Mathematics College

A sample of 20 observations has a standard deviation of 4. the sum of the squared deviations from the sample mean is:

Answers

Answer 1

Answer: 304.

Step-by-step explanation:

The formula to calculate the sample standard deviation is given by :-

[tex]s=\sqrt{\dfrac{\sum(x-\overline{x})^2}{n-1}}[/tex]

, where x = sample element.

[tex]\overline{x}[/tex] = Sample mean

s=sample standard deviation.

n= Number of observations.

[tex]\sum(x-\overline{x})^2[/tex] = sum of the squared deviations from the sample mean

As per given , we have

s=4

n= 20

Substitute theses values in the above formula , we get

[tex]4=\sqrt{\dfrac{\sum(x-\overline{x})^2}{20-1}}[/tex]

[tex]4=\sqrt{\dfrac{\sum(x-\overline{x})^2}{19}}[/tex]

Square root on both sides , we get

[tex]\Righatrrow\ 16=\dfrac{\sum(x-\overline{x})^2}{19}\\\\\Righatrrow\ \sum(x-\overline{x})^2=16\times19=304[/tex]

Hence, the sum of the squared deviations from the sample mean is 304.

Answer 2

Sum of squared deviations: [tex]\( 16 \times (20 - 1) = 304 \),[/tex]  given a standard deviation of 4 and sample size of 20.

To find the sum of the squared deviations from the sample mean, we'll use the formula for variance. Since the standard deviation is the square root of the variance, we'll square the standard deviation to get the variance. Then, we'll multiply by the sample size minus 1 to get the sum of the squared deviations.

Given:

Standard deviation (σ) = 4

Sample size (n) = 20

First, let's find the variance:

[tex]\[ \text{Variance} = \sigma^2 = 4^2 = 16 \][/tex]

Now, we'll use the formula for the sum of squared deviations:

[tex]\[ \text{Sum of squared deviations} = \text{Variance} \times (n - 1) \]\[ \text{Sum of squared deviations} = 16 \times (20 - 1) \]\[ \text{Sum of squared deviations} = 16 \times 19 = 304 \][/tex]

So, the sum of the squared deviations from the sample mean is 304.

Related Questions

The equation d=13/v shows that the density of a particular substance equals a mass of 13 grams divided by the volume of the substance. What happens to the density as the volume approaches 0?

Answers

d = M/V where M=mass and V = volume

Assume the Mass is 1 kg and the Volume = 1 cm³, so d= 1/1 kg/cm³

for V=0.1 → d = 1/0.1 = 10 kg.cm³
for V = 0.01 → d = 100.kg.cm³
for V = 0.001 → d = 1000.kg.cm³
for V = 0.000001 → d = 1,000,000.kg.cm³
and when Volume → 0. density →∞
.

Answer: the density approaches infinity

Step-by-step explanation:

ok so what is is the square root of 1234 i dot know

Answers

sqrt(1234) = 35.1283

 you don't say how it should be rounded, so round off as needed

Between 2005 and 2008, the average rate of inflation was about3.4 per year. If a cart of groceries cost $140 in 2005, what did it cost in 2008

Answers

The formula is
A=p (1+r)^t
A future value?
P current value 140
R rate of inflation 0.034
T time 2008-2005=3 years
A=140×(1+0.034)^(3)
A=154.77 round your answer to get
A=155

What is the reciprocal of 2 2/3

Answers

[tex]\bf 2\frac{2}{3}\implies \cfrac{2\cdot 3+2}{3}\implies \cfrac{8}{3}\qquad reciprocal\implies \cfrac{3}{8}[/tex]
3/8, because you make the mixed number an improper fraction(8/3), then you flip it (3/8)

How do you convert 6 feet into meters?

Answers

1.8288 is the corect answer. There are unit converters online.

6 feet is equal to 1.829 m exactly.

Find a general solution to the differential equation 2y''-5y'-3y=0

Answers

We want a general solution for the ODE
2y'' - 5y' - 3y = 0

The characteristic equation is
2m² - 5m - 3 = 0
(2m + 1)(m - 3) = 0
which yields
m = -1/2, 3

Answer:
The general solution is
[tex]y(x)=c_{1}e^{-x/2}+c_{2} e^{3x}[/tex]
where c₁ and c₂ are constants.

a garden table and a bench cost 817 dollars combined. The garden table costs 83 less than the bench. what is the cost of the bench

Answers

table=t
bench=b


t=b-83

t+b=817
b-83+b=817
2b=900
b=450 ($)



"Non nobis, Domine, non nobis, sed Nomini tuo da gloriam."



Regards M.Y.

Which of the following is closest to 27.8 times 9.6? A. 280. B 300. C 2,800. D 3,000

Answers

A 280. you really couldn't use a calculator?
The answer would be A because multiplying the 2 numbers give you 266.88

Find a nonzero vector normal to the plane

Answers

Find a nonzero vector normal to the plane z - 3 (x - 1) = -3 (4 - y).

What is the answer, with the correct number of decimal places, for this problem? 4.392 g + 102.40 g + 2.51 g =?

Answers

The summation of 4.392 g + 102.40 g + 2.51 g with three decimal places is 109.302 g.

What is summation?

A summation, also abbreviated as a sum, is the outcome of adding two or more numbers or quantities. Here are always an integer number of terms in a summation. There could be only two terms, but there could be one hundred, thousand, or a million.

Given the expression for sum,

4.392 g + 102.40 g + 2.51 g

⇒ (4.392 + 102.40 + 2.51)g

⇒ 109.302 g

Hence "The summation of 4.392 g + 102.40 g + 2.51 g with three decimal places is 109.302 g".

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Final answer:

The sum of the masses 4.392 g, 102.40 g, and 2.51 g is 109.30 g.

Explanation:

A summation, which can sometimes be shortened to "sum," is the result of multiplying two or more quantities by one another. A summation always has an integer number of terms. One hundred, thousand, or a million phrases could exist, but there could only be two.

The sum of the masses 4.392 g, 102.40 g, and 2.51 g is 109.302 g.

To ensure the correct number of decimal places, we need to consider the measurement with the least number of decimal places, which is 2.51 g.

Since 2.51 g has two decimal places, we round the sum to two decimal places as well.

Therefore, the answer is 109.30 g.

Consider the following.
Point
(-5, 4)
 Line   
x + y = 7
(a) Write the slope-intercept form of the equation of the line through the given point and parallel to the given line.

(b) Write the slope-intercept form of the equation of the line through the given point and perpendicular to the given line.

Answers

x + y = 7....y = -x + 7....the slope here is -1

A. a parallel line will have the same slope
    y = mx + b
    slope(m) = -1
    (-5,4)...x = -5 and y = 4
    sub and find b, the y int
    4 = -1(-5) + b
    4 = 5 + b
    4 - 5 = b
    -1 = b
so ur parallel line is : y = -x - 1 <==

B. perpendicular lines have negative reciprocal slopes. That means our perpendicular line will have a slope of 1
   y = mx + b
   slope(m) = 1
   (-5,4)...x = -5 and y = 4
   now we sub and find b, the y int
   4 = 1(-5) + b
   4 = -5 + b
   4 + 5 = b
   9 = b
so ur perpendicular line is : y = x + 9 <==

Find The Perimeter Of The Shaded Region

90 ft
58 ft
24 ft
38 ft

Answers

l  = 14 - 6 = 8
w = 15 - 4 = 11

P of shaded = 2(8+9) = 2 (19) = 38

answer
last one 38ft

Answer:

38 ft

Step-by-step explanation:

Perimeter of the rectangle = 2* length + 2* width

Length of shaded part = Length of the larger rectangle - 4 = 11ft

width of the shaded part = width of the larger rectangle - 6 = 8 ft

Perimeter of the rectangle = 2* length + 2* width

Plug in the values of length and width

Perimeter of the shaded rectangle= 2(11) + 2(8)=  22+ 16= 38   feet

Solve for the indicated variable

D = 2zv for v

Answers

2zv=D  divide both sides by 2z

v=D/(2z)

First option is correct i.e. [tex]v = \frac{D}{2z}[/tex] .

What is variable in an equation?

Variable is a symbol( usually a letter) standing in for an unknown numerical value in an equation.

How to solve an equation for the variable?

To solve or isolate a variable means to get the variable on one side of the equation by itself.

According to the given question

we have an equation

D = 2zv and to solve for variable v

For solving the above equation for the variable v, make the variable v on one side of the equation by itself.

⇒ [tex]\frac{D}{2z} = \frac{2zv}{2z}[/tex]    ( dividing both the sides by 2z)

⇒ [tex]v = \frac{D}{2z}[/tex]

Hence, option first is correct.

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Two trains leave a train station traveling different directions. The first train travels 12 miles west, then 6 miles north. The second train travels 20 miles east, then 35 miles north.
a. The train station is the origin. What is the coordinate of each train?
b. Using the city center and the stop point of the first train, what is the slope of the line? Is it horizontal, vertical or neither? Write the equation of the line in slope-intercept form and standard form.
c. The city wants to build a train station 2 miles directly north of the first train station. They are going to build a train track parallel to the path the first train would’ve traveled if it were a direct route from the city center. What would be the equation of the line in slope intercept form of the new track?

Answers

Draw a diagram to illustrate the problem as shown below.
The origin (0, 0) is the train station.

Part a.
The first train travels 12 miles west and 6 miles north to arrive at A.
It's coordinate is (-12, 6).

The second train travels 20 miles east and 35 miles north to arrive at B.
It's coordinate is (20, 35).

Part b.
The slope of the line from the origin to A is
m = (6 - 0)/(-12 - 0) = -1/2.
The slope is neither vertical nor horizontal.
The y-intercept is 0.

The line OA is given in slope-intercept form by
y = -(1/2)x
In standard form, the line is
y - 6 = -(1/2)*(x - (-12))
or
y - 6 = -(1/2)*(x + 12)

Part c.
The new train station is located at (0, 2) because it is 2 miles north of the old station.
If a new track is built parallel to OA, then it should have a slope of -1/2.
Because it's y-intercept is 2, its equation in slope-intercept form is
y = -(1/2)x + 2.

Answer:a. first (-12,6) second (20,35)

b. y = -1/2x, 2y + 1x = 0 (neither horizontal or vertical)

c. y= -1/2x + 2.

Step-by-step explanation:

One card is selected at random from an ordinary deck of 52 playing cards. let a = event a face card is selected

Answers

we have three face card and 4 groups of cards
3*4=12
12/52=3/13
p(a)=3/13

Suppose a​ least-squares regression line is given by modifyingabove y with caret equals 4.302 x minus 3.293y=4.302x−3.293. what is the mean value of the response variable if x equals 20x=20

Answers

Final answer:

The mean value of the response variable y when x equals 20 in the least-squares regression line equation y = 4.302x - 3.293 is 82.041.

Explanation:

The given equation is y = 4.302x - 3.293, which is a least-squares regression line. In this formula, x is the independent variable and y is the resulting dependent variable or response. The goal is to find the mean value of the response variable when x is 20. This can be achieved simply by plugging 20 in place of x in our equation and calculating the resulting value for y.

We will substitute x = 20 into the equation y = 4.302x - 3.293. Therefore, the value of y when x is 20 is:

y = 4.302(20) - 3.293 = 82.041

So, when x = 20, the mean value of the response variable y or the predicted y value is 82.041.

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Find the standard form of the equation of the parabola with a focus at (-4, 0) and a directrix at x = 4. (2 points)

Answers

To find the focus you have to find the center between the to, do you remember the formula's?

check the picture below.

since the focus point is at -4, 0 and the directrix is a vertical line at  x = 4, is a horizontal parabola, and it opens to the left-hand-side.

now, notice the distance "p", is just 4 units, however, the parabola is opening to the left-side, thus "p" is negative, then is -4, the vertex is half-way between the focus point and the directrix.

[tex]\bf \textit{parabola vertex form with focus point distance}\\\\ \begin{array}{llll} \boxed{(y-{{ k}})^2=4{{ p}}(x-{{ h}})} \\\\ (x-{{ h}})^2=4{{ p}}(y-{{ k}}) \\ \end{array} \qquad \begin{array}{llll} vertex\ ({{ h}},{{ k}})\\\\ {{ p}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}\\\\ -------------------------------\\\\ \begin{cases} h=0\\ k=0\\ p=-4 \end{cases}\implies (y-0)^2=4(-4)(x-0)\implies y^2=-16x \\\\\\ -\cfrac{1}{16}y^2=x[/tex]

3 1/6 divided by 5/8

Answers

The result of 3 1/6 divided by 5/8 is equal to 76/15.

To divide a mixed number by a fraction, we need to convert the mixed number into an improper fraction.

In this case, 3 1/6 can be written as an improper fraction as (3 × 6 + 1) / 6 = 19/6.

Next, we can multiply the numerator of the fraction by the reciprocal of the divisor.

The reciprocal of 5/8 is 8/5.

So, (19/6) ÷ (5/8) = (19/6) × (8/5) = (19 × 8) / (6 × 5) = 152/30.

The fraction 152/30 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which in this case is 2. So, (152/30) ÷ 2 = 76/15.

Therefore, 3 1/6 divided by 5/8 is equal to 76/15.

Final answer:

To find the result of 3 1/6 divided by 5/8, convert the mixed number to an improper fraction, multiply by the reciprocal of the divisor, and simplify the resulting fraction. The answer is 5 1/15.

Explanation:

The student's question 3 1/6 divided by 5/8 is a mathematics problem that involves division of mixed numbers and fractions. To solve this problem, the student first needs to convert the mixed number into an improper fraction. To do this, the student multiplies the whole number by the denominator of the fractional part and then adds the numerator:

Multiply 3 (the whole number) by 6 (the denominator of the fractional part): 3 x 6 = 18.

Add the numerator (the fractional part's numerator, which is 1): 18 + 1 = 19. So, 3 1/6 becomes 19/6.

The next step is to divide 19/6 by 5/8. In division of fractions, you multiply by the reciprocal of the divisor. The reciprocal of 5/8 is 8/5.

Therefore, you multiply 19/6 by 8/5: 19/6 x 8/5.

Perform the multiplication of numerators and denominators: 19 x 8 = 152 and 6 x 5 = 30.

The result is 152/30. This fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2.

The simplified answer is 76/15, or as a mixed number, 5 1/15.

This shows that 3 1/6 divided by 5/8 is 5 1/15.

negative 2 to the 3 power

Answers

-2^3 = -2 * -2 * -2 = -8
2 to the power of 3 is 8

A new basketball costs $25.00 at the sporting goods store. If the store is having a going-out-of-business sale and everything is 60% off, what is the actual cost of the basketball?

Answers

Final answer:

To calculate the discounted price of the basketball, multiply the original price ($25.00) by 60% to find the discount ($15.00), and subtract this from the original price to get the final price ($10.00).

Explanation:

To find out the actual cost of the basketball after a 60% discount, we start by calculating the amount of the discount. A 60% discount on a $25.00 basketball means the discount is 60/100 times $25.00. To do the calculation:

First, we convert the percentage to a decimal: 60% = 0.60.Then, we multiply the original price by the decimal: $25.00 × 0.60 = $15.00.This $15.00 is the amount of the discount.

To find the discounted price, we subtract the discount from the original price: $25.00 - $15.00 = $10.00. Therefore, the discounted price of the basketball is $10.00.

From the 11

male and 6

female sales representatives for an insurance​ company, a team of 3

men and 2

women will be selected to attend a national conference on insurance fraud.
In how many ways can the team of 5

be​ selected?

Answers

Selecting r objects out of n objects, can be done in C(n, r) many ways.

For example selecting groups of 4 people out of 10 people can be done in
C(10, 4) many ways.


C(n, r) is calculated as follows: [tex]C(n, r)= \frac{n!}{r!(n-r!)} [/tex], 

where n! is 1*2*3*...*(n-1)*n


3 men out of 11 men, and 2 women out of 6 women are to be selected.

This can be done in C(11, 3) and C(6,2) ways respectively.

Since any of the selected men group can be combined with any of the selected women group, there are C(11, 3)*C(6,2) many ways of selecting the team of 5.


[tex]C(11, 3)*C(6,2) = \frac{11!}{8!3!} * \frac{6!}{4!2!}= \frac{11*10*9*8!}{8!*3!}* \frac{6*5*4!}{4!*2!}= \frac{11*10*9}{3*2*1} * \frac{6*5}{2*1}= [/tex]

165*15=2475


Answer: 2475

i need to know the solution using a fraction or integer to 3 more than the product of 7 and a number x is less than 26

Answers

so.. the number is "x", now, the product of "x" and 7 is just 7*x or 7x.

3 more than that? is just 7x + 3

so, we know is less than 26, 7x + 3 < 26

[tex]\bf 7x+3\ \textless \ 26\implies 7x\ \textless \ 26-3\implies 7x\ \textless \ 23\implies x\ \textless \ \cfrac{23}{7} \\\\\\ \boxed{x\ \textless \ 3\frac{2}{7}}\qquad \qquad 3\frac{2}{7}\implies \cfrac{3\cdot 7+2}{7}\implies \cfrac{23}{7}[/tex]

hat are the dimensions of the lightest​ open-top right circular cylindrical can that will hold a volume of 1728 cm^3?

Answers

The product of height and square of the radius of the open-top right circular cylindrical should be equal or more than 550 cm³ in order to hold a volume of 1728 cm³.

What is volume?

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

The volume of the cylinder is = πr²h
In order to hold the volume of 1728 cm³,
πr²h ≥ 1728
r²h ≥ 550

Thus, the product of height and square of the radius of the open-top right circular cylindrical should be equal to or more than 550 cm³ in order to hold a volume of 1728 cm³.

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Find the surface area of x^2+y^2+z^2=9 that lies above the cone z= sqrt(x^@+y^2)

Answers

The cone equation gives

[tex]z=\sqrt{x^2+y^2}\implies z^2=x^2+y^2[/tex]

which means that the intersection of the cone and sphere occurs at

[tex]x^2+y^2+(x^2+y^2)=9\implies x^2+y^2=\dfrac92[/tex]

i.e. along the vertical cylinder of radius [tex]\dfrac3{\sqrt2}[/tex] when [tex]z=\dfrac3{\sqrt2}[/tex].

We can parameterize the spherical cap in spherical coordinates by

[tex]\mathbf r(\theta,\varphi)=\langle3\cos\theta\sin\varphi,3\sin\theta\sin\varphi,3\cos\varphi\right\rangle[/tex]

where [tex]0\le\theta\le2\pi[/tex] and [tex]0\le\varphi\le\dfrac\pi4[/tex], which follows from the fact that the radius of the sphere is 3 and the height at which the sphere and cone intersect is [tex]\dfrac3{\sqrt2}[/tex]. So the angle between the vertical line through the origin and any line through the origin normal to the sphere along the cone's surface is

[tex]\varphi=\cos^{-1}\left(\dfrac{\frac3{\sqrt2}}3\right)=\cos^{-1}\left(\dfrac1{\sqrt2}\right)=\dfrac\pi4[/tex]

Now the surface area of the cap is given by the surface integral,

[tex]\displaystyle\iint_{\text{cap}}\mathrm dS=\int_{\theta=0}^{\theta=2\pi}\int_{\varphi=0}^{\varphi=\pi/4}\|\mathbf r_u\times\mathbf r_v\|\,\mathrm dv\,\mathrm du[/tex]
[tex]=\displaystyle\int_{u=0}^{u=2\pi}\int_{\varphi=0}^{\varphi=\pi/4}9\sin v\,\mathrm dv\,\mathrm du[/tex]
[tex]=-18\pi\cos v\bigg|_{v=0}^{v=\pi/4}[/tex]
[tex]=18\pi\left(1-\dfrac1{\sqrt2}\right)[/tex]
[tex]=9(2-\sqrt2)\pi[/tex]

Milla and Luka are 3 kilometers apart and walking toward each other. Milla's average speed is 5 kilometers per hour and Luka's is 4 kilometers per hour.

Which equation can be used to find t, the time it takes for Milla and Luka to meet?
5t + 4t = 1
5t + 4t = 3
5t – 4t = 0
5t – 4t = 3

Answers

Answer: Second option is correct.

Step-by-step explanation:

Since we have given that

Speed of Milla = 5 km per hour

Speed of Luka = 4 km per hour

Distance between Milla and Luka = 3 km

Let the time be 't'.

As we know that

[tex]Distance=Speed\times time[/tex]

So, it becomes,

Distance covered by Milla + Distance covered by Luka = Total distance

[tex]5t+4t=3[/tex]

Hence, Second option is correct.

Anoav uses which statistical distribution to determine the significance of the results

Answers

In statistics, ANOVA means Analysis of Variance. This is a statistical tool that helps in determining if the effect of the independent variable on the dependent variable is significant or not. It uses the F-distribution to determine the difference of means. That is why the other name for ANOVA is the F-test. It was named in honor of Ronald Fisher. It is a table consisting of F values which is simply the ratio of two variances. It depends on the degrees of freedom and the α to be used. A sample of the F-table is shown in the picture.

Find the volume: in cm 7cm high 3cm wide 2 cm long

Answers

v=l×w×h
so 7×3×2=42 cm3
The answer is 42 cm cubed


If $3500 is invested at the rate of 8%, compounded quarterly, what will be the value of the investment 17 years from now, assuming no withdrawals?

Answers

We will use the compound interest formula, which is

A = P(1+r/n)^(n*t)

The variables are

A = amount in the account after t years
P = initial amount invested
r = interest rate (in decimal form)
n = compounding frequency
t = number of years

In this case

A = unknown (we're solving for this)
P = 3500
r = 0.08 (8% = 8/100 = 0.08)
n = 4 (compound quarterly ---> compound 4 times a year)
t = 17

------------------------------------------

Plug all these values into the equation to get...

A = P(1+r/n)^(n*t)
A = 3500(1+0.08/4)^(4*17)
A = 3500(1+0.02)^(4*17)
A = 3500(1.02)^(4*17)
A = 3500(1.02)^(68)
A = 3500(3.8442505025456)
A = 13454.8767589096
A = 13454.88

This means that you will have $13454.88 in the account after 17 years

Final Answer: 13454.88

How to solve this problem?

Answers

11)

 x*y = -5*2 = -10, absolute value is 10

y*z = 2 * -2 = -4, absolute value is 4

10+4 = 14

8meters long 4 meters wide and 2 meters deep.What is the volume of the pond.

Answers

Volume of a 3 dimensional object is Length x Width x Height. The length is 8 meters, the width is 4 meters, and the height (the depth rather) is 2 meters. Therefore, the volume of the pond is equal to 8 x 4 x 2

8 x 4=32 x 2=64

The volume of the pond is 64 meters
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