There are 10 members on board of directors_ of them must be elected to the offices of president; vice-president, secretary, and treasurer, then how many different slates of candidates are possible? Assume that no board member may be elected to more than one of these offices.

The probability that he gets four or fewer questions correct is 0.9984

Let p be probability of getting correct answer and q be probability of getting in correct answer.

Number of trails :  n = 6

Number of Successes : x = 4

By using binominal distribution ,

P(x≤4) = 1 - P(x>4)

= 1 - [P(x = 5) + P(x = 6)]

= 1 - [ ⁶C₅ p⁵ q +⁶C₆ p⁶ ]

solving combination ,

= 1 - [ 6 × 4/(5⁶) + 1 /(5⁶) ]

= 1 - (24 + 1 / 625)

= 1 - 25 / 625

= 624/625 = 0.9984

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The answer is option B: 54,000,000/mL. The sperm concentration is 0.54 million per cubic centimeter, or 54 million per milliliter.

To calculate the sperm concentration using a Neubauer counting chamber, we can use the following formula:

Sperm concentration = (number of sperm counted ÷ number of counting squares) ÷ dilution factor

In this case, we have:

Number of sperm counted = 54

Number of counting squares = 5

Dilution factor = 1:20

First, we need to calculate the total volume of the diluted sperm sample that was loaded onto the counting chamber. To do this, we can use the following formula:

Total volume = volume of loaded sample ÷ dilution factor

Since the dilution factor is 1:20, this means that the volume of loaded sample is 1/20th of the total volume. The total volume depends on the depth of the chamber and is usually 0.1 mL (or 100 μL) for a standard Neubauer counting chamber. Therefore:

Total volume = 0.1 mL ÷ 20 = 0.005 mL

Next, we can calculate the sperm concentration using the formula above:

Sperm concentration = (54 ÷ 5) ÷ 1/20

Sperm concentration = 54 ÷ 5 × 20

Sperm concentration = 54 ÷ 100

Sperm concentration = 0.54 million/cc

Therefore, the answer is option B: 54,000,000/mL. The sperm concentration is 0.54 million per cubic centimeter, or 54 million per milliliter.

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Your question is incomplete, but probably the complete question is :

Using a 1:20 dilution and the 5 RBC counting squares of the Neubauer counting chamber, an average of 54 sperm is counted. The sperm concentration is:

A. 54,000/cc

B. 54,000,000/mL

C. 108,000/cc

D. 108,000,000/mL

Answer:

9/2

Step-by-step explanation:

2/3 + 3/4 + 5/6 + 4/8 + 3/12 + 3/2 =

= 16/24 + 18/24 + 20/24 + 12/24 + 6/24 + 36/24

= 108/24

= 54/12

= 9/2

Answer:

B. |-6| < |-8|

Step-by-step explanation:

The absolute value will always make the number positive. B is the only option in which (once absolute value is used) will make a true statement.

|-6| < |-8| = 6 < 8

( 6 is less than 8 )

Jane's opportunity cost of pork is 0.1 pounds of beans per pound of pork, and her opportunity cost of beans is 10 pounds of pork per pound of beans. With the discovery of a lower-cost method of producing computers, the supply of computers will increase. A binding price ceiling in the market would result in a shortage.

1. Jane's opportunity cost of pork can be calculated by dividing the hours required to produce pork (10 hours) by the hours required to produce beans (5 hours). Therefore, her opportunity cost of pork is 0.1 pounds of beans per pound of pork. Similarly, her opportunity cost of beans is calculated by dividing the hours required to produce beans (5 hours) by the hours required to produce pork (10 hours), resulting in an opportunity cost of 10 pounds of pork per pound of beans.

2. Although the U.S. can produce more televisions per hour of labor than China, it does not necessarily mean that the U.S. should specialize in television production. Comparative advantage considers the opportunity cost of producing other goods. If the U.S. has a lower opportunity cost in producing a different good, it may be more beneficial for the U.S. to specialize in that particular area and trade with China for televisions.

3. The discovery of a lower-cost method of producing computers would lead to an increase in the supply of computers. With lower production costs, producers can offer computers at a lower price, stimulating demand and expanding the quantity supplied.

4. Immediately after a price increase for natural gas, the price elasticity of demand is expected to be more inelastic. In the short term, consumers may not have immediate alternatives or the ability to switch to other heating methods. Over time, as consumers adjust to the price increase and explore alternative options, the price elasticity of demand for natural gas would likely become more elastic.

5. A binding price ceiling, which sets a maximum price below the equilibrium price, would result in a shortage in the market. The price ceiling prevents the market from reaching equilibrium, leading to excess demand and insufficient supply. Suppliers may not find it profitable to provide goods or services at an artificially low price, resulting in a shortage as consumers compete for the limited available quantity.

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Answer:

3731.2 pounds

Step-by-step explanation:

Aquarium will hold 4.4 * 2.5 * 5.3 = 58.3 cubic feet of sea water.

For 3 cubic feet of sea water, weight is 192 pounds

For 58.3 cubic feet of sea water,

( 192 * 58.3) / 3 = 11193.6 / 3 = 3731.2 pounds

Answer:

The answer might be 2-5 (-9/5) -3

Step-by-step explanation:

The distance between Casey and the base of the lighthouse is 49 ft.

The angle of elevation refers to the angle formed by the straight horizontal line and an object. The crosshair of an observer is usually above the horizontal. 

The angle of depression is the angle formed by the horizontal and a downward angle to an object. The crosshair of an observer is usually above below the horizontal.

The distance between Casey and the base of the lighthouse can be determined by using the tangent of trigonometry.

(TOA)

\(\mathbf{tan \theta = \dfrac{opp}{adj}}\)

\(\mathbf{tan \ 58 = \dfrac{78}{x}}\)

\(\mathbf{x= \dfrac{78}{1.6003}}\)

x ≅ 49 ft

The height of the goal post can be determined by using the tangent of trigonometry.

\(\mathbf{tan \theta = \dfrac{opp}{adj}}\)

\(\mathbf{tan 17 = \dfrac{x}{131}}\)

x = (tan 17) × 131

x = 0.3057 × 131

x ≅ 40 ft

The horizontal distance between Zack and the water fountain is calculated by using the tangent of trigonometry.

\(\mathbf{tan \theta = \dfrac{opp}{adj}}\)

\(\mathbf{tan \ 28 = \dfrac{75}{x}}\)

\(\mathbf{x = \dfrac{75}{0.5317}}\)

x = 141 ft

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To calculate this probability, we need to use the cumulative binomial probability formula:

P(X ≤ k) = Σ(i=0 to k) (n choose i) p^i (1-p)^(n-i)

Where:
- X is the number of heads obtained
- k is the number of heads we want to calculate the probability for (in this case, the same number of heads obtained)
- n is the total number of coin flips (10 in this case)
- p is the probability of getting heads on a single flip (0.5 for a fair coin)
- (n choose i) is the binomial coefficient, which represents the number of ways to choose i heads out of n flips

For this problem, we want to calculate P(X ≤ 10), since we're interested in the probability of obtaining as many heads as we did or less. Plugging in the values, we get:

P(X ≤ 10) = Σ(i=0 to 10) (10 choose i) 0.5^i 0.5^(10-i)
          = (10 choose 0) 0.5^0 0.5^10 + (10 choose 1) 0.5^1 0.5^9 + ... + (10 choose 10) 0.5^10 0.5^0
          = 0.00098 + 0.00977 + 0.04395 + 0.11719 + 0.20508 + 0.24609 + 0.20508 + 0.11719 + 0.04395 + 0.00977 + 0.00098
          = 0.9453

Therefore, the probability of obtaining as many heads as we did or less when flipping a fair coin 10 times is 0.9453.

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Answer:

D

Step-by-step explanation:

C and D are the location for -1 and 1

....-2  -1  0  1  2 ...

The ratio of the volume divided by the temperature for the first data pair is 0.0026 using the significant figures.

The ratio of two number is the fraction part, which represent that how a number is more or less compare to the other.

The value of the volume is 0.72 and the value of temperature is 276 for the first data pair. The image of all the values of the volume and temperature table is attached below.

The ratio of the volume to the temperature is,

\(\dfrac{V }{ T} =\dfrac{ 0. 72}{276 }\\\dfrac{V }{ T} =0.002608695652\)

The above value is the ratio of volume to the temperature. Now this value has to be written with significant figure.

Let's correct the value, after the 4 places of the decimal point. As the value of fifth place is zero, then the value of 4 place will remain as it is.

Thus, the ratio is,

\(\dfrac{V }{ T} =0.0026\)

The ratio of the volume divided by the temperature for the first data pair is 0.0026 using the significant figures.

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The correct statement regarding the linear functions is given as follows:

f(-2) = g(–2).

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

For function f(x), we have that when x = 0, y = -2, hence the intercept b is given as follows:

b = -2.

When x increases by 0.75, y decays by 2, hence the slope m is given as follows:

m = -2/0.75

m = -2.67.

Hence the function is defined as follows:

f(x) = -2.67x - 2.

For function g(x), we have that when x = 0, y = 6, hence the intercept b is given as follows:

b = 6.

When x increases by 6, y increases by 6, hence the slope m is given as follows:

m = 6/6

m = 1.

Hence the function is:

g(x) = x + 6.

Then the numeric values are:

Meaning that the closest statement is:

f(-2) = g(–2)

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The equations of the parabola are y = (x - 1)(x - 7), y = -(x + 1)(x - 5) and y = (x + 8)(x + 4)

Other properties are below

The equation of a parabola in factored form is represented as

y = a(x - x₁)(x - x₂)

Where

x₁ and x₂ are the x-intercepts of the function

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

Function 1

y = a(x - 1)(x - 7)

Using the points in the graph, we have

a(4 - 1)(4 - 7) = -9

a = 1

So, the function is

y = (x - 1)(x - 7)

Set x = 0 for the y-intercept

y-intercept = (0 - 1)(0 - 7)

y-intercept = (0, 7)

The x-intercepts are (1, 0) and (7, 0)

Lastly the vertex is (4, -9)

Function 2

y = a(x + 1)(x - 5)

Using the points in the graph, we have

a(2 + 1)(2 - 5) = 9

a = -1

So, the function is

y = -(x + 1)(x - 5)

Set x = 0 for the y-intercept

y-intercept = -(0 + 1)(0 - 5)

y-intercept = (0, 5)

The x-intercepts are (-1, 0) and (5, 0)

Lastly the vertex is (2, 9)

Function 3

y = a(x + 8)(x + 4)

Using the points in the graph, we have

a(-6 + 8)(-6 + 4) = -4

a = 1

So, the function is

y = (x + 8)(x + 4)

Set x = 0 for the y-intercept

y-intercept = (0 + 8)(0 + 4)

y-intercept = (0, 32)

The x-intercepts are (-8, 0) and (-4, 0)

Lastly the vertex is (-6, -4)

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Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.

To determine when tan(theta) is undefined on the unit circle, we need to remember the definition of the tangent function.
Tangent is defined as the ratio of the sine and cosine of an angle. Specifically, tan(theta) = sin(theta)/cos(theta).

Now, we know that cosine can never be equal to zero on the unit circle, since it represents the x-coordinate of a point on the circle and the circle never crosses the x-axis. Therefore, the only way for tan(theta) to be undefined is if the cosine of theta is equal to zero.
There are two values of theta on the unit circle where cosine is equal to zero: pi/2 and 3pi/2.

At theta = pi/2, we have cos(pi/2) = 0, which means that tan(pi/2) = sin(pi/2)/cos(pi/2) is undefined.
Similarly, at theta = 3pi/2, we have cos(3pi/2) = 0, which means that tan(3pi/2) = sin(3pi/2)/cos(3pi/2) is also undefined.
Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.

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The tallest bar in a frequency distribution with a bar graph is A bar representing a frequency of 30​

A frequency distribution is a representation, either in a graphical or tabular format, that displays the number of observations within a given interval.

Given that, a frequency distribution represented by a bar graph, we need to identify which will be the tallest, among the given frequencies,

A bar chart is one of the most commonly used representation or visually translate groups of data. It is drawn in such a way that the x-axis of the graph would represent the items and the y-axis will be for the frequency.

Out of the choices given, the tallest among the bars will be that would frequency is 30.

Hence, the answer to this is A bar representing a frequency of 30​

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The express in the form of a + bi would be 0 + 5i.

Complex numbers are those expressed as a + ib, where a, b are real numbers and 'i' is a fictitious number called a "iota." i is equal to  (√-1). A pair of real and imaginary numbers combined in the form a + bi.

When a and b are real numbers, a complex number is one with the formula a + bi. The complex number has two parts: real component (a) and imaginary part (b). If both the real and imaginary components of two complex numbers are identical, only then are the two complex numbers equal.

Let the given expression be \($\sqrt{-25}$$\).

We have to evaluate the expression.

\($$\begin{aligned}\sqrt{-25} & =\sqrt{-1 \cdot 25} \\& =\sqrt{-1} \sqrt{25} \\& =i(5) \\& =5 i\end{aligned}$$\)

The express in the form of a + bi = 0 + 5i.

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The tanker has been filling the reservoir for 4 minutes given that it fills at a rate of 10 1/4 gallons per minute.

Rate refers to the relationship of two quantities of different units. Usually, it is a measure or quantity of something per unit time.

rate = amount / time

If a tank truck fills the gas station's reservoir at the rate of 10 1/4 gallons per minute, and if the reservoir is empty at the start and become 41 gallons full, we can determine how long the tanker has been filling the reservoir by dividing the final amount by the rate.

time = amount / rate

where amount = 41 gallons

rate = 10 1/4 gallons per minute

time = 41 gallons / 10 1/4 gallons per minute

time = 4 minutes

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Answer:

No

Step-by-step explanation:

The jump from each of the numbers is 3 but from 25 to 27 is 2 therefore it is not an arithmetic  sequence.

Answer: x-1)(x-5)=0 x=1 and 5

Step-by-step explanation:

Answer:

  a) see attached

  b) 15015 meters

Step-by-step explanation:

You want the voltage, current, resistance, and power for each component of the circuit shown in the diagram.

The relevant circuit relations are ...

Given current and resistance for element 1, we immediately know its voltage is ...

  V = IR = (4)(10) = 40 . . . . volts

Given the voltage on element 3, we know that parallel element 2 has the same voltage: 30 volts.

Given the voltage at T is 90 volts, the sum of voltages on elements 1, 2, and 4 must be 90 volts. That means the voltage on element 4 is ...

  90 -(40 +30) = 20

The current in elements 1, 4, and T are all the same, because these elements are in series. They are all 4 amperes.

That 4 ampere current is split between elements 2 and 3. The table tells us that element 2 has a current of 1 ampere, so element 3 must have a current of ...

  4 - 1 = 3 . . . . amperes

The resistance of each element is the ratio of voltage to current:

  R = V/I

Dividing the V column by the I column gives the values in the R column.

Note that power source T does not have a resistance of 22.5 ohms. Rather, it is supplying power to a circuit with an equivalent resistance of 22.5 ohms.

Power is the product of voltage and current. Multiplying the V and I columns gives the value in the P column.

Note that the power supplied by the source T is the sum of the powers in the load elements.

We found that the transmitter is receiving a power of 90 watts, so its operating frequency is ...

  (90 W)×(222 Hz/W) = 19980 Hz

Then the wavelength is ...

  λ = c/f

  λ = (3×10⁸ m/s)/(19980 cycles/s) ≈ 15015 m/cycle

The wavelength of the broadcast is about 15015 meters.

__

Additional comment

The voltage and current relations are "real" and used by circuit analysts everywhere. The relationship of frequency and power is "made up" specifically for this problem. You will likely never see such a relationship again, and certainly not in "real life."

Kirchoff's voltage law (KVL) means the sum of voltage rises (as at T) will be the sum of voltage drops (across elements 1, 2, 4).

Kirchoff's current law (KCL) means the sum of currents into a node is equal to the sum of currents out of the node. At the node between elements 1 and 2, this means the 4 amps from element 1 into the node is equal to the sum of the currents out of the node: 1 amp into element 2 and the 3 amps into element 3.

As with much of math and physics, there are a number of relations that can come into play in any given problem. You are expected to remember them all (or have a ready reference).

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Answer:

There are 192 possible system configurations.

The customer can choose one of six amplifiers, one of four compact disc players, and one of eight speaker models. The number of possible system configurations is the product of these three numbers, which is 6 * 4 * 8 = 192.

Here is another way to calculate the number of possible system configurations:

There are 6 ways to choose an amplifier.

For each amplifier, there are 4 ways to choose a compact disc player.

For each amplifier and compact disc player combination, there are 8 ways to choose a speaker model.

Therefore, there are 6 * 4 * 8 = 192 ways to choose an amplifier, a compact disc player, and a speaker model.

Step-by-step explanation:

Answer:

C(x) = 38,250 + 1900x

..........

The expression data.index(20) evaluates to c) 1.

The expression data.index(20) is used to find the index position of the value 20 within the list data. In this case, data refers to the list [10, 20, 30].

When the expression is evaluated, it searches for the value 20 within the list data and returns the index position of the first occurrence of that value. In this case, the value 20 is located at index position 1 within the list [10, 20, 30]. Therefore, the expression data.index(20) evaluates to 1.

The list indexing in Python starts from 0, so the first element of a list is at index position 0, the second element is at index position 1, and so on. In our case, the value 20 is the second element of the list data, so its index position is 1.

Therefore, the correct answer is option c) 1.

It's important to note that if the value being searched is not present in the list, the index() method will raise a Value Error exception. So, it's a good practice to handle such cases by either using a try-except block or checking if the value exists in the list before calling the index() method.

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The hypotheses for the test are H₀: σ₁² = σ₂² and H₁: σ₁² ≠ σ₂². This is a two-tailed test to assess if there is a difference in the standard deviations of sound levels between the areas designated as "casualty doors" and operating theaters. The claim being investigated is whether or not there is a difference in the standard deviations.

The hypotheses for the test are:

H₀: σ₁² = σ₂² (There is no difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

H₁: σ₁² ≠ σ₂² (There is a difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

This hypothesis test is a two-tailed test because the alternative hypothesis is not specifying a direction of difference.

To substantiate the claim that there is a difference in the standard deviations, we will conduct a two-sample F-test at a significance level of 0.10, comparing the variances of the two groups.

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The statements below that show y = x² 2x - 1 being converted to vertex form. The conversion of y = x² + 2x - 1 to vertex form is y = (x + 1)² - 2.

To convert the quadratic equation y = x² + 2x - 1

to vertex form, we need to complete the square.

Here's how:
1. Write the equation:

y = x² + 2x - 1
2. Take half of the coefficient of x and square it:

(2/2)² = 1
3. Add the result from step 2 to both sides of the equation:

y + 1 = x² + 2x + 1 - 1
4. Simplify:

y + 1 = (x + 1)² - 1
5. Rewrite the equation in vertex form:

y = (x + 1)² - 2
So, the conversion of

y = x^2 + 2x - 1

to vertex form is

y = (x + 1)² - 2.

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