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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Solve (x - 2 < 5) ∩ (x + 7 > 6).
1. Ø
2. {x | x < -1 x < 7}
3. {x | -1 < x < 7}
Answer:
c2
Step-by-step explanation:
A four-person committee is chosen from a group of eight boys and six girls.
If students are chosen at random, what is the probability that the committee consists of all boys?
•4/1001
• 15/1001
•10/143
•133/143
Answer:
The answer is 10/143
Step-by-step explanation:
Priya wants to sketch a graph of the polynomial f defined by f(x)=x^3+5x^2+2x-8. She knows f(1)=0, so she suspects that (x-1) could be a factor of x^3+5x^2+2x-8 and writes (x^3+5x^2+2x-8) = (x-1) (?x^2+?x+?) and draws a diagram.
1. Finish Priya's diagram
2. Write f(x) as the product of (x-1) and another factor.
3. Write f(x) as the product of three linear factors.
4. Make a sketch of y=f(x).
Given the polynomial f(x)=x³+5x²+2x-8 and f(1)=0.
Factorization is the process of determining the components of a given value or mathematical statement. The integers that are multiplied to create the original number are known as factors. The components of 18 include, for instance, 2, 3, 6, 9, and 18, as well as;
18 = 2 x 9
18 = 2 x 3 x 3
18 = 3 x 6
In a similar way, the factors in the case of polynomials are the polynomials that are multiplied to create the original polynomial. For instance, (x + 2) (x + 3) are the elements of x2 + 5x + 6. The original polynomial is produced when we multiply both x +2 and x +3. We can also locate the polynomials' zeros after factorization. Zeroes in this situation are x = -2 and x = -3.
2. Now, to write f(x) as the product of (x-1) and another factor.
x³+5x²+2x-8 = (x-1)(x²-6x+8).
3. Now, to write f(x) as the product of three linear factors.
x³+5x²+2x-8 = (x-1)(x²-6x+8)= (x-1)(x-4)(x-2)
4. Look at the sketch below.
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What is the value of y?
Enter your answer in the box
Y=_
Answer:
the angles of a triangle always equal 180 so
34+x-5+4y=180
simplify
29+x+4y=180
-29
x+4y=151
-4y
x=-4y+151
then put this into the original equation
29-4y+151+4y=180
simplify
29+151=180
so this proves that this works
-1/4x-151=y
Hope This Helps!!!
can you help me solve this question
Answer: Coordinates: (1,3) length RS: 3 length RT: 2 ST: 3.6
Step-by-step explanation:
a^2+b^2=c^2
3^2+2^2=c^2
9+4=c^2
13=c^2
3.6=c
Mr. T has 784 marbles. he has 263 marbles more than Indie. how many marbles do they have altogether?
Answer:
Step-by-step explanation:
784-263=521
784+521=1305
answer=1305
Use the multiplication law for logarithm to expand the following expression:[tex]log_{8} (21)[/tex]
- worth 20pt
Answer:
[tex]\log_8{(3)} + \log_8{(7)}[/tex]
Step-by-step explanation:
Product Rule for Logarithms
[tex]\log_b{(mn)} = \log_b{(m)} + \log_b{(n)}[/tex]
Instead of 21 you can write 3 · 7, because 21 = 3 · 7.
[tex]\log_8{(21)} = \\= \log_8{(3 \cdot 7)} =\\= \log_8{(3)} + \log_8{(7)}[/tex]
What is the solution to this equation log(2x-100)=3
What is the parent graph of f(x) = |(x/2 + 4)^2 +6|
Answer
The answer is A. y = x²
(Giving 75 points! Please do not answer without showing work and do not answer if you do not know the answer.)
Since we know U is the midpoint, we can say TU=
substituting in our values for each we get:
? =12x−1
Solve for x
We now want to solve for x.
−4x+11=−1
−4x= ?
x= 3
Solve for TU, UV, and TV
This is just the first part of our question. Now we need to find TU, UV, and TV. Lets start with TU and UV.
TU=8x+11 We know that x=3 so let’s substitute that in.
TU=8(?)+11
TU= ?
We will do the same for UV. From our knowledge of midpoint, we know that TU should equal UV, however let’s do the math just to confirm.
UV=12x−1 We know that x=3 so let’s substitute that in.
UV=12(3)−1
UV= 35
Using the segment addition postulate we know:
TU+UV=TV
35+35=TV
TV= 70
Answer:
x = 3
TU = 35
UV = 35
TV = 70
Step-by-step explanation:
As U is the midpoint of TV:
⇒ TU = UV
⇒ 8x + 11 = 12x - 1
⇒ 8x + 11 - 11 = 12x - 1 - 11
⇒ 8x = 12x - 12
⇒ 8x - 12x = 12x - 12 - 12x
⇒ -4x = -12
⇒ -4x ÷ -4 = -12 ÷ -4
⇒ x = 3
Substitute the found value of x into the expression for TU:
⇒ TU = 8x + 11
⇒ TU = 8(3) + 11
⇒ TU = 24 + 11
⇒ TU = 35
Using the transitive property of equality:
As UV = TU and TU = 15 then UV = 35
Using the segment addition postulate:
⇒ TV = TU + UV
⇒ TV = 35 + 35
⇒ TV = 70
Hence
TU=8(3)+11=35UV=12(3)-1=35TV=2(35)=703. Find the measure of angle TOS in the figure below.
∠ROQ and ∠TOS are vertically opposite angles, so must be equal, which means they are 122°
∠TOS = 122°You are drawing an angle in standard position and you swing the terminal side until an angle of 281 is made. how many more degrees can you continue swinging so that the terminal side is at the same position as the initial side
Answer:
79°
Step-by-step explanation:
An angle in standard position has it "initial" side glued on to the positive x-axis. The other ray that makes the angle swings around the origin, (0,0) like a hand of a analog clock (but moving backwards) straight up is 90°, straight to the left is 180° straight down is 270°. And all the way back to the start is 360°.
If the angle is 281° it can go 79° more degrees before getting back to the start.
360° - 281° = 79°
Triangle abc is represented. points d and f are marked on side ab and points e and g are marked on side ac. segments de and fg are drawn.
if , then line segment
is parallel to line segment
.
If points d and f are on side ab and points e ang g are on side ac then line segment de and fg are parallel.
Given There is a triangle abc.
Parallel lines are those lines that do not meet at any point. If we draw a triangle abc and plot points d and f are marked on side ab and points e and g are marked on side ac then the line segment fg is parallel to de because both the line segments are drawn from the points which are on the sides opposite to each other. We have assumed a simple triangle because no description is given for the triangle.
Hence the line segment fg is parallel to de if drawn points d and f marked on ab and points e and g are marked on ac.
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Answer:D-E is parallel to FG which is parallel to B-C meaning all three are parallel
Step-by-step explanation:
Simplify the expression below using the order of operations. 10+(6-3) 22-4-1 Simplify the expression below using the order of operations . 10+ ( 6-3 ) 22-4-1
The expression is 17.
What is expression?An expression is a sentence with a minimum of two numbers or variables and at least one math operation.
Given:
10+(6-3) 22-4-1
Using the BODMAS rule,
First solve the bracket term
10+ 3 * 22 -4-1
Now, perform multiplication
10+66-4-1
Now, subtraction
10+66-5
=10+61
And lastly addition
=71.
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Answer:
17
Step-by-step explanation:
the answer is 17 :)
i need this answer a.s.a.p!!!
Answer:
Should have ended with "at most -15, not "at least -15."
Step-by-step explanation:
[tex]\leq[/tex] -15 means less than or equal to -15
So it can be -15, but also anything less than -15. The phrase "at most -15, not "at least -15" says exactly that.
Which is not a characteristic of the absolute value parent function?
Answer:
B
Step-by-step explanation:
the range of y=|x| is not all real numbers its [0,inf)
sign - ...
Zekrom
The side length of a square is 3x^2 . Find The area of the square
Answer: A=9x^4
Step-by-step explanation:
Hii, do you need to find the area of a square with a side length of 3x^2? Let me help you out! (:
AreaTo find the area of a square, you need to square its side length.
Sounds strange, right?
The formula is shown below.
[tex]\LARGE\boldsymbol{A=a^2}[/tex]
Here "A' (capital A) denotes the area
"a" (lower-case a) denotes the side length
The 2 above the a tells us that we need to multiply the side length times itself.
Alright, now it's just a matter of sticking in the known values...
[tex]\sf A=(3x^2)^2[/tex]
Simplify
[tex]\sf A=9x^4[/tex]
Voila! There's our answer, cheers! (;
_________Hope I helped! Best wishes! (:
Reach far. Aim high. Dream big.
________[tex]\underbrace[/tex]
Please help!!!
Consider the segment UV.
Type the correct answer in each box. Use numerals instead of words.
Find x intercept for n and find y intercept for m
What is the product? Assume x>0.
(√3x + √5)√15x+2√30
O 3x√√5+3√165x+10-√√6
O 3x√5 +6√10x +5√3x +10√/6
O 3x√5+10√6
0 6√3x+10√6
Step-by-step explanation:
well you can distribute the sqrt(15x) to the (√3x + √5) and then combine the radicals using the product property of radicals: [tex]\sqrt[n]{a} * \sqrt[n]{b} = \sqrt[n]{ab}[/tex].
[tex](\sqrt{3x} + \sqrt{5})\sqrt{15x} + 2\sqrt{30}\\(\sqrt{3x} * \sqrt{15x}) + (\sqrt{5} * \sqrt{15x}) + 2\sqrt{30}\\\sqrt{45x^2} + \sqrt{75x} + 2\sqrt{30}\\[/tex]
Now we can simplify the radicals using the same property we used to combine them but instead of combining into one radical we'll separate them into two radicals where one of the radicals simplifies into a number without a radical
[tex](\sqrt{9} * \sqrt{x^2} * \sqrt{5}) + (\sqrt{25} * \sqrt{3x}) + 2\sqrt{30}\\3x\sqrt{5} + 5\sqrt{3x} + 2\sqrt{30}[/tex]
I
1
8 in
Find h.
13 in
= √[?] in.
as the following pic you can see the answer.
#diameter is 8 so radius is 4
A fuel tank is 1/6 full. When 2 gallons of gasoline are added, the tank becomes 1/4 full. What is the total fuel capacity of the tank in gallons?
Answer:
24 gallons
Step-by-step explanation:
Since the 2 gallons of gas increased the fill ratio from 1/6 to 1/4, we can find how much of the tank the 2 gallons filled by solving the equation 1/4 - 1/6 = 1/12. This means that each gallon of gas is 1/24th of the tank.
Thus, the tank has a fuel capacity of 24 gallons.
Answer:
24
Step-by-step explanation:
Let x be the total fuel capacity of the tank, in gallons.
Then from the given information
x/6 + 2 = x/4,
Multiplying both sides by 12 to remove the fractions, we get
2x + 24 = 3x so x = 24.
Therefore, the total fuel capacity of the tank is 24 gallons.
There are 12 ducks and 11 geese in a certain park. Find the ratio of geese to ducks.
I need help with this question, I'm not sure what to do
If Bruce can deduct 40% from other interest then the total interest deducted is $2927.
Given Adjusted gross income=$36500, mortgage interest =$2787 and other interest $350.
It is said that 40% of other interest can be deducted by Bruce but it is not said that nothing will be deducted by Bruce from Mortgage interest so we will deduct full of mortgage interest and 40% of other interest. So,
Mortgage interest =$2787
Other interest=$350
Other interest deductable=40%*350
=$140
So the total will be 2787+140 =$2927.
Hence the interest deducted by Bruce is $2927if only 40% of other interest is deductable.
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A student committee is to consist of 2 freshmen, 5 sophomores, 4 juniors, and 3 seniors. If 6 freshmen, 13 sophomores, 8 juniors, and 14 seniors are eligible to be on the committee, in how many ways can the committee be chosen
Delete the commas if necessary.
============================================================
Explanation:
There are 6 freshmen total and we want to pick 2 of them, where order doesn't matter. The reason it doesn't matter is because each seat on the committee is the same. No member outranks any other. If the positions were labeled "president", "vice president", "secretary", etc, then the order would matter.
Plug n = 6 and r = 2 into the nCr combination formula below
[tex]n C r = \frac{n!}{r!(n-r)!}\\\\6 C 2 = \frac{6!}{2!*(6-2)!}\\\\6 C 2 = \frac{6!}{2!*4!}\\\\6 C 2 = \frac{6*5*4!}{2!*4!}\\\\ 6 C 2 = \frac{6*5}{2!}\\\\ 6 C 2 = \frac{6*5}{2*1}\\\\ 6 C 2 = \frac{30}{2}\\\\ 6 C 2 = 15\\\\[/tex]
This tells us there are 15 ways to pick the 2 freshmen from a pool of 6 total.
Repeat those steps for the other grade levels.
n = 13 sophomores, r = 5 selections leads to nCr = 13C5 = 1287. This is the number of ways to pick the sophomores.
You would follow the same type of steps shown above to get 1287. Let me know if you need to see these steps.
Similarly, 8C4 = 70 is the number of ways to pick the juniors.
Lastly, 14C3 = 364 is the number of ways to pick the seniors.
-----------------------------
To recap, we have...
15 ways to pick the freshmen1287 ways to pick the sophomores70 ways to pick the juniors364 ways to pick the seniorsMultiply out those values to get to the final answer.
15*1287*70*364 = 491,891,400
This massive number is a little under 492 million.
Determine the inequality that can be used to model when the population of bacteria will be greater than or equal to 656,100. Then solve the inequality for t.
The inequality is 100*[tex]3^{t}[/tex]≤ 656100.
The correct option is (B).
What is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Given:
From the table attached below:
a=300, r= 900/300 = 3
As, it is GP
Now,
f(t) = [tex]ar^{t-1}[/tex]
f(t) = [tex]300*3^{t-1}[/tex]
f(t) = 300/3 *[tex]3^{t}[/tex]
f(t) = 100*[tex]3^{t}[/tex]
Inequality is used to determine greater than or equal to 656100
100*[tex]3^{t}[/tex]≤ 656100
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Find all solutions of the equation in the interval .
Write your answer in radians in terms of .
If there is more than one solution, separate them with commas.
The solutions to the trigonometric equation in the desired interval are given as follows:
[tex]\theta = \frac{\pi}{3}, \theta = \frac{5\pi}{3}[/tex]
What is the solution to the trigonometric equation?The trigonometric equation is given by:
[tex]\sqrt{3}\cot{\theta} - 1 = 0[/tex]
Solving it similarly to an equation, we have that:
[tex]\sqrt{3}\cot{\theta} = 1[/tex]
[tex]\cot{\theta} = \frac{1}{\sqrt{3}}[/tex]
Since [tex]\cot{\theta} = \frac{1}{\tan{\theta}}[/tex], we have that the equation is equivalent to:
[tex]\tan{\theta} = \sqrt{3}[/tex]
The tangent is positive in the first and in the fourth quadrant. In the first quadrant, the angle [tex]\theta[/tex] with [tex]\tan{\theta} = \sqrt{3}[/tex] is:
[tex]\theta = \frac{\pi}{3}[/tex]
In the fourth quadrant, the equivalent angle is:
[tex]\theta = 2\pi - \frac{\pi}{3} = \frac{5\pi}{3}[/tex]
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Help please I only have 10 minutes TT
1. 5:15 = 1/3
scale factor is 1/3going from bigger to smaller
2. 2/8 = 1/4
14 x 1/4 = 3.5
X = 3.5
I’m confused nd stuck
Answer:
B. (4,2)
Step-by-step explanation:
The answer is where the lines intersect.
Hope this helps!
If not, I am sorry.
Answer:
(4,2)
Step-by-step explanation:
the solution is where both lines intersect. We would write the point as (x,y). That’s why the answer is (4,2) not (2,4)
HELP ASAP PLS ILL MARK YOU BRAINLIEST
Answer:
c is the answer.
