4(6x + 87)

9(5 x 89p)

(45 - 9) x 12

To find the partial derivative of z with respect to x, we need to differentiate the equation f(x,y) with respect to x while treating y as a constant. Using the formal definition of the partial derivative, we have:

∂z/∂x = lim(h→0) [f(x+h,y) - f(x,y)]/h
= lim(h→0) [(12(x+h)² - 9(x+h)y + 16y²) - (12x² - 9xy + 16y²)]/h
= lim(h→0) [24xh + 12h² - 9yh]/h
= lim(h→0) (24x + 12h - 9y)
= 24x - 9y

Similarly, to find the partial derivative of z with respect to y, we differentiate the equation with respect to y while treating x as a constant:

∂z/∂y = lim(k→0) [f(x,y+k) - f(x,y)]/k
= lim(k→0) [12x² - 9x(y+k) + 16(y+k)² - (12x² - 9xy + 16y²)]/k
= lim(k→0) (32k - 9x)
= -9x

Therefore, the partial derivatives of z with respect to x and y are:

∂z/∂x = 24x - 9y
∂z/∂y = -9x

This is the explanation for finding the partial derivatives of z with respect to x and y using the formal definition of the partial derivative. The derivative is a measure of the rate at which a function changes with respect to its input variables, while an equation is a statement that two expressions are equal. In this case, we used an equation to represent a function of two variables and found its partial derivatives with respect to each variable using the formal definition of the partial derivative.

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A bar graph would be the best graphical representation to display this type of data.

Given data ,

A random sample of 50 purchases from a particular pharmacy was taken.

The type of item purchased was recorded, and a table of the data was created.

Now , Item Purchased Health & Medicine Beauty Household Grocery

Number of Purchases 10 18 15 7

A bar graph would be the best graphical representation to display this type of data. The bar graph would have four bars representing the different categories of items purchased, and the height of each bar would represent the number of purchases in that category.

Hence , the bar graph is solved

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Opportunity cost is the price of giving up an option. An opportunity cost is the price you pay for selecting a particular option over another. Opportunity cost is the benefits you lose by choosing one alternative over another one.”

The value of the next-highest-valued alternative use of a resource is what economists mean when they talk about its "opportunity cost." You cannot, for instance, read a book at home during the time you would have spent seeing a movie and spend the money you would have spent on something else.

Opportunity cost is frequently referred to as the second-best option. The loss of benefit that would have been realized if a different option had been taken is sometimes referred to as the alternative cost. The loss of advantage as a result of a change in decision is another way to explain it.

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Answer:

She owes her brother $7.

Step-by-step explanation:

Subtract $18 made from dogsitting from the total (which is $25).

addition expression : $18 + x =$25

                      check :  $25 - $18 = $7

$7 is what she needs to finish paying back.  

For the information given in the statement you have:

*For Joan

Because the pack of socks is $ 7 and x is the cost of each T-shirt.

*For Kylie

Because the cost of the water balloon package is $3 and x is the cost of each T-shirt.

Answer:   B

Step-by-step explanation:Because you look at the the value place and make sure it is under zero and also make sure it is in the correct spot.

plz leave a like

Answer:

6 percent?

Step-by-step explanation:

.

It is true that in a one-way ANOVA situation, if the overall F value is statistically significant, then you know that all of the means are significantly different from one another.

ANOVA, which represents the analysis of variance, is a statistical test used to examine the distinction between the means of more than two groups.

One independent variable is used in a one-way ANOVA, while two independent variables are used in a two-way ANOVA.

In a one-way ANOVA scenario, the overall F value must be statistically significant for more than two of the means to be significantly different.

thus we can say that the given statement is true.

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The total volume of the two circular cylinders intersecting perpendicularly is\(V=πr2+πr3=πr2(1+r)\).

The volume of the two circular cylinders intersecting perpendicularly can be calculated using the triple integral formula in rectangular coordinates. The triple integral formula is V=∫∫∫dzdydx.

We can separate the integral into three components. The x-component is ∫dx from \(-√r2-y2 to √r2-y2\). The y-component is ∫dy from -r to r. The z-component is ∫dz from 0 to r.

Substituting the components into the equation for the triple integral, we get \(V=∫-rrdr∫-√r2-y2√r2-y2dx∫0rdz\).

We can solve the integral by splitting the y-component into two pieces:

\(V=∫-rrdr∫-r0dx∫0rdz+∫-rrdr∫0√r2-y2dx∫0rdz\)

The first integral can be solved easily and yields V=πr2. The second integral can be solved using the substitution u=r2-y2 and yields V=πr3.

Hence, the total volume of the two circular cylinders intersecting perpendicularly is V=πr2+πr3=πr2(1+r).

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The coefficient of determination is a measure of how well the regression model fits the observed data. The proportion of the total variation in the dependent variable that is explained by the independent variable(s).

The coefficient of determination (R-squared) is calculated as the square of the correlation coefficient (r) between the dependent and independent variables. In other words, R-squared = r^2. Given that the result is r = 0.653, we can calculate the coefficient of determination as follows: R-squared = (0.653)^2 = 0.426409. To express this as a percentage, we can multiply by 100: R-squared = 0.426409 * 100 = 42.64%.

Therefore, the coefficient of determination for the research project is approximately 42.64%. It indicates that 42.64% of the total variation in the dependent variable can be explained by the independent variable(s) included in the regression model.

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Answer:

The average rate of change of the function over the given interval is -6

Step-by-step explanation:

The function we want to find its average rate of change is;

F(x) = 17 - x^2

Mathematically, the average rate of change of a function F(x) over an interval (a,b) can be calculated as;

{F(b) - F(a)}/(b-a)

According to this question, a = 1 and b = 5

F(a) = F(1) = 17 -(1)^2 = 17 -1 = 16

F(b) = F(5) = 17 - 5^2 = 17-25 = -8

So making the substitution; we have

(-8)-16/(5-1) = -24/4 = -6

Answer:

A: -6

Step-by-step explanation:

When the measurement scale provides information regarding greater than or less than, but not how much greater or less, it is in the form of ordinal data.

Ordinal data is a type of categorical data, which is a type of data that fits into discrete categories, such as gender, or levels of education. Ordinal data does not provide numerical values for comparison, only information on the order of the categories.

For example, a survey may ask respondents to rate their opinion of a product on a scale of one to five. The scale provides information on the order of the categories (one being least favorable and five being most favorable), but it does not provide numerical values that can be used to calculate the average opinion of the product.

Mathematically, ordinal data is usually represented using an ordered set of numbers, with each number representing the order of the categories. For example, the survey mentioned above would be represented this way: 1, 2, 3, 4, 5. This set of numbers can then be used to calculate the median, mode, and range of the data. For example, the median value of the example survey would be 3, the mode would be 5, and the range would be 4 (5 - 1 = 4).

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In this triangle it is clear that the unknown side x is the hypotenuse of both the triangles that are being formed . So , let us take any one of the triangles and with it's length let us find the length of their hypotenuse which is side x .

= 5² + 5² = x² ( according to the pythagorean theorem the square on the hypotenuse will be equal to the sum of the squares on the other two legs )

= 25 + 25 = x²

= 50 = x²

= 7.0710678119 = x

But they have given that we have to round it off to the nearest tenths , so ;

= 7.0710678119 will be equal to = 7.10

= 7.1 = x

Therefore , the length of the unknown side x = 7.1 .

Part A

We were told that the submarine descends 480 feet in 24 seconds. Since it is descending,the distance would be negative. Let x represent the descent in 1 second. Thus, the expressions would be

- 480 = 24

x = 1

By cross multiplying, we have

x * 24 = 480 * 1

24x = - 480

x = - 480/24

Thus, the correct option is the thrd one

Part B

Let the constant rate be x ft/sec

This means that after 8 seconds, the elevation change would be

8 * x

= 8 feet

Finding the Least Common Multiple (LCM) of the denominators will allow us to turn the supplied fractions into like fractions by matching their denominators.

Any number of equal portions, or parts of a whole, are described by fractions. Fractions in standard English indicate the number of pieces of a specific size. 8, 3/4 of .Part of an entire is a fraction. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. When a fraction is true, its numerator is smaller than its denominator.

Finding the Least Common Multiple (LCM) of the denominators will allow us to turn the supplied fractions into like fractions by matching their denominators. Once this is done, the numerators of the fractions can be simply compared.

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True. The values that can be entered into a field are determined by the data type of the field.

The data type specifies what type of data can be stored in the field, such as text, numbers, dates, or boolean values. This helps ensure data consistency and accuracy within the field.
Field values that may be entered into a field are determined by the data type of the field. The data type defines the kind of values that can be stored in that specific field, ensuring that the information entered is consistent and accurate.

Data are collected by techniques such as measurement, observation, interrogation or analysis and are often represented as numbers or symbols that can be further processed. Data fields are data stored in unmanaged fields. Test data is data created during the execution of the test. Data analysis uses techniques such as computation, reasoning, discussion, presentation, visualization, or other post-mortem analysis. Before analysis, raw data (or raw data) is usually cleaned: outliers are removed and obvious devices or incorrect input data are corrected.

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Answer:

6.0 x 10^11

Step-by-step explanation:

Let me know if this is wrong :) I tried

a.  The probability that a randomly chosen bolt has a width between 947 and 958 mm is approximately 0.4060.

b. The approximate value of C such that a randomly chosen bolt has width less than C with probability 0.8531 is approximately 960.7 mm

a) To find the probability that a randomly chosen bolt has a width between 947 and 958 mm, we need to find the area under the normal curve between these two values. We can standardize the values using the z-score formula:

z1 = (947 - 950) / 10 = -0.3

z2 = (958 - 950) / 10 = 0.8

Using a standard normal distribution table or calculator, we can find the probabilities associated with these z-scores:

P(z < -0.3) = 0.3821

P(z < 0.8) = 0.7881

Then, the probability that a randomly chosen bolt has a width between 947 and 958 mm is:

P(947 < x < 958) = P(-0.3 < z < 0.8) = P(z < 0.8) - P(z < -0.3)

= 0.7881 - 0.3821

= 0.4060

Therefore, the probability that a randomly chosen bolt has a width between 947 and 958 mm is approximately 0.4060.

b) To find the approximate value of C such that a randomly chosen bolt has width less than C with probability 0.8531, we need to find the z-score corresponding to the 85.31th percentile of the standard normal distribution. We can use a standard normal distribution table or calculator to find this value:

z = 1.07

Then, we can use the z-score formula to find the corresponding value of C:

z = (C - 950) / 10

Solving for C, we get:

C = z * 10 + 950 = 1.07 * 10 + 950 = 960.7

Therefore, the approximate value of C such that a randomly chosen bolt has width less than C with probability 0.8531 is approximately 960.7 mm.

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The probability that a standard normal random variable z is between -2.4 and 0.4 is approximately 0.6472.

To find the probability that a standard normal random variable z is between -2.4 and 0.4, we can follow these steps:

Step 1: Look up the cumulative probability corresponding to -2.4 in the standard normal distribution table. The cumulative probability at -2.4 is approximately 0.0082.

Step 2: Look up the cumulative probability corresponding to 0.4 in the standard normal distribution table. The cumulative probability at 0.4 is approximately 0.6554.

Step 3: Subtract the cumulative probability at -2.4 from the cumulative probability at 0.4 to find the probability between the two values:

P(-2.4 < z < 0.4) = 0.6554 - 0.0082

= 0.6472.

Therefore, The probability that z is between -2.4 and 0.4, when z is a standard normal random variable, is approximately 0.6472. This means that there is a 64.72% chance that a randomly selected value from a standard normal distribution falls within the range of -2.4 to 0.4.

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In physics, work done refers to the transfer of energy that occurs when a force acts upon an object and displaces it in the direction of the force. Work can be categorized into three types: positive, negative, and zero work done.

Positive work is done when the force and displacement are in the same direction, resulting in the transfer of energy to the object. Negative work occurs when the force and displacement are in opposite directions, indicating that energy is being taken away from the object. Zero work is done when there is no displacement, regardless of the magnitude of the force applied.

The law of conservation of energy states that energy cannot be created or destroyed; it can only be transferred or transformed from one form to another. This principle holds that the total amount of energy in an isolated system remains constant over time.

In other words, energy can change its form (e.g., from potential to kinetic or thermal energy), but the total energy within the system remains unchanged. This fundamental law is crucial in understanding various phenomena and calculations in physics and plays a key role in analyzing the behavior of energy in different systems.

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Answer:

the answer is $5,000

Step-by-step explanation:

the question is asking what the initial value of the painting is and in the equation, they are trying to find out how much the painting will cost after t years. the 1.098 is how much the painting decreases each year and it is being multiplied by &5000 so $5000 is the original value of the painting.

Answer:

\(\boxed{44}\)

Step-by-step explanation:

\([-5+(-7)]^2-(7+3)^2\)

Resolving Parenthesis

\((-5-7)^2-(10)^2\\(-12)^2-100\\144-100\)

=> 44

Answer:

\(\boxed{44}\)

Step-by-step explanation:

\([-5+(-7)]^2-(7+3)^2\)

Solve for brackets first.

\([-12]^2-(10)^2\)

Solve the exponent or power.

\(144-100\)

Subtract the numbers.

\(=44\)

Answer:

5/2

Step-by-step explanation:

We know,

Equation of the slope is, y = mx + c.   Where m is the slope.

y - 4 = 5/2*(x-2)

y = 5/2*(x-2) + 4

y = (5/2)x - 5 + 4

y = (5/2)x - 1

y = (5/2)x + (-1)      [y = mx + c form]

Slope, m = 5/2

Hope this will help. Please mark me brainliest.

Simplify 52⋅(x−2)52⋅(x-2). Apply the distributive property. y−4=5/2x+5/2⋅−2 Combine 5252 and x

y−4=5x2+5/2⋅−2 Cancel the common factor of 2.Factor 2 out of −2

y−4=5x2+52⋅(2(−1))y-4=5x2+52⋅(2(-1))

Cancel the common factor.

y−4=5x2+52⋅(2⋅−1)y-4=5x2+52⋅(2⋅-1)

Rewrite the expression.

y−4=5x2+5⋅−1y-4=5x2+5⋅-1

Multiply 55 by −1-1.

y−4=5x2−5

Add 44 to both sides of the equation.

y=5x2−5+4y=5x2-5+4

Add −5-5 and 44.

y=5x2−1

Reorder terms.

y=52x−1

THE ANSWER IS M = 5/2

The extreme values of f(x, y) = xy occur at the points (2, 1) and (-2, -1) on the ellipse \(3x^{2} +2y^{2} =1\).

To find the extreme values of f(x, y) = xy on the ellipse \(3x^{2} +2y^{2} =1\), we can use the method of Lagrange multipliers.

Define the function g(x, y) = \(3x^{2} +2y^{2} -1\). We need to find points (x, y) where the gradient of f is proportional to the gradient of g:

∇f = λ∇g

The gradient of f is ∇f = (y, x), and the gradient of g is ∇g = (6x, 4y). Therefore, we have the following system of equations:

y = 6λx
x = 4λy

Substitute the second equation into the first:

y = 6λ(4λy)
y = \(24λ^{2y}\)

If y ≠ 0, then 1 = \(24λ^{2}\), and λ = ±1/2. Plugging this value into the second equation gives x = ±2. Thus, we have two potential extreme points: (2, 1) and (-2, -1).

Now consider the case when y = 0. The constraint equation becomes \(3x^{2} =1\), and x = ±1/√3. However, these points correspond to f(x, y) = 0, which is not an extreme value.

Therefore, the extreme values of f(x, y) = xy occur at the points (2, 1) and (-2, -1) on the ellipse \(3x^{2} +2y^{2} =1\).

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Step-by-step explanation:

S = (2 * pi * r^2) + (2 * pi * r * h)

S = (2 * pi * 4^2) + (2 * pi * 4 * 5)

S = (32 pi) + (40 pi) = 72pi = 226.08 ANS.

The equation that satisfies the data in the table is,

y = -4x - 4 [Option D]

Definition of an Equation:

An equation is defined as a mathematical assertion in which you use mathematical symbols to demonstrate the equality of two amounts. A combination of expressions with variables and constants on either side of the equality sign make up an equation.

The (x, y) coordinates from the given table are,

(-1,0), (0, -4), (1, -8)

Now, these points must satisfy the required equation.

Considering the first point (-1, 0), if we substitute these values of x and y coordinates in y=4x-4, the equality is no longer maintained.

Similarly, (-1,0) does not satisfy the second and third equations, that are, y = -x + 4 and y = x + 4, respectively, either.

Taking the fourth equation, y = -4x - 4

Putting x = -1 in this equation, we get,

y = -4(-1) - 4

y = 4 - 4

y = 0

Likewise, this equation satisfies the rest of the data in the table too.

Therefore, y = -4x - 4 is the required equation.

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(n-1) x (n-2)! ways of seating arrangements are possible if Fred (a boy) and Carrie (a girl) must be seated next to each other.

A permutation is the act of putting things or numbers in a certain order. Combinations are a method of picking things or numbers from a set of objects or collections without regard for their order.

Let's say there are n seats in total.

Then, there are (n-1) gaps between the seats that Fred and Carrie can be placed in.

If we place Fred and Carrie in one of these gaps, there will be (n-2)! possible arrangements for the rest of the seats.

Therefore, there will be (n-1) x (n-2)! total possible seating arrangements for Fred and Carrie if they must be seated next to each other.

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Answer:

Rate of change = 150%

Rate of change = 100%

Rate of change = 100%

Step-by-step explanation:

Find:

Rate of change

x=2 and x=5

x=3 and x=6

x=2 and x=4

Rate of change = [(5-2)/2]100

Rate of change = 150%

Rate of change = [(6-3)/3]100

Rate of change = 100%

Rate of change = [(4-2)/2]100

Rate of change = 100%

Answer:

2 4 8         next : increases

Step-by-step explanation:

The statement that the set SN(R) of n x n real matrices with trace zero form a subspace of the overall vector space MN(R) of n x n real matrices is true.

The set SN(R) of n x n real matrices with trace zero does, indeed, form a subspace of the overall vector space MN(R) of n x n real matrices. This means that SN(R) has its properties and is distinct from the larger set of matrices.

It also means that SN(R) is closed under addition and scalar multiplication, meaning that if two matrices in SN(R) are added or multiplied by a scalar, the result is another matrix in SN(R).

In conclusion, the statement that the set SN(R) of n x n real matrices with trace zero form a subspace of the overall vector space MN(R) of n x n real matrices is true. This is an important concept to understand when it comes to matrices and linear algebra.

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