A biologist is doing an experiment on the growth of a certain bacteria culture. After 8 hours the following data has been recorded: t(x) 0 1 2 3 4 5 6 7 8 on p (y) 1.0 1.8 3.3 6.0 11.0 17.8 25.1 28.9 34.8 where t is the number of hours and p the population in thousands. Integrate the function y = f(x) between x - O to x-8, using Simpson's 1/3 rule with 8 strips.

Answers

Answer 1

the value of the integral of y = f(x) between x = 0 to x = 8, using Simpson's 1/3 rule with 8 strips is 287.4.

We need to calculate the integral of y = f(x) between the interval 0 to 8.Using Simpson's 1/3 rule, we have, The width of each striph = (8-0)/8 = 1 So, x₀ = 0, x₁ = 1, x₂ = 2, ...., x₈ = 8.

Now, let's calculate the values of f(x) for each xi as follows,

The value of f(x) at x₀ is f(0) = 1.0

The value of f(x) at x₁ is f(1) = 1.8

The value of f(x) at x₂ is f(2) = 3.3

The value of f(x) at x₃ is f(3) = 6.0.

The value of f(x) at x₄ is f(4) = 11.0

The value of f(x) at x₅ is f(5) = 17.8

The value of f(x) at x₆ is f(6) = 25.1

The value of f(x) at x₇ is f(7) = 28.9

The value of f(x) at x₈ is f(8) = 34.8.

Using Simpson's 1/3 rule formula, we have,

∫₀⁸ f(x) dx = 1/3 [f(0) + 4f(1) + 2f(2) + 4f(3) + 2f(4) + 4f(5) + 2f(6) + 4f(7) + f(8)]

hence, the value of the integral is,

∫₀⁸ f(x) dx ≈ 1/3 [1.0 + 4(1.8) + 2(3.3) + 4(6.0) + 2(11.0) + 4(17.8) + 2(25.1) + 4(28.9) + 34.8]

= 287.4 (rounded to one decimal place).

Therefore, the value of the integral of y = f(x) between x = 0 to x = 8, using Simpson's 1/3 rule with 8 strips is 287.4.

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Related Questions

a sports guard thickness of about mm is desirable for heavy contact sports in which injuries are more likely. group of answer choices 1 2 4 8

Answers

Answer:

What is the question?! I don't understand, sry?!

Step-by-step explanation:

is y= 3/2x linear or nonlinear

Answers

Answer: It is linear

Step-by-step explanation:

When you graph the equation, it is a straight line, meaning it is linear.

If you graphed the equation and it wasn't a straight line, it would be nonlinear.

Which is the best option?

Which is the best option?

Answers

C is the best option

Is the following a function ?

Is the following a function ?

Answers

Yes it is a function

find the equation of a straight line which is parallel to the line with equation 5x+7y=14 and passes through a point (-2,-3)​

Answers

Answer:

\(7y=-5x-11\)

Step-by-step explanation:

Since it says the lines are parallel both of their gradients will be same.

so gradient of line 1 = \(y=\frac{14-5x}{7}\) = \(y=\frac{14}{7}-\frac{5x}{7}\)= \(-\frac{5}{7}\)

so equation of line 2 = \(y-y_{1}=m(x-x_{1} )\)

                                   = \(y-(-3)_{}=\frac{-5}{7} (x-(-2)_{} )\)

                                   = \(y +3=-\frac{5}{7}x+\frac{10}{7}\)

                                   = \(y =-\frac{5x+10}{7}-3\)

                                   = \(7y=-5x-11\)

Step-by-step explanation:

basically a line equation typically looks like

y = ax + b

with a being the slope, and b bent the y-intercept (y value when x = 0).

5x + 7y = 14

7y = -5x + 14

y = -5/7 x + 14/7 = -5/7 x + 2

so, wie know the slope of the original line : -5/7 .

any line parallel to it must have the same slope.

our desired line looks like

y = -5/7 x + b

to get b we use the provided point (-2, -3).

-3 = -5/7 × -2 + b = 10/7 + b

-21/7 = 10/7 + b

-31/7 = b

and the full equation is

y = -5/7 x - 31/7

7y = -5x - 31

5x + 7y = -31

Which number line best shows how to solve −4 − (−6)? (5 points)

A number line from negative 10 to 10 is shown, with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 4. Another arrow points from negative 4 to 6.
A number line from negative 10 to 10 is shown, with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 4. Another arrow points from negative 4 to negative 6.
A number line from negative 10 to 10 is shown, with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 4. Another arrow points from negative 4 to negative 2.
A number line from negative 10 to 10 is shown, with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 4. Another arrow points from negative 4 to 2.

Answers

Answer:

the last one

Step-by-step explanation:

-4 - (-6) is actually -4 + 6, which equals 2

pls help asap will give brainliest

pls help asap will give brainliest

Answers

Answer:

270.5

Step-by-step explanation:

*sigh* here we go again ok

separate it into a rectangle and semicircle

12*16=192

circle is pi(r)^2/2   so

5^2=25

25*3.14=78.5

78.5+192=270.5

For every 3 packages that Marcella wraps, she uses 12 of a roll of wrapping paper. If she uses 212 rolls of wrapping paper, how many packages has she wrapped?

Answers

Answer:

She wrapped 27 packages also can i have brain or heart

a quality control expert at life batteries wants to test their new batteries. the design engineer claims they have a variance of 8100 with a mean life of 1192 minutes. if the claim is true, in a sample of 72 batteries, what is the probability that the mean battery life would be greater than 1173.8 minutes? round your answer to four decimal places.

Answers

The probability that the mean battery life would be greater than 1173.8 minutes is 0.9588

We can solve this problem using the central limit theorem, which tells us that the distribution of sample means from a population with a known variance becomes approximately normal as the sample size increases.

The standard error of the mean can be calculated as

SE = σ / sqrt(n)

where σ is the population standard deviation, n is the sample size

Here, we are given that the population variance is 8100, so the population standard deviation is the square root of 8100, which is 90.

SE = 90 / sqrt(72) = 10.6066

Next, we need to standardize the sample mean using the z-score formula

z = (X - μ) / SE

where X is the sample mean, μ is the population mean.

Here, the population mean is given as 1192 minutes and the sample mean we are interested in is 1173.8 minutes.

z = (1173.8 - 1192) / 10.6066 = -1.7356

We want to find the probability that the sample mean is greater than 1173.8 minutes. Since we have a negative z-score, we need to find the area to the right of this value on a standard normal distribution. We can use a z-table or a calculator to find this probability.

Using a standard normal distribution table, we find that the area to the right of z = -1.7356 is 0.9588.

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Please help! Will mark brainliest if correct! No guessing! Please help quickly

Please help! Will mark brainliest if correct! No guessing! Please help quickly

Answers

Answer:

D. 12.0    i believe

Step-by-step explanation:

Slant height of a cone:

s = √(r2 + h2)

The spray from a sprinkler reaches 21 feet from the sprinkler and creates a circle as it spins. What is the circumference of the circle sprayed by the sprinkler? Use
22
7
for π.
21 ft
66 ft
120 ft
132 ft

Answers

Answer:

D: 132 ft

Step-by-step explanation:

C= π2r

So, take pi and multiply that by two..

π2= 6.28

Now, take your radius and multiply it by 6.28.

21 x 6.28= 131.88

Round it two the nearest whole number, which is 132!

Hope this helps!

Answer:

132

Step-by-step explanation:

a) what is the cumulative frequency for a weight of 27.5 pounds?

Answers

Cumulative frequency for a weight of 27.5 pounds is 42.

1. First, arrange the data in ascending order.

2. Identify the weights given and their corresponding frequencies.

3. Calculate the cumulative frequency by adding up the frequencies for weights less than or equal to 27.5 pounds.

4. In this case, the cumulative frequency for 27.5 pounds would be the sum of the frequencies for all weights less than or equal to 27.5 pounds.

5. If the given data is in a frequency table, simply find the cumulative frequency value corresponding to the weight of 27.5 pounds.

6. If the data is not given in a frequency table, you can create one by counting the occurrences of each weight and then calculating the cumulative frequencies.

7. Once you have the cumulative frequencies for all weights, find the value corresponding to 27.5 pounds.

8. The obtained value is the cumulative frequency for a weight of 27.5 pounds.

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Solve the following inequality: 38 < 4x+3+7 – 3x.
a. x < 28
b. x > 28
c. x < 4
d. x > 4

Answers

To solve the given inequality, first we have to simplify the given inequality.38 < x + 10 After simplification we get, 38 - 10 < x or 28 < x.

The correct option is B.

The given inequality is 38 < 4x + 3 + 7 - 3x. Simplify the inequality38 < x + 10  - 4x + 3 + 7 - 3x38 < -x + 20 Combine the like terms on the right side and simplify 38 + x - 20 < 0 or x + 18 < 0x < -18 + 0 or x < -18. The given inequality is 38 < 4x + 3 + 7 - 3x. To solve the given inequality, we will simplify the given inequality.

Simplify the inequality38 < x + 10  - 4x + 3 + 7 - 3x38 < -x + 20 Combine the like terms on the right side and simplify 38 + x - 20 < 0 or x + 18 < 0x < -18 + 0 or x < -18. Combine the like terms on the right side and simplify38 + x - 20 < 0 or x + 18 < 0x < -18 + 0 or x < -18.So, the answer is  x > 28. In other words, 28 is less than x and x is greater than 28. Hence, the answer is x > 28.

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what are numerical or verbal descriptions that usually result from measurements of some sort?

Answers

The numerical or verbal descriptions that usually result from measurements are called data or observations.

When measurements are conducted, whether in scientific experiments, surveys, or other data collection processes, the outcome is typically a set of data or observations.

These measurements can be represented numerically, such as numerical values or quantities, or verbally, using descriptive terms or categories.

Numerical descriptions provide precise quantitative information, such as measurements of length, weight, temperature, time, or any other measurable attribute. These measurements are often expressed using numbers or units of measurement.

Verbal descriptions, on the other hand, use words or qualitative descriptions to convey information about the observations.

For example, when conducting a survey, respondents might provide verbal responses that describe their opinions, preferences, or experiences.

Both numerical and verbal descriptions play important roles in data analysis and interpretation.

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help please

plz plz plz​

help pleaseplz plz plz

Answers

Step-by-step explanation:

Here,

y= 2x

and x € (1,2,3)

now,

when x=1 , when x=2 , when x= 3

y=2x y= 2x y=2x

= 2×1 = 2×2 = 2×3

= 2 = 4 = 6

Therefore, y = (2,3,6)

candy had some money. she bought a drink for £1.45 and a piece of cake for £1.20 she now has two thirds of her money left. how much money did candy to start with? i suck at fraction

Answers

The amount of money Candy started with after spending on drinks and cakes is £7.95

How to find the amount of money she started with?

She bought a drink for £1.45 and a piece of cake for £1.20.

She has two thirds of here money left.

Let the money she has initially  = x

Therefore,

2 / 3 x = x - 1.45  - 1.20

2 / 3 x = x - 2.65

subtract x from both sides

2 / 3 x - x = - 2.65

2x - 3x / 3 = - 2.65

- x / 3 = - 2.65

cross multiply

-x = - 2.65 × 3

- x = -7.95

x = £ 7.95

Therefore, Candy started with £7.95

l

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Solution to 2 variable equations 2x+3y=12

Answers

Answer:

x= -3/2y + 6

Step-by-step explanation:

Let's solve for x.

2x+3y=12

Step 1: Add -3y to both sides.

2x+3y+−3y=12+−3y

2x=−3y+12

Step 2: Divide both sides by 2.

2x

2

=

−3y+12

2

Orlando is 12 years older than Omar. Carl is three times older than Orlando. The sum of their ages is 68.Find the ratio of Omar’s age to Carl’s age to Orlando’s age.

Answers

Step-by-step explanation:

let's name the variables for the age of the people as the people themselves :

orlando = omar + 12

carl = 3×orlando

carl + orlando + omar = 68

using the first equation in the second equation, and then that result and the first equation in the third equation :

carl = 3×(omar + 12)

3×(omar + 12) + (omar + 12) + omar = 68

3×omar + 36 + omar + 12 + omar = 68

5×omar + 48 = 68

5×omar = 20

omar = 4

orlando = omar + 12 = 4 + 12 = 16

carl = 3×orlando = 3×16 = 48

the ratio omar : carl : orlando

4 : 48 : 16 = 1 : 12 : 4

Given the following assignments:
num1 = 12 num2 = 5 num3 = 10 num4 = 3
What are the results of the following expressions?

Answers

The results of the expressions are as follows: num1 + num2 = 17; num3 - num4 = 7; num1 * num4 - num2 = 31; num3 / num2 = 2; num1 % num4 = 0.

To determine the results of the expressions, we can evaluate them using the given assignments:

num1 + num2:

Result: 12 + 5 = 17

num3 - num4:

Result: 10 - 3 = 7

num1 * num4 - num2:

Result: 12 * 3 - 5 = 31

num3 / num2:

Result: 10 / 5 = 2

num1 % num4:

Result: 12 % 3 = 0

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Raj correctly determined that ray LH is the bisector of AngleGLI. Which information could he have used to determine this?

AngleGLH Is-congruent-to AngleILM
mAngleKLM = 5mAngleILM
mAngleGLI = 2mAngleGLH
mAngleGLI = mAngleGLH + mAngleHLI

Answers

The information could he have used to determine this is C. ∠GLI = 2∠GLH.

What is an angle?

An angle is formed from the intersection of two lines. The types of angles are acute, obtuse, and scalene.

∠GLI is bisected by LH, hence:

∠GLH = ∠HLI (definition of bisection)

∠GLI = ∠GLH + ∠HLI (angle addition)

∠GLI = 2∠GLH

The information that can be used to determine this is ∠GLI = 2∠GLH.

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Answer: its C

Step-by-step explanation: on edge

Question 6: How many miles are there in 4 kilometers?Hint: 1 km 0.6 mi
Round your answer to the nearest tenth.
O 24
O 2.4
2.40
24.0

Question 6: How many miles are there in 4 kilometers?Hint: 1 km 0.6 miRound your answer to the nearest

Answers

Answer:

B

Step-by-step explanation:

C would also be the correct answer but its not rounded to the nearest tenth.

Which expression is equivalent to x^6 – 5

Answers

Answer:

Amdjss

Step-by-step explanation:

b) If a, b, c are three rational numbers where a =
a = 3
3,6 = and c =
olů
Verify: a + (b + c) = (a + b) + C​

Answers

Step-by-step explanation:

a =

a = 3

3,6 = and c =

olů

what is this please write this clearly

Pleas answer part A!!!!!!

Pleas answer part A!!!!!!

Answers

Answer:

y=120x

Step-by-step explanation:

You can just divide all of the points (y/x) and they all equal to 120. And when you add it to the equation its y=120x

7th grade math help me pleasee

7th grade math help me pleasee

Answers

Answer:

5a. 30

5b. 32

5c. 60

u have to cross multiply on all of them

Step-by-step explanation:

Someone plz help me I’m in mine last question

Someone plz help me Im in mine last question
Someone plz help me Im in mine last question

Answers

Step-by-step explanation:

21)

Frog C - Frog B

318.5-199.25=119.25 cm

22)

Frog A = 213.33

to the nearest whole number= 213 cm

Given the graphs of f(x) = X - 8 and g(x) = -4x + 2, find the solution to this system of equations: Y - X = -8 and 4x + y = 2 A) (0, 2) B) (0.-8) C) (2, -6) D)​

Given the graphs of f(x) = X - 8 and g(x) = -4x + 2, find the solution to this system of equations: Y

Answers

Answer

The Answer is C) 2, -6

Step-by-step explanation:

Look at the graph as you can see there is only one solution to that graph and on the line intersected there is one point which that would be 2, -6.

Note: Understand that when asking about the point or something else look for the lines intersected each other then you could find your answer. If there is only one line then it is infinite solutions but if the lines don't intersect then it is a no solution.

Have a good day :)

For hotels in New York City, a travel web site wants to provide information comparing hotel costs (high, average, low) versus the quality ranking of the hotel (excellent, good, fair, poor). A useful way to summarize these data is to construct a(n)

Answers

For hotels in New York City, a travel web site wants to provide information comparing hotel costs (high, average, low) versus the quality ranking of the hotel (excellent, good, fair, poor). A useful way to summarize these data is to construct a scatter plot.

A scatter plot is a graph that shows the correlation between two variables. A horizontal x-axis and a vertical y-axis are used to plot data points in a scatter plot. Each data point represents a single observation on both the x-axis and the y-axis, and each point on the scatter plot represents a single observation.

The data set, including hotel costs and quality rankings, would be plotted on a scatter plot. The data is plotted using the independent variable on the x-axis and the dependent variable on the y-axis. The data points are spread over the plot in a scattered pattern.

For example, the independent variable is hotel costs, and the dependent variable is quality rankings in this example. A scatter plot is a helpful tool for identifying trends and predicting outcomes. To make sense of the data, a scatter plot can be used to generate a trend line that connects the data points. The trend line is also referred to as a regression line and is used to predict future values of the dependent variable based on the independent variable.

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OMG HELP PLS IM PANICKING OMG OMG I GOT A F IN MATH AND I ONLY HAVE 1 DAY TO CHANGE MY GRADE BECAUSE TOMORROW IS THE FINAL REPORT CARD RESULTS AND I DONT WANNA FAIL PLS HELP-

OMG HELP PLS IM PANICKING OMG OMG I GOT A F IN MATH AND I ONLY HAVE 1 DAY TO CHANGE MY GRADE BECAUSE

Answers

Answer:

2/5 bucket

Step-by-step explanation:

1/2 and 3/4 are equal. So 2/5 is wrong.

hope this helped, and please mark as Brainliest <3

The number of miles a car travels varies directly with the number of gallons of gas in its tank of a car with 20 gallons of gas can drive 560 miles which equation represents the number of miles an

Answers

Answer:

28 miles per gallon

560/20=28

Step-by-step explanation:

Plz give me brainliest

Number of miles a car travels are 28.

What is division?

The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken.

Number of gallons of gas = 20

A car with 20 gallons of gas can drive 560 miles

Based on the given conditions,

= \(\frac{560}{20}\)

= 28

Hence, number of miles are 28.

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