Answer:
0.999945 = 99.9945% probability that at least two of the alarms are triggered.
Step-by-step explanation:
For each alarm, there are only two possible outcomes. Either it is triggered, or it is not. The probability of an alarm being triggered is independent of any other alarm, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [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]
And p is the probability of X happening.
A home security system is designed to have a 90% reliability rate.
This means that [tex]p = 0.9[/tex]
Suppose that 6 home equipped with this system experience an attempted burglary.
This means that [tex]n = 6[/tex]
Find the probability that at least two of the alarms are triggered.
This is:
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
In which
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{6,0}.(0.9)^{0}.(0.1)^{6} = 0.000001[/tex]
[tex]P(X = 1) = C_{6,1}.(0.9)^{1}.(0.1)^{5} = 0.000054[/tex]
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.000001 + 0.000054 = 0.000055[/tex]
Then
[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.000055 = 0.999945[/tex]
0.999945 = 99.9945% probability that at least two of the alarms are triggered.
What is the distance of 39 from zero? Hellpppppppp
Answer: 39
Step-by-step explanation: the distance is always positive, 39 + 0 = 39
Answer:
39
Step-by-step explanation:
39 is 39 numbers away from zero. it really doesn't get simpler.
Find the area of the triangle. round your answer to the nearest tenth
Answer:
use photo math
Step-by-step explanation:
cuz i said so
What is the approximate sector area of a sector defined by minor arc CB?
Answer:
d. 7.5 cm²
Step-by-step explanation:
Area of sector = central angel/360 × πr²
Central angle = 180° - 84° = 96° (supplementary angles)
BA = radius (r) = ½(6) = 3 cm
Plug in the values
Area of sector = 96/360 × π*3²
= 7.53982238
= 7.5 cm² (nearest tenth)
The probability distribution for the number of defects in a shipment of alarm clocks, based on past data, is given below. Find the expected number of defects in a shipment of alarm clocks.Number of defects, n: 0, 1, 2, 3, 4Probability of n defects: 0.82, 0.11, 0.04, 0.02, 0.01
Answer:
0.29
Step-by-step explanation:
Given :
n : ___ 0 _____ 1 ____ 2 ____ 3 ____ 4
P(n) : 0.82___ 0.11 ___0.04 _0.02 ___0.01
The expected number of defect in a shipment can be obtained using the expected value formula :
Expected value, E(X) = Σx*p(x)
Σx*p(x) = (0*0.82) + (1*0.11) + (2*0.04) + (3*0.02) + (4*0.01)
E(X) = 0.29
Hence, the expected number of defect in shipment is 0.29
Determine whether the triangles are similar. If so, write a similarity
statement.
Answer:
yes that are similar
Step-by-step explanation:
because the angles are both 50 degrees
similarity statement:
triangle DEF= triangle JEH
hope that helps bby<3
Graph the linear function y= -x + 3.
For which equation is the solution set {-5,2}? *
Step-by-step explanation:
14 For which equation is the solution set {-5,2}?. 15 Which equation has the same solutions as. 2x. 2 + x - 3 = 0.
Given (x+y)^12, find the coefficient of the 7th term.
200
495
792
924
Answer: 924
Step-by-step explanation:
1. Use the combination formula nCr = n!/(n-r)!r!
Using this formula gets you 16 (n) C 6 (r) = 12!/6!6! Which is also 12 • 11 • 10 • 9 • 8 • 7 • 6 • 5 • 4 • 3 • 2 • 1 / 6 • 5 • 4 • 3 • 2 • 1 • 6 • 5 • 4 • 3 • 2 • 1
2. Cancel out matching multiples that are in the numerator and denominator
This gets you 12 • 11 • 10 • 9 • 8 • 7 / 6 • 5 • 4 • 3 • 2 • 1 or 665280/720 when you simplify which leads you to the answer 924
Hope this helps!
Answer:
924
Step-by-step explanation:
What is the quotient of ? 2^4/2^-4
Answer:
[tex] \frac{ {2}^{4} }{ {2}^{ - 4} } \\ = {2}^{4} . {2}^{4} \\ = {2}^{8} \\ = 256[/tex]
Answer:
2⁸
Step-by-step explanation:
2⁴ ÷ 2⁻⁴ = 2⁸
if the bases are the same and you're dividing then you subtract the exponents
According to a bridal magazine, the average cost of a wedding reception for an American wedding is $8213. Assume that the average is based on a random sample of 450 weddings and that the standard deviation is $2185.a. What is the point estimate of the corresponding population mean
Answer:
Point estimate of the corresponding population mean = $8,213
Step-by-step explanation:
Given:
Average cost of a wedding reception (x) = $8,213
Total number of sample (n) = 450
Standard deviation = $2185
Find:
Point estimate of the corresponding population mean
Computation:
Average cost of a wedding reception (x) = Point estimate of the corresponding population mean
Point estimate of the corresponding population mean = $8,213
NO LINKS OR ELSE YOU'LL BE REPORTED! Only answer if you're very good at Math.No guessing please.
A company manufactures video games with a current defect rate of 0.95%.To make sure as few defective video games are delivered as possible,they are all tested before delivery.The test is 98% accurate at determining if a video game is defective.If 100,000 products are manufactured and delivered in a month, approximately how many defective products are expected to be delivered?
A: 950
B: 2,000
C: 20
D: 50
====================================================
Work Shown:
0.95% = (0.95)/100 = 0.0095
0.95% of 100,000 = 0.0095*(100,000) = 950
We expect about 950 games will be defective.
Answer:
A: 950
Step-by-step explanation:
Evaluate the expression:
3x + 2y when X=10 and y=4
Answer:
38
Step-by-step explanation:
3x + 2y when X=10 and y=4
3(10) + 2(4)
30 + 8
38
PLEASE ANSWER ASAP FOR BRAINLEST!!!!!!!!!!!!!!!!!
Answer: C) Next year, 7 out of every 60 students will be taking music.
Step-by-step explanation:
A is wrong because it is an opinion which a table cannot prove.
B is wrong because it says "A representative sample of 60 students) while the answer incorrectly says 30.
C is correct because on the table it says 7 people are taking music and correctly identifies that it's out of 60 students.
D is incorrect for the same reason B is incorrect except this time it says 120.
Lauren woke up one morning and saw frost on the windows. It was -2°C outside. Later in the day, the frost melted. At 3 p.m. it was 9°C outside. Which expression represents the difference between the two temperatures?
Answer:
9-(-2) or 9+2
Step-by-step explanation:
To find the difference of something, subtract one value from the other. It become addition because two negatives make a positive
HELP PLEASE I"LL GIVE 50 POINTS. what is the ratio in simplest form between the length of a side in ΔMNO and the length of it's corresponding side in ΔXYZ
Answer:
1 : 2
Step-by-step explanation: trust
Answer:
3/1 Hope that helps
Step-by-step explanation:
Enlarge the triangle by scale factor 3
Answer:
The triangle will triple in size.
Which state ment is true regarding the graphed function
F(4)= g(4)
F(4)= g(-2)
F(2)= g(-2)
F(-2)= g(-2)
Answer:
F(-2)= g(-2)
Step-by-step explanation:
F(-2)= g(-2), both function have the same points of intersect.
-3(4x-6)=7-12x(solve)(show work)
Hi there!
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I believe your answer is:
There is no solution to the equation.
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Calculating the Answer...}}\\\\-3(4x-6)=7-12x\\-------------\\\rightarrow -12x+18 = 7 - 12x\\\\\rightarrow -12x + 18 - 18 = 7 - 18 -12x\\\\\rightarrow -12x=-12x-11\\\\\rightarrow-12x+12x = -12x+12x - 11\\\\\rightarrow 0 = -11\\\\\boxed{\text{This is a \underline{contradiction}. There is no solution.}}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Help meeeee and plz get it right
A technical machinist is asked to build a cubical steel tank that will hold of water. Calculate in meters the smallest possible inside length of the tank. Round your answer to the nearest .
Answer:
The smallest possible length is 0.83m
Step-by-step explanation:
Given
[tex]Volume = 565L[/tex]
Required
The smallest length of the tank
Since the tank is cubical, then the volume is:
[tex]Volume = Length^3[/tex]
This gives:
[tex]565L= Length^3[/tex]
Express as [tex]m^3[/tex]
[tex]\frac{565m^3}{1000} = Length^3[/tex]
[tex]0.565m^3 = Length^3[/tex]
Take cube roots of both sides
[tex]0.8267m = Length[/tex]
Rewrite as:
[tex]Length = 0.8267m[/tex]
Approximate
[tex]Length = 0.83m[/tex]
If the following data were linearized using logarithms, what would be the
equation of the regression line? Round the slope and y-intercept of the
regression line to three decimal places.
х
y
1
1
13
N
55
3
349
4
2407
5 16,813
Answer:
the equation of the regression line will be 1
EI NHS de Evergreen está diseñando un nuevo jardín.
El jardín será un rectángulo. Sea x el ancho del jardín.
La longitud del jardín será el doble del ancho más 4 pies.
Calcula el área y el perímetro del jardín.
¿Cuál es la expresión de la longitud?
Answer:
Area= 2(x^2 + 4)
Perímetro=6x + 8
Step-by-step explanation:
Ancho = x
Longitud = 2x + 4
Area= ancho × longitud
Area= x × 2x + 4
Area= 2x^2 + 4
Area= 2(x^2 + 4)
Perímetro= ancho+ancho+longitud+longitud
Perímetro=2ancho + 2longitud
Perímetro=2(x) + 2(2x+4)
Perímetro=2x + 4x + 8
Perímetro=6x + 8
Is 4/pi rational or irrational?
Answer:
Pi is an irrational number, same is pi/4.
Step-by-step explanation:
Find the area of the triangle.
35 cm
24 cm
Answer:
A =420 cm^2
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh where b is the length of the base and h is the height
A = 1/2 ( 24) * 35
A =420 cm^2
Answer:
The area of triangle is 420 cm ².
Step-by-step explanation:
Given : -Base of triangle = 24 cmHeight of triangle = 35 cmTo Find :-Area of triangleFormula Used :-Area of triangle = 1/2 × base × height
Solution :-Using Formula
Area of triangle = 1/2 × base × height
substitute the values into the formula
Area of triangle = 1/2 × 24 cm × 35 cm
multiply,
Area of triangle = 1/2 × 840 cm ²
Divide, we get
Area of triangle = 420 cm ²
Therefore, The area of triangle is 420cm².
Twelve skateboards have 48 wheels. What is the value of the ratio of skateboards to wheels, in simplest form? A. 1/4 B. 4/12 C. 12/48 D. 16/20
Answer:
1/4
Step-by-step explanation:
Skateboards : wheels
12 : 48
Divide each part by 12
12/12 : 48/12
1 :4
[tex]\huge\mathbb{\fcolorbox{red}{lavenderblush}{✰Answer}}[/tex]
There are Twelve skateboards have 48 wheels.,
we need to find the ratio of skateboards to wheels, in simplest form;
Hence,
Ratio of skateboard to wheel
[tex]\sf{\dfrac{skateboard}{wheels} }[/tex] [tex]\sf{\dfrac{12}{48} }[/tex] [tex]\sf{\dfrac{\cancel{12}^{^{1}}}{\cancel{48}_{_{4}}} }[/tex] [tex]\bold{\dfrac{1}{4} }[/tex]Anyone no how to do this?..
The top part is the areas of the rooms in feet. You need to find the inches instead. Multiply them by 12.
20 x 12
20 x 12= 240
12 x 12=144
So the first one will be:
240 x 144
Second:
96 x 96
Third:
96 x 114
Fourth:
240 x 196
Fifth:
240 x 240
Sixth:
120 x 240
Prove the formula that:
((∃x)(F(x)∧S(x))→(∀y)(M(y)→W(y)))∧((∃y)(M(y)∧¬W(y)))
⇒(∀x)(F(x)→¬S(x))
Step-by-step explanation:
Given: [∀x(L(x) → A(x))] →
[∀x(L(x) ∧ ∃y(L(y) ∧ H(x, y)) → ∃y(A(y) ∧ H(x, y)))]
To prove, we shall follow a proof by contradiction. We shall include the negation of the conclusion for
arguments. Since with just premise, deriving the conclusion is not possible, we have chosen this proof
technique.
Consider ∀x(L(x) → A(x)) ∧ ¬[∀x(L(x) ∧ ∃y(L(y) ∧ H(x, y)) → ∃y(A(y) ∧ H(x, y)))]
We need to show that the above expression is unsatisfiable (False).
¬[∀x(L(x) ∧ ∃y(L(y) ∧ H(x, y)) → ∃y(A(y) ∧ H(x, y)))]
∃x¬((L(x) ∧ ∃y(L(y) ∧ H(x, y))) → ∃y(A(y) ∧ H(x, y)))
∃x((L(x) ∧ ∃y(L(y) ∧ H(x, y))) ∧ ¬(∃y(A(y) ∧ H(x, y))))
E.I with respect to x,
(L(a) ∧ ∃y(L(y) ∧ H(a, y))) ∧ ¬(∃y(A(y) ∧ H(a, y))), for some a
(L(a) ∧ ∃y(L(y) ∧ H(a, y))) ∧ (∀y(¬A(y) ∧ ¬H(a, y)))
E.I with respect to y,
(L(a) ∧ (L(b) ∧ H(a, b))) ∧ (∀y(¬A(y) ∧ ¬H(a, y))), for some b
U.I with respect to y,
(L(a) ∧ (L(b) ∧ H(a, b)) ∧ (¬A(b) ∧ ¬H(a, b))), for any b
Since P ∧ Q is P, drop L(a) from the above expression.
(L(b) ∧ H(a, b)) ∧ (¬A(b) ∧ ¬H(a, b))), for any b
Apply distribution
(L(b) ∧ H(a, b) ∧ ¬A(b)) ∨ (L(b) ∧ H(a, b) ∧ ¬H(a, b))
Note: P ∧ ¬P is false. P ∧ f alse is P. Therefore, the above expression is simplified to
(L(b) ∧ H(a, b) ∧ ¬A(b))
U.I of ∀x(L(x) → A(x)) gives L(b) → A(b). The contrapositive of this is ¬A(b) → ¬L(b). Replace
¬A(b) in the above expression with ¬L(b). Thus, we get,
(L(b) ∧ H(a, b) ∧ ¬L(b)), this is again false.
This shows that our assumption that the conclusion is false is wrong. Therefore, the conclusion follows
from the premise.
15
Encuentra el resultado de la ecuación mediante la formula general
Step-by-step explanation:
de hecho, la respuesta está en la imagen de arriba
A boat heading out to sea starts out at
Point A, at a horizontal distance of 796 feet
from a lighthouse/the shore. From that
point, the boat's crew measures the angle
of elevation to the lighthouse's beacon-light
from that point to be 10°. At some later
time, the crew measures the angle of
elevation from point B to be 4º. Find the
distance from point A to point B. Round
your answer to the nearest foot if
necessary.
The distance from point A to point B is about 1211 feet.
What is trigonometric ratio?Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.
Let h represent the height of the light house. At point A:
tan(10) = h / 796
h = 140.36 feet
At point B, let d represent the horizontal distance from B to light house:
tan(4) = 140.36/d
d = 2007 feet
The distance from A to B = 2007 - 796 = 1211 feet
The distance from point A to point B is about 1211 feet.
Find out more on trigonometric ratio at: https://brainly.com/question/24349828
Consider the expression 25 – 10 ÷ 2 + 3.
Part A
Which shows a way to rewrite the expression using parentheses so that the expression equals 23?
Select all that apply.
A. (25 – 10) ÷ 2 + 3 = 23
B. 25 – 10 ÷ (2 + 3) = 23
C. (25 – 10) ÷ (2 + 3) = 23
D. 25 – (10 ÷ 2) + 3 = 23
Part B
Which shows a way to rewrite the expression using parentheses so that the expression equals 3?
A. (25 – 10) ÷ 2 + 3 = 3
B. 25 – 10 ÷ (2 + 3) = 3
C. (25 – 10) ÷ (2 + 3) = 3
D. 25 – (10 ÷ 2) + 3 = 3
Given:
The expression is:
[tex]25-10\div 2+3[/tex]
To find:
Part A: The expression using parentheses so that the expression equals 23.
Part B: The expression using parentheses so that the expression equals 3.
Solution:
Part A:
In option A,
[tex](25-10)\div 2+3=15\div 2+3[/tex]
[tex](25-10)\div 2+3=7.5+3[/tex] [Using BODMAS]
[tex](25-10)\div 2+3=10.5[/tex]
In option B,
[tex]25-10\div (2+3)=25-10\div 5[/tex]
[tex]25-10\div (2+3)=25-2[/tex] [Using BODMAS]
[tex]25-10\div (2+3)=23[/tex]
In option C,
[tex](25-10)\div (2+3)=15\div 5[/tex]
[tex](25-10)\div (2+3)=3[/tex]
In option D,
[tex]25-(10\div 2)+3=25-5+3[/tex]
[tex]25-(10\div 2)+3=28-5[/tex] [Using BODMAS]
[tex]25-(10\div 2)+3=23[/tex]
After the calculation, we have [tex]25-10\div (2+3)=23[/tex] and [tex]25-(10\div 2)+3=23[/tex].
Therefore, the correct options are B and D.
Part B: From part A, it is clear that
[tex](25-10)\div (2+3)=3[/tex]
Therefore, the correct option is C.
