Splitting up [0, 3] into [tex]n[/tex] equally-spaced subintervals of length [tex]\Delta x=\frac{3-0}n = \frac3n[/tex] gives the partition
[tex]\left[0, \dfrac3n\right] \cup \left[\dfrac3n, \dfrac6n\right] \cup \left[\dfrac6n, \dfrac9n\right] \cup \cdots \cup \left[\dfrac{3(n-1)}n, 3\right][/tex]
where the right endpoint of the [tex]i[/tex]-th subinterval is given by the sequence
[tex]r_i = \dfrac{3i}n[/tex]
for [tex]i\in\{1,2,3,\ldots,n\}[/tex].
Then the definite integral is given by the infinite Riemann sum
[tex]\displaystyle \int_0^3 2x^2 \, dx = \lim_{n\to\infty} \sum_{i=1}^n 2{r_i}^2 \Delta x \\\\ ~~~~~~~~ = \lim_{n\to\infty} \frac6n \sum_{i=1}^n \left(\frac{3i}n\right)^2 \\\\ ~~~~~~~~ = \lim_{n\to\infty} \frac{54}{n^3} \sum_{i=1}^n i^2 \\\\ ~~~~~~~~ = \lim_{n\to\infty} \frac{54}{n^3}\cdot\frac{n(n+1)(2n+1)}6 = \boxed{18}[/tex]
Round 219.371 to the nearest one tenth and hundredths
Answer:
219.4
Step-by-step explanation:
Find the number in the tenth place 3 and look at the one place to the right for rounding digit 7. Round up if this number is greater than or equal to 5 and round down if it is less than 5. So the answer is 219.4
What value of b will cause the system to have an infinite number of solutions y=6x+b
-3x+1/2y=-3
A-(-6)
B(-3)
C(3)
D(6)
Answer: -6
Step-by-step explanation:
[tex]-3x+\frac{1}{2}y=-3\\\\\frac{1}{2}y=3x-3\\\\y=6x-6[/tex]
For there to be infinite solutions, b = -6.
Will mark brainliest
[tex]x^3[/tex] is strictly increasing on [0, 5], so
[tex]\max\{x^3 \mid 0\le x\le5\} = 5^3 = 125[/tex]
and
[tex]\min\{x^3 \mid 0 \le x\le5\} = 0^3 = 0[/tex]
so the integral is bounded between
[tex]\displaystyle \boxed{0} \le \int_0^5x^3\,dx \le \boxed{125}[/tex]
Una química tiene 3 soluciones acidas de varias concentraciones. La primera es 10% acida; la segunda 20% y la tercera 40%. ¿Cuántos mililitros de cada una debe ella usar para hacer 100ml de una solución al 18%, si tiene que usar cuatro veces mas de la solución al 10% que de la solución al 40%?
Based on the percentage of the first, second, and third acids, the milliliters of each acid that should be used to make 100 ml of 18% are:
10% acid = 40 ml20% acid = 50 ml40% acid = 10 mlWhat concentrations are needed to make the solution?Assuming the concentration of the 40% acid is denoted as x, the other acid concentrations would be:
10% acid = 4x
20% = 100 - 5x
The target solution is 100ml of 18%.
Solving gives:
(10% × 4x) + (20% × (100 - 5x)) + (40% × x) = 18% x 100
(80% × x) + 20 - x = 18
(80x - 100x) / 100 = 18 - 20
-20x / 100 = -2
20x = 200
x = 200 / 20
x = 10 ml
The 10% solution:
= 10 x 4
= 40 ml
20% acid:
= 100 - (5 x 10)
= 50 ml
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What must be true for line EF to not intersect plane L?
Answer:
If line EF is parallel to line CD, it will not intersect plane L.
From the sample space S={1,2,3,4,...,15} a single number is to be selected at random. Given the following events, find the indicated probability.
A. the selected number is even
B. the selected number is a multiple of 4.
C. the selected number is a prime number.
P(BIA)
The probabilities of the given events are:
A. P(even) = P(A) = 7/15
B. P(multiple) = P(B) = 3/15
C. P(prime) = 6/15
D. P(B|A) = 3/7
What is probability?Probability is defined as the ratio of the number of favorable outcomes of an event to the total number of possible outcomes.
P(E) = n(E)/n(S)
Calculation:The given sample space is S = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}
So, n(S) = 15
A. The selected number is even:
Consider the event as A.
The set of even numbers in the given sample is {2,4,6,8,10,12,14}
So, n(A) = 7
Then, the required probability is
P(A) = n(A)/n(S)
= 7/15
B. The selected number is a multiple of 4:
Consider the event as B.
The set of multiples of 4 in the given sample is {4,8,12}
So, n(B) = 3
Then, the required probability is
P(B) = n(B)/n(S)
= 3/15
C. The selected number is prime:
Consider the event as C.
The set of prime numbers in the given sample is {2,3,5,7,11,13}
So, n(C) = 6
Then, the required probability is
P(C) = n(C)/n(S)
= 6/15
D. calculate P(B|A):
Since events B and A are dependent events of the same sample,
n(A∩B) = 3 and the set is {4,8,12}. Then, P(B|A) is
P(B|A) = n(A∩B)/n(A)
⇒ P(B|A) = 3/7
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I neeeeed heeeelp please
Answer:
10b/y^2
Step-by-step explanation:
Hope this helps! :)
Which answer choice shows that the set of irrational numbers is not closed under addition? π+(-π)=0
1/2+(-1/2)=0
π+π=2π
1/2+1/2=1
Answer:
(a) π + (-π) = 0
Step-by-step explanation:
You want a counterexample for the statement that irrationals are closed under addition.
Closed setA set is closed under addition if adding members of the set always results in a member of the set.
π + (-π) = 0This shows that adding members of the set can result in a rational number. This is the counterexample you're looking for.
(1/2) + (-1/2) = 0Irrelevant. 1/2 is rational, so is not a member of the set of irrationals.
π + π = 2πAn example of a sum that is an element of the set. This is not a counterexample.
(1/2) +(1/2) = 1Irrelevant. 1/2 is rational, so is not a member of the set of irrationals.
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Evaluate each expression given the variable. 3x+7, when x=2
Answer:
13
Step-by-step explanation:
3x + 7
x = 2
3 × 2 + 7 = 6 + 7 = 13
Hi there.
3x+7
x=2 :
3(2)+7
6+7
13
That's it.
I NEED HELP ASAP PLS!!!
Answer:
C looks most correct
Step-by-step explanation:
Can someone please simplify this 9+4t=-3(1-2t)?
Answer:
simplification of the original equation is below/
Step-by-step explanation:
9+4t=-3(1-2t) can be simplified into
9+4t=-3+6t because of distributing the -3 to both the 1 and -2t.
however, this can simplified to
4t-6t=-3-9
and this can simplify to
-2t=-12
which can simplify to
t = 6
give brainliest please!
hope this helps :)
Explain insurable interest and give an example
The examples of insurable interest is an employer under certain arrangements.
Insurable interest is a investment that protects anything subject to a financial loss. A person or entity has an insurable interest in an item, event, or action when the damage or loss of the object would cause a financial loss or other hardshapes. In order to have an insurable interest a person or entity would take out an insurance policy protecting the person,item, or event in question. The insurance policy is able to mitigate the risk of loss if something happens to the asset-like becoming damaged or lost.
Examples of insurable interest are:
YourselfYour spouse or former spouseYour children or grandchildrenA special needs adult childAn aging parentAn employer (under arrangements)Hence the examples of insurable interest is an employer under certain arrangements.
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Answer: Insurable interest means you must have a financial stake in the risk being insured. You can’t claim insurance for a risk that you don’t face directly.
If Rob’s dad’s car is stolen, his father will receive the insurance money, not Rob.
Step-by-step explanation: Edmentum
Rebecca drew a graph with these key features:
The function is decreasing.
The left end is approaching a constant.
Which function could be represented by Rebecca’s graph?
Answer that was correct for me was: f(x) =-2(5/4)^x+3
The function that could be represented by Rebecca’s graph is f(x) =-2(5/4)^x+3
How to determine the function that could be represented by Rebecca’s graph?The properties are given as:
The function is decreasing.The left end is approaching a constant.For an exponential function to keep decreasing, one or more the following must be true:
The rate is less than 1The leading factor is negative and the rate is greater than 1For the left end of an exponential function to approach a constant, the following must be true:
The leading factor is negative and the rate is greater than 1The equation that has the above properties is f(x) =-2(5/4)^x+3
Hence, the function that could be represented by Rebecca’s graph is f(x) =-2(5/4)^x+3
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question in image
ddddddddddddddddd
Step-by-step explanation:
"congruent" for lines simply means they are equally long.
15. yes. AB = EF = 3
16. yes. BD = DF = 8
17. no. AC = 5, CD = 6
18. yes. AC = DE = 5
19. no. BE = 13, CF = 14
20. no. CD = 6, DF = 8
Please put answer as a mixed number! :)
1 and 3/8* 1.5 + 5 and 5/8 ÷ 0.4 =
Answer: 7 1/16 and 1 9/16
Step-by-step explanation: 1 3/8 x 1.5 is 1 3/8 x 1 5/10 11/8 x 15/10 which is 165/80. We divide it by 5/5 to get 33/16. This as a mixed number is 2 1/16. We add 5 to get 7 1/16.
5/8 divided by 0.4 is 5/8 divided by 2/5. We divide this by first finding the reciprocal of 2/5 which is 5/2. 5/8 x 5/2 = 25/16. This as a mixed number is 1 9/16.
Please help me quick. I don’t understand please give me the answer
Answer:
m = -2
Step-by-step explanation:
to find the answer you must put rise over run
rise is (y2 - y1) and run is (x2 - x1)
lets use the bottom two points for thisd
y2 is 0 and y1 is 2
x2 is 1 and x1 is 0
0 - 2 = -2
1 - 0 = 1
-2/1 = -2
that is the slope
An electrician plans to install solar panels on a rectangular section of roof with an area 180m2. This width of this section of roof is 7 1/5 m across. What is the length of this section of roof?
The length of the rectangular section of the roof is 25 m
Calculating areaFrom the question, we are to determine the length of the section of the roof
From the given information,
The area of the rectangular section = 180 m²
The width of the rectangular section = 7 1/5 m = 7.2 m
Using the formula for area of a rectangle
A = l × w
Where A is the area
l is the length
and w is the width
Then,
180 = l × 7.2
l = 180/7.2
l = 25 m
Hence, the length of the rectangular section of the roof is 25 m
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Answer:
25
Step-by-step explanation:
Just did it on Khan Academy.
If s(x) = 2 - x and t(x) = 3x, which value is equivalent to (s•f)(-7)?
Answer:
Step-by-step explanation:
t(-7)= 3(-7)= -21
s(-21)= 2-(-21)= 2 + 21= 23
Please help me this is due Monday!
Answer:
1.
2. Additive Identity
3. Associative Property
4. Multiplication Inverse Property
5. Multiplication Property of 0
6. Commutative Property
7.
8.
Step-by-step explanation:
Select the correct answer.
What is the equation of the line that has a slope of 3 and goes through the point (-3,-5)?
OA.
y=3x+4
OB. y=3x-14
OC. y=3x-4
OD. y=3x + 12
Answer: [tex]\Large\boxed{A.~y=3x+4}[/tex]
Step-by-step explanation:
Given information
Slope = 3
Point = (-3, -5)
Given the format of the equation
Slope-intercept form: y = mx + b
m = Slopeb = y-interceptSubstitute values into the equation
y = (3)x + b
y = 3x + b
Substitute the given point into the equation to get the value of [ b ]
(-5) = 3(-3) + b
-5 = -9 + b
b = -5 + 9
b = 4
Therefore, the equation of the line is [tex]\Large\boxed{y=3x+4}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
If f(x) = -5^x - 4 and g(x) = -3x - 2, find (f - g) (x).
Answer:
-5^x + 3x - 2.
Step-by-step explanation:
(f - g) (x) = f(x) - g(x)
= -5^x - 4 - (-3x - 2)
= -5^x - 4 + 3x + 2
= -5^x + 3x - 2.
Given: LM ∥ KN
LP ⊥ KN , KL = MN
KN = 30, LM = 20
m∠KLM=126°
Find: LP
An angle is produced at the point where two or more lines meet. Thus the value of LP required in the question is approximately 14.
Two lines are said to be perpendicular when a measure of the angle between them is a right angle. While parallel lines are lines that do not meet even when extended to infinity.
From the question, let the length of LP be represented by x.
Thus, from the given question, it can be deduced that;
LM ≅ PN = 20
KP = KN - PN
= 30 - 20
KP = 10
LP = x
Also,
<MLP is a right angle, so that;
< KLP = < KLM - <PLM
= 126 - 90
<KLP = [tex]36^{o}[/tex]
So that applying the Pythagoras theorem to triangle KLP, we have;
Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
Tan 36 = [tex]\frac{10}{x}[/tex]
x = [tex]\frac{10}{Tan 36}[/tex]
= [tex]\frac{10}{0.7265}[/tex]
x = 13.765
Therefore the side LP ≅ 14.
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mrs smith had 46$more than mrs wilson at first mrs wilson spent 4/7 of her money on some clothes and mrs smith spent 3/5 of her on household items after that they had an equal amount of money left find the total amount of money the two ladies spent.
please solve it as soon as posible
Using a system of equations, it is found that the total amount of money the two ladies spent was of $782.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Amount Mrs. Smith had initially.Variable y: Amount Mrs. Wilson had initially.Mrs smith had $46 more than Mr.s Wilson at first, hence:
x = y + 46.
Mrs Wilson spent 4/7 of her money on some clothes and, and Mrs. Smith spent 3/5 of her on household items, then they remained with an equal amount, so:
[tex]\frac{2}{5}x = \frac{3}{7}y[/tex]
Since x = y + 46, we have that:
[tex]\frac{2}{5}(y + 46) = \frac{3}{7}y[/tex]
14(y + 46) = 15y
y = 14 x 46
y = $644
x = 644 + 46 = $690
Hence the amount they spent is given as follows:
[tex]\frac{3}{5}x + \frac{4}{7}y = \frac{3}{5} \times 690 + \frac{4}{7} \times 644 = 782[/tex]
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please help urgently
Answer: no real solution
Thus, the function has no x- intercept
Step-by-step explanation:
Find the equation of the line that passes through point (6,1) with the x-intercept of 2.
Answer:
y=1/4x-1/2
Step-by-step explanation:
(x+ 3/8 ) 2 + y 2 =1
what is the radius & units?
The radius of the circle of the circle equation (x + 3/8)^2 + y^2 = 1 is 1 unit
How to determine the radius of the circle?The circle equation of the graph is given as:
(x + 3/8)^2 + y^2 = 1
The general equation of a circle is represented using the following formula
(x - a)^2 + (y - b)^2 = r^2
Where the center of the circle is represented by the vertex (a, b) and the radius of the circle is represented by r
By comparing the equations (x - a)^2 + (y - b)^2 = r^2 and (x + 3/8)^2 + y^2 = 1, we have the following comparison
(x - a)^2 = (x + 3/8)^2
(y - b)^2 = y^2
1 = r^2
Rewrite the last equation as follows:
r^2= 1
Take the square root of both sides of the equation
√r^2 = √1
Evaluate the square root of 1
√r^2 = 1
Evaluate the square root of r^2
r = 1
Hence, the radius of the circle of the circle equation (x + 3/8)^2 + y^2 = 1 is 1 unit
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Which is a true statement about the function f(x)= 8x^3
Answer:
The function is odd because f(-x) = -f(x)
Step-by-step explanation:
[tex]f(x)=8x^3[/tex]
[tex]f(-x)=8(-x)^3[/tex]
[tex]f(-x)=-8x^3[/tex]
[tex]-f(x)=-(8x^3)[/tex]
[tex]-f(x)=-8x^3=f(-x)[/tex]
[tex]f(-x)=-f(x)[/tex], therefore the function is odd
The function is odd because f(-x)=-f(x).
What is a function?A relation is a function if it has only One y-value for each x-value.
The given function is f(x)=8x³.
We need to find which statement would be true in the given options.
Let us find this by taking x as -x.
f(-x)=8(-x)³
We know that when a negative sign is multiplied three times we get negative sign.
f(-x)=-8x³
-f(x)=-(8x³)
-f(x)=-8x³=f(-x)
f(-x)=-f(x)
By the definition of odd function f(-x)=-f(x).
Hence, the function is odd because f(-x)=-f(x).
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the cost of living is 230% of what it was 10 years ago. what mixed number is this?
Answer:
Step-by-step explanation:
23
which description from the list below accurately describe the relationship between QRS and TUV? check all that apply
Triangle QRS was translated to form triangle TUV, hence both triangles have the same shape, same size and are congruent.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are reflection, translation, rotation and dilation.
Rigid transformation preserves the shape and size of the figure. Reflection, translation, rotation are rigid transformations.
Triangle QRS was translated to form triangle TUV, hence both triangles have the same shape, same size and are congruent.
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Answer: All of the above
Step-by-step explanation:
I did the test
if 6m of a uniform iron rod weighs 21 kg what will be the weight of 16 m of the same rod?
Answer:
56kg
Step-by-step explanation:
If 6m of a rod is 21 kg, then 21/6 will give us the weight of 1m of the rod. 21/6 = 3.5 kg
16*3.5 = 56 kg
