we want to find the number of hours (or rather days) until only 4.25% of the drives fail.
that means for an exponential distribution we have
P(X < x) = 1 - e^(-Lx)
L = 1/mean = 1/12500
and we need to find x, so that P(X <x) = 0.0425 (that is 4.25% converted into a probability).
so, we get
0.0425 = 1 - e^(-x/12500)
0.0425 - 1 = -e^(-x/12500)
-0.9575 = -e^(-x/12500)
0.9575 = e^(‐x/12500)
ln(0.9575) = -x/12500
-x = ln(0.9575)×12500
x = -ln(0.9575)×12500 = - -0.043429558...×12500 =
= 0.043429558...×12500 = 542.8694741... hours
after 542.8694741... hours = 22.61956142... days
it is expected that 4.25% of the hard drives fail.
you left out to what decimal this should be rounded. and if you need hours or days. in case of doubt use hours (as the only other time information is given in hours).
please round yourself as you need.
please help me, i will mark the brainliest pls!
Answer:
YES
Step-by-step explanation:
The blanks would be (5 x 6) - (5 x 3) hope this helps :)
Represent absolute value, not brackets. Calculate the value of this expression: |-7|×|5|+18÷|-6|. -38, -35, 32, 38.
Answer:
38
Step-by-step explanation:
|-7|×|5|+18÷|-6|
First take the absolute value of each number, which means take the positive value
7×5+18÷6
Multiply and divide from left to right
35 + 3
Then add
38
brainliest to correct quickly
Learning Task 3 Answer the questions that follow. Put a check mark (/) on the space provided. Copy and answer in your math notebook. 1. The units for Volume are always ______squared _____cubed 2. Volume is the amount of space an object takes up. ___True ___False Calculate for the volume of solid. 3. Chona is selling Pringle Chips to raise money for a field trip. The container has a diameter of 9 inches and a height of 32 inches. 4. A 3-tier cake with the same height of 10 in and radius of 12 in, 8 in, 5 in respectively is to be delivered to a birthday party. How much space does this cake take up? Use 3.14 for π. 5. A Styrofoam model of a volcano is in the shape of a cone. The model has a circular base with a diameter of 48 centimeters and a height of 12 centimeters. Find the volume of foam in the model to the nearest tenth. Use 3.14 for π.
3. The volume of the Pringle Chips container is approximately 2034.72 cubic inches.
4. The cake takes up approximately 7317 cubic inches of space.
5. The volume of foam in the model of the volcano is approximately 7234.08 cubic centimeters.
1. The units for Volume are always cubed.
2. Volume is the amount of space an object takes up. True.
3. To calculate the volume of the Pringle Chips container, we need to find the volume of a cylinder. The formula for the volume of a cylinder is V = πr^2h, where π is a constant (approximately 3.14), r is the radius, and h is the height. Given that the diameter is 9 inches, the radius would be half of that, which is 4.5 inches. Substituting the values into the formula, we have:
V = 3.14 * (4.5)^2 * 32
V = 3.14 * 20.25 * 32
V ≈ 2034.72 cubic inches
4. To find the volume of the 3-tier cake, we need to find the volume of each tier separately and then add them together. Since all the tiers are cylinders, we can use the formula V = πr^2h.
Tier 1:
V1 = 3.14 * (12)^2 * 10 = 4521.6 cubic inches
Tier 2:
V2 = 3.14 * (8)^2 * 10 = 2010.4 cubic inches
Tier 3:
V3 = 3.14 * (5)^2 * 10 = 785 cubic inches
Total volume:
Total V = V1 + V2 + V3
Total V = 4521.6 + 2010.4 + 785
Total V ≈ 7317 cubic inches
5. To find the volume of the Styrofoam model of the volcano, we can use the formula for the volume of a cone, V = (1/3)πr^2h. Given that the diameter is 48 centimeters, the radius would be half of that, which is 24 centimeters. Substituting the values into the formula, we have:
V = (1/3) * 3.14 * (24)^2 * 12
V = (1/3) * 3.14 * 576 * 12
V ≈ 7234.08 cubic centimeters
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i dont understand this
We can Add 7 black beads to make ratio 3 : 1.
Since we can only change the number of black beads, decide how many black beads you will add based on how many white beads there are.
There are three white beads in the picture.
Total beads we will have (b meaning black)b : 3
Ratio black : white beads 3 : 1
Use the common ratio, which is a number that both sides of the original ratio multiply by to get to the new ratio.
Find common ratio by dividing total by ratio white beads: 3/1 = 3
Multiply ratio black beads by common ratio. 3 X 3 = 9
We need 9 black beads in total.
Check answer
9 : 3
Both sides divisible by 3; reduce ratio
= 3 : 1
Which is Correct ratio
Hence, There will be a total of 9 black beads, but we already have 2 black beads:
(9 total) - (2 original) = (7 to add)
Therefore , we need to add 7 black beads.
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This graph represents the demand for health supplements in Oklahoma. Match each section of the function to the description of how the y-value changes as the x-value increases. increases quickly increases slowly decreases slowly decreases quickly A arrowRight B arrowRight C arrowRight D arrowRight
The appropriate description of the graph is as follows
1. The demand for health supplements in Oklahoma A: increases slowly.
2. The demand for health supplements in Oklahoma B: Decreases quickly.
3. The demand for health supplements in Oklahoma for C: Increases quickly.
4. The demand for health supplements in Oklahoma for D: decreases slowly.
How to interpret lines on a graph?To interpret lines on a graph, we must first note that those lines mean a number of things but ultimately, the tell or show is the relationship between two or more variables.
In the case of the Oklahoma graphs, we know that the lines represents the deman for health supplements. However, what we don't know are those factors that are causing the demands to increase or decrease.
The above answer is for the graph below that has been attached.
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help me please i will heart the first correct comment
Fill in the blanks to complete the rule
uh i could never, sorry
Use vectors to find the interior angles of the triangle with the given vertices. (Enter your answers as a comma-separated list. Enter your answers in terms of degrees. Round your answers to two decimal places.)
(−2, 4), (−3, 8), (6, 8)
Please Help ASAP
Answer:
77.47°
75.96°
26.57°
Step-by-step explanation:
Given vertices of the triangle:
A = (−2, 4)B = (−3, 8)C = (6, 8)Find the vectors from A to B, B to C and A to C:
\(\begin{aligned}AB = B - A &=(x_B-x_A,y_B-y_A) \\&=(-3-(-2), 8-4)\\& = (-1, 4) \end{aligned}\)
\(\begin{aligned}BC=C-B &=(x_C-x_B,y_C-y_B)\\ &=(6-(-3),8-8)\\&=(9,0)\end{aligned}\)
\(\begin{aligned}AC = C - A &=(x_C-x_A,y_C-x_A)\\&= (6-(-2), 8-4) \\&= (8, 4)\end{aligned}\)
Use Pythagoras Theorem to calculate the magnitudes of the vectors:
\(|AB| = \sqrt{(-1)^2+4^2}=\sqrt{17}\)
\(|BC|=\sqrt{9^2+0^2}=9\)
\(|AC| = \sqrt{8^2+4^2}=4\sqrt{5}\)
\(\boxed{\begin{minipage}{6 cm}\underline{Dot Product of two vectors}\\\\$a \cdot b=|a||b| \cos \theta$\\\\where:\\ \phantom{ww}$\bullet$ $|a|$ is the magnitude of vector a. \\ \phantom{ww}$\bullet$ $|b|$ is the magnitude of vector b. \\ \phantom{ww}$\bullet$ $\theta$ is the angle between $a$ and $b$. \\ \end{minipage}}\)
Rearrange the dot product formula to make θ the subject:
\(\implies \theta=\cos^{-1}\left(\dfrac{a \cdot b}{|a||b|}\right)\)
Use the rearranged dot product formula to find the angles between two pairs of vectors.
\(\boxed{\begin{minipage}{4 cm}\underline{Dot Product}\\\\$\textbf{u} \cdot \textbf{v}=u_1v_1+u_2v_2$\\\\where:\\ \phantom{ww}$\bullet$ $\textbf{u}=\left\langle u_1,u_2 \right\rangle$ \\\phantom{ww}$\bullet$ $\textbf{v}= \left\langle v_1,v_2 \right\rangle$ \\ \end{minipage}}\)
Angle A
\(\implies A=\cos^{-1}\left(\dfrac{AB \cdot AC}{|AB||AC|}\right)\)
\(\implies A=\cos^{-1}\left(\dfrac{-1 \cdot 8+4 \cdot4}{\sqrt{17} \cdot 4 \sqrt{5}}\right)\)
\(\implies A=\cos^{-1}\left(\dfrac{8}{4 \sqrt{85}}\right)\)
\(\implies A=77.47^{\circ}\; \sf (2 \; d.p.)\)
Angle C
\(\implies C=\cos^{-1}\left(\dfrac{BC \cdot AC}{|BC||AC|}\right)\)
\(\implies C=\cos^{-1}\left(\dfrac{9 \cdot 8+0 \cdot4}{9 \cdot 4 \sqrt{5}}\right)\)
\(\implies C=\cos^{-1}\left(\dfrac{72}{36 \sqrt{5}}\right)\)
\(\implies C=26.57^{\circ}\; \sf (2 \; d.p.)\)
Interior angles of a triangle sum to 180°.
\(\implies B=180^{\circ}-A-C\)
\(\implies B=180^{\circ}-77.47^{\circ}-26.57^{\circ}\)
\(\implies B=75.96^{\circ}\)
Therefore, the interior angles of the triangle with the given vertices are:
77.47°75.96°26.57°On a map, 1 inch equals 20 miles. If two cities are 3 inches apart on the map, how far are they actually apart?
Answer: 60 miles
Step-by-step explanation:
1 in. times 3 = 3 in
20 mi times 3 = 60 mi.
What system of equations is shown on the graph below
Answer:
A.
Step-by-step explanation:
x-2y=4 has a x-intercept of 4, a slope of 1/2, and a y-intercept of -2. 2x+y=4 has a x-intercept of -2, a slope of 2, and a y-intercept of -4.
For the student council meeting after school, Mr. Aggie brought 7 loaves of homemade raisin bread. Each loaf was cut into 20 equal pieces. The sixth grade students ate 1 whole loaf and 4 slices of raisin bread. The seventh grade students ate 9 slices of raisin bread. The eighth grade students ate 6 slices of raisin bread. Which expression below can be used to show the amount of raisin bread eaten by the student council members?
Answer:
proportion of ratio will be used
Answer:
C. 1 4/10 + 9/10 + 6/10
got it right
Based on the figure, which statement provides enough information to conclude that line ris
perpendicular to line p?
O m/2 = 90°
O m26 = 90°
O m/1+ m26 = 90°
O m/3 + m24 = 90°
Answer:
m<6 = 90°
Step-by-step explanation:
If lines are perpendicular, the angles form by their intersection measure 90°.
Answer: m<6 = 90°
Based on the figure, correct statement provides enough information to conclude that line r is perpendicular to line p is,
⇒ m ∠6 = 90 degree
We have to given that,
Three lines r, n and p are shown in figure.
Now, We know that,
If a line is perpendicular to another line then it make a right angle in between them.
Hence, By given figure, correct statement provides enough information to conclude that line r is perpendicular to line p is,
⇒ m ∠6 = 90 degree
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Which inequality is equivalent to the given inequality? -4(x+7)< 3(x-2)
An equivalent inequality to the given \(-4(x + 7) < 3(x - 2)\) is \(7x > -22.\)
To find an equivalent inequality, we can start by simplifying the given inequality and then make adjustments to preserve its truth.
Let's simplify the given inequality step by step:
\(-4(x + 7) < 3(x - 2)\)
Expanding both sides:
\(-4x - 28 < 3x - 6\)
Grouping like terms:
\(-4x - 3x < -6 + 28\)
Simplifying:
\(-7x < 22\)
To maintain the direction of the inequality, we need to multiply both sides by -1.
However, when we multiply or divide both sides of an inequality by a negative number, the direction of the inequality is reversed.
Therefore, we need to flip the inequality sign:
\(7x > -22\)
Hence, an equivalent inequality to the given \(-4(x + 7) < 3(x - 2)\) is
\(7x > -22.\)
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A positive integer is 1 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is 2, then find the two integers.
The two integers are 1 and 2.
What do you mean by Integers?An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.
Integer is a Latin word which means 'whole' or 'intact'. This means integers do not include fractions or decimals.
A number is positive if it is greater than zero, so they are positive integer.
A number is negative if it is less than zero, so they are negative integer.
A number line is a visual representation of numbers on a straight line. This line is used for comparison of numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally.
Given:
x be a positive number
x + 1 = y
The sum of reciprocal of the smaller and twice the reciprocal of the larger number
Substitute
\(\frac{1}{x} + \frac{2}{y} = 2\)
\(\frac{1}{x} + \frac{2}{x + 1} = 2\)
\(\frac{x+ 1 + 2x}{x(x +1)} = 2\)
\(x + 1 + 2x = 2x^2 + 2x\)
Subtracting 2x on both sides, we get
x + 1 + 2x - 2x = 2x² + 2x - 2x
x + 1 = 2x²
2x² - x - 1 = 0
2x² - 2x + x - 1 = 0
2x(x - 1) + 1(x - 1) = 0
(2x + 1)(x - 1) = 0
x = -1/2 and x = 1
But x = -1/2 is not possible. Becuase x is a positive number.
So, x = 1
y = x + 1
y = 2
The two integers are 1 and 2.
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Which choice shows (50 + 20) + 30 correctly rewritten using the associative
property and then correctly simplified?
Answer:
100Step-by-step explanation:
BIDMAS
do the bracket first
50+20=70
70+30=100
FILL IN THE BLANK.A point that moves on a coordinate line is said to be in simple ___ ___ if its distance d from origin at time t is given by either d=a sinωt or d=a cosωt.
"A point that moves on a coordinate line is said to be in simple harmonic motion if its distance d from origin at time t is given by either d = a sinωt or d = a cosωt."
Any function which is written in the form 'a sin(ωt+Ф)' and 'a cos(ωt+Ф)' is said to be a simple harmonic motion.
One definition of a periodic motion is a straightforward harmonic motion. The acceleration of the particle at any location is directly proportional to the displacement from the mean position in simple harmonic motion, which is an oscillatory motion.
Simple harmonic motion, or SHM, is a specific type of repeated or periodic motion that describes the motion of the pendulum. The oscillating object's location changes sinusoidally over time.
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A package in the shape of a rectangular prism has a length of 412 feet, a width of 234 feet, and a height of 213 feet.
What is the volume, in cubic feet, of the package?
Answer:
b , 16 11/12
Step-by-step explanation:
Mr. Jackson was born on January 1, 1970. His daughter Lea was born on
January 1, 1992. In what year was Mr. Jackson exactly three times as old
as Lea?
2003 - Lea would be 11, and as there is 22 years between them Mr Jackson would be 33, which is 11 X 3.
Review the graph.
On a coordinate plane, a circle has center (4, 0) and radius 4. Another circle has center (2, negative 3) and radius 6. The area inside of the first circle and outside of the second circle between the 2 circles is shaded.
Which system of inequalities is shown in the graph?
36 > (x + 3)2 + (y – 2)2 and 16 > (x – 4)2 + y2
36 > (x – 2)2 + (y + 3)2 and 16 > (x – 4)2 + y2
36 < (x + 3)2 + (y – 2)2 and 16 > (x – 4)2 + y2
36 < (x – 2)2 + (y + 3)2 and 16 > (x – 4)2 + y2
Answer:
36 < (x - 2)² + (y + 3)² and 16 > (x - 4)² + y²
Step-by-step explanation:
This is because the shaded area is inside the first circle (centered at (4, 0) with a radius of 4) but outside the second circle (centered at (2, -3) with a radius of 6). The inequalities reflect these conditions by setting the inequality signs accordingly. The inequality with "<" for the first circle ensures that the shaded area is within the circle, and the inequality with ">" for the second circle ensures that the shaded area is outside the circle.
1) write the equation of the
line in slope intercept form
that passes through (0,-2)
and (2,1).
Answer:
y=3/2x-2
Step-by-step explanation:
Find the slope first:
\(m=\frac{y_{2-y_{1} } }{x_{2}-x_{1} } =\frac{1-(-2)}{2-0}=\frac{3}{2}\)
Then solve for y-intercept:
\(y=\frac{3}{2}x+b\\-2=\frac{3}{2}(0)+b\\-2=b\)
Now, write out your complete equation:
y=3/2x-2
Which chart has an equation of y = 2.75x?
Answer:
None of it.
Step-by-step explanation:
Notice the slope is 2.75 this means for EVERY X the graph goes up by 2.75 in the Y axis. For example.
If at X=1 y=0
Then for X=2 y=2.75
and for X=3 y=2.75+2.75=5.5
also the graph must pass thought point (0,0), the origin, and none of the graph follow this.
You can also compare the slopes of each equations
for graph A, from x=1 to x=2 the height Y goes from 3 to 3.5, this is a slope of 0.5 (not the 2.75 we are looking for)
for graph A, from x=1 to x=2 the height Y goes from 1 to 2.5, this is a slope of 1.5 (not the 2.75 we are looking for)
for graph A, from x=1 to x=2 the height Y goes from 1 to 2.75 this is a slope of 1.75 (not the 2.75 we are looking for)
notice the last is similar to equation y=1.75X+b, just in case.
Answer:
none
Step-by-step explanation:
A person buy a lot of tickets for Rs.136 each execution class ticket cost rupees12 and each local class ticket cost for Rs 4 each make an equation and fine explain possible solutions
Answer:
3.98
Step-by-step explanation:
Answer:
the second method may be through graph
) In a geometric progression, the sum of the first two terms is equal to 16. The sum to infinity is equal to 25. Find the possible values of the first term.
There are no possible real values for the first term 'a' that satisfy both equations.
Let's denote the first term of the geometric progression as 'a' and the common ratio as 'r'.
The sum of the first two terms can be expressed as:
a + ar = 16
To find the sum to infinity, we can use the formula:
Sum to infinity = a / (1 - r)
Given that the sum to infinity is 25, we have:
25 = a / (1 - r)
We now have two equations:
a + ar = 16
a / (1 - r) = 25
We can solve these equations simultaneously to find the possible values of 'a'.
From the first equation, we can factor out 'a' to get:
a(1 + r) = 16
Dividing both sides of the second equation by 25, we have:
a / (1 - r) = 1
We can rearrange this equation to get:
a = 1 - r
Substituting this expression for 'a' in the first equation, we get:
(1 - r)(1 + r) = 16
Expanding the equation, we have:
1 - r^2 = 16
Rearranging the terms, we get:
r^2 = -15
Since we are dealing with a geometric progression, the common ratio 'r' must be a real number. However, we observe that r^2 = -15 has no real solutions. Therefore, there are no possible real values for the first term 'a' that satisfy both equations.
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Given ΔMNO, find the measure of ∠MNO.
Triangle MNO with segment LM forming a straight angle with segment MO and segment OP forming a straight angle with segment MO, the measure of angle NOP is 104 degrees, and segment MN and NO are marked congruent.
28 degrees
38 degrees
52 degrees
76 degrees
I know the answer is 28 degrees , I just am not sure how to work out this problem .
Answer:10907
Step-by-step explanation 10907
Answer:
The answer is 28
Step-by-step explanation:
Hope this helps,
have a great day
A smart phone manufacturer wants to determine the average battery time that its new smart phone will get. The manufacturer will test 100 smart phones. Match the strategies to their corresponding sampling techniques.
a. The manufacturer tests 20 smart phones from each of its five equally sized distributors.
b. The manufacturer tests every 1000th smart phone that comes off the assembly line.
c. The manufacturer uses a computer to randomly select 150 smart phone serial numbers and tests all 150 phones with these serial numbers.
d. The manufacturer asks 100 of her friends who have the phone if she can borrow their phones to test.
e. The manufacturer finds three small communities that have dry moderate and humid climates and every smart phone from each of these three communities is tested.
1. Simple Random Sampling
2. Cluster Sampling
3. Stratified Sampling
4. Convenience Sampling
5. Systematic Sampling
Using sampling concepts, it is found that the matches of the strategies to their corresponding sampling techniques are given by:
a - 3.b - 5.c - 1.d - 4.e - 2.How are samples classified?Samples are classified as:
Convenient: Drawn from a conveniently available pool.Random: All the options into a hat and drawn some of them.Systematic: Every kth element is taken. Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.Stratified: Also divides the population into groups. Then, a equal proportion of each group is surveyed.Item a:
Population divided into equally-sized groups(by distributors), and the same number from each is taken, hence stratified sampling is used, and the matching is a - 3.
Item b:
Every kth piece, hence systematic sampling is used, and the matching is b - 5.
Item c:
150 phones are chosen randomly, hence random sampling and the matching is c - 1.
Item d:
Asks friends, so by convenience sampling, hence the matching is d - 4.
Item e:
Divided into groups(by communities), all elements are surveyed, hence cluster sampling and the matching is e - 2.
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Trying to do this question.
The algorithm is tripping! It won't let me post a legit explanation. Sorry!
E09 Review
Scores on "The ability to do quantitative thinking" test are normally distributed with a mean of 250 and a standard deviation of
25. Brandi scored at the 81st percentile on this test. What was her test score?
is the test score for Brandi.
Answer:
272 is the test score for Brandi.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
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.
Mean of 250 and standard deviation of 25:
This means that \(\mu = 250, \sigma = 25\)
Brandi scored at the 81st percentile on this test. What was her test score?
The z-score of her score of X has a p-value of 0.81. This means that her score is given by X when Z = 0.88.
\(Z = \frac{X - \mu}{\sigma}\)
\(0.88 = \frac{X - 250}{25}\)
\(X - 250 = 0.88*25\)
\(X = 272\)
272 is the test score for Brandi.
What is the probability that a student chosen randomly from the class does not have a cat
Answer:
20/27 or 0.74
Step-by-step explanation:
The total number of people is: 2+6+5+14 = 27
Total number of people that don't have a cat is: 6+14 = 20
20/27 = 0.74
A house was valued at $299,000 . Over several years, the value decreased by, 9% giving the house a new value.
(a) Fill in the blank to write the new value in terms of the old value.
Write your answer as a decimal.
(b) Use your answer in part (a) to determine the new value.
A) - The NEW VALUE in terms of the old value is 0.91 times the old value.
B) - The NEW VALUE of the HOUSE is: 299,000 * 0.91 = $272,090
Step-by-step explanation:Make A Plan:
A) - Calculate the Percentage of the Value Remaining After the Decrease
B) - Calculate the NEW VALUE of the house
SOLVE THE PROBLEM:
A) - The PERCENTAGE of the VALUE REMAINING AFTER the DECREASE
100% - 9% = 91%
As A DECIMAL:0.91
B) - Calculate the NEW VALUE of the house:
NEW VALUE = OLD VALUE * REMAINING PERCENTAGE
NEW VALUE = 299,000 * 0.91
Draw the conclusion:
A) - The NEW VALUE in terms of the old value is 0.91 times the old value.
B) - The NEW VALUE of the HOUSE is: 299,000 * 0.91 = $272,090
I hope it helps!