The points (7,3) and (w,9) fall on a line with a slope of -2. What is the value of w?

The probability of drawing a winning pair which is a pair with the same color OR same letter 0.9388.

The problem we are dealing with is related to probability which is referred to as Probability is essentially how likely something is to happen. At whatever point we're uncertain approximately the result of an occasion, we will conversation around the probabilities of certain outcomes—how likely they are.

Since we are provided with four red cards and four green cards so, the total possible combination of the  8 cards will be

C(8,2) = 28

out of which  2*C(4,2)=12 are the  pairs of the same color

therefore the probability of picking a pair with the same color OR same letter is

1 - (12*4)/28^2 = 0.9388

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The Big M method is a technique used in linear programming to solve problems with constraints and objective functions. It is an extension of the simplex method that handles cases where some constraints have strict inequalities (i.e., ">") or the objective function includes a term to be minimized.

To construct the first simplex tableau using the Big M method, follow these steps:

1. Write the objective function in standard form:
\(Z = 2x₁ + 3x₂ + x₃\)

2. Introduce slack variables to convert the inequalities into equations:
  \(x₄ = 8 - x₁ - 4x₂ - 2x₃\\x₅ = 6 - 3x₁ - 2x₂\)

3. Add a big M term to the objective function for each slack variable:
  \(Z = 2x₁ + 3x₂ + x₃ + M₁x₄ + M₂x₅\)

4. Convert the inequalities into equations by adding surplus variables for ">=" constraints:
 \(x₆ = x₁ + 4x₂ + 2x₃ - 8\\x₇ = 3x₁ + 2x₂ - 6\)

5. Add a big M term to the objective function for each surplus variable:
  \(Z = 2x₁ + 3x₂ + x₃ + M₁x₄ + M₂x₅ + M₃x₆ + M₄x₇\)

6. Write the initial simplex tableau using the augmented matrix:

```
   [  2  3  1  0  0  0  0  0 ]
   [ -1 -4 -2  1  0  0  0  8 ]
   [ -3 -2  0  0  1  0  0  6 ]
   [  1  4  2  0  0  1  0 -8 ]
   [  3  2  0  0  0  0  1 -6 ]
```

7. Identify the entering and leaving basic variables:
  - The entering variable is the column with the most negative coefficient in the objective row.

In this case, it is the second column (x₂).
  - The leaving variable is the row with the smallest non-negative ratio of the right-hand side to the entering variable's coefficient.

In this case, it is the third row (x₆).

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Using the Big M method, the complete first simplex tableau for the given linear programming problem is constructed as follows:

┌─────────────┬──────┬───────┬───────┬─────┬─────┬─────────────┐

│     BV      │  x₁  │   x₂  │   x₃  │  s₁ │  s₂ │      RHS    │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────────────┤

│      Z      │  2   │   3   │   1   │  0  │  0  │      0      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────────────┤

│  x₁ + 4x₂ + │  1   │   4   │   2   │ -1  │  0  │     -8      │

│     2x₃ - M  │      │       │       │     │     │             │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────────────┤

│  3x₁ + 2x₂  │  3   │   2   │   0   │  0  │ -1  │      6      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────────────┤

│     x₁      │  1   │   0   │   0   │  1  │  0  │      0      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────────────┤

│     x₂      │  0   │   1   │   0   │  0  │  1  │      0      │

├─────────────┼──────┼───────┼───────┼─────┼─────┼─────────────┤

│     x₃      │  0   │   0   │   1   │  0  │  0  │      0      │

└─────────────┴──────┴───────┴───────┴─────┴─────┴─────────────┘

The initial entering basic variable is x₁, which has the most negative coefficient in the objective row. The leaving basic variable is x₃, determined by selecting the row with the smallest positive ratio of the right-hand side (RHS) to the entering column's coefficient. In this case, the ratio for the fourth row (0/1) is the smallest, so x₃ leaves the basis.

To construct the complete first simplex tableau using the Big M method, we first convert the given problem into standard form by introducing slack variables (s₁ and s₂) for the inequalities and a large positive value (M) to penalize the artificial variable in the objective function.

The first row represents the objective function, where the coefficients of the decision variables x₁, x₂, and x₃ are taken directly from the given problem. The slack and artificial variables (s₁ and s₂) have coefficients of 0 since they don't appear in the objective function.

The subsequent rows represent the constraints. Each row corresponds to one constraint, where the coefficients of the decision variables, slack variables, and the artificial variable are taken from the original problem. The right-hand side (RHS) values are also copied accordingly.

The initial entering basic variable is determined by selecting the most negative coefficient in the objective row, which is x₁ in this case. The leaving basic variable is determined by finding the smallest positive ratio of the RHS to the entering column's coefficient. Since the ratio for the fourth row (0/1) is the smallest, x₃ leaves the basis.

The resulting tableau serves as the starting point for applying the simplex method to solve the linear programming problem iteratively.

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Answer:

A. $3.59

Step-by-step explanation:

10+5=15 dollars, that handed Mark

15-4.23 = 10.77 costs 3 sets of fasteners

10.77/3 = 3.59 cost each set of fasteners

===========================================================

Explanation:

10+5 = 15 dollars was handed over to the cashier.

He got back $4.23 in change, which means the total price is 15-4.23 = 10.77 dollars.

Divide this over 3 to find the cost of each fastener set.

10.77/3 = 3.59 dollars

----------------

An algebraic approach:

x = cost of 1 fastener set

3x = cost of 3 fastener sets

3x+4.23 = add on the change received

3x+4.23 = 10+5

3x+4.23 = 15

3x = 15-4.23

3x = 10.77

x = 10.77/3

x = 3.59 dollars

a) To find out how much L is needed to produce 400 toys per hour when K is equal to 20, we can use the production function formula provided, which is Q = 4K + 5L.

To solve for L, we can rearrange the formula as follows: Q - 4K = 5L 400 - 4(20) = 5L 320 = 5L L = 64

Therefore, to produce 400 toys per hour with K = 20, the manufacturer would need 64 units of labor input per hour.

b) Similarly, to find out how much K is needed to produce 500 toys per hour when L is equal to 40, we can use the production function formula: Q = 4K + 5L

Substituting the given values, we get: 500 = 4K + 5(40) 500 = 4K + 200 4K = 300 K = 75

Therefore, to produce 500 toys per hour with L = 40, the manufacturer would need 75 units of capital input per hour.

In conclusion, the production function formula provides a useful tool for toy manufacturers to produce a desired level of output. By manipulating the formula, the manufacturer can also calculate the maximum output possible given a certain combination of inputs.

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Answer:

16 meters

Step-by-step explanation:

Factors of 64: 1, 2, 4, 8, 16, 32, 64

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The greatest common factor of 64 and 48 is 16.

Answer:

Step-by-step explanation:

To find the length of the longest scale that can measure 64 m and 48 m exactly, we need to find the greatest common factor (GCF) of 64 and 48. The GCF is the largest number that divides both numbers without leaving a remainder. One way to find the GCF is to list the factors of both numbers and find the largest one that they have in common. For example:

Factors of 64: 1, 2, 4, 8, 16, 32, 64

Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The largest factor that both numbers have in common is 16. Therefore, the GCF of 64 and 48 is 16.

This means that the longest scale that can measure both lengths exactly is 16 m. We can check this by dividing both lengths by 16 and seeing that there is no remainder:

1664​=4

1648​=3

A recent report estimates that four out of every five dentists recommend a brand of toothpaste situation involves Inferential statistics.

Inferential statistics are widely employed to compare the differences between the treatment groups. Inferential statistics compare the treatment groups and make generalizations about the subject population using data from the experiment's sample of subjects. To offer answers for a situation or phenomena, inferential statistics is helpful. It differs fundamentally from descriptive statistics, which do not allow for result extrapolations and merely report the data that has already been measured.

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Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, there is not sufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools.

To determine if there is sufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools, we can use a two-sample z-test for the difference in proportions.

The null hypothesis is that there is no difference between the proportions of students with ear infections at the two schools, while the alternative hypothesis is that there is a difference.

Let p1 be the proportion of students with ear infections at the first school and p2 be the proportion at the second school. The test statistic is given by:

z = (p1 - p2) / sqrt(p_hat * (1 - p_hat) * (1/n1 + 1/n2))

where p_hat is the pooled proportion, n1 and n2 are the sample sizes from the first and second schools, respectively.

The pooled proportion is given by:

p_hat = (x1 + x2) / (n1 + n2)

where x1 and x2 are the number of students with ear infections in each school.

Using the given data, we have:

n1 = 40, n2 = 30

x1 = 11, x2 = 12

p1 = x1/n1 = 11/40 = 0.275

p2 = x2/n2 = 12/30 = 0.4

p_hat = (x1 + x2) / (n1 + n2) = (11 + 12) / (40 + 30) = 0.355

The test statistic is:

z = (0.275 - 0.4) / sqrt(0.355 * 0.645 * (1/40 + 1/30)) = -1.197

Using a standard normal table or calculator, the p-value for a two-tailed test with a test statistic of -1.197 is approximately 0.231.

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The required volume of the given composite space figure is 1512 \(cm^3\).

Given that, the rectangular pyramid fits exactly on top of a rectangular prism. The length of the prism is 18 cm, width is 6 cm and height is 9 cm. The length of the pyramid is 18 cm, width is 6 cm and height is 15 cm.

To find the volume of the composite figure formed by the rectangular pyramid on top of the prism, find the volume of prism and pyramid and then add it .

The volume of the prism is given by V1 = length × width × height.

The volume of the pyramid is given by V2 = length × width × height.

The volume of the composite figure is V = V1 +V2.

By using the given data and formula, find the volume of the prism,

Volume of prism V1 = length × width × height.

Volume of prism V1 = 18 × 6 × 9.

Thus, Volume of prism V1 = 972 \(cm^3\) .

By using the given data and formula, find the volume of the pyramid,

Volume of pyramid V2 = (length × width × height)/3.

Volume of pyramid V2 = (18 × 6 × 15)/3.

Thus, Volume of pyramid V2 =  1620/3= 540 \(cm^3\) .

By using above volumes, find the volume of the composite figure.

V = V1 +V2.

V = 972 + 540.

V = 1512 \(cm^3\) .

Hence, the required volume of the given composite space figure is

1512 \(cm^3\)

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The estimated probability is 0.0294

To estimate the probability of getting between 45 and 50 correct answers on the multiple-choice test, we can use the binomial probability formula and a calculator.

The binomial probability formula is given by P(X = k) = (nCk) * p^k * q^(n-k), where n is the number of trials, k is the number of successes, p is the probability of success on a single trial.

q is the probability of failure (1 - p), and nCk represents the number of combinations.

In this case, n = 160 (number of questions), p = 0.25 (probability of guessing a correct answer), and we want to find P(45 ≤ X ≤ 50), which means the probability of getting between 45 and 50 correct answers.

Using a calculator such as TI-83, TI-83 Plus, or TI-84, we can calculate the individual probabilities for each value of X (45, 46, 47, 48, 49, 50) using the binomial probability formula.

Then, we sum up these probabilities to find the total probability of getting between 45 and 50 correct answers.

By performing the calculations, we find that the estimated probability is 0.0294, rounded to four decimal places.

This means that with random guessing, there is approximately a 2.94% chance of getting between 45 and 50 correct answers on the multiple-choice test.

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Answer:

b. F' (3, 0), G' (-6, -1), H' (-5, -3)

The simplified version of (sec a - cosec a) / (sec a + cosec a)  is cosec 2a(cosec 2a - 2) / (sec²a - cosec²a).

The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.

Given:

(sec a - cosec a) / (sec a + cosec a)

Multiply the numerator and denominator by (sec a - cosec a)

(sec a - cosec a) / (sec a + cosec a)  × (sec a - cosec a)

(sec²a + cosec²a -2sec a cosec a) / (sec²a - cosec²a)

As we know,

\(sec^2a + cosec^2a = sec^2a \ cosec^2a\)

sec² a cosec² a - 2sec a cosec a /  (sec²a - cosec²a)

sec a cosec a (sec a cosec a - 2) / (sec²a - cosec²a)

cosec 2a(cosec 2a - 2) / (sec²a - cosec²a)

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Answer:

64 gallons

Step-by-step explanation:

Ask yourself; if

 16gallons = 1minute

     ?           = 4minutes

Cross multiply;

(16 × 4) ÷ (1) = 64

PART A:

In the expression -7 - (-9), we can combine both negative signals and create a positive signal, so the expression will be -7 + 9.

That means in the number line we start at the number -7 and go 9 units to the right.

So Karissa is not correct, because she said a different starting point and a different direction to add the 9 units.

PART B:

Let's solve the equation:

We can see that the equation is not true, since the final statement is false. So Hugo is not correct, because the final values of each side of the equation didn't match.

The exact value of cscθ is (35 * √(1190)) / 1190.

To find the value of cscθ (cosecant θ) given that cosθ = 1/√35 and sinθ < 0, we can use the reciprocal relationship between sine and cosecant.

Recall that cscθ is the reciprocal of sinθ. Since sinθ is negative, we can determine its value based on the quadrant in which θ lies.

In the unit circle, the cosine is positive in the first and fourth quadrants, while the sine is negative in the third and fourth quadrants.

Given that cosθ = 1/√35 and sinθ < 0, we can conclude that θ lies in the fourth quadrant.

Using the Pythagorean identity, sinθ = √(1 - cos^2θ), we can calculate the value of sinθ:

sinθ = √(1 - (1/√35)^2)

     = √(1 - 1/35)

     = √(34/35)

     = √34 / √35

     = (√34 / √35) * (√35 / √35)     [Multiplying numerator and denominator by √35 to rationalize the denominator]

     = √(34 * 35) / 35

     = √(1190) / 35

Now, since cscθ is the reciprocal of sinθ, we have:

cscθ = 1 / sinθ

     = 1 / (√(1190) / 35)

     = 35 / √(1190)

     = (35 * √(1190)) / 1190.

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Answer:

FV= PV*(1 + g)^n

Step-by-step explanation:

Giving the following information:

Present Value (PV)= 120

Growth rate (g)= 6.5% per year

To calculate the future value of the population in any given year "n", we need to use the following formula:

FV= PV*(1 + g)^n

For example, in 10 years:

FV= 120*(1.065^10)

FV= 225

The value of p is 2 and 4.

What is a quadratic equation?

Any equation that can be written in the standard form where x is an unknown value, a, b, and c are known quantities, and a 0 is a quadratic equation. Any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.

Here, we have

Given: p² - 6p + 8

we have to solve the quadratic formula or complete the square.

= p² - 6p + 8

= p² -4p - 2p + 8

= p(p-4) -2(p-4)

= (p-4)(p-2)

(p-4)(p-2) = 0

p-4 = 0,

p-2 = 0

p = 4, 2

Hence, the value of p is 2 and 4,

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The probability that James will take the same mode of transportation twice is 1/9.

To find the probability that James will take the same mode of transportation twice, we need to calculate the probability of each individual transportation option and then multiply them together.

In the morning, James has 3 transportation options: bus, cab, or train. Since he randomly chooses his ride, the probability of selecting any particular option is 1 out of 3 (assuming all options are equally likely).

Therefore, the probability of James selecting the same transportation mode in the morning and evening is 1/3.

Hence, the probability that James will take the same mode of transportation twice is 1/3 multiplied by 1/3:

P(same mode of transportation twice) = 1/3 * 1/3 = 1/9.

Therefore, the probability that James will take the same mode of transportation twice is 1/9.

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When the second derivative of a function equals zero, it indicates a possible point of inflection or a critical point where the concavity of the function changes. It is a significant point in the analysis of the function's behavior.

The second derivative of a function measures the rate at which the slope of the function is changing. When the second derivative equals zero at a particular point, it suggests that the function's curvature may change at that point. This means that the function may transition from being concave upward to concave downward, or vice versa.

Mathematically, if the second derivative is zero at a specific point, it is an indication that the function has a possible point of inflection or a critical point. At this point, the function may exhibit a change in concavity or the slope of the tangent line.

Studying the second derivative helps in understanding the overall shape and behavior of a function. It provides insights into the concavity, inflection points, and critical points, which are crucial in calculus and optimization problems.

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When the second derivative of a function equals zero, it indicates a critical point in the function, which can be a maximum, minimum, or an inflection point.

The second derivative of a function measures the rate at which the slope of the function is changing. When the second derivative equals zero, it indicates a critical point in the function. A critical point is a point where the function may have a maximum, minimum, or an inflection point.

To determine the nature of the critical point, further analysis is required. One method is to use the first derivative test. The first derivative test involves examining the sign of the first derivative on either side of the critical point. If the first derivative changes from positive to negative, the critical point is a local maximum. If the first derivative changes from negative to positive, the critical point is a local minimum.

Another method is to use the second derivative test. The second derivative test involves evaluating the sign of the second derivative at the critical point. If the second derivative is positive, the critical point is a local minimum. If the second derivative is negative, the critical point is a local maximum. If the second derivative is zero or undefined, the test is inconclusive.

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to find the equation of sencond line we should find slope of first line , because when we multiple slopes of 2 prependicular line we will get -1 .

\(5x - 2y = - 6 \\ 5x + 6 = 2y \\ \frac{5x}{2} + \frac{6}{2} = \frac{2y}{2} \\ \frac{5x}{2} + 3 = y \\ \\ y = mx + b \\ so \: slope(m)is \frac{5}{2} \\ \\ slope \: of \: second \: line \: is \: \frac{ - 2}{5} \)

to write equation of line we use this formula

\(y - y1 = m(x - x1) \\ y - ( - 4) = \frac{ - 2}{5} (x - 5) \\ y + 4 = \frac{ - 2}{5} x + \frac{10}{5} \\ y + 4 = \frac{ - 2}{5} x + 2 \\ y = \frac{ - 2}{5} x + 2 - 4 \\ y = \frac{ - 2}{5} x - 2\)

so the options ( A , D , B ) are correct

PLEASE MARK ME AS BRAINLIEST

The correct answer is that the probability of a cash flow being between $16,000 and $19,000 is approximately 18.59%.

To calculate the probability of a cash flow being between $16,000 and $19,000, we can use the standard deviation and assume a normal distribution.

We are given that the average cash flow is $14,000 with a standard deviation of $5,000. These values are necessary to calculate the probability.

The probability of a cash flow falling within a certain range can be determined by converting the values to z-scores, which represent the number of standard deviations away from the mean.

First, we calculate the z-score for $16,000 using the formula: z = (x - μ) / σ, where x is the cash flow value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z1 = (16,000 - 14,000) / 5,000.

z1 = 2,000 / 5,000 = 0.4.

Next, we calculate the z-score for $19,000: z2 = (19,000 - 14,000) / 5,000.

z2 = 5,000 / 5,000 = 1.

Now that we have the z-scores, we can use a standard normal distribution table or calculator to find the corresponding probabilities.

Subtracting the probability corresponding to the lower z-score from the probability corresponding to the higher z-score will give us the probability of the cash flow falling between $16,000 and $19,000.

Looking up the z-scores in a standard normal distribution table or using a calculator, we find the probability for z1 is 0.6554 and the probability for z2 is 0.8413.

Therefore, the probability of the cash flow being between $16,000 and $19,000 is 0.8413 - 0.6554 = 0.1859, which is approximately 18.59%.

So, the correct answer is that the probability of a cash flow being between $16,000 and $19,000 is approximately 18.59%.

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The probability of a cash flow between $16,000 and $19,000 is approximately 18.59%.

To calculate the probability of a cash flow being between $16,000 and $19,000, we can use the standard deviation and assume a normal distribution.

We are given that the average cash flow is $14,000 with a standard deviation of $5,000. These values are necessary to calculate the probability.

The probability of a cash flow falling within a certain range can be determined by converting the values to z-scores, which represent the number of standard deviations away from the mean.

First, we calculate the z-score for $16,000 using the formula: z = (x - μ) / σ, where x is the cash flow value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z1 = (16,000 - 14,000) / 5,000.

z1 = 2,000 / 5,000 = 0.4.

Next, we calculate the z-score for $19,000: z2 = (19,000 - 14,000) / 5,000.

z2 = 5,000 / 5,000 = 1.

Now that we have the z-scores, we can use a standard normal distribution table or calculator to find the corresponding probabilities.

Subtracting the probability corresponding to the lower z-score from the probability corresponding to the higher z-score will give us the probability of the cash flow falling between $16,000 and $19,000.

Looking up the z-scores in a standard normal distribution table or using a calculator, we find the probability for z1 is 0.6554 and the probability for z2 is 0.8413.

Therefore, the probability of the cash flow being between $16,000 and $19,000 is 0.8413 - 0.6554 = 0.1859, which is approximately 18.59%.

So, the correct answer is that the probability of a cash flow being between $16,000 and $19,000 is approximately 18.59%.

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The investment's expected return is 5.95%.

The expected return of an investment is calculated by multiplying the probabilities of each possible return by their respective returns and summing them up. In this case, Gautney Enterprises has provided the probabilities and returns for the investment. By applying the formula, we find that the expected return is 5.95%.

To calculate the standard deviation, we need to determine the variance first. The variance is computed by taking the difference between each possible return and the expected return, squaring those differences, multiplying them by their respective probabilities, and summing them up. Once we have the variance, the standard deviation is simply the square root of the variance. The standard deviation measures the degree of risk associated with an investment.

In this scenario, the expected return of the investment is 5.95%, but we need to consider the standard deviation as well to assess the risk. If the standard deviation is high, it indicates a greater level of uncertainty and potential volatility in returns. A low standard deviation implies a more stable investment.

Without the specific values for each return and their respective probabilities, we cannot calculate the exact standard deviation. However, Gautney Enterprises should compare the calculated expected return and the associated standard deviation to their risk tolerance and investment objectives. If the expected return meets their desired level of return and the standard deviation aligns with their risk appetite, they may consider investing in this security.

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Answer:

x=15

Step-by-step explanation:

One can solve a proportion by cross multiplying.

Or simplifying one side:

35/7 = x/3

since 35/7 =5

we can say

5 = x/3

then multiply by 3 to undo the /3

5 = x/3

*3

15 = x

Answer:

x=15

Step-by-step explanation:

35/7 = x/3

5x7/7=x/3

The probability of a random sample of 225 students having a mean score of less than 600 is very low, at about 0.01%.

To find the probability of a sample mean greater than 625, we need to calculate the z-score for this value: z = (625 - 610) / (σ / √(225)) where σ is the population standard deviation.

Let's assume for this example that σ is equal to 30.

Plugging in these values, we get: z = (625 - 610) / (30 / sqrt(225)) = 3.75 U

sing a standard normal distribution table or a calculator, we can find that the probability of a z-score greater than 3.75 is approximately 0.0001.

Therefore, the probability of a random sample of 225 students having a mean score of more than 625 is very low, at about 0.01%.

To find the probability of a sample mean less than 600, we can use a similar process: z = (600 - 610) / (σ / sqrt(225)) = -3.75

Using the same standard normal distribution table or calculator, we can find that the probability of a z-score less than -3.75 is also approximately 0.0001. (0.01%)

So, the answer of the probability is 0.01%.

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The measurements of a rectangular plot of land with a perimeter of 70 km and an area of 300 km is 20 and 15.

Given that,

We have to find what are the measurements of a rectangular plot of land with a perimeter of 70 km and an area of 300 km.

We know that,

Let a and b be the side lengths of the rectangle

The perimeter is 70 km,

So, 2a+2b=70 equation(1)

The area is 300 km

So, a×b=380 equation(2)

To solve this system of 2 equations,

We express b in terms of a in eq 1 -> b=35-a

Then we substitute for b in eq 2 -> a×(35-a)=300

Some transformation leads to a²-35a+300=0

a²-20a-15a+300=0

a(a-20)-15(a-20)=0

(a-20)(a-15)=0

a=20,15

Now, substitute a in equation (1)

2a+2b=70

a+b=35

20+b=35

b=35-20

b=15

Now,

15+b=35

b=35-15

b=20

Therefore, the measurements of a rectangular plot of land with a perimeter of 70 km and an area of 300 km is 20 and 15.

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The area of the given triangle is 87.55 square centimeter.

From the given triangle, base=17 cm and height=10.3 cm.

The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.

Here, area of a triangle = 1/2 ×17×10.3

= 87.55 square centimeter

Therefore, area of the given triangle is 87.55 square centimeter.

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Answer:

-0.4 or 2.3

Step-by-step explanation:

simple

each box is 0.1 unit

Answer:

Step-by-step explanation:

The answer is where the graph cuts the x-axis.

I can't see it very well but it looks like x = -0.4 and 2.3.

The measure that gives the most common year of birth is the mode.

The mode is the value that appears most frequently in a given dataset. In the context of the football team, each member reported the year they were born, and the mode would be the birth year that is reported by the highest number of team members.

On the other hand, the mean is calculated by summing up all the values in the dataset and dividing by the total number of values. The mean provides the average value and may not necessarily represent the most common year of birth.

The median, on the other hand, is the middle value in a dataset when it is arranged in ascending or descending order. If there is an odd number of data points, the median is the value at the center. If there is an even number of data points, the median is the average of the two middle values. While the median can give us the middle point of the dataset, it does not necessarily indicate the most common year of birth.

Therefore, if you want to find the most common year of birth reported by the football team members, you should look for the mode.

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Answer:

Step-by-step explanation:

There are no solutions to this equation

3 + 6z = 13 + 6z              Subtract 6z from both sides

  - 6z =       - 6z

3 = 13

There is no way on this planet using this numbering system that you can get 3 = to 13