Answer:
6
Step-by-step explanation:
I did it
Odessa starts counting the frogs in the small pond that the forest service just set up by her house. She marks the data in this graph. If y equals the number of frogs and x equals the number of months that have passed, the frog population can be described by the mathematical formula y = x.
Answer:
Answer is 2
Step-by-step explanation:
If it shows a graph with Frog Population on top
6 - 8x = 22 whats the answer?
Answer:
x = -2
Step-by-step explanation:
subtract the 6 from 22
then divide -8x and 16 by -8
then you get your anser
The solution to the equation 6 - 8x = 22 is x = -2. The equation was solved by rearranging and isolating 'x', and then dividing by the coefficient -8.
Explanation:The question is a simple linear equation. Let's solve it step by step:
First, let's rearrange 6 - 8x = 22 to find the value of 'x'. We can do this by subtracting 6 from both sides, which gives us -8x = 22 - 6.So, -8x = 16.Next, we solve for 'x' by dividing both sides of the equation by -8. This gives us x = 16 / -8.x = -2 is the solution to the equation 6 - 8x = 22.Learn more about Solving linear equationshttps://brainly.com/question/2030026
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Answer and how to do it
Answer:
[tex] (x - 9)^2 + y^2 = 36 [/tex]
Step-by-step explanation:
The equation of a circle in standard form is
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
You are given
[tex] x^2 + y^2 - 18x + 45 = 0 [/tex]
In order to put the equation in standard from, we need to complete the square. Since there is no y term, the y part is simply y^2, and there is no need to complete the square for y. For x, we do have an x term, so we must complete the square in x.
Start by grouping the x terms and subtracting 45 from both sides.
[tex] x^2 - 18x + y^2 = -45 [/tex]
Now we need to complete the square for x.
[tex] x^2 - 18x ~~~~~~+ y^2 = -45 [/tex]
The number that completes the square will go in the blank above, and it will also be added to the right side of the equation.
To find the number you need to add to complete the square, take the coefficient of the x term. It is -18. Divide it by 2. You get -9. Now square -9 to get 81. The number that completes the square in x is 81. Now you add it to both sides of the equation.
[tex] x^2 - 18x + 81 + y^2 = -45 + 81 [/tex]
[tex] (x - 9)^2 + y^2 = 36 [/tex]
Answer: [tex] (x - 9)^2 + y^2 = 36 [/tex]
Clark Heter is an industrial engineer at Lyons Products. He would like to determine whether there are more units produced on the night shift than on the day shift. A sample of 60 day-shift workers showed that the mean number of units produced was 334, with a population standard deviation of 23. A sample of 68 night-shift workers showed that the mean number of units produced was 341, with a population standard deviation of 28 units.At the .10 significance level, is the number of units produced on the night shift larger?1. This is a (Click to select)twoone-tailed test.2. The decision rule is to reject H0: μd ≥ μn if z < . (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)3. The test statistic is z = . (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)4. What is your decision regarding H0?
Answer:
Step-by-step explanation:
Let the subscripts d and n represent day and night respectively
The null hypothesis is
H0 : μd ≥ μn
The alternative hypothesis is
H1 : μd < μn
it is a one-tailed and also a right left test because of the greater than symbol in the alternative hypothesis.
The decision rule is to reject H0: μd ≥ μn If 0.10 > p value
Since the population standard deviations are known, we would use the formula to determine the test statistic(z score)
z = (xd - xn)/√σd²/nd + σn²/nn
Where
xd and xn represents sample means for day and night respectively.
σd and σn represents population standard deviations for day and night respectively.
nd and nn represents number of samples
From the information given,
xd = 334
xn = 341
σd = 23
σ2 = 28
nd = 60
nn = 68
z = (334 - 341)/√23²/60 + 28²/68
= - 7/√20.34607843138
z = - 1.55
From the normal distribution table, the probability value corresponding to the z score is 0.061
Since the level of significance, 0.1 > 0.061, we would reject H0
Therefore, there is enough evidence to conclude that there are more units produced on the night shift than on the day shift.
Final answer:
Clark Heter is conducting a one-tailed test to compare the mean production of day and night shifts. The decision to reject the null hypothesis that day shift production is greater or equal to night shift production is based on a critical value of -1.28 linked to a significance level of 0.10. The test statistic is computed from the given means and standard deviations for both samples.
Explanation:
Conducting a Two-Sample Z-Test
Clark Heter wants to determine if more units are produced on the night shift than on the day shift. Given the samples:
- Day-shift (n=60): mean = 334, population standard deviation = 23.
- Night-shift (n=68): mean = 341, population standard deviation = 28.
The significance level is 0.10.
A marble is selected at random from a jar containing 4 red marbles, 2 yellow marbles, and 3 green marbles.
Home
What is the probability that the marble is red?
Answer:
4 / 9 probability of getting a red
Step-by-step explanation:
How many marbles are there total?
4 red + 2 yellow + 3 green = 9 marbles total
P( red marble) = 4 red / 9 total = 4/9
Answer:
Step-by-step explanation:
Red marbles- 4
Yellow marbles-2
Green marbles-3
Total marbles=9
Probability= 4/9
=0.4444
the train to hogwarts is moving at a speed of 120 mph. if hogwarts is 420 miles away, how long will the students train ride be ?
Answer:
The train ride is 3.5 hours
Step-by-step explanation:
We know that distance is equal to rate times time
d = rt
We know the distance and the rate
420 = 120*t
Divide each side by 120
420/120 = 120t/120
3.5 =t
The train ride is 3.5 hours
Answer:
3.5 hrs
3 hrs and 30 min
210 min
A circular dining room table can seat 11 people. Each person has about 2 feet of space along the edge of the table. What is the radius of the table, rounded to the nearest half-foot?
Answer:bruh
Step-by-step explana
The radius of the table, rounded to the nearest half-foot, is 3.5 feet.
To determine the radius of the circular dining room table, we can use the formula for the circumference of a circle, which is:
C = 2 π r
where:
C - circumference
r - radius
Given that each person has about 2 feet of space along the edge of the table, the circumference of the table must be able to accommodate the seating for 11 people. Each person occupies 2 feet of space, so the total space needed around the edge of the table is:
11 × 2 = 22 feet
We can set up an equation using the circumference formula:
C = 2 π r = 22
To find the radius (r), we divide both sides of the equation by 2π:
r = [tex]\frac{22}{2 \pi}[/tex]
Now, let's calculate the value:
r = [tex]\frac{22}{2 \pi}[/tex] = [tex]\frac{22}{2 \times 3.14}[/tex] = [tex]\frac{22}{6.28}[/tex] = 3.503
Rounding to the nearest half-foot, we get:
r = 3.5 feet
Question 1 (1 point)
in a local raffle, first prize is $100, second prize is $75, third prize is $50 and fourth prize is $25. If 15 people enter the raffle, how many ways
can 4 be selected to win the prizes?
There are 32,760 ways to select 4 winners from 15 participants in a local raffle where the order of prizes matters according to permutation.
Explanation:To find out how many ways 4 winners can be selected from 15 participants in a local raffle with given prizes, we can use the concept of permutation because the order in which the prizes are awarded matters (i.e., the prizes are not identical).
The total number of different ways to select 4 winners from 15 participants is represented by the permutation of 15 things taken 4 at a time (since the order of selection matters for different prizes).
The formula for permutation is: P(n, k) = n! / (n-k)! where n is the total number of items, k is the number of items to choose, and '!' represents a factorial.
For this problem, we calculate P(15, 4):
Therefore, there are 32,760 ways to select 4 winners from 15 participants.
What is the mean for the data set?
8 10 6 4
12 6 8 14
Answer:
8.5
Step-by-step explanation:
To find mean, we simply take the average of all the numbers in the data set, and divide in by the amount of values!
[tex]8+10+6+4+12+6+8+14= 68\\[/tex]
68 ÷ 8 = 8.5!
Answer:
[tex]8\frac{1}{2}[/tex]
Step-by-step explanation:
First add up all the numbers:
8+10+6+4+12+6+8+14=68
Now you have to divide the sum by the amount of numbers. There are 8 numbers.
[tex]\frac{68}{8}=\frac{34}{4}=\frac{17}{2}[/tex]
[tex]\frac{17}{2}=8\frac{1}{2}[/tex]
An experiment consists of randomly selecting a marble from a bag, replacing it, and then selecting another marble. The bag contains 3 yellow marbles and 2 white marbles? What is the probability of selecting a white marble and then a yellow marble?
Answer:
6/25 probability
Step-by-step explanation:
We have 5 marbles total, 3 + 2 = 5
Find P( white marble, yellow marble with replacement)
= P(white, yellow) = (2/5)*(3/5) = 6 / 25
Apply the Pythagorean Theorem to find the distance between points A and B. A) 6 units B) 18 units C) 27 units D) 81 units
Answer:
A: 6 Units
Step-by-step explanation:
mr. winter has 32 students in his class. he puts 6 student into each group. if Mr winter gives each group five pieces of chart paper, how many sheets will he need for the whole class?
PART A. which equation can be used to find the answer?
32-6x5=S
32÷5x6=S
32÷6x5=S
32x6÷5=S
Part B. Complete the statement.
Mr. Winter needs _____ sheets of chart paper.
Answer: A) 32÷6x5=S
B) 30 sheets of chart paper.
Step-by-step explanation:
we have 32 students.
he puts 6 students into each group.
he gives each group 5 pieces of chart paper.
32/6 will give us the number of groups
32/6 = 5.33
This means that we have 5 complete groups 6 students, and one group with 2 students. (a total of 6 groups)
And each of these groups need 5 pieces of paper, so we have the equation:
(32/6)*5 = S
and S = 26.66
now, for the 5 complete groups we need 5 pieces of paper for each, and 5*5 = 25 pieces of papper.
For the group of 2 persons we have the oter 1.66 ( or 2 if we round up) pieces of papper.
but this is a group, so they also should receive 5 pieces of papper regardless that they are only 2 integrants, then the total number of paper pieces is 30.
Nana Akosua Owusu – Ansah, a financial manageress for a company is considering two competing investment proposals. For each of these proposals, she has carried out an analysis in which she has determined various net profit figures and has assigned subjective probabilities to the realization of these returns. For proposal A, her analysis shows net profits of GHȼ 20,000.00, GHȼ 30,000.00 or GHȼ 50,000.00 with respective probabilities 0.2, 0.4 and 0.4. For proposal B, she concludes that there is a 50% chance of successful investment, estimated as producing net profits of GHȼ 100,000.00, and of an unsuccessful investment, estimated as a break – even situation involving GHȼ 0.00 of net profit. Assuming that each proposal requires the same Ghana cedi investment, which of the two proposals is preferable solely from the standpoint of expected monetary return?
Answer:
Proposal B
Step-by-step explanation:
This problem can be solved by comparing the expected returns on both options.
The expected return is the sum of the possible outcomes multiplied by its probabilities of occurrence.
For proposal A, the net profits are $20,000, $30,000 and $50,000, with respective probabilities 0.2, 0.4 and 0.4. Then, the expected return can be calculated as:
[tex]E(A)=\sum_{i=1}^3p_iR_i\\\\E(A)=p_1R_1+p_2R_2+p_3R_3\\\\E(A)=0.2*20,000+0.4*30,000+0.4*50,000\\\\E(A)=4,000+12,000+20,000\\\\E(A)=36,000[/tex]
The proposal A has a expected net profit of $36,000.
The proposal B has a 50% chance of having a net profit of $100,000 and a 50% of break even (zero net profit). We applied the same calculation for the expected profit and we have:
[tex]E(B)=\sum_{i=1}^2p_iR_i\\\\E(B)=p_1R_1+p_2R_2\\\\E(B)=0.5*100,000+0.5*0\\\\E(B)=50,000[/tex]
The proposal B has a expected net profit of $50,000.
Assuming that each proposal requires the same investment, the proposal B has more expected monetary return (GHȼ 50,000) than proposal A (GHȼ 36,000).
5. The numbers of blocked intrusion attempts on each day during the first two weeks of the month were 56, 47, 49, 37, 38, 60, 50, 43, 43, 59, 50, 56, 54, 58 After the change of firewall settings, the numbers of blocked intrusions during the next 20 days were 53, 21, 32, 49, 45, 38, 44, 33, 32, 43, 53, 46, 36, 48, 39, 35, 37, 36, 39, 45. (a) Construct a 95% confidence interval for the difference between the average number of intrusion attempts per day before and after the change of firewall settings. (b) Can we claim a significant reduction in the rate of intrusion attempts
To construct a 95% confidence interval for the difference between the average number of daily intrusion attempts before and after changing firewall settings, you determine the standard deviation and mean for both periods. Use these in the formula for the confidence interval. If the interval doesn't include zero, it indicates a significant difference in the average number of daily intrusion attempts, and thus, potentially a significant reduction in intrusion attempts.
Explanation:To perform this analysis, we first need to calculate the mean of the numbers of intrusion attempts for both periods - before and after the change of firewall settings. Then, we need to calculate the standard deviation for the numbers of intrusion attempts for both periods. The formula for the confidence interval is Mean Difference ± (Z*Standard Error). Where Z is a standard score value retrieved from the Z distribution table for a particular confidence level, in this case, 95%. The confidence levels you will be working with depend on the number of samples, in this case 14 and 20 respectively.
Once you have the confidence interval, it will give you the range in which the actual difference between the two means lies with 95% certainty. If the interval does not include zero, it indicates a significant difference between the means. By observing whether the values are predominantly positive or negative, we can infer about the significant reduction in the rate of intrusion attempts.
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What is the side length of a square with a perimeter of 52 meters
Answer:
13 meters
Step-by-step explanation:
The perimeter is the sum of all the sides.
As a square has four identical sides, to calculate the length of one side you would simply divide 52 by 4,which gives you 13.
1) Divide 52 by 4.
[tex]52/4=13meters[/tex]
Answer:
13m
Step-by-step explanation:
52/4 = 13
What is the equation of the following graph?
Enter our answer
help me please !!
What is mBC?
A.70
B.140
C.28
D.56
What is mBCD
A.168
B.192
C.220
D.82
Answer:
is there more to the question?
Step-by-step explanation:
Answer:
1. is 56
2. is 82
Step-by-step explanation:
Just took the quiz and got it right (Like it please so people know its the correct answer)
A company produces fruit juice in 10 different flavors. a local supermarket sells the product, but has only sufficient shelf space to display 3 of the company's 10 fruit juice flavors at a time. How many possible combinations of 3 flavors can the fruit juice company display on the local supermarket shelf?
Answer:
120.
Step-by-step explanation:
This is the number of combinations of 3 from 10.
This = 10C3
= 10! / 3! (10-3)!
= 10*9*8 / 3*2*1
= 120 combinations.
Answer:
120
Step-by-step explanation:
In 1999 the population of Austria was one-third the population of Nepal. At that time the number of people living in Austria was 8,100,000. How many people were living in Nepal
At the post office, Tiffany paid, $11.04. for 2 stamps. At this rate, how much would it cost for Tiffany yo buy 18 stamps?
Answer: $$$99.36
Step-by-step explanation:
It's 11.04 for 2 stamps
U have to buy 18 stamps
18÷2=9
9×11.04=99.36
Answer:
It costs $5.52 to Sam to buy 12 stamps.now multiply
Step-by-step explanation:
Consider the accompanying data on breaking load (kg/25 mm width) for various fabrics in both an unabraded (U) condition and an abraded (A) condition. Use the paired t test to test: H0: μD = 0 versus Ha: μD > 0 at significance level 0.01. (Use μD = μU-A.) Note: The data below is formatted such that you can copy and paste it into R. Fabric 1 2 3 4 5 6 7 8 U = c( 36.3, 55.0, 51.1, 38.8, 43.2, 48.8, 25.6, 49.5) A = c( 28.5, 20.0, 46.0, 34.5, 36.5, 52.5, 26.5, 46.5) Calculate the mean difference and standard deviation. d = sd = Compute the test statistic value. (Round your answer to three decimal places.) t = p-value = State the conclusion in the problem context. Fail to reject H0. The data does not suggest a significant mean difference in breaking load for the two fabric load conditions. Reject H0. The data does not suggest a significant mean difference in breaking load for the two fabric load conditions. Fail to reject H0. The data suggests a significant mean difference in breaking load for the two fabric load conditions. Reject H0. The data suggests a significant mean difference in breaking load for the two fabric load conditions.
Rejection region(s)
t > 2.998
Test statistic value
t = 2.89
Fail to reject H0. The data does not suggest a significant mean difference in breaking load for the two fabric load conditions. Option B is the right choice.
State the hypotheses
H0: μD = 0
Ha: μD > 0
State the rejection region
Since the alternative hypothesis is one-sided, we use a one-tailed test. The rejection region for a one-tailed t-test with significance level 0.01 and 7 degrees of freedom is:
t > 2.998
Compute the test statistic
The test statistic for a paired t-test is calculated as follows:
t = ([tex]\bar x[/tex]D - μD) / (sdD / √n)
where:
[tex]\bar x[/tex]Dis the mean difference between the unabraded and abraded breaking loads
sdD is the standard deviation of the difference between the unabraded and abraded breaking loads
n is the sample size
Calculating the mean difference:
[tex]\bar x[/tex]D = (36.3 - 28.5) + (55.0 - 20.0) + (51.2 - 46.0) + (38.6 - 34.0) + (43.2 - 36.5) + (48.8 - 52.5) + (25.6 - 26.5) + (49.6 - 46.5) = 6.85
Calculating the standard deviation of the difference:
sdD = √[((36.3 - 28.5)^2 + (55.0 - 20.0)^2 + (51.2 - 46.0)^2 + (38.6 - 34.0)^2 + (43.2 - 36.5)^2 + (48.8 - 52.5)^2 + (25.6 - 26.5)^2 + (49.6 - 46.5)^2) / 7] = 10.87
Calculating the test statistic:
t = (6.85 - 0) / (10.87 / √8) = 2.89
Make a decision
Since the test statistic (2.89) is less than the critical value (2.998), we fail to reject the null hypothesis.
The correct choice is option d. Fail to reject H0. The data does not suggest a significant mean difference in breaking load for the two fabric load conditions.
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Question:-
Consider the accompanying data on breaking load (kg/25 mm width) for various fabrics in both an unabraded condition and an abraded condition. Use the paired t test to test H0: ?D = 0 versus Ha: ?D > 0 at significance level 0.01. (Use ?D = ?U ? ?A.)
State the rejection region(s). (If the critical region is one-sided, enter NONE for the unused region. Round your answers to three decimal places.)
t ? _______
t ? ________
Compute the test statistic value. (Round your answer to three decimal places.)
t = _____
State the conclusion in the problem context.
a.Reject H0. The data suggests a significant mean difference in breaking load for the two fabric load conditions.Fail to b.reject H0. The data suggests a significant mean difference in breaking load for the two fabric load conditions. c.Reject H0. The data does not suggest a significant mean difference in breaking load for the two fabric load conditions.
d.Fail to reject H0. The data does not suggest a significant mean difference in breaking load for the two fabric load conditions
HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing. Check all that apply.
Answer:
A, B, and D.
Step-by-step explanation:
The absolute value function is V shaped, goes through the origin, and never dips below the x axis, meaning that it is in the 1st and 2nd quadrants. The left side resembles a line with slope -1, which means that choice C is incorrect. Hope this helps!
The combined math and verbal scores for students taking a national standardized examination for college admission, is normally distributed with a mean of 820 and a standard deviation of 200. If a college requires a student to be in the top 15 % of students taking this test, what is the minimum score that such a student can obtain and still qualify for admission at the college calculator
Answer: 1007.28
Step-by-step explanation:
Given : The combined math and verbal scores for students taking a national standardized examination for college admission, is normally distributed with
[tex]\mu=820\ \ \ ,\ \sigma=200[/tex]
If a college requires a student to be in the top 15 % of students taking this test, it means that they want the students that score 85 percentile or above.
Let X be the scores of any random student, we require
[tex]P(X<x)=0.85[/tex], where x is minimum score that such a student can obtain and still qualify for admission at the college.
Formula for z-score = [tex]z=\frac{x-\mu}{\sigma}=\frac{x-820}{200}[/tex] ...(i)
From normal z-value table , [tex]P(z<1.036)=0.85[/tex]...(ii)
From (i) and (ii) , we get
[tex]\frac{x-820}{200}=1.0364\\\\\Rightarrow\ x-820=207.28\\\\\Rightarrow\ x=207.28+820=1007.28[/tex]
Hence, the minimum score that such a student can obtain and still qualify for admission at the college is 1007.28.
Square M N O P is shown. Angle M is (4 t + 20) degrees and angle N is (7 f + 6) degrees.
MNOP is a square. What are the values of t and f?
t =
f =
Answer:
t = 17.5°
f = 12°
Step-by-step explanation:
MNOP is a square and the angle M is (4t + 20)° and the angle N is (7f + 6)°. The value of t and f can be calculated below.
A square is a quadrilateral and all the sides are equal. Opposite sides are parallel to each other . Each angle of a square is equal to 90°.
Since ∠M = 4t + 20
This means ∠M
4t + 20 = 90
4t = 90 - 20
4t = 70
t = 70/4
t = 17.5°
∠N = 7 f + 6
7 f + 6 = 90
7f = 90 -6
7f = 84
f = 84/7
f = 12°
Answer:
t=17.5
f=12
Step-by-step explanation:
What is the value of x in the equation x/-4=7?
Answer: -28
Step-by-step explanation: Since x is being divided by -4, to solve for x, multiply both sides of the equation by -4.
On the left side, the -4's will cancel
and on the right side, 7(-4) is -28.
So x = -28.
Please do not try to do this problem in your head.
Show the work that it takes to get x by itself.
Answer:
x= - 28
Step-by-step explanation:
-4/1[x/-4 = 7]
x = -28
A publishing company has just published a new college textbook. Before the company decides the price at which to sell this textbook, it wants to know the average price of such textbooks in the market. The research department at the company took a sample of 25 comparable textbooks and collected information on their prices. This information produced a mean of $145 for this sample. It is known that the standard deviation of all such textbooks is $35 and the population of such prices is normal.
a. What is the point estimate of the mean price of all such college textbooks?
b. Construct a 90% confidence interval for the mean price of all such college textbooks.
Answer:b
Step-by-step explanation:
a. The point estimate of the mean price of college textbooks is $145. b. A 90% confidence interval for the mean price is ($133.49, $156.52).
Given a sample of 25 comparable textbooks with a mean price of $145 and a known population standard deviation of $35, the following steps will help answer the questions:
a. Point Estimate:
The point estimate of the mean price of all such college textbooks is simply the sample mean, which is $145.
b. 90% Confidence Interval:
To construct a 90% confidence interval for the mean price of college textbooks, we follow these steps:
Identify the sample mean [tex]ar_{x}[/tex] = $145, sample size (n) = 25, and population standard deviation [tex]\sigma[/tex] = $35.Determine the z-score for a 90% confidence level. The z-score corresponding to a 90% confidence level is 1.645.Calculate the standard error (SE) of the mean using the formula: SE = [tex]\sigma[/tex] / [tex]\sqrt{n}[/tex] = $35 / √(25) = $7.Compute the margin of error (ME) using the formula: ME = [tex]z \times SE[/tex] = 1.645 × $7 = $11.515.Determine the confidence interval using the formula: ([tex]\bar{x}[/tex] - ME, [tex]\bar{x}[/tex]} + ME) = ($145 - $11.515, $145 + $11.515) = ($133.485, $156.515).Thus, the 90% confidence interval for the mean price of all college textbooks is ($133.49, $156.52).
a new play premieres on saturday, october 1, and 420 people attend. attendance then decreases by 30% each day. find the attendance on tuesday , october 4
Answer:
The attendance on tuesday, october 4, is of 144 people.
Step-by-step explanation:
The attendance after t days is given by the following equation:
[tex]A(t) = A(0)(1-r)^{t}[/tex]
In which A(0) is the attendance on the first day and r is the daily decrease rate.
Premieres on saturday, october 1, and 420 people attend.
This means that [tex]A(0) = 420[/tex]
Attendance then decreases by 30% each day.
This means that [tex]r = 0.3[/tex]
So
[tex]A(t) = A(0)(1-r)^{t}[/tex]
[tex]A(t) = 420(1-0.3)^{t}[/tex]
[tex]A(t) = 420(0.7)^{t}[/tex]
Find the attendance on tuesday , october 4
This is 4-1 = 3 days after saturday. So this is A(3).
[tex]A(3) = 420(0.7)^{3} = 144[/tex]
The attendance on tuesday, october 4, is of 144 people.
To find the attendance on Tuesday, October 4, after a 30% daily decrease from an initial attendance of 420 people on Saturday, October 1, we calculate the exponential decay for three days to get approximately 144 attendees.
The student's question involves an exponential decay math problem where the attendance of a play decreases by a percentage each day. To calculate the attendance on Tuesday, October 4, we begin with the initial attendance of 420 people on Saturday, October 1. We then apply a 30% decrease for each subsequent day:
Sunday, October 2: 420 - (0.30 × 420) = 294 peopleMonday, October 3: 294 - (0.30 × 294) = 205.8 peopleTuesday, October 4: 205.8 - (0.30 × 205.8) = approximately 144.06 peopleSince we cannot have a fraction of a person attending, we would generally round to the nearest whole number, which means about 144 people attended the play on Tuesday, October 4.
Fill in the blanks in the following proof, which shows that the sequence defined by the recurrence relation
sk = sk − 1 + 2k, for each integer k ≥ 1
s0 = 3.
satisfies the formula
sn = 3 + n(n + 1) for every integer n ≥ 0.
Proof (by mathematical induction):
To prove that the sequence defined by the recurrence relation satisfies the formula sn = 3 + n(n + 1), we need to show that the base case holds and then prove the inductive step.
Explanation:To prove that the sequence defined by the recurrence relation satisfies the formula , we need to show that the base case holds and then prove the inductive step.
Base case:
When , we have . This matches the formula, so the base case holds.
Inductive step:
Assume that the formula holds for some . We want to show that it holds for .
Using the recurrence relation, we have:
sn+1 = sn + 2(n+1)
Using the induction hypothesis, we can substitute in the expression:
sn+1 = (3 + n(n + 1)) + 2(n+1)
Expanding the expression:
sn+1 = 3 + n(n + 1) + 2n + 2
Combining like terms:
sn+1 = 3 + n(n + 1) + 2(n+1)
sn+1 = 3 + (n+1)((n + 1) + 1)
This matches the formula for , so the inductive step holds. Therefore, the formula holds for all integers .
Can someone help.....
Answer:
7
Step-by-step explanation:
formula for circumference of a circle is [tex]\pi[/tex]d
7[tex]\pi[/tex] = [tex]\pi[/tex]d
d = 7
simplify the expression below. (-3x2 + 2x - 4) + (4x2 + 5x +9)
Answer: =x2+7x+5
Step-by-step explanation:
−3x2+2x−4+4x2+5x+9
=−3x2+2x+−4+4x2+5x+9
Combine Like Terms:
=−3x2+2x+−4+4x2+5x+9
=(−3x2+4x2)+(2x+5x)+(−4+9)
=x2+7x+5
Answer:
=x2+7x+5
Answer:
x^2+7x+5
Step-by-step explanation:
Remove parentheses: -3x^2+2x-4+4x^2+5x+9
Group like terms: -3x^2+4x^2+2x+5x-4+9
Add similar elements: x^2+2x+5x-4+9
Add/subtract the numbers: x^2+7x+5