suppose a cell phone carrier can collect data from each customer to check that within one week, how many times he/she talks to someone on the phone for more than 20 minutes. this type of data is considered . g

If the point (3, -2) were reflected across the y-axis what would be the new y-coordinate is same as before, which is -2.

If a point (x, y) is reflected across the y-axis, its x-coordinate becomes its opposite (-x), while its y-coordinate remains the same.

In this case, the point is (3, -2). If we reflect this point across the y-axis, its x-coordinate will become its opposite, which is -3. The new coordinates of the reflected point will be (-3, -2).

Therefore, the new y-coordinate is still -2, as the point is only being reflected across the y-axis and not moving up or down in the y-direction. The change is only in the x-coordinate, which becomes its opposite.

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The solution to the equation (a - b) / (a + b) = 3/5 in terms of b is a = 4b.

A statement that affirms the equivalence of two expressions joined by the equals symbol "=" is known as an equation.

Your steps are correct, and here's the solution to the equation:

(a - b) / (a + b) = 3/5

To solve for a in terms of b, we cross multiply:

5(a - b) = 3(a + b)

Expanding the brackets, we get:

5a - 5b = 3a + 3b

Simplifying the equation by combining like terms, we get:

5a - 3a = 8b

2a = 8b

Dividing both sides of the equation by 2, we get:

a = 4b

Therefore, the solution to the equation (a - b) / (a + b) = 3/5 in terms of b is a = 4b.

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The complete question is:

The equation given is A = 4b. Please write an appropriate question related to this equation.

The solution of the given simultaneous equations is x = 3 and y = 5.

The given equations are:

3x + 2y = 19

x + 2y = 13

To solve them using the elimination method, we need to eliminate one variable from the equations. In this case, we can eliminate y by subtracting the second equation from the first equation, as follows:

(3x + 2y) - (x + 2y) = 19 - 13

Simplifying the left-hand side, we get:

2x = 6

Dividing both sides by 2, we obtain:

x = 3

Now that we have found the value of x, we can substitute it back into one of the original equations to find the value of y. Let's substitute it into the second equation:

x + 2y = 13

3 + 2y = 13

Subtracting 3 from both sides, we get:

2y = 10

Dividing both sides by 2, we obtain:

y = 5

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Original statement: Any valid argument has a true conclusion. Negation: There exists a valid argument with a false conclusion.

To write a negation for a statement, we use the word “not” or its equivalent to express the opposite of the original statement. For example, the negation of “All dogs are mammals” is “Not all dogs are mammals” or “Some dogs are not mammals”. Here are the negations for the given statements:

a. The negation of “Any valid argument has a true conclusion” is “Not any valid argument has a true conclusion” or “Some valid arguments do not have a true conclusion”.

b. The negation of “Every real number is positive, negative, or zero” is “Not every real number is positive, negative, or zero” or “There exists a real number that is not positive, negative, or zero”.

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To summarize:

- The relation is not reflexive.

- The relation is not symmetric.

- The relation is transitive.

A homogeneous relation R over the set A, which comprises the elements x, y, and z, is known as a transitive relation. If R relates x to y and y to z, then R likewise relates x to z.

To determine whether each relation is reflexive, symmetric, or transitive, we need to examine the properties individually. Let's analyze each property for the given relation R on Z, where x, y ∈ Z and xRy if and only if (x + y)² ≡ ±1.

(a) Reflexive: A relation R is reflexive if every element in the set is related to itself. In this case, we need to check if (x + x)² ≡ ±1 for all x ∈ Z.

If we simplify (x + x)², we get (2x)² = 4x². Since we are looking for the relation (x + y)² ≡ ±1, this relation is not reflexive because 4x² is not equivalent to ±1 for all integers x.

(b) Symmetric: A relation R is symmetric if whenever x is related to y, then y is also related to x. In this case, we need to check if (x + y)² ≡ ±1 implies (y + x)² ≡ ±1 for all x, y ∈ Z.

Let's consider a counterexample to show that it is not symmetric. Suppose we have x = 1 and y = 2. (1 + 2)² = 9, which is not equivalent to ±1. However, (2 + 1)² = 9, which is also not equivalent to ±1. Since the relation is not symmetric for these values, we can conclude that it is not symmetric for all values.

(c) Transitive: A relation R is transitive if whenever x is related to y and y is related to z, then x is related to z. In this case, we need to check if (x + y)² ≡ ±1 and (y + z)² ≡ ±1 imply (x + z)² ≡ ±1 for all x, y, z ∈ Z.

To show that this relation is transitive, we need to verify that if (x + y)² ≡ ±1 and (y + z)² ≡ ±1, then (x + z)^2 ≡ ±1.

Expanding (x + y)², we have (x + y)² = x² + 2xy + y². Similarly, expanding (y + z)², we have (y + z)² = y² + 2yz + z².

Now, if we add these two equations, we get:

(x + y)² + (y + z)² = x² + 2xy + y² + y² + 2yz + z² = x² + 2xy + 2yz + z² + 2y².

We want this expression to be equivalent to ±1, so we need to consider the cases when it is equal to ±1:

Case 1: (x² + 2xy + 2yz + z² + 2y²) ≡ 1

In this case, (x + z)² ≡ 1, which satisfies the transitive property.

Case 2: (x² + 2xy + 2yz + z² + 2y²) ≡ -1

In this case, (x + z)² ≡ -1, which also satisfies the transitive property.

Therefore, the given relation is transitive.

To summarize:

- The relation is not reflexive.

- The relation is not symmetric.

- The relation is transitive.

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There is one specific type of transformation that can cause a change in the period of a tangent or cotangent function, and that is a dilation.

A dilation is a transformation that stretches or compresses a function horizontally or vertically. When a tangent or cotangent function is dilated horizontally, the period of the function changes. The period of a tangent function is π, while the period of a cotangent function is also π.

If the function is dilated by a factor of k, then the new period will be π/k. This means that the function will oscillate faster if it is compressed horizontally (k > 1) and slower if it is stretched horizontally (k < 1). Therefore, it is important to consider the effects of dilations when analyzing the period of a tangent or cotangent function.

The type of transformation that could cause a change in the period of a tangent or cotangent function is called a "horizontal stretch" or "horizontal compression." These transformations affect the frequency of the function by scaling it horizontally, which in turn alters the period of the tangent or cotangent function.

In mathematical terms, the general form of a tangent function is y = A * tan(B(x - C)) + D, and for a cotangent function, it's y = A * cot(B(x - C)) + D. In these expressions, A represents the amplitude, B determines the horizontal stretch or compression, C is the phase shift, and D is the vertical shift.

The factor B directly affects the period of the function. For a tangent or cotangent function, the standard period is π. To find the new period after a horizontal transformation, you can use the formula: new period = (standard period) / |B|. Thus, by changing the value of B, the period of the tangent or cotangent function will be affected accordingly.

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The amount of the check is $94.08.

To calculate the amount of the check, we need to consider the cost per dozen shirts, the number of dozens purchased, and any applicable discounts.

Given information:

Cost per dozen shirts: $16

Number of dozens purchased: 6

Cost per shirt from the wholesaler: $16.32

Terms of the sale: 2/15, n/30 (meaning a 2% discount if paid within 15 days, and the full amount is due within 30 days)

Invoice paid on: March 29

Let's break down the calculations step by step:

Cost of 6 dozen shirts:

Cost per dozen shirts = $16

Cost of 6 dozen shirts = 6 * $16 = $96

Applying the discount:

Discount percentage = 2% = 0.02

Discount amount = 0.02 * $96 = $1.92

Total amount after discount = $96 - $1.92 = $94.08

Check the payment due date:

The invoice was paid on March 29, which is within the 30-day period. Therefore, there is no additional penalty or interest.

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The degree of the polynomial P(x) is 2.

Let the degree of the polynomials P(x) and Q(x) be 'm' and 'n' respectively.

deg {P(x)} = m

deg {Q(x)} = n

So deg {P(x²)} = 2m

and deg {Q³(x)} = 3n

Given that the degree of polynomial {P(x²).Q³(x)} is 12.

So, 2m*3n = 12

6mn = 12

mn = 12/6

mn = 2

n = 2/m ..................... (i)

Again, deg {P³(x)} = 3m

deg (Q(x)) = n

Now given that, deg[P³(x)/Q(x)] = 7

So, 3m/n = 7

3m = 7n

3m = 7*(2/m) [Using the equation (i)]

3m² = 14

m² = 14/3

m = 2 (approximating to nearest whole number)

Hence, the degree of the polynomial p(x) is 2.

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The primal and dual problems have the same optimal value.

What is inequalities?

In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal.

The primal problem is:

minimize c'x

subject to Ax ≥ b

x ≥ 0

The dual problem is:

maximize b'y

subject to A'y ≤ c

y ≥ 0

To convert the dual problem into an equivalent minimization problem, we can negate the objective function and switch the direction of the inequalities:

minimize -b'y

subject to -A'y ≥ -c

y ≥ 0

The dual problem is identical to the primal when the following conditions are satisfied:

The primal and dual are both feasible (i.e., there exists a feasible solution to both problems).

The objective functions of both problems are bounded.

The optimal values of both problems are equal.

To satisfy these conditions, we need to ensure that:

A is a full-rank matrix.

The rows of A are linearly independent.

There exists a vector x such that Ax = b and x ≥ 0.

The objective function c is a linear combination of the rows of A.

An example of a problem that satisfies these conditions is:

minimize 3x1 + 4x2 + 5x3

subject to x1 + 2x2 + 3x3 ≥ 6

2x1 + x2 + 3x3 ≥ 7

x1 + x2 + 2x3 ≥ 4

x1, x2, x3 ≥ 0

The corresponding dual problem is:

maximize 6y1 + 7y2 + 4y3

subject to y1 + 2y2 + y3 ≤ 3

2y1 + y2 + y3 ≤ 4

3y1 + 3y2 + 2y3 ≤ 5

y1, y2, y3 ≥ 0

We can verify that the conditions for strong duality are satisfied:

Both problems are feasible. For example, x = (0, 0, 2) is feasible for the primal problem, and y = (0, 2, 1) is feasible for the dual problem.

The objective functions of both problems are bounded.

We can find a vector x such that Ax = b and x ≥ 0. For example, x = (0, 0, 2) satisfies Ax = b, where b = (6, 7, 4).

The objective function c is a linear combination of the rows of A. Specifically, c = (3, 4, 5) is a linear combination of the rows of A.

Therefore, the primal and dual problems have the same optimal value.

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Since ABCD is an isosceles trapezoid, we know that AB = CD. Additionally, we know that AD = BC. Therefore, we can set up two equations:

AB = CD

AD = BC

Using the fact that B = x + 10 and C = 2x - 30, we can substitute those values into the equations:

AB = CD

x + 10 + AD = 2x - 30 + BC

Since AD = BC, we can simplify the second equation to:

x + 10 + AD = 2x - 30 + AD

x + 10 = 2x - 30

x = 40

Now that we know x, we can find the measures of angles B and C:

B = x + 10 = 50

C = 2x - 30 = 50

Since ABCD is an isosceles trapezoid, we know that angles B and C are congruent. Therefore, each of them measures 50 degrees. Since the sum of the angles in a quadrilateral is 360 degrees, we can set up the equation:

A + B + C + D = 360

Substituting in the values we have:

A + 50 + 50 + D = 360

Simplifying the equation:

A + D = 260

Since ABCD is an isosceles trapezoid, we know that angles A and D are congruent. Therefore, we can set up the equation:

A + D = 2D

Substituting in the value we have:

2D = 260

Simplifying the equation:

D = 130

Therefore, the measure of angle D is 130 degrees.

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a. The rate diagram is given below.

b. The balance equations using matrix methods, we get the limiting probabilities.

c. The average number of hamburgers on the grill is 2.3721.

d. The owner should pay his employee at most $14.18 per hour to ensure that the restaurant makes an average profit of at least $150 per day.

e. The percentage of customers who leave happy can be calculated as:

Percentage of customers who leave happy = 100% * (1 - P0)

What is matrix?

The term "matrix of order m by n," sometimes known as "m x n matrix," refers to a rectangular array of m x n numbers (real or complex), organised into m rows and n columns.

a) The states for the CTMC are:

- State 0: No hamburgers on the grill

- State 1: 1 hamburger on the grill

- State 2: 2 hamburgers on the grill

- State 3: 3 hamburgers on the grill

- State 4: 4 hamburgers on the grill

The transitions between states are as follows:

- From state 0 to state 1 at rate λ, where λ is the rate of hamburger orders (1 customer every 5 minutes).

- From state i to state i+1 at rate μ, where μ is the rate of hamburger cooking (1 hamburger cooked every 8 minutes).

- From state i to state i-1 at rate 4μ, where 4μ is the rate of hamburgers leaving the grill (1 hamburger leaves the grill every 2 minutes on average).

The rate diagram is as follows:

```

   λ

0 -----> 1

^        |

|μ       |4μ

|        v

4 <----- 3

   μ

```

b) The balance equations are:

- For state 0:

λ * P₀ = 4μ * P₁

P₀ + P₁ + P₂ + P₃ + P₄ = 1

- For states 1 to 3:

λ * Pi = μ * (i+1) * Pi+1 + 4μ * (i-1) * Pi-1

P₀ + P₁ + P₂ + P₃ + P₄ = 1

- For state 4:

λ * P₄ = μ * 4 * P₄

P₀ + P₁ + P₂ + P₃ + P₄ = 1

Solving the balance equations using matrix methods, we get the limiting probabilities:

P₀ = 0.1504

P₁ = 0.3008

P₂ = 0.3008

P₃ = 0.2005

P₄ = 0.0474

c) The average number of hamburgers on the grill can be calculated as:

E[number of hamburgers on grill] = P₁ + 2*P₂ + 3*P₃ + 4*P₄

                                 = 2.3721 hamburgers

d) Let C be the cost of the employee per hour. The expected profit per hour can be calculated as:

Expected profit per hour = 8 * (λ - μ) * (P₁ + 2P₂ + 3P₃ + 4P₄) - C * 5

To make an average profit of at least $150 per day (i.e., $30 per hour), we can set up the following inequality:

8 * (λ - μ) * (P₁ + 2P₂ + 3P₃ + 4P₄) - C * 5 ≥ 30

Substituting the values of λ, μ, and the limiting probabilities, we get:

8 * (1/5 - 1/8) * (0.3008 + 2*0.3008 + 3*0.2005 + 4*0.0474) - C * 5 ≥ 30

Solving for C, we get:

C ≤ $14.18 per hour

Therefore, the owner should pay his employee at most $14.18 per hour to ensure that the restaurant makes an average profit of at least $150 per day.

e) The percentage of customers who leave happy can be calculated as:

Percentage of customers who leave happy = 100% * (1 - P0)

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Yao Ming was 24 inches taller than Earl Boykins, as 7 feet is equal to 84 inches and 5 feet 5 inches is equal to 65 inches. Therefore, 84 - 65 = 19 inches, and Ming was 19 inches taller than Boykins.

Yao Ming, standing at 7'5" (7 feet 5 inches), was significantly taller than Earl Boykins, who was 5'5" (5 feet 5 inches) tall in the NBA in 2003. To calculate the difference in height, first convert their heights to inches: Yao Ming = (7 * 12) + 5 = 89 inches and Earl Boykins = (5 * 12) + 5 = 65 inches. Now subtract Boykins' height from Ming's: 89 - 65 = 24 inches. Yao Ming was 24 inches taller than Earl Boykins.

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The correct answer is either (a) if the p-value is less than 0.05, or (b) if the p-value is greater than 0.05.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

Without knowing the specific p-value for the relationship between sales rep age and customer satisfaction rating, it is not possible to determine the correct answer to this question.

In general, a p-value less than 0.05 indicates that there is a statistically significant relationship between the predictor variable and the outcome variable.

However, it is important to interpret the p-value in the context of the specific analysis and research question.

If the p-value for the relationship between sales rep age and customer satisfaction rating is greater than 0.05, it would suggest that the relationship is not statistically significant and may be due to chance.

However, if the p-value is less than 0.05, it would suggest that there is a statistically significant relationship between sales rep age and customer satisfaction rating, and the relationship is not likely due to chance.

Therefore, the correct answer is either (a) if the p-value is less than 0.05, or (b) if the p-value is greater than 0.05.

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Answer:

30 meters

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Answer:

30 meters

Step-by-step explanation:

If circle is having radius as 4 cm, then the length of the rectangle inscribed in circle is 5.29 cm.

The "Rectangle" is inscribed in the circle, So, its diagonal will be equal to the diameter of circle.

So, diagonal of rectangle has a length of = 2 × radius,

⇒ Diagonal = 2×4 = 8 cm.

We also know that width of rectangle is = 6 cm. To find length of  rectangle, we use the property, which states that in "right-triangle", the sum of the squares of the "length" and "width" is equal to the square of "diagonal".

Let "h" denote "length" of rectangle which is inscribed in circle,

So, We have, h² + 6² = 8²,

⇒ h² + 36 = 64,

⇒ h² = 28,

⇒ h ≈ 5.29,

Therefore, the length of rectangle is approximately 5.29 cm.

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The given question is incomplete, the complete question is

The circle has a radius of 4cm. The vertices of the rectangle lie on the circumference of the circle. The rectangle has a width of 6 cm.

Calculate the length of the rectangle.

The length of CB is 4√(3), and we used the Pythagorean theorem and the perpendicular bisector theorem to solve for it.

By the perpendicular bisector theorem, if a point lies on the perpendicular bisector of a line segment, then it is equidistant from the endpoints of the segment. Therefore, in triangle ABC, since ray DB is the perpendicular bisector of AC, it follows that BD = DC.

Let x be the length of CB. Then, by the Pythagorean theorem in triangle ABC, we have:

[tex]AB^2 + BC^2 = AC^2[/tex]

Substituting AB = 12 and BD = DC = x/2, we get:

[tex]12^2 + x^2 = (2x)^2[/tex]

[tex]144 + x^2 = 4x^2[/tex]

[tex]3x^2 = 144[/tex]

[tex]x^2[/tex]= 48

x = √(48) = 4√(3)

Therefore, the length of CB is 4√(3), and we used the Pythagorean theorem and the perpendicular bisector theorem to solve for it.

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In summary: Mean (μ): 120, Standard deviation (σ): 6.93, Minimum usual value (μ - 2σ): 106.14 and Maximum usual value (μ + 2σ): 133.86

To find the mean mu μ of the binomial distribution, we use the formula mu = n*p. Therefore, mu = 200*0.6 = 120.

To find the standard deviation sigma σ, we use the formula sigma = sqrt(n*p*(1-p)). Therefore, sigma = sqrt(200*0.6*0.4) = 6.93.

Using the range rule of thumb, we can estimate the minimum usual value by subtracting 2 times the standard deviation from the mean, and the maximum usual value by adding 2 times the standard deviation to the mean. Therefore, the minimum usual value is mu - 2*sigma = 120 - 2*6.93 = 106.14, and the maximum usual value is mu + 2*sigma = 120 + 2*6.93 = 133.86.

So, in summary, the mean mu μ of the binomial distribution is 120, the standard deviation sigma σ is 6.93, the minimum usual value mu minus 2 sigma μ−2σ is 106.14, and the maximum usual value mu plus 2 sigma μ+2σ is 133.86.
For a binomial distribution, the mean (μ) and standard deviation (σ) can be calculated using the formulas:

μ = n * p
σ = √(n * p * (1 - p))

Given n = 200 and p = 0.6, we can find μ and σ:

μ = 200 * 0.6 = 120
σ = √(200 * 0.6 * (1 - 0.6)) = √(200 * 0.6 * 0.4) = √48 ≈ 6.93

Next, we can use the range rule of thumb to find the minimum and maximum usual values:

Minimum usual value (μ - 2σ):
120 - (2 * 6.93) = 120 - 13.86 ≈ 106.14

Maximum usual value (μ + 2σ):
120 + (2 * 6.93) = 120 + 13.86 ≈ 133.86

In summary:
Mean (μ): 120
Standard deviation (σ): 6.93
Minimum usual value (μ - 2σ): 106.14
Maximum usual value (μ + 2σ): 133.86

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In the long run, the likelihood of indifferent weather in Columbus on a given day is approximately 29.3%.

To find the long-term likelihood of indifferent weather in Columbus, we need to find the steady-state probabilities of the stochastic matrix provided. The matrix is given as:

P = | 0.6  0.5  0.4 |
     | 0.3  0.2  0.3 |
     | 0.1  0.3  0.3 |

1. First, find the transpose of the matrix P:
P^T = | 0.6  0.3  0.1 |
          | 0.5  0.2  0.3 |
          | 0.4  0.3  0.3 |

2. Next, subtract the identity matrix I from the transpose of P:
P^T - I = | -0.4  0.3  0.1 |
               |  0.5 -0.8  0.3 |
               |  0.4  0.3 -0.7 |

3. To find the steady-state probabilities, we need to solve the system of linear equations:
(-0.4)x + 0.3y + 0.1z = 0
0.5x - 0.8y + 0.3z = 0

We also have an additional constraint since the sum of probabilities must equal 1:
x + y + z = 1

4. Solve this system of linear equations using any method (substitution, elimination, or matrix method). The resulting probabilities are:
x = 0.432 (good weather probability)
y = 0.293 (indifferent weather probability)
z = 0.275 (bad weather probability)

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Answer:

Based on the information provided, the correct choice is:

fail to reject it

Here are the key points:

• The mean depression score for the sample of 20 4th graders was 4.4.

• The counselor tested the null hypothesis that these 4th graders were less depressed than the general 4th grader population.

• The t score calculated was 2.8.

To reject the null hypothesis and conclude the sample differs from the population, we would need a high enough t score. But the t score of 2.8 is not conclusively high enough here.

Some additional considerations:

• The general 4th grader population mean is 5, so the sample mean of 4.4 is a bit lower, but not drastically. This suggests the sample may not differ hugely from the population.

• There is no information on the variation or standard deviation for either the sample or population. Without this, we can't determine if a t score of 2.8 actually signifies a statistically significant difference.

• The sample size of 20 is decent but not very large. Larger sample sizes provide more conclusive results.

• No p-value is given, making it hard to judge if the t score of 2.8 is high enough to reject the null hypothesis. By convention, p<0.05 is often used but we don't have the p-value here.

So overall, there is not enough definitive evidence provided to conclusively reject the null hypothesis. The t score of 2.8 alone is probably not high enough, given the considerations around sample size, variation, and lack of a p-value. More data and analysis would be needed to make a firm decision either way.

Therefore, the correct choice is: "fail to reject it". There is not enough information given in this question and results to conclusively reject the null hypothesis.

Step-by-step explanation:

One more time-consuming method to check for normality of a distribution that only works for large data sets is to use the Shapiro-Wilk test.

The Shapiro-Wilk test is a statistical test that checks whether a given sample of data comes from a normally distributed population. It works by calculating the test statistic W, which measures the deviation of the sample from a normal distribution. The test then compares the value of W to a critical value, which depends on the sample size and significance level.

While the Shapiro-Wilk test is a powerful tool for assessing normality, it is computationally intensive and may not be practical for smaller data sets. Moreover, it can be sensitive to sample size, so it may not provide reliable results for very small or very large samples.

In general, it is recommended to use multiple methods for checking normality, such as visual inspection of a histogram or Q-Q plot, in addition to formal statistical tests like the Shapiro-Wilk test.

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Answer:

Account A:

[tex]4750 {e}^{.0375 \times 7} = 6175.84[/tex]

Account B:

[tex]5100 {(1 + \frac{.03875}{12}) }^{12 \times 5} = 6188.41[/tex]

Account B has a larger balance.

The orthocenter will lie in the interior of a(n) acute triangle.  In Euclidean geometry, the orthocenter is a point where the three altitudes of a triangle intersect.

All three angles in an acute triangle are less than 90 degrees.  If we draw the altitudes from each vertex, they will all intersect inside the triangle. Therefore, the orthocenter of an acute triangle will always be located in the interior of the triangle.

On the other hand, in an obtuse triangle, at least one angle is greater than 90 degrees. In this case, one of the altitudes will lie outside of the triangle, so the orthocenter will be located outside of the triangle.

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Based on the above, the height from which the stone is said to be dropped is approximately 176.4 meters.

Looking at the question given, the formula to calculate the height from which an object that is dropped will be:

h = 4.9t²

where:

h = the height (m)

t  = time (seconds)

So by substituting t = 6 seconds into the formula, we will  have:

h = 4.9 x 6²

h = 4.9 x 36

h = 176.4

Therefore, the height from the point that the stone is dropped is 176.4 meters.

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To calculate the height, in meters, from which an object is dropped, knowing the time it takes to reach the ground, the following formula is used: h equals 4.9 t squared, where h is the height and t is the time in seconds. What is the height from which a stone is dropped that takes 6 seconds to hit the ground? The height is meters

This alternative hypothesis is either greater than or less than 0.87, but not exactly equal to it.

The alternative hypothesis (H1) is the hypothesis that is tested when the null hypothesis (H0) is rejected.

The null hypothesis is that the population proportion using the new drug that have a quick recovery is 0.87.

The alternative hypothesis would be that the population proportion using the new drug that have a quick recovery is different from 0.87.

This can be expressed as:

H1: p ≠ 0.87

The alternative hypothesis in this scenario would be that the new drug being tested is effective in increasing the chance of a quick recovery in people who have come down with the flu in the past week.

The alternative hypothesis would state that the population proportion of those who use the new drug and experience a quick recovery is greater than 0.87.
The alternative hypothesis is necessary because it allows us to determine whether the results of the study are statistically significant.

If the null hypothesis is accepted, it means that there is no significant difference between the rate of quick recovery with or without the new drug.

The alternative hypothesis is accepted, it means that the new drug has a significant effect on increasing the rate of quick recovery.
To test this hypothesis, a statistical analysis will need to be performed using the data collected from the study.

This analysis will allow us to determine whether the results are statistically significant and whether we can reject the null hypothesis in favor of the alternative hypothesis.

Ultimately, this will provide valuable information on the effectiveness of the new drug and whether it should be recommended for use in treating the flu.

The "≠" symbol means "not equal to".

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The null hypothesis (H0) is that the proportion of clients who have high-risk stocks is equal to or greater than 15%, while the alternative hypothesis (H1) is that the proportion of clients who have high-risk stocks is less than 15%. In other words, the null hypothesis assumes that p >= 0.15 and the alternative hypothesis assumes that p < 0.15.

To Test These hypotheses, the brokerage firm can collect a sample of clients and determine the proportion of those clients who have high-risk stocks in their portfolio. If the sample proportion is significantly lower than 15%, the firm can reject the null hypothesis and conclude that there is evidence to suggest that the true proportion of clients with high-risk stocks is less than 15%.

If the sample proportion is not significantly lower than 15%, the firm fails to reject the null hypothesis and cannot conclude that the true proportion of clients with high-risk stocks is less than 15%.

It is important for the brokerage firm to accurately determine the proportion of clients with high-risk stocks, as this information can help them manage their clients' portfolios more effectively and reduce the overall risk of their business.

By testing these hypotheses, the firm can gain a better understanding of the risk level of their clients' investments and make informed decisions about how to allocate their resources.

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Answer:

The correct answer is B. In set B, the input of -2 does not correspond to exactly one output.

Answer:

72 cm²

Step-by-step explanation:

We can split this composite figure into 3 simple shapes:

First, we can solve for the area of the rectangles:

A(rect) = length × width

A(rect1) = 4 × (9 - 3) = 24

A(rect2) = 10 × 3 = 30

Next, we can solve for the area of the triangle:

A(triangle) = (1/2) × base × height

A(triangle) = (1/2) × (10 - 4) × 6

A(triangle) = 3 × 6 = 18

Finally, we can add each the simple shapes' areas together to get the area of the whole figure.

A = A(rect1) + A(rect2) + A(triangle)

A = 24 + 30 + 18

A = 72 cm²

the probability of choosing exactly 5 red marbles when 12 marbles are chosen at random is approximately 0.028.

This is a hypergeometric probability problem .

The total number of ways to choose 12 marbles from 27 is:

${{27}\choose{12}} = \frac{27!}{12!15!} = 10,!626,!766$

The number of ways to choose 5 red marbles and 7 blue marbles is:

$ {{15}\choose{5}}\cdot{{12}\choose{7}} = \frac{15!}{5!10!}\cdot\frac{12!}{7!5!} = 300,!450$

So the probability of choosing exactly 5 red marbles is:

$P(\text{5 red}) = \frac{300,!450}{10,!626,!766} \approx 0.028$

what is probability?

Probability is the measure of the likelihood or chance of an event occurring. It is a quantitative measure that ranges from 0 to 1, where 0 indicates an impossible event and 1 indicates a certain event.

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The volume of the completed rectangular prism that have a height of 7 cubes will be 63 cubic units.

The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height of the prism. In this case, the base of the prism has 3 x 3 cubes, which means the length and width are both 3 cubes.

Therefore, l = 3 and w = 3. The height of the prism is given as 7 cubes. Thus, h = 7.

Substituting the given values in the formula for volume, we get:

V = lwh

= 3 x 3 x 7

= 63

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