List the different combinations of heads and tails that can occur when 3 ordinary coins are tossed. Use h for heads and t for tails. One combination is hht. List the other combinations, taking order into account (Use a comma to separate answers) More i () a Enter your answer in the answer box ere to search

Final answer:

To find the probability that the mean weight of a sample of 107 babies differs from the population mean by less than 40 grams, we can use the Central Limit Theorem. The probability is approximately 0.0441.

Explanation:

To find the probability that the mean weight of a sample of 107 babies differs from the population mean by less than 40 grams, we can use the Central Limit Theorem. According to the Central Limit Theorem, the distribution of sample means will be approximately normal as long as the sample size is large enough. In this case, our sample size is 107, which is considered large enough.

The formula to calculate the standard deviation of the sampling distribution of the sample mean is sigma/sqrt(n), where sigma is the population standard deviation and n is the sample size. Plugging in the values, we have 446/sqrt(107) = 42.96 grams.

To find the probability, we need to calculate the z-score for a difference of 40 grams from the population mean. The z-score formula is (x - mu) / (sigma / sqrt(n)), where x is the desired difference, mu is the population mean, sigma is the population standard deviation, and n is the sample size.

Plugging in the values, we have (40 - 3242) / (446/sqrt(107)) = -1.7. We want to find the probability that the z-score is less than -1.7. Using a standard normal distribution table or calculator, we find that the probability is approximately 0.0441.

To solve this question, we can use the Central Limit Theorem (CLT), which implies that the sampling distribution of the sample means will be normally distributed if the sample size is large enough (usually n > 30 is considered sufficient). Since we are dealing with a sample of 107 babies, which is quite large, we can safely use the CLT.
According to the CLT, the mean of the sample means will be equal to the population mean (μ), and the standard deviation of the sample means (often called the standard error, SE) will be equal to the population standard deviation (σ) divided by the square root of the sample size (n).
Given:
- The population mean (μ) = 3242 grams
- The population standard deviation (σ) = 446 grams
- The sample size (n) = 107 babies
First, we must calculate the standard error (SE):
SE = σ / √n
SE = 446 grams / √107
SE ≈ 446 grams / 10.344
SE ≈ 43.13 grams
Now, we want to find the probability that the mean weight of the sample babies would differ from the population mean by less than 40 grams. This means we are looking at weights from (μ - 40) grams to (μ + 40) grams.
So we will find the z-scores corresponding to (μ - 40) grams and (μ + 40) grams:
Z = (X - μ) / SE
For the lower limit (μ - 40 grams = 3202 grams):
Z Lower = (3202 - 3242) / 43.13
Z Lower ≈ -40 / 43.13
Z Lower ≈ -0.927
For the upper limit (μ + 40 grams = 3282 grams):
Z Upper = (3282 - 3242) / 43.13
Z Upper ≈ 40 / 43.13
Z Upper ≈ 0.927
Using the standard normal distribution (Z-distribution), we can find the probability that a Z-score falls between -0.927 and 0.927. These values correspond to the area under the standard normal curve between these two Z-scores.
If we look these values up in a Z-table, or use a calculator:
- The probability of Z being less than 0.927 is approximately 0.8238.
- The probability of Z being less than -0.927 is approximately 0.1762.
So, the probability of the mean weight being between μ - 40 grams and μ + 40 grams is the area between these two Z-scores, which can be found by subtracting the lower probability from the upper probability:
P(-0.927 < Z < 0.927) = P(Z < 0.927) - P(Z < -0.927)
P(-0.927 < Z < 0.927) = 0.8238 - 0.1762
P(-0.927 < Z < 0.927) = 0.6476
Rounding to four decimal places:
P(-0.927 < Z < 0.927) ≈ 0.6476
Therefore, the probability that the mean weight of the sample babies would differ from the population mean by less than 40 grams is approximately 0.6476, or 64.76%.

Answer: 0.5507

Step-by-step explanation:

The cumulative distribution function for exponential distribution:-

[tex]P(X\leq x)=1-e^{-\lambda x}[/tex]

Given : The life of a light bulb is exponentially distributed with a mean of 1,000 hours.

Then , [tex]\lambda=\dfrac{1}{1000}[/tex]

Then , the probability that the bulb will last less than 800 hours is given by :-

[tex]P(X\leq 800)=1-e^{\frac{-800}{1000}}\\\\=1-e^{-0.8}=0.5506710358\approx0.5507[/tex]

Hence, the probability that the bulb will last less than 800 hours = 0.5507

The probability that the bulb will last less than 800 hours is 0.550

An incandescent light bulb is an electric light with a wire filament heated to such a high temperature that it glows with visible light. The filament of  an incandescent light bulb is protected from oxidation with a glass or fused quartz bulb that is filled with inert gas or a vacuum. The exponential distribution is the probability distribution of the time between events in a Poisson point process. It is a particular case of the gamma distribution. While the arithmetic mean is the central value of a discrete set of numbers: specifically, the sum of the values divided by the number of values

The life of a light bulb is exponentially distributed with a mean of 1,000 hours. What is the probability that the bulb will last less than 800 hours?

What is the probability that the light bulb will have to replaced within 800 hours?

[tex]\lambda = \frac{1}{1000}[/tex]

[tex]P(x<=800) = 1 - e^{(-\lambda*x)} = 1-e^{[(-\frac{1}{1000} )*800]} = 1-e^{-0.8} = 1-0.449 = 0.550[/tex]

Grade:  5

Subject:  math

Chapter:  probability

Keywords:  mean, bulb, hours, exponential, light

Answer:

95%

Step-by-step explanation:

We have a normal distribution with a mean of 6 students and standard deviation of 26.

To solve this problem, we're going to need the help of a calculator.

P(16<z<120) = 0.9545 ≈ 95.45%

Rounding, we can say that 95% of the students scored between 16 and 120.

Answer: 0.5

Step-by-step explanation:

Binomial probability formula :-

[tex]P(x)=^nC_x\ p^x(q)^{n-x}[/tex], where P(x) is the probability of getting success in x trials , n is the total trials and p is the probability of getting success in each trial.

Given : The probability that the adults follow more than one game = 0.30

Then , q= 1-p = 1-0.30=0.70

The number of adults surveyed : n= 15

Let X be represents the adults who follow more than one sport.

Then , the probability that fewer than 4 of them will say that football is their favorite sport,

[tex]P(X\leq4)=P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)\\\\=^{15}C_{0}\ (0.30)^0(0.70)^{15}+^{15}C_{1}\ (0.30)^1(0.70)^{14}+^{15}C_{2}\ (0.30)^2(0.70)^{13}+^{15}C_{3}\ (0.30)^3(0.70)^{12}+^{15}C_{4}\ (0.30)^4(0.70)^{11}\\\\=(0.30)^0(0.70)^{15}+15(0.30)^1(0.70)^{14}+105(0.30)^2(0.70)^{13}+455(0.30)^3(0.70)^{12}+1365(0.30)^4(0.70)^{11}\\\\=0.515491059227\approx0.5[/tex]

Hence, the probability rounded to the nearest tenth that fewer than 4 of them will say that football is their favorite sport =0.5

Answer:

Step-by-step explanation:

The x-intercept exists when y = 0; the coordinate takes on the form (    , 0)

The y-intercept exists when x = 0; the coordinate takes on the form (0,   ).

We will fill in the blanks in a sec.

If the x-intercept exists when y = 0, then we fill in 0 for y and solve for x:

-3(0) - x = -9 so

-x = -9 and

x = 9

The coordinate is (9, 0) for the x-intercept.

If the y-intercept exists when x = 0, then we fill in 0 for x and solve for y:

-3y - 0 = -9 so

-3y = -9 and

y = 3

The coordinate is (0, 3) for the y-intercept.

Answer: 77.45 %

Step-by-step explanation:

We assume that the measurements are normally distributed.

Given : Mean : [tex]\mu=39[/tex]

Standard deviation : [tex]\sigma=4.0[/tex]

Let x be the randomly selected measurement.

Now we calculate z score for the normal distribution as :-

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x = 35, we have

[tex]z=\dfrac{35-39}{4}=-1[/tex]

For x = 45, we have

[tex]z=\dfrac{45-39}{4}=1.5[/tex]

Now, the p-value = [tex]P(35<x<45)=P(-1<z<1.5)[/tex]

[tex]=P(z<1.5)-P(z<-1)\\\\=0.9331927-0.1586553=0.7745374\approx0.7745[/tex]

In percent , [tex]0.7745\times100=77.45\%[/tex]

Hence, the percent of measurements should fall between 35 and 45 = 77.45 %

Final answer:

Approximately 68% of the hardness measurements on the Rockwell C scale should fall between 35 and 45, according to the empirical rule and the provided mean and standard deviation.

Explanation:

To determine the percentage of hardness measurements that fall between 35 and 45 on the Rockwell C scale, we utilize the concept of standard deviation and the empirical rule.

Given the average (or mean) Rockwell C value is 39 and the standard deviation is 4.0, the range from 35 to 45 encompasses from one standard deviation below to one standard deviation above the mean.

According to the empirical (68-95-99.7) rule, about 68% of data within a normal distribution falls within one standard deviation of the mean.

Since the range from 35 to 45 represents this bracket around the mean, we can conclude that approximately 68% of the hardness measurements should fall within this range, assuming a normal distribution of the measurements.

Answer: 0.7264

Explanation:

The number of independent questions (n)  = 100

Probability of answering a question (p) = 0.80

Let X be the no. of questions that need to be answered.

[tex]\therefore[/tex] random variable X follows binomial distribution

The probability function of a binomial distribution is given as

[tex]P(X=x) = \binom{n}{x}\times p^{x}(1-p)^{n-x}[/tex]

Now , we nee to find P(74 ≤ X ≤ 84)

[tex]\therefore P(74\leq X\leq 84) = P(X=74) + P(X=75).........+ P(X=84)[/tex]

P(74 ≤ X ≤ 84) = [tex]\sum_{74}^{84}\binom{100}{x}\times (0.80)^{x}(0.20)^{100-x}[/tex]

P(74 ≤ X ≤ 84) = 0.7264

Answer:

650 milliliters.

Step-by-step explanation:

Amount in the Jug = 1.5 * 1000 = 1,500 mls.

She pours out 250 mls and 0.6 * 1000 = 600 mls

The amount left = 1500 - 250 - 600

= 650 milliliters.

The amount of chocolate milk left in the jug is; D: 650 milliliters

We are told;

Amount of chocolate milk in the jug = 1.5 litres

She fills one cup with 250 mL = 0.25 liters

She fills another cup with 0.6 liters

Thus;

Total amount used = 0.6 +  0.25 = 0.85 litres

Amount left = 1.5 - 0.85 = 0.65 Liters

Converting to mL gives; 650 milliliters

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Answer:

discount= $94.5

Proceeds=$2605.5

Step-by-step explanation:

amount Dawin has to pay= $2700

in 6 months time

at a discount rate of 7%

here future value = $2700

D= discount before m months is given by

[tex]D= \frac{FV\times r\times m}{1200}[/tex]

m= 6 months, r= 7% and FV= 2700

putting values

[tex]D= \frac{2700\times 7\times 6}{1200}[/tex]

solving we get

D= $94.5

now present value = future value - discount

=2700-94.5= $ 2605.5

here PV(present valve )= Proceeds= $2605.5

The distribution of X is a normal distribution with a mean of 66 inches and a standard deviation of 2.5 inches. To find the probability that a person's height is between 64 and 69 inches, we need to determine the z-scores for each height value and use a z-table or calculator to find the probabilities.

A) Give the distribution of X.
X ~ Normal(66, 2.5)
B) Find the probability that the person is between 64 and 69 inches.
P(64 ≤ X ≤ 69)

To find this probability, we need to calculate the z-score for each height value using the formula z = (X - μ) / σ. Then, we can use a z-table or a calculator to find the corresponding probabilities.

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The height X of Asian adult males follows a normal distribution with parameters X ~ N(66, 2.5). The probability that one randomly chosen male is between 64 and 69 inches tall can be found using Z-scores and the area under the normal curve.

The distribution of the height X for Asian adult males according to the given study is X ~ N(66, 2.5), where 66 is the mean height in inches and 2.5 is the standard deviation.

Probability that the height is between 64 and 69 inches

To find the probability that the height of a randomly chosen Asian adult male is between 64 and 69 inches, we can use the properties of the normal distribution. We first convert the raw scores to Z-scores using the formula Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

The probability statement is P(64 < X < 69). To calculate this probability, we find the Z-scores for 64 and 69 inches and then find the area under the normal curve between these two Z-scores using a standard normal distribution table or a calculator with normal distribution functions.

Answer:

The commission would be $ 920.

Step-by-step explanation:

Given,

Sales in 1997 ​= $ 9500,

Since, there is a commision of 8 % on the first $ 7500 of​ sales, 16% on the next $ 7500 of​ sales, and 20% on sales over $ 15,000,

If x represents the total sales,

Commission for x ≤ 7500 = 8% of x = 0.08x,

Commission for 7500 < x ≤ 15000 = 8% of 7500 + 16% of (x-7500)

= 600 + 0.16(x-7500),

Commission for 7500 < x ≤ 15000 = 8% of 7500 + 16% of 7500 + 20% of (x-15000)

= 600 + 1200 + 0.20(x-15000)

= 1800 + 0.20(x-15000)

Thus, the function that shows the given situation,

[tex]f(x)=\left\{\begin{matrix}0.08x & x \leq 7500\\ 600+0.16(x-7500) & 7500 < x \leq 15000\\ 1800+0.20(x-15000) & 15000 < x\end{matrix}\right.[/tex]

Since, 9500 lies between 7500 and 15000,

Therefore, the commission would be,

f(9500)= 600 + 0.16(9500 - 7500) = 600 + 320 = $ 920

Shelby's gross commission for July 1997 on sales of $9500 is calculated as  $920.

Kelly Price sells college textbooks on commission, and the structure of her commission is a tiered rate: 8% on the first $7500 of sales, 16% on the next $7500 of sales, and 20% on sales over $15,000.

For Shelby’s sales totaling $9500 in July 1997, we must calculate her gross commission for that month.

Here is the step-by-step calculation:

Therefore, Shelby’s gross commission for July 1997 is $920.

Answer: First option.

Step-by-step explanation:

It is important to remember that the line intersects the x-axis when [tex]y=0[/tex].

So, given the line [tex]3x+4y=12[/tex], you need to substitute [tex]y=0[/tex] into the equation and solve for "x", in order to find the x-intercept of this line.

Therefore, this is:

[tex]3x+4y=12\\\\3x+4(0)=12\\\\3x+0=12\\\\3x=12\\\\x=\frac{12}{3}\\\\x=4[/tex]

Therefore, this line intersects the x-axis at this point:

[tex](4,0)[/tex]

Answer:  0.317

Step-by-step explanation:

Let A be the event that the selected household is prosperous and B the event that it is educated.

Given : P(A)=0.138,   P(B)=0.261

P(A and B)=0.082

We know that for any events M and N ,

[tex]\text{P(M or N)=P(M)+P(N)-P(M or N)}[/tex]

Thus , [tex]\text{P(A or B)=P(A)+P(B)-P(A or B)}[/tex]

[tex]\text{P(A or B)}=0.138+0.261-0.082\\\\\Rightarrow\text{ P(A or B)}=0.317[/tex]

Hence, the probability P(A or B) that the household selected is either prosperous or educated = 0.317

Final answer:

The probability that a randomly selected American household is either prosperous or educated is 0.317.

Explanation:

We are asked to find the probability P(A or B) that a randomly selected American household is either prosperous (income over $100,000) or educated (householder completed college). To calculate the probability of the union of two events A and B, we use the formula:

P(A or B) = P(A) + P(B) - P(A and B).

According to the given data:

P(A) is the probability that a household is prosperous, which is 0.138.

P(B) is the probability that a household is educated, which is 0.261.

P(A and B) is the probability that a household is both prosperous and educated, which is 0.082.

Now we apply the given probabilities to the formula:

P(A or B) = 0.138 + 0.261 - 0.082 = 0.317.

Therefore, the probability that a selected household is either prosperous or educated is 0.317.

Recall that for [tex]|z|<1[/tex], we have

[tex]\dfrac1{1-z}=\displaystyle\sum_{n\ge0}z^n[/tex]

Then

[tex]\dfrac1{1-z}=-\dfrac1z\dfrac1{1-\frac1z}=-\dfrac1z\displaystyle\sum_{n\ge0}z^{-n}=-\sum_{n\ge0}z^{-n-1}[/tex]

valid for [tex]|z|>1[/tex], so that

[tex]\dfrac1{1-z^2}=-\dfrac1{z^2}\dfrac1{1-\frac1{z^2}}=-\dfrac1{z^2}\displaystyle\sum_{n\ge0}z^{-2n}=-\sum_{n\ge0}z^{-2n-2}[/tex]

also valid for [tex]|z|>1[/tex].

Answer:

The answer is Parallel-forms reliability.

Parallel-forms reliability describes a measure used to compare two different tests with the same group of participants to see how closely correlated the two sets of scores are with each other.

Test-retest reliability is a measure used to compare the results of two instances of the same test taken by the same group of participants to establish how closely correlated the two sets of scores are.

The measure used to compare two different tests with the same group of participants to see how closely correlated the two sets of scores are with each other is called test-retest reliability.

In essence, test-retest reliability measures the consistency of results when a test is administered more than once. The higher the correlation between the two sets of scores, the higher the test’s reliability. For example, if a group of students were to take a vocabulary test one week, and then the same test a week later, a high correlation between the results would suggest that the test is reliable.

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Answer:

  16.053 inches

Step-by-step explanation:

Many such probability questions are easily answered by a suitable calculator or spreadsheet.

Answer:

C (0, 9)

Step-by-step explanation:

First, X is reflected across the line x=2.

X(4, -7) becomes X'(0, -7).

Next, X' is reflected across the line y=1.

X'(0, -7) becomes X"(0, 9).

Answer: 0.1052

Step-by-step explanation:

Given : Mean :[tex]\mu= 120[/tex]

Standard deviation : [tex]\sigma= 5.6[/tex]

We assume the variable is normally distributed.

The formula for z-score is given by :-

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x=120.4

[tex]z=\dfrac{120.4-120}{5.6}=0.0714285714286\approx0.07[/tex]

For x=121.9

[tex]z=\dfrac{121.9-120}{5.6}=0.339285714286\approx0.34[/tex]

The p-value =[tex]P(0.07<z<0.34)=P(0.34)-P(0.07)[/tex]

[tex]=0.6330717-0.5279031=0.1051686\approx0.1052[/tex]

The probability that the individual's pressure will be between 120.4 and 121.9 mm Hg = 0.1052

Answer:

The number of adult tickets sold was 121

Step-by-step explanation:

The general equation is: S + A = T    ;where S means student tickets, A means adult tickets and T means total tickets. We know that S is two times A and T is 363. So, S will be 2x and A will be x. Then, the new equation is 2x + x = 363.

S + A = T  

2x + x = 363  

3x = 363  

x = 363 / 3

x = 121

Adult tickets: A = x = 121

Student tickets: S = 2x = 2 * 121 = 242

Final answer:

To solve for the number of adult tickets sold, set the number of adult tickets as x, the student tickets as 2x, and use the total of 363 tickets to create the equation 3x = 363. Solving for x, you find that 121 adult tickets were sold.

Explanation:

The numerical problem given is about determining the number of adult tickets and student tickets sold for a school play, with the total number of tickets sold being 363, and the number of student tickets being twice the number of adult tickets sold.

Let the number of adult tickets be x. Then the number of student tickets is 2x. The total number of tickets sold is the sum of the adult tickets and student tickets, which is x + 2x = 3x. Since we know that 363 tickets were sold in total, we can write the equation:

3x = 363

Now, solve for x:

Therefore, 121 adult tickets were sold.

Answer:

a) Velocity of the galaxy=573.756 km/s

b) Distance to the galaxy=716 Mpc

Step-by-step explanation:

a) [tex]v=H_0 D\\Where\ v=Velocity\ of\ the\ galaxy\\H_0= Hubble\ constant=69.8\pm 1.9\ as\ of\ 16\ July\ 2019\\D= Proper\ distance=8.22\ Mpc\\\Rightarrow v=69.8\times 8.22\\\therefore v=573.756\ km/s\\[/tex]

b)[tex]v=H_0 D\\v=50000\ km/s\\H_0= Hubble\ constant=69.8\pm 1.9\\\Rightarrow D=\frac{v}{H_0}\\\Rightarrow D=\frac{50000}{69.8}\\\therefore D=716\ Mpc[/tex]

one rupee coin be z

50 paisa coins=2z

25 paisa coins=4z

50/25=2 2z*2=4z

z+2x+4x=175

7z=175

7z/7=175/7

z=25

one rupee coin=25 value

50 paisa rupee coins=50 value

25 rupee coin=100 value

50/25=2 50*2=100

25+50+100=175

Answer is b) Rs 175. I think this is the answer.

Answer:

The list of bijections from A into B are shown below.

Step-by-step explanation:

A function f is called one-to-one or injective, if and only if

[tex]f(x)=f(y)\Rightarrow x = y[/tex]

for all x and y in the domain of f.

A function f from X to Y is called onto or surjective, if and only if

for every element y∈Y there is an element x∈X with f(x)=y.

If a function is one-one and onto, then it is called bijective.

Part (a):

A={q,r,s} and B={2,3,4}

We need to find all the bijections from A into B.

(1) [tex]A\rightarrow B=\{(q,2),(r,3),(s,4)\}[/tex]

(2) [tex]A\rightarrow B=\{(q,2),(r,4),(s,3)\}[/tex]

(3) [tex]A\rightarrow B=\{(q,3),(r,2),(s,4)\}[/tex]

(4) [tex]A\rightarrow B=\{(q,3),(r,4),(s,2)\}[/tex]

(5) [tex]A\rightarrow B=\{(q,4),(r,2),(s,3)\}[/tex]

(6) [tex]A\rightarrow B=\{(q,4),(r,3),(s,2)\}[/tex]

Part (b):

A={1,2,3,4} and B={5,6,7,8}

We need to find all the bijections from A into B.

(1) [tex]A\rightarrow B=\{(1,5),(2,6),(3,7),(4,8)\}[/tex]

(2) [tex]A\rightarrow B=\{(1,5),(2,6),(3,8),(4,7)\}[/tex]

(3) [tex]A\rightarrow B=\{(1,5),(2,7),(3,6),(4,8)\}[/tex]

(4) [tex]A\rightarrow B=\{(1,5),(2,7),(3,8),(4,6)\}[/tex]

(5) [tex]A\rightarrow B=\{(1,5),(2,8),(3,6),(4,7)\}[/tex]

(6) [tex]A\rightarrow B=\{(1,5),(2,8),(3,7),(4,6)\}[/tex]

(7) [tex]A\rightarrow B=\{(1,6),(2,5),(3,7),(4,8)\}[/tex]

(8) [tex]A\rightarrow B=\{(1,6),(2,5),(3,8),(4,7)\}[/tex]

(9) [tex]A\rightarrow B=\{(1,6),(2,7),(3,5),(4,8)\}[/tex]

(10) [tex]A\rightarrow B=\{(1,6),(2,7),(3,8),(4,5)\}[/tex]

(11) [tex]A\rightarrow B=\{(1,6),(2,8),(3,5),(4,7)\}[/tex]

(12) [tex]A\rightarrow B=\{(1,6),(2,8),(3,7),(4,5)\}[/tex]

(13) [tex]A\rightarrow B=\{(1,7),(2,6),(3,5),(4,8)\}[/tex]

(14) [tex]A\rightarrow B=\{(1,7),(2,6),(3,8),(4,5)\}[/tex]

(15) [tex]A\rightarrow B=\{(1,7),(2,5),(3,6),(4,8)\}[/tex]

(16) [tex]A\rightarrow B=\{(1,7),(2,5),(3,8),(4,6)\}[/tex]

(17) [tex]A\rightarrow B=\{(1,7),(2,8),(3,6),(4,5)\}[/tex]

(18) [tex]A\rightarrow B=\{(1,7),(2,8),(3,5),(4,6)\}[/tex]

(19) [tex]A\rightarrow B=\{(1,8),(2,6),(3,7),(4,5)\}[/tex]

(20) [tex]A\rightarrow B=\{(1,8),(2,6),(3,5),(4,7)\}[/tex]

(21) [tex]A\rightarrow B=\{(1,8),(2,7),(3,6),(4,5)\}[/tex]

(22) [tex]A\rightarrow B=\{(1,8),(2,7),(3,5),(4,6)\}[/tex]

(23) [tex]A\rightarrow B=\{(1,8),(2,5),(3,6),(4,7)\}[/tex]

(24) [tex]A\rightarrow B=\{(1,8),(2,5),(3,7),(4,6)\}[/tex]

Answer:

Length of B is 7.4833

Step-by-step explanation:

The vector sum of A and B vectors in 2D is

[tex]C=A+B=(a_1+b_1,a_2+b_2)[/tex]

And its magnitude is:

[tex]C=\sqrt{(a_1+b_1)^2+(a_2+b_2)^2} =9[/tex]

Where

[tex]a_1=Asinx[/tex]

[tex]a_2=Acosx[/tex]

[tex]b_1=Bsin(x+90)[/tex]

[tex]b_2=Bcos(x+90)[/tex]

Using the properties of the sum of two angles in the sin and cosine:

[tex]b_1=Bsin(x+90)=B(sinx*cos90+sin90*cosx)=Bcosx[/tex]

[tex]b_2=Bcos(x+90)=B(cosx*cos90-sinx*sin90)=-Bsinx[/tex]

Sustituying in the magnitud of the sum

[tex]C=\sqrt{(Asinx+Bcosx)^2+(Acosx-Bsinx)^2} =9[/tex]

[tex]C=\sqrt{A^2sin^2x+2ABsinxcosx+B^2cos^2x+A^2cos^2x-2ABsinxcosx+B^2sin^2x} =9[/tex]

[tex]C=\sqrt{A^2(sin^2x+cos^2x)+B^2(cos^2x+sin^2x)}[/tex]

[tex]C=\sqrt{A^2+B^2} =9[/tex]

Solving for B

[tex]A^2+B^2 =9^2[/tex]

[tex]B^2 =9^2-A^2[/tex]

Sustituying the value of the magnitud of A

[tex]B^2=81-5^2=81-25=56[/tex]

[tex]B= 7. 4833[/tex]

The calculation reveals that vector B should be approximately 7.48 in length when magnitude of A s 5.00 and magnitude of their vector sum is 9.00.

The subject question asks for the length of vector B given that it is at right angles to vector A, whose magnitude is 5.00, to ensure that the magnitude of their vector sum is 9.00. To solve this problem, we can use the Pythagorean theorem because the vectors are at right angles to each other.

Let's designate the magnitude of vector B as |B|. According to the Pythagorean theorem for right-angled triangles, we have:
|A|² + |B|² = |A + B|²
So, if |A| = 5.00 and the resultant |A + B| = 9.00, we can substitute these values to find |B|:
5.00² + |B|² = 9.00²
|B|² = 9.00² - 5.00²
|B|² = 81.00 - 25.00
|B|² = 56.00

Therefore, |B| = √(56.00)

|B| = 7.48.

So the length of B should be approximately 7.48 to get a resultant magnitude of 9.00 when added to A.

Answer:

1,460 hours per year.

113,880 hours in a lifetime.

Step-by-step explanation:

Great question, it is always good to ask away and get rid of any doubts that you may be having.

Let's assume that on an average day Americans drive 4 hours a day. This includes going and coming from work as well as any groceries they might need to do. Since there are 365 days in a year we can multiply this by the hours a day driven.

[tex]365*4 = 1,460[/tex]

We can "guesstimate" that on average an American drives 1,460 hours per year.

Based on my research the average lifetime of an American is 78 years old. We can now multiply this by the number of hours driven in a year to have an idea of the number of hours driven in a lifetime.

[tex]1,460*78 = 113,880[/tex]

On average we "guesstimate" that an American drives 113,880 hours in a lifetime.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

[tex]x^2-6x + 8=x^2-6x+9-1=(x-3)^2-1[/tex]

Answer:

(x - 3)^2 - 1.

Step-by-step explanation:

x2 – 6x + 8.

We divide the coefficient of x by 2:

-6 / 2 = -3 so the contents of the parentheses is x - 3:

x^2 - 6x + 8

= (x - 3)^2 - (-3)^2 + 8

= (x - 3)^2 - 1.

Answer: 1.49

Step-by-step explanation:

We know that the standard deviation in a binomial distribution is given by :-

[tex]\sigma=\sqrt{n\cdot p\cdot (1-p)}[/tex], where n is the number of trials and p is the probability of success.

Given : The number of trials : [tex]n=10[/tex]

The probability of success = [tex]p=\dfrac{1}{3}[/tex]

Then , the standard deviation will be :-

[tex]\sigma=\sqrt{10\cdot \dfrac{1}{3}\cdot (1-\dfrac{1}{3})}\\\\\Rightarrow\ \sigma=1.490711985\approx1.49[/tex]

The standard deviation of a given binomial distribution with 10 trials and a probability of success of 1/3 is calculated using the formula σ = √npq, resulting in approximately 1.49. This value helps us understand the spread of successes in the experiment.

To compute the standard deviation of a given binomial distribution with 10 trials and a probability of success p=1/3, we first identify the probability of failure, which is q=1-p=2/3. The formula for the standard deviation (σ) of a binomial distribution is σ = √npq, where n is the number of trials, p is the probability of success, and q is the probability of failure.

By substituting the given values into the formula:

We get σ = √(10)(1/3)(2/3) = √(20/9) ≈ 1.49. Therefore, the standard deviation of the binomial distribution is approximately 1.49.

This calculation helps us understand the dispersion or spread of the distribution of successes in our binomial experiment, indicating how far the number of successes can deviate from the expected value on average.

Answer:

Given

[tex]f(m+n)=f(m)f(n)[/tex]

If we assume

[tex]f(x)=ae^{x}\\\\f(m+n)=ae^{m+n}\\\\\therefore f(m+n)=ae^{m}\times ae^{n}(\because x^{a+b}=x^{a}\times x^{b})\\\\\Rightarrow f(m+n)=f(m)\times f(n)[/tex]

Similarly

We can generalise the result for

[tex]f(x)=am^{x }[/tex] where a,m are real numbers

2)

[tex]f(m\cdot n)=f(m)+f(n)\\\\let\\f(x)=log(x)\\\therefore f(mn)=log(mn)=log(m)+log(n)\\\\\therefore f(mn)=f(m)+f(n)[/tex]

Answer: True, hope this helps! :)

Answer:

Yes! There are 3 different explanations I have. Pick your favorite.

Step-by-step explanation:

So we are asked to see if the following equation holds:

[tex]\frac{4 \text{ ft }}{6 \text{ ft}}=\frac{12 \text{ sec }}{18 \text{sec}}[/tex]

The units cancel out ft/ft=1 and sec/sec=1.

So we are really just trying to see if 4/6 is equal to 12/18

Or you could cross multiply and see if the products are the same on both sides:

[tex]\frac{4}{6}=\frac{12}{18}[/tex]

Cross multiply:

[tex]4(18)=6(12)[/tex]

[tex]72=72[/tex]

Since you have the same thing on both sides then the ratios given were proportional.

OR!

Put 4/6 and 12/18 in your calculator.  They both come out to have the same decimal expansion of .66666666666666666(repeating) so the ratios gives are proportional.

OR!

Reduce 12/18 and reduce 4/6 and see if the reduced fractions are same.

12/18=2/3  (I divided top and bottom by 6)

4/6=2/3  (I divided top and bottom by 2)

They are equal to the same reduced fraction so they are proportional.

Answer:

The height of tower is 322.7 feet.

Step-by-step explanation:

Given

Distance between a building and tower= 250 feet

BCDE is a rectangle .Therefore, we have  BC=ED and CD=BE=250 feet

In triangle ABE

[tex]tan\theta=\frac{perpendicula \; side }{hypotenuse}[/tex]

[tex]\theta=38^{\circ}[/tex]

[tex] tan38^{\circ}=\frac{AB}{BE}[/tex]

[tex]\frac{AB}{250}=0.781[/tex]

[tex] AB=0.781\times250[/tex]

AB=195.25 feet

In triangle EDC

[tex]\theta=27^{\circ}[/tex]

[tex]tan27^{\circ}=\frac{ED}{CD}[/tex]

[tex]\frac{ED}{250}=0.509[/tex]

[tex]ED=250\times0.509[/tex]

ED=127.25 feet

ED=BC=127.25 feet

The height of tower=AB+BC

The height of tower=195.25+127.25=322.5 feet