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.
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.
Find the volume: in cm 7cm high 3cm wide 2 cm long
Find a nonzero vector normal to the plane
negative 2 to the 3 power
How do you convert 6 feet into meters?
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.
How to solve this problem?
11)
x*y = -5*2 = -10, absolute value is 10
y*z = 2 * -2 = -4, absolute value is 4
10+4 = 14
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?
Answer: the density approaches infinity
Step-by-step explanation:
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?
Find the standard form of the equation of the parabola with a focus at (-4, 0) and a directrix at x = 4. (2 points)
Find the surface area of x^2+y^2+z^2=9 that lies above the cone z= sqrt(x^@+y^2)
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
Find The Perimeter Of The Shaded Region
90 ft
58 ft
24 ft
38 ft
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
hat are the dimensions of the lightest open-top right circular cylindrical can that will hold a volume of 1728 cm^3?
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.
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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ok so what is is the square root of 1234 i dot know
sqrt(1234) = 35.1283
you don't say how it should be rounded, so round off as needed
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
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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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?
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:
What is the reciprocal of 2 2/3
Find a general solution to the differential equation 2y''-5y'-3y=0
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
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.
What is the answer, with the correct number of decimal places, for this problem? 4.392 g + 102.40 g + 2.51 g =?
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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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.
3 1/6 divided by 5/8
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.
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?
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.
Solve for the indicated variable
D = 2zv for v
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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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
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?
Which of the following is closest to 27.8 times 9.6? A. 280. B 300. C 2,800. D 3,000
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
8meters long 4 meters wide and 2 meters deep.What is the volume of the pond.
Anoav uses which statistical distribution to determine the significance of the results
One card is selected at random from an ordinary deck of 52 playing cards. let a = event a face card is selected