Answer:
45360 arrangements
Step-by-step explanation:
Given the word 'robberies'
Number of letters = 9 letters in total
Repeated letters ; r = 2 ; b = 2 ; e = 2
Therefore, the number of distinct arrangement of letters is :
(total letters)! / repeated letters!
The number of distinct arrangement of letters is :
9! / (2! * 2! * 2!) = (9*8*7*6*5*4*3*2*1) / (2*2*2)
362880 / 8 = 45360 arrangements
10% of 360 is how much more than 5% of 360
10% of 360 is 18 more than 5% of 360.
What is the percentage?The percentage is defined as ratio expressed as a fraction of 100.
What are Arithmetic operations?
Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
Given data as :
10% of 360
5% of 360
Firstly, we have to determine 10% of 360,
⇒ 10% of 360
⇒ (10/100)360
⇒ (0.10)360
So, 10% of 360 is 36.
⇒ 5% of 360
⇒ (5/100)360
⇒ (0.05)360
So, 5% of 360 is 18.
Since 10% of 360 is more than 5% of 360
So, substract 18 from 36, and
⇒ 36 - 18
⇒ 18
Hence, 10% of 360 is 18 more than 5% of 360.
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The number of typing errors made by a typist has a Poisson distribution with an average of three errors per page. If more than three errors appear on a given page, the typist must retype the whole page. What is the probability that a randomly selected page does not need to be retyped
Answer:
0.6472 = 64.72% probability that a randomly selected page does not need to be retyped.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Poisson distribution with an average of three errors per page
This means that [tex]\mu = 3[/tex]
What is the probability that a randomly selected page does not need to be retyped?
Probability of at most 3 errors, so:
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498[/tex]
[tex]P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494[/tex]
[tex]P(X = 2) = \frac{e^{-3}*3^{2}}{(2)!} = 0.2240[/tex]
[tex]P(X = 3) = \frac{e^{-3}*3^{3}}{(3)!} = 0.2240[/tex]
Then
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0498 + 0.1494 + 0.2240 + 0.2240 = 0.6472[/tex]
0.6472 = 64.72% probability that a randomly selected page does not need to be retyped.
NEED HELP ASAP
Find the area of the irregular figure.
12 in.
6 in.
1
A = [? ]in.2
4 in.
13 in
4 in
5 in.
Answer:
Step-by-step explanation:
use the figure to find y
Answer:
y = 3
Step-by-step explanation:
6sin(30) = 3
Write the quadratic equation in standard form:
7x + 8 + 2x2
2x + 1 + x2
Answer:
[tex]3x^2 + 9x +9[/tex]
Step-by-step explanation:
Given
[tex](7x + 8 + 2x^2) + (2x + 1 + x^2)[/tex]
Required
The result in standard form
We have:
[tex](7x + 8 + 2x^2) + (2x + 1 + x^2)[/tex]
Remove brackets
[tex]7x + 8 + 2x^2 + 2x + 1 + x^2[/tex]
Collect like terms
[tex]7x+ 2x + 8 + 1 + 2x^2+ x^2[/tex]
[tex]9x + 9+ 3x^2[/tex]
The standard form of a quadratic equation is:
[tex]ax^2 + bx + c[/tex]
So, we have:
[tex]9x + 9+ 3x^2[/tex]
[tex]3x^2 + 9x +9[/tex]
The function ƒ(x) = (x − 1)^2 + 5 is not one-to-one. Find a portion of the domain where the function is one-to-one and find an inverse function.
The restricted domain for ƒ is ?
Answer:
f(x)=(x-1)^2+5 with domain x>1 and range y>5 has inverse g(x)=sqrt(x-5)+1 with domain x>5 and range y>1.
Step-by-step explanation:
The function is a parabola when graphed. It is in vertex form f(x)=a(x-h)^2+k where (h,k) is vertex and a tells us if it's reflected or not or if it's stretched. The thing we need to notice is the vertex because if we cut the graph with a vertical line here the curve will be one to one. So the vertex is (1,5). Let's restrict the domain so x >1.
* if x>1, then x-1>0.
* Also since the parabola opens up, then y>5.
So let's solve y=(x-1)^2+5 for x.
Subtract 5 on both sides:
y-5=(x-1)^2
Take square root of both sides:
Plus/minus sqrt(y-5)=x-1
We want x-1>0:
Sqrt(y-5)=x-1
Add 1 on both sides:
Sqrt(y-5)+1=x
Swap x and y:
Sqrt(x-5)+1=y
x>5
y>1
(3 A sum of money doubles itself in 6 years. In how many years, it becomes 5 times?
Answer:
In 24 years.
Step-by-step explanation:
Let the sum of money be 100 which amounts to 200 ( doubles itself ) in 6 years time. Interest on 100rs. Is 100. Putting the following in simple interest formula. You get :
[tex]100=\dfrac{100\times R\times 6}{100}\\\\R=\dfrac{100}{6}[/tex]
Now when 100 will become 5 times i.e 500 the interest will be 400rs.
Putting in simple interest formula:
[tex]400=\dfrac{\dfrac{100\times 100}{6T}}{100}\\\\T=\dfrac{2400}{100}\\\\=24\ yrs[/tex]
So, in 24 years, it will become 5 times.
Second to last question, Find I
50 points
Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.
Remember: SOH-CAH-TOA
Looking from angle I, we know the opposite side and the hypotenuse. Therefore, we should use sine.
sin(I) = [tex]\frac{\sqrt{39}}{\sqrt{51}}[/tex]
To solve, you can use your calculator and the inverse sine function (sin^-1).
I = sin^-1([tex]\frac{\sqrt{39}}{\sqrt{51}}[/tex])
I = 61 degrees
Hope this helps!
A tank contains 200 L of salt solution which contains 100 grams of salt. Pure water enters the tank ata rate of 4 L/min, but the thoroughly mixed solution leaves the tank at a rate of 2 L/min.Write andsolve an IVP to determiney, the number of grams of salt in the tank at timet.
Answer:
a. dy/dt = - 2y/(200 + 2t) where y(0) = 100 g
b. y = 20000/(200 + t)
Step-by-step explanation:
a. Write an IVP to determine y, the number of grams of salt in the tank at time, t.
Let y be the mass of salt.
The net flow into the tank dy/dt = mass flow in - mass flow out
Since only water flows into the tank, the mass flow in = 0 g/min
Let m be the mass of salt in the tank at time t. Since the volume of the tank is 200 L and water flows in at a rate of 4 L/min and out at a rate of 2 L/min, the net rate of increase of the volume of the tank is rate in - rate out = 4 L/min - 2 L/min = 2L/min. So, in time, t, the volume of the water in the tank increases by 2t. So, the volume of the tank in time, t is V = 200 + 2t.
So, the concentration of salt in the tank at time t is mass/volume = m/(200 + 2t).
Since the well mixed solution leaves at a rate of 2 L/min, the mass flow out is concentration × volume flow out = y/(200 + 2t) × 2 = 2y/(200 + 2t)
The net flow into the tank dy/dt = mass flow in - mass flow out
dy/dt = 0 - 2y/(200 + 2t)
dy/dt = - 2y/(200 + 2t)
Since the initial mass of salt in the tank is 100 g, y(0) = 100 g
So, the initial value problem IVP is
dy/dt = - 2y/(200 + 2t) where y(0) = 100 g
b. Solve an IVP to determine, the number of grams of salt in the tank at time, t.
Solving the IVP, we have
dy/dt = - 2y/(200 + 2t) where y(0) = 100 g
Separating the variables, we have
dy/y = - 2dt/(200 + 2t)
Integrating both sides, we have
∫dy/y = - ∫2dt/(200 + 2t)
㏑y = - ㏑(200 + t) + ㏑C
㏑y + ㏑(200 + t) = ㏑C
㏑[y(200 + t)] = ㏑C
y(200 + t)] = C
y = C/(200 + t) since y(0) = 100, we have
100 = C/(200 + 0)
100 = C/200
C = 100 × 200
C = 20000
So, y = C/(200 + t)
y = 20000/(200 + t)
can someone help me with this question
9514 1404 393
Answer:
local minima: at x=-1, x=3local minimum values: -2 and -1 (respectively)Step-by-step explanation:
A local minimum is where the curve stops going down and starts going up. It is the bottom of any U-shaped spot. Here, those are identified with dots at the coordinates (-1, -2) and (3, -1).
(a) the x-values at which f has a local minimum are -1 and 3.
(b) the local minimum values of f are -2 and -1 at those x-values.
work out the equasion 39+(−13)
Answer:
39-13=26
Step-by-step explanation:
plus(minus)=minus
Subtract the second equation from the first.
8x + 3y = 14
(4x + 3y = 8)
-
O A. 6y = 22
O B. 4x = 6
O c. -6y = 6
D. 12x = 22
Please help
Answer:
B
Step-by-step explanation:
Subtracting second equation from first, term by term , gives
(8x - 4x) + (3y - 3y) = (14 - 8) , that is
4x + 0 = 6, so
4x = 6 → B
Find the lateral area of this square based pyramid. 10in 5in (in the image)
Answer:
100 in²
Step-by-step explanation:
4 triangles, each of them has area = 10*5/2
so total area = (10*5/2)*4
= (10*5*2)
= 100 in²
Answered by GAUTHMATH
The lateral surface area of the pyramid is 100 in²
What is surface area?The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.
The pyramid has four triangular faces and one rectangular base we need to calculate the lateral surface area so we will calculate the area of the four triangles and sum up all the triangles.
4 triangles, each of them has an area = 10 x ( 5/2 )
So total area = (10 x 5/2) x 4
Total area = (10 x 5 x 2)
Total area = 100 in²
Therefore the lateral surface area of the pyramid is 100 in²
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The elevation E, in meters, above sea level at which the boiling point of a certain liquid ist degrees Celsius is given by the function shown below. At what elevation is the boling point 99.5*7 100°?
E() - 1200(100-1) • 580(100 - 1)
At what elevation is the boiling point 99.5?
E (90.5*)=. meters
At what elevation is the boiling point 100"?
E(100*)-meters
Answer:
Given E(t)=1100(100-t)+580(100-t)^2
Put t = 99.5, we get
E(99.5)=1100(100-99.5)+580(100-99.5)^2
E(99.5)=1100(0.5)+580(0.5)^2
E(99.5)=1100(0.5)+580(0.25)
E(99.5)=550+145
E(99.5)=695m
Step-by-step explanation:
It can be concluded that -
E(99.5) = 695
E(100) = 0
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is the function as follows -
E(t) = 1100(100 - t) + 580(100 - t)²
The given function is -
E(t) = 1100(100 - t) + 580(100 - t)²
At → E(99.5)
E(99.5) = 1100(100 - t) + 580(100 - t)²
E(99.5) = 1100(100 - 99.5) + 580(100 - 99.5)²
E(99.5) = 1100(0.5) + 580(0.5)²
E(99.5) = 550 + 145
E(99.5) = 695
At → E(100)
E(100) = 1100(100 - t) + 580(100 - t)²
E(100) = 1100(100 - 100) + 580(100 - 100)²
E(100) = 0
Therefore, it can be concluded that -
E(99.5) = 695
E(100) = 0
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Use the diagram to determine the height of the tree.
where's the diagram?
A lot is in the shape of a trapezoid. The sum of the bases is 180 feet. If the area of the lot is 8100 square feet, what is the distance across the lot, i.e., the altitude of the figure?
Answer: The altitude is 90.
Step-by-step explanation: the formula to calculate a trapezoid: A = (.5)(B+b)h.
plug the values in.
8100 = (.5)(180)h
8100 = 90h
h = 8100/90
h = 90
Which inequality is shown in the graph?
Answer:
A.
Step-by-step explanation:
the equation of the parabola shown in the graph is y=x²-5, then the inequality is y≥x²-5 (inside the parabola).
Select the correct answer.
Each statement describes a transformation of the graph of y=x. Which statement correctly describes the graph of y= x - 13?
OA. It is the graph of y= x translated 13 units to the right.
OB. It is the graph of y=xwhere the slope is decreased by 13.
It is the graph of y= x translated 13 units to the left.
OD. It is the graph of y= x translated 13 units up.
ОС.
minus sign ironically makes it go to the right
because the function crosses the y axis at -13
It is the graph of y = x translated 13 units down is the statement describes a transformation of the graph of y=x.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The equation y = x - 13 represents a transformation of the graph of y = x. To find the type of transformation, we have to compare the two equations and look for changes.
In the equation y = x - 13, we subtract 13 from the value of x.
This means that the graph of y = x is shifted 13 units downwards,
since every point on the graph has 13 subtracted from its y-coordinate.
Hence, It is the graph of y = x translated 13 units down is the statement describes a transformation of the graph of y=x.
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Which of these is a key feature of an experimental study?
A.
The treatment in the experiment should be simple enough for each individual in the experimental group to understand.
B.
The treatment in the experiment must vary for each individual in the experimental group.
C.
The treatment in the experiment must be applied to each of the individuals in the experimental group.
D.
The treatment in the experiment should be short so that each individual is tested quickly.
3) Consider the sequence -11 ; 2sin3x ; 15; ...
3.1.1) Determine the values of x in the interval [0 ; 90] for whichthe sequence will be arithmetic.
You are walking from home to a grocery store you stop for a rest after 2/5 miles the grocery store is actually 3/4 miles from home how much farther do you have to walk
Answer:
7/20 mile farther
Step-by-step explanation:
Subtracting 2/5 mile from 3/4 mile results in the distance you still have to walk:
3/4 - 2/5 = ?
Here the LCD is 20. Thus, 3/4 becomes 15/20 and 2/5 becomes 8/20.
Then 3/4 - 2/5 = 15/20 - 8/20, or 7/20.
You still have 7/20 mile to walk to get home.
Help please!!!!!A student needs to select 3 books from 3 different mathematics, 3 different physics and 1 history book. what is the probability that one of them is mathematics and the other 2 are either physics or history books ? A. 3/15 B.9/25 C. 15/35 D. 18/35
===========================================
Explanation:
There are 3 ways to select the single math book and 4*3/2 = 12/2 = 6 ways to pick the two other books that are either physics or history (order doesn't matter). This is effectively because we have 3+1 = 4 books that are either physics or history, and we're using the nCr combination formula.
Overall, there are 3*6 = 18 ways to select the three books such that one is math, and the other two are either physics or history.
-------------------
There are 3+3+1 = 7 books total. Since we're selecting 3 of them, we use the nCr formula again and you should get 35.
Or you could note how (7*6*5)/(3*2*1) = 210/6 = 35
This says there are 35 ways to select any three books where we can tell the difference between any subject (ie we can tell the difference between the math books for instance).
-------------------
We found there are 18 ways to get what we want out of 35 ways to do the three selections. Therefore, the answer as a fraction is 18/35
The lengths of the three sides of a triangle are 3, 15, and 16. Classify it as acute, obtuse, or right.
Answer:
Obtuse Scalene Triangle
Step-by-step explanation:
Sum of the squares of the smaller 2 sides < longest side squared = Obtuse Scalene Triangle
What are the solutions to the equation
Answer:
(0,1) and (3,4)
Step-by-step explanation:
It's the points where they meets, judging the graph, it's x = 0, y = 1 and x = 3, y = 4
put them in the equation and you'll see the the values satisfies the equation
Answered by GAUTHMATH
he ride a bike for 15 miles oer hour how many miles did he ride
graph a circle with General form.x^2 +y^2+8x-12y+24=0
Answer:
jhshejwjabsgsgshshsnsjs
Answer:
Step-by-step explanation:
Put the equation into center-radius form.
x² + y² + 8x - 12y + 24 = 0
x² + y² + 8x - 12y = -24
(x²+8x) + (y²-12y) = -24
(x²+8x+4²) + (y²-12y+6²) = 4²+6²-24
(x+4)² + (y-6)² = 28
Center: (-4,6)
radius: √28
16. Which symbol will make the number sentence |-12? 12 true? (1 point)
0=
O=\
O<
O >
Answer:
0>
Step-by-step explanation:
I am having troubles finding x, need an explanation
Answer:
56+35=180 then solve it thanks
Answer:
Step-by-step explanation:
we have a two right triangle, with one side 115
lets say that the other side of the big right triangle is y
-in the big triangle find the third angle
180 -90 -35 = 55, because the sum of all interior angles in a triangle is 180
tan 55 = opp. /adj= y / 115
y = 115 * tan 55
-in the small right triangle
tan 56 = opp./ adj. = 115 / y-x
y-x = 115/ tan 56 , subtract y from both sides
- x= -y +( 115/tan 56), multiply by -1 both sides
x= y -(115/tan56), substitute y for 115 * tan 55
x= (115*tan 55)- (115/tan56)
x≅86.6685
-3u-17=(u+8)
simplify
Answer:
-25/4 = u
Step-by-step explanation:
-3u-17=(u+8)
Add 3u to each side
-3u+3u-17=(u+3u+8)
-17 = 4u +8
Subtract 8 from each side
-17-8 = 4u+8-8
-25 = 4u
Divide by 4
-25/4 = 4u/4
-25/4 = u
Eddie is using his phone's calculator app to calculate 16,544 × 70. He accidentally enters 16,544 × 7 instead. How can he correct his mistake
Answer:
Multiply the product of 16,544 x 7 by 10 as it id the same as multiplying 16,544 x 70.
