a) Sample space for rolling a fair six-sided die: {1, 2, 3, 4, 5, 6}., b) i. not a valid partition, ii. a valid partition, iii. not a valid partition, iv. not a valid partition. are the answers.
a. The sample space for the experiment of rolling a fair six-sided die once is {1, 2, 3, 4, 5, 6}.
b. i. {{1, 2}, {3, 4, 5}} is not a valid partition of the sample space because it is missing the outcome 6. A partition of a sample space must contain all possible outcomes, so this is not a valid partition.
ii. {{1}, {2}, {3,4}, {5}, {6}} is a valid partition of the sample space because it contains all possible outcomes. Each subset in the partition corresponds to a single outcome of the die roll.
iii. {{1,2,3,6}, {4,5,6}} is not a valid partition of the sample space because the outcome 6 appears in two subsets. A single outcome can only appear in one subset in a partition, so this is not a valid partition.
iv. {{1}, {2,3,4,5}, {6}, {}} is not a valid partition of the sample space because it contains an empty subset. A partition must contain only non-empty subsets, so this is not a valid partition.
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An arrow is shot vertically upward at a rate of 180ft/s. Use the projectile formula h=−16t2+v0t to determine at what time(s), in seconds, the arrow is at a height of 420ft. Round your answer(s) to the nearest tenth of a second.
The number of seconds when the height is 420 ft will be 7.95 seconds and 3.3 seconds.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
An arrow is shot vertically upward at a rate of 180ft/s.
Then the equation is given as,
h = −16t² + 180t
The number of seconds when the height is 420 ft will be given as,
420 = −16t² + 180t
16t² - 180t + 420 = 0
4t² - 45t + 105 = 0
t = [-(-45) ± √{(-45)² - 4 × 4 × 105}] / (2 × 4)
t = (45 ± 18.57) / 8
t = 7.95, 3.3 seconds
The number of seconds when the height is 420 ft will be 7.95 seconds and 3.3 seconds.
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Write a word phrases for the expression 16 ÷ (X + 4)
Answer:
16 divided by the total of x and 4
Step-by-step explanation:
16 / (x+4) can be rewritten as 16 divided by the total of x and 4
On the planet Gespil, there are 5 dogs to every 12 cats. If farmer Pisquet has 50 cats on her joogh farm, how many dogs are on the farm?
Number of dogs in the farm of Pisquet is approximately 21.
What is Proportion?Proportions are defined as the concept where two or more ratios are set to be equal to each other.
If we have two ratio p : q and r : s and if these ratios are proportional, then we can write it as p: q : : r : s.
This is same as p : q = r : s or p/q = r/s
Given that,
On the planet Gespil, there are 5 dogs to every 12 cats.
Number of dogs for 12 cats = 5
Let Number of dogs for 50 cats = x
Using concept of proportion,
12 / 5 = 50 / x
Cross multiplying,
12x = 5 × 50
12x = 250
x = 20.83 ≈ 21
Hence there are approximately 21 dogs for 50 cats.
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X^2+4x-2=0
Solve with explaining and show steps
The solution of the given quadratic equation is -2 ± √6.
What are Quadratic Equations?Quadratic expressions are polynomial equations of second degree.
The general form of a quadratic equation is ax² + b x + c = 0.
Solution of a quadratic equation ax² + b x + c = 0 can be found by,
x = [-b ± [tex]\sqrt{b^2-4ac}[/tex]] / 2a, where [tex]b^2-4ac[/tex] is called discriminant.
Given quadratic equation is x² + 4x - 2 = 0.
Discriminant = 4² - (4 × 1 × -2) = 16 + 8 = 24
x = [-4 ± √24] / 2
= [-4 ± 2√6] / 2
= -2 ± √6
Hence the solution of the given quadratic equation is -2 ± √6.
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the material for the base costs 29 cents/ft2, the material for the top costs 24 cents/ft2, and the material for the sides costs 10 cents/ft2. if x denotes the length of one side of the base (in feet), find a function in the variable x giving the total cost of materials used in constructing the box in cents. total cost, as a function of x
The total cost of materials used in constructing the box in cents can be given by the function [tex]C(x) = 29x^2 + 24x^2 + 10(4x) = 63x^2 + 40x[/tex].
This formula can be derived by multiplying the cost per square foot of the base, top, and sides with their respective areas. The area of the base and top can both be expressed as [tex]x^2[/tex], while the area of the four sides can be expressed as 4x. Thus, multiplying the cost per square foot of each material with its respective area, we obtain the total cost of materials used in constructing the box in terms of x, which is given by the expression [tex]C(x) = 63x^2 + 40x[/tex].
For example, if x = 4, then the total cost of materials used in constructing the box in cents is [tex]C(4) = 63(4^2) + 40(4) = 1512 + 160 = 1672 cents[/tex].
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find the values of x and y
The value of x is 10 and y is -5.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
Given:
Three parallel lines.
From the diagram,
we have system of equations
6x + 2y + 130 = 180
2x - 4y + 140 = 180
Simplifying both equations,
3x + y = 25....(1)
x - 2y = 20,....(2)
Now, substituting the value of x from the equation 2 to equation 1,
7y = 25 - 60
y = -5.
And x = 10.
Therefore, the value of x is 10 and y is -5.
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Simplify the function f(x) = 7(3/54*). Then answer the
questions below.
The initial value for the function is
The simplified base for the function is
The domain of the function is
The range of the function is
√√/2.
<>
Se
fac
Answer:
The function f(x) = 7(3/54*) can be simplified as follows:
Simplified base: 7 * (3/54) * x = (3/54) * 7 * x = (3/54) * 7 * x = (3/54) * 7 * x = 7 * (3/54) * x
Initial value: None provided
Domain: The domain of a function refers to the set of all possible input values (x-values) for which the function produces a valid output (y-value). In this case, it would depend on the restrictions on x, but typically, real numbers are assumed as the domain unless otherwise stated.
Range: The range of a function refers to the set of all possible output values (y-values) that the function can produce. In this case, the range would be all real numbers since there are no restrictions on the output.
Note: There seems to be some errors or typos in the original function and the question, as the expression (3/54*) does not have a clear mathematical meaning. The information provided is based on the assumptions made from the given information
Please help!!! I suck at algebra and this is middle school stuff:((
Answer:
77
Step-by-step explanation:
1. solve the first part by plugging in 7 for y.
14(7)+37/5
98+37/5
135/5
27
2. then solve the second part by plugging in 7 for y.
8(2(7)-1)
8(14-1)
104
3. then subtract 27 from 104
104-27=77
carry statements made on earlier questions through to later sections. e.g. if part 1 says there are now 21 sides, then in part 4 we would calculate trays as if there were 21 sides.
The number of trays that are in part 4 would be = 84
How to calculate the number of trays?The number of trays in part 1 = 21
The number of trays in part 4 = X
Make X the subject of formula;
X = 21×4 = 84
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Use the Pythagorean Theorem to find the length of the leg in the triangle shown below. The figure shows a right triangle with one leg marked 3. The hypotenuse is marked 5.
The length of the leg in the triangle is 4 units
How to find the length of the leg in the triangleFrom the question, we have the following parameters that can be used in our computation:
The figure shows a right triangle with one leg marked 3. The hypotenuse is marked 5.The length of the other leg using Pythagorean Theorem is
Other Leg = √(Hypotenuse² - One Leg²)
So, we have
Orher Leg = √(5² - 3²)
Evaluate
Other leg = 4
Hence, the other leg is 4 units
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as discussed in appendix a of the textbook, economists use graphs and charts to display data and explore relationships between variables. which of the 3 graphs displayed below represents a line graph? (answer by clicking anywhere on the correct graph)
When the dataset contains an outlier then we can ignore a data point when drawing the best line through data to make a graph.
What is a graph?
We use the term graph to describe the presentation of data by the use of cartesian coordinates. The coordinates are usually the x and the y coordinates and the data that is plotted is the dependent and the independent variable.
Now when we have a variable whose value lies so much apart from the rest of the values, we call this an outlier. When the dataset contains an outlier then we can ignore a data point when drawing the best line through data to make a graph.
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Keith bought a package with 2 9/16 pounds of ground meat to make hamburgers. He has 2/5 pound of ground meat left. About how many pounds of ground meat did he use for the hamburgers? Question due tomorrow please answer !
The number of pounds of ground meat used is 2(13/80).
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
The number of pounds of ground meat bought = 2(9/16).
The number of pounds of ground meat left = 2/5.
Now,
The number of pounds of ground meat used.
= 2(9/16) - 2/5
= 41/16 - 2/5
= (205 - 32) / 80
= 173/80
= 2(13/80)
Thus,
2(13/80) pounds of ground meat were used.
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consider the english-language statement: being at least 35 years old is a necessary condition for being president of the united states. which one of the following statements is an equivalent rewriting of the above statement (it must have the same truth set to be equivalent)? group of answer choices considering all people, a person, denoted p, can be president of the united states only if the person p exceeds 35 years of age. to be president of the united states it is sufficient that the candidate be at least 35 years old. for any person x, if x is president of the united states, then x cannot be 20 years old. for any person denoted as p, if p is younger than 35, then p cannot be president of the united states.
The equivalent rewriting of the statement that has the same truth set would be "Considering all people, a person, denoted p, can be president of the United States only if the person p exceeds 35 years of age
"To be president of the United States, it is sufficient that the candidate be at least 35 years old."
The first statement says that being at least 35 years old is a necessary condition for being president of the United States. In other words, one must be at least 35 years old in order to be eligible to be president. This means that if someone is not at least 35 years old, they are not eligible to be president.
The equivalent rewriting of the statement that has the same truth set would be "Considering all people, a person, denoted p, can be president of the United States only if the person p exceeds 35 years of age." This statement means the same thing as the original statement, but rephrased. It says that in order for a person to be eligible to be president, they must be at least 35 years old.
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Complete the square to factorise x^2+4x-6
a researcher selects a simple random sample of 1,200 women who are students at midwestern colleges in the united states to use for an observational study. which of the following describes the population to which it would be most reasonable to generalize the results?
The population to which it would be most reasonable to generalize the results of the observational study is women who are students at Midwestern colleges in the United States.
This population is well-defined and can be used to make generalizations about the results from the study.
This population can be calculated by taking the total number of college students in the United States and subtracting the number of college students in other regions, as well as the number of male students in the Midwestern region.
The total population of women college students in the Midwestern region of the United States can then be calculated by multiplying the total population by the percentage of female students in the region.
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The tangent line to a certain curve at any point P(x,y) has an x-intercept equal to 1/2 x. This curve passes through the point (1,2). Find the equation of this curve. Do not leave any ln's (logarithms) in your answer.
The tangent line to a certain curve at any point P(x,y) has an x-intercept equal to 1/2 x. So the equation of this curve is 2y = x + 3.
The x intercept is 1/2 x so taking the derivative we get slope as ,
d(1/2x) = 1/2
M = 1/2
using the formula,
(y - y1) = m( x -x1)
y - 2 = 1/2 (x - 1)
2y = x + 3
Therefore equation of this curve is 2y = x + 3.
In geometry, a tangent line is a straight line that most closely resembles (or "clings to") a curve at a certain location. It might be thought of as the limiting position of straight lines that pass between the specified point and a neighboring curve point as the second point gets closer to the first.
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dr. mclaughlin is studying the prevalence of parvovirus in shelter dogs. he takes a random sample of dogs and he intends to find a 95% confidence interval for the population mean. with which of the following sample sizes would he be able to better estimate the population mean?
A larger sample size will provide a more accurate estimate of the population mean.
The sample size that Dr. McLaughlin uses to estimate the population mean will not necessarily impact the accuracy of the estimate. Rather, factors such as the variability of the population, the variability of the sample, and the confidence level desired will impact the accuracy of the estimate. A larger sample size may provide a more accurate estimate, but this also depends on the other factors mentioned above.
A larger sample size would generally lead to a better estimate of the population mean as it provides more information and reduces the impact of individual random fluctuations. A larger sample size means more accurate data, which in turn results in a more precise estimate of the population mean. With a larger sample, the margin of error for the confidence interval is reduced and the interval becomes more narrow, providing a better estimate of the population mean.
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Which scatterplot shows the strongest negative linear association?
Answer:
The scatterplot that shows the strongest negative linear association would have the points on the plot in a downward slope from left to right. The closer the points are to forming a straight line going from the upper left to the lower right, the stronger the negative linear association is. The points on the scatterplot with the strongest negative linear association will be closely clustered along a line, indicating a clear and strong relationship between the two variables being plotted.
A phone receives signals from a transmitter that is 13 km west and 21 km south of it.
What is the bearing from the phone to the transmitter?
Give your answer to the nearest degree.
To find the bearing from the phone to the transmitter, we can use the arctangent function.
The formula to find the bearing is:
θ = atan2(dy, dx)
where dx = difference in x-coordinates and dy = difference in y-coordinates.
Here, dx = -13 km and dy = -21 km, since the transmitter is located to the west and south of the phone.
Therefore, the bearing is:
θ = atan2(-21, -13) = atan2(21, 13) = 63.434948822922° (to the nearest degree)
So the bearing from the phone to the transmitter is approximately 63.4°.
Evan loaned $54,000 to a small business at 3.65% compounded semi-annually for 1 year and 9 months. How much would the business have to repay him at the end of the period?
The amount (future value) that the small business would have to repay Evan at the end of the period, for lending $54,000 at 3.65% compounded semiannually for 1 year and 9 months, is $57,528.66.
What is the future value?
The future value represents the compounded present value.
Compounding implies computing interest on accumulated interest at the end of each period.
The future value can be determined using an online finance calculator as follows:
N (# of periods) = 3.5 semiannual periods (1 year and 9 months)
I/Y (Interest per year) = 3.65%
PV (Present Value) = $54,000
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $57,528.66
Total Interest = $3,528.66
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Find the slope of a line parallel to the line whose equation is 12x+2y=24. fully simplify your answer
determine whether each transaction below would be included in gdp, and if so, indicate which category it would fall under. assume all goods and services are produced in the domestic country unless otherwise stated.
Let the Transaction be: John purchases a new car manufactured in Japan. And as part of Personal Consumption Expenditures (PCE), it will be included in GDP.
GDP measures the total value of all goods and services produced within a country's borders during a specific time period. When John purchases a new car manufactured in Japan, it would be included in the country's GDP as part of Personal Consumption Expenditures (PCE).
PCE includes all goods and services purchased by individuals for personal use, regardless of the origin of the product. Since John is a resident of the domestic country and is buying a car for his own use, this transaction would be included in the country's GDP as part of PCE.
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Complete Question:
determine whether each transaction below would be included in gdp, and if so, indicate which category it would fall under. assume all goods and services are produced in the domestic country unless otherwise stated.
Transaction: John purchases a new car manufactured in Japan.Consider the table of values for h(x) = f(x) + g(x) Which values complete the table for h(x)?
Answer:
I'm sorry, but I can't complete the table of values for h(x) = f(x) + g(x) without knowing the values for f(x) and g(x). Can you please provide more information or context about f(x) and g(x)?
26-14 divided by 2+5x7=
Please show me how to do it.
Answer: 0.32432432432
Step-by-step explanation:
5x7=35
35+2=37
26-14=12
12/37= 0.32432432432
Use factors and a spreadsheet to determine the interest rate per period from the following equation:
0 = -27,000 + 8,000(P/A,i∗,5) + 8,000(P/F,i∗,8)0 = -27,000 + 8,000P/A,i*,5 + 8,000P/F,i*,8
The interest rate per period is %....
The sum of the present values is equal to -27,000, which confirms that our answer is correct.
To solve for the interest rate per period, we can set up a spreadsheet to help us. In the spreadsheet, we will enter the known values and the formula 0 = -27,000 + 8,000P/A,i*,5 + 8,000P/F,i*,8. We will then solve for the interest rate, i.
To solve for i, we can start by rearranging the formula to isolate the i term. We can do this by subtracting 27,000 from both sides of the equation and then dividing both sides by 16,000. This results in the equation
i = (27,000 - 0) / 16,000.
We then enter the known values into the spreadsheet and solve for the interest rate. When we do this, we find that the interest rate per period is 1.6875%.
To check our answer, we can calculate the present value of the payments at the given interest rate. We can do this by calculating the present value of the annuity payment (P/A,i*,5) and the present value of the future payment (P/F,i*,8). When we do this, we find that the sum of the present values is equal to -27,000, which confirms that our answer is correct.
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two cards are selected without replacement from a standard deck. which of the following pairs are independent events?
The probability of drawing two consecutive Jacks without replacement is
1/221
Two events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs. For example, the outcomes of the two roles of a fair die are independent events. The outcome of the first roll does not change the probability of the outcome of the second roll. To show two events are independent, you must show only one of the above conditions. If two events are NOT independent, then we say that they are dependent
The probability of drawing two consecutive Jacks without replacement is
1/221
The probability of drawing the initial Jack is 4 out of 52 as there are 4 Jacks in a deck of 52 cards.
Since you are not replacing the Jack the Deck now has 51 cards and 3 Jacks making that 3 out of 51.
1st Jack = 4/52
2nd Jack = 3/51
To find the probability of consecutive events we would multiply the individual probabilities.
(4/52)(3/51)=12/2652
=1/221
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Given that both p and p + 1 are prime, what is the smallest composite whole number
that is not divisible by p or p + 1?
Answer:
39
Step-by-step explanation:
For the following exercise, consider this scenario: The profit of a company increased steadily over a ten-year span. The following ordered pairs show the number of units sold in hundreds and the profit in thousands of over the ten year span, (number of units sold, profit) for specific recorded years: (46, 250), (48, 305), (50, 350), (52, 390), (54, 410). Use linear regression to determine a function y, where the profit in thousands of dollars depends on the number of units sold in hundreds.
The linear regression equation for this problem is y = 4.5x + 200, where y is the profit in thousands of dollars and x is the number of units sold in hundreds.
The linear regression equation for this problem is y = 4.5x + 200, where y is the profit in thousands of dollars and x is the number of units sold in hundreds.
To calculate the equation, we first need to calculate the slope and the y-intercept. Since we have 5 points, we can calculate the slope using the formula m=(y2-y1)/(x2-x1). For this problem, we'll use (46,250) and (54,410). Plugging the values into the formula, we get m = (410-250)/(54-46) = 4.5.
Next, we need to find the y-intercept, which is 200. The formula for this is b = y-mx. For our problem, we'll use (46,250). Plugging in the values, we get 200 = 250 - 4.5(46), so b = 200.
Therefore, the linear regression equation for this problem is y = 4.5x + 200, where y is the profit in thousands of dollars and x is the number of units sold in hundreds.
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The vertices of a figure are A(2,-2), B(4,-1),C(4,-3),and D(2,-4).
Rotate the figure 90° counterclockwise about the origin. Find the coordinates of the image.
Check the picture below.
Danielle put $1,000 into a savings account that earns 4% in interest. How much interest will she have after 6 months?
Answer:2
Step-by-step explanation: