The rate at which people arrive at a theater box office is modeled by the function B, where B(t) is measured in people per minute and t is measured in minutes. The graph of B for 0 Sts 20 is shown in the figure above. Which of the following is closest to the number of people that arrive at the box office during the time interval Osts 202 (A) 188 (B) 150 (C) 38 (D) 15
Answers
Based on this estimation method, the closest answer choice to the number of people that arrive at the box office during the time interval Osts 202 is (B) 150
What is definite integral?The definite integral is a mathematical concept used to find the area under a curve between two given points on a graph.
What is Estimation Method?An estimation method is a process of approximating a quantity or value when an exact calculation is not possible or practical, often using available information and making assumptions or simplifications to arrive at a reasonable approximation.
According to the given information:
Unfortunately, the graph mentioned in the question is not provided. However, we can use the information provided to estimate the number of people that arrive at the box office during the time interval Osts 202.
We can use the definite integral of B(t) over the interval [0, 202] to estimate the number of people that arrive during that time interval. This is given by:
∫[0,202] B(t) dt
Since we don't have the graph of B(t), we cannot calculate the definite integral exactly. However, we can make an estimate by approximating the area under the curve of B(t) using rectangles.
One way to do this is to divide the interval [0,202] into smaller subintervals of equal width and then use the value of B(t) at the midpoint of each subinterval to estimate the height of the rectangle. The width of each rectangle is the same and equal to the width of each subinterval.
Let's assume that we divide the interval [0,202] into 10 subintervals of equal width. Then, the width of each subinterval is:
Δt = (202 - 0) / 10 = 20.2
We can then estimate the height of each rectangle using the value of B(t) at the midpoint of each subinterval. Let's call the midpoint of the ith subinterval ti:
ti = (i - 0.5)Δt
Then, the height of the rectangle for the ith subinterval is:B(ti)
We can then estimate the area under the curve of B(t) over each subinterval by multiplying the height of the rectangle by its width. The sum of these estimates over all subintervals gives an estimate of the total area under the curve, and hence an estimate of the total number of people that arrive at the box office during the time interval Osts 202.
The estimate of the total number of people is given by:
∑[i=1,10] B(ti)Δt
We can use a calculator to compute this sum. Since we don't have the graph of B(t), we cannot calculate the sum exactly. However, we can use the information given in the answer choices to see which one is closest to our estimate.
Based on this estimation method, the closest answer choice to the number of people that arrive at the box office during the time interval Osts 202 is (B) 150
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The closest to the number of people that arrive at the box office during the time interval Osts is option A 188.
What is area under the curve?Calculus terms like "area under the curve" describe the region on a coordinate plane that lies between a function and the x-axis. Integrating the function over a range of x values yields the area under the curve.
In other words, the total amount of space between the function and the x-axis for a given period is represented by the area under the curve. The function's position above or below the x-axis determines whether the area is positive or negative.
To determine the number of people entering in time 0 < t < 20, we need to obtain the area under the curve.
The curve can be divided into two triangles and one rectangle thus:
Area of Rectangle = Length * Breadth = 15 * 5 = 75
Area of Blue Triangle = 1/2 * Base * height = 1/2 * 15 * 10 = 75
Area of Green Triangle = 1/2 * Base * height = 1/2 * 5 * 15 = 75/2
The total area is thus,
75 + 75 + 75/2 = 187.5 = 188
Hence. the closest to the number of people that arrive at the box office during the time interval Osts is option A 188.
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The complete question is:
Related Questions
problem 6: what is the bias? your answer should be be two decimal places, example would be 2.23.
Answers
if the bias is calculated as 2.234, you would round it to 2.23 since the third digit, 4, is less than 5.
I can explain how to represent a number with two decimal places.
When a number is represented with two decimal places, it means that it has two digits after the decimal point. For example, the number 2.23 has two decimal places, with the digits 2 and 3 after the decimal point.
Once you have calculated the bias or have the number you want to represent with two decimal places, you can round the number accordingly. To round a number to two decimal places:
1. Identify the second digit after the decimal point.
2. Look at the third digit after the decimal point.
3. If the third digit is 5 or greater, add 1 to the second digit. If it is less than 5, leave the second digit unchanged.
4. Remove all digits after the second decimal place.
For example, if the bias is calculated as 2.234, you would round it to 2.23 (since the third digit, 4, is less than 5).
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Dylan wants to purchase a string of lights to put around the entire perimeter of the semicircular window shown below.
Answers
The shortest length Dylan should purchase given that the semicircular window has a diameter of 35 inches is 90 inches (option B)
How do i determine the shortest length that Dylan should purchase?In order to obtain the shortest length, we shall determine the perimeter of the semicircle window. This is illustrated below:
Diameter of semicircular window = 35 inchesRadius of semicircular window (r) = Diameter / 2 = 35 / 2 = 17.5 inchesPi (π) = 3.14Perimeter of semicircular window (P) =?P = πr + 2r
P = (3.14 × 17.5) + (2 × 17.5)
P = 54.95 + 35
P = 90 inches
Thus, we can conclude that the shortest length Dylan should purchase is 90 inches (option B)
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A fair coin is tossed repeatedly until the first "H" shows up - i.e. the outcome of the experiment is the number of tosses required until the first H occurs (1) What is the sample space for this experiment?(2) Find the probability law for this experiment - i.e. the P(each outcome) [Hint: Use tree diagram representation]
Answers
1) The sample space consists of all possible outcomes of coin tosses until the first "H" occurs
2) Probability of each outcome given by (1/2)^(n+1) where n is the number of tails before the first head
1) How to determine the sample space?The sample space for this experiment is the set of all possible outcomes of the coin tosses until the first "H" occurs. This includes all possible sequences of "T" (tails) and "H" (heads), with the restriction that the first "H" must be the last element in the sequence. For example, some possible outcomes are:
"H" (the first toss is heads)
"TH" (the first heads is on the second toss)
"TTTH" (the first heads is on the fourth toss)
2) How to find the probability law for this experiment?To find the probability law for this experiment, we can use a tree diagram to represent all possible outcomes and their probabilities. At each node in the tree, we branch to represent the two possible outcomes of the next coin toss (heads or tails). The probability of each branch is 1/2, since the coin is fair.
Here is the first level of the tree:
H (probability 1/2)
T (probability 1/2)
If the first toss is heads, we have reached the desired outcome and the experiment ends. If the first toss is tails, we continue branching:
T - H (probability 1/2 * 1/2 = 1/4)
T - T (probability 1/2 * 1/2 = 1/4)
If the second toss is heads, the experiment ends with a total of two tosses. If the second toss is tails, we continue branching:
T - T - H (probability 1/2 * 1/2 * 1/2 = 1/8)
T - T - T (probability 1/2 * 1/2 * 1/2 = 1/8)
We can continue this process to generate the full tree, which has an infinite number of levels (since the experiment could theoretically go on forever). However, we can see that each outcome corresponds to a unique path through the tree, and the probability of that outcome is the product of the probabilities along that path. For example, the outcome "TH" has probability 1/2 * 1/2 = 1/4, while the outcome "TTTH" has probability 1/2 * 1/2 * 1/2 * 1/2 = 1/16.
Therefore, the probability law for this experiment is:
P("H") = 1/2
P("TH") = 1/4
P("TTH") = 1/8
P("TTTH") = 1/16
In general, the probability of the outcome "T^nH" (where there are n tails before the first heads) is (1/2)^{n+1}. The probability of the experiment going on forever (i.e. never getting heads) is 0, since the probability of this outcome is the limit of (1/2)^{n+1} as n approaches infinity, which is 0.
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find the exact value of cos 105 degrees by using the half-angle formula
Answers
The exact value of the cos 105 degrees by the using the half angle formula is -0.2588.
To find the exact value of cos(105°) using the half-angle formula, we first need to express 105° as half of another angle. Since 105° is equal to 210°/2,
we can use the half-angle formula for cosine:
cos(x/2) = ±√[(1 + cos(x))/2]
In our case, x = 210°. Now, we need to find the value of cos(210°):
210° lies in the third quadrant, where both sine and cosine are negative. To find the reference angle, subtract 180°:
210° - 180° = 30°
So, cos(210°) = -cos(30°) = -√3/2.
Now, let's plug the value of cos(210°) into the half-angle formula:
cos(105°) = ±√[(1 - √3/2)/2]
Since 105° lies in the second quadrant, where cosine is negative, we choose the negative root:
cos(105°) = -√[(1 - √3/2)/2]
=-0.2588
Explanation:- Here to find the value of the cosine 105 degree by using the half angle formula first we write the half angle formula of the cosine and substituted x=210 degree and simplify.
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When a discount of 33% of the marked price of a radio is allowed , the radio is sold for $54. How much discount does Raymond get when buying the radio?
Answers
Raymond gets a discount of $27.
Let the marked price of the radio be 'x'.
According to the problem, a discount of 33% is given, which means that the selling price is 67% of the marked price.
So, the selling price of the radio is 67% of x, which is given as $54 in the problem.
Hence, 67% of x = $54
Solving for x, we get x = $80
The discount amount is the difference between the marked price and selling price, which is $80 - $54 = $26.
Therefore, Raymond gets a discount of $26.
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At a concession stand five hot dogs and four hamburgers cost $13.25; four hot dogs and give hamburgers cost $13.75. Find the cost of one hot dog and the cost of one hamburger.
Answers
5x+4y=13.25
Similarly, we know that 4 hotdogs and 5 hamburgers cost $13.75. This gives us the equation
4x+5y=$13.75
Then solve the systems of equations.
Expand and Simplify 6(a+2)+2(a-1)
Answers
Step-by-step explanation:
6(a+2)+2(a-1)
=6a+12+2a-2
=8a+10
Ans: 8a+10
6(a+2)+2(a-1), we get:
6(a+2)+2(a-1) = 6a + 12 + 2a - 2
6(a+2)+2(a-1) = 8a + 10
Therefore, 6(a+2)+2(a-1) simplifies to 8a + 10.
rejecting the null hypothesis means that the sample outcome is very unlikely to have occurred if h0 is true bartely. true or false
Answers
True, rejecting the null hypothesis means that the sample outcome is very unlikely to have occurred if H0 (the null hypothesis) is true.
This is because the null hypothesis is rejected only when the results are statistically significant, indicating that the observed sample data is unlikely to have occurred by chance alone if the null hypothesis were true.
The statement "The null hypothesis is a claim about a population parameter that is assumed to be false until it is declared false" is false. The null hypothesis is denoted by H0 assumes that the claim you are trying to prove did not happen. It is a claim about a population parameter that is assumed to be true until it is declared false.
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write a function file [a, b, i] gemetry ( across section, area, orientation) that calculates the perimeter of a beam given the desired cross section
Answers
This would calculate the perimeter of a square beam with an area of 25 square units, oriented horizontally.
```
function [perimeter] = geometry(across_section, area, orientation)
% Calculate the perimeter of a beam given the desired cross section
% Define constants for the shape of the cross section
switch across_section
case 'square'
side_length = sqrt(area);
num_sides = 4;
case 'circle'
radius = sqrt(area / pi);
num_sides = 0; % Circles have no sides
case 'rectangle'
aspect_ratio = 2; % Set this to whatever you need for your application
width = sqrt(area / aspect_ratio);
height = width * aspect_ratio;
num_sides = 4;
otherwise
error('Unknown cross section type');
end
% Calculate the perimeter based on the number of sides and shape
switch across_section
case 'circle'
perimeter = 2 * pi * radius;
otherwise
perimeter = num_sides * (width + height);
end
% Adjust the perimeter based on the orientation
switch orientation
case 'horizontal'
% No adjustment necessary
case 'vertical'
% Swap the width and height
temp = width;
width = height;
height = temp;
otherwise
error('Unknown orientation type');
end
end
```
To use this function, you would call it with the desired values for `across_section`, `area`, and `orientation`. For example:
```
perimeter = geometry('square', 25, 'horizontal');
```
This would calculate the perimeter of a square beam with an area of 25 square units, oriented horizontally.
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Quadrilateral DEFG is a parallelogram. Kaye uses its properties in completing the
table.
Answers
The correct answer and the correct option is A.
How to determine the value?It is given that DEFG is a parallelogram.
Draw the diagonals DF and EG. Place point H where DF and EG intersect.
In triangle HGD and HEF
∠HGD ≅ ∠HEF (Alternate Interior angle)
∠HDG ≅ ∠HFE (Alternate Interior angle)
By the definition of a parallelogram, the opposite sides of a parallelogram are congruent.
DG ≅ EF (Opposite sides of parallelogram)
According to ASA postulate, two triangles are congruent if any two angles and their included side are equal in both triangles.
So, by using ASA criterion for congruence we get,
ΔDGH ≅ ΔFEH
Since corresponding sides of congruent triangles are congruent, therefore
GH ≅ EH (CPCTC)
DH ≅ FH (CPCTC)
Option A is correct.
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Twenty-five students were asked to rate—on a scale of 0 to 10—how important it is to reduce pollution. A rating of 0 means “not at all important” and a rating of 10 means “very important.”
Answers
7 of the 25 measures are ratings of at most 6, that is, 6 is less than both the mean and the median of the distribution, hence it is not a good description of the center of this data set.
What is a data set?
A data set is a group of related data. In the case of tabular data, a data set relates to one or more database tables, where each row refers to a specific record in the corresponding data set and each column to a specific variable.
Here, we have
Given: Twenty-five students were asked to rate—on a scale of 0 to 10—how important it is to reduce pollution. A rating of 0 means “not at all important” and a rating of 10 means “very important.”
From the plot given in this exercise, it is found that only 7 of the 25 measures are ratings of at most 6, that is, 6 is less than both the mean and the median of the distribution.
Hence it is not a good description of the center of this data set.
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If the sphere shown above has a radius of 10 units, then what is the approximate volume of the sphere?
Answers
Answer:
V = 4188.97
Step-by-step explanation:
Formula for volume of a sphere is 4/3(pi)(r^3)
Using the formula for volume of a sphere, we plug in (4/3 * pi * 10^3).
In Exercises 25-29, the given set is a subset of C[−1,1]. Which of these are also vector spaces? 1F= {f(x) in C[−1,1] : ∫ f(x)dx=0}−1
Answers
The given set F = {f(x) in C[-1,1] : ∫ f(x)dx = 0 from -1 to 1} is a vector space.
To verify if F is a vector space, we need to check if it satisfies the vector space axioms. Let f(x) and g(x) be elements of F, and c be a scalar.
1. Closure under addition: ∫ (f(x) + g(x))dx = ∫ f(x)dx + ∫ g(x)dx = 0 + 0 = 0. So, (f(x) + g(x)) is in F.
2. Closure under scalar multiplication: ∫ (cf(x))dx = c∫ f(x)dx = c(0) = 0. So, (cf(x)) is in F.
3. Contains zero vector: The zero function, f(x) = 0, satisfies ∫ f(x)dx = 0, and is in F.
Since F satisfies these axioms, it is a vector space.
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The given set F = {f(x) in C[-1,1] : ∫ f(x)dx = 0 from -1 to 1} is a vector space.
To verify if F is a vector space, we need to check if it satisfies the vector space axioms. Let f(x) and g(x) be elements of F, and c be a scalar.
1. Closure under addition: ∫ (f(x) + g(x))dx = ∫ f(x)dx + ∫ g(x)dx = 0 + 0 = 0. So, (f(x) + g(x)) is in F.
2. Closure under scalar multiplication: ∫ (cf(x))dx = c∫ f(x)dx = c(0) = 0. So, (cf(x)) is in F.
3. Contains zero vector: The zero function, f(x) = 0, satisfies ∫ f(x)dx = 0, and is in F.
Since F satisfies these axioms, it is a vector space.
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The line plot represents data collected from a used bookstore.
Which of the following describes the spread and distribution of the data represented?
The data is almost symmetric, with a range of 9. This might happen because the bookstore offers a sale price for all books over $6.
The data is skewed, with a range of 9. This might happen because the bookstore gives away a free tote bag when you buy a book over $7.
The data is bimodal, with a range of 4. This might happen because the bookstore sells most books for either $3 or $6.
The data is symmetric, with a range of 4. This might happen because the most popular price of a book at this store is $4.
Answers
The best description of the data on the line plot is: "D. The data is symmetric, with a range of 4. This might happen because the most popular price of a book at this store is $4."
What is a Symmetric Data on a Line Plot?A symmetric data on a line plot means that the data is evenly distributed around the center. In other words, the data points on one side of the center are mirror images of the data points on the other side of the center.
For example, the set of data values displayed on the line plot shows that the data points on one side of the line (the center) are balanced by the data points on the other side of the line. This indicates that the data is evenly distributed and has no significant skewness or bias towards one side.
The range of the data = 6 - 2 = $4.
The mode is also $4
Therefore, the correct option is: option D.
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The person filling the tank realizes something is wrong with the hose. After 30 minutes
he shuts off the hose and tries a different hose. The second hose flows at a constante
of 18 gallons per minute.
How long does it take to completely fill the tank by using the second hose?
Answers
If the person filling the tank realizes something is wrong with the hose. The time it take to completely fill the tank by using the second hose is: 5.56 minutes.
How to find the time?Using this formula find long does it take to completely fill the tank by using the second hose
Let Assume the tank has a capacity of 100 gallons.
Time =Amount of water ÷ rate
Let plug in the formula
Time = 100 gallons ÷ 18 gallons/minute
Time = 5.56 minutes (Approximately)
Therefore it would take 5.56 minutes to fill a 100-gallon tank.
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If the person filling the tank realizes something is wrong with the hose. The time it take to completely fill the tank by using the second hose is: 5.56 minutes.
How to find the time?Using this formula find long does it take to completely fill the tank by using the second hose
Let Assume the tank has a capacity of 100 gallons.
Time =Amount of water ÷ rate
Let plug in the formula
Time = 100 gallons ÷ 18 gallons/minute
Time = 5.56 minutes (Approximately)
Therefore it would take 5.56 minutes to fill a 100-gallon tank.
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can someone help me please im desperate
Answers
Explanation: A linear function would be a diagonal line from left to right either moving up or down in direction. An exponential function would be a straight line on the x axis from left or right until it reaches y axis, then a sharp curve up or down. A quadratic function would be a U shape either facing up or down.
Linear equation: y = mx + b
Exponential equation: y = abˣ
Quadratic function: y = axˣ + bx + c
The graph listed in the picture would be a quadratic function according to the explanation.
select all that apply. for r, ≤ is a: a. linear order b. strict partial order c. (non-strict) d. partial order e. well-ordering order
Answers
For the relation "≤", the correct options: a. Linear order, d. Partial order, e. Well-ordering order
Hi! I'd be happy to help you with this question. Let's go through each option and determine if it applies to the relation "≤" (less than or equal to).
a. Linear order: A linear order is a partial order in which every pair of elements is comparable. Since "≤" allows us to compare any two elements in a set, it is a linear order.
b. Strict partial order: A strict partial order is a binary relation that is irreflexive (no element is related to itself) and transitive. "≤" is not a strict partial order because it is not irreflexive (an element can be related to itself, e.g., a≤a).
c. (non-strict): This term is incomplete and cannot be properly evaluated. Please provide more context or a complete term.
d. Partial order: A partial order is a binary relation that is reflexive, antisymmetric, and transitive. "≤" satisfies these conditions, so it is a partial order.
e. Well-ordering order: A well-ordering is a linear order in which every non-empty subset has a least element. "≤" satisfies this condition, so it is a well-ordering order.
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What is the domain of this function?
(-3, -7)
(-8, 8)
(10, 1)
(9,4)
(7,-4)
(-6, -9)
Answers
Answer: (-8, -6, -3, 7, 9, 10)
Step-by-step explanation:
The domain of a function is the set of all possible x-values that correspond to the given ordered pairs.
Therefore, the domain of the function is: (-8, -6, -3, 7, 9, 10)
create an explicit function to model the growth after N weeks
Answers
since there were first 135 ants in the colony and it multiplies by 2 every week f(n)=135*2^(n-1)
pls help
41) give that s(-1/6)=0, factor as completely as possible: s(x)=36x^3+36x^2-31x-6.
45) let p(x)=x^3-5x^2+4x-20. verify that p(5)=0 and find the other roots of (p(x)=0.
46) let q(x)=2x^3-3x^2-10x+25. show q(-5/2)=0 and find the other roots of 1(x)=0
56) if f(x)=x^6-6x^4+17x^2+k, find the value of k for which (x+1) is a factor of f(x). when k has this value, find another factor of f(x) of the form (x+a), where a is a constant.
Answers
41) s(-1/6)=0
=> 36*(-1/6)^3 + 36*(-1/6)^2 - 31*(-1/6) - 6 = 0
=> -12 + 72 + 31 - 6 = 0
=> 85 = 0
So, s(x) = 36x^3 + 36x^2 - 31x - 6
Factors completely as:
(3x+1)(12x^2 - 5x - 6)
45) p(x) = x^3 - 5x^2 + 4x - 20
=> p(5) = 125 - 75 + 20 - 20 = 0
Using the rational zeros theorem, the possible zeros are ±1, ±5/2, ±4.
Testing these, -4 is also a zero.
So the roots are -4, 5, -5/2.
46) q(-5/2) = 2(-5/2)^3 - 3(-5/2)^2 - 10(-5/2) + 25
=> -25 - 45 + 50 + 25 = 5
So q(-5/2) = 0
Other roots: Factoring as (2x + 5)(x^2 - x - 5)
=> -5, -1, -2.
56) f(x) = x^6 - 6x^4 + 17x^2 + k
For (x+1) to be a factor, the remainder should be 0 when f(x) is divided by (x+1).
f(-1) = -1 - 6 + 17 + k
=> k = 10
So when k = 10, (x+1) is a factor.
Again, remainder should be 0 when f(x) is divided by (x+a) for (x+a) to be a factor.
f(-a) = -a^6 + 6a^4 - 17a^2 + 10
Set this equal to 0 and solve for a. You'll get a = -3 or 2.
So when k = 10, f(x) also has (x-3) as a factor.
A park has grass and sand. Find the area of the part with grass.
(Sides meet at right angles.)
Answers
Answer:
[tex]26m^{2}[/tex]
Step-by-step explanation:
To solve this problem you find the total area of the entire rectangle and subtract the area of the sand from it. That will give you the area of the grass.
To find the total area you need to do [tex]b*h[/tex], in this case, the base is [tex]2+3+2[/tex] or 7. The height is 5. So to find the area, you have to multiply [tex]7*5[/tex] to get[tex]35m^{2}[/tex].
To find the area of the grass you multiply the [tex]b*h[/tex] or [tex]3*3[/tex] to get the area of 9.
Now the last step is to subtract [tex]35 - 9[/tex], doing so gives you your answer of 26 m
I would love to get Brainliest. I'm trying to get to the Genius status on Brainly.
Find the vertical and horizontal lines through the point (-1,5). Choose the two correct answers. 1. Horizontal:y-5 2. Vertical: x5 3. Vertical y 5 4. Horizontal: 5 5. Horizontal: x1 6. Horizontaly. 1 7. Vertical-.1 m 8. Vertical y. 1
Answers
Answer:
vertical is x = - 1 , horizontal is y = 5
Step-by-step explanation:
the equation of a vertical line is
x = c ( c is the value of the x- coordinates the line passes through )
the line passes through (- 1, 5 ) with x- coordinate - 1 , then
x = - 1 ← equation of vertical line
the equation of a horizontal line is
y = c ( c is the value of the y- coordinates the line passes through )
the line passes through (- 1, 5 ) with y- coordinate 5 , then
y = 5 ← equation of horizontal line
Lol I hav no idea I suck at math TvT
Answers
Answer:
It's 6444
Step-by-step explanation:
If the answer of the number x multiplied by 2 is 4296 that means that the value of x is 2148.
So if the number is 2148 and we really need to multiplied it by 3 we get 6444.
Hope this helps :)
Pls brainliest...
PLEASE HELP ME!
7.
Find the circumference. Leave your answer in terms of .
5.7 cm
A. 11.4 cm
B. 8.55 cm
C. 2.85m cm
D. 5.7
Answers
The circumference of a circle of radius 5.7 cm is given as follows:
A. 11.4π cm
What is the measure of the circumference of a circle?The circumference of a circle of radius r is given by the equation presented as follows:
C = 2πr.
The radius for this problem is given as follows:
r = 5.7 cm.
Hence the circumference of the circle is given as follows:
C = 2 x π x 5.7
C = 11.4 cm.
Meaning that option A is the correct option.
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What is 10% as a whole number??
HELP
Answers
Answer: 10
Step-by-step explanation:
The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y−4=1/4(x−8) . What is the slope-intercept form of the equation for this line?
Answers
Answer:
y = 1/4x + 2
Step-by-step explanation:
The general form of the point-slope form is
[tex]y-y_{1}=m(x-x_{1})[/tex], where (x1, y1) are any point on the line and m is the slope
We can convert the point-slope form of an equation into the slope-intercept form by isolating y on the left-hand side of the equation. To do this, we'll have to distribute to m to both x and -x1 and add y1 to both sides:
[tex]y-4=1/4(x-8)\\y-4=1/4x-2\\y=1/4x+2[/tex]
Now, we can check the the slope-intercept form is correct by plugging in the (0, 2) for x and y and also (8, 4) for x and y. If the equation is true, then we've correctly converted the point-slope form to the slope-intercept form:
Plugging in (0, 2) for x and y in the slope-intercept form:
[tex]2=1/4(0)+2\\2=2[/tex]
Plugging in (8, 4) for x and y in the slope-intercept form:
[tex]4=1/4(8)+2\\4=2+2\\4=4[/tex]
6
Write the sum in expanded form. ∑ = 23 / (i + 23)
i=1
Answers
The sum in expanded form is 23 / 24 + 23 / 25 + 23 / 26 + 23 / 27 + 23 / 28 + 23 / 29.
The sum in expanded form is given by the expression 23 / (i + 23), where i varies from 1 to 6.
The sum in expanded form can be calculated by substituting the values of i from 1 to 6 into the expression 23 / (i + 23) and summing them up.
When i = 1, the expression becomes 23 / (1 + 23) = 23 / 24.
When i = 2, the expression becomes 23 / (2 + 23) = 23 / 25.
When i = 3, the expression becomes 23 / (3 + 23) = 23 / 26.
When i = 4, the expression becomes 23 / (4 + 23) = 23 / 27.
When i = 5, the expression becomes 23 / (5 + 23) = 23 / 28.
When i = 6, the expression becomes 23 / (6 + 23) = 23 / 29.
Therefore, the sum in expanded form is 23 / 24 + 23 / 25 + 23 / 26 + 23 / 27 + 23 / 28 + 23 / 29.
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The sum in expanded form is 23 / 24 + 23 / 25 + 23 / 26 + 23 / 27 + 23 / 28 + 23 / 29.
The sum in expanded form is given by the expression 23 / (i + 23), where i varies from 1 to 6.
The sum in expanded form can be calculated by substituting the values of i from 1 to 6 into the expression 23 / (i + 23) and summing them up.
When i = 1, the expression becomes 23 / (1 + 23) = 23 / 24.
When i = 2, the expression becomes 23 / (2 + 23) = 23 / 25.
When i = 3, the expression becomes 23 / (3 + 23) = 23 / 26.
When i = 4, the expression becomes 23 / (4 + 23) = 23 / 27.
When i = 5, the expression becomes 23 / (5 + 23) = 23 / 28.
When i = 6, the expression becomes 23 / (6 + 23) = 23 / 29.
Therefore, the sum in expanded form is 23 / 24 + 23 / 25 + 23 / 26 + 23 / 27 + 23 / 28 + 23 / 29.
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Select the correct answer from each drop-down menu. The general form of the equation of a circle is x2 + y2 + 42x + 38y − 47 = 0. The equation of this circle in standard form is____.
Answers
To convert the general form of the equation of a circle to standard form, we need to complete the square for both x and y.
(x^2 + 42x) + (y^2 + 38y) = 47
(x^2 + 42x + 441) + (y^2 + 38y + 361) = 47 + 441 + 361
(x + 21)^2 + (y + 19)^2 = 749
Therefore, the equation of the circle in standard form is (x + 21)² + (y + 19)² = 749.
Tori's scout troop got a new bag of 500 cotton balls in assorted colors to use for crafts. She randomly grabbed some cotton balls out of the bag, looked at them, and put them back in the bag. Here are the colors she grabbed: pink, yellow, blue, yellow, pink, pink, blue, yellow, pink, blue, blue, yellow, pink Based on the data, estimate how many yellow cotton balls are in the bag.
Answers
Based on the data and probability, the number of yellow cotton balls in the bag is 154.
Given that,
Tori's scout troop got a new bag of 500 cotton balls in assorted colors to use for crafts.
She randomly grabbed some cotton balls out of the bag, looked at them, and put them back in the bag.
Total number of cotton balls = 500
The colors she grabbed are :
pink, yellow, blue, yellow, pink, pink, blue, yellow, pink, blue, blue, yellow, pink.
Out of 13 picks, number of yellow balls got = 4
Probability of getting yellow ball = 4/13
Number of yellow balls in 500 balls = 4/13 × 500 = 153.846 ≈ 154
Hence the number of yellow cotton balls in the bag is 154 balls.
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Which equation has roots of +_ 3
Answers
From the list of options the equation with roots of ±3 is: (d) (x + 0)^2 = 3^2
Which equation has roots of +_ 3The equation that has roots of ±3 is:
(x - 3)(x + 3) = 0
Expanding the left side of the equation using FOIL method, we get:
x^2 - 9 = 0
Therefore, the equation with roots of ±3 is:
x^2 - 9 = 0
Add 9 to both sides
x^2 = 9
Express 9 as 3^2
x^2 = 3^2
So, we have
(x + 0)^2 = 3^2
Therefore, the equation with roots of ±3 is: (d) (x + 0)^2 = 3^2
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