A) The approximation of the definite integral ∫₀³ (2x - 1) dx using a right-endpoint approximation with four subintervals is 8.25.
B) The total area between f(x) = 2x and the x-axis over the interval [-5, 5] is 0.
C) The approximation of the definite integral ∫₋₂² (1/(x^2 + 1)) dx using a right-endpoint approximation with four subintervals is approximately 2.2
D) The derivative of s(x) is 0, which means the function s(x) is constant; s'(5) is also equal to 0.
How to evaluate the definite integral?A) To evaluate the definite integral ∫₀³ (2x - 1) dx using a right-endpoint approximation, we divide the interval [0, 3] into subintervals and approximate the area under the curve using rectangles. Let's use four subintervals:
Δx = (3 - 0) / 4 = 0.75
The right endpoints of the subintervals are: 0.75, 1.5, 2.25, 3.0
For each subinterval, we evaluate the function at the right endpoint and multiply it by the width Δx:
f(0.75) = 2(0.75) - 1 = 1.5 - 1 = 0.5
f(1.5) = 2(1.5) - 1 = 3 - 1 = 2
f(2.25) = 2(2.25) - 1 = 4.5 - 1 = 3.5
f(3.0) = 2(3.0) - 1 = 6 - 1 = 5
The Riemann sum is the sum of these areas:
R4 = Δx * [f(0.75) + f(1.5) + f(2.25) + f(3.0)]
= 0.75 * [0.5 + 2 + 3.5 + 5]
= 0.75 * 11
= 8.25
Therefore, the approximation of the definite integral ∫₀³ (2x - 1) dx using a right-endpoint approximation with four subintervals is 8.25.
B) The total area between the function f(x) = 2x and the x-axis over the interval [-5, 5] can be found by evaluating the definite integral ∫₋₅⁵ (2x) dx.
Since the function f(x) = 2x is a linear function, the area between the function and the x-axis is the area of a trapezoid. The base of the trapezoid is the interval [-5, 5], and the height is the maximum value of the function within that interval.
The maximum value of the function f(x) = 2x occurs at x = 5, where f(5) = 2(5) = 10.
The area of the trapezoid is given by the formula: Area = (base1 + base2) * height / 2.
In this case, base1 = -5 and base2 = 5, and the height = 10.
Area = (base1 + base2) * height / 2
= (-5 + 5) * 10 / 2
= 0
Therefore, the total area between f(x) = 2x and the x-axis over the interval [-5, 5] is 0.
C) To calculate R4 for the function g(x) = 1/(x^2 + 1) over the interval [-2, 2], we'll use a right-endpoint approximation with four subintervals.
Δx = (2 - (-2)) / 4 = 1
The right endpoints of the subintervals are: -1, 0, 1, 2
For each subinterval, we evaluate the function at the right endpoint and multiply it by the width Δx:
g(-1) = 1/((-1)² + 1) = 1/(1 + 1)
g(-1) = 1/(1 + 1) = 1/2
g(0) = 1/(0² + 1) = 1/1 = 1
g(1) = 1/(1² + 1) = 1/2
g(2) = 1/(2² + 1) = 1/5
The Riemann sum is the sum of these areas:
R4 = Δx * [g(-1) + g(0) + g(1) + g(2)]
= 1 * [1/2 + 1 + 1/2 + 1/5]
= 1 * [5/10 + 10/10 + 5/10 + 2/10]
= 1 * [22/10]
= 22/10
= 2.2
Therefore, the approximation of the definite integral ∫₋₂² (1/(x^2 + 1)) dx using a right-endpoint approximation with four subintervals is approximately 2.2.
D) To determine s'(5) for the function s(x) = 9(6x)/(x³), we need to find the derivative of s(x) with respect to x and evaluate it at x = 5.
Let's first find the derivative of s(x):
s(x) = 9(6x)/(x³)
Using the quotient rule to differentiate s(x), we have:
s'(x) = [9(6)(x³) - (9)(6x)(3x²)] / (x³)²
= [54x³ - 54x³] / x⁶
= 0 / x⁶
= 0
Therefore, The derivative of s(x) is 0, which means the function s(x) is constant; s'(5) is also equal to 0.
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7(2x+3)-x(14-y)
[tex]7(2x + 3y) - x(14 - y)[/tex]
Answer:
[tex]y(x+21)[/tex]
Step-by-step explanation:
[tex]7(2x+3y)-x(14-y)\\=14x+21y-14x+xy\\= 21y+xy\\= y(x+21)[/tex]
Find the area of the shaded region.
Answer:
69.53 ft
Step-by-step explanation:
area of a box: 18*18 = 324
area of a circle: (pi)*9^2 = 254.47
324-254.47 = 69.53 ft
The total weight of three kittens is 14 ounces kitten one weighs 1/4 pound kit in two weighs 5.5 ounces how many ounces does kitten three weigh?
Answer:
4.5 ounces
Step-by-step explanation:
Given data
Total weight=14 ounces
1st kitten= 1/4pound = 4 ounces
2nd kitten= 5.5 ounces
3rd kitten = x ounces
Let the expression for the total weight be
4+5.5+x=14
solve for x
9.5+x=14
x= 14-9.5
x=4.5 ounces
Hence the 3rd kitten weighs 4.5 ounces
What is the point-slope form of a line with slope
(-3, 6)?
nun
that contains the point
A. y- 3 = (x+3)
B. y+6 = {(x+3)
O C. y- 6 = - 3(x+ 3)
O D. y-6 = {(x+3)
Let X be a standard normal random variable. Another random variable is determined as follows. We flip a fair coin (independent from X). In case of Heads, we let Y=X. In case of Tails, we let Y=−X.
Is Y normal? Justify your answer.
yes
no
not enough information to determine
Compute Cov(X,Y).
Cov(X,Y)=
Are X and Y independent?
yes
no
not enough information to determine
Problem 3. Problem 1(c)
Find P(X+Y≤0).
P(X+Y≤0)=
Based on these considerations, it can be concluded that Y is not a normal random variable.
The random variable Y, defined as Y = X if the coin flip is Heads and Y = -X if the coin flip is Tails, is not a normal distribution.
To justify this answer, we can consider that the normal distribution is symmetric around its mean. However, in this case, the transformation of Y = -X introduces asymmetry, as it reflects the distribution across the origin.
Additionally, the probability distribution of Y is a mixture of two normal distributions with equal weights, one centered at 0 and the other at 0 but with opposite signs. This combination results in a distribution that is not normal.
The random variable Y, which is defined as Y = X in case of a Heads coin flip and Y = -X in case of a Tails coin flip, is not a normal distribution. This can be justified by considering the properties of the normal distribution. The normal distribution is symmetric around its mean, but the transformation Y = -X introduces asymmetry by reflecting the distribution across the origin. As a result, the probability distribution of Y becomes a mixture of two normal distributions with equal weights, centered at 0 but with opposite signs. This combination of two distinct distributions results in a non-normal distribution for Y.
Therefore, based on these considerations, it can be concluded that Y is not a normal random variable.
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Please help asap. This is khan acadamy
Answer:
xr 30 degrees
Step-by-step explanation:
the angles always add up to 180 sooo
53+97=150
180-150=30
there's how u solve these kinds of problems
hope this helps
у
80
The graph of quadratic function
is shown on the grid.
What is a solution to r(x) = 0?
60
40
A -50
20
B 4
х
-4
4
8
12
- 16 -12 -8
16
C 14
-20
D-60
vo
-60
-80
Answer:
C 14
Step-by-step explanation:
2,900 Written in scientific notation
The number 2,900 in scientific notation is 2.9 * 10³
How to write the number in scientific notationFrom the question, we have the following parameters that can be used in our computation:
Number = 2,900
Multiply the number by 1
So, we have
Number = 2,900 * 1
Express 1 as 1000/1000
So, we have
Number = 2,900 * 1000/1000
Divide
Number = 2.9 * 1000
Express 1000 as 10³
So, we have
Number = 2.9 * 10³
Hence, the number in scientific notation is 2.9 * 10³
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Please Please help me
Answer:
1. 30
Step-by-step explanation:
First, place the numbers from least to greatest.
11,13,23,37,45,58
Then, find the middle number (or two middle numbers).
In this case, the middle numbers are 23 and 37.
Third, we find the mean of these numbers.
23+37=60
60/2=30
So your answer is 30.
Repeat this method for the other problems.
Express the following in form, where p and q are integers and q≠ . (0.1282828) find the answer please and thank you
Answer: [tex]\dfrac{127}{990}[/tex].
Step-by-step explanation:
Let x=0.1282828...
Multiply 10 on both sides , we get
10 x = 1.282828... (i)
Now multiply 100 on both sides , we get
1000x=128.2828... (ii)
Eliminate (i) from (ii), we get
[tex]990x=127\\x=\dfrac{127}{990}[/tex]
Hence, the required [tex]\dfrac{p}{q}[/tex] form: [tex]\dfrac{127}{990}[/tex].
another, these are tricky to me.
Answer:
It would be D ^^
Step-by-step explanation:
I learned this 2 years ago lol <3
Name the decimal and fraction for R on the number line.
Click the icon to view the number lines.
The decimal is 1.
The fraction is
Ben's dad is making a large pot of pasta sauce that calls for 3.5 kilograms of tomatoes. If he triples the amount of tomatoes for the recipe, how many grams of tomatoes will he use? Enter your answer in the box.
Answer: 10,500 gm
Step-by-step explanation:
Given
Pasta requires 3.5 kg of tomatoes
we know, [tex]1\ kg=1000\ mL[/tex]
If the amount is triples, the quantity of tomatoes is [tex]3\times 3.5=10.5\ kg[/tex]
[tex]\Rightarrow 10.5\ kg\equiv 10.5\times 1000=10,500\ gm[/tex]
Thus, he uses 10,500 gm of tomatoes
PLEASE ANSWER THIS ASAP
Answer:
Option D
is the correct....
helpppp please
On a map, 2 inches represent an actual distance of 28 miles. If the actual distance
between two cities is 322 miles, how many inches apart will the two cities be on the
map?
644 inches
23 inches
2 inches
28 inches
Jamal needs the order the four cards shown in increasing order .which would be the correct order of cards
Answer:
It's C, not D
Step-by-step explanation:
The solution is, Jamal needs the order the four cards shown in increasing order , D > A > B > C would be the correct order of cards.
option A.
What is number?A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.
here, we have,
given that,
Jamal needs the order the four cards shown in increasing order
we have,
A. -2/9 = -0.22
B. -.25 = - 0.25
C. -29% = -0.29
D. -1/5 = -0.2
we know that,
-0.2> -0.22> -0.25 > -0.29
so, the correct order of cards is:
D > A > B > C
Hence, The solution is, Jamal needs the order the four cards shown in increasing order , D > A > B > C would be the correct order of cards.
option A.
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Pharoah Limited purchased a computer for $8,600 on January 1, 2020. Straight-line depreciation is used for the computer, based on a five-year life and a $900 residual value. In 2022, the estimates are revised. Pharoah now expects the computer will be used until December 31, 2023, when it can be sold for $700. Calculate the 2022 depreciation expense.
The depreciation expense for 2022, based on the purchase price for the computer of $8,600, the revised estimate in 2022, using the straight-line method is $2,410 per year
What is the straight line depreciation method?The straight-line depreciation method is method for calculating the depreciation of an asset in which the value of the asset is uniformly reduced within each period until the salvage value of asset is reached.
The depreciation on the computer = $8,600 - $900 = $7,700
The annual depreciation rate for the computer in the first two years, using the straight line depreciation method is; $7,700/5 = $1,540 per year
The depreciation of the computer by the end of 2021 = 2 × $1,540 = $3,080
Therefore, the net book value of the computer at the end of 2021 = $8,600 - $3,080 = $5520
The estimates are revised with Pharoah expecting to use the computer until December 2022, to sell for $700, therefore;
The revised depreciable amount for the computer = $5,520 - 700 = $4,820
The revised depreciation rate for the years, 2022 and 2023 is therefore;
Depreciation = $4,820/2 = $2,410 per year
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The ratio of carrots to potatoes in a garden was 1:2. The ratio of potatoes to tomatoes was 1:3. If there are 45 carrots in the garden, how many tomatoes are in the garden?
Answer:
270 tomatoes
Step-by-step explanation:
Lets organize the Info
Carrots to Potatoes is 1:2
Potatoes to Tomatoes is 1:3
There are 45 Carrots
So lets input it in the ratio Carrots : Potatoes
45 : 2(45)
45 : 90
There are 90 Potatoes in the garden
Lets input that info to the ratio Potatoes : Tomatoes
90: 3(90)
90 : 270
Summarize:
There are :
45 carrots
90 potatoes
270 tomatoes
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
270 tomatoes
Step-by-step explanation:
If Ann travels 50 meters North, 200 meters East and 150 meters South, what is her total distance travelled ? A. 150 meters B.400 meters C. 250 meters D. 0 meter
Answer:
400 meters
Step-by-step explanation:
50 + 200 + 150 = 400
If the family plans to move to their retirement home in 10 years, which pool would be more cost effective to install? How do
you know?
Answer:
Step-by-step explanation:
but is their any answer choices
Can someone please help me with this question
Answer
180 - x
Step-by-step explanation:
opposite angles of a quadrilateral inscribed in a circle are supplementary
Answer:
180-x !!!
Step-by-step explanation:
i had some time to think about it
PLSSSSSSSSSSSSSS HELPPP FOR REAL SOMEBODDYY REWARD BRAINLIEST!!!!!!!!!!!!!!!!!
Answer:
1. x = 3
2. (1, 0)
3. x = 3, -2
4. 144
5. -3 + 4√3
Step-by-step explanation:
The school band has 8 alto saxophones and 2 baritone saxophones. What is the ratio of baritone saxophones to alto saxophones?
Answer:
4:1
Step-by-step explanation:
8/2 = 4:1 cause 2 can go into 8, 4 times.
Determine the equation of the circle graphed below
The equation of the circle graphed below is (x - 2)² + (y + 3)² = 25.
To determine the equation of a circle, we need the center and the radius of the circle. In the graph below, the center appears to be at (2, -3) and the radius appears to be 5.
Therefore, we can use the standard equation of a circle,
which is (x - h)² + (y - k)² = r²,
where (h, k) is the center of the circle and r is the radius.
Substituting the values of the center and radius, we obtain the equation of the circle as follows:(x - 2)² + (y + 3)² = 25
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PLEASE HELP!!
In a geometric sequence, a2=2, a3=12, and a4=72. Which equation can be used to find the nth term of the sequence, an?
an=2⋅10n−1
an=6⋅2n−1
an=13⋅6n−1
an=2n−1
Ik this is late, but people who are looking for the answer can see this.
Answer:
an =1/3*6^n-1
Step-by-step explanation:
You should plug in 2 for n in each equation, which, the correct one should give you 2. Then, to make sure, you plug in 3 in the equations that gave you 2.
Example:
an = 1/3 * 6 ^n-1
Plug in 2.
an = 1/3 * 6 ^2-1
an = 1/3 * 6 ^1
1/3 * 6 = 2
Step 2.
an = 1/3 * 6 ^3-1
an = 1/3 * 6 ^2
1/3 * 36 = 12
Hope this helps.
The correct equation which can be used to find the nth term of the sequence, an is,
⇒ a (n) = 1/3 × 6ⁿ⁻¹
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.
Given that;
In a geometric sequence,
⇒ a₂ = 2, a₃ = 12 and a₄ = 72
Now, From option 3;
The equation is,
⇒ a (n) = 1/3 × 6ⁿ⁻¹
Put n = 2
⇒ a (2) = 1/3 × 6²⁻¹
⇒ a (2) = 1/3 × 6
⇒ a (2) = 2
Hence, This is the correct equation which can be used to find the nth term of the sequence, an.
Thus, The correct equation which can be used to find the nth term of the sequence, an is,
⇒ a (n) = 1/3 × 6ⁿ⁻¹
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Find the missing length
Answer:
15
Step-by-step explanation:
Answer:
15
Step-by-step explanation:
A² + B² = C²
9 • 9 = 81
12 • 12 = 144
81 + 144 = 225
Sqrt
√255 = 15
Bernard works for a business that sells and repairs tires. He can repair tires in an hour work day. What is Bernard's unit rate for the number of tires repaired in one hour?
Answer:
3 tires per hour
Step-by-step explanation:
Bernard works for a business that sells and repairs tires. He can repair 24 tires in an 8 hour work day. What is Bernard's unit rate for the number of tires repaired in one hour?
Number of tires repaired per day = 24 tires
Number of time used to repair tire per day = 8 hours
What is Bernard's unit rate for the number of tires repaired in one hour?
Number of tires repaired in one hour = Number of tires repaired per day / Number of time used to repair tire per day
= 24 tires / 8 hours
= 3 tires per hour
The unit rate for the number of tires repaired in one hour is 3 tires per hour
4. A Tesla dealership is having a sale on their cars. This week you can save 15% off
the total price. If the retail price of the Tesla is $30,190, what is the discount?
Answer:
25,661.5
Step-by-step explanation:
30160x15%=4528.50
30160-4528.50=25,661.50
Is j+j+j+j and j with the power of four equivalent?
Answer:
No, they are not equivalent.
Step-by-step explanation:
j + j + j + j = 4j
j^4
Let's say j = 2
4j = 8
j^4 = 16
Answer:
NO
Step-by-step explanation:
j+j+j+j
remember multiplication is repeated addition!
j+j+j+j = 4j
THIS IS DIFFERENT! powers are repeated MULTIPLICATION.
j^4 = j to the power of 4 = j * j * j * j, NOT j+j+j+j !!!!!
If 3/4 of a cup of a snack food gives you your daily value of calcium, then what fraction of your daily value of calcium is in 1 cup of the snack food? (Enter a fraction in the form A/B, where A and B are whole numbers. Do not include any words or calculations.)
The fraction of your daily value of calcium in 1 cup of the snack food is 4/3.
Given information:
If 3/4 fraction of a cup of a snack food gives you your daily value of calcium
To find:
what fraction of your daily value of calcium is in 1 cup of the snack food?
Solution:
If 3/4 of a cup of a snack food gives you your daily value of calcium, then 1/4 of a cup of a snack food would give you 1/3 of the daily value of calcium.
Now, 1 cup of the snack food would give you four times that amount of 1/3 of the daily value of calcium.
Thus, the fraction of daily value of calcium in 1 cup of the snack food would be 4 x 1/3= 4/3
Answer: Therefore, the fraction of your daily value of calcium in 1 cup of the snack food is 4/3.
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