15.2, 3,6,11,18, ...
Describe the pattern. Then write the next three numbers

Answer:

E

Step-by-step explanation:

\sqrt 6 is an irrational number, as it cannot be written as the ratio of 2 numbers.

It is also a real number, as it does not include the square root of a negative number.

Therefore, E is the correct option.

Answer:

y= 4x

Step-by-step explanation:

2*4=8

3*4=12

4*4=16

5*4=20

6*4=24

7*4=28

The maximum rate of change of function [tex]f(x,y)=ln(x^2+y^2)[/tex] is  [tex]\frac{\sqrt(2)}{2}[/tex] and the direction is [tex](\frac{-1}{2}, \frac{1}{2})[/tex]

Given data:

To find the maximum rate of change of the function [tex]f(x,y)=ln(x^2+y^2)[/tex] at the point (-2, 2), calculate the gradient vector (∇f) and evaluate it at that point.

The gradient vector is a vector that points in the direction of the steepest ascent of the function and its magnitude represents the rate of change of the function at that point.

To find the gradient vector (∇f), calculate the partial derivatives of f(x, y) with respect to x and y:

[tex]\frac{df}{dx} = \frac{(2x)}{ (x^2 + y^2)}[/tex]

[tex]\frac{df}{dy} = \frac{(2y)}{ (x^2 + y^2)}[/tex]

Evaluating these partial derivatives at the point (-2, 2):

[tex]\frac{df}{dx}_{-2,2}=-1/2[/tex]

[tex]\frac{df}{dy}_{-2,2}=--1/2[/tex]

So, the gradient vector (∇f) at the point (-2, 2) is (∇f) = (-1/2, 1/2).

The maximum rate of change of the function occurs in the direction of the gradient vector (∇f). Therefore, the direction in which the maximum rate of change occurs is in the direction of the vector (-1/2, 1/2).

Note that the magnitude of the gradient vector (∇f) represents the maximum rate of change. In this case, the magnitude of (∇f) is:

|∇f| = [tex](\frac{-1}{2}^2 + \frac{1}{2}^2)[/tex]

= √(1/4 + 1/4)

= √(1/2)

= 1/√(2)

[tex]=\frac{\sqrt(2)}{2}[/tex]

Hence, the maximum rate of change of f(x, y) at the point (-2, 2) is [tex]\frac{\sqrt(2)}{2}[/tex], and it occurs in the direction of the vector [tex](\frac{-1}{2}, \frac{1}{2})[/tex].

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Answer:

21,31

Step-by-step explanation:

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Answer:

5

Step-by-step explanation:

Remember:

Two negatives make a positive

A negative flips a sign

2 - (-4) + 3 + (-6) - (-2)

=

2+4+3-6+2

9-6+2

=5

Answer:

$64

Step-by-step explanation:

Otto had x dollars.

He spent 3/4x which equals to $48

Otto had $64 before he bought the game

Answer:

64

Step-by-step explanation:

distribute the [tex]7[/tex] and [tex]5[/tex]:

[tex]7(4+t)-5(t+1)=\\28+7t -5t -5[/tex](collect like-terms)

[tex]28-5 +7t-5t=\\23+2t[/tex]

[tex]23+2t[/tex] or [tex]2t+23[/tex] is your answer. hope this helps <3

Answer:

x+5x=84

6x=84

6x/6=84/6

x=14

so therefore

14+5(14)

14+70

The numbers are 14 and 70

The two parts are x = 70 and y = 14

We have a 2 - digit number -  84.

We have to split it into two parts such that one part is five times the other part.

Assume the two numbers to be x and y.

x + y = 24

A/Q -

y  = 3x

x + 3x =24

4x = 24

x = 6

and y = 3 x 6 = 18.

According to question, we have -

Number = 84

Assume the first part be x.

Then, the other part = [tex]\frac{x}{5}[/tex]

Therefore -

x + [tex]\frac{x}{5}[/tex] = 84

5x + x = 84 x 5

6x = 420

x = 70

and

y = [tex]\frac{x}{5} =\frac{70}{5}[/tex] = 14

Hence, the two parts are x = 70 and y = 14

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Answer: See below; x=1/6

Step-by-step explanation:

This problem may seem intimidating, but all you need to know are your exponent rules. Let's first work inside the parenthesis. Since the bases are the same, we can directly subtract the exponents.

[tex]\frac{3}{4} -\frac{3}{8}[/tex]                             [common denominator]

[tex]\frac{6}{8} -\frac{3}{8}[/tex]                             [subtract]

[tex]\frac{3}{8}[/tex]

Now, our new answer is [tex](3^\frac{3}{8} )^\frac{4}{9}[/tex].

Unfortunately, the answer is asking for an exponent with a single base. One of the properties is when the exponents are separated by parenthesis, you multiply them together.

[tex]\frac{3}{8} *\frac{4}{9}[/tex]                              [cross cancel to simplify]

[tex]\frac{1}{2} *\frac{1}{3}[/tex]                              [multiply]        

[tex]\frac{1}{6}[/tex]

Our final answer is [tex]3^\frac{1}{6}[/tex].

The value is x is [tex]\frac{1}{6}[/tex] since [tex]3^\frac{1}{6}[/tex] is equal to [tex]3^x[/tex], we know that [tex]x=\frac{1}{6}[/tex].

Correlation is a quantitative measure of the strength of a non-linear association between two variables.

Statement B is false because the r value measures the linear association between two variables. In other words, it tells us how good a linear fit we have with a scatterplot of data. So this is why statement A is true.

As r gets closer to +1, then we have a stronger positive linear correlation. If r = 1 exactly, then all points fall on the same straight line with positive slope (the slope isn't necessarily m = 1). Conversely, if r = -1, then the points fall on the same straight line with negative slope (not necessarily m = -1). As r gets closer to r = 0, the strength of the linear relationship weakens. All of this points to statements A, C, and D to be true statements.

Answer:

Correlation is a quantitative measure of the strength of a non-linear association between two variables.

Step-by-step explanation:

Correlation specifically measures the strength and direction of a linear association between two variables.  So we can't use it for all variables or for non-linear associations.

Answer:

x = [tex]\frac{36}{7}[/tex]

Step-by-step explanation:

Given

12x - 17 = 5x + 19 ( subtract 5x from both sides )

7x - 17 = 19 ( add 17 to both sides )

7x = 36 ( divide both sides by 7 )

x = [tex]\frac{36}{7}[/tex]

Answer:

This is false

Step-by-step explanation:

Because we have to understand that some times sample mean may be very high that is they may be practically significant but are not statistically significant because the calculated p-value is not less than alpha value which could only mean that they could occur as a result of mere chance.

Answer:

-1

Step-by-step explanation:

-3x(-5)-16

15-16

-1

Answer:

n=-37

Step-by-step explanation:

9+n/4 = -7

First, we multiply each side by 4:

9+n= -28

Subtract 9 from both sides

n= -37

Hope this helps!!!

Answer:

n=8

Step-by-step explanation:

[tex]-9+\frac{n}{4}=-7\\ \frac{n}{4}=-7+9\\\frac{n}{4}=2\\ n=4*2\\n=8[/tex]

Answer:

(5,-6)

Step-by-step explanation:

Answer: 82 sq. units .

Step-by-step explanation:

Answer:

He was correct

Step-by-step explanation:

100÷ 19.678= 5

5 meters for seconds

Answer:

rational, Natural, Integer, whole

Step-by-step explanation:

remember your perfect squares

the sqrt of 25 is a perfect square

sqrt of 25 is 5

5 is all except irrational

Answer:

Sample  1 : independent

Sample  2 :   dependent

Step-by-step explanation:

From the question we are told that

   The  given date is  

                   Sample 1: Pre-training blood pressure of 17 people

                    Sample 2: Post-training blood pressure of 17 people

Now  Sample 1 is independent because  the Pre-training blood pressure of 17 people does not depend of Post-training blood pressure of 17 people

While  

        Sample 2  is  dependent because the Post-training blood pressure of 17 people is  dependent on the Pre-training blood pressure of 17 people

Answer:

1.)6.68% ; 2)84.13% ; 3)84.13% ; 4)1168 ; 5)1105

Step-by-step explanation:

Given a normal distribution with:

Mean (m) = 1000

Standard deviation (sd) = 200

1) What percentage of the persons who take the test score above 1300?

X = 1300

Zscore = (x - m) / sd

Zscore = (1300 - 1000) / 200 = 300/200 = 1.5

P(z > 1.5) = 1 - p(z < 1.5) ;

From the z distribution table:

p(z < 1.5) = 0.9332 ; 1 - 0.9332 = 0.0668 = 6.68%

2) What percentage score above 800?

X = 800

Zscore = (x - m) / sd

Zscore = (800 - 1000) / 200 = - 200/200 = - 1

P(z > - 1) = 1 - p(z < - 1) ;

From the z distribution table:

p(z < - 1) = 0.1587 ; 1 - 0.1587 = 0.8413 = 84.13%

3) What percentage score below 1200?

X = 1200

Zscore = (x - m) / sd

Zscore = (1200 - 1000) / 200 = 200/200 = 1

p(z < 1)

From the z distribution table:

p(z < 1) = 0.8413 = 84.13%

Above what score do 20% of the test takers score?

P(z > Zscore) = 0.2 = P(z > Zscore) = 1 - 0.2 = 0.8

P(z < Zscore) = 0.8

0.8 is closest to a Zscore of 0.84

From the formula:

Zscore = (x - m) / sd

0.84 = (x - 1000) / 200

168 = x - 1000

x = 168 + 1000 = 1168

Above what score do 30% of the test takers score?

P(z > Zscore) = 0.3 = P(z > Zscore) = 1 - 0.3 = 0.7

P(z < Zscore) = 0.7

0.8 is closest to a Zscore of 0.525

From the formula:

Zscore = (x - m) / sd

0.525 = (x - 1000) / 200

105 = x - 1000

x = 105 + 1000 = 1105

Step-by-step explanation:

the line QP is a part of the line PR and PN

Answer:

n> −1 and n < 1/3

Step-by-step explanation:

Answer:

The first blank is 81[tex]x^{2}[/tex]+9=x-1

The second blank is 9x+3=x^2-1

Step-by-step explanation:

For the first part, you must set up the equation (9x+3)^2       then you must multiply the exponent to the inside exponents [tex]9^{2} x^{2}[/tex]+[tex]3^{2}[/tex] next, simplify.

81[tex]x^{2}[/tex]+9=x-1

For part two, set up equation. [tex]x^{2} -1^{2}[/tex] Then simplify 9x+3= [tex]x^{2} -1[/tex]

9x + 3 = x - 1

Squaring the left side and simplifying results in​ 81x² + 53x + 10 = 0.

Squaring the right side and simplifying results in x² - 11x - 2 = 0.

Given,

9x + 3 = x -1

We need to square on the left side and right side separately and find the results.

(A + B)² = A² + 2AB + B²

(A - B)² = A² - 2AB + B²

We have,

9x + 3 = x - 1

Squaring the left side.

( 9x + 3)² = x - 1

(9x)² + 2 x (9x) x 3 + 3² = x - 1

81x² + 54x + 9 = x - 1

81x² + 54x - x + 9 + 1 = 0

81x² + 53x + 10 = 0

Now,

9x + 3 = x - 1

Squaring right side

9x + 3 = ( x - 1 ) ²

9x + 3 = x² - 2 x (x) x 1 + 1²

9x + 3 = x² -2x + 1

x² - 2x - 9x + 1 - 3 = 0

x² - 11x - 2 = 0

Thus the results after simplifying 9x + 3 = x - 1 are

Squaring on the left sides:

81x² + 53x + 10 = 0

Squaring on the right sides:

x² - 11x - 2 = 0

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Answer: 7 pt

Step-by-step explanation:

1 U.S pt is 2 cups

take 14 divided by 2

= 7

Answer: r=2

Step-by-step explanation:

We can use the given 2 points to find slope. Since we are given the slope, we can plug it into the formula and solve for r.

[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} } =2[/tex]                                        [plug in values]

[tex]\frac{12-r}{-6-(-11)} =2[/tex]                                   [combine like terms]

[tex]\frac{12-r}{5} =2[/tex]                                          [multiply both sides by 5]

[tex]12-r=10[/tex]                                      [subtract both sides by 12]

[tex]-r=-2[/tex]                                          [divide both sides by -1]

[tex]r=2[/tex]

Answer:

48 mL 5% vinegar, 192 mL 15% vinegar

Step-by-step explanation:

If x is volume of 5% vinegar, and y is volume of 15% vinegar, then:

x + y = 240

0.05 x + 0.15 y = 0.13 (240)

Solve with substitution:

0.05 x + 0.15 (240 − x) = 0.13 (240)

0.05 x + 36 − 0.15 x = 31.2

0.10 x = 4.8

x = 48

y = 192

Answer:

so just be you

Step-by-step explanation:

A product concept statement, sometimes referred to as just a "concept statement" represents the vision that a business owner and his design team has for a product or service. It describes the product or service, explains its purpose and considers the consumer demographics that the product is market toward.

Answer:

18 on the left 29 on the right

Step-by-step explanation:

LEFT SIDE

There is one row of 10 cubes and one row of 8 cubes making 18

RIGHT SIDE

There are two rows of 10 cubes and 1 row of 9 cubes making 29

Answer:

x = -3 , y = 4 , z = 0

Step-by-step explanation:

Solve the following system:

{x - 3 y + z = -15

2 x + y - z = -2

x + y + 2 z = 1

Hint: | Choose an equation and a variable to solve for.

In the first equation, look to solve for z:

{x - 3 y + z = -15

2 x + y - z = -2

x + y + 2 z = 1

Hint: | Solve for z.

Subtract x - 3 y from both sides:

{z = 3 y + (-x - 15)

2 x + y - z = -2

x + y + 2 z = 1

Hint: | Perform a substitution.

Substitute z = -15 - x + 3 y into the second and third equations:

{z = -15 - x + 3 y

15 + 3 x - 2 y = -2

x + y + 2 (-15 - x + 3 y) = 1

Hint: | Expand the left hand side of the equation x + y + 2 (-15 - x + 3 y) = 1.

x + y + 2 (-15 - x + 3 y) = x + y + (-30 - 2 x + 6 y) = -30 - x + 7 y:

{z = -15 - x + 3 y

15 + 3 x - 2 y = -2

-30 - x + 7 y = 1

Hint: | Choose an equation and a variable to solve for.

In the second equation, look to solve for x:

{z = -15 - x + 3 y

15 + 3 x - 2 y = -2

-30 - x + 7 y = 1

Hint: | Isolate terms with x to the left hand side.

Subtract 15 - 2 y from both sides:

{z = -15 - x + 3 y

3 x = 2 y - 17

-30 - x + 7 y = 1

Hint: | Solve for x.

Divide both sides by 3:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

-30 - x + 7 y = 1

Hint: | Perform a substitution.

Substitute x = (2 y)/3 - 17/3 into the third equation:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

(19 y)/3 - 73/3 = 1

Hint: | Choose an equation and a variable to solve for.

In the third equation, look to solve for y:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

(19 y)/3 - 73/3 = 1

Hint: | Isolate terms with y to the left hand side.

Add 73/3 to both sides:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

(19 y)/3 = 76/3

Hint: | Solve for y.

Multiply both sides by 3/19:

{z = -15 - x + 3 y

x = (2 y)/3 - 17/3

y = 4

Hint: | Perform a back substitution.

Substitute y = 4 into the first and second equations:

{z = -x - 3

x = -3

y = 4

Hint: | Perform a back substitution.

Substitute x = -3 into the first equation:

{z = 0

x = -3

y = 4

Hint: | Sort results.

Collect results in alphabetical order:

Answer: {x = -3 , y = 4 , z = 0

Answer: $25

Step-by-step explanation: