Find the equation for the tangent plane to the surface z=8x^2-9y^2 at the point (2,1,23)

Answer:

Carlos did 49 more jumping jacks than John.

Step-by-step explanation:

Carlos = 138

John = 89

138 - 89 = 49

The probability that the randomly selected point is in the bullseye = 15/16.

To calculate the probability that the randomly selected point is in the bullseye, we shall first evaluate the area of each of the circles:

The area of the larger circle (outer circle) with radius 8 cm is given:

A_outer = πr² = π(8)² = 64π

The area of the smaller circle (inner circle) with radius 2 cm is given:

A_inner = πr² = π(2)² = 4π

The area of the bullseye (the region between the two circles) = the difference between the areas of the two circles:

A_bullseye = A_outer - A_inner

= 64π - 4π = 60π

Therefore, the probability that a randomly selected point is in the bullseye:

P = A_bullseye / A_outer

= (60π) / (64π)

P = 15/16

x

Therefore, the probability that the randomly selected point is in the bullseye = 15/16.

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Answer:-30c

Step-by-step explanation:

you subtract 8 from 3c which is -5c than multiply by 6 which is -30c

Answer: B) 1/2

Step-by-step explanation: Hope this helps! :)

The answer is 1/3. I looked it up on gpt and also got a 100 on this quiz

Answer: See attached.

Step-by-step explanation:

     First, we will create an equation with the slope given.

y = [tex]\frac{3}{4}[/tex]x + b

     Then, we will substitute this value in and solve for b (our y-intercept). Then we will graph the equation.

y = [tex]\frac{3}{4}[/tex]x + b

(-1) = [tex]\frac{3}{4}[/tex](-4) + b

-1 = -3 + b

b = 2

     Our final equation:

           y = [tex]\frac{3}{4}[/tex]x  + 2

     See attached for the graph. We will plot the point (0, 2) for our y-intercept and then move 3 units up for every four units right, according to the slope.

A linear equation which shows a proportional relationship include the following: A. y = 2x.

In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 2/1 = 4/2 = 6/3 = 8/4

Constant of proportionality, k = 2.

Therefore, the required linear equation is given by;

y = kx

y = 2x

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The J curve impact is an financial wonder that happens when domestic currency  increases in value in esteem relative to other monetary forms within the remote trade advertise. The J curve impact is named for the shape of the bend that's made when the adjust of exchange and the esteem of a country's currency are plotted against time.

Within the brief run, when a country's money increases in value, its sends out ended up more costly and imports ended up cheaper. This implies that the request for a country's sends out will diminish, whereas the request for imports will increase. As a result, the adjust of exchange will at first

compound, which implies that the nation will have a exchange shortfall.

Be that as it may, within the long run, the J curve impact predicts that the adjust of exchange will in the long run progress, and the exchange shortage will turn into a exchange overflow. This happens because the increment within the cost of sends out due to the appreciation of the currency will in the long run lead to a diminish within the amount of trades requested. At the same time, the diminish within the price of imports due to the appreciation of the money will in the long run lead to an increment within the amount of imports requested. Over time, these changes in request will cause a move within the adjust of exchange, coming about in a exchange excess.

In this manner, the Jcurve impact portrays the short-term weakening within the adjust of exchange that happens when a money increases in value, taken after by a long-term enhancement within the adjust of exchange. This impact is named after the shape of the bend that's shaped when the adjust of exchange and the esteem of a country's cash are plotted against time, which looks like a "J" shape.

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This interval is wider than the confidence interval in part (a) and the prediction interval in part (b) because it is based on the entire population of metal pieces, not just a sample.

(a) To find a 99% confidence interval on the mean diameter, we can use the t-distribution with n-1 degrees of freedom since the population standard deviation is not known. The formula for the confidence interval is:

CI = x ± tα/2,s/√n

where x is the sample mean, s is the sample standard deviation, n is the sample size, and tα/2 is the t-value with (n-1) degrees of freedom for the desired level of confidence α.

Plugging in the values, we get:

CI = 1.0056 ± t0.005/2,0.0246/√9

= 1.0056 ± 0.025

= (0.9806, 1.0306)

Therefore, we can be 99% confident that the true mean diameter of the metal pieces produced by the machine is between 0.9806 and 1.0306 centimeters.

(b) To compute a 99% prediction interval on a measured diameter of a single metal piece taken from the machine, we can use the formula:

PI = x ± tα/2,s(1 + 1/n)√(1 + 1/n)

where x is the point estimate of the diameter (in this case, the sample mean), s is the sample standard deviation, n is the sample size, and tα/2 is the t-value with (n-1) degrees of freedom for the desired level of confidence α.

Plugging in the values, we get:

PI = 1.0056 ± t0.005/2,0.0246(1 + 1/9)√(1 + 1/9)

= 1.0056 ± 0.052

= (0.9536, 1.0576)

Therefore, we can be 99% confident that a single metal piece produced by the machine will have a diameter between 0.9536 and 1.0576 centimeters.

(c) To find the 99% tolerance limits that will contain 95% of the metal pieces produced by this machine, we can use the formula:

TL = x ± kσ

where x is the sample mean, σ is the population standard deviation (which is estimated by the sample standard deviation s), k is the number of standard deviations from the mean that will contain the desired percentage of the population (in this case, 95% or 1.96 standard deviations for a normal distribution).

Plugging in the values, we get:

TL = 1.0056 ± 1.96(0.0246)

= (0.9573, 1.0539)

Therefore, we can be 99% confident that 95% of the metal pieces produced by the machine will have diameters between 0.9573 and 1.0539 centimeters. This interval is wider than the confidence interval in part (a) and the prediction interval in part (b) because it is based on the entire population of metal pieces, not just a sample.

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Check the picture below.

Answer:

Step-by-step explanation:

A = length x width = (2w + 5)(w) = 2w² + 5w

P = 2(2w + 5) + 2w = 6w + 10

To graph:  sorry, Brainly doesn't have graphing tools so I'll just have to describe it

A:  parabola, opens up, vertex at (-1.25, -3,124), crosses x axis at (-2.5, 0) and (0,0)

P:  straight line, slants up, with a slope of 6, y-intercept of 10, crosses x axis at (-1.667, 0)

FYI, the 2 graphs intersect at 2 points:  (-2, 2) and (2.5, 25)

There were 3097 6th-grade students who went on the field trip to see the play at the theater.

We have,

If 95% of the 3260 seats in the theater were filled by the 6th-grade students,

We can find the total number of students by multiplying the total number of seats by the fill percentage as a decimal:

Number of 6th graders = 3260 x 0.95

Number of 6th graders = 3097

Therefore,

There were 3097 6th-grade students who went on the field trip to see the play at the theater.

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The following statements are always true regarding the given diagram having angles: m<3+m<4+m<5=180, m<5+m<6=180, m<2+m<3=m<6.

Statement 2 is always true because the sum of the three angles in a triangle is always 180 degrees.

Statement 3 is always true because the sum of the angles on a straight line is 180 degrees.

Statement 4 is always true because angles 2, 3, and 6 are opposite angles, which means they are congruent.

Thus, statements 1 and 5 are not always true. The sum of angles 3, 4, and 5 could be greater or less than the measure of angle 5. The sum of angles 2, 3, and 5 could be greater or less than the measure of angle 3.

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The radius of the diameter X is 6cm. Option D

To determine the radius of the circle, we have;

It is important to that the formula for diameter

The formula for calculating the diameter is given as;

d = r/2

Such that the parameters are given as;

From the information given, we have that;

Diameter, d = 12cm

Now, we have to substitute the values

Radius =diameter/2

Radius = 12/2

Radius = 6cm

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The perimeter of the shape above is 22.22 units

the area of the shape above is 26 square units

We can see from the diagram shown, that the shape is made up of a semicircle below and a triangle above.

Now, the formula for calculating the area of a triangle is expressed as;

A = 1/2bh

Such that the parameters are;

Now, substitute the values

Area = 1/2 × 7 ×6

Multiply the values

Area = 42/2

Area = 26 square units

The formula for perimeter of a triangle is;

Perimeter = (a + b + c)

Perimeter = 6 + 7 + 9. 22

Add the values

Perimeter = 22. 22 units

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Answer: the visitor would save $8 with the coupon.

Step-by-step explanation: 10% of $80 = 0.1 x $80 = $8

The x-intercepts represent a zero profit.

The maximum value of the graph represents the maximum profit.

The function increases up till the vertex and decreases after it.

This means that the profit increases as it reaches the peak at the vertex.

It decreases after the vertex up till it reaches zero.

On the left of the first zero and on the right of the second zero, the profits are negative.

An approximate average rate of change of the graph from x = 3 to x =5 represents the reduction in profit from 3 to 5

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The original sample box had a volume of 343 cubic cm, which is half the volume of the new sample box.

Since the height of the new sample box is twice as long as the original box, its height will be 2×7=14 cm.

The length and width remain the same at 7 cm.

The volume of the new sample box is given by the formula:

V = lwh

Substituting the values, we get:

V = (7)(7)(14) = 686 cubic cm

Therefore, the volume of the new sample box is 686 cubic cm.

Comparing the volumes of the two boxes, we see that the new sample box has a larger volume than the original sample box.

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When we create a budget for television purchase as a technique, this can help you avoid overspending and ensure that you stay within your means.

It is best to ensure we you are purchasing a television that meets your needs and is within your budget. We can look for reviews, compare prices and features of different models to make an informed decision.

One can also try to purchase during sales, holidays and special events which is when retailers offer discounts and promotions.

Finally, when we create a budget, this can help you avoid overspending and ensure that you stay within your means. By setting a limit on how much you're willing to spend, you can focus on finding the best deal within your budget.

Full question "The discussion above offers a third tip for saving money on purchases which is create a budget. Write a short paragraph, consisting of 125 words or more, that applies these techniques to purchasing a television".

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The velocity of the meteorite is 4 km per sec.

Given that, a meteorite is approaching the earth and is 10000 km away from earth,

we need to find the velocity,

v = k / √d

v = 400 / √10000

v = 400 / 100

v = 4 km per sec.

Hence, the velocity of the meteorite is 4 km per sec.

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The velocity at a distance of 6,889 kilometers is 6.795 Km/ sec.

We have,

The velocity v of a meteorite approaching earth is V = k/√d.

The distance from center of Earth = 8836

and, Velocity = 6 Km/ s

So, using the formula for velocity

6 = k/√8836

6 = k/94

k= 564 Km

Now, velocity at 6689 Km

V = 564/ √6889

V =6.795 km/sec

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The point that satisfies y = -3-x is (0,-3), the point that satisfies y = x-3 is (0,-3), the point that satisfies y = 3x+2 is (0,2), the point that satisfies y = 3x -2 is (0,-2), the point that satisfies y = -3x+2 is (0,2). The graph is shown below.

To find the points that satisfy the equation y = -3 - x, we can substitute different values of x and solve for y.

When x = 0, y = -3 - 0 = -3, so one point is (0, -3).

When x = 1, y = -3 - 1 = -4, so another point is (1, -4).

When x = -1, y = -3 - (-1) = -2, so another point is (-1, -2).

By repeating this process for different values of x, we can find more points that satisfy the equation.

To find the points that satisfy the equation y = x - 3, we can again substitute different values of x and solve for y.

When x = 0, y = 0 - 3 = -3, so one point is (0, -3).

When x = 1, y = 1 - 3 = -2, so another point is (1, -2).

When x = -1, y = -1 - 3 = -4, so another point is (-1, -4).

To find the points that satisfy the equation y = 3x + 2, we can once again substitute different values of x and solve for y.

When x = 0, y = 3(0) + 2 = 2, so one point is (0, 2).

When x = 1, y = 3(1) + 2 = 5, so another point is (1, 5).

When x = -1, y = 3(-1) + 2 = -1, so another point is (-1, -1).

To find the points that satisfy the equation y = 3x - 2, we can once again substitute different values of x and solve for y.

When x = 0, y = 3(0) - 2 = -2, so one point is (0, -2).

When x = 1, y = 3(1) - 2 = 1, so another point is (1, 1).

When x = -1, y = 3(-1) - 2 = -5, so another point is (-1, -5).

To find the points that satisfy the equation y = -3x + 2, we can once again substitute different values of x and solve for y.

When x = 0, y = -3(0) + 2 = 2, so one point is (0, 2).

When x = 1, y = -3(1) + 2 = -1, so another point is (1, -1).

When x = -1, y = -3(-1) + 2 = 5, so another point is (-1, 5).

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The figure that has two more faces than a rectangular prism is a Square pyramid.

There are precisely six faces that a rectangular prism contains, which consists of a pair of identical rectangles for its top and bottom planes as well as four lateral faces consisting of corresponding right-angled, congruent rectangles. Hence, a solid figure that has two more sides than the aforementioned rectangular prism could only have eight total faces without exception.

An example of such an entity is a square pyramid whose base constitutes of four equal-length sides with four corresponding triangular surfaces converging at one single vertex on the summit's tip. Within this context, it possesses five faces (one square and four isosceles triangles), thus exceeding by two faces compared to the former geometric model.

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Answer:

Colbie did not complete the square correctly.

Colbie failed to add the square of half the coefficient of the term in x to both sides of the equation. She only added 25 to the left side of the equation. She also factored x² + 10x + 25 incorrectly by using a subtraction sign in the binomial rather than an addition sign.

Step-by-step explanation:

Given quadratic equation:

[tex]2x^2+20x-48=0[/tex]

As the leading coefficient is not one, to complete the square we must first divide both sides of the equation by the leading coefficient, 2:

[tex]\dfrac{2x^2+20x-48}{2}=\dfrac{0}{2}[/tex]

[tex]x^2+10x-24=0[/tex]

Now move the constant to the right side of the equation by adding 24 to both sides of the equation:

[tex]\begin{array}{rcr}x^2+10x-24&=&0\\\vphantom{\dfrac12}+24 & &+24\\\cline{1-3}\vphantom{\dfrac12}x^2+10x\phantom{-24.}&=&24\end{array}[/tex]

We need to make the left side of the equation a perfect square trinomial. To do this, add the square of half the coefficient of the term in x to both sides of the equation.

The coefficient of the term in x is 10. Therefore, the square of half of this is 25:

[tex]\left(\dfrac{10}{2}\right)^2=5^2=25[/tex]

This is the point at which Colbie made her first mistake. She didn't add the square of half the coefficient of the term in x to both sides of the equation - she only added it to the left side.

Add 25 to both sides of the equation:

[tex]x^2+10x+25=24+25[/tex]

[tex]x^2+10x+25=49[/tex]

To continue to solve the equation, factor the perfect square trinomial on the left side of the equation:

[tex](x+5)^2=49[/tex]

↑ Colbie made her second mistake here. She factored x² + 10x + 25 incorrectly by using a subtraction sign in the binomial rather than an addition sign.

Square root both sides:

[tex]\sqrt{(x+5)^2}=\sqrt{49}[/tex]

[tex]x+5=\pm7[/tex]

Subtract 5 from both sides:

[tex]x+5-5=-5\pm7[/tex]

[tex]x=-5\pm7[/tex]

Therefore, the solutions are:

[tex]x=-5+7=2[/tex]

[tex]x=-5-7=-12[/tex]

Answer:

Step-by-step explanation:

1. The line of best fit must have an equal number of points above and below the line

2. The line of best fit could be used as a predictions showing a trend in data

The total number of employees in the company is 297 if  ratio of union members to nonunion members working for a company is 4 to 7

The given ratio of union members to nonunion members, which is 4 to 7. This means that for every 4 union members, there are 7 nonunion members.

We are also given that there are 108 union members working for the company.

The total number of employees in the company be "x".

Let us from a proportional equation

4/11 = 108/x

To solve for x, we can cross-multiply and simplify:

4x = 1188

x = 297

Therefore, the total number of employees in the company is 297.

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1.) [tex]6p=30[/tex]

2.) Sebastian bought a pack of 30 mechanical pencils and plans to give the same number of pencils each to 6 friends.

Let a varible such as p be the number of pencils given by him to each students.

Now we need to find p we need to divide 30 by 6, we get

[tex]p = \frac{30}{6}[/tex]    

 [tex]to[/tex]

[tex]6p = 30[/tex]

Thus, the equation can he use to find p, the number of pencils each friend will receive is: [tex]6p = 30[/tex]

Answer:

[tex]6p = 30[/tex]

Step-by-step explanation:

3dxnn have's the explanation.

Step-by-step explanation:

the volume of a sphere is

4/3 × pi × r³

the original sphere had a radius of 3.

now, after a dilation of factor 4 the radius is 3×4 = 12.

the volume of that sphere is then

4/3 × pi × 12³ = 4/3 × pi × 1728 = 2304pi

Let's assume the price of a citron is "x" units and the price of a fragrant wood apple is "y" units.

From the given information, we can form two equations:

7x + 9y = 135 ...(1)

9x + 7y = 137 ...(2)

We can solve this system of equations using the elimination method. Multiplying equation (1) by 9 and equation (2) by 7, we get:

63x + 81y = 1215 ...(3)

63x + 49y = 959 ...(4)

Subtracting equation (4) from equation (3), we get:

32y = 256

y = 8

Substituting the value of y in equation (1), we get:

7x + 9(8) = 135

7x + 72 = 135

7x = 63

x = 9

Therefore, the price of a citron is 9 units and the price of a fragrant wood apple is 8 units.

The solution to the multiplication of both functions is:

2x³ - x² - 4x + 3

To multiply a function by another function, multiply their outputs. For example, if f (x) = 2x and g(x) = x + 1, then fg(3) = f (3) × g(3) = 6 × 4 = 24. fg(x) = 2x(x + 1) = 2x² + x.

We are told that the domain for f(x) and g(x) is the set of all real numbers.

The functions are given as:

f(x) = 2x² + x - 3

g(x) = x - 1

Thus:

f(x) · g(x) = (2x² + x - 3) * (x - 1)

= 2x³ + x² - 3x - 2x² - x + 3

= 2x³ - x² - 4x + 3

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Answer: 9

Step-by-step explanation: volume is l x w x h, so 9 x 9 x height = 729

9 x 9 = 81, so 81 x height = 729

by dividing 729 / 81, you get 9

Answer: The answer is H=9.

The reason of this is because the branch of mathematics concerned with the shape of individual objects, spatial relationships among various objects, and the properties of surrounding space.

Hence,

We can see that thats the answer because volume is l x w x h, so 9 x 9 x height = 7299 x 9 = 81, so 81 x height = 729by divide 729 / 81, you get 9

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Step-by-step explanation: Please give Brainliest.

Hope this helps!!!!

I can answer more questions if you want.