Question 7
Central Middle School has an enrollment of 800 students. Its enrollment is expected to increase by 75 students per year. Nichols Middle School has an enrollment of 890 students. Its enrollment is expected to increase by 60 students per year. After how many years will the enrollment at the two schools be equal?

The conditions for inference are indeed met. The correct option is:
Yes, the conditions for inference are met.

The conditions for inference are met when conducting a confidence interval for a proportion if the following conditions are satisfied:

Random Sample: The sample should be a simple random sample or a random sample from a well-defined sampling frame. This ensures that the sample is representative of the population of interest.

Large Counts Condition: The sample size should be large enough so that both the number of successes (defective chips) and failures (non-defective chips) in the sample are at least 10. This ensures that the sampling distribution of the proportion is approximately normal.

Independence: The individual observations in the sample should be independent of each other.

In this scenario, the quality control specialist took a random sample of 100 chips from the day's production, which satisfies the random sample condition.

Now, let's check the Large Counts Condition.

The quality control specialist found 12 defective chips in the sample. To satisfy the Large Counts Condition, both the number of defective chips and the number of non-defective chips should be at least 10.

In this case, the number of defective chips is 12, and the number of non-defective chips is 100 - 12 = 88.

Both numbers are greater than 10, so the Large Counts Condition is met.

Since both the random sample condition and the Large Counts Condition are met, the conditions for inference are indeed met. Therefore, the answer is:

Yes, the conditions for inference are met.

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The probability of Akhil picking two oranges is 11/105 OR 10.476%.

To find the probability of Akhil picking two oranges, we need to consider the total number of fruits and the number of oranges in the basket.

The total number of fruits is 8 green apples + 11 red apples + 5 nectarines + 12 oranges = 36 fruits.

The probability of picking the first orange is 12 oranges / 36 fruits = 1/3.

After eating the first orange, there are now 35 fruits left and 11 oranges.

The probability of picking the second orange is 11 oranges / 35 fruits.

So, the probability of Akhil picking two oranges (P(two oranges)) is the product of the individual probabilities: (1/3) * (11/35) = 11/105.

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The maximum height of Anna's golf ball is approximately 7.81 units.

The equation y = [tex]x - 0.04x^2[/tex] represents the height of Anna's golf ball, where x is the horizontal distance the ball has traveled.

To find the maximum height of the ball, we need to determine the vertex of the parabolic equation. The x-coordinate of the vertex can be found using the formula x = -b/2a, where a = -0.04 and b = 1.

x = -b/2a = -1/(2(-0.04)) = 12.5

So, the maximum height of the ball occurs when it has traveled a horizontal distance of 12.5 units. To find the maximum height, we substitute x = 12.5 into the equation:

[tex]y = 12.5 - 0.04(12.5)^2 = 7.81[/tex]

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The critical point is x = -1/2, the function has a local minimum at x = 1 and an absolute maximum at x = 4, and the absolute minimum is at x = -1/2.

a. The critical point is x = -1/2.

To find the critical point(s), we need to find where the derivative of the function is equal to zero or undefined. In this case, we have:

f(x) = -4x - x^2 + 2

f'(x) = -4 - 2x

Setting f'(x) equal to zero, we get:

-4 - 2x = 0

-2x = 4

x = -2/2

x = -1

However, we need to check if this value is in the given interval (1-4, 4). Since -1 is not in the interval, it is not a critical point.

Next, we check the endpoints of the interval.

When x = 1, f(x) = -4 - 1^2 + 2 = -3.

When x = 4, f(x) = -4 - 4^2 + 2 = -22.

So the function has a local minimum at x = 1, and an absolute maximum at x = 4, and no local maximum.

b. The local maximum is at x = 4, and the local minimum is at x = 1.

We can use the First Derivative Test to locate the local maximum and minimum points. If the derivative changes sign from positive to negative at a point, then it is a local maximum. If the derivative changes sign from negative to positive at a point, then it is a local minimum.

In this case, we have f'(x) = -4 - 2x. It is negative for x < -2 and positive for x > -2. Therefore, the function is decreasing for x < -2 and increasing for x > -2. Since the interval is (1-4, 4), the critical points are -2 and 4.

For x = 4, we have f'(4) = -4 - 2(4) = -12, which is negative, so x = 4 is a local maximum.

For x = 1, we have f'(1) = -4 - 2(1) = -6, which is negative, so x = 1 is a local minimum.

Therefore, the local maximum is at x = 4, and the local minimum is at x = 1.

c. The absolute maximum is at x = 4, and the absolute minimum is at x = -1/2.

To find the absolute maximum and minimum, we need to evaluate the function at the critical points and endpoints of the interval, and choose the largest and smallest values, respectively.

We have already found that the local maximum is at x = 4, and the local minimum is at x = 1. We also found that x = -1/2 is a critical point, but it is not in the given interval, so we can ignore it.

Evaluating the function at the endpoints of the interval, we get:

f(1) = -3

f(4) = -22

Therefore, the absolute maximum is at x = 4, and the absolute minimum is at x = 1/2.

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The calculated number of police cadets in the group is 25

From the question, we have the following parameters that can be used in our computation:

Scouts = 8/13

Police cadets = the rest

This means that

Police cadets = 1 - 8/13

Evaluate

Police cadets = 5/13

Also, we have

Prefects = 3/8 or 15 of scouts

This means that

3/8 * Scouts = 15

Scouts = 40

So, we have

Total = 40/(8/13)

Total = 65

Recall that

Police cadets = 5/13

So, we have

Police cadets = 5/13 * 65

Evaluate

Police cadets = 25

Hence, the number of police cadets in the group is 25

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Answer:

740

Step-by-step explanation:

37 times 20

Answer:

740 miles

Step-by-step explanation:

37 miles in 1 day

So we need to multiply 37*20 to find the number of miles for 20 days

So, he travels 740 miles

The height of the tree is approximately equal to the tangent of 768 radians multiplied by 50 meters, rounded to the nearest meter.

To find the height of the tree, we can use trigonometry. Let's assume that the height of the tree is represented by the variable "h."

In a right triangle formed by the forester, the base of the tree, and the top of the tree, the tangent of the angle is equal to the opposite side (height of the tree, h) divided by the adjacent side (distance from the base of the tree, 50 m).

Using the tangent function, we can write:

tan(angle) = [tex]\frac{h }{ 50}[/tex]

We can rearrange this equation to solve for h:

h = tan(angle) * 50

Now we can substitute the given angle into the equation and calculate the height:

h = tan(768) * 50

Calculating this in degrees might result in an error because the tangent function expects the angle to be in radians.

Therefore, we need to convert the angle to radians before evaluating the tangent.

There are 180 degrees in pi radians, so we can convert the angle as follows:

angle_radians = [tex]\frac{768 \* \pi }{ 180}[/tex]

Substituting this value into the equation:

h = tan(angle_radians) * 50

Now we can calculate the height using a calculator:

h ≈ [tex]tan(\frac{768 \pi }{ 180}) 50[/tex]

After evaluating this expression, we get the height of the tree. Rounding the answer to the nearest meter will give us the final result.

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The clockwise rotation about the origin from the pre-image to the image​ include the following: a rotation of 90° clockwise.

In Mathematics, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Additionally, the rotation of a point 90° about the center (origin) in a clockwise direction would produce a point that has these coordinates (y, -x).

Next, we would apply a rotation of 90° clockwise to the coordinate of triangle ABC as follows;

(x, y)                               →            (y, -x)

Coordinate A = (1, 1) → Coordinate A' = (1, -(1)) = (1, -1)

Coordinate B = (1, 4) → Coordinate B' = (4, -(1)) = (4, -1)

Coordinate C = (5, 1) → Coordinate C' = (1, -(5)) = (1, -5)

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Circumference of circle is 31.4 and area of circle is 78.6

Given, C(-1,6) is center and A(3, 9) is a point on circle.

CA is the radius of the circle.

Using Distance Formula

[tex]r=\sqrt{(3-(-1))^2+(9-6)^2}[/tex]

[tex]r=\sqrt{(4)^2+(3)^2}[/tex]

[tex]r=\sqrt{16+9}[/tex]

[tex]r=\sqrt{25}=5[/tex]

We know the the formula for circumference of circle C = 2πr

C = 2*22/7*5

= 31.428

Rounding to nearest tenth

C = 31.4

Area of the circle = [tex]\pi r^2[/tex]

[tex]A=\frac{22}{7}(5)^2[/tex]

= 78.571

Rounding to nearest tenth

A = 78.6

Hence, circumference of circle is 31.4 and area of circle is 78.6.

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Molly gave away 90 trading cards, which is option (c).

Let's start by figuring out how many trading cards Marcus gave away. We know that Molly gave away n trading cards, so she has 250 - n cards left. Marcus gave away three times as many cards as Molly did, so he gave away 3n cards. That means he has 430 - 3n cards left.

We also know that Molly and Marcus have the same number of trading cards left, so:

250 - n = 430 - 3n

Simplifying and solving for n, we get:

2n = 180

n = 90

Therefore, Molly gave away 90 trading cards, which is option (c).

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A nonspecific defense, also known as innate immunity, is the first line of defense that the body uses against pathogens, such as bacteria, viruses, and fungi.

This defense is considered nonspecific because it is not targeted towards a particular pathogen but rather provides a general defense mechanism that helps the body to prevent and fight infections. Examples of nonspecific defenses include physical barriers such as skin and mucous membranes, chemical barriers such as stomach acid and lysozyme, and cellular defenses such as phagocytic cells and natural killer cells.

2. The body's second line of defense is also part of the innate immune system and involves the activation of nonspecific leukocytes, including neutrophils, monocytes/macrophages, and natural killer cells. This defense takes effect when pathogens manage to breach the physical and chemical barriers of the body and enter into the tissues. These leukocytes then recognize and attack the invading pathogens through various mechanisms such as phagocytosis, release of cytotoxic substances, and activation of the complement system.

3. Nonspecific leukocytes play critical roles in the body's second line of defense by recognizing and attacking foreign pathogens. Neutrophils are the most abundant leukocytes in the body and are the first responders to infection. They are recruited to the site of infection and destroy pathogens through phagocytosis and release of antimicrobial substances. Monocytes/macrophages also play a crucial role in phagocytosis and release cytokines that activate other immune cells. Natural killer cells are responsible for recognizing and killing virus-infected cells and tumor cells.

Lastly, question 4. When Jera's skin became red and warm around the cut, it was a sign of inflammation, which is a normal response of the immune system to infection. Inflammation is characterized by redness, heat, swelling, and pain, and is caused by the release of chemicals such as histamine and cytokines in response to infection. The purpose of inflammation is to increase blood flow to the site of infection, bringing immune cells and nutrients to aid in the fight against the invading pathogens.

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The perimeter is indeed 26 feet, which means they have used all the extra fencing.

Let's start by assuming that the length and width of the garden patch are whole numbers of feet, since we are asked to use only whole numbers.

Let's call the length of the garden patch "L" and the width "W".

We know that Liam has 26 feet of fencing left over. This fencing will be used to make the perimeter of the garden patch, which is given by:

Perimeter = 2L + 2W

We can substitute the value of the perimeter with the amount of fencing that Liam has:

26 = 2L + 2W

Simplifying this equation, we get:

13 = L + W

Since we want to use all the extra fencing, we know that the perimeter of the garden patch must be 26 feet. We can use this information to write another equation:

Perimeter = 2L + 2W = 26

We can substitute the value of 13 for L + W in this equation:

2L + 2W = 26

2L + 2(13-L) = 26

2L + 26 - 2L = 26

26 = 26

This equation is true, which means that our assumption that L and W are whole numbers is correct.

Therefore, the dimensions of the garden patch that Liam and his brother can make for their sister are 6 feet by 7 feet.

To check, we can calculate the perimeter:

Perimeter = 2L + 2W = 2(6) + 2(7) = 12 + 14 = 26

So the perimeter is indeed 26 feet, which means they have used all the extra fencing.

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The greatest common what is the greatest common factor of 6a2b2 and 15a4b37 is option d.

To find the greatest common factor (GCF) of 6a^2b^2, 15a^4b^3, 7a^3b, and 3a^2b^2, follow these steps:

Step 1: Find the GCF of the numerical coefficients: The GCF of 6, 15, 7, and 3 is 1.

Step 2: Find the GCF of the 'a' terms: The lowest power of 'a' is a^2, so the GCF is a^2.

Step 3: Find the GCF of the 'b' terms: The lowest power of 'b' is b, so the GCF is b.

Combine the results from steps 1, 2, and 3: The GCF of 6a^2b^2, 15a^4b^3, 7a^3b, and 3a^2b^2 is 1a^2b.

Therefore, the GCF of 6a^2b^2 and 15a^4b^3 is 3a^2b^2, which is option (d).

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Let's label the 3 points as A;B;C, where BC is the hypotenuse and AB is the shortest side, and x as AH.

We can see that triangle AHC is similar to triangle CAB, and triangle ACH is similar to triangle BCA, so therefore triangle AHC is similar to triangle CHA (i might've messed up the order but you get it)

Because they are similar, we get the ratio : x/12 = 40/x, or x^2 = 480.

So, x = [tex]\sqrt{480}[/tex], or 21.9 (1 d.p)

Answer:

-----------------------

According to the right triangle altitude theorem:

We see x is the altitude and 12 & 40 are the segments formed on the hypotenuse.

Applied to the given triangle, we get following equation:

Answer:

Point in the original figure: (5,4)

Point in the final figure: (0,-2)

Step-by-step explanation:

hope this works and helps! :)

Ans. Correct option in (c) 12!/11!

we know that

the formula of nPr is n! / (n−r)!.

in this question

n = 12 and r = 1

so putting values we get ,

= 12! / (12-1)!

=  12!/11!

Answer:

I got you

Step-by-step explanation:

it's c -103 cause you first have to get 180 degrees

Answer:

a + 5b - 7c

Step-by-step explanation:

Let the number to be added by X

then,

a - 2b + 3c + X = 2a + 3b - 4c

X =  a + 5b - 7c

Answer:

27

Step-by-step explanation:

The complete system of inequalities for Anduray's package is:

x ≤ 22

y ≤ 22

x + y ≤ 30

14xy ≤ 3696

Let's define:

x: length of the package in inches

y: width of the package in inches

Then, the system of inequalities that represents the delivery service requirements is:

x ≤ 22 (length must be 22 inches or less)

y ≤ 22 (width must be 22 inches or less)

x + y ≤ 30 (length plus width must be no more than 30 inches)

We also know that Yuriy's package has a height of 7 inches, so we can add the following constraint:

4xy ≤ 840 (the product of length, width, and height must be no more than 840 cubic inches)

Therefore, the complete system of inequalities for Yuriy's package is:

x ≤ 22

y ≤ 22

x + y ≤ 30

4xy ≤ 840

Anduray's package has a height of 14 inches, so we can add the following constraint to his system of inequalities:

14xy ≤ 3696 (the product of length, width, and height must be no more than 3696 cubic inches)

Therefore, the complete system of inequalities for Anduray's package is:

x ≤ 22

y ≤ 22

x + y ≤ 30

14xy ≤ 3696

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Answer:

B, A, C

Step-by-step explanation:

The rate is the another name for the slope.

A:

Change in y over the change in x.  You find the change by subtracting

[tex]\frac{7-3}{5-3}[/tex] = [tex]\frac{4}{2}[/tex] = 2

The rate is 2.

B:

Change in y over the change in x. You find the change by subtracting.

[tex]\frac{0-3}{-5-0}[/tex] = [tex]\frac{-3}{-5}[/tex] = [tex]\frac{3}{5}[/tex]

The rate is [tex]\frac{3}{5}[/tex].

C:

The rate is the number before the x in the equation.

The rate is 3.

Helping in the name of Jesus.

The number of triangles that can be formed using 14 points in a plane such that 4 points are collinear is 360.

If 4 points are collinear, then we can choose any 3 of those points to form a line segment, which cannot be extended to form a triangle.

we need to choose 3 points from the 14 points such that no 3 of them are collinear.

The number of triangles that can be formed from n non-collinear points in a plane is given by the formula:

                  C(n,3) = n(n-1)(n-2)/6

where C(n,3) is the binomial coefficient for choosing 3 items out of n.

So, to find the number of triangles that can be formed using 14 points in a plane such that 4 points are collinear,

we first need to find the number of ways to choose 3 points from 14 points, and then subtract the number of ways to choose 3 points from the 4 collinear points.

That is:

Total number of triangles = C(14,3) - C(4,3)

Total number of triangles = 364 - 4

Total number of triangles  = 360

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The size of each section in a graph tells in relation to the portion of the data :

The magnitude of a graphic's segment indicates a specific attribute of the data being presented. In charts like pie charts or stacked bar graphs, each component's size denotes the relative frequency or proportion of data points in a particular category.

This implies that larger fragments reflect an increased number of data points for its associated categories whereas smaller ones represent categories with lesser data points.

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The values of m and n are

m = 0 and n = 3.125

The graph is attached

The values of m and n are solved using the relationship between miles and kilometers. This type of relationship is a linear proportional relationship. Linear relationship implies the graph will be a straight line graph.

This relationship is that 1 mile equals 0.625 km hence the linear equation is

y = 0.625x

when x = 0, we have that

y = 0.625 * 0

y = 0

when x = 5, we have that

y = 0.625 * 5

y = 3.125

Where x is kilometers and y is miles

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The number of people left after one week is approximately 157286.

The population of a city with 750,000 people is devastated by a unknown virus that kills 20% of the population per day.

Therefore, each day, 20% of the people are killed by the virus.

Hence, let's find the number of people left as follows:

Therefore,

7 days = 1 week

number of people left = 750,000(1 - 20%)⁷

number of people left = 750,000(1 - 0.2)⁷

number of people left = 750,000(0.8)⁷

number of people left = 750,000(0.2097152)

number of people left = 157286.4

Therefore,

number of people left after 1 week =  157286.4

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The distance between Town A and Town B is 550 km.

Let's denote the distance between Town A and Town B as D.

When the two cars first passed each other, let's assume that car A traveled a distance of x km and car B traveled a distance of D - x km.

Let's also denote the initial speeds of car A and car B as 6s and 5s, respectively, where s is some constant representing the speed of the slower car.

The time it took for the two cars to pass each other can be calculated using the formula:

time = distance / speed

For car A, the time it took to travel x km was:

x / (6s)

For car B, the time it took to travel D - x km was:

(D - x) / (5s)

Since the two cars traveled the same amount of time until they passed each other, we can set these two expressions equal to each other:

x / (6s) = (D - x) / (5s)

Solving for x, we get:

x = 6Ds / (11s)

After the speeds of both cars were reduced, car A's speed was (5/6) * 6s = 5s, and car B's speed was (3/4) * 5s = (15/4)s.

Let's denote the time it took for car A to travel the remaining distance from x to D as t.

Then, the time it took for car B to travel a distance of (D - x - 54) km is also t.

Using the new speeds, we can write the equation:

[tex](D - x - 54) = (15/4)s * t[/tex]

Solving for t, we get:

[tex]t = (4/15)(D - x - 54) / s[/tex]

The distance car A traveled after the two cars passed each other is:

D - x = D - 6Ds / (11s) = (5/11)D

The time it took for car A to travel this distance is:

[tex]t + x / (6s) = (4/15)(D - x - 54) / s + 6Ds / (66s)[/tex]

Setting these two expressions equal to each other and solving for D, we get:

D = 550 km

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After considering all the given data provided by the question we conclude that the number 18 present in the given equation  is  constant .

The equation for the sunflower's height is h = 18 + 2.5w.
Here, the number 18 shows the height of the sunflower during the time it was planted, so it is the constant term present in the equation and hence it does not relie on the duration of weeks that have passed.
The coefficient of w is 2.5, which represents the rate at which the sunflower grows in height per week.
Therefore, after one week, the sunflower would be 20.5 inches tall (18 + 2.5 x 1), after two weeks it would be 23 inches tall (18 + 2.5 x 2), after four weeks it would be 28 inches tall (18 + 2.5 x 4), and after six weeks it would be 33 inches tall (18 + 2.5 x 6).

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The amount of profit when there are 0 visitors.

In the context of the given quadratic function, the y-intercept represents the amount of profit when there are 0 visitors.

To explain, the y-intercept is the point at which the function intersects the y-axis. This occurs when the x-value (number of visitors in thousands) is 0. In the given table, the y-intercept corresponds to the data point (0, 0), meaning there is a profit of $0 thousands when there are 0 visitors.

Looking at the table, we can see that when the number of visitors is 0, the profit is also 0. Therefore, the y-intercept of the function represents the amount of profit when there are 0 visitors.

So the correct option is: "the amount of profit when there are 0 visitors".

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To maximize Q = xy with the constraint x + y = 332, and given x = 4, we need to express the objective function in terms of y.

Since x = 4, we can rewrite the constraint as: 4 + y = 332

Now, solve for y:
y = 332 - 4
y = 328

Now, substitute the value of x into the objective function:
Q = (4)(y)

So, the objective function in terms of y is:
Q = 4y

To write the objective function in terms of y, we can solve for x in the constraint equation:

x + 332 = 4

x = 4 - 332

x = -328

Now we can substitute this value of x into the equation for Q:

Q = xy

Q = (-328)y

Q = -328y

Therefore, the objective function in terms of y is Q = -328y.

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