Answer:
26
Step-by-step explanation:
The mean of a set of number is the average the set of number, it is the ratio of the total sum of the terms to the sum of terms.
The standard deviation is the variation of a set of numbers to their mean. A low standard deviation means the value are close to the mean and a high standard deviation means the values are far from the mean. The standard deviation is given as:
[tex]\sigma=\sqrt{\frac{\Sigma (x_i-\mu)^2}{n} }\\ \\\mu=mean,n=number\ of\ terms, \sigma=standard\ deviation[/tex]
Given the numbers:
86, 81, 87, 82. mean = μ = 84
[tex]\Sigma(x_i-\mu)^2=(86-84)^2+(81-84)^2+(87-84)^2+(82-84)^2=4+9+9+4=26[/tex]
Sum of squared deviations = 26
The sum of the squared deviations of the scores from the mean is 26.
-----------------------
The observations are: 86, 81, 87 and 82.The mean of the observations is 84.The sum of the squared deviations of the scores from the mean is the sum of the differences squared of each observation and the mean.Thus:
[tex]S_{ds} = (86-84)^2 + (81-84)^2 + (87-84)^2 + (82-84)^2 = 4 + 9 + 9 + 4 = 26[/tex]
The sum of the squared deviations of the scores from the mean is 26.
A similar problem is given at https://brainly.com/question/17327780
Write the equation of the line that passes through the points (-7, -5) and
(-7,–7). Put your answer in fully reduced point-slope form, unless it is a vertical or
horizontal line.
Answer:
vertical
Step-by-step explanation:
Is 10 closer to 3 or 4?
Answer:
4
Step-by-step explanation:
Answer:
If there's a zero in the tenths place and your round down, keep the zero in your answer. For example, 4.03 rounded to the nearest tenth in 4.0.
6 tenths+3 thousandths
-30=5k+5 solve for k
Answer:
The answer is -7
5k=-30-5.
5k=-35.
k= -7.
Hi there! Hopefully this helps!
---------------------------------------------------------------------------------------------------
Answer: [tex]\boxed{k = -7}[/tex] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[tex]-30=5k+5[/tex]
Swap sides so that all variable terms are on the left hand side.
[tex]5k+5=-30[/tex]
Subtract 5 from both sides.
[tex]5k=-30-5[/tex]
Subtract 5 from −30 to get −35.
[tex]5k=-35[/tex]
Divide both sides by 5.
[tex]k=\frac{-35}{5}[/tex]
Divide −35 by 5 to get, you guessed it, -7!You can also do "5(-7) + 5 = ??" For proof.
is pie a natural number?
Nope
Step-by-step explanation:
Pi is an irrational number because it can not be expressed by a simple fraction.
Answer: No it's a rational number
Step-by-step explanation:
When a negative and positive number is added, is the sum going to be negative or positive?
Answer:negative
Step-by-step explanation:
Answer:
It depends on the values of the numbers.Step-by-step explanation:
If the positive number has a greater value than the negative number,adding them together will give you a positive answer.But,if the negative number has a greater value than the positive number, adding them together will give you a negative answerA boat whose speed is 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream is ___ km/hr.
Answer:
The speed of the stream is 5 km/hr.
Step-by-step explanation:
- Let's assume that the speed of stream is = x km/h
- Speed of boat in still water v = 15 km/h
- Total time taken = 4 hour and 30 mins or 9/5 hrs
- Distance covered (one way) = 30 km/s
Then,
Speed of boat downstream =( 15 + x ) km/h
Time taken downstream = (30/15 + x ) hrs
As time = distance / speed
Speed of boat upstream = ( 15 - x ) km/h
Time taken upstream =( 30/15 - x ) hrs
Now,
Total time taken = Time taken downstream + Time taken upstream
or, 9/2 = (30/15 + x ) + (30/15 - x )
or, x = 5 km/h
The speed of the stream is 5 km/h
I hope my answer helps
A line passes through the points (−4, −18) and (0, 2). Which is an equation of the line?
Answer:
y=5x+2
Step-by-step explanation:
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
First, let's find what m is, the slope of the line...
The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.
For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:
So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (-4,-18), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=-4 and y1=-18.
Also, let's call the second point you gave, (0,2), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=0 and y2=2.
Now, just plug the numbers into the formula for m above, like this:
m= (2 - -18)
------------
(0 - -4)
or...
m= 20
-------
4
or...
m=5
So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:
y=5x+b
Now, what about b, the y-intercept?
To find b, think about what your (x,y) points mean:
(-4,-18). When x of the line is -4, y of the line must be -18.
(0,2). When x of the line is 0, y of the line must be 2.
Because you said the line passes through each one of these two points, right?
Now, look at our line's equation so far: y=5x+b. b is what we want, the 5 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (-4,-18) and (0,2).
So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.
You can use either (x,y) point you want..the answer will be the same:
(-4,-18). y=mx+b or -18=5 × -4+b, or solving for b: b=-18-(5)(-4). b=2.
(0,2). y=mx+b or 2=5 × 0+b, or solving for b: b=2-(5)(0). b=2.
See! In both cases we got the same value for b. And this completes our problem.
The equation of the line that passes through the points
(-4,-18) and (0,2)
is
y=5x+2
What would be a good lower bound for the number of jelly beans in the jar?
Answer:
I think you need to link the question or a picture of the jar
Step-by-step explanation:
Question 8 The measurements of the length and width of a rectangular kitchen are 5.34 m and 3.48 m respectively. a Calculate in m² the exact area of the kitchen. b Write down both the length and the width correct to 1 dp. just answer b
Answer:
a) 18.5832 m^2
b) length 5.34 ≈ to one decimal point 5.3m
width 3.48 ≈ to one decimal point 3.5m
Step-by-step explanation:
Samuel currently has an account balance of $3,439.96. He opened the account five years ago with a deposit of $3,104.31. If the interest compounds quarterly, what is the interest rate on the account?
Answer:
The interest rate on the account is 2.1%
Step-by-step explanation:
Compound interest is one that is added to the initial capital and on which new interests are generated. Money, in this case, has a multiplier effect because interest produces new interest. In other words, the initial capital increases in each period because the interests add up.
To calculate the final capital, the initial capital is multiplied by one plus the interest, raised to the number of periods:
[tex]A=P*(1+\frac{r}{n}) ^{n*t}[/tex]
where
A = Accumulated amount (principal + interest) P = Principal amount r = the interest rate n = the number of times the interest is compounded per year t = Time Involved in yearsIn this case:
A = $3,439.96P = $3,104.31r = ?n = 4t = 5Replacing, you get:
[tex]3,439.96=3,104.31*(1+\frac{r}{4}) ^{4*5}[/tex]
Now, solving:
[tex]\frac{3,439.96}{3,104.31} =(1+\frac{r}{4}) ^{20}[/tex]
[tex]\sqrt[20]{1.1081} =(1+\frac{r}{4})[/tex]
[tex]1.00514 =1+\frac{r}{4}[/tex]
[tex]1.00514 -1=\frac{r}{4}[/tex]
[tex]0.00514=\frac{r}{4}[/tex]
r=0.0051*4
r= 0.02056
In percentage it is expressed as: r= 2.056 %≅ 2.1 %
The interest rate on the account is 2.1%
A new community sports complex is being build in Madison. The perimeter of the rectangular playing field is 466 yards. The length of the field is 7 years less than quadruple the width. What are the dimensions of the playing field?
Answer:
The dimensions of the field is 185 yards by 48 yards
Step-by-step explanation:
Here, we are interested in calculating the dimensions of the field.
Let the width of the field be x yards
From the question, we are made to know that the length of the field is 7 yards less than quadruple ( 4 times) the width
So mathematically, the length of the field will be ;
(4x -7) yards
The perimeter of the field mathematically is:
2(l + b)
Thus;
2(x + 4x- 7) = 466
2(5x -7) = 466
divide both side by 2
5x - 7 = 466/2
5x - 7 = 233
5x = 233 + 7
5x = 240
x = 240/5
x = 48 yards
Length of field is; 4x -7 = 4(48) -7 = 192 - 7 = 185 yards
5a+6b-10d=15c SOLVE FOR B
if 5 a solution of 3x + 30 = 9x?
Answer:
5 is a solution
What is the difference between -4 and 6?
-10
-2
2
10
Answer:
the answer is 10
Step-by-step explanation:
*please give me brainliest, i only need four more*
Answer:
-10
I did the math
(-4)-6
TIMED QUESTION!!!!!!!
Answer: (2 1/2, 0) (the last option)
Step-by-step explanation:
I guess the function is:
f(x) = (2 1/2) - (3 1/2)*x
now, the rule for f-1(x) that we know is:
f-1( f(x) ) = x.
So if we want to find the x-intercept of f-1(x), we must evaluate it in f(0)
f-1(f(0)) = 0.
And we have that f(0) = (2 1/2) - (3 1/3)*x = 2 1/2
This means that the x-intercept of f-1(x) will be when x= 2 1/2, so the intercept is:
(2 1/2, 0)
The sum of three consecutive even integers is 108 what is the largest number
Answer:
38
Step-by-step explanation:
if x is an even integer then the two other even integers are x+2 and x+4.
x+x+2+x+4=108
3x+6=108
3x=108-6
3x=102
x=102/3
x=34.
⇒the largest number from x, x+2 and x+4 is x+4.
x+4=34+4=38
Answer:
38
Step-by-step explanation:
good luck on your assignment
Fill in the blank with a constant, so that the resulting quadratic is the square of a binomial. \[x^2 + \dfrac{4}{5}x + \underline{~~~~}\]
Answer:
4/25Step-by-step explanation:
Given the incomplete quadratic equation [tex]\[x^2 + \dfrac{4}{5}x + \underline{~~~~}\][/tex], we are to complete it so that the result will be the square of a binomial. To do that, we will use the completing the square method.
Completing the square method is a way of completing a quadratic equation by solving for a constant to add that will make the quadratic equation a perfect square of a binomial.
To get the constant term using the method, we will take the square of the alf of the coefficient of x in the equation given.
Coefficient of x = 4/5
half of the coefficient of x = 1/2(4/5)
half of the coefficient of x = 4/10 = 2/5
Square of the half of the coefficient of x = (2/5)²
Square of the half of the coefficient of x = 4/25
Hence the constant that we will use to complete the equation to make if a square of a binomial is 4/25
The equation will become:
[tex]= \[x^2 + \dfrac{4}{5}x +\dfrac{4}{25} \\\\= \[x^2 + \dfrac{4}{5}x +(\dfrac{2}{5})^2\\\\= (x +\dfrac{2}{5})^2[/tex]
Hence the constant value that will make the resulting quadratic the square of a binomial is 4/25
Answer:
4/25
Step-by-step explanation:
Suppose the quadratic is the square of the binomial $x+c.$ We have $(x+c)^2 = x^2+2cx + c^2.$ Comparing the linear term of $x^2 + 2cx+c^2$ to the linear term of $x^2 + \frac{4}{5}x + \underline{~~~~},$ we have $2c = \dfrac{4}{5},$ so $c = \dfrac{2}{5}.$ Therefore, the constant term is
\[c^2 = \left(\dfrac{2}{5}\right)^2 = \boxed{\frac{4}{25}}.\]
if a turtle moves at 1 1/3 kilometers per hour how long would it take for the turtle to travel 9 kilometers.
Answer:
33 hours
Step-by-step explanation:
[tex]\frac{11}{3} *9 =33[/tex]
Answer:
6 3/4 hours
Step-by-step explanation:
divide 9 by 1 1/3. You get 6.75 which is converted to 6 and 3/4 hours.
what is 5+10/5 i cant find the answer
we'll divide 10 by 5..the answer is 2 then we'll add it to the other 5 making it to be 7
Answer: 7
How to: To add fractions, find the LCD and then combine.
which expressions are equivalent too the square root of 252
Answer:
[tex]6\sqrt{7}[/tex]
Step-by-step explanation:
If you bring 252 to its prime numbers, its 2, 2, 3, 3, and 7. Just multiply 2 and 3 and you get 6 root 7.
The expression equivalent to the square root of 252 is 6[tex]\sqrt{7}[/tex].
What are prime numbers?That number which can be divided by itself or 1 only. eg. 2, 3, 5, 7, 11, 13 etc.
Given value,
252
Expressed in prime numbers as:
252 = 2x2x3x3x7 or [tex]2^{2}[/tex] x [tex]3^{2}[/tex] x 7
∴ [tex]\sqrt{252}[/tex] = 2x3 [tex]\sqrt{7}[/tex] = 6 [tex]\sqrt{7}[/tex]
Hence [tex]\sqrt{252}[/tex] can be expressed as 6 [tex]\sqrt{7}[/tex]. Similarly any real number can be represented as the product of prime numbers.
To learn more about prime numbers, refer to the link:
https://brainly.com/question/9315685
#SPJ2
Simplify (2 raised to- 1 x 3 raised to 2 )/ (2 raised to 2 x 3 raised to -4 )the who raised to 7/2 x (2 raised to -2 multiplied by 3 raised to 3 )/ (2 raised to 3 multiplied by 3 raised to -5) whole raised to -5/2
Answer:
12
Step-by-step explanation:
Given the expression:
[tex](\dfrac{(2^{-1}\times 3^2)}{(2^{2}\times 3^{-4})})^\frac{7}{2} \times (\dfrac{(2^{-2}\times 3^3)}{(2^{3}\times 3^{-5})})^\frac{-5}{2}[/tex]
We have to simplify the above expression.
Let us have a look at a few formulas:
[tex]1.\ a^b = \dfrac{1}{a^{-b}}[/tex]
[tex]2.\ a^b\times a^c = a^{b+c}[/tex]
[tex]3.\ (a^b ) ^c = a^{bc}[/tex]
Now, let us try to solve the given above expression using the formulas:
[tex]\Rightarrow (\dfrac{(3^{4}\times 3^2)}{(2^{2}\times 2^{1})})^\frac{7}{2} \times (\dfrac{(3^{5}\times 3^3)}{(2^{3}\times 2^{2})})^\frac{-5}{2}[/tex]
[tex]\Rightarrow (\dfrac{(3^{4+2})}{(2^{2+1})})^\frac{7}{2} \times (\dfrac{(3^{5+3})}{(2^{3+2})})^\frac{-5}{2}\\\Rightarrow (\dfrac{3^{6}}{2^{3}})^\frac{7}{2} \times (\dfrac{3^{8}}{2^{5}})^\frac{-5}{2}\\\Rightarrow (\dfrac{3^{\frac{42}{2}}}{2^{\frac{3\times 7}{2}}})\times (\dfrac{2^{5}}{3^{8}})^\frac{5}{2}\\\Rightarrow (\dfrac{3^{21}}{2^{\frac{21}{2}}})\times (\dfrac{2^{\frac{5\times 5}{2}}}{3^{\frac{8\times 5}{2}}})[/tex]
[tex]\Rightarrow (\dfrac{3^{21}}{2^{\frac{21}{2}}})\times (\dfrac{2^{\frac{25}{2}}}{3^{20}})\\\Rightarrow {3^{1}}\times {2^{\frac{25-21}{2}}}\\\Rightarrow 3\times 4 \\\Rightarrow \bold{12}[/tex]
is -6/11 a rational or irrational number?
Answer: I am pretty sure it is a rational number!
Step-by-step explanation:
d) Make a is the subject of the formula, ab + bc = ad
e) Define Pythagoras' Theorem.
Answer:
(D) ab + bc =ad
ab-ad = -bc
a(b-d) =bc
a = bc / b-d
(e) The Pythagoras Theorem states that in a Right angled triangle the {hypotenuse}^2 = {opposite}^2 + {adjacent}^2
Step-by-step explanation:
If their is 300 unicorns and 200 dragons and 50 dragons fly away then 30 unicorns walk away how many are of each left?
Pls help.
Answer:
If 30 unicorns out of 300 walk away then it will be 300-30=270 unicorns left.
If 50 dragons fly away out of 200 then it will be 200-50=150.
Therefore there are 270 unicorns and 150 dragons left.
I hope this helps you...Thank you...
A basketball player scored 8 points in the 1st quarter 5 points during 2nd quarter 2 points in the 3rd quarter and 20 in the 4th quarter
Answer: 25
Step-by-step explanation: He scored 25 in the game
If B is the midpoint of AC, AC=CD, AB=3x+4, AC=11x-17, and CE=49, find DE.
Answer:
11
Step-by-step explanation:
AB = 3x + 4 and AC which is twice of AB is equal to 11x - 17
2 (3x + 4) = 11x - 17
6x + 8 = 11x - 17
8 + 17 = 11x - 6x
25 = 5x
5 = x
AC = CD = 11x - 17 ➡ 11×5 - 17 = 38
CD = 38 and DE = 49 - 38 = 11
Horatio went to the movies and spent $15 on his ticket and snacks. If the snacks cost $8, how much did his ticket cost? -Answer?
Answer:
$7
Step-by-step explanation:
t = ticket price
We know the total cost of the ticket and snacks was $15, and just the snacks were $8 so:
t + $8 = $15
To find the amount of the ticket, subtract $8 from each side
t + $8 - $8 = $15 - $8
The $8 cancels and you're left with
t = $7
So the ticket costs $7
The remaining cost after the snack cost is the cost of the movie ticket and it is $7.
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects.
In a different sense, subtraction refers to a mathematical procedure where two values will be subtracted to produce a new value.
Total spent = cost of snacks + cost of a movie ticket
Given that,
Total spent = $15
Cost of snacks = $8
So,
15 = 8 + cost of movie ticket
Cost of movie ticket = 15 - 8 = $7
Hence "The remaining cost after the snack cost is the cost of the movie ticket and it is $7".
For more about subtraction,
https://brainly.com/question/1927340
#SPJ2
please solve and explain!!!
Answer:
I think thats false
Step-by-step explanation:
Tell them false there isn't much evidence and if you tried to search it up thats not correct or the correct way to solve it theyre trying to trick you.
Josh takes a load of dress shirts to the dry cleansers the amount he pays for dry cleaning (f) is given by the equation f=3-2s where is the number of shirts what is the constant of proportionally in terms of the cost per shirt
Answer:
s= number of shirts
3/2= constant of proportionality
Step-by-step explanation:
Josh takes a load of dress shirts to the dry cleaners. The amount he pays for dry cleaning (
f. is given by the equation f=3/2s, where s is the number of shirts. What is the constant of proportionality in terms of the cost per shirt?
Given:
f= 3 / 2s
Where,
f= amount Josh paid for dry cleaning
s= number of shirts
3= constant of proportionality
2= amount paid per shirt
For example, if Josh took 3 shirts to the dry cleaner, the amount Josh will pay is
f= 3 / 2s
= 3 / 2(3)
= 3 / 6
= 1 / 2
f= 1 /2