Decreasing half of a number by 19.7 results in â€""4.1. what is the number? use the given equation to find the number. one-halfx â€"" 19.7 = â€""4.1 what is the number? 7.8 15.6 31.2

We need to calculate the partial derivatives, set them equal to zero, and analyze the values within the given range.

To find the critical points, we need to calculate the partial derivatives of f(x, y) with respect to x and y and set them equal to zero.

∂f/∂x = 2x - y - 2 = 0

∂f/∂y = -x + 2y + 2 = 0

Solving these equations simultaneously, we find x = 2 and y = 1. Thus, (2, 1) is a critical point.

Next, we evaluate the function at the critical point (2, 1) and the boundary values (-2, -2, 2, 2) to find the absolute minimum and absolute maximum.

f(2, 1) = (2)² - (2)(1) + (1)² - 2(2) + 2(1) = 1

Now, evaluate f at the boundary values:

f(-2, -2) = (-2)² - (-2)(-2) + (-2)² - 2(-2) + 2(-2) = 4

f(-2, 2) = (-2)² - (-2)(2) + (2)² - 2(-2) + 2(2) = 16

f(2, -2) = (2)² - (2)(-2) + (-2)² - 2(2) + 2(-2) = 8

f(2, 2) = (2)² - (2)(2) + (2)² - 2(2) + 2(2) = 4

From these evaluations, we can see that the absolute minimum is 1 at (2, 1), and the absolute maximum is 16 at (-2, 2).

Therefore, the critical point is (2, 1), the absolute minimum is 1, and the absolute maximum is 16 within the given range.

Learn more about partial derivatives here:

https://brainly.com/question/28751547

#SPJ11

(a-1) The value of the population mean is unknown.

(a-2) The best estimate of the population mean is the sample mean, which is 20 eggs.

(c) The value of t for a 95% confidence interval with 17 degrees of freedom is approximately 2.110.

(d) the 95% confidence interval for the population mean is approximately (17.902, 22.098).

(e-1) It would not be reasonable to conclude that the population mean is 17 eggs.

(e-2) It would be reasonable to conclude that the population mean is 18 eggs.

(a-1) The given information provides the sample mean (20 eggs) and the sample standard deviation (5 eggs), but it does not directly provide the population mean.

(a-2) In the absence of other information, the sample mean is a reasonable estimate of the population mean.

(c) For a 95% confidence interval, the value of t can be determined using the t-distribution with n-1 degrees of freedom, where n is the sample size. In this case, the sample size is 18, so the degrees of freedom is 18 - 1 = 17.

Using a t-distribution table or a statistical software, the value of t for a 95% confidence interval with 17 degrees of freedom is approximately 2.110.

(d) To determine the 95% confidence interval for the population mean, we can use the formula: Confidence interval = sample mean ± (t * standard error), where the standard error is the sample standard deviation divided by the square root of the sample size.

In this case, the sample mean is 20, the standard deviation is 5, the sample size is 18, and the value of t is 2.110. Plugging in these values, the confidence interval is 20 ± (2.110 * (5 / √18)), which evaluates to approximately 20 ± 2.098.

(e-1) The 95% confidence interval calculated in part (d) does not include 17 eggs, indicating that it is unlikely for the population mean to be 17 eggs.

(e-2) The 95% confidence interval calculated in part (d) includes 18 eggs, suggesting that it is plausible for the population mean to be 18 eggs.

For more such questions on population mean

https://brainly.com/question/31101410

#SPJ8

Answer:

(280+7) ÷ (7+7)

Step-by-step explanation:

hopefully this helps ya

The equation that is equal to 287 ÷ 7 is (280 + 7) ÷ (7 + 7). The correct option is C.

An equation is a statement in mathematics that shows that two expressions are equal. It has two sides that are separated by an equal sign.

To find the value of 287 ÷ 7, we can use the following methods:

We can simplify 287 ÷ 7 as follows:

287 ÷ 7 = 280 ÷ 7 + 7 ÷ 7

Note that 7 ÷ 7 simplifies to 1, so we have:

287 ÷ 7 = 280 ÷ 7 + 1

Therefore, the answer is C. (280 + 7) ÷ (7 + 7) = 287 ÷ 14 = 20.5.

For more details regarding equation, visit:

https://brainly.com/question/29657983

#SPJ2

Answer:

(3, -4)

Step-by-step explanation:

Lines are intersecting at points (3, -4).

So, the solution of the given system of equations is (3, -4).

Hope it helps you in your learning process.

Answer:

\(\circ\ \ 36\sqrt{3}\)

Step-by-step explanation:

\(CD=12\times \sin(60) =12\times \frac{\sqrt{3} }{2}\)

Important Note:………………………………………………………………………………………

ABC is an equilateral triangle because it has 2 angles of measure 60

===========================================================

According to the note AB = 12

Final answer :

\(\text{Area of triangle ABC} =\frac{AB\times CD}{2}\)

                                  \(=\frac{12\times 6\sqrt{3} }{2}\)

                                  \(=\frac{72\sqrt{3} }{2}\)

                                  \(=36\sqrt{3}\)

The solution is, 76,000 mg chlorine is in the pool.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

The pool has 2.5 milligrams of chlorine per liter of water.

There are 8000 gallons of water in the swimming pool.

we know,

1 gallon = 3.785 liters

Water in pool = 8000 x 3.785

Water in pool = 30,280 liters

so, we get,

Chlorine dosage = 2.5 mg / liter

Chlorine = 2.5 x 30,280

Chlorine = 75,700 mg

To the nearest thousand milligram:

Chlorine = 76,000 mg

Hence, The solution is, 76,000 mg chlorine is in the pool.

To learn more on multiplication click:

brainly.com/question/5992872

#SPJ9

Performing a linear transformation involves applying a mathematical operation to each data point in a dataset to transform it into a new set of values and can be useful for various data analysis purposes.

A linear transformation, we are applying a mathematical operation to each data point in a dataset to transform it into a new set of values.

Specifically, a linear transformation involves multiplying each data point by a constant value and adding another constant value to the result.

The general formula for a linear transformation is:

y = a × x + b

y is the transformed value of x, a is the scaling factor, x is the original value of the data point, and b is the constant shift.

Performing a linear transformation can be useful for several reasons.

To rescale data that has different units or scales, or to adjust the distribution of the data to meet certain statistical assumptions.

Here are some common examples of linear transformations:

Scaling:

Multiplying each data point by a constant factor to convert it to a different unit or scale.

Converting temperature from Celsius to Fahrenheit by multiplying by 1.8 and adding 32.

Standardizing:

Subtracting the mean value of a dataset from each data point and then dividing by the standard deviation to transform the data into z-scores.

This helps to rescale the data to a standard normal distribution with a mean of zero and a standard deviation of one.

Centering:

Subtracting a constant value from each data point to shift the distribution to a different location.

Centering the data around zero by subtracting the mean value from each data point.

Normalizing:

Dividing each data point by the sum of all data points to transform the data into proportions or percentages that add up to one.

This can be useful for analyzing relative frequencies or proportions.

For similar questions on linear

https://brainly.com/question/12788590

#SPJ11

Answer:

The measure or what?

Step-by-step explanation:

Answer:

we need a measure

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the first three terms be a/r, a, ar... where a is the first term and r is the common ratio of the geometric sequence.

If the sum of the first two term is 24, then a/r + a = 24...(1)

and the sum of the first three terms is 26.. then a/r+a+ar = 26...(2)

Substtituting equation 1 into 2 we have;

24+ar = 26

ar = 2

a = 2/r ...(3)

Substituting a = 2/r into equation 1 will give;

(2/r))/r+2/r = 24

2/r²+2/r = 24

(2+2r)/r² = 24

2+2r = 24r²

1+r = 12r²

12r²-r-1 = 0

12r²-4r+3r -1 = 0

4r(3r-1)+1(3r-1) = 0

(4r+1)(3r-1) = 0

r = -1/4 0r 1/3

Since a= 2/r then a = 2/(-1/4)or  a = 2/(1/3)

a = -8 or 6

All the geometric sequence can be found by simply knowing the formula for heir nth term. nth term of  a geometric sequence is expressed as

if r = -1/4 and a = -8

Tn = -8(-1/4)^(n-1)

if r = 1/3 and a = 6

Tn = 6(1/3)^(n-1)

The nth term of the sequence above can be used to find all the geometric sequence where n is the number of terms

Answer:

9.30918

Step-by-step explanation:

For a sample of Lead-218, with half-life time period of 0.25 minute, the percent of the sample decays away every minute is equals to the 93.75%.

We have a half-life time period of Lead-218 is equals to the 0.25 minute.

Initial sample amount of lead-218 = 100 mg

The equation which is used to modeled the situation or decay equation is written as \(A(t) = 100(\frac{1}{2})^{4t}\)

where, t --> time period ( in minutes)

We have to determine percent of the sample decays away every minute. So, we determine the decay value of A(t) at t = 1 minute then change the amount in percent form. Substitute, t = 1 minutes

=> \(A(t) = 100(\frac{1}{2})^{4× 1}\)

\(= 100(\frac{1}{2^4})\)

\(= \frac{100}{16}\)

= 6.25

Conversion in percentage : \( (\frac{100 - 6.25}{100})100%\)

= 93.75%

Hence, decay Percent is 93.75% in every minute.

For more information about half life, visit:

https://brainly.com/question/15575933

#SPJ4

To determine if a matrix is a linear combination of other matrices, we need to check if it can be written as a weighted sum of those matrices where the weights are scalar values (numbers).

If a matrix can be expressed in this way, it is said to be a linear combination of the other matrices.

For example if we have matrices: A, B & C and we can write matrix D as follows:

Then D is a linear combination of matrices A, B and C. This concept is important in linear algebra as it allows us to express one matrix in terms of others. Making it easier to manipulate & analyze the matrices. A matrix is a linear combination of other matrices if it can be expressed as a weighted sum of those matrices where the weights are scalar values.

Learn more about linear combination brainly.com/question/8881662

#SPJ4

Answer:

Graphical method

The solution to the system of equations is x = 8/3 and y = 41/43.

To find the solution for the given system of equations, we can use the method of substitution or elimination. Let's use the method of elimination:

Given equations:

3x + 2y = 22 ---(1)

-x + 15y = 21 ---(2)

To eliminate one variable, we can multiply equation (2) by 3 and equation (1) by -1, then add the resulting equations:

-3x + 45y = 63 ---(3) (multiplying equation (2) by 3)

-3x - 2y = -22 ---(4) (multiplying equation (1) by -1)

Adding equations (3) and (4) eliminates the x variable:

43y = 41

Dividing both sides by 43 gives us:

y = 41/43

Now we can substitute this value of y into either equation (1) or (2). Let's use equation (1):

3x + 2(41/43) = 22

Multiplying both sides by 43 to eliminate the fraction:

129x + 82 = 946

Subtracting 82 from both sides:

129x = 864

Dividing both sides by 129:

x = 864/129

Simplifying:

x = 8/3

For more such questions on equations visit:

https://brainly.com/question/17145398

#SPJ8

Answer:

Graph Y

Step-by-step explanation:

This is since the points on the table match up with the line on the Y graph.

Answer:

Step-by-step explanation:

Let d and r be the diameter and radius, respectively.

d² + 12² = 15²

d² = 15² - 12² = 81

d = √81 = 9

r = d÷2 = 4.5 mm

Answer:

3.5

Step-by-step explanation:

28 days = 4 weeks

28 divided by 4 = 1 week

14 gallons divided by 4 = 3.5

Why not? Because it fails the vertical line test. Here it is possible to draw a single straight vertical line through more than one point on the curve. That's why choice D is not a function. Choices A,B,C are functions because it's impossible to draw a single vertical line through more than two points on the curve, and therefore we can say they pass the vertical line test.

Side note: choices B and C fail the horizontal line test, so these functions are not one-to-one.

Answer:

{3,4,5,.........,49,50}

Step-by-step explanation:

All these numbers are greater than 2, but less than 51.

Answer:

-(x - 4)² + 6

Max height: 6

Step-by-step explanation:

Step 1: Factor out negative

0 = -(x² - 8x + 10)

Step 2: Divide by -1

0 = x² - 8x + 10

Step 3: Move 10 over

-10 = x² - 8x

Step 4: Complete the Square

-10 + 16 = x² - 8x + 16

6 = (x - 4)²

Step 5: Move 6 over

(x - 4)² - 6

Step 6: Multiply by -1

-(x - 4)² + 6

The maximum height of the puck is 6 feet. We look at k in f(x) = a(bx - h)² + k.

Answer:

-(x-4)^2+6=0

maximum point (4,6)

max=6

Step-by-step explanation:

−x^2 + 8x − 10 use the formula (b/2)^2 to create a new term to complete the square: b=8 so the new term is (8/2)^2 = 16

−x^2 + 8x − 10+16=0

factorize : -x^2+8x+16-10

-(x-4)^2+6=0

to find the maximum value : x= -b/2a b=8 and a=-1

x=-8/-2

x=4 substitute the value of x in the equation:

-4^2+8(4)-10=-16+32-10=6

To improve the design of this experiment, the researchers could have used a double-blind design, where both the participants and the researchers are unaware of the group allocation.

In the given experiment, the researchers have not employed any form of blinding, which could be a potential source of bias. Blinding is a critical aspect of experimental design, where the participants or the researchers are unaware of the group allocation or the treatment being administered. Blinding is used to eliminate any potential sources of bias that may arise due to the expectations or beliefs of the researchers or participants. In this particular study, the lack of blinding could have led to two possible sources of bias. Firstly, the participants in the first group who received the meditation session could have had higher expectations of improvement in their flexibility due to the meditation. These expectations could have led to higher motivation and effort during the flexibility measurement, leading to an artificial improvement in their flexibility scores. Secondly, the researchers who were measuring the flexibility of the participants could have been biased towards finding a difference between the groups due to their knowledge of the group allocation. This could have led to a subconscious alteration in the measurement process, leading to a false conclusion about the effect of meditation on flexibility.

hence To improve the design of this experiment, the researchers could have used a double-blind design, where both the participants and the researchers are unaware of the group allocation. For instance, the participants could have been assigned a unique identification number, and the researchers could have used coded labels to differentiate the groups. This would have eliminated any potential sources of bias due to expectations or beliefs and would have made the results more reliable.

To know more about double-blind design click here:

brainly.com/question/30450870

#SPJ4

Answer:

  c

Step-by-step explanation:

Work out the composition and see what you get.

  \((f\circ g)(x)=f(g(x))=f(7x+10)=\dfrac{(7x+10)-10}{7}=\dfrac{7x}{7}=x\)

This is your first clue that the functions are inverses of each other, so we expect that g(f(x)) = x will be true, too. We can work that out to confirm it.

  \((g\circ f)(x)=g(f(x))=g\left(\dfrac{x-10}{7}\right)=7\left(\dfrac{x-10}{7}\right)+10\\\\=(x-10)+10=x\)

So, the appropriate choice is as shown below.

Answer:

x= -2 y= -1

Step-by-step explanation:

To solve by Substitution you would make this equation equal to each other x+1=3x+5 from there you would solve for x subtract x on both sides. and subtracting 5 from both sides 2x= -4 then divide by 2 to get x by itself x=-2 since we now found what the value of x is you can now plug in x into one of the origunal equations and get your answer for y which is y=-1

Answer:

Step-by-step explanation:

the rest are incorrect

The general solution of the given differential equation is \(y = C_1e^{4x} + C_2xe^{4x} + \frac{3}{16}e^{4x}\), where \(C_1\) and \(C_2\) are constants.

To find the general solution of the given differential equation using the method of undetermined coefficients, we assume a particular solution in the form of \(y_p = A e^{4x}\), where \(A\) is a constant to be determined.

We'll start by finding the first and second derivatives of \(y_p\):

\(y_p' = 4Ae^{4x}\) and \(y_p'' = 16Ae^{4x}\).

Substituting these into the original equation, we get:

\(16Ae^{4x} - 8(4Ae^{4x}) + 16(Ae^{4x}) = 3e^{4x}\).

Simplifying the equation, we have:

\(16Ae^{4x} - 32Ae^{4x} + 16Ae^{4x} = 3e^{4x}\),

\(0 = 3e^{4x}\).

Since the exponential function \(e^{4x}\) is never equal to zero, this equation has no solutions. Therefore, we need to modify our assumption for the particular solution.

Since the differential equation is of the form \(y'' - 8y' + 16y = 3e^{4x}\), which resembles the form of the homogeneous equation \((D^2 - 8D + 16)y = 0\), we'll modify the particular solution assumption to \(y_p = A x e^{4x}\), where \(A\) is a constant to be determined.

Taking the first and second derivatives of \(y_p\):

\(y_p' = (A + 4Ax)e^{4x}\) and \(y_p'' = (4A + 8Ax + 4A)e^{4x}\).

Substituting these into the original equation, we get:

\((4A + 8Ax + 4A)e^{4x} - 8(A + 4Ax)e^{4x} + 16(Ax)e^{4x} = 3e^{4x}\).

Simplifying the equation, we have:

\((8A + 16Ax)e^{4x} - (8A + 32Ax)e^{4x} + 16Ax e^{4x} = 3e^{4x}\),

\(16Ax e^{4x} = 3e^{4x}\).

By comparing the coefficients of \(e^{4x}\), we find that \(16Ax = 3\).

Solving for \(A\), we get:

\(A = \frac{3}{16x}\).

Therefore, the particular solution is:

\(y_p = \frac{3}{16x} x e^{4x} = \frac{3}{16}e^{4x}\).

Now, to find the general solution, we need to solve the corresponding homogeneous equation:

\(y'' - 8y' + 16y = 0\).

The characteristic equation is:

\(r^2 - 8r + 16 = 0\).

Factoring the quadratic, we get:

\((r-4)^2 = 0\).

This equation has a repeated root \(r = 4\). Thus, the general solution to the homogeneous equation is:

\(y_h = C_1e^{4x} + C_2xe^{4x}\), where \(C_1\) and \(C_2\) are arbitrary constants.

Finally, combining the particular and homogeneous solutions, we obtain the general solution to the given differential equation:

\(y = y_h + y_p = C_1e^{4x} + C_2xe^{

Learn more about coefficients from the given link:

https://brainly.com/question/1594145

#SPJ11

Answer:

P = A/1+rt

Step-by-step explanation:

Given: A = P + Prt

Applying the distributive principle: A = P( 1 + rt)

Dividing both sides by (1 + rt):

A/1 + rt = P

The measure of the missing angles are d= 77° , e= 31° ,and f = 72°.

As given in the question,

Angle e is vertically opposite to the given angle 31°

⇒Measure of angle e = 31°

Angle d is vertically opposite to the given angle 77°

⇒Measure of angle d = 77°

Angle e , Angle f and angle d are linear pairs

⇒∠e +∠f +∠d =180°

⇒31° +∠f + 77°=180°

⇒ ∠f =180° -108°

⇒ ∠f =72°

Therefore, the measure of the missing angles are d = 77° , e = 31° and

f = 72°.

Learn more about angles here

brainly.com/question/28451077

#SPJ1

Answer:

No

Step-by-step explanation:

The Side-Angle-Side rule of congruence

two triangles are congruent if two sides and one included angle in a given triangle are equal to the corresponding two sides and one included angle in another triangle.