Answer:
[tex]\mu = 22.04[/tex] represent the mean in seconds for the 200 m Dash in 1988
[tex]\sigma = 0.24[/tex] represent the deviation in seconds for the 200 m Dash in 1988
We assume that the parameters are the same for 2000. And we know that Pauline Davis won gold with a time of 22.27 seconds, we want to find the z score so we can use the following formula:
[tex] z=\frac{X -\mu}{\sigma}[/tex]
And replacing we got:
[tex] z= \frac{22.27- 22.04}{0.24}= 0.96[/tex]
Step-by-step explanation:
For this case we have the follwing parameters given:
[tex]\mu = 22.04[/tex] represent the mean in seconds for the 200 m Dash in 1988
[tex]\sigma = 0.24[/tex] represent the deviation in seconds for the 200 m Dash in 1988
We assume that the parameters are the same for 2000. And we know that Pauline Davis won gold with a time of 22.27 seconds, we want to find the z score so we can use the following formula:
[tex] z=\frac{X -\mu}{\sigma}[/tex]
And replacing we got:
[tex] z= \frac{22.27- 22.04}{0.24}= 0.96[/tex]
what is 1/4 x 1/4 x 1/4
Answer:
1/64
Step-by-step explanation:
1/4 × 1/4 × 1/4
Multiply the fractions.
1/4³
= 1/64
Answer:
The answer is 1/64.
Step-by-step explanation:
1/4 x 1/4 x 1/4 = 1/64
In other ways, you can write this as: 1/4³
Hope this helped!
Which statement is true about the graphs of the two lines y = –6 and x = ?
The lines are perpendicular to each other because the graph of y = –6 is a horizontal line with a slope that is undefined, and the graph of x = is a vertical line with a slope of 0.
The lines are perpendicular to each other because the graph of y = –6 is a vertical line with a slope that is undefined, and the graph of x = is a horizontal line with a slope of 0.
The lines are perpendicular to each other because the graph of y = –6 is a vertical line with a slope of 0, and the graph of x = is a horizontal line with a slope that is undefined.
The lines are perpendicular to each other because the graph of y = –6 is a horizontal line with a slope of 0, and the graph of x = is a vertical line with a slope that is undefined.
Answer:
if x is positive the answer is the 4th statement and if it is negative the answer is the 3rd statement
Step-by-step explanation:
We have the statement that tells us: "the graphs of the two lines y = –6 and x =?" x, we do not know it, but from the y coordinate we can do it by discard.
In the case of y-coordinate we have that y = -6 is a horizontal line with a slope of 0, therefore of the 4 statements it is reduced to 2, the third and the fourth.
Depending on the sign that has the value of x, if it is positive or negative it would be the 3rd and 4th answer.
if x is positive it is a vertical line with a slope that is undefined, but if it is negative it is a horizontal line with a slope that is undefined.
What is the value of - x^2 -4 x -11 if x =.3
Answer: -32
Step-by-step explanation:
I'm just going to plug in and break down the equation to make it more understandable and easier to comprehend
-(3^2) - (4*3) -11
-(9)- (12) -11
-9 - 12 - 11
-21 -11
-32
According to a 2017 survey conducted by the technology market research firm The Radicati Group, U.S. office workers receive an average of 121 emails per day.† Suppose for a particular office the number of emails received per hour follows a Poisson distribution and that the average number of emails received per hour is three. (Round your answers to four decimal places.) (a) What is the probability of receiving no emails during an hour? (b) What is the probability of receiving at least three emails during an hour? (c) What is the expected number of emails received during 15 minutes? (d) What is the probability that no emails are received during 15 minutes?
Answer:
Step-by-step explanation:
The interval of interest is per hour. This means 60 minutes. Since the number of emails received per hour follows a Poisson distribution and that the average number of emails received per hour is three, it means that
Mean, μ = 3
x is a random variable representing the number of mails received per hour
a) The probability of receiving no emails during an hour is expressed as
P(x = 0)
From the Poisson distribution calculator,
P(x = 0) = 0.0498
b) the probability of receiving at least three emails during an hour is expressed as P(x ≥ 3).
P(x ≥ 3) = 0.577
c) the expected number of emails received during 15 minutes is
3 × 15/60 = 0.75
d) mean = 0.75
From the poisson distribution calculator, P(x = 0) = 0.47
A population consists of 500 elements. We want to draw a simple random sample of 50 elements from this population. On the first selection, the probability of an element being selected is
A. 0.100
B. 0.010
C, 0.001
D. 0.002
Answer:
D. 0.002
Step-by-step explanation:
Given;
total number of sample, N = 500 elements
50 elements are to be drawn from this sample.
The probability of the first selection, out of the 50 elements to be drawn will be = 1 / total number of sample
The probability of the first selection = 1 / 500
The probability of the first selection = 0.002
Therefore, on the first selection, the probability of an element being selected is 0.002
The correct option is "D. 0.002"
On the first selection, the probability of an element being selected is 0.002. Option D is correct.
Given information:
A population consists of 500 elements. so, the total number of samples will be [tex]N = 500[/tex] .
We want to draw a simple random sample of 50 elements.
The probability is defined as the preferred outcomes divided by the total number of samples.
So, the probability of first selection will be calculated as,
[tex]P=\dfrac{1}{500}\\P=0.002[/tex]
Therefore, on the first selection, the probability of an element being selected is 0.002.
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Which function is graphed below?
Answer:
Piecewise function;
y = 2x - 2 where x < 2
4 where 2 ≤ x ≤ 5
y = x + 1 where x > 5
Step-by-step explanation:
Function graphed represents the piecewise function.
1). Equation of the line with y-intercept (-2) and slope 'm'.
Since, slope of the line = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
= [tex]\frac{2}{1}[/tex]
= 2
Therefore, equation of this segment will be in the form of y = mx + b,
⇒ y = 2x - 2 where x < 2
2). Equation of a horizontal line,
y = 4 where 2 ≤ x ≤ 5
3). Equation of the third line in the interval x > 5
Let the equation of the line is,
y = mx + b
Where m = slope of the line
b = y-intercept
Here, slope 'm' = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
= [tex]\frac{2}{2}[/tex]
= 1
Equation of this line will be,
y = 1(x) + b
y = x + b
Since, this line passes through (5, 6),
6 = 5 + b
b = 6 - 5 = 1
Therefore, equation of this line will be,
y = x + 1 where x > 5
Graphed piecewise function is,
y = 2x - 2 where x < 2
4 where 2 ≤ x ≤ 5
y = x + 1 where x > 5
What is the best description of the transformation shown?What is the best description of the transformation shown?
Answer:
the correct answer is a reflection over the y axis
Step-by-step explanation:
The best description of the transformation shown will be;
''Reflection over the y - axis.''
What is Translation?
A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
The transformation is shown in figure.
Now,
Clearly, A'B'C'D' is the mirror image of the ABCD across the y - axis.
So, The best description of the transformation shown will be;
''Reflection over the y - axis.''
Thus, The best description of the transformation shown will be;
''Reflection over the y - axis.''
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Find the value of x for which a ll b
Answer:
x=35
Step-by-step explanation:
John played a note on his tuba that vibrated the air 50 times per second. If
he played the note for 2 seconds, how many times did the air vibrate?
Answer:
100 times
Step-by-step explanation: vibration per second: 50 times
vibration for 2 seconds; 50*2=100 times
Answer:
100 times
Step-by-step explanation:
2 seconds=100 times
100÷50=2
So now you can do
50×2=100
Use the graph to find the roots of the equation x^2 – 2x – 3 = 0
Answer:
The roots are where the graph intercepts the x-axis
Step-by-step explanation:
Alternatively, you could factor and then solve algebraically.
Which relations are functions?
For a relation to be a function every x value will have a single y value.
The first one has two x values of -2 but their y values are different so can’t be a function.
The second one has two 10’s with different y values so isn’t a function.
The 3rd one has 1 and -1 with the same y value, so isn’t a function.
The correct answer is the 4th choice
Complete the following exercises by applying polynomial identities to complex numbers. Show your work. Factor x^2 + 64. Check your work. Factor 16x^2 + 49. Check your work. Find the product of (x + 9i)^2. Find the product of (x − 2i)^2. Find the product of (x + (3+5i))^2.
Answer:
Step-by-step explanation:
Hello,
Factor x^2 + 64.
[tex]\boxed{x^2+64=x^2+8^2=x^2-8^2i^2=(x-8i)(x+8i)}[/tex]
Factor 16x^2 + 49.
[tex]\boxed{16x^2+49=(4x)^2-(7i)^2=(4x-7i)(4x+7i)}[/tex]
Find the product of (x + 9i)^2.
[tex]\boxed{(x+9i)^2=x^2+18xi+(9i)^2=x^2+18xi-81=x^2-81+18xi}[/tex]
Find the product of (x − 2i)^2.
[tex]\boxed{(x-2i)^2=x^2-4xi-4=x^2-4-4xi}[/tex]
Find the product of (x + (3+5i))^2.
[tex]\boxed{(x + (3+5i))^2=x^2+(3+5i)^2+2x(3+5i)=x^2+9-25+30i+6x+10xi}\\\boxed{=x^2+6x-16+(30+10x)i}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
What is the solution to the system of equations?
y=-3x – 2
5x + 2y = 15
0 (-40. 19)
(-19.55)
(19-40)
(55.-19)
Answer:
Step-by-step explanation:
y = -3x - 2
5x + 2y = 15
5x + 2(-3x -2) = 15
5x -6x - 4 = 15
-x - 4 = 15
-x = 19
x = -19
y = -3(-19) - 2
y = 57 - 2
y = 55
(-19, 55)
solution is b
In order to estimate the average electric usage per month, a sample of 196 houses was selected, and their electric usage determined. a) Assume a population standard deviation of 350 kilowatt hours. Determine the standard error of the mean. b) With a 0.95 probability, determine the margin of error. c) If the sample mean is 2,000 KWH, what is the 95% confidence interval estimate of the population mean
Answer:
a) SE = 25
b) MOE = 41
c) CI = 1951 ; 2049
Step-by-step explanation:
Normal distribution
Population mean unknown
Population standard deviation σ = 350 Kwh
a) The standard error of the mean SE is
SE = σ/√
SE = 350 /√196
SE = 350/14
SE = 25
b) If confidence nterval is 95% or 0,95 then
α = 0,05
And from z table we get z(c) = 1,64
MOE = z(c) * SE
MOE = 1,64 * 350/√196
SE = 1,64 * (350)/14
SE = 41
MOE = And from z tabl we get z(c) = 1,64
MOE = 1,64 * 350/√196
MOE = 1,64 * (350)/14
MOE = 1,64 * 25
MOE = 41
c) The confidence interval is:
Z = 2000
α = 1- 0,95
α = 0,05 ⇒ α/2 = 0,025
CI = Z - z(α/2) * σ/√n ; Z + z(α/2) * σ/√n
z(α/2) from z-table is: z(0,025) = 1,96
CI = 2000 - 1,96* 350/√196 ; 2000 + 1,96* 350/√196
CI = 2000 - 1,96*25 ; 2000 + 1,96*25
CI = 2000 - 49 ; 2000 + 49
CI = 1951 ; 2049
–9(w + 585) = –360 w = ______
Answer:
w = 15
Step-by-step explanation:
-9(w + 585) = -360w
-9w -5265 = -360w
351w = 5265
w=15
What is the algebraic expression . The club earned$20 more than twice what it earned last year
Answer:
algebraic expression is Y = 2x + 20
where x is the earning for last year
Y is the earning for this year
Step-by-step explanation:
Let the earning of club in last year be x
given
The club earned$20 more than twice what it earned last year
twice the earning of last year = 2x
$20 more than twice the earning of last year = 2x +20
Earning this year = 2x +20
where x is the earning for last year
let the earning for this year be y
Y = 2x +20
Thus, algebraic expression is Y = 2x + 20
Pleaseeee hheeelppp mmmeee
Answer:
A
90 degrees
anticlockwise.
Step-by-step explanation:
It looks much more complicated than it really is. I don't know how to explain this in any other form but to give the answers.
1 A
The center of rotation is where the 90 degree angle has its vertex. So that would be A.
1 B
Follow x. It rotates 90 degrees. So every point must rotate 90 degrees.
1 C
The direction is against the way the clock tells time, so the direction of rotation is anticlockwise.
What is the product?
(3a^2b^7) (5a^3b^8)
Answer:
[tex]\boxed{\sf \ \ \ 15a^5b^{15} \ \ \ }[/tex]
Step-by-step explanation:
hello,
[tex](3a^2b^7) (5a^3b^8)=15a^{2+3}b^{7+8}=15a^5b^{15}[/tex]
hope this helps
What is the solution to arccos 0.5 express answer in radians
Answer:
arccos (0.5) is [tex]\frac{\pi}{3}[/tex]
Step-by-step explanation:
With the arccos(0.5) in this problem, you are asked which angle renders its cosine equal to 0.5 (or 1/2).
Recall that there are special angles in the unitary circle that render well know values like 1/2. There are two angle values between 0 and the full circle ([tex]2\pi[/tex] radians), that render cosine function equal 1/2, and they are: [tex]\frac{\pi}{3}[/tex], and [tex]-\frac{\pi}{3}[/tex].
The arccos uses just the first one as answer over the restricted domain between 0 and [tex]\pi[/tex], since otherwise it will not be considered a function.
So the answer is that the arccos (0.5) is [tex]\frac{\pi}{3}[/tex]
The angles of a
quadrilateral, taken in order
are y, 5y, 4y
and
2y.
Find these angles
Answer:
30, 150, 120, and 60 degrees
Step-by-step explanation:
Since the sum of the interior angles in a quadrilateral is 360 degrees:
y+5y+4y+2y=360
12y=360
y=30
2y=60, 4y=120, 5y=150
Hope this helps!
Step-by-step explanation:
y+5y+ 4y + 2y=360°(sum of a Quadrilateral)
12y=360°
divide both sides by 12
y=30°
5y=(5×30)=150°
4y=(4×30)=120°
2y=(2×30)=60°
Assume that the probability of the binomial random variable will be approximated using the normal distribution. Describe the area under the normal curve that will be computed. Find the probability that at leastat least 3535 households have a gas stove.
This is not the correct question, the correct question is;
Assume that the probability of the binomial random variable will be approximated using the normal distribution. Describe the area under the normal curve that will be computed. Find the probability that at least 35 households have a gas stove.
Answer: p ( x > 34.5 ) The area to the right of 34.5
Step-by-step explanation:
Given that, x = 35
when using normal approximation
Using continuity correction
so
p ( x ≥ 35 ) = p ( x > 34.5 )
More than means the area is towards the right.
Therefore, the area under the normal curve is,
p ( x > 34.5 ) The area to the right of 34.5
Find the intersection point for the following linear functions. f(x) = 2x + 3 g(x) = -4x − 27
Answer:
(- 5, - 7 )
Step-by-step explanation:
Equate f(x) and g(x), that is
2x + 3 = - 4x - 27 ( add 4x to both sides )
6x + 3 = - 27 ( subtract 3 from both sides )
6x = - 30 ( divide both sides by 6 )
x = - 5
Substitute x = - 5 into either of the 2 functions for y- coordinate
Substituting into f(x)
f(- 5) = 2(- 5) + 3 = - 10 + 3 = - 7
Thus point of intersection = (- 5, - 7 )
solving the equation 2x+3(3x-5)=51 for x gives x = 6 what is the complete solution
Answer:
x = 6
Step-by-step explanation:
2x + 3(3x - 5) = 51
Expand the brackets.
2x + 9x - 15 = 51
Add like terms.
11x - 15 = 51
Add 15 on both sides.
11x = 51 + 15
11x = 66
Divide both sides by 11.
x = 66/11
x = 6
The solution to the equation 2x+3(3x-5)=51 is x = 6
How to determine the complete solution?The equation is given as:
2x+3(3x-5)=51
Expand
2x + 9x - 15 = 51
Evaluate the like terms
11x = 66
Divide both sides by 11
x = 6
Hence, the solution to the equation 2x+3(3x-5)=51 is x = 6
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What is the range of this function?
Answer:
c
Step-by-step explanation:
outputs are on the right, which are the y-values.
Solve by quadratic Formula:
Answer:
x = 1, x = .333
Step-by-step explanation:
Answer:
x = 1 and x = 1/3
Step-by-step explanation:
Here the coefficients of this quadratic are a = 3, b = -4 and c = 1.
The discriminant is b^2 - 4ac, or (-4)^2 - 4(3)(1) = 16 - 12 = 4.
Thus, the roots are:
-(-4) ± √4 4 ± 2
x = ---------------- = ------------- => x = 1 and x = 1/3
2(3) 6
Approximate the area under the curve y = x^3 from x = 2 to x = 5 using a Right Endpoint approximation with 6 subdivisions.
Answer:
182.8125
Step-by-step explanation:
Given:
y = x^3
from [2,5] using 6 subdivisions
deltax = (5 - 2)/6 = 3/6 = 0.5
hence the subdivisions are:
[2, 2.5]; [2.5, 3]; [3, 3.5]; [3.5, 4]; [4, 3.5]; [4.5, 5]
hence the right endpoints are:
x1 = 2.5; x2 = 3; x3 = 3.5; x4 =4; x5 = 4.5; x6 = 5
now the area is given by:
A = deltax*[2.5^3 + 3^3 + 3.5^3 + 4^3+ 4.5^3 + 5^3]
A = 0.5*365.625
A = 182.8125
Area using Right Endpoint approximation is 182.8125
The area of the region is an illustration of definite integrals.
The approximation of the area of the region R is 182.8125
The given parameters are:
[tex]\mathbf{f(x) = x^3}[/tex]
[tex]\mathbf{Interval = [2,5]}[/tex]
[tex]\mathbf{n = 6}[/tex] ------ sub intervals
Using 6 sub intervals, we have the partitions to be:
[tex]\mathbf{Partitions = [2,2.5]\ u\ [2.5, 3]\ u\ [3,3.5]\ u\ [3.5,4]\ u\ [4,4.5]\ u\ [4.5,5]}[/tex]
List out the right endpoints
[tex]\mathbf{x= 2.5,\ 3,\ 3.5,\ 4,\ 4.5,\ 5}[/tex]
Calculate f(x) at these partitions
[tex]\mathbf{f(2.5) = 2.5^3 = 15.625}[/tex]
[tex]\mathbf{f(3) = 3^3 = 27}[/tex]
[tex]\mathbf{f(3.5) = 3.5^3 = 42.875}[/tex]
[tex]\mathbf{f(4) = 4^3 = 64}[/tex]
[tex]\mathbf{f(4.5) = 4.5^3 = 91.125}[/tex]
[tex]\mathbf{f(5) = 5^3 = 125}[/tex]
So, the approximated value of the definite integral is:
[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx \frac{1}{2}(\sum f(x))}[/tex]
This becomes
[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx \frac{1}{2}(15.625 + 27 + 42.875 + 64+91.125 + 125)}[/tex]
[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx \frac{1}{2} \times 365.625}[/tex]
[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx 182.8125}[/tex]
Hence, the approximation of the area of the region R is 182.8125
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On the distant planet Cowabunga, the weights of cows have a normal distribution with a mean of 479 pounds and a standard deviation of 40 pounds. The cow transport truck holds 15 cows and can hold a maximum weight of 7350. If 15 cows are randomly selected from the very large herd to go on the truck, what is the probability their total weight will be over the maximum allowed of 7350
Answer: 0.1435
Step-by-step explanation:
Given : Mean = 479 pounds
Standard deviation = 40 pounds.
Let X denote the weights of cows.
[tex]X\sim N(\mu=479,\sigma=40)[/tex]
The cow transport truck holds 15 cows and can hold a maximum weight of 7350.
i.e. mean weight of cow in this case =[tex]\overline{x}=\dfrac{7350}{15}=490\text{ pounds}[/tex]
If 15 cows are randomly selected from the very large herd to go on the truck, what is the probability their total weight will be over the maximum allowed of 7350 will be:-
[tex]P(\overline{x}>490)=P(\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{490-479}{\dfrac{40}{\sqrt{15}}})\\\\=P(z>1.065)\ \ [\because\ z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-P(z\leq1.065)\\\\=1- 0.8565=0.1435\ \ [\text{By z-table}][/tex]
Hence, If 15 cows are randomly selected from the very large herd to go on the truck, the probability their total weight will be over the maximum allowed of 7350 = 0.1435
So, the probability their mean weight will be over 479 is [tex]0.53836.[/tex]
Z-score:A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean.
It is given that,
[tex]\mu=479\\\sigma=40\\n=15\\X=maximum\ weight=7350[/tex]
Then,
[tex]\bar{x}=\frac{\sum x}{n}\\ =\frac{7350}{15}\\ =490[/tex]
Now, calculating Z-score:
[tex]Z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n} } } \\Z=\frac{490-479}{\frac{40}{\sqrt{15} } }\\ Z=1.07[/tex]
Using z table =1.07
[tex]P(Z < 1.07)=0.46164\\P(Z > 1.07)=1-P(Z < 1.07)\\=1-0.46164\\=0.53836[/tex]
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Solve the equations. 8x + 7y = 39 4x – 14y = –68
Answer:
y = 5, x= 1/2
Step-by-step explanation:
8x+7y = 39
4x - 14y = -68
x = 39/8 - 7/8y
4(39/8 - 7/8y) -14y = -68
19.5 - 3.5y -14y = -68
-17.5y = -87.5
y = 5
x = 39/8 - 7/8(5)
x = 0.5 or 1/2
What are the steps for constructing a copy of an angle using only a compass and
a straightedge?
Answer:
1. Use a straightedge
2. Draw dots on the line to mark the starting point
3. Place the point of the compass on the point you made or was given
4. Extend the compass so that the pencil is on the 2nd point & make a an arc thru point B
5. Place the compass point on the starting point dot on the line and draw w/ the pencil to create an arc crossing the line.
Answer:
Step 1: Mark the point that will be the vertex of the new angle, and label it P.
Step 2: Draw a ray from P in any direction, with any length. This ray will be one of the sides of the new angle.
Step 3: Place the compass point on the vertex of the original angle, and adjust the compass width to a convenient size.
Step 4: Use the compass to draw an arc intersecting both rays of the original angle at two points, J and K.
Step 5: Move the compass (without changing the width) to point P, and make an arc intersecting the existing ray of the angle. Mark the intersection point, and label it M.
Step 6: Set the compass point on the original angle at point J, and set its width to the length of line segment JK.
Step 7: Move the compass point to M on the new angle, and draw an arc cutting the previous arc. Mark the intersection point and label it L.
Step 8: Draw a ray from point P through point L. The new angle is a copy of the original angle.
Step-by-step explanation:
edmentum
The city of Raleigh has 9500 registered voters. There are two candidates for city council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 350 randomly selected registered voters was conducted. 112 said they'd vote for Brown, 207 said they'd vote for Feliz, and 31 were undecided.
a. What is the population of this survey?
b. What is the size of the population?
c. What is the size of the sample?
d. Give the sample statistic for the proportion of voters surveyed who said they'd vote for Brown.
e. Based on this sample, we might expect how many of the 9500 voters to vote for Brown?
Answer:
a. The population is represented by the registered voters of the Raleigh city
b. The population size is 9,500
c. The sample size is 350
d. The proportion of people that voted for Brown was 32% >> (112 x 100) / 350 = 32%
e. The expected number of Brown's voters is 3,040 >> (32 x 9,500) / 100 = 3,040
Step by step explanation:
In statistics, a population includes all the dataset from the study, while a sample is represented by one or more observations obtained from this dataset. The proportion can be represented by two fractions (ratios) which are equivalent to each other. Finally, the estimated size of the total population can be estimated by multiplication of the observed ratio in the sample and the size of the population (32 % x 9,500), and then dividing this number by the total ratio value.