Answer:
Mean = 81°F.
S. dev. = 5°F.
Step-by-step explanation:
When we have a set of data:
{x₁, x₂, ..., xₙ}
The mean can be calculated as:
M = (x₁ + x₂ ... + xₙ)/N
Where N is the number of data points that we have:
in this case the set is:
{ 74°F , 79°F , 76°F, 85°F, 87°F, 83°F, 86°F, 78°F }
So N = 8.
Then the mean is:
M = ( 74°F + 79°F + 76°F + 85°F + 87°F + 83°F + 86°F + 78°F )/8
M = 81°F.
Now, the standard deviation can be calculated as.
Sd = √ ( (1/N)*∑(xₐ - M)^2)
where the summation is over xₐ, which represents a summation over all the points in the data set.
Then we can write the standard deviation as:
Sd = √(1/8)*√( (74°F - 81°F)^2 + (79°F - 81°F)^2 + (76°F - 81°F)^2 + (85°F - 81°F)^2 + (87°F - 81°F)^2 + (83°F - 81°F)^2 + (86°F - 81°F)^2 + (78°F - 81°F)^2)
Sd = 4.58°F.
That we should round up to 5°F (because our mean has no digits after the decimal point)
50 POINTS Iann bought a carpet to cover 500 square feet. He wants to cover a room that is 10feet and 5 inches long by 9 feet and 7 inches. About how much will he have left over for the rest of the house?
Answer:
20.85 ft
Step-by-step explanation:
first convert 7 in to ft than add 9 to it
10×5×9.583 = 479.15ft that's how much carpet he needs for his room
500-479.15= 20.85ft left for the rest of his house
The town of hillside has an elevation of 50 feet above sea level. The town of Lakeside has an elevation of -35 feet. A bicyclist rides from Lakeside to Hillside,and wants to find his change in elevation. He finds the difference between his final elevation, 50 feet, and his starting elevation, -35 feet. What is the difference?
Answer:
The difference is 85 ft.
Step-by-step explanation:
Elevation 1: 50 ft
Elevation 2: -35 ft
Difference = Elevation 1 - Elevation 2
Difference = 50 - (-35)
I can simplify this expression, as subtracting a negative number is the same as adding a positive number:
Difference = 50 + 35
Difference = 85
Answer: The difference is 85 ft.
feet
12. Darcy and Danny were diving on a trip in
the Bahamas. When they stopped to look at a
school of fish, Darcy was 178 feet below the
surface of the water, and Danny was
2
feet
below the surface. Who was closest to the
is
Ire
surface of the water
Danny was closest to the surface of the water.
Here,
Darcy and Danny were diving on a trip in the Bahamas.
When they stopped to look at a school of fish, Darcy was [tex]\sqrt{78}[/tex] feet below the surface of the water and Danny was 17/2 feet below the surface.
What is square root?
A square root of a number x is a number y such that [tex]y2 = x[/tex].
Now,
Darcy was [tex]\sqrt{78}[/tex] feet below the surface of the water.
⇒[tex]\sqrt{78} = 8.83[/tex]
Danny was 17/2 feet below the surface.
[tex]\frac{17}{2} = 8.5[/tex]
Clearly, [tex]8.5 < 8.85[/tex]
Hence, Danny was closest to the surface of the water.
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The momentum of an object, p, is determined by its mass, m, and its velocity, v. The formula p=mv shows this relationship. Which equation shows the formula p=mv correctly solved for v?
A.
v=pm
B.
v=p/m
C.
v=p−m
D.
v=m/p
On solving for [v], we get v = p/m.
What is momentum?Momentum is defined as the product of mass and velocity of a body. Mathematically, we can write vector as -
p = mv
It is a vector quantity. In a three dimensional coordinate, the momentum vector can be resolved as -
[p] = p[x] a[x] + p[y] a[y] + p[z] a[z]
[p] = m {v[x] a[x] + v[y] a[y] + v[z] a[z]}
Given is the momentum of an object whose formula is p=mv.
We have the formula for momentum as -
p = mv
We can solve for [v] as -
p = mv
Divide by [m] on both sides, we get -
p/m = mv/m
v = p/m
Therefore, on solving for [v], we get v = p/m.
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15 divided by 266 I need R
Answer:
Step-by-step explanation:
You could use a calculator or you could perform long division to find the remainder of 15/266. There is no integer quotient, other than 0 (zero). That means 15 is the remainder.
Supposing you were dealing with 266/15 (which is really a different problem). This division produces an integer quotient and a remainder:
266
------- = 17 r. 11
15
Double-check to ensure that you've copied this problem down correctly.
Which expression is equivalent to 6x2−(4x+10)−3+(4x2−5x)? 100 points and brainly for fast answer
Answer:
1
Step-by-step explanation:
12-4x-10-3+(8x-5x)
collect like terms
12-4x-10-3+(3x)
remove the parenthesis
12-4x-10-3+3x= 1
Answer:
10x² - 9x - 13
Step-by-step explanation:
6x² - (4x + 10) - 3 + (4x² - 5x)
~Remove parenthesis
6x² - 4x + 10 - 3 + 4x² - 5x
~Combine like terms
10x² - 9x - 13
Best of Luck!
what is p-9/3=2 what is p?
p-9/3 = 2
p-9 = 2×3
p-9 = 6
p = 6+9
p = 15... Hope this will help...
What is the value of f(15) if the function is f(x)=(x)(2x+5)
integrate x^2+5 please i need it fast
Answer:
[tex]\frac{1}{3}[/tex] x³ + 5x + c
Step-by-step explanation:
Using the power rule
∫ a[tex]x^{n}[/tex] dx = [tex]\frac{a}{n+1}[/tex] [tex]x^{n+1}[/tex]
Thus
∫ x² + 5 dx
= [tex]\frac{1}{3}[/tex] x³ + 5x + c ← c is the constant of integration
Sovle for x. 2x + 6 = - r - 15
Answer:
[tex]x = \frac{-r - 21}{2}[/tex]
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Remember to do the opposite of PEMDAS.
PEMDAS =
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
First, subtract 6 from both sides:
2x + 6 (-6) = -r - 15 (-6)
2x = -r + (-15 - 6)
2x = -r + (-21)
2x = - r - 21
Next, divide 2 from both sides:
[tex]\frac{2x}{2} = \frac{-r - 21}{2}[/tex]
[tex]x = \frac{-r - 21}{2}[/tex]
~
please help asap! thanks
Answer:
its the last one i believe
Step-by-step explanation:
because u have to get m by its self so
you divide 5 square from both sides and boom
whats 4x4 +65x67-5+8+9=
4,383 I hope I got that right, Hope it helps!
HELPPPPP
Find the sum of the series 18 +12 +8+16/3...
Answer: who knows what the answers is bruh
Step-by-step explanation:
A florist can order roses in bunches of 12 and tulips in bunches of 8. Last month she ordered the same number of roses and tulips. If she ordered no more than 100 of each kind of flower, how many bunches of each could she have ordered? Find all the possible combinations
Answer
196
Step-by-step explanation:
12*8=96+100=196
Math problem whoever answers it right gets brainlist
Answer:
the 2nd one
Step-by-step explanation:
look at it again its simple
Solve the following proportion for x. x/5 = 17/11
Answer:
x=85/11
Step-by-step explanation:
[tex]\frac{x}{5}= \frac{17}{11} \\\\5*\frac{x}{5} =\frac{17}{11} \\\\x=\frac{85}{11}[/tex]
What is the domain of the relation {(1,-5), (2,3), (-6, -1), (2, 3), (-7, 8), (2, 3)}?
Answer:
all work is pictured and shown
Help with the ones marked in red.
Answer:
number 5 is 22
Step-by-step explanation:
Solve this
equation for m
y = mx + b
Answer:
m is represented as the slope
Step-by-step explanation:
what is the answer to 1/4 - 2/5
Answer:
0.15
Step-by-step explanation:
longerrrrrrrrrrrrr
Peter leaves Mitchell's house traveling 30 mph. Mitchell leaves 15 min later, trying to catch up to peter, going 40 mph, if they drive along the same route how long will it take Mitchell to catch Peter?
Given :
Peter velocity , P = 30 mph .
Mitchell velocity , M = 40 mph .
Mitchell leaves 15 min later .
To Find :
If they drive along the same route how long will it take Mitchell to catch Peter.
Solution :
Distance covered by Peter in 15 min .
[tex]D = 30\times \dfrac{15}{60}=7.5\ miles[/tex]
Let , time taken is x .
So , distance covered b them is equal :
[tex]7.5+30\times x=40\times x\\\\x=\dfrac{7.5}{10}=0.75\ hours\\\\x=0.75\times 60\ min\\\\x=45\ min[/tex]
Therefore , time taken by them is 45 minutes .
Hence , this is the required solution .
Use implicit differentiation to find the slope of the tangent line at the given point:
Answer:
[tex]\displaystyle \frac{dy}{dx}\Big|_{(1, 1)}=0[/tex]
Step-by-step explanation:
We are given the equation:
[tex](x^2+y^2)^2=4x^2y[/tex]
And we want to find the slope of the tangent line at the point (1,1).
Recall that the slope of the tangent line to a point of a function is given by the function's derivative.
Thus, find the derivative of the equation. Take the derivative of both sides with respect to x:
[tex]\displaystyle \frac{d}{dx}\left[(x^2+y^2)^2\right]=\frac{d}{dx}\left[4x^2y\right][/tex]
Let's do each side individually.
Left:
We can use the chain rule:
[tex](u(v(x))'=u'(v(x))\cdot v'(x)[/tex]
Let v(x) be x² + y² and u(x) is x². Thus, u'(x) is 2x. Therefore:
[tex]\displaystyle \frac{d}{dx}\left[(x^2+y^2)^2\right]=2\left(x^2+y^2\right)\left(\frac{d}{dx}\left[x^2+y^2\right]\right)[/tex]
Differentiate:
[tex]\displaystyle \frac{d}{dx}[(x^2+y^2)^2]=2(x^2+y^2)\left(2x+2y\frac{dy}{dx}\right)[/tex]
Factor. Therefore, our left side is:
[tex]\displaystyle 4(x^2+y^2)\left(x+y\frac{dy}{dx}\right)[/tex]
Right:
We have:
[tex]\displaystyle \frac{d}{dx}\left[4x^2y\right][/tex]
We can move the constant multiple outside:
[tex]\displaystyle =4\frac{d}{dx}\left[x^2y\right][/tex]
We will use the Product Rule:
[tex]\displaystyle =4\left(\frac{d}{dx}\left[x^2\right]y+x^2\frac{d}{dx}\left[y\right]\right)[/tex]
Differentiate:
[tex]\displaystyle =4\left(2xy+x^2\frac{dy}{dx}\right)[/tex]
Therefore, our entire equation is:
[tex]\displaystyle 4(x^2+y^2)\left(x+y\frac{dy}{dx}\right)=4\left(2xy+x^2\frac{dy}{dx}\right)[/tex]
To find the derivative at (1,1), substitute and evaluate dy/dx when x = 1 and y = 1. Hence:
[tex]\displaystyle 4((1)^2+(1)^2)\left((1)+(1)\frac{dy}{dx}\right)=4\left(2(1)(1)+(1)^2\frac{dy}{dx}\right)[/tex]
Evaluate:
[tex]\displaystyle 4((1)+(1))\left(1+\frac{dy}{dx}\right)=4\left(2+\frac{dy}{dx}\right)[/tex]
Further simplify:
[tex]\displaystyle 8\left(1+\frac{dy}{dx}\right)=8+4\frac{dy}{dx}[/tex]
Distribute:
[tex]\displaystyle 8+8\frac{dy}{dx}=8+4\frac{dy}{dx}[/tex]
Solve for dy/dx:
[tex]\displaystyle 4\frac{dy}{dx}=0\Rightarrow \frac{dy}{dx}=0[/tex]
Therefore, the slope of the tangent line at the point (1, 1) is 0.
A cab company charges $ 2 per cab ride, plus an additional $ 1 per mile driven. How long is a cab ride that costs $ 45 ?
Divide. Write the quotient in lowest terms. 4 2/3 divided by 1/2
Answer:
9 1/3
Step-by-step explanation:
4 2/3 ÷ 1/2
Write the mixed number as an improper fraction
(3 * 4 +2)/3 = 14/3
14/3 ÷1/2
Copy dot flip
14/3 * 2/1
28/3
Divide 28 by 3
9 with 1 left over
Put the left over part on top of the denominator
9 1/3
Find the equation for the vertical line that goes through point M(−2, 6).
The equation for the vertical line that goes through point M(−2, 6) is x = -2.
The equation of a straight line is:
y = mx + b;
y, x are variables, m is the slope of the line and b is the y intercept.
The slope of a vertical is undefined. Since the line passes through the point M(−2, 6), hence the equation of the vertical line is:
x = -2
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Emily is thinking of a number, which she calls n. She finds 1/4 of the number and subtracts 3. Write an expression that represents Emily’s number.
Answer:
1/4n - 3
Step-by-step explanation:
1/4 of a number means multiplying 1/4 to n. So we can write 1/4n. Now we write the subtract 3 portion. 1/4n - 3.
The expression n = 1/4n - 3 shows that Emily's number can be obtained by adding 3 to one-fourth of her number.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
Emily's number can be represented as:
n
One-fourth of Emily's number can be represented as:
1/4n
Subtracting 3 from one-fourth of Emily's number gives us:
1/4n - 3
Therefore, the expression that represents Emily's number is:
n = 1/4n - 3
This expression shows that Emily's number can be obtained by adding 3 to one-fourth of her number.
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5) Determine the Distance between (-3, 1) and (5,-6). Round your answer 10 points
to the nearest tenth. *
22
3
4
5
-2
0
-4
-2
-3
-4
-5
-6
it is 10.63
Step-by-step explanation:
Used a calculator
Between which two integers does -13/3 lie?
A -3 and 4
B -2 and -3
C -5 and 6
D -4 and -5
Answer:
-4 and -5
Step-by-step explanation:
- 13/3 is equal to -4.3 so this is why i think this but it maybe wrong.
Triangle ABC was transformed to be triangle DBP using one
transformation
What transformation was performed?
O reflection
o translation
O rotation
O dilation
Answer:
reflection
Step-by-step explanation:
this is a reflection off y=-x
BRUH SOMEONE HELP ME
also explain:)
Answer:
[tex]x=7[/tex]
Step-by-step explanation:
So we have the function:
[tex]w(x)=3x-7[/tex]
And we want to find x when w(x) is 14.
So, substitute 14 for w(x):
[tex]14=3x-7[/tex]
Add 7 to both sides. The right cancels:
[tex]21=3x[/tex]
Divide both sides by 3:
[tex]x=7[/tex]
So, the value of x is 7.
The correct answer is the first option.