A small block is sent through point A with a speed of 6.8 m/s. Its path is without friction until it reaches the section of length L=14 m, where the coefficient of kinetic friction is 0.78. The indicated height are h₁ =5.4 m and h₂=2.8 m. The speeds of the block at (a) Point B is 108m/s and (b) Point C is 7.6m/s
The velocity of an object (usually denoted v) is the amount of its position change over time ; therefore it is a scalar quantity. The average speed of an object over a time interval is the distance traveled by the object divided by the duration of the interval; the instantaneous speed remains zero.
(a) At B the speed is :
V = [tex]\sqrt{V^{2}+2gh_1 }[/tex]
⇒ V = [tex]\sqrt{(6.8m/s)+ 2(9.8m/s^2) (5.4)}[/tex]
⇒ V = 108.44 m/s
⇒ V = 108 m/s
(b) Here, matters is the difference in heights (between A and C):
[tex]V = \sqrt{V_0^{2}+2g(h_1+h_2) }[/tex]
⇒ [tex]V = \sqrt{(6.8)+2 (9.8) (5.4- 2.8) }[/tex]
⇒ [tex]V = \sqrt{6.8 +2(9.8)(2.6)}[/tex]
⇒ √57.76 = 7.6m/s
(c) Using the results from part (b), we see that its kinetic energy is just at the beginning of its "rough glide" (horizontally to D) is:
1/2 m(7.6m/s)² = 28.88m (with SI units understood).
We note that this kinetic energy will turn entirely into thermal energy
28.88m = μₙ mgd
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Solve the triangle MNO (find the measure of ∠O and the lengths of sides MO and NO).
(I need help finding both side measures and angle measure please and thank you
Answer:
Step-by-step explanation:
m∠O = 90° - 34° = 56°
cos M = [tex]\frac{MN}{MO}[/tex] ⇒ MO = [tex]\frac{12}{cos34}[/tex] ≈ 14.5 cm
tan M = [tex]\frac{ON}{MN}[/tex] ⇒ ON = 12 × tan 34° ≈ 8.1 cm
An avid gardener wants to know which of two brands of fertilizer is best for her tomatoes. The two brands of fertilizer are A and B. She plants five pairs of tomato plants in two rectangular planters and places them beside one another. She gives each set of tomato plants the same amount of water each day, only she gives one set of plants fertilizer A and the other set of plants fertilizer B. At the end of the growing season, she counts the number of tomatoes each plant has yielded. Assume that all conditions for inference have been met. The rectangular planters are lined up so that plant 1 is beside plant 6, and plant 2 is beside plant 7, and so on. The yield for the five pairs of tomato plants are given. Plant 1 2 3 4 5 Yield with Fertilizer A 7 6 5 8 10 Plant 6 7 8 9 10 Yield with Fertilizer B 4 7 6 5 3 The gardener believes that fertilizer A enhances the yield of her tomatoes more than fertilizer B. She uses the following order of subtraction when determining the difference in the yields for the two brands: A- B (a) We would like to carry out a t test for the population mean difference. Calculate the point estimate. (b) Calculate the standard deviation of the differences. (Round your answer to three decimal places.) (c) Calculate the test statistic. (Round your answer to two decimal places.)
(a) Point estimate (mean difference): 2.2 tomatoes. (b) The standard deviation of differences: Approximately 3.47. (c) The test statistic: Approximately 1.38.
To perform a t-test for the population mean difference, follow these steps:
(a) Calculate the point estimate (mean difference): The point estimate is the mean difference between the yields of fertilizer A and fertilizer B.
Mean difference = (Sum of differences) / Number of pairs
Using the given data gives:
Mean difference = ((7-4) + (6-7) + (5-6) + (8-5) + (10-3)) / 5
Subtracting gives:
Mean difference = (3 - 1 - 1 + 3 + 7) / 5
Solving gives:
Mean difference = 11 / 5
Dividing gives:
Mean difference = 2.2
(b) Calculate the standard deviation of the differences:
To calculate the standard deviation of the differences, we need to calculate the squared differences, find their sum, divide by (n-1), and then take the square root.
Squared differences:[tex](3 - 2.2)^2, (-1 - 2.2)^2, (-1 - 2.2)^2, (3 - 2.2)^2, (7 - 2.2)^2[/tex]
Solving gives:
Sum of squared differences = (0.64 + 12.96 + 12.96 + 0.64 + 21.16)
Solving gives:
The sum of squared differences = 48.36
The standard deviation of the differences [tex]= \sqrt{48.36 / 4}[/tex]
Solving gives:
The standard deviation of the differences [tex]= \sqrt{2.09}[/tex]
Rounded to three decimal places
The standard deviation of the differences ≈ 3.47
c) Calculate the test statistic:
The test statistic (t) = (Point estimate - Null hypothesis value) / (Standard deviation /√(sample size))
Let's assume the null hypothesis is that there is no difference between the two fertilizers
(i.e., mean difference = 0).
[tex]t = (2.2 - 0) / (3.47 / \sqrt5)[/tex]
Substituting [tex]\sqrt 5 = 2.236[/tex]
t = 2.2 / (3.47 / 2.236)
Rounded to two decimal places
t ≈ 1.378
So, the test statistic is approximately 1.378.
The gardener can compare this test statistic to critical values from the t-distribution to determine whether the difference between the two fertilizers is statistically significant at a certain significance level. If the calculated test statistic is greater than the critical value, she ma
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The expression shown in red represents how many hockey pucks and hockey sticks come in one gym set. The expression shown in blue shows how many come in 3
sets.
Use the drop-down menus to complete the statements below to compare the values of the two expressions.
Answer:
three times
Step-by-step explanation:
Draw a diagram to help you set up an equation(s). Then solve the equation(s). Round all lengths to the neatest tenth and all angles to the nearest degree. (number 3)
The required distance the ship traveled from its starting point to its destination is approximately 44.8 miles.
How to use Pythagoras theorem to find distance?To solve this problem, we can use the Pythagorean theorem to find the distance the ship traveled from its starting point to its destination.
We can see that the ship traveled 35 miles east and 28 miles south, forming a right triangle. The distance from the starting point to the destination is the hypotenuse of this triangle.
Using the Pythagorean theorem, we can find the length of the hypotenuse:
[tex]$\begin{align*}\text{distance} &= \sqrt{35^2 + 28^2}\&= \sqrt{1225 + 784}\&= \sqrt{2009}\&\approx 44.8 \text{ miles}\end{align*}[/tex]
Therefore, the distance the ship traveled from its starting point to its destination is approximately 44.8 miles.
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Please help, due very soon !!
What is the solution to 3(2k + 3)= 6-(3k -5)
Answer:
[tex]\frac{11}{8}[/tex]
Step-by-step explanation:
3(2k+3)=6-(3k-5)
6k +9=6-3k+5
6k+3k=6+5
8k=11
k=[tex]\frac{11}{8}[/tex]
Answer: I think it is k=2/9
Step-by-step explanation:
30 points to help me!
Answer:
Step-by-step explanation:
5+3x/4 = 7/12
[(5*4)+3x]/4 = 7/12
(20+3x)/4 = 7/12
20+3x = 7/12*4
20+3x = 7/3
3x = 7/3 - 20
3x = [7-(20*3)]/3
3x = (7-60)/3
3x = -53/3
x = -53/3/3/1 ( reciprocal )
x = -53/3*1/3
x= -53/9
please answer i have 5 minutes i need an answer FAST!!!
(8.15x4 divided by 5) x 3.2 = _____.
Answer:
20.864
Step-by-step explanation:
8.15 x 4 is 32.6. I used a calculator but what I would do if I were solving on paper would be to double it, and then double it again.
Then, we divide 32.6 by five to get 6.52. I did this with a calculator, but if I were solving on paper, I would divide by 10 (move decimal point), and then double it.
Finally, we muliply 6.52 by 3.2. I did this with a calculator and got 20.864, but if I was doing this on paper, I would just solve using standard form!
Let me know if this helped by hitting brainliest! If you have any questions, comment and I'll get back to you ASAP.
Will give brainiest
Write the equation of the circle using the center and any one of the given points A, B, or C
Answer:
To write the equation of a circle given its center and a point on the circle, we need to use the standard form of the equation of a circle, which is:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center of the circle and r is the radius.
Let's use point A as the point on the circle. We are given that the center of the circle is (4, -2) and point A is (6, 1). We can use the distance formula to find the radius of the circle:
r = √[(6 - 4)^2 + (1 - (-2))^2] = √[4^2 + 3^2] = 5
Now we can substitute the center and radius into the standard form equation:
(x - 4)^2 + (y + 2)^2 = 5^2
Simplifying and expanding the right-hand side, we get:
(x - 4)^2 + (y + 2)^2 = 25Therefore, the equation of the circle is (x - 4)^2 + (y + 2)^2 = 25 and we used point A to find it.
please help me I have attached a photo below. thanks for your time
Therefore, the slope of the line passing through the points (0,5) and (2,0) is -5/2.
What is slope?In mathematics, slope refers to the measure of steepness of a line. It is the ratio of the change in y (vertical change) over the change in x (horizontal change) between any two points on the line. The slope of a line is represented by the letter "m" and can be calculated using the slope formula: m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are the coordinates of two points on the line.
Here,
To find the slope of a line, we use the formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are any two points on the line.
Using the given coordinates, we have:
x1 = 0, y1 = 5
x2 = 2, y2 = 0
slope = (0 - 5) / (2 - 0)
slope = -5/2
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Enter the values needed to find the
length BC. (Simplify your answer.)
A (-5x, 4y)
B (-2x, -4y)
BC=√([?])² + (3y)²
C (7x, -1y)
Distance Formula
d = √√(x₂ − ×₁)² + (y₂ − y₁)²
The missing value to find the length of BC is 9x.
What is distance formula?The distance formula is a formula for calculating the separation in coordinates between two places. It is provided by and deduced from the Pythagorean theorem by:
distance = √((x₂ - x₁)² + (y₂ - y₁)²)
The distance formula is used to compute distances between objects or places in many disciplines, including geometry, physics, and engineering.
The distance formula is given as:
distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Substituting the values of the coordinates of B and C we have:
distance = √((7x - (-2x))² + (-1y - (-4y))²)
distance = √((9x)² + (3y)²)
distance = √(81x² + 9y²)
distance = 3√(9x² + y²)
Hence, the missing value to find the length of BC is 9x.
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during the computer daze special promotion, a customer purchasing a computer and printer is given a choice of three free software packages. there are 8 different software packages from which to select. how many different groups of software packages can be selected?
Therefore, there are 336 different groups of software packages that can be selected from the 8 different software packages offered during the Computer Daze special promotion.
There are 8 different software packages to choose from during the Computer Daze special promotion. Since the customer purchasing a computer and printer is given a choice of 3 free software packages, this means that there are 336 different groups of software packages that can be selected.
To calculate this, the total number of possibilities can be found by using the formula nPr,
where n is the total number of choices, and r is the number of items chosen. This can be written as 8P3. 8P3 is equal to[tex]8x7x6 = 336.[/tex]
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Which pattern shows a quadratic relationship between the step number and the number of dots? Explain or show how you know.
Pattern B shοws a quadratic relatiοnship between the step number and the number οf dοts.
What is wοrd prοblem?Wοrd prοblems are οften described verbally as instances where a prοblem exists and οne οr mοre questiοns are pοsed, the sοlutiοns tο which can be fοund by applying mathematical οperatiοns tο the numerical infοrmatiοn prοvided in the prοblem statement. Determining whether twο prοvided statements are equal with respect tο a cοllectiοn οf rewritings is knοwn as a wοrd prοblem in cοmputatiοnal mathematics.
Here pattern B shοws a quadratic relatiοnship between the step number and the number οf dοts.
We can write quadradic equation as [tex]y=1+x^2[/tex]
Where y is number οf dοts and x is step number.
Then if x=0 and y=1
If x = 1 and y = 2
If x = 2 and y = 5
If x = 3 and y = 10
Hence Patten B fοllοws the quadratic realatiοnship.
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Use the quadratic formula to solve. Show work describe solution.
Answer:
Use the quadratic formula to solve. Show work describe solution.
Step-by-step explanation:
The quadratic formula is used to find the solutions (or roots) of a quadratic equation in the form ax^2 + bx + c = 0, where a, b, and c are constants.
The quadratic formula is:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
To use the quadratic formula, we need to plug in the values of a, b, and c from the given equation and solve for x.
For example, let's say we have the equation 2x^2 + 5x - 3 = 0.
Here, a = 2, b = 5, and c = -3.
Plugging these values into the quadratic formula, we get:
x = (-5 ± sqrt(5^2 - 4(2)(-3))) / 2(2)
Simplifying the expression inside the square root:
x = (-5 ± sqrt(49)) / 4
x = (-5 ± 7) / 4
We get two solutions:
x = (-5 + 7) / 4 = 1/2
x = (-5 - 7) / 4 = -3
So the solutions to the equation 2x^2 + 5x - 3 = 0 are x = 1/2 and x = -3.
These solutions represent the points where the quadratic curve intersects the x-axis. They can also be used to factor the quadratic equation or graph the quadratic function.
alexis created the two-way frequency table from information she gathered by asking 88 teenagers about their last online shopping experience. own money parents' money total completed purchase 16 34 50 just looked 22 16 38 total 38 50 88 about what percent of the teenagers purchased something with their parents' money?
The percentage of the teenagers who purchased something with their parents' money can be calculated from the two-way frequency table. About 38.64% of the teenagers purchased something with their parents' money.
There were a total of 88 teenagers who were surveyed by Alexis. 38 of them completed the purchase, and out of these 38 teenagers, 34 of them used their parents' money. So, the percentage of teenagers who purchased something with their parents' money can be calculated as follows:
Percent of teenagers who purchased something with their [tex]parents' money = \frac{Frequency of completed purchase}{Total Number of teenagers surveyed} *100[/tex]
Percent of teenagers who purchased something with their parents' money = [tex]\frac{34}{88} * 100%[/tex]%
Therefore percent of teenagers who purchased something with their parents' money = 38.64%
Therefore, about 38.64% of the teenagers purchased something with their parents' money.
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Which expressions are equivalent to
6
�
−
18
ℎ
6g−18h6, g, minus, 18, h?
Choose 2 answers:
Choose 2 answers:
(Choice A)
(
�
−
3
)
⋅
6
(g−3)⋅6left parenthesis, g, minus, 3, right parenthesis, dot, 6
A
(
�
−
3
)
⋅
6
(g−3)⋅6left parenthesis, g, minus, 3, right parenthesis, dot, 6
(Choice B)
2
⋅
(
3
�
−
18
ℎ
)
2⋅(3g−18h)2, dot, left parenthesis, 3, g, minus, 18, h, right parenthesis
B
2
⋅
(
3
�
−
18
ℎ
)
2⋅(3g−18h)2, dot, left parenthesis, 3, g, minus, 18, h, right parenthesis
(Choice C)
3
(
2
�
−
6
ℎ
)
3(2g−6h)3, left parenthesis, 2, g, minus, 6, h, right parenthesis
C
3
(
2
�
−
6
ℎ
)
3(2g−6h)3, left parenthesis, 2, g, minus, 6, h, right parenthesis
(Choice D)
(
−
�
−
3
ℎ
)
(
−
6
)
(−g−3h)(−6)left parenthesis, minus, g, minus, 3, h, right parenthesis, left parenthesis, minus, 6, right parenthesis
D
(
−
�
−
3
ℎ
)
(
−
6
)
(−g−3h)(−6)left parenthesis, minus, g, minus, 3, h, right parenthesis, left parenthesis, minus, 6, right parenthesis
(Choice E)
−
2
×
(
−
3
�
+
9
ℎ
)
−2×(−3g+9h)minus, 2, times, left parenthesis, minus, 3, g, plus, 9, h, right parenthesis
E
−
2
×
(
−
3
�
+
9
ℎ
)
−2×(−3g+9h)
You can use the distributive property of multiplication over addition and the fact that 18 is thrice of 6.
The given expression is equivalent to
Option C) [tex]3(2g-6h)[/tex]Option E) [tex]-2\times(-3g+9h)[/tex]What are equivalent expressions?Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.
What is the distributive property of multiplication over addition?[tex]a(b+c)=a\times b+a\times c[/tex]
(remember that many times, when using letters or symbols, we hide multiplication and write two things which are multiplied, close to each other. As in [tex]2\times x=2x[/tex])
The given expression is [tex]6g-18h[/tex]
We know that we can write
[tex]6=2\times3[/tex]
[tex]18=2\times9=3\times6[/tex]
Thus,
[tex]6g-18h=6\times g-6\times 3h=6(g-3h)=-6(-g+3h)[/tex]
[tex]6g-18h=2\times 3g-2\times 9h=2(3g-9h)=-2(-3g+9h)[/tex]
[tex]6g-18h=3\times 2g-3\times 6h=3(2g-6h)=-3(-2g+9h)[/tex]
All of the above forms are obtained from the same expression without altering its value but only forms, so their simplified forms are same so they are equivalent expressions.
Thus,
The given expression is equivalent to
Option C) [tex]3(2g-6h)[/tex]Option E) [tex]-2\times(-3g+9h)[/tex]Learn more about equivalent expressions here:
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Answer:C & D
Step-by-step explanation:
For each of the following elementary matrices, describe the corresponding elementary row operation and write the inverse.
a. E = 1 0 3
0 1 0
0 0 1
b. E = 0 0 1
0 1 0
1 0 0
c. E = 1 0 0
0 1/2 0
0 0 1
d. E = 1 0 0
-2 1 0
0 0 1
e. E = 0 1 0
1 0 0
0 0 1
f. E = 1 0 0
0 1 0
0 0 5
In the given elementary matrix, the corresponding elementary row operation is multiplication of the second row of a given matrix with a scalar of 5. The given matrix is an elementary matrix because it can be obtained by multiplying an identity matrix by an elementary matrix. The inverse of the given matrix can be obtained by multiplying a scalar of 1/5 to the second row of the identity matrix.
The given elementary matrix is:
[1 0 0]
[0 0 5]
[0 1 0]
The corresponding elementary row operation for this matrix is multiplication of the second row of a given matrix with a scalar of 5. This means that if we have a matrix A and we multiply the second row of A with a scalar of 5, we get a new matrix B which is represented by the above elementary matrix.
The inverse of the given matrix is:
[1 0 0]
[0 1/5 0]
[0 0 1]
The inverse of a given elementary matrix can be obtained by applying the inverse of the corresponding elementary row operation to an identity matrix. In this case, the inverse of the given elementary matrix can be obtained by multiplying a scalar of 1/5 to the second row of the identity matrix. This gives us the above inverse matrix.
Therefore, the corresponding elementary row operation for the given matrix is multiplication of the second row of a given matrix with a scalar of 5 and the inverse of the given matrix is:
[1 0 0]
[0 1/5 0]
[0 0 1]
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Need help with math
The new coordinates of the two points after rotating the parallel lines 180 degrees clockwise are (2, -7) and (-8, 5).
What are parallel lines?
In geometry, parallel lines can be defined as two lines in the same plane that are at equal distance from each other and never meet.
If the set of parallel lines contains the points (-2, 7) and (8, -5), then the two lines are parallel to each other and have the same slope. We can find the slope of the line that passes through these two points using the slope formula:
slope = (y2 - y1) / (x2 - x1)
slope = (-5 - 7) / (8 - (-2))
slope = -12 / 10
slope = -6 / 5
So, the equations of the two parallel lines are:
y - 7 = (-6 / 5)(x + 2) --- equation 1
y + 5 = (-6 / 5)(x - 8) --- equation 2
To rotate the lines 180 degrees clockwise, we need to negate both the x and y coordinates of the points on the lines. That is, we need to replace each point (x, y) with the point (-x, -y).
So, after the rotation, the new coordinates of the two points will be:
(-(-2), -7) = (2, -7) --- for point (-2, 7)
(-(8), -(-5)) = (-8, 5) --- for point (8, -5)
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C. Use Structure Why might Tavon have chosen
to multiply both sides of the equation by 10?
Could he have used another number? Explain.
By answering the presented question, we may conclude that In general, expressions it is often most convenient to choose numbers that are powers of ten.
what is expression ?In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.
Tavon may have chosen to multiply both sides of the equation by 10 because he wanted to remove the decimal point and work with integers. Then he can use his knowledge of integer multiplication and division to solve the equations more easily.
Tavon may have used a different number and removed the decimal point. For example, you could multiply both sides by 100 or 1000 instead of 10. However, you should carefully choose a number that is manageable and does not overcomplicate the problem. Multiplying by larger numbers complicates the calculations, and multiplying by smaller ones does not eliminate the decimal point entirely. In general, it is often most convenient to choose numbers that are powers of ten.
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The perimeter of a rectangle is 112 cm and its 10. A group
The tota
breadth is x cm.
(i) Find, in terms of x, an expression for the
length of the rectangle.
(ii) Given that the area of the rectangle is 597 cm²,
formulate an equation in x and show that it
reduces to x²-56x +597 = 0.
(iii) Solve the equation x²-56x + 597 = 0, giving
both answers correct to 2 decimal places.
(iv) Hence, find the length of the diagonal of
the rectangle.
Therefore, the length of the diagonal of the rectangle is approximately 193.57 cm or 49.43 cm, depending on which value of x is used.
What is perimeter?Perimeter is the total distance around the edge of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. For example, the perimeter of a rectangle is found by adding the lengths of its four sides.
Here,
(i) Let the length of the rectangle be y cm.
Then, the perimeter of the rectangle is given by:
2(x + y) = 112
x + y = 56
y = 56 - x
(ii) The area of the rectangle is given by:
Area = length x breadth
597 = yx
Substituting y = 56 - x, we get:
597 = x(56 - x)
597 = 56x - x²
x² - 56x + 597 = 0
(iii) Using the quadratic formula,
x = (-(-56) ± √((-56)² - 4(1)(597))) / (2(1))
x = (56 ± √(3136 - 2388)) / 2
x = (56 ± √(748)) / 2
x = (56 ± 2√(187)) / 2
x = 28 ± √(187)
Therefore, the two solutions are x = 28 + √(187) and x = 28 - √(187).
(iv) The length of the rectangle is y = 56 - x.
Using Pythagoras theorem, the length of the diagonal of the rectangle is given by:
d² = y² + x²
d² = (56 - x)² + x²
d² = 3136 - 112x + 2x²
d = √(3136 - 112x + 2x²)
Substituting the value of x from part (iii) into the above equation, we get:
d = √(3136 - 112(28 ± √(187)) + 2(28 ± √(187))²)
d = √(3136 - 3136 ± 112√(187) + 56 ± 56√(187) + 2(187))
d = √(37400 ± 168√(187))
d ≈ 193.57 cm (rounded to 2 decimal places) or d ≈ 49.43 cm (rounded to 2 decimal places)
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Salaries for teachers in a particular state have a mean of $ 52000 and a standard deviation of $ 4800. a. If we randomly select 17 teachers from that district, can you determine the sampling distribution of the sample mean? Yes If yes, what is the name of the distribution? normal distribution The mean? 52000 The standard error? b. If we randomly select 51 teachers from that district, can you determine the sampling distribution of the sample mean? ? If yes, what is the name of the distribution? The mean? The standard error? C. For which sample size would I need to know that population distribution of X, teacher salaries, is normal in order to answer? ? v d. Assuming a sample size of 51, what is the probability that the sampling error is within $1000. (In other words, the sample mean is within $1000 of the true mean.) e. Assuming a sample size of 51, what is the 90th percentile for the AVERAGE teacher's salary? f. Assuming that teacher's salaries are normally distributed, what is the 90th percentile for an INDIVIDUAL teacher's salary?
a. Yes, the sampling distribution of the sample mean is a normal distribution with a mean of $52000 and a standard error of $\frac{4800}{\sqrt{17}}$.
b. Yes, the sampling distribution of the sample mean is a normal distribution with a mean of $52000 and a standard error of $\frac{4800}{\sqrt{51}}$.
c. You would need to know that the population distribution of X, teacher salaries, is normal in order to answer the questions regarding any sample size.
d. Assuming a sample size of 51, the probability that the sampling error is within $1000 is approximately 0.84 or 84%.
e. Assuming a sample size of 51, the 90th percentile for the average teacher's salary is approximately $54488.
f. Assuming that teacher's salaries are normally distributed, the 90th percentile for an individual teacher's salary is approximately $56396.
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a survey of 50 people were taken 30 like chocolate 20 like vanilla 10 like both how mnay like choclate
From the survey of 50 people 20 people like chocolate.
A survey was conducted with 50 people, out of which 30 liked chocolate, 20 liked vanilla, and 10 liked both. The question is asking how many people like chocolate.
To determine the number of people who like chocolate only, we subtract the number of people who like both flavors from the total number of people who like chocolate.
The number of people who like chocolate alone = total number of people who like chocolate - the number of people who like both
= 30 - 10= 20
This means that out of the 50 people surveyed, 20 individuals like chocolate, while 10 people enjoy both chocolate and vanilla.
Therefore, 20 people like chocolate.
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plain why the statistic is misleading.
Wilson was 42 inches tall on Jan 1, 2000, and 51 inches tall on Jan 1, 2002. William was 5 feet tall on Jan 1, 2000, and 6 feet tall on Jan 1, 2002.
Conclusion: The difference between 42 and 51 is greater than the difference between 5 and 6, so Wilson grew more during one year.
Wilson and William were measured at various times, therefore drawing the inference that Wilson grew more over the course of a year than William is incorrect and the statistics is misleading.
What is descriptive statistics?Inferential statistics and descriptive statistics are two disciplines of statistics with distinct applications.
Summarizing and characterizing gathered data is the focus of descriptive statistics. It uses techniques including graphical presentations, measurements of variability, and measures of central tendency, such as mean, median, and mode (e.g., histograms, box plots). The purpose of descriptive statistics is to shed light on a sample's or population's properties, such as its distribution, dispersion, and shape.
Wilson and William were measured at various times, therefore drawing the inference that Wilson grew more over the course of a year than William is incorrect.
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growth models like those used in forecastx usually model situations well where a process grows multiple choice a. until reaching saturation. b. at a more or less constant rate. c. at an exponential rate. d. in a linear fashion.
This type of growth model is often used to model revenue or sales of a product, as these types of processes often grow in a linear fashion.
Growth models, like those used in ForecastX, are typically used to model situations where a process grows at an exponential rate. This is a type of growth where the rate of increase is proportional to the size of the process, meaning that the process increases quickly over time.
This type of growth model is often used to model population growth, technological growth, and financial growth. In these cases, the growth model is usually used to make predictions about future growth in the process.
In some cases, a growth model can be used to model a process that grows in a more or less constant rate. In this situation, the rate of increase is not proportional to the size of the process, and the rate of increase remains relatively stable over time. This type of growth model is often used to model natural resources, as these resources typically increase or decrease at a steady rate.
Finally, growth models can also be used to model a process that grows in a linear fashion. In this case, the rate of increase is constant and increases in a straight line over time.
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Each of the following passages contains a single argument. Using the letters "P" and "C," identify the premises and conclusion of each argument, writing premises first and conclusion last. List the premises in the order in which they make the most sense (usually the order in which they occur), and write both premises and conclusion in the form of separate declarative sentences. Indicator words may be eliminated once premises and conclusion have been appropriately labeled. The exercises marked with a star are answered in the back of the book.
Every art and every inquiry, and similarly every action and pursuit, is thought to aim at some good; and for this reason the good has rightly been declared to be that at which all things aim.
(Aristotle, Nicomachean Ethics)
As per the given question, we have to identify the premises and conclusions of different passages in the text of Aristotle's Nicomachean Ethics. It is a philosophical text that explains the ethical theory and how to live a good life. It is based on the concept of eudaimonia, which is translated as happiness or human flourishing. Here are the premises and conclusions of some of the passages:
Passage 1:
Premises: (P) All human beings have a natural desire for knowledge. (C) Therefore, philosophy is an important pursuit for all human beings.
Conclusion: Philosophy is an essential activity for all people because all humans have an innate desire for knowledge.
Passage 2:
Premises: (P) Virtues are habits that are formed by repeatedly practicing virtuous actions. (C) Therefore, becoming a virtuous person requires a lot of practice.
Conclusion: Being virtuous requires lots of practice because virtues are habits that are formed through repeated actions.
Passage 3:
Premises: (P) Moral virtues are acquired by habituation. (C) Therefore, becoming virtuous requires practicing virtuous actions.
Conclusion: One becomes virtuous by practicing virtuous actions because moral virtues are acquired through habituation.
Passage 4:
Premises: (P) Happiness is the highest good that humans can achieve. (C) Therefore, all human actions aim at achieving happiness.
Conclusion: All human actions are aimed at achieving happiness because happiness is the highest good that humans can attain.
Passage 5:
Premises: (P) All humans have a natural desire to be happy. (C) Therefore, achieving happiness is the ultimate goal of all human actions.
Conclusion: The ultimate goal of all human actions is to achieve happiness because all humans have a natural desire to be happy.
In summary, the text of Aristotle's Nicomachean Ethics explains the ethical theory and how to live a good life. It is based on the concept of eudaimonia, which is translated as happiness or human flourishing. The premises and conclusions of different passages have been identified in the given question, and we have explained them in detail.
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Ixl dilations-find the scale factor and center dilation
The scale factor is 2 and center dilation is reduced.
The scale factor is a ratio that describes how much a figure has been enlarged or reduced. It is calculated by dividing the length of the corresponding sides of the original and dilated figures. If the scale factor is greater than 1, then the figure is enlarged, and if it is less than 1, then the figure is reduced.
To find the scale factor in an IXL dilations problem, you need to compare the corresponding sides of the original and dilated figures.
If the original figure has a side length of 4 units, and the dilated figure has a corresponding side length of 8 units, then the scale factor is 8/4=2. This means that the dilated figure is twice as large as the original figure.
The center of dilation is the point about which the figure is enlarged or reduced. It is the fixed point that remains unchanged during the dilation process.
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In the given truss bridge, parallelograms ABCD and PQRS are congruent. If AB = 24 feet, what is PQ?
Answer:
D. 24 ft
Step-by-step explanation:
Congruent means equal. Since ABCD and PQRS are congruent they are the same.
Answer:
D
Step-by-step explanation:
Use Lagrange multipliers to find the point on the given plane that is closest to the following point. (Enter your answer as a fraction.)
x-y+z=3 (5,6,2)
To find the point on the given plane that is closest to the given point (5,6,2), we can use Lagrange multipliers.
Let f be the function that represents the plane x-y+z=3 and let g be the function that represents the point (5,6,2). Then, the point on the plane closest to (5,6,2) is the point that minimizes g=x2+y2+z2. We can use the method of Lagrange multipliers to solve this problem.
Let lambda be the Lagrange multiplier. Then, we need to solve the system of equations given by:
x2+y2+z2-2x-2y-2z=0x-y+z-3=0
By solving this system of equations, we obtain the point 13/14x=7/7y=11/7z=5/7, which is the closest point on the plane to the given point (5,6,2).
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10) A rectangle has a width of 2m+3. The length
is twice as long as the width. What is the length
of the rectangle?
Answer:
4m + 6
Step-by-step explanation:
Since the length is twice as long your equation should look like this
2(2m + 3) = L
which would be 4m + 6 as the length of the rectangle
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2. How do the sizes of the circles compare?
3. Are triangles ABC and DEF similar? Explain your reasoning.
4. How can you use the coordinates of A to find the coordinates of D?
The triangle DEF is twice the size of the triangle ABC and the triangles are similar triangles
How do the sizes of the circles compare?Given the triangles ABC and DEF
From the figure, we have
AB = 1
DE = 2
This means that the triangle DEF is twice the size of the triangle ABC
Are triangles ABC and DEF similar?Yes, the triangles ABC and DEF are similar triangles
This is because the corresponding sides of DEF is twice the corresponding sides of triangle ABC
How can you use the coordinates of A to find the coordinates of D?Multipliying the coordinates of A by 2 gives coordinates of D
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