Go, Paul is thinking of a number he say that the sum of the number 8×3/4 is equal to -12, which equation can be used to find gold Paul’s number?

Answer:

\(x=18,\:y=6\)

Step-by-step explanation:

Solve by substitution

\(\begin{bmatrix}x+y=24\\ 75x+60y=1710\end{bmatrix}\)

\(\mathrm{Substitute\:}x=24-y\)

\(\begin{bmatrix}75\left(24-y\right)+60y=1710\end{bmatrix}\)

\(\begin{bmatrix}1800-15y=1710\end{bmatrix}\)

\(\mathrm{For\:}x=24-y\)

\(\mathrm{Substitute\:}y=6\)

\(x=24-6\)

\(x=18\)

\(\mathrm{The\:solutions\:to\:the\:system\:of\:equations\:are:}\)

\(x=18,\:y=6\)

Answer:

-11, 4, and 22

Step-by-step explanation:

Expression: 3b-5

when b=-2

Expression: 3(-2)-5=-11

When b=3

Expre; 3(3)-5=4

When b=9

Expre; 3(9)-5=22

Answer:

.........................................

Step-by-step explanation:

.............................................................................................................................................................................................

In the game described, two players take turns playing. Initially, a positive integer n is written on the blackboard. However, without further information about the rules or objectives of the game, it is not possible to provide a detailed explanation or analysis.

To provide a comprehensive explanation or analysis of the game, we need more information about the rules, objectives, and the specific actions that players can take during their turns. This could include details about the possible moves, winning conditions, or any strategic considerations.

The nature of the game and the outcome of each turn would determine the strategies and tactics players employ. Without these specifics, it is not possible to provide a meaningful explanation of the game or analyze its dynamics.

If you could provide more information about the rules or objectives of the game, I would be glad to assist you in understanding and analyzing the game further.

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In a two-tailed test, the null hypothesis should be rejected when the test value falls into either of the two critical regions.

A two-tailed test is used when we are interested in determining if there is a significant difference between the sample data and the hypothesized population parameter in either direction. It allows for the possibility of a difference in either direction, rather than focusing on a specific direction of difference.

When conducting a hypothesis test, we set up the null hypothesis (H0) and the alternative hypothesis (Ha). The null hypothesis represents the status quo or the hypothesis of no difference, while the alternative hypothesis represents the hypothesis we are testing for a significant difference.

In a two-tailed test, we divide the significance level (α) equally between the two critical regions, which are the rejection regions. These regions are located in both tails of the distribution. The critical values that define these regions are determined based on the desired level of significance and the distribution of the test statistic.

If the calculated test statistic falls into either of the two critical regions, it means that the observed data is statistically significant and we reject the null hypothesis. This suggests that there is evidence to support the alternative hypothesis and that there is a significant difference between the sample data and the hypothesized population parameter, regardless of the direction of the difference.

In summary, in a two-tailed test, the null hypothesis should be rejected when the test value is in either of the two critical regions, indicating a statistically significant difference between the sample data and the hypothesized population parameter.

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As per the given question, based on performance and z-scores, Barney scored better than Fred.

To determine who scored better between Fred and Barney, it is required to compare their scores with respect to rest of the class. This can be done by calculating their z-scores.

Determining the score for Fred:

z-score = (x - μ) / σ

= (71 - 81) / 5

= -10/5

= -2

Determining the score for Barney:

z-score = (x - μ) / σ

= (84 - 95) / 8

= -11/8

= -1.375

Both z-scores are negative because both scores fall below the means of their respective classes. Although Barney's z-score of -1.375 is closer to the mean than Fred's z-score of -2.

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An observational study would be the most appropriate type of study to compare lawyer salaries to doctors' salaries.

When comparing lawyer salaries to doctors' salaries, conducting an observational study would be the most appropriate approach. An observational study involves observing and analyzing existing data without any intervention or manipulation of variables. In this case, researchers would collect salary data from a representative sample of lawyers and doctors and analyze the differences between the two groups.

Conducting an experiment without blinding, experiment with single blinding, or experiment with double blinding would not be suitable for this question. Blinding refers to the process of concealing information about the intervention or treatment from the participants or researchers to reduce bias. Since the question involves comparing salaries, there is no direct intervention or treatment that can be manipulated, making blinding unnecessary.

A case-control study would also not be appropriate for this question. A case-control study is typically used to investigate the association between an outcome (case) and potential risk factors (control). In the case of lawyer salaries versus doctors' salaries, there is no specific outcome or risk factor to compare; rather, the focus is on comparing the salaries themselves.

Therefore, an observational study would be the most suitable approach to compare lawyer salaries to doctors' salaries, as it allows for the collection and analysis of existing data without the need for manipulation or blinding.

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Answer:

-5/2

Step-by-step explanation:

Find the coordinates of the two points

(1,4) and (3,-1)

We can use the slope formula

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

   = (-1-4)/(3-1)

   = -5/2

Answer:

both answers are BMobile

Answer:

MyTalk has a lower monthly cost. Based on the graph it seems to be about $25 a month.

MyTalk has a lower cost after 4 months. If you look at the graph, 4 months costs $130 whereas BMobile costs $170 after 4 months.

Answer:

3 Pounds

Step-by-step explanation:

If 1 slice of pie = 8 ounces that means that 6 slices would be 48 ounces because of 6 slices * 8 ounces. Now we have to take the 48 ounces and divide them by 16 because 16 ounces = 1 pound. And in doing so, 6 slices would = 3 Pounds.

A. True

B. True

C. True

D. False

A. In a randomized block design, each block is a group of experimental units that are similar with respect to some known characteristic. Each block is randomly assigned to one treatment to reduce variability within blocks.

B. In a completely randomized experimental design ANOVA procedure, the MSE (mean square error) represents the within-treatment estimate of population variance. The MSE is a measure of the variability of the data within each treatment group.

C. For full factorial experimental design ANOVA procedure, the f-statistic can be calculated by taking the mean square due to treatments divided by the mean square due to error. The f-statistic is used to test whether the treatments have a significant effect on the response variable.

D. Randomization is the process of assigning the treatments to the experimental units in a random and unbiased manner to minimize the effect of extraneous variables. The goal of randomization is to ensure that the differences between the treatment groups are due to the treatments themselves and not to any systematic differences between the groups. Therefore, the statement that randomization is the process of assigning the treatments to the experimental units in a systematic or subjective basis is false.

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Answer:

positive

Step-by-step explanation:

because that's how math works

Kayla would have approximately $554.93 in the account after 12 years, rounded to the nearest dollar.

Learn more about To calculate the amount Kayla would have in the account after 12 years, we can use the formula for compound interest:

A = P * (1 + r/n)^(n*t)

Where:

A = the final amount

P = the principal amount (initial deposit)

r = the annual interest rate (in decimal form)

n = the number of times interest is compounded per year

t = the number of years

In this case, Kayla deposits $380 every quarter, so the principal amount (P) is $380. The annual interest rate (r) is 3.3% or 0.033 as a decimal. The interest is compounded quarterly, so n = 4. The number of years (t) is 12.

Plugging these values into the formula:

A = $380 * (1 + 0.033/4)^(4*12)

Calculating the exponent:

A = $380 * (1 + 0.00825)^(48)

A = $380 * (1.00825)^(48)

Using a calculator, we can calculate the value of (1.00825)^(48) ≈ 1.464096

A = $380 * 1.464096

A ≈ $554.93

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The first 3 terms of the sequence are 21, 24 and 29

From the question, we have the following parameters that can be used in our computation:

n² + 20

This means that

f(n) = n² + 20

The first 3 terms of the sequence is when n = 1, 2 and 3

So, we have

f(1) = 1² + 20 = 21

f(2) = 2² + 20 = 24

f(3) = 3² + 20 = 29

Hence, the first 3 terms of the sequence are 21, 24 and 29

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The largest even number that cannot be expressed as the sum of two composite numbers is 38.

A composite number is a number that has more than two factors, including 1 and itself. A prime number is a number that has exactly two factors, 1 and itself.

If we consider all even numbers greater than 2, we can see that any even number greater than 38 can be expressed as the sum of two composite numbers. For example, 40 = 9 + 31, 42 = 15 + 27, and so on.

However, 38 cannot be expressed as the sum of two composite numbers. This is because the smallest composite number greater than 19 is 25, and 38 - 25 = 13, which is prime.

Therefore, 38 is the largest even number that cannot be expressed as the sum of two composite numbers.

Here is a more detailed explanation of why 38 cannot be expressed as the sum of two composite numbers.

The smallest composite number greater than 19 is 25. If we try to express 38 as the sum of two composite numbers, one of the numbers must be 25. However, if we subtract 25 from 38, we get 13, which is prime. This means that 38 cannot be expressed as the sum of two composite numbers.

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When each data value in one sample is matched with a corresponding data value in another sample, the samples are known as paired samples.

Paired samples are a type of experimental design in which two sets of data are compared for a given set of variables.

The term “paired” refers to the fact that each data point in one set corresponds to a specific data point in the other set.

Paired samples are a statistical method that is used to compare two groups of data.

Each set of data must be obtained from a single source.

A paired sample is where each observation in one group is matched with an observation in the other group.

This is a statistical technique that is frequently used in experimental research to measure the effect of a treatment on a particular group.

An example of a paired sample is when the same set of people are tested twice to determine the effect of a drug.

The first test is performed before the drug is administered, and the second test is performed after the drug has been administered.

The results of the two tests are then compared to determine the effect of the drug on the group of people.

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1. Find the volume of the solid obtained by rotating the region enclosed by the curves y=21−x,y=9x+11 and x=−1 about the x-axis.

The region enclosed by the curves y=21−x,y=9x+11 and x=−1 is as follows:

Solid is obtained by rotating the region enclosed by the curves y=21−x,y=9x+11 and x=−1 about the x-axis is as follows:Let us express y=21−x and y=9x+11 in terms of x, to calculate the volume as follows:

y=21−xy=9x+11

∴ x=21−yx−1119−y94−y

Now, we can write as below:

VolumeV=∫−111π[R(y)]2dy,where R(y) is the radius of the cross-section at a distance y from the axis of rotation.Now, let us consider y=0 as the axis of rotation. Then we have, y=0 to y=10. The radius of the cross-section R(y) is the distance between the axis of rotation and the curve (solid region). So, we can write R(y)=21−x−(9x+11)=10−10x−1.Therefore, the volume of the solid is as follows:

V=∫0^10π[10−10x−1]2dy

=π∫0^10100−40xy+x2dy

=π[100y−20y2+13y3]0^10

=π[0]=0

Volume of the solid obtained by rotating the region enclosed by the curves y=21−x,y=9x+11 and x=−1 about the x-axis is 0 cubic units.

Then we have, x=2 to x=6, as the radius of the cross-section R(x) is the distance between the line x=6 and the curve (solid region). So, we can write R(x)=6−x.

The volume of the solid generated by revolving the region bounded by the graphs of the equations y=6−x, y=0, and x=2 about the line x=6 is as follows:

VolumeV=∫26π[6−x]2dx

=π∫26(x2−12x+36)dx

=π[1/3x3−6x2+36x]26

=π[128/3]=40π/3 cubic units.

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Answer: 19.6 feet

Step-by-step explanation:

Using the Pythagorean theorem,

\(x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6\)

The linear function that can be used to find the amount in dollars Luis can spend on entertainment is given by:

f(x) = (x - 35)/6.

A linear function is modeled by:

y = mx + b

In which:

In this problem:

Hence, the function is given by:

f(x) = (x - 35)/6.

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The identities among the given statements are:

tan x = sin x / cos x

sin x / tan x = cos x

We have,

Let's analyze each of the given statements to determine whether they are identities:

tan x = sin x / cos x:

This is an identity.

It is known as the fundamental identity of trigonometry, as it holds true for all values of x (except when cos x is equal to 0).

tan x cos x = sin x:

This is not an identity.

It is a specific equation that may be true for certain values of x, but it does not hold true for all values of x.

cos x = tan x sin x:

This is not an identity.

Similar to the previous statement, it is a specific equation that may be true for certain values of x, but it does not hold true for all values of x.

sin x / tan x = cos x:

This is an identity.

It can be derived from the fundamental identity by dividing both sides by cos x, resulting in sin x / cos x = cos x / cos x, which simplifies to sin x / tan x = cos x.

Thus,

The identities among the given statements are:

tan x = sin x / cos x

sin x / tan x = cos x

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Answer:

c is the correct answer

The probability of choosing the biased coin if you won a prize is 22/27 or 0.30556

What is probability?

The probability of any coin chose is 1/2.

Probability if biased chosen and win is 1/2(1-0.78).

The probability of win 1/2 (1-0.78) + 1/2 (1-0.5)

Therefore,

P(biased/win) = P(biased ∩ win) / P(win)

= 1/2(1-0.78) / [ 1/2 (1-0.78) + 1/2 (1-0.5) ]

= 1/2(0.22) / [ 1/2(0.22) +1/2(0.5) ]

= 22/27

= 0.30556

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Answer:

Y=-1

Step-by-step explanation:

Y-5=3-9y-18

y+9y=3-18+5

10y=-10

y=-1

there is the answer ................................

(a) The region for which f(x,y) > 0 is the region where the joint probability density function (pdf) is positive. In this case, f(x,y) = cx^2y. Since the pdf is only positive when cx^2y is positive, it means that the region is defined by the inequality cx^2y > 0. This implies that both x and y must be non-zero for f(x,y) to be positive. Therefore, the region where f(x,y) > 0 is the entire xy-plane excluding the x and y axes.

(b) To determine the value of c, we need to integrate the joint pdf over its entire support and set it equal to 1, since the joint pdf must integrate to 1 over its support to be a valid probability density function.

∫∫f(x,y) dxdy = ∫∫cx^2y dxdy

Since the region of integration is the entire xy-plane, we can integrate with respect to x first:

∫(∫cx^2y dx)dy = ∫(c/3 * x^3y)dy

Integrating with respect to y now, over the entire range of y:

∫(c/3 * x^3y)dy = c/3 * x^3 * [y^2/2] = c/6 * x^3 * y^2

To find the value of c, we set this expression equal to 1 and solve for c:

c/6 * x^3 * y^2 = 1

c = 6 / (x^3 * y^2)

(c) The marginal pdf of X can be obtained by integrating the joint pdf over the range of y:

fX(x) = ∫f(x,y) dy

∫cx^2y dy = c/2 * x^2 * y^2

To find the value of c, we integrate fX(x) over its entire support, which is the range of x:

∫fX(x) dx = ∫c/2 * x^2 * y^2 dx = 1

Integrating, we get:

c/2 * y^2 * [x^3/3] = 1

c * y^2 / 6 = 1

c = 6 / y^2

Therefore, the marginal pdf of X is fX(x) = (6 / y^2) * x^2.

Similarly, we can find the marginal pdf of Y by integrating the joint pdf over the range of x:

fY(y) = ∫f(x,y) dx

∫cx^2y dx = c/3 * x^3 * y

Integrating fY(y) over its entire support, which is the range of y, we get:

∫fY(y) dy = ∫c/3 * x^3 * y dy = 1

Integrating, we have:

c/3 * x^3 * [y^2/2] = 1

c * x^3 / 6 = 1

c = 6 / x^3

Therefore, the marginal pdf of Y is fY(y) = (6 / x^3) * y.

(d) The conditional pdf of X given Y=y can be obtained using the formula:

fX|Y(x|y) = f(x,y) / fY(y)

Substituting the values of f(x,y), fY(y), and c derived earlier:

fX|Y(x|y) = (cx^2y) / [(6 / x^3) * y] = cx^5 / 6

Therefore, the conditional pdf of X given Y=y is fX|Y(x|y) = cx^5 / 6.

(e) To determine if X and Y are independent, we need to check if the joint pdf f(x,y) can be expressed as the product of the marginal pdfs fX(x) and fY(y). However, in this case, the joint pdf f(x,y) = cx^2y cannot be factorized into the product of the marginal pdfs (6 / y^2) * x^2 and (6 / x^3) * y. Therefore, X and Y are not independent.

(f) To calculate P(X ≤ Y), we integrate the joint pdf f(x,y) over the region where X ≤ Y:

P(X ≤ Y) = ∫∫f(x,y) dxdy

Since f(x,y) = cx^2y, the integral becomes:

∫∫cx^2y dxdy

Integrating over the appropriate region, we get:

∫(∫cx^2y dx)dy

The limits of integration will depend on the specific range of x and y.

(g) To calculate P(X ≤ 0.4 | Y ≥ 0.5), we need to find the conditional probability of X being less than or equal to 0.4 given that Y is greater than or equal to 0.5. This can be computed by integrating the conditional pdf fX|Y(x|y) over the range where X ≤ 0.4 and Y ≥ 0.5, and dividing it by the probability of Y being greater than or equal to 0.5:

P(X ≤ 0.4 | Y ≥ 0.5) = ∫(∫fX|Y(x|y) dx) dy / P(Y ≥ 0.5)

The limits of integration will depend on the specific range of x and y in the given conditions.

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The probability that exactly five households say they would feel secure if they had $50,000 in savings is approximately 0.188 or 18.8% (rounded to three decimal places).

To find the probability that exactly five households say they would feel secure if they had $50,000 in savings, we can use the binomial probability formula. The formula is:

P(X = k) = (nCk) * p^k * (1 - p)^(n - k)

where P(X = k) is the probability of getting exactly k successes, n is the number of trials (sample size), p is the probability of success in a single trial, and (nCk) represents the number of combinations.

In this case, n = 8 (the number of randomly selected households), p = 0.45 (the probability that a household says they would feel secure), and k = 5.

Using the formula and substituting the values, we can calculate the probability:

P(5) = (8C5) * 0.45^5 * (1 - 0.45)^(8 - 5)

P(5) ≈ 0.188

Therefore, the probability that exactly five households say they would feel secure if they had $50,000 in savings is approximately 0.188 or 18.8% (rounded to three decimal places).

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Answer:

\(\huge\underline\mathtt\colorbox{cyan}{Alt-interior Angles}\)

Step-by-step explanation:

Angles 4 and 3 are a pair of alternate-interior angles which are equal in measure.

Answer:

x = 4

Step-by-step explanation:

In the modified model, considering a constant harvesting rate, the net rate of change of the fish population takes into account both the birth rate and the death rate, which is proportional to the square of the population. The model is given by dP/dt = k1P - k2P^2 - h, where P(t) represents the population of fish at time t, k1 is the constant of proportionality for the birth rate, k2 is the constant of proportionality for the death rate, and h is the harvesting rate.

The net rate at which the population of fish changes takes into account the birth rate, the death rate, and the harvesting rate. The birth rate is proportional to the population present at time t, represented by k1P(t). The death rate, on the other hand, is proportional to the square of the population present at time t, given by k2P^2(t). The harvesting rate, denoted by h, represents the constant rate at which fish are being harvested. Therefore, the net rate of change of the population, dP/dt, is equal to the birth rate minus the death rate minus the harvesting rate. This can be expressed as dP/dt = k1P - k2P^2 - h. This differential equation provides a model for the population dynamics of the fish, accounting for both natural processes (birth and death rates) and human intervention (harvesting rate).

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