there or 5 consecutive odd integers. the sum of 3 smallest is 3 more than the sum of the 2 largest, find the integers.

PLEASE HELP ASAP!

The degrees of freedom for a chi-square goodness-of-fit test are calculated as the number of categories minus 1.

Suppose we wish to determine if an ordinary-looking six-sided die is fair, or balanced, meaning that each face has a probability of 1/6

of arrival on top when the die is tossed. We could toss the die dozens, maybe hundreds, of times and compare the actual number of times each face arrival on top to the scheduled number, which would be 1/6

of the total number of tosses. We would not expect each number to be exactly 1/6 of the total, but it should be close.

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Answer:

Confidence Level z*-value

90% 1.645 (by convention)

95% 1.96

98% 2.33

99% 2.58

Step-by-step explanation:

the difference in sample means is 0.1, and the upper end of the confidence interval is 0.1 + 0.1085 = 0.2085 while the lower end is 0.1 – 0.1085 = –0.0085.

Answer:

Step-by-step explanation:

perp. -1/3

y + 4 = -1/3(x - 3)

y + 4 = -1/3x + 1

y = -1/3x - 3

The total number of possible outcomes containing exactly 3 heads when a coin is flipped eight times where each flip comes up either heads or tails are 56.

There are two possible outcomes i.e. heads and tails when a coin is flipped. If the coin is flipped 8 times, the total number of outcomes will be:-

\(2^8=256\)

We need exactly 3 heads , and hence exactly 5 tails, like

H H H T T T T T

Here H represents heads and T represents tails.

But H and T can come in any combination, for example:-

H T H H T T T T

Hence, total possible outcomes containing exactly 3 heads and 5 tails will be determined using the combinations formula :-

\(^{8}C_{3}=\frac{8!}{3!5!}=\frac{8*7*6*5!}{3*2*5!}=8*7=56\)

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Yes it is correct that the expected value of a random variable can be interpreted as a long-run average.

The expected value of a random variable is a concept used in probability theory and statistics. It is a way to summarize the average behavior or central tendency of the random variable.

To understand why the expected value represents the average value that the random variable would take in the long run, consider a simple example. Let's say we have a fair six-sided die, and we want to find the expected value of the outcomes when rolling the die.

The possible outcomes when rolling the die are numbers from 1 to 6, each with a probability of 1/6. The expected value is calculated by multiplying each outcome by its corresponding probability and summing them up.

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Answer:

Step-by-step explanation:

Given

To find

Solution

Answer: 20

The equation for the price of house after x years is,

Simplify the equation to obtain the equation for value of house after x years.

So option B is correct.

The z score that separate the middle 56% of the distribution from the area in the tails of the standard normal distribution is ±0.77.

Given that the z score separates the 56% of the distribution from the area in the tails of the standard normal distribution.

In a normal distribution in with mean μ and standard deviation σ, the z score of a measure X is as under:

Z=(X-μ)/σ

It is used to measure how many standard deviations the measure is from the mean.

After finding the z score we have to look at the z score table and find the p value associated with this z score, which is the percentile of X.

The normal distribution is symmetric which means that the middle 56% is between the 11th and 67th percentile. Looking at the z table the z scores are Z=±0.77.

Hence the z score that separate the middle 56% of the distribution from the area in the tails of the standard normal distribution is ±0.77.

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The probability of machine A breaking down in a year is 0.05.

The probability that neither machine breaks down in a 10-year period is approximately 0.605.



a) Since the probability of both machines breaking down is the product of their individual probabilities, we have:

P(A and B) = P(A) * P(B) = x * 0.01 = 0.0005

Solving for x, we divide both sides of the equation by 0.01:

x = 0.0005 / 0.01 = 0.05

Therefore, the probability that machine A breaks down in any given year is 0.05.

b) The probability that neither machine breaks down in a given year is the complement of the probability that either one or both machines break down. Since the events are independent, we can multiply the probabilities:

P(Neither A nor B breaks down) = P(A' and B') = P(A') * P(B') = (1 - 0.05) * (1 - 0.01)

To calculate the probability over a 10-year period, we raise the result to the power of 10:

P(Neither machine breaks down in a 10-year period) = (1 - 0.05) * (1 - 0.01)^10 ≈ 0.605

Therefore, the probability that neither machine will break down in a 10-year period is approximately 0.605.

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The probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours is approximately 0.9564, or 95.64%.

To find the probability that the average number of hours of overtime worked by a random sample of 140 employees exceeds 20 hours, we can use the Central Limit Theorem (CLT). The CLT states that for a large enough sample size, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution.

Given that the population mean is 18.9 hours and the population standard deviation is 7.8 hours, we can calculate the standard error of the mean using the formula: standard error = population standard deviation / sqrt(sample size).

For this problem, the sample size is 140, so the standard error is 7.8 / sqrt(140) ≈ 0.659.

To calculate the probability, we need to standardize the sample mean using the z-score formula: z = (sample mean - population mean) / standard error.

In this case, the sample mean is 20 hours, the population mean is 18.9 hours, and the standard error is 0.659. Plugging these values into the formula, we get z = (20 - 18.9) / 0.659 ≈ 1.71.

Now, we can use a standard normal distribution table or calculator to find the probability associated with a z-score of 1.71. Looking up this value in the table, we find that the probability is approximately 0.9564.

Therefore, the probability that the average number of hours of overtime worked last month by a random sample of 140 employees in the city exceeds 20 hours is approximately 0.9564, or 95.64%.

Here's a sketch to visualize the calculation:

                  |

                  |

                  |

                  |       **

                  |      *  *

                  |     *    *

                  |    *      *

                  |   *        *

                  |  *          *

                  | *            *

-------------------|--------------------------

      18.9        |       20

The area under the curve to the right of 20 represents the probability we're interested in, which is approximately 0.9564 or 95.64%.

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5/x = x/ 9

Cross-multiply

x² =45

Take the square root of both-side

x = 3√5 or 6.7082039325

Answer:

l is 6/10 w is 4/10

Step-by-step explanation:

width = 2/3 length and perimeter = 2l +2w which is 2ft you can sub w for 2/3l 2l + 2(2/3l) =2 so 6/3l +4/3l =2 10/3l =2 10l = 6 l = 6/10 w = 2/3l 2/3(6/10) is 4/10

\(\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}\)

Actually Welcome to the Concept of the areas.

Let the length be x and width be y, hence we get the relation as,

2(l+b) = perimeter, here l=x and b =y

2(x+y) = 2 feet, but since y = 2/3x

so we get as,

2(x+(2/3)*x)= 2 ft

===> 2x + (4/3)*x = 2 ft

===> taking the lcm

===> 6x + 4x = 6 ft

===> x = 6/10 = 0.6 ft

so x = 0.6 ft and y = (2/3)*(6/10) = 2/5 ft

hence, x = 3/5 feet and y = 2/5 feet

Answer:

VII

Step-by-step explanation:

The effective interest rate of the loan would be

In this case, we are given 4 options:

The formula of compounded interest rate is:

\(A = P (1+\frac{r}{n})^{nt}\)

Where:

A = amount, P = principal amount, r = interest rate, n = number of times interest rate compounded, t = time

Let’s assume the principal amount is $100 for 1 year

Loan L =

\(A = 100 (1+\frac{0.08254}{356})^{356x1}\)

A = $108.603

Loan M =

\(A = 100 (1+\frac{0.08474}{52})^{52x1}\)

A = $108.834

Loan N =

\(A = 100 (1+\frac{0.08533}{12})^{12x1}\)

A = $108.875

Loan O =

\(A = 100 (1+\frac{0.08604}{1})^{1x1}\)

A = $108.604

Therefore, the best effective interest rate for Craig is Loan L with nominal rate of 8.254% compounded daily.

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Answer:

x = 8√3

Step-by-step explanation:

The sampling variance of Spencer's estimator can be calculated using the formula for the variance of the sum or difference of two random variables.

In this case, Spencer's estimator is the average weight of the first and last apple, denoted as (X1 + Xn)/2.

The variance of the sum or difference of two independent random variables is the sum of their individual variances. Since the weights of the apples are independently distributed with mean µ and variance σ^2, the variance of each apple weight is σ^2.

To find the sampling variance of Spencer's estimator, we need to find the variance of (X1 + Xn)/2. Using the formula for variance, we can simplify the calculation as follows:

Var[(X1 + Xn)/2] = (1/4) * Var(X1 + Xn)

Since X1 and Xn are independent, the variance of their sum is the sum of their individual variances:

Var(X1 + Xn) = Var(X1) + Var(Xn) = 2σ^2

Plugging this back into the previous equation, we get:

Var[(X1 + Xn)/2] = (1/4) * 2σ^2 = σ^2/2

Therefore, the sampling variance of Spencer's estimator is σ^2/2.

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Answer:

y = 15

Step-by-step explanation:

y varies directly as x.

⇒y = kx where k is a constant.

find k:

when x = 4, y = 5

5 = k(4)

5 = 4k

k = 5/4

plug k into the equation:

y = 5/4 k

find y when x = 12:

when x = 12:

y= 5/4(12)

y = 5(3)

y = 15

The probability that a randomly selected home in Queens has 4 or more computers is 0.1 or 10%. The correct answer is (b) 0.10.

The given probability distribution table shows the probabilities of having 1, 2, or 3 computers in a randomly selected home in Queens. However, the probability of having 4 or more computers is not given in the table.

To find the probability of having 4 or more computers in a randomly selected home, we can use the complement rule. The complement rule states that the probability of an event happening is equal to 1 minus the probability of the event not happening. In this case, the event we are interested in is having 4 or more computers in a home, and the complement of this event is having 1, 2, or 3 computers in a home.

So, the probability of having 4 or more computers in a randomly selected home in Queens can be calculated as:

P(4 or more) = 1 - P(1 or 2 or 3)

P(1 or 2 or 3) = P(1) + P(2) + P(3) = 0.4 + 0.3 + 0.2 = 0.9

P(4 or more) = 1 - 0.9 = 0.1

Therefore, the probability that a randomly selected home in Queens has 4 or more computers is 0.1 or 10%. The correct answer is (b) 0.10.

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Answer:

60 mph

Step-by-step explanation:

Let 'S' be the velocity of the southbound car and 'E' be the velocity of the eastbound car. The distances traveled by each car are:

\(D_E=3E\\D_S=3S=3(E+15)\\D_S=3E+45\)

The distance between both cars is given by:

\(D^2=D_S^2+D_E^2\\225^2=(3E+45)^2+(3E)^2\\50,625=9E^2+270E+9E^2+2,025\\18E^2+270E-48,600=0\\\)

Solving the quadratic equation for the velocity of the eastbound car:

\(18E^2+270E-48,600=0\\E^2+15E-2,700\\E=\frac{-15\pm\sqrt{15^2-4*1*(-2,700)}}{2}\\E=45.0\ mph\)

The velocity of the southbound car is:

\(S=E+15=45+15\\S=60\ mph\)

The southbound car is driving at 60 mph.

Answer:

Total amount of investment = $1,531.51

Step-by-step explanation:

A = P(1+r/n)^(nt)

I don't see the picture. Can you send it in the message.

Answer:

385

Step-by-step explanation:

Answer:

The lines are straight the lines are at a 385 angle

Step-by-step explanation:

The reason they are straight lines is they are at a perfectly straight not curving to the side or bending like E and F how they have a 45 dgree angle I assume.

I not really sure if its right but umm if I am I hope this helps you out.

To find σg(X)^2, we need to calculate the variance of the function g(X) = 4X^2 + 2, where X is a random variable with a given density function. The density function is defined as f(x) = (3/2)(x + 1) for 0 ≤ x and 0 elsewhere. By calculating the variance of g(X), we can determine the value of σg(X)^2.

To calculate the variance of g(X), we first need to find the mean of g(X), denoted as E[g(X)]. For a continuous random variable, the mean is calculated as the integral of the function multiplied by the density function. In this case, we have:

E[g(X)] = ∫(4X^2 + 2) * f(x) dx

Substituting the given density function, we have:

E[g(X)] = ∫(4X^2 + 2) * (3/2)(X + 1) dx

After simplifying and evaluating the integral, we can find the value of E[g(X)].

Next, we calculate the variance of g(X), denoted as Var[g(X)]. The variance is calculated as the expectation of the squared difference between g(X) and its mean, E[g(X)]^2. In mathematical terms:

Var[g(X)] = E[(g(X) - E[g(X)])^2]

By substituting the values of g(X) and E[g(X)], we can evaluate this expression and find the value of Var[g(X)].

Finally, to find σg(X)^2, we take the square root of Var[g(X)], i.e., σg(X) = √Var[g(X)]. After calculating Var[g(X)], we can determine the value of σg(X) to three decimal places as needed.

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Answer:

Step-by-step explanation:

you can complete the square or use a calculator online that does it for you.

the equation is in the for y = a(x-h)^2 + k

it should be y = (x + 3)^2 + 3

Answer:

The correct answer is \(y = - (x - 3)^{2} +21\).

Step-by-step explanation:

To solve this equation (y = \(-x^{2} +6x + 12\)), we want to first complete the square. To do this, we want to add a -9 to the expression in order to achieve \(y = -x^{2} +6x - 9 + 12\).

Then, you want to add the -9 to the other side of the equation to get \(y - 9 = -x^{2} + 6x - 9 + 12\).

Then, we factor out the negative sign from the right side of the equation. This is a negative 1 that can therefore make the polynomial easier to factor. This leaves us with \(y - 9 = -(x^{2} -6x+9) + 12\).

Now, we use an identity in algebra that is difference of two squares identity. This says that \(a^{2} -2ab +b^{2} =(a-b)^{2}\).

So, we will then factor the trinomial -\(x^{2} -6x+9\) to get \(-(x-3)^{2}\). Our new and updated equation is \(y-9 = -(x-3)^{2} +12\).

Now, we move the constant of -9 to the right side of the equation. This just means we are going to add this to 12. This gives us \(y = -(x-3)^{2} +21\).

This is our final equation.

Answer:

x=12

Step-by-step explanation:

turn into and equation because angles in a triangle add up to 180°

so

6x-19+3x+7+84=180

collect like terms

9x+72=180

solve to find 'x'

9x=108

x=12

Therefore , the solution of the given problem of standard deviation comes out to be the CEO is informed that the mean scores for Cities A and B are identical.

Variance is a measure of difference used in statistics. The typical variance here between dataset and the mean is calculated using the multiplier of that figure. By comparing each figure to the mean, it incorporates those data points into its calculations, unlike other measurable measures of variability. Variations may result from internal or external factors and may include unintentional errors, inflated expectations, and changing economic or commercial circumstances.

Here,

It is clear that both offices share a comparable average score from the sentence "The CEO is informed that both City A or City B have the same mean score."

If City A is more reliable than City B, then City A will have a lower standard deviation.

A collection of data's variability or dispersion is measured by the standard deviation. The closer the data points are to the mean, the lower the standard deviation, and the less variable the data are.

So, the appropriate answer is:

The CEO is informed that the mean scores for Cities A and B are identical. However, due to the fact that City A's standard deviation is lower than City B's, City A is more reliable than City B.

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The answer is: x-component of vector = 5.0 cm/s, y-component of vector = 0 cm/s.

The given vector v has an x-component of 5.0 cm/s and a y-component in the negative x-direction. Since the y-component is in the negative x-direction, it means the y-component is negative and has the same magnitude as the x-component.

Given vector v = (5.0 cm/s, −x-direction).

The vector is having magnitude 5.0 cm/s along the negative x-direction.

x-component of vector = 5.0 cm/s (magnitude of vector)v and y-component of vector is 0 since there is no component of v along y-axis.

Therefore, the x- and y-components of the vector v are 5.0 cm/s and 0 cm/s respectively.

Hence, the answer is: x-component of vector = 5.0 cm/s, y-component of vector = 0 cm/s.

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The distance over which the power carried by the wave is reduced by 7.4 dB is approximately 0.4214 meters.

To determine the distance over which the power carried by the wave is reduced by 7.4 dB, we need to use the logarithmic formula for decibel (dB) calculations.

The decibel scale is logarithmic, and the relationship between power ratios and decibels is given by the formula:

dB = 10 * log10(P2 / P1)

where dB is the decibel value, P2 is the final power, and P1 is the initial power.

In this case, the power reduction is given as 7.4 dB. We can rearrange the formula to solve for the power ratio:

P2 / P1 = 10^(dB / 10)

Substituting the given dB value into the formula:

P2 / P1 = 10^(7.4 / 10)

Calculating the power ratio:

P2 / P1 ≈ 5.623

The power ratio is approximately 5.623.

Now, we know that power is inversely proportional to the square of the distance. So, we can write the power ratio as a distance ratio:

(D2 / D1)^2 = P1 / P2

Substituting the power ratio value:

(D2 / D1)^2 = 1 / 5.623

Simplifying:

(D2 / D1)^2 ≈ 0.1778

Taking the square root of both sides:

D2 / D1 ≈ √(0.1778)

D2 / D1 ≈ 0.4214

Now, we can solve for the distance ratio (D2 / D1):

D2 / D1 = 0.4214

To find the distance over which the power is reduced by 7.4 dB, we need to find D2 when D1 is known. Let's assume D1 is 1 meter.

D2 = D1 * (D2 / D1)

= 1 * 0.4214

≈ 0.4214 meters

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