Yes.
1467-776=691
Which means 776 believed the country was protected and 691 believed the country wasn't.
To determine if a majority of surveyed citizens in 1945 believed the US could develop protection against atomic bombs, a one-sample proportion test must be conducted. If the test results in a p-value less than the 0.01 level of significance, we can conclude that a majority did hold this belief. This involves concepts in hypothesis testing and statistics.
Explanation:The question you're asking requires a basic understanding of hypothesis testing in statistics. Let's denote the proportion of those who answered 'yes' as p and the total number of citizens surveyed as n.
In this case, p = 776 / 1467 = 0.529, meaning 52.9% of the sampled citizens responded yes leading to the claim that a majority believe the US could develop protection against atomic bombs.
However, to determine if this is truly a majority at a 0.01 level of significance, we need to conduct a one-sample proportion test. Our null hypothesis (H0) would state that the population proportion is 0.5 (no majority), while our alternative hypothesis (H1) would be that the population proportion is greater than 0.5 (there is a majority).
If we find a p-value less than the 0.01 level of significance from the test, we reject H0 and conclude that a majority of Americans did believe in the capacity for atomic bomb protection. If the p-value is greater than 0.01, we would fail to reject H0, concluding that a majority belief can't be inferred.
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How do you convert 7/2^6 to decimal please? ( seven over 2 to the power of 6)
You just put the expression in a calculator! We have
[tex]\dfrac{7}{2^6} = \dfrac{7}{64}=0.109375[/tex]
1) Find the lump that must be deposited today to have a future value of $ 25,000 in 5 years if funds earn 6 % componded annually.
Answer: $ 18681.45
Step-by-step explanation:
Given: Future value : [tex]FV=\$25,000[/tex]
The rate of interest : [tex]r=0.06[/tex]
The number of time period : [tex]t=5[/tex]
The formula to calculate the future value is given by :-
[tex]\text{Future value}=P(1+i)^n[/tex], where P is the initial amount deposited.
[tex]\Rightarrow\ 25000=P(1+0.06)^5\\\\\Rightarrow\ P=\dfrac{25000}{(1.06)^5}\\\\\Rightarrow\ P=18681.4543217\approx=18681.45[/tex]
Hence, the lump that must be deposit today : $ 18681.45
Evaluate: LaTeX: \int^8_6\frac{4}{\left(x-6\right)^3}dx ∫ 6 8 4 ( x − 6 ) 3 d x a. Diverges LaTeX: \left(\infty\right) ( ∞ ) b. Diverges LaTeX: \left(-\infty\right) ( − ∞ ) c. 0 d. LaTeX: \frac{1}{4} 1 4 e. LaTeX: \frac{2}{9} 2 9
Answer:
It diverges to positive infinity
Step-by-step explanation:
I see it was 4/(x-6)^3 not 4(x-6)^3... but still can't make out everything else.
[tex] \int_6^8 \frac{4}{(x-6)^3} dx [/tex]
The integrand does not exist at x=6.
[tex] \int_6^8 \frac{4}{(x-6)^3} dx [/tex]
[tex] \lim_{z \rightarrow 6^{+} } \int_z^8 4(x-6)^{-3} dx [/tex]
[tex] \lim_{z \rightarrow 6^{+} }\frac{4(x-6)^{-2}}{-2} |_z^8dx [/tex]
[tex] \lim_{z \rightarrow 6^{+} }[\frac{4(8-6)^{-2}}{-2} -\frac{4(z-6)^{-2}}{-2} ] [/tex]
[tex] \frac{1}{-2} - -\infty [/tex]
[tex] \infty [/tex]
So it diverges
Answer:
I could not properly read this but here was what I could make out
Step-by-step explanation:
Find the difference.
LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.
LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.
LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.
LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.
LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.
LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.
LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.
LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.
LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)Find the difference.
LaTeX: -\frac{5}{6}-\frac{17}{18}-\left(-\frac{2}{9}\right)
home this helped ;)
Calculate ∬y dA where R is the region between the disks x^2+y^2 <=1 & x^2+(y-1)^2 <=1
Show all work. (Also explain why you split up the regions)
Let's first consider converting to polar coordinates.
[tex]\begin{cases}x=r\cos\theta\\y=r\sin\theta\end{cases}\implies\begin{cases}x^2+y^2=1\iff r=1\\x^2+(y-1)^2=1\iff r=2\sin\theta\end{cases}[/tex]
We have
[tex]1=2\sin\theta\implies\sin\theta=\dfrac12\implies\theta=\dfrac\pi6\text{ or }\theta=\dfrac{5\pi}6[/tex]
Then [tex]\mathrm dA=r\,\mathrm dr\,\mathrm d\theta[/tex] and the integral is
[tex]\displaystyle\iint_Ry\,\mathrm dA=\int_{\pi/6}^{5\pi/6}\int_{2\sin\theta}^1r^2\sin\theta\,\mathrm dr\,\mathrm d\theta=\boxed{-\frac{\sqrt3}4-\frac{2\pi}3}[/tex]
Find the absolute maximum and minimum values of f(x.y)=x^2+y^2-2x-2y on the closed region bounded by the triangle with vertices (0,0), (2,0), and (0,2)
Try this suggested solution, note, 'D' means the region bounded by the triangle according to the condition. It consists of 6 steps.
Answers are underlined with red colour.
The equation P=31+1.75w models the relation between the amount of Tuyet’s monthly water bill payment, P, in dollars, and the number of units of water, w, used. Find Tuyet’s payment for a month when 12 units of water are used.
Answer: [tex]P = \$\ 52[/tex]
Step-by-step explanation:
We have the equation [tex]P = 31 + 1.75w[/tex] where P represents the payment and w represents the amount of water used.
To calculate the monthly payment that corresponds to 12 units of water you must do [tex]w = 12[/tex] in the main equation and solve for the variable P.
[tex]P = 31 + 1.75w[/tex]
[tex]P = 31 + 1.75(12)[/tex]
[tex]P = 31 + 21[/tex]
[tex]P = 52[/tex]
Tuyet's payment for a month when 12 units of water are used is $52.
Explanation:To find Tuyet's payment for a month when 12 units of water are used, we can substitute 12 for 'w' in the equation P = 31 + 1.75w and solve for P.
P = 31 + 1.75(12)
P = 31 + 21
P = 52
Therefore, Tuyet's payment for a month when 12 units of water are used is $52.
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Liz earns a salary of $2,500 per month, plus a commission of 7% of her sales. She wants to earn at least $2,900 this month. Enter an inequality to find amounts of sales that will meet her goal. Identify what your variable represents. Enter the commission rate as a decimal.
Answer:
The minimum amount in sales this month to meet her goal is [tex]\$5,714.29[/tex]
Step-by-step explanation:
Let
x----> amount in sales this month
we know that
[tex]7\%=7/100=0.07[/tex]
The inequality that represent this situation is equal to
[tex]2,500+0.07x\geq2,900[/tex]
Solve for x
Subtract 2,500 both sides
[tex]0.07x\geq2,900-2,500[/tex]
[tex]0.07x\geq400[/tex]
Divide by 0.07 both sides
[tex]x\geq400/0.07[/tex]
[tex]x\geq \$5,714.29[/tex]
therefore
The minimum amount in sales this month to meet her goal is [tex]\$5,714.29[/tex]
The weights of broilers (commercially raised chickens) are approximately normally distributed with mean 1387 grams and standard deviation 161 grams. What is the probability that a randomly selected broiler weighs more than 1,454 grams?
Answer:
Probability that a randomly selected broiler weighs more than 1454 g is 0.3372 or 34% (approx.)
Step-by-step explanation:
Given:
Weights of Broilers are normally distributed.
Mean = 1387 g
Standard Deviation = 161 g
To find: Probability that a randomly selected broiler weighs more than 1454 g.
we have ,
[tex]Mean,\,\mu=1387[/tex]
[tex]Standard\,deviation,\,\sigma=161[/tex]
X = 1454
We use z-score to find this probability.
we know that
[tex]z=\frac{X-\mu}{\sigma}[/tex]
[tex]z=\frac{1454-1387}{161}=0.416=0.42[/tex]
P( z = 0.42 ) = 0.6628 (from z-score table)
Thus, P( X ≥ 1454 ) = P( z ≥ 0.42 ) = 1 - 0.6628 = 0.3372
Therefore, Probability that a randomly selected broiler weighs more than 1454 g is 0.3372 or 34% (approx.)
How many equivalence relations are there on the set 1, 2, 3]?
Answer:
We need to find how many number of equivalence relations are on the set {1,2,3}
A relation is an equivalence relation if it is reflexive, transitive and symmetric.
equivalence relation R on {1,2,3}
1.For reflexive, it must contain (1,1),(2,2),(3,3)
2.For transitive, it must satisfy: if (x,y)∈R then (y,x)∈R
3. For symmetric, it must satisfy: if (x,y)∈R,(y,z)∈R then (x,z)∈R
Since (1,1),(2,2),(3,3) must be there is R, (1,2),(2,1),(2,3),(3,2),(1,3),(3,1). By symmetry,
we just need to count the number of ways in which we can use the pairs (1,2),(2,3),(1,3) to construct equivalence relations.
This is because if (1,2) is in the relation then (2,1) must be there in the relation.
the relation will be an equivalence relation if we use none of these pairs (1,2),(2,3),(1,3) . There is only one such relation: {(1,1),(2,2),(3,3)}
we can have three possible equivalence relations:
{(1,1),(2,2),(3,3),(1,2),(2,1)}
{(1,1),(2,2),(3,3),(1,3),(3,1)}
{(1,1),(2,2),(3,3),(2,3),(3,2)}
Equivalence relations on a set satisfy conditions of reflexivity, symmetry, and transitivity. The Bell number counts the number of partitions, or equivalence relations, on a set. Hence, for the set {1, 2, 3}, there are five equivalence relations.
Explanation:The subject of this question relates to equivalence relations on a set which is an important topic in discrete mathematics and set theory. In simple terms, an equivalence relation is a relation on a set that equates certain pair of elements. In your set {1, 2, 3}, an equivalence relation must meet three conditions: reflexivity (each number is equal to itself), symmetry (if 1 is related to 2, then 2 is related to 1), and transitivity (if 1 is related to 2 and 2 is related to 3, then 1 is related to 3).
To find the number of equivalence relations on a set, we refer to the Bell number. Bell numbers count the number of partitions of a set. For a set with 3 elements like yours, the third Bell number gives the number of equivalence relations, which is 5. Therefore, there are 5 equivalence relations on the set {1, 2, 3}.
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when are the expressions 3x +12 and 3(x+4) equvialent
Answer:
For any value of x
Step-by-step explanation:
Solve by using system of equations!
3x+12
3(x+4)=3x+12
3x+12=3x+12
x=x
This means that any value of x would create the same answer for both equations.
Answer:
Always.
Step-by-step explanation:
Always. This is true by distributive property.
The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.2 days and a standard deviation of 1.7 days. What is the probability of spending more than 2 days in recovery? (Round your answer to four decimal places.)
Answer: 0.9713
Step-by-step explanation:
Given : Mean : [tex]\mu = 5.2\text{ day}[/tex]
Standard deviation : [tex]\sigma = 1.7\text{ days}[/tex]
The formula of z -score :-
[tex]z=\dfrac{X-\mu}{\sigma}[/tex]
At X = 2 days
[tex]z=\dfrac{2-5.2}{1.7}=-1.88235294118\approx-1.9[/tex]
Now, [tex]P(X>2)=1-P(X\leq2)[/tex]
[tex]=1-P(z<-1.9)=1- 0.0287166=0.9712834\approx0.9713[/tex]
Hence, the probability of spending more than 2 days in recovery = 0.9713
Answer:
There is a 98.54% probability of spending more than 2 days in recovery.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 5.7, \sigma = 1.7[/tex]
What is the probability of spending more than 2 days in recovery?
This probability is 1 subtracted by the pvalue of Z when X = 2. So:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2 - 5.7}{1.7}[/tex]
[tex]Z = -2.18[/tex]
[tex]Z = -2.18[/tex] has a pvalue of 0.0146.
This means that there is a 1-0.0146 = 0.9854 = 98.54% probability of spending more than 2 days in recovery.
Which of the following graphs could represent a quartic function?
Answer:
Graph A
Basically a graph of a function will have no turns if linear, 1 turn if quadratic, 2 turns if cubic, and 3 terms if quartic.
Graph A has a small turn on its right side.
Step-by-step explanation:
I love the way this other guy explained it, basically you count the turns that it says. i.e quartic = 4, so 4 turns, so A in this case
This was so confusing and I've been learning it for over a week and never understood it but literally took me 2 seconds to read his answer and understand it perfectly
Suppose that the price p (in dollars) and the weekly sales x (in thousands of units) of a certain commodity satisfy the demand equation 4p cubedplusx squaredequals38 comma 400. Determine the rate at which sales are changing at a time when xequals80, pequals20, and the price is falling at the rate of $.20 per week.
Answer:
sales are increasing at the rate of 6000 units per week
Step-by-step explanation:
Your demand equation appears to be ...
4p³ +x² =38400
Then differentiation gives ...
12p²·p' +2x·x' = 0
Solving for x', we get ...
x' = -6p²·p'/x
Filling in the given values, we find the rate of change of sales to be ...
x' = -6(20²)(-0.20/wk)/80 = 6/wk . . . . . in thousands of units/wk
Sales are increasing at the rate of 6000 units per week.
You want to estimate the proportion of students at your college or university who are employed for 10 or more hours per week while classes are in session. You plan to present your results by a 95% confidence interval. Using the guessed value p* = 0.33, find the sample size required if the interval is to have an approximate margin of error of m = 0.06.
Answer: Hello your in college please help me with my latest problem please :(
Step-by-step explanation:
please help, Drag the values to order them from least to greatest, with the least at top
Step-by-step explanation:
The square root of 17 is 4.12. Minus one equals 3.12
The square root of 5 is 2.23.
pi+7 equals 10.142. Divided by five equals around 2.
so you end up with, 3.12, 2.23, and 2.1
The 5 hour energy drink should keep a person feeling awake while driving for 5 hours, regardless of their age. Stacy just doesn't believe it. So she has 50 twenty year olds, 50 thirty year olds, 50 forty year olds, and 50 fifty year olds consume a 5 hour energy drink, and then Stacy measured participants' awakeness after 5 hours of driving. What test should she use to analyze her results?
Answer:
a. Single-sample Z-Test
b. Single-sample t-test
c. Independent-measures t-test
d. Repeated-measures t-test (Paired-samples t-test)
e. Independent-measures ANOVA
Two Cars Start at a Given point and travel in the Same Direction at an Average Speeds of 45 Mph ,, and 52 Mph. So, The Question is How Far Apart Will they Be in 4 hours ???
Answer:
28 mi
Step-by-step explanation:
The cars are separating at the rate of 52 mi/h - 45 mi/h = 7 mi/h. Then after 4 hours, their separation distance will be ...
(7 mi/h)(4 h) = 28 mi
The two cars will be 28 miles apart after 4 hours.
Explanation:To find the distance between the two cars after 4 hours, we need to calculate the distance traveled by each car. The formula to find distance is speed multiplied by time. The first car travels at an average speed of 45 mph for 4 hours, so its distance traveled is 45 mph * 4 hours = 180 miles.
The second car travels at an average speed of 52 mph for 4 hours, so its distance traveled is 52 mph * 4 hours = 208 miles. Therefore, the two cars will be 208 miles - 180 miles = 28 miles apart after 4 hours.
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Help me ! Please for summer school
Answer:
The correct answer option is C. [tex]\frac{y_4-y_3}{x_4-x_3} \times \frac{y_2-y_1}{x_2-x_1} = -1[/tex].
Step-by-step explanation:
We are given that two line segments AB and CD are formed from the points A ([tex](x_1, y_1)[/tex], B ([tex](x_2, y_2)[/tex], C ([tex](x_3, y_3)[/tex] and D ([tex](x_4, y_4)[/tex].
We are to determine which condition needs to be met in order to prove that AB is perpendicular to CD.
When slopes of two perpendicular lines are multiplied, they give a product of -1.
Hence option C. [tex]\frac{y_4-y_3}{x_4-x_3} \times \frac{y_2-y_1}{x_2-x_1} = -1[/tex] is the correct answer.
Monitors manufactured by TSI Electronics have life spans that have a normal distribution with a standard deviation of 1800 hours and a mean life span of 20,000 hours. If a monitor is selected at random, find the probability that the life span of the monitor will be more than 17,659 hours. Round your answer to four decimal places.
Answer: 0.9032
Step-by-step explanation:
Given: Mean : [tex]\mu = 20,000\text{ hours}[/tex]
Standard deviation : [tex]\sigma = 1800 \text{ hours}[/tex]
The formula to calculate z is given by :-
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x= 17659
[tex]z=\dfrac{17659-20000}{1800}=−1.30055555556\approx-1.3[/tex]
The P Value =[tex]P(z>-1.5)=1-P(z<1.3)=1- 0.0968005\approx0.9031995\approx 0.9032[/tex]
Hence, the probability that the life span of the monitor will be more than 17,659 hours = 0.9032
To find the probability that the life span of the monitor will be more than 17,659 hours, use the z-score formula and the standard normal distribution table. The probability is approximately 0.0968.
Explanation:To find the probability that the life span of the monitor will be more than 17,659 hours, we need to calculate the z-score and use the standard normal distribution table. The z-score is calculated as:
z = (x - μ) / σ
Where x is the value we want to find the probability for, μ is the mean, and σ is the standard deviation. In this case, x = 17,659, μ = 20,000, and σ = 1800. Plugging these values into the formula, we get:
z = (17659 - 20000) / 1800 = -1.3
Now, we can look up the probability corresponding to the z-score -1.3 in the standard normal distribution table. The probability is approximately 0.0968. Therefore, the probability that the life span of the monitor will be more than 17,659 hours is approximately 0.0968.
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. Two algorithms takes n 2 days and 2 n seconds respectively, to solve an instance of size n. What is the size of the smallest instance on which the former algorithm outperforms the latter algorithm? Approximately how long does such an instance take to solve?
Answer:
n = 11 dayStep-by-step explanation:
n^2 is less than 2^n for n < 2 and for n > 4. The smallest size of n that is of interest is n=1. For that, n^2 = 1^1 = 1.
The n^2 algorithm will outperform the 2^n algorithm for n = 1. That problem size will take 1 day to solve.
_____
Please note that there are no algebraic methods for solving an inequality of the form x^2 < 2^x. We have solved it using a graphing calculator.
Final answer:
The smallest instance size where the n² days algorithm outperforms the 2n seconds algorithm is n=43200. However, it's not practical, as this size leads to a computation time of approximately 1.86496 × 10⁹ days for the first algorithm, showing that for any realistic value of n, the second algorithm is more efficient.
Explanation:
The student's question is about the comparison of the performance of two different algorithms. Specifically, the question asks at what size the algorithm, which takes n² days to solve an instance of size n, will outperform the 2n seconds algorithm.
To determine the smallest instance size at which the first algorithm outperforms the second, we must set the two times equal and solve for n. Let's denote the time taken by the first algorithm as T1 and the second algorithm as T2, where T1 = n² days and T2 = 2n seconds. We should convert both times to a common unit, which typically is seconds, as follows:
1 day = 24 hours = 86400 seconds
T1 in seconds: n² times 86400 seconds/day
T2 is already in seconds: 2n seconds
Now equate the two to find the smallest n:
n² times 86400 = 2n
n² times 86400 / 2 = n
n = 86400 / 2 = 43200
Thus, the smallest instance size n is 43200. To find how long this instance takes to solve by the first algorithm:
T1 = 43200² days
T1 ≈ 1.86496 × 109 days
This is impractically large, indicating that for any realistic value of n, the second algorithm is more efficient.
According to the growth model, how many trees will there be after 50 years? Details below
Answer: Third Option
[tex]f(t)=21,386[/tex]
Step-by-step explanation:
We know that the equation that models the number of trees in the forest is:
[tex]f(t)=\frac{32,000}{1+12.8e^{-0.065t}}[/tex]
Where t represents the time elapsed in years
To calculate the number of trees after 50 years substitute [tex]t = 50[/tex] in the equation
[tex]f(t)=\frac{32,000}{1+12.8e^{-0.065(50)}}[/tex]
[tex]f(t)=21,386[/tex]
XYZ Corp makes widgets 1% of the widgets are defective XYZ manufacturers 100000 widgets the number of defective widgets is expected to be
Answer:
the number to be expected is 1,000
Step-by-step explanation:
you multiply 100,000 by 1% which give you 1,000
Answer: 1000
Step-by-step explanation:
Given : The proportion of the defective widgets manufactured by XYZ corp= 1%
= 0.01 [we divide a percent by 100 to convert it into decimal to perform further calculations]
If the total number of widgets manufactured by XYZ = 100000
Then, the number of defective widgets is expected to be
(proportion of defective widgets) x (number of widgets manufactured by XYZ)
= 0.01 x 100000
= 1000
Hence, the number of defective widgets is expected to be 1000 .
A mile-runner’s times for the mile are normally distributed with a mean of 4 min. 3 sec. (This would have to be expressed in decimal minutes -- 4.05 minutes), and a standard deviation of 2 seconds (0.0333333··· minutes (the three dots indicate a repeating decimal)). What is the probability that on a given run, the time will be 4 minutes or less?
Answer: 0.0668
Step-by-step explanation:
Given: Mean : [tex]\mu=\text{4 min. 3 sec.=4.05 minutes}[/tex]
Standard deviation : [tex]\sigma = \text{2 seconds=0.033333 minutes }[/tex]
The formula to calculate z-score is given by :_
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x= 4 minutes , we have
[tex]z=\dfrac{4-4.05}{0.03333}\approx-1.5[/tex]
The P-value = [tex]P(z\leq-1.5)=0.0668072\approx0.0668[/tex]
Hence, the probability that on a given run, the time will be 4 minutes or less = 0.0668
The probability that on a given run, the time will be 4 minutes or less is approximately 6.68%.
Explanation:To find the probability that on a given run, the time will be 4 minutes or less, we need to calculate the z-score for 4 minutes and then use the standard normal distribution table to find the probability. The z-score can be calculated using the formula (x - mean) / standard deviation. In this case, the z-score is (4 - 4.05) / 0.0333333⋯ = -1.50. Looking up the z-score in the standard normal distribution table, we find that the probability is approximately 0.0668 or 6.68%.
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Two balls are drawn at random from an urn containing six white and nine red balls. Recall the equatio n for an. r) given below. C(n,r) (a) Use combinations to compute the probability that both balls are white. (b) Compute the probability that both balls are red. (a) The probability that both balls are white is (Type an integer or a decimal. Round to two decimal places as needed.)
Answer: (a) [tex]\dfrac{1}{7}[/tex] (b) [tex]\dfrac{12}{35}[/tex]
Step-by-step explanation:
Given: Number of white balls : 6
Number of red balls = 9
Total balls = 15
(a) The probability that both balls are white is given by :-
[tex]\dfrac{^6C_2}{^{15}{C_2}}\\\\=\dfrac{\dfrac{6!}{2!(6-2)!}}{\dfrac{15!}{2!(15-2)!}}=\dfrac{1}{7}[/tex]
∴ The probability that both balls are white is [tex]\dfrac{1}{7}[/tex] .
(b) The probability that both balls are red is given by :-
[tex]\dfrac{^9C_2}{^{15}C_2}\\\\=\dfrac{\dfrac{9!}{2!(9-2)!}}{\dfrac{15!}{2!(15-2)!}}=\dfrac{12}{35}[/tex]
∴ The probability that both balls are red is [tex]\dfrac{12}{35}[/tex] .
Prove that for all real numbers x, if 2x+1 is rational then x is rational
Answer with explanation:
It is given that, for all real numbers x, if 2 x+1 is rational .
When you will look at the expression ,2 x +1
⇒1 is rational
⇒2 x will be rational, because the expression , 2 x+1, is rational.
⇒2 x is rational, it means , x will be rational,because 2 is rational.
Some important rules considering rational and irrational
1.⇒Product of rational and rational is Rational.
2.⇒Product of Irrational and Rational is Irrational.
3.⇒Product of Irrational and Irrational may be irrational or rational.
≡2 x →is rational, 2 is rational number ,so x will be rational also.
If 2x+1 is rational, hence 2x is rational subtracting 1 which is also rational. Assuming 2x is expressible as a/b, then x is a/2b, again showing x is rational.
Explanation:To prove that if 2x+1 is rational, then x must also be rational, we must understand the definition of rational numbers and basic properties of arithmetic operations involving rational numbers. A number is considered rational if it can be written as the quotient of two integers (where the denominator is not zero). Given that the sum of two rational numbers is also rational, if 2x+1 is rational, and we know that 1 is rational (since 1 can be written as 1/1), then 2x must be rational because rational minus rational yields a rational result.
Now, assuming 2x is rational, we can express it as a fraction [tex]\frac{a}{b}[/tex], with a and b being integers and b non-zero. Since the multiplication of a rational number by an integer is also rational, and knowing that 2 is an integer, we can then say that x, which is [tex]\frac{a}{2b}[/tex], is also rational. This is because we can express the result of [tex]\frac{a}{2b}[/tex] with integers in the numerator and the denominator.
Suppose you have just received a shipment of 16 modems. Although you don't know this, 4 of the modems are defective. To determine whether you will accept the shipment, you randomly select 5 modems and test them. If all 5 modems work, you accept the shipment. Otherwise, the shipment is rejected. What is the probability of accepting the shipment?
[tex]|\Omega|={_{16}C_5}=\dfrac{16!}{5!11!}=\dfrac{12\cdot13\cdot14\cdot15\cdot16}{120}=4368\\|A|={_{12}C_5}=\dfrac{12!}{5!7!}=\dfrac{8\cdot9\cdot10\cdot11\cdot12}{120}=792\\\\P(A)=\dfrac{792}{4368}=\dfrac{33}{182}\approx18\%[/tex]
The probability of the event is defined as the ratio of the number of cases favourable to an occurrence, and the further calculation can be defined as follows:
4 of the 16 modems are defective, while the remaining 12 are not.
P(accepting shipment) = P (all 5 modems work)
[tex]\bold{^{12}C_{5}}[/tex] methods could be used to choose 5 non-defective modems from a pool of 12 non-defective modems.
[tex]\to \bold{^{12}C_{5} = \frac{12!}{ (12 -5)! \times 5! }}[/tex]
[tex]\bold{ = \frac{12!}{ 7! \times 5!}}\\\\\bold{ = \frac{12 \times 11 \times 10 \times 9 \times 8 \times 7!}{ 7! \times 5!}}\\\\\bold{ = \frac{12 \times 11 \times 10 \times 9 \times 8}{5 \times 4 \times 3 \times 2 \times 1}}\\\\\bold{ =11 \times 9 \times 8}\\\\\bold{=792}[/tex]
The total number of methods to choose 5 modems from a pool of 16 modems is [tex]\bold{^{16}C_{5}}[/tex].
[tex]\to \bold{^{16}C_{5} = \frac{16!}{ (16 -5)! \times 5! }}[/tex]
[tex]\bold{ = \frac{16!}{ 11! \times 5!}}\\\\\bold{ = \frac{16 \times 15 \times 14 \times 13 \times 12 \times 11 !}{ 11! \times 5!}}\\\\\bold{ = \frac{16 \times 15 \times 14 \times 13 \times 12}{ 5!}}\\\\\bold{ = \frac{16 \times 15 \times 14 \times 13 \times 12}{ 5\times 4\times 3 \times 2 \times 1}}\\\\\bold{ = 8 \times 3 \times 14 \times 13 }\\\\\bold{ = 4368 }\\\\[/tex]
P(accepting shipment) = P(all 5 modems work):
[tex]= \bold{\frac{^{12}C_5}{ ^{16}C_{5}}}[/tex]
[tex]\bold{=\frac{792}{4368}}\\\\\bold{=0.18131}\\\\\bold{=0.18131 \times 100= 18.131 \approx 18.131\%}\\\\[/tex]
Therefore, the final answer is "18.131%".
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Under the onslaught of the College Algebra second period class, a pile of homework problems decreased exponentially. It decreased from 1400 to 1000 problems in only 25 minutes. How long would it take until only 500 problems remained?
Step-by-step explanation:
Well it is simple.If he was able to solve 400 problems in just 25 ' then how long would it take him to solve 100(1/4 of 400)?It would take him 6.25' to solve 100 problems(1/4 of 25).So if he had to do another 500 (because 1000 -500=500) it would take him 31.25' (5*6.25) to complete them.If you have any further questions please contact me.
Yours sincerely,
Manos
PVC pipe is manufactured with mean diameter of 1.01 inch and a standard deviation of 0.003 inch. Find the probability that a random sample of n = 9 sections of pipe will have a sample mean diameter greater than 1.009 inch and less than 1.012 inch.
Answer: 0.8186
Step-by-step explanation:
Given: Mean : [tex]\mu=1.01\text{ inch}[/tex]
Standard deviation : [tex]\sigma=0.003\text{ inch}[/tex]
Sample size : [tex]n=9[/tex]
The formula to calculate z-score :-
[tex]z=\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
For x=1.009 inch
[tex]z=\dfrac{1.009-1.01}{\dfrac{0.003}{\sqrt{9}}}=-1[/tex]
For x=1.012 inch
[tex]z=\dfrac{1.012-1.01}{\dfrac{0.003}{\sqrt{9}}}=2[/tex]
Now, The p-value =[tex]P(-1<z<2)=P(2)-P(-1)=0.9772498-0.1586553=0.8185945\approx0.8186[/tex]
Hence, the required probability = 0.8186
a) You want to put down hard wood floors in your master bedroom. How much hard wood flooring would you need to buy?
Amount of hardwood floor =
Round your answer to 2 decimal places as needed.
b) You also want to put a trim on the bottom of each wall, except in front of the french doors, sliding doors, or hallway. How much trim should you buy?
Amount of trim to buy =
Round your answer to 2 decimal places as needed.
c) You want to paint your new bedroom. How much paintable space is there in the room?
We will assume the following:
- You are painting all walls and the inside of your french doors.
- You want to paint the ceiling as well.
- Your windows and sliding doors account for 73 square feet of surface that does not get painted (i.e. you will be painting above your sliding doors and above/below your window)
Amount of paintable space =
Round your answer to 2 decimal places as needed.
d) How many gallons of paint would you need to buy?
We will assume the following:
- The builder already put primer on all the paintable surfaces.
- One gallon of paint covers 350 square feet.
- You want to put on two coats of paint on every paintable surface.
Amount of paint needed = gallons.
Round your answer to 2 decimal places as needed.
Note: Paint is obviously not bought in hundredths of gallons, but we are still going to answer accordingly!
Answer:
Part a) The amount of hardwood floor is [tex]480\ ft^{2}[/tex]
Part b) The amount of trim to buy is [tex]78\ ft[/tex]
Part c) The amount of paintable space is [tex]1,297\ ft^{2}[/tex]
Part d) The amount of paint needed is [tex]7.41\ gallons[/tex]
Step-by-step explanation:
Part a) You want to put down hard wood floors in your master bedroom. How much hard wood flooring would you need to buy?
Find the area of the floor
[tex]A=(10+5+3)(10+5+10)+(2+6+2)(3)[/tex]
[tex]A=(18)(25)+(10)(3)[/tex]
[tex]A=480\ ft^{2}[/tex]
Part b) You also want to put a trim on the bottom of each wall, except in front of the french doors, sliding doors, or hallway. How much trim should you buy?
step 1
Find the perimeter of the master bedroom
[tex]P=2(25)+2(18)+2(3)[/tex]
[tex]P=50+36+6[/tex]
[tex]P=92\ ft[/tex]
step 2
Subtract the front of the french doors, sliding doors and hallway from the perimeter
[tex]92-(5+6+3)=78\ ft[/tex]
Part c) You want to paint your new bedroom. How much paintable space is there in the room?
step 1
Find the area of the ceiling
we know that
The area of the floor is equal to the area of the ceiling
so
The area of the ceiling is equal to [tex]A=480\ ft^{2}[/tex]
step 2
Find the area of the walls
Multiply the perimeter by the height
[tex]92*10=920\ ft^{2}[/tex]
step 3
Subtract 73 square feet of surface that does not get painted (windows and sliding doors ) and the area of the hallway
The amount of paintable space is equal to
[tex]A=480+920-73-3(10)=1,297\ ft^{2}[/tex]
Part d) How many gallons of paint would you need to buy?
we know that
One gallon of paint covers 350 square feet
Multiply the area by two (because You want to put on two coats of paint on every paintable surface)
so
[tex]1,297*(2)=2,594\ ft^{2}[/tex]
using proportion
[tex]1/350=x/2,594[/tex]
[tex]x=2,594/350[/tex]
[tex]x=7.41\ gallons[/tex]
8 x 10^-3 is how many times as great as 4 x 10^-6
Answer: The first number is 2000 times greater than second number.
Step-by-step explanation:
Let the first number be 'x' and second number be 'y'
We are given:
x = [tex]8\times 10^{-3}[/tex]
y = [tex]4\times 10^{-6}[/tex]
To calculate the times, number 'x' is greater than number 'y', we divide the two numbers:
[tex]\frac{x}{y}=\frac{8\times 10^{-3}}{4\times 10^{-6}}\\\\\frac{x}{y}=2\times 10^3\\\\x=2000y[/tex]
Hence, the first number is 2000 times greater than second number.
The number [tex]8\times 10^{-3}[/tex] is [tex]2000[/tex] times grater than the number [tex]4\times 10^{-6}[/tex].
Given information:
The number [tex]8 \times 10^{-3}[/tex]
And number [tex]4\times 10^{-6}[/tex]
Now , consider the first number as [tex]x[/tex] and number second as [tex]y[/tex].
So, according to the information given in the question we can write as:
[tex]\frac{x}{y} =\frac{8\times 10^{-3}}{4\times 10^{-6}}[/tex]
[tex]\frac{x}{y} = 2\times 10^3\\x=2000y[/tex]
Hence, We can conclude that the number [tex]8\times 10^{-3}[/tex] is [tex]2000[/tex] times the number [tex]4\times 10^{-6}[/tex].
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