Use the motion map to answer the question. A motion map. The position line is a long black arrow pointing right with x as the reference point at left. Above the line are 3 dots with short vector arrows moving toward x, then a dot, then 2 dots with longer vector arrows moving away from x. Describe the position and velocity of the object based on the motion map.
Answers
The direction and position of the fourth and fifth arrows indicate that the object then moves towards the origin, with a smaller velocity.
What are Motion maps?Motion maps are used to illustrate the direction and position of an object. Using the motion map, the description of the object position and velocity is as follows:
The object starts its movement from the origin with a large velocity, before moving back to the origin with a smaller velocity. It stops for 1 second in the origin, then moves away with a larger velocity, Finally, it moves back towards the origin with a smaller velocity.
See attachment for the motion map, where the number on each arrow in the map, represents the position of the object.
Note that; the long arrow means large velocity while the short arrow means small velocity.
We analyze the direction and position using the arrows
The first arrow shows that the object starts from the origin with a large velocity.The direction and length of the second arrow show that, the object then returned to the origin with a smaller velocity.There is a dot in front of the second arrow. This dot indicates that the object stops for one second.The third arrow means that, the object moved from the origin with a larger velocityThe direction and position of the fourth and fifth arrows indicate that the object then moves towards the origin, with a smaller velocity.Therefore, the direction and position of the fourth and fifth arrows indicate that the object then moves towards the origin, with a smaller velocity.
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Answer:
Based on the motion map, the object starts at the reference point "x" on the left side of the position line. The three dots with short vector arrows moving toward "x" indicate that the object is moving in the direction of the reference point and gaining speed. This suggests that the object is accelerating. Then, there is a single dot, which might indicate a momentary pause or a constant velocity. Afterward, the two dots with longer vector arrows moving away from "x" suggest that the object is decelerating or slowing down. In summary, the motion map shows an object that starts from rest, accelerates towards the reference point, maintains a constant velocity for a brief moment, and then decelerates away from the reference point.
Step-by-step explanation:
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Related Questions
Alyson deposits $500 in the bank for 12 years. The bank offers her a 4%
simple interest rate. How much money will be in her account at the end of
the 12 years? (Remember to round your answer to the nearest cent if
necessary.)
Answers
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &12 \end{cases} \\\\\\ A = 500[1+(0.04)(12)] \implies A = 740[/tex]
What is the sum of the geometric sequence −2, −6, −18, … if there are seven terms?
Group of answer choices
−728
−128
−1,458
−2,186
Answers
The sum of the first seven terms is given by -2186
What is a geometric progression?Any progression in which the ratio of adjacent terms is fixed is a Geometric Progression. The general form of representation of a geometric sequence is a, ar, ar², ar³, ...
The geometric sequence is given here by -2,-6,-18...
We can observe that the common ratio is r=3
thus the sequence of upto 7 terms is given by
-2,-6,-18,-54,-162,-486.-1458
Thus the sum of all seven terms is given by
S=-2-6-18-54-162-486-1458
=-2186
Hence, The sum of the first seven terms is given by -2186
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Solve the equation on the
interval [0, 2π).
3 sin x = sin x + 1
Answers
The solution to the equation on the interval is x = π/6 + 2πn, where n is any non-negative integer less than 2.
How to determine the solutionFrom the question, we have the following parameters that can be used in our computation:
3 sin x = sin x + 1
Interval = [0, 2π).
To solve the equation 3sin(x) = sin(x) + 1, we first subtract sin(x) from both sides to get 2sin(x) = 1.
So, we have
2sin(x) = 1
Then, we divide both sides by 2
sin(x) = 1/2.
Therefore, x = arcsin(1/2) + 2πn, where n is any integer.
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At a given point 67.7ft at ground level of a covered court, the angle of elevation of a roof worker from the bottom is 38.6⁰ and the angle of elevation of the roof from the top is 42.4 degrees find the height of the roof worker and the distance of the ø if someone is observing below.
Answers
The height is 114.83 ft and the distance of the ø if someone is observing below is 84.8.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
Given that at a given point of 67.7ft at the ground level of a covered court, the angle of elevation of a roof worker from the bottom is 38.6⁰ and the angle of elevation of the roof from the top is 42.4 degrees.
The base will be calculated as:-
tan(38.6) = P / B
tan(38.6) = 67.7 / B
B = 67.7 / tan(38.6)
B = 54.8 ft
The height will be calculated as:-
Cos(42.4) = B / H
H = 84.8 / Cos(42.4)
H = 114.83 ft
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The figure below is dilated by a factor of centered at the origin. Plot the resulting image.
Answers
A graph of the resulting image after a dilation by a factor of 1/4 centered at the origin is shown in the image attached below.
What is dilation?In Geometry, dilation simply refers to a type of transformation which typically changes the size of a geometric object, but not its shape.
Next, we would have to dilate the coordinates of the pre-image by using a scale factor of 1/4 centered at the origin as follows:
Ordered pair T (8, 8) → Ordered pair T' (8 × 1/4, 8 × 1/4) = Ordered pair T' (2, 2).
Ordered pair R (-8, -4) → Ordered pair R' (-8 × 1/4, -4 × 1/4) = Ordered pair R' (-2, -1).
Ordered pair S (4, -8) → Ordered pair S' (4 × 1/4, -8 × 1/4) = Ordered pair S' (1, -2).
Lastly, we would use an online graphing calculator to plot the resulting data points.
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Factor out the greatest common factor from the given polynomial 28X -2
Answers
The factorised for. of the given Polynomial expression using the greatest common factor is; 2 (14x - 1).
What is the factorised form of the given Polynomial expression?It follows from the task content that the factorised form of the given Polynomial expression is to be determined using the greatest common factor.
Since the given expression is; 28x - 2.
By careful observation of the two terms (28x and -2) in the polynomial expression; the greatest common factor is; 2.
Hence, the factorised form of the polynomial expression as required is; 2 (14x - 1).
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Find the average rate of change of the function on the interval specified for real number h.
p(x) = 2x + 5 on [2, 2 + h]
Answers
The average rate of change on the interval [2, 2 + h] is r = 2.
How to find the average rate of change?Wewant to find the average rate of change of p(x) = 2x + 5 on the interval [2, 2 + h]
Remember that the average rate of change on an interval [a, b] is:
r = ( p(b) - p(a))/(b - a)
So on this case, we have:
r = ( p(h + 2) - p(2))/(2 + h - 2)
r = ( 2*(x + h) + 5 - 2*x - 5)/h
r = (2h)/h
r = 2
The average rate of change is 2.
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Use the formula F =9 over 5 C + 32 to answer the following
Maha checked the outside temperature at noon one day and found it was 26° C. At 10 PM when she checked, the outside temperature was 18° C. How much, in degrees Fahrenheit, did the temperature drop between noon and 10 PM? Round your answer to the nearest tenth.
Answers
The temperature drop between noon and 10 PM is 14.4° F.
What is the conversion of Celsius to Fahrenheit?Celsius to Fahrenheit is the conversion of temperature from Celsius unit to Fahrenheit unit. Temperature scales provide a way of measuring how hot or cold a body is. Fahrenheit and Celsius are temperature scales.
The formula to convert Celsius to Fahrenheit is given by: °F = °C × (9/5) + 32.
Given that, Maha checked the outside temperature at noon one day and found it was 26° C.
So, the temperature in Fahrenheit is °F =26° ×(9/5)+32
= 46.8+32
= 78.8° F
At 10 PM when she checked, the outside temperature was 18° C.
So, the temperature in Fahrenheit is °F =18° ×(9/5)+32
= 32.4+32
= 64.4° F
Difference in temperature =78.8-64.4
= 14.4° F
Therefore, the temperature drop between noon and 10 PM is 14.4° F.
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division problem can be described using this model
Answers
The boxes are split in halves, and there is 4 boxes. The answer is 4 / 1/2.
What is division?
Division is a mathematical operation that involves dividing one number (the dividend) by another (the divisor). The result of this operation is called the quotient. Division is the inverse of multiplication, meaning that the product of a number divided by itself is equal to one. Division can also be used to find the number of times one number is contained in another. Division can be expressed in a variety of ways, such as by using fractions, decimals, or by using a long division algorithm.
When you look at the diagram, The boxes are split in halves, and there is 4 boxes. The answer is 4 / 1/2.
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Answer the questions in image!
(The answers are already there, just figure out which go where.)
50 points!
Answers
B: 1/3
C: 1/2
D: -4
E: 1
F: -5
Explanation: Parallel slopes tend to have the same slope but different equations of lines.
Perpendicular slope is the inverse of the slope.
an ordinary annuity pays 1000 quarterly for two years. how many payments are there?
Answers
The number of payments for the ordinary annuity that pays $1,000 quarterly for two years is 8.
What is an ordinary annuity?An ordinary annuity's cash flows or payments occur at the end of the period, unlike an annuity due.
For quarterly payments, in a year, payments are made 4 times, that is, every three months.
For two years, the payments will be made 8 times (4 x 2).
Thus, we expect the ordinary annuity to pay $8,000 ($1,000 x 2 x 4).
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in 2015, the national highway traffic safety administration reported the number of pedestrian fatalities in san francisco county was 24 and that the number in los angeles county was 209. can we conclude that pedestrians are safer in san francisco than in los angeles? why or why not? if you answered no, what additional data would allow us to make a conclusion about which county is safer for pedestrians?
Answers
No, we cannot conclude that pedestrians are safer in San Francisco than in Los Angeles based on the data provided. The number of pedestrian fatalities in a given county is only one factor in determining the safety of pedestrians in that county.
Other factors, such as the number of pedestrians in each county, the number of vehicles in each county, the number of traffic laws in each county, and the number of traffic enforcement officers in each county, all play a role in determining the safety of pedestrians in a given county.
We would also need to consider other factors such as the number of pedestrian-friendly infrastructure in each county, the number of pedestrian-friendly policies in each county, and the number of pedestrian-friendly initiatives in each county. With this additional data, we would be able to make a more informed conclusion about which county is safer for pedestrians.
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Barbara ran
after lunch.
3
of a mile before lunch and of a mile
8
12
How far did she run in all?
Answers
Answer:
Step-by-step explanation:
1/2 is your answer
Figure 1 and figure 2 are right triangles.
two right triangles labeled figure 1 and figure 2, where the legs of figure 1 are 3 units long and the legs of figure 2 are 4 units long
What scale factor was used to produce Figure 2 from Figure 1?
A. 3
B. 4
C. 3 over 4
D. 4 over 3
Answers
Answer:
4
Step-by-step explanation:
because its the factor
The scale factor of the dilation of triangles is k = 4/3
What is Dilation?Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent
The result of dilation is that the shapes and boundaries of objects in the input image are expanded or thickened. It is often used in conjunction with other morphological operations such as erosion, opening, and closing to manipulate and enhance images.
Given data ,
Let the scale factor of the dilation be represented as k
Now , the measure of leg of the first triangle is a = 3 units
The measure of leg of the second triangle is b = 4 units
So , the dilated triangle is given by
3 k = 4
Divide by 3 on both sides , we get
k = 4/3
Hence , the dilation factor is k = 4/3
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a manufacturer buys a new machine costing $180000 dollars. it is estimated that the machine has a useful lifetime of ten years and a salvage value of 6000 dollars at that time. assume the value of the machine varies linearly during this time. do not include dollar signs in your answers.
Answers
A manufacturer buys a new machine costing $180000 dollars. The value of the machine at the end of 10 years is $6000.
Calculate the annual depreciation of the machine.
Depreciation = (Purchase Price - Salvage Value) / Useful Life
Depreciation = (180000 - 6000) / 10
Depreciation = 174000 / 10
Depreciation = $17400 per year
Calculate the value of the machine at the end of each year.
Year 1: 180000 - 17400 = $162600
Year 2: 162600 - 17400 = $1452000
Year 3: 1452000 - 17400 = $1277600
Year 4: 1277600 - 17400 = $1103200
Year 5: 1103200 - 17400 = $928800
Year 6: 928800 - 17400 = $754400
Year 7: 754400 - 17400 = $580000
Year 8: 580000 - 17400 = $405600
Year 9: 405600 - 17400 = $231200
Year 10: 231200 - 17400 = $6000
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A friend has a 81% average before the final exam for a course. That score includes everything but the final, which counts for 25%
Answers
The best grade that can be earned is given as 0.8575
How to solve for the gradeIf he is able to get the sum of 100 percent in the final exam, trhis would count as 25 percent of the total grade that he has
100 - 25 = 75%
Then we would have
0.75 * 81 + 25 / 100
= 85.75 / 100
= 0.8575
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Question
A friend has a 81% average before the final exam for a course. That score includes everything but the final, which counts for 15% of the course grade.
What is the best course grade your friend can earn?
show me prymind with base length: 8 feet side length: 6.56 feet (calculated using the pythagorean theorem) height: 12 feet rmid
Answers
A diagram of a pyramid with the given measurements is not possible to generate.
But we can calculate he base length, side length and height of a pyramid using the Pythagorean theorem.
In a pyramid, the slant height (rmid) can be found using the Pythagorean theorem. If the base length (b) and the height (h) of the pyramid are known, the slant height (rmid) can be calculated using the formula:
rmid = sqrt(b^2 + h^2)
In this case,
rmid = sqrt(8^2 + 12^2) = sqrt(64 + 144) = sqrt(208) = 14.4
You can also use this information to find the side length of the pyramid, which is the length of one of the triangular faces. Using the Pythagorean theorem again:
side length = sqrt(rmid^2 - (b/2)^2)
In this case,
side length = sqrt(14.4^2 - (8/2)^2) = sqrt(207.36 - 16) = sqrt(191.36) = 6.56
So, based on the information provided, the base length of the pyramid is 8 feet, the side length is 6.56 feet and the height is 12 feet and the slant height is 14.4 feet.
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Expand a^2= (b-x)^2 +h^2
Answers
The expanded value of the given equation is a²+2bx = b² + x ²+ h² .
Expansion - what is it?Multiplication distributes over addition, so an expansion of a product of sums represents it as a sum of products.
Expansion is a scale-increasing affine transformation, sometimes known as enlargement or dilatation. It is also frequently referred to as an enlargement and is the polar opposite of a geometric contraction. An expansion and a translation are equivalent to a central dilation.
We must multiply out the brackets in order to expand and simplify an expression, and we must then collect like words in order to simplify the resulting expression.
Given : a^2= (b-x)^2 +h^2
a² = (b-x)² + h²
we know that (c-d)² = c²+d² + 2cd
So, a² = b² + x² -2bx + h²
a²+2bx = b² + x ²+ h²
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Homework 3x-5; x-5; an al 2x-14;.:. arithmetic sequence. Calculate the Value of x Find the Which term the First three are in Determine the general term of the Sequence Soth term the sequence is equal to -62 terms of
Answers
The value of x is found to be 3 and the arithmetic sequence is found to be 4, -2, -8, ... .
What is arithmetic sequence?
The nth term of an arithmetic progression is determined using the arithmetic sequence formula. The series where the common difference between any two next words stays constant is known as an arithmetic sequence.
The arithmetic sequence is 3x - 5, x - 5, 2x - 14, ....
If the numbers are in an arithmetic sequence, then the difference between the first and second term must be the same as the difference between the second and third term.
(x - 5) - (3x - 5) = (2x - 14) - (x - 5)
x - 5 - 3x + 5 = 2x - 14 - x + 5
-2x = x - 9
-2x - x = -9
-3x = -9
x = 3
The first three terms can be obtained by substituting the value of x in the terms -
The first term - 3(3) - 5 = 4
The second term - 3 - 5 = -2
The third term = 2(3) - 14 = -8
Therefore, the arithmetic sequence is 4, -2, -8, .....
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If a laborer weighing 895N and carrying bricks weighing 575N to scaffold up a ladder 3.1 m above the ground how much work has he done?
Answers
The amount of work that the laborer has done, given the weight of the bricks and the laborer is 4, 577 Joules .
How to find the work done ?To calculate the amount of work done by the laborer, we can use the formula:
work = force x distance x
where:
force is the force applied,
distance is the distance moved,
The force applied by the laborer is the combined weight of the laborer and the bricks:
= 895N + 575N
= 1, 470N
Therefore, the work done by the laborer is:
Work = 1, 470N x 3.1m
= 4577 Nm or Joules (J)
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Write the data in order from least to greatest and circle the median.
Of 3.50 7.99 3.25 4.00 3.50 7.50 3.65 3.50 4.00
Answers
Answer:
The answer to your questionis 3.65
Answer:
3.25, 3.50, 3.50, 3.50, 3.65, 4.00, 4.00, 7.50, 7.99
3.65 is the median.
Step-by-step explanation:
You're welcome.
Your grandparents started putting money away for you when you were born. If they put $100
each month into an account earning 3% compounded monthly, how much will be in the
account when you turn 18?
Answers
now, the assumption being that your granpa's are depositing the money at the beginning of the month.
[tex]~~~~~~~~~~~~\stackrel{\textit{deposits at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right)[/tex]
[tex]\begin{cases} A=\textit{accumulated amount} \\ pmt=\textit{periodic deposits}\dotfill & 100\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &18 \end{cases}[/tex]
[tex]A=100\left[ \cfrac{\left( 1+\frac{0.03}{12} \right)^{12 \cdot 18}-1}{\frac{0.03}{12}} \right]\left(1+\frac{0.03}{12}\right) \\\\\\ A=100\left[ \cfrac{(1.0025)^{216}-1}{0.0025} \right](1.0025) \implies \boxed{A \approx 28665.52}[/tex]
The size of a pentagon are given as x, x+1,x+3,x-2 and 6.If the perimeter is less than 78cm and x is an interger.Find the largest value of x
Answers
The largest value of x is 13.
What is perimeter?A closed shape's perimeter is the sum of the lengths of its outside boundaries. The lengths of all the sides are added to determine the measurement.
Given:
The size of a pentagon are given as x, x+1,x+3,x-2 and 6.
The perimeter is less than 78 cm and x is an integer.
The perimeter of the pentagon = the sum of all the sides.
x + x+1 + x+3 + x-2 + 6 < 78
4x + 10 - 2 < 78
4x < 70
x < 14
The largest value of x is 13.
Therefore, the largest value of x is 13.
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You are standing 143 feet away from the base of a building and your clinometer measures 17° when it’s looking at the top of the building. (This angle is the one between the ground and the top of the building). Please calculate the height of the building.
Answers
Answer:
The height of the building is 43.7 feet.
Step-by-step explanation:
Attached is a sketch of the problem.
We can use SOH CAH TOA to find our answer.
In this acronym, O is the opposite side, A is the adjacent side, and H is the hypotenuse. S is for the SIN function. C is for the COS function. T is for the TAN function.
We can calculate the height of the building by using the TAN function.
So we can say the tangent of angle x is the opposite side divided by the adjacent side.
[tex]tan(x)=\frac{O}{A}[/tex]
Lets solve for [tex]O[/tex].
Multiply both sides by [tex]A[/tex].
[tex]tan(x)*A=\frac{O}{A}*A[/tex]
Simplify the right side by cancelling the common factor of [tex]A[/tex].
[tex]tan(x)*A=O\\O=A*tan(x)[/tex]
Now lets evaluate the height of the building.
In this example we are given
[tex]x=17\\A=143[/tex]
[tex]O=143*tan(17)[/tex]
[tex]O=43.7195[/tex]
if we take a sample of reee's pieces has 1000 pieces. the manufacturer says that exactyl 40% of the candies are organe. if we select a sample of 50 pieces, how many will be oragne. let x
Answers
If we take a sample of 50 Reece's Pieces candies, we would expect about 20 of them to be orange.
The manufacturer says that exactly 40% of the candies are orange. We can use this information to find the expected value of the number of orange candies in a sample of 50 candies.
Expected value is found by multiplying the number of trials (in this case, 50) by the probability of success (in this case, 40% or 0.40)
x = (50)(0.40) = 20 candies.
So, if we take a sample of 50 Reece's Pieces candies, we would expect about 20 of them to be orange.
It's worth noting that this is an expectation, the actual number of orange candies in the sample of 50 candies may be different from the expected value.
The correct question of the following problem is:
If a sample of 1000 Reese's Pieces contains 40% orange candies, and a random sample of 50 Reese's Pieces is selected, how many orange candies can be expected to be in the sample of 50 Reese's Pieces? Let x be the number of orange candies in the sample of 50 Reese's Pieces.
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Angle
(Choice B)
B
Line
(Choice C)
C
Line segment
(Choice D)
D
Point
(Choice E)
E
Ray
(Choice F)
F
None of theseAngle
(Choice B)
B
Line
(Choice C)
C
Line segment
(Choice D)
D
Point
(Choice E)
E
Ray
(Choice F)
F
None of these
Answers
The correct answer is, the figure is a line segment.
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
here, we have,
from the given figure,
we get,
AB is a line segment.
Hence, The correct answer is, the figure is a line segment.
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A mathematics teacher wanted to see the correlation between test scores and homework. The homework grade (x) and test grade (y) are given in the accompanying table. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the projected test grade, to the nearest integer, for a student with a homework grade of 79.
Answers
The linear regression equation for this data is given as follows:
y = x - 6.
The projected grade for a student with homework grade of x = 79 is given as follows:
73.
How to obtain the equation for the regression line?The equation for the line of fit is obtained inserting the points of the data-set into a linear regression calculator.
The points from this data-set are given as follows:
(70, 55), (89, 92), (79, 81), (84, 74), (84, 77), (70, 65) and (64, 68).
Inserting these points into a calculator, the regression equation is given as follows:
y = x - 6.
The projected grade for a student with homework grade of x = 79 is obtained as follows:
y = 79 - 6
y = 73.
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Write an algebraic equation for the following.
Three times the sum of a number and seven is two less than five times the number.
Answers
Answer:
We dissect each statement from the problem above to fully understand it.
the sum of a number and 7 is (x + 7)
3 times this is 3(x + 7)
is means the equal sign here 3(x + 7) =
Two less then 5 times the number is 5x - 2.
Therefore, the answer is B, 3(x + 7) = 5x - 2
An experiment subject only to random fluctuation within a normal distribution collects the following set of unitless numerical values: 15.8, 17.8, 19.5, 20.0, 14.7, 16.6, 16.8, 19.4, 18.3
A number of hypotheses are put forward for the theoretical value of what is measured here. Select all of the theoretical values given below that can be ruled out by our usual 1-sigma uncertainty criterion. A. 15.6 B. 15.9 C. 19.5 D. 19.7 E. None of these theoretical values is confirmed by this data.
Answers
A one-sigma uncertainty criterion means that if a theoretical value falls within one standard deviation of the measured data, it is considered consistent with the data.
Using this criterion, we can rule out theoretical value D. 19.7, since it is outside the range of measured values.
The other theoretical values A. 15.6, B. 15.9, and C. 19.5 fall within one standard deviation of the measured data, so they cannot be ruled out by this criterion.
Therefore, the only theoretical value that can be ruled out by our usual 1-sigma uncertainty criterion is D. 19.7
It's worth noting that this method just gives a rough idea of the consistency of a theoretical value with the data.
Other methods, such as the chi-squared test, or Bayesian analysis could be used to find the best-fit theoretical value and its uncertainty, and confirm or rule out other theoretical values.
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Let ABCD be a parallelogram. Let M be the midpoint of line AB and N be the midpoint of line AD. Diagonal BD intersects line CM and line CN at P and Q, respectively. Find PQ/BD.
Answers
The value of PQ / BD of given parallelogram where Diagonal BD intersects line CM and line CN at P and Q, respectively = 1/3
Let's consider the two triangles BMP and DCP.
Here,
∠DPC = ∠BPM (because they are vertically opposite angles)
∠DCP = ∠BMP (because they are alternate interior angles of transversal CM with DC // BM)
∴△BMP∼△DCP (By AA theorem)
Thus,
ABCD is a parallelogram. Therefore AB = DC and AD = BC.
It is given that M is the midpoint of AB
BD = DQ + BQ BD = BP + PD
BD = 2BQ + BQ BD = 2PD + PD
BD = 3BQ BD = 3PD
therefore
BQ = PD And
Since DQ = 2BQ then DQ = 2PD and
PD + PQ = 2PD subtract PD from each side
PQ = PD
so BQ = PD = PQ
BD = PD + PQ + BQ
BD = PQ + PQ + PQ
BD = 3PQ
Therefore the value of PQ / BD of given parallelogram is PQ / BD = 1/3.
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