Moment generating function of a random variable is the expectation of a random variable. The moment generating function of the geometric(p) distribution is given by pe^{t}/ (1 - (1 - p)e^{t}.
A moment generating function can be described as
MGFₓ(t) = E( e^{tx})
For continuous x
E( e^{tx}) = ∫ₓ e^{tx}×f(x)×d(x) where f(x) is the probability density function.
For discrete x
E( e^{tx}) = ∑ₓ e^{tx}×P(x) where P(x) is the probability mass function.
A geometric distribution is a discrete probability distribution that provide us the probability that the 1st occurrence o success would need k independent trials of success probability p each. Thus probability mass function of geometric distribution is
P(X = k) = (1 - p)^{k} × p
So moment generating function can be obtained by
MGFₓ(t) = E( e^{tx}) = ∑ₓ e^{tx}×P(x)
MGFₓ(t) = ∑ₓ (e^{kt} × (1 - p)^{k} × p)
MGFₓ(t) = p×∑ₓ (e^{t} × (1 - p))^{k}
|e^{t} × (1 - p)| < 1 so applying property of sum of infinite geometric progression we have
MGFₓ(t) = p× e^{t}/ (1 - (1 - p)e^{t}
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Two researchers are gathering data on hours of video games played by school-aged children and young adults. They each randomly sample different groups of 150 students from the same school. They collect the following data.
Researcher A
Hours Played per Week Frequency Relative Frequency Cumulative Relative Frequency
0-2 26 0.17 0.17
2-4 30 0.20 0.37
4-6 49 0.33 0.70
6-8 25 0.17 0.87
8-10 12 0.08 0.95
10-12 8 0.05 1
Researcher B
Hours Played per Week Frequency Relative Frequency Cumulative Relative Frequency
0-2 48 0.32 0.32
2-4 51 0.34 0.66
4-6 24 0.16 0.82
6-8 12 0.08 0.90
8-10 11 0.07 0.97
10-12 4 0.03 1
Give a reason why the data may differ.
A) The researchers are studying different statistics, so there will be some variation in the data.
B) The researchers are studying different parameters, so there will be some variation in the data.
C) The researchers are studying the same statistic, so there will be some variation in the data.
D) The researchers are studying different samples, so there will be some variation in the data.
E) The researchers are studying the same population, so there will be some variation in the data.
The reason for data variation is that the researchers are studying different samples, so there will be some variation in the data.
What is meant by data?In mathematics, data is a collection of facts and figures that can take any shape, whether it be numerical or not. You can calculate numerical data, which is always gathered in number form and includes things like student test results, employee salaries, football team member heights, etc.
Write types of data.Qualitative, quantitative, discrete, continuous, primary and secondary are the types of data.
Since researches choose same school but group of 150 people is randomly chosen and different therefore, the reason for data variation is that the researchers are studying different samples, so there will be some variation in the data.
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)) A football team has $630 to spend on hats for their fans. Each hat costs $5. How many
hats can the team buy?
What is the position of E on the number line below?
Write your answer as a fraction or a mixed number.
E
The position of E as a mixed number is [tex]2\frac{4}{5}[/tex].
What is number line?
A number line is a diagram of a graduated straight line used to represent real numbers in elementary mathematics. It is assumed that every point on a number line corresponds to a real number, and that every real number corresponds to a point.
Let on a number line the position of E is given.
We have to find E as a mixed number.
As we can see there are 5 parts between 2 and 3.
So each part is 0.2 cm.
The position of E is in fourth part.
So, 4 x 0.2 = 0.8 cm
2 + 0.8 = 2.8 is the position of E.
2.8 can be written as.
28/10 = 2 8/10 = 2 4/5
Hence, the position of E as a mixed number is [tex]2\frac{4}{5}[/tex].
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Find the sum.
17x³ + (3x + 8x³) =
Journalizing, adjusting, adjusted trial balance
Harrison’s Repair Service shows opening balance for some accounts on 01 January 20X1: Cash: $36,000; Accounts Receivable: 60,500; Prepaid Rent: $2,400; Supplies: $2,500; Equipment: $13,900; Accumulated depreciation - Equipment: $3,150; Accounts Payable: $2,780; Notes Payable: 16,000; Unearned service revenue: 6,120; Share capital: 86,915; Retained Earnings: 15,335; Dividends: 15,000.
The following transactions in January were:
January 1 Paid the monthly rental fee, $790.
1 Made the monthly payment to Apple Company, $1,700 in order to decrease Accounts
Payable.
6 Purchased additional repair supplies on credit from Pineapple Company, $1820.
15 Received cash for repair service performed, $2,950.
20 Paid cash for an advertisement in the local newspaper, $370.
23 Paid Pineapple Company on account, $1,200
30 Collected payment for repair fees earned, $7,460.
30 Recorded a dividend paid to stockholders, $8,100.
Required
A, Prepare journal entries to record the January transactions.
B, Using the following information, record adjusting entries in the general journal and prepare the T- accounts for all accounts
1. One month of rent has expired. The rental policy is valid in one year starting from the first day of November 20X0.
2. The inventory of unused repair supplies is $1,520
3. The estimated depreciation on repair equipment is $350.
4. Accrued one-month interest expense on Note Payable that will be paid on February 1 (Borrowing Note was in 6-month; annual interest rate is 6%).
5. Accrued salaries for 2 employees at the end of the month, payment for each person is $500
6. Service Revenue still unearned at the end of the period is $3,675
7. Service revenue earned but not billed is $1,800
C. Prepare an adjusted trial balance from above T-accounts
Answer:
Step-by-step explanation: A. Prepare journal entries to record the January transactions.
Paid the monthly rental fee, $790.
Debit Credit
Rent Expense 790
Cash 790
Made the monthly payment to Apple Company, $1,700 in order to decrease Accounts Payable.
Debit Credit
Accounts Payable 1,700
Cash 1,700
Purchased additional repair supplies on credit from Pineapple Company, $1,820.
Debit Credit
Supplies 1,820
Accounts Payable 1,820
Received cash for repair service performed, $2,950.
Debit Credit
Service Revenue 2,950
Cash 2,950
Paid cash for an advertisement in the local newspaper, $370.
Debit Credit
Advertising Expense 370
Cash 370
Paid Pineapple Company on account, $1,200.
Debit Credit
Accounts Payable 1,200
Cash 1,200
Collected payment for repair fees earned, $7,460.
Debit Credit
Accounts Receivable 7,460
Cash 7,460
Recorded a dividend paid to stockholders, $8,100.
Debit Credit
Dividends 8,100
Cash 8,100
B. Using the following information, record adjusting entries in the general journal and prepare the T- accounts for all accounts
One month of rent has expired. The rental policy is valid in one year starting from the first day of November 20X0.
Debit Credit
Prepaid Rent 90
Rent Expense 90
The inventory of unused repair supplies is $1,520
Debit Credit
Supplies 1,520
Supplies Expense 1,520
The estimated depreciation on repair equipment is $350.
Debit Credit
Depreciation Expense 350
Accumulated Depreciation - Equipment 350
Accrued one-month interest expense on Note Payable that will be paid on February 1 (Borrowing Note was in 6-month; annual interest rate is 6%).
Debit Credit
Interest Expense 100
Interest Payable 100
Accrued salaries for 2 employees at the end of the month, payment for each person is $500
Debit Credit
Salaries Expense 1,000
Salaries Payable 1,000
Service Revenue still unearned at the end of the period is $3,675
Debit Credit
Unearned Service Revenue 3,675
Service Revenue 3,675
Service revenue earned but not billed is $1,800
Debit Credit
Service Revenue 1,800
Accounts Receivable 1,800
C. Prepare an adjusted trial balance from above T-accounts
Debit Credit
Cash 35,080
Accounts Receivable 63,080
Prepaid Rent 1,510
Supplies 1,300
Equipment 13,900
Accumulated Depreciation - Equipment 3,500
Accounts Payable 2,380
Notes Payable 16,100
Interest Payable 100
Salaries Payable 1,000
Unearned Service Revenue 3,675
Service Revenue 6,475
Rent Expense 870
Given the coordinates (0, 0) and (4, 1), the distance is
Answer:
distance = √17
Step-by-step explanation:
distance = √(y2 - y1)^2 + (x2 - x1)^2
distance = √(1 - 0)^2 + (4 - 0)^2
distance = √17
I hope my answer helps you.
Farah wants to have a cool million dollars to retire with when she is 55. How much must she invest today at age 19 into an account that pays 8% compounded monthly to accomplish this goal?
Sam also wants a cool million dollars when he is 55 but is willing to put away money every year. How much must he put away each year after his 21st birthday with same interest rate as Farah but his investment is compounded annually?
To calculate how much Farah must invest today at age 19 to have a cool million dollars when she is 55, we need to know how many years she has until she retires. Since Farah wants to retire at age 55, she has 55-19 = <<55-19=36>>36 years until she retires.
We also need to know the interest rate that the account pays and the frequency at which the interest is compounded. In this case, the interest rate is 8% and the interest is compounded monthly.
To calculate how much Farah must invest, we can use the formula for the future value of an annuity, which is given by:
FV = PMT * (((1 + i)^n - 1) / i)
where FV is the future value that Farah wants to have, PMT is the amount that Farah must invest each period, i is the interest rate per period, and n is the total number of periods.
Since Farah wants to have a cool million dollars, we can set FV equal to $1,000,000. We also know that the interest rate is 8% and that the interest is compounded monthly, so we can set i equal to 8% / 12 = 0.006667. Finally, we know that Farah has 36 years until she retires, so we can set n equal to 36 * 12 = 432, since there are 12 months in a year.
Substituting these values into the formula above, we get:
FV = PMT * (((1 + i)^n - 1) / i)
FV = PMT * (((1 + 0.006667)^432 - 1) / 0.006667)
To solve for PMT, we can divide both sides of the equation by ((1 + 0.006667)^432 - 1) / 0.006667, which gives us:
PMT = FV / (((1 + i)^n - 1) / i)
PMT = $1,000,000 / (((1 + 0.006667)^432 - 1) / 0.006667)
Calculating this value gives us a result of PMT = $176.72, which is the amount that Farah must invest each month to have a cool million dollars when she is 55.
Now, let's consider Sam's situation. Sam also wants to have a cool million dollars when he is 55, but he is willing to put money into his account every year instead of every month. This means that the frequency at which the interest is compounded will be annual instead of monthly.
To calculate how much money Sam must put into his account each year, we can use the same formula as above but with a few changes. In particular, we need to set i equal to 8% / 1 = 0.08, since the interest is compounded annually, and we need to set n equal to 55-21 = <<55-21=34>>34, since Sam has 34 years until he retires.
Substituting these values into the formula above, we get:
FV = PMT * (((1 + i)^n - 1) / i)
FV = PMT * (((1 + 0.08)^34 - 1) / 0.08)
Solving for PMT gives us:
PMT = FV / (((1 + i)^n - 1) / i)
PMT = $1,000,000 / (((
In the case of Regression Analysis, the dependent variable must be ________; in multiple discriminant analysis, the dependent variable is______ in nature.
a. Metric; nonmetric
b. Metric; nominal
c. Nominal; categorical
d. Categorical; nonmetric
b. Metric; nominal
In the case of regression analysis, the dependent variable must be metric; in multiple discriminant analysis, the dependent variable is nominal in nature. (Option B)
Regression analysis refers to a collection of statistical methods which are used for the estimation of relationships between a dependent variable and one or more independent variables. It can used to assess the strength of the relationship between variables and for modeling their future relationship. In regression analysis the dependent variable is metrically scaled (where distance between values can be calculated). Multiple discriminant analysis is a regression technique used in statistics to group objects into categories for analysis. In multiple discriminant analysis the dependent variable is nominally scaled (where characteristics can be distinguished).
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PLEASE HELP WILL MARK BARINLIEST
Answer:
d= 120
Step-by-step explanation:
c+d = 180 degree
d = 180-60 =120 degree
what is function for 3x-5
HELP PLEASE ASAP!!!
The entire graph of the function g is shown in the figure below. Write the domain and range of g as intervals or unions of intervals.
Answer:
D= [-4,-1) U (2,4)
R = [-3,5)
Read the following prompt and type your response in the space provided.
Sarah has a $30 music gift card. Each day she uses it to buy a $1.99 song download. For how many days will the gift card have still have a balance of more than $18?
Write an inequality to solve the problem and then solve showing your work. Explain what the solution to the inequality means.
Answer:
She will have a balance of more than $18 for up to 6 days
Step-by-step explanation:
Start with $30.
Each day, x, subtract $1.99 from $30.
30 - 1.99x
The amount must be greater than $18.
30 - 1.99x > 18
Subtract 30 from both sides.
-1.99x > -12
Divide both sides by -1.99. Remember than when you multiply or divide both sides of an inequality by a negative number, the inequality sign changes direction.
-1.99x/(-1.99) < -12/(-1.99)
x < 6.03
The number of days must be less than 6.03. Since we deal with whole days, she will have a balance of more than $18 for up to 6 days.
Is this correct? Or no?
Answer:
No
Step-by-step explanation:
No, this is not correct. When you divide both sides of an inequality by a negative number, the inequality symbol must be reversed. So in this case, dividing both sides of the inequality -3x > 9 by -3 would give us x < -3, which is not what Diego claimed.
Find the slope.
x
012345
y 3 6 9 12 15 18
The slope of the line is 3.
What is slope?The slope or gradient of a line is a number that describes both the direction and the steepness of the line.
Given that, are points of a line,
The slope of a line passing through two points is = (y₂-y₁)/(x₂-x₁)
Considering the points (0, 3) and (1, 6)
Therefore, slope = (6-3)/(1-0) = 3
Hence, the slope of the line passing through the given points is 3.
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Solve
7) 6-4(6 n+7) ≥122
The solution of the given inequality 6 - 4( 6 n+7 ) ≥ 122 is given by
n ≤ -6.
As given in the question,
Given inequality is :
6 - 4( 6 n+7 ) ≥ 122
Open the parenthesis of the given inequality we get,
⇒ 6 - 24n - 28 ≥ 122
⇒ 6 - 28 -24n ≥ 122
⇒ -22 -24n ≥ 122
Add 22 on both the side of inequality we get,
⇒ -22 + 22 -24n ≥ 122 + 22
⇒ -24n ≥ 144
Divide both the side by ( -24 ) we get,
⇒ n ≤ -144/ 24
⇒ n ≤ -6.
This shows that n has all the less than or equal to -6.
Therefore, the solution of the given inequality is equal to n ≤ -6.
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Question 6 A test of hypothesis was performed to determine, at 5% level of significance, if the majority of the engineering graduates pass the PE exam in their first try. If the computed value of the test statistic Z based on the sample information is z = 2.10, then the p-value for this test is: 0.00895 O 0.05 0.9821 None of these O 0.0179 N • Previous Not saved S
The p-value for the test is 0.9821.
What is hypothesis?
A statistical hypothesis test is a technique for determining if the available data are sufficient to support a specific hypothesis. We can make probabilistic claims regarding population parameters through hypothesis testing.
What is z-score?
You can plot a z-score on a normal distribution curve. The range of Z-scores ranges from -3 standard deviations (which would be on the far left of the normal distribution curve) to +3 standard deviations (which would fall to the far right of the normal distribution curve). You must be aware of the mean and population standard deviation in order to use a z-score.
Given that the test statistic Z based on the sample information is z = 2.10.
z = 2.1 + 0.00
From the z-score table the value of p is 0.9821.
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Find the derivative of f(x) = 3x² + 2x at 3. That is, find f '(3).
Answer:
20
Step-by-step explanation:
To find the derivative of f(x) = 3x² + 2x at x = 3, we can use the power rule:
f'(x) = 2*3x + 2
When x = 3, the derivative of f(x) is:
f'(3) = 2*3(3) + 2
f'(3) = 18 + 2
f'(3) = 20
Therefore, the derivative of f(x) = 3x² + 2x at x = 3 is f'(3) = 20.
Solve the system.
2x + y + 3z = 20
X + 2y - z = -11
3x - 2z = -3
Enter your answer as an ordered triple.
The solution to the system, as an ordered triple is: (3, -4, 6).
How to Solve a System of Equations?To solve the following given system of equations:
2x + y + 3z = 20 --> eqn. 1
x + 2y - z = -11 --> eqn. 2
3x - 2z = -3 --> eqn. 3
Multiply equation 1 by 2 to get eqn. 4:
4x + 2y + 6z = 40 --> eqn. 4
Subtract eqn. 4 from eqn. 2:
x + 2y - z = -11 --> eqn. 2
4x + 2y + 6z = 40 --> eqn. 4
-3x - 7z = -51 --> eqn. 5
Add equations 3 and 5 together:
3x - 2z = -3 --> eqn. 3
-3x - 7z = -51 --> eqn. 5
-9z = -54
z = -54/-9
z = 6
Substitute the value of z into equation 5:
-3x - 7(6) = -51 --> eqn. 5
-3x - 42 = -51
-3x = -51 + 42
-3x = -9
-3x/-3 = -9/-3
x = 3
Find the value of y by substituting the values of x and z into equation 1:
2(3) + y + 3(6) = 20 --> eqn. 1
6 + y + 18 = 20
24 + y = 20
y = 20 - 24
y = -4
The solution as an ordered triple is: (3, -4, 6).
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A group of 2342 students were surveyed about the courses they were taking at their college with the
following results:
1031 students said they were taking Dance.
1058 students said they were taking Science.
1059 students said they were taking English.
449 students said they were taking Science and Dance.
459 students said they were taking Science and English.
456 students said they were taking Dance and English.
218 students said they were taking all three courses.
Fill in the following Venn Diagram with the cardinality of each region then answer the questions
below.
Science
IV.
11.
VII.
V.
English
VI.
How many students took Science, Dance, or English?
How many students took Dance and English, but not Science?
How many students took Science or didn't take Dance?
How many students took none of the courses?
Dance
III.
How many students took Science or English, but not Dance?
VIII.
Hello,
I hope you and your family are doing well!
To find the number of students who took Science, Dance, or English, you can add the number of students in each individual category and then subtract the number of students who took all three courses, since those students were counted twice. This gives a total of 1031 + 1058 + 1059 - 218 = 3100 students.
To find the number of students who took Dance and English, but not Science, you can add the number of students in region VII and region VIII, which is 456 + 11 = 467 students.
To find the number of students who took Science or didn't take Dance, you can add the number of students in region I and region III, which is 1031 + 218 = 1249 students.
To find the number of students who took none of the courses, you can add the number of students in region II and region IV, which is 449 + 459 = 908 students.
To find the number of students who took Science or English, but not Dance, you can add the number of students in region V and region VI, which is 1059 + 459 = 1518 students.
----
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A random survey of 75 death row inmates revealed that the mean length of time on death row is 17.4 years with a standard deviation of 6.3 years. Conduct a hypothesis test to determine if the population mean time on death row could likely be 15 years. Is this a test of one mean or proportion? State the null and alternative hypotheses. H_o: H_a: Is this a right-tailed, left-tailed, or two-tailed test? What symbol represents the random variable for this test? In words, define the random variable for this test. Is the population standard deviation known and, if so. what is it? Calculate the following: Which test should be used? State the distribution to use for the hypothesis test. Find the p -value. Al a pre -conceived a = 0.05, what is your Decision: Reason for the decision: Conclusion (write out in a complete sentence):
At the null hypothesis, it is tested if the mean is of 15 years, that is:
[tex]H_0: \mu = 15[/tex]
At the alternative hypothesis, it is tested if the mean is different of 15 years, that is:
[tex]H_1: \mu \neq 15[/tex]
What is the test statistic?The equation that gives the test statistic is defined as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.The values of these parameters in this problem are given as follows:
[tex]\overline{x} = 17.4, \mu = 15, s = 6.3, n = 75[/tex]
Hence the test statistic is of:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{17.4 - 15}{\frac{6.3}{\sqrt{75}}}[/tex]
t = 3.30.
What is the p-value?Considering a two-tailed test, as we are testing if the mean is different of a value, with t = 3.30 and 75 - 1 = 74 df, the p-value of the test is of:
0.0015.
Since the p-value is less than the significance level of 0.05, the null hypothesis is rejected, meaning that there is enough evidence to conclude that prisoners spend a time different of 15 years in the death row.
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PLEASE HELP WILL GIVE 100 POINTS
Answer:
72y
Step-by-step explanation:
Perfect square monomials are in the form:
[tex]x^2+bx+\left(\dfrac{b}{2}\right)^2[/tex]
They factor as:
[tex]\left(x + \dfrac{b}{2}\right)^2[/tex]
To find the middle term of this polynomial, first factor 16 out of the expression.
[tex]16(y^2 \: + \: ?+5.0625)[/tex]
We know that the middle term will be in the form [tex]by[/tex], and the last term will be in the form [tex]\left(\dfrac{b}{2}\right)^2[/tex]. Using this information, we can solve for b.
[tex]5.0625 = \left(\dfrac{b}{2}\right)^2[/tex]
[tex]\sqrt{5.0625} = \dfrac{b}{2}\right[/tex]
[tex]4.5 = b[/tex]
Then, we can substitute that into the term [tex]by[/tex].
[tex]16(y^2 + 4.5y+5.0625)[/tex]
Finally, distribute the 16 and then take the middle term as the answer.
[tex]16y^2 + 72y+81[/tex]
72y
Answer:
72y or -72y-----------------------------
We are given a binomial and need to add a monomial to make it a perfect square.
Recall the identities for a square of a sum or difference of two numbers:
(a ± b)² = a² ± 2ab + b²Analyze the given and compare with the identity above:
16y² + ... + 81Here 16y² = (4y)² and 81 = 9², so a = 4y and b = 9.To complete the square we need to add ± 2ab, which is:
± 2ab = ± 2(4y*9) = ± 72yBy adding this we get:
16y² + 72y + 81 = (4y + 9)²or
16y² + (-72y) + 81 = (4y - 9)²d) an undeclared major thinks that the time it takes for a freshmen to pick their major has a standard deviation of 1 year. to find the average he surveys 10 freshmen and finds out how long it took them to pick a major. he does a confidence interval to find the average time it takes.
The time it takes a freshman to choose their major is thought to have a standard deviation of one year by an undeclared major. A t-distribution table can be used to determine the crucial value.
The confidence interval for the average time it takes for freshmen to pick a major can be found by taking the sample mean of the 10 freshmen surveyed and adding and subtracting
The margin of error is calculated by multiplying the sample standard deviation by the critical value from a t-distribution with degrees of freedom equal to (n-1), where n is the sample size.
The sample size in this instance is 10. A t-distribution table can be used to determine the crucial value.
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Let f (h) be the number of riders on a train h hours after 9 A.M. Explain the meaning of the
statement f (3) = 50.
Answer:
At 12:00 there were 50 riders
Step-by-step explanation:
3 hours after 9 would be noon. At that time there are 50 riders
. DIG DEEPER What is Descartes's number?
• It is less than 300.
• It is greater than 200.
• The ones digit is 2 more than the hundreds digit.
• The tens digit is 2 more than the ones digit.
●
Descartes's number is the 46.989, which is less than 47 and higher than 46.98.
Define Descartes's number.A Descartes number is an odd number with the formula n = m p, where m and p are coprime numbers and 2n = (m) (p + 1). P is regarded as a "spoof" prime in this formula. The only known example is the one that was provided. The invention of Cartesian or analytic geometry, which employs algebra to describe geometry, is one of Descartes's most enduring contributions. In equations, Descartes "introduced the convention of denoting unknowns by x, y, and z, and knowns by a, b, and c." A Descartes number is an odd integer that, if one of its composite elements were prime, would have been an odd perfect number.
Given,
Descartes's number is,
46.989, which is less than 47 and higher than 46.98.
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Ben bought 20 shares of stock at $10.00 per share and sold them for $12.00 per share.
What was his ROI (Return on Investment)?
You can spend at most $3.50 at a market. Apples cost $0.40 each, and pears cost $0.65 each. Let x be numbers of apples and y be numbers of pears. Write an inequality that represents the numbers of apples and pears you can buy. Is (3,4) a solution of the inequality?
Answer:
Step-by-step explanation:
.40x + .65 ≤3.50
(3, 4) I think it is a solution to the inequality. Because when you graph it (3, 4) looks like it is shaded meaning that it is a solution. (If wrong, I'm sorry)
The inequality that represents the numbers of apples and pears you can buy is 0.40x + 0.65y ≤ 3.50.
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.
Given;
The cost of the apples = $0.40 per apple
So, the cost of x apples is 0.40x.
The cost of the pears = $0.65 per pear
So, the cost of y pears is 0.65y.
The total cost of the apples and pears is the sum of the cost of the apples and the cost of the pears, which is 0.40x + 0.65y;
Since we can spend at most $3.50 at the market, the total cost of the apples and pears must be less than or equal to $3.50;
Therefore, the inequality that represents the numbers of apples and pears you can buy will be 0.40x + 0.65y ≤ 3.50;
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Alice has shared that her RSA public key is n = 33, e = 7. Her private key is d = 3. She was sent the encrypted number 21. Decrypt the number.
Answer: The encrypted number is 25 and this can be determined by using the formula from RSA algorithm.
Given :
Alice has shared that her RSA public key is n = = 33, e = 7.
The formula from the RSA algorithm is used to encrypt the number 16. The formula is given by:
where e = 7, n = 33 and m = 16.
Now, substitute the known values in the above equation.
Now, by using the modulo function the above expression becomes:
c = 25
So, the encrypted number is 25.
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Step-by-step explanation:
A satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by rotating a parabola around its axis of symmetry. The receiver is to be located at the focus. If the dish is 24 feet across at its opening and 2 feet deep at its center, where should the receiver be placed?
Find the equation of the parabola?
How far above the vertex should the receiver be placed?
Equation of parabola: y =ax² and receiver should be placed 18 feet above vertex.
Explanation:
Considering satellite dish as parabola we can have vertex as origin and concave upward.
So, equation of parabola will be justifying structure of satellite dish i.e
y = ax² -------(1)
Two points other than (0,0) are (-12,2) and (12,2), unit being feet.
This points will satisfy equation of parabola, substituting them in equation 1, we will calculate the value of constant 'a'.
a = [tex]\frac{2}{12^{2} }[/tex]
[tex]\frac{2}{2*6*12}\\ =\frac{1}{72}[/tex]
Substituting value of a = 1/72 in equation 1 we get
72y = x²
As receiver need to be located at focus, so it will be places at a distance of 'p' above the vertex
4p = 72
Dividing both sides by 4, we get
p = 18 feet
So, receiver will be placed at a distance of 18 feet above vertex.
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Compute the scalar surface integral ∬T(z+y)dS where T is the triangle (including its interior) with vertices (0,0,2), (0,1,0)( and (1,0,0)
the scalar surface integral ∬T(z+y)dS where T is the triangle (including its interior) with vertices (0,0,2), (0,1,0)( and (1,0,0) is 1
We can compute the scalar surface integral ∬T(z+y)dS using the parametric form of the surface integral.
Let S be the surface of the triangle. We can parameterize S as follows:
S(u,v) = (u, v, 2-u-v)
where 0 ≤ u ≤ 1 and 0 ≤ v ≤ 1-u.
Then, the scalar surface integral ∬T(z+y)dS is defined as:
∬T(z+y)dS = ∬S(u,v) (2-u-v + v) dudv
= ∫0→1∫0→1-u (2-u-v + v) dudv
= ∫0→1 [2u + (1-u)2 - (1-u)2u - u2(1-u)] du
= ∫0→1 (2u + 1 - 2u2 - u3) du
= [u2 + u - u4/4]0→1
= 1/4 + 1 - ¼
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What is 2 1/5 divided by 4/5 in mixed number form???