The height of the feeder is approximately 4 inches.
We can use the formula for the volume of a cone, which is V = (1/3)π[tex]r^{2}[/tex]h, where V is the volume, r is the radius, and h is the height. We know that V = 113.04 and r = 3, so we can solve for h:
113.04 = (1/3)*π*([tex]3^{2}[/tex])h
113.04 = 9πh
h = 113.04 / (9π)
h ≈ 4 inches
The y- intercept of a direct equation is the point where the line crosses the y- axis. It's the value of y when x is equal to 0. To graph a direct equation, you can compass the y- intercept on the y- axis, and also use the pitch to find other points on the line.
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A basket contains 8 green apples, 11 red apples, 5 nectarines, and 12 oranges. Akhil takes a piece of fruit, eats it,
then grabs another. What is the P(two oranges)?
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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2 Liam bought too much fencing and had 26 feet of it left over. He and his brother
decided to make a rectangle-shaped garden patch for their little sister. They wanted
to use all the extra fencing to outline her garden patch. What could be the dimen-
sions of the patch they make for their sister? (Use only whole numbers of feet. )
Show all your work.
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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help. 100 points guaranteed.
The Willis tower in Chicago is the second tallest building in the United States in his topped by a high intent. A surveyor on the ground makes the following measurements. The angle of elevation from her position to the top of the building is 34°. The distance from her position to the top of the building is 2595 feet. The distance from her position to the top of the antenna is 2760 feet. how far away from the base of the building is the surveyor located? How tall is the building? What is the angle of elevation from the surveyor to the top of the antenna? How tall is the antenna?
The surveyor is located about 239.6 feet away from the base of the Willis Tower.
The height of the Willis Tower is 165 feet.
The angle of elevation from the surveyor to the top of the antenna is about 3.41°.
The height of the antenna is about 135.9 feet.
How to solve for the angle of elevationLet's call the distance from the surveyor to the base of the Willis Tower "x", and let's call the height of the Willis Tower "h".
We can use trigonometry to solve for x and h. First, let's find x:
tan(34°) = h/x
x = h/tan(34°)
Now we can use the distance from the surveyor to the top of the building to solve for h:
h + 2595 = 2760
h = 165
So the height of the Willis Tower is 165 feet. Now we can solve for x:
x = 165/tan(34°) ≈ 239.6 feet
So the surveyor is located about 239.6 feet away from the base of the Willis Tower.
To find the angle of elevation from the surveyor to the top of the antenna, we can use trigonometry again:
tan(θ) = h/2760
θ = tan^(-1)(h/2760)
θ ≈ 3.41°
So the angle of elevation from the surveyor to the top of the antenna is about 3.41°.
Finally, we can use the height of the Willis Tower and the distance from the surveyor to the top of the antenna to solve for the height of the antenna:
tan(34°) = (h + a)/2760
a ≈ 135.9
So the height of the antenna is about 135.9 feet.
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Mr.Franklin drives 37 miles each day to and from work. How many miles does he drive in 20 work days
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
What is the maximum height of of Anna's golf ball? The equation is y=x−0. 04x2
The maximum height of Anna's golf ball is approximately 7.81 units.
Find the maximum height of Anna's golf ball with equation y=x−0. 04x2
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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What is the greatest common what is the greatest common factor of 6a2b2 and 15a4b37
a
3ab
b
3a4b3
с
6ab
d
3a2b2
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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Find the Circumference and area of the circle with the center C=(-1, 6) and a point on the circle A(3, 9). Round to the nearest tenth
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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Describe the clockwise rotation about the origin from the pre-image to the image
The clockwise rotation about the origin from the pre-image to the image include the following: a rotation of 90° clockwise.
What is a rotation?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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Helpppppppppppppppppppppppp
Answer:
Point in the original figure: (5,4)
Point in the final figure: (0,-2)
Step-by-step explanation:
hope this works and helps! :)
Chad is making a cake for the first time. His recipe calls for 280 grams of sugar, but he accidentally pours 295 grams on his first try. He uses a small spoon to remove the extra sugar. If he needs to remove 12 spoonfuls, how many milligrams of sugar does his spoon hold?
The number of milligrams of sugar his spoon holds is 1250 milligrams.
To find out how many milligrams of sugar Chad's spoon holds, we first need to know how much sugar he removed in total. To do this, we can subtract the amount of sugar he needed (280 grams) from the amount he poured (295 grams).
295 grams - 280 grams = 15 grams
Next, we need to divide the total amount of sugar Chad removed (15 grams) by the number of spoonfuls he used (12).
15 grams ÷ 12 = 1.25 grams per spoonful
Finally, we can convert grams to milligrams by multiplying by 1000.
1.25 grams x 1000 = 1250 milligrams
Therefore, Chad's spoon holds 1250 milligrams of sugar.
It's important to note that when cooking or baking, precise measurements are crucial to the success of the recipe. Even small changes can greatly affect the outcome. While it's great that Chad was able to remove the excess sugar, it's best to be as accurate as possible from the start.
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helppppppppppppplppppppooo
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.
what should be added to a-2b 3c to get 2a 3b-4c
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
Calculate the value of X, C is the center of the circle.
Answer:
38
Step-by-step explanation:
Formula
Inscribed angle = Central angle/2
Here
Inscribed angle = x
Central angle = 76
x = 76/2
x = 38
A car left Town A for Town b. Another car left Town B for Town A at the same time. The ratio of the speeds of the two cars was 6:5 initially. After the two cars passed each other, Car A's speed was reduced by 1/6 and car B's speed was reduced by 25%. When car A arrived at Town B, Car B was still 54 km away from Town A. Find the distance between Town A and Town B. Please I need the answer quickly :]
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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How do I solve for X with the base numbers on a right triangle. (Please give an explanation and an answer, I need to know how it works.)
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:
21.9 units-----------------------
According to the right triangle altitude theorem:
the altitude on the hypotenuse is equal to the geometric mean of line segments formed by altitude on the hypotenuse.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:
[tex]x=\sqrt{12*40} =\sqrt{480} =21.9\ units[/tex]find the number of triangles that can be formed using 14 points in a plane such that 4 points are collinear?
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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a. What does the size of each section tell you about that portion of the data? Select all that apply.
A. The relative importance of the category
B. The difference between the minimum and maximum values within the category
c. The count of data points within the category
D. The relative frequency of data within the category
The size of each section in a graph tells in relation to the portion of the data :
c. The count of data points within the categoryD. The relative frequency of data within the categoryWhat does the size show?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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Maximize Q = xy, where x and y are positive numbers such that x+ 332=4. Write the objective function in terms of y. Q= (Type an expression using y as the variable.)"
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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The volume of this rectangular prism is 3 cubic feet. What is the surface area?
Answer:
27
Step-by-step explanation:
What is a nonspecific defense?
What is the body’s second life of defense? When does it take effect?
Identify the roles of nonspecific leukocytes in the body’s second line of defense.
Jera cut her finger. The next day, the skin around the cut became red and warm. Why are these signs of infection?
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.
What is nonspecific defense?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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Identify 12P1 using factorials
a. 12!/13!
b. 12! times 11!
c. 12!/11!
d. 12!/1!
pls look at the pic
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!
Complete parts a rough for the given function f(x) = -4°-x+2:1-4,4) A. The critical point(a) is(ro) ot x - (Simplify your answer. Use a comma to separate wwers as needed) B. The function does not have a critical point b. Use the First Derivative Test to locate the local maximum and minimum values Select the correct choice below and recessary in the answer box to complete your choice (Simplify your answer. Use a comma to separate arvwers as needed) BA The local maximum/maximal/are at OD. The local minimumiminimais/are OC. The local minimumin nima infare at and the local maximum maxima are at OD. There is no local munimum and there is no local maximum e Identify the absolute maximum and minimum values of the function on the given interval (when they st) Select the correct the below and the web.com your choice (Simplify your answer Uses comma to separato answers as needed) A The absolute maxim is al and the absolute minimumis More 8 10
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.
How to find critical point?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.
How to find local maxima and minima?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.
How to found absouloute maxima and minima?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 population of a city with 750,000 people is devastated by a unknown virus that kills 20% of the population per day. How many people are left after 1 week
The number of people left after one week is approximately 157286.
How to find the number of people left?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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A computer company wants to determine the proportion of defective computer chips from a day’s production. A quality control specialist takes a random sample of 100 chips from the day’s production and determines that there were 12 defective chips. He wants to construct a 90% confidence interval for the true proportion of defective chips from the day’s production. Are the conditions for inference met?
Yes, the conditions for inference are met.
No, the 10% condition is not met.
No, the randomness condition is not met.
No, the Large Counts Condition is not met
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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Which describes the statement, "if point b is on ac and between points a and c,
then mab + mbc = mac"?
The statement "if point b is on ac and between points a and c, then mab + mbc = mac" describes the angle addition postulate in geometry.
In geometry, an angle is formed by two rays that share a common endpoint called a vertex. The measure of an angle is the amount of rotation between the two rays, usually measured in degrees or radians. The angle addition postulate states that if point B is on line segment AC and between points A and C, then the sum of the measures of angles MAB and MBC is equal to the measure of angle MAC. This postulate is used in various proofs and constructions in geometry, and it is also useful in real-world applications such as navigation, surveying, and engineering. The postulate is based on the fact that a straight angle measures 180 degrees, so if we know the measures of two angles that share a common ray, we can find the measure of the third angle by subtracting the sum of the first two angles from 180 degrees.
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At the beginning of spring, jin planted a small sunflower in his backyard. the sunflower's height in inches, h after w weeks, is given by the equation h=18+2.5w. what could the number 18 represent in the equation
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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what value of x is y/z
a-13
b-77
c-103
d-154
Answer:
I got you
Step-by-step explanation:
it's c -103 cause you first have to get 180 degrees
A forester is 50 m from the base of a tree and measures the angle between the ground and the top of the tree. If the angle is 768, fi nd the height of the tree. Round your answer to the nearest meter
The height of the tree is approximately equal to the tangent of 768 radians multiplied by 50 meters, rounded to the nearest meter.
How to determine the height of a tree using trigonometry and angle measurement?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 grass in the backyard
of a house is a square
with side length 10 m. A
square patio is placed in
the centre. If the side
length, in metres, of the patio is x, then the
area of grass remaining is given by the
relation A=-x^2+100
The problem presents a scenario where a square patio is placed in the centre of a 10m x 10m square backyard. The side length of the patio is given by x, and the remaining area of grass is expressed as A=-x^2+100.
To find the area of grass remaining, we can substitute different values of x into the equation.
For instance, if the patio is 5m x 5m, then x = 5 and the area of grass remaining is[tex]A = -5^2 + 100 = 75[/tex] square metres. Similarly, if the patio is 8m x 8m, then x = 8 and the area of grass remaining is [tex]A = -8^2 + 100 = 36[/tex] square metres.
As we can see, the area of grass remaining decreases as the size of the patio increases.
This problem illustrates the concept of content loaded and content remaining, where the initial content is the entire area of the square backyard, and the loaded content is the area of the square patio.
The remaining content is what is left after the loaded content is subtracted from the initial content. In this case, the loaded content is the patio area, and the remaining content is the grass area.
In summary, the area of grass remaining in the backyard after a square patio is placed in the centre can be calculated using the equation [tex]A=-x^2+100,[/tex] where x is the side length of the patio in metres.
The concept of content loaded and content remaining is also illustrated in this problem, where the loaded content is the patio area and the remaining content is the grass area.
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