find the linearization of the function f(x,y)=131−4x2−3y2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√ at the point (5, 3). l(x,y)= use the linear approximation to estimate the value of f(4.9,3.1) =

Answer:

9.8 gallons

Step-by-step explanation:

1900÷140=13.5714285714

round up to 14

0.7x14=9.8

Answer:

\(\frac{12}{3} - 5 +16 : 4 = 3\)

Step-by-step explanation:

\(\sqrt{144} = 12\\\sqrt[5]{243} = 3\\\\\sqrt[3]{64}= 4\)

Answer:

D

Step-by-step explanation:

If there are 500 students and only 350 are going then just divide 350 by 500. (350 / 500 = 0.7

Answer:

x = -5

Step-by-step explanation:

-3 - 3x = -4( 2x + 7 )

Distributive property

-4 * 2x - 4 * 7

-3 - 3x = -8x - 28

Add 3 on both sides

-3 + 3 - 3x = -8x - 28 + 3

-3x = -8x - 25

Add 8x on both sides

-3x + 8x = -8x + 8x - 25

5x = -25

Divide by 5 on both sides to isolate the variable

5x/5 = -25/5

x = -5

Hope this helped!

have a supercalifragilsticexpialidocious day!

Answer:

x = -5

Step-by-step explanation:

Rearrange terms

-3−3=−4(2+7)

−3−3=−4(2+7)

Distribute

−3−3=−4(2+7)

−3-3=−8−28

Add 3 to both sides of the equation

−3−3=−8−28

−3−3+3=−8−28+3

Simplify

Add the numbers:

−3−3+3=−8−28+3

−3=−8−28+3

Add the numbers:

−3=−8−28+3

−3=−8−25

Add 8 to both sides of the equation

−3=−8−25

−3+8=−8−25+8

Simplify

Combine like terms

−3+8=−8−25+8

5=−8−25+8

Combine like terms

5=−8−25+8

5=−25

Divide both sides of the equation by the same term

5=−25

5x/5 = -25/5

Simplify

Cancel terms that are in both the numerator and denominator

5x/5 = --25/5

x= -25/5

Divide the numbers

x= -25/5

x = -5

Answer:

  (d)  49p² -9

Step-by-step explanation:

You want to identify the difference of squares among the answer choices.

The odd exponent means the first term is not a square.

The plus sign (+) means the expression is not a difference. (It could be factored using complex numbers, but we expect you don't want to do that.)

The coefficient 10 is not a square.

This is the difference of squares: (7p)² -3².

Uma is correct, because getting an even number is an event.

The term probability refers to the likelihood of an event occurring.

Given that;

Bridget says that when a standard number cube is rolled getting an even number is an outcome.

And, Uma says that getting an even number is an event.

Now,

We know that;

When a standard number cube is rolled then getting an even number is an event.

Hence, Uma statement is correct.

Thus, Uma is correct, because getting an even number is an event.

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The value of the supplementary angle is 162 degrees.

If the measure of an angle is 18 degrees, the value of its supplementary angle is 162 degrees.

The supplementary angles are two angles whose sum is 180 degrees. Since one of the angles is 18 degrees, the other angle's value can be determined by subtracting 18 from 180 degrees. The result is 162 degrees.

Here's the calculation: Supplementary angle = 180 - measure of the angle

Supplementary angle = 180 - 18

Supplementary angle = 162

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Answer:

y = 163°

General Formulas and Concepts:

Geometry

Step-by-step explanation:

We see from the diagram that y and 163 are vertical angles. Therefore, y = 163. x and z would also be congruent to each other.

The intercept is an essential component of the regression model, as it helps to establish a baseline prediction for the number of shaped ski rentals before accounting for the effects of the independent variables.

Based on the previous multivariate regression model that used weekend, school break, and weather as predictors of shaped ski rentals, the value of the intercept refers to the estimated number of shaped ski rentals when all independent variables are equal to zero.

In this case, the intercept would represent the expected number of shaped ski rentals on a weekday during a non-school break period when the weather is average. Unfortunately, without the exact equation for the regression model, it's impossible to determine the specific value of the intercept.

However, it is important to note that the intercept is an essential component of the regression model, as it helps to establish a baseline prediction for the number of shaped ski rentals before accounting for the effects of the independent variables.

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Answer:

(x - 7)(x + 8)

Step-by-step explanation:

x² + x - 56
Multiples of 56 whose difference is 1: 7, 8
So, splitting the equation:
x² + 8x - 7x - 56
(x - 7)(x + 8)

The factored form of a quadratic expression is a way to rewrite the expression which shows the sums of products.

general form: \(y= a(x-r)(x-s)\)

when the a value is equal to zero:

\(y=x^2+x-56\)

\(y=(x+8)(x-7)\)

Any line can be graphed using two points. Select two x x values, and plug them into the equation to find the corresponding y y values. Tap for more steps.

:

The SS value for the first, second and third sample is 24, 26 and 18 respectively. Upon dividing the SS value by the sample size minus one, sample variance can be derived.

In the previous question, there were significant differences among the three treatments, partially due to the relatively small sample variances. Now, with the SS (sum of squares) values within each sample doubled, we need to calculate the new sample variances. The values provided in the previous question were 12.00, 13.00, and 8.00.

To calculate the sample variance for each of the three samples, we utilize the formula for variance, which is the sum of squared deviations from the mean divided by the sample size minus one.

For the first sample with a previous variance of 12.00, if the SS value is doubled, the new SS value would be 24.00. To calculate the new sample variance, we divide this SS value by the sample size minus one.

Similarly, for the second sample with a previous variance of 13.00, the doubled SS value would be 26.00. Again, we divide this SS value by the sample size minus one to calculate the new sample variance.

Lastly, for the third sample with a previous variance of 8.00, the doubled SS value would be 16.00. We divide this SS value by the sample size minus one to obtain the new sample variance.

By performing these calculations, we can determine the new sample variances for each of the three samples, which will reflect the changes resulting from the doubled SS values within each sample.

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Answer:

1 : 900

Step-by-step explanation:

18 m = 1800 cm

2:1800 reduced is 1:900

Answer:

A

Step-by-step explanation:

In A, the number of bags that had more than 19 skittles is 7 and the number of bags that had less than 19 skittles is 16, so A is true.

In B, the median package contained 18 candies.

In C, 5 bags contained 18 candies, while there were 8 bags in total for the 17 and 20 bags.

In D, the range is the highest value minus the lowest, so it's 22-12=10.

A total of 55.86 minutes have gone by since Greg started his run on the treadmill.

If Greg has completed 57% of his run, it means he has 43% of his run remaining.

To find out how many minutes have gone by, we can use proportions.

Let's say x is the total number of minutes Greg needs to complete his run:

x = 57% * 98 minutes

Evaluate

x =  minutes

Therefore, approximately 55.86 minutes have gone by since Greg started his run on the treadmill.

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The mood of the categorical syllogism in example 2 is AIO.

In your example, we have the following premises and conclusion:

1. Major Premise: No dogmatists are scholars who encourage free thinking.
2. Minor Premise: Some theologians are scholars who encourage free thinking.
3. Conclusion: Some theologians are not dogmatists.

The major premise in example 2 is an A proposition (All S are not P). The minor premise in example 2 is an I proposition (Some S are P). The conclusion in example 2 is an O proposition (Some S are not P).

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The answer of the equation 8(x-3) +7=2x(4-17) is x=1/2.

An equation is a statement that says that the value of two mathematical expressions is equal i.e., it is a mathematical sentence that has two equal sides separated by an equal sign.

We have the equation : 8(x-3) +7=2x(4-17)

Here we are not given Lin's solution so we can not find the error in her solution but we will solve this equation and find the value of x.

            8(x-3) +7= 2x (4-17)    

      ⇒  8x - 24 +7 = 2x(-13)

      ⇒  8x -17= -26x

      ⇒  34x = 17

      ⇒  x= 17/34

      ⇒ x =1/2.

The solution of the above equation is x= 1/2.

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Answer:

\(x = \frac{1}{4} \)

\(y = \frac{2}{4} \)

Answer:  \(\Big\{\pm 4\sqrt{5} \Big\}\)

This is the shorthand way of writing \(\Big\{4\sqrt{5}, -4\sqrt{5} \Big\}\)

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

Work Shown:

\(x^2 - 80 = 0\\\\x^2 = 80\\\\x = \pm\sqrt{80}\\\\x = \pm\sqrt{16*5}\\\\x = \pm\sqrt{16}*\sqrt{5}\\\\x = \pm4\sqrt{5}\\\\x = 4\sqrt{5} \ \text{ or } \ x = -4\sqrt{5}\\\\\)

The plus or minus is needed because squaring a negative leads to a positive. As another example, x^2 = 25 has x = 5 and x = -5 as the two solutions. Note that x^2 = (-5)^2 = (-5)*(-5) = 25.

Also, note that the 80 was broken up into 16*5. This was done to simplify the square root. We pull out the largest factor that's a perfect square.

So that's how we get to the solution set \(\Big\{\pm 4\sqrt{5} \Big\}\). The curly braces tell the reader that they are dealing with a set.

Answer: 0

Step-by-step explanation:

4y — 8 = 0 ———> 4(2) — 8 = 0

8 — 8 = 0

The kind of study that was conducted on the subjects who were given suplement and Placebo is termed as Experimental Study .

The active gathering of data from a primary source is observation. Observation of living things makes use of the senses. In science, observation can also entail the perception of information and the recording of that information using tools.

Because of ethical considerations or practical limitations, an observational study infers information from a sample to the population even when the researcher has no control over the independent variable.

An experiment is a technique used to confirm or deny a hypothesis, as well as assess the possibility or effectiveness of something that has never been done before. Experiments show what happens when a certain component is modified, which sheds light on cause-and-effect relationships.

The kind of study that was conducted on the subjects who were given suplement and Placebo is termed as Experimental Study .

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Job sharing is the name for this type of arrangement as Annette and Nathan share their work at Wood Grove Elementary.

A job share arrangement is a full-time of work of  job  and it is split between two individuals, each with responsibility for the success of the total job. Work sharing, sometimes known as work sharing, is a work arrangement in which two persons, or occasionally more, are kept on a part-time or reduced-time basis to carry out tasks that are typically completed by one person working full-time of job.

As a result, there is a net decrease in per-employee income. The individuals who share the job are jointly accountable for the workload of the shared job and work together to fulfill the task.

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Answer:

(-3/2, -13/2)

Step-by-step explanation:

To solve the system of equations graphically, we need to plot the two equations on the same set of axes and find the point of intersection.

To plot the first equation y = x - 5, we can start by finding the y-intercept, which is -5. Then, we can use the slope of 1 (since the coefficient of x is 1) to find other points on the line. For example, if we move one unit to the right (in the positive x direction), we will move one unit up (in the positive y direction) and get the point (1, -4). Similarly, if we move two units to the left (in the negative x direction), we will move two units down (in the negative y direction) and get the point (-2, -7). We can plot these points and connect them with a straight line to get the graph of the first equation.

To plot the second equation y = -x - 8, we can follow a similar process. The y-intercept is -8, and the slope is -1 (since the coefficient of x is -1). If we move one unit to the right, we will move one unit down and get the point (1, -9). If we move two units to the left, we will move two units up and get the point (-2, -6). We can plot these points and connect them with a straight line to get the graph of the second equation.

The point of intersection of these two lines is the solution to the system of equations. We can estimate the coordinates of this point by looking at the graph, or we can use algebraic methods to find the exact solution. One way to do this is to set the two equations equal to each other and solve for x:

x - 5 = -x - 8 2x = -3 x = -3/2

Then, we can plug this value of x into either equation to find the corresponding value of y:

y = (-3/2) - 5 y = -13/2

So the solution to the system of equations is (-3/2, -13/2).

Answer:

0.000001382 if you divide

Answer:

(21, 4)

Step-by-step explanation:

x+y=25

3x-2y=55

3x+3y=75

3x-2y=55

5y=20

y=4

x+4=25

x=21

Answer:

11/25 of the earnings were spent on new uniforms.

Step-by-step explanation:

Hope this helps! :)

Answer:

61

Step-by-step explanation:

straight line = 180 degree

to find the measure of angle QPR,

subtract 119 from 180

=>            180-119

=>            61

angle QPR = 61 degree

Answer:

Hope the picture will help you!!

It will take 57.78 years for your investment to reach $5000 with continuous compounding interest.

To determine how many years it will take for your investment to reach $5000 with continuous compounding interest, we can use the formula for continuous compound interest:

A = P * \(e^{rt}\)

Where:

A = Final amount (in this case, $5000)

P = Initial investment ($2000)

e = Euler's number (approximately 2.71828)

r = Interest rate (1.2% = 0.012)

t = Time (in years)

We can rearrange the formula to solve for t:

t = ln(A/P) / r

Substituting the given values:

t = ln(5000/2000) / 0.012

Calculating the value:

t ≈ ln(2.5) / 0.012

Using a calculator or software, we find:

t ≈ 57.78 years

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The probability that at least one child would draw the nickel too small is: P(X ≥ 1) = 1 - P(X = 0).

b) To find the probability that exactly 4 children would draw the nickel too small, we can use the binomial probability formula. The formula is: P(X = k) = (nCk) * (p^k) * (q^(n-k)), where n is the number of trials, k is the number of successes, p is the probability of success, and q is the probability of failure.

In this case, n = 8 (as 8 children are chosen), k = 4 (as exactly 4 children drawing the nickel too small), p = 0.15 (as the probability of a child drawing the nickel too small), and q = 1 - p = 1 - 0.15 = 0.85.

So, the probability that exactly 4 children would draw the nickel too small is: P(X = 4) = (8C4) * (0.15^4) * (0.85^(8-4)).

c) To find the probability that at least one child would draw the nickel too small, we can use the complement rule. The probability of at least one success is equal to 1 minus the probability of no success.

The probability of no success (all children drawing the nickel of the right size) is given by: P(X = 0) = (8C0) * (0.15^0) * (0.85^8).

Therefore, the probability that at least one child would draw the nickel too small is: P(X ≥ 1) = 1 - P(X = 0).

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