The total number of ways to assign employees to desks is 720 (6!), and the number of favorable outcomes is 144. Therefore, the probability is 144/720 = 1/5.
The total number of ways to assign six employees to six desks is 6! (6 factorial), which equals 720. Now we need to find the number of ways that the married couple will not have adjacent desks.
First, we can treat the married couple as one entity, which means we have 5 entities to assign to 6 desks. There are 6 possible ways to choose the position of the married couple in the row. For each of these positions, we can then assign the other 4 entities to the remaining 4 desks in 4! ways.
Therefore, the total number of ways to assign employees to desks without the married couple having adjacent desks is 6 x 4! = 144.
The probability of this happening is the number of favorable outcomes (144) divided by the total number of possible outcomes (720), which is 144/720 = 1/5.
The probability that the married couple will not have adjacent desks when six new employees are randomly assigned to six desks that are lined up in a row is 1/5.
We calculated this probability by first treating the married couple as one entity and then finding the number of ways to assign the remaining entities to the desks without the married couple being adjacent to each other. The total number of ways to assign employees to desks is 720 (6!), and the number of favorable outcomes is 144. Therefore, the probability is 144/720 = 1/5.
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which of the following is false about the margin of error of a confidence interval? as sample size increases, margin of error increases as well. as confidence level increases, margin of error increases as well. as standard deviation of the sample increases, margin of error increases as well.
The margin of error of a confidence interval is affected by multiple factors, including sample size, confidence level, and standard deviation. Understanding these relationships is essential for making accurate and reliable statistical inferences.
The margin of error of a confidence interval is a measure of the range of values within which the true population parameter is likely to lie. It reflects the amount of sampling error in the estimation process and is influenced by several factors.
Regarding the question, it is false that as sample size increases, the margin of error increases as well. In fact, the opposite is true. As the sample size increases, the margin of error decreases, since larger samples provide more information and reduce the uncertainty in the estimation. This relationship is inversely proportional and can be quantified by the formula: margin of error = z* (standard deviation / sqrt(n)), where z* is the critical value for the desired confidence level, n is the sample size, and standard deviation is the variability of the population.
On the other hand, it is true that as confidence level increases, the margin of error increases as well. This is because a higher confidence level requires a wider interval to capture a larger proportion of the population values, which results in a larger margin of error. For instance, a 99% confidence interval will be wider than a 95% confidence interval for the same sample size and standard deviation.
Finally, it is also true that as standard deviation of the sample increases, the margin of error increases as well. This is because a larger standard deviation implies a greater variability in the population and more uncertainty in the estimation, which requires a wider interval to account for the potential values. Thus, a larger standard deviation leads to a larger margin of error for the same sample size and confidence level.
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someone pls explain and help :(
Using the tables we can evaluate the given functions to get:
(f + g)(3) = 9(f times g)(-1) = -8f(g(2)) = 8g(f(0)) = 2How to evaluate the given functions?Here we have two tables for the functions f(x) and g(x), first we want to find the sum:
(f + g)(3) = f(3) + g(3)
Using the table we can see that:
f(3) = 8
g(3) = 1
Then:
(f + g)(3) = 8 + 1 = 9
For the second one we have:
(f times g)(-1) = f(-1)×g(-1)
Where:
f(-1)= -2
g(-1) = 4
Then we will get (f times g)(-1) = -2*4 = -8
Now we have the compositions:
f(g(2))
and g(2) = 3, then:
f(g(2)) = f(3) = 8
Finally:
g(f(0))
Where f(0) = 0
Then:
g(f(0)) = g(0) = 2
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can you help me with math
The linear function which represents the total cost is:
c = 11.95 + 48t
How to determine which linear function represents the total cost?The general form of linear function is:
c = mt + b
where m is the cost per ticket
b is the service fee ($11.95)
Total cost of 4 tickets = $203.95
Cost of 4 tickets without service fee = $203.95 - $11.95 = $192
Cost per ticket (m) = $192/4 = 48
Thus, the linear function which represents the total cost will be:
c = 48t + 11.95
c = 11.95 + 48t (When rearranged)
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Make a survey of the number of family and non family members living in their house
A survey was conducted to determine the number of family and non-family members living in their house. The results showed that out of 100 households surveyed, an average of 3.5 family members and 1.2 non-family members were living in each household.
Explanation:
The survey was conducted by randomly selecting 100 households in a particular area and asking them how many family and non-family members were living in their house. The results were then tabulated to determine the average number of family and non-family members per household.
The results showed that on average, each household had 3.5 family members and 1.2 non-family members living in their house. This information can be useful for various purposes, such as city planning, resource allocation, and understanding social dynamics within a community.
It's important to note that the results of this survey may not be representative of all households in the area, as the sample size is relatively small. Additionally, the definition of "family member" may vary from household to household, which could impact the results. Nevertheless, this survey provides some insight into the demographics of households in the area and can be used as a starting point for further research.
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given f(x)=3x+2 and g(x)= √x-1, determine the following: f(g(x))=
Answer:To find f(g(x)), we first substitute g(x) into the expression for f(x), then simplify:
f(g(x)) = f(√x-1)
= 3(√x-1) + 2 (substitute √x-1 for x in the expression for f(x))
= 3√x - 3 + 2
= 3√x - 1
Therefore, f(g(x)) = 3√x - 1.
Step-by-step explanation:
A right triangle abc is insribed in a circle k(O,r). Find the radius of this circle if m
The radius of given circle would be 18 cm.
Given that a right △ABC is inscribed in circle k(O, r) and m ∠C = 90°, AC = 18 cm, m ∠B = 30°.
We are asked to find the radius of the circle.
Draw a diagram that represent the given scenario. [check the attached diagram]
AB is diameter of circle O and it a hypotenuse of triangle ABC.
We will use sine of the angle to find side AB.
Sin x = AC/AB
Sin 30° = 18 / AB
AB = 36
So, the radius = 18 cm.
Therefore, the radius of given circle would be 18 cm.
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The complete question is =
A right △ABC is inscribed in circle k(O, r). Find the radius of this circle if:
m∠C = 90°, AC = 18 cm, m∠B = 30°.
the numbers of tomatoes growing on 7 different tomato plants are 2, 3, 3, 4, 7, 8, and 8. what is the range of this data set?
Answer:
range = 6
Step-by-step explanation:
the range is the difference between the maximum and minimum values in the data set.
maximum = 8 and minimum = 2 , then
range = 8 - 2 = 6
6 to the power of -4
Answer:
-4,096
Step-by-step explanation:
If you multiply:
4x4x4x4x4x4= 4,096
Then, just make that negative:
-4,069
Hope this helps :3
URGENT!!!!! Will give brainliest if correct :)
A regression line has a slope of 1.885. If the mean of the x-coordinates of the data points is 3.448, and the mean of the y-coordinates is 12.318, what is the y-value of the y-intercept of the line to three decimal places?
A. -5.819
B. - 19.771
C.19.771
D. 5.819
The equation of a regression line can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, the slope m is given as 1.885.
The y-intercept b can be found using the formula b = y_mean - m * x_mean, where x_mean and y_mean are the means of the x-coordinates and y-coordinates of the data points, respectively. Plugging in the given values, we get:
b = 12.318 - 1.885 * 3.448 b ≈ 5.819
So the y-value of the y-intercept of the line to three decimal places is approximately 5.819. The correct answer is D. 5.819.
Shandra is going to invest $530 and leave it in an account for 5 years. Assuming the interest is compounded daily, what interest rate, to the nearest hundredth of a percent, would be required in order for Shandra to end up with $700?
Answer: 5.56%
Step-by-step explanation:
Compound interest formula:
A = P(1 + r/n)^nt
A = final amount
P = principle amount (original amount of money)
r = interest rate
n = number of times interest in compounded per year
t = time
Step 1:
Fill in the formula
A = 700 (she ends up with this amount of money)
P = 530 (she started with this)
r = ?
n = 365 (it is compounded 365 times per year, or once a day)
t = 5 (she left the money in the account for 5 years)
700 = 530(1 + r/365)^365(5)
Step 2:
Solve the equation for r. You will get 0.055644...
Convert this to a percent and you get the final answer of 5.56%
Elizabeth goes to a restaurant and the subtotal on the bill was
�
x dollars. A tax of 6% is applied to the bill. Elizabeth decides to leave a tip of 21% on the entire bill (including the tax). Write an expression in terms of
�
x that represents the total amount that Elizabeth paid
The total amount Elizabeth paid can be expressed as 1.27x, where x is the subtotal on the bill.
To calculate the total amount, first, we need to add the tax to the subtotal, which gives us 1.06x. Then, we need to add the tip to the entire amount, which is 21% of the sum of the subtotal and the tax. This can be expressed as 0.21(1.06x) = 0.22386x. Finally, we add the tip to the subtotal and the tax, which gives us 1.06x + 0.22386x = 1.28386x. This is the same as multiplying the subtotal by 1.27, which gives us the expression 1.27x. Therefore, the total amount Elizabeth paid is 1.27 times the subtotal on the bill.
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What are the x-intercepts of the parabola? graph of parabola falling from the left, passing through 3 comma 2 to about 4 and one half comma negative one fourth, and rising to the right, passing through 6 comma 2
a (4.5, 0) and (5, 0)
b (0, 4.5) and (0, 5)
c (0, 5) and (0, 4)
d (5, 0) and (4, 0)
a
(4.5, 0) and (5, 0)
EXPLANATION:The x-intercept of the parabola represents the point where the parabola graph intersects the x-axis. In other words, these are the x values where the y coordinate is 0.
Using the information given, we can observe that the parabola falls from the left, passes through the point (3, 2), reaches the minimum point, then rises to the right and passes through the point (6, 2) .
Since the parabola intersects the x-axis at the x-intercept, we can conclude that the x-intercept is the point where the y-coordinate is 0. In this case, x values of 4.5 and 5 will have a y coordinate of zero. So the x-intercepts of the parabola are (4,5,0) and (5,0).
The function f(x)= -√√x is shown on the graph.
3+
2-
1+
--5-4-3-2-
H
2 3 4 5
Which statement is correct?
O The range of the graph is all real numbers greater
than or equal to 0.
O The domain of the graph is all real numbers greater
than or equal to 0.
O The range and domain of the graph are the same.
O The domain of the graph is all real numbers.
The domain and the range of the given function will be same and all the real numbers.
Given is a function f(x)= -√√x we need to see the range and the domain of the function,
Since the function is a root function, so the range and the domain will be all real numbers and hence equal.
Hence the domain and the range of the given function will be same and all the real numbers.
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The correct statement is: The range and domain of the graph are the same.
The function f(x) = -√-x is a valid function for all real numbers.
When x is negative, -x is positive and √-x is an imaginary number, which is then multiplied by -1 to make the function real.
Therefore, the range of the graph is all real numbers.
Thus, The range and domain of the graph are the same.
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Write two different quadratic functions whose graphs pass through (4,0) and (1,0)
The quadratic equation of function in the standard form is Y = -1.25 x² + 5x.
Since quadratic equation's x-intercepts are (-5, 0). That indicated that the quadratic equation's two elements are (x + 5) and (x -0).
f(x) = a (x + 5) (x - 0) (x - 0)
= ax+5a
The quadratic equation's graph goes through (4, 0). thus, we must change equation 1 to read x = 4 and f(x) = 0.
0 = a × 4² + (5 × 4)
0 = a × 16 +20
The quadratic equation is known to have the form ax² + bx + c = 0.
f(x) = -1.25 + 5x
Consider y= F(x)
∴ Y = -1.25 x² + 5x.
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John and Jane are married. The probability that John watches a certain television show is 0.7. The probability that Jane watches the show is 0.1. The probability that John watches the show, given that Jane does, is 0.8.
(a) Find the probability that both John and Jane watch the show.
(b) Find the probability that Jane watches the show, given that John does.
(c) Do John and Jane watch the show independently of each other? Yes or no?
(a) The probability that both John and Jane watch the show is 0.07.
(b) The probability that Jane watches the show, given that John does, is 0.11
(c) No. John and Jane do not watch the show independently of each other.
Probability(a) The probability that both John and Jane watch the show is given by the product of their individual probabilities:
P(John and Jane watch) = P(John watches) x P(Jane watches)
= 0.7 x 0.1
= 0.07.
(b) The probability that Jane watches the show, given that John does, is given by Bayes' theorem:
P(Jane watches | John watches) = P(John watches | Jane watches) x P(Jane watches) / P(John watches)
From the information given, we know that:
P(John watches | Jane watches) = 0.8P(Jane watches) = 0.1.To find P(John watches), we can use the law of total probability:
P(John watches) = P(John watches | Jane watches) * P(Jane watches) + P(John watches | not Jane watches) * P(not Jane watches)
= (0.8 x 0.1) + (0.7 x 0.9)
= 0.71
Therefore,
P(Jane watches | John watches) = 0.8 x 0.1 / 0.71 = 0.1127
(c) John and Jane do not watch the show independently of each other, since the probability that John watches the show changes depending on whether or not Jane watches it. In other words, the events "John watches the show" and "Jane watches the show" are dependent events.
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What is the rule for the reflection?
the length of a pregnancy from conception to birth is approximately normally dis- tributed with a mean of 272 days and a standard deviation of 9 days. a pregnancy is considered full-term if it lasts between 252 days and 298 days. what percentage of pregnancies are full-term?
The length of a pregnancy from conception to birth follows a normal distribution with a mean (μ) of 272 days and a standard deviation (σ) of 9 days. To find the percentage of pregnancies that are full-term, we need to calculate the probability of a pregnancy lasting between 252 and 298 days.
First, convert the days into z-scores:
z1 = (252 - μ) / σ = (252 - 272) / 9 ≈ -2.22
z2 = (298 - μ) / σ = (298 - 272) / 9 ≈ 2.89
Next, use a standard normal distribution table to find the probabilities corresponding to the z-scores:
P(z1) ≈ 0.0132
P(z2) ≈ 0.9981
To find the percentage of pregnancies that are full-term, subtract the lower probability from the higher probability:
Percentage = (P(z2) - P(z1)) × 100% = (0.9981 - 0.0132) × 100% ≈ 98.49%
Approximately 98.49% of pregnancies are full-term, lasting between 252 and 298 days.
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Which statement about the the slopes of JL and MP are true
A statement about the the slopes of JL and MP that is true include the following: A. The slope of JL is the same as the slope of MP because △JKL is similar to △MNP.
What are the properties of similar triangles?In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
Additionally, the lengths of corresponding sides or corresponding side lengths are proportional to the lengths of corresponding altitudes when two (2) triangles are similar and the slopes of side JL and side MP are equal;
Slope of side MP = NP/MN
Slope of side JL = KL/JK
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Explain step by step
Answer:
$40
Step-by-step explanation:
money made = $800 × 5%
= $800 × [tex]\frac{5}{100}[/tex] = $8 × 5 = $40
if abcd∼efgh, find the value of x
The calculated value of x in the similar shapes given that abcd ∼ efgh is 15
Calculating the value of x in the similar shapesFrom the question, we have the following parameters that can be used in our computation:
abcd ∼ efgh
By the corresponding ratio of similar shapes, we have the following equation
AB/AD = EF/EH
Using the above as a guide, we have the following:
8/14 = (x - 3)/(x + 6)
Cross multiply the equation
This gives
8(x + 6) = 14(x - 3)
When solved for x, we have
x = 15
Hence, the value of x in the shapes is 15
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HELP ON TIME LIMIT !!!!!Solve the system of equations. Be sure to check your work. Complete the ordered pair to show your answer.
Y=-2
Y=-x+5
Answer:( , )
Please helppp meeeeee
The length of segment BD is given as follows:
BD = 6.
What is the geometric mean theorem?The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.
The altitude segment for this problem is given as follows:
BD.
The bases for this problem are given as follows:
3 and 12.
Hence the length of segment BD is obtained as follows:
(BD)² = 3 x 12
(BD)² = 36
BD = 6 -> taking the square root.
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A scientist gathers data by weighing different fruits. The weight of each piece of fruit, in pounds, are as follows. 3/8, 1/4, 1/2, 1/2, 1, 1/8, 1/4, 1/2, 1/4, 1, 3/8, 3/8, 5/8
Create a line plot to represent this data set
A line plot for the weight of each piece of fruit, in pounds is shown in the image attached below.
What is a line plot?In Mathematics and Statistics, a line plot can be defined as a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.
In this scenario and exercise, we would use an online graphing calculator to graphically represent the weight of each piece of fruit, in pounds on a line plot as shown in the image attached below.
In conclusion, we can reasonably infer and logically deduce that the data set is skewed.
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Interest on $5.255 at 12% for 30 days (use ordinary interest) is: Multiple Choice:
a. $52.55 b. $5,307.55 c. $5.26 d. $5,260.26
The interest on $5.255 at 12% for 30 days using ordinary interest can be calculated using the formula:I = PRT,Where I is the interest, P is the principal amount, R is the rate of interest, and T is the time period.
Here, P = $5.255, R = 12% = 0.12 (as a decimal), and T = 30/365 = 0.08219 (in years, as the time is given in days).
So,
I = 5.255 x 0.12 x 0.08219 = $0.0518
Rounding to two decimal places, the interest on $5.255 at 12% for 30 days using ordinary interest is $5.26. Therefore, the correct answer is option (c).
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ABCD IS A KITE. (4x-2)cm A B AB= (4x-2) cm Jasper says that x could be 0.5 (a) Explain why Jasper cannot be correct.
Answer:
because if you substitute 0.5 for x you get zero as a result
Step-by-step explanation:
ABCD IS A KITE. (4x-2)cm A B AB= (4x-2) cm Jasper says that x could be 0.5 (a) Explain why Jasper cannot be correct.
I answer for what I understand, the question is not clear
because if you substitute 0.5 for x you get zero as a result
(4x - 2) =
4 × 0.5 - 2 =
2 - 2 = 0
How to calculate the Area of a cylinder
Answer:
Surface area of cylinder = 2 π r ² +2 π r h
Step-by-step explanation:
Surface area of cylinder =
area of both circle ends + area of curved surface
= 2 π r ² +2 π r h
A ferry traveled 1/6 of the distance between two ports 3/7 hour. The ferry travels at a constant rate . At this rate, what fraction of the distance between the two ports can the ferry travel in one hour?
start fraction, 3, divided by, 7, end fraction hour. The ferry travels at a constant rate.
At this rate, what fraction of the distance between the two ports can the ferry travel in one hour?
The ferry can travel 7/18 of the distance between the two ports in one hour.To determine the fraction of the distance between the two ports that the ferry can travel in one hour, we need to find the rate at which the ferry is traveling.
We know that the ferry traveled 1/6 of the distance between the two ports in 3/7 hour. This information allows us to find the rate of the ferry's travel.
The formula to calculate rate is:
Rate = Distance / Time
Let's assume the total distance between the two ports is represented by D. Therefore, the distance traveled by the ferry is 1/6 of D. Similarly, the time taken is 3/7 hour.
Plugging these values into the formula, we get:
Rate = (1/6)D / (3/7) = (1/6)D * (7/3) = (7/18)D
The rate of the ferry's travel is (7/18)D.
To find the fraction of the distance the ferry can travel in one hour, we need to divide the distance traveled in one hour by the total distance:
Fraction = Distance in one hour / Total Distance = Rate / D = (7/18)D / D = 7/18.
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Here are the ingredients needed to make 12 shortcakes.
50g of sugar
200g of butter
200g of flour
10ml of milk.
How many shortcakes does Dan make?
Answer:
He makes 12 shortcakes.
if martins mass is m kilogram , represent his mass after he gains 7 kilogram
If Martin's mass is initially m kilograms, his mass after gaining 7 kilograms would be:
m + 7 kilograms.
In the question, it's given that Martin's initial mass is m kilograms. This means that he weighs m kilograms at some point in time.
If Martin gains 7 kilograms, we need to add 7 to his initial mass to get his new mass. The formula for this is:
Martin's new mass = Martin's initial mass + the mass he gained
Martin's new mass = m + 7
So if Martin's initial mass is m kilograms, his mass after gaining 7 kilograms would be m + 7 kilograms. This means that he would weigh m + 7 kilograms at this point in time.
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from the fictitious study of gender and ear piercing in high school students. what can we conclude? check all that apply group of answer choices the sample provides evidence that is too weak to conclude that gender and ear piercing are dependent in the population of high school students. gender and ear piercing for high school students may be independent. the sample provides strong evidence that gender and ear piercing for high school students are dependent. the differences between observed and expected counts are statistically significant. the differences between observed and expected counts could be attributed to chance variation that occurs in random samples of high school students when gender and ear piercing are independent. conditions are not met for use of the chi-square test of independence. therefore, we cannot draw a conclusion based on this data.
Based on the fictitious study of gender and ear piercing in high school students, we can conclude that the sample provides evidence that is too weak to conclude that gender and ear piercing are dependent in the population of high school students. Gender and ear piercing for high school students may be independent.
The study did not provide strong evidence that gender and ear piercing for high school students are dependent. In addition, the differences between observed and expected counts could be attributed to chance variation that occurs in random samples of high school students when gender and ear piercing are independent.
Therefore, the conditions are not met for use of the chi-square test of independence, and we cannot draw a conclusion based on this data.
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