polynomial for the area of the square x7x

The contrapositive of the given statement is “If their graph is a linear function, then the two variables are directly proportional”, option B is correct.

The contrapositive of a conditional statement switches the order of the clauses and negates them both. In general, the contrapositive of a conditional statement has the same truth value as the original statement.

It can be a useful tool in logic and proofs because it can help simplify the statement and make it easier to prove or disprove. For example, if we wanted to prove the original statement, we could instead prove its contrapositive, option B is correct.

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The complete question is:

What is the contrapositive of the conditional statement?

A) If their graph is not a linear function, then the two variables are not directly proportional.

B) If their graph is a linear function, then the two variables are directly proportional.

C) If two variables are not directly proportional, then their graph is not a linear function.

D) If their graph is a non-linear function, then the two variables are not directly proportional.

The volume of the right rectangular prism is 156 cubic centimeters.

We have,

The formula for the volume of a rectangular prism is:

V = l x w x h

where V is the volume, l is the length, w is the width, and h is the height.

Using the given values, we can substitute them into the formula to find the volume of the rectangular prism:

V = 13 cm x 4 cm x 3 cm

V = 156 cm^3

Therefore,

The volume of the right rectangular prism is 156 cubic centimeters.

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The series converges for all values of p < -1, and diverges for all values of p ≥ -1.

To apply the Integral Test, we need to verify that the terms of the series are positive and decreasing for all n greater than some fixed integer. For this series, note that the terms are positive since both the base and the natural logarithm are positive. To show that the terms are decreasing, we take the ratio of successive terms:

[tex]a(n+1)/a(n) = [(n+1)ln(n+1)]^p / [nln(n)]^p[/tex]

[tex]= [(n+1)/n]^p * [(1+1/n)ln(1+1/n)]^p[/tex]

Since (n+1)/n > 1 and ln(1+1/n) > 0 for all n, it follows that the ratio is greater than 1 and therefore the terms are decreasing.

To use the Integral Test, we need to find a function f(x) such that f(n) = a(n) for all n and f(x) is positive and decreasing for x ≥ 3. A natural choice is [tex]f(x) = x(ln(x))^p[/tex]. Note that f(n) = a(n) for all n and f(x) is positive and decreasing for x ≥ 3. Then we have:

integral from 3 to infinity of f(x) dx = integral from 3 to infinity of x(ln(x))^p dx

To evaluate this integral, we use integration by substitution with u = ln(x):

[tex]du/dx = 1/x, dx = x du[/tex]

So the integral becomes:

integral from ln(3) to infinity of [tex]u^p e^u du[/tex]

This integral converges for p < -1, by the Integral Test for Improper Integrals.

Therefore, the series converges for all values of p < -1, and diverges for all values of p ≥ -1.

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The graph is attached.

Given is a triangle ABC, we need to find its coordinates if it is reflected over y = -x,

The rule of reflection over y = -x is,

(x, y) = (-x, -y)

So,

A = (-5, -4)

B = (1, -4)

C = (-1, -5)

After reflection,

A' = (5, 4)

B' = (-1, 4)

C' = (1, 5)

Hence the points after reflection are A' = (5, 4), B' = (-1, 4) and C' = (1, 5)

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Answer:

  75

Step-by-step explanation:

You want the value of y² +4y -2 when y=7.

Put the value where the variable is and do the arithmetic.

  7² +4·7 -2

  = 49 +28 -2

  = 77 -2

  = 75

The value of the expression is 75.

__

Additional comment

It is often easier to evaluate a polynomial when it is written in Horner form:

  (y +4)·y -2

  = (7 +4)·7 -2 = 11·7 -2 = 77 -2 = 75

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You read in a book about bridge that the probability that each of the four players is dealt exactly one ace is about 0.11. This means that (c) in a very large number of bridge deals, the percent of deals on which each player has one ace will be very close to 11%.

The correct answer is (c) in a very large number of bridge deals, the percent of deals on which each player has one ace will be very close to 11%. This is because the given probability is an estimate based on a large number of bridge deals, and the law of large numbers states that as the number of trials (bridge deals) increases, the observed percentage will approach the true probability. Option (a) is incorrect because the given probability is not a guarantee for every 100 bridge deals. Option (b) is incorrect because the number of deals with each player having one ace will vary and may not be exactly 110,000. Option (d) is incorrect because the given probability only refers to the likelihood of each player having one ace, not the average number of aces in a hand.

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The sample proportion of insomnia sufferers who did not enjoy a better night's sleep after the therapy is 0.694 (rounded to three decimal places).

We calculate the sample proportion of insomnia sufferers who did not enjoy a better night's sleep after the therapy. Here are the steps to find the answer:

1. Determine the total number of participants in the study (n): 72 insomnia sufferers.
2. Determine the number of participants who enjoyed a better night's sleep after the therapy: 22 participants.
3. Subtract the number of participants who enjoyed a better night's sleep from the total number of participants to find the number of participants who did not enjoy a better night's sleep: 72 - 22 = 50 participants.
4. Calculate the sample proportion (p) of insomnia sufferers who did not enjoy a better night's sleep after the therapy by dividing the number of participants who did not enjoy a better night's sleep by the total number of participants: p = 50 / 72.
5. Round the answer to three decimal places, if necessary: p ≈ 0.694.

Your answer: The sample proportion of insomnia sufferers who did not enjoy a better night's sleep after the therapy is approximately 0.694.

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The diameter of the given circle with a circumference of 28.6 centimeters is approximately 9.11 cm.

The circumference of a circle is given by the simple formula: C = πd, where C is the circumference, π is the constant pi and d is the diameter of the circle.

Given that the circumference of the circle is 28.6 cm, we can use the formula to find the diameter:

28.6 = πd

d = 28.6/π

Using 3.14 as an approximation for π, we get:

d ≈ 28.6/3.14 ≈ 9.11

Therefore, the diameter of the circle is approximately 9.11 cm.

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If two samples from the same population have the same mean and are both n = 100, they will probably still have different sample variances.

We have,

If two samples from the same population have the same mean and are both n=100, they will probably still have different sample variances.

This is because sample variance refers to the dispersion or spread of data points within each individual sample, and this can vary even if the samples have the same mean and sample size (n=100).

It's important to note that the other options (t-statistics, standard errors, and alpha values) are related to the sampling distribution or hypothesis testing, which may not be different simply due to having the same mean and sample size.

Thus,

If two samples from the same population have the same mean and are both n = 100, they will probably still have different sample variances.

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The intercepts of the equation 5x - 3y = -30 include the following:

x-intercept = (-6, 0).

y-intercept = (0, 10).

In Mathematics and Geometry, the x-intercept is the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" or y-value is equal to zero (0).

When the y-value = 0, the x-intercept can be calculated as follows;

5x - 3y = -30

5x - 3(0) = -30

5x = -30

x = -30/5

x = -6.

When the x-value = 0, the y-intercept can be calculated as follows;

5x - 3y = -30

5(0) - 3y = -30

3y = 30

y = 30/3

y = 10.

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Complete Question:

What are the intercepts of the equation 5x - 3y = -30?

Pierre's question is a common philosophical and scientific question about the nature of prediction and probability.

In the 18th century, there was not a comprehensive understanding of the scientific laws that govern the natural world as we have today. Therefore, the most reasonable response to Pierre's question would be that it depends on the probability model used. The probability of the sun rising tomorrow would be based on various factors such as astronomical observations, scientific knowledge of celestial mechanics, and weather patterns.

While we cannot predict the future with absolute certainty, we can use available data and knowledge to make informed predictions about the likelihood of the sun rising tomorrow.

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Answer:

14

Step-by-step explanation:

eere4

If a given certificate C is a legitimate answer to the instance, we can check in polynomial time if it is (B, S1, S2, ..., Sm, K) of SETCOVER. Hence, the language SETCOVER is in NP.

To prove that the language SETCOVER is in NP, we need to show that given an instance (B, S1, S2, ..., Sm, K) of SETCOVER and a certificate C, we can verify in polynomial time whether C is a valid solution to the instance.

The certificate C in this case is a subset IC of {1, 2, ..., m} of size K, which represents the indices of the sets that form a cover for B. To verify whether C is a valid solution, we need to check two things:

Verify that IC has size K: We can simply count the number of elements in IC and check if it equals K. This can be done in O(m) time, which is polynomial in the size of the input.

Verify that the sets S_i for i in IC form a cover for B: We can iterate through the elements in B and check whether each element is present in at least one of the sets S_i, where i is in IC. Since B has at most |B| elements, and each set S_i has at most |B| elements, this can be done in O(K |B|) time, which is polynomial in the size of the input.

Therefore, If a given certificate C is a legitimate answer to the instance, we can check in polynomial time if it is (B, S1, S2, ..., Sm, K) of SETCOVER. Hence, the language SETCOVER is in NP.

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Answer:

cos A = 45

Step-by-step explanation:

90 - sin A = 45 = cos A

90 Minus whatever the cos value for the angle is = the sin and vice versa.

The probability of choosing a black chip and then another black chip is,

⇒ 1/3

Since, There are 4 + 6 = 10 chips in the bag.

And, 6 of them are black .

Hence, The probability that the first chip chosen will be black is,

⇒ 6/10

⇒ 3/5.

After that, there is one black chip less in the bag, so there are 9 chips in the bag, 5 of them are black.

Hence, The probability that the second chip chosen will be black is,

⇒ 5/9

Now, Multiply the probabilities to find the probability that the first chip will be black and the second chip will be black:

⇒ 3/5 × 5/9

⇒ 1/3

Thus, The probability of choosing a black chip and then another black chip is,

⇒ 1/3

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The length of diagonal of square is 6√2 inch.

We have,

side length  = 6 inches

Now, the formula for diagonal length of square as

d = √2a

where a is the side of square.

So, the length of diagonal of square is

= 6√2 inch.

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To approximate f'(0.6) using the Second Derivative Midpoint Formula with the given table data points and h = 0.06, follow these steps:

1. Identify the relevant data points: f(0.54), f(0.6), and f(0.66).
2. Apply the Second Derivative Midpoint Formula: f'(0.6) ≈ (f(0.66) - 2f(0.6) + f(0.54)) / (h^2).

Unfortunately, I cannot provide a specific answer without the values for f(0.54), f(0.6), and f(0.66).

Please provide these values, and I will gladly help you complete the calculation.

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Answer:

x= 9 in

Step-by-step explanation:

Volume = L ×W ×h

153 in3 =2in ×8.5in × h

153 in3 = 17in2 ×h

h = 153 in3/17in2

h = 9 inch

so the height if the figure has 9in length

The cost of the wood for the walls of the playhouse is $1141.44.

To calculate the cost of the wood for the walls of the playhouse, we need to find the surface area of the walls and then multiply it by the cost per square foot.

The surface area of the walls of an octagonal pyramid can be calculated by finding the area of each trapezoidal face and adding them up. Since the side length of the pyramid is 3 feet and the slant height is 12 feet, we can use the Pythagorean theorem to find the height of each trapezoidal face:

h = √(12² - (3/2)²)

h = √(144 - 2.25)

h = √(141.75)

h ≈ 11.89 feet

The area of each trapezoidal face is:

A = 1/2 * (b1 + b2) * h

A = 1/2 * (3 + 3) * 11.89

A ≈ 35.67 square feet

There are 8 trapezoidal faces in the octagonal pyramid, so the total surface area of the walls is:

SA = 8 * A

SA ≈ 285.36 square feet

Finally, we can calculate the cost of the wood for the walls by multiplying the surface area by the cost per square foot:

Cost = SA * $4

Cost = 285.36 * $4

Cost = $1141.44

Therefore, the cost of the wood for the walls of the playhouse is $1141.44.

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The probability that the weight will be less than 4504 grams is 0.9713.

We need to standardize the value 4504 using the given mean and variance, and then use the standard normal distribution table to find the corresponding probability.

The standard deviation is the square root of the variance: √391876≈626.05

So, the z-score for a weight of 4504 grams is:

z=(4504−3315)/626.05≈1.8974

Using a standard normal distribution table, we find that the probability of a z-score being less than 1.8974 is approximately 0.9713.

Therefore, the probability that a newborn baby boy born at the local hospital will weigh less than 4504 grams is approximately 0.9713.

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The area of a regular polygon with perimeter of 58 and apothem 10 is 290 square units

It is important to note that the formula for calculating the area of a regular polygon is expressed as;

A = 1/2(ap)

This is so, such that the parameters of the formula are given as;

Now, substitute the values into the equation;

Area = 1/2 × 58 × 10

Multiply the values

Area = 580/2

Divide the values, we get;

Area = 290 square units

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The expected number of sample means falling between 174.2 and 177.2 can be estimated as:

Expected number = A * Total number of sample means.

(a) The mean of the sampling distribution of X is given as 176.5 and the standard deviation is 1.28.

(b) To determine the expected number of sample means that fall between 174.2 and 177.2 centimeters inclusive, we need to calculate the z-scores corresponding to these values and find the area under the normal curve between these z-scores.

The z-score for 174.2 can be calculated as:

z1 = (174.2 - 176.5) / 1.28

Similarly, the z-score for 177.2 can be calculated as:

z2 = (177.2 - 176.5) / 1.28

Using a standard normal distribution table or a calculator, we can find the area between these two z-scores.

Let's assume the area between z1 and z2 is A. The expected number of sample means falling between 174.2 and 177.2 can be estimated as:

Expected number = A * Total number of sample means.

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The number of frames that the welders would be able to complete in 4 hours would be 10 frames.

The time taken by one welder is 8 hours for one frame which means the work rate would be:

= 1 / 8

= 1 / 8 frames per hour

If we have 20 welders therefore, the work rate per hour would be :

= 1 / 8 x 20

= 2. 5 frames per hour

Given 4 hours, the number of frames they would make is:

= 2. 5 x 4 hours

= 10 frames

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First part of question is:

A welding company produces burglar frames for windows and doors. In order to complete one frame, one welder needs 8 hours.

Answer: Another simple way to help get the tears flowing is by yawning. “Try yawning a few times in a row to wake up the tear ducts. This may be helpful ...

Step-by-step explanation:

The original price of the ticket was $210 and the new price is $310.

To find the percentage increase, we can use the formula:

percentage increase = (new price - old price) / old price * 100%

So, the percentage increase in the ticket price is:

percentage increase = (310 - 210) / 210 * 100% = 47.62%

Therefore, the ticket price has increased by 47.62%.

If the airline charges an additional $50 baggage fee with the new ticket price of $310, then the new price will be $360.

To find the new percentage increase, we can use the same formula:

percentage increase = (new price - old price) / old price * 100%

So, the percentage increase in the ticket price with the additional $50 baggage fee is:

percentage increase = (360 - 210) / 210 * 100% = 71.43%

Therefore, the ticket price has increased by 71.43% with the additional $50 baggage fee.

Answer:

Percent Increase= 47.619% increase, With $50 baggage fee= 71.4286% increase

Step-by-step explanation:

Account A has a principal of  $15,000

Account B has a principal of $6250

Hence, account A will earn the highest interest in the first month.

When we talk about the simple interest, we mean the kind of interest that is charged only on the principal sum and not on the interest of the former year. Given that 18 months is 1.5 years and 15 months is 1.4 years we can now have that;

I= PRT/100

A = P + I

P = principal

I = interest

R = rate

T =time

Thus;

For account A

8.1 = P * 0.036 * 1.5/100

8.1 = 0.054P

P = $15,000

For account B;

19.25 = P * 0.022 * 1.4/100

P = 1925/0.308

P = $6250

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Answer:

A = 120; C = 95

Step-by-step explanation:

We will need a system of equations to solve for C, the number of child tickets and A, the number of adult tickets.

We know that the sum of the revenue earned from both the child tickets and the adult tickets = the total revenue

Thus, our first equation is 3C + 14A = 1965

We also know that the sum of the total number of child and adult tickets = the the total number of tickets

Thus, our other equation is C + A = 215

We can solve using substitution by first isolating c in the second equation:

[tex]C+A=215\\C=-A+215[/tex]

Now, we can plug in the equation we just made for C in the first equation in our system to solve for A:

[tex]3(-A+215)+14A=1965\\-3A+645+14A=1965\\11A+645=1965\\11A=1320\\A=120[/tex]

Finally, we can solve for C using the second equation in our system by plugging in 120 for A:

[tex]C+120=215\\C=95[/tex]

The given equation is a constant function with a horizontal line passing through (0, 1). Here option E is the correct answer.

The given equation, f(x) = 1, represents a constant function, where the output or value of the function is always equal to 1 for any input value of x. This is a special case of a linear function, where the slope is zero and the y-intercept is a non-zero constant value.

Among the four given options, none of them is a constant function. A reciprocal function, y = 1/x, has a variable slope and a vertical asymptote at x = 0. A square root function, y = √x, has a non-linear shape and a domain of x ≥ 0. An absolute value function, y = |x|, has a V-shaped graph and is symmetric around the y-axis. A cube root function, y = ∛x, is also non-linear and has a domain of all real numbers.

Therefore, the correct answer is not listed among the options, and the function f(x) = 1 does not belong to any of the parent functions mentioned. It is a simple constant function with a horizontal line as its graph, passing through the point (0, 1) on the y-axis.

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Complete question:

Which type of parent function does the equation f(x) = 1 represent?

A. Reciprocal

B. Square root

C. Absolute value

D. Cube root

E. None of these

The length of BD is 53 units.

We are given here that BD is (8x - 27) units and EC is (2x + 33) units. BD and EC are the diagonals of a trapezoid. As we know that diagonals of a trapezoid are equal. Therefore, we will equate the given diagonals of a trapezoid.

BD  =  EC

Substituting the given values of BD and EC

8x - 27  =  2x + 33

combining the like terms

8x - 2x  =  33 + 27

6x  =  60

x = 60/6

x = 10

Now, as we have to find BD, we will substitute the value of x in the given equation for BD.

BD = 8x - 27

BD = 8(10) - 27

BD = 80 - 27

BD = 53

Therefore, BD is 53 units.

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The complete question is " If BD = 8x - 27 and EC-2x + 33, find BD​ with respect to the image shown."