Which of the following quadrilaterals must have at least one pair of parallel sides?
Check all that apply.
Rectangle, Square, Trapezoid, Parallelogram, Kite, Rhombus.

Explain your answer.

The inequality in the expression 41-x < 17 is the less than inequality

The solution to the inequality is x > 24

The inequality is given as:

41-x < 17

Subtract 41 from both sides of the inequality

41 - 41 -x < 17 - 41

Evaluate the difference

-x < -24

Multiply both sides by -1

-1 * -x < -24 * -1

Evaluate the product

x > 24

Hence, the solution to the inequality is x > 24

See attachment for the number line

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Answer:

c = 0

Step-by-step explanation:

Step 1: Write equation

15 - 5(4c - 7) = 50

Step 2: Solve for c

Step 3: Check

Plug in c to verify it's a solution.

15 - 5(4(0) - 7) = 50

15 - 5(-7) = 50

15 + 35 = 50

50 = 50

Answer: The figure changed size.

Step-by-step explanation:  Dilations change the sizes of shapes.  They can either make them bigger or make them smaller.

Answer:

As x approaches 6:

\( \frac{6 - x}{ {x}^{2} - 36 } = - \frac{x - 6}{(x - 6)(x + 6)} = - \frac{1}{x + 6} = - \frac{1}{6 + 6} = - \frac{1}{12} \)

The limit of the given function as x approaches 6 is -1/12. This is achieved by factoring and revising the original function, and then substituting into the revised function.

The student is asking for the limit of the function (6-x) / (x²-36) as x approaches 6. In mathematics, this is a problem of calculus and specifically involves limits. Let's solve this by first factoring the denominator to get (6-x) / ((x-6)(x+6))

By realizing we can revise the numerator as -(x-6), we make it obvious that the limit can be directly computed by substituting x=6 after canceling out the (x-6) terms. The result is -1/12, therefore the limit of the function as x approaches 6 is -1/12.

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Alan will be 50 yrs old and Aron will be 20 yrs old

Answer:4

Step-by-step explanation:22-4=18-4=14-4=10-4=6=2

On a number line where A is at 5 and B is at 50, and X is the midpoint and T is somewhere between A and B, the coordinates of point T is 15 and the distance of XB is 22.5.

A number line is straight line divided by equal measures that serves as a visual representation of the real numbers.

If on a number line, a is at 5 and b is at 50, then AB = 50 - 5 = 45.

If point X is the midpoint of A and B, then X divides the distance of A to B into two equal parts.

let n = AX = XB

AB = AX + XB

45 = n + n

45 = 2n

n = 22.5

AX = XB = 22.5

If point T is 2/3 of the way from X to B, then

T = 2/3XB

T = 2/3(22.5)

T = 15

Hence, the coordinates of T is at 15 and the distance of XB is 22.5.

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The denominator can be calculated as the sum of the probabilities of all possible cases where X1 + X2 = m:

P(X1 + X2 = m) = Σ(P(X1 = k, X2 = m - k)), for k = 0 to m

We obtain the conditional distribution P(X1 = k | X1 + X2 = m) for k = 0 to m.

(a) To find the distribution of X, we can consider the cases where A catches k errors and B catches (X - k) errors, for k = 0 to X. The probability of A catching k errors is given by the binomial distribution:

P(X1 = k) = C(X, k) * p1^k * (1 - p1)^(X - k)

Similarly, the probability of B catching (X - k) errors is:

P(X2 = X - k) = C(X, X - k) * p2^(X - k) * (1 - p2)^(X - (X - k))

Since X is the number caught by at least one of the two proofreaders, the distribution of X is given by the sum of the

probabilities for each k:

P(X = x) = P(X1 = x) + P(X2 = x), for x = 0 to X

(b) To find E(X), we can sum the product of each possible value of X and its corresponding probability:

E(X) = Σ(x * P(X = x)), for x = 0 to X

(c) Assuming p1 = p2 = p, we can find the conditional distribution of X1 given that X1 + X2 = m using the concept of conditional probability. Let's denote X1 + X2 = m as event M.

P(X1 = k | M) = P(X1 = k and X1 + X2 = m) / P(X1 + X2 = m)

To find the numerator, we need to consider the cases where X1 = k and X1 + X2 = m:

P(X1 = k and X1 + X2 = m) = P(X1 = k, X2 = m - k)

Using the same logic as in part (a), we can calculate the probabilities P(X1 = k) and P(X2 = m - k) with p1 = p2 = p.

Finally, the denominator can be calculated as the sum of the probabilities of all possible cases where X1 + X2 = m:

P(X1 + X2 = m) = Σ(P(X1 = k, X2 = m - k)), for k = 0 to m

Thus, we obtain the conditional distribution P(X1 = k | X1 + X2 = m) for k = 0 to m.

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Because her initial speed is already above the speed limit. So, the problem is not solvable under the given conditions.

Let's call Amanda's initial speed "s" (in mph). We know that she drove for 4 hours at speed s, and then for the remaining time (which is 6 hours), she drove at speed s - 20 mph.

The total distance of the trip is 400 miles. Using the distance formula:

distance = rate × time

we can write two equations:

First part of the trip:

400 = s × 4

Second part of the trip:

400 = (s - 20) × 6

Now we can solve for s. Starting with the first equation:

400 = s × 4

Dividing both sides by 4 gives:

s = 100

So Amanda's initial speed was 100 mph.

Checking with the second equation:

400 = (s - 20) × 6

Substituting s = 100, we get:

400 = (100 - 20) × 6

400 = 80 × 6

400 = 480

This equation is not true, which means that there must be an error in our calculations. The error is that Amanda cannot possibly have driven at 100 mph for 4 hours and then slowed down to 80 mph for the remaining 6 hours, because her initial speed is already above the speed limit. So, the problem is not solvable under the given conditions.

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Answer:

x ≤3

Step-by-step explanation:

2(4+ 2x)≥ 5x+ 5

distribute

8+4x ≥ 5x+ 5

Subtract 4x from each side

8+4x-4x≥ 5x-4x+ 5

8  ≥ x+ 5

Subtract 5 from each side

8-5 ≥ x+ 5-5

3 ≥ x

x ≤3

Answer:

x ≤3

Step-by-step explanation:

The area of triangle ABC with vertices is 22 square units

The vertices are given as:

A(4, -3) B(9,-3) , and C(10, −11)

The area of the triangle is calculated using

Area = 0.5 * |Ax(By - Cy) + Bx(Ay - Cy) + Cx(Ay - By)|

This gives

Area = 0.5 * |4 * (-3 + 11) + 9 * (-3 + 11) + 10 * (-3 - 3)|

Evaluate the sum of products

Area = 0.5 * |44|

Remove the absolute bracket

Area = 0.5 * 44

Evaluate

Area = 22

Hence, the area of ABC with vertices is 22 square units

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Answer:

135/2

Step-by-step explanation:

In 1 day the dog eats 9/4 lbs

In 30 days the dog eats (9/4) * 30 lbs

                                     = (9 * 30) / 4

                                     =  135/2

\(\boldsymbol{\sf{\dfrac{4}{5}+\dfrac{9}{10} } }\)

The least common multiple of 5 and 10 is 10. Convert 4/5 and 9/10 to fractions with denominators of 10.

\(\boldsymbol{\sf{\dfrac{4\times2}{5\times2}+\dfrac{9}{10} \ \ \to \ \ Simplify }}\)

\(\boldsymbol{\sf{ \dfrac{8}{10}+\dfrac{9}{10} }}\)

Since 8/10 and 9/10 have the same denominator, join their numerators to add them.

\(\boldsymbol{ \sf{\dfrac{8+9}{10} \ \to \ \ Add }}\)

Simplify

\(\boldsymbol{\sf{ \dfrac{17}{10}= }}\boxed{\boldsymbol{\sf{1\frac{7}{10} }}}\)

The standard error of the mean for a sample of 256 middle managers, with a population standard deviation of $2,150.00 and a sample mean of $35,420.00, is approximately $134.38.

The standard error of the mean can be calculated using the formula: standard error = population standard deviation / square root of sample size.

Population standard deviation (σ) = $2,150.00

Sample size (n) = 256

Substituting these values into the formula, we can calculate the standard error of the mean:

Standard error = $2,150.00 / √256

Standard error ≈ $2,150.00 / 16

Standard error ≈ $134.38

Therefore, the standard error of the mean is approximately $134.38.

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The most likely cause for the change in pH after bubbling CO2 through the solution is the formation of carbonic acid.

When CO2 is bubbled through an aqueous solution, it can react with water to form carbonic acid (H2CO3). This reaction occurs due to the dissolution of CO2 in water, which undergoes a chemical equilibrium process. Carbonic acid is a weak acid that can release hydrogen ions (H+) into the solution, thus lowering the pH. The presence of carbonic acid lowers the pH value compared to the original pH of the solvent.

This phenomenon is commonly observed when CO2 is dissolved in water, such as in carbonated beverages. The carbonic acid formed from the reaction with CO2 contributes to the acidic properties of the solution. Therefore, the most likely cause for the change in pH after bubbling CO2 through the solution is the formation of carbonic acid, leading to a decrease in pH.

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Answer:

107, there is two lines after that so 108 109 and the last line is 110 so your answer will be 107 degrees.

Step-by-step explanation:

Answer:

\(\Large \boxed{\sf 107\°}\)

Step-by-step explanation:

The line is in between 106° and 108° so it is 107°

the volume of the silo is approximately 11,657.88 cubic meters.

To find the volume of the silo, we need to calculate the volumes of the cylinder and the cone separately, and then add them together.

The radius of the base of the silo is half the diameter, so it's 10 meters / 2 = 5 meters.

The height of the cylinder is given as 27 meters. Since the height of the cone is half the height of the cylinder, the height of the cone is 27 meters / 2 = 13.5 meters.

The volume of a cylinder is calculated using the formula:

Volume of Cylinder = π * radius^2 * height

Plugging in the values, we get:

Volume of Cylinder = π * 5^2 * 27 = 3375π cubic meters (approximately 10,598.07 cubic meters)

The volume of a cone is calculated using the formula:

Volume of Cone = (1/3) * π * radius^2 * height

Plugging in the values, we get:

Volume of Cone = (1/3) * π * 5^2 * 13.5 = 337.5π cubic meters (approximately 1059.81 cubic meters)

Adding the volumes of the cylinder and the cone, we get:

Volume of Silo = 3375π + 337.5π = 3712.5π cubic meters (approximately 11,657.88 cubic meters)

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The error of posting $50 as $500 can be detected by comparing the recorded amount to the expected amount. Here are the steps to detect this error:

1. Calculate the expected amount: Determine the correct amount that should have been posted. In this case, the expected amount is $50.

2. Compare the recorded amount with the expected amount: Check the posted amount and compare it to the expected amount. If the recorded amount shows $500 instead of $50, then an error has occurred.

3. Identify the discrepancy: Recognize that the recorded amount of $500 is significantly higher than the expected amount of $50.

4. Investigate the source of the error: Look for the cause of the error. It could be a data entry mistake, a typo, or a misunderstanding.

5. Take corrective actions: Once the error is detected, rectify it by posting the correct amount of $50. Additionally, ensure that the source of the error is addressed to prevent similar mistakes in the future.

By following these steps, the error of posting $50 as $500 can be detected, corrected, and prevented from happening again.

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The simplified value of the maximum weight is 9.62 and the minimum weight is 9.18. Also the function for the maximum and minimum weight is y + x and y - x

Here,

Given that, A package with a labeled weight of 9.4 pounds can have an actual weight plus or minus 0.22 pounds.
Let the weight labeled be y and the actual weight be x
Weight = y ± x
Maximum weight = y + x
Minimum weight = y - x

Weight = 9.4 ± 0.22
Now,
Maximum weight = 9.4 + 0.22 = 9.62 pounds
Minimum weight = 9.4 - 0.22 = 9.18 pounds

Thus, the simplified value of the maximum weight is 9.62 and the minimum weight is 9.18. Also, the function for the maximum and minimum weight is y + x and y - x

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The expression (3xy) is an algebraic expression

The equivalent expressions of (3xy) are (6xy)/2 and (9xy)/3

The expression is given as:

(3xy)

Multiply by 2/2

(3xy) = (6xy)/2

Multiply by 3/3

(3xy) = (9xy)/3

The above products means that, we multiply the expression by 1 (i.e. n/n) to get an equivalent expression

Hence, the equivalent expressions of (3xy) are (6xy)/2 and (9xy)/3

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The linear equation represents the total number of visits Jackson must make to earn a free movie ticket is 9.5x + 45 = 102 and the total number of visits to the movie theater he must make is 6.

Given :

The following steps can be used in order to determine the number of visits Jackson must make to earn a free movie ticket:

Step 1 - Let the total number of visits to the movie theater be 'x'.

Step 2 - So, the linear equation represents the total number of visits Jackson must make to earn a free movie ticket is:

9.5x + 45 = 102

Step 3 - Simplify the above linear equation.

9.5x = 57

x = 6

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Answer:

Function                         Not a function      

not a Function                   function

pg 2

B- explanation is that 2 inputs dont have the same output 8-1, 8-1,4-1,3-1

pg 3

1. yes; -5 is not in the set

2. yes; 2 is not in the set

3. no; .75 is 3/4

4. no; -4 is already in the set

Normal probability distribution is applied to a continuous random variable. The correct option is D.

The normal probability distribution, also known as the Gaussian distribution, is a probability distribution that is commonly used in statistics and probability theory. It is a continuous probability distribution that is often used to model the behavior of a wide range of variables, such as physical measurements like height, weight, and temperature.

The normal distribution is characterized by two parameters: the mean (μ) and the standard deviation (σ). It is a bell-shaped curve that is symmetrical around the mean, with the highest point of the curve being located at the mean. The standard deviation determines the width of the curve, and 68% of the data falls within one standard deviation of the mean, while 95% falls within two standard deviations.

The normal distribution is widely used in statistical inference and hypothesis testing, as many test statistics are approximately normally distributed under certain conditions. It is also used in modeling various phenomena, including financial markets, population growth, and natural phenomena like earthquakes and weather patterns.

Overall, the normal probability distribution is a powerful tool for modeling and analyzing a wide range of continuous random variables in a variety of fields.

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The inequality statements are 1 < 0, x > 0, x = x and x = 5

An empty set

An empty set is a set with no elements.

An inequality statement with no solutions results in an empty set.

One example of an inequality statement with no solutions is 1 < 0.

Some solution but not all real numbers

An inequality statement whose solution is some but not all real numbers is x > 0.

The solution set is the set of all positive real numbers, excluding 0.

The number line is represented as follows

|------------------------------------| 0  |----------------------------- |

All real numbers

A statement whose solution is all real numbers is x = x

The solution set is the set of all real numbers

The number line is represented as follows

|--------------------------- | ...  | -2  | -1  | 0  | 1  | 2  | ... |

Exactly one number

A statement whose solution is exactly one number is x = 5.

The solution set is the set containing only the number 5

The number line is represented as follows

|--------------------------- | ...  | 4  | ... |

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Answer:

3628800 ways if the women are always required to stand together.

To solve this problem, we can consider the number of ways to arrange the women and men separately, and then multiply the results together.

First, let's consider the arrangement of the women. Since no two men can be seated next to each other, the women must be seated in between the men. We can think of the 5 men as creating 6 "gaps" where the women can be seated (one gap before the first man, one between each pair of men, and one after the last man).

Out of these 6 gaps, we need to choose 7 gaps for the 7 women to sit in. This can be done in "6 choose 7" ways, which is equal to the binomial coefficient C(6, 7) = 6!/[(7!(6-7)!)] = 6.

Next, let's consider the arrangement of the 5 men. Once the women are seated in the chosen gaps, the men can be placed in the remaining gaps. Since there are 5 men, this can be done in "5 factorial" (5!) ways.

Therefore, the total number of ways to seat the 5 men and 7 women is 6 * 5! = 6 * 120 = 720.

There are 720 ways to seat the 5 men and 7 women in a row such that no two men are next to each other.

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Answer:

(-♾, ♾)

Step-by-step explanation:

A quadratic can accept any real x value. So the domain is All Real Numbers. This in interval notation is

(-♾, ♾)

This is read as negative infinity to positive infinity

The implied domain of g(x) = -2x² + 1 is (-∞, +∞), indicating that the function is defined for all real values of x.

To determine the implied domain of the function g(x) = -2x² + 1, we need to identify the set of all possible values for x that make the function defined and meaningful.

In this case, since the function is a quadratic polynomial, there are no restrictions on the input values of x. The function is defined for all real numbers.

Therefore, the implied domain of the function g(x) = -2x² + 1 is the set of all real numbers, which can be expressed in interval notation as (-∞, +∞).

This interval notation indicates that there are no specific limitations or exclusions on the values of x for the function. It includes all real numbers from negative infinity to positive infinity.

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Answer: it’s c

Step-by-step explanation:

Answer:

x=1

Step-by-step explanation:

-5x-3x = - 12-4

-8x=-16 multiply that by -8

x=2

Answer:

2

Step-by-step explanation:

Step 1:

- 5x + 4 = 3x - 12       Equation

Step 2:

4 = 8x - 12         Add 5x on both sides

Step 3:

16 = 8x       Add 12 on both sides

Step 4:

x = 16 ÷ 8       Divide

Answer:

x = 2

Hope This Helps :)