Price can be used to determine the profit when the price at which something is sold and the cost price of a product are known. The formula for calculating profit percentage is then applied, which is profit % = (profit/cost price) x 100 (A profit algorithm is used to determine how much profit was generated from the sale of a specific product.)

Cost Price= 4500000

Selling price= 540000

Profit = Selling price - cost price

Profit= 540000-450000

Profit = 90000

Profit as a percentage of cost price= [tex]\frac{90000}{45000}*100= 20%[/tex]

Therefore, the profit as a percentage of cost price is 20%.

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Answer:

y = [tex]\frac{25x+22}{6}[/tex]

Step-by-step explanation:

express the ratios in fractional form

[tex]\frac{5x+2}{y-2}[/tex] = [tex]\frac{6}{5}[/tex] ( cross- multiply )

6(y - 2) = 5(5x + 2) ← distribute parenthesis on both sides

6y - 12 = 25x + 10 ( add 12 to both sides )

6y = 25x + 22 ( divide both sides by 6 )

y = [tex]\frac{25x+22}{6}[/tex]

Answer:

6,435

Step-by-step explanation:

The number of different committees that can be chosen can be calculated using the combination formula, also known as "n choose k," which calculates the number of ways to choose k items from a set of n items without regard to the order.

In this case, the principal wants to assemble a committee of 7 students from a student council of 15 members. Therefore, the number of different committees that can be chosen is given by the formula:

C(15, 7) = 15! / (7! * (15-7)!)

Calculating this expression gives:

C(15, 7) = 15! / (7! * 8!)

Simplifying further:

C(15, 7) = (15 * 14 * 13 * 12 * 11 * 10 * 9) / (7 * 6 * 5 * 4 * 3 * 2 * 1)

C(15, 7) = 6435

Therefore, there are 6,435 different committees that can be chosen from the 15-member student council.

Answer: yes 2,0193-029712123,

Step-by-step explanation:

That's quadratic.

y=x^2

It's a very simple version of y=ax^2+bx+c. Just in this case, a = 1, b = 0 and c = 0.

The marginal cost (MC) function tells us the additional cost of producing one more unit of the Senior Executive model.

To find the average cost, we need to know the fixed costs, which are not given in the problem. Therefore, we cannot calculate the average cost.

To find the marginal cost, we need to take the derivative of the total cost function with respect to x:

MC(x) = dC(x) / dx

MC(x) = [tex]0.3x^2[/tex] - 16x + 500

Interpreting the results, the marginal cost (MC) function tells us the additional cost of producing one more unit of the Senior Executive model. It is an increasing function, which means that the cost of producing an additional unit increases as the production level increases. When MC is greater than the price of the product, it is not profitable to produce additional units, and the optimal production level is reached when MC equals the price.

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Question

Custom Office makes a line of executive desks. It is estimated that the total cost for making x units of their Senior Executive model is represented by the following function:

C(x) = 0.1x^3 - 8x^2 + 500x + 4000

where C(x) is measured in dollars/year.

The area of the figure will be 17 square centimeters.

The area of a two-dimensional figure is the area that its perimeter encloses. The quantity of unit squares that occupy a closed figure's surface is its region.

The area of the figure is the summation of the area of the two rectangles. Then the area of the figure is calculated as,

A = 3 x 5 + 1 x 2

A = 15 + 2

A = 17 square cm

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Steve is correct. Steve can find the difference in temperature between 7 AM and 12 PM on Wednesday by adding the distances from 0.

By using a number line, Steve can find the difference in temperature between 7 AM and 12 PM on Wednesday by adding the distances from 0. One temperature is negative and the other is positive, but by adding their distances, he can find the difference. Kelly's method of subtracting -5.1 from the temperature at 12 PM on Wednesday is not necessarily incorrect, but it does not give the exact difference in temperature between the two times. Therefore, using Steve's method, the change in temperature would be the sum of the distance from 0 to the temperature at 7 AM (which is 2.5) and the distance from 0 to the temperature at 12 PM (which is also 2.5), resulting in a difference of 5 degrees.

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The total number of atoms represented by Cd(CH₂CICO₂)₂ is 15.

In addition, items are combined and counted as a single large group. The process of adding two or more numbers together is known as addition in mathematics. The terms "addends" and "sum" refer to the numbers that are added and the result of the operation, respectively.

To find the total number of atoms represented by Cd(CH₂CICO₂)₂, we need to count the number of atoms of each element in the molecule and add them up.

Cd(CH₂CICO₂)₂ contains:

1 cadmium (Cd) atom

2 carbon (C) atoms

6 hydrogen (H) atoms

4 oxygen (O) atoms

2 chlorine (Cl) atoms

Adding these up, we get:

1 + 2 + 6 + 4 + 2 = 15

Therefore, the total number of atoms represented by Cd(CH₂CICO₂)₂ is 15.

The answer is (D) 15.

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Answer:

C. 3/20 of a meter

Step-by-step explanation:

Step 1: To find out how much ribbon Carl has left, we need to subtract the length of ribbon used from the total length of the ribbon.

Step 2:  To add the lengths of the ribbon used, we need to find a common denominator for the fractions used. The least common multiple of 5 and 4 is 20, so we can convert both fractions to twentieths.

Step 3: 2/5 of a meter is equivalent to 8/20 of a meter, and 1/4 of a meter is equivalent to 5/20 of a meter.

Step 4:  To add the lengths of ribbon used, we add the two fractions: 8/20 + 5/20 = 13/20.

Step 5:  To find the length of ribbon Carl has left, we subtract the fraction of the ribbon used from the total length of the ribbon: 4/5 - 13/20 = 16/20 - 13/20 = 3/20.

Step 6: Therefore, Carl has 3/20 of a meter of ribbon left.

Answer: (5x+6)(x+4)

Step-by-step explanation:

5x^2 + 26x + 24

5x^2 + 20x + 6x + 24

(5x^2 + 20x) + (6x + 24)

5x(x + 4) + 6(x + 4)

5x(x + 4) + 6(x + 4)

(5x + 6)(x + 4)

The solution of the exponential equation [tex]5^{({\frac{-x}{16})}}= 5[/tex] in terms of logarithms, or correct to four decimal places, is x ≈ -4.4431.

An exponential function is a mathematical function in the form of [tex]f(x) = a^x[/tex], where "a" is a constant and "x" is a variable. The value of the function at a particular value of "x" is found by raising "a" to the power of "x". Exponential functions are characterized by their rapid growth or decay.

We can solve for x by taking the logarithm of both sides with base 5:

[tex]5^{(\frac{-x}{16})} = 5[/tex]

[tex]log_5(5^{(\frac{-x}{16}))} = log_5(5)[/tex]

(-x/16)log₅(5) = 1

-x/16 = 1/log₅(5)

x = -16/log₅(5)

Using a calculator, we get:

x ≈ -4.4431

Therefore, the solution of the exponential equation [tex]5^{({\frac{-x}{16})}}= 5[/tex]  in terms of logarithms, or correct to four decimal places, is x ≈ -4.4431.

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The solutions are x = 0, 0, -2 and 5.

Given is a polynomial we need to solve it,

3x⁴-9x³-30x².

We know that a polynomial will have the number of solutions equal to its highest degree,

Here the highest degree of the polynomial is 4 so there will be 4 solutions.

3x⁴-9x³-30x²

[tex]= 3x^2\left(x^2-3x-10\right)[/tex]

[tex]= x^2-3x-10 =\quad \left(x+2\right)\left(x-5\right)[/tex]

[tex]= 3x^2\left(x+2\right)\left(x-5\right)[/tex]

Therefore, the solutions are x = 0, 0, -2 and 5.

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Step-by-step explanation:

First, let's find the square root of 30.6:

√30.6 ≈ 5.53 (rounded to two decimal places)

Now, let's multiply the square root by 2:

5.53 × 2 = 11.06

The length of side x to the nearest tenth is equal to 2.4 units.

In Mathematics and Geometry, an isosceles triangle simply refers to a type of triangle with two (2) sides that are equal in length (side lengths) and two (2) equal angles.

This ultimately implies that, an isosceles triangle comprises two (2) side lengths that are equal and two (2) angles with the same magnitude.

Therefore, we would apply Pythagorean theorem in order to find the length of side x as follows;

x² + x² = (√11)²

2x² = 11

x² = 11/2

x² = 5.5

x = 2.4 units.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The probability of not rolling a 1 when rolling a six-sided die is approximately 83%. This means that if you roll the die many times, you would expect to get a 1 about 1/6 of the time and not get a 1 about 5/6 of the time.

When you roll a six-sided die, there are six possible outcomes, each with equal probability. These outcomes are rolling a 1, 2, 3, 4, 5, or 6. If you want to find the probability of not rolling a 1, you can count the number of outcomes that are not 1 and divide by the total number of outcomes.

Since there are five outcomes that are not 1 (2, 3, 4, 5, and 6) and six total outcomes, the probability of not rolling a 1 is 5/6.

To write this as a percentage rounded to the nearest whole number, we can multiply by 100 and round to the nearest whole number:

5/6 × 100 ≈ 83%.

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Answer:

fg(x) = 3x² + 1

Step-by-step explanation:

f(g(x))

f(3x² - 1)

(3x² - 1) + 2

The calculated volumes of the figures are 11264 cubic units, 14482.28 cubic units, 3744 cubic units, 475.2 cubic units, 18824.14 cubic units and 91.99 cubic units

The cylinder

The volume is calculated as

V = πr²h

Where

r = Radius

h = Height

So, we have

V = 22/7 * (32/2)² * 14

Evaluate

Volume = 11264

The cylinder

The volume is calculated as

V = πr²h

Where

r = Radius

h = Height

So, we have

(2r)² = 40² - 32²

(2r)² = 576

So, we have

r = 12

So, we have

V = 22/7 * (12)² * 32

Evaluate

Volume = 14482.28

The rectangular prism

The volume is calculated as

V = lwh

Where

l = Length

w = Width

h = Height

So, we have

V = 8 * 12 * 39

Evaluate

Volume = 3744

The triangular prism

The volume is calculated as

V = 1/2lwh

Where

l = Length

w = Width

h = Height

So, we have

V = 1/2 * 11 * 5.4 * 16

Evaluate

Volume = 475.2

The sphere

The volume is calculated as

V = 4/3πr³

Where

r = Radius

So, we have

V = 4/3 * 22/7 * (33/2)³

Evaluate

Volume = 18824.14

The sphere

The volume is calculated as

V = 4/3πr³

Where

r = Radius

So, we have

V = 4/3 * 22/7 * 2.8³

Evaluate

Volume = 91.99

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The volume of the figures are;

4.  27. 18 in³

5. 3. 024 m³

6.  23 6/18 yd³

The formula for calculating the volume of a triangular prism is expressed with the equation;

V = Bl

Given that the parameters are;

4.  We have that;

Base area = 1/2 × 2.6 × 4.1

Multiply the values

Base area = 5. 33in²

Then,

Volume = 5.33 × 5.1

Volume = 27. 18 in³

5. Base area = 1/2 × 2. 4 × 1.4

Multiply the values

Base area = 1. 68 m²

Volume = 1.8 ×1.68

Multiply the values

Volume= 3. 024 m³

6. Base area = 1/2 × 10/3 × 14/3

Multiply the values

Base area = 7 14/18yd²

Volume = 140/18 × 3

Multiply the values

Volume = 23 6/18 yd³

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