Answer:
1. C. The researcher must compute an estimated standard error for the mean difference score to compute a t statistics.
2. B. 10
3. A. 12
Step-by-step explanation:
The degrees of freedom is number of independent variable factors that affect the range of parameters. The degrees of freedom is the calculation of number values that are free to vary. The degrees of freedom is calculated by N-1. Standard error is the estimated deviation of standard deviation from its sample mean distribution.
Please help me on question 4 and 5 I am really stuck thank you I would really appreciate it
Answer:
1. 5/4
2. 7
Step-by-step explanation:
1) Lets call the width as w
Therefore length would be:
w+4
To find the perimeter you use the formula:
2 (l+w)
Now substitute our values into this formula:
2 (w+4+w)
2( 2w+4)
4w+8
Now make this equal to 13:
4w +8 = 13
4w = 5
w = 5/4
2. In this question we will call length l
Therefore width would be:
l-5
Now we will do the steps we did above:
2 (l+l-5)
2 (2l-5)
4l -10
4l - 10 = 18
4l = 28
l = 7
6. A car dealership would like to estimate the mean mpg of its new model car with 90% confidence. The population is normally distributed; however we are taking a sample of 25 cars with a sample mean of 96.52 and a sample standard deviation of 10.70. Calculate a 90% confidence interval for the population mean using this sample data.
Answer:
92.9997<[tex]\mu[/tex]<99.5203
Step-by-step explanation:
Using the formula for calculating the confidence interval expressed as:
CI = xbar ± Z * S/√n where;
xbar is the sample mean
Z is the z-score at 90% confidence interval
S is the sample standard deviation
n is the sample size
Given parameters
xbar = 96.52
Z at 90% CI = 1.645
S = 10.70.
n = 25
Required
90% confidence interval for the population mean using the sample data.
Substituting the given parameters into the formula, we will have;
CI = 96.52 ± (1.645 * 10.70/√25)
CI = 96.52 ± (1.645 * 10.70/5)
CI = 96.52 ± (1.645 * 2.14)
CI = 96.52 ± (3.5203)
CI = (96.52-3.5203, 96.52+3.5203)
CI = (92.9997, 99.5203)
Hence a 90% confidence interval for the population mean using this sample data is 92.9997<[tex]\mu[/tex]<99.5203
The following data shows the number of home runs hit by the top 12 home run hitters in Major League Baseball during the 2011 season.
43 41 39 39 38 37 37 36 34 33 33 32
The lower limit for determining outliers for a box-and-whisker plot is______.
a. 23.75.
b. 20.0.
c. 22.5.
d. 25.25.
Answer:
d. 25.25.
Step-by-step explanation:
A whisker plot is a type of box plot which is graphical representation of five number summary. It is used for explanatory data analysis. The baseball league has data set whose median is 45. When the outliner are present in data set the median measures central tendency.
Which expression is equivaleny to 0.7 + p + 0.86p?
A.1 + 1.56p
B.p + 1.56
C.2.56p
D. -0.84p
Answer:
None of the above.
1.86p + 0.7
Step-by-step explanation:
Step 1: Write expression
0.7 + p + 0.86p
Step 2: Combine like terms
0.7 + 1.86p
None of those answer choices are correct unless you wrote the problem incorrectly.
∠3 and ∠6 can be classified as:
Answer:
Alternate Interior Angles
Step-by-step explanation:
Since they are inside the parallel lines, Alternate Exterior Angles and any other similar theorems can be ruled out.
Since they are on opposite sides of each other, Corresponding Angles and any other similar theorems can be ruled out.
Since they are far apart from each other, Supplementary Angles, Adjacent Angles, Vertical Angles, and any other similar definitions can be ruled out.
Therefore, we are left with Alternate Interior Angles.
Answer:
angle 3 and angle 6 are
1) Alternate Angles
2) Interior Angles
Step-by-step explanation:
(see attached for reference)
|5x|=3 please help me
x + y + z = -6 -2x – 2y – 2z = 12 5x + 5y + 5z = -30 find x y and z please
Answer:
x = s, y = t, z = -6 -s -t
Step-by-step explanation:
These are dependent equations. For some values s and t, the solution is ...
x = s, y = t, z = -6 -s -t
How much work is done in lifting a 1.4-kg book off the floor to put it on a desk that is 0.7 m high?
Use the fact that the acceleration due to gravity is g = 9.8 m/s^2. How much work is done in lifting a 21-lb weight 6 ft off the ground?
Answer:
Step-by-step explanation:
Work is said to be done when a force applied to an object cause the body to move in a specified direction.
Work-done = Force * Distance
Since Force = mass * acceleration due to gravity
Work-done = mass * acceleration due to gravity * distance
Given mass = 1.4kg, distance = 0.7m and g = 9.8m/s²
Workdone in lifting the book off the floor = 1.4*0.7*9.8
Workdone = 9.604Joules
- Similarly, work done in lifting a 21-lb weight book 6 ft off the ground is expressed using the same formula as above;
Given mass = 21-lb, g = 32ft/s² and distance = 6ft
Workdone = 21 * 32 * 6
Workdone = 4,032 lb-ft²/s²
Hence, work-done in lifting a 21-lb weight book 6 ft off the ground is 4,032 lb-ft²/s²
What is the x-intercept?
Find the sum of all solutions to this equation : ((2x-4)/x+1)) * ((2x+8)/2) * ((2x-70)/(x+2)) =0
Answer:
x=0 or x=2 or x=−4 or x= (7)(2)
Step-by-step explanation:
NEED HELP ASAP trig question!! Need to find y!!
Answer:
Hey there!
Tangent 70=12/y
Tangent 70y=12
y=12/Tangent 70
y=4.37 cm
Let me know if this helps :)
Find the sum of the first 12 terms of the sequence 512, 256, 128, …
Answer: 1023.75 (a)
Step-by-step explanation:
The sequence is a Geometric progression with the common ratio of ¹/₂ and first term of 512.
a = 512, r = ¹/₂. To determine the ratio, just divide the second term by the first term.
Now to calculate the sum, we consider two formula here and select the one that is most appropriate,
(1) a( rⁿ - 1 )/r - 1, when r is greater than 1
(2) a( 1 - rⁿ )/1 - rⁿ, when r is less than 1.
In this question, formula 2 shall be appropriate because r is less than 1.
so,
S₁₂ = 512( 1 - 0.5¹² )/1 - 0.5
512( 1 - 2.44 ₓ 10⁻⁴ )/0.5
= 512( 0,9998 )/0.5
= 511.875/0.5
= 1023.75
The answer is a
please answer! I need these points for grade!
∡NMO = 59°
Step-by-step explanation:if MO bisect =>
=> ∡LMN = 2∡LMO =>
=> 5x - 22 = 2(x + 31)
5x - 22 = 2x + 62
5x - 2x = 62 + 22
3x = 84
x = 28°
∡LMO = ∡NMO => ∡NMO = x + 31
=> ∡NMO = 28 + 31 = 59°
Y varies inversely with x. If Y=17 and k(The constant of variation) =76, what is x? Round to the nearest tenth if necessary.
Answer:
x ≈ 4.5
Step-by-step explanation:
Given y varies inversely with x then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
Here k = 76 and y = 17 , thus
17 = [tex]\frac{76}{x}[/tex] ( multiply both sides by x )
17x = 76 ( divide both sides by 17 )
x ≈ 4.5 ( to the nearest tenth )
You are to manufacture a rectangular box with 3 dimensions x, y and z, and volume v=8000. Find the dimensions which minimize the surface area of this box.
Answer:
20 by 20 by 20
Step-by-step explanation:
Let the total surface of the rectangular box be expressed as S = 2xy + 2yz + 2xz
x is the length of the box
y is the width and
z is the height of the box.
S = 2xy + 2yz + 2xz ... 1
Given the volume V = xyz = 8000 ... 2
From equation 2;
z = 8000/xy
Substituting into equation 1;
S = 2xy + 2y(8000/xy)+ 2x(8000/xy)
S = 2xy+16000/x+16000/y
Differentiating the resulting equation with respect to x and y will give;
dS/dx = 2y + (-16000x⁻²)
dS/dx = 2y - 16000/x²
Similarly,
dS/dy = 2x + (-160000y⁻²)
dS/dy = 2x - 16000/y²
Note that at the turning point, ds/dx = 0 and ds/dy = 0, hence;
2y - 16000/x² = 0 and 2x - 16000/y² = 0
2y = 16000/x² and 2x = 16000/y²
2y = 16000/(8000/y²)²
2y = 16000×y⁴/64,000,000
2y = y⁴/4000
y³ = 8000
y =³√8000
y = 20
Given 2x = 16000/y²
2x = 16000/20²
2x = 16000/400
2x = 40
x = 20
Since Volume of the box is V = xyz
8000 = 20(20)z
8000 = 400z
z = 8000/400
z = 20
Hence, the dimensions which minimize the surface area of this box is 20 by 20 by 20.
The dimensions which minimize the surface area of this box is 20 *20* 20. This can be calculated by using surface area and volumes.
The calculation for total surface area:Let the total surface of the rectangular box be expressed as:
S = 2xy + 2yz + 2xz
where,
x is the length of the box
y is the width and
z is the height of the box.
S = 2xy + 2yz + 2xz .................(1)
Given:
Volume V = xyz = 8000 .............(2)
From equation 2;
z = 8000/xy
Substituting into equation 1;
S = 2xy + 2y(8000/xy)+ 2x(8000/xy)
S = 2xy+16000/x+16000/y
Differentiating the resulting equation with respect to x and y will give;
dS/dx = 2y + (-16000x⁻²)
dS/dx = 2y - 16000/x²
Similarly,
dS/dy = 2x + (-160000y⁻²)
dS/dy = 2x - 16000/y²
Note that at the turning point, ds/dx = 0 and ds/dy = 0, hence;
2y - 16000/x² = 0 and 2x - 16000/y² = 0
2y = 16000/x² and 2x = 16000/y²
2y = 16000/(8000/y²)²
2y = 16000×y⁴/64,000,000
2y = y⁴/4000
y³ = 8000
y =³√8000
y = 20
Given 2x = 16000/y²
2x = 16000/20²
2x = 16000/400
2x = 40
x = 20
Since, Volume of the box is V = xyz
8000 = 20(20)z
8000 = 400z
z = 8000/400
z = 20
Hence, the dimensions which minimize the surface area of this box is 20*20*20.
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Complete each ordered pair so that it is a solution of the given linear equation.
x - 4y = 4; (_,3), (4,_)
Answer: (16,3) and (4,0)
Step-by-step explanation:
Using the equation x-4y=4 is asking what is the value of x if the value of y is 3. So plot it into the equation and solve for x.
x-4(3)=4 multiply the left side
x - 12 = 4 add 12 to both sides
x= 16
You will now have the coordinates (16,3)
In the second pair it gives the x coordinate which is 4 but we need to solve for y.
4 - 4y=4 subtract 4 from both sides
-4 -4
-4y = 0 Divide both sides by 4
y = 0
The ordered pair will be (4,0)
The perimeter of a rectangle is 80 inches, if the width is 18 inches what is the area of the rectangle? A.22 sq.in B.324 sq.in C.396 sq.in D.6,400 sq.in
Answer:
396 in^2
Step-by-step explanation:
The perimeter of a triangle is given by the formula:
● P = 2w+2L
L is the length and w is the width
■■■■■■■■■■■■■■■■■■■■■■■■■■
The width hereis 18 inches and the perimeter is 80 inches.
Replace w by 18 and P by 80 to find L.
● P= 2L+2w
● 80 = 2L + 2×18
● 80 = 2L + 36
Substrat 36 from both sides
● 80-36 = 2L+36-36
●44 = 2L
Divide both sides by 2
● 44/2 = 2L/2
● 22 = L
So the length is 22 inches
■■■■■■■■■■■■■■■■■■■■■■■■■■
The area of a rectangle is given by the formula:
● A= L×w
● A = 22×18
● A = 396 in^2
Assume that a random sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level.
Answer:
Margin of Error = z∝/2 * Standard Error
Step-by-step explanation:
The formula for standard error is given by
SE = [tex]\sqrt{\frac{pq}{n} }[/tex]
Where p is the probability or proportion of success q=1-p and n is the number of trials or samples.
Now Margin of Error is given by
ME = z∝/2 * Standard Error
The confidence level is used to estimate the value of alpha.
For example 90% confidence means alpha= 1-0.9= 0.1 and alpha by 2 would be 0.05 . So the value for alpha by 2 would be 1.96
What fraction of a ton is a pound?
Answer:
There are 2000 pounds in a short ton. To convert short tons to pounds, multiply the ton value by 2000.
Answer:
5/100000 tons
Step-by-step explanation:
PLZ HELP THANKS! Find the equation of the line passing through the pair points (-8,6) (-9,-9). The equation of the line in the form is Ax+By=C.
Answer:
The answer is
15x - y = - 126Step-by-step explanation:
To find the equation of the line we must first find the slope (m)
[tex]m = \frac{y2 - y1 }{x2 - x1} [/tex]
So the slope of the line using points
(-8,6) (-9,-9) is
[tex]m = \frac{ - 9 - 6}{ - 9 + 8} = \frac{ - 15}{ - 1} = 15[/tex]
So the equation of the line using point (-8,6) and slope 15 is
y - 6 = 15( x + 8)
y - 6 = 15x + 120
Writing the equation in the form
Ax+By=C
We have
15x - y = -120-6
The final answer is
15x - y = - 126Hope this helps you
Write 4–6 sentences explaining why it is important to have precise definitions in mathematics.
Complete the point-slope equation of the line through (2,3)(7,4). Use exact numbers. y-4=
Please help me, I would really appreciate it!
Answer:
The answer is
[tex]y - 4 = \frac{1}{5} (x - 7)[/tex]Step-by-step explanation:
To find the equation of a line given two points first find the slope and use the formula
[tex] y - y_{1} = m(x - x_{1})[/tex]Where m is the slope
To find the slope we use the formula
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]The slope of the line using points
(2,3)(7,4) is
[tex]m = \frac{4 - 3}{7 - 2} = \frac{1}{5} [/tex]Equation of the line using point (7,4) and slope 1/5 is
[tex]y - 4 = \frac{1}{5} (x - 7)[/tex]Hope this helps you
Answer:
y-4=1/5(x-3)
Step-by-step explanation:
We plug in the x's and the y's and find the slope with:
[tex](y-y_{1} )/ x-x_{1})=m[/tex]
Which of the following best defines the midpoint of a segment? A. The point that splits a line segment into two equal parts. B. Any point on a line segment in between the two endpoints. C. When a line segment is split into equal thirds, a midpoint is any point in the middle third. D. Any point that is closer to one endpoint of the segment than the other.
Answer:
A. The point that splits a line segment into two equal parts.
Step-by-step explanation:
A. The point that splits a line segment into two equal parts.
Midpoint, as the word suggests, means the point which lies in the middle of something. The correct option is A.
What does a midpoint mean?Midpoint, as the word suggests, means the point which lies in the middle of something. The midpoint of a line segment means a point which lies in the mid of the given line segment.
The statement that best describes the midpoint of a segment is the point that splits a line segment into two equal parts.
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Which of the following points IS a solution to the system: y > - 3x + 4 / y > 2x / - y < 7 Selected answer is not correct.
Answer:
Solution : Third Option
Step-by-step explanation:
The first step here is to make all the signs uniform. As you can see the third inequality has a less than sign, which we can change to a greater than sign by dividing negative one on either side, making the inequality y > - 7.
[tex]\begin{bmatrix}y>-3x+4\\ y>2x\\ y>-7\end{bmatrix}[/tex]
Now take a look at the third option. Of course the y - coordinate, 3, is greater than - 7, so it meets the third requirement ( y > - 7 ). At the same time 3 > 1( 2 ) > 2, and hence it meets the second requirement as well. 3 > - 3( 1 ) + 4 > - 3 + 4 > 1, meeting the first requirement.
Therefore, the third option is a solution to the system.
Use the gradient to find the directional derivative of the function at P in the direction of Q. g(x, y, z) = xye^z, P(2, 4, 0), Q(0, 0, 0)
Answer: Find answer in the attached files
Step-by-step explanation:
find the derivative of f(x)=3x^2✓x
Answer:
[tex]f'(x)=\dfrac{15x\sqrt{x}}{2}[/tex]
Step-by-step explanation:
The power rule applies.
d(x^n)/dx = nx^(n-1)
__
[tex]f(x)=3x^2\sqrt{x}=3x^{\frac{5}{2}}\\\\f'(x)=3(\frac{5}{2})x^{\frac{3}{2}}\\\\\boxed{f'(x)=\dfrac{15x\sqrt{x}}{2}}[/tex]
The perimeter of a rectangular garden is 43.8 feet. It's length is 12.4t . What is it's width ?
Answer:5
Step-by-step explanation:
A teacher shares sweets among 8 students so they get 6 each. How many sweets would they each have got if there had been 12 students?
Answer:
4 sweets
Step-by-step explanation:
we know that there is a total of 48 sweets being handed out, and we can tell that this is an example of inverse proportion:
when one increases the other decreases
So, we multiply 8 * 6 to get 48, and then divide that by 12 to get 4 which is how many each student gets
for some constant k -> xy/z=k
12) A traffic control engineer reports that 75% of the vehicles passing through a checkpoint are from within the state. What is the probability that fewer than 4 of the next 9 vehicles are from out of state
Answer:
0.8343
Step-by-step explanation:
From the question, we have the following values:
Probability of vehicles that pass within the check point that are from within the state = 75% = 0.75
Probability of vehicles that pass within the check point that are from outsode the state = 100 - 75 = 25% = 0.25
P = 0.25
n = number of random variables = 9
The probability that fewer than 4 of the next 9 vehicles are from out of state is calculated as:
P < 4 = P ≤ 3
n = 9
P(x) = n!/(n - x)! x! × p^x × q^(n - x)
x = 3
p = 0.25
q = 0.75
P(x) = 9! /(9 - 3)! × 3! × 0.25^3 × 0.75^(9 - 3)
P(x) =0.8343
The probability that fewer than 4 (x<4) of the next 9 vehicles are from out of state is 0.83427.
Given information:
75% of the vehicles passing through a checkpoint are from within the state.
So, the probability that the vehicle is from within the state is 0.75.
The probability that the vehicle is from outside the state will be 1-0.75=0.25.
Now, let x be the random variable. So, the value of n=9. and x<4
It is required to calculate the probability that fewer than 4 of the next 9 vehicles are from out of state.
So, [tex]x< 4[/tex], p=0.25 and q=0.75.
So, the required probability can be calculated as,
[tex]P(x\le3) =\sum ^nC_x\times p^x \times q^{(n - x)}\\P(x\le3)=\sum\dfrac{n!}{(n - x)! x!} \times p^x \times q^{(n - x)}\\P(x\le3)= \dfrac{9!}{(9 - 3)! 3!} \times 0.25^3 \times 0.75^{(9 - 3)}+\dfrac{9!}{(9 - 2)! 2!} \times 0.25^2 \times 0.75^{(9 - 2)}+\dfrac{9!}{(9 - 1)! 1!} \times 0.25^1 \times 0.75^{(9 - 1)}+\dfrac{9!}{(9 - 0)! 0!} \times 0.25^0 \times 0.75^{(9 - 0)}\\P(x\le3)=0.83427[/tex]
Therefore, the probability that fewer than 4 of the next 9 vehicles are from out of state is 0.83427.
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A bank account earned 3.5% continuously compounded annual interest. After the initial deposit, no deposits or withdrawals were made. At the end of an 8 year period, the balance in the account was $13231.30. What was the dollar amount of the initial deposit? Round your answer to the nearest dollar. Do not include a dollar sign ($) or comma in your answer.
Answer:
[tex]\large \boxed{\$10000.00}[/tex]
Step-by-step explanation:
We can use the formula for continuously compounded interest.
[tex]\begin{array}{rcl}A & = & Pe^{rt}\\13231.30& = & Pe^{0.035 \times 8}\\& = &Pe^{0.28}\\& = & P\times 1.3231298\\P & = &\dfrac{13231.30}{1.3231298}\\\\&=&\mathbf{10000.00}\\\end{array}\\\text{The initial deposit was $\large \boxed{\mathbf{\$10000.00}}$}[/tex]
