Answer:
a) P(4)=0.03
b) P(x≥3)=0.15
c) P(x<3)=0.85
d) µX=1.52
e) σX=1.69
Step-by-step explanation:
The question is incomplete:
The variable X has the following probability distribution:
x 1 2 3 4 5
P(x) 0.7 0.15 0.10 0.03 0.02
a) The probability P(x=4) can be read from the table
[tex]P(4)=0.03[/tex]
b) The probability that there are at least 3 occupants in the car is P(x≥3).
[tex]P(x\geq3)=P(3)+P(4)+P(5)\\\\P(x\geq3)=0.10+0.03+0.02\\\\P(x\geq3)=0.15[/tex]
c) The probability that a car has fewer than 3 occupants (P(x<3)) is:
[tex]P(x<3)=1-P(x\geq3)=1-0.15=0.85[/tex]
d) The mean can be calculated as:
[tex]\mu_x=\sum_{i=1}^5p_i\cdot x_i\\\\\mu_x=0.7*1+0.15*2+0.10*3+0.03*4+0.02*5\\\\\mu_x=0.7+0.30+0.30+0.12+0.10\\\\ \mu_x=1.52[/tex]
e) The standard deviation can be calculated as:
[tex]\sigma_x=\sqrt{\sum_{i=1}^5p_i(x_i-\mu_x)^2}}\\\\ \sigma_x=\sqrt{0.7(1-1.52)^2+ 0.15(2-1.52)^2+ 0.1(3-1.52)^2+ 0.03(4-1.52)^2 +0.02(5-1.52)^2}\\\\ \sigma_x=\sqrt{0.7*0.2704+0.15*0.2304+0.1*2.1904+0.03*6.1504+0.03*12.1104}\\\\\sigma_x=\sqrt{0.18928+0.06912+0.65712+0.738048+1.21104}\\\\ \sigma_x=\sqrt{2.8646}\\\\ \sigma_x=1.69[/tex]
The graph of the probability distribution of X is a bar graph. The mean of X is 1.65 and the standard deviation can be calculated using the variance formula. The probability that a car has at least 3 occupants is 0.12 and the probability that a car has fewer than 3 occupants is 0.85.
Explanation:The graph of the probability distribution of X is a bar graph where the x-axis represents the number of occupants and the y-axis represents the probability. You will have bars at x = 1, 2, 3, 4, and 5 with heights of 0.70, 0.15, 0.10, 0.02 respectively.(i) To calculate the mean of X, you multiply each possible value of X by its corresponding probability and sum them up. So, μX = 1*0.70 + 2*0.15 + 3*0.10 + 4*0.02 + 5*0 = 1.65. (ii) To calculate the standard deviation, you need to find the variance first. The variance is calculated by squaring the difference between each value of X and the mean, multiplying it by its corresponding probability, and summing them up. The standard deviation is the square root of the variance. (a) To find the probability that a car has at least 3 occupants, you need to sum up the probabilities of X being 3, 4, and 5. So, P(X≥3) = P(3) + P(4) + P(5) = 0.10 + 0.02 = 0.12. (b) To find the probability that a car has fewer than 3 occupants, you need to sum up the probabilities of X being 1 and 2. So, P(X<3) = P(1) + P(2) = 0.70 + 0.15 = 0.85.Suppose the number of prisoners held in a certain type of prison, measured in thousands, can be described by the polynomial - 2.02x + 78.47x + 744. The variable x represents the number of years since 1990, According to the polynomial, by how much did the prison population increase from 2002 to 2007?
M(8, 7) is the midpoint of RS. The coordinates of S are (9, 5). What are the coordinates of R?
Answer:
M(Mx, My), R(Rx, Ry), S(Sx, Sy)
M is midpoint of RS
=> Rx + Sx = 2Mx => Rx = 2Mx - Sx = 2 x 8 - 9 = 7
=> Ry + Sy = 2My => Ry = 2My - Sy = 2 x 7 - 5 = 9
=> R(7, 9)
Hope this helps!
:)
Answer:
(7,9)
Step-by-step explanation:
Let R:(x,y)
(x+9)/2, (y+5)/2 = 8 ,7
x + 9 = 16
x = 7
y + 5 = 14
y = 9
R: (7,9)
If you are driving at the speed of 90 km/hour. What is your speed in meter/second
Answer:
speed = 25 m/s
Step-by-step explanation:
Driving at a speed of 90 km / hour . what is the speed in meters per seconds.
converting from km to meter one have to multiply by 1000. This means 1 km is equal to 1000 meter. Converting 90 km to meter we have to multiply 90 by 1000.
90 × 1000 = 90000 meters
The time is in hours so we have to convert to seconds as required by the question.
60 minutes = 1 hour
Therefore,
1 minutes = 60 seconds
60 minutes = 3600 seconds
This means 1 hour = 3600 seconds
speed = 90000/3600
speed = 25 m/s
Jackson is testing different types of planting soil to determine which type is most effective for growing strawberry bushes. He purchases two different brands of planting soil from a local store. Jackson applies brand A to an area of the yard that receives full sunlight and brand B to another area of the yard that is in partial sunlight. He waters the area with brand B daily; he waters the area with brand A every other day. At the end of the study, Jackson concludes brand A is more effective in growing strawberry bushes. Is Jackson's conclusion valid? Explain why or why not.
Answer:
The answer to this question can be described as follows:
Step-by-step explanation:
In the outcome of Jackson isn't legitimate as product A and product B were n’t considered equal in watering the plants. It is the preparation for all two to be compared, Product A with only a region of the backyard, which receives direct energy, and Product B will be maintained regularly by the very same area of the yards, that is in minimal lighting.
No, The conclusion done by Jackson's is not valid for this situation.
What is effective soiling?Effective Soiling depth is the depth of soil material which is above the layer that impedes movement of air and water and growth in plant roots.
According to outcome of Jackson that isn't legitimate as product A and product B were considered equal in watering the plants. Then it is the preparation of two to be compare with product B, Product A with only a region of the backyard, which receives direct energy, and Product B will maintained regularly very same area of the yards, that is with minimal lighting.
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The number of withdrawals a bank processes in a day follows a random variable X. The number of deposits in a day is represented by Y. X and Y are independent and have the following moment generating functions \displaystyle {M}_{X}(t)=\frac{p}{1-q{e}^{t}} \displaystyle {M}_{Y}(t)={\left(\frac{p}{1-q{e}^{t}}\right)}^{r} q = 1 - p What is the expected number of transactions in a day?
Answer:
Check the explanation
Step-by-step explanation:
Number of transactions in a day is sum of number of withdrawals and number of deposits. So,
Number of transactions in a day, Z = X + Y
Moment Generating function of Z is,
T+1
Expected number of transactions in a day = E[Z]
[tex]= \frac{\mathrm{d} }{\mathrm{d} t}_{t=0}M_Z(t) = (r+1)\left ( \frac{p}{1-qe^t} \right )^{r} * \frac{-p}{(1-qe^t)^2} * (-qe^t) for t = 0[/tex]
[tex]= (r+1)\left ( \frac{p}{1-qe^0} \right )^{r} * \frac{-p}{(1-qe^0)^2} * (-qe^0)[/tex]
[tex]= (r+1)\left ( \frac{p}{1-q} \right )^{r} * \frac{-p}{(1-q)^2} * (-q)[/tex]
[tex]= (r+1)\left ( \frac{p}{p} \right )^{r} * \frac{-p}{(p)^2} * (-q)[/tex]
[tex]= \frac{(r+1)q}{p}[/tex]
Which sum or difference is modeled by the algebra tiles?
Answer:
The second one is the correct answer
Step-by-step explanation:
The third one is incorrect as she stated, I tried it and got it wrong when I did the retry I put the second one and I got it correct.
PLZZZZZ ANSWERR FASTTT
Corbin recorded the amount of money spent, in dollars, on food per meal at two different restaurants. He rounded the amounts to the nearest dollar and plotted the data on the box plots below. A box plot titled Dollars Spent at Restaurant 1. The number line goes from 0 to 15. The whiskers range from 6 to 14, and the box ranges from 7 to 12. A line divides the box at 8. Dollars Spent at Restaurant 1 A box plot titled Dollars Spent at Restaurant 2. The number line goes from 0 to 16. The whiskers range from 6 to 15, and the box ranges from 8 to 12. A line divides the box at 10. Dollars Spent at Restaurant 2 Which best explains at which restaurant the average meal costs the most money? Restaurant 1, because the interquartile range of Restaurant 1 is greater Restaurant 1, because more of the graph is located to the right of the median Restaurant 2, because the median of Restaurant 2 is greater Restaurant 2, because the range of Restaurant 2 is greater
Answer:
It’s c I got a 100
Step-by-step explanation:
e d g e n u I ty
The results of a History test and Calculus test are normally distributed. The History test had a mean score of 68 with a standard deviation of 8. The Calculus test had a mean score of 70 with a standard deviation of 7.2. Joseph scored 82 on the Calculus test and Zoe scored 82 on the History test. Which student had a higher percentile rank in their class?
Answer:
Zoe, at about the 96th percentile.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Zoe:
Zoe scored 82 on the History test. So X = 82.
The History test had a mean score of 68 with a standard deviation of 8. This means that [tex]\mu = 68, \sigma = 8[/tex]
Then, we find the z-score to find the percentile.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{82 - 68}{8}[/tex]
[tex]Z = 1.75[/tex]
[tex]Z = 1.75[/tex] has a pvalue of 0.9599.
So Zoe was at abouth the 96th percentile.
Joseph:
Joseph scored 82 on the Calculus test. This means that [tex]X = 82[/tex]
The Calculus test had a mean score of 70 with a standard deviation of 7.2. This means that [tex]\mu = 70, \sigma = 7.2[/tex]
Z-score
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{82 - 70}{7.2}[/tex]
[tex]Z = 1.67[/tex]
[tex]Z = 1.67[/tex] has a pvalue of 0.9525.
Joseph scored in the 95th percentile, which is below Zoe.
So the correct answer is:
Zoe, at about the 96th percentile.
A researcher with the Ministry of Transportation is commissioned to study the drive times to work (one-way) for U.S. cities. The underlying hypothesis is that average commute times are different across cities. To test the hypothesis, the researcher randomly selects six people from each of the four cities and records their one-way commute times to work.
Refer to the below data on one-way commute times (in minutes) to work. Note that the grand mean is 36.625.
Houston Charlotte Tucson Akron
45 25 25 10
65 30 30 15
105 35 19 15
55 10 30 10
85 50 10 5
90 70 35 10
74.167 36.667 24.833 10.833
524.167 436.667 82.167 14.167
Based on the sample standard deviation, the one-way ANOVA assumption that is likely not met is _____________.
A) the populations are normally distributed
B) the population standard deviations are assumed to be equal
C) the samples are independent
D) None of these choices is correct
Answer:
B
Step-by-step explanation:
For one-way ANOVA test results to be reliable, it has to be assumed that standard deviations of populations are equal. Here standard deviations of populatinos are not mentioned.
A huge ice glacier in the Himalayas initially covered an area of 454545 square kilometers. Because of changing weather patterns, this glacier begins to melt, and the area it covers begins to decrease exponentially.
The relationship between AAA, the area of the glacier in square kilometers, and ttt, the number of years the glacier has been melting, is modeled by the following equation.
A=45e^{-0.05t}A=45e
−0.05t
A, equals, 45, e, start superscript, minus, 0, point, 05, t, end superscript
How many years will it take for the area of the glacier to decrease to 151515 square kilometers?
Give an exact answer expressed as a natural logarithm
We have been given that a huge ice glacier in the Himalayas initially covered an area of 45 square kilo-meters. The relationship between A, the area of the glacier in square kilo-meters, and t, the number of years the glacier has been melting, is modeled by the equation [tex]A=45e^{-0.05t}[/tex].
To find the time it will take for the area of the glacier to decrease to 15 square kilo-meters, we will equate [tex]A=15[/tex] and solve for t as:
[tex]15=45e^{-0.05t}[/tex]
[tex]\frac{15}{45}=\frac{45e^{-0.05t}}{45}[/tex]
[tex]\frac{1}{3}=e^{-0.05t}[/tex]
Now we will switch sides:
[tex]e^{-0.05t}=\frac{1}{3}[/tex]
Let us take natural log on both sides of equation.
[tex]\text{ln}(e^{-0.05t})=\text{ln}(\frac{1}{3})[/tex]
Using natural log property [tex]\text{ln}(a^b)=b\cdot \text{ln}(a)[/tex], we will get:
[tex]-0.05t\cdot \text{ln}(e)=\text{ln}(\frac{1}{3})[/tex]
[tex]-0.05t\cdot (1)=\text{ln}(\frac{1}{3})[/tex]
[tex]-0.05t=\text{ln}(\frac{1}{3})[/tex]
[tex]t=\frac{\text{ln}(\frac{1}{3})}{-0.05}[/tex]
[tex]t=\frac{\text{ln}(\frac{1}{3})\cdot 100}{-0.05\cdot 100}[/tex]
[tex]t=\frac{\text{ln}(\frac{1}{3})\cdot 100}{-5}[/tex]
[tex]t=-\text{ln}(\frac{1}{3})\cdot 20[/tex]
[tex]t=-(\text{ln}(1)-\text{ln}(3))\cdot 20[/tex]
[tex]t=-(0-\text{ln}(3))\cdot 20[/tex]
[tex]t=20\text{ln}(3)[/tex]
Therefore, it will take [tex]20\text{ln}(3)[/tex] years for area of the glacier to decrease to 15 square kilo-meters.
In circle O, AC and BD are diameters.
Circle O is shown. Line segments B D and A C are diameters. A radius is drawn to cut angle C O C into 2 equal angle measures of x. Angles A O C and B O C also have angle measure x.
What is mArc A B?
72°
108°
120°
144°
Answer:
mArc A B = 120° (C)
Step-by-step explanation:
Question:
In circle O, AC and BD are diameters.
Circle O is shown. Line segments B D and A C are diameters. A radius is drawn to cut angle D O C into 2 equal angle measures of x. Angles A O D and B O C also have angle measure x.
What is mArc A B?
a)72°
b) 108°
c) 120°
d) 144°
Solution:
Find attached the diagram of the question.
Let P be the radius drawn to cut angle D O C into 2 equal angle measures of x
From the diagram,
m Arc AOC = 180° (sum of angle in a semicircle)
∠AOD + ∠DOP + ∠COP = 180° (sum of angles on a straight line)
x° +x° + x° =180°
3x = 180
x = 180/3
x = 60°
m Arc DOB = 180° (sum of angle in a semicircle)
∠AOB + ∠AOD = 180° (sum of angles on a straight line)
∠AOB + x° = 180
∠AOB + 60° = 180°
∠AOB = 180°-60°
∠AOB = 120°
mArc A B = 120°
Answer:
c
Step-by-step explanation:
For the data set 2.5, 6.5, 9, 19, 20, 2.5. What is the mean?
Answer:
9.9166667
Step-by-step explanation:
All of the numbers equal 59.5 then divide by 6 equals the answer above.
To calculate the mean of the given data set, sum all the data values and divide by the number of values. The mean of this data set is 9.9167.
To find the mean of the given data set: 2.5, 6.5, 9, 19, 20, 2.5, follow these steps:
Sum of the data values: 2.5 + 6.5 + 9 + 19 + 20 + 2.5 = 59.5Number of data values: There are 6 values in the data set.Calculate the mean: Mean = Sum of data values / Number of data values = 59.5 / 6 = 9.9167Hence, the mean of the data set is 9.9167.
Angle 1 and 2 are linear pair. If m<1=x-9 and m<2=x+47 find the measure of each angle
Answer:
m1 = 62°, m2 = 118°
Step-by-step explanation:
The definition of a linear pair of angles is a pair of angles that are adjacent and add up to 180°.
Then, we have the following equation
[tex]x-9+x+47 =180 [/tex]
Then,
[tex]2x+38=180[/tex]
Subtracting 38 on both sides
[tex] 2x = 180-38 = 142[/tex]
Dividing by two, we get x = 71. Then m1 = 71-9 = 62, m2 = 71+47=118[/tex]
Sharif's portfolio generated returns of 12 percent, 15 percent, −15 percent, 19 percent, and −12 percent over five years. What was his average return over this period?
3.8 percent
2.1 percent
17 percent
19 percent
Answer:
3.8 percent
Step-by-step explanation:
To find his average return over n years, we sum all of his returns, and divide by n.
In this problem:
5 years.
The sum is (12 + 15 - 15 + 19 - 12) = 19
19/5 = 3.8
So the correct answer is:
3.8 percent
Answer:
The answer is 3.82
Step-by-step explanation:
(12 + 15− 15− 12 + 19)/5 = 3.8 3.
John Legend sells, on average, 115,000 songs on itunes every two weeks. Michelle did some quick math, and concluded that based on those numbers, he must sell, on average, over 9,000 songs per day. Is Michelle's conclusion true or false?
Answer: Michelle's conclusion is wrong, he sells 8214.3 songs per day
Step-by-step explanation:
Sell 115000 songs every 2 weeks
Sell 115000 songs every 14 days
Sell (a) songs for 1 day
(a) =(115000x1) ➗ 14
(a) =115000 ➗ 14
(a) =8214.3
What is the average rate of change of h over the interval -2≤x≤2 in the equation h(x)=1/8x³-x²?
We have been given a function [tex]h(x)=\frac{1}{8}x^3-x^2[/tex]. We are asked to find the average rate of change of our given function over the interval [tex]-2\leq x\leq 2[/tex].
We will use average rate of change formula to solve our given problem.
[tex]\text{Average rate of change}=\frac{f(b)-f(a)}{b-a}[/tex]
[tex]\text{Average rate of change}=\frac{h(2)-h(-2)}{2-(-2)}[/tex]
[tex]\text{Average rate of change}=\frac{\frac{1}{8}(2)^3-2^2-(\frac{1}{8}(-2)^3-(-2)^2)}{2+2}[/tex]
[tex]\text{Average rate of change}=\frac{\frac{1}{8}(8)-4-(\frac{1}{8}(-8)-(4))}{4}[/tex]
[tex]\text{Average rate of change}=\frac{1-4-(-1-4)}{4}[/tex]
[tex]\text{Average rate of change}=\frac{-3-(-5)}{4}[/tex]
[tex]\text{Average rate of change}=\frac{-3+5}{4}[/tex]
[tex]\text{Average rate of change}=\frac{2}{4}[/tex]
[tex]\text{Average rate of change}=\frac{1}{2}[/tex]
Therefore, the average rate of change over the interval [tex]-2\leq x\leq 2[/tex] is [tex]\frac{1}{2}[/tex].
The average rate of change of h over the interval -2 ≤ x ≤ 2 in the equation h(x)=1/8x³-x² is 3/8.
Explanation:To find the average rate of change of h over the interval -2 ≤ x ≤ 2, we need to calculate the difference in the values of h at the endpoints of the interval and divide it by the change in x.
First, let's find the value of h at x = -2: h(-2) = (1/8) * (-2)^3 - (-2)^2 = -(1/2).
Next, let's find the value of h at x = 2: h(2) = (1/8) * (2)^3 - (2)^2 = 1.
The change in x is 2 - (-2) = 4. So, the average rate of change of h over the interval -2 ≤ x ≤ 2 is (1 - (-1/2))/4 = 3/8.
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The most expensive type of life insurance
The most expensive type of life insurance is cash-value (whole) life insurance due to its integrated savings component, investment aspect, and the management involved. These features add complexity and cost to the policy, making it more expensive than term life insurance, which only offers a death benefit.
The most expensive type of life insurance is typically cash-value (whole) life insurance. This kind of policy not only provides a death benefit to beneficiaries upon the insured individual's death but also includes a savings component known as the cash value. Over time, the policy accumulates a cash value that the policyholder can borrow against or even withdraw. Part of the premium goes towards life insurance, while another part is invested by the company, often in a conservative mix of investments. This investment aspect and the management involved make whole life insurance more expensive compared to term life insurance which only provides a death benefit without a savings component.
It is also worth noting that individuals purchasing life insurance are likely to have more knowledge about their own health risks than the insurance company. This information asymmetry can impact the pricing of life insurance policies. Moreover, the fundamental law of insurance states that the average person's premium payments over time must cover the claims, the insurer's costs, and profits. Therefore, insurance premiums, particularly for policies with cash values, reflect the cost of investment management and the integrated savings aspects, which can contribute to their higher costs.
What is the volume of a box that is 7cm by 11cm by 13cm?
Answer:
V = 1001
Step-by-step explanation:
This is rather simple question, but I can understand not knowing how to find volume.
The volume of a rectangular prism(as specified by the way the dimensions were given) is whl, when w is width, h is height, and l is length. It does not actually matter the order, due to the Commutative Property of Multiplication, which states that is does not matter what order you multiply things.
Plugging in the numbers, we end up with 1001.
Hope this helps!
Sera sells t-shirts at the beach. She believes the price of a t-shirt and the number of t-shirts sold are related. She has been experimenting with different prices for the
t-shirts. She has collected a data set with five pairs of
data: each consists of the price of a t-shirt and the
number of shirts sold.
The independent variable which will on on the x-axis is the price of a t-shirt.
The dependent variable which will on on the x-axis is the number of t-shirts sold.
The independent variable can be described as the variable that is used to determine the dependent variable. It is the variable that the researcher manipulates in the experiment.
The dependent variable is the variable whose value is determined in the experiment. The value of the dependent variable depends on the independent variable.
For example, assume that if the price of a shirt is $1. A person purchases 10 t shirts. If the price increases to $10, only one shirt would be sold. This means that the amount of shirts bought is dependent on the price of the t-shirt. The price of the shirt is the independent variable while the amount of shirts bought is the dependent variable.
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The nicotine content in cigarettes of a certain brand is normally distributed with mean (in milligrams) μ and standard deviation σ=0.1. The brand advertises that the mean nicotine content of their cigarettes is 1.5, but you believe that the mean nicotine content is actually higher than advertised. To explore this, you test the hypotheses H0:μ=1.5, Ha:μ>1.5 and you obtain a P-value of 0.052. Which of the following is true? A. At the α=0.05 significance level, you have proven that H0 is true. B. This should be viewed as a pilot study and the data suggests that further investigation of the hypotheses will not be fruitful at the α=0.05 significance level. C. There is some evidence against H0, and a study using a larger sample size may be worthwhile. D. You have failed to obtain any evidence for Ha.
Answer:
Step-by-step explanation:
This is a test of a single population mean since we are dealing with mean.
From the information given,
Null hypothesis is expressed as
H0:μ=1.5
The alternative hypothesis is expressed as
Ha:μ>1.5
This is a right tailed test
The decision rule is to reject the null hypothesis if the significance level is greater than the p value and accept the null hypothesis if the significance level is less than the p value.
p value = 0.052
Significance level, α = 0.05
Since α = 0.05 < p = 0.052, the true statement would be
At the α=0.05 significance level, you have proven that H0 is true. B.
Final answer:
The P-value of 0.052 provides some evidence against the null hypothesis H0, although not enough to reject it at the α = 0.05 significance level. A study with a larger sample size may be worthwhile to investigate the true mean nicotine content further.
Explanation:
With a P-value of 0.052 for the hypothesis test, comparing it against a significance level alpha (α) = 0.05 determines whether the null hypothesis (H0) is rejected or not. Despite the P-value being slightly above the significance level, the correct interpretation is Option C: 'There is some evidence against H0, and a study using a larger sample size may be worthwhile.' This suggests that while there isn't enough evidence to reject the null hypothesis at α = 0.05, the result is close enough to warrant further investigation.
We cannot claim that the null hypothesis has been proven true as statistical hypothesis testing never proves a hypothesis, but only provides evidence against it (Option A is incorrect). The data suggests that further investigation could be useful, instead of being unfruitful (Option B is an incorrect view). Lastly, there is evidence pointing towards the alternative hypothesis (Ha), it's not that there's no evidence at all (Option D is incorrect).
α = 0.05Decision: Do not reject null hypothesis.Reason for decision: p-value > αConclusion: There is insufficient evidence to conclude that the mean nicotine content is higher than 1.5 at the 5 percent level, but further research might be beneficial.
f(n)= 64 + 6n complete the recursive formula of f(n)
We want to find a recursive formula for f(n) = 64 + 6n
The recursive formula is f(n) = f(n - 1) + 6
First, a recursive formula is a formula that gives the value of f(n) in relation to the value of f(n - 1) or other previous terms on the sequence.
We know that:
f(n) = 64 + 6n
f(n - 1) = 64 + 6*(n - 1) = 64 + 6*n - 6
Then we can rewrite:
f(n) = 64 + 6n + 6 - 6
f(n) = ( 64 + 6n - 6) + 6
And the thing inside the parenthesis is equal to f(n - 1)
Then we have:
f(n) = f(n - 1) + 6
This is the recursive formula we wanted to get.
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The volume of the cylinder is 307.9 cubic meters. Find the height. Round your answer to the nearest whole number.
In response to the question, we may say that the height of the cylinder is 6.
what is cylinder?A cylinder is a three-dimensiοnal geοmetric shape made up οf twο parallel cοngruent circular bases and a curving surface cοnnecting the twο bases. The bases οf a cylinder are always perpendicular tο its axis, which is an imaginary straight line passing thrοugh the centre οf bοth bases. The vοlume οf a cylinder is equal tο the prοduct οf its base area and height.
A cylinder's volume is computed as V = r²h,
where
"V" represents the volume,
"r" represents the radius of the base, and
"h" represents the height of the cylinder.
Thus,
307.9 = 7²h
307.9 = 49h
h = 307.9/49
h 6.283
h = 6 (rounding to the nearest whole)
Thus, The height of the cylinder is 6.
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Your company manufactures hot water heaters. The life spans of your product are known to be normally distributed with a mean of 13 years and a standard deviation of 1.5 years. You want to set the warranty on your product so that you do not have to replace more than 5% of the hot water heaters that you sell. How many years should you claim on your warranty
Answer:
You should claim 10.5325 years on your warranty.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 13, \sigma = 1.5[/tex]
Want's to replace no more than 5% of the products.
This means that the warranty should be 5th percentile, that is, the value of X when Z has a pvalue of 0.05. So X when Z = -1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.645 = \frac{X - 13}{1.5}[/tex]
[tex]X - 13 = -1.645*1.5[/tex]
[tex]X = 10.5325[/tex]
You should claim 10.5325 years on your warranty.
What is the mode of the following numbers?
9,10,6,5,6
Answer:
6
Step-by-step explanation:
The mode is the number which appears most often in a set of numbers in this case that would be 6 because it appears twice
The mode of a set of values is the one that appears most frequently. In your list: 9, 10, 6, 5, 6 - the number 6 appears twice, more than any other number, making 6 the mode.
Explanation:In statistics, the mode of a set of values is the value that appears most frequently. An easy way to find the mode is to count the frequency of each number. Looking at your list of numbers: 9, 10, 6, 5, 6. The number 6 is the only number that appears more than once.
So, the mode of the given set of numbers is 6 because it appears more frequently than the other numbers.
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Which functions have a maximum value greater than the maximum of the function g(x) = –(x + 3)2 – 4? Check all that apply. f(x) = –(x + 1)2 – 2 f(x) = –|x + 4| – 5 f(x) = –|2x| + 3
Answer:
A
C
D
Step-by-step explanation:
which number line shows the solution to 6 + (-6)
Answer
it is 0
Step-by-step explanation: you have to add 6 yto negative six so it is zero
Answer:
its is the option that shows the first line at six then 0
Orlando invests $1000 at 6% annual interest compounded daily and Bernadette invests $1000 at 7%
simple interest. After how many whole years will Orlando's investments be worth more than
Bernadette's investments?
Answer:
6 Years
Step-by-step explanation:
Orlando invests $1000 at 6% annual interest compounded daily.
Orlando's investment = [tex]A=1000(1+\frac{0.06}{365})^{(365\times t)}[/tex]
Bernadette invests $1000 at 7% simple interest.
Bernadette's investment = A = 1000(1+0.07×t)
By trail and error method we will use t = 5
Bernadette's investment will be after 5 years
1000(1 + 0.07 × 5)
= 1000(1 + 0.35)
= 1000 × 1.35
= $1350
Orlando's investment after 5 years
[tex]A=1000(1+\frac{0.06}{365})^{(365\times 5)}[/tex]
= [tex]1000(1+0.000164)^{1825}[/tex]
= [tex]1000(1.000164)^{1825}[/tex]
= 1000(1.349826)
= 1349.825527 ≈ $1349.83
After 5 years Orlando's investment will not be more than Bernadette's.
Therefore, when we use t = 6
After 6 years Orlando's investment will be = $1433.29
and Bernadette's investment will be = $1420
So, after 6 whole years Orlando's investment will be worth more than Bernadette's investment.
Solve for x in the diagram below.
Answer:
x = 12
Step-by-step explanation:
20° + (6x - 2) = 90°
18° + 6x = 90°
6x = 90° - 18°
6x = 72°
x = 72°/6
x = 12
Answer:
Hope it helps buddy! Mark as brainlist please.
Find two matrices A and B such that 2A-3B= [5 0
-1 2]
(5 & 0 are on top; -1 & 2 are on the bottom— it’s a 2x2 matrix)
The easy answer: If, say, B is the zero matrix, i.e.
[tex]B=\begin{bmatrix}0&0\\0&0\end{bmatrix}[/tex]
then
[tex]2A=\begin{bmatrix}5&0\\-1&2\end{bmatrix}\implies A=\begin{bmatrix}\dfrac52&0\\\\-\dfrac12&1\end{bmatrix}[/tex]
Exclude leap years from the following calculations. (a) Compute the probability that a randomly selected person does not have a birthday on March 14. (b) Compute the probability that a randomly selected person does not have a birthday on the 2 nd day of a month. (c) Compute the probability that a randomly selected person does not have a birthday on the 31 st day of a month. (d) Compute the probability that a randomly selected person was not born in February.
Answer:
a) 99.73% probability that a randomly selected person does not have a birthday on March 14.
b) 96.71% probability that a randomly selected person does not have a birthday on the 2 nd day of a month.
c) 98.08% probability that a randomly selected person does not have a birthday on the 31 st day of a month.
d) 92.33% probability that a randomly selected person was not born in February.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
A non-leap year has 365 days.
(a) Compute the probability that a randomly selected person does not have a birthday on March 14.
There are 365-1 = 364 days that are not March 14. So
364/365 = 0.9973
99.73% probability that a randomly selected person does not have a birthday on March 14.
(b) Compute the probability that a randomly selected person does not have a birthday on the 2 nd day of a month.
There are 12 months, so there are 12 2nds of a month.
So
(365-12)/365 = 0.9671
96.71% probability that a randomly selected person does not have a birthday on the 2 nd day of a month.
(c) Compute the probability that a randomly selected person does not have a birthday on the 31 st day of a month.
The following months have 31 days: January, March, May, July, August, October, December.
So there are 7 31st days of a month during a year.
Then
(365-7)/365 = 0.9808
98.08% probability that a randomly selected person does not have a birthday on the 31 st day of a month.
(d) Compute the probability that a randomly selected person was not born in February.
During a non-leap year, February has 28 days. So
(365-28)/365 = 0.9233
92.33% probability that a randomly selected person was not born in February.
The probability that a person does not have a birthday on March 14, on the 2nd day of a month, on the 31st day of a month, or is not born in February is approximately 0.9973, 0.9671, 0.9808, and 0.9233 respectively. These probabilities were computed by subtracting the fraction of the year representing the specific days or month from 1. These solutions are based on a standard non-leap year of 365 days.
To solve the probability questions, we will assume a non-leap year with 365 days.
(a) Probability that a randomly selected person does not have a birthday on March 14:
There is only one day out of the year that is March 14. Therefore, the probability that a person does have a birthday on March 14 is:
P(March 14) = 1/365
Consequently, the probability that a person does not have a birthday on March 14 is:
P(Not March 14) = 1 - 1/365 = 364/365 ≈ 0.9973
(b) Probability that a randomly selected person does not have a birthday on the 2nd day of a month:
Since there are 12 months in a year, there are 12 days which fall on the 2nd day of each month.
P(2nd day) = 12/365
Therefore, the probability that a person does not have a birthday on the 2nd day of any month is:
P(Not 2nd day) = 1 - 12/365 = 353/365 ≈ 0.9671
(c) Probability that a randomly selected person does not have a birthday on the 31st day of a month:
There are only 7 months with 31 days (January, March, May, July, August, October, December).
P(31st day) = 7/365
Therefore, the probability that a person does not have a birthday on the 31st day of any month is:
P(Not 31st day) = 1 - 7/365 = 358/365 ≈ 0.9808
(d) Probability that a randomly selected person was not born in February:
February has 28 days out of the year.
P(February birthday) = 28/365
Therefore, the probability that a person was not born in February is:
P(Not February) = 1 - 28/365 = 337/365 ≈ 0.9233