This question is solved using probability concepts.
A probability is given by the number of desired outcomes divided by the number of total outcomes.The order in which the balls are chosen don't matter, which means that the combinations formula is used to find the number of outcomes.Doing this, we get that:
[tex]\frac{1}{1200}[/tex] probability that you win the jackpot.
------------------------------------------
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
----------------------------------------------------
Total outcomes:
3 white from a set of 10(numbered from $1 to $10).1 red from a set of 10(numbered from $11 to $20).Thus:
[tex]T = C_{10,3}C_{10,1} = \frac{10!}{7!3!} \times \frac{10!}{1!9!} = 120 \times 10 = 1200[/tex]
Desired outcomes:
The correct balls, order does not matter, so only one outcome, that is, [tex]D = 1[/tex]
What is the probability that you win the jackpot?
[tex]p = \frac{D}{T} = \frac{1}{1200}[/tex]
[tex]\frac{1}{1200}[/tex] probability that you win the jackpot.
A similar question is given at https://brainly.com/question/23966554
Answer:
6/7200=1/1200
Step-by-step explanation:
[3! ways to arrange the three white balls] over [10x9x8 ways to pick three white balls and 10 ways to pick a red] =3x2x1/10x9x8x10=6/72x100=6/7200=1/1200
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create another show real life multi-step function problems with Solutions in quadratics
Answer:
Kazan also SOS jz zks zj sj aka always zks. aiwow
You want to make a nut mix that has almonds, cashews, and peanuts. Almonds cost $7 per pound, cashews are $5 per pound, and peanuts are $2 per pound. If you want to make a 10 pound mix with a $20 budget find the possible mix combinations of almonds, cashews, and peanuts. How many pounds of almonds should you use
Answer and explanation:
Assume Almond is a
Cashew is c
Peanuts is p
The system of equations satisfies this thus:
a+c+p= 10
7a+5c+2p= $20
The system of equations has three unknowns. Solving for the unknown variables here would yield parametric equations or dependent system where given x y z we may find x in terms of y and z in terms of x, in that form. This would give many results for our problem which may not be very accurate.
How do I find out the square root of a perfect square
(1-sinx+cosx)^2 = 2(1+sinx)(1+cosx)
If you're trying to establish an identity, the given equation is not an identity. The proper identity would be as follows:
(1 - sin(x) + cos(x))² = (1 - sin(x))² + 2 (1 - sin(x)) cos(x) + cos²(x)
… = (1 - 2 sin(x) + sin²(x)) + 2 (1 - sin(x)) cos(x) + cos²(x)
… = 2 - 2 sin(x) + 2 (1 - sin(x)) cos(x)
… = 2 - 2 sin(x) + 2 cos(x) - 2 sin(x) cos(x)
… = 2 (1 - sin(x) + cos(x) - sin(x) cos(x))
… = 2 (1 - sin(x) + cos(x) (1 - sin(x)))
… = 2 (1 - sin(x)) (1 + cos(x))
But if you're trying to solve an equation:
(1 - sin(x) + cos(x))² = 2 (1 + sin(x)) (1 + cos(x))
2 (1 - sin(x)) (1 + cos(x)) = 2 (1 + sin(x)) (1 + cos(x))
(1 - sin(x)) (1 + cos(x)) - (1 + sin(x)) (1 + cos(x)) = 0
(1 + cos(x)) (1 - sin(x) - 1 - sin(x)) = 0
-2 sin(x) (1 + cos(x)) = 0
sin(x) = 0 or 1 + cos(x) = 0
sin(x) = 0 or cos(x) = -1
[x = arcsin(0) + 2nπ or x = arcsin(0) + π + 2nπ] or
… [x = arccos(-1) + 2nπ]
We have arcsin(0) = 0 and arccos(-1) = π, so the solution set reduces to
x = 2nπ or x = (2n + 1)π
(where n is any integer)
Plane R and Plane U intersect at which of the following?
Answer:
do you have any images with the questions?
Step-by-step explanation:
Element X is a radioactive isotope such that every 42 years, its mass decreases by
half. Given that the initial mass of a sample of Element X is 50 grams, how long
would it be until the mass of the sample reached 45 grams, to the nearest tenth of a
year?
Answer:
6.38548 years
Step-by-step explanation:
1 = 2 [tex]e^{42k}[/tex]
1/2 = [tex]e^{42k}[/tex]
ln(1/2) = 42k ln(e)
ln(1/2)/42 = k
k = -0.01650
~~~~~~~~~~~~~~
45 = 50 [tex]e^{-0.01650t}[/tex]
45/50 = [tex]e^{-0.01650t}[/tex]
ln(45/50) = -0.01650 t ln(e)
ln(45/50)/ -0.01650 = t
t = 6.38548 years
The number of years for the radioactive element to reach a mass of 45 grams is given by t = 6.384129 years
What is half-life of an element?The half-life of a radioactive isotope is the amount of time it takes for one-half of the radioactive isotope to decay. The half-life of a specific radioactive isotope is constant; it is unaffected by conditions and is independent of the initial amount of that isotope.
Half-life (symbol t½) is the time required for a quantity (of substance) to reduce to half of its initial value
The decay constant λ is = 0.693/t½
where t½ is the half-life of the element
Given data ,
Let the number of years be t
Let the initial mass of the element be a = 50 grams
The final mass of the element be ( a - x ) = 45 grams
Now , Element X is a radioactive isotope such that every 42 years, its mass decreases by half
And , half life t½ = 42 years
So , the decay constant k = 0.693/t½
k = 0.693 / ( 42 )
k = 0.0165
And , k= 2.303/t {log (a/a-x)}
So , t = 2.303 / ( 0.0165 ) log ( 50/45 )
On simplifying , we get
t = 6.384129 years
Hence , the number of years for the radioactive element to reach 45 grams is 6.384129 years
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Can someone explain this
=========================================================
Explanation:
Let x be the unknown angle we want to find. This angle is in degrees.
The diagram shows 19 is the opposite of this angle, and the side 35 is adjacent to the angle.
We use the tangent ratio to tie the two sides together
[tex]\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}\\\\\tan(x) = \frac{19}{35}\\\\x = \tan^{-1}\left(\frac{19}{35}\right)\\\\x \approx 28.4956386\\\\x \approx 28\\\\[/tex]
Note: The notation [tex]\tan^{-1}[/tex] refers to the inverse tangent, or arctangent.
help me please its confusing pleasee
Answer:
a) -8x³+x²+6x
d) 16x²-9
Step-by-step explanation:
a) -2x(x+4x²)+3(x²+2x)
Expand each bracket:
-2x(x+4x²)
As the -2x is on the outside of the bracket, you have to times everything inside the bracket by -2x.
-2x times x equals -2x²
-2x times 4x² equals -8x³
Then we expand the other bracket:
3(x²+2x)
3 times x² equals 3x²
3 times 2x equals 6x
We then put all of it together:
-2x²-8x³+3x²+6x
Collect like terms:
-8x³+x²+6x
b) (4x-3)(4x+3)
We will use the FOIL method:
F-First
O-outer
I-Inner
L-Last
Times the first two terms in each bracket:
4x times 4x equals 16x²
Times the outer terms in the bracket:
4x times 3 equals 12x
Times the inside terms in the bracket:
-3 times 4x equals -12x
Times the last terms in the bracket:
-3 times 3 equals -9
Put it together:
16x²+12x-12x-9
The 12x and -12x cancel out to leave 16x²-9
Hope this helps :)
A rectangle has a perimeter of 50m, the ratio between the two side is 32 . Caculator the area of that rectangle?
Answer:
Area of rectangle = 150 cm
Step-by-step explanation:
Given the following data;
Ratio = 3:2 Perimeter = 50mTo find the area of the rectangle;
First of all, we would determine the dimensions (length and width) of the rectangle;
For length;
Length, L = 2x
For width;
Width, W = 3x
Mathematically, the perimeter of a rectangle is given by the formula;
P = 2(L + W)
50 = 2(2x + 3x)
50 = 2(5x)
50 = 10x
x = 50/10
x = 5
Length, L = 2x = 2 * 5 = 10 cm
Width, W = 3x = 3 * 5 = 15 cm
Now, we would find the area of the rectangle;
Mathematically, the area of a rectangle is given by the formula;
Area of rectangle = length * width
Area of rectangle = 10 * 15
Area of rectangle = 150 cm
What's 672 divided by 32
Find the distance between the two points.
(-2,5)
✓ [?]
(4,-2)
Enter the number that
goes beneath the
radical symbol.
Enter
Answer:
√85
Step-by-step explanation:
We can find the distance between two points by using this formula
d = √(x2 - x1)² + (y2 - y1)²
Where the x and y values are derived from the two given points
The two given points are (-2,5) and (4,-2)
Remember that coordinates are written as (x,y)
Next we want to define our variables ( x2, x1, y2 and y1 are the variables)
x2 = 4
x1 = -2
y2 = -2
y1 = 5
Now to find the distance between the two points we simply substitute the values of the variables into the formula
Formula: d = √(x2 - x1)² + (y2 - y1)²
x2 = 4, x1 = -2, y2 = -2 and y1 = 5
d = √(4 - (-2))² + (-2 - 5)²
The two negative signs before the 2 cancel out and it changes to + 2
d = √(4 + 2)² + (-2 - 5)²
Add 4 and 2
d = √6² + (-2 - 5)²
Subtract -2 and -5
d = √6² + -7²
Apply the exponents
d = √36 + 49
Add 36 and 49
d = √85
We can conclude that the distance between the two points is √85
worth 10pts if someone can help!
Answer:
y=-x
I found the points then simplified it down
Answer:
hmm maybe trying using 2y=5x-2
Step-by-step explanation:
how i came to this was just looking at point y which was just 2 and then since point x was at 5,-2 all i did was simply it into 2y=5x-2
maybe that's the answer if it is can i get brainlist ?! pretty please if not let me know so i can see what i got wrong
Please help me answer this question:
(D 3, 3, 5, 5, 6, 7, 8, 9, 11
Answer:
According to the graph presented within the proposed interrogate, the answer to such is identified as ‘C’: 2, 3, 5, 5, 6, 7, 8, 10, 11.
Step-by-step explanation:
To evaluate for such a problem, a comprehension of the “Whisker” plots is obligated.
- The box geometric figure with the vertical line contained within represents the average of the numbers presented.
* In this peculiar case, 6 is acknowledged as the individual value responsible for the mean.
Thus far, browsing at such answer choices, we are obligated to appoint an answer where 6 is the standard deviation or the mean (where 6, and only 6, is found in the middle of the set of numbers provided).
The only answer choice in which certifies to all conditions thus far declared is disseminated as “C”.
*I hope this helps.
Qual o valor da expressão? 155÷2+4−55+1,5−6×5+6?
Answer:
Step-by-step explanation:
Hello!
(155/2)+4−55+1,5−(6×5)+6=
77,5 +4-55 +1,5 -30 +6= 4
Instructions: Use the images to answer the questions below.
Graph A
Graph B
Graph C
5108
6 4 8
7046
8 2 2 2 6 66
90 000 24
50,1,2,
63,8,9,
71,3,4,
8 2,4,6,7,
glo,
57 39
68 5 1
7 3 0 0
824
919
an
11.11
1. What type of graph is displayed? stem-and-leaf plot •
2. The data is quantitative
3. Which graph is made correctly? Graph A :
4. The data in the correctly made graph is negatively skewed . This indicated that the mean is
the same or approximately the same as the median.
5. The population size of the data set in the correctly made graph is 5
Some of the sub-questions have been answered. I will provide explanation to the already answered questions and then answer the unanswered parts
1. The graph type
The three graph displayed are stem-and-leaf plots. The single numbers at the left-hand side are referred to as the stem, while the numbers at the right are called leaves.
2. The type of data
The three graphs display numerical data (i.e. numbers). Hence, the data are quantitative
3. The correct graph
To know the correct graph; the leaves on each line must be in ascending order and the delimiter to use is a blank space.
Only graph A obey the above illustration
4. Skewness
In graph A, the length of the leaves increases as we move from one stem to the other. This means that the graph is negatively skewed.
For a negative skewed stem plot, the mean is less than the median
5. The population size
This means that we count the number of leaves in the stem plot
The leaves are:
[tex]Leaves = \{0,8,4,8,0,4,6,2,2,2,6,6,6,0,0,0,0,2,4\}[/tex]
So, the population size is: 19
6. The data set
To do this, we include the stem to the corresponding leaves.
So, we have:
[tex]Dataset= \{50,58,64,68,70,74,76,82,82,82,86,86,86,90,90,90,90,92,94\}[/tex]
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∫(x+1)/(x2+2)2x−3dx need help with this question. can you show the process
do you need to include the wiggle infront of the first bracket? if not;
(x+1) ÷ [(x^2+2) x (2x-3dx)]
x^2 x 2x = 2x^3
x^2 x -3dx = -3dx^3
2 x 2x = 4x
2 x -3dx = - 6dx
i cant find a way to make it equal 0 so i think the answer is just
x+1 over 2x^3 - 3dx^3 + 4x - 6dx as a fraction
is 23/17 a rational number?
Answer:
rational number
Step-by-step explanation:
a rational number can be written as a/b where a and b are integers
23/17 = a/b where a = 23 and b = 17
This is a rational number
What are the coordinates of the vertices of the image?
A) A'(9,8), B'(-3,-4), C'(1, 2), and D'(1,-2)
B) A'(3,4), B'(3,-4), C'(-5, 2), and D'(1, 2)
C) A'(3,8), B'(-3, 4), C'(1,-2), and D'(-1,2)
D) A'(-3, 4), B'(3,4), C'(5,-2), and D'(-1,-2)
Answer:
D
Step-by-step explanation:
I took the quiz
27x + 24y= 4.5
1.5x + y =0.225
Answer:
x = 0.1, y = 0.075
Step-by-step explanation:
Given the 2 equations
27x + 24y = 4.5 → (1)
1.5x + y = 0.225 → (2)
Multiplying (2) by - 24 and adding to (1) will eliminate the y- term
- 36x - 24y = - 5.4 → (3)
Add (1) and (3) term by term to eliminate y
- 9x = - 0.9 ( divide both sides by - 9 )
x = 0.1
Substitute x = 0.1 into either of the 2 equations and solve for y
Substituting into (2)
1.5(0.1) + y = 0.225
0.15 + y = 0.225 ( subtract 0.15 from both sides )
y = 0.075
Answer:
the values for x AND y are 0.1 and 0.075 respectively
PLS HELP WILL GIVE BRAINLY!!
What is the weight (in grams) of a liquid that exactly fills a 182.8 milliliter container if the density of the liquid is 0.135grams over milliliter? Round to the nearest hundredth when necessary, and only enter numerical values, which can include a decimal point
Answer:
24.68 gram
Step-by-step explanation:
Given that :
Volume = 182.8 ml
Density of liquid = 0.135 gram/ml
Recall :
Density = mass (g/ml) / volume (ml)
Substitute the value into the equation :
0.135 = mass / 182.8
Mass = 0.135 * 182.8
Mass = 24.678 gram
Hence, weight = 24.678 grams
find the mean value of the following. 5, 11, 4, 10, 8, 6
please help
solve (4-w)(5w+3)=0
Answer:
4=w w = -3/5
Step-by-step explanation:
(4-w)(5w+3)=0
Using the zero product property
4-w = 0 5w+3 =0
4 =w 5w= -3
4=w w = -3/5
Answer:
4 & -3/5
Step-by-step explanation:
the "trick" is to set each factor = to zero
4-w = 0
w = 4
~~~~~~~~~~~
5w + 3 = 0
5w = -3
w=-3/5
Which rule is a recursive rule for the sequence
1, – 6, 36, – 216,
...?
Ο o An
-
6. An-1
ο o an
.
6
An-1
o an
6. An-1
1
ο o an
-
.
6
an-1
1
2
3
Apply the distributive property to factor out the greatest common factor.
44+48=
Answer:
(40+4)+(40+48)
=40+(4+8)+4+8(40)
=44+48+12×40
if u add all
=104×40
=4160
Step-by-step explanation:
Its in the picture!!!1
answer please and no links .....thank you
Answer:
8,3,-1,3,15
Step-by-step explanation:
y=x^2-1
y(-3)=8
y(-2)=3
y(0)=-1
y(2)=3
y(4)=15
I need help with this
Answer:
45
Step-by-step explanation:
Use the first five terms of the binomial theorem to approximate (-1.4)^8
Answer:
14.75789056
Step-by-step explanation:
I think so...
The first five terms of the binomial theorem to approximate (-1.4)⁸ answer would be 14.056.
What is the Binomial Theorem?The binomial theorem states the principle for expanding the algebraic expression (x + y)ⁿ and describes it as the total of the phrases involving the unique exponents of the x and y variables. Each word in a binomial expansion has a coefficient, which is a numerical value.
According to the binomial theorem, it is possible to expand any non-negative power of binomial (x + y) into a sum of the form,
(x+y)ⁿ = ⁿC₀xⁿy₀ + nC₁ xⁿ⁻¹y₁ + nC₂ xⁿ⁻² y2 + ... + nC x¹yⁿ⁻¹ + nCn x°yⁿ
where n ≥ 0 is an integer and each ⁿCₓ is a positive integer known as a binomial coefficient.
Given expression as (- 1.4)⁸
as a result, if you have raised a negative integer to an even power, the response will be positive.
Eliminating the negative sign.
⇒ (1.4)⁸ = (1+0.4)⁸
⇒ 1⁸+8*1⁷*0.4+28*1⁶*0.4²+56*1⁵*0.4³+70*1⁴*0.4⁴
⇒ 1+3.2+4.48+3.584+1.792
⇒ 14.056
If we used one more term we would get 14.62944
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Emma earns a $39,000 salary in the first year of her career. Each year, she gets a 5% raise. How much does Emma earn in total in the first 11 years of her career?
Answer:
554,000
Step-by-step explanation:
that is the answer
Emma earns $554,064.80 in total in the first 11 years of her career
We are to determine the future value of $39,000 each year for 11 years given the growth rate of 5%
The formula for calculating future value:
FV = P (1 + r)^n
Where :
FV = Future value
P = Present value
R = interest rate
N = number of years
First year = $39,000
Second year = 39,000 x (1.05) = $40,950
Third year = 39,000 x (1.05)^2 = $42,997.50
Fourth year = 39,000 x (1.05)^3 = $45,147.38
Fifth year = 39,000 x (1.05)^4 = $47,404.75
Sixth year = 39,000 x (1.05)^5 = $49,774.99
seventh year = 39,000 x (1.05)^6 = $52,263.74
eighth year = 39,000 x (1.05)^7 = $54,876.93
ninth year = 39,000 x (1.05)^8 = $57,620.78
tenth year = 39,000 x (1.05)^9 = $60,501.82
eleventh year = 39,000 x (1.05)^10 = $63,526.91
Sum of the earnings for the first eleven years = $554,064.80
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5
In the diagram, rhombus ABCD has sides of length 5 cm each and the length of the
diagonal AC is 8 cm.
(a) Find ABC
(b) Calculate the area of rhombus ABCD
Answer:
a) the angle ABC is approximately 106 degrees b) 24
Step-by-step explanation:
1) Using the law of cos
AC*AC= AB*AB+BC*BC-2*AB*BC*cosB
8*8= 5*5+5*5-2*5*5*cosB
64= 50- 50c0sB
cosB= 14/(-50)= -7/25.
B= arccosB= arccos(-7/25)= 106degrees.
2) sinB*sinB= 1- CosB*cosB= 1-49/625= 576/625
sinB= 24/25 (SinB doesn't equal -24/25, because B is between 0 and 180 degrress, so sin B is positive)
3) S= AB*BC*sinB= 5*5*24/25= 24 (area of the rhombus is 24)
