Answer:
about 10 hershy kisses
Step-by-step explanation:
Sorry If wrong :(
hey! please help explaining this!!
Answer:
a
Step-by-step explanation:
correct anwer is A
Kelly has a hula hoop with a radius of 2.4 feet. what is the diameter.
Answer:
4.8
Step-by-step explanation:
Radius is 1/2 of the diameter so just do 2.4 and multiply it by 2
hope this helps :)
You create a new hypothesis test on data 11, ... , I 100 with the null assumptions that they are Normally distributed with mean 10 and variance 4. You decide to use a custom hypothesis test with p-value = 0 4/100 Recall that I is the sample mean of the data. You will reject the test if p-value <0.01. a) What is the type I error rate of this test? 10 b) If 11, ..., 1 100 are Normally distributed with mean 11 and variance 4, what is the type Il error rate of this test? c) If 11, ... , I 100 are Normally distributed with mean 9 and variance 16, what is the type Il error rate of this test?
Without specific alternative hypotheses and distribution parameters, it is not possible to determine the type I error rate.
a) The type I error rate of this test is 0.01, which is the significance level chosen for the test. It represents the probability of rejecting the null hypothesis when it is actually true. In this case, if the data is indeed normally distributed with a mean of 10 and variance of 4, there is a 1% chance of incorrectly rejecting the null hypothesis.
b) To determine the type II error rate, we need to know the specific alternative hypothesis and the distribution parameters under that hypothesis. Without this information, we cannot calculate the type II error rate.
c) Similarly, without knowing the specific alternative hypothesis and the distribution parameters under that hypothesis (mean and variance), we cannot calculate the type II error rate for the scenario where the data is normally distributed with a mean of 9 and a variance of 16.
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A current-carrying conductor is located inside a magnetic field within an electric motor housing. It is required to find the force on the conductor to ascertain the mechanical properties of the bearing and housing. The current may be modelled in three-dimensional space as: 1 = 2i + 3j – 4k and the magnetic field as: B = 3i - 2j + 6k Find the Cross Product of these two vectors to ascertain the characteristics of the force on the conductor (i.e., find I x B).
The cross product of the current vector (1 = 2i + 3j – 4k) and the magnetic field vector (B = 3i - 2j + 6k) is obtained by calculating the determinant of a 3x3 matrix formed by the coefficients of i, j, and k. The resulting cross product is 26i + 18j + 13k.
To find the cross product (I x B), we can calculate the determinant of the following matrix:
|i j k |
|2 3 -4 |
|3 -2 6 |
Expanding the determinant, we have:
(i * (3 * 6 - (-2) * (-4))) - (j * (2 * 6 - 3 * (-4))) + (k * (2 * (-2) - 3 * 3))
Simplifying the expression, we get:
(26i) + (18j) + (13k)
Therefore, the cross product of the current vector (1 = 2i + 3j – 4k) and the magnetic field vector (B = 3i - 2j + 6k) is 26i + 18j + 13k. This cross product represents the force on the conductor within the electric motor housing. The resulting force has components in the i, j, and k directions, indicating both the magnitude and direction of the force acting on the conductor.
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Consider the following data.
−11, −11, −9, −11, 0, 0, 0
Step 1 of 3 :
Determine the mean of the given data. and median and no mode unimodal, bimodal or multimodal
The mean of the data set is -6.
The median of the data set is - 9.
The mode of the data set, is - 11.
What is the mean, median and mode of the data?The mean of the data set is calculated by applying the following formula as follows;
mean = total number of data sample /number of data sample
mean = ( -11 - 11 - 9 - 11 + 0 + 0 + 0 ) / 7
mean = ( -42 ) /7
mean = -6
The median of the data set is calculated as follows;
-11, - 11, - 11, - 9, 0, 0, 0
The median number = - 9
The mode of the data set, is the most occurring number or the number with the highest occurrence.
mode = - 11
The data sample is unimodal because it has only one mode.
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64 over 81= 8 over 9 what is the exponent
Answer: 64/81=8/9 is that what you trying to say. O and the answer is False
Step-by-step explanation: Hope this help :D
I need help with this question please help.
Its gt geometry
Answer: First one is 140, second one is 70
Step-by-step explanation: They’re corresponding angles
(-4,9);m=-1/2
Write the equation in point slope form
1/4(16p+8) ÷ 2(p+2)
someone help
Answer: 1/2(16p+8)(p+2)
Explanation: There is a lot to do, but basically you must simplify the equation and then multiply by 4 on both sides
z=xe^y,x=u^2−v^2,y=u^2 v^2, find ∂z/∂u and ∂z/∂v. the variables are restricted to domains on which the functions are defined.
[tex]z=xe^y,\ x=u^2-v^2,\ y=u^2 v^2[/tex]. Using partial differentiation, ∂z/∂u = [tex]2ue^y + 2uv^2xe^y[/tex] and ∂z/∂v = [tex]-2ve^y + 2u^2\ vxe^y[/tex].
How to apply partial differentiation?
To find the partial derivatives ∂z/∂u and ∂z/∂v, we will differentiate the function [tex]z = xe^y[/tex] with respect to u and v while keeping other variables constant.
Given:
[tex]z = xe^y,\\x = u^2 - v^2,\\y = u^2v^2.[/tex]
First, let's express z in terms of u and v by substituting the expressions for x and y into z:
[tex]z = (u^2 - v^2)e^{u^2v^2}[/tex]
Now, we can find the partial derivatives.
Partial derivative ∂z/∂u:
To find ∂z/∂u, we differentiate z with respect to u while treating v as a constant. Applying the chain rule, we have:
∂z/∂u = (∂z/∂x)(∂x/∂u) + (∂z/∂y)(∂y/∂u).
∂z/∂x = [tex]e^y[/tex],
∂x/∂u = 2u,
∂z/∂y =[tex]x * e^y[/tex],
∂y/∂u = [tex]2uv^2[/tex].
Substituting these values, we get:
∂z/∂u = [tex](e^y)(2u) + (x * e^y)(2uv^2)[/tex].
∂z/∂u = [tex]2ue^y + 2uv^2xe^y[/tex].
Partial derivative ∂z/∂v:
To find ∂z/∂v, we differentiate z with respect to v while treating u as a constant. Applying the chain rule, we have:
∂z/∂v = (∂z/∂x)(∂x/∂v) + (∂z/∂y)(∂y/∂v).
∂z/∂x = [tex]e^y[/tex],
∂x/∂v = -2v,
∂z/∂y = [tex]x * e^y[/tex],
∂y/∂v = [tex]2u^2v[/tex].
Substituting these values, we get:
∂z/∂v = [tex](e^y)(-2v) + (x * e^y)(2u^2v)[/tex].
∂z/∂v = [tex]-2ve^y + 2u^2vxe^y[/tex].
Therefore, the partial derivatives are:
∂z/∂u = [tex]2ue^y + 2uv^2xe^y[/tex],
∂z/∂v =[tex]-2ve^y + 2u^2\ vxe^y.[/tex]
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I’ll give the Brainliest to who answers these questions with reasonable explanations.
1. The manager of the soda shop decides that you’re a good customer, you may use a flavour as many times as you’d like. How many different possible mixtures can you make know (remember, you have 13 flavours available to you and you must choose 6)?
2. You realize that, despite what you expected, the soda actually tastes different depending on which flavour you choose first, second, etc. With this in mind, how many different sodas can you make?
Answer:
Answer
5.0/5
1
sana112704
Answer:
i think the answer is 10,296
Step-by-step explanation:
The first one is still 13C6
Review the definition of combina
Step-by-step explanation:
Answer:
what is the answer to part one ?
and the answer too part 2 ?
the answers down below wereńt clear enough .
Step-by-step explanation
A semi circle of diameter 6cm is cut from rectangle with sides 6cm and 8cm.
Calculate the perimeter of the shaded shape correct to 1 decimal place.
(My words) Add working steps if possible :)
A spring attached to a wall was displaced horizontally to model simple periodic motionWhich function represents the oscillations of the spring it it had amplitude of 5, a frequency of 3/(2pi) and midine of 4? Do not show me a link I want the answer the question is in the picture
Answer:b
Step-by-step explanation:
The function f(t) = 5sin(3t) + 4 represents the oscillations of the spring it had an amplitude of 5, a frequency of 3/(2pi), and a midline of 4 option second is correct.
What is the frequency?It is defined as the number of waves that crosses a fixed point in one second known as frequency. The unit of frequency is per second.
We have amplitude A = 5
Frequency f = 3/(2π)
Midline m = 4
The equation for the simple periodic motion is given by:
f(t) = Asin(wt+∅) + m
Here phase angle ∅ = 0
We know:
w = 2πf
w = 2π(3/2π)
w = 3
Put all the values in the equation:
f(t) = 5sin(3t) + 4
Thus, the function f(t) = 5sin(3t) + 4 represents the oscillations of the spring it had an amplitude of 5, a frequency of 3/(2pi), and a midline of 4
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A technique of: 40 mAs with 60 kV an exposure of 100mR. If we change to 20 mAs value what should the new kV value be to maintain exposure?
To maintain the same exposure of 100mR with a new technique of 20 mAs, the new kV value should be increased to approximately 120 kV.
The exposure received by a patient during an X-ray examination is determined by the product of milliamperes-seconds (mAs) and kilovolts (kV).
In this case, the initial technique of 40 mAs with 60 kV resulted in an exposure of 100mR.
To calculate the new kV value, we can use the mAs reciprocity law, which states that if the mAs is halved, the kV should be doubled to maintain the same exposure. In other words, the product of mAs and kV should remain constant.
In the initial technique, the product of mAs (40) and kV (60) is 2400. When the mAs value is reduced to 20, we need to find the new kV value that, when multiplied by 20, gives the same product of 2400.
By rearranging the equation, we find that the new kV value should be approximately 120, obtained by dividing the constant (2400) by the new mAs value (20).
To maintain the same exposure of 100mR with a reduced mAs value of 20, the new kV value should be increased to approximately 120 kV. This adjustment ensures that the product of mAs and kV remains constant, as dictated by the mAs reciprocity law.
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I will give 50 points for the answer
Answer:
nosee
Step-by-step explanation:
the bearing of c from a is 210°
(i) find the bearing of B from A
(ii) find the bearing of A from B
if you could also solve the question above I'd be very grateful
I need it in at least 10 minutes so please answer it!! ♡♡
Answer:
(a) His speed when he runs from C to A is [tex]4.\overline {285714}[/tex] m/s
(i) The bearing of B from A is approximately 127.18°
(ii) The bearing of A from B is approximately 307.18°
Step-by-step explanation:
(a) The given parameters are;
The distance from A to B = 120 m
The speed with which Olay runs from A to B, v₁ = 4 m/s
The distance from B to C = 180 m
The speed with which Olay runs from B to C, v₂ = 3 m/s
The distance from C to A = 150 m
His average speed for the whole journey = 3.6 m/s
We find
The total distance of running from A back to A, d = 120 m + 180 m + 150 m = 450 m
The time it takes to run from A to B, t₁ = 120 m/(4m/s) = 30 seconds
The time it takes to run from B to C, t₂ = 180 m/(3m/s) = 60 seconds
Let t₃ represent the time it takes Olay to run from C to A
We have;
The total time it takes to run from A back to A = t₁ + t₂ + t₃
Therefore;
[tex]Average \ velocity = \dfrac{Total \ distance }{Total \ time} = \dfrac{d}{t_1 + t_2 + t_3}[/tex]
Substituting the known values for the average velocity, 'd', 't₁' and 't₂' gives;
[tex]Average \ velocity = 3.6 \, m/s = \dfrac{450 \, m}{30 \, s + 60 \, s + t_3}[/tex]
3.6 m/s × (30 s + 60 s + t₃) = 450 m
3.6 m/s × 30 s + 3.6 m/s × 60 s + 3.6 m/s × t₃ = 450 m
108 m + 216 m + 3.6 m/s × t₃ = 450 m
∴ 3.6 m/s × t₃ = 450 m - (108 m + 216 m) = 126 m
t₃ = 126 m/(3.6 m/s) = 35 s
The speed with which Olay runs from C to A, v₃ = Distance from C to A/t₃
The speed with which he runs from C to A = 150 m/(35 s) = 30/7 m/s =[tex]4.\overline {285714}[/tex] m/s
(i) The given bearing of C from A = 210°
By cosine rule, we have;
a² = b² + c² - 2·b·c·cos(A)
∴ cos(A) = (b² + c² - a²)/(2·b·c)
Where;
a = The distance from B to C = 180 m
b = The distance from C to A = 150 m
c = The distance from A to B = 120 m
We find;
cos(A) = (150² + 120² - 180²)/(2 × 150 × 120) = 0.125
A = arccos(0.125) ≈ 82.82°
The bearing of B from A ≈ 210° - 82.82° ≈ 127.18°
The bearing of B from A ≈ 127.18°
(ii) The angle, θ, formed by the path of the bearing of A from B is an alternate to the supplementary angle of the bearing of B from A
Therefore, we have;
θ ≈ 180°- 127.18° ≈ 52.82°
The bearing of A from B = The sum of angle at a point less θ
∴ The bearing of A from B = 360° - 52.82° ≈ 307.18°
The bearing of A from B ≈ 307.18°.
8 ft
Find the area of the figure.
if a = 2 and b = 7 then b^a =
Answer:
49
Step-by-step explanation:
7^2 mean 7x7 which is 49
Write the Algebraic expression for six more three times a number n
suppose that number is ( x ).
three time of it means : 3 × x
six more means : + 6
So;
Six more three times a number means :
3x + 6
Thus, f ( x ) = 3x + 6
HELP!!!!! URGENT!!! A student surveyed his classmates to determine their favorite sport. According to the circle graph which statement must be true?
Answer:
25.5 / 3 = 8.5
8.5 times more student prefer basketball over soccer
Step-by-step explanation:
Answer:
C: Half the people surveyed liked baseball or football
Step-by-step explanation:
25% + 25% = 50% which is 1/2 of the surveyed population
What statement is used to prove that quadrilateral ABCD is a parallelogram? (5 points)
a) Opposite angles are congruent.
b) Opposite sides are congruent.
c) Diagonals bisect each other.
d) Consecutive angles are supplementary.
The statement that is used to prove that quadrilateral ABCD is a parallelogram is opposite sides are congruent. In a parallelogram, opposite sides are parallel, and their opposite angles are congruent. A quadrilateral is a polygon with four sides. A parallelogram is a quadrilateral with two pairs of opposite and parallel sides, which means that the opposite sides in the parallelogram are congruent.
So, a statement that is used to prove that quadrilateral ABCD is a parallelogram is that opposite sides are congruent. It is one of the necessary and sufficient conditions to prove a quadrilateral as a parallelogram. Therefore, option (b) is the correct answer.Apart from this, the other statements that could have been options are:Option (a) - Opposite angles are congruent. It is a property of a parallelogram but is not sufficient to prove that a quadrilateral is a parallelogram. If only opposite angles are congruent, then it is not necessary that opposite sides are parallel.Option (c) - Diagonals bisect each other. This property is only applicable to a parallelogram, and not to any other quadrilateral. However, it is not sufficient to prove a quadrilateral as a parallelogram because this property is only one of the properties of a parallelogram.Option (d) - Consecutive angles are supplementary. This property is common to all quadrilaterals, not just parallelograms. Therefore, it is not sufficient to prove that a quadrilateral is a parallelogram.
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The statement that is used to prove that quadrilateral ABCD is a parallelogram is "Opposite sides are congruent".
A parallelogram is a quadrilateral with two pairs of parallel sides.
There are some properties of parallelograms which include:
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent
Consecutive angles are supplementary
Diagonals bisect each other
Now let's look at the answer options available:
a) Opposite angles are congruent: This statement is used to prove that a quadrilateral is not necessarily a parallelogram, but it is a kite.
b) Opposite sides are congruent: This statement is used to prove that quadrilateral ABCD is a parallelogram.
c) Diagonals bisect each other: This statement is used to prove that quadrilateral is a parallelogram or rectangle. But it cannot prove that ABCD is a parallelogram.
d) Consecutive angles are supplementary: This statement is used to prove that quadrilateral is a parallelogram or rectangle. But it cannot prove that ABCD is a parallelogram.
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Suppose we test H0: p=0.3 versus Ha: p≠0.3 and that a random sample of n=100 gives a sample proportion p ˆ = 0.2. Use the p-value to test H0 versus Ha by setting the level of significance α to 0.10, 0.05, 0.01 and 0.001. What do you conclude at each value of α
At α = 0.10, 0.05,0.01, and 0.001, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the population proportion is not equal to 0.3.
What are the verdicts ?Given
H₀: p = 0.3 (null hypothesis)
Hₐ: p ≠ 0.3 (alternative hypothesis)
Sample size (n) = 100
Sample proportion (p)= 0.2
To calculate the p-value, we can follow these steps -
Calculate the test statistic z -
z = (pa - p₀) /√(p₀ * (1 - p₀) / n)
where pa is the sample proportion, p₀ is the hypothesized population proportion,and n is the sample size.
Calculate the p-value -
For a two-tailed test, the p-value is calculated as:
p-value =2 * P(Z ≤ -|z |), where Z is the standard normal distribution.
Now let's calculate the test statistic and p-value for each level of significance α
For α = 0.10:
p₀ = 0.3
The test statistic is
z =(0.2 - 0.3) / √(0.3 * (1 - 0.3) / 100)
z ≈ -4.714
The p-value for a two-tailed test is calculated like this
p-value = 2 * P(Z ≤ -|z|)
≈ 2 * P(Z ≤ -4.714)
Using a standard normal distribution table or calculator,the p-value is approximately < 0.001
At α = 0.10 - We reject the null hypothesis and conclude that there is sufficient evidence to suggest that the population proportion is not equal to 0.3.
At α = 0.05 - We reject the null hypothesis and conclude that there is sufficient evidence to suggest that the population proportion is not equal to 0.3.
At α = 0.01 - We reject the null hypothesis and conclude that there is sufficient evidence to suggest that the population proportion is not equal to 0.3.
At α = 0.001 - We reject the null hypothesis and conclude that there is sufficient evidence to suggest that the population proportion is not equal to 0.3.
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F(X)= 6Xt3
F(7)= what does it mean
The average price of homes sold in the U.S. in the past year was $220,000 (population mean). A random sample of 81 homes sold this year showed an average price of $210,000. It is known that the standard deviation of the population is $36,000. At a 5% level of significance, test to determine if there has been a significant decrease in the average price of homes. a. State the null and alternative hypotheses to be tested. b. Determine the critical value for this test. c. Compute the test statistic. d. What do you conclude? And interpret it. e. Compute the p-value.
The statistical analysis indicates a significant decrease in the average price of homes based on the given data. The test statistic of -2.5 is lower than the critical value, and the p-value is approximately 0.0062, supporting the conclusion of a significant decrease.
a. The null hypothesis (H0) assumes no significant decrease in the average price of homes, while the alternative hypothesis (Ha) assumes a significant decrease.
b. To determine the critical value, we consider a one-tailed test at a 5% level of significance. Looking up the critical value in the z-table for a one-tailed test, we find it to be -1.645.
c. The test statistic is calculated using the formula z = (sample mean - population mean) / (population standard deviation / sqrt(sample size)). Substituting the given values, we get z = (-10,000) / (36,000 / sqrt(81)) = -2.5.
d. Since the test statistic (-2.5) is less than the critical value (-1.645), we reject the null hypothesis. This indicates that there is evidence of a significant decrease in the average price of homes.
e. The p-value represents the probability of observing a test statistic as extreme as -2.5 or more extreme, assuming the null hypothesis is true. By looking up the p-value corresponding to a z-score of -2.5 in the z-table, we find it to be approximately 0.0062. This indicates strong evidence against the null hypothesis, further supporting the conclusion of a significant decrease in the average price of homes.
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Can someone help me with this. Will Mark brainliest.
Answer:
[tex]\sqrt{53}[/tex]
Step-by-step explanation:
ANSWER PLEASEEEEEE !!!!!!!!!!!!!!
Zack placed $900 into a savings account. What is the total value of the account in 6 months at 3.5% rate?
Step-by-step explanation:
Interest=P×R×T/100
= 900×3.5×6/100
= 9×3.5×6. cancelling 900 by 100
= $189 Answer
You may need to use the appropriate appendix table to answer this question. A person must score in the upper 2% of the population on an admissions test to qualify for membership in society catering to highly intelligent individuals. If test scores are normally distributed with a mean of 140 and a standard deviation of 5, what is the minimum score a person must have to qualify for the society? (Round your answer to the nearest integer).
To calculate the minimum, score a person must have to qualify for the society catering to highly intelligent individuals, given that test scores are normally distributed with a mean of 140 and a standard deviation of 5, you may need to use the appropriate appendix table to answer this question.
The Z-score formula is useful for calculating the minimum score a person must have to qualify for the society catering to highly intelligent individuals. The formula for Z-score is given below: Z = (X - μ) / σwhere, X is the minimum scoreμ is the mean σ is the standard deviation Z is the z-score
From the given data, we can find the Z-score as follows: Z = (X - μ) / σZ = (X - 140) / 5
Given that the person must score in the upper 2% of the population, the area under the normal curve is 0.02.
Since the curve is symmetric, the area under the curve to the right of the mean will be 0.5 - 0.02/2 = 0.49. Since we need to find the minimum score, we can use the inverse normal distribution table or appendix table. From the inverse normal distribution table, the Z-score for 0.49 is 2.06. Now we can substitute the Z-score in the above formula and find the minimum score: X = Zσ + μX = (2.06) (5) + 140X = 151.3The minimum score a person must have to qualify for the society catering to highly intelligent individuals are 151 (rounded to the nearest integer).
Therefore, the correct answer is 151.
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Is 1.75 less or greater than 1 1/2
Answer:
Greater 1 1/2 is 1.50
Step-by-step explanation:
Please Brainliest if right <3
Answer:
Yes cuz 1.75= 1 3/4 while 1 1/2= 1 2/4
Step-by-step explanation:
A.) Use the definition of the definite integral to evaluate
∫_0^3(2x−1)dx. Use a right-endpoint approximation to generate the Riemann sum.
B.)What is the total area between f(x)=2x and the x-axis over the interval [−5,5]?
C) Calculate R4 for the function g(x)=1/x2+1 over [−2,2].
D)Determine s′(5) to the nearest tenth when s(x)=9(6x)/x3. (Do not include "s′(5)=" in your answer.)
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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