As the sample size (n) increases, the number of degrees of freedom increases, and the t-distribution approaches a normal distribution.
What is degrees of freedom ?
The variety of degrees of freedom is the amount of values within the final calculation of a datum that are liberal to vary. Estimates of applied math parameters are often primarily based upon totally different amounts information|of knowledge or data.
Main Body:
Degrees of freedom typically equals the quantity of observations (or items of information) minus the quantity of parameters calculable. once you perform regression, a parameter is calculable for each term within the model, and and every one consumes a degree of freedom. Therefore, as well as excessive terms during a multivariate analysis model reduces the degrees of freedom on the market to estimate the parameters' variability.
Hence the number of degrees of freedom increases,as the sample size (n) increases.
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a recent survey found that 70% of all adults wear sunglasses for driving. in a random sample of 10 adults, what is the probability that at least five wear sunglasses?
The probability that at least five wear sunglasses is 0.9464
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty. The higher the probability of an event, the more likely it is that the event will occur. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%).
In a random sample of 10 adults, the probability that at least five wear sunglasses
P(X ≥ 5) = P(X = 5) + P(X = 6 ) + P(X=7) + P(X=8) + P(X=9) + P(X=10)
P(X ≥ 5) = 10[tex]C_{5}[/tex] × [tex](0.7)^{5}[/tex]×[tex](0.3)^{5}[/tex] + 10[tex]C_{6}[/tex]×[tex](0.7)^{6}[/tex]× [tex](0.3)^{4}[/tex]+ 10[tex]C_{7}[/tex]×[tex](0.7)^{7}[/tex]×[tex](0.3)^{3}[/tex] + 10[tex]C_{8}[/tex]× [tex](0.7)^{8}[/tex]×[tex](0.3)^{2}[/tex] +10[tex]C_{9}[/tex] ×[tex](0.7)^{9}[/tex]×[tex](0.3)^{1}[/tex]+10[tex]C_{10}[/tex]×[tex](0.7)^{10}[/tex]×[tex](0.3)^{0}[/tex]
P(X ≥ 5) = 0.9464
The probability that at least five wear sunglasses is 0.9464
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which expression is equivalent to -24-12w
Answer:
Simplest form = -w - 2
Step-by-step explanation:
Given expression,
→ -24 - 12w
→ -12w - 24
Simplifying the expression,
→ -12w - 24
→ (-12w - 24)/12
→ -w - 2
Hence, the answer is -w -2.
Examine the triangles, which are similar.
12 mm
18 mm
y
?
12 mm
© 2017 StrongMind. Created using GeoGebra.
How many millimeters long is the missing side?
Note: The triangles may not be drawn to scale.
The missing side of the first triangle is 8 millimeters long.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The relations between variables, either direct or inversely proportional, can be built to find the desired measures in the problem.
We have been given that;
The first triangle has a side length of 12 millimeters, which corresponds to the second triangle's side of 18 millimeters.
The missing side of the first triangle corresponds to a side of 12 millimeters on the second triangle.
Therefore, The relationship between them is;
12/ n = 18/12
n = 12 x 12/18
n = 144 /18
n = 8
Therefore, the missing side of the first triangle is 8 millimeters long.
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the standard deviation of utterance is the average number of morphemes that communicators use in their sentences. true or false
The statement which said that "the standard deviation of utterance is the average number of morphemes that communicators use in their sentences", is false.
What is the standard deviation?
Standard deviation is a statistical value that shows the distribution of data in the sample so that it can show how close each point is to the sample mean value. The amount of data that differs from the average can be identified by the standard deviation value.
In conclusion, the standard deviation of utterance is the number of morphemes that are different from the average morpheme used by the communicator in his sentence.
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For his phone service, Alonzo pays a monthly fee of $17, and he pays an additional $0.07 per minute of use. The least he has been charged in a month is $115.56. What are the possible numbers of minutes he has used his phone in a month? Use m for the number of minutes, and solve your inequality for m .
Answer:
at least 1,408 minutes
Step-by-step explanation:
Let m be the number of minutes.
[tex]17 + .07m \geqslant 115.56[/tex]
[tex].07m \geqslant 98.56[/tex]
[tex]m \geqslant 1408[/tex]
Questions 11 - 13. Given a standard beta distribution with the following parameters: a = 5 and B = 2 Question 13: Compute P(X<0.2) A. 0.039 B. 0.0149 C. 0.0016 D. 0.026
The P(X<0.2) with standard beta distribution parameters α = 5 and β = 2 is 0.0016.
How to calculated the probability density function in standard beta distribution?
Beta distribution is one of the continuous probability distributions set at interval (0, 1) intervals with two positive parameters α and β.
Probability density function can be calculated by this formula
[tex]\frac{x^{\alpha -1}(1-x)^{\beta -1}}{B(\alpha ,\beta) }[/tex]
B(α,β) is beta function = Γ(α)Γ(β)/Γ(α+β)
Γ(α) is gamma function of alpha
Γ(β) is gamma function of beta
P(X<0.2) = [tex]\frac{0.2^{5-1}(1-0.2)^{2-1}}{B(5,2) }[/tex]
= 0.0016
Excel formula for beta distribution is
=BETA.DIST(x;α;β;TRUE)
Thus, the P(X<0.2) with standard beta distribution parameters α = 5 and β = 2 is 0.0016.
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consider the equation y+4=-1/2(x+8)
The equation of the line in standard form is x + 2y = -16
What are linear equations?Linear equations are the set of equations that have constant slopes or gradient
How to put the equation of a line into standard form?From the question, we have the following equation that can be used in our computation:
y+4=-1/2(x+8)
Rewrite the above equation properly
So, we have the following representation
y + 4 = -1/2(x + 8)
Multiply through the equation by -2
So, we have the following equation
-2(y + 4) = -1/2(x + 8) * -2
Evaluate the products
-2y - 8 = x + 8
To rewrite as standard form is to make the variable stand alone
So, we have
-x -2y = 8 + 8
Evaluate the like terms
So, we have the following representation
-x -2y = 16
Multiply through by -1
x + 2y = -16
Hence, the equation is x + 2y = -16
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Possible question
consider the equation y+4=-1/2(x+8)
Put the equation of a line into standard form
help me with the question on the attached photo please
The width of the shade along line AB, using relations in a right triangle, is of:
337.8 mm.
What are the relations in a right triangle?There are three relations in a right triangle, given as follows:
The sine of an angle of the triangle is represented by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle of the triangle is represented by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle of the triangle is represented by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.The width of the shade along-side line AB is of:
100 mm + e1 + e2.
Considering a bisection at the top corner of the shade, we have that:
e1 is the length opposite side to an angle of 50º in a right triangle with hypotenuse of 150 mm, hence:
sin(50º) = e1/150
e1 = 150 x sin(50º)
e1 = 114.9 mm.
Considering a bisection at the bottom corner of the shade, we have that:
e2 is the length opposite side to an angle of 55º in a right triangle with hypotenuse of 150 mm, hence:
sin(55º) = e2/150
e2 = 150 x sin(55º)
e2 = 122.9 mm.
Hence the total width of the shade is of:
100 mm + e1 + e2 = 100 + 114.9 + 122.9 = 337.8 mm.
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The volume of a rectangular prism is represented by the function x3 9x2 6x − 16. the length of the box is x 2, while the height is x 8. find the expression representing the width of the box. x − 4 x − 1 x 1 x 4
The expression that represents the width of the box is (x - 1) , the correct option is (b) .
In the question ,
it is given that ,
the Volume of the rectangular prism is = x³ + 9x² + 6x – 16
the measure of the length of the box = x+2
the measure of the height of the box = x+8
formula for Volume of Prism is
Volume = l × w × h
where l = length of the prism,
w = width of the prism and
h = height of the prism.
Substituting the values ,
we get ,
x³ [tex]+[/tex] 9x² [tex]+[/tex] 6x – 16 [tex]=[/tex] (x [tex]+[/tex] 2) * (x [tex]+[/tex] 8) * width
On dividing the equation (x³ + 9x² + 6x – 16) with (x+2)
and then dividing the result with (x+8) , we get
width = (x-1) .
Therefore , The expression that represents the width of the box is (x - 1) , the correct option is (b) .
The given question is incomplete , the complete question is
The volume of a rectangular prism is represented by the function x³ + 9x² + 6x – 16. The length of the box is x + 2 while the height is x + 8. Find the expression representing the width of the box
(a) x - 4
(b) x - 1
(c) x + 1
(d) x + 4
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Answer:
B
Step-by-step explanation:
Asked my teacher to help me.
A coffee table is on sale for 20% off tej original price of $115.If there is a 7.5% sales tax, what is the final price of the coffee table
Answer:
$85.10
Step-by-step explanation:
115 * .20 = 23
115 - 23 = 92
92 * 0.075 = 6.9
92 - 6.9 + 85.10
prime factorization for gcf and lcm for 25 and 60.
The gcf of 25 and 60 is 5
the lcm of 25 and 60 is 300
What is prime factorization?The process of determining which prime numbers combine to form the original number is known as prime factorization.
Prime factorization of 25 = 5 * 5
Prime factorization of 60 = 2 × 2 × 3 × 5
the greatest common factor, gcf of 25 and 60 is 5
The lowest common multiple, lcm of 25 and 60
= 2 * 2 * 3 * 5 * 5
= 300
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25 POINTS!! ANSWER FOR BRAINLIST AND SHOW WORK!!!
Answer:
See attached "Image 2" for graph
3 points that are in the system
[tex](6,1)\\(8,-2)\\(7,5)[/tex]
3 points that are not in the system:
[tex](0,0)\\(-2,-6)\\(-8,4)[/tex]
Step-by-step explanation:
Start by writing the equation in slope-intercept form so they can be graphed.
[tex]\left \{ {{y+5 < 2x} \atop {3y\geq -2x+6}} \right. \\\\\left \{ {{y < 2x-5} \atop {y\geq -\frac{2}{3} x+2}} \right. \\\\[/tex]
Now, graph just the lines - LIGHTLY- on the coordinate plane. See the first attached image.
Now, you can shade the correct areas. In the first equation y is LESS THAN the function, so you would shade BELOW the line, and draw the line as a dashed line, not a solid line. This is because y is not EQUAL to the function.
In the second equation y is GREATER than or EQUAL to the function, so draw the line as a solid line and you would SHADE above the line.
In a system of inequalities, the correct area to shade is where the two shaded areas overlap. See the attached image 2 to see how that looks.
Some points that are in the system of inequalities are:
[tex](6,1)\\(8,-2)\\(7,5)[/tex]
These points are NOT in the system:
[tex](0,0)\\(-2,-6)\\(-8,4)[/tex]
1.
What are the rational zeros of the function
f(x) = 5x² - 35x - 300?
A -12,5
B-12, -5,5
-5, 12
D-5, 5, 12
For the given function f(x) = 5x² - 35x -300 the rational zeroes of the given function are 12 and -5.
As given in the question,
Given function is equal to:
f(x) = 5x² - 35x -300
Simplify the given function f(x) = 5x² - 35x -300 to get the rational zeros of the function,
f(x) = 0
⇒ 5x² - 35x -300 = 0
⇒ 5( x² - 7x - 60) = 0
As 5≠ 0 ,
⇒ x² - 7x - 60 = 0
⇒ x² - 12x + 5x- 60 = 0
⇒(x-12) (x+ 5) = 0
⇒ x = 12 or -5
Therefore, for the given function f(x) = 5x² - 35x -300 the rational zeroes of the given function are 12 and -5.
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Write an equation in point-slope form that passes through (-4, -6) and is parallel to y= -7/2x+6. I'm stuck, please help.
Answer:
y= -7/2x-20
Step-by-step explanation:
parallel line so same slope
the equation given is in y=mx+b form so take out m:
m= -7/2
now input the coordinates and slope(m) given into y=mx+b to find b:
-6=-7/2(-4)+b
-6=28/2+b
-6=14+b
-6-14=b
b=-20
now write equation using slope(m) and y intercept(b)
y= -7/2x-20
Please mark as brainliesttt
The equation in point-slope pass through the given point will be y = -7/2x-20
What is an equation?Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.
The same slope due to a parallel line,
Take away m from the above equation since it is in the y = mx+b form:
m= -7/2
Now, enter the given coordinates and slope(m) into y=mx+b to determine b:
-6 =-7/2 (-4) + b
-6 = 28/2 + b
-6 = 14 + b
b = -20
Slope(m) and y-intercept are now used to create an equation (b),
y = -7/2x-20
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SOLVES FOR 50 POINTS AND BARINLISTEST
Answer:
(-2, 3 1/3)
2nd one
Step-by-step explanation:
2/3*-3=-2 so x=-2
2/3*5=10/3= 3 1/3 so y= 3 1/3
(-2, 3 1/3)
Many bank accounts never go below zero. But some banks will allow a negative balance, at least for a short time, called an overdraft. It means someone has taken out, or 'drafted', more money than was in the account to begin with. Madeline's account went into overdraft. To get back to a positive balance, she deposited mone at a steady rate of $29.06 per week. After 8 weeks, she had $190.69 in the account. What was the balance when the account went into overdraft?
Answer:
-41.79
Madeline was overdrawn $41.79.
Step-by-step explanation:
If she deposited $29.06 a week for 8 weeks, she put
8 × 29.06
= 232.48
$232.48 into her account. But they're saying she now has only $190.69. Some of the money went to payback the negative balance she had.
Balance+232.48=190.69
Balance=190.69-232.48
Balance = -41.79
Madeline had a negative balance of $41.79.
what is 20.72 divided by 8 with work shown
Answer:
2.59
Step-by-step explanation:
Answer shown in picture.
Bill started west on road u. S. 50, riding a bicycle at an average rate of 9 mph. Four hours later charles started after bill on a motor cycle and overtook him in 2 hours. What was charles' rate? which equation could be used to solve for charles' rate if it is represented by x? 6 x = 54 2 x = 54 2 x = 36.
The equation could be used to solve for charles' rate if it is represented by x is 2x=54.
In the given question wehave to find the equation could be used to solve for charles' rate if it is represented by x.
Bill riding a bicycle at an average rate of 9 mph.
Charles' rate is x.
So the relative rate = x−9 mph
Distance traveled by Bill in 4 hours = 9*4 =36 mph
Charles' overtook Bill in 2 hours. So
Relative Rate = Distance/Time
x−9=36/2
Multiply by 2 on both side. We get
2(x−9)=36
Simplifying
2x−18=36
Add 18 on both side, we get
2x=36+18
2x=54
Hence, the equation could be used to solve for charles' rate if it is represented by x is 2x=54.
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an airplane flying with the wind can cover 560 miles in 2 hours. the return trip against the wind takes 2 1 2 hours. what is the speed of the plane? the speed of the plane is miles per hour. what is the speed of the air? the wind's speed is miles per hour.
The speed of the plane is 252 miles per hour and the speed of the wind is 28 miles per hour .
In the question ,
it is given that ,
the airplane covers the distance of 560 miles in 2 hours with the wind,
So , the speed of the airplane with the wind is 560/2 = 280 miles per hour
also given that
airplane covers the distance of 560 miles in 2.5 hours against the wind ,
So , the speed of the plane with the wind = 560/2.5 = 224 miles per hour .
let the speed of the airplane be "a" miles per hour ,
and let the speed of the wind be "b" miles per hour ,
So , equation of speed with the wind is denoted by
a + b = 280
and the equation of speed against the wind is denoted by
a - b = 224
Adding both the equations , we get
2a = 504
a = 504/2
a = 252 miles per hour
and b = 280 - 252 = 28 miles per hour .
Therefore , The speed of the plane is 252 miles per hour and the speed of the wind is 28 miles per hour .
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Simplify to a single power of 4:
(44) 5
Answer:
4²0=4×5=20=4²0 арлатат
Choose the expression that is equivalent to 1/4 x 12
Answer:
4%12
Step-by-step explanation:
Determine whether each number is an integer, a rational number that is not an integral or an irrational number
The integers are 3√25, -185/5, rational = -1/4, 0.75, 3√25, -185/5, 4√8, irrational = √13,
An integer is the number zero (0), a positive natural number (1, 2, 3, etc.) or a negative integer with a minus sign.
A rational number is any number that can be written as a fraction, where both the numerator na demoninator that is the top and the bottom number are integers, and the denominator is cannot be zero
An irrational number is a type of real number which cannot be represented as a simple fraction.
A integer can always be a rational number but vice versa is not true.
Integer = 3√25 = 3x5 = 15
-185/5 = -37
rational = -1/4, 0.75, 3√25, -185/5, 4√8
irrational = √13,
Therefore, the integers are 3√25, -185/5, rational = -1/4, 0.75, 3√25, -185/5, 4√8, irrational = √13,
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please help me with this
The inequality shown on the number line is -3 < x ≤ 2
Inequality means when the two values that are not equal is defined by inequalities. Inequality means unequal.
When two values are not equal we will greater than or less than sign .
" < " means less than
" >" means greater than
"≤ " means less than and equal to
"≥ " means greater than and equal to
(a) Inequality -4 < n ≤ 5
here , -4 is not included so, the Number line starts from -3
5 is included so, number line will end on 5
(b) The number line shows ,
line is starting from -3 but the dot is not filled means it is not included
The line ends at 2 so,
Inequality is -3 < n ≤ 2
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Factor the expression in the image please
To factorize this,the answer is [tex]\frac{1}{3} x^{4} y^{2} (\frac{1}{4} y^{} -\frac{1}{3} x)[/tex]
What is Factorization?Factorization is when you break a number down into smaller numbers that, when multiplied together, give you that original number.
The expression above can only be determined by looking at the common factors and using it to answer the question. [tex]\frac{1}{12} x^{4}y^{3} -\frac{1}{9}x^{5}y^{2}[/tex]
To factorize the fractions by looking at the common factor between the both[tex]\frac{1}{3} (\frac{1}{4} -\frac{1}{3} )[/tex]To factorize the indices by looking at the common factor[tex]x^{4}y^{2} (y-x)[/tex]
So, to factorize the expression above[tex]\frac{1}{3} x^{4} y^{2}(\frac{1}{4} y-\frac{1}{3} x)[/tex]
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What is the main difference between vulnerability scanning and penetration testing?.
The main difference between vulnerability scanning and penetration testing is a vulnerability scan is an automated, high-level test that looks for and reports potential vulnerabilities. A penetration test is a detailed hands-on examination by a real person that tries to detect and exploit weaknesses in your system.
vulnerability scanning:
These scans are typically automated and give a beginning look at what could possibly be exploited.
High-quality vulnerability scans can search for over 50,000 vulnerabilities and are required as per PCI DSS, FFIEC, and GLBA mandates.
penetration testing:
A penetration test simulates a hacker attempting to get into a business system through hands-on research and the exploitation of vulnerabilities. Actual analysts, often called ethical hackers, search for vulnerabilities and then try to prove that they can be exploited. Using methods like password cracking, buffer overflow, and SQL injection, they attempt to compromise and extract data from a network in a non damaging way.
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It costs $0.75 each to make color copies at a copy
center. At this price, how many copies can be purchased with $60.00?
Answer: 80 copies can be purchased with $60.00.
Step-by-step explanation:
If it costs $0.75 for each color copy, then you would have to divide $60.00 by $0.75, which equals 80 copies.
pls help!
Simplify the expression to a + bi form:
√4 + √−45 + √49 + √−45
Answer: 9+6i√5
Step-by-step explanation:
√4 + √−45 + √49 + √−45
2 + √45i + 7 + √45i
9 + 3i√5 + 3i√5
9+6i√5
If the average product of labor is seven units of output per worker per day, the total output of 15 workers will be ______________ units per day.
The total output of 15 workers will be 105 units per day.Work and time are correlated so using this we could solve the question.
What is work and time?
Time is the duration of any activity or work that occurs or continues.
Work is a task or set of activities designed to achieve a specific result.
Main Body:
This can be done by simply multiplying both number of days and total work in one day.Hence the equation become:
total output = total workers*total work done by one person.
Total output = 7*15
hence,total output = 105 units
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determine if the following orders pairs
The given ordered pair (x, y) represents a linear function
Consider first point (-1, -3) and (0, -1)
The slope of the line is the change in y coordinate with respect to the change in x coordinate of the line.
The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the value in the equation
The slope of the line = (-1-(-3)) / (0 -(-1)
= (-1+3) / 1
= 2
Consider the next set of points (1, 1) and (2, 3)
The slope of the line = (3-1) / (2-1)
= 2
Here slope of the line is same, therefore it is linear function
Hence, the given ordered pair (x, y) represents a linear function
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What is the difference between the graph of y=x+3 and the graph of y=x-3?
Answer:
y
=
x
+
3
y
=
x
−
3
Step-by-step explanation: