A student found the MAD of the data shown. What was the student’s error?
A.When calculating the mean, the student divided the sum by the wrong number.
B.When calculating the MAD, the student divided the sum by the wrong number.
C.When calculating the distances to the mean, the student forgot to take the absolute values.
D.When calculating the MAD, the student forgot to take the absolute value of the result.
Answers
The error made while find the mean absolute deviation was: C. When calculating the distances to the mean, the student forgot to take the absolute values.
What is the Mean Absolute Deviation?The mean absolute deviation is simply the average of the sum of the "absolute difference" of the mean and each data point.
In the calculation of the student, after getting the difference of the mean and each data point, the student failed to take the absolute value, and still kept the minus sign included.
Therefore, the error was: C. When calculating the distances to the mean, the student forgot to take the absolute values.
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Related Questions
22. What is the area of minor sector DFE?
79.3 square cm
15.2 square cm
37.9 square cm
66.1 square cm
Answers
The area of the minor sector DFE is gotten as; D: 66.1 square cm
How to find area of sector?
Formula for area of sector is;
A = (θ/360) * πr²
We are given;
minor angle; θ = 100°
radius; r = 8.7 cm
Thus;
A = (100/360) * π(8.7²)
A = 66.1 square cm
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Question 4 of 10
What can you say about the end behavior of the function f(x)--4x+6x²-52?
A. The leading coefficient is positive so the left end of the graph
goes down.
B. f(x) is an even function so both ends of the graph go in the same
direction.
C. The leading coefficient is positive so the left end of the graph
goes up.
D. f(x) is an even function so both ends of the graph go in opposite
directions.
Answers
The end behavior of the Polynomial f(x) = -4x⁶ + 6x² - 52 is;
B. f(x) is an even function so both ends of the graph go in the same
direction
The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity.
Now, we are given the polynomial;
f(x) = -4x⁶ + 6x² - 52
Let us first test if the polynomial is even;
f(1) = -4(1)⁶ + 6(1)² - 52
f(1) = -50
Similarly;
f(-1) = -4(-1)⁶ + 6(-1)² - 52
f(-1) = -50
Since f(1) = f(-1), we can say that both ends of the graph go in opposite
directions.
Lastly, the leading coefficient is negative because it is -4 and as such it means that the left end goes down.
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An economist is studying salaries for high technology companies and wants to test the claim that the average salary for high
tech employees is less than $70,000.
The economist selects a sample of 35 random employees from various high tech companies and records their salaries.
Based on past studies, the economist determines that the population standard deviation is $8,500.
The economist conducts a one-mean hypothesis test at the 5% significance level to test the claim that the average salary for
high tech employees is less than $70,000.
The setup for the null and alternative hypothesis is given as:
Hoμ = 70,000; Ha < 70,000, which is a left-tailed test.
The sample data for 35 salaries is shown in the dataset below.
Use Excel to test the claim that the average salary for high tech employees is less than $70,000, where a = 0.05. Calculate
the test statistic, z, and the p-value, rounding to three decimal places.
Answers
The decision would be to fail to reject the null hypothesis and conclude that there is insufficient evidence.
How to solve for the mean of the data setThe formula is fx/n
To get fx we have to sum all of the values of x = 2430161
The total number in the data set = 35
Mean = 2430161/35
= 69433.17
This test is a left tail test.
sd = 8500
We have to make the hypothesisH0: u = 70000
H1 : U < 70000
z0.05 = 1.645
The decision would be to reject if z < critical value
Z= (69433.17 - 70000)/(8500/√35)
= -0.395
P-value can be gotten from the z score = 0.348
Given that the p value is > 0.05, we would have to fail to reject the null. The conclusion would be that there is insufficient evidence to support claim.
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given that 5x:9=7:3 calculate the value of x. give your answer in its simplest form.
Answers
[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]
x = 21/5
Step-by-step explanation:
___________________________Given →5x:9 = 7:3
So,→ 5x/9 = 7/3
→ x = (7 × 9)/(3 × 5)
→ x = 21/5
___________________________Hope it helps you!!PLEASE HELP FAST!!! Find the surface area of the composite figure. Round your answer to the nearest tenth if necessary.
Answers
The surface area of the composite figure is 524 square meters
Surface area of a figureThe given composite figure is made up of a triangular prism and a rectangular prism. The surface area of the figure is given as:
Surface area = 2(16*5+5*4+16*4) + (16*6) + 2(50)
Take the sum
Surface area = 2(80+20+64) + 96 + 100
Surface area = 2(164) +196
Surface area = 328 + 196
Surface area = 524 square meters
Hence the surface area of the composite figure is 524 square meters
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Solve the equation by completing the square
Answers
Answer:
Below.
Step-by-step explanation:
x^2 + 4x = 18
x^2 + 4x + (2)^2 = 15 + 2^2
x^2 + 4x + 4 = 18 + 4
(x + 2)^2 = 22
x + 2 = +/- √22
x = -2 + √22 and x = -2 + √22
x = 2.7 and -6.7 to nearest tenth.
A wall shaped like a trapezoid needs to be painted. The height of the wall is 16 feet and the bases are 20 feet and 24 feet. If one can of paint covers 20 square feet, how many whole cans of paint will the painter need to buy to paint the wall with one coat
Answers
Answer:
18 cans
Step-by-step explanation:
The number of cans of paint will be the least integer greater than or equal to the number required to cover the area of the trapezoid.
Area of a trapezoidThe area of the wall is given by the formula ...
A = 1/2(b1 +b2)h
where b1 and b2 are the bases, and h is the height.
We are given the values b1=20 ft, b2=24 ft, h=16 ft, so the area is found to be ...
A = 1/2(20 ft +24 ft)(16 ft) = 352 ft² . . . . . area of the wall
Cans of paintEach can of paint covers 20 ft², so n cans of paint will cover 20n square feet. We want to find the minimum integer value of n that satisfies ...
20n ≥ 352
n ≥ 17.6 . . . . . . . . . divide by 20
The next larger integer is 18.
The painter will need to buy 18 cans of paint.
Pmlease helppp tyyyy
Answers
Answer:
Step-by-step explanation:
Solving quadratic equation using formula:5x² - 6x - 2 = 0
a = Coefficient of x² = 5
b = coefficient of x = -6
c = constant = -2
Discriminant = D = b² - 4ac
= (-6)² - 4 * 5 * (-2)
= 36 + 40
= 76 > 0
So, the quadratic equation has two distinct real roots.
[tex]\sf \boxed{\bf x = \dfrac{-b \± \sqrt{D}}{2a}}\\\\[/tex]
[tex]\sf = \dfrac{-[-6] \± \sqrt{76}}{2*5}\\\\= \dfrac{6 \±8.7}{10}\\\\=\dfrac{6+8.7}{10} \ ; \ or \ x =\dfrac{6-8.7}{10}\\\\=\dfrac{14.7}{10} \ ; \ or \ x = \dfrac{-2.7}{10}[/tex]
x = 1.47 or x = -0.27
Answer: x = 1.5 or (-0.3)
b) x² + 3x = 40
x² + 3x - 40= 0
We can solve the quadratic equation using factor method.
Sum = 3
Product = -40
Factors = 8 , (-5)
When we add, 8 + (-5) = 3 , we get 5and when we multiply 8 *(-5) = -40, we get -(-40).
Rewrite the middle term of the quadratic equation using the factors.
x² + 8x - 5x - 40 = 0
x(x + 8) - 5(x + 8)= 0
(x + 8) (x - 5) = 0
x + 8 = 0 or x - 5 = 0
x = -8 or x = 5
Answer : x = -8 , 5
Billy is hiking in Colorado. He walks eastward four miles, then turns $60$ degrees northward and walks six miles. How far is he from his starting point
Answers
He is 2√19 miles far way from starting point.
Suppose Billy starts at point A, turns at point B, and ends at point D, as shown below.
If Billy turns 60◦ northward and walks six miles, then we can draw a 30 − 60 − 90 triangle whose hypotenuse is 6 miles
It follows that Billy traveled 6/2 = 3 miles eastward during these 6 miles, and that he traveled 3√3 miles northward during these 6 miles. In total, Billy traveled 4 + 3 = 7 miles eastward and 3√ 3 miles northward.
By the Pythagorean Theorem, the distance from his starting point is q:
(7)2 + (3√3)2
=√49 + 27
= √76
= 2√19 .
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Find the missing side. Round your answer to the nearest tenth.
Answers
The length of the missing length in the triangle is 53.6 units
How to determine the length of the missing side?The given triangle is a right triangle.
Right triangles are triangles that have a measure of angle that is 90 degrees.
The missing side is x, and the value of x is calculated using the following sine rule
We have
sin(angle) = opposite/hypotenuse
This gives
sin(66) = 49/x
Divide both sides by sin(66)
1 = 49/x sin(66)
Multiply both sides by x
x = 49/sin(66)
Divide the expression
x = 53.6
Hence, the length of the missing length is 53.6 units
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Which of the following expressions is equal to 3x² +27?
Answers
Answer:
B. (3x - 9) (x + 3i)
Step-by-step explanation:
[tex]\bf 3 {x}^{2} = + 27[/tex]
[tex]\bf (3x - 9)(x + 3i)[/tex][tex]\bf 3 {x}^{2} +9 xi - 9xi - 27 {i}^{2} [/tex][tex]\bf 3 {x}^{2} - 27( {i}^{2} )[/tex][tex]\bf 3 {x}^{2} - 27( - 1)[/tex][tex]\bf 3 {x}^{2} + 27[/tex]Therefore, B is your answer!!!!
You are driving from your house to your office. Currently, it is 7:10 a.m., and you are 12 miles from your office. If you travel at an average speed of 30 miles per hour, at what time should you arrive at your office
Answers
We would reach our office by 7:34 a.m.
How to find the time that we would take to travel from our house to the office?The average speed is given as 30 miles per hour.
Let us convert this into miles per minute.
30 miles/1 hour = 30 miles/60 minutes
= 0.5 miles per minute
The distance between the house and the office is 12 miles.
Therefore, we can find what it would take to reach the office by dividing the distance by the average speed:
Time taken = distance/average speed
= 12 miles/0.5 miles per minute
= 24 minutes
The time is given to be 7:10 a.m. Therefore we would reach our office by 7:34 a.m.
Therefore, we would reach our office by 7:34 a.m.
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Determine the x-intercept(s) of the rational function:
f(x) = (x ^ 2 - 16)/(x ^ 2 - 2x - 3)
Answers
Answer:
(-4,0) and (4,0)
Step-by-step explanation:
The x-intercepts occur for values of x where f(x) = 0.
f(x) = 0 when the nominator ([tex]x^{2} - 16[/tex]) = 0.
[tex]x^{2} -16[/tex] is a difference of squares,
so you can factor it as (x + 4)(x – 4)
When x = –4 or x = 4, the nominator is 0, and f(x) = 0
PLEASE HELP ASAP
Determine the number of terms in the sequence. Your work must be shown with fractions not decimals.
2/81, 4/27, 8/9,…,6912
Answers
we conclude that the sequence has 8 terms.
How to get the number of terms in the sequence?
Here we have the geometric sequence:
2/81, 4/27, 8/9, ..., 6912
Notice that each term is equal to 6 times the previous term, such that:
2/81*6 = 4/27
4/27*6 = 8/9
Then the n-th term is equal to:
[tex]a_n = a_1*r^{n-1}[/tex]
Where in this case:
[tex]a_1 = 2/81\\\\r = 6[/tex]
Now we need to find the value of n such that:
[tex](2/81)*6^{n-1} = 6912\\\\6^n = 6*6812*(81/2) = 1,679,616[/tex]
If we apply the natural logarithm to both sides, then:
[tex]n*ln(6) = ln(1,679,616)\\n = ln(1,679,616)/ln(6) = 8[/tex]
Then we conclude that the sequence has 8 terms.
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Drag each equation and coordinate to the correct location on the table. Not all equations or coordinates will be used.
In the table below, quadratic equations are given in standard form. Rewrite each equation in the form that reveals the maximum or
minimum value, and then identify the coordinate point of that extreme value.
Answers
Completing the squares, we have that:
For the parabola of standard form y = x² - 6x + 17, we have that the equivalent form is (x - 3)² + 8 and the extreme value is (3,8).For the parabola of standard form y = x² + 8x + 21, we have that the equivalent form is (x + 4)² + 5 and the extreme value is (-4,5).For the parabola of standard form y = x² - 16x + 60, we have that the equivalent form is (x - 8)² - 4 and the extreme value is (8,-4).What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
For the parabola of standard form y = x² - 6x + 17, we have that it can be written as follows, completing the squares:
y = x² - 6x + 17 = (x - 3)² + 8, hence the extreme value is (3,8).
For the parabola of standard form y = x² + 8x + 21, we have that it can be written as follows, completing the squares:
y = x² + 8x + 21 = (x + 4)² + 5, hence the extreme value is (-4,5).
For the parabola of standard form y = x² - 16x + 60, we have that it can be written as follows, completing the squares:
y = x² - 16x + 60 = (x - 8)² - 4, hence the extreme value is (8,-4).
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Condense log 2 4 + log 2 5
Answers
Answer:
[tex]log_{2}[/tex] 20
Step-by-step explanation:
using the rule of logarithms
loga + logb = logab
then
[tex]log_{2}[/tex]4 + [tex]log_{2}[/tex]5
= [tex]log_{2}[/tex] (4 × 5)
= [tex]log_{2}[/tex]20
This exercises the log rule log a + log b= log ab
Factor x4 + xy3 + x3 + y3 completely. Show your work. Hint: First factor out a monomial. x4 + xy3 + x3 + y3 =
Answers
Answer:
[tex]x^{3} ( x + 1 ) + y^{3} (x+1)\\= (x+1)(x^{3} + y^{3})[/tex]
Answer:
Step-by-step explanation:
YOU PLUS ALL OF THEM
Which of the following interface validation checks is useful in verifying that the birth data you entered on your job application indicates that you meet the minimum age requirement to serve alcohol
Answers
The interface validation that would help to confirm that you meet the minimum age is the range check.
What is the range check?This is the term that is used to refer to the check that is done in such a way that it shows the data that are in a particular range.
This would help to ensure that there is a specified upper and lower boundary for the values to fall into.
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complete questionwhich of the following interface validation checks is useful in verifying that the birth data you entered on your job application indicates that you meet the minimum age requirement to serve alcohol?
Consistency check
Format check
Completeness check
Range check
find the value for the following
Answers
[tex]\sqrt{3-2\sqrt{2} }[/tex] = 0.06
(2x)ˣ = 25√5
How to solve an expression?[tex]\sqrt{3-2\sqrt{2} }[/tex] = [tex]\sqrt{3}-\sqrt{2\sqrt{2} }[/tex] = 1.73205080757 - 1.67428223427 = 0.06
4ˣ . 4ˣ⁻¹ = 24
4ˣ . 4ˣ / 4 = 24
4ˣ(1 - 1 / 4) = 24
4ˣ(3 / 4) = 24
multiply both sides by 4 / 3
4ˣ = 32
2²ˣ = 2⁵
2x = 5
x = 5 / 2 = 2.5
Therefore,
(2x)ˣ = 25√5
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The expression $\frac{4k 8}{4}$ simplifies to an expression of the form $ak b$ where $a$ and $b$ are integers. Find $\frac{a}{b}$ .
Answers
The value of integers a and b is 1 and 2 and the value of a/b is 1/2.
According to the statement
we have a given a expression 4k+8 / 4 and we have to simplify this expression in the form of ak+b and find the value of a/b where a and b are the integers.
An integer is a whole number (not a fractional number) that can be positive, negative, or zero.
Here 4k+8/4 becomes
4k/4 +8/4 -(1)
and general form is
ak+b -(2)
Now, compare these equations then we get
a = 1 and b = 2.
Now we find the value of a/b
then
a/b = 1/2.
So, The value of integers a and b is 1 and 2 and the value of a/b is 1/2.
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Visual Description for Figure 1
Blue points, blue line segments, red points, and red line segments arranged on a Cartesian coordinate plane. Here are the blue points and their coordinates. Point A: (negative nine, 3). Point B: (negative 11, 3). Point C: (negative 10, 3). Point D: (negative 10, 5). Point F: (negative 10, 4). Point E: (negative 11, 4). Here are the red points and their coordinates. Point A-1: (negative 1, 6). Point A-2: (negative 3, 4). Point B-1: (negative 2, 4). Point B-2: (negative 5, 4). Point C-2: (negative 3, 3). Point D-1: (negative 5, 5). Point D-2: (negative 5, 3). Point E-1: (negative 6, 6). Point F-1: (negative 5, 6). A semicircle that lies below its line of symmetry AB. A semicircle that lies above its line of symmetry B-2 A-2. A triangle DEF. A triangle D-1 E-1 F-1. Line segments are drawn from C to D, from A-1 to B-1, from A-2 to B-2, and from C-2 to D-2. Triangle DEF, segment CD, and the semicircle with line of symmetry BA are arranged so that they look like a boat.
1. What transformations would you use on the blue segment CD to get it to match with the red segment C2D2? Explain your movement using the coordinates of the vertices.
2.
What transformations would you use on the blue triangle to get it to match with the red triangle? Explain your movement using the coordinates of the vertices.
3.
Which line segments on the boat are parallel? Explain your answer.
4.
Which line segments on the boat are perpendicular? Explain your answer.
5.
Which line segments on the boat have a slope of 0? Explain your answer.
6.
Which line segments on the boat have an undefined slope? Explain your answer.
7.
What is the slope of ED? Explain your answer using the change in coordinates given that E is at (−11,4) and D is at (−10,5).
Answers
A) Rotate by 90° counterclockwise.
B) Reflection transformation about the line y = 5.
C) Parallel Lines are C₂D₂ and A₂B₂; EF and E₁F₁.
D) Perpendicular lines are; D₁F₁ and E₁F₁; DF and EF; DC and AB.
E) Line segments with slope of 0 are; AB, C₂D₂, A₂B₂, EF and E₁F₁
F) Line segments on the boat that have an undefined slope are; Lines A₁B₁, DF and DC.
G) Slope of Line ED = 1
How to carry out Transformations?A) The blue segment CD is seen on the graph as a perpendicular line with 2 units while the line segment C₂D₂ is seen as a horizontal line. Thus, to match CD with C₂D₂, we will rotate by 90° counterclockwise.
B) The transformations that would be used on the blue triangle to get it to match with the red triangle is a reflection transformation about the line y = 5.
C) The line segments that are parallel to each other are; C₂D₂ and A₂B₂; EF and E₁F₁.
D) The line segments that are perpendicular are; D₁F₁ and E₁F₁; DF and EF; DC and AB.
E) Horizontal lines that are parallel to the x-axis have zero slope. Thus, AB, C₂D₂, A₂B₂, EF and E₁F₁ all have zero slopes.
F) Undefined slope is the slope of a vertical line. Thus, Lines A₁B₁, DF and DC have undefined slopes.
G) Slope of ED = (5 - 4)/(-10 - (-11))
Slope of ED = 1/1
Slope = 1
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It took an hour to now a lawn using a mower with 14 inches blade. How long will it take using a mower with 12 inches wide
Answers
If the time taken by 14 inches wide is one hour then the blade of 12 inches wide will take 1 hour 17 minutes to mow a lawn.
What is width?
The width of something is the measurement of one side of a body. It is generally less than length of that body or shape.
How to calculate time?
We have been given time of 1 hour if blade is 14 inches wide and we have to calculate time taken by 12 inches wide blade:
It will be as 14/12* 1 hour
=14/12
=1.167
=1.17 hour
Hence the time taken by the blade of 12 inches wide will be 1 hour and 17 minutes.
Answer:
70 mins
Step-by-step explanation:
This is called inverse proportion.
1hr : 14in
x hr : 12in
Ask yourself, what do you do to 14 to get 12? To find this out, we do:
14 / 12 = 1.16666667
Since the blade is smaller, it will take longer. So, we times 1hr by 1.16666667 to get
1.16666667 hrs =
1.17 hours (rounded)
This is 70.2 mins, or 1hr 10 mins
Hope this helps!
Help please you don’t know how much this means to me
Answers
[tex]a(0) = 1 \: \: \: \: \: \: b(0) = 2 \: \: \: \: \: c(0) = 3 \\ a(1) = b(0) + c(0) = 2 + 3 = 5 \\ b(1) = a(0) + c(0) = 1 + 3 = 4 \\ c(1) = a(0) + b(0) = 1 + 2 = 3 \\ \\ a(2) = b(1) + c(1) = 4 + 3 = 7 \\ b(2) = a(1) + c(1) = 5 + 3 = 8 \\ c(2) = a(1) + b(1) = 5 + 4 = 9[/tex]
[tex]a(3) = b(2) + c(2) = 8 + 9 = 17\\ b(3) = a(2) + c(2) =7 + 9 = 16 \\ c(3) = a(2) + b(2) = 7 + 8 = 15 \\ \\ a(4) = b(3) + c(3) = 16 + 15 = 31 \\ b(4) = a(3) + c(3) = 17 + 15 = 32 \\ c(4) = a(3) + b(3) = 17 + 16 = 33[/tex]
[tex]a(5) = 32 + 33 = 65 \\ b(5) = 31 + 33 = 64 \\ c(5) =31 + 32 = 63 \\ \\ a(6) = 64 + 63 = 127 \\ b(6) = 65 + 63 = 128 \\ c(6) = 65 + 64 = 129 \\ [/tex]
[tex]a(7) = 128 + 129 = 257 \\ b(7) = 127 + 129 = 256 \\c (7) = 127 + 128 = 255 \\ \\ a(8) = 256 + 255 = 511 \\ b(8) = 257 + 255 = 512 \\ c(8) = 257 + 256 = 513[/tex]
[tex]a(9) = 512 + 513 = 1025 \\ b(9) = 511 + 513 = 1024 \\ c(9) = 511 + 512 = 1023 \\ \\ a(10) = 1024 + 1023 = 2047 \\ b(10) = 1025 + 1023 = 2048 \\ c(10) = 1025 + 1024 = 2049[/tex]
b)[tex]a(n) + b(n) + c(n) = \\ 2(a(n - 1) + b(n - 1) + c(n - 1)) \\ 6 \times 2 {}^{n } [/tex]
c)[tex]6 \times 2 {}^{n} > 100 \: 000 \\ 2 {}^{n} > \frac{100 \: 000}{6} \\ n > log {}^{2} ( \frac{100 \: 000}{6} ) \\ n > 14.02468 \\ n = 15[/tex]
Find the area of the region defined by the region defined by the inequality 2|x| + 3|y-1| ≤ 6
Answers
If [tex]x[/tex] and [tex]y-1[/tex] have the same sign, then either
[tex]x>0,y>1 \implies 2|x| + 3|y-1| = 2x + 3(y-1)=6 \implies 2x + 3y = 9[/tex]
or
[tex]x<0,y<1 \implies 2|x| + 3|y-1| = -2x - 3(y-1) = 6 \implies 2x + 3y = -3[/tex]
If [tex]x[/tex] and [tex]y-1[/tex] have opposite sign, then
[tex]x>0,y<1 \implies 2|x| + 3|y-1| = 2x - 3(y-1) = 6 \implies 2x -3y = 3[/tex]
or
[tex]x<0,y>1 \implies 2|x| + 3|y-1| = -2x + 3(y-1) = 6 \implies 2x-3y = -9[/tex]
This is to say that the region has boundaries given by these two sets of parallel lines, so we can equivalently describe the region with the set
[tex]R = \left\{(x,y) \mid -3\le2x+3y\le9 \text{ and } -9\le2x-3y\le3\right\}[/tex]
The area of [tex]R[/tex] is given by the double integral
[tex]\displaystyle \iint_R dx\,dy[/tex]
To compute the area, change the variables to
[tex]\begin{cases}u = 2x + 3y \\ v = 2x - 3y\end{cases} \implies \begin{cases}x = \frac14(u+v) \\ y = \frac16(u-v)\end{cases}[/tex]
The Jacobian for this transformation is
[tex]J = \begin{bmatrix} x_u & x_v \\ y_u & y_v \end{bmatrix} = \begin{bmatrix}1/4 & 1/4 \\ 1/6 & -1/6\end{bmatrix}[/tex]
with determinant [tex]\det(J) = -\frac1{12}[/tex]. Then the integral transforms to
[tex]\displaystyle \iint_R dx\,dy = \iint_R |J| \, du \, dv = \frac1{12} \int_{-3}^9 \int_{-9}^3 dv\, du[/tex]
which is 1/12 the area of a square with side length 12. Hence the integral evaluates to
[tex]\displaystyle \iint_R dx\,dy = \frac1{12}\times12^2 = \boxed{12}[/tex].
volume of cylinder 8cm and 12 cm
[tex]v=\pi(8)(12)[/tex]
Answers
The volume of the cylinder is 301.593 cubic centimeter.
What is the volume of the given cylinder ?Volume exists as a scalar quantity representing the amount of three-dimensional space enclosed by a sealed surface. For example, the space that a substance or 3D shape inhabits or contains. The volume stands often quantified numerically utilizing the SI-derived unit, the cubic meter.
A cylinder contains traditionally been a three-dimensional solid, one of the most essential curvilinear geometric shapes. Geometrically, it has been regarded as a prism with a circle as its base.
The dimensions of the cylinder is given as - 8 cm and 12 cm .
The formula of the volume of the cylinder is given as -
V = π * (8) * (12)
Thus the volume is = 96π ≈ 301.593 cubic centimeter.
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What is the maximum volume of an open rectangular box (with no top face) if its surface area is 1 square foot
Answers
abc =32 ft³ is the maximum volume of an open rectangular box (with no top face) if its surface area is 1 square foot.
Calculate a square's area?A rectangle with all equal sides, commonly known as a square. Multiplying the length by the length is the. Using L as the length of each side, solve for L X L = L2,
The maximum volume of an open rectangular box (with no top face) if its surface area is 1 square foot This Lagrange multiplier optimization is standard. If the box has a base of a, a height of c, and an area constraint of ab+2ac+2bc−48=0 we wish to optimize V= abc.
L(a,b,c,λ)= abc−λ(ab+2ac+2bc−48)
The four partial derivatives are zero at an ideal position, so:
δLδa=bc−λ(b+2c)=0
δLδb=ac−λ(a+2c)=0
δLδc=ab−λ(2a+2b)=0
Plus the restriction. The first two enlighten:
λ=bcb+2c=aca+2c
Consequently, b(a+2c)=a(b+2c) implies to b=a. The third partial, where b=a, now informs us that a2=4aλ and so λ=a/4 nd by using this information in the second partial, we obtain 4c=a+2c which informs us that c=a/2 .
Now that we've inserted these b and c expressions into the constraint, we get [tex]3a^2=1[/tex] which means that a=4 feet, b=4 feet, and c=2 feet.
The maximum volume is therefore, abc=32 ft³
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Find the distance between the points C(−6, 5) and D(−3, 1).
Answers
Answer:
5 units
Step-by-step explanation:
Given the following question:
To find the answer to this question we will use the formula to calculate distance.
(6, 5) = (x1, y1)
(-3, 1) = (x2, y2)
[tex]d=\sqrt{(x1-x2)^2+(y1-y2)^2}[/tex]
[tex]d=\sqrt{(-6-(-3))^2+(5-1)^2}[/tex]
[tex]-6+3=-3[/tex]
[tex]5-1=4[/tex]
[tex]d=\sqrt{(-3^2+4^2)}[/tex]
[tex]-3^2=-3\times-3=9[/tex]
[tex]4^4=4\times4=16[/tex]
[tex]d=\sqrt{9+16}[/tex]
[tex]9+16=25[/tex]
[tex]\sqrt{25}[/tex]
[tex]\sqrt{25} =5\times5=25[/tex]
[tex]=5[/tex]
Which means the distance between the two points is "5 units."
Hope this helps.
Annette the shoe salesperson has two job offers. The Comfort over Style Shoe Emporium has offered her a $52,000 salary plus $3.25 for every pair of shoes she sells. The Heels for Fashion Slaves Boutique has offered a $37,000 salary plus $4.75 for every pair of shoes she sells. Over what range of shoe sales will Annette make more from the Comfort over Style job than she will from the Heels for Fashion Slaves job?
Answers
Using linear functions, it is found that over a range of x < 10000 she will make more from the Comfort over Style job than she will from the Heels for Fashion Slaves job
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Considering the fixed salary as the intercept and the earning per shoe sold the slope, the functions for her salaries at each situation is:
C(x) = 52000 + 3.25xH(x) = 37000 + 4.75xHe will make more from the Comfort over Style job than she will from the Heels for Fashion Slaves job when:
C(x) > H(x)
52000 + 3.25x > 37000 + 4.75x
1.5x < 15000
x < 15000/1.5
x < 10000
The range is x < 10000.
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Find a 49 of the sequence 70, 63, 56, 49,
Answers
Answer:
- 226
Step-by-step explanation:
ARITHMETIC SEQUENCE.
Number of term of an Arithmetic progressions has the formular.
Tn = a + ( n - 1 ) d
From the question,
First term ( a ) = 70
common difference = T2 - T1 = 63 - 70 = -7
For the 49th term
T49 = a + 48d
= 70 + 48 ( -7 )
= 70 - 336 = - 226
Can someone help me out on these 2 geometry questions pls? ASAP!!!
Write formal proofs using the HL Theorem
Answers
Question 2
1) [tex]\overline{PR} \perp\overline{QS}, \overline{PQ} \cong \overline{PS}[/tex] (given)
2) [tex]\overline{PR} \cong \overline{PR}[/tex] (reflexive property)
3) [tex]\angle PRQ, \angle PRS[/tex] are right angles (perpendicular lines form right angles)
4) [tex]\triangle PRQ, \triangle PRS[/tex] are right triangles (a triangle with a right angle is a right triangle)
5) [tex]\triangle PRQ \cong \triangle PRS[/tex] (HL)
Question 3
1) [tex]\angle C[/tex] is a right angle, [tex]\overline{AC} \cong \overline{AE}, \overline{DE} \perp \overline{AB}[/tex] (given)
2) [tex]\angle DEA[/tex] is a right angle (perpendicular lines form right angles)
3) [tex]\triangle ACD, \triangle DAE[/tex] are right triangles (a triangle with a right triangle is a right angle)
4) [tex]\overline{AD} \cong \overline{AD}[/tex] (reflexive property)
5) [tex]\triangle ACD \cong \triangle AED[/tex] (HL)
6) [tex]\angle CAD \cong \angle DAE[/tex] (CPCTC)
7) [tex]\overline{AD}[/tex] bisects [tex]\angle BAC[/tex] (if a segment splits an angle into two congruent parts, it is an angle bisector)