what is the probability of having no defectives in a sample of size 3 from a lot of 24 items with 5 known defectives.

Answer:

$28

Step-by-step explanation:

\(22 + x - 12 = 38\)

\(x + 1 0 = 38\)

\(x = 28\)

Answer:

5 men

Step-by-step explanation:

4m × 4h = 12

xm × 8h=36

x m = 4.5

(a) Approximately 4.849056 units of work are needed to stretch the spring from 40 cm to 48 cm. (b) The spring will be stretched approximately 1062.67 cm beyond its natural length with a force of 35 N.

To find the exact answers to both parts of the question, we can use Hooke's Law, which states that the force required to stretch or compress a spring is directly proportional to the displacement from its natural length.

(a) Let's find the work needed to stretch the spring from 40 cm to 48 cm.

The work done is given by the formula:

Work = (1/2) * k * (x² - x0²)

Where:

k is the spring constant (which we need to find)

x is the final displacement (48 cm)

x0 is the initial displacement (40 cm)

Given that 43 units of work are needed to stretch the spring from 36 cm to 53 cm, we can set up a proportion to find the value of k:

43 / (53² - 36²) = k / (48² - 40²)

Simplifying the equation and solving for k:

k = (43 / (53² - 36²)) * (48² - 40²)

k ≈ 0.032946

Now we can find the work needed to stretch the spring from 40 cm to 48 cm:

Work = (1/2) * k * (48² - 40²)

= (1/2) * 0.032946 * (48² - 40²)

≈ 4.849056 units of work

Therefore, the exact answer for part (a) is approximately 4.849056 units of work.

(b) To find how far beyond its natural length the spring will be stretched with a force of 35 N, we can rearrange Hooke's Law equation:

F = k * x

Solving for x:

x = F / k

= 35 / 0.032946

≈ 1062.67 cm

Therefore, the exact answer for part (b) is approximately 1062.67 cm beyond its natural length.

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Answer:

12x+24≤60 for x≤3

Step-by-step explanation:

Given that she had $60 and spent $24 on food and drinks

Her balance will be 60-24=$36

We are told that she went on 12 rides with the balance of $36

Let the cost of each ride be x, so

12x=36

Divide both sides by 12

x=36/12

x=3

This means that the cost of each ride is $3 and cannot be more

Therefore the inequality is given as

12x+24≤60 for x≤3

Answer:

yes its 50

Step-by-step explanation:

if you need an explanation let me know!

The probability that at least one of the test scores is more than 1070 when 4 test scores are picked at random is 0.643.

Given that the scores on a college entrance examination are normally distributed with a mean of 1000 and a standard deviation of 100, we have to find the probability that at least one of the test scores is more than 1070 when 4 test scores are picked at random.

So, let's calculate the probability of each test score being less than or equal to 1070.

P(Z < (1070 - 1000) / 100)

= P(Z < 0.7)

= 0.758

Therefore, the probability of each test score being less than or equal to 1070 is 0.758.

So, the probability that all 4 test scores are less than or equal to 1070 is:

P(All 4 scores ≤ 1070)

= (0.758)⁴

= 0.357

Now, the probability that at least one of the test scores is more than 1070 is

P(At least one score > 1070)

= 1 - P(All 4 scores ≤ 1070)

= 1 - 0.357

= 0.643

Therefore, the probability that at least one of the test scores is more than 1070 when 4 test scores are picked at random is 0.643.

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Certify Completion Icon Tries remaining: 3 A high school has 52 players on the football team. The summary of the players' weights is given in the box plot. The median weight of the players on the football team is 160 pounds.

The box plot shows that the median weight of the players is the middle value of the distribution. In this case, the median weight is halfway between the 26th and 27th players, which is 160 pounds.

The box plot also shows that the minimum weight of the players is 150 pounds and the maximum weight is 212 pounds. The interquartile range, which is the range of the middle 50% of the data, is 20 pounds.

In conclusion, the median weight of the players on the football team is 160 pounds. This means that half of the players on the team weigh more than 160 pounds and half of the players weigh less than 160 pounds.

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Answer:

Step 3 is wrong. If 3x+28=15, then 3x= 15-28

Answer:

Where is the polygon?

An isosceles trapezoid LMNO has the side LO is congruent to side MN, the diagonal LN is congruent to diagonal MO, and the angle L is congruent to angle M. Hence correct options are a), c), and e)

Given :

Trapezoid LMNO.

The following are the conditions that show any trapezoid is an isosceles trapezoid:

Condition 1 -- Both the legs are of the same length.

Condition 2 -- The base angles are of the same measure.

Condition 3 -- Diagonals are of the same length.

So, the given trapezoid LMNO is an isosceles trapezoid when:

The side LO is congruent to side MN.

The diagonal LN is congruent to diagonal MO.

The angle L is congruent to angle M.

Therefore, the correct option is a), c), and e).

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Answer:

it'sssssss 2.51

Step-by-step explanation:

========≈==================

(a) Alice's strategy is not a winning strategy. Bob can always win against this strategy by mirroring Alice's moves. Whenever Alice takes a square from the top row, Bob takes the corresponding square from the bottom row, and vice versa. By doing so, Bob can always ensure that he takes the last remaining square, thereby winning the game.

In the game of CHOMP, the player who takes the last remaining square loses. Alice's strategy of always taking a single square from the top row if possible, or from the bottom row if the top row is all gone, does not guarantee a win. Bob can exploit this strategy by mirroring Alice's moves. This means that whenever Alice takes a square from the top row, Bob takes the corresponding square from the bottom row, and vice versa.

By employing this strategy, Bob can ensure that he takes the last remaining square. For example, if Alice takes the square in the top-left corner, Bob will take the corresponding square in the bottom-left corner. This leaves a smaller board of 1×4. Bob can continue mirroring Alice's moves until there is only one square left, which he will take, winning the game. Therefore, Bob has a winning strategy against Alice's strategy in CHOMP.

(b) If Bob goes first and Alice still uses the same strategy, Bob will always win the game. Bob can adopt the strategy of always taking a single square from the top row if possible, or from the bottom row if the top row is all gone, just like Alice's strategy. Since Bob moves first, he can make the same move as Alice would have made in the first turn. By doing so, Bob puts himself in the same advantageous position that Alice would have been in. From this point on, Bob can employ the mirroring strategy mentioned above and guarantee a win.

(c) If both players use the same strategy of always taking a single square from the top row if possible, or from the bottom row if the top row is all gone, the game will end in a draw. Both players will continue mirroring each other's moves, resulting in a symmetrical game progression. Eventually, all squares will be taken, and no player will be left with the last square. Hence, there is no winning strategy for either player when both follow this strategy.

Bonus: A winning strategy for the first player can be achieved by modifying the initial strategy. The first player should intentionally leave a specific square for the opponent to take, such that it leads to a losing position. By strategically choosing their moves, the first player can force the second player into a position where they have no choice but to take the last square, resulting in a win for the first player. This requires careful planning and analysis of the game state to identify the optimal moves that lead to a winning position.

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The equation of the line that is parallel to the line y= -3x+8 and passes through the point (9,-8) is y = -3x +19 .

Given line y = -3x + 8 The given line is in slope-intercept form, y = mx + c, where m is the slope of the line and c is the y-intercept.

The given line y = -3x + 8 can be written as y = -3x + 8 + 0. The slope of the given line is -3.As the line parallel to the given line, which means the slope of the required line is also -3.

Now, we have the slope of the line and a point (9, -8) that the line passes through.

Using the slope-intercept form, we get the required equation: y = mx + b⇒ y = -3x + b (as the slope m = -3)The line passes through the point (9, -8).

Therefore, substituting the values of x and y in the above equation, we get-8 = -3(9) + b⇒ b = -8 + 27 = 19

Putting the value of b in the equation, y = -3x + 19

Therefore, the required equation of the line is y = -3x + 19.

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To find the length of A'B', we first need to find the coordinates of A' and B' after the dilation. The length of A'B' is 6√20.

Using the formula for dilation:
A' = 6*(-2,5) + (-4,8) = (-16,38)
B' = 6*(2,3) + (-4,8) = (8,26)
Now that we have the coordinates of A' and B', we can use the distance formula to find the length of A'B':
A'B' = √[(8 - (-16))^2 + (26 - 38)^2]
= √[(24)^2 + (-12)^2]
= √(720)
= 12√5
Therefore, the length of A'B' after the dilation is 12√5.
To find the length of A'B', the image of AB after a dilation by a factor of 6 centered at point C(-4, 8), you can follow these steps:
1. Find the length of AB using the distance formula: √((x2 - x1)² + (y2 - y1)²) = √((2 - (-2))² + (3 - 5)²) = √(4² + (-2)²) = √(16 + 4) = √20.
2. Calculate the length of A'B' using the dilation factor: A'B' = Dilation Factor × Length of AB = 6 × √20 = 6√20.

Hence, So, the length of A'B' is 6√20.

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n(t) = 360 * 1.05^t. This formula assumes the growth rate of the student population remains constant at 5% per year. In reality, the growth rate may vary from year to year depending on various factors such as the school's reputation, enrollment policies, and local demographics

The formula for the function n(t) is based on the assumption that the student population grows by 5% per year. To calculate the number of students attending the charter school t years after 1994, we start with the initial number of students in 1994, which is 360, and then multiply it by 1.05 raised to the power of t.

For example, if we want to know how many students are attending the school in 2023 (29 years after 1994), we plug in t=29 into the formula:

n(29) = 360 * 1.05^29

≈ 1,188 students

This formula assumes that the growth rate of the student population remains constant at 5% per year. In reality, the growth rate may vary from year to year depending on various factors such as the school's reputation, enrollment policies, and local demographics. However, the formula provides a useful estimate of the school's enrollment over time based on a simple, consistent assumption.

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Answer:

C) ATUS-ABCS

Step-by-step explanation:

ΔTUS ΔBSC would also be a right answer, but remember that the order of the points matter.

Both of these triangles share a point S, so the order of where the S is placed should be the same.

In this answer, ΔTUS ΔBCS, notice that the S is in the end of the triangle notation.

However, in this answer,  ΔTUS ΔBSC, the S is in the end of ΔTUS while the S is in the middle of ΔBSC even S is the correspondent point for both triangles.

Hence, ΔTUS ΔBCS is the correct notation and correct answer.

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The value of the expression when x = 3 and y = -5 is -213

Algebraic expressions are expressions made up of variables and constants with mathematical operations such as addition, subtraction, division, multiplication, etc

From the expression given;

3(x+y)^2-(xy)2

Where:

Substitute the values into the expression

3 ( 3 + -5)^2 - ( 3 × -5 )^2

3 ( -2)^2 - ( -15)^2

3(4) - ( 225)

-12

Thus, the value of the expression when x = 3 and y = -5 is -213

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The driving time along this stretch was reduced by 36% for a person who always drives at the speed limit.

To calculate the percent reduction in driving time along the stretch, we need to consider the effects of both the distance decrease and the speed increase.

First, let's assume the original distance of the stretch was D. After the reconstruction, the distance is now 0.8D (since it was decreased by 20%).

Next, let's assume the original speed limit was S. After the reconstruction, the speed limit is now 1.25S (since it was increased by 25%).

To calculate the original driving time along the stretch, we would use the formula: time = distance / speed. So the original driving time would be D/S.

After the reconstruction, the driving time would be (0.8D) / (1.25S) = 0.64D/S.

To calculate the percent reduction in driving time, we can use the formula: (original time - new time) / original time * 100%.

Plugging in the values we calculated, we get:

(original time - new time) / original time * 100% = (D/S - 0.64D/S) / (D/S) * 100% = 36%.

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(a) correctly describes the relationship between a parameter and a statistic.

The correct description is:

a) A statistic is calculated from sample data and is generally used to estimate a parameter.

In statistics, a parameter refers to a characteristic or measure that describes a population, while a statistic is a characteristic or measure calculated from sample data. Statistics are often used to estimate or infer the corresponding parameters of the population. Therefore, option (a) correctly describes the relationship between a parameter and a statistic.

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The required measure of the angle ∠C in the given triangle is 20°.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should be equal to 180°

Here,
For the given triangle,
the sum of the interior angle should be equal to 180,
∠C + 73 + 87 = 180
∠C = 180 - 87 - 73
∠C = 20°

Thus, the required measure of the angle ∠C is given as  ∠C = 20°.

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The volume of the given solid using polar coordinates is 0.

First, let's consider the equation of the plane: 6xy - z = 8. We need to find the region below this plane.

To do this, we'll rewrite the equation of the plane in terms of polar coordinates. We have:

x = r*cos(θ)

y = r*sin(θ)

z = 6xy - 8

Substituting these values into the equation of the plane, we get:

6r*cos(θ)*r*sin(θ) - 8 = 8

6\(r^2\)*cos(θ)*sin(θ) = 16

\(r^2\)*cos(θ)*sin(θ) = 16/6

\(r^2\)*sin(2θ) = 8/3

Now, let's consider the disk defined by \(x^2 + y^2 \leq 1\), which represents a circle centered at the origin with radius 1. We need to find the region above this disk.

In polar coordinates, the disk equation becomes:

\(r^2\) ≤ 1

Since the solid is bounded above by the plane and below by the disk, the limits of integration for r will be from 0 to 1, and the limits of integration for θ will be from 0 to 2π.

The volume integral can be set up as follows:

V = ∫∫∫ dV

  = ∫∫∫ r dz dr dθ

  = ∫[0,2π]∫[0,1]∫[0, \(r^2\) *sin(2θ) = 8/3] r dz dr dθ

To evaluate the integral and find the volume of the solid, we can start by simplifying the expression:

V = ∫[0,2π]∫[0,1]∫[0,\(r^2\)*sin(2θ) = 8/3] r dz dr dθ

Integrating with respect to z first, we have:

∫[0,\(r^2\)*sin(2θ) = 8/3] r dz = r * [z] evaluated from 0 to \(r^2\) *sin(2θ) = 8/3

= r * (\(r^2\)*sin(2θ) = 8/3 - 0)

= (8/3) *\(r^3\) * sin(2θ)

Next, we integrate with respect to r:

∫[0,1] (8/3) * \(r^3\) * sin(2θ) dr

= (8/3) * (∫[0,1] \(r^3\) dr) * sin(2θ)

= (8/3) * (1/4) *\(r^4\) * sin(2θ) evaluated from 0 to 1

= (8/3) * (1/4) * (\(1^4\)) * sin(2θ) - (8/3) * (1/4) * (\(0^4\)) * sin(2θ)

= (2/3) * sin(2θ)

Finally, we integrate with respect to θ:

∫[0,2π] (2/3) * sin(2θ) dθ

= (-1/3) * (1/2) * cos(2θ) evaluated from 0 to 2π

= (-1/3) * (1/2) * (cos(4π) - cos(0))

= (-1/3) * (1/2) * (1 - 1)

= 0

Therefore, the volume of the given solid is 0.

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Answer:

I

Step-by-step explanation:

The probability of selecting 19 homeowners and 1 renter in a random sample of 20 residents in a small village with 190 homeowners and 110 renters.

To calculate the probability of randomly selecting a homeowner and a renter from a small village of 300 residents with 190 homeowners and 110 renters in a sample of 20 residents, follow these steps:
1. Calculate the probability of selecting a homeowner (P(homeowner)).
P(homeowner) = Number of homeowners / Total number of residents = 190 / 300
2. Calculate the probability of selecting a renter (P(renter)).
P(renter) = Number of renters / Total number of residents = 110 / 300
3. Calculate the number of ways to choose 19 homeowners and 1 renter from the sample (Combination).
C(190,19) × C(110,1) = (190! / (19! × (190-19)!)) × (110! / (1! × (110-1)!))
4. Calculate the number of ways to select a random sample of 20 residents (Combination).
C(300,20) = 300! / (20! × (300-20)!)
5. Calculate the probability of selecting 19 homeowners and 1 renter from the random sample of 20 residents.
Probability = (C(190,19) × C(110,1)) / C(300,20)
By calculating these values, you will find the probability of selecting 19 homeowners and 1 renter in a random sample of 20 residents in a small village with 190 homeowners and 110 renters.

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It takes a machine at a seafood company 20 seconds to clean 3 pounds of shrimp. The rate of the machine is 0.15 pound per second

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

It takes a machine at a seafood company 20 seconds to clean 3 pounds of shrimp. Hence:

Rate of the machine = 3 pounds / 20 seconds = 0.15 pound per second

It takes a machine at a seafood company 20 seconds to clean 3 pounds of shrimp. The rate of the machine is 0.15 pound per second

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Answer:

only ingrid

Step-by-step explanation:

\(\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{ \textit{we'll use this one} }{a^{log_a (x)}=x} \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_2(16x)=4\implies 2^{\log_2(16x)}=2^4\implies 16x=2^4\implies x=\cfrac{2^4}{16}\implies x=1\)

Answer:

1st and 2nd

Step-by-step explanation:

I'm not so sure but I think it's the first and second one