Question 1 : solve 12 < 2x ≤ 32

After considering the given data we conclude that the answer for the given sub question regarding combination are
a) the number of different groups of 10 employees that can be selected is 14,307,292
b) the number of possible groups of 10 employees that consist only of employees who either take public transit or drive to work is 77
c) employees who take public transit is 66
d) employees who drive to work is 11
e) employees that do not include anyone who takes public transit is 184,756
f) employees that do not include anyone who drives to work is 352,716
g) employees that consist of at least one person who drives to work is 14,054,576
h) employees that consist of at least one person who drives to work is 14,054,576
i) employees that consist of 5 people who take public transit and 5 people who drive to work is 365,904
j) employees that consist of 4 people who take public transit, 3 people who drive to work, and 3 people who do neither is 6,270,840

a) This is a combination problem, where the order of selection does not matter. The formula for the number of combinations of n objects taken r at a time is \(nCr = n! / (r! * (n-r)!)\), where n is the total number of objects and r is the number of objects being selected. In this case, there are 32 employees and we want to select 10 of them, so the number of different groups of 10 employees that can be selected is:
\(32C10 = 32! / (10! * (32-10)!) = 14,307,292\)

b) We can add the number of groups that consist only of employees who take public transit to the number of groups that consist only of employees who drive to work. To find the number of groups that consist only of employees who take public transit, we can choose 10 employees from the 12 who take public transit. Similarly, to find the number of groups that consist only of employees who drive to work, we can choose 10 employees from the 11 who drive to work. Therefore, the number of possible groups of 10 employees that consist only of employees who either take public transit or drive to work is:
\(12C10 + 11C10 = 66 + 11 = 77\)

c) We can choose 10 employees from the 12 who take public transit, so the number of possible groups of 10 employees that consist entirely of employees who take public transit is:
\(12C10 = 66\)

d) We can choose 10 employees from the 11 who drive to work, so the number of possible groups of 10 employees that consist entirely of employees who drive to work is:
\(11C10 = 11\)

e) We can choose 10 employees from the 20 who either drive to work or do neither, so the number of possible groups of 10 employees that do not include anyone who takes public transit is:
\((20C10) = 184,756\)
f) We can choose 10 employees from the 21 who either take public transit or do neither, so the number of possible groups of 10 employees that do not include anyone who drives to work is:
\((21C10) = 352,716\)

g) We can subtract the number of possible groups of 10 employees that do not include anyone who takes public transit from the total number of possible groups of 10 employees. Therefore, the number of possible groups of 10 employees that consist of at least one person who takes public transit is:
\(32C10 - 20C10 = 14,122,536\)

h) We can subtract the number of possible groups of 10 employees that do not include anyone who drives to work from the total number of possible groups of 10 employees. Therefore, the number of possible groups of 10 employees that consist of at least one person who drives to work is:
\(32C10 - 21C10 = 14,054,576\)

i) We can choose 5 employees from the 12 who take public transit and 5 employees from the 11 who drive to work. Therefore, the number of possible groups of 10 employees that consist of 5 people who take public transit and 5 people who drive to work is:
\(12C5 * 11C5 = 792 * 462 = 365,904\)

j) We can choose 4 employees from the 12 who take public transit, 3 employees from the 11 who drive to work, and 3 employees from the 9 who do neither. Therefore, the number of possible groups of 10 employees that consist of 4 people who take public transit, 3 people who drive to work, and 3 people who do neither is:
\(12C4 * 11C3 * 9C3 = 495 * 165 * 84 = 6,270,840\)
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Answer:

The discount percentage is 11.1%

Step-by-step explanation:

Here, we want to find the percentage of discount

We simply place the discount amount over the sales price multiplied by 100

we have this as;

50/450 * 100%

= 1/9 * 100%

= 100%/9

= 11.1%

The true mean additional tax owed for estate tax returns is between approximately $3056 and $3832. This means option C is the correct answer: One can be 90% confident that the mean additional tax owed is between the lower and upper bounds.

Based on a random sample of 100 audited estate tax returns, the mean amount of additional tax owed was estimated to be $3444, with a standard deviation of $2504. Using this data, a 90% confidence interval for the mean additional amount of tax owed can be calculated. The lower bound of the confidence interval is approximately $3056, and the upper bound is approximately $3832. Therefore, one can be 90% confident that the true mean additional tax owed for estate tax returns falls between these two values.

To construct the 90% confidence interval, we can use the formula:

Confidence Interval = mean ± (critical value) * (standard deviation / sqrt(sample size))

Since the sample size is large (n = 100), we can assume a normal distribution and use the z-score critical value. The critical value for a 90% confidence interval is 1.645.

Plugging in the values, we have:

Confidence Interval = $3444 ± 1.645 * ($2504 / sqrt(100))

= $3444 ± 1.645 * ($2504 / 10)

= $3444 ± 1.645 * $250.4

= $3444 ± $411.86

Calculating the lower and upper bounds:

Lower bound = $3444 - $411.86 ≈ $3056

Upper bound = $3444 + $411.86 ≈ $3832

Therefore, we can say with 90% confidence that the true mean additional tax owed for estate tax returns is between approximately $3056 and $3832. This means option C is the correct answer: One can be 90% confident that the mean additional tax owed is between the lower and upper bounds.

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Answer:

first option

Step-by-step explanation:

Using the rule of exponents

\((\frac{a^{m} }{a^{n} }) ^{p}\) = \(\frac{a^{mp} }{a^{np} }\) , then

\((\frac{2^{5} }{^{2} } )^{4}\)

= \(\frac{2^{5(4)} }{3^{2(4)} }\)

= \(\frac{2^{20} }{3^{8} }\)

By examining the dotplot, you can see the frequency and distribution of the miles run by Roger. For example, there are 4 instances where Roger ran 0.5 miles, 3 instances where he ran 4 miles, and so on.

The dotplot that displays the data correctly is the one titled "Roger's Training" with a number line labeled "Miles Run" that goes from 0.5 to 5 in increments of 0.5. The dotplot should have the following data points:
0.5, 4
1, 1
1.5, 2
2, 2
2.5, 3
3, 2
3.5, 0
4, 3
4.5, 2
5, 1
This dotplot accurately represents the number of miles Roger ran each day over a 20-day period. Each dot represents a data point from the given list of miles run. The number line indicates the range of miles run, starting from 0.5 and ending at 5, with increments of 0.5.
By examining the dotplot, you can see the frequency and distribution of the miles run by Roger. For example, there are 4 instances where Roger ran 0.5 miles, 3 instances where he ran 4 miles, and so on. This visual representation allows you to easily interpret the data and observe any patterns or trends in Roger's training.

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The minimized SOP expression for F(A,B,C,D,E) using a five-variable Karnaugh map is D'E' + BCE'. A five-variable Karnaugh map is a graphical tool used to simplify Boolean expressions.

The map consists of a grid with input variables A, B, C, D, and E as the column and row headings. The cell entries in the map correspond to the output values of the logic function for the respective input combinations.

To find the minimized SOP expression, we start by marking the cells in the Karnaugh map corresponding to the minterms given in the function: 2m(4,5,6,7,9,11,13,15,16,18,27,28,31). These cells are identified by their binary representations.

Next, we look for adjacent marked cells in groups of 1s, 2s, 4s, and 8s. These groups represent terms that can be combined to form a simplified expression. In this case, we find a group of 1s in the map that corresponds to the term D'E' and a group of 2s that corresponds to the term BCE'. Combining these groups, we obtain the expression D'E' + BCE'.

The final step is to check for any remaining cells that are not covered by the combined terms. In this case, there are no remaining cells. Therefore, the minimized SOP expression for the given logic function F(A,B,C,D,E) is D'E' + BCE'.

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The population density for each animal is given as follows:

The population density is calculated as the division of the total population by the total area.

The area for this problem is given as follows:

2.22 million acres = 2,220,000 acres.

Hence the densities are given as follows:

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Answer:

-2

Step-by-step explanation:

3*(-2)=-6

-6*(-2)=12

12*(-2)=-24

Step-by-step explanation:

7x - 5 = 8

7x = 8 + 5

7x = 13 (divide both sides by 7 to get x)

7x/7 = 13/7

x = 1.85714285714

Answer:

Step-by-step explanation:

line AB, line CD and line EF

line AB parallel to line CD

line CD perpendicular to line EF.

Answer:

Option

Step-by-step explanation: The way tell what the answer is are the similar lines. The single yellow line helps indicate that it's a similar angle.

We can change the base formula by:

                           logₐ b = logₓ a /logₓ b

                                         OR

                           logₓ a, logₓ b = logₓ a

The change of base formula is used to change the base of a logarithm.  We know that "log" stands for a logarithm of base 10 and "ln" stands for a logarithm of base e. But there is no option to calculate the logarithm of a number with any other bases other than 10 and e.

The change of base formula solves this issue of changing base from e to 10, and from base 10 to e. Also, it is used in solving several logarithms problems.

Base Formula: -

The change of base formula is used to write a logarithm of a number with a given base as the ratio of two logarithms each with the same base that is different from the base of the original logarithm. This is a property of logarithms. You can see the change of base formula here.

Change of base formula

                            logₐ b = logₓ a /logₓ b

                                         OR

                            logₓ a, logₓ b = logₓ a

Change of Base Formula

Change of base formula can be represented as follows. Here the base of the given logarithm is also changed to a logarithm with a new base. The basic logarithm with a base is transformed to two logarithms with a new and same base. The change of base formula is:

                          logₐ  b = [logₐ x] / [logₐ y]

In this formula,

Change of Base Formula Derivation

Change of base formula derivation can be understood from the following steps. Let us assume that

log ₐ b = p, logₙ a = q, and logₙ b = r.

By converting each of these into exponential form, we get,

a = \(b^{p}\), a = \(x^{q}\), and b = \(n^{r}\)

From the first two equations,

\(x^{q}\) = \(n^{r}\)

Substituting b =  \(n^{r}\) (which is from third equation) here,

(\(n^{r}\))\(^{p}\) = \(x^{q}\)

\(n^{r}\))\(^{p}\) = \(x^{q}\)(Using a property of exponents)

p r = q

p = q / r

Substituting the values, we get,

logₐ  b = [logₐ x] / [logₐ y]
For Example:

Evaluate the value of log₆₄ 8 using the change of base formula.

Solution:

We will apply the change of base formula (by changing the base to 10). Note that log₁₀ is same as log.

log₆₄ 8 = [log 8] / [log 64]

            = [log 8] / [log 82]

            = [log 8] / [2 log 8]              [∵ log am = m log a]

            = 1 / 2

Answer: log₆₄ 8 = 1 / 2

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Answer:

light blue

Step-by-step explanation:

If the family size sunscreen bottle holds 12 fl oz (fluid ounces) of sunscreen, while the regular bottle has 75% less, we will then convert the percentage into fluid ounces with the following calculation:

75/100×12=9

From the calculation above, we know the difference in the liquid content between both bottles; the regular size bottle of sunscreen has 9 fl oz (fluid ounces) less liquid content. So the liquid content of a regular sunscreen bottle is 3 fl oz (fluid ounces)

You asked an incomplete question, so I assume your complete question was:

"The family size bottle of sunscreen holds 12 fluid ounces of sunscreen. The regular bottle holds 75% less. How many fewer fluid ounces does the regular bottle hold?"

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Answer:

See below

Step-by-step explanation:

Number of distinct variations:

3

\(\left[\begin{array}{ccc}1&5\\2&4\\3&3\end{array}\right]\)

The answer to x + y = 6 can pretty much be anything that equals 6 but in addition so for example 3 + 3!

The percentage of the bulbs that have lifetimes that lie within 2 population standard deviations to either side of the population mean is 95.00%.

To solve the problem, we can use the Empirical Rule or the 68-95-99.7 rule, which states that

Approximately 68% of the data falls within one standard deviation of the mean

Approximately 95% of the data falls within two standard deviations of the mean

Approximately 99.7% of the data falls within three standard deviations of the mean

In this case, we want to find the percentage of bulbs that have lifetimes within 2 standard deviations of the mean. We know that the population mean is 153 hours and the population standard deviation is 17 hours.

To find the range of lifetimes that is within 2 standard deviations of the mean, we can use the formula:

Range = mean ± (standard deviation × number of standard deviations)

So, the range of lifetimes that is within 2 standard deviations of the mean is

Range = 153 ± (17 × 2) = 119 to 187

Therefore, approximately 95% of the bulbs have lifetimes that lie within this range.

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The square of a binomial, the value of the constant \(c\) should be equal to half the coefficient of the linear term squared, which in this case is \(c = \left(\frac{22}{2}\right)^2 = 121\). Therefore, the constant that needs to be filled in is 121.

To express the quadratic expression \(x^2 + 22x + c\) as the square of a binomial, we need to find a binomial of the form \((x + a)^2\) that expands to \(x^2 + 22x + c\). Expanding \((x + a)^2\) gives \(x^2 + 2ax + a^2\). Comparing the coefficients of the expanded binomial and the given quadratic expression, we can equate the linear terms to find \(2ax = 22x\), which gives \(a = 11\). Substituting this value of \(a\) back into the expanded binomial, we have \(x^2 + 22x + 121\). Therefore, the constant that needs to be filled in is 121.

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The statement 'When you try to find the most appropriate input probability distribution in a simulation model, you first have to choose the most appropriate family, and then you have to select the most appropriate member of that family' is generally true because in simulation modeling, input probability distributions are used to represent uncertain or random factors in the system being modeled.

These distributions are often classified into different families, such as normal, exponential, uniform, and so on, based on their properties and mathematical characteristics.

When selecting an appropriate distribution for a simulation model, it is important to first identify the family of distributions that best represents the underlying random process being modeled.

For example, if the data is symmetric and bell-shaped, then the normal distribution might be a suitable family to consider. However, if the data is non-negative and skewed, then the exponential or gamma distribution might be more appropriate.

Once the appropriate family of distributions is selected, the next step is to identify the most appropriate member or parameter values of that family that best fit the data being modeled.

This often involves using statistical methods to estimate the parameters of the distribution based on historical data or expert knowledge.

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Answer:

143

Step-by-step explanation:

A = \(\frac{Base1 + Base2}{2}\) x h

A = \(\frac{8 + 18}{2}\) x 11

A = \(\frac{26}{2}\) x 11

A = 13 x 11

A = 143

Answer:

none of the multiple choice are right, it's 143

Step-by-step explanation:

use trapezoid formula

a+b

------- h

2

26

----- h

2

13×11= 143

Answer: 15

Step-by-step explanation:

To determine the maximal velocity from an acceleration vs. time graph, you need to follow these steps:

Identify the time interval during which the acceleration remains constant or nearly constant. This interval can be identified as a straight line on the graph.

Calculate the acceleration value during this interval by finding the slope of the line. The slope is the change in acceleration divided by the change in time.

Use the acceleration value and the time interval to calculate the change in velocity during this interval using the formula:

Δv = aΔt

Where Δv is the change in velocity, a is the acceleration, and Δt is the time interval.

Add the change in velocity to the initial velocity at the start of the time interval to obtain the maximal velocity. If the initial velocity was zero, then the maximal velocity will be equal to the change in velocity.

vmax = vi + Δv

Where vmax is the maximal velocity and vi is the initial velocity.

Note that this method assumes that the acceleration is constant or nearly constant during the time interval of interest. If the acceleration changes significantly during this time interval, you will need to break it down into smaller intervals and repeat the above steps for each interval to determine the maximal velocity.

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Answer:

20÷25

Step-by-step explanation:

20÷25=0.8

0.8 as a fraction is 8/10 which can be simplified down to 4/5

25 and 20 both go into 5. so that means that we know the numerator is 5. how many 5's go into 25? 5. how many 5's go into 20? 4. so we know it's 4/5

The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches zero:

f'(a) = lim (h → 0) [f(a + h) - f(a)] / h

What is derivative?

The derivative of a function in calculus measures the function's sensitivity to changes in its input variable. Specifically, at a particular point, it represents the function's rate of change with respect to its input variable at that moment.

The derivative of a function f(x) at a point x = a is defined as the limit of the difference quotient as h approaches zero:

f'(a) = lim (h → 0) [f(a + h) - f(a)] / h

This limit represents the instantaneous rate of change or slope of the function at the point x = a. The difference quotient is the change in the function value divided by the change in the input variable (or the distance between two points on the graph of the function).

The derivative is a fundamental concept in calculus, and it has many applications in various fields of science, engineering, and economics. It allows us to calculate important quantities such as velocity, acceleration, and marginal cost, and it is used to optimize functions and solve many real-world problems.

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The players who play this game expected to lose $0.98 per ticket with a standard deviation of $145.87.

The probability distribution of X is given as follows:

X P(x)

-2 0.998

-1 0.002

5 0.1

10 0.005

1000 0.0006

5000 0.0001

To calculate the expected value of X, we can use the formula:

Expected value of X =  ΣxP(x)

Therefore, the expected value is:

Expected Value of X = (-2) (0.998) + (-1) (0.002) + (5) (0.1) + (10) (0.005) + (1000) (0.0006) + (5000) (0.0001) = -0.98

The standard deviation of X is given by the expression:

Standard deviation of X = √(Σ(x-μ)²P(x))

Where μ is the expected value of X.

In this case, μ = -0.98

Therefore, the standard deviation of X is:

Standard deviation of X = √(((-2 - (-0.98))²) (0.998) + ((-1 - (-0.98))²) (0.002) + ((5 - (-0.98))²) (0.1) + ((10 - (-0.98))²) (0.005) + ((1000 - (-0.98))²) (0.0006) + ((5000 - (-0.98))²) (0.0001))

= √(145.87)

= 12.07

Therefore, the players who play this game expected to lose $0.98 per ticket with a standard deviation of $145.87.

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Answer:

rhombus

Step-by-step explanation:

Answer: I'd go with Option (C.<3 AND 4, <6 AND 4)

Answer: The answer is D

Step-by-step explanation: