Answer:
Hence the correct option is option c has a Binomial distribution with n=21 and p=50%.
Step-by-step explanation:
1)
A coin is tossed 19 times,
P(Head)=0.5
P(Tail)=0.5
We have to find the probability of a total number of heads in all the coin tosses equals 9.
This can be solved using the binomial distribution. For binomial distribution,
P(X=x)=C(n,x)px(1-p)n-x
where n is the number of trials, x is the number of successes, p is the probability of success, C(n,x) is a number of ways of choosing x from n.
P(X=9)=C(19,9)(0.5)9(0.5)10
P(X=9)=0.1762
2)
A fair die is rolled twice.
Total number of outcomes=36
Possibilities of getting sum as 9
S9={(3,6),(4,5)(5,4),(6,3)}
The total number of spots showing in all the die rolls equals 9 =4/36=0.1111
3)
The event of getting a good number of spots on a die roll is actually no different from the event of heads on a coin toss since the probability of a good number of spots is 3/6 = 1/2, which is additionally the probability of heads. the entire number of heads altogether the tosses of the coin plus the entire number of times the die lands with a good number of spots has an equivalent distribution because the total number of heads in 19+2= 21 tosses of the coin. The distribution is binomial with n=21 and p=50%.
Write the piecewise defined function for the total cost of parking in the garage. That is, state the function C(x), where x is the number of hours a car is parked in the garage.
Answer:
[tex]C(x) = \left[\begin{array}{ccc}4x &0 \le x \le 2& \\4 +2x &2 < x \le 6& \\16 &6<x\le 8& \end{array}\right[/tex]
Step-by-step explanation:
Given
See attachment for question
Required
The piece-wise function
From the attachment, we have:
(1) $4/hr for first 2 hours
This is represented as:
[tex]C(x) = 4x[/tex]
The domain is: [tex]0 \le x \le 2[/tex]
(2) $2/hr for next 4 hours
Here, we have:
[tex]Rate = 2[/tex]
The total cost in the first 2 hours is:
[tex]C(x) = 4x[/tex]
[tex]C(2) = 4*2 = 8[/tex]
So, this function is represented as:
[tex]C(x) = C(2) + Rate * (Time - 2)[/tex] ----- 2 represents the first 2 hours
So, we have:
[tex]C(x) = C(2) + Rate * (Time - 2)[/tex]
[tex]C(x) =8 + 2(x - 2)[/tex]
Open brackets
[tex]C(x) =8 + 2x - 4[/tex]
Collect like terms
[tex]C(x) =8 - 4+ 2x[/tex]
[tex]C(x) =4+ 2x[/tex]
The domain is:
[tex]2 < x \le 2 + 4[/tex]
[tex]2 <x \le 6[/tex]
(3) 0 charges for the last 2 hours
The maximum charge from (2) is:
[tex]C(x) =4+ 2x[/tex]
[tex]C(6) = 4 + 2*6[/tex]
[tex]C(6) = 4 + 12[/tex]
[tex]C(6) = 16[/tex]
Since there will be no additional charges, then:
[tex]C(x) = 16[/tex]
And the domain is:
[tex]6 < x \le 8[/tex] --- 8 represents the limit
So, we have:
[tex]C(x) = \left[\begin{array}{ccc}4x &0 \le x \le 2& \\4 +2x &2 < x \le 6& \\16 &6<x\le 8& \end{array}\right[/tex]
A soccer team wants new uniforms. A jersey costs $42, shorts cost $26, socks cost $6, and shinguards cost $18. How much does one
uniform cost?
$62
$74
$83
$92
Answer:
$92
Step-by-step explanation:
42 + 26 + 6 + 18 = 92
A baseball team plays in a stadium that holds 58000 spectators. With the ticket price at $12 the average attendance has been 25000. When the price dropped to $9, the average attendance rose to 29000. Assume that attendance is linearly related to ticket price.
Required:
a. Find the demand function p(x), where x is the number of the spectators.
b. How should ticket prices be set to maximize revenue?
Answer:
We need to assume that the relationship is linear.
a) Remember that a linear relation is written as:
y = a*x + b
then we will have:
p(x) = a*x + b
where a is the slope and b is the y-intercept.
If we know that the line passes through the points (a, b) and (c, d), then the slope can be written as:
y = (d - b)/(c - a)
In this case, we know that:
if the ticket has a price of $12, the average attendance is 25,000
Then we can define this with the point:
(25,000 , $12)
We also know that when the price is $9, the attendance is 29,000
This can be represented with the point:
(29,000, $9)
Then we can find the slope as:
a = ($9 - $12)/(29,000 - 25,000) = -$3/4,000 = -$0.00075
Then the equation is something like:
y = (-$0.00075)*x + b
to find the value of b we can use one of the known points.
For example, the point (25,000 , $12) means that when x = 25,000, the price is $12
then:
$12 = (-$0.00075)*25,000 + b
$12 = -$18.75 + b
$12 + $18.75 = b
$30.75 = b
Then the equation is:
p(x) = (-$0.00075)*x + $30.75
b) We want to find the ticket price such that it maximizes the revenue.
The revenue will be equal to the price per ticket, p(x) times the total attendance, x.
Then the revenue can be written as:
r(x) = x*p(x) = x*( (-$0.00075)*x + $30.75 )
r(x) = (-$0.00075)*x^2 + $30.75*x
So we want to find the maximum revenue.
Notice that this is a quadratic equation with a negative leading coefficient, thus the maximum will be at the vertex.
Remember that for an equation like:
y = a*x^2 + bx + c
the x-value of the vertex is:
x = -b/2a
Then in our case, the x-value will be:
x = -$30.75/(2*(-$0.00075)) = 20,500
Then the revenue is maximized for x = 20,500
And the price for this x-vale is given by:
p( 20,500) = (-$0.00075)*20,500 + $30.75 = $15.375
which should be rounded to $15.38
K.Brew sells a wide variety of outdoor equipment and clothing. The company sells both through mail order and via the internet. Random samples of sales receipts were studied for mail-order sales and internet sales, with the total purchase being recorded for each sale. A random sample of 18 sales receipts for mail-order sales results in a mean sale amount of $81.90 with a standard deviation of $22.25. A random sample of 8 sales receipts for internet sales results in a mean sale amount of $88.30 with a standard deviation of $23.25. Using this data, find the 90% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases. Assume that the population variances are not equal and that the two populations are normally distributed. Construct the 98% confidence interval.
Answer:
kdjdeoksndoddmsnsksndjdjd
Mrs. Hanson has 3 pies for a party. She calculates that if she splits the pies evenly among the guests, they will each receive
1/6
of a pie. How many guests are there?
Answer:
18 guests.
Step-by-step explanation:
To find the number of guests, we can simply divide 1/6 from 3. The result gives us 18.
round 12.5478 to the nearest hundredths
Answer:
12.04
Step-by-step explanation:
Find the number in the hundredth place 4 and look one place to the right for the rounding digit 1 . Round up if this number is greater than or equal to 5 and round down if it is less than 5 .
I NEED HELP PLEASE!!!
A researcher utilizes a t-test to compare the average amount of beta-lactamase produced by two different types of bacteria. The Levene's test for equality of variances has a p value of 0.01. You know this means:
Answer:
The answer is "T-test results must not be presented if the same variations are expected".
Step-by-step explanation:
A t-test is used by a scientist to compare the average beta-lactamase of two distinct strains of bacteria. The Levene equality test does have a p-value of 0.01. Researchers know that all this means that research should report t-test findings with a failed assumption of identical variances because the Log-rank equality test has a p-value of 0.01 of less than 0.05 that shows different twp population variance.
Determine the quadrant in which the terminal side of the given angle lies.
115°
Answer:
Quadrant 2
Step-by-step explanation:
Given
[tex]\theta = 115^o[/tex]
Required
The quadrant
We have:
[tex]0^o < \theta < 90^o[/tex] --- quadrant 1
[tex]90^o < \theta < 180^o[/tex] --- quadrant 2
[tex]180^o < \theta < 270^o[/tex] --- quadrant 3
[tex]270^o < \theta < 360^o[/tex] --- quadrant 4
So, by comparison; we have:
[tex]90^o < \theta < 180^o[/tex]
Substitute 115 for [tex]\theta[/tex]
[tex]90^o < 115 < 180^o[/tex]
The above is true for quadrant 2
If f(x) is an exponential function where f(-1.5) 26 and
f(5.5) = 7, then find the value of f(10), to the nearest hundredth.
Answer:
[tex]f(10) = 1147.25[/tex]
Step-by-step explanation:
Given
[tex]f(-1.5) = 26[/tex]
[tex]f(5.5) = 7[/tex]
Required
f(10)
An exponential function is represented as:
[tex]f(x) = ab^x[/tex]
[tex]f(-1.5) = 26[/tex] impleies that:
[tex]26 = ab^{-1.5}[/tex] --- (1)
[tex]f(5.5) = 7[/tex] implies that
[tex]7 = ab^{5.5}[/tex] --- (2)
Divide (2) by (1)
[tex]26/7 = ab^{-1.5}/ab^{5.5}[/tex]
[tex]3.71429 = b^{-1.5+5.5}[/tex]
[tex]3.71429 = b^{4}[/tex]
Take 4th root
[tex]b = 1.39[/tex]
Substitute [tex]b = 1.39[/tex] in [tex]26 = ab^{-1.5}[/tex]
[tex]26 = a * 1.39^{-1.5}[/tex]
[tex]26 = a * 0.6102[/tex]
Solve for (a)
[tex]a = 26/0.6102[/tex]
[tex]a = 42.61[/tex]
f(10) is calculated as:
[tex]f(10) = ab^{10}[/tex]
[tex]f(10) = 42.61 * 1.39^{10}[/tex]
[tex]f(10) = 1147.25[/tex]
Ray’s weight increased by 11% in the last two years. If he gained 16.5 pounds, what was his weight two years ago?
Answer:
Ray weighed 150 pounds two years ago.
Step-by-step explanation:
11/100 = 16.5/x
11x = 16.5(100)
11x = 1,650
(11x)/11 = (1,650)/11
x = 150
About time that he should start going to the gym!
The answer to the picture please
the required ans is 3√b+b/3b
Answer pleaseeeeeeeeee
Answer:
[tex]y=-\frac{8}{7}x+4[/tex]
Step-by-step explanation:
A line is perpendicular to another if its slope is the negative reciprocal of the other.
Your lines are in slope intercept form here, y=mx+b, where m is the slope. We can see the given line has slope [tex]\frac{7}{8}[/tex]. The negative reciprocal of that is [tex]-\frac{8}{7}[/tex], which is the slope of the third answer choice.
Is this the correct answer?
Answer:
25.40
Step-by-step explanation:
tickets ( 2 at 10.95 each) = 2* 10.95 = 21.90
popcorn ( 1 at 7.50) = 7.50
Total cost before discount
21.90+7.50=29.40
subtract the discount
29.40-4.00 =25.40
Answer:
Yep! That's correct!
Step-by-step explanation:
We know that Marilyn and her sister are each getting a ticket that cost $10.95. They are also getting a $7.50 popcorn to share. Let's add those values up.
(10.95 * 2) + 7.50 {Multiply 10.95 by 2 to get 21.90.}
21.90 + 7.50 {Add 7.50 to 21.90 to get 29.40}
$29.40 (without the credit) in toal
A credit on a movie reward card functions as a discount, so what we need to do next is subtract 4 from 29.40. That will get us $25.40 as the total cost.
After doing the math, I can deduce that your answer is correct!
What percentages of participants in the study were American?
If Jan can weed the garden in 2 hours and her husband can weed it in 1 hour and 30 minutes, find how long it takes them to weed the garden together.
Answer:
3 hours 30 minutes
Step-by-step explanation:
Jan :2 hours
her husband : 1 hour 30 minutes
2hr + 1 ½ hrs = 3 ½ hrs...that is 3 hours 30 minutes....?
solve for x : 2(x^2+9)-4=0
Answer:
no solution
Step-by-step explanation:
multiply 2 and get 2x^2+18-4=0
combine like terms
2x^2+14=0
subtract 14
2x^2=-14
there can't be a square root of a negative number so there's no solution
Answer:
x = ±i sqrt(7)
Step-by-step explanation:
2(x^2+9)-4=0
Add 4 to each side
2(x^2+9)-4+4=0+4
2(x^2+9)=4
Divide by 2
2(x^2+9)/2=4/2
(x^2+9)=2
Subtract 9 from each side
x^2 +9-9 = 2-9
x^2 = -7
Taking the square root of each side
sqrt(x^2) =sqrt(-7)
x = sqrt(-1 *7)
x = ±i sqrt(7)
Given the data, identity the type of data for each variable. (For example, determine whether the variable Day is categorical or quantitative data). Which variable is most appropriate to summarize using ungrouped frequency distributions
Answer:
Kindly check explanation
Step-by-step explanation:
The variables in the heavenly chocolate dataset is attached below :
Variables are classed as either Categorical or Quantitative.
Categorical variables are used for non - numeric variables which are used to group values based on labels whole quantitative variables are those which are numeric.
Therefore, the variables ;
Customer = Quantitative (represented with number values)
Day = Categorical (Non-numeric)
Browser = Categorical (Non - numeric)
Time = Quantitative (contains numeric values)
Pages viewed = Quantitative (contains numeric values)
Amount spent = Quantitative (contains numeric values)
Quantitative variables are most appropriate to summarize using ungrouped frequency as the attributed of the data can be adequately ibtia Ed without have to seperates or place data into categories.
A textbook store sold a combined total of 473 chemistry and sociology textbooks in a week. The number of sociology textbooks sold was 59 less than the number of chemistry textbooks sold. How many textbooks of each type were sold?
Answer:
I. C = 266 textbooks.
II. S = 207 textbooks.
Step-by-step explanation:
Let the chemistry textbook be C.
Let the sociology textbook be S.
Translating the word problem into an algebraic expression, we have;
C + S = 473 ..... equation 1
S = C - 59 ..... equation 2
Substituting eqn 2 into eqn 1, we have;
C + C - 59 = 473
2C - 59 = 473
2C = 473 + 59
2C = 532
C = 532/2
C = 266 textbooks.
Next, we would determine the value of S;
S = C - 59
S = 266 - 59
S = 207 textbooks.
Check:
C + S = 473
266 + 207 = 473
473 = 473
A Basketball team won 8 games and lost 7 games. What are the odds in favor of winning a basketball game
Answer:
0.47
Step-step explanation:
Add 8+7 which gives you 15. So 7/15. Then turn it into decimal form which is 0.47. Hope this helps!
Please solve the problem
Answer:
does this have to do with graphs
A window is to be built in the shape of a rectangle surmounted by an isosceles triangle. The area of the window must be 6 square meters. Use Lagrange Multipliers to find the width and height of the rectangle for which the perimeter of the window will be as small as possible
Answer:
x = 2.536 m
y = 2 m
Step-by-step explanation:
Considering the three sides of the rectangle and the isosceles triangle
when resolving the width and height of the rectangle to achieve the smallest possible perimeter.
step 1 :
Area of window = xy + 1/2 xz , perimeter = x + 2y + 2c
c = [tex]\sqrt{z^2 + 1/4 x^2 }[/tex]
we are tasked with minimizing the perimeter ( p ) subject to A = 6
attached below is the detailed solution of the given problem
f(x)=8x−4x+4 , then f(x−1)=
Answer: [tex]4x[/tex]
Step-by-step explanation:
[tex]f(x)=8x-4x+4\\f(x-1)=8(x-1)-4(x-1)+4\\f(x-1)=8x-8-4x+4+4\\f(x-1)=4x-8+4+4\\f(x-1)=4x[/tex]
The functions q and r are defined as follows
q(x)=-2x-2
r(x)=x^2+1
Find the value of r(q(4)).
plug-in
-2(4) - 2
-8 - 2
-10
-10^2 + 1
-100 + 1
Your answer: -99
Use the substitution methed to solve the system of equations. Choose the correct ordered pair.
2y+5x=13
2y+3x=5
Solve both equations for 2y :
2y + 5x = 13 ==> 2y = 13 - 5x
2y + 3x = 5 ==> 2y = 5 - 3x
Solve for x :
13 - 5x = 5 - 3x
8 = 2x
x = 4
Solve for y :
2y = 13 - 5×4
2y = -7
y = -7/2
As an ordered pair, the solution is then the point (x, y) = (4, -7/2).
If a house is worth $125,000 and depreciates by 7.5% per year, how much is it worth in two years
Answer:
Solution given;
principal [P]=$125,000
depreciated rate[R]=7.5%
time[t]=2 years
worth price of house [A]=???
we have
Worth price[A]=[tex]\large \bold P(1-\frac{R}{100})^{t}[/tex]
=[tex]125,000(1-\frac{7.5}{100})^{2}[/tex]
=125,000*0.925²
=125,000*0.855625
=106953.125
its worth price is $106953.125work for 12 hours and earn $140 find the unit rate
Answer:
11.60
Step-by-step explanation:
To find unit rate, you need to use the formula:
(amount of money) ÷ (amount of hours)
Since we have both, we can plug in
140 ÷ 12 will give you approximately 11.6
So, you receive $11.60 every hour.
5
13
The probabilities that three men win their respective races are 1/3,3/5and 3/4.what is theprobability that
a) all of them win their races)
b) only one of them win his race?
Answer:
a
Step-by-step explanation:
1/3 x 3/5 x 3/4 =7/12 so therefore that's what the answer isn't
In a residual plot against x that does NOT suggest we should challenge the assumptions of our regression model, we would expect to see a _____. a. parabolic band of points b. band of points having a slope consistent with that of the regression equation c. horizontal band of points centered near 0 d. widening band of points
Answer:
In a residual plot against x that does NOT suggest we should challenge the assumptions of our regression model, we would expect to see a _____.
c. horizontal band of points centered near 0
Step-by-step explanation:
This residual graph or plot shows the residual values (or the difference between the observed y-value (from scatter plot) and the predicted y-value (from regression equation line) on the vertical axis and displays the independent variable on the horizontal axis. A linear regression model becomes appropriate for a dataset when the points are randomly dispersed around the horizontal axis near 0; otherwise, a nonlinear model becomes more appropriate.
A well-known brokerage firm executive claimed that 60% of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over a two week period, found that in a sample of 100 people, 69% of them said they are confident of meeting their goals. Test the claim that the proportion of people who are confident is larger than 60% at the 0.01 significance level.
The null and alternative hypothesis would be:________
a. H0:μ=0.6H0:μ=0.6
H1:μ≠0.6H1:μ≠0.6
b. H0:μ=0.6H0:μ=0.6
H1:μ<0.6H1:μ<0.6
c. H0:μ=0.6H0:μ=0.6
H1:μ>0.6H1:μ>0.6
d. H0:p=0.6H0:p=0.6
H1:p≠0.6H1:p≠0.6
e. H0:p=0.6H0:p=0.6
H1:p>0.6H1:p>0.6
f. H0:p=0.6H0:p=0.6
H1:p<0.6H1:p<0.6
The test is:________
a. two-tailed
b. left-tailed
c. right-tailed
The test statistic is:_______ (to 3 decimals)
The p-value is:_______ (to 4 decimals)
Based on this we:________
a. Fail to reject the null hypothesis
b. Reject the null hypothesis
We are testing a hypothesis. So, first we identify the null and the alternative hypothesis, then we find the test statistic, and with the test statistic, the p-value is found.
Null and alternative hypothesis:
Claim the the proportion is of 60%, thus, the null hypothesis is:
[tex]H_0: p = 0.6[/tex]
Test if the proportion is greater than 60%, thus, the alternative hypothesis is:
[tex]H_1: p > 0.6[/tex]
And the answer to the first question is given by option c.
Classification:
We are testing if the proportion is greater than a value, so it is a right-tailed test.
Test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.6 is tested at the null hypothesis:
This means that [tex]\mu = 0.6, \sigma = \sqrt{0.4*0.6}[/tex]
Survey, conducted over a two week period, found that in a sample of 100 people, 69% of them said they are confident of meeting their goals.
This means that [tex]n = 100, X = 0.69[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.69 - 0.6}{\frac{\sqrt{0.4*0.6}}{\sqrt{100}}}[/tex]
[tex]z = 1.837[/tex]
The test statistic is z = 1.837.
p-value:
The p-value of the test is the probability of finding a sample proportion above 0.69, which is 1 subtracted by the p-value of z = 1.837.
Looking at the z-table, z = 1.837 has a p-value of 0.9669.
1 - 0.9669 = 0.0331
The p-value is 0.0331.
Decision:
The p-value of the test is 0.0331 > 0.01, and thus:
a. Fail to reject the null hypothesis
For another example of a problem of a test of hypothesis, you can take a look at:
https://brainly.com/question/24166849
