A company has 7000 arrivals of Internet traffic over a period of 16,780 thousandths of a minute. Let the random variable
× represent the number of such Internet traffic arrivals in one thousandth of a minute. It appears that these Internet
-M
arrivals have a Poison distribution. If we want to use the formula ply= l"•é
to find the probability of exactly 3
X!
arrivals in one thousandth of a minute, what are the values of y, ×, and e that would be used in that formula?
Answers
The values we used in the Poisson probability formula are:
μ = λ = 0.4168
x = 3
e ≈ 2.718
What is Poisson probability?The Poisson probability distribution is a statistical distribution that models the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence of the events.
The Poisson distribution has a mean and variance of λ. Therefore, in this case, the mean and variance of the number of Internet traffic arrivals in one thousandth of a minute are equal to λ.
We can find the value of μ by dividing the total number of arrivals (7000) by the total time period (16,780):
μ[tex]= 7000/16,780 = 0.4168[/tex]
We can use μ as the value of λ in the Poisson distribution since they are equal.
To find the probability of exactly 3 arrivals in one thousandth of a minute, we use the Poisson probability formula:
P(x=3) = (e^(-λ) * λ^x) / x!
where x = 3.
Substituting the values we have:
[tex]P(x=3)[/tex][tex]= (e^(-0.4168) * 0.4168^3) / 3![/tex]
Using a calculator, we can evaluate e^(-0.4168) to be 0.6596, and simplify the denominator:
[tex]P(x=3) = (0.6596 * 0.0287) / 6[/tex]
[tex]P(x=3) ≈ 0.000305[/tex]
Therefore, the values we used in the Poisson probability formula are:
μ = λ = 0.4168
x = 3
e ≈ 2.718
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The values we used in the Poisson probability formula are:
μ = λ = 0.4168
x = 3
e ≈ 2.718
What is Poisson probability?The Poisson probability distribution is a statistical distribution that models the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence of the events.
The Poisson distribution has a mean and variance of λ. Therefore, in this case, the mean and variance of the number of Internet traffic arrivals in one thousandth of a minute are equal to λ.
We can find the value of μ by dividing the total number of arrivals (7000) by the total time period (16,780):
μ[tex]= 7000/16,780 = 0.4168[/tex]
We can use μ as the value of λ in the Poisson distribution since they are equal.
To find the probability of exactly 3 arrivals in one thousandth of a minute, we use the Poisson probability formula:
P(x=3) = (e^(-λ) * λ^x) / x!
where x = 3.
Substituting the values we have:
[tex]P(x=3)[/tex][tex]= (e^(-0.4168) * 0.4168^3) / 3![/tex]
Using a calculator, we can evaluate e^(-0.4168) to be 0.6596, and simplify the denominator:
[tex]P(x=3) = (0.6596 * 0.0287) / 6[/tex]
[tex]P(x=3) ≈ 0.000305[/tex]
Therefore, the values we used in the Poisson probability formula are:
μ = λ = 0.4168
x = 3
e ≈ 2.718
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Related Questions
in the diagram below, DE is parallel to AB. if the length of AB is the same as the length of DG, AC=17, and DE=6, find the length of DC.
Answers
The length of the side DC is 10.099 units.
What are similar triangles?Similar triangles are those triangles whose corresponding sides are in the same ratio. And the corresponding angles measure the same. It is denoted by the ‘~’ symbol.
Given that DE is parallel to AB. Therefore, the two triangles, ΔCDE and ΔABC are similar to each other.
For a similar triangle, the ratio of the corresponding sides are in the same ratio, therefore, it can be written as,
DC/AC = DE/AB = CE/BC
Take the first two terms,
DC/AC = DE/AB
DC × AB = DE × AC
As the length of AB is the same as the length of DC,
DC × DC = DE × AC
DC² = 6 units × 17 units
DC² = 102 units²
DC = 10.099 units
Hence, the length of the side DC is 10.099 units.
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The complete question with the image of the triangle is mentioned below.
Question: In the diagram below, DE is parallel to AB. if the length of AB is the same as the length of DC, AC=17, and DE=6, find the length of DC.
Lindsey estimated the amount of liquid in a container to be 5 oz. The actual amount
of liquid was 4 oz.
What is the percent error?
10%
15%
20%
25%
Answers
The percent error is 25%
How to calculate the percent error ?
The first step is to calculate the error
= 5 - 4
= 1
The percent error can be calculated as follows
= 1/4 × 100
= 0.25 × 100
= 25%
Hence the percent error is 25%
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Joel has $100 more than Mike. After Joel gave half of his money to Mike, Mike had $500 more than Joel. How much did they have altogether?
Answers
ANSWER:
They have $1,100 altogether.
EXPLANATION:
- Originally, Mike had $500, while Joel had $600. That adds up to $1,100, and it makes Joel have $100 more than Mike.
- Half of Joel’s $600 is $300, which he gave to Mike. That makes Joel now have $300 himself.
- Adding $300 to Mike’s $500 is $800, which means Mike now has $800.
- $800 (Mike’s new amount) minus $300 (Joel’s new amount) is $500, which works because Mike now has $500 more than Joel.
-$300 + $800 is, of course, still $1,100.
Find the missing coefficient
Answers
Answer:
To fill in the blank, let's first expand the left-hand side of the equation:
(2d-5)(2d-4)
= 2d * 2d + 2d * (-4) -5 * 2d -5 * (-4) (using the distributive property)
= 4d^2 - 8d - 10d + 20
= 4d^2 - 18d + 20
Now, we can compare this with the right-hand side of the equation, which is 4d^2 + blank d + 20.
Comparing the coefficients of the like terms, we can see that the blank should be filled with -18, since the coefficient of d on the left-hand side is -18 (from -8d - 10d) and the coefficient of d on the right-hand side is blank.
So, the filled-in equation becomes:
(2d-5)(2d-4) = 4d^2 - 18d + 20
Brainlyest!?
Answer:
Step-by-step explanation:
(2d - 5) x (2d - 4)
= 4d^2 - 8d - 10d + 20
= 4d^2 - 18d + 20
Therefore Answer is -18.
What does f equal in f/3 + 22 = 17
Answers
Answer:
f = -15
Step-by-step explanation:
Use algebra to solve!
f/3 + 22 = 17
f/3 = 17 - 22 (bring 22 to the other side, this changes the sign from plus to minus)
f/3 = -5 {because 17-22 = (-5)}
f = (-5) (3) {to eliminate 3 from the denominator of f, you do the opposite of division which is multiplication, so -5 times 3}
therefore, f = -5
You can also check this answer by putting it back into the original equation, -15/3 is -5 and then -5 + 22 = 17.
A student surveyed some friends about their favorite type of ice cream. The results are shown in the bar graph below.
Part A: Choose one ice cream flavor. Determine the percentage of friends who named the flavor you chose. Show all necessary work. (3 points)
Part B: Based on the student's findings, are you able to determine that the most popular ice cream flavor for the general population is the Pistachio and Vanilla? Explain your reasoning. (2 points)
Answers
Part(A),
The percentage of friends who named Chocolate Chip is 18%.
Part(B),
We cannot determine that the most popular ice cream flavour for the general population is Pistachio and Vanilla based solely on the student's findings.
A bar chart is a graphical representation of data that uses bars of varying heights or lengths to represent the values of a set of data. The bars can be horizontal or vertical, and they are usually spaced equally apart to represent the categories or groups being compared.
Part A:
Let's say we choose the Chocolate Chip flavour. From the bar graph, we can see that 18% of the surveyed friends named Chocolate Chip as their favourite flavour. Therefore, the percentage of friends who named Chocolate Chip is 18%.
Part B:
We cannot determine that the most popular ice cream flavour for the general population is Pistachio and Vanilla based solely on the student's findings. The survey only represents a small sample size of the student's friends, and may not accurately reflect the preferences of the entire population. It is possible that the most popular flavour for the general population is different from what was found in the survey.
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Find the measure of each indicated side. Round your answer to the nearest tenth.
Answers
Answer:
Step-by-step explanation:
By the law of cosines, [tex](59.7)^2=52^2+41^2-2\cdot 52 \cdot 41 \cos(\angle R).[/tex]
Thus, after solving for [tex]\cos(\angle R)[/tex], we get [tex]\cos(\angle R) = 0.1925211.[/tex] So taking the inverse cosine then yields [tex]\boxed{\angle R = 1.377 \text{ rad}}.[/tex]
Answer:
Step-by-step explanation:
By the law of cosines, [tex](59.7)^2=52^2+41^2-2\cdot 52 \cdot 41 \cos(\angle R).[/tex]
Thus, after solving for [tex]\cos(\angle R)[/tex], we get [tex]\cos(\angle R) = 0.1925211.[/tex] So taking the inverse cosine then yields [tex]\boxed{\angle R = 1.377 \text{ rad}}.[/tex]
Add. (2x^4+c^3-4^2+3)+(4x^4-2x^3-x^2+10x+2)
Answers
The value of (2x^4+x^3-x^2+3)+(4x^4-2x^3-x^2+10x+2) is 6x⁴-x³-2x²+10x+5
What is addition of expression?Expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)
Adding two expressions together requires to collect like terms. like terms are terms with similar variable. For example, in 2x²+6x+x² , x² and 2x² are like terms.
Therefore, 2x⁴+x³-x²+3 + 4x⁴-2x³-x²+10x+2 can be simplified as;
2x⁴+4x⁴+x³-2x³-x²-x²+10x+2+3
= 6x⁴-x³-2x²+10x+2
therefore, the value of 2x⁴+4x⁴+x³-2x³-x²-x²+10x+2 is 6x⁴-x³-2x²+10x+5.
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Suppose currently Samsung's common stock is selling for $216. The company announced that it will give $1.14 dividend next year and it plans to grow the dividend by 5% every year. Given the information what is the market's required rate of return for the stock? (Round your answer to two decimal points)
Answers
The market's required rate of return for Samsung's common stock is 5.53%, rounded to two decimal points
What is meant by the rate of stock?
The rate of stock refers to the price at which a particular stock is being bought or sold in the stock market, which can vary based on supply and demand.
What is decimal?
A decimal is a number system that uses the base 10 and includes a decimal point to separate the integer part from the fractional part. It is commonly used in mathematics and everyday life for expressing fractions, percentages, and monetary values.
According to the given information
We can use the constant-growth dividend discount model to calculate the market's required rate of return for the stock. The model is:
Current stock price = Dividend next year / (Required rate of return - Dividend growth rate)
We know the current stock price is $216, the dividend next year is $1.14, and the dividend growth rate is 5%. We need to solve for the required rate of return.
216 = 1.14 / (r - 0.05)
Multiplying both sides by (r - 0.05), we get:
216(r - 0.05) = 1.14
Expanding the left side, we get:
216r - 10.8 = 1.14
Adding 10.8 to both sides, we get:
216r = 11.94
Dividing both sides by 216, we get:
r = 0.0553 or 5.53%
Therefore, the market's required rate of return for Samsung's common stock is 5.53%, rounded to two decimal points
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The market's required rate of return for Samsung's common stock is 5.53%, rounded to two decimal points
What is meant by the rate of stock?
The rate of stock refers to the price at which a particular stock is being bought or sold in the stock market, which can vary based on supply and demand.
What is decimal?
A decimal is a number system that uses the base 10 and includes a decimal point to separate the integer part from the fractional part. It is commonly used in mathematics and everyday life for expressing fractions, percentages, and monetary values.
According to the given information
We can use the constant-growth dividend discount model to calculate the market's required rate of return for the stock. The model is:
Current stock price = Dividend next year / (Required rate of return - Dividend growth rate)
We know the current stock price is $216, the dividend next year is $1.14, and the dividend growth rate is 5%. We need to solve for the required rate of return.
216 = 1.14 / (r - 0.05)
Multiplying both sides by (r - 0.05), we get:
216(r - 0.05) = 1.14
Expanding the left side, we get:
216r - 10.8 = 1.14
Adding 10.8 to both sides, we get:
216r = 11.94
Dividing both sides by 216, we get:
r = 0.0553 or 5.53%
Therefore, the market's required rate of return for Samsung's common stock is 5.53%, rounded to two decimal points
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The remains of an ancient ball court include a rectangular playing alley with a perimeter of about 24 m. The length of the alley is two times the width. Find the length and the width of the playing alley.
Answers
How many liters each of a 50 % acid solution and a 65 % acid solution must be used to produce 60 liters of a 55 % acid solution? (Round to two decimal places if necessary.)
Answers
To produce 60 liters of a 55% acid solution, we would need 40 liters of the 50% acid solution and 20 liters of the 65% acid solution.
Let number of liters of 50% acid solution needed be = "x", and
Let number of liters of 65% acid solution needed to produce 60 liters of a 55% acid solution. be = y,
To solve for x and y, we can use the following system of equations:
The "total-volume" of the solution is 60 liters,
⇒ x + y = 60, ...equation(1)
We know that, the total amount of acid in the solution is equal to the concentration of the final solution times its volume;
⇒ 0.50x + 0.65y = 0.55(60) ...equation(2),
On simplifying equation(2),
We get,
⇒ 0.50x + 0.65y = 33,
From equation(1), we have ⇒ x = 60 - y,
Now, we substitute "x" into the second equation and solve for y)
⇒ 0.50(60 - y) + 0.65y = 33,
⇒ 30 - 0.50y + 0.65y = 33,
⇒ 0.15y = 3,
⇒ y = 20
So, we need 20 liters of the 65% acid solution.
⇒ x + y = 60,
⇒ x + 20 = 60,
⇒ x = 40,
Therefore, we need 40 liters of the 50% acid solution and 20 liters of the 65% acid solution to produce 60 liters of a 55% acid solution.
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Find the exact value of x.
Answers
Answer:
1) 13 **Explained below **
2) 4 **Explained below **
3) 6
4) 8
5) 15
6) 2.64575 **Explained below **
Step-by-step explanation:
All 6 problems can be solved using the Pythagorean theorem using the following two rules
If x is the hypotenuse and a, b are the shorter sides then
[tex]x = \sqrt{a^2 + b^2}[/tex]
If x is one of the shorter sides and a (or b) is the other shorter side and c is the hypotenuse then
[tex]x = \sqrt{c^2 - a^2\\[/tex] if a is the other shorter side
[tex]x = \sqrt{c^2 - b^2\\[/tex] if b is the other shorter side
I will just demonstrate for #1 , #2 and #6. You can figure out the reasoning behind the rest.
#1. x is the hypotenuse, 5 and 12 are legs(shorter sides)
[tex]x = \sqrt{5^2 + 12^2}\\\\x = \sqrt{25 + 144}\\\\x = \sqrt{169}\\\\x = 13\\\\[/tex]
# 2. x is one of the shorter sides (leg)
5 is the hypotenuse and 3 is the other shorter side
[tex]x = \sqrt{5^{2} - 3^{2}}\\\\x = \sqrt{5^{2} - 3^{2}}\\\\x = \sqrt{25 - 9}\\\\x = \sqrt{16}\\\\x = 4[/tex]
#6 hypotenuse is 4, short side = 3
[tex]x = \sqrt{4^{2} - 3^{2}}\\\\x = \sqrt{4^{2} - 3^{2}}\\\\x = \sqrt{16 - 9}\\\\x = \sqrt{7}\\\\x = 2.64575\\\\[/tex]
Experiment 4: You have a bag of 15 scrabble tiles. 3 of the
tiles are the letter O. And the other 2 tiles are the letter U.
a. What is the probability of getting an O on the first draw?
b. What is the probability of getting a U if you didn't replace the O?
c. What is the probability of getting O and then U if you don't
replace the O?
Answers
Step-by-step explanation:
a 1/15 for getting 0
b 2/14 for getting u
c 2/210 or 3/210
Angles in a Triangle
Answers
Answer:
x = 115°
Step-by-step explanation:
The interior angle adjacent to the 115° angle measures:
180° - 115° = 65°
x is an exterior angle, so x = 65° + 50°
x = 115°
Answer:
115
Step-by-step explanation:
X has to be supplementary to that adjacent angle, so first the angle next to the 115 has to be defined. 180-115 (as the must be supplementary) is 65. 65+ 50= 115, which should be x. The 2 opposite angles will equal the opposite outside angle. Hope this helps!
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Put the items in order from least steep to steepest rate of change
Answers
Answer:
1) Michele
2) f(t)
3) Elisa's puppy
4) g(x)
Step-by-step explanation:
This is because Michele's situation has a rate of change of -10, f(t) has -6.2, Elisa's puppy's situation has a rate of change of +5, and g(x) has 8.1
Hence,
-10 < -6.2 < 5 < 8.1
Hope this helps and be sure to mark this as brainliest! :)
Find the area I will give brainliest
Answers
The area of the triangle is 22 miles square
Finding the area of the triangleFrom the question, we have the following parameters that can be used in our computation:
The triangle
Where we have
Base = 11 miles
Height = 4 miles
using the above as a guide, we have the following:
Area = 1/2 * Base * Heigt
substitute the known values in the above equation, so, we have the following representation
Area = 1/2 * 11 * 4
Evaluate
Area = 22 miles square
hence, the area is 22 miles square
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Oliver is buying a new dishwasher. The dishwasher’s price is $285.10 after tax. He has a few payment options. He can put it on his debit card, which would take the money from his savings account. His savings account earns interest at a rate of 1.8% annually. He could also put it on one of two different credit cards. Card A has an annual interest rate of 9%, charged monthly, and charges a flat 1.2% fee on the initial value of the purchase (note: the fee accrues interest too). Card B has an annual interest rate of 12%, charged monthly, but no fee for purchases. Oliver thinks it will take five months for him to earn the additional money to offset the purchase. In all cases, the interest accrues according to this equation:
A = P(1 + r)n, where A is the final dollar amount, P is the principal (initial amount borrowed), r is the interest rate for each interest period, and n is the number of interest periods.
Answers
Oliver withdraws an amount of $285.10 from his saving account and the interest is $26.60
How to calculate the interest?Compound interest is a type of interest that is paid on the closing balance at the end of the previous year, which includes the interest paid in previous years.
His saving account earns 1.8% annually
The interest Oliver could have earned in five months:
Monthly interest = Annual interest ÷ 12
Monthly interest = 1.8% ÷ 12
Monthly interest = 0.018 ÷ 12 = 3/2000
A = P(1 + r)n
After five months = Principle × (1 + interest)ⁿ
After five months = 285.10 × (1 + 0.018)⁵
After five months = 311.70
Interest earned = 311.70 - 285.10 = $26.60
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The interior angles formed by the sides of a hexagon have measures that sum to 720°.
What is the measure of angle F?
Enter your answer in the box.
Answers
Answer:
140
Step-by-step explanation:
First you want to add up the numbers inside of the hexagon and set them equal to 720. Your starting equation should be 3x+240=720. Then your going to subtract 240 from each side giving you 3x=480. Next divide each side by 3 giving you x=160. Plug 160 in for x and you should get 160-20= 140.
Answer:
140
Step-by-step explanation:
First you want to add up the numbers inside of the hexagon and set them equal to 720. Your starting equation should be 3x+240=720. Then your going to subtract 240 from each side giving you 3x=480. Next divide each side by 3 giving you x=160. Plug 160 in for x and you should get 160-20= 140.
from orlando to syracuse is 1053 miles. flying into headwinds on the way down. The trip takes 2.75 hrs. on the way back . the wind is still blowing at the same speed. the trip takes 1.75 hrs. so, what is the speed in the still air and how fast is the wind blowing
Answers
Step-by-step explanation:
distance / rate = time s = plane speed w = wind speed
Flying with wind 1053 / ( s+ w) = 1.75
solve for s = 601.714 -w
Flying against wind 1053 / (s-w) = 2.75 sub in for s (above)
1053 / ( 601.714 - w -w ) = 2.75
solve for w = 109.27 mi/hr
sub this 'w' into one of the equations to solve for 's'
1053 / ( s + 109.273) = 1.75 shows s = 492.44 mi/hr
Write the polynomial in standard form.
Answers
Answer:
[tex] - 9 {g}^{3} + {g}^{2} + 10g - 5[/tex]
Determine the amount thabang will receive if they decided to share their money according to hours
Answers
If Thabang and Ndivhu decided to share their money according to hours, then Thabang will receive R240.
Thabang worked for 3 hours and Ndivhu worked for 2 hours.
Together, they worked for a total of 5 hours. They were paid R400 for their work,
So, we calculate their hourly-rate by dividing the total amount by the total number of hours worked;
⇒ Hourly rate = (Total amount paid)/(Total number of hours worked),
⇒ Hourly rate = R400/5,
⇒ Hourly rate = R80 per hour,
Now, we find amount Thabang will receive if it is decided to share the money according to "hours-worked".
Thabang worked for 3 out of the total 5 hours, so he should receive 3/5 of the total amount paid,
⇒ Amount Thabang will receive = (Hours Thabang worked / Total hours worked) × Total amount paid,
⇒ Amount Thabang will receive = (3/5) × R400,
⇒ Amount Thabang will receive = R240,
Therefore, Thabang will receive R240 if they decided to share their money according to hours worked.
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The given question is incomplete, the complete question is
Thabang and his friend Ndivhu share a job of cleaning a neighbors yard and they were paid R400, Thabang worked 3 hours and Ndivhu worked for 2 hours. Determine the amount Thabang will receive if they decided to share their money according to hours.
Select the statement that shows equivalent measurements.
14 grams = 0.14 decagrams
14 grams = 1.4 decigrams
14 grams = 140 centigrams
14 grams = 14,000 milligrams
Answers
Answer:
14 grams = 14,000 milligrams
Step-by-step explanation:
since multiply the grams by 1000 will convert it to milligrams
It is given that M is the midpoint of and . Midpoints divide a segment into two congruent segments, so . Since and perpendicular lines intersect at right angles, and are right angles. Right angles are congruent, so . The triangles share , and the reflexive property justifies that . Therefore, by the SAS congruence theorem. Thus, because _____________. Finally, ΔPKB is isosceles because it has two congruent sides.
Answers
Complete paragraph proof would be detailed proof.
Given that M is the midpoint of PK and PK ⊥ MB, we need to prove that △PKB is isosceles.
Proof,
Since M is the midpoint of PK, PM ≅ KM.
Also, since PK ⊥ MB, we have ∠PMB and ∠KMB are right angles.
Since right angles are congruent, we have ∠PMB ≅ ∠KMB.
Now, by the SAS congruence theorem, we have △PMB ≅ △KMB because they share side MB, and PM ≅ KM and ∠PMB ≅ ∠KMB.
Thus, we have BP ≅ BK because corresponding parts of congruent triangles are congruent.
Therefore, △PKB has two congruent sides and isosceles by definition.
Hence, we have proven that △PKB is isosceles.
Correct Question :
Complete the paragraph proof. Given: M is the midpoint of PK PK ⊥ MB Prove: △PKB is isosceles It is given that M is the midpoint of PK and PK ⊥ MB. Midpoints divide a segment into two congruent segments, so PM ≅ KM. Since PK ⊥ MB and perpendicular lines intersect at right angles, ∠PMB and ∠KMB are right angles. Right angles are congruent, so ∠PMB ≅ ∠KMB. The triangles share MB, and the reflexive property justifies that MB ≅ MB. Therefore, △PMB ≅ △KMB by the SAS congruence theorem. Thus, BP ≅ BK because . Finally, △PKB is isosceles because it has two congruent sides.
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The price of a
home is $224,000. The bank requires a 20% down payment and three points at the time of closing. The cost of the home is financed with a 30-year fixed-rate mortgage at 7%. Complete parts (a) through (e) below.
Answers
(a) 20% of $224,000 is $44,800.
(b) 3 points on a $224,000 mortgage is $6,720.
(c) $44,800 + $6,720 is $51,520. So the total down payment and closing costs are $51,520.
(d) The mortgage amount is $224,000 - $51,520 = $172,480.
(e)
Monthly payment = $172,480 * (7%/12%)(30 years) = $1,234.15
Total interest paid over 30 years = $172,480 * 7% * 30 years = $243,720
Martina is learning different kinds of Latin dance she went to 6 salsa lessons and 12 rumba lessons. Each cost four dollars. let T equal the total number of lessons let c equal the total cost of classes .write an equation to find the total number of the lessons and ration to find the total cost of the lessons
Answers
The equation to find the total number of lessons is T = 6 + 12 = 18, and the ratio to find the total cost of the lessons is c:T = 72:18 or 4:1.
The equation to find the total number of lessons (T) can be written as:
T = number of salsa lessons + number of rumba lessons
Substituting the given values, we get:
T = 6 + 12 = 18
The ratio to find the total cost of the lessons (c) can be written as:
c = cost per lesson x total number of lessons
Substituting the given values, we get:
c = $4 x 18 = $72
Therefore, the equation to find the total number of lessons is T = 6 + 12 = 18, and the ratio to find the total cost of the lessons is c:T = 72:18 = 4:1.
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Given the following probabilities, determine whether the events A and B are
independent or dependent.
P(A) = 2/3
P(B) = 1/4
P(A and B)= 2/7
Answers
If P(A)= [tex]\frac{2}{3}[/tex], P(B) = [tex]\frac{1}{4}[/tex] and P(A and B)= [tex]\frac{2}{7}[/tex], then the events A and B are dependent.
By comparing the probability of events A and B intersection (P(A and B)) to the product of their individual probabilities (P(A) * P(B)), we can find out whether the events are independent or dependent.
Condition of independent events,
If P(A) * P(B) = P(A and B)
Condition of dependent events,
If P(A) * P(B) ≠ P(A and B)
Given,
P(A) = [tex]\frac{2}{3}[/tex]
P(B) = [tex]\frac{1}{4}[/tex]
P(A and B) = [tex]\frac{2}{7}[/tex]
Calculating P(A) * P(B) and compare it to P(A and B):
P(A) * P(B) = [tex]\frac{2}{3}[/tex] * [tex]\frac{1}{4}[/tex] = [tex]\frac{2}{12}[/tex] = [tex]\frac{1}{6}[/tex]
Since P(A and B) ≠ P(A) * P(B), therefore events A and B are dependent.
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CAN SOMEONE HELP WITH THIS QUESTION?
Answers
The area under the curve is 522 units².
What is the area under the curve?The area under the curve is calculated by integrating the function and finding the definite integra as shown below.
f(x) = 8x + 10
The integra of the function;
f(x)' = 4x² + 10x
Find the definite integra at the boundaries, x = 19 and x = 22
f(19)' = 4(19)² + 10(19)
F(19)' = 1,634
f(22)' = 4(22)² + 10(22)
F(22)' = 2,156
Area = 2,156 - 1,634 = 522 units²
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NEED HELP WITH THIS TRIG QUESTION
Answers
The distance from the ball to the center of the green (CD) is approximately 13.2 yards.
How to find distance using trignometric ratios?Determine the values given: Determine the known angles and distances that are involved in the issue.Choose the proper trigonometric function: To link the angle and the distances, select the proper trigonometric function (such as sine, cosine, or tangent) based on the given angle and the sides of the triangle created by the points.Use the trigonometric formula: Using the selected function and the unknown distance as the variable, write the trigonometric equation and replace the specified values .Calculate the distance: To determine the unknown distance on one side of the equation, use algebraic methods and according to the requirements of the problem, round the final response to the specified number of significant figures or decimal places.Given:
AB = 110 yards (distance from marker to center of the green)
BC = 45 yards (distance from marker to golfer's ball)
angle BAC = 115° (angle formed when golfer turns towards the ball)
To find CD (distance from ball to center of the green):
Apply the cosine function to angle BAC:
cos(115°) = AB/BC (∵cos θ = Adjacent side/ Hypotenuse)
Substitute the given values:
cos(115°) = 110/45
Calculate cos(115°):
cos(115°) ≈ -0.2924 (rounded to four decimal places)
Multiply both sides by BC to solve for AB:
AB = BC * cos(115°)
AB ≈ 45 * -0.2924
AB ≈ -13.16 yards (rounded to two decimal places)
Note: (The AB is negative, as the ball is moving in the opposite direction of the golfer's turn.)
CD = |AB| ≈ 13.16 yards (rounded to two decimal places)
CD ≈ 13.2 yards (rounded to one decimal point)
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Students are painting a mural. So far the mural is painted one fourth blue two 8 red and three 12 green
Answers
One fourth blue can be written as 1/4, two 8 red is equivalent to 1/4 (since 2/8 reduces to 1/4), and three 12 green is equivalent to 1/4 (since 3/12 reduces to 1/4).
Therefore, the fraction of the mural that has been painted is:
1/4 + 1/4 + 1/4 = 3/4
So, the students have painted 3/4 of the mural so far.
Give a recursive definition for the following set of ordered pairs of positive integers ([tex]a|b[/tex] means that a is a factor of b): [tex]S=[/tex]{[tex](a,b)|a \in Z^+, b \in Z^+, a|b[/tex]}
Answers
A recursive definition for the set S of ordered pairs of positive integers (a,b) where a is a factor of b can be given as follows:
1. The ordered pair (1, b) is in S for all positive integers b.
2. If a is a factor of b, then (a, b) is in S if and only if (a, b/a) is in S.
The first rule establishes the base case for the recursion, stating that (1, b) is in S for all b. The second rule provides the recursive step, stating that (a, b) is in S if and only if (a, b/a) is in S, where b/a is an integer division of b by a, and a is a factor of b. This recursive definition ensures that all pairs (a, b) in S have a as a factor of b.