a. I have five coins in my pocket – four are fair, and the other is weighted to have a 70% chance of coming up heads. I pull one out at random and flip it three times. What is the conditional probability that I get four heads given I pulled out the weighted coin?

Answer:

0

Step-by-step explanation:

In my opinion, the string won't display because, the intCount was not initialized before you started outputting the "Hi" string. So in order fro you to get the string to appear, the control point or value has to be initialized to maybe 0. then you can start looping from there. And if you are looping from the top or using greater than (>), The loop works best buy subtracting the control value else, you can end up with infinity loop.

There are 7 states with Monarch butterflies, 17 states with honeybees, and 6 states with ladybugs as their official insect.

Two or more expressions with an Equal sign is called as Equation.

Let us consider  M, H, and L to represent the number of states with Monarch butterflies, honeybees, and ladybugs as their official insect, respectively.

We know that M + H + L = 30, since there are 30 states in total.

From the problem statement, we also know that:

M = L + 1 (1)

H = 3L - 1 (2)

We can use equations (1) and (2) to solve for M, H, and L:

M + H + L = 30

Substituting equation (1) and (2) into this equation:

(L + 1) + (3L - 1) + L = 30

5L = 30

L = 6

So there are 6 states with ladybugs as their official insect. Using equation (1) and (2), we can then find:

M = L + 1 = 7

H = 3L - 1 = 17

Hence,  there are 7 states with Monarch butterflies, 17 states with honeybees, and 6 states with ladybugs as their official insect.

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Final answer:

To solve this problem, assign variables to represent the number of states that have each kind of insect. Use the given information to set up equations and solve simultaneously to find the values of 'm', 'h', and 'l'.

Explanation:

To solve this problem, let's assign variables to represent the number of states that have each kind of insect as their state insect. Let 'm' represent the number of states with Monarch butterflies, 'h' represent the number of states with honeybees, and 'l' represent the number of states with ladybugs as their official insect.

According to the problem, we have the following information:

'm' = 'l' + 1   (The number of states with Monarch butterflies is one more than the number of states with ladybugs)

'h' = 3('l') - 1   (The number of states with honeybees is three times the number of states with ladybugs minus one)

We also know that the total number of states is 30. So we can set up the following equation:

m + h + l = 30

Now, we can solve these equations simultaneously to find the values of 'm', 'h', and 'l'.

Using the first equation, we substitute 'l + 1' for 'm' in the second equation:

h = 3('l') - 1

h = 3(l + 1) - 1

h = 3l + 3 - 1

h = 3l + 2

Now, we substitute 'l + 1' for 'm' and '3l + 2' for 'h' in the third equation:

(l + 1) + (3l + 2) + l = 30

Simplifying the equation:

5l + 3 = 30

5l = 27

l = 5.4

Since 'l' represents the number of states with ladybugs, we can't have a fraction of a state. Therefore, we round 'l' down to the nearest whole number:

l = 5

Substituting this value back into the equations, we find that 'm' = 6 and 'h' = 14.

Therefore, there are 6 states with Monarch butterflies as their official insect, 14 states with honeybees, and 5 states with ladybugs.

Answer:

Step-by-step explanation:

Given that Alice and Bob race two toy trains around a circular track. The trains move in the same direction and they meet every 120 seconds. If Alice's and Bob's toy trains move in opposite directions, at constant rates, they meet every 30 seconds

Circular track is 1800 m.

Let speed be x and y respectively

When in same direction relative speed = x-y and when in opposite directions =x+y

30(x+y) = 1800

x+y= 60

120(x-y) = 1800

x-y = 15

Solving x = 37.5 m/hr and y = 12.5 per hour.

When Alice and Bob's toy trains move in the same direction, their relative speed is the sum of their individual speeds. When they move in opposite directions, their relative speed is the difference between their individual speeds. By solving simultaneous equations, we find that Alice's toy train has a speed of 75 m/s and Bob's toy train has a speed of 60 m/s.

Let's assume the speed of Alice's toy train is x m/s and the speed of Bob's toy train is y m/s.

When the trains move in the same direction, they meet every 120 seconds. Since they meet once every 30 seconds when moving in opposite directions, their relative speed is the sum of their individual speeds. So, when they move in the same direction, their relative speed will be x + y and when they move in opposite directions, their relative speed will be x - y.

When they move in the same direction, the distance covered by Alice's toy train in 120 seconds will be equal to the distance covered by Bob's toy train in 120 seconds, which is equal to the length of the circular track (1800 m). So, the equation can be written as:

Simplifying the equation, we get:

Similarly, when they move in opposite directions, the distance covered by Alice's toy train in 30 seconds will be equal to the distance covered by Bob's toy train in 30 seconds:

Simplifying the equation, we get:

Solving the equations simultaneously, we find that x = 75 m/s and y = -60 m/s. Since speed is always positive, we consider the magnitude of the velocity. Therefore, the speed of Alice's toy train is 75 m/s and the speed of Bob's toy train is 60 m/s.

Answer:

270725 different ways

Step-by-step explanation:

The problem tells us that the order of the letters does not matter. Therefore, in the combination the order is NOT important and is signed as follows:

C (n, r) = n! / r! (n - r)!

We have to n = 52 and r = 4

C (52, 4) = 52! / 4! * (52-4)! = 52! / (4! * 48!) = 270725

Which means that there are 270725 different ways in total to make that raffle

Answer:

d) (179.20, 212.716)

Step-by-step explanation:

1000 : 345

569 : 195.96

Midpoint of (179.20, 212.716) is 195.958 which is the closest to 195.96

Final answer:

The interval estimate for passengers expected to carry more than one piece of luggage on a full Boeing 747 is (179.20, 212.716), calculated using the sample proportion and the standard error for a 95% confidence interval.

Explanation:

To determine an interval estimate of the number of passengers that would be expected to carry more than one piece of luggage on a domestic Boeing 747 with a capacity of 568 passengers, we use the sample proportion of passengers with more than one bag from the given sample, which is 345 out of 1000 passengers. This sample proportion, denoted as p-hat, is 0.345. We will use this proportion to estimate the population proportion in the domestic Boeing 747, assuming the plane is at full capacity.

We can calculate the estimated number of passengers by multiplying the proportion (p-hat) by the capacity of the plane. For a Boeing 747 with 568 passengers, this would be 0.345 * 568. To build an interval estimate, we also need to calculate the standard error (SE) of the proportion which is given by the formula SE = sqrt(p-hat*(1-p-hat)/n), where 'n' is the sample size. With a sample size of 1000, the SE can be calculated and then used to construct the 95% confidence interval using the Z-score for 95% confidence (approximately 1.96).

After calculating the interval estimate, we find that the confidence interval falls within one of the options provided. The correct interval estimate of the number of passengers expected to carry more than one piece of luggage on the plane, assuming it's full, would be (179.20, 212.716), which corresponds to option d.

Answer:

C

Step-by-step explanation:

A function is a special kind of relation in which each valid input gives exactly one output.

C {(22, 10), (23, 10), (24, 7), (25, 5)}

So C is the correct option.

Answer:

Step-by-step explanation:

1/2 3

Answer: Area of sector = 11.8 square meters

Step-by-step explanation:

The formula for determining the area of a sector is expressed as

Area of sector = θ/360 × πr²

Where

θ represents the central angle.

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

Radius, r = 3 m

θ = 150 degrees

Therefore,

Area of sector = 150/360 × 3.14 × 3²

Area of sector = 11.8 square meters rounded up to the nearest tenth.

Answer: 59106

Step-by-step explanation:

We would apply the formula for exponential decay which is expressed as

A = P(1 - r)^ t

Where

A represents the population after t years.

t represents the number of years.

P represents the initial population.

r represents rate of growth.

From the information given,

P = 60000

r = 0.1% = 0.1/100 = 0.001

t = 2015 - 2000 = 15 years

Therefore

A = 60000(1 - 0.001)^15

A = 60000(0.999)^15

A = 59106

The predicted population of Adams County in the year 2015 is calculated using the initial population and applying a yearly decrease of 0.1% over 15 years, resulting in approximately 59,106 residents.

The question involves calculating the predicted population of Adams County in the year 2015 based on a yearly decrease of 0.1% from the year 2000.

To find the population in 2015, we need to apply the percentage decrease for each year from 2000 to 2015, which is a total of 15 years. The formula to calculate the population after a certain number of years with a consistent percentage change is: [tex]P = P_0 (1 - r)^t[/tex] where P is the final population, P₀ is the initial population, r is the rate of decrease, and t is the number of years.

Using the given data, P0 = 60,000, r = 0.001 (0.1% expressed as a decimal), and t = 15 years.

So, the calculation will be: P = 60,000 (1 - 0.001)¹⁵ = 60,000 (0.999)¹⁵ = 60,000 (0.985075) ≈ 59,106

Therefore, the predicted population of Adams County in the year 2015 is approximately 59,106 residents.

Answer:

Step-by-step explanation:

Let x represent the total sales made in a year.

Employees at Driscoll's Electronics as a base salary plus a 20% Commission on their total sales for the year. If the base salary is $40,000, it means that if the employee makes a total sales of $x in a year, the total equation to represent earnings would be

0.2x + 40000

b) if Stewart wants to make $65,000 this year, it means that

0.2x + 40000 = 65000

0.2x = 65000 - 40000

0.2x = 25000

x = 25000/0.2

x = 125000

c) 52,000 + 0.3s = 82,000

The base salary is $52000

The percentage of commission from sales is 30%

Answer:

The answer to the question is

The probability of winning second prize (that is, picking five of the six winning numbers) with a 6/44 lottery, as played in Connecticut, Missouri, Oregon, and Virginia is 3.49905×10⁻⁵≡ 0.00003 to five decimal places.

Step-by-step explanation:

The probability of winning the second prize or picking five of the six winning numbers) with a 6/44 lottery is given by

Number of 5 sets of numbers in 44 = ₄₄C₅ = 1086008 ways

Number of 5 set of winning numbers in 44 = 1

Number of ways of picking the last number to make it 6 numbers is given by

44 - 5 lucky numbers - The 1 winning number = 38

Therefore, there are 38 ways from 1086008 of selecting the 5 second place winning numbers

Therefore the probability of picking the 5 second place winning numbers is [tex]\frac{38}{1086008}[/tex] = 3.49905×10⁻⁵

hope it helps you!!!!!

Answer:

(a)Area of the bedroom=96 square inches

(b)Area of the living room =144 square inches

(c)Area of the dollhouse that is not of the bedroom or living room =336 square inches.

Step-by-step explanation:

The area of the bedroom is 1/6 the area of the entire dollhouse

The area of the living room is 3/2 times the area of the bedroom.

The area of the entire dollhouse is 576 square inches

Let the area of bedroom=b

Let the area of living room=l

(a) The area of the bedroom is 1/6 the area of the entire dollhouse

[tex]b=\frac{1}{6}X576=96[/tex] square inches

(b)The area, in square inches, of the living room

The area of the living room is 3/2 times the area of the bedroom

l= [tex]\frac{3}{2}X96=144[/tex] square inches

(c)The total area of the house =576 square inches

Area of the bedroom=96 square inches

Area of the living room =144 square inches

Area of the dollhouse that is not of the bedroom or living room

=576-(96+144)=576-240=336 square inches.

The area of the living room is 3/2 times the area of the bedroom

This is gotten by subtracting the area of the bedroom and living room from the total area of the house.

Final answer:

To calculate John Worker's tax, we need to use the tax rate schedule. Assuming the taxable income is $31,000, we can refer to the tax rate schedule to determine the tax. If the tax rate for the income range $30,001 to $40,000 is 20%, then John Worker's tax would be 20% of his taxable income of $31,000, which equals $6,200.

Explanation:

To calculate John Worker's tax, we need to use the tax rate schedule. Assuming the taxable income is $31,000, we can refer to the tax rate schedule to determine the tax.

From the given information, we don't have the specific tax rate for $31,000. However, we can use the tax rates provided in the table to calculate the tax.

For example, if the tax rate for the income range $30,001 to $40,000 is 20%, then John Worker's tax would be 20% of his taxable income of $31,000, which equals $6,200.

Answer:

The center of the circle is (-2 , 3) ⇒ 3rd answer

Step-by-step explanation:

The equation of a circle is (x - h)² + (y - k)² = r², where

∵ The equation of the circle is x² + 4x + y² - 6y = 12

- Lets make a completing square for x² + 4x

∵ x² = (x)(x)

∵ 4x ÷ 2 = 2x

- That means the second term of the bracket (x + ...)² is 2

∴ The bracket is (x + 2)

∵ (x + 2)² = x² + 4x + 4

∴ We must add 4 and subtract 4 in the equation of the circle

∴ (x² + 4x + 4) - 4 + y² - 6y = 12

Lets make a completing square for y² - 6y

∵ y² = (y)(y)

∵ -6y ÷ 2 = -3y

- That means the second term of the bracket (y + ....) is -3

∴ The bracket is (y - 3)

∵ (y - 3)² = y² - 6y + 9

∴ We must add 9 and subtract 9 in the equation of the circle

∴ (x² + 4x + 4) - 4 + (y² - 6y + 9) - 9= 12

Now lets simplify the equation

∵ (x + 2)² + (y - 3)² - 13 = 12

- Add 13 to both sides

∴ (x + 2)² + (y - 3)² = 25

- Compare it with the form of the equation of the circle to

   find h and k

∵ (x - h)² + (y - k)² = r²

∴ h = -2 and k = 3

The center of the circle is (-2 , 3)

Answer:

The answer to your question is the last option

Step-by-step explanation:

Process

1.- To calculate the rate of change, calculate slope

Formula

             m = (y2 - y1) / (x2 - x1)

x1 = 1           y1 = 1200

x2 = 2         y2 = 2400

2.- Substitution

             m = (2400 - 1200) / (2 - 1)

3.- Simplification

             m = 1200 / 1

4.- Result

             m = 1200 meters / minute

Answer:

(d) 1200 Meters per minute

Step-by-step explanation:

Answer:

a) The approximate probability that more than 25 chips are defective is 0.1075.

b)  The approximate probability of having between 20 and 30 defecitve chips is 0.44.

Step-by-step explanation:

Lets call X the total amount of defective chips. X has Binomial distribution with  parameters n=1000, p =0.02. Using the Central Limit Theorem, we can compute approximate probabilities for X using a normal variable with equal mean and standard deviation.

The mean of X is np = 1000*0.2 = 20, and the standard deviation is √np(1-p) = √(20*0.98) = 4.427

We will work with a random variable Y with parameters μ=20, σ=4.427. We will take the standarization of Y, W, given by

[tex] W = \frac{Y-\mu}{\sigma} = \frac{Y-20}{4.427} [/tex]

The values of the cummmulative distribution function of the standard normal random variable W, which we will denote [tex] \phi [/tex] , can be found in the attached file. Now we can compute both probabilities. In order to avoid trouble with integer values, we will correct Y from continuity.

a)

[tex]P(X > 25) = P(X > 25.5) \approx P(Y>25.5) = P(\frac{Y-20}{4.427} > \frac{25.5-20}{4.427}) =\\P(W > 1.2423) = 1-\phi(1.2423) = 1-0.8925 = 0.1075[/tex]

Hence the approximate probability that more than 25 chips are defective is 0.1075.

b)

[tex]P(20<X<30) = P(20.5 < X < 29.5) \approx P(20.5<Y>29.5) = \\P(\frac{20.5-20}{4.427} < \frac{Y-20}{4.427} < \frac{29.5-20}{4.427}) = P(0.1129 < W < 2.14) = \phi(2.14)-\phi(0.1129) = \\0.9838-0.5438 = 0.44[/tex]

As a result, the approximate probability of having between 20 and 30 defecitve chips is 0.44.

Final answer:

To approximate the probabilities of defective chips where 2% are defective from a lot of 1000, the binomial distribution is used, with more complex probability calculations often requiring statistical software. Both (a) more than 25 defective and (b) between 20 and 30 defective scenarios can be estimated using normal approximation due to the large sample size and small defect probability.

Explanation:

To approximate the probability of defective chips in the scenario where 2% of the semiconductor chips produced are defective, we can use the binomial distribution as an approximation because the sample size is large (n=1000) and the probability of a defect (p=0.02) is small.

For part (a), more than 25 chips are defective, we are looking for P(X>25). The calculation for this is more complex and typically done using statistical software or a calculator with binomial capabilities.

For part (b), between 20 and 30 chips are defective, we need to find the probability that X is between 20 and 30 inclusively, or P(20 ≤ X ≤ 30). This requires calculating the cumulative probability for 20 through 30 and then subtracting the lower end from the higher end.

In real-world applications, as the number of trials is large and the probability of success is small, the binomial distribution can be approximated by a normal distribution. The mean (μ) of the distribution is np and the variance (σ2) is np(1-p), which would give us μ = 20 and σ2 = 19.6 for this example. We can then use the standard normal table or a calculator to find the probabilities for parts (a) and (b).

Answer:

x+2x+$3+$5=$1131

Step-by-step explanation:

Take students to be x then the adults be 2x and the dollars being played and the total money.Then you will take the $3+$8 and subtract from $1131 dollars then you'll get x

Answer: The system of equations that represent this situation is

x = 2y

5x + 3y = 1131

Step-by-step explanation:

Let x represent the number of adult tickets sold on the first night of the play.

Let y represent the number of student tickets sold on the first night of the play.

On the first night of the play, twice as many adults attended the play as students. This means that

x = 2y

Students tickets cost $3 and adults tickets cost $5. The total amount of money earned from tickets sales was $1,131. This means that

5x + 3y = 1131- - - - - - - - - 1

Answer: 0.206

Step-by-step explanation: the probability of employees that needs corrective shoes are =8%= 8/100 = 0.08

Probability of employees that needs major dental work = 15% = 15/100 = 0.15

Probability of employees that needs both corrective shoes and dental work = 3% = 3/100 = 0.03

The probability that an employee will need either corrective shoes or major dental work = (Probability an employee will need correct shoes and not need dental work) or (probability that an employee will need dental work or not corrective shoes)

Probability of employee not needing corrective shoes = 1 - 0.08 = 0.92

Probability of employee not needing dental work = 1 - 0.15 = 0.85

The probability that an employee will need either corrective shoes or major dental work = (0.08×0.85) + (0.15×0.92) = 0.068 + 0.138 = 0.206 = 20.6%

The probability that an employee will need either corrective shoes or dental work = 0.206.

Please note that the word "either" implies that we must choose one of the two options (corrective shoes or dental work) and not both.

The  probability that an employee selected at random will need either corrective shoes or major dental work is 0.206.

Since

The exams showed that 8% of the employees needed corrective shoes, 15% needed major dental work, and 3% needed both corrective shoes and major dental work.

So,

Probability of employee not needing corrective shoes should be

= 1 - 0.08

= 0.92

And,

Probability of employee not needing dental work should be

= 1 - 0.15

= 0.85

So final probability should be

= (0.08×0.85) + (0.15×0.92)

= 0.068 + 0.138 = 0.206

= 20.6%

hence, The  probability that an employee selected at random will need either corrective shoes or major dental work is 0.206.

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Answer:

[tex]t=\frac{70.1-65.2}{\frac{2.52}{\sqrt{30}}}=10.65[/tex]    

[tex]p_v =P(t_{(29)}>10.65)=7.76x10^{-12}[/tex]  

And the best conclusion for this case would be:

D. The p-value is less than 0.00001. There is sufficient data to reject the null hypothesis.

Step-by-step explanation:

Data given and notation  

[tex]\bar X=70.1[/tex] represent the sample mean

[tex]\sigma=2.52[/tex] represent the population standard deviation  

[tex]n=30[/tex] sample size  

[tex]\mu_o =65.2[/tex] represent the value that we want to test

[tex]\alpha[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is higher than 65.2, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 65.2[/tex]  

Alternative hypothesis:[tex]\mu > 65.2[/tex]  

If we analyze the size for the sample is = 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

[tex]t=\frac{70.1-65.2}{\frac{2.52}{\sqrt{30}}}=10.65[/tex]    

P-value

The first step is calculate the degrees of freedom, on this case:  

[tex]df=n-1=30-1=29[/tex]  

Since is a one side right tailed test the p value would be:  

[tex]p_v =P(t_{(29)}>10.65)=7.76x10^{-12}[/tex]  

And the best conclusion for this case would be:

D. The p-value is less than 0.00001. There is sufficient data to reject the null hypothesis.

The correct option is D. The p-value is less than [tex]0.00001.[/tex] There is sufficient data to reject the null hypothesis.

Hypotheses:

Null hypothesis [tex](\(H_0\)): \(\mu_1 = \mu_2\)[/tex] (the mean height of contemporary males is equal to the mean height of eighteenth-century males)

Alternative hypothesis [tex](\(H_1\)): \(\mu_1 > \mu_2\)[/tex] (the mean height of contemporary males is greater than the mean height of eighteenth-century males)

Given Data:

Sample mean for contemporary males [tex](\(\bar{x}_1\)) = 70.1 inches[/tex]

Sample standard deviation for contemporary males [tex](\(s_1\)) = 2.52 inches[/tex]

Sample size for contemporary males [tex](\(n_1\)) = 30[/tex]

Sample mean for eighteenth-century males [tex](\(\bar{x}_2\)) = 65.2 inches[/tex]

Sample standard deviation for eighteenth-century males [tex](\(s_2\)) = 3.51\ inches[/tex]

Sample size for eighteenth-century males [tex](\(n_2\)) = 30[/tex]

Test Statistic:

We use a two-sample t-test for the difference of means:

[tex]\[t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}\][/tex]

Substituting the given values:

[tex]\[t = \frac{70.1 - 65.2}{\sqrt{\frac{2.52^2}{30} + \frac{3.51^2}{30}}}\][/tex]

First, calculate the variances and their respective terms:

[tex]\[s_1^2 = 2.52^2 = 6.3504, \quad s_2^2 = 3.51^2 = 12.3201\][/tex]

[tex]\[\frac{s_1^2}{n_1} = \frac{6.3504}{30} = 0.21168, \quad \frac{s_2^2}{n_2} = \frac{12.3201}{30} = 0.41067\][/tex]

[tex]\[\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} = \sqrt{0.21168 + 0.41067} = \sqrt{0.62235} = 0.7889\][/tex]

Now calculate the t-value:

[tex]\[t = \frac{70.1 - 65.2}{0.7889} = \frac{4.9}{0.7889} = 6.21\][/tex]

Degrees of Freedom:

Since the sample sizes are the same, we can use the following approximation for degrees of freedom [tex]df[/tex]

[tex]\[df = n_1 + n_2 - 2 = 30 + 30 - 2 = 58\][/tex]

P-value:

Using a t-distribution table or a calculator for a one-tailed test with [tex]58[/tex] degrees of freedom, we find that a t-value of [tex]6.21[/tex] corresponds to a p-value much less than [tex]0.00001.[/tex]

Answer: the power required to do the same work in 1 hour is 30 j/h

Step-by-step explanation:

If two variables vary inversely, an increase in one of the variables causes a decrease in the other variable and vice versa.

The power P required to do a fixed amount of work varies inversely as the time t. If we introduce a constant of variation, k, the expression would be

P = k/t

If a power of 15 J/h is required to do a fixed amount of work in 2 hours, it means that

15 = k/2

k = 15 × 2 = 30

The equation becomes

P = 30/t

Therefore, the power required to do the same work in 1 hour is

P = 30/1 = 30 j/h

The quadratic function in vertex form is [tex]y=\frac{1}{2} (x-5)^{2}-2[/tex].

Solution:

The equation of a quadratic in  vertex form  is [tex]y=a(x-h)^{2}+k[/tex].

where  (h, k) are the coordinates of the vertex and "a"  is a multiplier.

Here (h, k) = (5, –2)

Substitute this in the vertex form.

[tex]y=a(x-5)^{2}+(-2)[/tex]

[tex]y=a(x-5)^{2}-2[/tex] – – – – (1)

Passes through the point (7, 0).

Here x = 7 and y = 0.

Substitute this in equation (1), we get

[tex]0=a(7-5)^{2}-2[/tex]

[tex]0=4a-2[/tex]

Add 2 on both sides.

2 = 4a

Divide 2 on both sides, we get

[tex]$a=\frac{1}{2}[/tex]

Substitute the value of a in equation (1),

[tex]$y=\frac{1}{2} (x-5)^{2}-2[/tex]

The quadratic function in vertex form is [tex]y=\frac{1}{2} (x-5)^{2}-2[/tex].

Answer:

There is no such point where the given curve has a tangent line with slope 2.

Step-by-step explanation:

We have been given a curve [tex]y=4x^3+7x-5[/tex]. We are asked to show that the given curve has no tangent line with slope 2.

First of all, we will find the derivative of given curve as shown below:

[tex]y'=\frac{d}{dx}(4x^3)+\frac{d}{dx}(7x)-\frac{d}{dx}(5)[/tex]

[tex]y'=4\cdot 3x^{3-1}+7x^{1-1}-0[/tex]

[tex]y'=12x^{2}+7x^{0}[/tex]

[tex]y'=12x^{2}+7(1)[/tex]

[tex]y'=12x^{2}+7[/tex]

We know that derivative represents slope of tangent line, so we will equate derivative of the given curve with 2 and solve for the point (x), where the slope of tangent line will be equal to 2 as:

[tex]12x^2+7=2[/tex]

[tex]12x^2+7-7=2-7[/tex]

[tex]12x^2=-5[/tex]

[tex]x^2=-\frac{5}{12}[/tex]

We know that square of any real number could never be negative, therefore, there is no such point where the given curve has a tangent line with slope 2.

Final answer:

The proof involves finding the derivative of the given curve y = 4x³ + 7x - 5, setting it equal to the desired slope (2), and showing that the resulting equation has no real solutions, proving that no tangent line with slope 2 exists for this curve.

Explanation:

The question is about proving that the curve y = 4x³ + 7x - 5 does not have any tangent line with slope 2. To do this, we first need to find the derivative of the curve, which gives us the slope of the tangent at any point (x). The derivative of y with respect to x is given by y' = 12x² + 7. To determine if a tangent with slope 2 exists, we set the derivative equal to 2 and solve for x: 12x² + 7 = 2.

Solving this equation gives us 12x² = -5, which has no real solution since the left side of the equation (a squared term) cannot be negative. This means there is no value of x for which the slope of the tangent (derivative) is equal to 2, proving that no such tangent line exists for the given curve.

Answer:

C) -5

Step-by-step explanation:

-1 4/5 x= 9.

Change the left side to an improper fraction

(5*1+4)/5 = 9/5

-9/5 x =9

Multiply each side by -5/9 to isolate x

-5/9 * 9/5x = 9 * (-5/9)

x = -5

Answer:

x=-5

Step-by-step explanation:

-1 4/5x=9

-9/5x=9

-9x=9*5

-9x=45

x=45/(-9)

x=-5

Answer:

8 headbands can be made.

Step-by-step explanation:

dividing both sides by 16.5, the material needed for one, leaves the equation as h=8, because 132 divided by 16.5 equals 8

Brinley can make 8 hands from the elastic she has.

What is the unitary method?

The unitary method is a method in which you find the value of a unit and then the value of a required number of units. Suppose you go to the market to purchase 6 apples. The shopkeeper tells you that he is selling 10 apples for Rs 100. In this case, the apples are the units, and the cost of the apples is the value.

Given here, A headband needs 16 and a half inches of elastic and Brinley has 132 inches of elastic

Therefore the number of headbands that she could make is

= 132/16.5

=8 Headbands.

Hence, Brinley can make 8 hands from the elastic she has.

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Answer:

D. 28

Step-by-step explanation:

If a distribution is negatively skewed, the mean of the distribution is always less than the median.

If the median of a negatively skewed distribution is 31, then from the given options, the only value that is less than 31 is 28.

Therefore the mean could be 28.

The correct answer is D

Answer:

Correct option: 3. Cluster Sampling.

Step-by-step explanation:

Cluster sampling method is the type of sampling where first the entire population is divided into groups and then a random sample of fixed size is selected from each group.

In this case also, the researcher first divides the population of students in Scion School of Business into groups according to their class standing.

Then he selects 50 students from each of these groups to create a representative sample of the entire student body.

Thus, the sampling method used is Cluster Sampling.

Answer:

A.

Step-by-step explanation:

The problem states that -3 is our y-intercept, so (0,-3) must be one of the answer choices. Next, just graph the equation to find the other two coordinate pairs are (1,-1) and (2,1).

Answer:

Correct option is b. Procedure results in a binomial distribution.

Step-by-step explanation:

Consider that X is Binomial random variable. The properties that are satisfied by X are:

Suppose a roulette wheel is spun and the number of times the ball lands on '16' is observed.

If the random variable X is defined as the number of times the ball lands on '16', then the random variable X follows a Binomial distribution.

Because,

Thus, the correct option is b. Procedure results in a binomial distribution.

Answer:

The correct option is

d) (179.20, 212.716)

Step-by-step explanation:

We have out of a random sample of 1000, 345 carried more than a bag

Therefore in the question our X = 345 passengers carry more than a piece of luggage

n = 1000

Therefore the probability of a passenger carrying more than one luggage = 345/1000 = 0.345

The confidence interval estimator of p is given by

[tex]p'+/-z_{\alpha/2}\sqrt{\frac{p'(1-p')}{n} }[/tex] where p' = 0.345 = probability of desired outcome

n = 1000 = Population size

z at 95 %   = Confidence interval estimate, the value is sought from the distribution table as z value is 1.96 at 95 % confidence level

We have  [tex]0.345+/-1.96\sqrt{\frac{0.345*(0.655)}{1000} }[/tex] which gives

0.3745 or 0.3155

Which gives the range of confidential interval estimate as

212.695 to 179.224 which is equivalent to

d) (179.20, 212.716).

To determine the interval estimate of the number of passengers carrying more than one piece of luggage on the plane, we use the formula for the confidence interval for a proportion. The interval estimate is (0.3132, 0.3768), so we can expect the number to be between 313 and 377 passengers.

To determine the interval estimate of the number of passengers that you would expect to carry more than one piece of luggage on the plane, we can use the formula for the confidence interval for a proportion. First, we calculate the sample proportion of passengers carrying more than one bag, which is 345/1000 = 0.345. Then, we find the standard error using SE = sqrt(p(1-p)/n), where p is the sample proportion and n is the sample size. Substituting the values, we get SE = sqrt(0.345(1-0.345)/1000) = 0.0162.

Next, we find the margin of error by multiplying the standard error by the critical value for the desired level of confidence. Since the problem does not specify a level of confidence, we will use a 95% confidence level, which corresponds to a critical value of 1.96. The margin of error is therefore 1.96 * 0.0162 = 0.0318.

Finally, we construct the confidence interval by subtracting and adding the margin of error from the sample proportion. The interval estimate is given by (0.345 - 0.0318, 0.345 + 0.0318), which simplifies to (0.3132, 0.3768). Therefore, we can expect the number of passengers carrying more than one piece of luggage on the plane to be between 313 and 377.

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The swimmer will travel a distance of 55.92 meters when swimming from one corner to the opposite corner of an Olympic-size swimming pool.

Given, the length and width of the pool form the two sides of the right-angled triangle, and the distance the swimmer will travel is the hypotenuse.

Using the Pythagorean theorem, we can calculate the distance as follows:

Distance² = Length² + Width²

Distance² = 50² + 25²

Distance² = 2500 + 625

Distance² = 3125

Distance = √3125

Distance = 55.90 meters

Therefore, a swimmer will travel approximately 55.92 meters.

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Final answer:

To determine the distance a swimmer travels across an Olympic-sized pool from corner to opposite, the Pythagorean theorem is used, giving approximately 55.90 meters as the distance.

Explanation:

The student's question entails calculating distances and speeds in different swimming and water current scenarios, which is a classic physics problem involving kinematics and geometry. However, since it involves calculations and applying formulae, particularly the Pythagorean theorem, and rate, time, and distance relationships, it falls under the subject of Mathematics.

To Calculate the Distance Swum Across an Olympic-sized Pool

For an Olympic-sized pool that is 50 meters in length and 25 meters in width, a swimmer traveling from one corner to the opposite would traverse a diagonal. To calculate this diagonal distance, we use the Pythagorean theorem:

Diagonal2 = Length2 + Width2

Diagonal = √(Length2 + Width2)

Substitute the given values:

Diagonal = √(502 + 252) = √(2500 + 625)

Diagonal = √(3125) meters

The swimmer will travel approximately √(3125) meters, which is about 55.90 meters.