Consider the error formulas.

|E| ≤

(b − a)3

12n2

[max |f ''(x)|], a ≤ x ≤ b

Trapezoidal Rule

|E| ≤

(b − a)5

180n4

[max |f (4)(x)|], a ≤ x ≤ b

Simpson's Rule

Use these to estimate the errors in approximating the integral, with n = 4, using the Trapezoidal Rule and Simpson's Rule.


6 1 (x − 1)2 dx 2

Answer:

B. x=negative 7

Step-by-step explanation:

sana nakatulong :-)

Answer:

Inequality: 0.08x + 2300 ≥ 2800

Liz needs to sell products of $6250 at least.

Step-by-step explanation:

Given that:

Per month salary of Liz = $2300

Commission = 8% = \(\frac{8}{100}}\) = 0.08

Amount Liz wants to earn = $2800

Let,

x be the amount of sales.

0.08x + 2300 ≥ 2800

0.08x ≥ 2800 - 2300

0.08x ≥ 500

Dividing both sides by 0.08

\(\frac{0.08x}{0.08}\geq \frac{500}{0.08}\\x\geq 6250\)

Hence,

Liz needs to sell products of $6250 at least.

At 15 hours the amount of bacteria is 1345. It takes 47 hours to get 350000 bacteria.

Let y represent the amount of bacteria after n hours

Since the bacteria doubles after every 4 hours, hence, this can be represented by exponential function:

y = abⁿ

where a is the initial value and b is the multiplier.

Since it doubles every 4 hours and the initial amount of bacteria is 100, this can be represented by:

a)

\(y=100(2)^\frac{n}{4}\\\\At\ 15hours:\\\\y=100(2)^\frac{15}{4}\\\\y=1345\ bacteria\)

b) y = 350000

\(350000=100(2)^\frac{n}{4}\\\\3500=(2)^\frac{n}{4}\\\\taking\ ln:\\\\ln(3500)=\frac{n}{4} ln(2)\\\\\frac{n}{4}=11.77\\\\n=47\ hours\)

Therefore at 15 hours the amount of bacteria is 1345. It takes 47 hours to get 350000 bacteria.

Find out more at: https://brainly.com/question/3127939

The x-coordinate of the absolute maximum for the function f(x) = 3 + 5ln(x), x > 0, is x = 1.

To find the x-coordinate of the absolute maximum, we need to analyze the behavior of the given function within its domain.

First, let's find the derivative of f(x) to determine the critical points. Taking the derivative of 3 + 5ln(x) with respect to x, we get:

f'(x) = 5/x

Setting f'(x) equal to zero, we find that x = 0 is a critical point. However, since the domain of the function is x > 0, we exclude x = 0 from consideration.

Next, we need to examine the endpoints of the domain, which in this case is x = 0. Since the function is not defined at x = 0, we cannot consider it for finding the absolute maximum.

Now, we evaluate the function at the critical point x = 1 and compare it with the function values at the endpoints:

f(1) = 3 + 5ln(1) = 3

f(2) = 3 + 5ln(2) ≈ 6.609

Comparing the values, we see that f(2) > f(1). Therefore, the absolute maximum occurs at x = 1.

Learn more about x-coordinate

brainly.com/question/28913580

#SPJ11

Answer:

Step-by-step explanation:

Answer:

Perimeter of rectangle 1=4x+4

Perimeter of rectangle 2=4x+4

Step-by-step explanation:

Two squares with the same dimension

Square 1: let length=x

Square 2: let length=x

Since they have same dimensions

He added two inches to the length of square 1 to make it a rectangle

Rectangle 1: width=x, length=x+2

Perimeter=2(l+w)

=2{(x+2)+x}

=2(x+2+x)

=2(2x+2)

=4x+4

He added two inches to the width of square 2 to make it a rectangle

Rectangle 2: length=x, width=x+2

Perimeter=2(l+w)

=2{(x+(x+2)}

=2(x+x+2)

=2(2x+2)

=4x+4

The two rectangles have equal perimeter

Answer:

I think you mean 1/9.

If so, Sarah gets 2/9 of the money.

Step-by-step explanation:

1 = 9/9

1-(1/9)= 8/9

Colin : Sarah, altogether is 8

6 : 2

Thus, Sarah get 2/9

Answer:

Sarah proportion is 25% of the momey

Solution:

Given that;

The price of a house decreased from $400, 000 to $300, 000 in one year

The difference is

The percentage decrease will be

Hence, the percentage decrease is 25%

The maximum profit is achieved when approximately 312.5 units of lab equipment are sold.

The revenue function R(x) represents the amount of money the company earns from selling x units of lab equipment. It is given by the equation:

R(x) = -0.32x^2 + 270x

The costs function C(x) represents the expenses incurred by the company for producing and selling x units of lab equipment. It is given by the equation:

C(x) = 70x + 52

To determine the company's profit, we subtract the costs from the revenue:

Profit = Revenue - Costs

P(x) = R(x) - C(x)

Substituting the given revenue and costs functions:

P(x) = (\(-0.32x^2 + 270x)\) - (70x + 52)

Simplifying the equation:

P(x) = -0.32x^2 + 270x - 70x - 52

P(x) = -\(0.32x^2\)+ 200x - 52

The profit function P(x) represents the amount of money the company makes from selling x units of lab equipment after deducting the costs. It is a quadratic function with a negative coefficient for the x^2 term, indicating a downward-opening parabola. The vertex of the parabola represents the maximum profit the company can achieve.

To find the maximum profit and the corresponding number of units sold, we can use the vertex formula:

x = -b / (2a)

For the profit function P(x) = -\(0.32x^2 + 200x\)- 52, a = -0.32 and b = 200.

x = -200 / (2 * -0.32)

x = 312.5

Therefore, the maximum profit is achieved when approximately 312.5 units of lab equipment are sold.

for more such question on profit visit

https://brainly.com/question/29785281

#SPJ8

Assuming the population is in Hardy-Weinberg equilibrium, the individuals have green hair are equal to 91% .

From the data present in problem,

Hardy and Weinberg proved mathematically that in a population all dominant and recessive alleles include all alleles for a given gene. Mathematically, denoted as p + q = 1.0

Where, p = frequency of dominant alleles (C)

q = frequency of recessive alleles (c) = 0.3

Number of population individua's = 100

Hardy and Weinberg described all the possible genotypes for a gene with two alleles. The binomial expansion representing this is,

p² + 2pq + q² = 1.0

Where, p² = proportion of homozygous dominant individuals (Green)

• q² = proportion of homozygous recessive individuals (White)

2pq = proportion of heterozygotes (Green)

Since, p+ q = 1.0

=>p = 1 - q = 1 - 0.3 = 0.7

=>p = 0.7

The genotypic frequencies are as follows:

CC (p²) = (0.7) = 0.49

Cc (2pq) = 2x(0.3)(0.7) = 0.42

cc (9²) = (0.3)² = 0.09

p² + 2pq + q² = (0.49) + (0.42)+(0.09)= 1.0

The expected number for each genotype are as follows: CC (p²) = (0.49×100) = 49

Cc (2pq) = (0.42×100)= 42

cc(q²) = (0.09×100) = 9

The number of individuals have green hair is as follows: (p²)+(2pq) = 49+42= 91

Thus, required individuals percentage is 91%.

To learn more about Hardy-Weinberg equilibrium, refer:

https://brainly.com/question/14669053

#SPJ4

The fraction of washers with thicknesses greater than 2.4 millimeters. We need to understand the normal distribution of washer thicknesses. In a normal distribution, data is centered around the mean value, and the standard deviation (SD) determines the spread.

For this problem, we need the mean thickness and SD of the washers being produced.

Once we have the mean and SD, we can calculate the z-score, which represents the number of standard deviations a data point is from the mean. The formula for the z-score is:

Z = (X - mean) / SD

Where X is the specified thickness (2.4 millimeters in this case). After calculating the z-score, we can use a standard normal distribution table (also known as a z-table) to find the corresponding area to the right of the z-score. This area represents the fraction of washers that are expected to be greater than 2.4 millimeters thick.

Unfortunately, without the mean and standard deviation values, we cannot provide a specific answer to your question. However, once you have those values, you can follow the steps above to find the fraction of washers with thicknesses greater than 2.4 millimeters.

Learn more about fraction  here:

https://brainly.com/question/10708469

#SPJ11

Answer:

factor: 7(x+7y+3)

simplifies: There are no like terms.

Step-by-step explanation:

Answer:

rip

Step-by-step explanation:

its been 5 min

Answer:

t = 4.7 days

Step-by-step explanation:

The half life formula is

N = No * e ^ (-kt)

Where No is the initial amount of the substance

N = 45 e ^ (-.1483 t)

We want 1/2 of the substance left

22.5 is half of 45 grams

22.5 = 45 e ^ (-.1483 t)

Divide each side by 45

1/2 = e ^ (-.1483 t)

Take the natural log of each side

ln(1/2) = ln (e ^ (-.1483 t))

ln(1/2) = -.1483t

Divide each side by -.1483

ln(1/2) / -.1483 = t

t=4.67395

Rounding to the nearest tenth

t = 4.7 days

Based on the formula of the quadratic function y=-x^2+6x-5, we know that its graph is a downward-facing parabola that opens wide, with a vertex at (3,-14), and an axis of symmetry at x=3.

Based on the formula of the quadratic function y=-x^2+6x-5, we can determine several properties of its graph, including its shape, vertex, and axis of symmetry.

First, the negative coefficient of the x-squared term (-1) tells us that the graph will be a downward-facing parabola. The leading coefficient also tells us whether the parabola is narrow or wide. Since the coefficient is -1, the parabola will be wide.

Next, we can find the vertex using the formula:

Vertex = (-b/2a, f(-b/2a))

where a is the coefficient of the x-squared term, b is the coefficient of the x term, and f(x) is the quadratic function. Plugging in the values for our function, we get:

Vertex = (-b/2a, f(-b/2a))

= (-6/(2*-1), f(6/(2*-1)))

= (3, -14)

So the vertex of the parabola is at the point (3,-14).

Finally, we know that the axis of symmetry is a vertical line passing through the vertex. In this case, it is the line x=3.

Know more about quadratic function here;

https://brainly.com/question/18958913

#SPJ11

Answer:

Pythagorean Theorom: \(a^2+b^2=c^2\)

Triangle #1

\(21^2+x^2=29^2\)

\(x^2=29^2-21^2\)

\(x=\sqrt{841-441} =\sqrt{400}=20\)

Triangle #2

\(1.6^2+3.0^2=x^2\)

\(x=\sqrt{1.6^2+3.0^2}=\sqrt{11.56} =3.4\)

Triangle #3

\(x^2+40^2=41^2\)

\(x=\sqrt{41^2-40^2}=\sqrt{81} =9\)

I hope this helps!

50%

since 98/2 = 49

Thats it

The confidence interval can be expressed as:

p ± E = 0.888 ± 0.111

To express the confidence interval 0.777 < p < 0.999 in the form p ± E, we need to first calculate the point estimate of the population proportion p.

The point estimate is simply the midpoint of the confidence interval, which is given by:

Point estimate = (lower limit + upper limit) / 2

= (0.777 + 0.999) / 2

= 0.888

Next, we need to calculate the margin of error (E) using the formula:

E = (upper limit - point estimate) = (0.999 - 0.888) = 0.111

Therefore, the confidence interval can be expressed as:

p ± E = 0.888 ± 0.111

So the confidence interval is 0.777 < p < 0.999, which can also be written as p ± 0.111.

know more about confidence interval visit :

https://brainly.com/question/24131141

#SPJ1

Step-by-step explanation:

In a parallelogram, opposite sides are equal and parallel. Therefore,

QT = PS = 3y ...(1)

PT + TR = PS

y + 2x + 1 = 3x + 9

2x - y = 4 .....(2)

PR = QT = 3y

PR = SQ = 3x + 9 ....(3)

From equations (1) and (3), we can see that:

3y = 3x + 9

y = x + 3

Substitute this value of y in equation (2):

2x - (x + 3) = 4

x = 7

To find the value of y, we can substitute x = 7 in equation (2):

2(7) - y = 4

y = 10

Therefore, x = 7 and y = 10.

The weekly standard deviation of the stock price calculated from this sample is 42.957

Given info,

Bear Stearns' stock price closed at $98, $103, $58, $29, and $4 over five successive weeks,

To find the weekly standard deviation of the stock price calculated from this sample,

We use,

μ = (98 + 103 + 58 + 29 + 4) / 5

μ = 58.4

The mean of this sample is 58.4

The standard deviation is,

σ = \(\sqrt{\frac{(98-58.4)^2+(103-58.4)^2+(58 - 58.4)^2+(29-58.4)^2+(4-58.4)^2}{(5-1)} }\)

σ = √1845.3

σ = 42.957

Hence, the standard deviation is 42.957

To learn more about mean click here:

brainly.com/question/23631778

#SPJ4

Answer:

3\(\sqrt{3}\)

Step-by-step explanation:

Using the rule of radicals

\(\sqrt{a}\) × \(\sqrt{b}\) ⇔ \(\sqrt{ab}\)

Simplifying \(\sqrt{12}\)

\(\sqrt{12}\)

= \(\sqrt{4(3)}\)

= \(\sqrt{4}\) × \(\sqrt{3}\)

= 2\(\sqrt{3}\)

Then

\(\sqrt{3}\) + \(\sqrt{12}\)

= \(\sqrt{3}\) + 2\(\sqrt{3}\)

= 3\(\sqrt{3}\)

Answer:

I think 500 is the answer. I don't remember but I think 1 milliliter is one gram.

So that means one gram is equal to a milliliter.

Step-by-step explanation:

Hope this helped.

A brainliest is always appreciated.

Answer:

500 gm ( for water)

Step-by-step explanation:

answer can be different, as 500 ml water will be 500 gm , but 500 ml oil will be higher than 500gm

Answer:

6 cookies

____________________

Christine has 2 MORE than Matt.

2 + 2 = 4(Christine)

4 + 2 = 6(total)

The required equation of the line is 3x + 2y = 8.

What is an equation?

Algebra is concerned with two types of equations: polynomial equations and the particular case of linear equations. Polynomial equations have the form P(x) = 0, where P is a polynomial, while linear equations have the form ax + b = 0, where a and b are parameters, when there is only one variable. To solve equations from either family, algorithmic or geometric approaches derived from linear algebra or mathematical analysis are used. Algebra also explores and solves Diophantine equations with integer coefficients. The approaches employed are unique and derive from number theory. In general, these equations are complex; one frequently searches just for the existence or lack of a solution, and, if they exist, the number of solutions.

The required equation of the line is

(y-4) = (0+6)/(4-8) (x-0)

or, y - 4 = 6/(-4) x

or, y - 4 = -3/2 x

or, 2y - 8 = -3x

or, 3x + 2y = 8

To know more about an equation, click on the link

https://brainly.com/question/27893282

#SPJ13

The given vector equation represents a twisted tube or helix in three-dimensional space. The given vector equation r(s, t) = s sin(5t), s², s cos(5t) represents a parametric surface in three-dimensional space.

To identify the surface, let's analyze the components of the vector equation:

x = s sin(5t)

y = s²

z = s cos(5t)

From the equation, we can observe that the variable s appears in all three components. This suggests that the surface is radial, meaning it extends outward from the origin (0, 0, 0) or contracts towards it.

The trigonometric functions sin(5t) and cos(5t) indicate periodic behavior along the t direction. These functions oscillate between -1 and 1 as t varies.

The component s² indicates that the surface extends or contracts based on the square of s. When s > 0, the surface expands outward, and when s < 0, it contracts towards the origin.

Considering these observations, we can identify the surface as a twisted tube or a helix that extends or contracts radially while twisting in a periodic manner along the t direction.

In summary, the given vector equation represents a twisted tube or helix in three-dimensional space.

Learn more about vectors here: brainly.com/question/24256726

#SPJ11