10. Circle the irrational number in the list below.
√196
7.27
5/9
√15

You did not post enough information.

The direction in which the maximum rate of change of f occurs at the point (5, 6, -1) is approximately (-0.17, -0.11, -0.98).

To find the maximum rate of change of the function f at the given point (5, 6, -1) and the direction in which it occurs, we can calculate the gradient of f at that point.

The gradient vector represents the direction of maximum increase of the function, and its magnitude represents the rate of change in that direction.

The gradient vector (∇f) of f(x, y, z) = (8x + 5y)/z can be found by taking the partial derivatives with respect to each variable:

∂f/∂x = 8/z

∂f/∂y = 5/z

∂f/∂z = -(8x + 5y)/z^2

Evaluated at the point (5, 6, -1), we have:

∂f/∂x = 8/(-1) = -8

∂f/∂y = 5/(-1) = -5

∂f/∂z = -((8(5) + 5(6))/(-1)^2) = -46

So, the gradient vector (∇f) at the point (5, 6, -1) is (-8, -5, -46).

The maximum rate of change of f at this point is given by the magnitude of the gradient vector:

|∇f| = √((-8)^2 + (-5)^2 + (-46)^2) = √(64 + 25 + 2116) = √2205 = 47.

Therefore, the maximum rate of change of f at the point (5, 6, -1) is 47.

To determine the direction in which this maximum rate of change occurs, we normalize the gradient vector by dividing it by its magnitude:

Direction vector = (∇f) / |∇f| = (-8/47, -5/47, -46/47).

Hence, the direction in which the maximum rate of change of f occurs at the point (5, 6, -1) is approximately (-0.17, -0.11, -0.98).

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The expression can be written as the trinomial below.

3x2 - 14x + 15

Here we just need to expand the expression:

(x - 3)*(3x - 5)

Just expanding that product we will get:

(x - 3)*(3x - 5)

x*(3x) - 3*(3x) + x*(-5) - 3*(-5)

3x^2 - 9x - 5x + 15

3x2 - 14x + 15

So we have 3 terms now, thus, this is a trinomial.

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Answer:

8. 600

9. 4200

10. 149

11.  yes he is correct

Step-by-step explanation:

The value of angles in inscribed quadrilateral are μ(∠zyx) is 92⁰ and μ(∠yxw) is 65⁰.

An inscribed quadrilateral is a quadrilateral that can be inscribed in a circle, meaning that its vertices all lie on the circumference of a circle. In other words, the four vertices of an inscribed quadrilateral are concyclic.

The opposite angles of an inscribed quadrilateral are supplementary, which means that they add up to 180 degrees. This property is known as the "interior angle sum" of a quadrilateral.

μ(∠zyx) + μ(∠xwz) = 180⁰ (opposite angle of cyclic quadrilateral are supplementary)

μ(∠xwz) = 88⁰

μ(∠zyx) = 180⁰ - 88⁰ = 92⁰

μ(∠yzw) is an inscribed angle that intercepts the arc 112⁰ and 118⁰. Therefore,

μ(∠yzw)

= (112⁰ + 118⁰)/2

= 230⁰/2

= 115⁰

μ(∠yxw) + μ(∠yzw) = 180⁰  (opposite angle of cyclic quadrilateral are supplementary)

μ(∠yxw) = 180⁰ - 115⁰ = 65⁰

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Answer:

we note that there 52 ways to choose the first card, 51 ways to choose the second card, and 50 ways to choose the third card, for a total of 52x51x50=132,600 ways.

Step-by-step explanation:

Answer:

4; 3 of spades, 3 of clubs, 3 of diamonds, and 3 of hearts

Step-by-step explanation:

A population of 600 organisms is expected to increase by 50.

We can use the equation I = k * n to determine whether the anticipated growth (I) of an organism population is directly related to the size of the current population (n).

Where k is a proportionality constant that connects the anticipated growth to the current population.

We can use the details provided in the problem to determine the value of k. We can write: 20 = k * 240 to represent an increase of 20 in a sample of 240 organisms.

We can calculate k as follows: k = 20 / 240 = 1 / 12.

Now that we know the value of k, we can use it to calculate the predicted growth for a population of 600:

I = (1 / 12) * 600 = 50

Therefore, a population of 600 organisms is expected to increase by 50.

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The measure of the smallest exterior angle of the quadrilateral is: 30°.

Regardless of the polygon, the sum of all its exterior angles are equal to 360 degrees, therefore, the sum of all the exterior angles of a quadrilateral would be equal to 360 degrees.

The exterior angles of the quadrilateral given are:

x°, 2x°, 4x°, and 5x°.

Therefore:

x + 2x + 4x + 5x = 360

Combine like terms

12x = 360

12x/12 = 360/12

x = 30

Find the measure of each angle:

x° = 30°

2x° = 2(30) = 60°

4x° = 4(30) = 120°

5x° = 5(30) = 150°

Therefore, the smallest exterior angle has a measure of 30°.

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The minimum price necessary for the firm to earn a profit is $30.

Hence,.option C is correct

The profit of a firm is calculated as the difference between total revenue and total cost. To find the minimum price necessary for a firm to earn a profit, we need to determine the revenue and cost functions first. Then we can find the break-even point and determine the minimum price for the firm to earn a profit.

Total cost function: TC = 50 + 2q²

where

q = quantity produced

We know that the profit equation is:

Total revenue (TR) = price (p) x quantity (q)

Profit (π) = TR - TC

Now we need to determine the revenue function:TR = p × q

We can substitute this into the profit equation to obtain:π = TR - TCπ = p × q - (50 + 2q²)

To find the break-even point, we can set the profit to zero:

0 = p × q - (50 + 2q²)

p × q = 50 + 2q²

We can rearrange this equation to solve for p:p = (50 + 2q²) / q

Let's substitute q = 5:p = (50 + 2(5)²) / 5 = $30

Therefore, the minimum price necessary for the firm to earn a profit is $30. So, the correct option is O c. p-$30.

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The median number of newspapers sold over seven weeks is 223.

The median is the middle score for a data set arranged in order of magnitude. The median is less affected by outliers and skewed data.

The formula for the median is as follows:

Find the median number of newspapers sold. (87, 87, 215, 154, 288, 235, 231)

We'll first arrange the data in ascending order.87, 87, 154, 215, 231, 235, 288

The median is the middle term or the average of the middle two terms. The middle two terms are 215 and 231.

Median = (215 + 231)/2

= 446/2

= 223

In statistics, the median measures the central tendency of a set of data. The median of a set of data is the middle score of that set. The value separates the upper 50% from the lower 50%.

Hence, the median number of newspapers sold over seven weeks is 223.

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Answer: #x^3

Step-by-step explanation:

        x^3

note: An algebraic expression doesn't have an equal sign (=)

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Answer:

there i tried :)

Step-by-step explanation:

Answer:

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

The bottom part is a cylinder with:

The top is a cone with:

Find the total volume of the solid by adding up the volumes.

Volume of the cylinder:

Volume of the cone:

Volume of the solid:

The volume of the solid is 2880.43 ft³ .

The object is made up of a cylinder and a cone. The volume of the object would be the sum of the volume of the cylinder and the volume of the cone.

Volume of the cylinder = πr²h

Where:

π = pi = 3.14

r = radius = diameter / 2 = 16 / 2 = 8

h = height = 12.5

3.14 x 8² x 12.5 = 2512 ft³

Volume of a cone = 1/3 πr²h

H = 18 - 12.5 = 5.5 feet

1/3 x 3.14 x 8² x 5.5 = 368.43 ft

Volume of the solid = 2512 ft³ + 368.43 ft = 2880.43 ft³

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The output of each function include the following:

u'(1) = 0.

v'(5) = -2/3

By critically observing the graph of the functions f and g, we can logically deduce the following parameters;

f(1) = 2         f(5) = 3

g(1) = 1         g(5) = 2

f'(1) = 2         f'(5) = -1/3

g'(1) = -1        g'(5) = 2/3

Next, we would take the first derivative of u with respect to x and then, substitute the x-value into the composite function, and then evaluate as follows;

u(x) = f(x)g(x)

u'(x) = f'(x)g(x) + g'(x)f(x)

u'(1) = f'(1)g(1) + g'(1)f(1)

u'(1) = 2(1) + (-1)2

u'(1) = 2 - 2

u'(1) = 0.

For v'(5), we have the following function by applying quotient rule:

\(v'(x) = \frac{f'(x)g(x)\;-\;f(x)g'(x)}{g^2(x)} \\\\v'(5) = \frac{f'(5)g(5)\;-\;f(5)g'(5)}{g^2(5)} \\\\v'(5) = \frac{\frac{-1}{3} \times 2 - (3 \times \frac{2}{3}) }{2^2}\)

v'(5) = -8/3 × 1/4

v'(5) = -2/3

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

By using the digits 0 to 9, the boxes are filled with their respective numerical values to make the chart accurate as shown in the image attached below.

A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables.

In Mathematics, there are different types of functions and these include the following;

A logarithm function can be defined as a type of function that represents the inverse of an exponential function. Mathematically, a logarithm function is written as follows:

y = logₐₓ

y = log₁₀10

y = log₁₀10 = 1.  

Therefore, if log₁₀x < 1, then, x < 10.  Also, if log₁₀x > 1, then, x > 10.

For this exercise, you should take note of this deductive points:

In conclusion, by using the digits 0 to 9, the boxes are filled with their respective numerical values to make the chart accurate as shown in the image attached below.

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Answer:

120 inches

Step-by-step explanation:

the first box on the bottom is 72 because 12 x 2 x 3 is 72 and the bottom on is 48 because 2 x 4 x 6 is 48. then add 72 plus 48 and it gives you 120 inches.

Answer:

C. P = 30

Step-by-step explanation:

Parallelogram opposite (or parallel) sides are equal,

so:

2x = x + 2

5y - 9 = 2y + 3

For x:

2x = x + 2

2x - x = 2

x = 2

For y:

5y - 9 = 2y + 3

5y - 2y = 3 + 9

3y = 12

y = 4

the smallest sides are equal 2x and x + 2 => 2 * 2 = 4

the biggest sides are equal 5y - 9 and 2y + 3 => 2 * 4 + 3 = 11

P = 2 * (a + b)

P = 2 * (4 + 11)

P = 2 * 15

P = 30

To calculate the mass of the Earth, we can use the following formula:

M = (4π²rₑₘ³) / (Gtₘ²)

Where:

M is the mass of the Earth

rₑₘ is the distance from the center of the Earth to the center of the Moon (384 million meters)

G is the gravitational constant (approximately 6.67430 x 10^-11 m³/(kg·s²))

tₘ is the orbital period of the Moon around the Earth (27.3 days converted to seconds)

Let's plug in the values and calculate the mass of the Earth:

M = (4π² * (384 x 10^6)³) / (6.67430 x 10^-11 * (27.3 x 24 x 60 x 60)²)

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The probability that a customer waits less than or equal to 90 seconds is approximately 0.7769, or 77.69%.

To calculate the probability that a customer waits a certain amount of time at the local Subway sandwich shop, we can use the exponential distribution formula:

\(P(X > t) = e^{(-t/u)}\)

Where:

P(X > t) is the probability that the waiting time (X) is greater than a specific value (t).

e is the base of the natural logarithm (approximately 2.71828).

t is the specific value of waiting time.

μ is the mean of the exponential distribution.

In this case, the mean waiting time (μ) is given as 60 seconds. Let's calculate the probability of a customer waiting less than or equal to a specific time, which is the complement of waiting longer than that time:

P(X ≤ t) = 1 - P(X > t)

For example, to calculate the probability a customer waits less than or equal to 90 seconds, we have:

P(X ≤ 90) = 1 - P(X > 90)

\(= 1 - e^{(-90/60)}\\= 1 - e^{(-1.5)}\)

≈ 1 - 0.2231

≈ 0.7769

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The probability that a customer waits less than 30 seconds is approximately 0.3935, or 39.35%.

The probability that a customer waits less than a certain amount of time can be calculated using the exponential distribution. In this case, the mean waiting time is given as 60 seconds.

To calculate the probability that a customer waits less than a specific time, we can use the formula for the cumulative distribution function (CDF) of the exponential distribution.

Let's say we want to calculate the probability that a customer waits less than 30 seconds. We can plug the values into the formula:

\(P(X < 30) = 1 - e^(-λt)\)

Where λ is the rate parameter, which is the reciprocal of the mean (λ = 1/60), and t is the desired time (30 seconds).

\(P(X < 30) = 1 - e^(-1/60 * 30) = 1 - e^(-1/2) ≈ 0.3935\)

Therefore, the probability that a customer waits less than 30 seconds is approximately 0.3935, or 39.35%.

Similarly, we can calculate the probability for other desired waiting times by plugging in the appropriate values into the formula.

Keep in mind that this calculation assumes that the waiting times follow an exponential distribution with a mean of 60 seconds.

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Answer:

\(c = \sqrt{52}\)

Step-by-step explanation:

\(c^{2} = a^{2} + b^{2}\)

\(c^{2} = 4^{2} + 6^{2}\)

\(c^{2} = 16 + 36\\\)

\(c^{2} = 52\)

\(\sqrt{c^{2} } = \sqrt{52}\)

\(c = \sqrt{52}\)

Answer:

28.3 (explaination below)! :)

Step-by-step explanation:

Use the formula for cicrumfrence: C=2πr

Radius can be found by splitting the given number in half, (unless you were given the radius already, then you'd just multiply by 2).

Plug in our numbers. C= 2π4.5

Then, multiply.

You'd get 28.27433388230814.

Rounding to the first decimal place, you'd have a final answer of  28.3.

Hope this helps!

This integral is quite complex and does not have an analytical solution is 2pi ∫\(0^2\) \(e^{-r sin(\theta)\)) r (1 - 2\(r^2\)\(cos^{2}(\theta)\) (2\(-r^2\)) dr dtheta

To evaluate the triple integral of e^(x-y) over the region enclosed by the surfaces z=\(x^2-1, z=1-x^2, y=0,\) and y=8, we will use the cylindrical coordinates since the region is symmetric about the z-axis.

In cylindrical coordinates, we have:

x = r cos(theta)

y = r sin(theta)

z = z

The limits of integration for r, theta, and z are as follows:

0 <= r <= 2

0 <= theta <= 2pi

\(x^2\)-1 <= z <= 1-\(x^2\)

Substituting the cylindrical coordinates into the integral, we get:

∫∫∫ e^(x-y) dv = ∫∫∫ \(e^{(r cos(\theta) - r sin(\theta))\)r dz dr dtheta

Now, we need to determine the limits of integration for z in terms of r. Solving for z in the two equations that define the boundaries of the region, we get:

z =\(x^2\)- 1 -> z = \(r^2\)\(cos^2(\theta)\) - 1

z = 1 - \(x^2\) -> z = 1 - \(r^2\) \(cos^2(\theta)\))

Thus, the limits of integration for z become:

\(r^2 cos^2\)(theta) - 1 <= z <= 1 -\(r^2\) \(cos^2(\theta)\)

Substituting these limits into the integral and performing the integrations, we get:

∫∫∫ \(e^{r cos(\theta)\) - r sin(theta)) r (1 - \(r^2\) \(cos^2(\theta)\)) - \(r^2\) \(cos^2(\theta))\) dz dr dtheta

= ∫\(0^8\)∫\(0^2\)pi ∫\(0^2\) \(e^{r cos(\theta)\) - r sin(theta)) r (1 - 2\(r^2\) \(cos^2(\theta))\)dz dr dtheta

= 2pi ∫\(0^2\) \(e^{-r sin(\theta))\)r (1 - 2\(r^2\) \(cos^2(\theta))\) (2-\(r^2\)) dr dtheta

This integral is quite complex and does not have an analytical solution. Therefore, we need to evaluate it numerically using a computer or calculator.

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#1

No

#2

We can see f(1) has 3 values so it's not a function as it's failed in vertical line test

#3

f(10) has two values -2 and 11

So not a function

#4

As per definition of function

So it's not a function

Answer:

cos a = 12/13

tan a = 5/12

You use these properties to solve the question,

sin²a+cos²a=1

tana=sina/cosa

The polynomial x⁵ - 4x³ + x² - 4 will have a remainder of -8 when divided by x² - x + 1 and the result can be written in the form (x³ + x² - 4x + 4) - 8/(x² - x + 1).

Using the long division method will require us to; divide, multiply, subtract, bring down the next number and repeat the process to end at zero or arrive at a remainder

We shall divide the polynomial x⁵ - 4x³ + x² - 4 by x² - x + 1 as follows;

x⁵ divided by x² equals x³

x² - x + 1 multiplied by x³ equals x⁵ - x⁴ + x³

subtract x⁵ - x⁴ + x³ from x⁵ - 4x³ + x² - 4 will result to x⁴ - 5x³ + x² - 4

x⁴ divided by x² equals x²

x² - x + 1 multiplied by x² equals x⁴ - x³ + x²

subtract x⁴ - x³ + x² from x⁴ - 5x³ + x² - 4 will result to -4x³ - 4

-4x³ divided by x² equals -4x

x² - x + 1 multiplied by -4x equals -4x³ + 4x² - 4x

subtract 4x³ + 4x² - 4x from -4x³ - 4 will result to 4x² - 4x - 4

4x² divided by x² equals 4

x² - x + 1 multiplied by 4 equals 4x² - 4x - 4

subtract 4x² - 4x - 4 from 4x² - 4x - 4 will result to a remainder of -8.

Therefore, the polynomial x⁵ - 4x³ + x² - 4 divided by x² - x + 1 gives a quotient x³ + x² - 4x + 4 and a remainder of -8 and can be written as (x³ + x² - 4x + 4) - 8/(x² - x + 1).

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Answer:

She needs to save $500 each month over the next 2 years to fulfill her first year of tuition.

Step-by-step explanation:

Consider the provided information.

She needs $48,000 per year for tuition.

The university offered financial aid that covers 50% of her tuition expenses.

It means she needs to pay only 50% of $48,000 per year for the tuition fee.

\(50\% \times 48,000=\frac{50}{100}\times48,000\)

                      \(=24,000\)

Now she needs $24,000 for tuition expenses.

Her parents contribute $10,000 for tuition each year and she receives a local scholarship for $2,000.

Now, for the first year of tuition, she needs=$24,000-$10,000-$2000

                                                                       =$12,000

In 2 years there are 24 months, which means she needs to save $12,000 in 24 months.

Amount she needs to save each month = \(\dfrac{\$12000}{24}=\$500\)

Hence, she needs to save $500 each month over the next 2 years to fulfill her first year of tuition.

The value of p in the given equation is -1.

Given is an equation p-3 = -4, we need to find the value of p,

So,

p-3 = -4

p = -4+3

p = -1

Hence, the value of p in the given equation is -1.

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Answer:

\(a_{n}\) = 5n + 5

Step-by-step explanation:

The nth term of an arithmetic progression is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 10 and d = a₂ - a₁ = 15 - 10 = 5 , then

\(a_{n}\) = 10 + 5(n - 1) = 10 + 5n - 5 = 5n + 5