39. Find the minimized Boolean expression for the functions defined by each of the following truth tables a) x у Z F 0 0 0 X 0 0 1 X 10 1 0 1 0 1 1 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 b) w x y Z F 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 1 0 0 х 0 1 0 1 0 0 1 1 0 X 0 1 1 0 1 10 0 0 1 1 0 D 1 X 1 10 1 0 х 1 0 1 1 X 1 1 0 0 X 1 1 0 1 1 1 1 1 0 X 1 1 1 X

Answer:

3

Step-by-step explanation:

Find the prime factorization of 9

9 = 3 × 3

Find the prime factorization of 33

33 = 3 × 11

To find the GCF, multiply all the prime factors common to both numbers:

Therefore, GCF = 3

Answer:

if a joke i dont know

Answer:

75x = 300

x = 4

So he has

4 quarters

3x = 3*4 = 12 dimes

4x = 4*4 = 16 nickels

Step-by-step explanation:

Answer:

x > 3/7

Step-by-step explanation:

7x-5>-2

7x > (-2+5)

x > 3/7

Answer:

x>3/7

Step-by-step explanation:

7x-5>-2  add 5 to both sides

7x>3 divide both sides by 7

x > 3/7

The probability that a student makes more than 7 mistakes on the exam is 0.39.

In science, the probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%. T

Now, let X be the number of mistakes a student makes on the exam. Then, the X follows a binomial distribution with n=16 and some unknown probability of success p (i.e., the probability of answering a question correctly).

We know that P(X<5) = 0.47 and P(5<=X<=7) = 0.14. Using the complement rule, we can find P(X>7) as follows:

P(X>7) = 1 - P(X<=7)

= 1 - P(X<5) - P(5<=X<=7)

= 1 - 0.47 - 0.14

= 0.39. Therefore, the probability that a student makes more than 7 mistakes on the exam is 0.39.

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Step-by-step explanation:

Given that the number of amoeba is 1

in 1 hour it divides to form 2

1 hour later (2 hours): 1 amoeba(forms 2), 1 amoeba(forms 2)= 4  

1 hour again(3 hours):   1=2,1=2,1=2,1=2 hence a total of 8 after 3 hours

Question and answers

1. How many amoebas are there after 1 hour

=2 amoebas

2. How many amoebas are there after 2 hours

=4 amoebas

3. Write an expression for the number of amoebas after 6 hours.

let the number of amoeba be y, and the time be n

so in 6 hours n= 6

\(y=2^n\)

\(y= 2^6\\\\y= 64 amoebas\)

Answer:11

Step-by-step explanation:

The interquartile range of the set of values given is: 11 - 4 =7

To find the interquartile range, you first begin by defining the lower half, the median, and the upper half. The median of the set of figures given is 8. Then the upper half begins at 11 while the lower half begins and ends at 4.

So, to define the interquartile range, we would subtract 7 from 11 to get 4. So, the interquartile range of the values in the dataset is 4.

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Complete Question:

A data set is made up of these values 3,4,5,8,9,11,12 Find the interquartile range

Option (D), the last option is the correct statement, If heights in inches of 200 graduating seniors were summarized in the frequency table;

The median height is greater than or equal to 60 inches but less than 66 inches.

The median is the number value that separates the lower and upper values to halves. The median height is determined by arranging all the given heights in order either from the smallest to highest or from highest to smallest without skipping any measurement of the heights.

After arranging all the heights in order, the median height is usually at the middle.

The reason as to why the median height is greater than or equal to 60 inches but less than 66 inches is because the middle height should not be same as the largest height of 66 inches. It is possible to have multiple 60 inch heights from the 200 seniors. It is also possible to have multiple 66 inch of heights from the 200 seniors.

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Answer:

Thus, the length of the arc AB will be 5/18 of the circumference of the circle, which equals 2πr, according to the formula for circumference. length of arc AB = (5/18)(2πr) = (5/18)(2π(18)) = 10π. Thus, the length of arc AB is 10π.

Step-by-step explanation:

A normal distribution curve with mean 110 and standard deviation 10.  Percentages of students scoring below 90, higher than 115, lower than 115, and between IQ score cut offs for the top 15% and the middle 36% of students were 105.7 and 114.3. The percentage of students falling between IQ scores of 95.6 and 105 is  23.5%..

To find the percentage of students who scored below a 90, we need to find the area under the normal distribution curve to the left of 90. Using a standard normal distribution table or calculator, we find that this area is about 0.16 or 16%.

To find the percentage of students who scored higher than a 115, using a standard normal distribution table or calculator, we find that this area is about 0.16 or 16%. To find the percentage of students who scored lower than a 115, we need to find the area under the normal distribution curve to the left of 115, which is about 84%.

To find the IQ score cutoff for the top 15% of students, using a standard normal distribution table or calculator, we find that the z-score is about 1.04. We can then use the formula z = (x - μ) / σ to solve for x, the IQ score cutoff:

1.04 = (x - 110) / 10

x = 121.04

So the IQ score cutoff for the top 15% of students is about 121.04.

To find the IQ scores, using a standard normal distribution table or calculator, we find that the z-scores are about -0.43 and 0.43. We can then use the formula z = (x - μ) / σ to solve for x, the IQ score cutoffs:

-0.43 = (x - 110) / 10

x = 105.7

0.43 = (x - 110) / 10

x = 114.3

So the IQ score cutoffs for the middle 36% of students are about 105.7 and 114.3.

To find the percentage of students who fall between IQ scores of 95.6 and 105, we find that the z-scores are about -1.04 and -0.46. Using a standard normal distribution table or calculator, we find that the area between these z-scores is about 0.235 or 23.5%.

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Answer:

120

Step-by-step explanation:

The probability that 3 out of the 4 captured elk have been tagged is approximately 0.0053.

We can use the concept of combinations.

The total number of ways to choose 4 elk out of 24 is given by the combination formula:

C(24, 4) = 24! / (4!(24-4)!) = 10,626

Now, we need to consider the number of ways to choose 3 tagged elk out of the 8 tagged elk and 1 untagged elk. The number of ways to do this is given by:

C(8, 3) * C(1, 1) = 8! / (3!(8-3)!) * 1! / (1!(1-1)!) = 56

Therefore, the probability that 3 out of the 4 captured elk have been tagged is:

P = (Number of ways to choose 3 tagged elk out of 8 tagged elk and 1 untagged elk) / (Total number of ways to choose 4 elk out of 24)

P = 56 / 10,626

Calculating this division gives us the probability:

P ≈ 0.0053

So, the probability that 3 out of the 4 captured elk have been tagged is approximately 0.0053 .

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Answer:

(6m² + 12m + 2) / (6m + 1)

Step-by-step explanation:

multiply both sides by m.

we get m² - 1 = 6m

move the -1 to the other side, so it becomes +1

m² =  6m + 1

so m² + 1/m² = (6m + 1) + 1/(6m + 1)

get a common denominator by squaring (6m + 1)

(6m + 1)².

we now have (6m + 1)² / (6m + 1)  + 1/(6m + 1).

we now add the numerators.

(6m + 1)² + 1 = (6m² + 6m + 6m + 1) + 1 = 6m² + 12m + 2.

numerator over denominator = (6m² + 12m + 2) / (6m + 1)

First, we plot the graph of the equation y=-4x+3, to do this, we only need two points

In green it is shaded the ponts that satisfy the inequality, that is because the y value must be below (that's why it has the sigh <) this graph.

Answer:

1/2

Step-by-step explanation:

When you roll a 6-sided die, there are 6 possible outcomes:

1, 2, 3, 4, 5, 6

3 of the outcomes are even, and 3 of the outcomes are odd.

p(A) = p(even) = 3/6 = 1/2

p(Ac) = 1 - p(A) = 1 - 1/2 = 1/2

Answer: Any number less than 9.

Step-by-step explanation: The inequality is x is less than 9, that’s what < means, so you can say x is 8, 7, 6, 6.9, etc, x is anything less than 9.

Richard's net pay for the week, considering Social Security, Medicare, and FIT deductions, can be calculated by subtracting the total deductions from his gross earnings.

First, let's determine the amount deducted for Social Security. The Social Security rate is 6.2%, and the maximum earnings subject to this deduction are $118,500. Since Richard is $1,000 below the maximum level, the amount subject to Social Security deduction is $1,000. Therefore, the Social Security deduction is 6.2% of $1,000.

Next, we calculate the Medicare deduction. The Medicare rate is 1.45%, and it is applied to the entire earnings of $1,700.

To calculate the FIT deduction, we need additional information about Richard's taxable income, tax brackets, and exemptions. Without this information, we cannot provide an accurate calculation for the FIT deduction.

Finally, we subtract the total deductions (Social Security, Medicare, and FIT) from Richard's gross earnings of $1,700 to obtain his net pay for the week.

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The value of y can be an infinite number of answers such as 1,2,3,4,5,6,7,8,9 ......n(infinity)

Let's go with the first statement;

If y = 1

Then ; 1× 9 = 9+ 8 = 17÷ 9 = 1 remainder 8

If y = 2 2 × 9 = 18+8 = 26÷9 = 2 remainder 8

If y= 3 3×9 = 27+8 = 35÷9 = 3 remainder 8

For the second statement;

If y = 1

Then; 1×8 = 8+7 = 15/8 = 1 remainder 7

If y = 2 2×8 = 16+7 = 23/8 = 2 remainder 7

For third statement;

If y = 1

Then; 1×7 = 7+6 = 13/6 = 1 remainder 5

For fourth statement;

if y = 1

Then; 1×6 =6+5 = 11/6 = 1R5

For fifth statement;

If y = 1

Then; 1×5 = 5+4 = 9/5= 1R4

For sixth statement;

if y = 1

Then ; 1×4 = 4+3 = 7/4 = 1R3

For seventh statement;

if y = 1

Then ; 1×3= 3+2 = 5/3 = 1R2

For eight statement;

if y = 1

Then; 1×2 = 2+1 = 3/2 = 1R1

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The volume V of solid S is e - 1 cubic unit.

What is Volume?

Volume refers to the measure of three-dimensional space occupied by an object or a region. It quantifies the amount of space enclosed by the boundaries of an object or contained within a given region. In mathematical terms, volume is often calculated by integrating the cross-sectional areas of the object or region along a particular axis. Volume is typically expressed in cubic units, such as cubic meters (m^3) or cubic centimeters (cm^3). It is an essential concept in geometry, physics, engineering, and other scientific fields where the measurement of three-dimensional space is involved.

To find the volume of solid S, we need to integrate the areas of the cross sections perpendicular to the x-axis along the interval \([e, \infty).\)

The area of each square cross-section is equal to the square of the side length, which in this case is \(y = \sqrt{\ln(x)}.\)

Therefore, the volume V of solid S can be calculated as:

\(V = \int_{e}^{\infty} (\sqrt{\ln(x)})^2 dx\)

To evaluate this integral, we can simplify the expression:

\(V = \int_{e}^{\infty} \ln(x) dx\)

Using integration by parts, we let \(u = \ln(x)\)and dv = dx:

\(du = \frac{1}{x} dx\\v = x\)

Applying the integration by parts formula:

\(V = [uv] - \int v du= [x \ln(x)] - \int x \left(\frac{1}{x}\right) dx= x \ln(x) - \int dx= x \ln(x) - x + C\)

Evaluating the definite integral:

\(V = [x \ln(x) - x]_{e}^{\infty}= (\infty \cdot \ln(\infty) - \infty) - (e \cdot \ln(e) - e)= \infty - 0 - (1 - e)= e - 1\)

Therefore, the volume V of solid S is e - 1 cubic unit.

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A telephone call center uses two customer service representatives (csrs) during the 8:30 a.m. to 9:00 a.m. time period. the standard service rate is 2.0 minutes per telephone call per csr. assuming a target labor utilization rate of 70 percent, Therefore, these two CSRs can handle approximately 3 calls during this half-hour period.

Given a telephone call center uses two customer service representatives (CSRs)

during the 8:30 a.m. to 9:00 a.m. time period, and the standard service rate is 2.0 minutes per telephone call per CSR. Assuming a target labor utilization rate of 70%,

we have to determine the number of calls these two CSRs can handle during this half-hour period.

The formula to calculate the number of calls that can be handled during this half-hour period is:

Number of calls = (number of servers x utilization rate x service time) / arrival rate

                          = (2 x 0.70 x 2) / 1

                          = 2.8 calls (rounded to the nearest whole number)

Therefore, these two CSRs can handle approximately 3 calls during this half-hour period.

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Answer:

base of triangle is 18 cm

Step-by-step explanation:

Perimeter of triangle: P = a + b + c

if a is the base

then b = a + 3

and c = a - 5

so a + b + c = P

a + (a + 3) + (a - 5) = 52

3a - 2 = 52

3a = 54

a = 54/3 = 18

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Answer:

xy = 3

d/dt(xy) = d/dt(3)

ydx/dt + xdy/dt = 0

y = 3/x so substitute 3/5 for y, 5 for x, and 5 for dy/dt; and solve for dx/dt.

3/5(dx/dt) + 5(5) = 0

3/5(dx/dt) = -25

dx/dt = -125/3

Step-by-step explanation:

this should be able to help you :)

Answer:

Step-by-step explanation:

(3+1)/2= 4/2 = 2

(-8+2)/2= -6/2= -3

(2, -3)

Answer:

A

Step-by-step explanation:

The probability that if you choose 2 people randomly, exactly one will need an x-ray is 0.4.

The probability that if you choose 2 people randomly from the 16 in the hospital, exactly one will need an x-ray is as follows:
Firstly, calculate the probability of choosing one person who needs an X-ray and one person who doesn't.

There are 4 people who need an x-ray and 12 who don't, so the probability for this is (4/16) * (12/15).

Now, calculate the probability of choosing one person who doesn't need an X-ray and one person who does. This is (12/16) * (4/15).

Now, add the probabilities to find the total probability.

The probability that exactly one person will need an x-ray is

(4/16) * (12/15) + (12/16) * (4/15) = 2/5

=0.4.

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The probability that if you choose 2 people randomly, exactly one will need an x-ray is 0.4 or 40%.

If there are 16 people in a hospital and 4 need an xray, the probability that if you choose 2 people randomly, exactly one will need an xray is 0.56.

Total number of people in a hospital = 16

Number of people who need an x-ray = 4

Thus, the probability that if you choose 2 people randomly, exactly one will need an x-ray is given by;

P(one needs an x-ray) = (Number of people who need an x-ray × Number of people who do not need an x-ray) / Total number of people × Total number of people - 1

P(one needs an x-ray) = (4 × 12) / 16 × 15

P(one needs an x-ray) = 0.08

P(one doesn't need an x-ray) = (Number of people who need an x-ray × Number of people who do not need an x-ray) / Total number of people × Total number of people - 1

P(one doesn't need an x-ray) = (12 × 4) / 16 × 15

P(one doesn't need an x-ray) = 0.32

Now, we have to add both the probabilities of exactly one person needing an x-ray and exactly one person not needing an x-ray;

P(exactly one person needs an x-ray) = P(one needs an x-ray) + P(one doesn't need an x-ray)

P(exactly one person needs an x-ray) = 0.08 + 0.32P(exactly one person needs an x-ray) = 0.4

The probability that if you choose 2 people randomly, exactly one will need an x-ray is 0.4 or 40%.

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Answer:

n=5

Step-by-step explanation:

6(n-2)-8=22+4(2-n)

open brackets

6n-12-8=22+8-4n

collect like terms

6n+4n=22+8+12+8

10n=50

n=50/10

n=5