A moving sidewalk in an airport moves people between gates. It takes Jason's 8-year-old

daughter Josie 44 sec to travel 176 ft walking with the sidewalk. It takes her 7 sec to walk 21 ft

against the moving sidewalk in the opposite direction). Find the speed of the sidewalk and find

Josie's speed walking on a non-moving ground.

The side walk moves at Ft/sec

Step-by-step explanation:

1km = 9000 m

1 min = 60 sec

So 60 min = 3600 sec

In this way Matty jogs 9000m /3600sec

Matty's speed of 9 km/hr is equivalent to 2.5 m/s when converted using the relationship where 1 km equals 1000 meters and 1 hour equals 3600 seconds.

To compute Matty's speed in meters per second (m/s), we need to convert from kilometers per hour (km/h) to m/s. To do this, we can use the conversion rate where 1 km equals 1000 meters, and 1 hour equals 3600 seconds.

First, we convert Matty's speed to meters:
9 km/h = 9 × 1000 m/h = 9000 m/h.

Then, we convert hours to seconds:
9000 m/h × (1 h / 3600 s) = 9000 m / 3600 s = 2.5 m/s.

Therefore, Matty's speed in meters per second is 2.5 m/s.

Answer:

Mrs. Potts needs 72 feet of fencing.

Step-by-step explanation:

You find the perimeter of the rectangular garden, which is 24 yards. You then convert the yards to feet. There are 3 feet in a yard. You multiply 24 by 3 to get your final answer of 72 feet.

Answer:

$38 + 15% off

Step-by-step explanation:

to do this, multiply each original price by the coupon percentage, (38 being .15, and 44 being .4,) and subtract the answers. when this is done and you compare, you will see that the $38 sweatshirt is less money by $2.90.

The cost of the sweatshirt both in-store and online after applying the respective discounts shows that it is better to buy the sweatshirt online, saving Nathan $2.90.

This problem relates to the mathematics field of percentage or discount calculations. To solve this problem, we need to calculate the cost of the sweatshirt after applying the discounts both in-store and online.

First, let's calculate the amount of the 20% discount for the in-store purchase. To find the discount, we multiply the cost of the sweatshirt by the discount rate: $44 * 20% = $8.80. So the total cost for the sweatshirt in-store after the discount would be $44 - $8.80 = $35.20.

Secondly, let's calculate the online price with a 15% discount. The discount on the online price would be calculated as: $38 * 15% = $5.70. Therefore, the cost of the sweatshirt online after the discount is $38 - $5.70 = $32.30.

Based on these calculations, buying online is the better deal by $35.20 - $32.30 = $2.90.

Learn more about Discount Calculations here:

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Answer:

About 296 households have more than three children.

Step-by-step explanation:

The complete question is:

Carmen used a random number generator to simulate a survey of how many children live in the households in her town. There are 1,346 unique addresses in her town with numbers ranging from zero to five children. The results of 50 randomly generated households are shown below. Children in 50 Households Number of Children Number of Households 0 5 1 11 2 13 3 10 4 9 5 2 Using a proportion, what can you infer about the number of households in her town that have more than three children? About 242 households have more than three children. About 269 households have more than three children. About 296 households have more than three children. About 565 households have more than three children.

Solution:

The data provided for the number of children and number of households is:

Number of Children (X)          Number of Households (f (X))

               0                                                   5

               1                                                    11

               2                                                   13

               3                                                   10

               4                                                    9

               5                                                    2

           TOTAL                                             50

Compute the probability of households having more than three children as follows:

P (More than 3 children) = P (4 children) + P (5 children)

                                        [tex]=\frac{9}{50}+\frac{2}{50}[/tex]

                                        [tex]=\frac{11}{50}[/tex]

                                        [tex]=0.22[/tex]

Let the random variable Y be defined as the number of households having more than three children.

The probability of the random variable Y is, p = 0.22.

The entire population, i.e. total number of addresses in Carmen's town with numbers ranging from zero to five children, consists of N = 1,346 households.

Compute the expected number of households having more than three children as follows:

[tex]E(Y) =N\times p[/tex]

         [tex]=1346\times 0.22\\=296.12\\\approx 296[/tex]

Thus, about 296 households have more than three children.

Answer:

Mark will use 153 no of trays to accomplish his task.

Final answer:

Mark can use 9 trays to distribute 153 hot dogs and 171 hamburgers evenly by finding the Greatest Common Divisor (GCD) of the two numbers, which is 9.

Explanation:

Mark has 153 hot dogs and 171 hamburgers and wants to distribute them evenly across the greatest number of trays. To do this, Mark needs to find the Greatest Common Divisor (GCD) of the two numbers, which is the largest number that can evenly divide both 153 hot dogs and 171 hamburgers. The GCD of 153 and 171 is 9.

Therefore, Mark can use 9 trays, with 17 hot dogs and 19 hamburgers on each tray, to distribute them evenly.

Answer:

The mean of the sampling distribution(SRS 49) of the sample mean is 420 and the standard deviation is 3.

The mean of the sampling distribution(SRS 576) of the sample mean is 420 and the standard deviation is 0.875.

By the Central Limit Theorem, the sample size does not influence the sample mean, but it does decrease the standard deviation of the sample

Step-by-step explanation:

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.

Population

mean = 420, standard deviation = 21.

Sample of 49

Mean = 420, standard deviation [tex]s = \frac{21}{\sqrt{49}} = 3[/tex]

The mean of the sampling distribution of the sample mean is 420 and the standard deviation is 3.

Sample of 49

Mean = 420, standard deviation [tex]s = \frac{21}{\sqrt{576}} = 0.875[/tex]

The mean of the sampling distribution of the sample mean is 420 and the standard deviation is 0.875.

Increasing the sample size from 49 to 576 in a simple random sample from a population with a mean of 420 and a standard deviation of 21 keeps the mean of the sampling distribution the same but decreases the standard deviation.

When taking a simple random sample (SRS) from a population where the mean (μ) is 420 and the standard deviation (σ) is 21, and using a sample size (n) of 49, the sampling distribution of the sample mean will have:

When the sample size increases to 576, the sampling distribution of the sample mean will still have a mean of 420, but the standard deviation will decrease because it is inversely proportional to the square root of the sample size. The new standard deviation will be 21/√576 = 21/24 = 0.875.

The effect of increasing the sample size is that while the mean of the sampling distribution remains the same, the standard deviation decreases, leading to a more narrow distribution. This indicates that there is less variability in the sample means, and they will be closer to the population mean, which is in accordance with the Central Limit Theorem.

Answer:

  12,765

Step-by-step explanation:

The exponential formula for the population can be written as ...

  population = (initial population)(1 -decay rate)^t

where t is in years, and the decay rate is the loss per year.

The given numbers make this ...

  population = 100,000(0.9918^t)

In 250 years, the population will be about ...

  population = 100,000(0.9918^250) ≈ 12,765.15

There will be about 12,765 butterflies in 250 years.

In 250 years, there will be approximately 12,765 butterflies in the population.

This figure is obtained by applying the exponential decay formula with a 0.82% decrease rate per year from an initial population of 100,000 butterflies.

To determine the butterfly population in 250 years given a yearly decrease rate of 0.82%, we utilize the exponential decay formula:

[tex]\[ P(t) = P_0 \times (1 - r)^t \][/tex]

where:

- (P(t)) represents the population after (t) years,

- (P_0) is the initial population, which is 100,000,

- (r) is the annual decrease rate in decimal form, which is 0.82% or 0.0082,

- (t) is the time in years, here 250 years.

By substituting the given values into the formula:

[tex]\[ P(250) = 100,000 \times (1 - 0.0082)^{250} \][/tex]

Upon calculation, the population after 250 years is found to be approximately 12,765, rounding to the nearest whole number for practical purposes. This result is based on the principle of exponential decay, reflecting how a consistent percentage decrease affects the population over a prolonged period.

Answer:

Step-by-step explanation:

f(g(x)) = f of g of x

f(x) · g(x)  = f at x times g at x, which is not the same thing.

The sample size needed with 99% confidence and 3% margin of error is 1843.

To estimate the sample size needed:

Determine the critical value for 99% confidence, which is 2.576.

Calculate the minimum sample size using the formula:

n = (Z^2 * p * q) / E^2

Substitute Z = 2.576, p = 0.5, q = 0.5, and E = 0.03.

Calculate to get the sample size, which is approximately 1843.

Answer:

  0.72

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you that the relation of interest is ...

  Cos = Adjacent/Hypotenuse

Then the cosine of angle C is ...

  cos(C) = CD/CB = 21/29

  cos(C) ≈ 0.72

Answer:

Step-by-step explanation:

Answer:

a)We are 95% confident that the average commuting time for route A is between 1.3577 and 4.6423 minutes shorter than the average committing time for rout B.  

(b) No, because the confidence internal does not contain —5, which corresponds with an average of 5 minutes shorter for route A.

Step-by-step explanation:

Given:  

n_1 = 20

x_1= 40

s_1 = 3

n_2 = 20

x_2= 43

s_2 = 2

d_f = 33.1

c = 95%. 0.95

(a) Determine the t-value by looking in the row starting with degrees of freedom df = 33.1 > 32 and in the column with c = 95% in the Student's t distribution table in the appendix:  

t[tex]\alpha[/tex]/2 = 2.037  

The margin of error is then:  

E = t[tex]\alpha[/tex]/2 *√s_1^2/n_1+s_2^2/n_2

E = 2.037  *√3^2/20+s_2^2/20

  = 1.64

The endpoints of the confidence interval for u_1 — u_2 are:  

(x_1 — x_2) — E = (40 — 43) — 1.6423 = —3 — 1.6423= —4.6423

(x_1 - x_2)  + E   = (40 — 43) + 1.6423 = —3 + 1.6423= —1.3577  

a)We are 95% confident that the average commuting time for route A is between 1.3577 and 4.6423 minutes shorter than the average committing time for rout B.  

(b) No, because the confidence internal does not contain —5, which corresponds with an average of 5 minutes shorter for route A.

To subtract 143-79 by breaking apart, round 79 to 80, subtract it from 143 to get 63, and add 1 back for rounding to get the final answer of 64.

The question involves breaking apart numbers to subtract 143-79. This is a technique used in math to simplify subtraction by splitting numbers into parts that are easier to work with.

The final answer is 64.

Answer: x = 3

Step-by-step explanation

This is a simultaneous equation. So to find x , we solve to ascertained the coordinate or point of intersection of the too lines.

y = 4x + 2, and 6x - y = 4

To solve , we need to rearrange first

y = 4x + 2 will be

4x - y = -2 -------------------------1

Equation 2 is in order

6x - y = 4 -------------------------- 2

Now solve the two equation for x by using any methods you are familiar with.

4x - y = -2

6x - y = 4, now subtract equation 2 from 1 in order to eliminate y,

we now have

-2x = -6, now divide through by 2

x = 3.

Hence y could be find by substitution for x in any of the equation above and now check.

4x - y = -2

4(3) - y = -2

12 - y = = -2

y = 12 + 2

y = 14.

Now let check

6x - y = 4

6(3) - 14

18 - 14

= 4.

Therefore, the value of x is 3

Google translation

2/3 of a basket of apples rot. We eat 4/5 of the rest and use the remaining 25 to make jam. How many apples were in the basket

Answer:

375

Step-by-step explanation:

Since the basket was full, ⅔ rot so the remaining for any use will be 1-⅔=⅓

Since we only eat 4/5 of this remaining quantity, we use the 1-4/5=1/5 of ⅓ for making jam

1/5 of ⅓=1/5*⅓=1/15

If 1/15 equals 25 pieces then the full basket had

25*15/1=375 pieces

Answer:

If your asking what 4.7kg is to grams then it is 4700g

Answer:

4700 g

Step-by-step explanation:

1 kg = 1000g

Using this rule, 4.7 kg would be 4700g

4.7 x 1000 = 4700

Answer:

The probability of a Type II error is 0.3446.

Step-by-step explanation:

A type II error is a statistical word used within the circumstance of hypothesis testing that defines the error that take place when one is unsuccessful to discard a null hypothesis that is truly false. It is symbolized by β i.e.  

β = Probability of accepting H₀ when H₀ is false

  = P (Accept H₀ | H₀ is false)

In this case we need to test the hypothesis whether the voter turnout during the most recent elections in Texas was higher than 54%.

The hypothesis can be defined as:

H₀: The voter turnout during the most recent elections in Texas was 54%, i.e. p = 0.54.

Hₐ: The voter turnout during the most recent elections in Texas was higher than 54%, i.e. p > 0.54.

A type II error would be committed if we conclude that the voter turnout during the most recent elections in Texas was 54%, when in fact it was higher.

The information provided is:

X = 54

n = 90

α = 0.02

true proportion = p = 0.67

Compute the mean and standard deviation as follows:

[tex]\mu=p=0.54[/tex]

[tex]\sigma=\sqrt{\frac{0.54(1-0.54)}{90}}=0.053[/tex]

Acceptance region  = P (Z < z₀.₀₂)

The value z₀.₀₂ is 0.6478.

Compute the sample proportion as follows:

[tex]z=\frac{\hat p-\mu}{\sigma}\\2.054=\frac{\hat p-0.54}{0.053}\\\hat p=0.6489[/tex]

Compute the value of β as follows:

β = P (p < 0.54 | p = 0.67)

  [tex]=P(\frac{\hat p-\mu}{\sigma}<\frac{0.6489-0.67}{0.053})\\=P(Z<-0.40)\\=0.34458\\\approx 0.3446[/tex]

Thus, the probability of a Type II error is 0.3446.

Yes, it is possible for a 7 x 7 matrix to not be diagonalizable even if it has three eigenvalues.

Yes, it is possible for a 7 x 7 matrix to not be diagonalizable even if it has three eigenvalues. A matrix is diagonalizable if and only if it has n linearly independent eigenvectors, where n is the size of the matrix. In this case, since we have one eigenspace two-dimensional and one eigenspace three-dimensional, we have a total of 5 linearly independent eigenvectors. Since 5 is less than 7, the matrix is not diagonalizable.

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Yes, it is possible that matrix A is not diagonalizable. For a square matrix to be diagonalizable, it must have a complete set of eigenvectors.

Yes, it is possible that matrix A is not diagonalizable. For a square matrix to be diagonalizable, it must have a complete set of eigenvectors. In this case, we have a 7 x 7 matrix with three eigenvalues, but only two eigenspaces are given (a two-dimensional eigenspace and a three-dimensional eigenspace). Since we don't have eigenvectors for all the eigenvalues, matrix A is not guaranteed to be diagonalizable.

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Answer:

  6

Step-by-step explanation:

Freda lives in house 6. Lamar lives 3 houses from Freda, so lives in house 3. Jay lives next to Lamar, but not in house 2, which is Bart's. So, Jay lives in house 4 and Davina lives in house 5, on the other side of Jay from Lamar.

Davina lives in house 5, so has the most DVDs.

__

Since Freda gave p DVDs to Jay, she has 17-p. Lamar has p-2, Bart has p+4, Tara has 4p-13, and Davina has the most at 3(p-2).

We want Davina to have the most DVDs, so there are some inequalities that must be true:

  3(p-2) > 4p-13   ⇒   p < 7

  3(p-2) > p +4   ⇒   p > 5

The only value of p satisfying both of these requirements is p = 6.

_____

Tara lives in house 1 and has 11 DVDs.

Bart lives in house 2 and has 10 DVDs.

Lamar lives in house 3 and has 4 DVDs.

Jay lives in house 4 and has 6 DVDs.

Davina lives in house 5 and has 12 DVDs. (the most)

Freda lives in house 6 and has 11 DVDs.

Answer:

The probability of  the student will pass the quiz = .0546

Step-by-step explanation:

Given -

Total no of question = 10

If the student guesses on each question there are two outcomes true of false

the probability  of guesses  question correctly =  [tex]\frac{1}{2}[/tex]

the probability  of success is (p) =  [tex]\frac{1}{2}[/tex]

the probability  of guesses  question incorrectly = [tex]\frac{1}{2}[/tex]

the probability  of failure is (q) = 1- p = [tex]\frac{1}{2}[/tex]

If the student guesses on each question he must answered at least 8 question correctly

the probability of  the student will pass the quiz = [tex]P(X\geq8 )[/tex]

= P(X = 8 ) + P(X = 9) + P(X = 10 )

= [tex]\binom{10}{8}(p)^{8}(q)^{10 - 8} + \binom{10}{9}(p)^{9}(q)^{10 - 9} + \binom{10}{10}(p)^{10}(q)^{10 - 10}[/tex]

= [tex]\frac{10!}{(2!)(8!)}(\frac{1}{2})^{8}(\frac{1}{2})^{10 - 8} +\frac{10!}{(1!)(9!)} (\frac{1}{2})^{9}(\frac{1}{2})^{10 - 9} + \frac{10!}{(0!)(10!)}(\frac{1}{2})^{10}(\frac{1}{2})^{10 - 10}[/tex]

= [tex]45\times\frac{1}{2^{10}} + 10\times\frac{1}{2^{10}} + 1\times\frac{1}{2^{10}}[/tex]

= [tex]\frac{56}{2^{10}}[/tex]

= .0546

Final answer:

The probability of a student passing the true or false quiz by guessing and getting at least 8 out of 10 questions correct is 7/128. This is calculated by finding the binomial probabilities for 8, 9, and 10 correct guesses and summing them.

Explanation:

To determine the probability that the student passes the quiz by guessing, we need to calculate the chances of them getting at least 8 out of 10 true or false questions correct. Since each question can only be true or false, there's a 1/2 chance of guessing each question correctly, and therefore, a 1/2 chance of guessing incorrectly.

The scenarios in which a student can pass are by getting 8, 9, or 10 questions correct. We will use the binomial probability formula, which is P(X=k) = (n choose k) * (p)^k * (1-p)^(n-k), where 'n' is the number of trials (questions), 'k' is the number of successes (correct answers), and 'p' is the probability of success on an individual trial (1/2 for true/false questions).

The probability of getting exactly 8 questions right is (10 choose 8) * (1/2)^8 * (1/2)^(10-8).

The probability of getting exactly 9 questions right is (10 choose 9) * (1/2)^9 * (1/2)^(10-9).

The probability of getting all 10 questions right is (10 choose 10) * (1/2)^10 * (1/2)^(10-10).

We add these individual probabilities together to find the total probability of passing the quiz.

Using a calculator or the binomial coefficients, we find:

P(getting 8 right) = 45 * (1/2)^10,

P(getting 9 right) = 10 * (1/2)^10,

P(getting 10 right) = 1 * (1/2)^10.

Adding these together gives us the total probability:
P(8 or more correct) = [45 + 10 + 1] * (1/2)^10 = 56 * (1/2)^10

After simplifying, we find that the probability of passing the quiz with at least 8 correct answers is thus 56/1024, which can be reduced to 7/128.

Answer:

A = πr²

Step-by-step explanation:

Answer:

Answer = 11/46

Step-by-step explanation:

Answer:

There are NO parallel sides.

Step-by-step explanation:

Look at them.

Answer: Bottom left, lamins have no parrellel sides

Step-by-step explanation: All of them have no parrellel sides. Hope this helps!

Answer:

Margin of error = Critical value x Standard error of the sample.

Step-by-step explanation:

The margin of error can be calculated in two ways, depending on whether you have parameters from a population or statistics from a sample: Margin of error = Critical value x Standard deviation for the population. Margin of error = Critical value x Standard error of the sample.

Its C. ME= (z*s)/ sqrt n

The opposite of a coordinate in mathematics is obtained by changing the sign of the given number. Without the specific coordinate for point D, the opposite cannot be determined from the provided options.

The question seems to refer to the notion of opposite coordinates in a coordinate system. In mathematics, particularly in the context of a coordinate plane, the opposite of a coordinate is simply the same number with its sign changed. If the original coordinate for point D is not given in the question, it's impossible to determine the correct opposite coordinate from the options provided.

Step-by-step explanation:

The bacteria is always doubled because in the sequence we multiply the number by 2

3 x 2 = 6 x 2 = 12 x 2 = 24 x 2 = 48 x 2 = 96

Answer:

(a) The value of P (X = 4) is 0.1465.

(b) The probability that all 5 of them land heads up is 0.0313.

(c) The probability that the student answers correctly on less than 4 of these questions is 0.6980.

Step-by-step explanation:

A Binomial distribution is the probability distribution of the number of successes, X in n independent trials with each trial having an equal probability of success, p.

The probability mass function of a Binomial distribution is:

[tex]P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0,1,2,3...,\ 0<p<1[/tex]

(1)

The information provided is:

X = 4

n = 8

p = 0.31

Compute the value of P (X = 4) as follows:

[tex]P(X=4)={8\choose 4}0.31^{4}(1-0.31)^{8-4}\\=70\times 0.00923521\times 0.22667121\\=0.146535\\\approx 0.1465[/tex]

Thus, the value of P (X = 4) is 0.1465.

(2)

The probability of heads, on tossing a single fair coin is, p = 0.50.

It is provided that n = 5 fair coins are tossed together.

Compute the probability that all 5 of them land heads up as follows:

[tex]P(X=5)={5\choose 5}0.50^{5}(1-0.50)^{5-5}\\=1\times 0.03125\times 1\\=0.03125\\\approx 0.0313[/tex]

Thus, the probability that all 5 of them land heads up is 0.0313.

(3)

There are 5 possible answers for every multiple choice question. Only one of the five options is correct.

The probability of selecting the correct answer is, p = 0.20.

Number of multiple choice questions, n = 14.

Compute the probability that the student answers correctly on less than 4 of these questions as follows:

P (X < 4) = P (X = 0) + P (X = 1) + P (X = 2) + P (X = 3)

              [tex]=\sum\limits^{3}_{x=0}{{14\choose x}0.20^{x}(1-0.20)^{14-x}}\\=0.0439+0.1539+0.2501+0.2501\\=0.6980[/tex]

Thus, the probability that the student answers correctly on less than 4 of these questions is 0.6980.

The final probabilities are P(4 successes) ≈ 0.146, P(5 heads) ≈ 0.03125, and P(less than 4 correct answers) ≈ 0.5972.

Solutions to Probability Questions

Let's tackle each of your probability questions step-by-step:

Question 1 To find P(x) using the binomial probability formula, given n = 8, p = 0.31, and x = 4, we use the formula:

Where:

Calculating:

So, P(4) ≈ 70 * 0.009235 * 0.226981 ≈ 0.146.

Question 2 If 5 fair coins are tossed, the probability that all 5 of them land heads up is calculated as:

Question 3 For a student answering a multiple-choice quiz with 14 questions where each question has 5 possible answers, and we are to find the probability of correctly answering less than 4 questions, we use the binomial distribution with n = 14, p = 0.2 (since only one answer out of five is correct), and x < 4:

Answer:

Expected no of stops=N(1-exp(-10/N)

Step-by-step explanation:

Using equation

X=∑[tex]I_{m}[/tex]

where m lies from 1 to N

solve equation below

E(X)=N(1-exp(-10/N)

Given Information:

Distribution = Poisson

Mean = 10

Required Information:

Expected number of stops = ?

Answer:

[tex]E(N) = N(1 - e^{-0.1N} )[/tex]

Explanation:

The number of people entering on the elevator is a Poisson random variable.

There are N floors and we want to find out the expected number of stops that the elevator will make before discharging all of its passengers.

Mean = μ = 10

The expected number of stops is given by

[tex]E(N) = N(1 - e^{-mN} )[/tex]

Where m is the decay rate and is given by

Decay rate = m = 1 /μ = 1/10 = 0.10

Therefore, the expected number of stops is

[tex]E(N) = N(1 - e^{-0.1N} )[/tex]

If we know the number of floor (N) then we can the corresponding expected value.

Answer:

A. (-3,4), (6,2), (-7,1), (2,2)

Step-by-step explanation:

Functions cannot have the x repeating. All the other answers have one of their x-values repeating, so they are not functions.