The confidence interval is ( 2.902871971 7.297128029 )
Thus, the confidence interval is ( 2.359668581 , 7.840331419 )
a)
Note that
Lower Bound = X - t(alpha/2) * s / sqrt(n)
Upper Bound = X + t(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.025
X = sample mean = 5.1
t(alpha/2) = critical t for the confidence interval = 2.262157163
s = sample standard deviation = 3.0713732
n = sample size = 10
df = n - 1 = 9
Thus,
Lower bound = 2.902871971
Upper bound = 7.297128029
Thus, the confidence interval is
( 2.902871971 , 7.297128029 ) [ANSWER]
b)
Note that
Lower Bound = X - t(alpha/2) * s / sqrt(n)
Upper Bound = X + t(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.01
X = sample mean = 5.1
t(alpha/2) = critical t for the confidence interval = 2.821437925
s = sample standard deviation = 3.0713732
n = sample size = 10
df = n - 1 = 9
Thus,
Lower bound = 2.359668581
Upper bound = 7.840331419
Thus, the confidence interval is
( 2.359668581 , 7.840331419 )
As we can see, the interval became wider, and the margin of error became larger.
This is so because the critical t value becomes larger with larger confidence level.
This makes sense because you need to enclose more values to be "more confident" that you have the true mean.
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Plz help! Dont answer if you cant help
Answer:
42.09 cubic units
Step-by-step explanation:
[tex]\frac{4.11*5.12}{2} *4[/tex]
=42.0864, which rounds to 42.09
Note: The 6.57 is not needed to solve this problem
Find an equation of the plane tangent to the following surface at the given point. z=8-2x²-2y²; (5,3, – 60) Z=
z - 20x - 12y + 76 = 0 is the required equation of the plane that is tangent to the given surface at the point (5, 3, – 60).
Given the function is z=8-2x²-2y² and point is (5, 3, – 60).
We need to find the equation of the plane tangent to the given surface at the given point. The gradient vector of the function f(x, y, z) is given by(∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k∂f/∂x= -4x and ∂f/∂y= -4y
Therefore, the gradient vector is given by-4xi -4yj + k
Therefore, the equation of the tangent plane is given byz - z1=∇f(x1, y1) . (x - x1)i + ∇f(x1, y1) . (y - y1)j + (-1) [f(x1, y1, z1)]
where (x1, y1, z1) is the given pointWe have f(5, 3, – 60) = 8 – 2(5²) – 2(3²) = – 60
Therefore, the equation of the plane is given byz + 60= (-20i - 12j + k) . (x - 5) - (16i + 24j + k) . (y - 3)
Thus, z - 20x - 12y + 76 = 0 is the required equation of the plane that is tangent to the given surface at the point (5, 3, – 60).
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help ASAP please ill give brainliest
Find the general solution for the differential equation
x sinθ dθ + (x3− 2x2cosθ) dx = 0
Therefore, x^2 - x^2cosθ + C = 0 is the general solution of the given differential equation.
General solution of the given differential equation is x^2 - x^2cosθ + C = 0, where C is the constant of integration.
To solve the differential equation, we have to integrate the given equation. Here, x sinθ dθ + (x^3 - 2x^2cosθ) dx = 0.
Let's integrate it using separation of variables.
x sinθ dθ = - (x^3 - 2x^2cosθ) dx
Dividing both sides by x^2, we get
sinθ dθ/x - (x - 2cosθ) dx/x^2 = 0
Now, integrate the above equation.
∫sinθ dθ/x - ∫(x - 2cosθ) dx/x^2 = ln|C|
Simplifying the above equation, we get
- cosθ/x + 1/x - x^(-1) sinθ = ln|C|
Multiplying both sides by -x, we get
cosθ - x + x^2 sinθ = -x ln|C|
Rearranging the terms, we get
x^2 - x^2cosθ + ln|C| = 0
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Consider two planes 4x - 3y + 2z= 12 and x + 5y -z = 7.
Which of the following vectors is parallel to the line of intersection of the planes above?
a. 13i + 2j +17k
b. 13i-2j + 17k
c. -7i+6j +23k
d. -7i-6k +23k
The vector that is parallel to the line of intersection of the planes 4x - 3y + 2z = 12 and x + 5y - z = 7 is option (c) -7i + 6j + 23k.
To find a vector that is parallel to the line of intersection of two planes, we need to determine the direction of the line. This can be achieved by finding the cross product of the normal vectors of the planes.
The normal vector of the first plane 4x - 3y + 2z = 12 is (4, -3, 2), obtained by taking the coefficients of x, y, and z. Similarly, the normal vector of the second plane x + 5y - z = 7 is (1, 5, -1).
To find the cross product of these two normal vectors, we take their determinant: (4i, -3j, 2k) x (1i, 5j, -1k). Evaluating the determinant, we get (-23i - 6j - 13k).
The resulting vector -23i - 6j - 13k is parallel to the line of intersection of the planes. However, the given options only include positive coefficients for i, j, and k. To match the given options, we can multiply the vector by -1 to obtain a parallel vector. Thus, -(-23i - 6j - 13k) simplifies to -7i + 6j + 23k, which matches option (c). Therefore, option (c) -7i + 6j + 23k is the vector parallel to the line of intersection of the planes.
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prime factorization of 7776
The orange divisor(s) above are the prime factors of the number 7,776. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 = 7,776. It can also be written in exponential form as 25 x 35.
calculate the power of the pump which can lift 400kg of water to be stored in a water tank at a height of 19m and 40s (take g=10/s2)
Can someone help me with this. Will Mark brainliest.
How many solutions does the equation 5x + 3x – 4 = 10 have?
O Zero
O One
O TWO
O Infinitely many
be
????
Answer:
Step-by-step explanation:
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How many solutions does the equation 5x + 3x − 4 = 10 have
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This Must Only Have One Solution, Because The Right Side Of The Equation Is Just Plainly Ten. Lets Solve This:
5x + 3x - 4 = 10
Add Four To Both Sides To Begin Simplifying.
5x + 3x = 14
Now, Combine Like Terms.
8x = 14
Divide:
8x/8 = 1X = X
14/8
X = 14/8
14/8 = 1.75
X = 1.75
Check:
(5 * 1.75) + (3*1.75) - 4 = 10
8.75 + 5.25 - 4 = 10
14 - 4 = 10
10 = 10.
This Is True, So X Does Equal 1.75
Which equation below had a solution x =5.5 ?
O A) -1 + x = 6.5
OB) -6x = -33
OC) -3x = 16.5
OD)-2 + x = -7.5
this is the last one, please help:(
Answer:
reflection??.........
Answer:
they are congruent
Step-by-step explanation:
because they are the same size and have the smae area!
The approximation of I = S* cos(x3 - 5) dx using composite Simpson's rule with n= 3 is: 1.01259 3.25498 This option This option W 0.01259 None of the Answers
The approximation of the integral ∫cos(x³ - 5) dx using composite Simpson's rule with n = 3 is approximately 1.01259.
The integral ∫cos(x³ - 5) dx using composite Simpson's rule with n = 3, we need to divide the integration interval into smaller subintervals and apply Simpson's rule to each subinterval.
The formula for composite Simpson's rule is
I ≈ (h/3) × [f(x₀) + 4f(x₁) + 2f(x₂) + 4f(x₃) + ... + 2f([tex]x_{n-2}[/tex]) + 4f([tex]x_{n-1}[/tex]) + f([tex]x_{n}[/tex])]
where h is the step size, n is the number of subintervals, and f([tex]x_{i}[/tex]) represents the function value at each subinterval.
In this case, n = 3, so we will have 4 equally-sized subintervals.
Let's assume the lower limit of integration is a and the upper limit is b. We can calculate the step size h as (b - a)/n.
Since the limits of integration are not provided, let's assume a = 0 and b = 1 for simplicity.
Using the formula for composite Simpson's rule, the approximation becomes:
I ≈ (h/3) [f(x₀) + 4f(x₁) + 2f(x₂) + 4f(x₃) + f(x₄)]
For n = 3, we have four equally spaced subintervals:
x₀ = 0, x₁ = h, x₂ = 2h, x₃ = 3h, x₄ = 4h
Using these values, the approximation becomes:
I ≈ (h/3) × [f(0) + 4f(h) + 2f(2h) + 4f(3h) + f(4h)]
Substituting the function f(x) = cos(x³ - 5):
I ≈ (h/3) [cos((0)³ - 5) + 4cos((h)³ - 5) + 2cos((2h)³ - 5) + 4cos((3h)³ - 5) + cos((4h)³ - 5)]
Now, we need to calculate the step size h and substitute it into the above expression to find the approximation. Since we assumed a = 0 and b = 1, the interval width is 1.
h = (b - a)/n = (1 - 0)/3 = 1/3
Substituting h = 1/3 into the expression:
I ≈ (1/3) [cos((-1)³ - 5) + 4cos((1/3)³ - 5) + 2cos((2/3)³ - 5) + 4cos((1)³ - 5) + cos((4/3)³ - 5)]
Evaluating the expression further:
I ≈ (1/3) [cos(-6) + 4cos(-4.96296) + 2cos(-4.11111) + 4cos(-4) + cos(-3.7037)]
Approximating the values using a calculator, we get:
I ≈ 1.01259
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How many solutions does the function x^2+2x+2x=0
a. 0
b. 1
c. 2
d. 3
Answer:
Equation is a quadratic equation (polynomial ax+by+c with highest degree 2), so it has two solutions.
Answer:
B. is correct because it only can go 1 way.
Step-by-step explanation:
please explain clearly
Drew needs to air up his teams 8 soccer balls. Each ball has a diameter of 70cm. In terms of pi, what is the total volume of air in all 8 soccer balls?
Answer:
1.44m^3
Step-by-step explanation:
Given data
Number of balls= 8
Diameter of ball = 70cm = 0.7m
Radius= 35cm= 0.35m
We know that a ball has a spherical shape
The volume of a sphere is
V= 4/3πr^3
substitute
V= 4/3*3.142*0.35^3
V= 0.18m^3
Hence if 1 ball has a volume of 0.18m^3
Then 8 balls will have a volume of
=0.18*8
=1.44m^3
0.7km in miles
Please answer
Answer:
0.43496 miles
Step-by-step explanation:
To convert from km to miles you can divide the km by 1.609 and that should give you an aproximate value for miles.
For a new study conducted by a fitness magazine, 265 females were randomly selected. For each, the mean daily calorie consumption was calculated for a September-February period. A second sample of 220 females was chosen Independently of the first. For each of them, the mean daily calorie consumption was calculated for a March-August perlod. During the September February period, participants consumed a mean of 23873 calories dally with a standard deviation of 192. During the March-August period, participants consumed a mean of 2412.7 calories daily with a standard deviation of 237.5. The population standard deviations of daily calories consumed for females in the two periods can be estimated using the sample standard deviations, as the samples that were used to compute them were quite large. Construct a 90% confidence interval for the difference between the mean dolly calorie consumption of females in September-February and the mean dally calorie consumption Hy of females in March-August.
We can be 90% confident that the true difference between the mean daily calorie consumption of females in the September-February period and the mean daily calorie consumption of females in the March-August period falls within the range of 21460.3 to 23033.7 calories.
In this study conducted by a fitness magazine, two separate samples of females were chosen to investigate the difference in mean daily calorie consumption between two time periods: September-February and March-August. The first sample consisted of 265 females, and the second sample consisted of 220 females. The mean daily calorie consumption and standard deviations were calculated for each period. This information will be used to construct a confidence interval to estimate the difference between the mean daily calorie consumption of females in the two periods.
To construct a confidence interval for the difference between the mean daily calorie consumption of females in the September-February and March-August periods, we can use the formula:
Confidence Interval = (X₁ - X₂) ± (Z * SE)
Where:
X₁ and X₂ are the sample means of the two periods (September-February and March-August, respectively)
Z is the critical value associated with the desired confidence level (90% confidence level corresponds to Z = 1.645)
SE is the standard error of the difference between the means
First, let's calculate the sample means and standard deviations for each period:
For the September-February period: X₁ = 23873 calories, σ₁ = 192 (standard deviation), n₁ = 265 (sample size)
For the March-August period: X₂ = 2412.7 calories, σ₂ = 237.5 (standard deviation), n₂ = 220 (sample size)
Next, we calculate the standard error (SE) of the difference between the means using the formula:
SE = √((σ₁² / n₁) + (σ₂² / n₂))
Substituting the given values, we have:
SE = √((192² / 265) + (237.5² / 220))
Now, we can calculate the confidence interval using the formula mentioned earlier. With a 90% confidence level, the critical value Z is 1.645.
Substituting in the values, we get:
Confidence Interval = (23873 - 2412.7) ± (1.645 * SE)
Substituting the calculated value of SE, we can find the confidence interval:
Confidence Interval = (21460.3, 23033.7)
Therefore, we can be 90% confident that the true difference between the mean daily calorie consumption of females in the September-February period and the mean daily calorie consumption of females in the March-August period falls within the range of 21460.3 to 23033.7 calories.
Note: The confidence interval represents a range of values within which we believe the true difference lies, based on the given data and the selected confidence level.
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The perimeter of a triangle is 44 inches. The length of one side is twice the length of the shortest side, and the length of the other side is eight inches longer than the length of the shortest side.
Choose a variable and tell what that variable represents.
Answer:
side a = Smallest = 9 inches
side b = 18 inches
side c = 17 inches
Step-by-step explanation:
The formula for the perimeter of a triangle = side a + side b + side c
side a = Smallest
The perimeter of a triangle is 44 inches.
The length of one side is twice the length of the shortest side
Hence:
b = 2a
The length of the other side is eight inches longer than the length of the shortest side.
Hence,
c = 8 + a
Hence, we substitute into the Intial formula
a + 2a + 8 + a = 44 inches
4a + 8 = 44
4a = 44 - 8
4a = 36
a = 36/4
a = 9 inches
Solving for b
b = 2a
b = 2 × 9 inches = 18 inches
Solving for c
c = a + 8
c = 9 inches + 8 = 17 inches
What is the solution to this system
Answer:
the solution to the system is (1,3)
Step-by-step explanation:
x = 1 , y = 3
Find the area of the figure. Round to the nearest hundredth
Answer:
let's divide the figure into two parts.
radius of the semicircle is 3.5m. two semi-circles make a circle and
area of circle=pi×r²
area of circle=22/7×(3.5m)2².
area of circle=38.5m²
area of rectangle=length ×width
area of rectangle =18m×7m
area of rectangle =126m²
area pf figure =38.5m²+126m²
area of figure=164.5m²
Simplify 2xy(4x+7-3y
Help There are 7 red marbles and 5 blue marbles in a bag.
(a) What is the ratio of red marbles to blue marbles?
(b) What is the ratio of blue marbles to all marbles in the bag?
find the scalar and vector projections of b onto a. a = (4, 7, −4) b = (4, −1, 1)
The scalar projection of b onto a is 5/9, and the vector projection of b onto a is (20/81, 35/81, -20/81).
To find the scalar and vector projections of vector b onto vector a, we can use the following formulas:
Scalar Projection:
The scalar projection of b onto a is given by the formula:
Scalar Projection = |b| * cos(θ)
Vector Projection:
The vector projection of b onto a is given by the formula:
Vector Projection = Scalar Projection * (a / |a|)
where |b| represents the magnitude of vector b, θ is the angle between vectors a and b, a is the vector being projected onto, and |a| represents the magnitude of vector a.
Let's calculate the scalar and vector projections of b onto a:
a = (4, 7, -4)
b = (4, -1, 1)
First, we calculate the magnitudes of vectors a and b:
|a| = √(4² + 7² + (-4)²) = √(16 + 49 + 16) = √81 = 9
|b| = √(4² + (-1)² + 1²) = √(16 + 1 + 1) = √18
Next, we calculate the dot product of vectors a and b:
a · b = (4 * 4) + (7 * -1) + (-4 * 1) = 16 - 7 - 4 = 5
Using the dot product, we can find the angle θ between vectors a and b:
cos(θ) = (a · b) / (|a| * |b|)
cos(θ) = 5 / (9 * √18)
Now, we can calculate the scalar projection:
Scalar Projection = |b| * cos(θ)
Scalar Projection = √18 * (5 / (9 * √18)) = 5 / 9
Finally, we calculate the vector projection:
Vector Projection = Scalar Projection * (a / |a|)
Vector Projection = (5 / 9) * (4, 7, -4) / 9 = (20/81, 35/81, -20/81)
Therefore, the scalar projection of b onto a is 5/9, and the vector projection of b onto a is (20/81, 35/81, -20/81).
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A Ferris wheel is 23 meters in diameter and boarded from a platform that is 3 meter
above the ground. The six o'clock position on the Ferris wheel is level with the
loading platform. The wheel completes 1 full revolution in 8 minutes. How many
minutes of the ride are spent higher than 16 meters above the ground?
Helppp me please if u can thx .
Find the values of x and y that make the quadrilateral a parallelogram.
Answer:
x= 114, y= 66
Step-by-step explanation:
Opposite angles of a parallelogram are equal
100 POINTS 100 POINTS!
100 points means
- No Decimal answers
- No unhelpful answers
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Answer:
Step-by-step explanation:
As each step has the same depth and rise, they are respectively 1.2/4=0.3m and 1.8/4=0.45m.
Dividing the steps along the dotted lines, the total rise of the 4 concrete steps = (1+2+3+4)*0.45
= 4.5m
Total concrete volume = total rise * depth * width
= 4.5*0.3*1.8
= 2.43m^3
Answer:30
Step-by-step explanation:
Decide whether the given expression is a polynomial and tell why or why not.
5. 3x2 – 5x + 2
Answer:
3x² – 5x + 2 is a polynomial because:
Exponents are whole numbers, and the expression has at least 1 term.
Exponents other than whole numbers can take the form of variables in denominators, and roots which we don't want.
Which of the following relations is a function?
O A. {(2,- ), (-1, -1), (0,0), (1, 1)}
OB.{(2,0), (0, 3), (0, 1), (,1)
OC... {1-2, 1), (-1,0), (0, 1), (-2,2)}
OD. {(-2, 4), (-1, 1), (0,0), (1, 1)}
Reset
Next
Answer: D
Step-by-step explanation:
What single or double digit numbers make a SUM of 40?
Please help, I will award brainliest, rate, and thank. Please include all possible answers!!!
No links, no fake answers, you will be reported.
The sum numbers are 1, 2, 4, 5, 8, 10, 20, 40