Use these equations to find ∂z/∂x and ∂z/∂y for the following.
x8 + y8 + z5 = 6xyz

Answer:

(4, -2)

Step-by-step explanation:

The midpoint of two points is found by averaging the X coordinates and averaging the Y coordinates to create a new pair.

X: (5+3)/2     = 4

Y: (-10+6)/2   = -2

Answer:

(4,-2)

Step-by-step explanation:

add the x and divide by two. do the same with the y. this is the same as finding the average

Answer:

1875

Step-by-step explanation:

750 x 2.5 = 1,875

Answer:

lateral surface area =perimeter of base×height=

={4+7+7+11)×6=174 km²

Step-by-step explanation:

Answer:

[tex]14/50\\[/tex]

Step-by-step explanation:

The equation for sine is sine = opposite/ hypotenuse

The opposite of W is 14 and the hypotenuse the the side across the 90° angle, which is 50.

So, when you set up the equation it should be [tex]14/50[/tex].

Answer:

[tex]\frac{75}{4\pi }[/tex] inches or approximately 5.97 inches  

Step-by-step explanation:

Use the cone volume formula: V = [tex]\pi[/tex]r²[tex]\frac{h}{3}[/tex]

The diameter is 8 inches, so the radius will be 4 inches.

Plug in the radius and volume, and solve for h

V = [tex]\pi[/tex]r²[tex]\frac{h}{3}[/tex]

100 = [tex]\pi[/tex](4²)([tex]\frac{h}{3}[/tex])

100 = 16[tex]\pi[/tex][tex]\frac{h}{3}[/tex]

Divide each side by 16[tex]\pi[/tex]

[tex]\frac{25}{4\pi }[/tex] = [tex]\frac{h}{3}[/tex]

Cross multiply and solve for h:

4[tex]\pi[/tex]h = 75

h = [tex]\frac{75}{4\pi }[/tex]

So, the cone's height is [tex]\frac{75}{4\pi }[/tex] or approximately 5.97 inches  

The measure of each angle in the triangle is 24 degrees, 36 degrees, and 120 degrees.

Let's denote the three angles of the triangle as A, B, and C. According to the given ratio of 2:3:10, we can assign the values 2x, 3x, and 10x to angles A, B, and C, respectively, where x is a common factor.

The sum of the angle measures in a triangle is always 180 degrees. Therefore, we can set up the following equation:

2x + 3x + 10x = 180

Simplifying the equation, we get:

15x = 180

Dividing both sides by 15, we find:

x = 12

Now we can substitute x back into the expressions for each angle:

Angle A = 2x = 2(12) = 24 degrees

Angle B = 3x = 3(12) = 36 degrees

Angle C = 10x = 10(12) = 120 degrees

Therefore, the measure of each angle in the triangle is 24 degrees, 36 degrees, and 120 degrees.

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Step-by-step explanation:

x - 3 > -4

= x > -4+3

= x > -1 _ Answer

The general solution of the given equation, x^2(dw/dx) = sqrt(w)(3x+2), expressed explicitly as a function of the independent variable, is w(x) = (1/27)((9x^2 + 6x + C)^3), where C is an arbitrary constant.

To solve the given equation, we can separate the variables and integrate.

First, rewrite the equation as

(1/sqrt(w))dw = (3x+2)/x^2 dx.

Integrate both sides with respect to their respective variables:

∫(1/sqrt(w))dw = ∫(3x+2)/x^2 dx.

The integral of (1/sqrt(w)) with respect to w is 2√w, and the integral of (3x+2)/x^2 with respect to x can be found using partial fractions or another suitable method.

After integrating and simplifying, we obtain:

2√w = (1/27)(9x^2 + 6x + C),

where C is the arbitrary constant.

To find the explicit solution, isolate w by squaring both sides:

w(x) = (1/27)((9x^2 + 6x + C)^3),

where w(x) is the function expressing the solution explicitly in terms of the independent variable x, and C is the arbitrary constant.

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Answer:

Just do 8.4 times 7

Step-by-step explanation:

8.4 times 7 = 58.8

a. Using the z-score, the probability of a randomly chosen mouse having a mass of less than 20.7 grams is approximately 0.2794.

b. The probability that a randomly chosen mouse has a mass more than 21.02g is 0.0985

c.  The probability of a mouse having a mass between 20.65 and 20.95 grams is approximately 0.6474.

d. About 10% of all mice have a mass of less than 20.5649 grams.

a) To find the probability that a randomly chosen mouse has a mass of less than 20.7 grams, we can use the normal distribution.

First, we need to standardize the value of 20.7 grams using the formula: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

The z-score for the data is;

z = (20.7 - 20.8) / 0.17 = -0.5882

P = 0.2794

b) To find the probability that a randomly chosen mouse has a mass of more than 21.02 grams, we also need to standardize the value:

z = (21.02 - 20.8) / 0.17 = 1.2941

P = 0.0985

Using the standard normal distribution table or a calculator, we find that the probability corresponding to this z-value is approximately 0.0985.

c) To find the proportion of mice that have a mass between 20.65 and 20.95 grams, we can standardize both values:

For 20.65 grams:

z₁ = (20.65 - 20.8) / 0.17 = -0.8824

For 20.95 grams:

z₂ = (20.95 - 20.8) / 0.17 = 0.8824

Using the standard normal distribution table or a calculator, we can find the probabilities corresponding to these z-values. The probability of a mouse having a mass between 20.65 and 20.95 grams is approximately 0.6474.

d) To find the mass of mice that corresponds to the 10th percentile, we need to find the z-score associated with the 10th percentile. We can use the standard normal distribution table or a calculator to find this value.

The z-score associated with the 10th percentile is approximately -1.2816.

Next, we can use the z-score formula to find the corresponding mass value:

z = (x - μ) / σ

-1.2816 = (x - 20.8) / 0.17

Solving for x, we get:

x = -1.2816 * 0.17 + 20.8 ≈ 20.5649 grams

Therefore, 10% of all mice have a mass of less than 20.5649 grams.

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The set of vectors (b) (-3,0,4), (5,-1,2), (1,1,3) are linearly dependent. The other given sets of vectors in R3 are linearly independent.

Let's review the given sets of vectors in R₃ to determine which ones are linearly dependent.

(a) (4.-1,2), (-4, 10, 2).

To check if the given set is linearly dependent or not, we need to check whether there are non-zero scalars such that their linear combination is equal to

0.a(4,-1,2) + b(-4,10,2) = (0,0,0).

The system of equations can be written as;

4a - 4b = 0-1a + 10b = 00a + 2b = 0.

Clearly, a = b = 0 is the only solution.

So, the set is linearly independent.

(b) (-3,0,4), (5,-1,2), (1, 1,3)

To check if the given set is linearly dependent or not, we need to check whether there are non-zero scalars such that their linear combination is equal to

0.a(-3,0,4) + b(5,-1,2) + c(1,1,3) = (0,0,0).

The system of equations can be written as;

-3a + 5b + c = 00a - b + c = 00a + 2b + 3c = 0

Clearly, a = 2, b = 1, and c = -2 is a solution.

So, the set is linearly dependent.

(c) (8.-1.3). (4,0,1).

To check if the given set is linearly dependent or not, we need to check whether there are non-zero scalars such that their linear combination is equal to

0.a(8,-1,3) + b(4,0,1) = (0,0,0).

The system of equations can be written as;

8a + 4b = 01a + 0b = 0-3a + b = 0.

Clearly, a = b = 0 is the only solution.

So, the set is linearly independent.

(d) (-2.0, 1), (3, 2, 5), (6,-1, 1), (7,0.-2).

To check if the given set is linearly dependent or not, we need to check whether there are non-zero scalars such that their linear combination is equal to

0.a(-2,0,1) + b(3,2,5) + c(6,-1,1) + d(7,0,-2) = (0,0,0)

The system of equations can be written as;

-2a + 3b + 6c + 7d = 00a + 2b - c = 00a + 5b + c - 2d = 0

Clearly, a = b = c = d = 0 is the only solution.

So, the set is linearly independent.

Therefore, The set of vectors (b) (-3,0,4), (5,-1,2), (1,1,3) are linearly dependent. The other given sets of vectors in R₃ are linearly independent.

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Answer:(2,36)and (3,54)

Step-by-step explanation:

Answer:

(2, 36) and (3, 54)

Step-by-step explanation:

I just answer the question from iready and I got it correct.

Answer:

a=25

b=7

Step-by-step explanation:

Answer:

GASOLINE The table gives the cost of a

gallon of gasoline at two stations.

How much more does gasoline cost at

Gas For Less than at Cut-Rate?

Step-by-step explanation:

Answer:

Selling price of the laptop is $600.

Step-by-step explanation:

Let the sale price of the laptop = $x

Regular price of the laptop = $750

Discount on each computer = 20%

Selling price of the laptop 'x' = 750 - (20% of 750)

                                                = 750 - [tex](\frac{20}{100}\times 750)[/tex]

                                                = 750 - 150

                                                = $600

Therefore, selling price of the laptop is $600.

Answer:

£139

Step-by-step explanation:

£12.50 * 11 = 137.50

137.50 + 1.50 = £139

Answer:

137.5 + 1.50 = £139

Step-by-step explanation:

Please Give brainliest

Answer:

c

Step-by-step explanation:

circumference = perimeter around circle

Answer:

e) yes, symmetric around the y-axis

f) minimum at (0,0)

g) x-intercept at 0

Step-by-step explanation:

Answer:

You add (9+3)

Step-by-step explanation:

because PEMDAS evaluates the parenthesis first,

Answer:

It' B

Step-by-step explanation:

I got a 100 on the test

The sum of the given function is  2x^3 +  log(x+4) + 100

Given the following functions

f(x)=2x^3 and;

g(x) = log(x+4) + 100

Take the sum of the functions

f(x) + g(x) = 2x^3 +  log(x+4) + 100

Hence the sum of the given function is  2x^3 +  log(x+4) + 100

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The joint density f(x, y) = 1 for -y < x < y and 0 < y < 1, or 0 elsewhere, the variables X and Y are uncorrelated but not independent.

The problem requires the determination of whether the random variables X and Y are independent and uncorrelated. For that, the expectation of the product of X and Y is needed. Evaluating E(XY). For the two variables X and Y, their joint density is given as:

f(x, y) = 1 for -y < x < y and 0 < y < 1, or 0 elsewhere

To evaluate the expectation of XY, multiply the variables X and Y as follows: E(XY) = ∫∫xy f(x,y) dy dx.

We evaluate the above equation over the range of the variables.

Since the domain of the density function is given by -y < x < y and 0 < y < 1, E(XY) = ∫∫xy f(x,y) dy dx = ∫0¹ ∫-[tex]y^{y}[/tex] xy dy dx

The above equation can be simplified as:

E(XY) = ∫0¹ (1/3)*y³ dy = 1/12

Hence the covariance between X and Y is given by: Cov (X, Y) = E(XY) - E(X)E(Y) = E(XY) = 1/12.

The variance of X is calculated as follows: E(X) = ∫∫xf(x, y) dy dx

For the two variables X and Y, their joint density is given as: f(x, y) = 1 for -y < x < y and 0 < y < 1, or 0 elsewhere.

Thus, E(X) = ∫∫x f(x, y) dy dx= ∫0¹ ∫-[tex]y^{y}[/tex] x dy dx= 0.

Hence, Var(X) = E(X²) - [E(X)]² = E(X²) - 0² = E(X²).

The variance of X² is calculated as follows:

E(X²) = ∫∫x² f(x, y) dy dx. For the two variables X and Y, their joint density is given as: f(x, y) = 1 for -y < x < y and 0 < y < 1, or 0 elsewhere.

Thus, E(X²) = ∫∫x² f(x, y) dy dx= ∫0¹ ∫-[tex]y^{y}[/tex] x² dy dx= 1/3

Hence, Var(X) = E(X²) - [E(X)] ² = 1/3 - 0 = 1/3

The variance of Y² is calculated as follows: E(Y²) = ∫∫y² f(x, y) dy dx

For the two variables X and Y, their joint density is given as: f(x, y) = 1 for -y < x < y and 0 < y < 1, or 0 elsewhere. Thus, E(Y²) = ∫∫y² f(x, y) dy dx= ∫0¹ ∫-[tex]y^{y}[/tex]y² dy dx= 1/3

Hence Var(Y) = E(Y²) - [E(Y)]² = 1/3 - [E(Y)]²

The covariance between X and Y is given by: Cov (X, Y) = E(XY) - E(X)E(Y) = 1/12 - 0 = 1/12.

We can evaluate the correlation between X and Y as: Corr (X, Y) = Cov (X, Y) / √Var (X) Var(Y)= (1/12) / [(1/3) * (1/3)] = 1/4

Thus, the variables X and Y are uncorrelated but not independent.

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Answer:

40 units

Step-by-step explanation:

For a square, all the sides are equal and the interior angles are equal and all equal to 90. Hence;

m<BOJ = 90 degrees

m<BOJ = 4x - 6

Equating both to get x;

4x - 6 = 90

4x = 90+6

4x = 96

x = 96/4

x = 24

Since all the sides are equal, hence BO = JO = 2x-8

JO = 2x - 8

Substitute x = 24 into JO

JO = 2(24) - 8

JO = 48 - 8

JO = 40

Hence the measure of JO is 40 units

The standard deviation for the given test scores is 20, and the variance is 400

We have,

To find the standard deviation and variance for the given test scores, we can follow these steps:

Calculate the mean (average) of the test scores:

Mean (μ) = (92 + 92 + 92 + 52 + 52) / 5 = 80

Calculate the deviation of each test score from the mean:

Deviation = Test score - Mean

For the given test scores:

Deviations = (92 - 80), (92 - 80), (92 - 80), (52 - 80), (52 - 80)

= 12, 12, 12, -28, -28

Square each deviation:

Squared Deviations = Deviation²

Squared Deviations = 12², 12², 12², (-28)², (-28)²

= 144, 144, 144, 784, 784

Calculate the variance:

Variance = (Sum of Squared Deviations) / (Number of Scores)

Variance = (144 + 144 + 144 + 784 + 784) / 5

= 2000 / 5

= 400

Calculate the standard deviation:

Standard Deviation = √Variance

Standard Deviation = √400

= 20

Therefore,

The standard deviation for the given test scores is 20, and the variance is 400.

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Answer:

72 cm

Step-by-step explanation:

It would be multiplied by 8 so the length would become 72 cm

Answer:

the answer is B

I hope it helps have a great day

Answer:

2 + n < 14

Step-by-step explanation:

Hey!

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

Let's work this word by word.

"Two more than a number is less than 14"

--------------------------------------------------------------------------------------------------------------

"Two more than"

⇒ 2 +

"A number"

⇒ 2 + n

"Is less than"

⇒2 + n <

"14"

⇒2 + n < 14

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

Hope I Helped, Feel free to ask any questions to clarify :)

Have a great day!

More Love, More Peace, Less Hate.

       -Aadi x

The random variable x is uniformly distributed between 10 and 20. To compute the probability of 10 ≤ x ≤ 15, Hence, the probability of 10 ≤ x ≤ 15 is 0.5.

Since x is uniformly distributed between 10 and 20, the probability density function (PDF) of x is a constant within this range. The PDF is given by the reciprocal of the range, which in this case is 1/10.

To find the probability of 10 ≤ x ≤ 15, we need to calculate the area under the PDF curve between 10 and 15. Since the PDF is constant, the area under the curve corresponds to the proportion of the total range that falls within this interval.

The width of the interval 10 ≤ x ≤ 15 is 15 - 10 = 5. The total range of x is 20 - 10 = 10. Therefore, the proportion of the total range that falls within the interval is 5/10 = 0.5.

Hence, the probability of 10 ≤ x ≤ 15 is 0.5. This means that there is a 50% chance that a randomly chosen value of x will fall within the interval from 10 to 15.

It is important to note that in a uniform distribution, the probability of any subinterval within the range is proportional to the width of that subinterval. In this case, since the subinterval 10 ≤ x ≤ 15 has a width of 5 out of the total range of 10, the probability is 0.5 or 50%.

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The correct interpretation of `f(6) = 44,500` is that in the year 2011, a company that opened in 2005 will produce 44,500 units of products is the answer.

Given, `f(t)` be the number of units produced by a company `t` years after opening in 2005.

According to the question, `f(6) = 44,500`. It means six years after the company opened, which is in the year 2011, the company will produce 44,500 units of products.

The statement "six years from now, 44,500 units will be produced" (option a) is not correct because the year is not specified. The company will produce 44,500 units of products in the year 2011, not six years from the present.

The statement "in 2009, 44,500 units are produced" (option b) is not correct because in the year 2009, the company will only have been open for four years, and not enough information is provided to calculate the number of units produced.

The statement "in 2006, 44,500 units are produced" (option c) is not correct because in the year 2006, the company will have only been open for one year, and not enough information is provided to calculate the number of units produced.

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Answer:

972 cubic feet

Step-by-step explanation:

12 by 9 by 7.5

+

1.5 by 9  by 12

Answer:

891 ft³

Step-by-step explanation:

First I'll find the volume of the rectangular prism. (l * w * h)

12 * 9 * 7.5

Multiply 12 by 9 to get 108.

108 * 7.5

Now, multiply 108 by 7.5 to get 810. (756 + 54 = 810)

810

Now for the triangular prism. (1/2(l * w * h))

1/2(12 * 9 * 1.5) (I figured the height was 1.5 since the height of the rectangular prism was 7.5; the entire figure's height was 9)

Multiply 12 by 9 to get 108.

1/2(108 * 1.5)

Multiply 108 by 1.5 to get 162. (108 + 54 = 162)

1/2(162)

Multiply 162 by 1/2 to get 81. (162/2)

81

Now add that to 810 to get 891.

810 + 81

891 ft³

The volume of the garage is 891 ft³.