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ederal Government Employee E-mail Use It has been reported that 88% of federal government employees use e-mail. If a sample of 210 federal government employees is selected, find the mean, variance, and standard deviation of the number who use e-mail. Round your answers to three decimal places.
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The mean, variance, and standard deviation of the number of federal government employees who use e-mail can be calculated using the binomial distribution formula.
Given that 88% of federal government employees use e-mail, we can define the probability of success (p) as 0.88 and the number of trials (n) as 210.
The mean of a binomial distribution is given by μ = np, where μ is the mean and n is the number of trials. Therefore, the mean of the number of federal government employees who use e-mail is μ = 210 * 0.88 = 184.8.
The variance of a binomial distribution is given by [tex]\sigma^2 = np(1-p)[/tex], where [tex]\sigma^2[/tex] is the variance and n is the number of trials. Therefore, the variance of the number of federal government employees who use e-mail is σ^2 = 210 * 0.88 * (1-0.88) = 21.504.
The standard deviation of a binomial distribution is the square root of the variance. Therefore, the standard deviation of the number of federal government employees who use e-mail is σ = sqrt(21.504) ≈ 4.637.
In summary, the mean of the number of federal government employees who use e-mail is 184.8, the variance is 21.504, and the standard deviation is approximately 4.637. These values represent the average, spread, and deviation from the mean, respectively, for the number of federal government employees who use e-mail in a sample of 210 individuals.
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Simplify 2xy(4x+7-3y
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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
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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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help ASAP please ill give brainliest
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Hopes this helps!!!!!
0.7km in miles
Please answer
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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.
Can someone help me with this. Will Mark brainliest.
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explanation: using midpoint formula
Mrs. Baxter deposits $2,000 in an account that earns 5% sample
interest, How much interest does Mrs Batter's investment en ter
8 years
The answer is $480!
Answers
Answer:
$800 in interest
Step-by-step explanation:
T = A(1 + rt)
T = 2,000(1 + .05(8))
T = 2,000(1.4)
T = 2800
2800 - 2000 = 800
100 POINTS 100 POINTS!
100 points means
- No Decimal answers
- No unhelpful answers
- No spamming
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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:
Find the values of x and y that make the quadrilateral a parallelogram.
Answers
Answer:
x= 114, y= 66
Step-by-step explanation:
Opposite angles of a parallelogram are equal
please explain clearly
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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.
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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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prime factorization of 7776
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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.
What is the solution to this system
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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
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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
Write the equation of the
line that is parallel to
y = 1.5x – 6 and passes
through the point (4,2).
Answers
:)
The equation of the line is (y - 2) = 1.5(x - 4)
What is line ?
Euclid described a line as an "unextended length" that "stands equally with respect to its points"; he introduced the postulates as the main unprovable properties from which he constructed all of geometry, now called Euclidean geometry to avoid confusion with other geometries introduced from the late 19th century (such as non-Euclidean, projective and affine geometry).
In modern mathematics, given the multiplicity of geometries, the concept of line is closely related to the way geometry is described. For example, in analytic geometry, a plane line is often defined as a set of points whose coordinates correspond to a given linear equation, but in a more abstract setting, such as drop geometry, the line may be an object other than the set. of the points located on it.
When geometry is described by a set of axioms, the concept of line is usually left undefined (so-called primitive object). The properties of the lines are then determined by the axioms that refer to them. One of the advantages of this approach is the flexibility it gives users of the geometry. Thus, in differential geometry a line can be interpreted as a geodesic (shortest path between points), while in some projective geometries a line is a 2-dimensional vector space (all linear combinations of two independent vectors). This flexibility also extends beyond mathematics and allows physicists, for example, to think of the path of a light ray as a line.
Given, [tex]y = 1.5x - 6....(1)[/tex]
We are comparing equation (1) with y = mx+c and get m = 1.5
It is also given required equation passes through the point (4,2)
We know, if slope of a equation m and the equation passes through (a,b) then equation of the line (y-b) = m (x-a)
Here,
[tex]m = 1.5 \\ a = 4 \\ b = 2[/tex]
So, required equation of the line [tex](y - 2) = 1.5(x - 4)[/tex]
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Find an equation of the plane tangent to the following surface at the given point. z=8-2x²-2y²; (5,3, – 60) Z=
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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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this is the last one, please help:(
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Answer:
reflection??.........
Answer:
they are congruent
Step-by-step explanation:
because they are the same size and have the smae area!
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
Answers
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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Find the general solution for the differential equation
x sinθ dθ + (x3− 2x2cosθ) dx = 0
Answers
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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Decide whether the given expression is a polynomial and tell why or why not.
5. 3x2 – 5x + 2
Answers
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.
Helppp me please if u can thx .
Answers
= $67.5 x 6 Days
= $405.00
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?
Answers
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
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.
Answers
The sum numbers are 1, 2, 4, 5, 8, 10, 20, 40
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
Answers
Answer: D
Step-by-step explanation:
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)
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I hope this help...
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.
Answers
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
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?
Answers
ratio of blue to all is : 5/12
(b) 7 + 5 = 12 total marbles
Ratio would be 5:12 (blue to total)
How many solutions does the function x^2+2x+2x=0
a. 0
b. 1
c. 2
d. 3
Answers
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:
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?
Answers
How many solutions does the equation 5x + 3x – 4 = 10 have?
O Zero
O One
O TWO
O Infinitely many
be
????
Answers
Answer:
Step-by-step explanation:
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cecewiliams23
08/12/2016
Mathematics
High School
answered
How many solutions does the equation 5x + 3x − 4 = 10 have
2
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Answer
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MathGeek289
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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