The standard deviation is $8,000. So, the standard deviation measured in thousands of dollars, is 8. and The mean is the average. So the average, measured in thousands of dollars, is 56.
Average salary: 56
Standard deviation of the salary: 8
$56,000 dollars is 56 thousand dollars.
$8,000 is 8 thousand dollars.
The mean is the average. So the average, measured in thousands of dollars, is 56.
The standard deviation is $8,000. So, the standard deviation measured in thousands of dollars, is 8.
complete question
Let X denote the average starting salary for 2014 U.S. college graduates, measured in dollars. Suppose that the average annual salary is $56,000 dollars, with a standard deviation of 8,000. Find the mean and standard deviation when salary is measured in thousands of dollars.
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explain why 1/12+1/12+1/12+1/12 is the same as 1/3.
Answer:
Step-by-step explanation:
It is equivalent
4/12
1/3
1x4=4
_
3x4=12
"The solid has ( a circular base, a trapezoidal base, a triangular base, or a rectangular base) in the xy-plane.
The solid has ( a circular face, a trapezoidal face, a triangular face, or a rectangular face) in the xz-plane.
The solid has ( a circular face, a trapezoidal face, a triangular face, or a rectangular face) in the yz-plane.
The solid has ( a circular face, a trapezoidal face, a triangular face, or a rectangular face) in the plane z = 1 - x.
The solid has ( a circular face, a trapezoidal face, a triangular face, or a rectangular face) in the 0plane y = 9 - 9z.
As x increases, the top of the region (decreases, increases, or remains constant).
As y increases, the top of the region (decreases, increases, or remains constant)."
The solid has a triangular face in the xy-plane.
The solid has a rectangular face in the xz-plane.
The solid has a trapezoidal face in the yz-plane.
The solid has a triangular face in the plane z = 1 - x.
The solid has a rectangular face in the plane y = 9 - 9z.
As x increases, the top of the region decreases.
As y increases, the top of the region remains constant.
The solid whose volume is given by the iterated integral, integral 0 to 1 integral 0 to (1-x) integral 0 to (9 - 9z) dy dz dx. This is a three-dimensional solid, that has been defined by three nested integrals. The outer integral is with respect to x, the second integral is with respect to y and the inner integral is with respect to z.
In the xz-plane, the solid has a rectangular face: the integral bounds for x are 0 to 1 and for z, it is 0 to (9 - 9z)
In the yz-plane, the solid has a trapezoidal face: the integral bounds for y are 0 to (1-x) and for z, it is 0 to (9 - 9z)
In the plane z = 1 - x, the solid has a triangular face: the integral bounds for x are 0 to 1 and z = 1 - x
In the plane y = 9 - 9z, the solid has a rectangular face: the integral bounds for y are 0 to (1-x) and y = 9 - 9z
As x increases, the top of the region decreases: the limit for y decreases from 9 to 0 as x increases from 0 to 1
As y increases, the top of the region remains constant: y = 9 - 9z is a constant value, as y increases, the integral bounds for z decrease from 9 to 0
This solid is a rectangular pyramid with a trapezoidal base. The rectangular face is located in the xz-plane, the trapezoidal face is located in the yz-plane, the triangular face is located in the plane z = 1
--The question is incomplete, answering to the question below
"The solid whose volume is given by the iterated integral,
∫ [0 to 1] ∫ [0 to (1-x)] ∫ [0 to (9 - 9z)] (dy dz dx)
The solid has ( a circular face, a trapezoidal face, a triangular face, or a rectangular face) in the xz-plane.
The solid has ( a circular face, a trapezoidal face, a triangular face, or a rectangular face) in the yz-plane.
The solid has ( a circular face, a trapezoidal face, a triangular face, or a rectangular face) in the plane z = 1 - x.
The solid has ( a circular face, a trapezoidal face, a triangular face, or a rectangular face) in the plane y = 9 - 9z.
As x increases, the top of the region (decreases, increases, or remains constant).
As y increases, the top of the region (decreases, increases, or remains constant)."
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Please help with with this 9th grade math question
We can observe from the graph that plan B is less expensive for the interval [0, 4], however plan A is better if you watch 4 or more movies each month.
How do I obtain the cost equations?We know that Plan A costs $14 per month + $2 each movie, thus the total cost if you see x movies is:
C₁(x) = $14 + $2*x
Plan B costs $10 a month + $3 per movie, therefore the total cost if you see x movies is:
C₂(x) = $10 + $3*x
The graph at the end may now be used to compare expenses. The blue line is C2(x), while the green line is C1(x).
The blue line in the graph may be seen between x = 0 and x = 4.
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a new real estate agent earns 5% of the cost of the sold house his first sale is a $219,000 house
Answer:
The new real state agent earns:
$10,950
Step-by-step explanation:
5% = 5/100 = 0.05
219000 * 0.05 = 10950
Estimate the product by rounding the numbers so that the resulting arithmetic can easily be performed by hand or in
your head. Then use a calculator to perform the computation. How reasonable is your estimate when compared to
the actual answer?
17% of 279,394
-The estimated product is. (Type an integer.) I need help for this math please
The value of 17% of 279,394 is 47496.98.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
We have to find the value of 17% of 279,394
Convert 17% to decimal value by dividing with 100
17/100=0.17
Now multiply 0.17 with 279394
0.17×279394
47496.98
Hence, the value of 17% of 279,394 is 47496.98.
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In order to set premiums at profitable levels, insurance companies must estimate how much they will have to pay in claims on cars of each make and model, based on the value of the car and how much damage it sustains in accidents. Let C be a random variable that represents the cost of a randomly selected car of one model to the insurance company. The probability distribution of C is given below. C $0 $1500 $5000 $15000 PC 0.60 0.05 0.13 0.22 The expected value for the above distribution is $4025. Which of the following is the best interpretation of expected value? (In the choices below. "Exp(C)" represents the expected value).
O If the company insures a large number of these cars, they can expect the variability in cost per car to average approximately Exp(C). O If the company Insures a large number of these cars, they can expect the cost per car to average approximately Exp(C). O The maximum cost to the company for insuring this car model is Exp(C) per car. O If the company insures 10 cars of this model, they know they will incur 10xExp(C) in costs. O The company must insure at least Exp(C) of these cars to make a profit
The expected value for a random variable is defined as the sum of the product of the values and probabilities of the variable.
In this case, the expected value for C is calculated by multiplying each possible value by its probability and adding the products. This is represented mathematically as:
Exp(C) = 0 x 0.60 + 1500 x 0.05 + 5000 x 0.13 + 15000 x 0.22 = 4025
The expected value of C can be interpreted as the average cost that the insurance company can expect to pay out for a randomly selected car of this model. This means that if the company insures a large number of these cars, they can expect the cost per car to average approximately $4025. The expected value does not represent the maximum cost for insuring this car model, or the cost for insuring a set number of cars. Instead, it provides an estimate of what the average cost per car will be.
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HELP ME OUT PLEASE!!!!!!!
What is the domain of the function shown in the graph below?
Answer:
X ≥ -4
Step-by-step explanation:
Remember domain only focuses on the X values, so we can immediately rule out the answers containing Y. We can observe that the graph has a closed circle over x=-4. This tells us it will be included and so we must have "≥" in the answer choice. By simple process of elimination A, the first answer choice is the correct answer.
Also note that it would be read as "X is greater than or equal to negative 4," which is exactly what our graph depicts. The second choice, which looks like it could be correct at first would be read as "X is greater than negative 4," which excludes negative 4 in the answer. We need that negative 4 for it to be correct.
In a Premier League match between Man. United and Arsenal FC, there are 22 players altogether and 3 match officials on the pitch. a. Find the probability Man. United wins the match. b. If a person is selected at random from the pitch, what is the probability that he is an official? c. If both coaches decide to play 4 defenders, 3 midfielders and 3 attackers from each side, find the probability that a player selected at random is i. a goalkeeper. ii. an attacker. iii. a defender
Answer:
a. Without any additional information provided, it is impossible to determine the probability of Manchester United winning the match. The outcome of a football match can be influenced by many factors such as player performance, tactics, and luck.
b. There are 22 players + 3 officials = 25 people on the pitch. The probability that a person selected at random from the pitch is an official is 3/25.
c. i. Since there are 2 goalkeepers on the pitch, the probability that a player selected at random is a goalkeeper is 2/22 = 1/11
ii. Since there are 3 attackers on the pitch, the probability that a player selected at random is an attacker is 3/22 = 1/7
iii. Since there are 8 defenders on the pitch, the probability that a player selected at random is a defender is 8/22 = 4/11
The number of solutions of (x2 + 1)2 + 2(x2 + 1) - 3 = 0 is equal to
A. 1
B. 2
C. 3
D. 4
Answer:
I'm pretty sure it's 3. I say that because I get 3 different answers.
x = -1 / 8
x = -0.125
x = -2^3
Those are the answers I got to solve the equation. There also is an answer if I were to rewrite the equation which is... 8x = -1
I hope this helps in any way <3
Step-by-step explanation:
f(x) is a direct variation function
f(3)= 12
f(x)= ?
f(2)= ?
The function f(x) will be : f(x) = 4x and f(2) = 8.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine the order of operations and other aspects of logical syntax.
Given that f(x) is a direct variation function.
Direct variation of {y} with {x} means that as {x} increases, {y} increases uniformly with it. Mathematically -
{K} = y/x = constant
Scale factor {K} is a dimensionless value that indicates the constant ratio value indicating direct variation.
It is given that -
f(3) = 12
We can write the slope of f(x) as -
m = (12 - 0)/(3 - 0)
m = 12/3
m = 4
So, f(x) will be -
f(x) = 4x
f(2) will be -
f(2) = 8
Therefore, the function f(x) will be : f(x) = 4x and f(2) = 8.
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The math department at a small school has 5 teachers. The ages of these teachers are 23, 34, 37, 42, and 58. Suppose you selected a random sample of 3 teachers and calculated the sample median.
(a) List all 10 possible samples of size 3. Calculate the sample median for each sample.
(b) Display the sampling distribution of the sample median.
When we select a random sample of 3 teachers and calculated the sample median from ages of 5 teachers in maths department, we get three samples of sample median 34, four samples of sample median 37 and three samples of sample median 42.
a. To list all 10 possible samples of size 3, we can use the combination formula C(5,3) = 5! / (3! * 2!) = 10.
The possible samples are:
Sample 1: (23, 34, 37) - Sample Median: 34
Sample 2: (23, 34, 42) - Sample Median: 34
Sample 3: (23, 34, 58) - Sample Median: 34
Sample 4: (23, 37, 42) - Sample Median: 37
Sample 5: (23, 37, 58) - Sample Median: 37
Sample 6: (23, 42, 58) - Sample Median: 42
Sample 7: (34, 37, 42) - Sample Median: 37
Sample 8: (34, 37, 58) - Sample Median: 37
Sample 9: (34, 42, 58) - Sample Median: 42
Sample 10: (37, 42, 58) - Sample Median: 42
b. To display the sampling distribution of the sample median, we can create a frequency table that shows how many times each sample median appears in the list of possible samples.
Sample Median Frequency
34 3
37 4
42 3
This table shows that the sample median of 34 appears in 3 out of the 10 possible samples, the sample median of 37 appears in 4 out of the 10 possible samples, and the sample median of 42 appears in 3 out of the 10 possible samples.
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A rectangular prism has a length of 10 meters, a width of 5 meters, and a height of 2 meters.
Which equations could be used to determine the volume, V, of the prism?
The volume equation of a rectangular prism is:
V = Bh orV = lwh,Where V - volume, l, w, h are dimensions, B - area of base (same as lw)
By substituting values we get:
V = 10*5*2 = 100 m³x + 3x + 10 solve for x
Answer:
x = 2.5
Step-by-step explanation:
I am assuming that this is the entire equation and that it equates to 0 otherwise the answer will just be [tex]4x + 10[/tex]
[tex]x + 3x +10 = 0 \\4x + 10 = 0\\4x = 10\\x = \frac{10}{4} \\x = 2.5[/tex]
given the 27 blocks represented by the mccumber cube; give an example item which would fulfill any 9 of the blocks.
The McCumber Cube, which bears the name of its inventor, John McCumber, demonstrates the interdependence of the many elements of information security.
What is the McCumber Cube used for?
The McCumber Cube, which bears the name of its inventor, John McCumber, demonstrates how the many elements of information security are interconnected. You may view availability, integrity, and confidentiality on one side. All three of these include crypto in a significant way.
Information Characteristics, Information States, and Security Countermeasures are the three McCumber cube dimensions. The three CIA triangle pillars of confidentiality, integrity, and availability make up information characteristics.
The McCumber Cube, which John McCumber developed in 1991, is a reference framework for developing and assessing information security (also known as information assurance) initiatives. This security model is presented as a grid that resembles the Rubik's Cube in three dimensions.
The McCumber Cube shows three proportions. If theorized, the three dimensions of each axis become a 3 × 3 × 3 cube with 27 cells representing areas that must be addressed to secure today’s information systems. To ensure system security, each of the 27 areas must be properly addressed during the security process (McCumber, 1991).
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perpendicular to line y=1/2x-8 passes through (7,-6) point slope form
An equation that is perpendicular to line y = 1/2x - 8 and passes through (7, -6) in point-slope form is y + 6 = -2(x - 7).
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.From the information provided, an equation of the first line is given by;
y = 1/2x - 8
Therefore, slope (m) = 1/2
In Mathematics, a condition that must be met for two lines to be perpendicular is given by:
m₁ × m₂ = -1
1/2 × m₂ = -1
m₂ = -2
Note: m represents the slope.
At point (7, -6), an equation of the line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - (-6) = -2(x - 7)
y + 6 = -2(x - 7)
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Complete Question:
Write an equation perpendicular to line y = 1/2x - 8 and passes through (7, -6) in point-slope form.
How did you find the answer to the problem?
Answer:
-4.44
because -pi means -22/7 so that means it is -3.14... and -11/3 means -3.6 and -4.123...leave your answer in exact form (in terms of pi, without spaces). the radius of each circle is r. if two circles are shown, r is the radius of the smaller circle and r is the radius of the larger circle. r
The small radius =5 cm; and the Long radius =5+4=9 cm.
Area (a + b) = 106 * pi cm^2 (given)
radius of a = x : radius of b = (x + 4)
Area a =[tex]pi * r^2 = pi * x^2\\[/tex]
Area b = [tex]pi * r^2 = pi * (x + 4)^2[/tex]
Area (a + b) = [tex]pi * x^2 + pi * (x + 4)^2[/tex] = 106 * pi cm^2
Area (a + b) =[tex]pi * x^2 + pi * (x^2 + 8x + 16)[/tex] = 106 * pi cm^2
Area (a + b) = pi * ([tex]2x^2[/tex]+ 8x + 16) = 106 * pi cm^2
Area (a + b) = [tex]2x^2 + 8x - 90 = 0[/tex]
2x^2 + 8x - 90 = x^2 + 4x - 45 = 0
x^2 + 4x - 45 = (x + 9)(x -5) = 0
x = 5 or x = -9
Therefore: radius a = 5 cm and radius b = 9 cm
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The question is incomplete
The sum of the areas of the two circles is 106pi cm^2 and the radius of the larger circle is 4cm longer than the radius Of the smaller circle. How could I find the length of the radii?
create an applab turtle project that uses loops and random numbers to create a background and 2 unique shapes.
A combination of loops and random numbers, a unique background and two unique shapes can be created.
The Applab Turtle project uses a combination of loops and random numbers to create a background and two unique shapes. The program starts by setting the background color of the canvas to a random number from 0 to 255. A for loop is then used to create a series of random circles. The loop is set to run 10 times, and each iteration uses the random number function to set the size of the circle and its position, resulting in a unique pattern of circles on the canvas. Following this, two for loops are used to create two unique shapes. The for loops are set to run a set number of times, and each iteration uses the random number function to set the size and position of the shape. By using a combination of loops and random numbers, a unique background and two unique shapes can be created.
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For a melon selected at random from distributor j, what is the probability that the melon will have a diameter greater than 137 mm?
The probability that the melon will have a diameter greater than 137 mm is 21.19%.
What is probability?Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes. The likelihood of an event occurring might range from 0 to 1.
Given A grocery store purchases melons from two distributors, J & K,
for distributor J,
mean of melons = μ = 133 mm
standard deviation = σ = 5 mm
to find the probability that the melon will have a diameter greater than 137 mm,
x = 137 mm
P(x > 137)
using z score formula
z = (x - μ)/σ
z = (137 - 133)/5
z = 0.8
P-value from Z-Table:
P(x < 137) = 0.78814
P(x > 137) = 1 - P(x < 137) = 0.21186
probability in percent = P(x > 137) = 0.21186*100 = 21.186%
P(x > 137) = 21.19%
Hence probability for melon will have a diameter greater than 137 mm is 21.19%.
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The complete question is,
A grocery store purchases melons from two distributors, J & K. Distributor J provides melons from organic farms. The distribution of the diameters of the melons from distributor J is approximately normal with mean with 133 millimeters and standard deviation 5 mm. For a melon selected at random from distributor J, what is the probability that the melon will have a diameter greater than 137mm?
let a and b be two possible events when a random number generator is used once. suppose you are told that a and b are mutually exclusive. this implies that
It implies that the two events are mutually exclusive, meaning that they cannot occur simultaneously. This means that if event A occurs, event B cannot occur, and vice versa.
It implies that the two events are mutually exclusive, meaning that they cannot occur simultaneously. This means that if event A occurs, event B cannot occur, and vice versa.
1. Two possible events, A and B, are given when a random number generator is used once.
2. It is stated that the two events are mutually exclusive.
3. This implies that the two events cannot occur simultaneously.
4. If event A occurs, event B cannot occur and if event B occurs, event A cannot occur.
It implies that the two events are mutually exclusive, meaning that they cannot occur simultaneously. This means that if event A occurs, event B cannot occur, and vice versa.
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12 Select the correct answer from each drop-down menu. Graph shows two triangles plotted on a coordinate plane. One triangle is at A (minus 4, 4), B (minus 8, 2), and C (minus 6, minus 6). Another triangle is at A prime (4, minus 2), B prime (2, 2), and C prime (6, 0). A sequence of transformations maps ∆ABC to ∆A′B′C′. The sequence of transformations that maps ∆ABC onto ∆A′B′C′ is a followed by a .
None of the transformations followed between the two given triangles. None of the options are correct.
What are Similar triangles?Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.
Here,
The graph shows two triangles plotted on a coordinate plane. One triangle is at A (-4, 4), B (-8, 2), and C (-6, -6). Another triangle is at A '(4, -2), B '(2, 2), and C '(6, 0).
As we can see in the graph, the triangles are completely different, so the transformation of either of the ΔABC to ΔA'B'C' or ΔA'B'C' to ΔABC is not possible.
Thus, None of the transformations followed between the two given triangles. None of the options are correct.
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Dinesh is a mason and he takes Rs 3,250 for 5 days working everyday. If he received only Rs 7,800 in two weeks, how many days was he absent in his work?
Answer:
2 days
Step-by-step explanation:
He was paid 3,250 for 5 days that means 1 day is 3250/5 = 650
So, then 7,800/650 = 12 days(number of days he came to work) but two weeks is 14 days so the number of days he was absent was 14-12= 2
Jorge wrote the inequality −14 °F <−2 °F to compare the temperatures at 7 A.M. and 7 P.M. It was colder at 7 P.M. than at 7 A.M. What was the temperature at 7 A.M.? Complete the explanation.
The temperature at 7 A.M. is,
−2 °F.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Given:
Jorge wrote the inequality −14 °F < −2 °F to compare the temperatures at 7 A.M. and 7 P.M.
It was colder at 7 P.M. than at 7 A.M.
That means,
−14 °F is the temperature at 7 P.M.
The temperature at 7 A.M. is,
−2 °F.
Therefore, the temperature at 7 A.M. is −2 °F.
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An experiment is performed where a 3-color spinner is spun and then a 4-color spinner is spun. The possible outcomes for each event are red (R), blue (B), and yellow (Y) for the 3-color spinner and red (R), blue (B), yellow (Y), and green (G) for the 4-color spinner. Identify the sample space for this experiment.
The sample space for this experiment is given as follows:
{RR, RB, RY, RG, BG, BB, BY, BG, YR, YB, YY, GG}.
What is a sample space?A sample space is a set that contains all possible outcomes in the context of an experiment.
Then the sample space for this problem is composed by two letters, and the meaning of each letter is given as follows:
First letter: outcome of the 3-color spinner.Second letter: outcome of the 4-color spinner.Hence, as an example, the outcome RB means that the color of the 3-color spinner was red and the color of the 4-color spinner was blue.
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in a large high school, 37% of the teachers believe that five minutes is not enough time for students to change classes. however, 89% of the students believe that five minutes is not enough time for students to change classes. let p hat subscript upper f and p hat subscript s be the sample proportions of teachers and students, respectively, who believe that five minutes is not enough time for students to change classes. suppose 28 teachers and 100 students are selected at random and asked their opinion on the amount of time students have to change class. which of the following is the correct calculation and interpretation of the standard deviation of the sampling distribution of p hat subscript upper f baseline minus p hat subscript s ?
The difference (faculty-student) in the sample proportions of those who think that students should have five minutes to switch classes usually varies by roughly 0.096 from the actual difference in proportions.
What is the standard deviation?A low standard deviation shows that the values tend to be close to the mean (also known as the expected value) of the set, whereas a high standard deviation suggests that the values are spread out over a broader range.
The standard deviation is a measure of variance or dispersion in statistics.
So, the sampling distribution's standard deviation is calculated as follows:
[tex]\begin{aligned}& \sigma_{\mathrm{F}}-\sigma_{\mathrm{s}}=\sqrt{\frac{0.37 \times(1-0.37)}{28}+\frac{0.89 \times(1-0.89)}{100}} \\& \sigma_{\mathrm{F}}-\sigma_{\mathrm{s}}=0.096\end{aligned}[/tex]
The actual proportional difference between those who believe five minutes is not enough time for pupils to switch courses and those who believe this is generally 0.096.
Therefore, the difference (faculty-student) in the sample proportions of those who think that students should have five minutes to switch classes usually varies by roughly 0.096 from the actual difference in proportions.
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Correct question:
n a large high school, 37% of the teachers believe that five minutes is not enough time for students to change classes. However, 89% of the students believe that five minutes is not enough time for students to change classes. Let p hat Subscript Upper F and p hat Subscript Upper S be the sample proportions of teachers and students, respectively, who believe that five minutes is not enough time for students to change classes. Suppose 28 teachers and 100 students are selected at random and asked their opinion on the amount of time students have to change class. Which of the following is the correct shape and justification of the sampling distribution of p hat Subscript Upper F Baseline minus p hat Subscript s ?
Shade each model. Then write each fraction as a decimal
Answer: 0.25
Step-by-step explanation:
1/4 = 0.25
An international food festival charges for admission and for each sample of food. Admission and 7 samples cost $9.25. Admission and 9 samples cost $11.25. Write a linear
function rule to model the cost y for any number of samples x.
The linear function rule is y=
In rhombus ABCD, points E,F,G and H are the midpoints of AB, BC, CD and DA respectively. Quadrilateral EFGH has area 14 and perimeter 16. Find the side length for rhombus ABCD.
Side length of Rhombus ABCD is 8+2√2 unit
EFGH is a rectangle :
We know that ,
E, F , G , H are midpoints of AB, BC, CD , DA respectively
Since ABCD is a rhombus
AB = BC = CD = DA
AB ll CD and BC ll DA
since, E, F , G , H are midpoints of AB, BC, CD , DA respectively
from the figure below we can say that ,
1) AB ll CD ll FH and AB= CD = FH
2) BC ll DA ll GE and BC = DA = GE
Using mid point theorem we can say that ,
GH = EF = 1/2 AC and FG= EH = 1/2 BD
Since for the figure EFGH opposite sides are equal and and parallel , and the diagonals are equal in length we can say that EFGH is a rectangle.
Perimeter of a rectangle = 2(a+b) = 2( GH + EH ) = 2 (EF + GF) = 2 ( 1/2 AC + 1/2 BD )
= 2 x 1/2 ( AC + BD ) = 16
⇒ AC + BD = 16 (1)
now area of a rectangle is given by
A = ab = GH x EH = EF x GF = 1/2 AC x 1/2 BD = 1/4 (AC x BD) = 14
⇒AC x BD = 14 x 4 = 56
from equation (1)
AC ( 16 - AC) = 56
= 16 AC - AC ^2 = 56
⇒ AC^2 - 16 AC + 56 = 0
AC = 8 +/- 2√2
BD = ( 16 - AC) = 8 +/- 2 √2 = side length of rhombus ABCD
Side length of Rhombus ABCD is 8+2√2 unit EFGH is - 1
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A certain skin cream is 80 percent effective in curing a common rash. A random sample of 100 people with the rash will use the cream. Which of the following is the best description of the shape of the sampling distribution of the sample proportion of those who will be cured? А Bimodal B Uniform
с Approximately normal D Strongly skewed to the left E) Strongly skewed to the right
The best description of the shape of the sampling distribution is Approximately normal. The correct option is C.
The sampling distribution of the sample proportion of those who will be cured with the skin cream is approximately normal. A sampling distribution is the distribution of a statistic calculated from a random sample of data. In this case, the statistic is the sample proportion of those who will be cured with the skin cream. The Central Limit Theorem states that the sampling distribution of a statistic will be approximately normal if the sample size is large enough, regardless of the shape of the underlying distribution.
Since the sample size of 100 people is large enough, the sampling distribution of the sample proportion of those who will be cured with the skin cream is approximately normal.
Hence the correct option is C.
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Dr. Chandler wants to print copies of
his thesis in hardcover book format. He
could use Washington Printing, paying a
setup fee of $41 and $6 for every book
printed. Or, he could go through Fairfax
University, paying an up-front fee of
$32 and $9 per book. For how many
books will the costs be the same? How
much is that?
On solving the equations y1 = 41 + 6x and y2 = 32 + 9x, it is obtained that -
For 3 books the cost will be the same.
The cost that will be same is $59.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The cost at Washington Printing is = $41 and $6 per book
The cost at Fairfax University is = $32 and $9 per book
Let the number of books be x.
Let y1 represent the total cost at Washington Printing.
Let y2 represent the total cost at Fairfax University.
So, the equations are -
y1 = 41 + 6x
y2 = 32 + 9x
According to the question -
y1 = y2
41 + 6x = 32 + 9x
Collect all the like terms together -
6x - 9x = 32 - 41
- 3x = - 9
x = 9/3
x = 3
Therefore, the number of books is 3.
The total cost can then be determined by the substituting the value of x in the equations -
41 + 6x = 41 + 6(3) = 41 + 18 = 59
32 + 9x = 32 + 9(3) = 32 + 27 = 59
Therefore, the total cost is $59.
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