Answer:
0.7588 = 75.88% probability that more than 1 vessel transporting nuclear weapons was destroyed
Step-by-step explanation:
The vessels are destroyed without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
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]
In this question:
Fleet of 17 means that [tex]N = 17[/tex]
4 are carrying nucleas weapons, which means that [tex]k = 4[/tex]
9 are destroyed, which means that [tex]n = 9[/tex]
What is the probability that more than 1 vessel transporting nuclear weapons was destroyed?
This is:
[tex]P(X > 1) = 1 - P(X \leq 1)[/tex]
In which
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]
So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,17,9,4) = \frac{C_{4,0}*C_{13,9}}{C_{17,9}} = 0.0294[/tex]
[tex]P(X = 1) = h(1,17,9,4) = \frac{C_{4,1}*C_{13,8}}{C_{17,9}} = 0.2118[/tex]
Then
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.0294 + 0.2118 = 0.2412[/tex]
[tex]P(X > 1) = 1 - P(X \leq 1) = 1 - 0.2412 = 0.7588[/tex]
0.7588 = 75.88% probability that more than 1 vessel transporting nuclear weapons was destroyed
Please help
Solve the inequality.
-1 < 2x + 5 < 4
[?] sxs H
Answer:
-1-5<2x+5-5<4-5
-6<2x<-1
-3<x<-1/2
Evaluate f(g(3)) if f(x)=6x−4 and g(x)=x2.
(Please Explain! Thank you)
Answer: 50
Step-by-step explanation:
f(x) = 6x-4 and g(x) = x^2
f(g(3)) means what is the value of the function f when it is evaluated at the value of g(3).
So g(x) is x^2 so g(3) is 3^2 = 9
Therefore we put 9 in for f(g(3))= f(9) = 6(9) - 4 = 54 - 4 = 50
What is the Square root of 30 ,12,36
Answer:
the square root of:
30: 5.477225575
12: 3.464101615
36: 6 <-- explanation of square root: any number that when multiplied by itself equals your wanted number (in this case 36) will be the square root of your wanted number.
Identifying properties used to solve liner equation.
Options are:
Addition property of Equality
subtraction property of Equality
multiplication property of Equality
division property of Equality
simplifying
distributive
Need a better explaination
Please help explanation if possible
Answer:
10% gain
Step-by-step explanation:
[P2-P1]/P1
(33-30)/30=3/30=.1 or 10% gain.
Answer:
10%
Step-by-step explanation:
→ Minus the new share from the old one
33 - 30 = 3
→ Divide the answer by the original price
3 ÷ 30 = 0.1
→ Multiply the answer by 100
0.1 × 100 = 10%
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
3x + 6y = -42
Answer:
y = -1/2x -7
Step-by-step explanation:
3x + 6y = -42
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
Subtract 3x from each side
3x-3x+6y = -3x-42
6y = -3x-42
Divide each side by 6
6y/6 = -3x/6 - 42/6
y = -1/2x -7
Ginny writes down a secret number on her palm. She says that it is a three-digit even number. The units digit is 1 more than the hundreds digit. The tens digit is twice the sum of the units digit and the hundreds digit.
Answer:
Hello,
Answer 162
Step-by-step explanation:
Let say n the searched number.
[tex]n=\overline{abc}\\a>0\\c=a+1\\b=2*(a+c)\\\\.T.\ means\ True.\\\\\\\begin{array}{c|c|c|c}a&c&b&ok\\1&2&6&.T.\\3&4&14&.F.\\5&6&22&.F.\\7&8&30&.F.\end{array}\\\\\\\boxed{Answer\ n=162}\\[/tex]
Terry got 27 out of 50 for his Maths test. What is his mark as a percentage?
Answer:
54%
Step-by-step explanation:
Concepts:
A percent is a value indicating hundredth parts of any number. 1%/one percent would be equal to a hundredth part, and 100% would be the entire quantity.Solving:
Let's solve this problem by going through the steps to find the percentage.
1. Find out the entire amount
Since Terry got 27/50 on his math test, we can assume he got 27 questions right out of 50 questions. This means, in total, there was 50 questions.2. Divide the number you want expressed as a percent by the total quantity
The number we want in this question to be expressed as a percent is 27, and the total quantity is 50.27 ÷ 50 = 0.543. Multiply the resulting value by 100
The result we got when we divided 27 by 50 is 0.540.54 · 100 = 544. Add the percent symbol (%) at the end of the value
The value we got was the number 5454%Therefore, Terry's marks as a percentage is 54%.
a word problem on proportions using a unit rate
Lashonda made $273 for 13 hours of work.
At the same rate, how many hours would she have to work to make $231?
hours
Х
?
eleven hours - 11 hours
Solve.
x^2 - 9x + 3 = 0
x= or x=
Answer:
Step-by-step explanation:
x^2 - 9x + 3 = 0 is a quadratic whose coefficients are a = 1, b = -9 and c = 3.
Use the quadratic formula to solve it.
The discriminant, b^2 - 4ac, is 81 - 4(1)(3), or 81 - 12, or 69.
The roots are:
-b ± √(discriminant)
x = -------------------------------
2a
And these roots in this particular problem are:
-(-9) ± √69 9 ± √69
= ------------------------------- = ----------------
2(1) 2
A principal of $4000 is placed in a savings account at 6% per annum compounded annually. How much interest is earned in the account after three years
The interest earned in the account after three years is $720.
The formula for simple interest= P×T × R/100
Principal (P) = $4000
Time( T) = 3 years
Rate(R) = 6%
interest(I)= 4000×3 × 6/100
I = 72000 ÷ 100
I = 720
Therefore, the interest earned in the account after three years is $720.
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please help solve for y!
As both angles are supplementary
[tex]\\ \Large\sf\longmapsto 3x+(2x+3y)=180°[/tex]
[tex]\\ \Large\sf\longmapsto 3x+2x+3y=180[/tex]
[tex]\\ \Large\sf\longmapsto 5x+3y=180[/tex]
[tex]\\ \Large\sf\longmapsto 3y=180-5x[/tex]
[tex]\\ \Large\sf\longmapsto y=\dfrac{180-5x}{3}[/tex]
And
[tex]\\ \Large\sf\longmapsto 3x=90[/tex]
[tex]\\ \Large\sf\longmapsto x=\dfrac{90}{3}[/tex]
[tex]\\ \Large\sf\longmapsto x=30[/tex]
Now
Putting value[tex]\\ \Large\sf\longmapsto y=\dfrac{180-5x}{3}[/tex]
[tex]\\ \Large\sf\longmapsto y=\dfrac{180-5(30)}{3}[/tex]
[tex]\\ \Large\sf\longmapsto y=\dfrac{180-150}{3}[/tex]
[tex]\\ \Large\sf\longmapsto y=\dfrac{30}{3}[/tex]
[tex]\\ \Large\sf\longmapsto y=10[/tex]
If f(x) = 3x + 10 and g(x) = 2x - 4, find (f+ g)(x).
Answer:
5x+6
Step-by-step explanation:
f(x) = 3x + 10
g(x) = 2x - 4
(f+ g)(x)= 3x + 10 + 2x - 4
Combine like terms
= 5x+6
Evaluate the variable expression x y for the given values of x and y. (If an answer is undefined, enter UNDEFINED.) x = 0; y = 21
Write an algebraic expression that represents three less than the square of a number k.
Answer:
2k-3
Step-by-step explanation:
the square of k is k times k so 2k (two times k) and less than three means minus three.
Question 1 of 10
Is (0,0) a solution to this system?
A. No. (0,0) does not satisfy either inequality.
B. No. (0,0) satisfies y< x2 + 2x + 1 but does not satisfy yz x2 + x - 4.
C. No. (0,0) satisfies ya x2 + x - 4 but does not satisfy y< x2 + 2x + 1.
O
D. Yes. (0,0) satisfies both inequalities.
Answer:
D
Step-by-step explanation:
0=> 0+0-4, 0=>-4 TRUE
0<0+0+1, 0<1 TRUE
Which box holds more popcorn?
Answer:
Amanda's popcorn container holds more popcorn
Step-by-step explanation:
First we'll have to find the volume.
The Volume helps us determine which is bigger.
Step 1
We'll find Amanda's popcorn container
10cm*10cm*13.5cm=1350cm
Step 2
We'll find Mary's popcorn container
8cm*8cm*20cm=320cm
Step 3
Since Amanda's popcorn container has 1350cm (volume) and Mary's popcorn container has 320cm (volume) we'll have this. 1350cm>320cm. We can determine the Amanda's popcorn container has holds more,
Final Answer
Amanda's popcorn container holds more popcorn
How many unit cubes are on each layer of the cube?
6
3
12
9
Answer:
6
Step-by-step explanation:
Remember: Each layer has 6 cubes. Step 3 Count the cubes. cubes Multiply the base and the height to check your answer. So, the volume of Jorge's rectangular prism is cubic centimeters. if wrong very sorry
Answer:
9
Step-by-step explanation:
took the test
Which improper fraction is equivalent to 17.8?
89/10
93/10
89/5
Answer:
17.8.
Step-by-step explanation:
89/5
= 17 4/5
= 17.8.
The correct improper fraction which is equivalent to 17.8 is,
⇒ 17.8 = 89 / 5
What is Rational number?A number which can be written in the form of fraction p / q , where q is non zero, are called Rational numbers.
We have to given that;
The number is,
⇒ 17.8
Now,
We can simplify the number as;
⇒ 17.8
⇒ 178 /10
⇒ 89 / 5
Therefore, The correct improper fraction which is equivalent to 17.8 is,
⇒ 17.8 = 89 / 5
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If f(×)=16×-30 and g(×)=14×-6, for which value of x does (f-g)(x)=0
Answer: [tex]x=12[/tex]
Step-by-step explanation:
[tex]f(x)=16x-30\\g(x)=14x-6[/tex] are the equations that you've given us.
Now if we plot these two equations on the graph we notice there's an intersection at (12,162). Therefore meaning that [tex]x=12[/tex].
We can prove that by doing the following calculations to prove that both sides are equal to each other.
The left side of the equal sign:
Step 1: Write the equation down:
[tex]16x-30[/tex]
Step 2: Substitute x for the numerical value we found.
[tex]16(12)-30[/tex]
Step 3: We will multiply [tex]16*20[/tex] first, giving us 192.
[tex]192-30[/tex]
Step 4: Subtract 192 from 30. Which gives us 162.
[tex]162[/tex]
The right side of the equal sign:
Step 1: Write the equation down:
[tex]14x-6[/tex]
Step 2: Substitute x for the numerical value we found.
[tex]14(12)-6[/tex]
Step 3: We will multiply [tex]14*12[/tex] first, giving us 168.
[tex]168-6[/tex]
Step 4: Subtract 168 from 6. Which gives us 162.
[tex]162[/tex]
We know that [tex]x=12[/tex] because when substituting x with 12, we get 162 on both sides. Therefore making this statement true and valid.
[tex]162=162[/tex]
Complete the table. Round your entries to the
nearest thousandth.
a
b
C
dz
ex
ASAP
a=2,5937
b=2,7048
c=2,7181
d=2,7183
e=2,7183
Graph: y – 3 = 1/2 (x + 2)
Answer:
The x-intercept is -8, the y-intercept is 4, and the slope is 1/2.
Step-by-step explanation:
The x-intercept is -8, the y-intercept is 4, and the slope is 1/2.
Answer: See below
Concept:
There are different forms of linear equations:
Slope-intercept form: y = mx + bPoint-slope form: y - y₁ = m (x - x₁)Standard form: Ax + By = CIntercept form: x / x₁ + y / y₁ = 1Solve:
Given: y - 3 = 1/2 (x + 2)
Here, we can see the linear equation is in the form of point-slope form.
x₁ = -2
y₁ = 3
m = 1/2
Point included in the graph = (-2, 3)
Slope of the graph = 1/2
Hope this helps!! :)
Please let me know if you have any questions
Two professional gamers subscribe to twitch streamers. Jonah has 430$ saved up, and spends 45$ a month on
subscriptions. Rodrick has 310$ saved up, and spends 25$ a month on subscriptions.
A) Create an equation that can be used to find m, the number of months it will take for both gamers to have the
same amount of money left?
B) After how many months will the gamers have the same amount of money?
Answer:
A) [tex]430-45m = 310-25m[/tex]
B) 6 months
Step-by-step explanation:
A) for Jonah, the equation would be [tex]430-45m[/tex]
Because the money is being spent on the subs, you subtract that from his original savings.
The same thing is said for Rodrick, but his equation would be [tex]310-25m[/tex]
to find out the number of months it will take for both gamers to have the
same amount of money left, you set their equations equal to each other:
[tex]430-45m = 310-25m[/tex]
B) you solve for m.
[tex]430-45m = 310-25m[/tex]
first by subtracting 310 on both sides to get:
[tex]430-310-45m=-25m[/tex]
[tex]120-45m=-25m[/tex]
then add 45m on both sides because we cant have negative months
[tex]120=-25m+45m[/tex]
[tex]120=20m[/tex]
divide by 20 on both sides to get the number of months
[tex]\frac{120}{20} =\frac{20m}{20}[/tex]
[tex]m=6[/tex]
Please if anyone can help me
ixl area of sectors. I am struggling on this question
Answer:
español :/
Step-by-step explanation:
Answer:
256/5 pi
Step-by-step explanation:
= angle/360 × pi×r^2
= 72/360 × pi × 16^2
= 51.2 pi
= 256/5 pi
Can you please help me with this question
Answer:
Where is the question?
Step-by-step explanation:
Python is an interpreted high-level general-purpose programming language. Python's design philosophy emphasizes code readability with its notable use of significant indentation.
Are 3(3x - y) and 12 ( x - 4y ) equivalent expression?
Answer:
No, they are not.
Step-by-step explanation:
If you distributed 12(x - 4y), you would get 12x - 48y. If you distributed 3(3x-y), you would get 9x- 3y. 12x - 48y and 9x - 3y are not equivalent. Hope this helped!
Suppose you have 3 bags. Two of them contain a single $10 bill, and the third contains a single $5 bill. Suppose you pick one of these bags uniformly at random. You then add a $5 bill to the bag, so it now contains two bills. The bag is shaken, and you randomly draw a bill from the bag without looking into the bag. Suppose it turns out to be a $5 bill. If a you draw the remaining bill from the bag, what is the probability that it, too, is a $5 bill
Answer:
1/2
Step-by-step explanation:
Number of bags = 3
number of bags with $10 bill initially = 2
number of bags with $5 bill initially = 1
assume :
event you pick a $5 bill at first draw = A
event you pick a $5 bill at second draw = B
hence : P ( A n B ) = 1/3 * 1 = 1/3
P( A ) = ( 1/3 * 1 ) + ( 1/3 * 1/2 + 1/3 * 1/2 ) = 2/3
therefore P( that the second drawn bill is $5 )
P( B | A ) = P(A n B ) / P ( A )
= (1/3) / (2/3) = 1/2
The probability that it, too, is a $ 5 bill is 33.33%.
Since you have 3 bags, and two of them contain a single $ 10 bill, and the third contains a single $ 5 bill, supposing you pick one of these bags uniformly at random and you then add a $ 5 bill to the bag, so it now contains two bills, and the bag is shaken, and you randomly draw a bill from the bag without looking into the bag, supposing it turns out to be a $ 5 bill, if a you draw the remaining bill from the bag, to determine what is the probability that it, too, is a $ 5 bill, the following calculation must be performed:
3 bags = 2 with a 10 bill and 1 with a 5 bill 1/3 = 0.3333 0.3333 x 100 = 33.33
Therefore, the probability that it, too, is a $ 5 bill is 33.33%.
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write your answer as an integer or as a decimal rounded to the nearest tenth
Answer:
8.6
Step-by-step explanation:
VW = WX / cos (36°)
= 7 / 0.81
= 8.6
Answer:
8.65
Step-by-step explanation:
cos 36° = 7 / VW
VW = 7 / cos 36°
VW = 8.65
Find the area of the shaded regions.
Answer:
around 22, or 21.98
Step-by-step explanation:
[tex]s1 = {r}^{2} \times \pi = 9 \times 3.14 = 28.26[/tex]
[tex]s2 = 1 \times 3.14 = 3.14[/tex]
[tex]s3 = 28.26 - (3.14 \times 2) = 28.26 - 6.28 = 21.98[/tex]
