The average value of the function f(x) = 3x2 + 4x on the interval [-1, 2] is about 4.67.
To find the average value fave of the function f(x) = 3x2 + 4x on the interval [-1, 2], solve the definite integral of f(x) over the interval and then divide by the interval length.
The definite integral of f(x) over the interval [-1, 2] can be calculated as follows:
[tex]∫[-1,2] (3x^2 + 4x) dx = [x^3 + 2x^2] between x = -1 and x = 2 = (23 + 2(22)) - ((-1)^3 + 2(-1)^2) \s= 14[/tex]
The interval length is 2 - (-1) = 3.
As a result, the average value fave of f(x) on the interval [-1, 2] is as follows:
fave =[tex](1/3) * ∫[-1,2] (3x^2 + 4x) dx \s= (1/3) * 14 \s[/tex]= 4.67 (rounded to two decimal places) (rounded to two decimal places)
As a result, the average value of the function f(x) = 3x2 + 4x on the interval [-1, 2] is about 4.67
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.
verify that the correlation is about 0.5. what feature of the datais responsible for reducing the correlation to this value despitea strong straight-line association between x and y in most of theobservations?
The correlation of 0.5 indicates that the data points are not perfectly related - there is some degree of variation, which could be caused by a number of factors. If some data points have significantly different values than others, they can reduce the overall correlation.
Alternatively, the data could also have other confounding variables, such as additional features that are not considered in the linear relationship between x and y. These additional variables could also reduce the correlation, as they introduce noise into the analysis. In either case, the correlation of 0.5 could be due to the presence of outliers and/or confounding variables.
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Please help
Write a story that could represent this math problem. (2 points)
Answer:
yes
Step-by-step explanation:
7. Mark starts out the week with $8. Every day he gives sister $2. Write an equation and
graph the situation. What is the meaning of the values when x is greater than 4?
Answer:
y = -2x + 8
When x = 4, Mark has no more money , so when x is greater than 4, Mark is in debt or is not able to give his sister any more money.
Step-by-step explanation:
Harvey has some 1 bills and some 5 in all he has 6 bills worth 22 let x be the number of 1 bills and let y be the number of 5 bills write a system of equations to represent the information and use substitution
The distance between Dallas and Houston is about 364 kilometers. There are approximately 8 kilometers in 5 miles. Which measurement is closest to the number of miles between these two towns?
Answer: Approximately 226 miles
Step-by-step explanation:
Km. to Mi.
364 = 226
6 What is the area of the shaded region?
3 in.
F 15 in²
G25 in²
H 40 in²
J 55 in²
5 in.
8 in.
5 in.
The area of the shaded region is 12.5 square inches.
How to find the area of the shaded regionFirst we can subtract the area of the smaller triangle from the area of the larger triangle.
The larger triangle has a base of 8 inches and a height of 5 inches, so its area is:
(1/2) * base * height = (1/2) * 8 in. * 5 in. = 20 in²
The smaller triangle has a base of 3 inches and a height of 5 inches, so its area is:
(1/2) * base * height = (1/2) * 3 in. * 5 in. = 7.5 in²
Subtracting the area of the smaller triangle from the area of the larger triangle, we get:
20 in² - 7.5 in² = 12.5 in²
Therefore, the area of the shaded region is 12.5 square inches.
Therefore the option is F. 15 in² (none of the given answer choices match the calculated area of 12.5 in²)
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PLS SHOW FULL WORK AND FULL ANSWERS ONLY OR WILL BE REPORTED
The rationalized form of the surd is;
1) 25/13
2) 144/3
3) 36
How do you rationalize a surd?We have to note that the term surd would have to refer to an irrational number as we know it.
1) The conjugate of the surd is;
5/4 + √3
Rationalizing we have;
5/4 - √3 * 5/4 + √3
25/16 + 4√3 - 4√3 -3
25/13
2) The conjugate is √7 - 2
Rationalizing we have;
12/√7 + 2 * 12/√7 - 2
144/7 -2√7 + 2√7 -4
144/3
3) The conjugate of the surd is √2 + √3
Rationalizing we have;
6/ √2 - √3 * 6/ √2 + √3
36/4 +√6 - √6 - 3
36/1 = 36
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Identify the figure below. Select 2 names that apply
A. quadrilateral
B.parallelogram
C. Rhombus
D. Square
E. Trapezoid
P.S hurry I have to summit this soon (1-10 mins)
Answer: a and b
Step-by-step explanation: lol it obvious
Answer: Quadrilateral, Parallelogram
Step-by-step explanation:
A Quadrilateral is any closed 4 sided figure
A Parallelogram is a quadrilateral with two sets of parallel and opposite sides.
Danielle earns a 7.75% commission on everything she sells at the electronics store where she works. She also earns a base salary of $725 per week. What were her sales last week if her total earnings for the week were $1,058.25?
Danielle's sales last week were $
Danielle's sales last week were $. At her job at an electronics store, Danielle receives a $4,295.16 commission on every sale.
What is an electronics store?
Courses in calculus (single and multivariable), complex analysis, differential equations (both ordinary and partial), linear algebra, and probability are typically required for jobs in electronics engineering. Additionally, topics like Z-transforms and Fourier analysis are frequently covered in electrical engineering curricula.More mathematics is required for electronics and telecommunications technicians, such as complex numbers, trigonometry, basic geometry, fundamental statistics, and differential and integral calculus.Every subject wants their students to be able to examine mathematics using technology, such as spreadsheets.Let's start by first finding out how much commission Danielle earned last week. We know that her total earnings were $1,058.25 and her base salary was $725 per week. Therefore, her commission must have been:
$1,058.25 - $725 = $333.25
We also know that Danielle earns a 7.75% commission on everything she sells. Let's use "x" to represent her total sales last week. Then we can set up an equation to solve for x:
0.0775x = $333.25
Solving for x, we get:
x = $333.25 / 0.0775
x = $4,295.16
Therefore, Danielle's sales last week were $4,295.16.
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pls hurry! Write the equation for the line in slope-intercept form: y=mx+b.
given 20 people, what is the probability that, among the 12 months in the year, there are 4 months containing exactly 2 birthdays and 4 containing exactly 3 birthdays?
the probability of having 4 months containing exactly 2 birthdays and 4 months containing exactly 3 birthdays among 20 people is approximately 0.000008, or about 0.0008%
The problem of calculating the probability of a certain pattern of birthdays among a group of people can be approached using the techniques of combinatorics and probability. To calculate the probability of having 4 months containing exactly 2 birthdays and 4 months containing exactly 3 birthdays among 20 people, we can use the following steps: First, we need to choose which 4 months will have exactly 2 birthdays and which 4 months will have exactly 3 birthdays. There are 12 months to choose from, so the number of ways to make these choices is given by the binomial coefficient: C(12, 4) × C(8, 4). This is the number of ways to choose 4 months out of 12 to have exactly 2 birthdays, multiplied by the number of ways to choose 4 months out of the remaining 8 to have exactly 3 birthdays. Next, we need to assign the people to the months. To do this, we can use the principle of inclusion-exclusion, which states that the number of ways to assign the people to the months so that each of the chosen months has the correct number of birthdays is: N = (20!/(2!²× 3!⁴)) × (4¹² - 6 × 3¹² + 4 × 2¹²). This expression counts the number of ways to distribute the 20 people among the 12 months so that the chosen months have the correct number of birthdays, and subtracts the cases where one or more of the chosen months have too many or too few birthdays. The factor (20!/(2!⁸ × 3!⁴)) accounts for the fact that we are counting distinguishable arrangements of people. Finally, we can calculate the probability of the desired pattern of birthdays by dividing the number of favorable outcomes (N) by the total number of possible outcomes, which is simply the total number of ways to assign the people to the months, given by: 12²⁰. Putting it all together, we get: P(4 months with 2 birthdays, 4 months with 3 birthdays) = N / 12²⁰. Evaluating this expression gives: P(4 months with 2 birthdays, 4 months with 3 birthdays) ≈ 0.000008. Therefore, the probability of having 4 months containing exactly 2 birthdays and 4 months containing exactly 3 birthdays among 20 people is approximately 0.000008, or about 0.0008%.
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which of the following is an example of a statistic? a.) average number of all high school graduates who will attend college b.) standard deviation of tuition costs for all private universities c.) 25 random students are asked how much they spent on books d.) summary value of a population
25 random students are asked how much they spent on books is an example of a statistic.
The primary areas of study in statistics include data collection, organization, organization, analysis, interpretation, and presentation. It is customary to begin with a statistical population or a statistical model that will be examined when applying statistics to a scientific, industrial, or social problem. There are many different groups of people or things that can be referred to as populations, such as "each person living in a country" or "each atom making up a crystal." Every aspect of data is covered by statistics, including the planning of data collection in terms of survey and experiment design. Statisticians gather data using custom experiment designs and survey samples in the absence of census data.
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there are women and men in a department. part: 0 / 30 of 3 parts complete part 1 of 3 (a) how many ways can a committee of people be selected? number of ways to select a committee of people is .
If there are 8 men and 5 women , then the number of ways of selecting a 4 people committee is 715 ways .
The number of ways to select a committee of 4 people from a group of 13 people, where 5 are women and 8 are men, is calculated by Combination ;
where , "n" is = total number of people, "r" is = number of people to be selected,
In this case, we have:
the total number of people is = 8 + 5 ⇒ n = 13 ;
the number of committee member to be selected is "r" = 4 ;
So, the number of ways to select a committee of 4 people from a group of 13 people is : ¹³C₄ = 715 ways ;
Therefore, there are 715 ways to select a committee of 4 people from a group of 5 women and 8 men.
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The given question is incomplete , the complete question is
There are 5 women and 8 men is a department . Find the Number of ways can a committee of 4 people be selected ?
1) At a fund-raising event, 60% of the people were males and the rest were females. 20% of the females left the event in the afternoon. In the evening, after 33 males and 35 females left the event, 75% of the people at the event were males. (a) What percentage of the people left the event in the afternoon? (b) How many people were there at the start of the fund-raising event?
(a) The percentage of people that left the event in the afternoon is 8%
(b) The total number of people that were there at the start of the fund-raising event were 68.
How did we get these values?Let x be the number of people at the start of the event. Then, 0.6x were males and 0.4x were females.
In the afternoon, 0.2 * 0.4x = 0.08x females left the event.
So, there were 0.4x - 0.08x = 0.32x females left at the event.
In the evening, 33 + 35 = 68 people left the event, and x - 68 people were left.
Out of the x - 68 people, 0.6(x - 68) were males.
So, we have 0.75 * (x - 68) = 0.6 * (x - 68).
We can now solve for x:
0.75 * (x - 68) = 0.6 * (x - 68)
0.15 * (x - 68) = 0
x - 68 = 0
x = 68
Thus, there were 68 people at the start of the fund-raising event.
(a) The percentage of people who left the event in the afternoon was 0.08x / x * 100% = 0.08 * 100% = 8%.
(b) There were 68 people at the start of the fund-raising event.
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Which ordered pair is a solution of the equation? y=4x-7
A only (2,1)
B only (4, 9)
C both ( 2,10) and (4,9)
D neither
Answer: To find the ordered pair that is a solution of the equation y = 4x - 7, we need to substitute the values of x and y into the equation and see if it is true.
If (x, y) is a solution, then y = 4x - 7 must be true for that particular x and y.
Option A: (2, 1)
Substituting x = 2 and y = 1 into the equation, we get:
1 = 4 * 2 - 7
1 = 8 - 7
1 = 1
Since the equation is true for x = 2 and y = 1, (2, 1) is not a solution of the equation.
Option B: (4, 9)
Substituting x = 4 and y = 9 into the equation, we get:
9 = 4 * 4 - 7
9 = 16 - 7
9 = 9
Since the equation is true for x = 4 and y = 9, (4, 9) is a solution of the equation.
Option C: Both (2, 10) and (4, 9)
Substituting x = 2 and y = 10 into the equation, we get:
10 = 4 * 2 - 7
10 = 8 - 7
10 = 3
Since the equation is not true for x = 2 and y = 10, (2, 10) is not a solution of the equation.
So, the only ordered pair that is a solution of the equation y = 4x - 7 is (4, 9). The answer is B) only (4, 9).
Step-by-step explanation:
there are seniors and juniors in a particular social organization. in how many ways can seniors and juniors be chosen to participate in a charity event?
Total ways can 4 seniors and 2 juniors be chosen to participate in a charity event is 1,91,100.
There are 16 seniors and 15 juniors in a particular social organization and
4 seniors and 2 juniors had to be chosen to participate in a charity event.
Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements. The number of combinations of n different things taken r at a time, denoted by [tex]^nC_r[/tex] and it is given by, [tex]^nC_r = \frac{n!}{r!(n-r)!}[/tex] , where 0 ≤ r ≤ n.
Therefore the total ways that 4 seniors and 2 juniors be chosen to participate in a charity event = [tex]^{16}C_{4}.^{15}C_{2}[/tex]
= [tex]\frac{16!}{4!(16-4)!}$\times \frac{15!}{2!(15-2)!}[/tex]
= 1820 × 105
= 1,91,100
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The complete question is:
There are 16 seniors and 15 juniors in a particular social organization. In how many ways can 4 seniors and 2 juniors be chosen to participate in a charity event?
What are some fast animals you can think of? What are some slow wins? How can fast can you run? Think about how you can predict who would win this race. Research the speed of at least four different animals. Then time how long it takes you to run 1/4 mile. If you and these four types of animals ran a marathon at those speed to win? How far into the race with the four other racers be when the winner cross the finish line? Would a sport article or research or record a sports new cast to predict the outcome of this race. Use the information you learned in this topic to justify your predictions. PLEASE HURRY!!!!
The answers include the following:
Some fast animals are cheetah, falcon.Some slow animals are snail, slug etc.Speed of cheetah is 114 km/hr, speed of lion is 81 km/hr. speed of snail is 0.048km/hr and speed of deer is 48.2km/hr.The time it will take me to run 1/4 mile is 2 minutes.Yes, a sport article or research or record a sports new cast to predict the outcome of this race.What is Speed?This is referred to as the ratio of distance to the time in which the distance was covered and it is a scalar quantity.
Sport article or research or record a sports new cast will be able to predict the outcome of this race due to the data being gathered which will provide more information about the race.
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Aubrey is making bead kits. Each one contains 20 red beads and 15 gold beads.
Part A
Drag numbers to complete the table to show how many red beads and gold beads are in different numbers of bead kits.
Numbers may be used once, more than once, or not at all.
75 added to
75803515401003060
Kits Red Beads Gold Beads
1 20
15
2
40
30
3
60
45
4
80
60
5
100
75
Part B
Use the drop-down menus to complete the rule for each bead color.
Red: Add
20
.
Gold: Add
15
.
Part C
Choose all the ordered pairs that represent the number of red beads and gold beads in kits.
A.
(
20
,
15
)
B.
(
20
,
40
)
C.
(
30
,
45
)
D.
(
80
,
60
)
E.
(
100
,
75
)
Part D
Which of the following graphs shows the relationship between the number of red beads and gold beads in kits?
A.
A graph named “Bead Kits” on a coordinate plane with “Number of Red Beads” on x-axis and “Number of Gold Beads” on y-axis is shown. The diagonal line is going up and to the right. The line passes through the points (0, 0), (15, 20), (30, 40) and (45, 60).
B.
A graph named “Bead Kits” on a coordinate plane with “Number of Red Beads” on x-axis and “Number of Gold Beads” on y-axis is shown. The diagonal line is going up and to the right. The line passes through the points (0, 0), (30, 20), (45, 30), (60, 40), (75, 50) and (90, 60).
C.
A graph named “Bead Kits” on a coordinate plane with “Number of Red Beads” on x-axis and “Number of Gold Beads” on y-axis is shown. The diagonal line is going up and to the right. The line passes through the points (10, 0), (20, 10), (40, 30) and (60, 50).
D.
A graph named “Bead Kits” on a coordinate plane with “Number of Red Beads” on x-axis and “Number of Gold Beads” on y-axis is shown. The diagonal line is going up and to the right. The line passes through the points (0, 0), (20, 15), (40, 30), (60, 45) and (80, 60).
Part E
What would the ordered pair
(
60
,
45
)
represent? Use the drop-down menus to show your answer.
When there are 60
red
beads in kits, there will be 45
gold
beads.
1 / 7
The ordered pair that represent the number of red beads and gold beads is A. D, and E.
What is ratio and proportion?Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion.
From the table we observe that the number of red beads and the gold beads are in the proportion x : y = 4 : 3.
Using the proportion we see that:
A: (20, 15) = 20 : 15 = 4 : 3
D: (80,60) = 4: 3
E = (100, 25)= 4:3
Hence, the ordered pair that represent the number of red beads and gold beads is A. D, and E.
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Use the net to find the surface area of the prism.
5 in.
12 in.
13 in.
8 in.
Step-by-step explanation:
Rather than give you the full answer, let me point out the things that you need to know to work this out for yourself.
The surface area of the solid is the sum of all of the areas of its faces.
The area of a right triangle is a well-known formula. You should already know this.
Please help with 3 4 and 5
5. Solve for x.
S
(14x-15)
139⁰
V
U
T
The price of a car increased from £10,506
to £11,288. Calculate the percentage
change (to 1dp where needed).
Trigonometry question
The value of sin (θ/2) in the trigonometry is π/9
How to find sin (theta / 2)Information given in the problem
tan θ = 7/8,
where
0 < θ < π/2
solving for θ, from tan θ = 7/8
tan θ = 7/8
θ = arc tan (7/8)
θ = 0.7188 radians
soling for sin (θ/2)
= sin (θ/2)
= sin (0.7188/2)
= 0.3517 approximately π / 9
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At a local fair , Lin purchases necklaces and bracelets. Necklaces cost $4 each and bracelets cost $1 each, Lin spends $20 on these items. Let n represent the number of necklaces Lin buys and b represent the number f bracelets Lin buys
After solving the equation for n and b we find out that Lin bought 1 necklace and 4 bracelets.
We can set up the following system of equations based on the given information: n = number of necklaces, b = number of bracelets
4n + b = 20 (Lin spends $20 on necklaces and bracelets)
where 4n represents the cost of n necklaces and b represents the cost of b bracelets. This system of equations can be used to solve for n and b. we can solve for n and b using the system of equations:
n + 1b = 5
4n + 1b = 20
We can use the first equation to solve for n in terms of b: n = 5 - b
Substitute this expression for n into the second equation: 4(5 - b) + b = 20
Simplifying this equation, we get: 20 - 4b + b = 20
Solving for b, we get: b = 4
Substituting this value of b back into n = 5 - b, we get: n = 1
Therefore, Lin bought 1 necklace and 4 bracelets
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Complete Question
At a local fair , Lin purchases necklaces and bracelets. Necklaces cost $4 each and bracelets cost $1 each, Lin spends $20 on these items. Let n represent the number of necklaces Lin buys and b represent the number f bracelets Lin buys. Find the number of necklaces and bracelets Lin purchased.
Simplify the following using the properties of exponents.
Answer:
Step-by-step explanation:
7/x^-8 = 7x^8
Calculate the volume of the solid generated by rotating the figure below around the vertical axis. Express
answer in terms of pi or m. For example, if your answer is 10 x , write answer as 10m or 10pi.
The volume of the solid of revolution is equal to 21π cubic units.
How to determine the volume of a solid of revolution
In this problem we find the representation of a figure, whose area is also shown and whose solid of revolution is can be defined by following formula:
V = π · A
Where:
V - Volume of the revolution, in cubic units.A - Area of the representation, in square units.First, the area of the representation is found by summing the areas of two compounding rectangles:
A = 5 · 3 + 2 · 3
A = 21
Second, compute the volume of the solid of revolution:
V = 21π
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12. Given the quadratic function f(x) = 4x² +7x+c, where c is some real number constant.
(a) If c = 3, are the zeroes of f(x) rational or irrational numbers? Explain how you arrived at your choice.
[3 points]
(b) Determine all values of c for which the graph of y=f(x) will have no x-intercepts. Show all work.
[3 points]
Step-by-step explanation:
A.Rational because by using the discrmant formula, Since our coefficients are integers, and if we get a perfect square, inside a radicand , we will have a rational numbers.
For example:
[tex] \sqrt{ {7}^{2} - 4(4)(3) } = \sqrt{49 - 48} = \sqrt{1} = 1[/tex]
Since root 1, is a perfect square, we will have rational roots.
B.
[tex] {b}^{2} - 4ac < 0[/tex]
[tex]49 - 16c < 0[/tex]
[tex] - 16c < - 49[/tex]
[tex]c > \frac{49}{16} [/tex]
If c is greater than 49/16, we will have no x intercepts.
A triangle has an area of 30 inches² and a height of 12 inches. What is the length, in inches, of the base?
Answer:
Plug your values into the equation A=1/2bh and do the math. First multiply the base (b) by 1/2, then divide the area (A) by the product. The resulting value will be the height of your triangle!
Step-by-step explanation:
solve the equation x^3-x^2-18=0 given that x-3 is a factor of x^3-x^2-18
The solutions to the equation x³ - x² - 18 = 0 are given as follows:
x = 3, x = -1 ± 2.236i.
How to obtain the solutions to the equation?The equation for this problem is defined as follows:
x³ - x² - 18 = 0
x - 3 is a factor, hence one solution is given as follows:
x - 3 = 0
x = 3.
Also considering that x - 3 is a factor, and x - 3 is of the first degree while the equation is of the third degree, we have that:
(x - 3)(ax² + bx + c) = x³ - x² - 18
ax³ + (b - 3a)x² + (c - 3b)x - 3c = x³ - x² - 18
Hence the coefficients are given as follows:
a = 1.b - 3 = -1 -> b = 2.-3c = -18 -> c = 6.Hence the remaining solutions are given as follows:
x² + 2x + 6 = 0.
Using a quadratic function calculator:
x = -1 ± 2.236i.
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can someone help please
Answer: x=3, y=-1
Step-by-step explanation:
2x+y=5
2y=2x-8
In equation 1, y=5-2x.
Substitute this value in equation 2.
2(5-2x)=2x-8
10-4x=2x-8
Thus,
4x+2x=10+8 (collecting terms)
6x=18
x=3
Now, we said earlier that y=5-2x.
Therefore, y=5-2(3) [because x=3]
y=5-6
y=-1
Hope this helps :]
