Explicit formula for

1,5,3,6,12

Answer:

The t-distribution is used, as we have the standard deviation of the sample.

The 95% confidence interval for the population mean time wasted is between 7.12 hours and 8.88 hours.

Step-by-step explanation:

We have the standard deviation for the sample, which meas that the t-distribution should be used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 81 - 1 = 80

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 80 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 1.99

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 1.99\frac{4}{\sqrt{81}} = 0.88[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 8 - 0.88 = 7.12 hours.

The upper end of the interval is the sample mean added to M. So it is 8 + 0.88 = 8.88 hours.

The 95% confidence interval for the population mean time wasted is between 7.12 hours and 8.88 hours.

Answer:

[tex]\frac{1}{5}[/tex]

Step-by-step explanation:

[tex]\frac{9}{10} -\frac{7}{10} =\frac{2}{10} =\frac{1}{5}[/tex]

Answer:

6x+8

Step-by-step explanation:

Brainliest?

Answer:

0 = 0

Step-by-step explanation:

Subtract 4 from both sides of the equation

3 + 4 − 4 = 3 + 4 − 4

Simplify

Subtract the numbers

3 = 3 + 4 − 4

3 = 3

Subtract 3x from both sides of the equation

3 − 3 = 3 − 3

Combine like terms

0 = 3 − 3

Result

0 = 0

Answer:

a) 0.0000001024 probability that he will answer all questions correctly.

b) 0.1074 = 10.74% probability that he will answer all questions incorrectly

c) 0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

d) 0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

Step-by-step explanation:

For each question, there are only two possible outcomes. Either he answers it correctly, or he does not. The probability of answering a question correctly is independent of any other question. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Each question has five answers, of which only one is correct

This means that the probability of correctly answering a question guessing is [tex]p = \frac{1}{5} = 0.2[/tex]

10 questions.

This means that [tex]n = 10[/tex]

A) What is the probability that he will answer all questions correctly?

This is [tex]P(X = 10)[/tex]

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} = 0.0000001024[/tex]

0.0000001024 probability that he will answer all questions correctly.

B) What is the probability that he will answer all questions incorrectly?

None correctly, so [tex]P(X = 0)[/tex]

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074[/tex]

0.1074 = 10.74% probability that he will answer all questions incorrectly

C) What is the probability that he will answer at least one of the questions correctly?

This is

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

Since [tex]P(X = 0) = 0.1074[/tex], from item b.

[tex]P(X \geq 1) = 1 - 0.1074 = 0.8926[/tex]

0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

D) What is the probability that Richard will answer at least half the questions correctly?

This is

[tex]P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 5) = C_{10,5}.(0.2)^{5}.(0.8)^{5} = 0.0264[/tex]

[tex]P(X = 6) = C_{10,6}.(0.2)^{6}.(0.8)^{4} = 0.0055[/tex]

[tex]P(X = 7) = C_{10,7}.(0.2)^{7}.(0.8)^{3} = 0.0008[/tex]

[tex]P(X = 8) = C_{10,8}.(0.2)^{8}.(0.8)^{2} = 0.0001[/tex]

[tex]P(X = 9) = C_{10,9}.(0.2)^{9}.(0.8)^{1} \approx 0[/tex]

[tex]P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} \approx 0[/tex]

So

[tex]P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0264 + 0.0055 + 0.0008 + 0.0001 + 0 + 0 = 0.0328[/tex]

0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

Answer:

Just Plus the 2 Given and Minus in the 360 Because 360 It has a Fourside The Answer is 168degrees

Answer:

B and D

Step-by-step explanation:

A would be:

57 + 2j

C would be:

13-t

Step-by-step explanation:

[tex]sinθ = \frac{3}{5} \: \: cosθ = \frac{4}{5} \\ now \\ tanθ = \frac{sinθ}{cos θ } \\ = \frac{3}{5 } \div \frac{4}{5} \\ = \frac{3}{5} \times \frac{5}{4} \\ = \frac{3}{4} [/tex]

Hope it will help :)❤

Answer:

df(t)/dt = 10 - 0.8f(t)

Step-by-step explanation:

The net rate of change, df(t)/dt = rate in - rate out

The rate in = rate litter forms on ground = 10 g/cm²/yr

Since f(t) is the amount of litter present at time, t, in g/cm² the rate out = rate of decomposition = the percentage rate × f(t) = 80% per year × f(t) = 0.8f(t) g/cm²/yr

Since df(t)/dt = rate in - rate out

df(t)/dt = 10 - 0.8f(t)

So the desired differential equation is

df(t)/dt = 10 - 0.8f(t)

Answer:

8/3

Step-by-step explanation:

x : 4 = 4 :  6

x = 16/ 6

x = 8/3

Answer:

0.1

Step-by-step explanation:

Answer:

NO POSSIBLE TRIANGLES

Step-by-step explanation:

Answer:

no possible triangles

Step-by-step explanation:

Answer:

5/14 + 5/14 + 2/14​ = 12/14 = 6/7

Step-by-step explanation:

Answer:Nancy completed more of the essay.

Step-by-step explanation:4/6 + 2/6 = 6/6 = Nancy

3/6 + 2/6 = 5/6 = Evan

Therefore Nancy did more of the essay.

Answer:

Its 5,...................

Answer:

5

Step-by-step explanation:

simplify the exponent

35/8-1

simplify

35/7

simplify

5

Answer:

Slope would be -3/1

Answer:

-3/1 is the slope since you are going down 3 and going to the right one time.

Answer:

62

Step-by-step explanation:

Since you are simply finding the perimeter, I assume they just want you to add all the sides. 13 + 15 + 10 + 10 + 14 = 62

Answer:

231+X = 231+X

Step-by-step explanation:

Hope it helps!!!!!!!!

Answer:

0.98 = 98% probability that the average midterm score of these students is at most 75 points.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The average midterm score of students in a certain course is 70 points.

This means that [tex]\mu = 70[/tex]

29 students are randomly selected and the standard deviation of their scores is found to be 13.15 points.

This means that [tex]\sigma = 13.15, n = 29, s = \frac{13.15}{\sqrt{29}} = 2.44[/tex]

Find the probability that the average midterm score of these students is at most 75 points.

This is the pvalue of Z when X = 75. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{75 - 70}{2.44}[/tex]

[tex]Z = 2.05[/tex]

[tex]Z = 2.05[/tex] has a pvalue of 0.98.

0.98 = 98% probability that the average midterm score of these students is at most 75 points.

Answer:

19x - 25

steps:

(8x + 11x) + (-7 - 18)

19x + (-25)

positive x negative = negative

19x - 25

Answer:

19x - 25

Step-by-step explanation:

(8x + 11x) + (-7 - 18) <------- add the bold ones (combine like terms)...

19x + (-7 - 18) <--------------- subtract the bold ones...

(19x) - 25 <-------------------- eliminate parenthases

19x - 25 <--------------------- solution...

Answer:

r = 4.90228481 in

d = 9.80456963 in

Answer:

12) Between 40 and 64 = 0.815

13) Between 32 and 40 = 0.0235

14) Between 56 and 64 = 0.34

15) At most 56 = 0.515

16) At least 72 = 0.025

17) At most 64 = 0.855

Explanation:

To answer this, we will convert each of the values into their standardized form to make this easier.

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ

x = Each value

μ = Mean = 56

σ = Standard deviation = 8

12) Between 40 and 64

For 40,

z = (x - μ)/σ = (40 - 56)/8 = (-16/8) = -2

For 64

z = (x - μ)/σ = (64 - 56)/8 = (8/8) = 1

So,

Between 40 and 64 = Between -2 and 1

From the curve, noting that the central point is the mean, with standard score of 0, the lines before it move in step of 1 standard deviation towards the negative side, that is, -1, -2, etc. And the lines before the central point move towards the positive side, that is, 1, 2, 3, etc.

So,

Between -2 and 1 = 0.135 + 0.34 + 0.34 = 0.815

13) Between 32 and 40

For 32,

z = (x - μ)/σ = (32 - 56)/8 = (-24/8) = -3

For 40,

z = (x - μ)/σ = (40 - 56)/8 = (-16/8) = -2

So,

Between 32 and 40 = Between -3 and -2 = 0.0235

14) Between 56 and 64

For 56,

z = (x - μ)/σ = (56 - 56)/8 = (0/8) = 0

For 64,

z = (x - μ)/σ = (64 - 56)/8 = (8/8) = 1

Between 56 and 64 = Between 0 and 1 = 0.34

15) At most 56

For 56,

z = (x - μ)/σ = (56 - 56)/8 = (0/8) = 0

At most 56 = At most 0 = 0.0015 + 0.0235 + 0.15 + 0.34 = 0.515

All the regions before z = 0)

16) At least 72

For 72,

z = (x - μ)/σ = (72 - 56)/8 = (16/8) = 2

At least 72 = At least 2 = 0.0235 + 0.0015 = 0.025

(All the regions from z = 2 to the end)

17) At most 64

For 64,

z = (x - μ)/σ = (64 - 56)/8 = (8/8) = 1

At most 64 = At most 1 = 0.0015 + 0.0235 + 0.15 + 0.34 + 0.34 = 0.855

(All the regions before z = 1)

Hope this Helps!!!

Answer:

Length of pendulum = 72 feet

Step-by-step explanation:

Given:

Time period (T) = 9.42

pi = 3.14

According to question,

T = 2 x pi x root(L/32)

9.42 = 2 x 3.14 x root(L/32)

9.42 = 6.28 × root (L/32)

9.42/6.28 = root(L/32)

1.5 = root(L/32)

Squaring both sides,

2.25 = L/32

L = 2.25 x 32

L = 72

Answer:

L=72

Step-by-step explanation:

T=2pi[tex]\sqrt{L/32\\}[/tex]

9.42 = (2 x 3.14)[tex]\sqrt{L/32}[/tex]

1.5=[tex]\sqrt{L/32}[/tex]

2.25 = L/32   (I squared both sides)

L=72

Hope this Helps

Answer:

The identity property of addition

Step-by-step explanation:

It is the identity property of addition.

Answer:

0.7823 = 78.23% probability that the response time is between 3 and 9 minutes.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Normal distribution with a mean of 7.2 minutes and a standard deviation of 2.1 minutes.

This means that [tex]\mu = 7.2, \sigma = 2.1[/tex]

Probability that the response time is between 3 and 9 minutes.

This is the pvalue of Z when X = 9 subtracted by the pvalue of Z when X = 3. So

X = 9

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{9 - 7.2}{2.1}[/tex]

[tex]Z = 0.86[/tex]

[tex]Z = 0.86[/tex] has a pvalue of 0.8051

X = 3

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{3 - 7.2}{2.1}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a pvalue of 0.0228

0.8051 - 0.0228 = 0.7823

0.7823 = 78.23% probability that the response time is between 3 and 9 minutes.

Answer:

At the moment in question, we have a 5-12-13 right triangle.

x^2 + y^2 = 13^2

2x dx/dt + 2y dy/dt = 0

2(5)(2/3) + 2(12) dy/dt = 0

dy/dt = -5/18 ft/s

the area is 1/2 xy, so

da/dt = 1/2 y dx/dt + 1/2 x dy/dt

= (1/2)((12)(2/3) + (5)(-5/18))

= 119/36

Step-by-step explanation:

Answer:

Option C.

Step-by-step explanation:

You can find this by doing ratios. 1/1.1266=x/700. Then, solve for x and you will get 621.3385.

Answer:

3.7%

Step-by-step explanation:

simple

Answer:

There are two paramount differences between art and science. The first is that art is subjective while science is objective. The second is that art expresses knowledge, most often in the form of subjective representation, while science is the system of acquiring knowledge.

Answer:

There are two differences

Step-by-step explanation:

Art expresses knowledge, most often in the form of subjective representation, while science is the system of acquiring knowledge.