A standard deviation (or σ) is a tool to measure how dispersed the data is in relation to the mean. While, in statistics, a central tendency is a central or typical value for a probability distribution. Some of the most common measures of central tendency consist of the arithmetic mean, the median, and the mode. Deviation means a change or a distance. But change is always followed by the word 'from'. Hence standard deviation is a measure of change or the distance from a measure of central tendency- which is normally the mean. Hence, standard deviation is different from a measure of central tendency.
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Find the value of a for which v = [6 -10 4 a] is in the set H = span
The value of a for which v is a linear combination is given as follows:
a = -8.
How to obtain the value of a?
A vector generated by adding two or more vectors (with various orientations) and multiplying by scalar values is known as a linear combination of two or more vectors.
v will be a linear combination of the set H if it can be obtained as the solution of a system of equations from the set H.
From the vectors, the system is defined as follows:
-x = -1.
2x - y = 4.
5x + 4y - 3z = -6.
-x + 3y - z = a.
From the first equation, the value of x is obtained as follows:
-x = -1
x = 1.
From the second equation, the value of y is obtained as follows:
2x - y = 4
2 - y = 4
y = 2 - 4
y = -2.
From the third equation, the value of z is obtained as follows:
5x + 4y - 3z = -6.
5 - 8 - 3z = -6
3z = 3
z = 1.
Then the value of a needed for the linear combination is of:
a = -x + 3y - z
a = -1 - 6 - 1
a = -8.
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At what annual percent rate would you need to invest $12,000 and make $2,880 in interest after 8 years?
Differentiate the following function F(x)Ã gnments F(x)= (x5 -6x)2 jdy Plan A-¡ ii x-A>> X Li. adebooK hapter = (x^5 - 6x)^2
Differentiating F(x) gives 10[tex]x^{9}[/tex] - 72[tex]x^{5}[/tex] + 72[tex]x[/tex].
Differentiation, also referred to as derivatives, determines the rate at which one variable changes in relation to another, in this case, f(x) in relation to x. Finding the greatest or minimum conditions, or the best solution, is possible through differentiation. There are certain fundamental guidelines for differentiating functions.
lf c is any real number and if f(x) = c for all x, then f ' (x) = 0 for all x . That is, the derivative of a constant function is the zero function.
Partial derivatives in calculus are derivatives of multivariate functions taken with respect to only one variable in the function, treating other variables as though they were constants.
F(x) = ([tex]x^{5}[/tex] -6[tex]x[/tex])²
= [tex]x^{10}[/tex] -12[tex]x^{6}[/tex] + 36[tex]x^{2}[/tex]
dF(x)/dx = d( [tex]x^{10}[/tex] -12[tex]x^{6}[/tex] + 36[tex]x^{2}[/tex] )/dx
= 10[tex]x^{9}[/tex] -12 (6[tex]x^{5}[/tex]) + 36([tex]2x[/tex])
= 10[tex]x^{9}[/tex] - 72[tex]x^{5}[/tex] + 72[tex]x[/tex]
Thus, differentiating F(x) gives 10[tex]x^{9}[/tex] - 72[tex]x^{5}[/tex] + 72[tex]x[/tex].
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Johnny just became a personal trainer and is finalizing his pricing plans. One plan is to charge $74 for the initial consultation and then $64 per session. Another plan is to charge $20 for the consultation and $66 per session. Johnny realizes that the two plans have the same cost for a certain number of sessions. What is that cost? How many sessions is that?
The cost when the two plans are the same is $1802. The number of sessions where the plans would be the same is 27.
What is the cost and the number of sessions?The linear equation that represents the total cost of the first plan: initial consultation + charge per session x number of sessions)
= $74 + $64s
The linear equation that represents the total cost of the second plan: $20 + $66s
When the two plans are the same, the two linear equations would be the same.
$20 + $66s = $74 + $64s
In order to determine the value of s, take the following steps:
Combine similar terms:
$66s - $64s = $74 - $20
Add similar terms:
$2s = $54
Divide both sides of the equation is $2
s = $54 / 2
s = 27
Total cost when s is 27: $20 + $66(27)
$20 + 1782 = $1802
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the edge of a cube is growing at a rate of 6 inches per second at the instant when the edge of the cube has a length of 11 inches. what is the rate of change of the volume of the cube at that instant?
The edge of a cube is growing at a rate of 6 inches per second at the instant when the edge of the cube has a length of 11 inches. Hence, the rate of change of the volume of the cube at that instant will be 2178 [tex]inches^3[/tex] /s.
The volume of the cube V = [tex]a ^ 3[/tex]
where 'a' is the edge.
Rate of increase of volume = dV / dt = 3a^2 da/dt.
da/dt = 6 inches /s
dV / dt = 3 [tex]a^2[/tex] da/dt.
When a = 11 inches.
dV /dt = 3 x [tex]11 ^2[/tex] x 6
= 3 x 121 x 6
= 2178 [tex]inches^3[/tex] /s
Hence, the rate of change of the volume of the cube at that instant will be 2178 [tex]inches^3[/tex] /s.
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determine weather the relationship between the two quantitates is porptional
The answer to the provided question is No, because the graph of the line connecting the ordered pairs does not pass through the origin.
what is proportionality?When two numbers or variables are linearly connected in mathematics, the term "proportional" is used. Both quantities increase by two times when one increases by two. Each variable declines in proportion to the other when it falls below 1/100th of its former value.
The relationship has the following form when two linear variables are directly proportional.
=> y = mx
where the constant ratio of change between the variables is denoted by m.
The graph of the direct proportion is a straight line that goes through the origin, which is one of its key characteristics.
You can see in the example image, though, that the line generated by those points won't cross the coordinate system's origin.
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the questionnaire is a carefully constructed measurement instrument. group of answer choices true false
Yes, its true that the questionnaire is very carefully constructed by an individual to provide the measurement instrument.
A questionnaire is a studies device which includes a sequence of questions for the motive of amassing facts from respondents. Questionnaires may be concept of as a form of written interview. A questionnaire is a listing of questions or gadgets used to collect facts from respondents approximately their attitudes, experiences, or opinions.
Questionnaires may be used to acquire quantitative and/or qualitative facts. Questionnaires are generally utilized in marketplace studies in addition to withinside the social and fitness sciences. Questionnaires are typically taken into consideration to be excessive in reliability. This is due to the fact it's miles feasible to invite a uniform set of questions. Any troubles withinside the layout of the survey may be ironed out after a pilot study. The greater closed questions used, the greater dependable the studies.
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in a local election, votes were cast for mr. dyer, ms. frau, and mr. borak in the ratio of 4:3:2. if there were no other candidates and none of the 2,700 voters cast more than one vote, how many votes did mr. dyer receive?
To calculate the number of votes that Mr. Dyer received, we need to multiply the ratio with the total votes. Mr. Dyer received 1,080 votes.
Ratio of votes = 4:3:2
Total votes = 4 + 3 + 2 = 9
Total votes cast = 2,700
Mr. Dyer's votes = (4/9) x 2,700 = 1,080 votes
The ratio of votes cast for Mr. Dyer, Ms. Frau and Mr. Borak was 4:3:2 respectively. This means that for every 9 votes cast, 4 votes were for Mr. Dyer, 3 votes were for Ms. Frau and 2 votes were for Mr. Borak. Since none of the 2,700 voters cast more than one vote, the total votes cast for each candidate would be 2,700. To calculate the number of votes that Mr. Dyer received, we need to multiply the ratio with the total votes. Therefore, Mr. Dyer received 1,080 votes (4/9 x 2,700).
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The vector (4/-3) translates a to b what is the vector that translates b to a
The required vector converting b to a is (4/3) when a to b is translated by the vector (4/-3).
Given that,
a to b is translated by the vector (4/-3)
We have to find what is the vector converting b to a.
We know that,
What is a vector?Quantities with both magnitude and direction are referred to as vectors. Additionally, it refers to the type of the quantity.
Here,
We have a vector,
ab=(4/-3)
Its direction will be reversed to translate the vector in the other way,
For
ba=-(4/-3)
ba=4/3
Therefore, The required vector converting b to a is (4/3) when a to b is translated by the vector (4/-3).
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You are standing on a ledge and throw a ball from 10 feet above the ground. The speed the ball leaves your hand is 16 feet per second and the acceleration of gravity is -16 feet per second squared.
How many seconds does it take to reach the highest point (vertex)?
Options for what the answer could be that i was given are:
18 seconds
1 second
0.5 seconds
9 seconds
The time taken is 1 second to reach the highest point by using std equations of velocity, time and displacement .
What are 3 std equations of velocity, time and displacement ?
The three standard equations are given as :
1st std equation : v = u + at
2nd std equation : s = u*t + (1/2)at²
3rd equation : 2as = v²-u²
By using 1st std equation:
At highest point final velocity will be zero(0).
So, v = 0
u = 16
a = -16
0 = 16 + -16*t
t = 1sec
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How do you solve 16/48 = n/36?
Answer:
n = 12
Step-by-step explanation:
16/48 = n/36
cross multiply
16 × 36 = 48n
576 = 48n
n = 576/48
n = 12
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What is -2/3 to the 5th power?
-2/3 to the 5th power is equal to -0.008. To do this, we first need to raise -2/3 to the 1st power.
-2/3 to the 5th power can be calculated by raising -2/3 to the 5th power. To do this, we first need to raise -2/3 to the 1st power. This is equal to -2/3. We then need to multiply this result by itself four more times (since it is to the 5th power).
-2/3 * -2/3 = 4/9
4/9 * -2/3 = -8/27
-8/27 * -2/3 = 16/81
16/81 * -2/3 = -32/243
-32/243 * -2/3 = 64/729
Therefore, -2/3 to the 5th power is equal to 64/729. To simplify this, we can divide the numerator and denominator by 64. This gives us 1/11.5 which is equal to -0.008.
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A certain small town, whose population consists of 100 families, has 30 families with 1 child, 50 families with 2 children, and 20 families with 3 children. The birth rank of one of these children is 1 if the child is the firstborn, 2 if the child is the secondborn, and 3 if the child is the thirdborn. (a) A random family is chosen (with equal probabilities), and then a random child within that family is chosen (with equal probabilities). Find the PMF, mean, and variance of the child’s birth rank. (b) A random child is chosen in the town (with equal probabilities). Find the PMF, mean, and variance of the child’s birth rank.
a) A random family is chosen and then a random child within that family is chosen the mean is 1.45 and the variance is 0.38.
b) A random child is chosen in the town, the mean is 1.579 and the variance is 0.454.
For part A:
A random family is chosen and then a random child within that family.
P(X=1)= P(X=1 | family with one child). P(family with one child)
+ P(X=1 | family with two children).P(family with two children)
+P(X=1 | family with three children).P(family with three children)
= 1.30/100 + 1/2 . 50/100 + 1/3 . 20/100 = 37/60
P(X=2)=P(X=2 | family with one child). P(family with one child)
+ P(X=2 | family with two children).P(family with two children)
+P(X=2 | family with three children).P(family with three children)
= 0.30/100 + 1/2 . 50/100 + 1/3 . 20/100 = 19/60
P(X=3)=P(X=3 | family with one child). P(family with one child)
+ P(X=3 | family with two children).P(family with two children)
+P(X=3 | family with three children).P(family with three children)
= 0.30/100 + 0 . 50/100 + 1/3 . 20/100 = 4/40
hence, using these probabilities we can find,
E(X) = 1(37/60) + 2(19/60) + 3(4/60) = 1.45,
therefore, Var(x) = 149/60 − [tex]1.45^{2}[/tex] = 457/1200 ≈ 0.38
hence, the mean of the child's birth is 1.45 and the variance of the child's birth ranks 0.38.
For part B,
When a random child is chosen in the town with equal probabilities.
There are 1 x 30 + 2 x 50 + 3 x 20 = 190 children in the town where 100 of them are first born, 70 of them are second born, and 20 of them are third born. Let X be a random variable that marks the birth rank of a child.
Hence,
E(X) = 1(100/190) + 2(70/190) + 3(20/190) ≈ 1.579
and
Var(X) = 2.947 − [tex]1.579^{2}[/tex] ≈ 0.454
For a random child chosen, the mean of the child's birth is 1.579 and the variance of the child's birth ranks 0.454.
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Evaluate the integral by reversing the order of integration. Double integrate e^x^2 dxdy=
the integral by reversing the order of integration. Double integrate e^x^2 dxdy= 1/3x e^x^3 + C
The integral can be written as:
∫ ∫ e^x^2 dx dy
∫ ∫ e^x^2 dy dx
Applying the formula for double integrals, the answer is:
∫ e^x^2 dy × ∫ dx
Since the inner integral is a constant, it is simply equal to x.
The answer is therefore:
∫ e^x^2 dy × x = x × ∫ e^x^2 dy
The outer integral is a standard antiderivative, and is equal to:
1/3e^x^3 + C
Therefore, the final answer is:
1/3x e^x^3 + C
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for each graph caculate the slope of each line
Answer: -5/4
Step-by-step explanation:
The slope is rise/run or y2 - y1/ x2 - x1
The two points are (-6,-3) (-2, -8)
The y decreases by 5 and the x increase by 4
So the slope is -5/4
What is the graph of this compound inequality?
Answer:
The second one
Step-by-step explanation:
The first graphic would be correct if the connector was "AND" instead of "OR"
"AND" --> Both conditions must ALWAYS be fulfilled
"OR" ---> It's only necessary that one of the conditions is fulfilled
does the data provide sufficient evidence to conclude that the number of errors in auditing technique a is greater than the number of errors in auditing technique b at the 0.1 level of significance? select the [rejection region, decision of reject (rh0) or failure to reject (frh0)]. (hint: the samples are dependent)
Therefore ,we reject the null hypothesis,[tex]H_{0}[/tex]= [tex]u_{d}[/tex] ≤ 0
What is standard deviation ?The square root of the variance is used to calculate the standard deviation, a statistic that gauges a dataset's dispersion from its mean. The standard deviation, which is proportional to the square root of variance, is calculated by comparing the variance of each data point to its mean.
Here,
The null hypothesis,[tex]H_{0}[/tex]= [tex]u_{d}[/tex] ≤ 0
Alternate hypothesis , [tex]H_{A}[/tex]= [tex]u_{d}[/tex] ≥ 0
thus,
[tex]d^{'}[/tex]=(14 + 11 + 7 + 11 -2 + 5 + 0 +5)/9
[tex]d^{'}[/tex]=4.44
[tex]S_{d}[/tex]=6.747
t=[tex]\frac{d^{'}-D}{\frac{S_{d}}{\sqrt{n} } }[/tex]
Putting values in above equation
[tex]d_{f}[/tex]=9-1=8
α=0.10 => t(0.1,8)
t=[tex]\frac{d^{'}-D}{\frac{S_{d}}{\sqrt{n} } }[/tex] = 1.397
Therefore ,we reject the null hypothesis,[tex]H_{0}[/tex]= [tex]u_{d}[/tex] ≤ 0
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If the area of an equilateral triangle is
[tex]64 \sqrt{3} cm {}^{2} [/tex]
find its perimeter
The perimeter of the equilateral triangle is 48 cm
How to find the perimeter of an equilateral triangle?equilateral triangle
An equilateral triangle is a type of triangle in which all three sides are equal in length and all three angles are also equal, measuring 60 degrees each.
Given that: the area of an equilateral triangle is 64√3 cm²
The formula for the area of an equilateral triangle is given by:
A = (√3)/4 × a²
Where a is the length of the side
64√3 = (√3)/4 × a²
4 × 64√3 = (√3) × a²
4 × 64 = a²
a² = 4 × 64
a² = 256
a = √256
a = 16 cm
Perimeter of the equilateral triangle = a + a + a = 3a
Perimeter of the equilateral triangle = 3 × 16 = 48 cm
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25. The value of y is directly proportional to x. Y =
54, when x = 9. What is the value of y when x
= 3.5?
Answer:
y = 21
Step-by-step explanation:
You need to find k
y = x
54 = 9k Divide both sides by 9
6 =k
y = 6(3.5)
y = 21
A pilot flies in a straight path for 1 h 30 min. She then makes a course correction, heading 10 degrees to the right of her original course, and flies 2 h in the new direction. If she maintains a constant speed of 670 mi/h, how far is she from her starting position?
On solving the provided question, we got to know that - distance she covered from her starting position is 2731 miles
What is equation?If two things are equal, an equation declares it. A "=" equals sign will appear in the format: 7 + 2 = 10 − 1 What is on the left (7 + 2) equals what is on the right (10 1), according to that equation. The statement "this equals that" is analogous to an equation.
The flight's first leg is 1020 miles long and lasts (1.5 hours) at 680 mph. We'll refer to this as our triangle's side B.
The second leg of the journey is 1360 miles (2 hours x 680 mph) long. We'll refer to this as the triangle's side C.
The law of cosines allows us to determine the triangle's side a's length.A is a 170° angle between the two sides whose lengths we are aware of. (180° - 10° = 170°).
[tex]a^2 = b^2 + c^2 - (2)*(a)*(b)*cos(A)[/tex]
[tex]a^2 = (1020 miles)^2 + (1360 miles)^2 - (2)*(1020 miles)(1360 miles)*cos(170)\\ a^2 = 1040400 miles^2 + 1849600 miles^2 - (2774400 miles2)*cos(170)\\ cos(170) = -0.9848\\ a^2 = 2890000 miles^2 + 2732251 miles^2 = 5622250.6 miles^2\\ a = (5622250.6 miles^2)^{\frac{1}{2} } = 2371 miles[/tex]
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Hi can someone please help me with this!!!
Answer:
q = 50
r = 75
s = 115
t = 30
Step-by-step explanation:
The Quotient of a number b and four plus seven is two
The algebraic form of the statement is b/4 + 7 = 2 and the value of b is -20.
What is the numerical value of the b?Given the statement; the quotient of a number b and four plus seven is two.
First, we convert the statement into an algebraic equation.
Quotient of a number b and 4 ⇒ b/4Plus 7 ⇒ + 7 Is two ⇒ = 2Now, combine the terms and equality sign.
b/4 + 7 = 2
Next, solve for the numerical value of b.
b/4 + 7 = 2
Subtract 7 from both sides
b/4 + 7 - 7 = 2 - 7
Simplify the left-hand side
b/4 = 2 - 7
Subtract 7 from 2
b/4 = -5
Next, multiply both sides by 4
b/4 × 4 = -5 × 4
b = -5 × 4
b = -20
Therefore, the numerical value of b is -20.
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Liam deposits $3,500 in a saving account that pays 1.5% interest, compounded quarterly.
a.Find the balance after a year.
B. Compare the interest compounded annually.
Therefore the balance after a year comes out to be $3552.80 and the balance comes out to be after compounded annually is $3552.50
What is compound interest ?Compound interest is the interest on savings that is computed using both the original principal and the interest accrued over time.
It is believed that Italy in the 17th century was where the idea of "interest on interest" or compound interest first emerged. It will accelerate the growth of a sum more quickly than simple interest, which is only applied to the principal sum.
Money multiplies more quickly through compounding, and the higher the
Here,
The Liam deposits $3,500 in a saving account that pays 1.5% interest,
Thus rate=1.5% and principle amount =3500
Therefore it is compounded quartely ,
The balance after year=
C=P[tex]e^{rt}[/tex]
C=3500*[tex]e^{1.5*4}[/tex]
C=3552.80
Therefore the balance after a year comes out to be $3552.80
Therefore the balance comes out to be after compounded annually is
$3552.50
So there is only $0.30 difference between the amounts
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suppose you have 1/6 chance of winning with a scratch-off lottery ticket. if you buy 30 ticket what is the probability of winning with all 3
Answer: 18%
Step-by-step explanation:
I gogled
if you have worked 52 % of the total 440 minutes, what percent of the 440 minutes do you have left to work?
The time that is needed to complete the pending work is 211.2 minutes.
To calculate the percentage, divide the value by the total value and then multiply the resultant by 100.
If the amount of work is 52%.
100% - 52% = 48%
The total minutes that are required is 440 minutes.
you have 48% of the 440 minutes left to work.
48% / 100 = .48 * 440 =211.2
Therefore, the time that is needed to complete the pending work is 211.2 minutes.
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Please help, giving thanks and brainliest:) (Please give an explanation if possible and please dont give a fake answer)
The value of x in the triangle is 22.
The angles in the triangle are 22, 29 and 127.
What are the values?A triangle is a three-sided polygon with three edges and three vertices. the sum of angles in a triangle is 180 degrees. A scalene triangle is a triangle that has three different angles.
x + (x + 7) + 127 = 180
In order to determine the value of x, take the following steps:
2x + 134 = 180
2x = 180 - 134
2x = 44
x = 44/2
x = 22
x + 7 = 22 + 7 = 29
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the function f is defined by f(x)={2x−1for x<3for x≥3. what is the value of ∫51f(x)dx?
The value of the given function f (x) is 10
What is the value of the given function ?[tex]f (x) = \left \{ {{2 \text{ for x} < 3} \atop {x- 1 \text { for x } \geq 3} \right. \\\\[/tex]
Integrating the given functions,
[tex]\int\limits^5_1 {f(x)dx = \int\limits^3_1 2dx + \int\limits^5_3 (x- 1)dx[/tex]
[tex]\int\limits^5_1 {f(x)dx =2x + [\frac{x^{2}} {2} - x][/tex]
Applying the limits,
[tex]\int\limits^5_1 {f(x)dx =[2(3)-2(1)]+ [\frac{5^{2}} {2} - 5-\frac{3^{2}} {2} + 3][/tex]
[tex]\int\limits^5_1 {f(x)dx =[6- 2]+ [\frac{25} {2} - 5-\frac{9} {2} + 3][/tex]
[tex]\int\limits^5_1 {f(x)dx = 4 + 6[/tex]
[tex]\int\limits^5_1 {f(x)dx = 10[/tex]
The value of the given function on integrating using the limits is 10
What is integration?Integration is a technique for combining slices to discover the total. Finding areas, volumes, central points, and many other important things may be done with integration. When infinitesimal data are combined, notions such as displacement, area, and volume can be created. An integral assigns numbers to functions in a way that describes these concepts. Integration is the action of locating integrals. The integrals listed here are those that fall under the category of definite integrals, which can be thought of as the signed area of the region in the plane that is enclosed by the graph of a particular function between two points on the real line.Integration is a fundamental, crucial operation of calculus, along with differentiation.To learn more about integration, refer:
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How do you use demoivre's theorem to simplify (1+i)^12?
By using demovire's theorem to determine the complex numbers to simplify (1+i)^12 we get [tex]z^{12}=-2^6=-64[/tex]
first, we have to find the argument. As the complex number, z=1+i will be in the 4th quadrant
we proceed according to conditions in demovire's theorem
[tex]r=\sqrt{(1)^2+(1)^2}\\ \\r=\sqrt{2}[/tex]
so from this our angle becomes
[tex]\alpha =2\pi -tan^{-1}=- \frac{\pi }{4}[/tex]
so putting r and alpha in the formula of demovier's of complex numbers
[tex]z^{n}=r^{n}(cos\alpha +isin\alpha )\\\\z^{12}=(\sqrt{2} )^{\112} }(cos\((\frac{-\pi }{4}) +isin(\frac{-\pi }{4}) )\\\\z^{12}=2^6(-1-0)\\\\z^{12}=-2^6=-64[/tex]
we get z to the power 12 equals to negative times sixty-four.
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How to do perimeter of the given coordinates(quadrilateral)? Number 32?
Answer:
27.21 to nearest hundredth
Step-by-step explanation:
You find the lengths of the 4 sides and add them.
AB = 4 - (-2) = 6
BC = 4 - (--1) = 9
CD = √(-1-(-5)^2 + (-2-4)^2)
= √(16 + 36)
= √52
AD = 5
So, the perimeter
= 6 + 9 + 5 + √52
= 20 + √52
= 27.21 to nearest hundredth.
If 5 dollars can be exchanged for 7.7095 units of some foreign currency, how much of that currency can be obtained for 6 dollars?
If 5 dollars can be exchanged for 7.7095 units of some foreign currency, the unit of that currency that can be obtained for 6 dollars will be
How do we calculate how much currency can be obtained for 6 dollars?5 dollars can be exchanged for 7.7095 units. This means that 1 dollar equals to:
5 dollars / 5 = 7.7095 units / 5
1 dollar = 7.7095 units / 5
1 dollar = 1.5419 units.
Now, for 6 dollars, the foreign currency that can be obtained is:
= 6 * 1.5419 units
= 9.2514 units. Therefore, 9.2514 unit of the foreign currency can be obtained for 6 dollars.
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