Answer:
see below
Step-by-step explanation:
\(y=-3(x-4)^2+2\)
\(x=-3(y-4)^2+2\)
\(x-2=-3(y-4)^2\)
\(\frac{1}{3}(2-x) =(y-4)^2\)
\(\sqrt{\frac{1}{3}(2-x)}=y-4\)
\(f^{-1}(x)=\sqrt{ \frac{1}{3}(2-x)}+4\)
Consider the following scenario to understand the relationship between marginal and average values. Suppose Lorenzo is a professional b. player, and his game log for free throws can be summarized in the following table.
The missing points from the Column is:
Game Free-Throw Percentage: 60 20 60 80
Average Free-Throw Percentage: 70 60 55 56.67
Game Game Total Game Average
Result Free-Throw Free-Throw
Percentage Percentage
1 8/10 8/10 80 80
2 6/10 14/20 60 70
3 1/5 15/25 20 60
4 3/5 18/30 60 55
5 8/10 26/40 80 56.67
In the "Total" column, we keep track of the cumulative number of successful free throws out of the total attempts.In the "Game Free-Throw Percentage" column, we calculate the percentage of successful free throws made in each game.In the "Average Free-Throw Percentage" column, we calculate the average free-throw percentage up to that game by dividing the cumulative successful free throws by the cumulative total attempts and multiplying by 100.Learn more about Cumulative Frequency here:
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The question attached here seems to be incomplete, the complete question is
Fill in the columns with Dmitri's free-throw percentage for each game and his overall free-throw average after each game.
Game Game Result Total Game Free-Throw Percentage Average Free-Throw Percentage
1 8/10 8/10 80 80
2 6/10 14/20
3 1/5 15/25
4 3/5 18/30
5 8/10 26/40
The sum of a number and 16 times it's reciprocal is 10. Find the numbers
Answer:
The answer is 2 and 8!
Hope this helped :D
A certain culture of the bacterium Rhodobacter sphaeroides initially has 25 bacteria and is observed to double every 6 hours. (a) Find an exponential model n(t) = n02t/a for the number of bacteria in the culture after t hours.
Estimate the number of bacteria after 13 hours. (Round your answer to the nearest whole number.)
After how many hours will the bacteria count reach 1 million? (Round your answer to one decimal place.)
Since the culture is observed to double every 6 hours, we know that the growth rate is constant at r = ln(2)/6 per hour.
To calculate growth rates, divide the difference between the starting and ending values for the period under study by the starting value. The most frequent time intervals for growth rates are annually, quarterly, monthly, and weekly.
We can use the formula for exponential growth to model the number of bacteria in the culture after t hours:
n(t) = n0e^(rt)where n0 is the initial number of bacteria.
Substituting in the values given in the problem, we get:
n(t) = 25e^[(ln(2)/6)t]Simplifying this expression using the properties of logarithms, we can rewrite it in the form:
n(t) = 25(2)^(t/6)This is the exponential model for the number of bacteria in the culture after t hours.
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The exponential model for population of bacteria, \(n(t) = n_0{2}^{\frac{t}{a} }\) can be written \(n(t) = 25 \times {2}^{\frac{t}{6} }\) for the number of bacteria in the culture after t hours. The estimate number of bacteria after 13 hours is equals to the 112. In 92 hours, the bacteria count will reach to 1 million.
We have a certain culture of the bacterium Rhodobacter.
Initial population, n₀ = 25
The population become doubles in every 6 months. The exponential model
\(n(t) = n_0{2}^{\frac{t}{a} }\) for the number of bacteria in the culture after t hours. Now, the population become double in 6 hours, so a = 6 , then exponential equation is \(n(t) = 25 \times {2}^{\frac{t}{6} }\).
We have to estimate the number of bacteria after 13 hours. That is t = 13 hours, \(n( t) = 25( 2)^{\frac{t}{6}}\)
Substitute t = 13 hours
\( = 25( 2)^{\frac{13}{6}}\)
\(= 25( 2)^{2.16}\)
= 111.728713807 ~ 112
So, n(13) = 112
We have to determine the value of t in hours for n(t) = 1 million = 1000000, using the above equation, \(1000000 = 25( 2)^{\frac{t}{6}}\)
\(40000 = ( 2)^{\frac{t}{6}}\)
Taking natural logarithm both sides
=>\( ln( 40000) = ln(( 2)^{\frac{t}{6}})\)
=> \(ln(40000) = \frac{t}{6} ln(2)\)
=> \(t = \frac{6 ln( 40000)}{ ln(2)}\)
= 91.7262742773 ~ 92
Hence, required value is 92 hours..
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Simplify
50(x^2+7x+6)
Distribute \(50\) to every term inside the parentheses.
\(50\cdotx^2+50\cdot7x+50\cdot6\)
Simplify with multiplication.
\(\huge\boxed{50^2+350x+300}\)
You can't simplify further by adding, so leave the answer as-is.
Answer:
50x^2 + 350x + 300
Step-by-step explanation:
Original Equation:
50(x^2+7x+6)
Distribute 50 to all 3 #'s:
50x^2 + 350x + 300
Divide:
43
Remainder
)982
im using long division
if you 43÷982 you'd get 0.0438 you could also express 43/982 as a mixed fraction
982 divided by 43 equals 22 with a reminder of 36.
brainliest me this is all i can do for youWrite the quotient and remainder when we divide (x^3 -4x^2 + 2x + 5) by (x - 2)
Answer:
Step-by-step explanation:
Sorry I can't explain how it is done. It is very difficult to explain on paper.
Last year, the population of a small town was 1,140 people. This year, the population incrreased by 15%. What is the
population of the town this year?
Answer:
171
Step-by-step explanation:
1140 * 15
3. (a) Find the student's total displacement for the entire trip.
(b) What was his total time for the entire trip?
(c) What was his average velocity for the entire trip?
4. (a) What was the student's total distance (the length of his path) for the entire trip?
Plz help
Answers:
1, It took him 21 minutes to reach the end.
2, He biked 8 kph/mph
3, He went 2.9 km/ 1.8 mi.
ur welcome
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a corporate board contains twelve members. the board decides to create a five-person committee to hide corporation debt. suppose four members of the board are accountants. what is the probability that the committee will contain two accountants and three nonaccountants?
The probability that the committee will contain 2 accountants and 3 non-accountants is (6 × 56) / 792 = 6/66 = 3/33.
What do you mean by corporate board?A corporate board refers to a governing body of a corporation, usually consisting of elected or appointed members, who are responsible for overseeing the management of the company and making important decisions related to its strategy, finances, operations, and other aspects. The board serves as a representative of the shareholders and is responsible for overseeing the actions of the CEO and other executives, ensuring that the company is run in a manner that benefits its stakeholders.
The probability that the committee will contain two accountants and three non-accountants can be calculated as follows:
The number of ways to choose 2 accountants out of 4 is 4 choose 2, or 4C2 = 6.
The number of ways to choose 3 non-accountants out of 8 (12-4) is 8C3 = 56.
The total number of ways to choose 5 people from 12 is 12C5 = 792.
Therefore, the probability that the committee will contain 2 accountants and 3 non-accountants is (6 × 56) / 792 = 6/66 = 3/33.
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which of these random samples represents a representative sample of the systolic blood pressure of all patients in a hospital?
A representative sample based on the hospital scenario is option A
What is representative sample?A subset of a larger population that accurately reflects the traits, diversity, and distribution of the total population is referred to as a representative sample.
Due to time, financial, or logistical limitations, it is frequently not possible or practical to investigate an entire population when conducting research or gathering data. In these situations, researchers choose a representative sample from which to deduce generalizations about the total population.
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Alexandra's drafting class is building a scale model of the school's courtyard. Alexandra chose to make a model of a campus oak tree for the assignment as shown. The tree is 10 yards tall and the base of the tree is 5 yards away from the edge of a park bench. She calculated that her oak tree model should be 0.4 yards tall. What is the distance, in yards, from the base of the model tree to the edge of the model bench?
Answer:
It's 0.20
Step-by-step explanation:
The distance between the base of the model tree to the edge of the model bench is 0.2 yard.
Similar triangle :A diagram is attached which describe the statement of question.
From diagram attached below, It is observed that both triangles are similar triangles.
The ratio of corresponding sides are same in the similar triangles.
the distance between the base of the model tree to the edge of the model bench is x.
\(\frac{5}{x}=\frac{10}{0.4}\\ \\ 10x=2\\\\x=2/10=0.2yard\)
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Bobby and his brother had 3/4 of a pizza leftover after dinner. Their father came home and are 1/2 of the leftover pizza .how much pizza did their father eat
Answer:
3/8 of the pizza
Step-by-step explanation:
3/4*reciprocal of 2
3/4*1/2
3/8
3/8
3/4÷1/2= 0.375
0.375= 3/8
The length of Rectangle A is 5 inches more than its width. The perimeter of Rectangle B is 17. The difference between the perimeters of the rectangles is less than 9. What are the possible integer values for the width of Rectangle A?
Based on the perimeter value, the width of the rectangle is 1.75 inches
What are perimeters?The perimeter of a shape is the sum of the side lengths of the shape
For all regular quadrilaterals, you add up the side lengths to determine the perimeter
How to determine the width of the rectangle?The given parameters about the rectangle are
Perimeter = 17
Length = Width + 5
Rewrite the above equations as
l = w + 5
p = 17
The perimeter of a rectangle is
p = 2 x (l + w)
Substitute p = 17 in the above equation
So, we have
2 x (l + w) = 17
Substitute l = w+ 5 in the above equation
So, we have
2 x (w + 5 + w) = 17
Evaluate the like terms in the above equation
So, we have
2 x (2w + 5) = 17
Open the bracket in the above equation
So, we have
4w + 10 = 17
Evaluate the like terms in the above equation
So, we have
4w = 7
Divide both sides of the above equation by 4
So, we have
w = 1.75
Hence, the width of the rectangle is 1.75 inches
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Answer: hi, the answer is 1 in. 2 in., and 3 in.
Step-by-step explanation:
I took the quiz! :)
Factor 8y^2+18. Please show work!!!
Answer:
2*(4y² + 9)
Step-by-step explanation:
Factorize the expression:8y² = 2 * 2 * 2 * y²
18 = 2 * 3 * 3
GCF = 2
8y² + 18 = 2* 4y² + 2*9
= 2*(4y² + 9)
Please help me with this difficult question i will mark taht guy as brainliest please request
Let's consider an example with hypothetical data for two crops, Wheat and Rice, obtained from five farmers:
| Farmer | Rabi Crop (tons/ha) | Kharif Crop (tons/ha) |
|--------|--------------------|----------------------|
| F1 | 4.5 | 6.2 |
| F2 | 3.8 | 5.5 |
| F3 | 4.2 | 6.0 |
| F4 | 5.1 | 7.3 |
| F5 | 4.9 | 6.5 |
```
To calculate the selling price and profit, you would need additional information such as the selling price per ton for each crop and the cost of production. Let's assume the selling price for Wheat is $200 per ton and for Rice is $250 per ton. We will also assume a production cost of $150 per ton for both crops.
To calculate the profit for each farmer, you can use the following formula:
Profit = (Selling Price - Production Cost) * Production
For example, let's calculate the profit for Farmer F1 with the given data:
Profit for Wheat = (200 - 150) * 4.5 = $225
Profit for Rice = (250 - 150) * 6.2 = $620
Repeat this calculation for each farmer and crop combination to obtain the profits for all.
Once you have the data for production, selling price, and profit, you can create a double bar graph to compare the production of Wheat and Rice in the farmers' fields. The x-axis will represent the farmers, and the y-axis will represent the production (tons/ha). Each farmer will have two bars, one for Wheat and one for Rice, showing the respective production amounts.
Please note that the actual selling price, production costs, and profits may vary based on various factors, and you would need specific data and current market information to calculate accurate values.
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change the following to binary numbers .
a) 16.55ten
b) 26.24ten
c) 0.5625ten
The binary numbers are:
a) (16.55)₁₀ = (10000.100011)₂
b) (26.24)₁₀ = (11010.001111)₂
c) (0.5625)₁₀ = (0.1001)₂
How do you convert decimal numbers to binary numbers?The following are the steps to convert an integral part of a decimal number to a binary equivalent:Divide the decimal number by 2, then record the remainder.Divide the quotient in step 1 by 2. Until the quotient is equal to zero, repeat step 2.The reverse of all remainders would be the equivalent binary number.The following are the steps to convert the fractional part of decimal to binary equivalent :Multiply the fractional decimal part by 2.The first digit of the binary fraction will be an integral part of the resulting decimal number.Follow step 2 after repeating step 1 using only the fractional portion of the decimal number.To obtain the binary number combine both the integral and fractional parts.a) (16.55)₁₀
⇒ 16 ÷ 2 = 8, Remainder = 0
8 ÷ 2 = 4, Remainder = 0
4 ÷ 2 = 2, Remainder = 0
2 ÷ 2 = 1, Remainder = 0
1 ÷ 2 = 0, Remainder = 1
So, (16)₁₀ = 10000₂
Now, for the fractional part
0.55 × 2 = 1 + 0.1
0.1 × 2 = 0 + 0.2
0.2 × 2 = 0 + 0.4
0.4 × 2 = 0 + 0.8
0.8 × 2 = 1 + 0.6
0.6 × 2 = 1 + 0.2
0.55 is equivalent to the binary number 0.100011.
Hence, (16.55)₁₀ = (10000.100011)₂
b) (26.24)₁₀
⇒ 26 ÷ 2 = 13, Remainder = 0
13 ÷ 2 = 6, Remainder = 1
6 ÷ 2 = 3, Remainder = 0
3 ÷ 2 = 1, Remainder = 1
1 ÷ 2 = 0, Remainder = 1
So, (26)₁₀ = 11010₂
Now, for the fractional part
0.24 × 2 = 0 + 0.48
0.48 × 2 = 0 + 0.96
0.96 × 2 = 1 + 0.92
0.92 × 2 = 1 + 0.84
0.84 × 2 = 1 + 0.68
0.68 × 2 = 1 + 0.36
Hence, (26.24)₁₀ = (11010.001111)₂
b) (0.5625)₁₀
⇒ Here, we only have the fractional part
0.5625 × 2 = 1 + 0.125
0.125 × 2 = 0 + 0.25
0.25 × 2 = 0 + 0.50
0.50 × 2 = 1 + 0
Hence, (0.5625)₁₀ = (0.1001)₂
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State whether the data described below are discrete or continuous, and explain whyThe numbers of voters that are registered with a certain political party in different regionsChoose the correct answer below:A. The data are continuous because the data can take on any value in an interval.B. The data are discrete because the data can take on any value in an interval.C. The data are continuous because the data can only take on specific values.D. The data are discrete because the data can only take on specific values.
Given: The numbers of voters that are registered with a certain political party in different regions
This can't be continous because we can't figure out how many people are registered with a certain political party.
It is like tracking how many push ups you can do. You can only do a certain amount and it varies. One day you can do 10 another 6 and another day 12. It is easier to make a chart of the people in a political party than to make a graph so that eliminates A and C.
And it can't be B because it is describing continuous data so it has to be D.
Answer:
D. The data are discrete because the data can only take on specific values.
how to solve 3x-2
…………..
The value of x for the system is 1. What is the value of y?*
1 point
3x + y = 9
y = -4x + 10
1. Substitute the value of y in the first equation:
2. Combine like terms:
3. Apply the subtraction property of equality:
4. Apply the division property of equality:
3x + (-4x + 10) = 9
-x+ 10 = 9
-X = -1
x = 1
O y = 14
O y = 12
O y = 6
O y=3
When loesolved
system lisin
bstitution bet7
TA
Which of the following algebraic represents shows a dilation that is an enlargement ?
The algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y). (Option D)
A dilation is a type of transformation that changes the size of the shape or object. It refers to a process of changing an object’s size by decreasing or increasing its dimensions by a scaling factor. A dilation produces an image that has the same shape as the original image but is a different size.
A dilation that results in a larger image is called an enlargement while a dilation that generates a smaller image is called a reduction. A dilation is described using the scale factor and the center of the dilation (which is a fixed point in the plane).
For a scale factor > 1, the image is an enlargement; for a scale factor < 1 and > 0, the image is a reduction; and for a scale factor = 1, the figure and the image are congruent. Hence, for a point (x,y), algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y) as the scale factor is greater than 1. For the remaining options, the scale factor is between 0 and 1, hence they are reduction.
Note: The question is incomplete. The complete question probably is: Which of the following algebraic representation shows a dilation that is an enlargement? A) (1/3 x,1/3 y) B) (0.1x, 0.1y) C) (5/6 x,5/6 y) D) (5/2 x,5/2 y)
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Here is the setup for a non-traditional casino game: You draw a card from a well shuffled full deck and if the card is a king you win $100. The game costs $2 to play and you decide to play the game until you win the $100. Each time you draw a card you pay $2, and if the card is not a king, the card is put back in the deck, and the deck is reshuffled. How much money should you expect to spend on this game?
The answer is $26 - I just don't know how this amount is derived. Please be specific with which statistical technique is used to determine this.
You should expect to spend $26 to win $100 playing this casino game.
This is a classic example of a geometric distribution, where each trial has two possible outcomes (win or lose) and the probability of winning remains constant at 1/13 (4 kings in a deck of 52 cards) across all trials.
The expected number of trials to win is 13, so the expected cost to win is 13 times the cost per trial, which is $2, giving an expected cost of $26. Note that this is the expected cost, not the guaranteed cost, and it is possible to spend more or less than $26 before winning.
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In a market survey, 100 traders sell fruits. 40 sell apples, 46 oranges, 50 mangoes, 14 apples and oranges, 15 apples and mangoes and 10 sell all three fruits each of the 100 traders sell at least one of the three fruits. (A) how many traders sell only one fruit. (B) how many traders sell only two fruits.
a) The number of traders who sell only one fruit is given as follows: 88.
b) The number of traders who sell only two fruits is given as follows: 9.
How to obtain the amounts?The amounts are obtained using Venn sets in the context of this problem.
The sets are given as follows:
Set A: sells apples.Set B: sells oranges.Set C: sells mangoes.10 sell all three fruits, hence:
A ∩ B ∩ C = 10.
15 vendors sell apples and mangoes, hence:
(A ∩ C) + (A ∩ B ∩ C) = 15
(A ∩ C) = 5.
14 vendors sell apples and oranges, hence:
(A ∩ B) + (A ∩ B ∩ C) = 14
(A ∩ B) = 4.
Hence the number who sell two of them is of:
(A ∩ B) + (A ∩ C) = 4 + 5 = 9.
50 vendors sell mangoes, hence:
C + (A ∩ C) + (A ∩ B ∩ C) = 50
C = 35.
46 vendors sell oranges, hence:
B + (A ∩ B) + (A ∩ B ∩ C) = 46
B = 32.
40 vendors sell apples, hence:
A + (A ∩ B) + (A ∩ C) + (A ∩ B ∩ C) = 40.
A + 9 + 10 = 40
A = 21.
Hence the number of vendors who sell only one fruit is given as follows:
A + B + C = 21 + 32 + 35 = 88.
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help plsssssssssssss
Answer:
Step-by-step explanation:
the third equation shows a positive rate of change as for every increase in x, the value of y will increase.
Select all the sets of conditions that will create only one unique triangle.
researchers are studying a population of small plants on an island. before and after a major drought, they dug up a random sample of plants and measured their root length. during the drought, no plant reproduction took place. what can be concluded from the plot below?
The correct conclusion that can be drawn from the plot is that the plant population had a significantly lower mean root length after the major drought occurred.
Explanation:
A frequency polygon is a graphical representation of a frequency distribution using line segments connected to points that indicate the midpoint of each class interval.
The horizontal axis shows the measurement variable, while the vertical axis shows the number of occurrences of the variable for each bin. The midpoint of each bin is used to represent the distribution of data that falls within that bin's range.
Since the values of adjacent bins overlap, the lines are connected. The points are connected by straight lines in a frequency polygon.
In this case, the conclusion that can be drawn from the plot is that the plant population had a significantly lower mean root length after the major drought occurred.
The peak of the frequency polygon has shifted to the left, indicating that the majority of plants have a shorter root length. The decrease in the mean root length of the plant population is due to the impact of the major drought on the island.
As a result, no plant reproduction took place, indicating a decrease in the plant population.
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the differce of a number and twenty four is equal to forty six
Answer:
n - 24 = 46
Step-by-step explanation:
Answer:
It is 70 because when you add 24 and 46 it is 70
so when you subtract 24 from 70, you get 46
:)
Step-by-step explanation:
local park is in the shape of a square. A map of the local park is made with a scale 1 inch to 200 feet.
If a straight path in the park is 700 feet long, how long would the path be when represented on a map?
Answer:
3.5 in
Step-by-step explanation:
help with this please i suck at math
Answer:
You're asked to find the cube root of 125.
That is,to cancel the power of y, you'd have to cube root both sides.
answer is 5
Given the function defined in the table below, find the average rate of change,
in simplest form, of the function over the interval 12 ≤ ≤ 36.
0
12
36
48
60
37
34
31
28
25
22
The average rate of change of \(f(x)\) on \(12\le x\le36\) is the difference quotient
\(\dfrac{f(36) - f(12)}{36 - 12} = \dfrac{28 - 34}{24} = \boxed{-\dfrac14}\)
I need this done before tomorrow please help
Answer:
If im not mistaken angle B nad D should have the same meausurement which would be 128°