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
for a science fair project javier is recording the amount of water that evaporate from a bucket in a month he creates a table like this i will give point for the best answer
week 1 2/16 inch
week 2 1/16 inch
week 3 3/16 inch
week 4 2/16 inch
how much water had evaported from the bucket at the end of week 2
what was the total amount of water that evaported in the four weeks
if javier orignally put 4 inches of water in the bucket how many inches of water were left after the experment was completed
Answer: [tex]\dfrac{3}{16},\ \dfrac{1}{2}, \dfrac{7}{2}\ \text{inch}[/tex]
Step-by-step explanation:
Given
Javier created a table for the amount of water evaporated in each week
After two weeks, the amount of water evaporated is
[tex]\Rightarrow \dfrac{2}{16}+\dfrac{1}{16}\\\\\Rightarrow \dfrac{2+1}{16}=\dfrac{3}{16}\ \text{inch}[/tex]
Total amount of water evaporated in four weeks is
[tex]\Rightarrow \dfrac{2}{16}+\dfrac{1}{16}+\dfrac{3}{16}+\dfrac{2}{16}\\\\\Rightarrow \dfrac{2+1+3+2}{16}=\dfrac{8}{16}\\\Rightarrow \dfrac{1}{2}\ \text{inch}[/tex]
If Javier originally puts 4 inches of water, amount of water left in the bucket
[tex]\Rightarrow 4-\dfrac{1}{2}\\\\\Rightarrow \dfrac{4\times 2}{2}-\dfrac{1}{2}\\\\\Rightarrow \dfrac{8-1}{2}=\dfrac{7}{2}\ \text{inch}[/tex]
Find the equivalent exponential expression.
(543
Answer:
(5) we have multiple the powers
f(x)=2x1 + 16x2 + 7x3 + 4x4 -> min
Step-by-step explanation:
f(x)=(2x-1)square=0
it can be 0 or greater than 0
Hence,maximum value of (2x- 1)square=0
maximum value of (2x- 1square)+3=0+3=3
Hannah ran 12 laps for 8 days. How many laps did she run in total if she take a break of 1 complete day and 1 half day.
Answer:
The correct answer would be - 9.75 laps (if runs 12 laps in 8 days) or 78 laps (if 12 laps each day for 8 days)
Step-by-step explanation:
Given:
a) Laps covered in 8 days = 12
interval = 1 and half day
total laps = ?
Solution:
To know the total laps with intervals we need to calculate the laps run each day :
= 12/8 laps per day
= 3/2 laps per day
Now multiply the daily run with days
= (3/2)*6.5 (due to 8 - 1.5 = 6,5 days)
= 9.75 laps
B) Given:
Laps covered in 8 days = 12*8 =96
interval = 1 and half day
total laps = ?
Solution:
To know the total laps with intervals we need to calculate the laps run each day :
= 96/8 laps per day
= 12laps per day
Now multiply the daily run with days
= 12*6.5 (due to 8 - 1.5 = 6,5 days)
= 78 laps
What is the value of y?
Enter your answer, as an exact value, in the box.
Answer:
y=4√3 units
Step-by-step explanation:
Hi there!
We are given ΔABC, which is a right triangle (m<C=90°), m<A=60°, AB=8, and BC=y
We need to find the value of y (BC)
The side AB is the hypotenuse of the (the side opposite from the right angle).
BC is a leg, which is a side that makes up the right angle.
Now, if we have a right triangle that has one of the acute angles as 60°, the side OPPOSITE from that 60° angle (in this case, BC) is equal to [tex]\frac{a\sqrt{3}}{2}[/tex], where a is the length of the hypotenuse
Since we have the hypotenuse given as 8, the length of BC (y) is [tex]\frac{8\sqrt{3}}{2}[/tex], or 4√3
so y=4√3 units
Hope this helps!
in a class of 38 student,30 are good in mathematics and 22 are good in physics how many students are good in both mathematics and physics
Answer:
8 are bad in math and 16 in physics
Step-by-step explanation:
On a coordinate plane, 2 triangles are shown. The first triangle has points A (negative 1, negative 2), B (negative 4, negative 2), C (negative 1, negative 4). The second triangle has points A prime (1, 2), B prime (4, 2), C prime (1, 4). What rule describes the rotation about the origin? (x, y) → How many degrees was the figure rotated about the origin?
9514 1404 393
Answer:
(x, y) ⇒ (-x, -y)180°Step-by-step explanation:
Each image point has its signs reversed from the pre-image point.
(x, y) ⇒ (-x, -y) . . . . describes the rotation
Rotation from the third quadrant (A) to the first quadrant (A') is a rotation of 180°.
Answer:
3rd and 2nd option
Step-by-step explanation:
Many electronics follow a failure rate described by an exponential probability density function (PDF). Solar panels are advertised to last 20 years or longer, but panels made in China are failing at a higher rate. The time-to-failure of this device is usually exponentially distributed with mean 13 years. What is the probability of failure in the first 5 years
Answer:
The right answer is "0.3193".
Step-by-step explanation:
According to the question,
Mean,
[tex]\frac{1}{\lambda} = 13[/tex]
[tex]\lambda = \frac{1}{13}[/tex]
As we know,
The cumulative distributive function will be:
⇒ [tex]1-e^{-\lambda x}[/tex]
hence,
In the first 5 years, the probability of failure will be:
⇒ [tex]P(X<5)=1-e^{-\lambda\times 5}[/tex]
[tex]=1-e^{-(\frac{1}{13} )\times 5}[/tex]
[tex]=1-e^(-\frac{5}{13})[/tex]
[tex]=1-0.6807[/tex]
[tex]=0.3193[/tex]
If A = {x, y, z} then the number of non-empty subsets of A is ________.
a) 8 b) 5 c) 6 d) 7
Answer:
(d) 7
Step-by-step explanation:
The total number of subsets that can be derived from a set with n elements is given by;
2ⁿ
Out of these subsets, there is one empty set. Therefore, the total number of non-empty subsets is given by;
2ⁿ - 1
Given:
A = {x, y, z}
Set A has 3 elements. This means that n = 3
Therefore, the total number of subsets that can be derived from set A is
2ⁿ = 2³ = 8
One of these 8 subsets is an empty set, therefore, the total number of non-empty subsets of A is;
2ⁿ - 1 = 2³ - 1
8 - 1 = 7
This can be checked by writing all the possible subsets of A as follows;
∅
{x}
{y}
{z}
{x, y}
{y, z}
{x, z}
{x, y, z}
Removing the empty set ∅, the non-empty subsets of A are;
{x}
{y}
{z}
{x, y}
{y, z}
{x, z}
{x, y, z}
Which would result in a lower price to first discount an item by 10% and then by a further 15%, OR to first discount an item by 15% and then by a further 10%. Justify your reasoning.
Answer:
Neither one. They will both result in the same price.
Step-by-step explanation:
To discount an item 10%, you charge 90% of the price of the item. To find 90% of a price, you multiply the price by 0.9.
To discount an item 15%, you charge 85% of the price of the item. To find 85% of a price, you multiply the price by 0.85.
Since multiplication is commutative, multiplying a number by 0.9 and then by 0.85 is the same as multiplying the number by 0.85 first and then by 0.9.
Let's say the item costs x.
Take off the 10% discount first: 0.9x
Now take off the 15% discount: 0.85 * (0.9x)
Now do it the other way.
Take off the 15% discount first: 0.85x
Now take off the 10% discount: 0.9 * (0.85x)
Since 0.85 * 0.9 * x = 0.9 * 0.85 * x, the results are the same.
Answer: neither
The cardinal number of {200, 201, 202, 203, ..., 1099}
Answer:
I have not been able to answer it sorry
The following figure appears in a math workbook. Students are asked to reflect the polygon across the line, then rotate it 90 degrees clockwise . Which figure shows the result of the two transformations?
Answer:
C
Step-by-step explanation:
tracing paper is your friend
One-ninth of all sales at a local Subway are for cash. If cash sales for the week were $690, what were
Subway's total sales?
Select one:
O a. $22,600
O b. $2,611
O c. $6,210
O d. $2,610
e. None of these
Answer:
c. $6,210Step-by-step explanation:
Total sales = x
x*1/9 = 690x = 690*9x = 6210Correct choice is C
Why is underfind the square root of a negative number?
Answer:
The square root of a negative number is undefined, because anything times itself will give a positive (or zero) result. Note: Zero has only one square root (itself). Zero is considered neither positive nor negative
Answer:
sjshzhshshdhdgdgdhdhdgshshshshshwywhwhw
Explain how to divide a decimal by a decimal
Answer:
To divide a decimal by another decimal:
Move the decimal point in the divisor to the right until it is a whole number.
Move the decimal point in the dividend to the right by the same number of places as the decimal point was moved to make the divisor a whole number.
Then divide the new dividend by the new divisor
Step-by-step explanation:
see in the example
The formula for the lateral area of a right cone is LA = pi rs, where is the radius of the base and s is the slant height of the cone.
Answer:
r is the radius of the base and s is the slant height of the cone. From the options given, We can make s the subject of the formula. Hence: Option a) s equals StartFraction L A Over pi r EndFraction
Two equivalent equations are s = LA/πr and r = LA/πs
What is cone?A cone is a shape formed using a series of line segments or lines that connect a common point, called a apex or vertex, to all points on the base of a circle that do not contain a vertex. The distance from the apex of the cone to the base is the height of the cone. A circular base has a measured radius value. And the length from the apex of the cone to any point around the base is the height of the slope. Equations for the surface area and volume of a cone can be derived from these quantities
Volume(V) = ⅓ πr²h cubic units
The total surface area of the cone = πrs + πr²
where, r is radius of the base, s is slant height and h is height of the cone
Given,
Lateral area of cone is denoted by LA
Lateral area of cone = πrs
where r is radius and s is slant height
⇒ LA = πrs
⇒ s = LA/πr
⇒ r = LA/πs
Hence, s = LA/πr and r = LA/πs are two equivalent equations in the given options.
Learn more about cone here:
https://brainly.com/question/16394302
#SPJ7
calculate the cost of 4 liters of gasoline if 10 Liters of gasoline cost $8.20 (using proportional relationship).
A . $3.28
B. $4.20
C. $8.20
D.$10
Test 21,753 for divisibility by 2,3,5,9 and 10
Answer:
Step-by-step explanation:
21,753
at unit place=3 not an even number,not equal to 5 and not equal to 0
so 21,753 is not divisible by 2,5 and 10
again
2+1+7+5+3=18 divisible by 3 and 9.
so 21,753 is divisible by 3 and 9.
A boy leaves station X on a bearing of 035' to station Y. which is 21km away. He then travels to another station Z on a bearing of 125 degrees . If Z is directly East of X, what is the distance from X to his present position?
9514 1404 393
Answer:
36.6 km
Step-by-step explanation:
We assume the initial bearing of the boy is 35°. Then he will make a 90° turn to a heading of 125°. A diagram shows the distance of interest is the hypotenuse of a right triangle in which 35° is the angle opposite the side of length 21 km.
The relevant trig relation is ...
Sin = Opposite/Hypotenuse
sin(35°) = (21 km)/XZ
XZ = (21 km)/sin(35°) ≈ 36.61 km
The distance from X to Z is about 36.61 km.
_____
The attached diagram has the angles measured in the usual way for a Cartesian plane: CCW from the +x axis. This will correspond to bearing measures if we relabel the axes so that +x is North, and +y is East.
I’ll mark u plz help
Answer:
D is the answer
Step-by-step explanation:
all sides and angles are equal
hope it helps!! let me know if it does
24
4
3+
2+
2
1
-3
-
-1
1
1
2
3
4
-1+
-2 +
-3+
4
What is the slope of the line?
Answer:
1.5/2
Step-by-step explanation:
slope formula = y2-y1/ x2 - x1
point one (2,0)
point 2 (0, 1.5)
you dont really need to subtract anything because the intercepts, so the slope is 1.5/2
(slope or m = 1.5 - 0 / 2 - 0 )
x intercept = value of x when y is 0
y intercept = value of y when x is 0
Un automóvil consume 4 galones de gasolina al recorrer 180 kilómetros y para recorrer 900 kilómetros necesita 20 galones ¿cuántos kilómetros recorre por galón? ¿Cuantos galones consumirá en 2700 kilómetros?
Answer:
45 km por galón
60 galones en 2700 Km
Step-by-step explanation:
180 / 4
45 km por galón
900 / 45
20 galones
2700 / 45
60 galones en 2700 Km
A farmer picks pumpkins from a large field. The farmer makes samples of 260 pumpkins and inspects them. If one in fifty pumpkins are not fit to market and will be saved for seeds, what is the standard deviation of the mean of the sampling distribution of sample proportions?
Answer:
[tex]\mu = 5.2[/tex]
[tex]\sigma = 2.257[/tex]
Step-by-step explanation:
Given
[tex]n = 260[/tex] -- samples
[tex]p = \frac{1}{50}[/tex] --- one in 50
Solving (a): The mean
This is calculated as:
[tex]\mu = np[/tex]
[tex]\mu = 260 * \frac{1}{50}[/tex]
[tex]\mu = 5.2[/tex]
Solving (b): The standard deviation
This is calculated as:
[tex]\sigma = \sqrt{\mu * (1-p)}[/tex]
[tex]\sigma = \sqrt{5.2 * (1-1/50)}[/tex]
[tex]\sigma = \sqrt{5.2 * 0.98}[/tex]
[tex]\sigma = \sqrt{5.096}[/tex]
[tex]\sigma = 2.257[/tex]
FREE
Circle O has a circumference of approximately 250 ft.
What is the approximate length of the diameter, d?
O 40 ft
O 80 ft
O 125 ft
O 250 ft
Save and Exit
Next
Submit
Mark this and return
Answer:
Step-by-step explanation:
circumference = πd ≅ 250 ft
d ≅ 250/π ≅80 ft
log2(6x) – log2 (x)-2
Answer:
xlog(64)−xlog(2)−2
Step-by-step explanation:
Simplify 6log(2) by moving 6 inside the logarithm.
log(2^6)x − log(2)x − 2
Raise 2 to the power of 6.
log(64)x − log(2)x − 2
Reorder factors in log(64)x − log(2)x −2.
Midsegments geometry acellus pls helppfpfpff
Answer:
BC = 28
Step-by-step explanation:
The midsegment DF is half the measure of the third side BC , then
BC = 2 × DF = 2 × 14 = 28
when price of indomie noodles was lowered from #50 to #40 per unit, quantity demanded increases from 400 to 600 units per week. calculate the coefficient of price elasticity of demand and determine whether by lowering price this firm has made a wise decision
Answer:
The price elasticity of demand is -10
Step-by-step explanation:
Given
[tex]p_1,p_2 = 50,40[/tex]
[tex]q_1,q_2 = 400,500[/tex]
Solving (a): The coefficient of price elasticity of demand (k)
This is calculated as:
[tex]k = \frac{\triangle q}{\triangle p}[/tex]
So, we have:
[tex]k = \frac{500 - 400}{40 - 50}[/tex]
[tex]k = \frac{100}{-10}[/tex]
[tex]k = -10[/tex]
Because |k| > 0, then we can conclude that the company made a wise decision.
5. In 2015, Texas led the nation in the percentage of people who lacked health insurance (21.6% of the population). It is known that, nationally, 5% of patients account for 50% of the costs of healthcare. These are the “high cost” patients Assume* that: Being a high cost patient and being uninsured are independent characteristics Insured and uninsured people become “patients” at the same rate The uninsured and high cost patients in Texas are evenly distributed across the state, and that high cost patients are evenly distributed across insured and uninsured patient populations a. What is the probability that a patient in a Texas healthcare facility will be a high cost patient who is uninsured?
Answer: 0.108
Step-by-step explanation:
Since the probability of the uninsured is 21.6% of the population, then the probability of insured will be:
= 1 - 21.6%
= 78.4%
The probability of high cost patients is 5%. Therefore, the probability that a patient in a Texas healthcare facility will be a high cost patient who is uninsured will be:
= 5% × 21.6%
= 0.05 × 0.216
= 0.108
Melanie has D dimes and Q quarters. She has no less than $4 worth of coins altogether. Write this situation as an inequality.
Step-by-step explanation:
D(.10) + Q(.25) = 4
I think
Answer:
D(.10) + Q(.25) = 4
Step-by-step explanation:
Suppose a large shipment of televisions contained 9% defectives. If a sample of size 393 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 3%
Answer:
0.9624 = 96.24% probability that the sample proportion will differ from the population proportion by less than 3%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Suppose a large shipment of televisions contained 9% defectives
This means that [tex]p = 0.09[/tex]
Sample of size 393
This means that [tex]n = 393[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.09[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.09*0.91}{393}} = 0.0144[/tex]
What is the probability that the sample proportion will differ from the population proportion by less than 3%?
Proportion between 0.09 - 0.03 = 0.06 and 0.09 + 0.03 = 0.12, which is the p-value of Z when X = 0.12 subtracted by the p-value of Z when X = 0.06.
X = 0.12
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.12 - 0.09}{0.0144}[/tex]
[tex]Z = 2.08[/tex]
[tex]Z = 2.08[/tex] has a p-value of 0.9812
X = 0.06
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.06 - 0.09}{0.0144}[/tex]
[tex]Z = -2.08[/tex]
[tex]Z = -2.08[/tex] has a p-value of 0.0188
0.9812 - 0.0188 = 0.9624
0.9624 = 96.24% probability that the sample proportion will differ from the population proportion by less than 3%
