A TV station is going to air a movie marathon with 11 movies. It will consist of 6 science fiction movies and 5 horror movies. The horror movies will be aired later in the evening. So, all of the horror movies will be aired last (after all of the science fiction movies). In how many ways can the station air the movie marathon?

The probability of the values of X that are less than 21 is 0.97725.

We have,

The term "standard deviation"  refers to a measurement of the data's dispersion from the mean.

A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Given:

u = 20

and SD = 2.25

To find P(X < 21)

So, P(X < 21 )

= 1 - P(X > 21)

Now, P(X > 21)

= P(Z >  [(21–20)/2.25]

= P( Z > 1/2.25)

= P(Z > 0.444)

= 0.02275

So, the required probability = P(Z < 21) = 1 - 0.02275= 0.97725

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complete question:

Let X be a normally distributed random variable with a mean of 20 and a standard deviation of 2.25. Using Excel, find the proportion of the values of X that are less than 21.

Answer:

  (-2, 10)

Step-by-step explanation:

You want the point that would be a solution to the inequalities ...

It can be useful to graph the inequalities, or develop a mental picture of what the graph would look like. Both boundary line slopes are fairly steep, and the lines cross in the third quadrant. The V-shaped space above that intersection  is the solution space.

The attachment shows the point (-2, 10) is a solution.

From the shape and location of the solution space, we can eliminate the choices ...

  (-8, 2) — too close to the x-axis in the far left part of the 2nd quadrant

  (10, -3) — no part of the 4th quadrant is in the solution space

It can work nicely to rewrite the inequalities as a comparison to zero.

  5x -2y +4 ≤ 0 . . . . . the first inequality in general form

  point (-2, 10): 5(-2) -2(10) +4 = -10 -20 +4 = -26 ≤ 0 . . . a solution

  point (4, 9): 5(4) -2(9) +4 = 20 -18 +4 = 6 > 0 . . . . . . . not a solution

  4x +y +7 ≥ 0 . . . . . . the second inequality in general form

  point (-2, 10): 4(-2) +(10) +7 = -8 +10 +7 = 9 ≥ 0 . . . . . . a solution

  point (4, 9): don't need to test (already known not a solution)

Point (-2, 10) is a solution.

__

Additional comment

We chose the use of "general form" inequalities for evaluating answer choices because ...

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If triangle ABC is translated 5 units down, the coordinates of the image vertices are A′(1, −7), B′(9, −7), C′(5, −3).

The correct option among the given choices is A′(1, −7), B′(9, −7), C′(5, −3).

To determine the coordinates of the image if triangle ABC is translated 5 units down, we need to subtract 5 from the y-coordinate of each vertex of the triangle.

The given vertices of triangle ABC are A(1, -2), B(9, -2), and C(5, 2).

To translate the triangle 5 units down, we subtract 5 from the y-coordinate of each vertex.

The new coordinates of the vertices after the translation are:

A': (1, -2 - 5) = (1, -7)

B': (9, -2 - 5) = (9, -7)

C': (5, 2 - 5) = (5, -3)

Therefore, the correct option among the given choices is A′(1, −7), B′(9, −7), C′(5, −3).

In summary, if triangle ABC is translated 5 units down, the coordinates of the image vertices are A′(1, −7), B′(9, −7), C′(5, −3).

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Answer:

149 sq. ft

Step-by-step explanation:

For the triangle:

Base = 16-9 = 7 ft

Area of Triangle = 1/2 of  b.h

= 1/2 of 7 * 6

= 21 sq. ft

Area of Rectangle = l.b

= 5 * 16

= 128 sq. ft

Total Area = 149 sq. ft

The algebraic expression for the sentence "5 subtracted from 3 times p" is given as follows:

A. 5 - 3p.

The sentence in the context of this problem is defined as follows:

"5 subtracted from 3 times p"

The expression that represents 3 times p is given as follows:

3p.

(that is, 3 and p are multiplied).

Then 5 subtracted from 3 times p means that the number 5 subtracts the above expression, hence the expression is given as follows:

5 - 3p.

Meaning that option A gives the correct answer in the context of this problem.

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The approximation of [tex]\sqrt{44}[/tex], to the hundredths place, is given as follows:

[tex]\sqrt{44} = 6.63[/tex]

The estimate of a non-exact square root of x is done finding two numbers, as follows:

For this problem, we want to estimate the root to the hundredth's place, hence the number that we must compare is:

44 x 10^4 = 440000.

(as each 10² is equivalent to the square root of a decimal digit).

Then the numbers are:

Hence the square root is approximated as follows:

663/100 = 6.63.

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This transformation of the polygon ABCD to A'B'C'D' is a by a factor of 2√5.

The coordinates are given as:

First polygon: A (-3, 7), B (-4, 9), C (-7, 9), and D (-4, 5).

Second polygon: A' (3, -4), B'(3, 6), C'(8, 2.8), and D'(7.2, -1.9)

Calculate the distance AB and A'B' using:

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

⇒ AB = √ (-4 + 3)² + (9 - 7)²

⇒ AB = √1 + 4

⇒ AB = √5

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

⇒ A'B' = √ (3 - 3)² + (6 + 4)²

⇒ A'B' = 10

This gives, Divide A'B' by AB to determine the scale factor (k)

k = 10 / √5

k = 2√5

Hence, this transformation is a by a factor of 2√5

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Answer:

Reflection and 2

Step-by-step explanation:

for plato

Step-by-step explanation:

The 'solution ' is the point where the two lines intersect :    ( 0,-1)

Answer:

5)  17.62 units² (2 d.p.)

6)  338.29 units² (2 d.p.)

7)  246.20 units² (2 d.p.)

Step-by-step explanation:

To find the area of a triangle given two sides and the included angle, use the Sine Rule (Area of a Triangle) formula:

[tex]\boxed{\begin{minipage}{6 cm}\underline{Sine Rule (Area of a triangle)}\\\\$A=\dfrac{1}{2}ab \sin C$\\\\\\where: \\ \phantom{ww}$\bullet$ $a$ and $b$ are adjacent sides. \\ \phantom{ww}$\bullet$ $C$ is the includ\:\!ed angle.\\\end{minipage}}[/tex]

[tex]\hrulefill[/tex]

Given values:

The two sides of the triangle are 'a' and 'c', and the included angle is 'B'.

Substitute the given values into the formula and solve for area:

[tex]\begin{aligned}\implies \textsf{Area}\; \triangle ABC&=\dfrac{1}{2} ac \sin B\\\\&=\dfrac{1}{2} \cdot 7 \cdot 8 \cdot \sin 141^{\circ}\\\\&= 28 \sin 141^{\circ}\\\\& = 17.6209709...\\\\&= 17.62\; \sf square\;units\;(2\;d.p.)\end{aligned}[/tex]

[tex]\hrulefill[/tex]

Given values:

The two sides of the triangle are 'a' and 'b', and the included angle is 'C'.

Substitute the given values into the formula and solve for area:

[tex]\begin{aligned}\implies \textsf{Area}\; \triangle ABC&=\dfrac{1}{2} ab \sin C\\\\&=\dfrac{1}{2} \cdot 30\cdot 24 \cdot \sin 70^{\circ}\\\\&= 360\sin 70^{\circ}\\\\&= 338.289343...\\\\& = 338.29\; \sf square\;units\;(2\;d.p.)\end{aligned}[/tex]

[tex]\hrulefill[/tex]

Given values:

The two sides of the triangle are 'b' and 'c', and the included angle is 'A'.

Substitute the given values into the formula and solve for area:

[tex]\begin{aligned}\implies \textsf{Area}\; \triangle ABC&=\dfrac{1}{2} bc \sin A\\\\&=\dfrac{1}{2} \cdot 20 \cdot 25 \cdot \sin 100^{\circ}\\\\&= 250 \sin 100^{\circ}\\\\&= 246.201938...\\\\& = 246.20\; \sf square\;units\;(2\;d.p.)\end{aligned}[/tex]

The histogram will show the distribution of the athletes' mile running times. It will provide a visual representation of the frequency or count of athletes falling within different time intervals.

1. Determine the time intervals or "bins" for the histogram. For example, you might have bins of 5-second intervals, such as 0-5 seconds, 5-10 seconds, and so on.

2. Count the number of athletes who fall within each bin. For instance, if three athletes completed the mile in the 0-5 second bin, and five athletes completed it in the 5-10 second bin, record those counts.

3. Plot the bins on the x-axis of the histogram and the corresponding frequency or count on the y-axis.

4. Draw rectangles (or bars) on the histogram, with the height of each bar representing the frequency or count of athletes within each bin.

5. Label the axes and add a title to the histogram for clarity.

The resulting histogram will provide a visual representation of how the athletes' mile running times are distributed, allowing you to observe any patterns or trends.

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78,624,000 different license plates are possible if letters and digits cannot be repeated.

For the letters:

There are 26 letters in the English alphabet, and we need to choose three of them without repetition.

This can be calculated as a permutation of 26 letters taken 3 at a time:

P(26, 3) = 26! / (26 - 3)!

= 26! / 23!

= 26 x 25 x 24

= 15,600

For the digits:

There are 10 digits (0-9), and we need to choose four of them without repetition.

This can be calculated as a permutation of 10 digits taken 4 at a time:

P(10, 4) = 10! / (10 - 4)! = 10! / 6!

= 10 x 9 x 8 x 7

= 5,040

To find the total number of different license plates possible, we multiply the number of possibilities for the letters by the number of possibilities for the digits:

Total possibilities = P(26, 3) x P(10, 4)

= 15,600 x 5,040

= 78,624,000

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Answer:

To find Salina Grant's gross pay, we need to calculate the pay for each range and add them together.

For the first 25 chairs, Salina will be paid $10 for each chair, so her pay for this range is:

25 chairs x $10 per chair = $250

For the next 15 chairs (26-40), Salina will be paid $13 for each chair, so her pay for this range is:

15 chairs x $13 per chair = $195

For the remaining 7 chairs (over 40), Salina will be paid $17.50 for each chair, so her pay for this range is:

7 chairs x $17.50 per chair = $122.50

Adding up all three ranges, Salina's gross pay is:

$250 + $195 + $122.50 = $567.50

Therefore, Salina Grant's gross pay for assembling 47 chairs in one week is $567.50.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the values of p, q, and r in the expression albici = Vabac, we need to equate the corresponding parts on both sides.

From the given equation, we have:

p * (a * b) * (c * i) = q * (a * b * a * c)

Comparing the exponents of a, b, and c on both sides, we get:

p = q * a^2

1 = q * c

To determine the value of r, we can use the fact that albici and Vabac are equivalent. The radical symbol (√) represents taking the square root.

√(a * b * c * i) = √(a * b * a * c)

This implies that:

√(a * b * c * i) = √(a^2 * b * c)

Comparing the exponents of a, b, and c on both sides, we get:

1/2 = 2 * p * q * r

Combining all the equations, we have:

p = q * a^2

1 = q * c

1/2 = 2 * p * q * r

To find the specific values of p, q, and r, we need additional information or equations involving a, b, and c. Without more context or equations, it is not possible to determine the exact values of p, q, and r.

Answer:    D.   <4 and <7

Step-by-step explanation:

Consecutive means one after the other

Interior means within the parallel lines

So we are looking for 2 to angles inside the parallelel lines that are 1 after the other on the same side

D.   <4 and <7

Answer:

the answer is C. Horizontal translation

Step-by-step explanation:

trust fr

The numbers arranged in the correct order are:

-3 = -3

-3 < | -1 |

0 < | 1 |

2 > | 0 |

3 > | 1 |

We have,

-3 = -3:

This is a true statement because -3 is indeed equal to -3.

-3 < | -1 |:

This is also a true statement.

The absolute value of -1 is 1, so we are comparing -3 and 1.

Since -3 is less than 1, the inequality is true.

0 < | 1 |:

Again, this is a true statement.

The absolute value of 1 is 1, so we are comparing 0 and 1.

Since 0 is less than 1, the inequality holds true.

2 > | 0 |:

This is also a true statement.

The absolute value of 0 is 0, so we are comparing 2 and 0.

Since 2 is greater than 0, the inequality is true.

3 > | 1 |:

Once again, this is a true statement.

The absolute value of 1 is 1, so we are comparing 3 and 1.

Since 3 is greater than 1, the inequality holds true.

Therefore,

By arranging the given numbers in this order: -3, -3, -1, 0, 1, 2, 3, all of the number sentences become true.

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a) The triangles are congruent by the AAA criterion.

b) The triangles are congruent by the SAS criterion.

a) In the first triangle the interior angles are 40 degrees and 30 degrees.

The other interior angle would be 180 - (40 + 30) = 110 degrees.

As per the diagram, the triangles have equal proportionate-sized side lengths.

Therefore, the triangles are congruent by the AAA criterion.

b) Both the triangles are right triangles and their adjacent side is 2 and the hypotenuse side is 4 centimeters.

Therefore, the triangles are congruent by the SAS criterion.

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The percentage of people borrowing from financial institutions generally exceeds borrowing from friends or family due to formality, legal protection, larger loan amounts, privacy, expertise, and long-term implications.

The percentage of people who would borrow from a financial institution compared to the percentage of people who would borrow from friends or family can vary depending on various factors such as cultural norms, economic conditions, individual preferences, and access to financial services. However, in general, borrowing from financial institutions is often more common and prevalent than borrowing from friends or family for several reasons.

Formality and Legal Protection: Borrowing from financial institutions offers a more formal and legally protected process. When individuals borrow from a financial institution, they enter into a contractual agreement that outlines the terms and conditions of the loan. This agreement provides a legal framework that protects both the borrower and the lender. In contrast, borrowing from friends or family often lacks the same level of formality and legal protection, which can lead to ambiguity and strain personal relationships.

Access to Larger Loan Amounts: Financial institutions typically have more capital and resources to lend larger amounts of money compared to friends or family members. If someone requires a substantial loan, such as for purchasing a home or starting a business, they are more likely to turn to a financial institution. These institutions have processes in place to evaluate creditworthiness, collateral, and other factors, allowing them to provide loans that meet the borrower's specific needs.

Privacy and Independence: Borrowing from a financial institution offers a level of privacy and independence that may be preferred by individuals. Some people might feel uncomfortable disclosing personal financial details or discussing their financial challenges with friends or family. Financial institutions provide a professional environment where individuals can maintain privacy and retain control over their financial matters.

Expertise and Financial Advice: Financial institutions employ professionals with expertise in lending and financial management. When borrowing from a financial institution, borrowers can benefit from the advice and guidance of these professionals. They can help borrowers understand the terms of the loan, explore different options, and make informed financial decisions. Friends and family members may not possess the same level of financial knowledge or experience, limiting their ability to provide comprehensive advice.

Long-Term Implications: Borrowing from friends or family can have long-term implications for personal relationships. Financial transactions have the potential to create tension, conflicts, or misunderstandings among individuals, especially if there are difficulties in repaying the borrowed amount. Relying on financial institutions can help maintain healthy personal relationships, as the borrowing and lending processes are conducted on a professional level, minimizing the emotional and relational strain that can arise from borrowing from loved ones.

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The solution is :  (5-b ) is the expression that shows the number of books Hazel checked out.

Here, we have,

given that,

Bill checked out 5 books from the library.

Hazel checked out b fewer books than Bill.

now, we have to find the expression that shows the number of books Hazel checked out.

let,

that shows the number of books Hazel checked out = x

so, we have,

that shows the number of books Hazel checked out =  b fewer books than Bill.

as, Bill checked out 5 books from the library.

so, we get,

the number of books Hazel checked out = 5 - b

so, we have,

x = 5-b

Hence, The solution is :  (5-b ) is the expression that shows the number of books Hazel checked out.

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Based on the fraction of the sugar sprinkled on the Brownies, Brandon sprinkles 0.4 cups of sugar on the brownies

The amount of sugar sprinkled on the Brownies by Brandon is determined as follows:

Data given:

Brandon sprinkles 1/10 of the sugar onto the plate of brownies

Since he has 4 cups of powdered sugar in total

The amount of sugar he sprinkles on the brownies can be calculated as:

The amount of sugar he sprinkles on the brownies = 1/10 * 4 cups

The amount of sugar he sprinkles on the brownies  = 0.4 cups

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The expected value for a person who buys a ticket is $0.35.

We have,

Number of tickets sold = 100

Price of each ticket = $1

Prize value (1st prize) = $25

Prize value (2nd prize) = $10

Let's calculate the expected value step by step:

Calculate the probability of winning each prize:

Since there is only one 1st prize and one 2nd prize, the probability of winning each prize is:

Probability of winning the 1st prize = 1/100

Probability of winning the 2nd prize = 1/100

Calculate the expected value:

Expected value = (Probability of winning 1st prize x Value of 1st prize) + (Probability of winning 2nd prize x Value of 2nd prize)

= (1/100 x $25) + (1/100 x $10)

= $0.25 + $0.10

= $0.35

Therefore, the expected value for a person who buys a ticket is $0.35.

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a) The given symbolic logic statement can be translated into English as follows:

"Not exists x such that (P(x) and Q(x)), and for all y, if R(y) then P(y)."

b) Potential ambiguities in the translated statement:

The scope of the negation symbol "¬" is not explicitly defined. It can be interpreted as applying only to the first part of the statement or to the entire statement.

The scope of the quantifiers (∃x) and (∀y) is not explicitly defined. It is unclear which parts of the statement they apply to.

c) To eliminate ambiguities while maintaining the original meaning, the statement can be rewritten as follows:

"(∀x)(¬(P(x) ∧ Q(x))) ∧ (∀y)(R(y) → P(y))"

In the revised statement: The negation symbol "¬" applies to the entire first part of the statement, indicating that there does not exist any x for which both P(x) and Q(x) are true.

The quantifiers (∀x) and (∀y) explicitly indicate that the following predicates apply universally to all values of x and y.

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The values are given as:

a. Mean = 19

Median = 20

Mode = 22

Standard deviation = 7.2

Range  = 24

b. Mean = 75

Median  =  80

Mode  = 90

Standard deviation  = 16

Range = 100

The three measures of central tendency include;

The measures of dispersions are;

From the information given, if 4 is added to all the measures, we get;

Mean = 15 + 4 = 19

Median = 16 + 4 = 20

Mode = 18 + 4 = 22

Standard deviation = 3.2 + 4 = 7.2

Range = 20 + 4 = 24

If the values are multiplied by 5

Mean = 15(5) = 75

Median = 16(5) =  80

Mode = 18(5) = 90

Standard deviation = 3.2(5) = 16

Range = 20(5) = 100

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Answer: x= —5/9

Step-by-step explanation:

The period of the function is given as follows:

C) 4.

A periodic function is a function that has the behavior repeating in intervals over the domain.

Then the period of the function is defined as the difference between two points in which the function has the same behavior.

The function in this problem has the behavior repeating at these following points:

x = 0, x = 4, x = 8, ...

Hence the period is given as follows:

4 - 0 = 8 - 4 = 4.

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Answer:

B. making an inference.

Step-by-step explanation:

The drama teacher's decision to add another performance time on Saturday is a result of making an inference based on the information that 80% of last year's sold-out plays occurred during weekend performances. By observing this pattern, the drama teacher infers that adding another performance on Saturday will likely attract a larger audience and increase the chances of having a sold-out show.

Answer:

0.5

Step-by-step explanation:

So what do we mean by half? Half means there are two of the thing, and so all you need to do is divide it by two. Half of 4/4 is just another way of saying 4/4 divided by 2:

: 4/4 ÷ 2

Now we know that "half" means to divide by 2, how do we half 4/4? Remember that a fraction a part of the whole, so the higher the denominator is, the smaller the piece. The answer is that the numerator stays the same and we multiply the denominator by 2:

: 4/4 x 2 = 4/8

Here's a little bonus calculation for you to easily work out the decimal format of half 4/4. All you need to do is divide the numerator by the denominator and you can convert any fraction to decimal:

: 4/8 = 0.5

The graph that shows the solution set of the inequality is the second one.

Here we have the following inequality:

y < |x + 3|

Notice that we have the symbol "<", then we know that the graph of the absolute value must be with dashed lines (because the points that lie on the graph aren't solutions).

Also, y is smaller than that, then the shaded region must be below the graph.

With that in mind, we conclude that the correct option is the second one.

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