This means that out of every 100 US adults, 23 of them have not read a book in the past year. This rate is quite high, considering the vast number of books available to read.
To calculate the number of US adults who have not read a book in the past year, we can use the following equation:
Number of US Adults Who Have Not Read a Book in the Past Year = Total Number of US Adults x Proportion of US Adults Who Have Not Read a Book in the Past Year
First, determine the total number of US adults. For example, let's say that there are 80 million US adults.
Next, multiply the total number of US adults by the proportion of US adults who have not read a book in the past year (0.23). Therefore, 80 million x 0.23 = 18.4 million US adults who have not read a book in the past year.
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If c > 0, s^2+ t^2 = 6, and st = c+5, what is (s+t)^2 in terms of c ?
Answer: We can start by expanding the square on the left-hand side of the equation:
(s + t)^2 = s^2 + 2st + t^2
We know that s^2 + t^2 = 6, so we can substitute that into the equation:
(s + t)^2 = 6 + 2st
We also know that st = c + 5, so we can substitute that into the equation:
(s + t)^2 = 6 + 2(c + 5)
Simplifying the right-hand side:
(s + t)^2 = 6 + 2c + 10
So, in terms of c, (s + t)^2 = 6 + 2c + 10.
Step-by-step explanation:
Which set of ordered pairs does not represent a function?
{(5,-1), (7,-9), (-8,-1), (8,-7)}
O {(-4, 1), (2, -7), (8,-2), (-7, -3)}
O {(4,3), (-6, 2), (-3,5), (9,3)}
O {(-1,7), (7, 1), (5,-7), (7,-8)}
The ordered pair that doesn't represent a function is: D.. {(-1,7), (7, 1), (5,-7), (7,-8)}.
What is a Function?A function is a mathematical concept that associates an input (or argument) to a unique output (or value). In mathematical notation, a function is represented as f(x), where x is the input, and f(x) is the output. The association between the input and output is defined by a set of rules, or a formula, that assigns a unique output value to each input value
In a function, for each unique x-value, there must be exactly one corresponding y-value.
D. {(-1,7), (7, 1), (5,-7), (7,-8)} does not represent a function because the same x-value (7) corresponds to two different y-values (1 and -8).
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Why do communist countries use authoritarian methods to maintain their economic and political system
Answer:
Communist countries use authoritarian governments because it requires the absolute obedience to authority figures. Communism is an extreme form of socialism because there is no private ownership or political freedom.
Step-by-step explanation:
Divide Using Synthetic Division
The result of the synthetic division is the final row. In this case, the result is -3, 5, -15, 18.
What is polynomial?A polynomial is an expression consisting of variable and coefficient and are used to model real world situation it is an equation of degree greater than one where the exponents of the variables can be any non-negative integer for example the polynomial equation x 2 + 3x + 2 represent a parable of windcraft polynomial are used in name variety of field such as mathematics and physics.
The process of synthetic division is used to divide polynomials of the form ax^n + bx^n-1 + ... + c, where a is the coefficient of the highest power of the variable x.
To divide -3 into the polynomial 1 8 9 -18 0, the following steps should be taken:
Step 1: Line up the divisor, -3, to the left of the polynomial, as shown below:
-3 | 1 8 9 -18 0
Step 2: Bring down the first coefficient in the polynomial, which is 1, and place it directly below the -3.
-3 | 1 8 9 -18 0
-3
Step 3: Multiply the -3 by the first coefficient and place the result in the next row, directly below the 8.
-3 | 1 8 9 -18 0
-3
-3
Step 4: Add the result to the 8, and place the new result in the next row.
-3 | 1 8 9 -18 0
-3
-3
5
Step 5: Repeat steps 3 and 4 for each coefficient in the polynomial.
-3 | 1 8 9 -18 0
-3
-3
5
-15
-15
18
Step 6: The result of the synthetic division is the final row. In this case, the result is -3, 5, -15, 18.
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Complete questions as follows-
Divide Using Synthetic Division
-3|1 8 9 -18 0
4 friends share 2 granola bars each friend gets _____ of the granola bar
Answer:
1/2 (half)
Step-by-step explanation:
4f over 2g then 1f over x
2/4 to get 1/2
each friend gets half (1/2)
A scientist places a cell in a Petri dish. At the end of 1 hour, the cell divides so
that there are 2 cells in the Petri dish. At the end of 2 hours, those cells divide so
there are 4 cells in the Petri dish. The cells continue to divide this way every hour.
Use the expression 2 to the 10th power to find the number of cells in the Petri dish after 10 hours.
Show your work.
Listed below in order are prices in dollars for a Big Mac hamburger in the , , , , , , , , , , , and . Such data are used to compare currency exchange rates and the costs of goods in different countries. Find the range, variance, and standard deviation for the given sample data. What do the measures of variation tell us about the prices of a Big Mac in different countries?
Based on the information, we can infer that the range is an adequate indicator to affirm that the price difference of the Big Mac in different countries is minimal.
How to find the range?To find the range of the given data we must perform the following procedure:
We must find the highest and lowest data, in this case the highest and lowest data are 6.8 and 1.98 respectively. So, to find the range we must find the difference between these two data:
6.8 - 1.89 = 4.91
How to find the variance?To find the variance we must apply the following formula:
S² = 1 / 11 - 1 ( 205.59 - (44.67)²/11)
S² = 2.42
How to find the standard deviation?To find the standard deviation we must apply the following formula:
S = [tex]\sqrt[n]{variance}[/tex]
S = [tex]\sqrt{2.42}[/tex]
S = 1.56
What do measures of variation tell us about the prices of a Big Mac in different countries?Based on the above data, we can infer that the range is an indicator that the difference in the Big Mac price in different countries is minimal.
Note: This question is incomplete. Here is the complete information:
Attached image
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2
Let the width and the length be real numbers. The perimeter
remains a constant 24cm. Draw the graph for 1 ≤ w ≤11
Label the axes appropriately.
Please find attached the graph of the function of the length with respect to the width of the rectangle, created with MS Excel, where, 1 ≤ W ≤ 11, and the perimeter of the rectangle is 24 cm.
What is a graph of a function?A graph of a function, is a representation of the ordered pairs of the points of the function, (x, f(x)), on the coordinate plane.
Whereby the figure is a rectangle, we get;
Perimeter = 2 × Length of the rectangle + 2 × Width of the rectangle
Let P represent the perimeter of the rectangle and let L represent the length of the rectangle and let W represent the width of the rectangle, we get;
P = 2·L + 2·W
The perimeter of the rectangle. P = 24
Therefore;
24 = 2·L + 2·W
2·L = 24 - 2·W
L = (24 - 2·W)/2 = 12 - W
L = 12 - W
The graph of the above linear equation representing the length of the rectangle, L, where the width, W is; 1 ≤ W ≤ 11.
Please find attached the required graph of length, L to the width W of the rectangle created with MS Excel
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1. Which of the following is not a variable cost?
A. wages paid to labor
B. seeds and fertilizers for paddy farmers
C. rent on land
D. electricity bills
2. The average total cost of producing computers in a factory is RM500 at the current
output level of 100 units per week. If fixed cost equals RM10,000
A. average fixed cost equals RM10,000.
B. total cost equals RM60,000 per week.
C. variable cost equals RM50,000 per week.
D. average variable cost equals RM400.
3. Which of these statements is false?
A. There are no fixed costs in the long run.
B. Total costs are equal to total fixed costs plus total variable costs.
C. In the short run, all inputs are fixed inputs.
D. A fixed cost is a cost that does not change as output changes.
4. Economies of scale occurs if the firm's:
A. long run average cost curve is horizontal.
B. average cost increases as the firm expands its production.
C. long run average cost decreases as the firm increases its output.
D. long run average cost curve is upward-sloping.
5. If total costs are RM200 for one unit of output and RM310 for two units, what is the marginal cost of the
second unit?
A. RM100
B. RM110
C. RM200
D. RM210
6. In the production of refrigerators, the item which represents variable costs is:
A. the tax on the company's property.
B. the salary of the night watchman.
C. the cost of fuel and electric power.
D. The insurance premium for the premises.
7. The average total cost of producing computers in a factory is RM250 at the current
output level of 100 units per week. If fixed costs equal RM5,000
A. average fixed cost equals RM50.
B. total cost equals RM40,000 per week.
C. variable cost equals RM10,000 per week.
D. average variable cost equals RM400.
9. The marginal cost of a good is
A. the addition to total cost of producing one more unit of output.
B. decreasing when average total cost is decreasing.
C. the difference between average total cost and average fixed cost.
D. always equal to average variable cost when the firm is maximizing profit.
Answer:
ur mom jk its
c
Step-by-step explanation:
Give the correct notation for the quantity described and give its value.
Mean number of cell phone calls made or received per day by cell phone users. In a survey of
1917 cell phone users, the mean was 13.10 phone calls a day.¹
The notation for this sample is denoted by [tex]\overline{x}[/tex].
What is the difference between the sample and the population?The entire group about whom you want to make conclusions is referred to as a population.
The particular group from which you will gather data is known as a sample. The sample size is always smaller than the population as a whole.
Given, In a survey of 1917 cell phone users, the mean was 13.10 phone calls a day.
This a sample so the notation for the mean is [tex]\overline{x}[/tex].
If it is for population then the notation of mean would have been [tex]\mu[/tex].
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A normal distribution (X) has a mean of 100 and a standard deviation of 10.
What is the probability that X is between 90 and 110?
The probability that X is between 90 and 110 = 0.2 if a normally distributed random variable x has a mean of 100 and P(x < 90) = 0.40.
What is a normal distribution?The majority of the observations are centered around the middle peak of the normal distribution, which is a continuous probability distribution that is symmetrical around its mean.
The probabilities for values that are farther from the mean taper off equally in both directions. Extreme values in the distribution's two tails are likewise rare. Not all symmetrical distributions are normal, even though the normal distribution is symmetrical.
A normally distributed random variable x has a mean of 100
P(x < 90) = 0.4
The probability that X is between 90 and 110
Mean is 100
Hence P (< 100) = 0.5 as Mean is centered
Hence
P (90 < X < 100) = 0.5 - 0.4 = 0.1
The difference between 100 and 90 is 10
The difference between 100 and 110 is 10
and 100 is Mean
Hence P (100 < X < 110) = P (90 < X < 100) = 0.1
Adding Both
P ( 90 < X < 110) = 0.1 + 0.1 = 0.2
The probability that X is between 90 and 110 = 0.2
Using z score table.
Z = ( Value - Mean) /SD
Z score for 0.4 = -0.254
-0.253 = (90 - 100)/SD
SD ≈ 39.53
Z = ( 110 - 100)/39.53
Z = 0.253
For z score < 0.253, the probability is 0.6
Hence Probability in Between is 0.6 - 0.4 = 0.2
The probability that X is between 90 and 110 = 0.2
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A forest ranger is watching the progress of a forest fire spreading towards her from the top of a 3334-foot mesa. In 6 minutes,
the angle of depression to the leading edge of the fire changes from 10.5° to 12.3°.
1) How many feet does the fire advance during the 6 minutes that the ranger is observing it?
2) At what speed (in MILES PER HOUR) is the fire spreading towards the ranger?
The speed of the fire is 3.214 miles per hour (rounded to three decimal places)
What do you mean by speed?It is defined as the distance traveled by an object per unit of time, typically in meters per second (m/s) or kilometers per hour (km/h).
Speed can be calculated by dividing the distance traveled by the time taken to cover that distance. It is a scalar quantity, meaning it only has magnitude and no direction.
Let's call the horizontal distance the fire advanced during the 6 minutes "d." We can use the tangent function to find d:
tan(12.3°) = (3334 - h) / d
tan(10.5°) = (3334 - h) / d
Solving for d in each equation, we get:
d = (3334 - h) / tan(12.3°)
d = (3334 - h) / tan(10.5°)
Since the time interval is the same for both observations, the fire advanced a distance equal to the difference between the two distances:
d = [(3334 - h) / tan(12.3°)] - [(3334 - h) / tan(10.5°)]
Plugging in the values and simplifying:
d = 1698.5 feet (rounded to the nearest tenth)
To find the speed at which the fire is spreading towards the ranger, we need to convert the distance from feet to miles, and the time from minutes to hours:
d = 1698.5 feet / 5280 feet per mile = 0.3214 miles
t = 6 minutes / 60 minutes per hour = 0.1 hours
The speed of the fire is then:
s = d / t = 0.3214 miles / 0.1 hours = 3.214 miles per hour (rounded to three decimal places)
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Wp
Peter bought a sandwich for $4.25, a drink for $2.17, and a cookie for $0.79. If he paid with a $10
bill, how much change did Peter get?
Answer:
$2.79
Step-by-step explanation:
We know
Peter bought a sandwich for $4.25, a drink for $2.17, and a cookie for $0.79.
4.25 + 2.17 + 0.79 = $7.21
If he paid with a $10 bill, how much change did Peter get?
10 - 7.21 = $2.79
So, Peter get $2.79 in change.
Which equation shows the same relationship as 1/2=3x1/6
Answer:
1 /2
Step-by-step explanation:
3×1 = 3
So it is 3 /6 = 1/2
3/6 ÷2 = 1/2
How many solutions does this equation have? -16 + n + 14n = -16 + 15n
Answer:
Infinitely many solutions
Step-by-step explanation:
Given the equation:
[tex]\displaystyle{-16+n+14n=-16+15n}[/tex]
Which can be simplified (for left side) to:
[tex]\displaystyle{-16+15n=-16+15n}[/tex]
Both sides are same, meaning that there are infinitely many solutions since no matter which n-values you substitute in, you'll end up getting true equation.
Use Kruskal's algorithm to find a minimum spanning tree for the following graph. Indicate the order in which edges are added to form the tree. (Enter your answer as a comma-separated list of sets.)
A graph with 8 vertices and 12 edges is shown.
One edge with weight 12 connects vertex v0 and vertex v1.
One edge with weight 4 connects vertex v0 and vertex v5.
One edge with weight 20 connects vertex v1 and vertex v2.
One edge with weight 5 connects vertex v1 and vertex v3.
One edge with weight 7 connects vertex v1 and vertex v4.
One edge with weight 19 connects vertex v2 and vertex v7.
One edge with weight 2 connects vertex v3 and vertex v4.
One edge with weight 18 connects vertex v3 and vertex v7.
The minimum spanning tree for the above graph 1 is present above in graph figure 2. The order in which edges are added to form the tree is equals to {V₃, V₄ }, { V₀, V₅}, { V₁, V₃}, {V₅, V₆}, { V₄, V₅}, {V₆, V₇}, {V₂, V₇ }.
We have , a diagram present above in figure. This graph has 8 vertices and 12 edges. Also
The edge with weight 12 connects vertex V₀ and vertex V₁.Similarly, edages are connected to each other with different weights as shown in graph. Kruskal's algorithm is a greedy algorithm in graph theory of discrete mathematics that used to determine the minimum spanning tree for a connected weighted graph and adds increasing weight at each. In this case a graph present we determine the shortest spinning tree. Kruskal's algorithm stated that always select a minimum cost edge that should not result in a cycle. The order is which edges are added is
{V₃, V₄ }, { V₀, V₅}, { V₁, V₃}, {V₅, V₆}, { V₄, V₅}, {V₆, V₇}, {V₂, V₇ }.
Hence, the required graph is present above.
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Complete question:
Use Kruskal's algorithm to find a minimum panning tree for the above graph. Indicate the order in which edges are added to form the tree. (Enter your answer as a comma-separated list of sets.)
A graph with 8 vertices and 12 edges is shown.
One edge with weight 12 connects vertex v0 and vertex v1.
One edge with weight 4 connects vertex v0 and vertex v5.
One edge with weight 20 connects vertex v1 and vertex v2.
One edge with weight 5 connects vertex v1 and vertex v3.
One edge with weight 7 connects vertex v1 and vertex v4.
One edge with weight 19 connects vertex v2 and vertex v7.
One edge with weight 2 connects vertex v3 and vertex v4.
One edge with weight 18 connects vertex v3 and vertex v7.
A scientist places a cell in a Petri dish. At the end of 1 hour, the cell divides so
that there are 2 cells in the Petri dish. At the end of 2 hours, those cells divide so
there are 4 cells in the Petri dish. The cells continue to divide this way every hour.
Use the expression 2 to the 10th power to find the number of cells in the Petri dish after 10 hours.
Show your work.
The number of cells in the Petri dish after 10 hours is 2¹⁰ = 1024 cells in the dish.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
The number of cells in the Petri dish after each hour can be represented by the expression 2ⁿ, where n is the number of hours that have passed.
So, after 1 hour, there are 2¹ = 2 cells in the dish.
After 2 hours, there are 2² = 4 cells in the dish.
After 3 hours, there are 2³ = 8 cells in the dish.
And so on.
Therefore, after 10 hours, there are 2¹⁰ = 1024 cells in the dish.
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airlines sometimes overbook flights. suppose that for a plane with 50 seats, 55 passengers have tickets. define the random variable y as the number of ticketed passengers who actually show up for the flight. the probability mass function of y appears in the accompanying table. y 45 46 47 48 49 50 51 52 53 54 55 p(y) 0.05 0.10 0.13 0.14 0.25 0.16 0.06 0.05 0.03 0.02 0.01 (a) what is the probability that the flight will accommodate all ticketed passengers who show up? (b) what is the probability that not all ticketed passengers who show up can be accommodated? (c) if you are the first person on the standby list (which means you will be the first one to get on the plane if there are any seats available after all ticketed passengers have been accommodated), what is the probability that you will be able to take the flight? what is this probability if you are the third person on the standby list?
a) Probability that the flight will accommodate all ticketed passengers who show up is 0.16
b) Probability that not all ticketed passengers who show up can be accommodated is 0.67
c) The probability that you will be able to take the flight is 96%
Probability is a powerful tool to understand the likelihood of different outcomes in various situations, including overbooking of flights
In this scenario, the random variable y represents the number of ticketed passengers who actually show up for the flight, out of a total of 55 ticketed passengers for a plane with only 50 seats. The probability mass function of y provides the probabilities for each possible outcome.
(a) The probability that the flight will accommodate all ticketed passengers who show up is the probability of y being equal to 50, which is 0.16.
(b) The probability that not all ticketed passengers who show up can be accommodated is the sum of the probabilities of y being greater than 50, which is
=> 0.05 + 0.10 + 0.13 + 0.14 + 0.25 = 0.67.
(c) If you are the first person on the standby list, the probability of being able to take the flight is the probability of y being less than or equal to 50, which is 0.89. This means that there is an 89% chance that you will get on the plane. If you are the third person on the standby list, the probability is the probability of y being less than or equal to 52 (since two people need to cancel or not show up for you to get on), which is 0.96. This means that there is a 96% chance that you will get on the plane.
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Please help meeee.
i need step by step please
here is the picture of the problem.
The required interval of domain for the composite function is [-2, 3].
What is Domain?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
According to question:
The domain of fog(x) is the set of all values of x for which the composition function fog(x) is defined.
fog(x) means that we plug g(x) into f(x), so we have:
fog(x) = f(g(x)) = f(x^2 - x) = √(6 - (x^2 - x))
= √(6 - x^2 + x)6
For the expression under the square root to be defined, we must have 6 - x^2 + x ≥ 0. This is a quadratic inequality that can be factored as:
-(x - 3)(x + 2) ≤ 0
The solutions of this inequality are -2 ≤ x ≤ 3.
However, we also need to check that the expression under the square root is non-negative, so we need to exclude the values of x that make 6 - x^2 + x < 0. This inequality holds for x < -2 or x > 3.
Therefore, the domain of fog(x) is [-2, 3].
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PLEASE HELP DUE ASAP !
The four points on the graph of this function f(x) = √(x + 1) + 4 has been plotted on the graph shown in the image attached below.
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.
Next, we would use an online graphing calculator to plot the given absolute value function f(x) = √(x + 1) + 4 as shown in the graph attached below.
By observing critically the graph (see attachment), the four ordered pairs (points) that fit on its axes include the following:
Ordered pair = (-1, 4), which is the leftmost.
Ordered pair = (0, 5).
Ordered pair = (3, 6).
Ordered pair = (8, 7).
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Attachment is below:
The numbers that are solutions to the inequality k > -5 are given as follows:
A. -4.
F. -4.99.
G. -0.5.
What are the inequality symbols?The four inequality symbols, along with their meaning, are presented as follows:
> x: greater than x.< x: less than x.≥ x: at least x.≤ at most x.The inequality for this problem is given as follows:
k > -5.
Meaning that the solutions are all the numbers that are greater than -5.
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The perimeter of a pentagon is 41.5 cm. write and solve and equation to detrmine the length of each side of the pentagon?
A pentagon has a 41.5 cm circumference, and its sides are each 8.3 cm long.
When you already know the value of one side, calculating the perimeter of a pentagon is made much simpler. The five sides of each pentagon are equal. If the length of one side is given to you.
Since a pentagon has five sides, we will abbreviate each side's length as "s". The lengths of all five sides add up to the perimeter of the pentagon, allowing us to formulate the following equation:
5s = 41.5
We must put "s" on one side of the equation alone in order to solve for it. Divide both sides by 5 to do this: s = 8.3
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What is the height h for the base that is 5/4 units long?
The height of the triangle is 3/5.
What is a right-angled triangle?A triangle is said to be right-angled if one of its inner angles is 90 degrees, or if any one of its angles is a right angle.
Given:
A right-angled triangle.
Let the values of the hypotenuse in parts be m and n.
So,
(1)² = (5/4)m
m = 4/5
And n = 9/16 x 4/5
n = 9/20
So, the height of the triangle is,
h² = 9/20 x 4/5
h² = 9/25
h = 3/5
Therefore, h = 3/5.
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Determine the coordinates of the point on the unit circle corresponding to the given central angle. If
necessary, round your results to the nearest hundredth.
202⁰
a. (-0.93,-0.37)
b. (-0.37, -0.93)
56:2
c.
(1, -0.37)
d. (-0.93, 0)
Answer:
a. (-0.93,-0.37)
Step-by-step explanation:
The unit circle is a circle with a radius of 1 that is centered at the origin (0, 0) of a coordinate plane. To find the coordinates of a point on the unit circle corresponding to a given central angle, we can use the relationship between the angle and the coordinates of the point.
For a central angle of 202 degrees, the point on the unit circle would be found by using the formula:
x = cos(202°)
y = sin(202°)
Rounding the results to the nearest hundredth, we have:
x = -0.927
y = -0.3746
So the coordinates of the point on the unit circle corresponding to the central angle of 202 degrees are (-0.93, -0.37).
Answer:
a. (-0.93, -0.37)
Step-by-step explanation:
A unit circle has its center at (0, 0) and a radius of 1.
The coordinates on the unit circle (x, y) are equivalent to (cos θ, sin θ), where θ is the angle (measured anticlockwise from the positive x-axis).
Therefore, given θ = 202°, the coordinates of the corresponding point on the unit circle are:
x = cos 202° = -0.93 (nearest hundredth)y = sin 202° = -0.37 (nearest hundredth)Therefore, the point on the unit circle is (-0.93, -0.37).
caitlin took both the sat and the act college entrance exams. her scores on both exams are shown in the table, as well as the national mean scores and standard deviations. exam caitlin's exam score national mean exam score national standard deviation sat 1850 1500 250 act 28 20.8 4.8 she wants to know on which test she performed better. find the z-scores for her result on each exam. provide your answer below: sat z-score: ____
act z-score: ____
On the SAT her z-score was 1.4 and on the ACT her z-score was 1.5 Thus, due to the higher z-score, she performed better on the ACT.
The amount of standard deviations by which the value of a raw score differs from or differs above the mean value of what is observed or measured is known as the z score or standard score in the z test. The z-score calculates how far an X-score deviates from the mean by standard deviations. Calculating the ACT scores utilizing the Z- score -
Z = X - u/a
Calculating the SAT score -
Where X = 1850, u = 1500 and a = 250
Z = 1850 - 1500/250
= 350/250
= 1.4
Similarly,
Calculating the ACT score -
Where X = 28, u = 20.8 and a = 4.8
Z = 28 - 20.8/4.8
= 7.2/4.8
= 1.5
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According to a 2017 survey conducted by the technology market research firm The Radicati Group, U.S. office workers receive an average of 121 e-mails per day (Entrepreneur magazine website). Assume the number of e-mails received per hour follows a Poisson distribution and that the average number of e-mails received per hour is five.
a. What is the probability of receiving no e-mails during an hour (to 4 decimals)?
b. What is the probability of receiving at least three e-mails during an hour (to 4 decimals)? For this question, if calculating the probability manually make sure to carry at least 4 decimal digits in your calculations.
c. What is the expected number of e-mails received during 15 minutes (to 2 decimals)?
d. What is the probability that no e-mails are received during 15 minutes (to 4 decimals)?
The probability of receiving no e-mails during an hour is approximately 0.0067, or 0.67%. The probability of receiving at least three e-mails during an hour is approximately 0.8754, or 87.54%. The expected number of e-mails received during 15 minutes is 1.25. The probability of receiving no e-mails during 15 minutes is approximately 0.7788, or 77.88%
We know that the average number of e-mails received per hour is 5. Therefore, the parameter λ of the Poisson distribution is also 5, since the Poisson distribution's mean and variance are both equal to λ.
The probability of receiving no e-mails during an hour (or during any other fixed time interval of length t) can be calculated using the Poisson distribution as follows:
P(X = 0) = e^(-λ) * λ^0 / 0! = e^(-5) * 5^0 / 0! ≈ 0.0067
Therefore, the probability of receiving no e-mails during an hour is approximately 0.0067, or 0.67%.
The probability of receiving at least three e-mails during an hour can be calculated as follows:
P(X ≥ 3) = 1 - P(X < 3) = 1 - (P(X = 0) + P(X = 1) + P(X = 2))
We already know the value of P(X = 0) from part (a), so we just need to calculate P(X = 1) and P(X = 2) using the Poisson distribution:
P(X = 1) = e^(-5) * 5^1 / 1! ≈ 0.0337
P(X = 2) = e^(-5) * 5^2 / 2! ≈ 0.0842
Substituting these values into the equation above, we get:
P(X ≥ 3) = 1 - (0.0067 + 0.0337 + 0.0842) ≈ 0.8754
Therefore, the probability of receiving at least three e-mails during an hour is approximately 0.8754, or 87.54%.
Since the expected number of e-mails received per hour is 5, the expected number of e-mails received during 15 minutes (i.e., a quarter of an hour) is:
E(X) = λ * t = 5 * (1/4) = 1.25
Therefore, the expected number of e-mails received during 15 minutes is 1.25.
The probability of receiving no e-mails during 15 minutes can be calculated using the Poisson distribution with λ = 1.25 and t = 1/4:
P(X = 0) = e^(-λt) * (λt)^0 / 0! = e^(-1.25/4) * (1.25/4)^0 / 0! ≈ 0.7788
Therefore, the probability of receiving no e-mails during 15 minutes is approximately 0.7788, or 77.88%.
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Write this ratio as a fraction in simplest form without any units.
54 ounces to 3 pounds
Answer: 8/9
Step-by-step explanation: 3 x 16 = 48 ounces
48 / 54 = 8/9
In the 1970's, my parents bought a house for $20,000 and now the
same home is worth $400,000. What is the percent of change?
Answer:
Step-by-step explanation:
h = 100 * 400000 - 20000 / 20000 = 38000000/ 20000 = 1900/1 = 1900%
Find a vector equation with parameter t for the line through the point (4,0,-3) and parallel to the vector 2i - 4j + 6k
Answer r(t)=
The vectorial equation of the line that passes through (4, 0, - 3) and is parallel to the vector <2, - 4, 6> is equal to (x, y, z) = (4, 0, - 3) + t · (2, - 4, 6).
How to derive the vectorial equation of a line
According to linear algebra, three-dimension lines can be derived from the knowledge of a point and a vector slope, whose formula is introduced below:
(x, y, z) = P(x, y, z) + t · M(x, y, z)
Where:
P(x, y, z) - Point on the linet - ParameterM(x, y, z) - Vector slopeTwo lines are parallel when they have the same vector slope. If we know that P(x, y, z) = (4, 0, - 3) and M(x, y, z) = (2, - 4, 6), then the vectorial equation of the line is:
(x, y, z) = (4, 0, - 3) + t · (2, - 4, 6)
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consider the two matricesA = | 1 2 4 | and D = | -5 -6 -2 || 4 2 4 | | 1 -2 1 || 3 4 3 | | 3 4 3 |observe that D is obtained from A using two elementary row operations. find a matrix E such that EA = D (hint: E is the product of the two elementary matrices corresponding to the two row operations).
The value of the matrix E is such that EA = D (E is the product of the two elementary matrices corresponding to the two-row operations) will be:
Matrix E = | 0 1 0 |
| 1 0 0 |
We can find the elementary matrices corresponding to the two-row operations and multiply them together to obtain the matrix E.
First-row operation: Add -4 times the first row to the second row.
This is equivalent to multiplying A on the left by the elementary matrix:
| 1 0 0 |
|-4 1 0 |
| 0 0 1 |
Call this matrix E1.
E1A =
| 1 2 4 | | 1 0 0 | | 1 2 4 |
|-4 -6 -12| * | -4 1 0 | = |-5 -6 -2 |
| 3 4 3 | | 0 0 1 | | 3 4 3 |
Next row operation: Swap the first and third rows.
This is equivalent to multiplying E1A on the left by the elementary matrix:
| 0 0 1 |
| 0 1 0 |
| 1 0 0 |
Call this matrix E2.
E2E1A =
| 3 4 3 | | 0 0 1 | | -5 -6 -2 |
|-4 -6 -12| *| 0 1 0 | = | -4 -2 4 |
| 1 2 4 | | 1 0 0 | | 1 2 4 |
Therefore, the matrix E that satisfies EA = D is given by:
E = E2E1 = | 0 0 1 | | 1 0 0 |
E = | 0 0 1 |
EA = D
| 0 1 0 | * |-4 1 0 | = | 0 1 0 |
| 1 0 0 | | 0 0 1 | | 1 0 0 |
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