Answers
1)
a) the mean is µ = 2.5.
b) the variance is σ² = 1.25.
c) Standard Deviation σ = 1.12
2)
a) the mean is µ = 6.40.
b) the variance is σ² = 2.12
c) Standard Deviation σ = 1.46.
1) To find the mean (µ), we can multiply each value of x by its corresponding probability (P(x)), and then add up the products: (See attached table I)
Sum | 1 | 2.5
Therefore, the mean is µ = 2.5.
To find the variance (σ²), we need to find the squared differences between each value of x and the mean, multiply each squared difference by its corresponding probability, and then add up the products:
See table II
Sum | 1 | | 5 | 1.25
Therefore, the variance is σ² = 1.25.
Finally, to find the standard deviation (σ), we can take the square root of the variance:
σ = √(σ²) = √(1.25) ≈ 1.12.
2)
To find the mean (µ), we can multiply each value of x by its corresponding probability (P(x)), and then add up the products: See table III...
Sum | 1.00 | 6.40
Therefore, the mean is µ = 6.40/1.00 = 6.40.
To find the variance (σ^2), we need to find the squared differences between each value of x and the mean, multiply each squared difference by its corresponding probability, and then add up the products: See table IV
Sum | 1.00 | | 40.80 | 2.1200
Therefore, the variance is σ² = 2.1200.
Finally, to find the standard deviation (σ), we can take the square root of the variance:
σ = √(σ²) = √(2.1200) ≈ 1.46.
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Related Questions
Pete scored 3/9 of the goals in a game. If Pete scored 9 goals, how many goals were scored in total
Answers
Answer:
then he's scored all the goals 9/9
Find the exact area of a circle is the circumference is 58 π
Answers
Answer:
2640.74
Step-by-step explanation:
Circumference : π * 2r
Area of circle : π * [tex]r^{2}[/tex]
For this particular circumference,
Circumference : π * 58
58 = 2r
So by dividing we learn that,
r = 29
When we substitute the radius into the equation for area, we get,
Area of circle : π * [tex]29^{2}[/tex]
Area of circle : π * 841
Area of circle : 2640.74
* I used 3.14 as π
Hope this helps ! Feel free to ask questions! : )
Answer the question correctly.
Answers
The ladder leaning on the wall will form the hypotenuse, so our hypotenuse is 24ft.
The length away from the house to the base of the ladder is one side length of 13ft.
Let’s use Pythagorean’s Theorem to find the height of the wall:
a^2 + b^2 = c^2
c = 24
b = 13
Let’s isolate what we want to solve for, a:
a^2 = c^2 - b^2
a = sqrt( c^2 - b^2 )
Plug in our c and b values:
a = sqrt( (24)^2 - (13)^2 )
a = sqrt( 576 - 169 )
a = sqrt( 407 )
a = 20.17
a = 20.2 ft
The ladder will reach 20.2 ft up the wall of her house.
11. Let’s first find Will’s distance:
a^2 + b^2 = c^2
a = 40
b = 40
c = sqrt( (40)^2 + (40)^2 )
c = sqrt ( 1600 + 1600 )
c = sqrt ( 3200 )
c = 56.6 yards
Now James’ distance:
a^2 + b^2 = c^2
a = 25
b = 35
a = sqrt( (25)^2 + (35)^2 )
a = sqrt( 625 + 1225 )
a = sqrt( 1850 )
a = 43.0 yards
Will ran a longer distance since 56.6 yards is longer than 43.0 yards.
Complete the following statement. Write your answer as a decimal or whole number.
__% of $3,000,000 = $2,250,000
Submit
Answers
Answer: 75
Step-by-step explanation:
[tex]x[/tex]% x 3000000 = 2250000
[tex]x[/tex]/100 x 3000000 = 2250000
[tex]x[/tex] x 30000 = 2250000
[tex]x[/tex] = 2250000/30000
[tex]x[/tex] = 75
The table above shows the price for different numbers of business cards. Which equation models the
total cost
Answers
Find the measure of angleq, the smallest angle in a triangle whose sides have lengths 4, 5, and 6. round the measure to the nearest whole degree. 34° 41° 51° 56°
Answers
The measure of the smallest angle, angle Q, is approximately 41°.
To find the smallest angle in the triangle with side lengths 4, 5, and 6, we can use the cosine rule.
The cosine rule states that for any triangle with sides a, b, and c and corresponding angles A, B, and C:
[tex]cos(A) = (b^2 + c^2 - a^2) / (2 * b * c)[/tex]
In our case, since we want to find the smallest angle, we need to find the angle opposite the smallest side.
The smallest side is 4, so we are looking for angle A.
The other sides, b and c, are 5 and 6 respectively.
Step 1: Plug in the side lengths into the cosine rule formula.
[tex]cos(A) = (5^2 + 6^2 - 4^2) / (2 * 5 * 6)[/tex]
Step 2: Calculate the values inside the parentheses.
cos(A) = (25 + 36 - 16) / (60)
Step 3: Simplify the equation.
cos(A) = (45) / (60)
Step 4: Divide the numbers.
cos(A) = 0.75
Step 5: Now, to find angle A, take the inverse cosine [tex](cos^(-1))[/tex] of the result.
A = cos^(-1)(0.75)
Step 6: Calculate the angle in degrees.
A ≈ 41.41°
Step 7: Round the angle to the nearest whole degree.
A ≈ 41°.
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Given the cost function C(x) = 0.75 + 63, 180 and the revenue
function R(x) = 1.92x, find the break-even point.
Answers
The break-even point is 54,000 units given the cost function and revenue function.
The break-even point is the moment at which a product's sales revenue equals its production costs. There is currently neither a gain nor a loss.
This problem's cost function is C(x) = 0.75x + 63,180, where x is the total number of created units. R(x) = 1.92x, where x is the quantity of units sold, is the revenue function.
We must set the revenue equal to the expense in order to determine the break-even point:
R(x) = C(x) (x)
1.92x = 0.75x + 63,180
1.17x = 63,180
x = 54,000
Thus, 54,000 units are needed to break even.
This means that the money earned will be equivalent to the cost of creating the product if the company produces and sells 54,000 units of it. The corporation will make money on any units sold over this threshold while losing money on any units sold below it.
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Please please, please someone help me I've been struggling for so long and my teacher won't help :(
Answers
Answer with explanation:
Slope:[tex]m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4-2}{2-1} = \frac{2}{1} = 2[/tex]
Substitute:
[tex]y-y_1 = m(x-x_1)[/tex] , Where:
y1: "y" of a point,
x1: "x" of a point and
m: slope
By substituting with the point (1,2):
[tex]y-2 = 2(x-1)[/tex]
Solve
[tex]y - 2 = 2x-2[/tex]
=
[tex]y = 2x - 0[/tex]
hope you find this easy to understand....
Have any questions? Write in the comments.
give me brainliest if you found this answer useful
What set of reflections and rotations would carry rectangle ABCD onto itself? Parallelogram formed by ordered pairs A at negative 4, 1, B at negative 3, 2, C at 0, 2, D at negative 1, 1. Rotate 180°, reflect over the x-axis, reflect over the line y = x Reflect over the x-axis, rotate 180°, reflect over the x-axis Rotate 180°, reflect over the y-axis, reflect over the line y = x Reflect over the y-axis, reflect over the x-axis, rotate 180°
Answers
The only transformation that would carry rectangle ABCD onto itself is a single rotation of 180 degrees in a parallelogram.
Rectangle ABCD's characteristics and how each transformation affects its orientation and location must be examined in order to identify the collection of reflections and rotations that would carry the rectangle onto itself of a parallelogram.
First, using the provided coordinates, let's determine the sides of the rectangle: AB is parallel to DC, and AD is parallel to BC. Also, we can observe that the lengths of AB and AD are equal to DC and BC, respectively, indicating that the opposite sides are congruent.
The rectangle is first suggested to be rotated 180 degrees. This transformation simply maps each point to its corresponding point on the rectangle; the rectangle's orientation is left unchanged. Hence, rectangle ABCD would be carried onto itself by this transformation alone.
The rectangle is first reflected over the x-axis, rotated 180 degrees, and then reflected once more over the x-axis is the second transformation suggested. This series of transformations flips the rectangle's orientation while mapping each point to its equivalent point on the other side of the rectangle. Hence, the rectangle ABCD would not be carried onto itself by this transformation sequence.
The third suggested transformation involves reflecting the rectangle first over the y-axis, then over the line y = x, and then back over the y-axis. The rectangle's orientation is maintained but its position is altered by this series of modifications. Hence, the rectangle ABCD would not be carried onto itself by this transformation sequence.
The rectangle is to be rotated 180 degrees, reflected over the line y = x, and then reflected over the x-axis as the fourth transformation suggested. Each point is moved and mapped to a point on the other side of the rectangle via this series of transformations. The rectangle's orientation is also altered, though. Hence, the rectangle ABCD would not be carried onto itself by this transformation sequence.
Hence, a single 180° rotation is the only transformation that could turn rectangle ABCD upon itself.
In conclusion, we studied the features of the rectangle and the consequences of each transformation on its orientation and location to find the set of reflections and rotations that would transport rectangle ABCD onto itself. In contrast to the other suggested transformations, we discovered that only a single rotation of 180 degrees would keep the rectangle's orientation and location intact.
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+10 and -10, are 10 units from 0 on the number line. Enter the correct answer.
Answers
It is true that +10 and -10, are 10 units from 0 on the number line
How to determine the true statementfrom the question, we have the following parameters that can be used in our computation:
Numbers = +10 and -10
The number of units of these numbers from 0 is calculated as
Units = |0 - Number|
So, we have
Units = |0 - 10| = 10
Units = |0 + 10| = 10
This means that the number of units is 10
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Pizza Paradise recently sold 15 pizzas, 5 of which were pepperoni pizzas. Consider this data, how many of the next 75 pizzas sold would you expect to be pepperoni pizzaas?
Answers
5/15 = x/75
Cross multiply:
5 • 75 = 15x
Simplify:
375 = 15x
Solve for x:
375 / 15 = x
x = 25
25 pizzas.
can someone help me with this please..........
Answers
Answer:
m = [tex]\frac{y-b}{x}[/tex]
Hope this helps!
Step-by-step explanation:
y = mx + b
mx = y - b
[tex]\frac{mx}{x}[/tex] = [tex]\frac{y-b}{x}[/tex]
m = [tex]\frac{y - b}{x}[/tex]
emily is repaving her backyard patio space in the shape shown below. to order the correct number of concrete pavers, she needs to calculate the area of the patio. what is the area of emily’s patio?
Answers
The area οf Emily's patiο is 1,896 square feet.
What is square?A square is a geοmetric shape with fοur equal sides and fοur equal angles (90 degrees each). It is a special case οf a rectangle where all sides are οf equal length. The area οf a square is calculated by multiplying the length οf οne side by itself, which is expressed as side^2 οr s^2, where s is the length οf a side.
Tο calculate the area οf the patiο, we need tο first find the dimensiοns οf each rectangle that make up the patiο.
The first rectangle has a length οf 15 feet and a width οf 20 feet. Its area is:
Area οf the first rectangle = length x width = 15 ft x 20 ft = 300 square feet
The secοnd rectangle has a length οf 38 feet and a width οf 42 feet. Its area is:
Area οf the secοnd rectangle = length x width = 38 ft x 42 ft = 1,596 square feet
Tο find the tοtal area οf the patiο, we need tο add the areas οf the twο rectangles:
Tοtal area οf the patiο = Area οf the first rectangle + Area οf the secοnd rectangle
Tοtal area οf the patiο = 300 square feet + 1,596 square feet = 1,896 square feet
Therefοre, the area οf Emily's patiο is 1,896 square feet.
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I need Helpppp my teacher sucks at teaching
Answers
4. A person has a beginning balance of $3,320. She charges $1,260 on the 10th day, and
she charges $270 on the 22nd day. What is her account's average daily balance?
a.
b.
d.
e.
$4,283
$4,367
$4,231
$4,345
$4,226
०२८
Ook d
Answers
Answer: (D) $4,345.
Step-by-step explanation:
Help what’s 5/8 divided by 6
Answers
hope this helps
Answer:
5/48
Step-by-step explanation:
the first thing you would do is change 6 into the reciprocal, which is 1/6. After, you multiply the fractions just like that.
hope this helps!! :3
What is 518.1 rounded to the nearest whole number?
Answers
Answer:
518
Step-by-step explanation:
Since you are rounding to the nearest whole number.
518.1 would need to be 518.5 or higher to be 519 so anything below that would just round up the 518
An isosceles trapezoid has a perimeter of 56.2 millimeters. Its shorter base measures 9.2 millimeters and its longer base measures 12.4 millimeters. The two remaining sides have the same length; what is that length?
Answers
The length of the remaining two equal sides is 17.3 millimeters.
What is Triangle ?
A triangle is a geometric shape that consists of three line segments or sides and three angles. Triangles are one of the basic shapes in geometry, and they are used extensively in many fields of mathematics, science, engineering, and art.
Let's denote the length of the remaining two equal sides by "x".
Since the trapezoid is isosceles, the two equal sides have the same length.
The perimeter of a trapezoid is the sum of the lengths of all its sides. Therefore, we can set up an equation based on the information given:
shorter base + longer base + 2(equal sides) = perimeter
Substituting the values we know, we get:
9.2 + 12.4 + 2x = 56.2
Simplifying the equation:
21.6 + 2x = 56.2
2x = 34.6
x = 17.3
Therefore, the length of the remaining two equal sides is 17.3 millimeters.
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a student has scores of 84%, 71%, 86%, and 73% on four exams. what grade does the student need on the next exam to have an overall mean of 80%?
Answers
Answer:
Step-by-step explanation:
So, first you add the four exam percentage which will be 314 then you multiply 80 and 5. We use 5 because there are total 5 exams which will give the mean of 80%. After you get the answer for 80x5 which will be 400. Then you do, 400 - 314 which will be 86. So, the answer is 86%. To figure out if that answer is right, You add all the scores percentage and divide that by 5 and you should get 80%.
To have an overall mean of 80% after five exams, the student needs to score 88% on the next exam.
To find the student's overall mean, we need to add up all the scores and divide by the number of exams.
We have 4 exams scores:84%, 71%, 86%, and 73%.
Therefore, the total of the four exam scores is:
84% + 71% + 86% + 73% = 314%
To find the overall mean after five exams, the total score after five exams should be 5 × 80% = 400%.
Therefore, to have an overall mean of 80%, the student must score (400 - 314)% on the fifth exam, which is equivalent to: 86%.
Hence, the student needs to score 86% on the next exam to have an overall mean of 80%.
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The surface of a cylinder is represented , where r is the radius of the cylinder and h is its height. Factor the right side of the formula.
Answers
The formula for the surface area of a cylinder is:
S = 2πrh + 2πr²
To factor the right side of the formula, we can first take out the common factor of 2πr:
S = 2πr(h + r)
Therefore, the right side of the formula can be factored as 2πr(h + r).
can yall help me this please?
Answers
Answer:
-31/30
Step-by-step explanation:
-5/6 + 1/3 Times -3/5
-5/6 - 1/5
pls answer need help
Answers
The equation of the graph are
y = -0.5x + 1How to find the equation of the graphsFor the straight line graph, the equation of a straight line is of the formula
y = mx + b
where m is the slope and b is the y intercept
solving for the slope, using (2, 0) and (6, -2)
m = (0 - -2) / (2 - 6)
m = 2 / -4
m = -0.5
Equation of a line of slope -0.5 passing through point (2, 0)
y - 0 = -0.5(x - 2)
y = -0.5x + 1
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A diagram of a porch is shown. If the distance are measured in meters, find the area or the porch.
28 m
32 m
40 m
24 m
Answers
Answer: The answer is B, or 32 m.
Step-by-step explanation:
Answer:
32
Step-by-step explanation:
Select the survey question that will produce categorical data. A. How long does it take to finish math homework each night? B. How much time do you spend on social media each day? C. What were the class scores on the last math quiz? D. What is your favorite snack food?
Answers
Answer:
3
Step-by-step explanation:
cdawwwwwwWhat is the answer to the question?
Answers
You can follow the order of operations with all of the other operations in the equation and treat the operations in the expression separately. Option 2.
Order of operationsThe order of operations is a set of rules that dictate the sequence in which mathematical operations should be performed in an expression. These rules are designed to ensure that the expression is evaluated correctly and consistently.
When interpreting an expression as a given quantity, you are essentially substituting a value for a variable in the expression. This does not contradict the order of operations because the rules still apply, but the variables in the expression are treated as known values rather than unknown variables.
For example, if you have the expression 2 + 3 × 4, following the order of operations, you would first perform the multiplication (3 × 4 = 12) and then add the result to 2 (2 + 12 = 14).
If you are asked to interpret this expression as a given quantity when x = 3, you would substitute 3 for x and get 2 + 3 × 4 = 14, which is the same result obtained by following the order of operations.
In short, interpreting an expression as a given quantity does not contradict the order of operations because the rules still apply, but the variables in the expression are treated as known values.
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a person on a 2,500 calorie diet states that they are healthier than a person on a 2,000 calorie diet because they eat more from veggies.Explain why this is or is not accurate.?????
please help i need it now pleas.
Answers
t is not accurate to claim that someone is healthier simply because they consume more calories or more vegetables. A variety of factors, including the quality and nutrient density of the food consumed, physical activity levels, genetics, and overall lifestyle choices, all contribute to overall health. Therefore, it is important to consider a comprehensive approach to evaluating health rather than relying solely on calorie intake as a metric.
What is genetic?
Genetics refers to the study of genes, heredity, and variation in living organisms. Genes are segments of DNA that contain instructions for building and maintaining an organism, and they are passed down from parents to their offspring through reproduction.
Simply comparing the number of calories consumed by two individuals is not a sufficient way to determine who is healthier. While consuming a diet with a variety of vegetables can certainly contribute to good health, there are many other factors that can affect overall health.
For example, the quality and nutrient density of the food consumed is important, not just the quantity. A person consuming 2,000 calories from nutrient-dense whole foods, including a variety of vegetables, may be healthier than someone consuming 2,500 calories from highly processed, nutrient-poor foods.
Additionally, individual factors such as physical activity levels, genetics, and overall lifestyle choices can also impact overall health. Therefore, it is important to take a comprehensive approach to evaluating health rather than relying solely on calorie intake as a metric.
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of 4 goats give 4 kg milks in 4 days so how much milk given by 9 goats in 9 days?
Answers
Answer:
Step-by-step explanation:
supply. /. time. /. work
4. / 4 /. 4
1 /. 4. /. 1
9. /. 4 / 9
9 /. 9 / 20.25
you need to divide 9 by 4 and them multiply your 9 by what you got from the the division which is 2.25
Write equations of circles in standard form from graphs
Answers
The equation of the circle in standard form is (x - 3)²+ y² = 1.
What is equation of circle in standard form?The standard form of the equation of a circle is:
(x - h)² + (y - k)² = r²
where (h, k) is the center of the circle and r is its radius.
This equation represents all points in the xy-plane that are equidistant from the center (h, k) of the circle. The squared terms (x - h)² and (y - k)² represent the distances between the center and any point (x, y) on the circle, and r² is the squared length of the radius of the circle.
In the given question,
The center of the circle is (3, 0), and the radius extends to the point (4, 0), which means the radius has a length of 1 unit.
Substituting the values of the center and radius into the standard form equation of a circle, we get:
(x - 3)² + (y - 0)² = 1²
Simplifying, we get:
(x - 3)² + y² = 1
Therefore, the equation of the circle in standard form is:
(x - 3)² + y² = 1.
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Find the surface area of the triangular prism.
list the length, width, height, and base.
Answers
The surface area of the given figure is 90sq inches which include 3 rectangular faces and two triangular faces.
EquationsArea of 1 rectangular face is 6.5x5=32.5.
Area of 2 rectangular face is 5x6=30
Area of 3 rectangular face is 2.5x5=12.5
Area of the two triangluar faces= 2.5x6x0.5x2=15
Total area is 90 sq inches.
What is surface area of joined figures?To find the surface area of a joined figure, we need to add up the surface areas of all the individual components of the figure.
For example, if we have a figure made up of a rectangular prism and a pyramid attached to the top, we can find the surface area by first calculating the surface area of the rectangular prism:
Surface area of the rectangular prism = 2lw + 2lh + 2wh
Surface area of the pyramid = (1/2)3.14 + B
Finally, we add the surface area of the rectangular prism to the surface area of the pyramid to get the total surface area of the joined figure.
Total surface area = Surface area of the rectangular prism + Surface area of the pyramid
This method can be applied to any joined figure made up of multiple components. We just need to find the surface area of each individual component and then add them up.
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C is the midpoint of BD. Are these triangles similar, congruent or neither? What theorem supports your answer?
options:
Similar: SSS
Similar: SAS
Similar: HL
Congruent: AAS
Congruent: SAS
Congruent: HL
Neither
Answers
The given triangles are congruent by AAS congruence. The solution has been obtained by using the concept of congruent triangles.
What are congruent triangles?
Triangles which have the same size and the same shape are said to be congruent. This implies that the respective sides and angles of the triangles are both equal.
We are given two triangles as ABC and CDE in which C is the midpoint of BD.
So, from this, we get
⇒ AC = EC (Given)
⇒ ∠ABC = ∠CDE (Right Angle)
⇒ ∠ACB = ∠ECD (Common Angle)
Hence, the triangles are congruent by the AAS congruence.
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