Answer:
0.9936 = 99.36% probability that during a year, you can avoid catastrophe with at least one working drive
Step-by-step explanation:
For each disk, there are only two possible outcomes. Either it works, or it does not. The probability of a disk working is independent of any other disk, 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.
Assume that there is a 8% rate of disk drive failure in a year.
So 100 - 8 = 92% probability of working, which means that [tex]p = 0.92[/tex]
Two disks are used:
This means that [tex]n = 2[/tex]
What is the probability that during a year, you can avoid catastrophe with at least one working drive?
This is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{2,0}.(0.92)^{0}.(0.08)^{2} = 0.0064[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0064 = 0.9936[/tex]
0.9936 = 99.36% probability that during a year, you can avoid catastrophe with at least one working drive
When converting 5 1/4% to decimal, Mark wrote 5.25. Explain why his answer is wrong and write the correct answer.
Answer:
Below
Step-by-step explanation:
It is 5 1/4 PERCENT not just 5 1/4.
5 1/4 % = 5.25%
= 5.25/100
= 0.0525.
Please help I’m really stuck this is my last attempt
What is the mode for the set of data?
Ages
Stem Leaves
5 0, 4, 6
6 0, 2, 3, 4, 8, 8, 9
7 0, 2, 3, 4, 4, 4, 8, 9
8 4, 5, 6, 8
5|0 = 50 years old
33
68
4
74
Answer:
I THINK IT IS 74 NOT 4
I HOPE THIS HELPS!!!!!
In the xy-plane, line / passes through the origin and is perpendicular to the line with equation 5x - 2y = 8.
Which of the following could be an equation of line /?
Answer:
[tex]ac - bd[/tex]
Step-by-step explanation:
[tex]ac - bd [/tex]
Choose the three formulas that can be used to describe complementary events.
Choose the three formulas that can be used to describe complementary events.
A. P(E') = 1 - P(E)
B. P(E) - P(E') = 1
C. P(E) + P(E') = 1
D. P(E) = 1/P(E')
E. P(E) = 1 - P(E')
F. P(E)/P(E') = 1
G. P(E') = 1/P(E)
Answer:
c
Step-by-step explanation:
A box contains 5 white balls, 3 black balls, and 2 red balls.A-What is the probability of drawing a white ball?B- How many white balls must be added to the box so that the probability of drawing a white ball is 3/4?C-How many black balls must be added to the original assortment so that the probability of drawing a white ball is 1/4?
Answer:
[tex](a)\ P(White) = \frac{1}{2}[/tex]
(b) 10 additional white balls
(c) 10 additional black balls
Step-by-step explanation:
Given
[tex]White = 5[/tex]
[tex]Black =3[/tex]
[tex]Red = 2[/tex]
Solving (a): P(White)
This is calculated as:
[tex]P(White) = \frac{White}{Total}[/tex]
[tex]P(White) = \frac{5}{5+3+2}[/tex]
[tex]P(White) = \frac{5}{10}[/tex]
[tex]P(White) = \frac{1}{2}[/tex]
Solving (b): Additional white balls, if [tex]P(White) = \frac{3}{4}[/tex]
Let the additional white balls be x
So:
[tex]P(White) = \frac{White+x}{Total+x}[/tex]
This gives:
[tex]\frac{3}{4} = \frac{5+x}{10+x}[/tex]
Cross multiply
[tex]30+3x = 20 + 4x[/tex]
Collect like terms
[tex]4x - 3x = 30 - 20[/tex]
[tex]x = 10[/tex]
Hence, 10 additional white balls must be added
Solving (c): Additional black balls, if [tex]P(White) = \frac{1}{4}[/tex]
Let the additional black balls be x
So:
[tex]P(White) = \frac{White}{Total+x}[/tex]
So, we have:
[tex]\frac{1}{4} = \frac{5}{10+x}[/tex]
Cross multiply
[tex]10+x = 5 * 4[/tex]
[tex]10+x = 20[/tex]
Collect like terms
[tex]x = 20 -10[/tex]
[tex]x = 10[/tex]
Hence, 10 additional black balls must be added
Question 1
Points 3
Rese
A carpet is in the shape of a right triangle. The longer leg
measures 8 feet. The hypotenuse is 4 feet more than the
length of the shorter leg. How long is the shorter leg?
Reset
after
assess
Answer:
6 feetStep-by-step explanation:
Given right triangle with:
Legs s and 8, and hypotenuse s + 4Use Pythagorean and solve for s:
(s + 4)² = s² + 8²s² + 8s + 16 = s² + 648s = 64 - 168s = 48s = 6The length of a rectangle is 6 meters more than its width. The area of the rectangle is 114 square meters. Which of the following quadratic equations represents the area of the rectangle? Suppose x is the width of the rectangle. x 2-6x - 114 = 0
A) x^2-6x-114=0
B) x^2-6x+114=0
C) x^2+6x+114=0
D) x^2+6x-114=0
Answer:
last one
Step-by-step explanation:
x = width
x+6 = length
Area = length times width
x(x + 6) = [tex]x^{2}[/tex] + 6x
[tex]x^{2}[/tex] + 6x = 114 (subtract 114 from both sides)
[tex]x^{2}[/tex] + 6x -114 = 0
1. 650 - 700 - 800 = ?
2. 25 - 45 + 23 ＝?
carry on learning
Answer:
- 850
3
Step-by-step explanation:
650 - 700 - 800
650 - 1500
- 850
25 - 45 + 23
- 20 + 23
3
A section of a deck is shaped like a trapezoid. For this section, the length of one base is 23 feet, and the length of the other base is 50 feet. The height is 20 feet. What is the area of this section of the deck?
The area for the section of the deck is ____ ft
Answer:
Area of a trapezoid= (big base+small base)/2 x height
A=(67+54)/2 x 18
A=60.5 x 18
A=1089
1. Come up with an integer that is BIGGER than 10.
2. Come up with an integer that is SMALLER than 10.
3. Come up with an integer that is BIGGER than 0.
4. Come up with an integer that is SMALLER than 0.
I need help pleaseeee
Answer:
1) any number that is greater than ten is considered an integer bigger than ten: for example, 11, 12, 100, 1000000, etc.
2) any number that is smaller than ten is considered an integer smaller than ten: for example, 9, 8, 7, -100, -100000, etc.
3) any number that is bigger than zero is considered an integer bigger than ten: for example, 1, 2, 10, 100, 100000, etc.
4) any number that is smaller than zero is considered an integer smaller than zero: for example, -1, -2, -3, -10, -100000, etc.
Step-by-step explanation:
An integer is any whole number
Answer:
Step-by-step explanation:
integer bigger than 10 is 11
integer smaller than 10 is 9
integer greater than 0 is 1.
integer smaller than 0 is -1.
Find the prime factorisation of each of the following numbers, leaving your answer in index notation..
(e) 117 800
plzz answer quick
Answer:
3x3x13 and 2 x 2 x 2 x 2 x 2 x 5 x 5
Step-by-step explanation:
A ice cream shop sells 8 different flavors of ice cream with A choice of three different styles of calls how many different ice cream cones are possible if you select one ice cream flavor with one type of ice cream cone
Explanation:
There are 8 different flavors and 3 types of cones. This means there are 8*3 = 24 different combos possible.
Imagine a table with 8 rows and 3 columns. Each row is a different flavor and each column is a different cone type. The table formed has 24 inner cells to represent a different combination of flavor + cone type. So that's why we multiplied those values earlier.
Note: This only works if you're only able to select one type of flavor.
Select the correct answer. Simplify. (3x^2y^3/z^3)^3 A. B. C. D.
Answer:
options aren't given but the correct answer will be [tex]\frac{27x^6y^9}{z^9}[/tex]
Step-by-step explanation:
The simplified form of (3x²y³/z³)³ is 27x⁶y⁹/z⁹.
To simplify the expression (3x²y³/z³)³, we apply the rules of exponents. When we raise a power to another power, we multiply the exponents.
First, let's apply the exponent of 3 to each term inside the parentheses:
(3x²y³/z³)³ = 3³ × (x²)³ × (y³)³ / (z³)³
Simplifying further:
= 27 × x⁶ × y⁹ / z⁹
Therefore, the simplified form of (3x²y³/z³)³ is 27x⁶y⁹/z⁹.
This means that each term inside the parentheses is raised to the power of 3, resulting in the expression 27x⁶y⁹/z⁹.
The final expression represents the cube of the original expression, where each term is cubed individually. The exponents are multiplied by 3 to reflect this operation.
In summary, the simplified form is 27x⁶y⁹/z⁹.
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Solve the system using elimination. x – y = –5 3x + y = 1
(–1, 4)
(–1, 2)
(2, –2)
(–3, 4)
Answer:
(–1,4)
Step-by-step explanation:
x – y = –5
3x + y = 1
You omit Ys due to their positive and negative signs and you got
4x = –4===> x= –1
and now place –1 inside the upper linear equation and there you have the Y, look
–1 – Y= –5===> –Y= –4===> Y = 4
(–1,4)
Keith used the following steps to find the inverse of f, but he thinks he made an error.
Х/10 is between 1/5
and 0.6. What could the value of x be?
Answer:
2 < x < 6
Step-by-step explanation:
x/10
1/5 = 2/10
.6 = 6/10
2 < x < 6
Tom swims a 1/2 kilometers every 1/4 hour. How far will he swim in one hour.
Answer:
2 kilometers
Step-by-step explanation:
every 1 kilometer is a 1/2 hour. double that and you get 2
How many voters should be sampled for a 95% confidence interval? Round up to the nearest whole number.
Answer:
467 voters
Step-by-step explanation:
Given
See attachment for complete question
Required
Sample size at 95% confidence interval
From the attachment, we have:
[tex]p = 65\% = 0.65[/tex]
[tex]E = 4.33\% = 0.0433[/tex]
[tex]CL = 0.95[/tex]
[tex]\alpha = 0.05[/tex] i.e. 1 - CL
First, we calculate the critical level
At [tex]CL = 0.95[/tex] and [tex]\frac{\alpha}{2}[/tex]
[tex]z^* = 1.96[/tex] --- the critical level
So, we have:
[tex]n = p * (1 - p) * (\frac{z^*}{E})^2[/tex]
[tex]n = 0.65 * (1 - 0.65) * (\frac{1.96}{0.0433})^2[/tex]
[tex]n = 0.65 * (1 - 0.65) * (45.3)^2[/tex]
[tex]n = 0.65 * 0.35 * 2052.1[/tex]
[tex]n = 466.9[/tex]
[tex]n = 467[/tex] --- approximated
Question 3
Solve In(x + 1) = 1.
A) X= 2
B) x = e + 1
C)x= e
D)x= e-1
Answer:
D) x = e - 1
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra II
Natural Logarithms ln and Euler's number eSolving logarithmic equationsStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle ln(x + 1) = 1[/tex]
Step 2: Solve for x
[Equality Property] e both sides: [tex]\displaystyle e^{ln(x + 1)} = e^1[/tex]Simplify: [tex]\displaystyle x + 1 = e^1[/tex][Equality Property] Isolate x: [tex]\displaystyle x = e - 1[/tex]Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 25% of the time, four events 30% of the time, three events 20% of the time, two events 15% of the time, one event 5% of the time, and no events 5% of the time. Find the probability that Javier volunteers for less than three events each month. P (x < 3) = 2 Find the expected number of events Javier volunteers in a month. 3.6 It is given that x must be below a certain value, which limits the rows to use in the PDF table. What is the sum of the probabilities of those rows?
Answer:
[tex]P(x < 3) = 25\%[/tex]
[tex]E(x) = 3[/tex]
Step-by-step explanation:
The given parameters can be represented as:
[tex]\begin{array}{ccccccc}x & {5} & {4} & {3} & {2} & {1}& {0} & P(x) & {25\%} & {30\%} & {20\%} & {15\%} & {5\%} & {5\%} \ \end{array}[/tex]
Solving (a): P(x < 3)
This is calculated as:
[tex]P(x < 3) = P(x = 0) + P(x = 1) + P(x =2)[/tex] ----- i.e. all probabilities less than 3
So, we have:
[tex]P(x < 3) = 5\% + 5\% + 15\%[/tex]
[tex]P(x < 3) = 25\%[/tex]
Solving (b): Expected number of events
This is calculated as:
[tex]E(x) = \sum x * P(x)[/tex]
So, we have:
[tex]E(x) = 5 * 25\% + 4 * 30\% + 3 * 20\% + 2 * 15\% + 1 * 5\% + 0 * 5\%[/tex]
[tex]E(x) = 125\% + 120\% + 60\% + 30\% + 5\% + 0\%[/tex]
[tex]E(x) = 340\%[/tex]
Express as decimal
[tex]E(x) = 3.40[/tex]
Approximate to the nearest integer
[tex]E(x) = 3[/tex]
The x intercepts of the function f(x) = 2x(x-5)^2(x+4)^3
are…
Answer:
[tex]\boxed{\sf x- intercepts = 0 , 5 \ and \ -4}[/tex]
Step-by-step explanation:
A function is given to us and we need to find the x Intercepts of the graph of the given function . The function is ,
[tex]\sf \implies f(x) = 2x( x - 5 ) ^2(x+4)^3 [/tex]
For finding the x intercept , equate the given function with 0, we have ;
[tex]\sf \implies 2x ( x - 5 )^2(x+4)^3= 0 [/tex]
Equate each factor with 0 ,
[tex]\sf \implies 2x = 0[/tex]
Divide both sides by 2 ,
[tex]\sf \implies\bf x = 0[/tex]
Again ,
[tex]\sf \implies ( x - 5)^2=0 [/tex]
Taking squareroot on both sides,
[tex]\sf \implies x - 5 = 0 [/tex]
Add 5 to both sides,
[tex]\sf \implies \bf x = 5[/tex]
Similarly ,
[tex]\sf \implies \bf x = -4 [/tex]
Hence the x Intercepts are -4 , 0 and 5 .
{ See attachment also for graph } .
What is the explicit formula for the geometric sequence with this recursive
formula?
a =
8
2.-1
(
O A... ----(3)
O B.
11
1
6
• (-4)(n-1)
OC. ,- 1.(-6)(n-1)
=
OD. 2, --5•()
160
Answer:
D)
[tex]an = -6 \times {( \frac{1}{4} )}^{n - 1} [/tex]
Step-by-step explanation:
(See the picture)
The explicit formula is given as [tex]T_n=-6(\frac{1}{4} )^{n-1}[/tex]
Geometric and recursive functionsThe general explicit formula for a geometric sequence is expressed as:
[tex]T_n=ar^{n-1}[/tex]Given the following recursive functions:
[tex]a_1=-6\\ a_n=a_{n-1}\cdot\frac{1}{4} [/tex]
Get the next two terms:
[tex]a_2=a_{1}\cdot\frac{1}{4} \\ a_2=-6\cdot\frac{1}{4} \\ a_2=\frac{-3}{2} [/tex]
For the third term:
[tex]a_3=a_{2}\cdot\frac{1}{4} \\ a_3=\frac{-3}{2} \cdot\frac{1}{4} \\ a_3=\frac{-3}{8} [/tex]
The common ratio for the sequence will be [tex]\frac{1}{4} [/tex]
The explicit formula is given as [tex]T_n=-6(\frac{1}{4} )^{n-1}[/tex]
Learn more on explicit functions here: https://brainly.com/question/10308651
what is the equation of the directx for the following parabola -8(x-5)=(y+1)^2
Answer:
x=7
Step-by-step explanation:
The directrix of a parabola is the vertical line found by subtracting
p from the x-coordinate h
of the vertex if the parabola opens left or right.
x=h-p
Substitute the known values of
p and h
into the formula and simplify.
x=7
2. The prices, in dollars per unit, of the three commodities X, Y and Z are x, y and z,
respectively
Person A purchases 4 units of Z and sells 3 units of X and 3 units of Y.
Person B purchases 3 units of Y and sells 2 units of X and 1 unit of Z.
Person C purchases 1 unit of X and sells 4 units of Y and 6 units of Z.
In the process, A, B and C earn $40, $50, and $130, respectively.
a) Find the prices of the commodities X, Y, and Z by solving a system of linear
equations (note that selling the units is positive earning and buying the units is
negative earning).
Answer:
Price of X is $24.81
Price of Y is $3.66
Price of Z is $11.36
Step-by-step explanation:
for person A, we know that earns $40, then we can write the equation:
-4*z + 3*x + 3*y = $40
For person B, we know that earns $50, then:
1*z + 2*x - 3*y = $50
For person C, we know that earns $130, then:
6*z - 1*x + 4*y = $130
Then we have a system of equations:
-4*z + 3*x + 3*y = $40
1*z + 2*x - 3*y = $50
6*z - 1*x + 4*y = $130
To solve the system, we need to isolate one of the variables in one of the equations.
Let's isolate z in the second equation:
z = $50 - 2*x + 3*y
now we can replace this in the other two equations:
-4*z + 3*x + 3*y = $40
6*z - 1*x + 4*y = $130
So we get:
-4*($50 - 2*x + 3*y) + 3*x + 3*y = $40
6*($50 - 2*x + 3*y) - 1*x + 4*y = $130
Now we need to simplify both of these, so we get:
-$200 + 11x - 9y = $40
$350 - 13*x + 28*y = $130
Now again, we need to isolate one of the variables in one of the equations.
Let's isolate x in the first one:
-$200 + 11x - 9y = $40
11x - 9y = $40 + $200 = $240
11x = $240 + 9y
x = ($240 + 9y)/11
Now we can replace this in the other equation:
$350 - 13*x + 28*y = $130
$350 - 13*($240 + 9y)/11 + 28*y = $130
Now we can solve this for y.
- 13*($240 + 9y)/11 + 28*y = $130 - $350 = -$220
-13*$240 - (13/11)*9y + 28y = - $220
y*(28 - (9*13/1) ) = -$220 + (13/11)*$240
y = ( (13/11)*$240 - $220)/(28 - (9*13/1) ) = $3.66
We know that:
x = ($240 + 9y)/11
Replacing the value of y, we get:
x = ($240 + 9*$3.66)/11 = $24.81
And the equation of z is:
z = $50 - 2*x + 3*y = $50 - 2* $24.81 + 3*$3.66 = $11.36
Then:
Price of X is $24.81
Price of Y is $3.66
Price of Z is $11.36
Consider a parallelogram in which one side is 3 inches long, another side measures 4 inches, and the measurement of one angle is 45°. How many parallelograms can you construct given these conditions? What are the lengths of the sides and the measurements of the angles for the parallelogram(s)? Using the given information, can you determine the lengths of all the sides of the parallelogram? If so, what are the side lengths?
9514 1404 393
Answer:
(a) one parallelogram
(b) opposite sides are 3 inches and 4 inches. Opposite angles are 45° and 135°
(c) yes, all side lengths can be determined, see (b)
Step-by-step explanation:
Opposite sides of a parallelogram are the same length, so if one side is 3 inches, so is the opposite side. Similarly, if one side is 4 inches, so is the opposite side. If sides have different lengths, they must be adjacent sides. The given numbers tell us the lengths of all of the sides.
The 4 inch sides are adjacent to the 3 inch sides. Thus the angle between a 4 inch side and a 3 inch side must be 45°. Opposite angles are congruent, and adjacent angles are supplementary, so specifying one angle specifies them all.
Only one parallelogram can be formed with these sides and angles. (The acute angle can be at the left end or the right end of the long side. This gives rise to two possible congruent orientations of the parallelogram. Because these are congruent, we claim only one parallelogram is possible. Each is a reflection of the other.)
What is the domain of the function f(x) =x+1/
X^2-6x+8?
Answer:
The domain of the function is all real values of x, except [tex]x = 4[/tex] and [tex]x = 2[/tex]
Step-by-step explanation:
We are given the following function:
[tex]f(x) = \frac{x+1}{x^2-6x+8}[/tex]
It's a fraction, so the domain is all the real values except those in which the denominator is 0.
Denominator:
Quadratic equation with [tex]a = 1, b = -6, c = 8[/tex]
Using bhaskara, the denominator is 0 for these following values of x:
[tex]\Delta = (-6)^2 - 4(1)(8) = 36-32 = 4[/tex]
[tex]x_{1} = \frac{-(-6) + \sqrt{4}}{2} = 4[/tex]
[tex]x_{2} = \frac{-(-6) - \sqrt{4}}{2} = 2[/tex]
The domain of the function is all real values of x, except [tex]x = 4[/tex] and [tex]x = 2[/tex]
change the standard form equation into slope intercept form 13x-7y=23.
If ABC is reflected across the y-axis, what are the coordinates of C?
A. (-8, -4)
B. (8,-4)
C. (-8,4)
D. (4,-8)
Answer:
c....................
Let f(x) = -2x + 7 and g(x) = -6x + 3. Find f.g and state its domain.
-14x^2 + 36x - 18; all real numbers
12x^2 - 48x + 21; all real numbers
-14x^2 + 36x - 18; all real numbers except x = 7
12x^2 - 48x + 21; all real numbers except x = 1
Answer:
Not sure if this is right, but I hope it helps. Please see attached pic
Step-by-step explanation:
Find the number of integers n that satisfy n^2 < 100.
Answer:
n=-9,-8,-7
Step-by-step explanation:
n<100
but that is the positive square root
\(-10 n is between the negative and positive square root of 100
thus, n=-9,-8,-7
The solution of the inequality n² < 100 will be less than 10.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The inequality is given below.
n² < 100
Simplify the equation, then we have
n² < 100
n² < 10²
n < 10
The solution of the inequality n² < 100 will be less than 10.
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