Using it's concept, it is found that the probabilities are given as follows:
a) 0.0527 = 5.27%.
b) 0.0088 = 0.88%.
c) 0.0098 = 0.98%.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
Item a:
6 out of 16 songs are of the Beatles, hence the probability of a single music being from the Beatles is:
[tex]pB = \frac{6}{16} = \frac{3}{8}[/tex]
Of three musics, the probability is:
[tex]p = \left(\frac{3}{8}\right)^3 = 0.0527[/tex]
Item b:
For the Rolling stones, the probability is:
[tex]pR = \frac{4}{16} = \frac{1}{4}[/tex]
For the four musics, the probability is:
[tex]p = \left(\frac{1}{4}\right)^2 \times \left(\frac{3}{8}\right)^2 = 0.0088[/tex]
Item c:
For the doors, the probability is:
[tex]pD = \frac{2}{16} = \frac{1}{8}[/tex].
For Beatles or Rolling stones, the probability is:
[tex]pBR = \frac{10}{16} = \frac{5}{8}[/tex]
For the three musics, the probability is:
[tex]p = \left(\frac{1}{8}\right)^2 \times \frac{5}{8} = 0.0098[/tex]
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A financial planner has three portfolios: A, B, and C. Because investors have different tolerances for risks, 35% of people are likely to invest in portfolio A, 25% are likely to invest in B, and 40% are likely to invest in C. Each portfolio has both stocks and bonds, and investors are equally likely to choose either.
This is a tree diagram that represents the probability of investors choosing the different financial products.
What is the probability of an investor choosing both stocks AND bonds from portfolio B?
The probability of an investor choosing both stocks AND bonds from portfolio B is 0.25 or 25%.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
A financial planner has three portfolios: A, B, and C.
Each portfolio has stocks and Bond
P(stock) = 0.5
P(bond) = 0.5
Customers are equally likely to choose stocks.
P(stock and bond from B) = P(stock, B) + P(bond, B)
= 0.25×0.5 + 0.25×0.5
= 0.25 or
= 25%
Thus, the probability of an investor choosing both stocks AND bonds from portfolio B is 0.25 or 25%.
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Factorise: 6 x2+ 7x -3
[tex] \:❏ \: \: \LARGE{\rm{{{\color{orange}{6 {x }^{2} \: + \: 7x \: - 3}}}}}[/tex]
Factorize the equation by breaking down the middle term.[tex] \large \blue\implies \tt \large \: 6 {x }^{2} \: + \: 7x \: - 3[/tex]
Let’s identify two factors such that their sum is 7 and the product is -18.Sum of two factors = 7 = 9 - 2
Product of these two factors = 9 × (-2) = 18
Now, split the middle term.[tex]\large \blue\implies \tt \large \:6 {x}^{2} \: + \: 9x \: - \: 2x \: - \: 3[/tex]
Take the common terms and simplify.[tex] \: \\ \large\blue\implies \tt \large \:3x(2x \: + \: 3)\: -1(2x \: + \: 3)[/tex]
[tex] \\ \large\blue\implies \tt \large \:(3x \: - \:1 ) \quad \: (2x \: + \: 3) \: = \: 0[/tex]
Thus, (3x - 1) and (2x + 3) are the factors of the given quadratic equation.
Solving these two linear factors, we get[tex]\large\blue\implies \tt \large \:x \: = \: \frac{1}{3} \: \: , \: \: \frac{ - 3}{2} \\ [/tex]
[tex] {6x}^{2} + 7x - 3 \\ \\ {6x}^{2} + 9x - 2x - 3 \\ \\ ( {6x}^{2} + 9x) - (2x + 3) \\ \\ 3x(2x + 3) - 1(2x + 3) \\ \\ (3x - 1)(2x + 3).[/tex]
What is the answer? i need help so bad....
Answer:
18
Step-by-step explanation:
(6 * 3 ) - (8 * 0) = 18
The charge for skating is $6.35 for skate rental, 1 hours
of skating at $18 per hour, and an additional $1 fee.
What is the total cost (c) for skating?
Answer:
c = 25.35
Step-by-step explanation:
Comment
Cost (c) = skate rental + time + miscellaneous
Givens
skate rental = 6.35 / hourusing the rink = 18.00miscellaneous = 1Answer
Cost = 6.35 + 18.00 + 1
Cost = 25.35 , but 24.35 is an hourly charge,
What is the period of the graph of y=1/2 sin (2x)-3?
A.3
B.2
C.1/2
D. Pi
The period of the y=1/2 sin (2x)-3 is 2.
We have given that,
y=1/2 sin (2x)-3
We have to determine the period
What is the period?
A period is the part of the menstrual cycle when a woman bleeds from her vagina for a few days.
Normally the period of sin(2x) is 2x, but the pi inside the sin(2x) is a horizontal compression by a factor of 1/pi.
So 2pi·1/pi = 2
The 1/2 and -3 do not impact the period. Those just impact the amplitude (vertical aspect) of the graph.
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Answer:
It's actually D. Pi.
Step-by-step explanation:
I have no clue what the other guy was saying. The period of this graph is Pi or π.
how can pascal's triangle be useful in finding probabilities? 30 point for thisss I need help
Answer: The coefficients of binomial expansions are calculated using Pascal's triangle.
7. Use the distributive property (and your wits!) to write each of the following expressions as a polynomial in standard form.
(u^7+u^3+1)(u-1)(u^5+u^4+u^3+u^2+u+1)
The simplification form of the provided polynomial is u¹³ + u⁹ -u⁷ + u⁶ - u³ - 1 after using the distributive property.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
We have an expression:
[tex]= \rm \left(u^7+u^3+1\right)\left(u-1\right)\left(u^5+u^4+u^3+u^2+u+1\right)[/tex]
After using the distributive property and simply it.
[tex]\rm =\left(u^8-u^7+u^4-u^3+u-1\right)\left(u^5+u^4+u^3+u^2+u+1\right)[/tex]
[tex]\rm =u^{13}+u^9-u^7+u^6-u^3-1[/tex]
Thus, the simplification form of the provided polynomial is u¹³ + u⁹ -u⁷ + u⁶ - u³ - 1 after using the distributive property.
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Hi I need help
1) -15+4r=-9
2)5-y/3=-1
3)42=5x-8
That's all, you don't have to show work, but I'd appreciate it:) asap pls
Equation #1:
-15+4r=-9We move all terms to the left:
-15+4r-(-9)=0
We add all the numbers together, and all the variables
4r-6=0
We move all terms containing r to the left, all other terms to the right
4r=6
r=6/4
r=1+1/2
Equation #2:
5-y/3=-1We move all terms to the left:
5-y/3-(-1)=0
We add all the numbers together, and all the variables
-y/3+6=0
We multiply all the terms by the denominator
-y+6*3=0
We add all the numbers together, and all the variables
-1y+18=0
We move all terms containing y to the left, all other terms to the right
-y=-18
y=-18/-1
y=+18
Equation #3:
Simplifying
42 = 5x + -8
Reorder the terms:
42 = -8 + 5x
Solving
42 = -8 + 5x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-5x' to each side of the equation.
42 + -5x = -8 + 5x + -5x
Combine like terms: 5x + -5x = 0
42 + -5x = -8 + 0
42 + -5x = -8
Add '-42' to each side of the equation.
42 + -42 + -5x = -8 + -42
Combine like terms: 42 + -42 = 0
0 + -5x = -8 + -42
-5x = -8 + -42
Combine like terms: -8 + -42 = -50
-5x = -50
Divide each side by '-5'.
x = 10
Simplifying
x = 10
Step-by-step explanation:
hope it's beneficial.
Draw my attention for further explanations.✨✨
How do I answer this question pls help me
Answer:
14.7 quarts
Step-by-step explanation:
Use the given equivalence figures to write a proportion. Solve the proportion for the unknown value.
__
quarts/liters = x/14 = 1/0.95 . . . . . the conversion is given as 1 qt = 0.95 L
Multiply by 14 to find x.
x = 14(1/0.95) ≈ 14.7
There are about 14.7 quarts in 14 liters.
_____
Additional comment
You are given a value in liters (14 liters) and asked for the equivalent in quarts. That means you want to change the units from liters to quarts. To do that, you can multiply the given value (14 liters) by a conversion factor that has quarts in the numerator and liters in the denominator. That is what the fraction 1/0.95 is in the above. You will note that units of liters cancel in this equation.
[tex](14\text{ liters})\times\dfrac{1\text{ quart}}{0.95\text{ liter}}=\dfrac{14}{0.95}\text{ quarts}\approx14.7\text{ quarts}[/tex]
This rule, "use a conversion factor that divides by the units you don't want and multiplies by the units you do want" applies to any units conversion problem. The conversion factor you use should always have equal quantities in the numerator and denominator. (Here, the equal quantities are 1 quart and 0.95 liters.)
You will notice that we treat units just like any variable. They can be multiplied, divided, cancelled, raised to a power. Only terms with like units can be added or subtracted.
* GEOMETRY
please help me show the work for number 15!!
Answer: (-2, -4)
Step-by-step explanation:
The translation that maps point A onto point B must also map point D onto point C.
Point A maps onto point B after a translation 8 units right and 6 units up, so point C maps onto point D after a translation 8 units left and 6 units down.
Thus, D has coordinates (-2, -4)
find the area of the shaded shape
Answer:
69 meters squared
Step-by-step explanation:
You can split the shape into two small rectangles by drawing a vertical line. Then, you can solve for the areas of the two rectangles separately and then add them together.
The larger rectangle would have an area of 5 * 12, or 60 m^2.
The smaller rectangle would have an area of 3 * 3, or 9 m^2.
Simply add those together and the total area would be 69 m^2.
Answer:
Area is 69 m
Step-by-step explanation:
When the product of 6 and the square of a number is increased by 5 times the number, the result is 4. which equation represents this situation? 6x2 5x - 4 = 0 6x2 5x 4 = 0 62x 5 x = 4 6 x2 5x = 4
Answer:
The answer would be 6x^2 + 5x - 4 = 0
This question is based on the box plot below: How is the data distributed?
The distribution is right skewed.
What is the data distribution?A box plot is graph that is used to display data. The box plot is made up of two whiskers that are on either sides of a box. The first line on the box is the first quartile, the second line is the median and the third line is the third quartile.
When the median is closer to the bottom of the box, and if the whisker is shorter on the lower end of the box, the data is right skewed.
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x + 3y > –3 and y < One-halfx + 1?
The complete question is
"Which is the graph of the system x + 3y > –3 and y < One-halfx + 1?"
The solution is the intersection region of all the solutions in the system of inequalities.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
We know that the lines are given as;
x + 3y = -3
y = 1/2 x + 1
Solving for "y" from the first line;
3y = -3 - x
y = -1 - x/3
For the line x + 3y = -3 the x-intercepts;
y = 0
y = -1 - x/3
0 = -1 - x/3
x/3 = -1
x = -3
And the y-intercept;
y = -1
For the line y = 1/2 x + 1 the x-intercepts;
y = 0
0= 1/2 x + 1
1/2x = -1
x = -2
And the y-intercept
x = 0
y = 1
Now we can graph both lines,
The solution is the intersection region of all the solutions in the system of inequalities.
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Calculate the difference in the proportion of males and the proportion of females that smoke. Give your answer to 2 decimal places
The difference in the proportion of males and the proportion of females that smoke is 0.08
Missing informationIn a sample of 61 males, 15 smoke, while in a sample of 48 females, 8 smoke.
How to determine the proportion difference?The given parameters are:
Male Female
Sample 61 48
Smokers 15 8
The proportion is calculated using:
p = Smoker/Sample
So, we have:
Male = 15/61 = 0.25
Female = 8/48 = 0.17
The difference is then calculated as:
Difference = 0.25 - 0.17
Evaluate
Difference = 0.08
Hence, the difference in the proportion of males and the proportion of females that smoke is 0.08
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Please help me i would really appreciate it, I really dont want to fail the assignment!!!
The ordered pair of the solution for the system of equation area are (2, -3) and (3, -3)
How to solve system of equation?f(x) = x² - 5x + 3
f(x) = -3
Therefore,
-3 = x² - 5x + 3
x² - 5x + 3 + 3 = 0
x² - 5x + 6 = 0
x² - 2x - 3x + 6 = 0
x(x - 2) - 3(x - 2) = 0
(x - 3)(x - 2) = 0
x = 3 or 2
when x = 2
f(x) = 4 - 10 + 3 = -3
when x = 3
f(x) = 9 - 15 + 3 = -3
Therefore, the ordered pair of the solution for the system of equation are (2, -3) and (3, -3)
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QUESTION 2
Evaluate x4 + 5x3-3x2 + 11x - 6 for x = 3
Answer:
The answer is (-84)
putting the value of X =(- 3)
2) X = 216
Hello!
We are going to evaluate the expression with our given x-value for question 2.
We know that our expression is: x^4 + 5x^3 - 3x^2 + 11x - 6
We also know that our x-value = 3
We will simply plug in "3" to "x" in our expression and solve.
Solve:
x^4 + 5x^3 - 3x^2 + 11x - 6
Plug in 3 to x:
(3)^4 + 5(3)^3 - 3(3)^2 + 11(3) - 6
Simplify:
(3)^4 + 5(3)^3 - 3(3)^2 + 11(3) - 6
81 + 5(3)^3 - 3(3)^2 + 11(3) - 6
81 + 135 - 3(3)^2 + 11(3) - 6
81 + 135 - 27 + 33 - 6
216 - 27 + 33 - 6
189 + 33 - 6
222 - 6 = 216
Therefore, our final answer would be 216.
Answer:
216
simplify √125+√45-√20
Answer:
[tex]6\sqrt{25}[/tex]
Step-by-step explanation:
[tex]\sqrt{125} = 5\sqrt{5} \\\sqrt{45} = 3\sqrt{5} \\\sqrt{20} = 2\sqrt{5} \\5\sqrt{5} + 3\sqrt{5} -2\sqrt{5} =6\sqrt{25}[/tex]
In triangle nql, point s is the centroid, ns = (x 10) feet, and sr = (x 3) feet. triangle n q l has centroid s. lines are drawn from each point to the midpoint of the opposite side to form line segments n r, q m, and l p. the length of line segment n s is x 10 and the length of line segment s r is x 3. what is rs? 4 feet 7 feet 10 feet 14 feet
The complete question is
"In triangle NQL, point S is the centroid, NS = (x + 10) feet, and SR = (x + 3) feet. Triangle N Q L has centroid S. Lines are drawn from each point to the midpoint of the opposite side to form line segments N R, Q M, and L P. The length of line segment N S is x + 10 and the length of line segment S R is x + 3.
What is RS?
4 feet, 7 feet, 10 feet, 14 feet"
Answer:
The Length of RS would be 7 ft. so the correct option is B.
What is a line segment?A line segment is a straight line with finite length, and thus, have to endpoints(points on either ends).
Given:
NS = (x + 10) ft
SR = (x + 3) ft
Based on the centroid theorem, the centroid, S will divide the median, line segment NR, into NS and SR,
NS : SR = 2 : 1.
Therefore:
NS = 2(SR)
x + 10 = 2(x + 3)
Solve for x
x + 10 = 2x + 6
x - 2x = -10 + 6
-x = -4
x = 4
SR = (x + 3) ft (SR is same as RS)
substitute the value of x
SR = (4 + 3) ft
SR = RS = 7 ft
Hence, The Length of RS would be 7 ft. so the correct option is B.
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Answer: B, 7 feet
Step-by-step explanation:
Write an equation for a circle with center (-2, 8) and radius 9.
The equation for a circle with a center (-2, 8) and a radius of 9 will be (x + 2)² + (y − 8)² = 81.
What is an equation of a circle?A circle can be characterized by its center's location and its radius's length.
Let the center of the considered circle be at the (h,k) coordinate.
Let the radius of the circle be 'r' units.
Then, the equation of that circle would be:
(x - h)² + (y - k)² = r²
Write an equation for a circle with a center (-2, 8) and a radius of 9.
Then the equation will be
(x + 2)² + (y − 8)² = 9²
(x + 2)² + (y − 8)² = 81
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One forth of one third of two fifths of a number is 15. What is the number?
A fourth of a third of two fifths is a thirtieth.
(1 x 1 x 2) / (4 x 3 x 5) = 2 / 60 = 1 / 30
A thirtieth of a number () is fifteen, the number is four hundred and fifty.
= 15 / (1 / 30) = 15 x 30 = 450
forty percent of four hundred and fifty is one hundred and eighty.
(450 / 100) x 40 = 180
Answer:
The number is 450
Step-by-step explanation:
One fourth is 1/4,
One third is 1/3
and two fifths is 2/5
let the number be x.
So,
One fourth of one third of two fifths of x is 15.
that is,
1/4 * 1/3 * 2/5 * x = 15
2/4*3*5* x = 15
2/60 * x = 15
1/30 * x = 15
1 * x = 15*30
x = 450
Therefore the number is 450
Variables y and x have a proportional relationship, and y = 21 when x = 14.
What is the value of x when y = 12?
Enter your answer in the box.
x =
please help
Answer:
18
Step-by-step explanation:
We know that y is 1.5 times x, so when x = 12, y = (1.5)(12)=18
This directly proportional relationship between p and q is written as p∝q where that middle sign is the sign of proportionality. The value of x is 8, when the value of y is 12.
What is the directly proportional and inversely proportional relationship?Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
p = kq
where k is some constant number called the constant of proportionality.
This directly proportional relationship between p and q is written as p∝q where that middle sign is the sign of proportionality.
In a directly proportional relationship, increasing one variable will increase another.
Now let m and n be two variables.
Then m and n are said to be inversely proportional to each other if
[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]
(both are equal)
where c is a constant number called the constant of proportionality.
This inversely proportional relationship is denoted by
[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]
As visible, increasing one variable will decrease the other variable if both are inversely proportional.
Given Variables y and x have a proportional relationship, therefore, we can write,
y ∝ x
y = k × x
21 = k × 14
21/14 = k
k = 1.5
Therefore, the equation for the relationship between x and y can be written as,
y = 1.5x
now, the value of x when the value of y is 12 is,
12 = 1.5 × x
x = 8
Hence, the value of x is 8, when the value of y is 12.
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You went to an electronics store and would like to buy a TV priced at $1200. You only have $1000 to
spend and the store gives 15% discount on the TV. Can you buy the TV? Explain
Using two six-sided number cubes, each labeled with the numbers 1 through 6, event A is defined by rolling a sum greater than 8Which of the following shows the sample space of event A?
Answer:{(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}
Step-by-step explanation:
Event A is defined by rolling a sum greater than 8 will be {(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}.
What is a random sample?Random sampling is the method of selecting the subset from the set to make a statical inference.
Utilizing two six-sided number solid shapes, each named with the numbers 1 through 6.
The number of the total events will be given as,
Total events = 6²
Total events = 6 x 6
Total events = 36
The total sample is given below.
(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)
Event A is defined by rolling a sum greater than 8 will be {(3, 6), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 3), (6, 4), (6, 5), (6, 6)}.
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y is directly proportianal to x when y is 30 x is 6. work out the equation connecting y and x
Answer:
Step-by-step explanation:
Solution
The general equation for this kind of problem is
y = k x
30 = k * 6 Divide both sides by 6
30/6 = 6k/6 Combine
5 = k
So the connection between x and y is that to get a value for y, you must divide it by 6.
Pls help!!!!!!!!!!!!!!!!
Answer:
D: 6.5, 3
C: 23.5, 9
I think
Answer:
C (23.5, 9)
D (6.5, 3)
Which of the following does the function [tex]y=-4cos(3x)-9[/tex] not have?
a) horizontal translation
b)vertical translation
c)horizontal compression
d)reflection
Answer:
horizontal translation ( this would require an x - k or x+k type of a factor)
Step-by-step explanation:
It DOES have :
vertical due to the -9
horizontal compression due to the 3x
reflection due to the -4
If h(x) = 5 + x and (x) =
XE
which expression is equivalent to (kh)(x)?
The value of composite function (koh)(x) is 1/(5+x) after plugging h(x) = 5+x in the k(x) option (B) is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The question is incomplete.
The question is:
if h(x)=5+x and k(x)=1/x which expression is equivalent to (koh)(x)
Answer options are:
A).(5+x)/xB). 1/(5+x)C). 5+(1/x)D). 5+(5+x)We have:
h(x) = 5 + x
k(x) = 1/x
To find the composite function:
(koh)(x):
= k(h(x))
= 1/(5+x)
Thus, the value of composite function (koh)(x) is 1/(5+x) after plugging h(x) = 5+x in the k(x) option (B) is correct.
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Geometry fence problem. Need help solving
Which expression is not a polynomial?
x³
x² - 2x
x³ +1
12x
Answer:
12x
Step-by-step explanation:
It has no exponent so it is not a polynomial