(a) Average velocity = -7(5^2-1^2) + 70(5-1) = -90 m/s.
(b) Average velocity = -7(4^2-1^2) + 70(4-1) = -62 m/s.
(c) Average velocity = -7(3^2-1^2) + 70(3-1) = -34 m/s.
(d) Average velocity = -7(1+h)^2 + 70(1+h-1) = -7h^2 + 70h m/s.
(a) Average velocity = -7(5^2-1^2) + 70(5-1) = -7(25-1) + 70(4) = -7*24 + 280 = -168 + 280 = -88 m/s.
(b) Average velocity = -7(4^2-1^2) + 70(4-1) = -7(16-1) + 70(3) = -7*15 + 210 = -105 + 210 = -95 m/s.
(c) Average velocity = -7(3^2-1^2) + 70(3-1) = -7(9-1) + 70(2) = -7*8 + 140 = -56 + 140 = -16 m/s.
(d) Average velocity = -7(1+h)^2 + 70(1+h-1) = -7(1+h)^2 + 70h = -7(1+h)^2 + 70h m/s. The average velocity of an object over a given period of time is calculated by taking the difference between the final and initial positions, and dividing it by the amount of time elapsed. In this exercise, we are given the position of an object along a line as a function of time, s(t) = -7t^2 + 70t. To solve each part, we can plug in the given time intervals into the function, and calculate the difference between the initial and final positions. We then divide this difference by the amount of time elapsed to find the average velocity. For example, in part (a), the average velocity is calculated as -7(5^2-1^2) + 70(5-1) = -90 m/s. In part (b), the average velocity is calculated as -7(4^2-1^2) + 70(4-1) = -62 m/s. In part (c), the average velocity is calculated as -7(3^2-1^2) + 70(3-1) = -34 m/s. Finally, in part (d), the average velocity is calculated as -7(1+h)^2 + 70h m/s
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Let a sphere of radius r be cut by a plane, thereby forming a segment of height h. Show that the volume of this segment is (∏h2(3r-h))/3
The volume of the segment formed when a sphere of radius r is cut by a plane is equal to (πh2(3r-h))/3. This can be found by using the formula for the volume of a spherical segment, where h is the height of the segment and r is the radius of the sphere.
Step 1: Calculate the volume of a sphere using the formula V = (4/3)πr3
Step 2: Calculate the volume of a cone using the formula V = (1/3)πr2h
Step 3: Calculate the difference between the two volumes to find the volume of the segment.
Step 4: The volume of the segment is (πh2(3r-h))/3.
To calculate the volume of the segment formed when a sphere of radius r is cut by a plane, we use the formula for the volume of a spherical segment. First, we calculate the volume of the sphere using the formula V = (4/3)πr3, then the volume of the cone using the formula V = (1/3)πr2h. By subtracting the two volumes, we find the volume of the segment, which is (πh2(3r-h))/3. This formula is useful in finding the volume of any segment formed when a sphere is cut by a plane.
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create the following tables and calculate the average: mean use the additional column to caculate the frequency subtotal
To create the tables and calculate the average mean, we need to have a set of data that we want to organize in a tabular form. The table should have columns for the data values, frequency, and frequency subtotal. The frequency column will show how many times a particular data value appears in the set.
The frequency subtotal column will be used to find the sum of the product of each data value and its corresponding frequency.
The average mean can be calculated by dividing the sum of the frequency subtotal by the total frequency.
Mean = ([tex]f_{1}x_{1}[/tex] + [tex]f_{2}x_{2}[/tex]+ [tex]f_{3}x_{3}[/tex]+ ... + [tex]f_{n}x_{n}[/tex]) / ([tex]f_{1}[/tex]+[tex]f_{2}[/tex]+[tex]f_{3}[/tex]+...+[tex]f_{n}[/tex])
By creating this table, we can easily see the distribution of the data and can calculate the average mean. This method of organizing data in tabular form is commonly used in statistics and data analysis, and it is an efficient way of summarizing and understanding large sets of data.
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tion. Then. determine how many books she will have after 4 years.
Answer:2x3x4
Step-by-step explanation:
What is BD?
In triangle ABC, the length of side AB is 12 and the length of side AD is 27. The line AC started from point A and cuts the side BD a point C. The length of BC is x and the length of CD is x + 5.
The procedures below can be used to determine a triangle's length BD.
In th that is presented;
The holding ratio is, therefore, as follows:
12 : x = 27 : x + 5
12 / x = 27 / (x + 5 )
When we cross multiply these, we obtain:
12 ( x + 5 ) = 27x
12x + 60 = 27x
Taking the x values on one side, we obtain:
27x - 12x = 60
15x = 60
x = 60/15
x= 4
The length of line BD is:
= BC + CD
= x + x + 5
After entering the value of x, we get
= 4 + 4 + 5
= 13
As a result, the length of the line BD is 13.
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According to Moore’s Law, the doubling time for the number of transistors that can be put on a computer chip is approximately two years. Recent data suggests that, as of 2013, the rate of growth predicted by Moore’s Law no longer holds. Growth has slowed to a doubling time of approximately three years. Find the new function that takes that longer doubling time into account with starting quantity A[0]. Enter the exact answer: f(t) =
The new function that takes that longer doubling time into account with starting quantity will be Aₙ = A₁ (1)ⁿ.
What is an exponent?Consider the function:
y = a (1 ± r)ˣ
Where x is the number of times this growth occurs, a = initial amount, and r = fraction by which this growth occurs.
As per Moore's Regulation, the multiplying time for the number of semiconductors that can be placed on a microprocessor is roughly two years. That's what ongoing information proposes, starting around 2013, the pace of development anticipated by Moore's Regulation does not hold anymore.
The rate is 0%, then the equation is given as,
Aₙ = A₁ (1 + 0)ⁿ
Aₙ = A₁ (1)ⁿ
The new function that takes that longer doubling time into account with starting quantity will be Aₙ = A₁ (1)ⁿ.
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Write an expression that is equivalent to 5 - 2(3x + 4).
Show you work please.
An expression which is equivalent to 5 - 2(3x + 4) is,
⇒ - 3 - 6x
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ 5 - 2 (3x + 4)
Now, We can solve the expression as;
⇒ 5 - 2 (3x + 4)
⇒ 5 - 2 × 3x - 2 × 4
⇒ 5 - 6x - 8
⇒ - 3 - 6x
Thus, The equivalent expression is,
⇒ - 3 - 6x
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2x+y=32
x+3y=36
solve the equation by elmination method
Answer: (x,y)=(12,8)
Step-by-step explanation:
Sample surveys show that fewer people enjoy shopping than in the past.
A recent survey asked a nationwide random sample of 2577 adults if they agreed or disagreed that "I like buying new clothes, but shopping is often frustrating and time-consuming."
The population that the poll wants to draw conclusions about is all U.S. residents aged 18 and over.
Suppose that in fact 62% of all adult U.S. residents would say "Agree" if asked the same questions.
What is the probability that 1610 or more of the sample agree?
The likelihood that at least 1610 members of the sample agree is 0.3385.
What is meant by probability?How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes how likely they are when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability. The quantity of possible outcomes is known as probability. all events that could possibly occur. For instance, there is a 1 in 2 chance of receiving a head when flipping a coin, and there are 2 possible outcomes overall (a head or tail). P(heads) = 12 is the formula.Probability is a measure of how likely it is for a given event to take place.Given,
sample std = sqrt[0.62 × 0.38/2577]
= 0.0096
sample proportion = 1610/2577
= 0.6240
z(0.6240) = (0.6240-0.62)/0.0096
= 0.4167
P(x >= 1610) = P(z >= 0.4167)
Then we get,
= 0.3385
Hence, The likelihood that at least 1610 members of the sample agree is 0.3385.
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Determine the point estimator you would use and calculate the value of the point estimate. Tonya wants to estimate what proportion of the seniors in her school plan to attend the prom. She interviews an SRS of 50 of the 750 seniors in her school and finds that 36 plan to go to the prom
According to the information provided, it should be noted that the 750 seniors in her school make up the population of interest, and the parameter of interest is the percentage of seniors who intend to attend the prom.
Given,
Additionally, a strictly random sample is required in order to create a confidence interval. Additionally, the sample size should be examined to see if it adequately represents the population.
Using the z critical of 1.645, a 90% confidence interval will be built. The sample proportion in this case will be:
= 36/50 = 0.72
Q = 1 - 0.72 = 0.28
n = 50
As a result, the standard error will be equal to 50 squared times the multiplication of 0.72 and 0.28. This amounts to 0.0635.
For a big sample randomly selected among 750 seniors, the interval on the context suggests that we are 90% confident that the fraction of those who desire to attend the prom falls within the interval.
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brainstorm consider what kind of program you would like to build. as you do, think about how your program can fulfill the coding requirements the college board outlines. remember, you need a list, an algorithm that uses sequencing, selection and iteration and a procedure that uses parameters.
The total score will be used to determine the student’s final admissions status.
I would like to build a program that calculates a student's score for a college admissions test. The program will be based on the coding requirements outlined by the college board, which include a list, an algorithm that uses sequencing, selection and iteration and a procedure that uses parameters.
The list will contain the student’s scores for each section of the admissions test. The algorithm will use sequencing to add the scores of each section together. Selection will then be used to determine whether the student has met the minimum requirements, and iteration will be used to keep track of any sections that were not completed. The procedure will be used to calculate the student’s total score, using parameters such as the number of sections completed and the scores for each section. The total score will be used to determine the student’s final admissions status.
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Consider the statements below. Which are not propositions? Mark all that apply.
(a) A delicious chocolate cake.
(b) College students should get more sleep.
(c) 3 + 5 = 8
(d) 5+ 3 = 53
(e) In Idaho, there are 15 temples for the Church of Jesus Christ of Latter-day Saints.
(f) No way!
(g) The great and spacious building.
(h) Will you be my Valentine?
The statements that are listed above that are not propositions include the following:
College students should get more sleep and Will you be my Valentine?. That is option B and H.What is a proposition statement?A proposition statement is defined as the statement that is either a true statement or false statement but can not be both.
From the given statements,the statement that is a true proposition include the following:
A delicious chocolate cake.3 + 5 = 8In Idaho, there are 15 temples for the Church of Jesus Christ of Latter-day Saints.No way!The great and spacious building.The statement that is a false proposition include the following:
5+ 3 = 53The statement will you be my valentine? is not a proposition but a declarative question that needs to be answered.
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Energy is generated from solar and wind power. Solar power must be at most 6units/day or the panels will burn out. Wind must be strong enough to power 1 unit/ day or else the turbines won’t turn. The wind power must be less than twice the solar power less one, or the batteries wont charge properly. Find the optimal production of wind and solar that will maximize overall power output
Efficiency.Compared to solar panels' efficiency range of 18% to 22%, wind turbines typically capture 60% of the energy that flows through them.
What is more efficient wind or solar energy?Efficiency.Compared to solar panels' efficiency range of 18% to 22%, wind turbines typically capture 60% of the energy that flows through them.This proves that a single home wind turbine can generate more electricity than a number of solar panels.By the movement of air in relation to the Earth's surface, wind energy, a type of solar energy, is created.When the Earth's surface is heated unevenly by the Sun, this type of energy is created. The Earth's rotation and surface topography then alter this energy.Photovoltaic (PV) panels or solar radiation-concentrating mirrors are two ways that solar technologies turn sunlight into electrical energy.Electricity can be produced from this energy, which can also be used to store energy thermally or in batteries.To learn more about solar energy refer
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Cola Root Beer Lemon-line
Under 21 years of age 40 25 20
Between 21 and 40 35 20 30
Over 40 years of age 20 30 35If one of the 255 subjects is randomly selected, find the probability that the person is over 40 years of age or that they drink root beer.
The probability of the person over 40 years of age who drinks root beer is equal to 0.1176.
As given in the question,
Total number of people is equal to 255
From the given table :
Number of people who drinks root beer and over 40 years of age is
= 30
Required probability who drinks root beer and over 40 years of age is given by :
= ( Number of favourable outcomes ) / ( total number of outcomes )
= ( 30 / 255 )
= 0.1176
Therefore, the required probability of the people over the age of 40 years and drinks root beer is given by 0.1176.
The above question is incomplete , the complete question is :
Cola Root Beer Lemon-line
Under 21 years of age : 40 25 20
Between 21 and 40 : 35 20 30
Over 40 years of age : 20 30 35 If one of the 255 subjects is randomly selected, find the probability that the person is over 40 years of age or that they drink root beer.
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Most sports drinks contain minerals. Research shows that the most effective sports drink has a magnesium to calcium ratio of 1: 2. The body absorbs about 87% of magnesium in a drink, and about 44% of calcium in a drink.
One serving of a particular sports drink contains
about 96 mg of calcium and 48 mg of magnesium. About how many milligrams of each mineral will the body absorb?
Answer:
41 mg magnesium
42 mg calcium
Step-by-step explanation:
87% of magnesium; 48 mg of magnesium
44% of calcium; 96 mg of calcium
87% × 48 mg magnesium = 0.87 × 48 mg magnesium = 41 mg magnesium
44% × 96 mg calcium = 0.44 × 96 mg calcium = 42 mg calcium
Find the general solution to
1/ln(t)(5e^t c) Enter your answer as y=…y=… .
Use C to denote the arbitrary constant in your answer.
y = c * 5e^t / ln(t) is the general solution to 1/ln(t)(5e^t c) .We can simplify this expression by applying the chain rule of differentiation. The chain rule states that if y = f(u) and u = g(x), then
dy/dx = dy/du * du/dx.
The given expression is 1/ln(t)(5e^t c) .
In this case, we can let y = 5e^t c and u = ln(t).
Taking the derivative with respect to t, we get:
dy/dt = 5e^t c * (du/dt) / u
Since u = ln(t), we can use the chain rule again to find du/dt:
du/dt = 1/t
Plugging this back into the original expression, we get:
dy/dt = 5e^t c * (1/t) / ln(t)
Now we can factor out the constant c, which is an arbitrary constant of integration, giving us the final answer:
y = c * 5e^t / ln(t)
So the final answer is: y = c * 5e^t / ln(t)
It's important to note that this is only the general solution of the function, if we have an initial condition then we can find the specific solution for the function
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I need help solving this
Answer:
110 cm^2 & 39 cm^3
Step-by-step explanation:
Volume = Length x Width x Height. With that in mind, volume is 39 cm^3
Surface Area = Area of all the shapes
2(13 x 1) + 2(13 x 3) + 2(3 x 1) =110 cm^
. let x denote the annual salary of scientists in the united states, measured in thousands of dollars. suppose that e[x]
The standard deviation is $8,000. So, the standard deviation measured in thousands of dollars, is 8. and The mean is the average. So the average, measured in thousands of dollars, is 56.
Average salary: 56
Standard deviation of the salary: 8
$56,000 dollars is 56 thousand dollars.
$8,000 is 8 thousand dollars.
The mean is the average. So the average, measured in thousands of dollars, is 56.
The standard deviation is $8,000. So, the standard deviation measured in thousands of dollars, is 8.
complete question
Let X denote the average starting salary for 2014 U.S. college graduates, measured in dollars. Suppose that the average annual salary is $56,000 dollars, with a standard deviation of 8,000. Find the mean and standard deviation when salary is measured in thousands of dollars.
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grass clippings are placed in a bin, where they decompose. for 0 30 t , the amount of grass clippings remaining in the bin is modeled by 6.687 0.931 t a t , where a t( ) is measured in pounds and t is measured in days. (a) find the average rate of change of a t over the interval 0 30 t . indicate units of measure
The average rate of change of a t over the interval 0 30 t is 0.03 pounds per day.
To find the average rate of change, we need to calculate the slope of the line representing the function a t( ) over the interval 0 to 30.
The slope is calculated by taking the change in a t over the change in t.
We can calculate the change in a t by subtracting the a t value at the start of the interval (0) from the a t value at the end of the interval (30):
a t (30) - a t (0) = 6.687 - 0 = 6.687
We can calculate the change in t by subtracting the t value at the start of the interval (0) from the t value at the end of the interval (30):
t (30) - t (0) = 30 - 0 = 30
We can now calculate the slope by dividing the change in a t by the change in t:
Slope = 6.687 / 30 = 0.03
The average rate of change of a t over the interval 0 30 t is 0.03 pounds per day.
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Why do companies stocks up on extra inventory
Answer:
allows companies to easily and quickly fulfill customer orders as soon as they come in
Step-by-step explanation:
Holding excess inventory will allow companies to easily and quickly fulfill customer orders as soon as they come in, all without having to worry about waiting on their stock to come in to ship an order out.
Neeedd helpppp !!!! I only have a little bit of time
The value of m∠1 is 50°. The solution is obtained using properties of angle and triangle.
What is an angle?
When two rays are brought together at a single point, an angle is created. The two rays in this instance are referred to as the arms of the angle, while the common point is known as the node or vertex. The symbol "∠" stands for an angle. Angle is a derivative of the Latin word "Angulus."
In the figure, we are given a right-angled triangle which means that one angle in the triangle measures 90°.
We are given an exterior angle equal to 140°.
We know that angles on a straight line form a linear pair which means that their sum is 180°.
Let the angle on the straight line be 'x'.
So, we get
⇒x + 140° = 180°
⇒x = 40°
Now, we know that in a triangle, the sum of all the angles is 180°.
Therefore,
⇒m∠1 + 90° + 40° = 180°
⇒m∠1 + 130° = 180°
⇒m∠1 = 50°
Hence, the value of m∠1 is 50°.
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state whether the standardized test statistic t indicates that you should reject the null hypothesis. explain.
No, the standardized test statistic t does not indicate that you should reject the null hypothesis.
The value of the test statistic t only tells you how much of an effect the independent variable has on the dependent variable. To determine whether to reject the null hypothesis, you must compare the value of t to a critical value based on the sample size, the level of significance, and the degrees of freedom.
The standardized test statistic t does not indicate whether you should reject the null hypothesis. To determine this, you must compare the value of t to a critical value based on the sample size, level of significance, and degrees of freedom.
No, the standardized test statistic t does not indicate that you should reject the null hypothesis.
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PLEASE HELP
C is the circumcenter of APQR.
PC=3x+7, RC=5x-15, & QC=51-x
S
Q
X=[ ? ]
Using circumcenter the value of x is 11.
What is circumcenter of triangle?
The center of a triangle's circumcircle is known as the circumcenter. It is located at the point where the perpendicular bisectors intersect. Let the circumcenter of ABC be O (x, y). Then, because there are no differences in the distances from the vertices to O, we have AO = BO = CO = Circumradius.
Here the given is PC=3x+7 , RC = 5x-15 and QC = 51-x
Now according to the circumcenter the distance of the vertices are same . Then,
=> PC = RC
=> 3x+7 = 5x-15
=> 5x-3x =15+7
=> 2x = 22
=> x = 11.
Hence the value of x is 11.
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Suppose that a hospital wants to evaluate whether a new drug works better than the drug it currently uses to treat a certain ailment. The hospital conducts a small experiment to assess the effectiveness of the new drug. To conduct the experiment, the hospital randomly assigns one group of patients to the new drug, which requires patients to drink an entire glass of water when it is taken, and a second group is assigned to the old drug, which does not require drinking.
What is an appropriate method of controlling for any confounding variables?
\
An appropriate method of controlling for any confounding variables is;
The group assigned to the old drug should also drink an entire glass of water with the drug
What is the confounding variable?In an experiment, there are three primary types of variables, namely;
Dependent variable
Independent variable or explanatory variable.
Confounding variable.
We know that explanatory variable seems to have some effects on the dependent variable but then confounding variable also affects the dependent variable in some way. Thus, confounding variables are having the hidden effect on the main variable.
A confounding variable is defined as an explanatory variable that was considered in a study whose effect cannot be distinguished from a second explanatory variable in the study.
Now, in this question we can say that the confounding variables could be;
-price of a daily ski pass
-temperature
-whether it has snowed recently
The method for controlling any of these is that The group assigned to the old drug should also drink an entire glass of water with the drug
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A student is trying to identify the composition of a pure metal block by determining its density. The student records the mass to be 20.0g. The rectangular block is 3.00cm x 4.00cm x 1.40cm. Calculate the density (in g/cm^3). Express your answer to the correct number of significant figures.
The block's density can be calculated using the equation d=25g/8.4 cm.
What are equations?Two things are equal, according to an equation.
For instance, 10 + 2 equals 6 + 6.
Simply put, this means that 10 plus 2 equals or is the same as 6 plus 6.
In an equation, the unknown could be present, as in 10 + x = 6 + 6.
So, find the block's volume first:
= Length * Width * Height
= 2 x 3 x 1.4
= 8.4 cm
Now that you know the volume and the mass, you can add them to the density formula, which is as follows:
= Mass / Volume
Assuming density is represented by the symbol b, the formula would be:
d = 25 g / 8.4 cm
Therefore, the block's density can be calculated using the equation d=25g/8.4 cm.
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Correct question:
A student is trying to identify the composition of a pure metal block by determining its density. The student records the mass of the sample to be 25.00 g. The rectangular block is 2.0 cm x 3.0 cm x 1.4 cm.
Which equation is necessary to determine the density sample?
Math Homework Unit 3 Section D
A carpenter has 590) nails in his tool bag. He finds a box with some nails in his truck.
Then, he uses 211 nails at a job site. Now, he has 520 nails. How many nails does the
carpenter find in his truck?
The carpenter finds
My answer is 141
591-211=379
520-379=141
Use drawings, numbers or words. Explain how you can use estimation to make sure your answer makes sense.
I need help on how to use estimation. Thanks!!
Answer:
Please see answer below
Step-by-step explanation:
An estimate is an answer to a problem that is close to the solution, but not necessarily exact. Estimation usually requires rounding
Usually you perform the estimate prior to computing actual values.
Let's look at the numbers
591 can be rounded to 600, 211 can be rounded to 200
Then, in your equations instead of using actual numbers we use the estimates
600 - 200 = 400
500 - 400 = 100
Note this is off quite a bit because we are rounding to the nearest 100
Instead if we round to the nearest tens we get
591 ==> 590
211 ==> 210
520==> 520
So we get
590 - 210 = 380
520 - 380 = 140
A little more work but a more accurate estimate
run a regression analysis on the following data set, where y is the final grade in a math class and x is the average number of hours the student spent working on math each week. hours/week x grade y 5 52 5 44 11 67.4 13 89.2 13 75.2 14 92.6 15 87 16 84.4 17 86.8 17 88.8 State the regression equation y=m⋅x+by=m⋅x+b, with constants accurate to two decimal places.
What is the predicted value for the final grade when a student spends an average of 8 hours each week on math?
Grade = Round to 1 decimal place.
Expert Answer
The regression equation is y = 15.98x + 43.76. The predicted value for the final grade when a student spends an equation of 8 hours each week on math is 87.8.
The regression equation is found by using a linear regression analysis. First, the data points are plotted on a graph. Then, the best-fit line is determined. The equation of the line is then calculated by finding the slope (m) and y-intercept (b).
The slope (m) is calculated by taking the difference between the two y-values divided by the difference between the two x-values.
m = (y2 - y1) / (x2 - x1)
The y-intercept (b) is calculated by substituting the values of m and one of the data points into the equation of a line, and solving for b.
b = y - mx
Once the values of m and b are determined, the regression equation can be determined:
y = mx + b
For this data set, the regression equation is y = 15.98x + 43.76.
To find the predicted value for the final grade when a student spends an average of 8 hours each week on math, the value of x is substituted into the equation, and the result is rounded to one decimal place.
y = 15.98(8) + 43.76
y = 87.8
Therefore, the predicted value for the final grade when a student spends an average of 8 hours each week on math is 87.8.
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Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Match each verbal description to its equivalent function rule as applied to the given function below.
The function f stretched vertically by a
factor of 4 and translated up by 9 units
arrowBoth
The function f stretched vertically
by a factor of 2 and translated up by 5 units
arrowBoth
The function f translated
6 units up and 2 units right
arrowBoth
The function f reflected about the y-axis
and translated 7 units left
arrowBoth
the final equations are.:
g(x) = 3x - 7g(x) = -3x - 28g(x) = 6x - 9g(x) = 12x - 19What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
We have the following function:
(x) = 3x - 7
The function f translated 6 units up and 2 units rights:
6 units up:
y = 3x - 7 + 6
2 units rigth:
y = 3(x-2) - 7 + 6
y = 3x - 6 - 7 + 6
Finally:
g(x) = 3x - 7
The function f reflected about the y-axis and translated 7 units left:
reflected about the y-axis:
y = 3(-x) - 7
y = -3x - 7
translated 7 units left:
y = -3(x+7) - 7
y = -3x - 21 - 7
y = -3x -28
Finally:
g(x) = -3x - 28
The function f stretched vertically by a factor of 2 and translated up by 5 units:
stretched vertically by a factor:
y = 6x - 14
translated up by 5 units:
y = 6x - 14 + 5
y = 6x - 9
Finally:
g(x) = 6x - 9
The function f stretched vertically by a factor of 4 and translated up by 9 units:
stretched vertically by a factor of 4:
y = 12x - 28
translated up by 9 units:
y = 12x - 28 + 9
y = 12x - 19
Finally:
g(x) = 12x - 19
Thus, the final equations are.:
g(x) = 3x - 7g(x) = -3x - 28g(x) = 6x - 9g(x) = 12x - 19Learn more about function here:
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Let f: X - Y, where X and Y are the set of all real numbers, and x and h are real numbers. a. Find a function f such that the equation / (x + h) = / (x) + f (h) is not true for all values of x and h. Justify your reasoning. b. Find a function / such that equation / (x + h) = / (x) + / (h) is true for all values of x and h. Justify your reasoning. c. Let /(x) = 2*. Find a value for x and a value for h that makes f(x + h) = f(x) + / (h) a true number sentence.
Answer:
a. A function f such that the equation f(x + h) = f(x) + f(h) is not true for all values of x and h is a function that is not linear. For example, a function f(x) = x^2 is not linear because it does not satisfy the equation f(x + h) = f(x) + f(h).
b. A function f such that the equation f(x + h) = f(x) + f(h) is true for all values of x and h is a linear function. For example, a function f(x) = mx + b, where m and b are constants, is a linear function because it satisfies the equation f(x + h) = f(x) + f(h).
c. Let f(x) = 2x. If we choose x = 3 and h = 2, then f(x + h) = f(3 + 2) = f(5) = 2(5) = 10, and f(x) + f(h) = f(3) + f(2) = 2(3) + 2(2) = 6 + 4 = 10. Therefore, the equation f(x + h) = f(x) + f(h) is true in this case.
2. A rectangle is graphed on a coordinate grid. Which transformation
will result in a rectangle that is NOT congruent to the original
rectangle?
180° anticlockwise rotation will turn the rectangle into one that is NOT consistent with the original rectangle.
The correct option is B.
What does a congruent rectangle mean?Two figures are referred to as congruent if their size and shape are the same. For instance, because they are the same size and shape, the rectangles ABCD and PQRS are congruent rectangles.
What do congruent shapes entail?Identical shapes are referred to as congruent shapes. The angles and sides that correspond to each other are the same. To accomplish this, we must examine each shape's sides and angles. Two congruent shapes will perfectly fit on top of each other.
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I understand that the question you are looking for is:
A rectangle is graphed on a coordinate grid. Which transformation will result in a rectangle that is NOT congruent to the original rectangle?
A. A dilation by a scale factor of
B. rotation of 180° counterclockwise
C. translation 90° units to the right
D. reflection across the x-axis
answer : A rotation of 180 digress counterclockwise
Find the volume of this cylinder. Give your answer to 1 decimal place 20 cm 9 cm
The volume of the given cylinder is 11304 cm³.
What is the volume?Volume is the measure of the capacity that an object holds.
Formula to find the volume of the object is Volume = Area of a base × Height.
Given that, radius of a cylinder is 20 cm and depth of a cylinder is 9 cm.
We know that, the volume of a cylinder is πr²h.
Now, volume = 3.14×20²×9
= 3.14×400×9
= 11304 cm³
Therefore, the volume of the given cylinder is 11304 cm³.
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Answer:
5089.4cm
Step-by-step explanation:
9² x pi x 20 =5089.3800
