Answer:\(x^{-2}\)
Have attached the solution below for better understanding of the question, hope that helps:
A new model of laptop computer can be ordered with one of three screen sizes (10 inches, 12 inches, 15 inches) and one of four hard drive sizes (50 GB, 100 GB, 150 GB, and 200 GB). Consider the chance experiment in which a laptop order is selected and the screen size and hard drive size are recorded.a. Display possible outcomes using a tree diagram.b. Let A be the event that the order is for a laptop with a screen size of 12 inches or smaller. Let B be the event that the order is for a laptop with a hard drive size of at most 100 GB. What outcomes are in AC ? In A ∪ B? In A ∩ B? c. Let C denote the event that the order is for a laptop with a 200 GB hard drive. Are A and C disjoint events? Are B and C disjoint?
A tree diagram for this scenario would have three branches for screen sizes (10, 12, 15 inches) and then four branches for each of those screen sizes representing the hard drive sizes (50, 100, 150, 200 GB).
b. - A ∩ B: {(10, 50), (10, 100), (12, 50), (12, 100)}
c-- B and C are disjoint events, as they have no common outcomes.
a. A tree diagram for this scenario would have three branches for screen sizes (10, 12, 15 inches) and then four branches for each of those screen sizes representing the hard drive sizes (50, 100, 150, 200 GB).
b.
- A (screen size of 12 inches or smaller): {(10, 50), (10, 100), (10, 150), (10, 200), (12, 50), (12, 100), (12, 150), (12, 200)}
- B (hard drive size of at most 100 GB): {(10, 50), (10, 100), (12, 50), (12, 100), (15, 50), (15, 100)}
- AC: {(10, 150), (10, 200), (12, 150), (12, 200)}
- A ∪ B: All outcomes except for {(15, 150), (15, 200)}
- A ∩ B: {(10, 50), (10, 100), (12, 50), (12, 100)}
c.
- C (order for a laptop with a 200 GB hard drive): {(10, 200), (12, 200), (15, 200)}
- A and C are not disjoint events, as they share common outcomes {(10, 200), (12, 200)}.
- B and C are disjoint events, as they have no common outcomes.
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The triangles below are similar. Which similarity statements describe the relationship between the two triangles? Check all that apply. Triangle C B A is similar to triangle F E D Triangle C B A is similar to triangle F D E Triangle B A C is similar to triangle E F D Triangle B A C is similar to triangle E D F Triangle A B C is similar to triangle D E F Triangle A B C is similar to triangle D F E
Complete Question
In triangle ABC: AC=10 , AB=5., Angle C = 30 degrees.
In Triangle DEF: ED= 7.5 , DF=15, Angle F =30 degrees , Angle E = 90 degrees.
Answer:
A, D and E
Step-by-step explanation:
The diagram is drawn and attached below.
Triangle ABC is similar to Triangle DEF. (Option E)Writing it backwards:
Triangle CBA is similar to Triangle FED. (Option A)Also,
Triangle BAC is similar to EDF. (Option D).Therefore, A, D and E are the similarity statements that describe the relationship between the two triangles.
Answer:
A, D and E
Step-by-step explanation:
find the value of each folloing in its simplest form 1/3 divided by 4
Answer:
1/12
Step-by-step explanation:
Answer:
1/3 divided by 4 is 1/12
Step-by-step explanation:
1/3 divided by 4
copy dot flip (as i was taught)
1/3 x 1/4
= 1/12
x acts as the "dot"
Change from rectangular to cylindrical coordinates. (Let r ≥ 0 and 0 ≤ θ ≤ 2π.)
(a) (−7, 7, 7)
(√98, 7π /4,7) Incorrect:
(b) (−7, 7 3 , 1)
(14, π /3,1) Incorrect:
The cylindrical coordinates of (−7, 7, 7) are (√98, -π/4, 7). cylindrical coordinate (−7, 7 3 , 1) is (14, -π/3, 1).
We must switch from rectangular to cylindrical coordinates in the provided problem. (let r ≥ 0 and 0 ≤ θ ≤ 2π.)
A)(−7, 7, 7)
Given rectangular coordinates(x, y, z) =(−7, 7, 7)
The cylindrical coordinates are (r, θ, z)
As a result, we determine each value of r and θ separately.
r = √x²+y²
r = √(-7)²+(7)²
r = √49+49
r = √98
θ = tan⁻¹ (y/x)
θ =tan⁻¹ (7/-7)
θ =tan⁻¹ (-1)
θ = -π/4
So cylindrical coordinate = (r, θ, z) = (√98, -π/4, 7)
B) (-7,7√3,1)
Given rectangular coordinates(x, y, z) = (-1,1,1)
The cylindrical coordinates are (r, θ, z)
As a result, we determine each value of r and θ separately.
r = √x²+y²
r = √(-7)²(7√3)²
r = √49+147
r = √196
r = 14
θ = (y/x)
θ = (7√3/-7)
θ = (-√3)
θ = -π/3
So cylindrical coordinate = (r, θ, z) = (14, -π/3, 1)
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help........................
since the powers are same, ignore 'em , and let's calculate the bases.
-16.(1/2)
-8.1 (upon cancellation)
ans = -8
hope it helps...!!!
HELPPPPPP PLSSSSSSSS
Answer:
hmmmm help rin ako po please
solve for x (x-1)(x-12)=0
Answer:
x = 1, 12
Step-by-step explanation:
Given the equation:
\(\displaystyle{(x-1)(x-12)=0}\)
This can be set as:
\(\displaystyle{x-1 = 0 \ \, \text{or} \ \, x - 12 = 0}\)
Solve equations like linear, add both sides by 1 for x - 1 and add both sides by 12 for x - 12:
\(\displaystyle{x-1 +1= 0+1\ \, \text{or} \ \, x - 12+12 = 0+12}\\\\\displaystyle{x= 1\ \, \text{or} \ \, x = 12}\)
Instead of using "or" for conjunction, we can simply write the solution as x = 1, 12 (or you can also write x = 12, 1)
Additional Info
If you see the equation in form of \(\displaystyle{(ax+b)(cx+d)=0}\) then you can just simply solve like linear separately and combine solutions together as one.
Find c Round to the nearest tenth 27 201 28 c=?cm
Answer:
\(56.3\)
Step-by-step explanation:
The Law of Sines works for any triangle and is given by \(\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}\) (the ratio of any angle and its opposite side is equal to the ratio of all other angles and their respective opposite sides).
Thus, we have:
\(\frac{\sin 28^{\circ}}{27}=\frac{\sin 102^{\circ}}{c},\\c=\frac{27\sin 102^{\circ}}{\sin 28^{\circ}}=56.2547070223\approx \boxed{56.3}\)
what's the importance of saving money
Answer:
saving money will help us in future.Today we save money tommorrow this saving money will need in work,business,etc.
Step-by-step explanation:
Saving money is important because it can help you with future expenses or debt, it can also help you for emergencies, specifically for medical emergencies, and for college funds. Saving money can also help you with buying a home for the future.
The vertices of triangle ABC are A (2,2) B(4,2) C(4,3). Please help me answer 1 and 2!
NO SCAMS OR LINKS! THANKS FOR THE HELP!
Answer:
1. C.
2. D.
Step-by-step explanation:
1. All coordinates are doubled
2. All coordinates are halved.
discuss how your understanding of Quartiles, variation, measure of dispersion and standard deviation. Are sampling always reliable? Why is standard deviation important. Give specific examples to illustrate your understanding.
Quartiles: Quartiles are values that divide a dataset into quarters. The first quartile, Q1, represents the value at which 25% of the data falls below it, the second quartile, Q2 (also known as the median), represents the value at which 50% of the data falls below it, and the third quartile, Q3, represents the value at which 75% of the data falls below it. Quartiles are useful for identifying the spread of a dataset, and they can be used in conjunction with box plots to visualize the distribution of the data.
Variation: Variation refers to the degree to which data points differ from one another. If the data points are all very similar, then there is little variation. If the data points are spread out across a wide range, then there is high variation. Variation can be measured using a variety of statistics, including range, interquartile range, variance, and standard deviation.
What is terms about?Measure of dispersion: Measures of dispersion are used to describe how spread out a dataset is. Common measures of dispersion include the range, interquartile range, variance, and standard deviation.
Standard deviation: The standard deviation is a measure of how spread out the data is from the mean. It tells us how much the data deviates from the average value. A smaller standard deviation indicates that the data is tightly clustered around the mean, while a larger standard deviation indicates that the data is spread out over a wider range.
Sampling reliability: Sampling is not always reliable because it is subject to sampling error, which occurs when the sample does not accurately represent the population being studied. The larger the sample size, the more reliable the sample is likely to be, but even with large sample sizes, there is always some degree of sampling error.
Importance of standard deviation: The standard deviation is an important statistic because it allows us to quantify the degree of variability within a dataset. It is particularly useful in comparing two or more datasets to determine which has a greater degree of variability. For example, if we are comparing the heights of two populations, we can use the standard deviation to determine which population has greater height variability.
Lastly, the Example: Let's say we have two datasets representing the ages of participants in two different races. Dataset A has a mean age of 30 and a standard deviation of 5, while Dataset B has a mean age of 30 and a standard deviation of 10. We can conclude that Dataset B has a greater degree of age variability than Dataset A, even though both datasets have the same mean age. This is important information if we are interested in understanding the differences between these two populations.
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HELP PLEASE!!
I'll give brainliest to whoever is correct! :)
Answer:
\( = \frac{p}{ - 2} < 9 \\ = p > 9( - 2) \\ = p > - 18\)
Choos all the values greater than -18...in this case it's
-17,-16,-15,-14
The expected number of defective parts produced on an assembly line per shift is 60 with a standard deviation of 4. Use Chebyshev's inequality to find the minimum probability that the number of defective parts on a particular shift will be between 46 and 74. (Round your answer to four decimal places. )
The minimum probability that the number of defective parts on a particular shift will be between 46 and 74 is equals to the 0.9184.
Chebyshev's inequality is a theory that is used to describe the maximum number of extreme values in a probability distribution. We have, The expected number of defective parts produced in assembly line per shift = 60
So, sample size = 60
Standard deviations = 4
Standardized score for 46 = (46 - 60)/4
= -3.5
Standardized score for 74 = (74 - 60)/4
= 3.5
Hence by Chebyshev's inequality,
Minimum probability that the number of defective parts on a particular shift will be between 46 and 74 = (1 - 1/3.52)
= 0.9184
Hence required probability is 0.9184.
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85 POINTSS!!! FOR 1 QUESTION!!
⦁ The table shows the soil density of several soil samples at different depths.
⦁ Depth (m) ⦁ 1 ⦁ 4 ⦁ 6 ⦁ 7 ⦁ 10 ⦁ 13 ⦁ 14 ⦁ 21 ⦁ 23 ⦁ 26 ⦁ 28
⦁ Soil density ( ) ⦁ 1040 ⦁ 1068 ⦁ 1122 ⦁ 1180 ⦁ 1201 ⦁ 1252 ⦁ 1269 ⦁ 1274 ⦁ 1255 ⦁ 1278 ⦁ 1293
⦁ .
⦁ Use the equation to estimate the soil density of a sample at a depth of 20m.Write the quadratic regression equation that models the data. Let x = depth below the surface and let y = soil density. Show your work.
This is prob wrong
1068/4=
267*20=
5,340
-7/8 - (-h) = -7/12
solve for h
pls show work
Answer:
The answer is 7/24.
Step-by-step explanation:
I attached a picture, but I'll try to walk through it here.
1) A negative and a negative makes a positive, so h becomes positive.
2) I added 7/8 to both sides, in order to "isolate the variable", which simply means to get h by itself, on one side of the equation (you'll likely hear it said both ways).
3) I multiplied 7/8 by 3/3, and multiplied -7/12 by 2/2. This is known as a common denominator, which in this case is 24. You can only add and subtract fractions that have a common denominator.
4) Multiply both of the fractions to get 21/24 + (-14/24). "Adding a negative" is the same thing as subtracting.
5) 21 - 14 = 7, and since our denominators are the same, the answer is 7/24.
You can confirm the answer by substituting, or "plugging" 7/24 into your original equation, in place of h.
what is the equation of the line with a slope of 3 and passing through the point (1, -3) slope-intercept form and point-slope form?
Answer:
from formula
slope(M)=Y2-Y1
X2-X1
you already have slope which is 3
3=Y-(-3)
X-1
then cros multiplication
3X-3=Y+3
from formula
Y=Mx-c
Y=3X-6--is answer
please help!
Set up a proportion to solve for x in the following similar triangles.
How does sample size affect t-value?
The standard normal distribution can roughly statistic estimate the t-value for small sample sizes, though it grows less sensitive to changes in sample size for large sample sizes.
Test statistic: What is it?The test statistic for something akin to a Z-test has been the Z-statistic, which shows the usual normal null hypothesis to be correct. Suppose you perform a 2 X y test with a 0.05 threshold of significance and, based on your data, you obtain a 2.5 R t (also defined as a Z-value). 0.0124 is the p-value for the this Z-value.
Here,
When the population size is small (typically less than 30) or when it is unclear what the population standard deviation will be, the t-value is a statistical measure that is used to determine the statistical significance of a difference of the two means.
This is so that there will be less sampling error and more accurate information the about population provided by the bigger sample size. As the sample size grows, the t-distribution gets more constrained and resembles the average more closely.
In conclusion, the t-value tends to rise as sample size rises, indicating the increased accuracy of the sample mean.
The standard normal distribution can roughly estimate the t-value for small sample sizes, though it grows less sensitive to changes in sample size for large sample sizes.
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a sample of 50 employees showed that the sample mean of hourly wage of $20.2106, and population standard deviation of $6. an economist wants to test if the average hourly wage differs from $22. (round your answers to 4 decimal places if needed) a. specify the null and alternative hypotheses. b. calculate the value of the test statistic. c. find the critical value at the 5% significance level. d. at the 5% significance level, what is the conclusion to the hypothesis test? e. calculate the 95% confidence interval and use the confidence interval approach to conduct the hypothesis test. is the result different from part d? explain.
On solving the provided query we have The test statistic (-2.5594) falls in equation the rejection zone since it is less than the threshold value (-2.009).
What is equation?A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.
a. The average hourly wage is equal to $22 under the null hypothesis, whereas it is not $22 under the alternative hypothesis.
A = $22 is the null hypothesis (H0).
Additional Hypothesis (Ha): $22
b. The test statistic's value can be determined as follows:
t = sqrt(sample size) / (population standard deviation / hypothesised mean) / (sample mean - hypothesised mean)
t = (20.2106 - 22) / (6 / sqrt(50))
t = -2.5594
c. The critical value with 49 degrees of freedom and a 5% significance level is 2.009.
d. The test statistic (-2.5594) falls in the rejection zone since it is less than the threshold value (-2.009).
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An electric company calculates a persons monthly bill from the number of kilowatt kWh, x, used
The function (in photo ) determines the bill
How much is the bill for a person who uses 400 kWh in a month
A. 50
B. 60
C. 40
D. 30
Answer:
Option (A)
Step-by-step explanation:
From the given piecewise function that represent the amount of bill from number of units of electricity used is 'x' kWh.
b(x) = 0.10x when x ≤ 200
0.15(x - 200) + 20 when x > 200
For x = 400 kWh,
Function which represents the expenses of the bill,
b(400) = 0.15(400 - 200) + 20 [Since x > 200]
= 0.15(200) + 20
= 30 + 20
= $50
Therefore, Option (A) will be the answer.
1 + 216 = (a + b)(a2 + ka +36), what does k equal?
PLEASE ANSWER NOW NOW NOW
Answer:k=−a3−a2b−36a−36b+217/a2+ab
Step-by-step explanation:Step 1: Flip the equation.
a3+a2b+a2k+abk+36a+36b=217
Step 2: Add -a^3 to both sides.
a3+a2b+a2k+abk+36a+36b+−a3=217+−a3
a2b+a2k+abk+36a+36b=−a3+217
Step 3: Add -a^2b to both sides.
a2b+a2k+abk+36a+36b+−a2b=−a3+217+−a2b
a2k+abk+36a+36b=−a3−a2b+217
Step 4: Add -36a to both sides.
a2k+abk+36a+36b+−36a=−a3−a2b+217+−36a
a2k+abk+36b=−a3−a2b−36a+217
Step 5: Add -36b to both sides.
a2k+abk+36b+−36b=−a3−a2b−36a+217+−36b
a2k+abk=−a3−a2b−36a−36b+217
Step 6: Factor out variable k.
k(a2+ab)=−a3−a2b−36a−36b+217
Step 7: Divide both sides by a^2+ab.
k(a2+ab)
a2+ab
=
−a3−a2b−36a−36b+217
a2+ab
k=
−a3−a2b−36a−36b+217
a2+ab
find the length of the curve r(t) = sqrt(2)ti
To find the length of the curve r(t) = sqrt(2)ti, we need to use the arc length formula:L = ∫[a,b] ||r'(t)|| dt,where ||r'(t)|| is the magnitude of the derivative of the curve.
First, we need to find r'(t):
r'(t) = (d/dt) [sqrt(2)ti] = sqrt(2)i
The magnitude of r'(t) is ||r'(t)|| = sqrt(2).
So, the length of the curve is:
L = ∫[0,1] sqrt(2) dt = sqrt(2) * [t] [0,1] = sqrt(2)
Therefore, the length of the curve r(t) = sqrt(2)ti is sqrt(2).
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What are the 5 positive integers that have a mode of 2 and 4, a median of 4 and a mean of 5
Answer:
10 i belive
Step-by-step explanation:
Hence, the five positive integers are 2, 2, 4, 4, 13.
What is a mean , median and mode?Mean- The arithmetic mean of a given data is the sum of all observations divided by the number of observations.
Median-The value of the middlemost observation, obtained after arranging the data in ascending or descending order, is called the median of the data.
Mode-The value which appears most often in the given data i.e. the observation with the highest frequency is called a mode of data.
Step by Step Solution:According to the question , it can be concluded that the total no. of observations are 5.
So , Let n=5
Let the integers be a, b, c, d and e
The question says that mode(s) are 2 and 4.
This indicates that 2 and 4 both have occurred more than once , and both have same frequency since both are modes.
Since we have only 5 integers , and 2 and 4 both are modes , so both these numbers have possibility to occur only twice.
Hence , it becomes , a=2 , b=2 , c=4 , and d=4
Hence we can say that out of five required integers ,four of them are 2 and 4.
Further , we are given that mean is 5.
therefore , using formula:
Mean = Sum of Observations / Number of observations(n)
Mean= (a+b+c+d+e) / 5
5 = (2+2+4+4+e) / 5
5 = (12+e)/5
Multiplying both sides by 5 , we get :
25 = 12+e
e=25-12
Hence , e = 13
So, the five positive integers are 2, 2, 4, 4, 13.
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already answered im good
Yes, based on what I can see, all the answers look fine.
P.S. Try to take a smaller snip of the screen, because now everyone can see who you are.
النسبه المئويه بين ٣٠٠ جرام و ٥‚١ كجم تساوي
Answer:
Step-by-step explanation:
1.5 kilogram = 1.5* 1000= 1500
percentage = 300/1500 = 1/5 = 20%
Formalize the following in terms of atomic propositions r, b, and w, first making clear how they correspond to the
English text. (a) Berries are ripe along the path, but rabbits have not been seen in the area.
(b) Rabbits have not been seen in the area, and walking on the path is safe, but berries are ripe along the path.
(c) If berries are ripe along the path, then walking is safe if and only if rabbits have not been seen in the area.
(d) It is not safe to walk along the path, but rabbits have not been seen in the area and the berries along the path are ripe.
e) For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to
pave been seen in the area.
Walking is not safe on the path whenever rabbits have been seen in the area and berries are ripe along the path.
Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path. This is formalized by using the →(if-then) and ∧(logical and) operators.
Given information and corresponding atomic propositions:
We need to formalize the given statements in terms of atomic propositions r, b, and w, which are defined as follows:
r: Rabbits have been seen in the area.
b: Berries are ripe along the path.
w: Walking on the path is safe.
Now, let us formalize each of the given statements in terms of these atomic propositions:
a) Berries are ripe along the path, but rabbits have not been seen in the area.
b: Rabbits have not been seen in the area, and walking on the path is safe, but berries are ripe along the path.
c: If berries are ripe along the path, then walking is safe if and only if rabbits have not been seen in the area.
d: It is not safe to walk along the path, but rabbits have not been seen in the area, and the berries along the path are ripe.
e) For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.
Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path.
The formalizations in terms of atomic propositions are:
a) b ∧ ¬r.b) ¬r ∧ w ∧
b.c) (b → w) ∧ (¬r → w).
d) ¬w ∧ ¬r ∧
b.e) (¬r ∧ ¬b) → w.b ∧
Berries are ripe along the path, but rabbits have not been seen in the area.
This is formalized by using the ∧(logical and) operator.
(¬r ∧ ¬b) → w: It means For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.
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Please Guys Please Help Me Please
Answer:45
Step-by-step explanation:
45 +15 =60
Name a pair of vertical angles in the diagram. **Be sure to start your answer with 'ANGLE'
Answer:
ANGLE LQM and ANGLE KQN
Step-by-step explanation:
Vertical angles are across from each other, so:
ANGLE LQM and ANGLE KQN are vertical angles.
Also, ANGLE LQK and ANGLE MQN are vertical angles.
The temperature at sunrise is 40°F. Each hour, the temperature rises 4°F. Write an equation that models the temperature y, in degrees Fahrenheit, after x hours. What is the graph of the equation?
Write an equation that models the temperature y, in degrees Fahrenheit, after x hours.
Answer:
y = 4x + 40
Step-by-step explanation:
At sunrise, 0 hours have passed, meaning x = 0.
When x = 0, the temperature is 40, meaning that 40 is the y-intercept.
And every x hours the temperature rises by 4 degrees F
Can someone on here tell me how to manipulate equations so a variable cancels? I'm on "Solving Systems of an Equation Algebraically"
Offering 25 points because I really need this. The program I am using is not a real help.