Answer:
10.94
Step-by-step explanation:
The standard deviation is calculated by using the following formula:
\(s=\sqrt{\frac{1}{N-1}sum(xi -x)^2}\)
This means that N is the total number of cases you want to take into account, times the sum of x at the ith position - x squared.
In other words, the standard deviation in your example implies the following:
26 is the first value, so i = 1, 34 is the second value, so i = 2, 18 where i = 3, and so on and so forth, until you reach the end, which is 6 (so the initial value is 1 and the last one is 6).
You're doing a sum over an iteration of all the numbers in your sample.
So applying the sum of all of the numbers, it gives us the following:
\((26-28)^2+(34 - 28)^2+(18 - 28)^2 ... (41 - 28)^2\)
\(= \frac{598}{5} \\=119.6\\\)
The sum of all of the numbers in your sample is equal to 119.6.
Substitute into the equation once again:
\(s=\sqrt{119.6}\)
Where the square root of 119.6 is 10.93617...
Rounded to two decimal places: 10.94
find the area of a rectangle with a length of (x^2+2x-3) and a width of (x+6)
Answer:
45
Step-by-step explanation:
6^2+2×6−3=45 is the correct answer
FIGURE ABCD BELOW IS A QUADRILATERAL. WHAT IS THE VALUE OF X ?
A. 15
B. 40
C. 45
D. 65
Answer:
x = 45
Step-by-step explanation:
Note that:
The sum of the interior angles of a quadrilateral is 360°.
Angle: ADC+BAD+ABC+BCD = 360°
Thus, Substitute ∠ABC = 3x, ∠BAD = (2x-5) , ∠ ADC = (x+15), ∠ BCD = 80 turn into ADC+BAD+ABC+BCD = 360° :
Also known as :
(x+15) +(2x-5) + 3x+80=360
Solving for x
Add the numbers
x + 90+2x+3x=360
Combine like terms
6x + 90=360
subtract 90 from both sides
6x = 270
x = 45
Hence the value of x = 45
Kavinsky
Answer:
C. 45
Step-by-step explanation:
1) Sum of the interior angles of any shape:
(n - 2) x 180, where n is the number of vertices of a shape. In this case, we have 4 vertices.
= (4 - 2) x 180
= 2 x 180
= 360°
2) Add all the given values equating to 360.
2x - 5 + 3x + 80 + x + 15 = 360
6x + 90 = 360
6x = 360 - 90
6x = 270
x = 270/6
x = 45
sume of angles of a triangel greater than 180 degrees when teh triange is so large that it extends to cosmological scales
In hyperbolic geometry, the angle sum of a triangle is always less than 180 degrees.
A lune is a wedge of a sphere with angle θ, represented by L(θ) in the proof.
α, β, and γ are the three angles of the triangle.
4πr²+4area[αβγ]=2L(α)+2L(β)+2L(γ)
2(2πr²+2area[αβγ])=2(L(α)+L(β)+L(γ))
2πr²+2area[αβγ]=L(α)+L(β)+L(γ)
At this point, we need to use a theorem that states that a lune whose corner angle is θ radians has an area of 2θr².
2πr²+2area[αβγ]=2αr²+2βr²+2γr²
2πr²+2area[αβγ]=2r²(α+β+γ)
π+area[αβγ]r²=α+β+γ
At this point, it is clear that the sum of the angles is equal to π plus the area[αβγ]r² (which cannot be zero).
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2 532-(4-1)]
2[32-(4-1)3]
Answer:
10
Step-by-step explanation:
2[32-(4-1)^3]
Use the Order of Operations (PEMDAS)
1.) 2[32-(3)^3]
2.) 2(32-27)
3.) 2(5)
4.) 10
Solve the equation 6(7-9w)-4w
Rearrange:
6(-9w+7)-4w
Distribute:
-54w+42-4w
Combine the like terms:
-54w-4w
-58w
So, you get...
-58w+42
the volume of a rectangular prism is 10 cubic feet. what could the dimensions of the prism be
Answer: 2x5x1, 1x10x1 (in any order) and any 3 multiples that make 10
Step-by-step explanation:
Answer:
There are multiple possible sets of dimensions for a rectangular prism with a volume of 10 cubic feet. Here are some possible solutions:
A rectangular prism with dimensions of 1 ft x 2 ft x 5 ft (length x width x height) would have a volume of 10 cubic feet, since 1 x 2 x 5 = 10.
A rectangular prism with dimensions of 2 ft x 1 ft x 5 ft (length x width x height) would also have a volume of 10 cubic feet, since 2 x 1 x 5 = 10.
A rectangular prism with dimensions of 0.5 ft x 1 ft x 20 ft (length x width x height) would also have a volume of 10 cubic feet, since 0.5 x 1 x 20 = 10.
A rectangular prism with dimensions of 5 ft x 1 ft x 2 ft (length x width x height) would have a volume of 10 cubic feet, since 5 x 1 x 2 = 10.
There are infinitely many other possible sets of dimensions for a rectangular prism with a volume of 10 cubic feet.
Someone please help me this is for a grade, it would mean a lot
to me. :)
Answer:
No equivalent, 8x + 4y = 4 (2x + y)
Step-by-step explanation:
In the example, 1 should be a coefficient of the variable y. Since there is no y variable, the example would be equal to 8x + 4. However, the answer choice selected still keeps the 2x, but adds a y variable in the place of the one, which, when we distribute, gives us 4y.
HELP!!???? Simplify.-7 + (-3)x + 5 + (-6)xa. 2 - 3xb. -12 - 3xc. -2 - 9xd. 12 - 9x
We have this expression and we have to simplify it:
\(\begin{gathered} -7+(-3)x+5+(-6)x \\ -7+5-3x-6x \\ -2+\left(-3-6\right)x \\ -2-9x \end{gathered}\)The answer is c. -2-9x
2) Simplify:
\(\begin{gathered} 7(7-3x)+6(x-6) \\ 7\cdot7+7\cdot(-3x)+6\cdot x+6\cdot(-6) \\ 49-21x+6x-36 \\ (-21+6)x+13 \\ -15x+13 \end{gathered}\)Figure ABCD Is a kite. Find x
Answer:
x = 8
Step-by-step explanation:
Diagonals of a kite cross at right angles. That gives us a relation that can be solved for x.
SetupThe measure shown is equal to the angle measure of 90°.
14x -22 = 90
SolutionWe can solve this 2-step linear equation in the usual way.
14x = 112 . . . . . . step 1, add the opposite of the constant to get x alone
x = 112/14 = 8 . . . step 2, divide by the coefficient of x
The value of x is 8.
The first term of a geometric sequence is 5 and the multiplier, or ratio, is –2. What is the sum of the first 5 terms of the sequence?
Step-by-step explanation:
s1 = 5
s2 = s1 × -2 = 5×-2 = -10
s3 = s2 × -2 = -10 × -2 = 20
...
now, we could do all that manually.
but there is also a formula for geometric sequence.
in fact, there are 2 - one for finite and one for infinite sequences.
and I was not completely honest, each of these 2 had some sub-forms depending on the size of the multiplier or ratio.
since we need the sum of the first 5 terms, which of the 2 do you think we need ?
of course, finite, because 5 is a normal number we can "touch". it is not infinity.
so, the formulas for finite sums of geometric sequences are :
if |r| < 1, Sn = a(1 - r^n)/(1 - r)
if |r| > 1, Sn = a(r^n - 1)/(r - 1)
if r = 1, Sn = na
if r = -1, then Sn = a or 0 depending on if n is odd or even.
the sequence is in general
s1 = a
sn = sn-1 × r
in our case a = 5, r = -2.
so, what form of the formula do we need ?
|-2| = 2, and 2 > 1, so ...
S5 = 5(-2^5 ‐ 1)/(-2 - 1) = 5(-32 - 1)/-3 = 5×-33/-3 =
= 5 × 11 = 55
quick check, as the 5 terms are
5
-10
20
-40
80
and their sum is : 55
correct !
He buys a jewel for $180 then sells it for $216 find his percentage profit
The difference between the selling price and the cost price is the profit he earned.
Profit = Selling Price - Cost Price
Profit = $216 - $180
Profit = $36
To find the percentage profit, we need to calculate what proportion of the cost price the profit represents, and express that as a percentage :
Percentage Profit = (Profit : Cost Price) * 100%
Percentage Profit = ($36 : $180) * 100%
Percentage Profit = 0.2 * 100%
Percentage Profit = 20%
Therefore, his percentage profit is 20%.
Eliana loves music, especially 80's punk rock. Eliana looked at the number of songs in her itunes account and she has 6 less than 4 times her best friend. Eliana's classmate David has 3 more than double her best friend. When talking to her Social Studies teacher, Eliana found out social study teacher has 7 more than two times the number of songs in his library than Eliana. Define a variable, then write and solve an equation. If the total number of songs is 382, how many songs does Eliana, her best friend, David and her social study teacher have?
Answer
Step by step explantion:
bsf= 26
Eliana:98
SS teacher=203
David=55
Step-by-step explanation:
m= music
bsf: m
eliana:4m-6
David:2m+3
SS teacher: 2(4m-6)+7
m+4m-6+2m+3+8m-12+7
382=15m-7
7+ +7
389=15m
/15m /15m
m=26
multiply 26 to each one of them
The ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 8 : 6. Terrence owns 36 models cars. How many model cars does Jim own?
The number of Jim's model car is 48
How to determine the number of JIm's carFrom the question, we have the following parameters that can be used in our computation:
Ratio of the number of model cars that Jim owns to the number of model cars Terrence owns is 8 : 6
This means that
Jim : Terrence = 8 : 6
Also from the question, we have
Terrence owns 36 models cars
This means that
Terrence = 36
Substitute the known values in the above equation, so, we have the following representation
Jim : 36 = 8 : 6
Multiply by 6
Jim : 36 = 48 : 36
So, we have
Jim = 48
Hence, the number of car is 48
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find dy/dx if y=1/✓x-1
Step-by-step explanation:
1/(2√x-1)
this is the answer
1
2
3
4
5
10
50
Which function has an inverse that is a function?
Ob(x) = x2 + 3
Od(x) = -9
Om(x) = -7x
O p(x) = 1x1
Which function has an inverse that is a function?
Step-by-step explanation:
an equation is a function, if it delivers for every possible input value x exactly one result value y.
b(x) = y = x² + 3
y - 3 = x²
x = sqrt(y -3)
our formally correct
y = sqrt(x - 3)
that is actually NOT a function, as a square root delivers for most x values 2 y values : a positive and a negative value.
d(x) = -9
that means for every possible value of x the result is -9.
reversing this means that the input value of -9 has infinitely many possible results
that is NOT a function.
m(x) = y = -7x
x = -y/7
or formally correct
y = -x/7
that is a normal function. every possible value of x leads to exactly one value of y.
p(x) = y = 1x¹ = x
y = x is its own inverse function.
and this is, of course, a function. every possible value of x leads to exactly one value of y.
What is the volume of this pyramid?
Enter your answer in the box.
Answer:
9576
Step-by-step explanation:
Area of the triangle × height
(1/2×28×19)×36
3 to the 4th power minus -6 to the 2nd power
Put the quadratic into vertex form
The vertex form of the quadratic function f(x) = 2x^2 + 8x + 7 is f(x) = 2(x + 2)^2 - 25.
How to find the vertex formTake a look at the quadratic function:
f(x) = 2x^2 + 8x + 7
In this situation, a = 2 and b = 8, yielding:
f(x) = 2(x^2 + 4x) + 7
It shtbe noted that to determine the value to add and subtract, multiply (b/2a)2 by (8/2(2))2 = 42 = 16. Inside the parenthesis, we add and subtract 16:
f(x) = 2(x^2 + 4x + 16 - 16) + 7
The expression inside the parenthesis can now be written as a perfect square:
f(x) = 2((x + 2)^2 - 16) + 7
Finally, the phrase is simplified by spreading the 2:
f(x) = 2(x + 2)^2 - 32 + 7
f(x) = 2(x + 2)^2 - 25
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What is the vertex form of the quadratic function f(x) = 2x^2 + 8x + 7
Which of the following would you see on a circle graph?
OA. Percentages
OB. Bars
C. Points
OD. A y-axis
A, percentages
You would see percentages on a circle graph, because it's how many parts of the whole that they take up.
Happy to help, have a great day! :)
Martha has 2 red beads for every 5 yellow beads on her necklace. If Martha has
18 fewer red beads than yellow beads, then how many yellow beads does she
have?
Answer:
30 yellow beads
Step-by-step explanation:
there is a difference of three beads if there are 5 yellow beads per 2 red beads. You're looking for a combination of numbers with a difference of 18. divide 18 by three, and you get 6. multiply 6 by each of the 2 numbers 2 and 5, to get 12 and 30. They have a difference of 18, and follow the ratio of red to yellow beads. Now just take the 30 yellow beads and give an answer
Differentiate the function with respect to x. Shot steps
The value of function after differentiation will be;
⇒ dy/dx = 2 / (x log3)
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The function is,
⇒ y = log ₃ 2x²
Now,
Since, The function is,
⇒ y = log ₃ 2x²
Differentiate with respect to x, we get;
⇒ dy/dx = 1 / (2x² log3) × d/dx (2x²)
= 1 / (2x² log3) × 4x
= 2 / (x log3)
Thus, The value of function after differentiation will be;
⇒ dy/dx = 2 / (x log3)
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Susan gave of a pizza to her brother, Joe. Then, she gave of what was left to her mother, and ate the rest herself. What percent of the pizza did Susan eat?
A.
6.25%
B.
5.625%
C.
93.75%
D.
56.25%
Your answer is A. 6.25%
Use the distributive property to simplify the expression:
3(x+8):
Answer:
3x+24
Step-by-step explanation:
3*x +3*8
=3x+24
Answer:
3x+24
Step-by-step explanation:
3(x+8)
3×x + 3×8
3x+24
Lcm of 36 75 80 is what if you know plz send the answer
Answer:
3600
Step-by-step explanation:
lcm stands for "lowest common multiple"
the lcm is 3600 when done with the prime factorization process
Answer:
3600
Step-by-step explanation:
Express each number as a product of its prime factors, that is
36 = 2² × 3²
75 = 3 × 5²
80 = \(2^{4}\) + 5
Now multiply each factor the greatest number of times it occurs in each of the 3 numbers.
2 → 4 times (that is \(2^{4}\) )
3 → twice (3² )
5 → twice (5² )
Thus
LCM = \(2^{4}\) × 3² × 5² = 16 × 9 × 25 = 3600
how many 10 digit phone number are possible if the first two digits must be nonzero write your answer in scientific notation
Answer:
3
Step-by-step explanation:
Please someone help me with this question what is the x and y
Answer:
x = -1y = 5Solution:
=> 6x + 5y = 19-3x - 4y = -17
=> 6x + 5y = 192(-3x - 4y = -17)
=> 6x + 5y = 19-6x - 8y = -34
=> -3y = -15=> 3y = 15=> y = 5Now, let's take one equation and substitute the value of y in it.
6x + 5y = 19=> 6x + 5(5) = 19=> 6x + 25 = 19=> 6x = 19 - 25=> 6x = -6=> x = -1Check:
=> -3x - 4y = -17=> -3(-1) - 4(5) = -17=> 3 - 20 = -17=> -17 = -17Hence, this is proven correct.
Hoped this helped.
\(BrainiacUser1357\)
Find the value of each variable
HELPP
Answer:
10. y=102,
11. x=103
12. x=145
Step-by-step explanation:
10.) 120+85+53+y=360
y+258=360
y=102,
11.) 117+100+105+115+x=540
x+437=540
x=103,
12.) 129+116+120+125+135+130+x=900
755+x=900
x=145
Answer:
10.) 102 11.) 103 12.) 145
Step-by-step explanation:
I am assuming you need help on all three questions.
10.) This shape, a trapezoid, has 4 angles. Therefore these angles are going to all add up to 360 degrees.
To solve... 360 - 120 - 85 - 53 = 102
OR...
120 + 85 + 53 = 258 then... 360 - 258 = 102
11.)This shape, a pentagon, has 5 angles. Therefore these angles are going to all add up to 540 degrees.
To solve... 540 - 117 - 100 - 105 - 115 = 103
OR...
117 + 100 + 105 + 115 = 437 then 540 - 437 = 103
12.)This shape, a heptagon, has 7 angles. Therefore these angles are going to all add up to 900 degrees.
To solve... 900 - 116 - 120 - 129 - 130 - 135 - 125 = 145
OR...
116 + 120 + 129 + 130 + 135 + 125 = then... 900 - 755 = 145
A company created a new container in the shape of a
triangular prism that will hold sunflower seeds. A three-
dimensional image of the container is shown below, as
well as a two-dimensional image of the base.
6 in.
3.2 in.
2 in.
3.2 in.
1 in.
square inches
1 in.
The container will be made from cardboard. How many
square inches of cardboard are needed to make one
container? Assume there are no overlapping areas.
The number of square inches of cardboard that are needed to make one
the container is 18.
We have,
The volume of the triangular prism.
= Area of the triangle x height
Now,
Height = 6 in
And,
To find the area of a triangle, we can use Heron's formula.
A = √(s(s-a)(s-b)(s-c))
where s is the semi-perimeter of the triangle, calculated as:
s = (a + b + c) / 2
In this case, the side lengths of the triangle are 3.2 in, 3.2 in, and 2 in.
Let's calculate the area using Heron's formula:
s = (3.2 + 3.2 + 2) / 2 = 4.2
A = √(4.2(4.2 - 3.2)(4.2 - 3.2)(4.2 - 2))
A = √(4.2 x 1 x 1 x 2.2)
A = √(9.24)
A ≈ 3.04 square inches
Now,
The volume of the triangular prism.
= Area of the triangle x height
= 3.04 x 6
= 18.24 in²
Now,
Area of one cardboard.
= 1² in²
= 1 in²
Now,
The number of square inches of cardboard that are needed to make one
container.
= The volume of the triangular prism / Area of one cardboard
= 18.24 in² / 1 in²
= 18.24
= 18
Therefore,
The number of square inches of cardboard that are needed to make one
the container is 18.
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cara played a card game using a deck of 52 cards after she dealt the same number of cards to 4 players she had 24 cards left over how many cards did each player get
Answer:
7Step-by-step explanation:
Assume each player get x cards. Total number of cards now is 4x+24=52.
Therefore, 4x=52-24=28.
Then, x= 28/4=7.
NO LINKS!! URGENT HELP PLEASE!!!
11. Write the equation for the graph
This is the same as writing y = sqrt(4(x+5)) - 1
===============================================
Explanation:
The given graph appears to be a square root function.
The marked points on the curve are:
(-4,1)(-1,3)(4,5)Reflect those points over the line y = x. This will have us swap the x and y coordinates.
(-4,1) becomes (1,-4)(-1,3) becomes (3,-1)(4,5) becomes (5,4)Recall the process of reflecting over y = x means we're looking at the inverse. The inverse of a square root function is a quadratic.
----------
Let's find the quadratic curve that passes through (1,-4), (3,-1) and (5,4).
Plug the coordinates of each point into the template y = ax^2+bx+c.
For instance, plug in x = 1 and y = -4 to get...
y = ax^2+bx+c
-4 = a*1^2+b*1+c
-4 = a+b+c
Do the same for (3,-1) and you should get the equation -1 = 9a+3b+c
Repeat for (5,4) and you should get 4 = 25a+5b+c
We have this system of equations
-4 = a+b+c-1 = 9a+3b+c4 = 25a+5b+cUse substitution, elimination, or a matrix to solve that system. I'll skip steps, but you should get (a,b,c) = (1/4, 1/2, -19/4) as the solution to that system.
In other words
a = 1/4, b = 1/2, c = -19/4
We go from y = ax^2+bx+c to y = (1/4)x^2+(1/2)x-19/4
----------
Next we complete the square
y = (1/4)x^2+(1/2)x-19/4
y = (1/4)( x^2+2x )-19/4
y = (1/4)( x^2+2x+0 )-19/4
y = (1/4)( x^2+2x+1-1 )-19/4
y = (1/4)( (x^2+2x+1)-1 )-19/4
y = (1/4)( (x+1)^2-1 )-19/4
y = (1/4)(x+1)^2- 1/4 - 19/4
y = (1/4)(x+1)^2 + (-1-19)/4
y = (1/4)(x+1)^2 - 20/4
y = (1/4)(x+1)^2 - 5
The equation is in vertex form with (-1,-5) as the vertex. It's the lowest point on this parabola. Placing it into vertex form allows us to find the inverse fairly quickly.
----------
The last batch of steps is to find the inverse.
Swap x and y. Then solve for y.
y = (1/4)(x+1)^2 - 5
x = (1/4)(y+1)^2 - 5
x+5 = (1/4)(y+1)^2
(1/4)(y+1)^2 = x+5
(y+1)^2 = 4(x+5)
y+1 = sqrt(4(x+5))
y = sqrt(4(x+5)) - 1
I'll let the student check each point to confirm they are on the curve y = sqrt(4(x+5)) - 1.
You can also use a tool like GeoGebra to verify the answer.