To use upper and lower sums to approximate the area of the region under the curve y = √6x, we need to divide the interval of integration into a certain number of subintervals of equal width.
Let's say that we want to divide the interval [a, b] into n subintervals of equal width. We can then define the points x0, x1, ..., xn as follows:
x0 = a
x1 = a + (b - a)/n
x2 = a + 2(b - a)/n
...
xn = b
The width of each subinterval is (b - a)/n.
We can then use these points to define the upper sum and lower sum as follows:
Upper sum = ∑ (b - a)/n * max(f(x))
Lower sum = ∑ (b - a)/n * min(f(x))
where the sum is taken over all subintervals, and max(f(x)) and min(f(x)) represent the maximum and minimum values of the function f(x) on each subinterval, respectively.
To calculate the upper and lower sums, we need to evaluate the function f(x) at each of the points x0, x1, ..., xn. For example, if we want to calculate the upper sum using 4 subintervals, we would evaluate the function at the points x0, x1, x2, and x3, and then use these values to calculate the upper sum using the formula above.
Once we have calculated the upper and lower sums, we can use them to approximate the area of the region under the curve. The area of the region is approximately equal to the average of the upper and lower sums.
For example, if the upper sum is 1.5 and the lower sum is 0.5, then the area of the region is approximately (1.5 + 0.5)/2 = 1.
In general, as we increase the number of subintervals, the upper and lower sums will get closer and closer to the actual area of the region, and the approximation will become more accurate.
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Suppose that the functions u and w are defined as follows.
u(x)=x² + 3
w (x)=√x+2
Find the following.
(wu) (2) =
(uw) (2) =
The values of composite functions are,
(w о u)(2) = √7 + 2
(u о w)(2) = 9 + 4√2
What is composite function?
Function composition is an operation о used in mathematics that takes two functions, f and g, and creates a function, h = g о f, such that h(x) = g. The function g is applied in this operation to the outcome of applying the function f to x.
Given:
u(x) = x^2 + 3
w(x) = √x+2
We have to find (w о u)(2) and (u о w)(2).
First to find (w о u)(x)
(w о u) = w(u(x))
= w(x^2 + 3)
(w о u) = √(x^2 + 3) + 2
⇒ (w о u)(2) = √(2^2 + 3) + 2
(w о u)(2) = √7 + 2
Now to find (u о w).
(u о w)(x) = u(w(x))
= u(√x+2)
= (√x+2)^2 + 3
= x + 4√x + 4 + 3
(u о w)(x) = x + 4√x + 7
⇒ (u о w)(2) = 2 + 4√2 + 7
(u о w)(2) = 9 + 4√2
Hence,
The values of composite functions are,
(w о u)(2) = √7 + 2
(u о w)(2) = 9 + 4√2
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elodie is putting on a fashion show and has five fabulous outfits for her five fabulous fashion models. however, on the day of the show, two of the outfits were ruined in an unfortunate permanent marker incident. regardless, the show must go on and the remaining outfits will be presented. if each outfit can only be worn by one model and there is no time for any model to wear more than one dress, how many different shows can elodie put on? (note: two shows are considered the same if they contain the same models wearing the same dresses.)
By analyzing the question, we find that there are a total of 5 * 4 * 3 = 60 different shows that Elodie can put on.
What is permutation?A permutation is an arrangement of a set of items in a specific order. Permutations are typically denoted using the notation "P" followed by the number of items being permuted and the number of items being chosen at a time.
What is the formula to calculate permutation?The formula for calculating permutations is as follows:
P(n,r) = n! / (n-r)!
where:
P(n,r) is the number of permutations of r items from a set of n items.
n! is the factorial of n, which is the product of all positive integers less than or equal to n.
There are five fashion models and three remaining outfits, which means there are 5 ways to choose the model who wears the first outfit, 4 ways to choose the model who wears the second outfit, and 3 ways to choose the model who wears the third outfit. Therefore, there are a total of 5 * 4 * 3 = 60 different shows that Elodie can put on.
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Which of the following is (x-8)(x+3)/(x+9)(x-1) simplified?
The simplified form of the given expression is [x² - 5x -24]/[x² + 8x -9].
What is an expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
Given expression is
(x-8)(x+3)/(x+9)(x-1)
Now applying the formula (x - a)(x + b) = x² -(a - b)x -ab in the numerator:
= [x² - (8 - 3)x -8×3]/(x+9)(x-1)
= [x² - 5x -24]/(x+9)(x-1)
Again applying the formula (x - a)(x + b) = x² -(a - b)x - ab in the denominator:
= [x² - 5x -24]/[x² - (1 - 9)x -9×1]
= [x² - 5x -24]/[x² + 8x -9]
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Use the Sport Shop data set below to calculate a 3 -year Weighted Moving Average (WMA) to predict the number of sports equipment that will be sold in 2022. Use the weights of 0.5, 0.3, and 0.2 0.5 , 0.3 , and 0.2 for the 3 3 -year WMA, where the first weight is used for the most recent year and the last weight is used for the least recent year. Round your answer to two decimal places, if necessary.
The 3-year Weighted Moving Average (WMA) for predicting the amount of sports equipment sales in 2022 is 1.7.
What is Weighted Moving Average?A Weighted Moving Average gives more weight to recent data and less weight to historical data. This is accomplished by multiplying the price of each bar by a weighting factor. WMA will track prices more precisely than a related Simple Moving Average due to its unique formula. A Weighted Moving Average (WMA) is a sort of moving average that prioritizes recent data over historical data. A moving average is a technical indicator that displays how the price has moved on average over a given time period.
Here,
weights=0.5, 0.3, and 0.2
(0.5×1+0.3×2+0.2×3) / (0.5+0.3+0.2) = 1.7
The 3-year Weighted Moving Average (WMA) to predict the number of sports equipment that will be sold in 2022 is 1.7.
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what is the answer to the question below
The equation of the area is 308 = 2 * (10 * x) + 2 * (2 * x) + 2 * (10 * 2) + 6 * (5 * 5) - 2 * (5 * 5)
How to determine the equation?From the question, we have the following parameters that can be used in our computation:
Area = 308
The formula used to calculate area
Area = S.A of the bottom + S.A of the top - 2 * Overlap
Using the given figure, we have
S.A of the top = 6 * (5 * 5)
S.A of the bottom = 2 * (10 * x) + 2 * (2 * x) + 2 * (10 * 2)
Overlap = 2 * (5 * 5)
So, we have
308 = 2 * (10 * x) + 2 * (2 * x) + 2 * (10 * 2) + 6 * (5 * 5) - 2 * (5 * 5)
Hence, the equation is (b)
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Suppose that the probability that the dart hit the area between the square of side length 14 and the square of side length 16
The probability of the area hit by the dart between the bigger square and the smaller square is equal to 0.7656.
As given in the question,
Total number of squares present = 2
Side length of the bigger square = 16 units
Side length of the smaller square = 14 units
Area of the bigger square = ( side length )²
= ( 16 )²
= 256 square units
Area of the smaller square = ( side length )²
= ( 14 )²
= 196 square units
Here favorable outcome is represented by small square and total outcome is represented by bigger square
Probability that the given dart hit the area between the square is
= 196 / 256
= 49/64
= 0.765625
≈ 0.7656
Therefore, the probability of the dart hitting the area formed by bigger square and smaller square is equal to 0.7656.
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An offshore oil well is 3 kilometers north off the coast that runs directly east to
west. A point, E, is labeled on the coast directly south of the oil well. The refinery
is located 4 kilometers east of point E. Laying pipe in the water costs $500,000 per kilometer and laying pipe on the coast costs $300,000 per kilometer.
What path should the pipe follow in order to minimize the cost?
Show all process leading to your answer.
Answer:
come ashore 1.75 km west of the refinerycost: $2.4 millionStep-by-step explanation:
You want to know the least-cost path of a pipeline from 3 km offshore to 4 km east of the closest point on shore. The cost of pipe in the water is $0.5M/km, and onshore is $0.3M/km.
Generic solutionThe solution in the general case for this kind of question is that the sine of the angle between the route directly to shore and the least-cost route is the ratio of the onshore cost to the in-water cost.
sin(α) = (0.3M/km)/(0.5M/km) = 3/5
The distance from the closest point onshore (E) to the least-cost onshore point is the product of the distance from shore and the tangent of this angle:
distance downshore = (3 km)·tan(arccos(3/5)) = 2.25 km
Since the refinery is 4 km downshore, this point is 1.75 km from the refinery.
The pipe should follow a direct path underwater from the well to a point 1.75 km west of the refinery, then downshore the remaining 1.75 km to the refinery.
Cost equationIf x represents the distance from the refinery to the point where the pipeline comes ashore, the cost of the route in millions will be ...
c = 0.5√(3² +(4-x)²) +0.3x
where the square root function is calculating the underwater length of the pipeline using the Pythagorean theorem.
MinimizationThis cost function will be minimized when its derivative with respect to x is zero.
c' = 0.5(1/2)(2x -8)/√(x² -8x +25) +0.3 = 0
0 = 0.5(x -4) +0.3√(x² -8x +25) . . . . . . numerator of the combined terms
4 -x = 0.6√(x² -8x +25) . . . . multiply by 2, add 4-x
16 -8x +x² = 0.36x² -2.88x +9 . . . . . . square both sides
0.64x² -5.12x +7 = 0 . . . . . subtract the right side
x = (5.12 -√(5.12² -4(0.64)(7)))/(2(0.64)) = 2.24/1.28 = 1.75
The route with lowest cost comes ashore 1.75 km from the refinery.
__
Additional comment
The cost of the pipeline will be ...
c = 0.5√(9 +(4-1.75)²) +0.3(1.75) = 0.5√14.0625 +0.525
c = 2.4 . . . . million dollars
The attached graph shows the cost function has a minimum of 2.4M at a distance of 1.75 km from the refinery. The cost is only 2.5M if the pipe runs directly from the well to the refinery (x=0).
One interior angle of a triangle is 43°, and the other two angles are congruent. Choose the equation that could be used to determine the degree measure of one of the congruent angles. 2x + 43 = 180 2x − 43 = 90 x + 43 = 180 x − 43 = 90
Answer:
x − 43 = 90
Step-by-step explanation:
2x + 43 = 180
2x − 43 = 90
x + 43 = 180
x − 43 = 90
ABCD is a rectangle find the length of AC and find the measures of a and 0
In the given triangle, length of AC = 12.3 units
α= 45⁰ and θ = 45⁰
Using Pythagoras theorem,
[tex]AC^{2} = AB^{2} + BC^{2}[/tex]
[tex]AC^{2}[/tex] = 9 + 144
AC = 12.37
Now, to find the angles:
AC is the diagonal.
Then AD=BC and AB=CD
And ∠ABC=∠BCA=∠CDA=∠DAB=90⁰
In ΔABC and ΔADC
∠ABC=∠ADC (Angle of rectangle)
AB=DC (Opposite side of rectangle)
AC=AC (Common side)
∴ΔABC≅ΔADC
∴∠ACD=∠ACB
∵∠ACD+∠ACB=90⁰ ..........[Angle ACB is the angle of rectangle]
∴2∠ACD=90⁰
⇒∠ACD=45⁰
⇒θ = 45⁰
similarly, α = 45⁰
Pythagoras theorem:
A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this rule, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse, or the side across from the right angle.
This theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, often called the Pythagorean equation:
[tex]a^{2} + b^{2} = c^{2}[/tex]
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BigPhone Company charges a connection fee of $200 and $0.15 per minute. LittlePhone Company charges a connection fee of $175 and $0.18 per minute.
Which phone plan would be cheapest if you spend 310 minutes on the phone?
Group of answer choices
LittlePhone Company is cheaper
Both companies will charge the same amount
BigPhone Company is cheaper
There is not enough information
The amount of Little phone company is $230.8 and of Big phone company is $246.5. Little Phone Company is cheaper. The correct option is B.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that Big phone Company charges a connection fee of $200 and $0.15 per minute. Little phone Company charges a connection fee of $175 and $0.18 per minute.
The cost for both companies for time 310 minutes will be calculated as,
Cbc= 0.15t + 200
Cbc = ( 0.15 x 310) + 200
Cbc = $246.5
The cost of little company,
Clc = 0.18t + 175
Clc = ( 0.18 x 310 ) + 175
Clp = $230.8
From the above costs, it is observed that the Little Phone Company is cheaper.
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a sequential circuit with two d flip-flops a and b, two inputs, x and y, and one output z is specified by the following next-state and output equations:
DB will appear at outputs A, and B.
Step 1
D flip flop stands for a delay flip flop that produces output that is identical to input after a brief delay. The flip flop's input and next state are equal.
Z is an output, and x and x inputs.
x'y + xA = DA= A*
B* = x'B + xA
z=A (output is independent of input) (output is independent of input)
The next states are A(t+1) and B(t+1). We must provide the next state value to D of the D flip flop in order to obtain the next states A(t+1), and B(t+1) for A, B(present state). So the sequential circuit will be:
Step 2
To get the next state as A(t+1)= x’A + xA, B(t+1)= x’B + xA, we have to give them to DA, DB of D flip flop because for D flip flop whatever is given to DA, DB will appear at output A, B.
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round 19.83 to the nearest tenth
Answer:
19.8
Step-by-step explanation:
19.83 rounded to the nearest tenth is 19.8.
To find the circumference of a circle, the measurement of the circle’s:
radius or diameter must be known.
area must be known.
base or height must be known.
tangent must be known.
None of these choices are correct.
Answer: Radius or Diameter
Step-by-step explanation: The formula for circumference is diameter times pi. Since radius is half of diameter, you could still easily find the circumference. You could also find it with area, but that involves multiple formulas and a lot of math. I hope this helped :)
suppose a runner claims that her mile run time is less than 9 minutes, on average. several of her friends do not believe her, so the runner decides to do a hypothesis test, at a 5% significance level, to persuade them. she runs 7 time trials, collects the proper data, and works through the testing procedure:H0: μ=9; Ha: μ<9α=0.1 (significance level)The test statistic isz0=x¯−μ0σn√=7.7−9112√=−4.5The critical value is −z0.1=−1.28.Conclude whether to reject or not reject H0 and interpret the results.Select all that apply:Reject H0. At the 10% significance level, the test results are statistically significant to conclude that the mean time is less than 9 minutes.There is NOT sufficient evidence at the 10% significance level to conclude that the mean time is less than 9 minutes.The test statistic falls within the rejection region.The test statistic is NOT in the rejection region.
The conclusion of the hypothesis test is;
B: Reject H₀. At the 10% significance level, the data provides sufficient evidence to conclude that the mean time is less than 9 minutes.
What is the conclusion of the hypothesis test?We are given;
Null Hypothesis; H₀: μ = 9;
Alternative Hypothesis; Hₐ: μ < 9
Significance level; α = 0.1
The critical value; z_0.1 = 1.28
Test statistic; z = -4.5
Now, the rejection rule here is that if the test statistic is below the critical value, we reject the null hypothesis at the significance level.
In this case, the the test statistic is less than the critical value and as such we reject the null hypothesis and conclude that the data provides sufficient evidence to conclude that the mean time is less than 9 minutes
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A chocolate chip cookie recipe calls for 2 3/4 cups of flour. You only have a 1/4-cup measuring cup and a 3/4-cup measuring cup that you can use.
a. What are different combinations of the measuring cups that you can use to get a total of 2 3/4 cups of flour?
b. Write each of the combinations as an addition equation.
The different combinations of the measuring cups that you can use to get a total of 2 3/4 cups of flour include 11 cups of 1/4 or 3.67 cups of 3/4.
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Since the chocolate chip cookie recipe calls for 2 3/4 cups of flour. You only have a 1/4-cup measuring cup and a 3/4-cup measuring cup that you can use.
The combination will be:.
= 2 3/4 ÷ 1/4.
= 11
The second combination will be:
= 2 3/4 ÷ 3/4
= 3.67
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a census is a statistical study in which an entire population is counted, not just a sample. which of the following stats is most likely to be based on a census?
true census is most likely to be based on a census There are many benefits to choosing a portion of the population selected to represent the population.
• Reducing the cost and time needed to conduct research. Researchers will save more time and money analyzing sample than the whole population.
• Reducing resource deployment. The manpower needed to analyze a sample is less than the manpower needed to analyze the whole population.
• Increasing data accuracy. Data taken from the sample will be more accurate than data taken from the whole population because the sample is more willing to join the research.
• Creating an intensive and exhaustive data. The data taken from a sample will be more intensive and exhaustive because the respondents are minimum.
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a line through the origin, rotates around the origin in such a way that the angle, theta, between the line and the positive x-axis changes at the rate of d/dt for time > 0. Which expression gives the rate at which the slope of the line is changing
The rate at which the slope of the line is changing with respect to time is dθ/dt.
The rate at which the slope of a line is changing with respect to time is a concept in calculus that is known as the derivative. The derivative measures the rate of change of a function with respect to one of its variables. In this case, we are looking at the rate of change of the slope of the line with respect to time. The slope of a line is determined by the angle, theta, between the line and the positive x-axis. Therefore, the rate of change of the slope of the line with respect to time is equal to the rate of change of the angle, theta, with respect to time. This can be expressed as dθ/dt, where dθ represents the change in theta and dt represents the change in time. Therefore, the expression which gives the rate at which the slope of the line is changing with respect to time is dθ/dt.
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Bill has to run some errands around town. Look at the map below to calculate his distance if he starts at home, goes to the video store, then the grocery store, grabs a fast snack, and ends at home. How many units did he walk?
Coordinate grid with points labeled home, video store, fast snacks, and grocery store. Home is located at negative 2, 3, video store is at 4, 3, fast snacks is at negative 2, negative 4, and grocery store is at 4, negative 4.
(4 points)
13 units
22 units
25 units
26 units
Answer:
26 units
Step-by-step explanation:
First he goes from home to the video store.
home (-2,3) --> video store (4,3)
There is no change in his y distance, so the distance he travels is only the change in x.
distance from home to video store = 4 - (-2) = 6 units
Then he goes from the video store to the grocery store
video store (4,3) --> grocery store (4,-4)
There is no change in his x distance, so the distance he travels is only the change in y.
distance from video store to the grocery store = 3 - (-4) = 7 units
Then he goes from the grocery store to the fast snacks
grocery store (4,-4) --> fast snacks (-2,-4)
There is no change in his y distance, so the distance he travels is only the change in x.
distance from the grocery store to the fast snacks = 4 - (-2) = 6 units
Finally he goes from the fast snack store to his house
fast snacks (2,-4) --> house (2,3)
There is no change in his x distance, so the distance he travels is only the change in y.
distance from the fast snacks to his house = 3 - (-4) = 7 units
therefore the total distance he traveled is 6 units + 7 units + 7 units + 6 units = 26 units
I hope this helps!
Which is the simplified form of the expression three 7/5 X +4-232 -5/4 X
The simplified form of the expression is 123/20 x - 228
How to determine the simplified form of the expression?From the question, we have the following parameters that can be used in our computation:
three 7/5 X +4-232 -5/4 X
Rewrite the above expression properly
So, we have the following representation
37/5 x + 4 - 232 - 5/4 x
Collect the like terms in the above expression
So, we have the following representation
37/5 x - 5/4 x + 4 - 232
Evaluate the like terms in the above expression
So, we have the following representation
123/20 x + 4 - 232
Solving further, we have
123/20 x - 228
Hence, the solution is 123/20 x - 228
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If t less than s and s less than r what is the relationship between the values t and r?
If t is less than s and s is less than r then the relationship between the values t and r is - t is less than r.
We are given that-
t is less than s i.e. t < s
and
s is less than r i.e. s < r
Now, let us find the relationship between the values of t and r.
t < s and s < r
this implies that - t < s < r
Hence, we get t < r.
Thus, we get that if t is less than s and s is less than r then the relationship between the values t and r is - t is less than r i.e. t < r.
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A popular social media platform has begun offering
stock shares to the public. In the past 2 years, the
price of the stock has generally increased. An
investment specialist gathers data on the stock price
over the past 2 years and proposes two models for
estimating the growth of the stock, as shown in the
scatterplots.
Based on the scatterplots, which type of model is
most suitable for estimating the stock price?
A) A power model is suitable because the scatterplot
of log(weeks) against log(stock price) shows a
curved relationship.
B) A linear model is suitable because the scatterplot
of weeks against log(stock price) shows a strong
linear relationship.
C) An exponential model is suitable because the
scatterplot of log(weeks) against log(stock price)
shows a curved relationship.
D) An exponential model is suitable because the
scatterplot of weeks against log(stock price) shows
a strong linear relationship.
Answer:
C) An exponential model is suitable because the scatterplot of log(weeks) against log(stock price) shows a curved relationship.
Step-by-step explanation:
Solve and graph the inequality on a number line:
42>g+27
The solution of the inequality 42 > g + 27 is 25 > g and the graph of the inequality has been plotted on a number line
The given inequality is
42 > g + 27
The inequality is the mathematical statement that shows the relationship between two expression with and inequality sign. The inequality maybe less than, less than or equal, greater than, greater than or equal etc. The equal sign will not be a part of inequality
Th given inequality is
42 > g + 27
Subtract both side of the inequality by 27
42 - 27 > g + 27 - 27
25 > g
Plot the inequality in number line
Therefore, the solution is 25 > g and the inequality has been plotted on the number line
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the augmented matrix is given for a system of equations. if the system is consistent, find the general solution. otherwise state that there is no solution.
The given matrix has no solution.
What is the system of equations?
system of equations, or simultaneous equations, In algebra, two or more equations to be solved together (i.e., the solution must satisfy all the equations in the system). For a system to have a unique solution, the number of equations must equal the number of unknowns. Even then a solution is not guaranteed.
According to the question, the matrix is:
[tex]\left[\begin{array}{ccc}1&-5&-4\\0&0&7\\ \end{array}\right][/tex]
The linear equation will be:
x - 5y = -4
and
0x + 0y = 7
i.e,
0 = 7 (Not possible)
Hence, the above given matrix has no solution.
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21. Which statement is a good definition?
Right angles are angles formed by two intersecting lines.
Skew lines are lines that do not intersect.
A
square is a rectangle with four congruent sides.
Parallel lines are lines that do not intersect.
The statement that is a good definition is D. Parallel lines are lines that do not intersect.
How to illustrate the information?A type of quadrilateral with all sides being equal and all angles being 90 degrees is a square.
Lines that do not cross each other but have a constant perpendicular distance are known as parallel lines. Right angles and skew lines are perpendicular to one another but not parallel. Therefore, a square is a type of rectangle in which all four sides are parallel to one another.
Therefore, based on the information, the correct option is D
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Use Taylor's Inequality to determine the number of terms of the Maclaurin series for e^x that should be used to estimate e^0.1 to within 0.0000001.
The number of terms of the Maclaurin series for eˣ that should be used to estimate [tex]e^{0.1}[/tex] to within 0.00001 is 4.
Taylor’s inequality:
If Rn( x ) = 0
Rn(x)=0
Rn(x)=0.
The given function is eˣ
Thus, all the derivatives of eˣ is eˣ itself.
Suppose that, the nth derivative of eˣ is eˣ
To estimate the value of [tex]e^{0.1}[/tex] substitute the value of x as 0.1.
Note that Taylor series is called Maclaurin series when a=0.
Usually, Maclaurin series will starts with n=2.
Increase the value of n until the reminder is less than 0.00001.
By Taylor’s inequality,
If | [tex]f^{n}[/tex](0.1) | = [tex]e^{0.1}[/tex]≤ M then | Rₙ(x) |≤[tex]\frac{M}{(n+1)!}[/tex] [tex]|0.1-0|^{n+1}[/tex]
Substitute the value of n as 2. Then,
[tex]|R2(x)|[/tex]≤[tex]\frac{M}{(2+1)!} |0.1-0|^{2+1}[/tex]
≤ [tex]\frac{e^{0.1}}{3!} |0.1|^{3}[/tex]
≤ [tex]\frac{e^{0.1}}{6} 0.001[/tex]
≤ 0.00018
Since [tex]|R2(x)|[/tex] ≥ choose the value of n as 3. Then,
[tex]|R3(x)|[/tex] ≤[tex]\frac{M}{(3+1)!} |0.1-0|^{3+1}[/tex]
≤ [tex]\frac{e^{0.1}}{4!} |0.1|^{4}[/tex]
≤ [tex]\frac{e^{0.1}}{24} 0.0001[/tex]
≤ 0.0000046
Therefore, [tex]|R3(x)|[/tex] ≤ 0.00001
That is, n=3 satisfies the inequality.
So, by adding the 4 terms (when n=0,1,2,and 3) of the Maclaurin series, it
is possible to estimate the value of [tex]e^{0.1}[/tex] to within 0.00001.
Thus, the number of terms of the Maclaurin series for eˣ that should be used to estimate [tex]e^{0.1}[/tex] to within 0.00001 is 4.
The number of terms of the Maclaurin series for eˣ that should be used to estimate [tex]e^{0.1}[/tex] to within 0.00001 is 4.
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Find the next permutation in lexicographic order About For each permutation of (1,2,3,4,5,6,7,give the next largest permutation or indicate that the permutation is the last one in lexicographic order (1,2,3,4,5,6,7) (7.6,5,4,3,2, 1) (1.7,6,4,2,3,5) (3,7,6,5,4,2,1) (5,4,7,6,3,2, 1)
On solving the provided question, we can say that In lexicographic order, the following variation will be (5,6,7,4,3,2,1).
What is a permutation?It is known as permuting the set in mathematics to rearrange the components of a set that is already ordered or, if the set is not already ordered, to place its members in a linear or sequential order. In this sense, "permutation" refers to the process of changing the linear order of an ordered set.It should be mentioned that a permutation is a mathematical concept that describes several potential arrangements of numbers or other objects.
The ascending numerical order is the lexicographic order when it comes to numbers. From left to right, the numbers are growing. The permutations of "1,2,3," for instance, are 123, 132, 213, 231, 312, and 321 in lexicographic order.
In lexicographic order, the following variation will be (5,6,7,4,3,2,1).
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What is the range of the data set?
{6.2,9.1,2.9,1.6,9.3,5.5,8.3}
Enter your answer as a decimal, rounded to the nearest tenth, like this: 4.2
The range of the data set { 6.2 , 9.1 , 2.9 , 1.6 ,9.3 , 5.5 , 8.3 } is 7.7 .
Given :
the range of the data set {6.2,9.1,2.9,1.6,9.3,5.5,8.3}
Enter your answer as a decimal, rounded to the nearest tenth .
Range :
In statistics, the range is the spread of your data from the lowest to the highest value in the distribution.
Range = highest value - lowest value
Arrange in ascending order = { 1.6 , 2.9 , 5.5 , 6.2 , 8.3 , 9.1 , 9.3 }
Here highest value = 9.3
Lowest value = 1.6
Range = 9.3 - 1.6
= 7.7
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What is the value of s?
10
units
The value of s for the given right angle triangle by Pythagoras' theorem will be 17.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
As per the given triangle, ABD is a right-angle triangle thus to Pythagora's theorem,
s² = 15² + 8²
s = 17
Hence "According to Pythagoras' Theorem, the value of s for the given right angle triangle is 17.".
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Four-Sided Dice A pair of four-sided dice-each with the numbers from 1 to 4 on their sides- -are rolled, and the num bers facing down are observed. (Note: A four-sided die is sim- ilar to a pyramid with a triangular base.) (a) List the sample space. (b) Describe each of the following events as a subset of the sample space i) Both numbers are even. (ii) At least one number is odd. iii Neither number is less than or equal to 2. (iv) The sum of the numbers is 7. (v) The sum of the numbers is greater than or equal to 6. (vi) The numbers are the same. (vii) A 2 or 3 occurs, but not both 2 and 3. (viii) No 4 appears.
Previous question
Answer:
Step-by-step explanation:
(a)
The sample space is
{(1,1), (2,2), (3,3), (4,4), (1,2), (1.3), (1,4), (2,1), (2,3), (2,4), (3,1), (3,2) (3,4), (4,1),(4,2), (4.3)}
(b)
i {(2,2), (4,4), (2,4), 4,2)}
ii {(1,1), (1,2), (3,3), (1,3), (1,4), (2,1), (2,3), (3,1), (3,2), (3,4), (4,1), (4,3)}}
iii {(1,1)}
iv {3,4), (4,3)}
v {(3,3), (2,4), (4,2), (3,4), (4, 3), (4,4)}
vi {(1,1), (2,2), (3,3), (4,4)}
vii {(1,2), (1,3), (2,1), (3,1), (2,2), (2,4), (3,3), (3,4), (4,2), (4,3)}
viii {(1,1), (2,2), (3,3), (1,2), (1.3), (2,1), (2,3), (3,1), (3,2)}
assume that the two samples are independent simple random samples selected from normally distributed populations. do not assume that the population standard deviations are equal. refer to the accompanying data set. use a significance level to test the claim that women and men have the same mean diastolic blood pressure.
Women
Men
Women
Men
71.0
69.0
63.0
63.0
94.0
64.0
72.0
79.0
81.0
69.0
56.0
91.0
66.0
60.0
59.0
79.0
71.0
64.0
79.0
87.0
79.0
71.0
73.0
63.0
57.0
59.0
69.0
71.0
50.0
40.0
65.0
78.0
71.0
67.0
66.0
75.0
87.0
66.0
83.0
57.0
68.0
83.0
54.0
65.0
60.0
75.0
75.0
84.0
71.0
53.0
75.0
71.0
1. Let μ1 be the mean diastolic blood pressure for women and let μ2 be the mean diastolic blood pressure for men. What are the null and alternative hypotheses?
2. Calculate the test statistic.(Round to two decimal places as needed.)
3. Find the P-value. (Round to three decimal places as needed.)
4. Make a conclusion about the null hypothesis and a final conclusion that addresses the original claim.
1)test the claim that women and men have the same mean diastolic blood pressure .Let p1 be the mean diastolic blood pressure for women and let u2 be the mean diastolic blood pressure for men
there for we test
H0: u1 = u2
H1 : u1 =!u2
2)t= overline X 1 - overline X 2 sqrt((S_{1} ^ 2)/n_{1} + (S_{2} ^ 2)/n_{2})
= (69.81 - 69.35)/(sqrt((10.46 ^ 2)/26 + (11.2l ^ 2)/26)
= 0.153
3) P-value.
t-statistic value = 0.153 , alpha=0.05 then
p-value for two tail test = 0.879 which is greater than n = 0.05(0.879 > 0.05) So we do not reject H0.
4)Make a conclusion about the null hypothesis and a final conclusion that addresses the original claim.
we concluded that the null hypothesis not rejected, at 95 % confidence H0:u1= u2 accepted.
that is we accept the claim that women and men have the same mean diastolic blood pressure.at 0.05 significance level.
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