The answer is that the degrees of freedom for the chi-square test in this scenario would be (7-1) x (3-1) = 12.
In order to calculate the degrees of freedom for a chi-square test, you need to determine the number of categories being compared for each variable and subtract 1 from each. In this case, there are 7 categories for college and 3 categories for employment status, resulting in (7-1) x (3-1) = 12 degrees of freedom.
Long Answer: The chi-square test is a statistical method used to determine whether there is a significant association between two categorical variables. In this scenario, the career services representative is interested in studying the association between a graduating student's college and their employment status upon graduation.
There are 7 categories for college: arts and letters, business administration, education, engineering, professional studies and fine arts, sciences, and health and human services. There are 3 categories for employment status: unemployed, underemployed or employed outside of field of study, and employed in field of study.
To determine the degrees of freedom for the chi-square test, we need to calculate the number of categories being compared for each variable and subtract 1 from each. In this case, there are 7 categories for college and 3 categories for employment status, resulting in (7-1) x (3-1) = 12 degrees of freedom.
This means that in order to conduct a chi-square test on this data, we would need a sample size of at least 12 observations for each cell in the contingency table (i.e., each combination of college and employment status). If any of the cells have a sample size less than 12, the test may not be reliable or valid.
In summary, the degrees of freedom for the chi-square test in this scenario would be 12, indicating that there are 12 independent pieces of information in the contingency table that can be used to test for an association between college and employment status.
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what is the price of 700g at £2 a kg
Answer:
£1.4
Step-by-step explanation:
700g = 0.7kg
0.7 x 2 = 1.4
a license plate has one letter (not i or o) followed by five digits. how many different plates are possible?]
There are 9,000,000 different possible license plates.
What is the total number of valid license plates consisting of one letter (excluding i and o) and five digits?Since the license plate has one letter followed by five digits, we need to consider two cases separately:
Case 1: The letter can be any of the 24 letters of the alphabet, excluding 'i' and 'o'.
Case 2: Each digit can be any of the 10 digits from 0 to 9.
For the first position, there are 24 choices for the letter. For the second position, there are 10 choices for the digit. Similarly, there are 10 choices for the third, fourth, fifth, and sixth positions.
Therefore, the total number of possible license plates is:
24 x 10 x 10 x 10 x 10 x 10 = 24 x 10^5 = 9,600,000
However, we need to exclude the license plates that contain 'i' or 'o'. There are 2 choices for the first position, and 10 choices for the remaining positions.
Therefore, the total number of license plates that contain 'i' or 'o' is:
2 x 10 x 10 x 10 x 10 x 10 = 2 x 10^5 = 200,000
So the final answer is:
24 x 10^5 - 2 x 10^5 = 9,600,000 - 200,000 = 9,000,000
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you are contracted to build a children's pool at the new public pool facility. the pool must be built on a fenced off 17 by 26 feet rectangular plot. the pool must be a 77 sq ft rectangle. furthermore, the facility manager wants the border fence to be the same distance, x, from all sides of the pool, except they want to put a lifeguard chair at one end of the length, so the fence should be twice as far away on that side. what are the dimensions of the pool?
The pool dimensions are approximately 12.22 by 21.22 feet.
To start, we know that the pool must be a 77 sq ft rectangle, so we can use the formula for the area of a rectangle (length x width = area) to solve for the dimensions.
77 = length x width
Next, we know that the fenced off plot is a 17 by 26 feet rectangle. We can use this information to set up an equation for the distance between the pool and the fence:
17 - 2x = length
26 - 2x = width
We also know that the fence should be twice as far away on the end where the lifeguard chair will be located, so we can set up another equation:
17 - 4x = length (on the side with the lifeguard chair)
Now we can substitute the expressions for length and width into the formula for the area of a rectangle:
77 = (17 - 2x)(26 - 2x)
Expanding the expression on the right side, we get:
77 = 442 - 86x + 4x^2
Rearranging and simplifying, we get a quadratic equation:
4x^2 - 86x + 365 = 0
Using the quadratic formula, we can solve for x:
x = (86 +/- sqrt(86^2 - 4(4)(365))) / (2(4))
x = (86 +/- sqrt(55284)) / 8
x = (86 +/- 234.85) / 8
x = 36.86 or 2.39
We can ignore the negative value, so x = 2.39 feet.
Now we can use the equations for length and width to solve for the dimensions of the pool:
length = 17 - 2x = 17 - 2(2.39) = 12.22 feet
width = 26 - 2x (except on the side with the lifeguard chair, where it is 4x) = 26 - 2(2.39) = 21.22 feet
So the pool dimensions are approximately 12.22 by 21.22 feet.
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a die is rolled twice. what is the probability that the number in the second roll will be higher than that in the first?
The probability of rolling a higher number on the second roll is 15/36 or approximately 0.42.
When rolling a die, each roll has an equal chance of landing on any of the six possible outcomes. Therefore, the probability of rolling any specific number on the first roll is 1/6, and the probability of rolling a number higher than the first on the second roll is also 1/6.
To find the probability of both events happening, we can use the multiplication rule of probability, which states that the probability of two independent events occurring together is equal to the product of their individual probabilities.
So, the probability of rolling a number on the first roll and then rolling a higher number on the second roll is:
P = (1/6) x (1/6)
However, since the question doesn't specify a particular number for the first roll, we need to consider all the possible outcomes for the first roll. These outcomes are mutually exclusive and have an equal chance of happening, so we can add their probabilities to find the overall probability of rolling a higher number on the second roll:
P = (1/6) x (5/6) + (1/6) x (4/6) + (1/6) x (3/6) + (1/6) x (2/6) + (1/6) x (1/6) + (1/6) x 0
Simplifying this expression, we get:
P = 15/36
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a consensus forecast is the average of a large number of individual analysts' forecasts. suppose the individual forecasts for a particular interest rate are normally distributed with a mean of 6 percent and a standard deviation of 1.4 percent. a single analyst is randomly selected. find the probability that his/her forecast is (a) at least 3.3 percent. (round the z value to 2 decimal places. round your answer to 4 decimal places.) (b) at most 7 percent. (round the z value to 2 decimal places. round your answer to 4 decimal places.) (c) between 3.3 percent and 7 percent. (round the z value to 2 decimal places. round your answer to 4 decimal places.)
The probability that his/her forecast is
(a) at least 3.3 percent 0.93
(b) at most 7 percent 0.0274.
(c) between 3.3 percent and 7 percent is 0.7337.
To calculate the probability of a single analyst's forecast being at least 3.3 percent, we need to find the z-score associated with that value. The z-score is a measure of how many standard deviations a data point is from the mean of a distribution. Using the formula:
z = (x - μ) / σ
where x is the value we want to find the z-score for, μ is the mean of the distribution, and σ is the standard deviation of the distribution, we can calculate the z-score for 3.3 percent:
z = (3.3 - 6) / 1.4 = -1.93
To find the probability of a single analyst's forecast being at least 3.3 percent, we need to find the area under the normal curve to the left of the z-score of -1.93. This can be done using a standard normal distribution table or a calculator. The probability is approximately 0.0274.
To calculate the probability of a single analyst's forecast being at most 7 percent, we need to find the z-score associated with that value. Using the same formula as before, we can calculate the z-score for 7 percent:
z = (7 - 6) / 1.4 = 0.71
To find the probability of a single analyst's forecast being at most 7 percent, we need to find the area under the normal curve to the left of the z-score of 0.71. This can also be done using a standard normal distribution table or a calculator. The probability is approximately 0.7611.
To calculate the probability of a single analyst's forecast being between 3.3 percent and 7 percent, we need to find the area under the normal curve between the z-scores of -1.93 and 0.71. This can also be done using a standard normal distribution table or a calculator. The probability is approximately 0.7337.
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if a>0 and b>0 then 3(a^0b^2)=
The expression can be simplified to get:
[tex]3*(a^0*b^2) = 3b^2[/tex]
How to simplify the given expression?Remember that for any real:
x > 0
We have that the power when the exponent is zero, is equal to one.
[tex]x^0 = 1[/tex]
Here we know that:
a > 0, b > 0.
And we have the expression:
[tex]3*(a^0*b^2)[/tex]
The first power can be removed, because that is equal to 1, then we can simplify our expression to get.
[tex]3*(a^0*b^2) = 3b^2[/tex]
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the sum of a number and the cube of a second number is 864. find the number so that the product is a maximum. calculus
To find the number that maximizes the product, we need to use calculus. Let's start by setting up the problem. Let x be the first number and y be the second number. We know that: x + y^3 = 864. We want to find the maximum value of xy.
Now, substitute this expression for x into our product function:
P(y) = (864 - y^3) * y
To find the maximum, we need to take the derivative of P(y) with respect to y and set it equal to 0:
dP/dy = -3y^4 + 864y - y^3(dy/dy)
dP/dy = -3y^4 + 864y - y^3(1)
Now, set dP/dy = 0 and solve for y:
0 = -3y^4 + 864y - y^3
It's a challenging polynomial to solve, but we can use numerical methods or technology to find the critical points of y.
Once we have the value(s) of y, we can plug it back into the equation x = 864 - y^3 to find the corresponding value(s) of x.
Finally, determine whether the critical points result in a maximum by checking the second derivative or analyzing the function's behavior around the critical points. The pair of numbers (x, y) will yield the maximum product.
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A 8-kg block is set moving with an initial speed of 6 m/s on a rough horizontal surface. If the force of friction is 12 n, approximately how far does the block travel before it stops?.
The block will cover the distance 12m before it stops.
Newton's second law of motion:According to Newton's second law of motion, the acceleration a
of a body of mass m is determined by the net force [tex]F_n_e_t[/tex] acting on it:
[tex]F_n_e_t[/tex] = ma.
The mass of a block, m = 8 kg
The initial speed of the block on rough horizontal surface , u = 6 m/s
The force of friction, F = 12N
We know that, the Newton's 2nd law: [tex]F_n_e_t[/tex] = ma.
Therefore, its final velocity is zero, v = 0
Since the only force that is acting on the body along the horizontal direction is the kinetic frictional force
[tex]F_n_e_t[/tex] = ma. ([tex]F_n_e_t[/tex] is acting in opposite direction to that of object motion)
a = [tex]\frac{f_n_e_t}{m}[/tex] = [tex]\frac{-12}{8} = -1.5m/s^2[/tex]
Negative sign shows that it is in the opposite direction to that of initial velocity.
By using the third kinematic equation, we get:
[tex]v^2=u^2+2as\\\\= > s = \frac{0-6^2}{2(-1.5)}\\ \\s = \frac{36}{3} = 12m[/tex]
Therefore, the block will cover the distance 12m before it stops.
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what is the probability that maximum speed differs from the mean value by at most 2.5 standard deviations?
The answer is that the probability that the maximum speed differs from the mean value by at most 2.5 standard deviations can be calculated using the normal distribution.
We first need to calculate the mean value and standard deviation of the speed data. Then, we can use the formula for the normal distribution to find the probability that the maximum speed falls within a certain range from the mean value.
Specifically, we can use the formula:
P(mean - 2.5SD < max speed < mean + 2.5SD) = P(z < 2.5) - P(z < -2.5)
where z is the z-score of the maximum speed, calculated as (max speed - mean)/SD.
We can find the probabilities P(z < 2.5) and P(z < -2.5) using a standard normal distribution table or calculator.
In general, if the maximum speed is normally distributed and the mean and standard deviation are known, we can use this formula to calculate the probability that the maximum speed falls within a certain range from the mean value.
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-17>6x+7
Solve the inequality for x
Answer:
x < -4
Step-by-step explanation:
-17>6x + 7
Switch it to: 6x + 7 <-17
6x + 7 < -17
Now, Subtract the opposite of 7 by both sides.
6x = -24
Divide both sides by 6
Answer : x < -4
Which best approximates the solution of 16 to the power of 2x = 125
Answer:
869
Step-by-step explanation:
Jeremiah is working on a model bridge. He needs to create triangular components, and he plans to use toothpicks. He finds three toothpicks of lengths 4 in., 5 in., and 1 in. Will he be able to create the triangular component with these toothpicks without modifying any of the lengths?
• Yes, according to the Triangle Inequality TheoremYes, according to the Triangle Sum Theorem
No, according to the Triangle Inequality Theorem
• No, according to the Triangle Sum Theorem
No, according to the triangle inequality theorem he will not be able to create the triangular component. That is option C
What is triangular inequality theorem?The triangular inequality theorem states that the sum of any two sides of a triangle is greater than the length of the third side.
That is;
a+b > c
a+ c > b
b+c > a
The lengths given include the following;
a = 4 in
b = 5 in
c = 1 in
Using the theorem;
a+b = 4+5 = 9 > 1
a+c = 4+1 = 5 = 5
b+c = 5+1 = 6> 4
Therefore he won't be able to create a triangular component using the three lengths of the tooth pick because is goes against the triangle inequality theorem rule.
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Answer:
Step-by-step explanation:
the answer is A
i took the text
5 to the power of 2x=20
The approximate value of x in the equation 5 to the power of 2x=20 is 0.93
Calculating the value of xFrom the question, we have the following parameters that can be used in our computation:
5 to the power of 2x=20
As an expression, we have
5^(2x) = 20
Take the natural logarithm of both sides
so, we have the following representation
2x = ln(20)/ln(5)
Evaluate the quotients
This gives
2x = 1.86
So, we have
x = 0.93
Hence, the value of x is 0.93
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z varies with y and inversely with x when z=6, x=4, and y=3
If z varies with y and inversely with and z = 6 when x = 4 and y = 3, then the value of Proportionality Constant is given by 8.
Proportion is a relation between two mathematical variables. If two variables vary directly that states if one increases another will also decrease and same for decrease.
If two variables are in inverse relation that states that if one variable increases then another decreases and if one variable decreases then another increases.
Given that, z varies with y and inversely with x. So,
z = k*(y/x), where k is the proportionality constant.
Given that, z = 6 when x = 4 and y = 3. So,
6 = k*(3/4)
k = (6*4)/3
k = 2*4
k = 8
Hence the value of Proportionality Constant is 8.
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The question is incomplete. The complete question will be -
"z varies with y and inversely with x when z=6, x=4, and y=3. Find the value of Proportionality Constant."
Magan invested $790 in an account paying an interest rate of 83% compounded
quarterly. Angel invested $790 in an account paying an interest rate of 8%
compounded continuously. After 7 years, how much more money would Magan have
in his account than Angel, to the nearest dollar?
Answer:3
Step-by-step explanation:
1437.9874-1444.882=3.1054
An SRS of 20 orangutans is selected, and 65 cc of blood is to be drawn from each orangutan using a 100 cc syringe. In the sample, the mean volume is 64 cc and the standard deviation is 12 cc. Assume that in the population of all such procedures, the amount of blood drawn follows a Normal distribution with mean ?.
Reference: Ref 17-1
We are interested in a 95% confidence interval for the population mean volume. The margin of error associated with the confidence interval is
Answer
A. 4.64.
B. 2.68.
C. 6.84.
D. 5.62.
The margin of error associated with the 95% confidence interval for the population mean volume is: D. 5.62.
To calculate the 95% confidence interval for the population mean volume, we can use the formula:
CI = x ± (t * (s/√n))
Where CI represents the confidence interval, x is the sample mean, t is the t-score associated with the desired confidence level (95%), s is the sample standard deviation, and n is the sample size.
In this case, x = 64 cc, s = 12 cc, and n = 20 orangutans. We need to find the t-score for a 95% confidence interval with 19 degrees of freedom (n-1). Using a t-table, we find that the t-score is approximately 2.093.
Now we can calculate the margin of error:
Margin of Error = t * (s/√n) = 2.093 * (12/√20) ≈ 5.62
Therefore, the margin of error associated with the 95% confidence interval for the population mean volume is: D. 5.62.
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an urn contains 13 white balls and 7 green balls. a sample of seven is selected at random. what is the probability that the sample contains at least one green ball?huffled standard 52-card deck of cards. what is the probability that the hand contains 4 jacks?
the probability of the sample containing at least one green ball when selecting 7 balls randomly is approximately 0.9779 or 97.79%.
To find the probability that the sample contains at least one green ball, it's easier to calculate the probability of the complementary event (not getting any green balls) and then subtract that from 1. The complementary event would be selecting all 7 balls as white balls.
1. Total balls in the urn = 13 white balls + 7 green balls = 20 balls
2. Calculate the probability of selecting 7 white balls:
- Number of ways to choose 7 white balls out of 13 = C(13,7) = 1716
- Number of ways to choose 7 balls out of 20 = C(20,7) = 77520
- Probability of selecting 7 white balls = 1716 / 77520 = 0.0221267
3. Calculate the probability of getting at least one green ball:
- Probability of at least one green ball = 1 - Probability of 7 white balls
- Probability of at least one green ball = 1 - 0.0221267 = 0.9778733
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Select the correct answer. Which value of x from the set {4, 5, 6, 7}, makes this equation true? 4(8 − x) = 8 A. 4 B. 5 C. 6 D. 7
Answer: c. 6
Step-by-step explanation:
Option-C is correct that is 6 number from the set {4 , 5, 6, 7} makes the equation 4(8 - x) = 8 true.
Given that,
We have to find which value of the x from the set {4 , 5, 6, 7} makes the equation 4(8 - x) = 8 true.
We know that,
What is a set?A group of well defined objects is referred to as a set. Only on the basis of simplicity are the objects of a set considered to be distinct.
A family or collection of sets are common names for a group of sets.
So,
The set has 4 numbers by substituting the numbers we get to know if the equation is true or false.
Take the equation,
4(8 - x) = 8
If x = 4,
4(8 - 4) = 8
4 × 4 = 8
16 ≠ 8
Now, If x = 5,
4(8 - 5) = 8
4 × 3 = 8
12 ≠ 8
Now, If x = 6,
4(8 - 6) = 8
4 × 2 = 8
8 = 8
And, If x = 7,
4(8 - 7) = 8
4 × 1 = 8
4 ≠ 8
Therefore, Option-C is correct that is number 6.
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If a bat catches a total of 560 bugs in 7 nights, and each night the bat catches the same number of bugs, how many bugs did the bat catch on the fifth night?
Answer:
400
Step-by-step explanation:
get the number of bugs caught in night and multiply it by five
The Blackburn family has a square field where they keep their cattle. The area of the field is 40,000 ft square, and Mr. Blackburn wants to put a fence diagonally through the field. What should the length of the fence be?
If "square-field" area is 40000 ft square, and Mr. Blackburn is planning to put a fence diagonally in field, then the length of fence should be 282.84 ft.
The area of the Blackburn's square-field is = 40000 ft²,
First, we equate this with area formula,
On Equating ,
We get,
⇒ (side)² = 40000,
⇒ side = 200,
substituting the "side-length" of the field as 200 ft, in the diagonal of a square formula,
we get,
⇒ Length of field's diagonal is = (side)√2,
⇒ Length of field's diagonal is = (200)√2,
⇒ Length of field's diagonal is ≈ 282.84 ft.
Therefore, the length of field's fence is 282.84 ft.
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consider the postfix expression: a-b c*(d*e-f)/(g h*k). the equivalent postfix (reverse polish notation) expression is: group of answer choices
The equivalent postfix (reverse Polish notation) expression for the infix expression "A-B+C*(DE-F)/(G+HK)" is option B: AB-CDEF-+GHK*+/.
The equivalent postfix (reverse Polish notation) expression for the given infix expression "A-B+C*(DE-F)/(G+HK)" is
AB-CDEF-+GHK*+/
Therefore, the correct answer is B), expression can be obtained by following the order of operations for postfix notation start from the left and push operands onto a stack until an operator is encountered. When an operator is encountered, pop the top two operands, perform the operation, and push the result back onto the stack.
Repeat until the end of the expression is reached, and the final result is the top value on the stack.
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--The given question is incomplete, the complete question is given
" Consider the postfix expression: A-B+C*(D*E-F)/(G+H*K). The equivalent postfix (reverse Polish notation) expression is:
A.
AB-C+DE*F-GH+K**/
B.
AB-CDE*F-*+GHK*+/
C.
ABC+-E*F-*+GHK*+/
D.
None of these"--
Sketch a curve y = f(x) that satisfies: f(0) = 3, and dy/dx =-2. What is f(x)?
The curve f(x) is f(x) = -2x + 3.
Given that dy/dx = -2, we can integrate both sides with respect to x to obtain:
dy/dx = -2
dy = -2 dx
Integrating both sides, we get:
y = -2x + C
where C is the constant of integration. To find the value of C, we use the initial condition f(0) = 3:
y = -2x + C
f(0) = 3
-2(0) + C = 3
C = 3
Thus, the equation of the curve is:
y = -2x + 3
Therefore f(x) is -2x + 3
We can sketch the curve by plotting a few points. For example, when x = 0, y = 3 (as required by the initial condition). When x = 1, y = 1. When x = -1, y = 5. We can also note that the slope of the curve is always -2, meaning that the curve is a straight line with a negative slope.
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Solve the equation 3x – 9 = 5x + 9
Answer:
x = -9
Step-by-step explanation:
3x - 9 = 5x + 9
3x - 5x = 9 + 9
-2x = 18
x = 18 / - 2x = -9
Answer:
x=-9
Step-by-step explanation:
(3 x -9) - 9 = -36
(5 x -9) + 9 = -36
what is true about quantitative versus qualitative research? multiple choice all of the statements about quantitative versus qualitative research are true. none of the statements about quantitative versus qualitative research are true. quantitative research is more subjective than qualitative research quantitative research is richer than qualitative research quantitative research is more time-consuming than qualitative research
None of the statements about quantitative versus qualitative research are true.
This is because the comparison between quantitative and qualitative research is not a matter of one being objectively better or more subjective, richer, or more time-consuming than the other. They are different approaches to research, each with its strengths and limitations, and the choice between them depends on the research question, the nature of the data, and the research design.
Quantitative research is characterized by the collection of numerical data that can be analyzed using statistical methods to identify patterns, relationships, and trends. This approach is used when the research question requires an objective measurement of variables that can be quantified and compared across groups. For example, a quantitative study may examine the relationship between height and weight in a population, using statistical techniques to identify the strength of the relationship and its significance.
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a couple decide they want to have 6 children. use binomial probability to find the probability of having the same number of boys and girls.
This means that there is a [tex]31.25%[/tex] chance of having the same number of boys and girls, or roughly [tex]0.3125.[/tex]
The binomial-probability formula can be used to determine the likelihood of having a specific number of boys and girls, assuming that the odds of having either a boy or a girl are equal, which is [tex]1/2:[/tex]
[tex]C(n,k) = P(X=k) * p^k * (1-p)^{n-k}[/tex]
Where:
k is the number of successes, which is the number of boys the couple wants to have and is also equal to the number of girls because they want an equal number of each; in this case,[tex]k = 6[/tex], where n is the number of tries, which is the number of children the couple expects to have. As a result,[tex]k = n/2 = 3[/tex] and p is the success-probability, which is equal to the likelihood of having a boy or girl, which is equals to [tex]1/2[/tex]. [tex]C(n,k) = n! / (k! * (n-k)!)[/tex], where! stands for the factorial function, is the number of combinations of n things taken k at a time.
[tex]0.3125.[/tex]
When these values are added to the formula:
[tex]P(X=3) = C(6,3) × (1/2)^3 * (1/2)^(6-3) \\= 20 * (1/2)^6\\= 0.3125[/tex]
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Assume a company has 7 departments and they want to assign unique 3-letter codes to each department. The first two characters of the code must be capital letters (A through Z) and the last character must be a digit ( 0 through 9 ). Therefore, a department code can be any string of the form: Letter-Letter-Digit. (i) How many different department codes are possible?
(ii) How many department codes are possible if no letter appears more than once? (iii) How many department codes are possible if no letter or digit appears more than once?
(i) To find the number of different department codes possible, we need to determine the number of choices available for each character in the code.
The first two characters can be any of the 26 capital letters of the alphabet, so there are 26 choices for each of these characters. The third character must be a digit, so there are 10 choices for this character. Therefore, the total number of different department codes possible is: 26 x 26 x 10 = 6,760.
(ii) If no letter appears more than once, then we have to choose three distinct letters for the code. There are 26 choices for the first letter, 25 choices for the second letter (since we've already used one letter), and 24 choices for the third letter (since we've already used two letters).
The third character must be a digit, so there are 10 choices for this character. Therefore, the total number of different department codes possible is: 26 x 25 x 24 x 10 = 15,600.
(iii) If no letter or digit appears more than once, then we have to choose three distinct characters (either letters or digits) for the code. There are 26 choices for the first character (since it can be any letter), 25 choices for the second character (since it can be any letter except the one we chose for the first character or any digit),
and 10 choices for the third character (since it can be any digit except the one we chose for the second character). Therefore, the total number of different department codes possible is:
26 x 25 x 10 = 6,500
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consider the function arctan(x^2) write a partial sum for the power series which represents this function consisting of the first four non zero terms
The partial sum for the power series of arctan[tex](x^2)[/tex] consisting of the first four non-zero terms can be written as: arctan[tex](x^2) ≈ x^2 - (1/3)x^6 + (1/5)x^10 - (1/7)x^14[/tex]
The power series representation of the function f(x) = arctan[tex](x^2)[/tex] is given by:
[tex]f(x) = ∑n=0^∞ (-1)^n x^(2n+1) / (2n+1)[/tex]
To find the partial sum consisting of the first four non-zero terms, we can simply substitute n = 0, 1, 2, and 3 into the above expression, and add up the resulting terms:
[tex]f(x) ≈ x - x^3/3 + x^5/5 - x^7/7[/tex]
This is the desired partial sum for the power series representation of arctan[tex](x^2)[/tex], consisting of the first four non-zero terms. Note that as we add more terms to this sum, we get a better and better approximation to the function f(x) over a wider range of x values.
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In 2010, the population of Appleville was 28000, and by 2020 the population had grown to 35000. The town of Treehill had a population of 41820 in 2015, and has been growing by 100 per year. If both towns continue to growth linearly at the same rate, in what year will the populations of the two towns be equal? Set up equations and solve algebraically!
The populations of the two towns will be equal in the year 2048.
Let's assume that the population of Appleville in the year "t" is "A(t)", and the population of Treehill in the year "t" is "T(t)". We know that the population of Treehill is increasing linearly by 100 per year. Therefore, we can express the population of Treehill in terms of "t" as follows:
T(t) = 41820 + 100t
The population of Appleville is also growing linearly, but we do not know the exact rate of growth. However, we can calculate this rate using the population data we have. The change in population from 2010 to 2020 is 35000 - 28000 = 7000. This change occurred over a period of 10 years. Therefore, the average annual growth rate is:
(35000 - 28000) / 10 = 700
We can use this rate to express the population of Appleville in terms of "t" as follows:
A(t) = 28000 + 700t
Now, we can set these two equations equal to each other to find the year when the populations of the two towns will be equal:
41820 + 100t = 28000 + 700t
Simplifying this equation, we get:
420t = 13820
t = 33
Therefore, the populations of the two towns will be equal in the year 2015 + 33 = 2048.
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A jet airplane reaches 846. Km/h on a certain flight. What distance does it cover in 13.0 min? Set the math up. But don't do any of it. Just leave your answer as a math expression. Also, be sure your answer includes all the correct unit symbols.
Answer:
Distance = (846 km/h) × (13.0 min × (1 h / 60 min))-----------------
To find the distance you can use the formula:
Distance = Speed × TimeGiven:
Speed = 846 km/hTime = 13.0 minFirst, we need to convert the time from minutes to hours:
13.0 min × (1 h / 60 min)Now, set up the equation using the given values and units:
Distance = (846 km/h) × (13.0 min × (1 h / 60 min))Find the volume of a pyramid whose square base is 10cm. And height 8cm
The volume of the pyramid is determined as 266.67 cm³.
What is the volume of pyramid?The volume of the pyramid is calculated by applying the following formula as shown below;
V = ¹/₃ Bh
where;
B is the base area of the pyramidh is the height of the pyramidThe volume of the pyramid is calculated as;
V = ¹/₃ x (10 cm)² x 8 cm
V = 266.67 cm³
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