Answer:
-0.28
Step-by-step explanation:
(1/5) : (-5/7)=(1*5)/(5*(-5))=-(7/25)=-0.28
Answer:
[tex]-7/25[/tex]
Step-by-step explanation:
[tex]1/5 \div -5/7[/tex]
Do the reciprocal of the second fraction.
[tex]1/5 \times 7/-5[/tex]
Multiply the first fraction by the reciprocal of the second fraction.
[tex]7/-25=-0.28[/tex]
The answer in decimal form is -0.28.
Given that 9 x − 4 y = 20 Find y when x = − 2 Give your answer as an improper fraction in its simplest form
Answer:
[tex]\boxed{\df\ \dfrac{-19}{2}}[/tex]
Step-by-step explanation:
Hi,
x=-2
it gives
9*(-2)-4y=20
<=> -18-4y=20
<=> 18-18-4y=20+18=38
<=> -4y=38
<=> y = -38/4=-19/2
hope this helps
According to the National Association of Theater Owners, the average price for a movie in the United States in 2012 was $7.96. Assume the population standard deviation is $0.50 and that a sample of 30 theaters was randomly selected.
Required:
a. Calculate the standard error of the mean.
b. What is the probability that the sample mean will be less than $7.75?
c. What is the probability that the sample mean will be less than $8.10?
d. What is the probability that the sample mean will be more than $8.20?
Answer:
(a) The standard error of the mean is 0.091.
(b) The probability that the sample mean will be less than $7.75 is 0.0107.
(c) The probability that the sample mean will be less than $8.10 is 0.9369.
(d) The probability that the sample mean will be more than $8.20 is 0.0043.
Step-by-step explanation:
We are given that the average price for a movie in the United States in 2012 was $7.96.
Assume the population standard deviation is $0.50 and that a sample of 30 theaters was randomly selected.
Let [tex]\bar X[/tex] = sample mean price for a movie in the United States
The z-score probability distribution for the sample mean is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean price for a movie = $7.96
[tex]\sigma[/tex] = population standard deviation = $0.50
n = sample of theaters = 30
(a) The standard error of the mean is given by;
Standard error = [tex]\frac{\sigma}{\sqrt{n} }[/tex] = [tex]\frac{0.50}{\sqrt{30} }[/tex]
= 0.091
(b) The probability that the sample mean will be less than $7.75 is given by = P([tex]\bar X[/tex] < $7.75)
P([tex]\bar X[/tex] < $7.75) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{7.75-7.96}{\frac{0.50}\sqrt{30} } }[/tex] ) = P(Z < -2.30) = 1 - P(Z [tex]\leq[/tex] 2.30)
= 1 - 0.9893 = 0.0107
The above probability is calculated by looking at the value of x = 2.30 in the z table which has an area of 0.9893.
(c) The probability that the sample mean will be less than $8.10 is given by = P([tex]\bar X[/tex] < $8.10)
P([tex]\bar X[/tex] < $8.10) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{8.10-7.96}{\frac{0.50}\sqrt{30} } }[/tex] ) = P(Z < 1.53) = 0.9369
The above probability is calculated by looking at the value of x = 1.53 in the z table which has an area of 0.9369.
(d) The probability that the sample mean will be more than $8.20 is given by = P([tex]\bar X[/tex] > $8.20)
P([tex]\bar X[/tex] > $8.20) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{8.20-7.96}{\frac{0.50}\sqrt{30} } }[/tex] ) = P(Z > 2.63) = 1 - P(Z [tex]\leq[/tex] 2.63)
= 1 - 0.9957 = 0.0043
The above probability is calculated by looking at the value of x = 2.63 in the z table which has an area of 0.9957.
Imagine you have a rectangular wooden block with dimensions of 10 cm x 3 cm x 8 cm (L x W x H). Required:a. What is the volume of your wooden block?b. What is the density of this wooden block if it has a mass of 168 g?
Answer:
a) The volume of the wooden block is 240 cm^3.
b) The density of the wooden block is 0.7 g/cm^3.
Step-by-step explanation:
The volume of the rectangular wooden block can be calculated as the multiplication of the length in each dimension: length, wide and height.
With dimensions 10 cm x 3 cm x 8 cm, the volume is:
[tex]V=L\cdot W\cdot H = 10\cdot 3\cdot 8=240[/tex]
The volume of the wooden block is 240 cm^3.
If we know that the mass of the wooden block is 168 g, we can calculate the density as:
[tex]\rho = \dfrac{M}{V}=\dfrac{168}{240}=0.7[/tex]
The density of the wooden block is 0.7 g/cm^3.
At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. Assume that the statistician also gave us the information that the distribution of serve speeds was mound- shaped and symmetric. What percentage of the player's serves were between 115 mph and 145 mph
Answer:
15.74% of the player's serves were between 115 mph and 145 mph
Step-by-step explanation:
When the distribution is normal, we use 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 question, we have that:
[tex]\mu = 100, \sigma = 15[/tex]
What percentage of the player's serves were between 115 mph and 145 mph
This is the pvalue of Z when X = 145 subtracted by the pvalue of Z when X = 115.
X = 145
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{145 - 100}{15}[/tex]
[tex]Z = 3[/tex]
[tex]Z = 3[/tex] has a pvalue of 0.9987
X = 115
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{115 - 100}{15}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
0.9987 - 0.8413 = 0.1574
15.74% of the player's serves were between 115 mph and 145 mph
Factor completely 6x to the second power - 36xy + 12x
Answer:
6x(x - 6y +2)
Step-by-step explanation:
Step 1: Write out expression
6x² - 36xy + 12x
Step 2: Factor out x
x(6x - 36y + 12)
Step 3: Factor out 6
6x(x - 6y + 2)
That is the most we can do. We can only take GCF to factor. Since we don't have an y² term we do not have binomial factors.
Where is my phone? I seem to have lost my phone. I know where I last saw it but it has been moved since then and I need help to locate it. It started at the following coordinates A (14, -12); B (14, -19); C (10, -19); D (10, -14); E (13, -14); F (13, -12). My Mom told me she translated it 6 units to the left Then my little brother said he had reflected it over the Y-axis My friend many found it and translated it 9 units up Dad said he tripped over it and reflected it over the X-axis My sister then rotated it 900 clockwise Uncle Jose translated it 5 units left and 4 units down Cousin Michelle then said she rotated it 900 clockwise Finally my dog picked it up and translated it 5 units down and 10 units to the right Where is my phone? Using the scenario on this page do the following. Graph the preimage using the given points. Label points (A, B, C, ...) Transform the objects using the information provided. Show each transformation and label. (A', B', C', ...) Determine the final location. Write a 2 to 3 sentence explain on how you found the phone location.
Answer:
see attached
Step-by-step explanation:
The attachments show the initial (brown) and final (blue) positions of the phone. The spreadsheet shows all the intermediate locations and the formulas used to determine them.
The two reflections cancel the total of 180° of CW rotation, so the net result is simply a translation. That translation is up by 9 units.
__
Translation up adds to the y-coefficient; translation right adds to the x-coefficient. Down or left use negative values.
90° CW does this: (x, y) ⇒ (y, -x)
Reflection across y does this: (x, y) ⇒ (-x, y)
Reflection across x does this: (x, y) ⇒ (x, -y)
A game popular in Nevada gambling casinos is Keno, which is played as follows: Twenty numbers are selected at random by the casino from the set of numbers 1 through 80. A player can select from 1 to 15 numbers; a win occurs if some fraction of the player’s chosen subset matches any of the 20 numbers drawn by the house. The payoff is a function of the number of elements in the player’s selection and the number of matches. For instance, if the player selects only 1 number, then he or she wins if this number is among the set of 20, and the payoff is $2.20 won for every dollar bet. (As the player’s probability of winning in this case is , it is clear that the "fair" payoff should be $3 won for every $1 bet). When the player selects 2 numbers, a payoff (of odds) of $12 won for every $1 bet is made when both numbers are among the 20.A) What would be the fair payoff in this case? Let P, k denote the probability that exactly k of the n numbers chosen by the player are among the 20 selected by the house. B) Compute Pn, k.C) The most typical wager at Keno consists of selecting 10 numbers. For such a bet, the casino pays off as shown in the following table. Compute the expected payoff.
The missing part in the question;
and the payoff is $2.20 won for every dollar bet. (As the player’s probability of winning in this case is [tex]\dfrac{1}{4}[/tex]........
Also:
For such a bet, the casino pays off as shown in the following table.
The table can be shown as:
Keno Payoffs in 10 Number bets
Number of matches Dollars won for each $1 bet
0 - 4 -1
5 1
6 17
7 179
8 1299
9 2599
10 24999
Answer:
Step-by-step explanation:
Given that:
Twenty numbers are selected at random by the casino from the set of numbers 1 through 80
A player can select from 1 to 15 numbers; a win occurs if some fraction of the player’s chosen subset matches any of the 20 numbers drawn by the house
Let assume X to represent the numbers of player chooses which are in the Casino-selected-set of 20.
Let assume the random variable X has a hypergeometric distribution with parameters N= 80 and m =20.
Then, the probability mass function of a hypergeometric distribution can be defined as:
[tex]P(X=k)=\dfrac{(^m_k)(^{N-m}_{n-k})}{(^N_n)}, k =1,2,3 ... n[/tex]
Now; the probability that i out of n numbers chosen by the player among 20 can be expressed as:
[tex]P(X=k)=\dfrac{(^{20}_k)(^{60}_{n-k})}{(^{80}_n)}, k =1,2,3 ... n[/tex]
Also; given that ; When the player selects 2 numbers, a payoff (of odds) of $12 won for every $1 bet is made when both numbers are among the 20
So; n= 2; k= 2
Then :
Probability P ( Both number in the set 20) [tex]=\dfrac{(^{20}_2)(^{60}_{2-2})}{(^{80}_2)}[/tex]
Probability P ( Both number in the set 20) [tex]= \dfrac{20*19}{80*79}[/tex]
Probability P ( Both number in the set 20) [tex]=\dfrac{19}{316}[/tex]
Probability P ( Both number in the set 20) [tex]=\dfrac{1}{16.63}[/tex]
Thus; the payoff odd for [tex]=\dfrac{1}{16.63}[/tex] is 16.63:1 ,as such fair payoff in this case is $16.63
Again;
Let assume X to represent the numbers of player chooses which are in the Casino-selected-set of 20.
Let assume the random variable X has a hypergeometric distribution with parameters N= 80 and m =20.
The probability mass function of the hypergeometric distribution can be defined as :
[tex]P(X=k)=\dfrac{(^m_k)(^{N-m}_{n-k})}{(^N_n)}, k =1,2,3 ... n[/tex]
Now; the probability that i out of n numbers chosen by the player among 20 can be expressed as:
[tex]P(n,k)=\dfrac{(^{20}_k)(^{60}_{n-k})}{(^{80}_n)}, k =1,2,3 ... n[/tex]
From the table able ; the expected payoff can be computed as shown in the attached diagram below. Thanks.
Can some help me if your good at maths
Answer:
36=2×3×3×3
36=2×3³Answer
[tex]36 = 2 \times 2 \times 3 \times 3 \\ \: \: \: \: \: \: \: \: = {2}^{2} \times {3}^{2} [/tex]
Step-by-step explanation:
First write the prime factors of 36 that you can see here
[tex]2 \: \: \: 2 \: \: \: 3 \: \: \: 3[/tex]
Now write 36 as a product of its prime factors.
[tex]36 = 2 \times 2 \times 3 \times 3 \\ \: \: \: \: \: \: \: \: = {2}^{2} \times {3}^{2} [/tex]
An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. The classes are open to any of the 100 students in the school. There are 28 students in the Spanish class, 26 in the French class, and 16 in the German class. There are 12 students who are in both Spanish and French, 4 who are in both Spanish and German, and 6 who are in both French and German. In addition, there are 2 students taking all 3 classes. If two students are randomly chosen, what is the probability that at exactly one of them does exactly two language classes.
Answer:
The probability that at exactly one of them does exactly two language classes is 0.32.
Step-by-step explanation:
We can model this variable as a binomial random variable with sample size n=2.
The probability of success, meaning the probability that a student is in exactly two language classes can be calculated as the division between the number of students that are taking exactly two classes and the total number of students.
The number of students that are taking exactly two classes is equal to the sum of the number of students that are taking two classes, minus the number of students that are taking the three classes:
[tex]N_2=F\&S+S\&G+F\&G-F\&S\&G=12+4+6-2=20[/tex]
Then, the probabilty of success p is:
[tex]p=20/100=0.2[/tex]
The probability that k students are in exactly two classes can be calcualted as:
[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{2}{k} 0.2^{k} 0.8^{2-k}\\\\\\[/tex]
Then, the probability that at exactly one of them does exactly two language classes is:
[tex]P(x=1) = \dbinom{2}{1} p^{1}(1-p)^{1}=2*0.2*0.8=0.32\\\\\\[/tex]
2.
√3x + 7 + √x + 1 =2
Answer:
x = -1
Step-by-step explanation:
The usual approach to these is to square the radicals until they are gone.
[tex]\displaystyle\sqrt{3x+7}+\sqrt{x+1}=2\\\\(3x+7) +2\sqrt{(3x+7)(x+1)}+(x+1) = 4\qquad\text{square both sides}\\\\2\sqrt{(3x+7)(x+1)}=-4x-4\qquad\text{subtract $4x+8$}\\\\(3x+7)(x+1)=(-2x-2)^2\qquad\text{divide by 2, square again}\\\\3x^2+10x +7=4x^2+8x+4\qquad\text{simplify}\\\\x^2-2x-3=0\qquad\text{subtract the left expression}\\\\(x-3)(x+1)=0\qquad\text{factor}\\\\x=3,\ x=-1\qquad\text{solutions to the quadratic}[/tex]
Each time the equation is squared, the possibility of an extraneous root is introduced. Here, x=3 is extraneous: it does not satisfy the original equation.
The solution is x = -1.
_____
Using a graphing calculator to solve the original equation can avoid extraneous solutions. The attachment shows only the solution x = -1. Rather than use f(x) = 2, we have rewritten the equation to f(x)-2 = 0. The graphing calculator is really good at showing the function values at the x-intercepts.
Margo borrows $1700, agreeing to pay it back with 4% annual interest after 6 months. How much interest
will she pay?
Round your answer to the nearest cent, if necessary.
Answer:
$1733.67
Step-by-step explanation:
Simple interest rate formula: A = P(1 + r)^t
Simply plug in your known variables
A = 1700(1 + 0.04)^0.5
A = 1733.67
Remember that t is time in years.
The answer to – 7x + y = -10
Step-by-step explanation:
y=7x-10
Answer:
[tex]\huge \boxed{y=7x-10}[/tex]
Step-by-step explanation:
[tex]-7x+y=-10[/tex]
[tex]\sf Add \ 7x \ on \ both \ sides.[/tex]
[tex]-7x+y+7x=-10+7x[/tex]
[tex]y=7x-10[/tex]
The television show 50 Minutes has been successful for many years. That show recently had a share of 20, meaning that among the TV sets in use, 20% were tuned to 50 Minutes. Assume that an advertiser wants to verify that 20% share value by conducting its own survey, and a pilot survey begins with 14 households have TV sets in use at the time of a 50 Minutes broadcast. Find the probability that none of the households are tuned to 50 Minutes.
Answer:
The probability that none of the households are tuned to 50 Minutes is 0.04398.
Step-by-step explanation:
We are given that the television show 50 Minutes has been successful for many years. That show recently had a share of 20, meaning that among the TV sets in use, 20% were tuned to 50 Minutes.
A pilot survey begins with 14 households have TV sets in use at the time of a 50 Minutes broadcast.
The above situation can be represented through binomial distribution;
[tex]P(X = r)= \binom{n}{r} \times p^{r} \times (1-p)^{n-r} ;x = 0,1,2,3,.........[/tex]
where, n = number of samples (trials) taken = 14 households
r = number of success = none of the households are tuned to 50 min
p = probability of success which in our question is probability that households were tuned to 50 Minutes, i.e. p = 20%
Let X = Number of households that are tuned to 50 Minutes
So, X ~ Binom(n = 14, p = 0.20)
Now, the probability that none of the households are tuned to 50 Minutes is given by = P(X = 0)
P(X = 0) = [tex]\binom{14}{0} \times 0.20^{0} \times (1-0.20)^{14-0}[/tex]
= [tex]1 \times 1 \times 0.80^{14}[/tex]
= 0.04398
Jack works in a supermarket. He earns $186 a week. How much does he earn in a 52 week year?
Answer:
9672 per year
Step-by-step explanation:
Take the amount he earns per week times the number of weeks he works
186* 52
9672 per year
Answer:
$9672
Step-by-step explanation:
Jack earns $186 in 1 week.
In 52 weeks,
186 × 52 = 9672
He earns $9672.
what is the volume of a cone with the given dimensions. radius=4 cm; height= 10 cm
Answer:
[tex] 167.47 \: {cm}^{3} [/tex]
Step-by-step explanation:
[tex]V_{cone} = \frac{1}{ 3} \pi {r}^{2}h \\ \\ = \frac{1}{ 3} \pi \times {4}^{2} \times 10 \\ \\ = \frac{1}{ 3} \times 3.14 \times 16 \times 10 \\ \\ = \frac{1}{ 3} \times \: 502.4 \\ \\ = 167.466667 \\ \\ = 167.47 \: {cm}^{3} [/tex]
The formula for the area of a parallelogram is A = bh,
where b is the base and h is the height.
(x-4) cm
(2x2 + 2x-6) cm
(Not drawn to scale)
Answer:
B) 2x³ – 6x² – 14x + 24 square centimetersStep-by-step explanation:
The question is incomplete and lacks the required diagram. Find the diagram attached. Here is also the complete question.
"The formula for the area of a parallelogram is A = bh, where b is the base and h is the height. Which simplified expression represents the area of the parallelogram? –4x3 + 14x – 24 square centimeters 2x3 – 6x2 – 14x + 24 square centimeters –4x3 – 14x + 24 square centimeters 2x3 + 6x2 + 14x + 24 square centimeters"
Area of a parallelogram = Base * Height.
Given the height of the parallelogram = (x-4)cm
Base = (2x² + 2x-6) cm
Area of the parallelogram = (x-4)cm * (2x² + 2x-6) cm
Area of the parallelogram = (x-4)(2x²+2x-6)
Area of the parallelogram = 2x³+2x²-6x-8x²-8x+24
= 2x³+2x²-8x²-6x-8x+24
= (2x³-6x²-14x+24)cm²
Solve for x: −3x + 3 < 6
Answer:x>-1
Step-by-step explanation:
Step 1: Subtract 3 from both sides.
-3x+3-3<6-3
-3x<3
Step 2: Divide both sides by -3.
-3x/-3<3/3
X>-1
A company makes wax candles shaped like rectangular prisms. Each candle is 7cm long, 2cm wide, and 10cm tall. If they used 5740cm^3 of wax, how many candles did they make?
Answer: 41 candles
Step-by-step explanation:
Multiply the dimensions of the candle first.
V = l*w*h
7 * 2 = 14
14 * 10 = 140
Now, divide the total amount of wax used by the amount of wax used for one candle.
5,740 / 140 = 41
there are only red counters and blue counters in a bag. Jim takes at random a counter from a bag. the probability that the counter is red is 0.45 Jim puts the counter back into the bag. Molly takes at random a counter from the bag. She puts the counter back in the bag. What is the probability that Jim and Molly take counters of different colours? Give your answer as a decimal
Answer:
0.495 probability that Jim and Molly take counters of different colours
Step-by-step explanation:
For each trial, there are only two possible outcomes. Either a blue counter is picked, or a red counter is picked. The counter is put back in the bag after it is taken, which means that we can use the binomial probability distribution 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.
The probability that the counter is red is 0.45
This means that [tex]p = 0.45[/tex]
Jim taken a counter, then Molly:
Two trials, so [tex]n = 2[/tex]
What is the probability that Jim and Molly take counters of different colours?
One red and one blue. So this is P(X = 1).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{2,1}.(0.45)^{1}.(0.55)^{1} = 0.495[/tex]
0.495 probability that Jim and Molly take counters of different colours
Please help !! Correct and first answer I’ll give you brainesttttt ! What is the equation of the line?
Step-by-step explanation:
can u give image PlZzzzz ....
Answer:
Hey!
Your answer should be Y=2x+4
Step-by-step explanation:
Hope this helps!
B
Round your answer to the nearest hundredth.
A
9
B
5
Answer:
56.25°
Step-by-step explanation:
The definition of the cosine function tells you that
cos(B) = BC/BA
B = arccos(BC/BA) = arccos(5/9)
B ≈ 56.25°
Please answer this correctly
Answer:
The number of employees classified into groups as shown below:
1 - 10: 3 6 (2companies)
11-20: 16 (1 company)
21-30: 25, 26, 27 (3 companies)
31-40: 34, 35, 35, 35, 36 (5 companies)
41-50: 41, 43, 48, 48 (4 companies)
Hope this helps!
Answer:
11-20 is 1
31-40 is 5
Step-by-step explanation:
Just count the amount
Hope that helps :D
Use the sample data and confidence level given below to complete parts (a) through (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n equals 1036 and x equals 583 who said "yes." Use a 90 % confidence level.
Required:
a. Find the best point estimate of the population proportion p.
b. Identify the value of the margin of error E =_______
c. Construct the confidence interval.
d. Write a statement that correctly interprets the confidence interval.
1. One has 99% confidence that the sample proportion is equal to the population proportion.
2. There is a 99% chance that the true value of the population proportion will fall between the lower bound and the upper bound.
3. One has 99% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.
Answer:
a. p=0.562
b. E = 0.0253
c. The 90% confidence interval for the population proportion is (0.537, 0.587).
d. We have 90% confidence that the interval (0.537, 0.587) contains the true value of the population proportion.
Step-by-step explanation:
We have to calculate a 90% confidence interval for the proportion.
The sample proportion is p=0.562.
[tex]p=X/n=583/1038=0.562[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.562*0.438}{1038}}\\\\\\ \sigma_p=\sqrt{0.000237}=0.0154[/tex]
The critical z-value for a 90% confidence interval is z=1.645.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot \sigma_p=1.645 \cdot 0.0154=0.0253[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=p-z \cdot \sigma_p = 0.562-0.0253=0.537\\\\UL=p+z \cdot \sigma_p = 0.562+0.0253=0.587[/tex]
The 90% confidence interval for the population proportion is (0.537, 0.587).
We have 90% confidence that the interval contains the true value of the population proportion.
Why do you think writing is an effective way to convince others
Answer:
Considering the audience helps a writer identify the types of details and language needed in the writing. Considering the audience helps the writer identify what is important to him or her. Considering the audience allows the writer to write about what he or she wants. Knowing the audience for a particular essay is important because it determines the content that will appear in the writing. If you are arguing for a change to occur, identifying the level at which you want this change to occur and/or the people you want to persuade to help create this change (audience) is important step by step
Justin spent $23 on fruit at grocery store. He spent a total of $25 at the store. What percentage of the total did he spend on fruit?
Step-by-step explanation:
In my opinion maybe he has spent 98%
You're pretty sure that your candidate for class president has about 6565% of the votes in the entire school. But you're worried that only 100100 students will show up to vote. How often will the underdog (the one with 3535% support) win? To find out, you
Answer:
You're pretty sure that your candidate for class president has about 55% of the votes in the entire school. but you're worried that only 100 students will show up to vote. how often will the underdog (the one with 45% support) win? to find out, you set up a simulation.
a. describe-how-you-will-simulate a component.
b. describe-how-you-will-simulate a trial.
c. describe-the-response-variable
Step-by-step explanation:
Part A:
A component is one voter's voting. An outcome is a vote in favor of our candidate.
Since there are 100 voters, we can stimulate the component by using two random digits from 00 - 99, where the digits 00 - 64 represents a vote for our candidate and the digits 65 - 99 represents a vote for the under dog.
Part B:
A trial is 100 votes. We can stimulate the trial by randomly picking 100 two-digits numbers from 00 - 99.
And counted how many people voted for each candidate. Whoever gets the majority of the votes wins the trial.
Part C:
The response variable is whether the underdog wins or not.
To calculate the experimental probability, divide the number of trials in which the simulated underdog wins by the total number of trials.
Construct a boxplot for the given data. Include values of the 5-number summary in all boxplots. The test scores of 40 students are listed below. Construct a boxplot for the data set.
25 35 43 44 47 48 54 55 56 57
59 62 63 65 66 68 69 69 71 72
72 73 74 76 77 77 78 79 80 81
81 82 83 85 89 92 93 94 97 98
Answer:
Minimum = 25
First quartile = 58
Second quartile = 72
Third quartile = 80
Maximum = 98
Step-by-step explanation:
y= -3/2x-6 x=15 plssssssssssssssssssssssss help
Answer:
-45/2 - 12/2 = -57/2
Step-by-step explanation:
Substitute 15 for x in the given equation: y = (-3/2)x - 6 becomes
y = (-3/2)(15) - 6 = -45/2 - 6 when x = 15. This is equivalent to -57/2
I NEED HELP ASAP PLEASE!!! I REALLY NEED HELP!
Answer:
D.
Step-by-step explanation:
One slope is positive and one negative, so one line should go up and one down. B or D.
y = 1/2 x - 1 line goes up and y-int. = - 1. Answer D.
y = - 1/2 x + 3 line goes up and y-int. = 3. Answer D.
Dr. Miriam Johnson has been teaching accounting for over 20 years. From her experience, she knows that 60% of her students do homework regularly. Moreover, 95% of the students who do their homework regularly generally pass the course. She also knows that 85% of her students pass the course.
a. What is the probability that a student will do homework regularly and also pass the course?
b. What is the probability that a student will neither do homework regularly nor will pass the course?
c. Are the events "pass the course" and "do homework regularly" mutually exclusive? Explain.
d. Are the events "pass the course" and "do homework regularly" independent? Explain.
Answer:
a) The probability that a student will do homework regularly and also pass the course = P(H n P) = 0.57
b) The probability that a student will neither do homework regularly nor will pass the course = P(H' n P') = 0.12
c) The two events, pass the course and do homework regularly, aren't mutually exclusive. Check Explanation for reasons why.
d) The two events, pass the course and do homework regularly, aren't independent. Check Explanation for reasons why.
Step-by-step explanation:
Let the event that a student does homework regularly be H.
The event that a student passes the course be P.
- 60% of her students do homework regularly
P(H) = 60% = 0.60
- 95% of the students who do their homework regularly generally pass the course
P(P|H) = 95% = 0.95
- She also knows that 85% of her students pass the course.
P(P) = 85% = 0.85
a) The probability that a student will do homework regularly and also pass the course = P(H n P)
The conditional probability of A occurring given that B has occurred, P(A|B), is given as
P(A|B) = P(A n B) ÷ P(B)
And we can write that
P(A n B) = P(A|B) × P(B)
Hence,
P(H n P) = P(P n H) = P(P|H) × P(H) = 0.95 × 0.60 = 0.57
b) The probability that a student will neither do homework regularly nor will pass the course = P(H' n P')
From Sets Theory,
P(H n P') + P(H' n P) + P(H n P) + P(H' n P') = 1
P(H n P) = 0.57 (from (a))
Note also that
P(H) = P(H n P') + P(H n P) (since the events P and P' are mutually exclusive)
0.60 = P(H n P') + 0.57
P(H n P') = 0.60 - 0.57
Also
P(P) = P(H' n P) + P(H n P) (since the events H and H' are mutually exclusive)
0.85 = P(H' n P) + 0.57
P(H' n P) = 0.85 - 0.57 = 0.28
So,
P(H n P') + P(H' n P) + P(H n P) + P(H' n P') = 1
Becomes
0.03 + 0.28 + 0.57 + P(H' n P') = 1
P(H' n P') = 1 - 0.03 - 0.57 - 0.28 = 0.12
c) Are the events "pass the course" and "do homework regularly" mutually exclusive? Explain.
Two events are said to be mutually exclusive if the two events cannot take place at the same time. The mathematical statement used to confirm the mutual exclusivity of two events A and B is that if A and B are mutually exclusive,
P(A n B) = 0.
But, P(H n P) has been calculated to be 0.57, P(H n P) = 0.57 ≠ 0.
Hence, the two events aren't mutually exclusive.
d. Are the events "pass the course" and "do homework regularly" independent? Explain
Two events are said to be independent of the probabilty of one occurring dowant depend on the probability of the other one occurring. It sis proven mathematically that two events A and B are independent when
P(A|B) = P(A)
P(B|A) = P(B)
P(A n B) = P(A) × P(B)
To check if the events pass the course and do homework regularly are mutually exclusive now.
P(P|H) = 0.95
P(P) = 0.85
P(H|P) = P(P n H) ÷ P(P) = 0.57 ÷ 0.85 = 0.671
P(H) = 0.60
P(H n P) = P(P n H)
P(P|H) = 0.95 ≠ 0.85 = P(P)
P(H|P) = 0.671 ≠ 0.60 = P(H)
P(P)×P(H) = 0.85 × 0.60 = 0.51 ≠ 0.57 = P(P n H)
None of the conditions is satisfied, hence, we can conclude that the two events are not independent.
Hope this Helps!!!