Step-by-step explanation:
For the charges that have same sign of charges will repel each other while for the charges that have different charges will attract each other. So, we can say that like charges repel and unlike charges attract each other.
The Coulomb's law of attraction of repulsion states that force between charges is directly proportion to the product of charges and inversely proportional to the square of distance between them. Mathematically, it is given by :
[tex]F=\dfrac{kq_1q_2}{r^2}[/tex]
Hence, all the given statements are true.
We want to use this information to determine if there is an effect of friendship. In other words, is the mean price when buying from a friend the same as (or different from) the mean price when buying from a stranger? Assume the two groups have the same population standard deviation, and use significance level 0.05. Suppose that mu1 is the true mean price when buying from a friend and mu2 is the true mean price when buying from a stranger. (a) What are the null and alternative hypotheses?
Answer:
H0 : mu1 = mu2
Ha : mu1 ≠ mu2
Which means
Null hypothesis H0; the true mean price when buying from a friend mu1 and the true mean price when buying from a stranger mu2 is the same/equal
Alternative hypothesis Ha; the true mean price when buying from a friend mu1 and the true mean price when buying from a stranger mu2 is different (not equal)
Step-by-step explanation:
The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean(i.e it tries to prove that the old theory is true). While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.
Therefore, for the case above;
H0 : mu1 = mu2
Ha : mu1 ≠ mu2
Which means
Null hypothesis H0; the true mean price when buying from a friend mu1 and the true mean price when buying from a stranger mu2 is the same/equal
Alternative hypothesis Ha; the true mean price when buying from a friend mu1 and the true mean price when buying from a stranger mu2 is different (not equal)
A group of n people enter an elevator in a building with k floors. Each person independently selects a floor uniformly at random (each with equal probability 1/k). The elevator stops at each floor selected (by at least one person). Let N be the number of stops. (a) [3 marks] Find a simple expression for EN, the average number of stops. Bonus [2 marks] Suppose that n
Answer:
Hence the person stop at floor by at least one person will be
E(X)=(summation from K=1 to k)[1-{(k-1)/k}^n]
Step-by-step explanation:
Given:
There are n peoples and k floors in a building.
Selects floor with 1/k probability .
To find :
Elevator stop at each floor by at least one person.
Solution:
Now
let K= number of floor at which at least one person will be stopping.
For getting E(X)
consider a variable Ak =1 if a least one person get of the elevator
and values for k=1,2,3.....k
K=(summation From k=1 to k)Ak
E(K)=((summation From k=1 to k) E[Ak]
=(summation From k=1 to k)[[tex]1-{(k-1/k)^n[/tex]
Hence the person stop at floor by at least one person will be
E(K)=(summation from K=1 to k)[1-{(k-1)/k}^n]
Find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit. Assume that revenue, Upper R (x ), and cost, Upper C (x ), are in thousands of dollars, and x is in thousands of units. Upper R (x )equals9 x minus 2 x squared, Upper C (x )equalsx cubed minus 3 x squared plus 4 x plus 1
Answer:
-1.39
Step-by-step explanation:
Revenue and cost as a function of units sold are [tex]u(x) = 9x-2x^{2}[/tex]and[tex]c(x)=x^{3}-3x^{2}+4x+1[/tex] respectively.
we are have to know for which value or input units are these functions at maximum which translates to for how many units is the revenue maximum and for how many same units is our cost minimum.
The police department in NYC is trying to determine if it is worth the cost to install a speed sensor and traffic camera on a highway near the city. They will install the speed sensor and traffic camera if convinced that more than 20% of cars are speeding. The police department selects a random sample of 100 cars on the highway, measures their speed, and finds that 28 of the 100 cars are speeding. A significance test is performed using the hypotheses.
Hoo: p=0 .20
Ha:p > 0.20
Where p is the true proportion of all cars on the highway that are speeding. The resulting p-value is 0.023. What conclusion would you make at the alpha level of 0.05 level?
A conclusion can be made that since the alpha level is less than the p-level, then we fail to reject the null hypothesis due p-value being 0.023 being greater than alpha level 0.05.
At a 5 percent significance level and with a p-value of 0.023, we reject the null hypothesis, concluding that more than 20% of cars are speeding.
Explanation:The question involves determining whether to reject the null hypothesis based on a p-value from a statistical test concerning the true proportion of cars that are speeding on a highway. Since the p-value of 0.023 is less than the alpha level of 0.05, we would reject the null hypothesis (H0: p = 0.20). At the 5 percent significance level, there is sufficient evidence to conclude that more than 20% of cars are speeding on the highway.
Since the p-value is less than the alpha level of 0.05, we reject the null hypothesis. Therefore, the police department should consider installing the speed sensor and traffic camera.
To determine if the police department should install a speed sensor and traffic camera based on a significance test, we need to examine the hypotheses:
H0: p = 0.20 (the true proportion of cars speeding is 20%)
H1: p > 0.20 (the true proportion of cars speeding is greater than 20%)
Given that in a random sample of 100 cars, 28 were speeding, the test resulted in a p-value of 0.023. At the alpha level of 0.05, since the p-value (0.023) is less than alpha (0.05), we reject the null hypothesis.
In conclusion, at the 5 percent significance level, there is sufficient evidence to conclude that the true proportion of cars speeding is greater than 20%, justifying the installation of the speed sensor and traffic camera.
Mr. Jackson had $110 to purchase school supplies for his class. He bought 32 boxes of colored pencils and 32 dry erase markers. Each box of colored pencils cost $2.40, and each dry erase marker cost $0.79. How much money did Mr. Jackson have left after these purchases?
Answer:
$7.92
Step-by-step explanation:
110 - ((32 x 2.40) + (32 x 0.79)) = $7.92
Answer:
$7.92 dollars left over
Step-by-step explanation:
32* 2.40= 76.8
32*0.79= 25.28
25.28+ 76.8= 102.08
110-102.08
===========7.92
PLZ HURRY!!!
THE QUESTION AND ANSWER BUBBLE IN PHOTO!
Which inequality is represented by this graph?
A student's tuition was 2800. They took a loan out for 6/7 of the tuition. How much was the loan
If $5000 is invested at a rate of 3% interest compounded quarterly, what is the value of the investment in five years?
A=P(1+r/n)^nt
Answer:
$5,805.92
Step-by-step explanation:
Lets use the compound interest formula provided to solve this:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
P = initial balance
r = interest rate (decimal)
n = number of times compounded annually
t = time
First, change 3% into a decimal:
3% -> [tex]\frac{3}{100}[/tex] -> 0.03
Since the interest is compounded quarterly, we will use 4 for n. Lets plug in the values now:
[tex]A=5,000(1+\frac{0.03}{4})^{4(5)}[/tex]
[tex]A=5,805.92[/tex]
The value of the investment after 5 years will be $5,805.92
Investment value after 5 years, compounded quarterly at 3%, is approximately $5,805.83.
let's calculate step by step.
1. First, let's convert the annual interest rate to decimal form:
[tex]\[ r = 3\% = \frac{3}{100} = 0.03 \][/tex]
2. Now, let's plug in the given values into the compound interest formula:
[tex]\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \][/tex]
where:
[tex]- \( P = $5000 \)\\ - \( r = 0.03 \)\\ - \( n = 4 \)\\ - \( t = 5 \)[/tex]
3. Substituting these values into the formula, we get:
[tex]\[ A = 5000 \left(1 + \frac{0.03}{4}\right)^{4 \times 5} \][/tex]
4. Simplifying inside the parentheses:
[tex]\[ A = 5000 \left(1 + 0.0075\right)^{20} \][/tex]
5. Calculating [tex]\( (1 + 0.0075) \):[/tex]
[tex]\[ 1 + 0.0075 = 1.0075 \][/tex]
6. Now, raise [tex]\( 1.0075 \)[/tex] to the power of [tex]\( 20 \):[/tex]
[tex]\[ (1.0075)^{20} \][/tex]
Using a calculator,[tex]\( (1.0075)^{20} \)[/tex] is approximately [tex]\( 1.161166 \).[/tex]
7. Finally, multiply this result by [tex]\( 5000 \):[/tex]
[tex]\[ A = 5000 \times 1.161166 \]\\ \[ A \approx 5,805.83 \][/tex]
So, the value of the investment in five years, compounded quarterly at a 3% interest rate, would be approximately $5,805.83.
here is complete question:-
"If $5000 is invested at a rate of 3% interest compounded quarterly, what is the value of the investment in five years?"
Create a list in steps, in order, that will solve the following equation. 3(x+1^2)=108
Answer: x=35
Step-by-step explanation:
1. Divide both by 3
2. Simplify-x+1=36
3. Subtract 1 form both sides
You answer will be x=35
Answer:
Divide Both Sides by 3
Take the Square Root of Both Sides
Subtract 1 from Both Sides
Step-by-step explanation:
Pray!
The caffeine content (in mg) was examined for a random sample of 50 cups of black coffee dispensed by a new machine. The mean and the standard deviation were 110 mg and 7.1 mg respectively. Use the data to construct a 98% confidence interval for the mean caffeine content for cups dispensed by the machine. Interpret the interval!
Answer:
We are 98% confident interval for the mean caffeine content for cups dispensed by the machine between 107.66 and 112.34 mg .
Step-by-step explanation:
Given -
The sample size is large then we can use central limit theorem
n = 50 ,
Standard deviation[tex](\sigma)[/tex] = 7.1
Mean [tex]\overline{(y)}[/tex] = 110
[tex]\alpha =[/tex] 1 - confidence interval = 1 - .98 = .02
[tex]z_{\frac{\alpha}{2}}[/tex] = 2.33
98% confidence interval for the mean caffeine content for cups dispensed by the machine = [tex]\overline{(y)}\pm z_{\frac{\alpha}{2}}\frac{\sigma}\sqrt{n}[/tex]
= [tex]110\pm z_{.01}\frac{7.1}\sqrt{50}[/tex]
= [tex]110\pm 2.33\frac{7.1}\sqrt{50}[/tex]
First we take + sign
[tex]110 + 2.33\frac{7.1}\sqrt{50}[/tex] = 112.34
now we take - sign
[tex]110 - 2.33\frac{7.1}\sqrt{50}[/tex] = 107.66
We are 98% confident interval for the mean caffeine content for cups dispensed by the machine between 107.66 and 112.34 .
Final answer:
A 98% confidence interval for the mean caffeine content of cups dispensed by the machine is calculated using the sample mean, the standard deviation, and the Z-score for a 98% confidence level, leading to an interval of (107.72 mg, 112.28 mg). We can be 98% confident that the true mean caffeine content lies within this range.
Explanation:
To construct a 98% confidence interval for the mean caffeine content of cups dispensed by the machine, we use the provided sample mean (μ), which is 110 mg, and the standard deviation (s), which is 7.1 mg, of the 50 cups sampled. Since the sample size is 50, which is more than 30, we can use the Z-distribution as an approximation of the T-distribution for this confidence interval as the Central Limit Theorem suggests that the distribution of sample means will be normally distributed if the sample size is large enough. Using a Z-score for 98% confidence, which typically is approximately 2.33 (you would obtain the exact value from a Z-table), the margin of error (E) can be calculated using the formula E = Z * (s/√n), where n is the sample size (50 in this case).
The margin of error is then 2.33 * (7.1/√50), which equals approximately 2.28 mg. The 98% confidence interval is therefore the sample mean plus or minus the margin of error, which is 110 mg ± 2.28 mg or (107.72 mg, 112.28 mg).
The interpretation of this confidence interval is that we can be 98% confident that the true mean caffeine content of all cups of coffee dispensed by the machine falls between 107.72 mg and 112.28 mg.
A textbook company claims that their book is so engaging that less than 55% of students read it. If a hypothesis test is performed that fails to reject the null hypothesis, how would this decision be interpreted?
a. There is sufficient evidence to support the claim that less than 55% of students read this text
b. There is not sufficient evidence to support the claim that less than 55% of students read this text
c. There is sufficient evidence to support the claim that no more than 55% of students read this text
d. There is not sufficient evidence to support the claim that no more than 55% of students read this text
Answer:
The answer is B.
Step-by-step explanation:
The example given in the question uses the null hypothesis versus the alternative hypothesis. Null hypothesis is the statement that is tested to be true or not and if it is not true, then the alternative hypothesis is accepted.
In the example, it is stated that the hypothesis test for the null hypothesis failed which means that the statement given on the percentage of students who read the book is false.
Then the option b is going to be interpreted which claims that the null hypothesis is false and there is not enough evidence to say that less than 55% of students read the textbook.
I hope this answer helps.
Final answer:
When a hypothesis test does not reject the null hypothesis with a p-value greater than the alpha level of 0.05, it indicates that there is not sufficient evidence to support the claim being tested, in this case, that less than 55% of students read the textbook.
Explanation:
If a hypothesis test is performed and fails to reject the null hypothesis, the interpretation depends on the results related to the alpha level and the p-value. In this case, where the claim is that less than 55% of students read the textbook and the p-value is greater than the alpha level (0.05 or 5%), the correct interpretation is that there is not sufficient evidence to support the claim that less than 55% of students read the text. This means that the sample data does not provide strong enough evidence to infer that the proportion of students who read the textbook is less than 55% for the entire population of students.
Therefore, the correct answer is:
b. There is not sufficient evidence to support the claim that less than 55% of students read this text.
If each edge equals 5 inches, what will be the surface area of the cube?? Need answer quick!
Answer:
C
Step-by-step explanation:
A cube has 6 faces
Each face is a square of area:
5² = 25
Surface area: 6 × 25
= 150 in²
Answer:
150 in^2
Step-by-step explanation:
The surface area of a cube is given by
SA = 6 s^2 where s is the side length
SA = 6 (5)^2
= 6 * 25
= 6*25
= 150 in^2
To the nearest tenth of a second, how much time would it take the penny to hit the ground?
0.5 seconds
0.6 seconds
0.7 seconds
0.8 seconds
Answer:0.6 sec
Step-by-step explanation:
Answer:
Step-by-step explanation:
0.6 is the answer just took the test
Full-price tickets for a concert cost $ 58.50. Students can purchase a discounted ticket for $ 48.50. If a total of 3250 tickets are sold and if the total amount of ticket sales was $ 160,045a) how many full-price tickets were sold? b) how many student tickets were sold?
Answer:
242 Full Tickets were sold; and
3008 Student Tickets were sold.
Step-by-step explanation:
Let the number of full tickets sold=x
Let the number of student tickets sold =y
A total of 3250 tickets were sold, therefore:
x+y=3250Cost of a Full Ticket =$58.50.
Cost of a Discounted Ticket=$48.50
Total Amount =(58.50. X Number of Full Tickets sold)+(58.50 X Number of Student Tickets sold)
Total amount of ticket sales was $ 160,045
Therefore:
58.50x+48.50y=160045We solve the two equations simultaneously to obtain the values of x and y.
From the First Equation, x=3250-y
Substitute x=3250-y into the Second Equation.
58.50x+48.50y=160045
58.50(3250-y)+48.50y=160045
Open the brackets
190125-58.50y+48.50y=160045
-10y=160045-190125
-10y=-30080
Divide both sides by -10
y=3008
Recall: x=3250-y
x=3250-3008
x=242
Therefore:
242 Full Tickets were sold; and
3008 Student Tickets were sold.
Final answer:
To solve for the number of full-price and student tickets sold, a system of two linear equations is set up and solved using the elimination method. The solution shows that 242 full-price tickets and 3008 student tickets were sold.
Explanation:
To solve this problem, we will use a system of linear equations. Let's define x as the number of full-price tickets and y as the number of student tickets. The two equations based on the information provided will be:
x + y = 3250 (the total number of tickets sold)
58.50x + 48.50y = 160,045 (the total revenue from ticket sales)
To find the number of full-price and student tickets sold, we need to solve this system of equations. We can do this using either the substitution or elimination method. I'll demonstrate the elimination method.
Step 1: Multiply the first equation by 48.50 to align the y terms.
48.50x + 48.50y = 157,625
Step 2: Subtract this new equation from the second equation.
58.50x + 48.50y = 160,045
- (48.50x + 48.50y = 157,625)
10x = 2,420
Step 3: Solve for x
x = 242
Step 4: Use the value of x to solve for y in the first equation.
242 + y = 3250
y = 3250 - 242
y = 3008
So, 242 full-price tickets were sold, and 3008 student tickets were sold.
A person has 5 tickets for a concert and she wants to invite 4 of her 8 best friends. How many choices does she have, if two of her friends do not get along and cannot be both invited?
Answer:
55
Step-by-step explanation:
Combinations formula is used to make choice of 'R' out of 'N' options =
N(C)R = N ! / [ R ! . (N-R)! ]
Total choices to choose 4 out of 8 friends = 8C4
= 8! / (4! 4!)
= 70
Choices for calling them 2 together = 2C2 x 6C2
= 1 x [ 6! / (2! 4!)]
= 15
So : Number of choices that the 2 friends are not called together = Total choices - choices they are called together
= 70 - 15 = 55
What is the area of the kite? A kite has a height of 10 meters and a base of 8 meters.
Answer:
80 meters (8*10=80)
Answer:
80
Step-by-step explanation:
10 times 8= 80
to find the area is always lenght × height × weight
to find the perimeter is always lenght × lenght × heigth × heigth
example...
a house with the height of 5 and the lenght of 1 .find the perimeter
5+5+1+1= 12
It has been estimated that only about 30% of California residents have adequate earthquake supplies. Suppose you randomly survey 11 California residents. We are interested in the number who have adequate earthquake supplies.What is the probability that at least 8 have adequate earthquake supplies?
Is it more likely that none or that all of the residents surveyed will have adequate earthquake
supplies? Why?
Answer:
[tex]P(X\geq 8)=0.0043\\\\[/tex]
It's more likely that all of the residents surveyed will have adequate earthquake supplies since it has a probability of 98.02% which is very close to 100%.
Step-by-step explanation:
-This is a binomial probability problem with the function:
[tex]P(X=x)={n\choose x}p^x(1-p)^{n-x}[/tex]
-Given p=0.3, n=11, the is calculated as:
[tex]P(X=x)={n\choose x}p^x(1-p)^{n-x}\\\\P(X\geq 8)=P(X=8)+P(X=9)+P(X=10)+P(X=11)\\\\={11\choose 8}0.3^8(0.7)^3+{11\choose 9}0.3^9(0.7)^2+{11\choose 10}0.3^{10}(0.7)^1+{11\choose 11}0.3^{11}(0.7)^0\\\\=0.0037+0.0005+0.00005+0.000002\\\\=0.0043[/tex]
Hence, the probability that at least 8 have adequate supplies 0.0043
#The probability that non has adequate supplies is calculated as;
[tex]P(X=x)={n\choose x}p^x(1-p)^{n-x}\\\\P(X= 0)={11\choose 0}0.3^{0}(0.7)^{11}\\\\=0.0198[/tex]
#The probability that all have adequate supplies is calculated as:
[tex]P(X=x)={n\choose x}p^x(1-p)^{n-x}\\\\P(X= All)=1-{11\choose 0}0.3^{0}(0.7)^{11}\\\\=1-0.0198\\\\=0.9802[/tex]
Hence, it's more likely that all of the residents surveyed will have adequate earthquake supplies since [tex]P(All)>P(None)\ \[/tex] and that this probability is 0.9802 or 98.02% a figure close to 1
Final answer:
The probability that at least eight California residents have adequate earthquake supplies when surveying 11 can be calculated with the binomial distribution, summing probabilities for exactly 8, 9, 10, and 11. None having adequate supplies is more likely than all, given the 30% success rate. The average number of surveys before finding a resident without supplies is close to 2, and before finding one with supplies, it is approximately 3.
Explanation:
The probability of at least eight California residents having adequate earthquake supplies when surveying 11 residents can be calculated using the binomial distribution formula. Given that the success probability (having adequate supplies) is 30% (0.3), we can calculate the probability for exactly 8, 9, 10, and 11 residents and sum these probabilities to get the total probability for 'at least 8'.
The random variable X can be defined as the number of successes in n independent Bernoulli trials, with success on each trial having probability p. Here, X represents the number of California residents with adequate earthquake supplies in our sample of 11. The values that X can take on are 0, 1, 2, ..., 11.
To find the probability of none or all residents having adequate supplies, we calculate the probabilities for X = 0 and X = 11. The probability of none (X = 0) would be 0.7¹¹, and the probability of all (X = 11) would be 0.3¹¹. Between these, the probability of none is higher due to the lower success probability.
For the expected number of surveys until finding a resident without adequate supplies, we can use the geometric distribution where the expected value E(X) is 1/p. In this case, p = 0.7 (probability of not having adequate supplies), so E(X) would be approximately 1.43, meaning on average we would have to survey close to one or two residents before finding one without adequate supplies.
Conversely, the expected number of surveys until finding one with adequate supplies would be 1/q, where q = 0.3 (probability of having adequate supplies), giving us an expected value of around 3.33 surveys.
An actor invested some money at 5% simple interest, and $41,000 more than 4 times the amount at 9%. The total annual interest earned from the investment was $35,260. How much did he invest at 5% and 9%?
Answer:
The amount invested at 5%=$77,000The amount invested at 9%=$349,000Step-by-step explanation:
Let the amount invested at 5% simple interest =$xHe invested $41,000 more than 4 times the amount at 9%.
This amount is: $(4x+41000)Total Annual Interest Earned = $35,260
Therefore, Time=1 year
Simple Interest[tex]=\frac{Principal X Rate X Time}{100}[/tex]
Therefore, his total interest
=Interest from Investment 1 + Interest from Investment 2
[tex]35260=\left(\frac{x*5*1}{100} \right)+\left(\frac{4x+41000*9*1}{100} \right)\\35260=0.05x+(0.36x+3690)\\35260-3690=0.05x+0.36x\\31570=0.41x\\\text{Divide both sides by 0.41}\\x=\$77000[/tex]
Therefore:
The amount invested at 5%=$77,000
The amount invested at 9%=$(4*77,000+41000)=$349,000
Evaluate \dfrac {15}k
k
15
start fraction, 15, divided by, k, end fraction when k=3k=3k, equals, 3.
Answer:
5
Step-by-step explanation:
We desire to evaluate the fraction: [tex]\dfrac{15}{k}[/tex] when k=3.
This is a simple substitution, so what is required is
Replace k with the given numberSimplify the resulting expressionTherefore, when k=3
[tex]\dfrac{15}{k}=\dfrac{15}{3}=5[/tex]
You can try the same for any value of k.
The question requires to evaluate the mathematical expression 15/k when k=3. Substituting k with 3, we get 15/3 which equals to 5.
In the subject of Mathematics, the expression 15/k represents a simple division. The value of this expression changes depending on the value assigned to k. In the case where k = 3, we simply substitute 3 in place of k in the expression. This gives us: 15/3 which equals 5. So, 15/3 = 5. So when k = 3, 15/k equals 5.
Learn more about Mathematical Expression here:
https://brainly.com/question/34902364
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0.24 + 4.25 equals what ?
Answer:
4.49
Step-by-step explanation:
Answer:
4.49
Step-by-step explanation:
*Imagine it as money, you have $4.25 and you find $0.24
1) 4.25 + 0.24= 4.49
You now have $4.49
Hoped that helped ;)
What percentage of job opening are published?
a. 10% - 15%
b. 15% - 20%
30% - 35%
35% - 40%
Please select the best answer from the choices provided
Ο
Α
Answer:
a. 10% - 15%
Step-by-step explanation:
The percentage of a job opening, that gets published, is 15% to 20%, just since just scarcely any occupations can be seen on a paper, commercials, and employment sheets. A large portion of the employment opportunities can be gotten notification from those representatives that worked inside the organization since there is only two job vacancies.
Answer:
the answer is b
Step-by-step explanation:
Question 2 of 10
2 Points
Which of the following is the solution to 4|x+32 8?
Nadia deposited $3000 into an account that earns annual simple interest. 13 points
After 6 years, she had earned $990 in interest. What was the interest rate
of the account? *
Your answer
To find the annual interest rate of Nadia’s account, we use the simple interest formula I = PRT. By rearranging the formula and plugging in the known values, we determine that the interest rate is 5.5%.
Explanation:To determine the interest rate of Nadia’s account, we can use the formula for simple interest I = PRT, where I is the interest earned, P is the principal amount deposited, R is the annual interest rate in decimal, and T is the time in years. In Nadia's case, we know that she earned $990 in interest (I), deposited $3000 (P), over 6 years (T).
We need to solve for R.
The formula thus becomes: $990 = $3000 × R × 6
To find R, we divide both sides of the equation by $3000 × 6:
R = $990 / ($3000 × 6)
R = $990 / $18000
R = 0.055 or 5.5%
Therefore, the annual interest rate Nadia received on her account was 5.5%.
1. A group of 400 town residents is asked to attend a
town hall meeting. Of the 400 residents asked to
attend, 36 were able to attend. What percentage of the
town residents were able to attend?
Answer:
9%
Step-by-step explanation:
36/400=9/100=9%
Angle measure represented by 36.7 rotations counterclockwise
Answer:
13,212° or 73.4π radiansStep-by-step explanation:
Each rotation is 360° or 2π radians. So, 36.7 rotations is ...
36.7×360° = 13,212°
or
36.7×2π = 73.4π radians
Lue is rolling a random number cube.The cube has six sides,and each one is labeled with a number 1 through 6. What is the probability that he will roll a sum of 12 in two rolls
Answer:
2%
Step-by-step explanation:
You do 12÷6×1=2
I used PEMDAS
Final answer:
The probability that Lue will roll a sum of 12 on two rolls of a standard six-sided die is 1/36 or about 2.78%, as only the combination (6,6) results in the sum of 12.
Explanation:
Probability of Rolling a Sum of 12
To calculate the probability that Lue will roll a sum of 12 on two rolls of a six-sided die, we need to consider all the possible combinations that can result in a sum of 12. These combinations are (6,6). Since each die is independent, we calculate the probability for one die and then square it for two dice, because there is only one way to get a six on a die, and there are six faces. Therefore, the probability of rolling a six is:
1/6
To find the probability of rolling two sixes, we multiply the probabilities of each independent event:
(1/6) × (1/6) = 1/36
So, the probability that Lue will roll a sum of 12 in two rolls is 1/36, or approximately 2.78%.
Certain car manufacturers install a gauge that tells the driver how many miles they can drive until they will run out of gas. A study was conducted to test the accuracy of these gauges. Each driver was assigned a certain gauge reading until empty to watch for. When their car announced it had that many miles remaining until empty, they began to measure their distance traveled. After they ran out of gas, they reported the distance they were able to drive (in miles) as well as the gauge reading they were assigned (in miles). Here is computer output showing the regression analysis: Regression Analysis: Distance versus Gauge Reading Predictor Coef SE Coet Constant -0.7928 3.2114 -0.2469 0.8060 Gauge 1.1889 0.0457 26.0310 0.0000 B = 7.0032 R-39 = 0.9326 2-3q(adj) = 0.9312 Identify and interpret the slope of the regression line used for predicting the actual distance that can be driven based on the gauge reading.
Answer:
that a hard question
Step-by-step explanation:
i tried to use a calculator and graphs to solve it but I couldn't
Answer:
Slope = 1.1889. The predicted distance the drivers were able to drive increases by 1.1889 miles for each additional mile reported by the gauge.
Step-by-step explanation:
The slope is the second value under the “Coef” column. The interpretation of slope must include a non-deterministic description (“predicted”) about how much the response variable (actual number of miles driven) changes for each 1-unit increment of change in the explanatory variable (the gauge reading) in context.
What is the probability that X is between 12 and 60?
An NBA fan named Mark claims that there are more fouls called on his team 1 point
any other team, but the commissioner says that the number of fouls called
against his team are no different than any other team. Mark finds that the
average number of fouls in any game in the NBA is 11.5. He takes a random
sample of 34 of games involving his team and finds that there are an
average of 12.2 fouls against his team, with a standard deviation of 1.6 fouls.
What is the correct conclusion? Use a = 0.05
a) The p value is 2.55 indicating insufficient evidence for his claim.
b)The p-value is 0.008, indicating sufficient evidence for his claim.
c)The p-value is 0.008, indicating insufficient evidence for his claim.
d)The p-value is 2.55, indicating sufficient evidence for his claim.
Answer:
[tex]t=\frac{12.2-11.5}{\frac{1.6}{\sqrt{34}}}=2.551[/tex]
[tex] df = n-1=34-1=33[/tex]
[tex]p_v =P(t_{(33)}>2.551)=0.008[/tex]
Since the p value is less than the significance level of 0.05 we have enough evidence to reject the null hypothesis in favor of the claim
And the best conclusion for this case would be:
b)The p-value is 0.008, indicating sufficient evidence for his claim.
Step-by-step explanation:
Information provided
[tex]\bar X=12.2[/tex] represent the sample mean fould against
[tex]s=1.6[/tex] represent the sample standard deviation
[tex]n=34[/tex] sample size
represent the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
System of hypothesis
We need to conduct a hypothesis in order to check if the true mean is higher than 11.5 fouls per game:
Null hypothesis:[tex]\mu \leq 11.5[/tex]
Alternative hypothesis:[tex]\mu > 11.5[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
The statistic is given by:
[tex]t=\frac{12.2-11.5}{\frac{1.6}{\sqrt{34}}}=2.551[/tex]
P value
The degreed of freedom are given by:
[tex] df = n-1=34-1=33[/tex]
Since is a one side test the p value would be:
[tex]p_v =P(t_{(33)}>2.551)=0.008[/tex]
Since the p value is less than the significance level of 0.05 we have enough evidence to reject the null hypothesis in favor of the claim
And the best conclusion for this case would be:
b)The p-value is 0.008, indicating sufficient evidence for his claim.
Suppose SAT Writing scores are normally distributed with a mean of 493 and a standard deviation of 108. A university plans to send letters of recognition to students whose scores are in the top 10%. What is the minimum score required for a letter of recognition
Answer:
The minimum score required for a letter of recognition is 631.24.
Step-by-step explanation:
Problems of normally distributed samples are 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 = 493, \sigma = 108[/tex]
What is the minimum score required for a letter of recognition
100 - 10 = 90th percentile, which is the value of X when Z has a pvalue of 0.9. So X when Z = 1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 493}{108}[/tex]
[tex]X - 493 = 1.28*108[/tex]
[tex]X = 631.24[/tex]
The minimum score required for a letter of recognition is 631.24.
Answer:
[tex]b=493 +1.28*108=631.24[/tex]
The minimum score required for a letter of recognition would be 631.24
Step-by-step explanation:
Let X the random variable that represent the writing scores of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(493,108)[/tex]
Where [tex]\mu=493[/tex] and [tex]\sigma=108[/tex]
On this questio we want to find a value b, such that we satisfy this condition:
[tex]P(X>b)=0.10[/tex] (a)
[tex]P(X<b)=0.90[/tex] (b)
Both conditions are equivalent on this case. We can use the z score again in order to find b.
As we can see on the figure attached the z value that satisfy the condition with 0.90 of the area on the left and 0.1 of the area on the right it's z=1.28. On this case P(Z<1.28)=0.9 and P(z>1.28)=0.1
If we use condition (b) from previous we have this:
[tex]P(X<b)=P(\frac{X-\mu}{\sigma}<\frac{b-\mu}{\sigma})=0.90[/tex]
[tex]P(z<\frac{b-\mu}{\sigma})=0.90[/tex]
[tex]z=1.28<\frac{b-493}{108}[/tex]
And if we solve for a we got
[tex]b=493 +1.28*108=631.24[/tex]
The minimum score required for a letter of recognition would be 631.24