human iq scores are approximately normally distributed with a mean of 100 and a standard deviation of 15. determine:

Answer:

390cm³

Step-by-step explanation:

6cm×5cm×13cm= 30cm²×13cm= 390cm³

The first partial derivatives of the function f(x, y, z) = xyz + 9yz are:

To find the first partial derivatives of the function f(x, y, z) = xyz + 9yz, we need to differentiate the function with respect to each variable (x, y, z) one at a time while treating the other variables as constants.

Let's start with finding the partial derivative with respect to x (fx):

fx(x, y, z) = ∂/∂x (xyz + 9yz)

Since y and z are treated as constants when differentiating with respect to x, we can simply apply the power rule:

fx(x, y, z) = yz

Next, let's find the partial derivative with respect to y (fy):

fy(x, y, z) = ∂/∂y (xyz + 9yz)

Again, treating x and z as constants, we differentiate yz with respect to y:

fy(x, y, z) = xz + 9z

Finally, let's find the partial derivative with respect to z (fz):

fz(x, y, z) = ∂/∂z (xyz + 9yz)

Treating x and y as constants, we differentiate yz with respect to z:

fz(x, y, z) = xy + 9y

Therefore, the first partial derivatives of the function f(x, y, z) = xyz + 9yz are:

fx(x, y, z) = yz

fy(x, y, z) = xz + 9z

fz(x, y, z) = xy + 9y

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Therefore, the linearization of f(x) = cos(x) at a = π/2 is L(x) = π/2 - x.

The linearization of a function f(x) at a point a is given by:

L(x) = f(a) + f'(a)(x - a)

where f'(a) denotes the derivative of f(x) evaluated at x = a.

In this case, we have:

f(x) = cos(x)

a = π/2

First, let's find f'(x):

f'(x) = -sin(x)

Then, we can evaluate f'(a):

f'(π/2) = -sin(π/2) = -1

Next, we can plug in the given values into the formula for linearization:

L(x) = f(a) + f'(a)(x - a)

L(x) = cos(π/2) + (-1)(x - π/2)

L(x) = 0 - x + π/2

L(x) = π/2 - x

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To find the amount of the discount, we can multiply the total bill by the discount rate of 20% (or 0.2):

Discount = 0.2 x $54.95

Discount = $10.99

What is percentage ?

Percentage is a way of expressing a fraction or proportion as a portion of 100. It is often used to represent rates, discounts, or increases/decreases in values.

So you would save $10.99 using your Hawk card.

To find the final amount you would pay after the discount, we can subtract the discount from the total bill:

Final amount = Total bill - Discount

Final amount = $54.95 - $10.99

Final amount = $43.96

So the final amount you would pay with the Hawk card discount is $43.96.
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   The equation that defines the parabola with vertex at the origin and focus at (0, -4) is

y = -x²/16

We define what a parabola is

 The parabola is a geometric shape that is formed from the intersection of a vertical plane in a cone.

  The canonical equation of a parabola is given by

(x - h)² = 4p(y - k)

   The parabola is a quadratic function, it is composed of a vertex, or inflection point, a focus and a directrix.

Since the vertex and the focal axis are on the same axis, we analyze that:

v = (0, 0)

f = (0, -4) This means that the focus is on the negative part of the y-axis, the form of the equation of this parabola is y = x²

(x - 0)² = 4p(y - 0)

Focus:

f = (0, 0 + p)

(x - 0)² = 4*-4(y - 0)

(x)² = 16(y)

y = -x²/16

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A. To determine if an integral is convergent, we analyze the function's behavior, integrability, apply integration techniques, and examine its limits, ensuring they are finite, leading to a finite result.

B. To determine if an integral is divergent, we look for infinite limits, vertical asymptotes, and erratic behavior within the integration interval, indicating the lack of a finite value for the integral.

A. To determine if an integral is convergent, we need to consider several approaches. First, we check for basic convergence criteria such as infinite limits or vertical asymptotes.

Then, we examine integrability, ensuring the function is continuous or has a finite number of discontinuities. Next, we simplify the integral using integration techniques.

Finally, we analyze the behavior of the function at infinity and apply comparison tests if necessary to establish convergence.

B. To determine if an integral is divergent, we follow a series of steps. First, we check for basic divergence criteria such as infinite limits or vertical asymptotes.

Then, we examine integrability, looking for discontinuities that prevent integration. Next, we simplify the integral using integration techniques. Finally, if the integral does not converge, it is deemed divergent.

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Answer:

aaalot I'm guessing I'm stu.pid

Answer:

I’m good LOVE

Step-by-step explanation:

Answer:

Good thank u for asking how abt u! xD

Answer:

Step-by-step explanation:

Change 2/5 to a decimal

2/5 = 0.4

Change 1 2/15 of a fluid ounce to a decimal.

1.133333

Set up your proportion.

0.4 / 1.133333 = x / 5               Cross multiply

0.4*5 = 1.133333*x

2 = 1.133333 x                         Divide by 1.1333333

2/1.33333 = x

x = 1.5 ounces.

He needs 1.5 ounces of red to make 5 ounces of purple.

Answer:

The net worth of those from 35 to 44 was about 5 times greater than those under 35.

Step-by-step explanation:

69,600 divided by 13,900 is around 5.

In summary, to find an interval of length 1 and having integer endpoints on which the function has a root, we can use a trial-and-error method to identify intervals that satisfy the given criteria. The choice of interval may depend on the specific function and there may be multiple intervals that satisfy these conditions.

To find an interval on which the function has a root, we need to consider the function's behavior and identify any potential zero crossings. An interval of length 1 with integer endpoints can be represented as [a, a+1] where a is an integer.
One approach to finding a root is to plot the function and visually identify where it crosses the x-axis. Another approach is to use algebra and solve for when the function equals zero. However, without knowing the specific function, we cannot use these methods.
Instead, we can use a trial-and-error method to identify an interval that satisfies the given criteria. For example, we can start by choosing an integer a and evaluating the function at a and a+1. If the function has opposite signs at these two endpoints, then by the Intermediate Value Theorem, the function must have at least one root in the interval [a, a+1].
We can continue this process until we find an interval that satisfies the given criteria. Note that there may be multiple intervals that satisfy these conditions, and the choice of interval may depend on the specific function.

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Answer:

1 answer is 2

2 answer 4

3 answer 10

Step-by-step explanation:

Add 1+1

get 2

Add 2+2

get 4

Add 3+7

get 10

Answer:

\( s = 6.1~cm \)

Step-by-step explanation:

\( s = \dfrac{n}{360^\circ} \times \pi d \)

\( s = \dfrac{50^\circ}{360^\circ} \times \pi \times 14~cm \)

\( s = 6.1~cm \)

Answer:

12.2 cm

Step-by-step explanation:

Since the circle has a diameter of 14cm, its radius is 7cm.

Using the formula s=rθ where s is the arc length of the circle, r is the radius of the circle, and θ is the central angle of the circle in radians, then the arc length is s = (14)(50°)(π/180) = (14)(50π/180) = 700π/180 ≈ 12.2 cm

Answer:

50 km/hr

Step-by-step explanation:

D = RT

Time for first part of trip = 80/60 = 4/3 hr.

Time for second part of trip = 20/30 = 2/3 hr.

total time for entire trip = 4/3 + 2/3 = 6/3 = 2 hr.

Total distance = 100 km

Average rate of speed for entire trip = 100/2 = 50 km/hr

answer is y=-3x+(-1/3)

The correct expression for the mathematical statement "Add 450 to 348, and then multiply by 7." is (450 + 348) × 7 , the correct option is (b).

An Algebraic Expression is defined as a mathematical phrase which contains one or more variables, numbers, and are joined by mathematical operators such as addition, subtraction, multiplication, and division.

The expression for the mathematical statement "Add 450 to 348, and then multiply by 7" is represented in ,option (b) (450 + 348) × 7 ;

Let the statement be read in two parts,

First "Add 450 to 348", which means we add 450 and 348 together, which is represented as "450+348";

In second part ,we "Multiply by 7", which means we multiply result in first part by 7.

Putting it all together, we get:

⇒ (450 + 348) × 7

Therefore , the correct Algebraic Expression is (b) (450 + 348) × 7.

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The given question is incomplete, the complete question is

Select the correct expression for the given mathematical statement. "Add 450 to 348, and then multiply by 7."

(a) 450 + 348 × 7

(b) (450 + 348) × 7

(c) 450 × 7 + 348

(d) 450 × (7 + 348)

\(x_2 = -1\\x_3 = 0\\x_4= -1\)

i.e, The method fails.

What is newton's method?

The Newton-Raphson technique, also referred to as the Newton-Raphson root-finding algorithm and named after Isaac Newton and Joseph Raphson, is a root-finding algorithm used in numerical analysis that generates progressively improved approximations to the roots of a real-valued function.

\(y= x^3 - 2x - 2\\\\x_1 = 0\\\\y= x^3 - 2x - 2\\\\\Rightarrow \ \ \ y'= 3x^2 - 2\)

\(x_{n+1} = x_n - \frac{y_n}{y'_n}\\\\x_{2} = x_1 - \frac{y_1}{y'_1}\\\\\Rightarrow \ \ \ x_{2} = 0 - \frac{(0)^3 - 2(0) - 2}{3(0)^2 - 2}\\\\\Rightarrow \ \ \ x_{2} = -1\)

\(x_{3} = x_2 - \frac{y_2}{y'_2}\\\\\Rightarrow \ \ \ x_{3} = -1 - \frac{(-1)^3 - 2(-1) - 2}{3(-1)^2 - 2}\\\\\Rightarrow \ \ \ x_{3} = -1 - (-1)\\\\\Rightarrow \ \ \ x_{3} =0\\\\\\x_{4} = x_3 - \frac{y_3}{y'_3}\\\\\Rightarrow \ \ \ x_{4} = 0 - \frac{(0)^3 - 2(0) - 2}{3(0)^2 - 2}\\\\\Rightarrow \ \ \ x_{4} = -1\)

\(x_2 = -1\\x_3 = 0\\x_4= -1\)

Hence, The method fails.

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Answer:

c)  y = 8\(\sqrt{3}\)

Step-by-step explanation:

in a 30-60-90° Δ the ratio of the sides, respectively, is 1: \(\sqrt{3}\) : 2

if the side opposite the 30°∡ is 8 then 'y' is 8\(\sqrt{3}\) and 'x' is 16

A change in the price of chicken, the good's own price, will cause a movement along the demand curve for chicken, a normal good, resulting in an increase in the quantity demanded.

The demand curve for chicken represents the relationship between the price of chicken and the quantity of chicken demanded by consumers. The law of demand states that there is an inverse relationship between the price of a good and the quantity demanded, holding all other factors constant. In other words, as the price of chicken decreases, the quantity demanded of chicken increases, and vice versa.

A movement along the demand curve for chicken occurs when there is a change in the price of chicken. When the price of chicken decreases, ceteris paribus, consumers are willing to purchase more chicken at the lower price, resulting in an increase in the quantity demanded along the demand curve. Conversely, when the price of chicken increases, consumers are willing to purchase less chicken at the higher price, resulting in a decrease in the quantity demanded along the demand curve.

Other factors that can shift the demand curve for chicken include changes in consumer income, the prices of substitute or complementary goods, and changes in consumer preferences. However, these factors cause a shift in the entire demand curve, rather than a movement along the curve.

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Answer:

3/4 of 5

= 3/4 × 5

= 15/4

= \(3\dfrac{3}{4}\)

Eric rode the rental scooter for a total of 221 minutes. Let's assume that Eric rode the scooter for x minutes. According to the given information, he paid a $6 fee to start the scooter and an additional 8 cents per minute.

Therefore, the cost of the ride can be represented by the equation 6 + 0.08x = 20.72. To find the value of x, we need to solve this equation. First, let's subtract 6 from both sides of the equation: 0.08x = 14.72. Then, we divide both sides by 0.08 to isolate x: x = 14.72 / 0.08 = 184. By substituting the value of x back into the equation, we can verify that the total cost of the ride is indeed $20.72. Thus, Eric rode the rental scooter for 184 minutes.

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Answer:

Step-by-step explanation:

The first man painted:

The second man painted:

If the first man painted 3 times more, then:

The 94th term of the arithmetic sequence -26,−37,−48 is -1049.

It is important to note that an arithmetic sequence is calculated by using the formula:

a + (n - 1)d

where a = -26

d = -37 + 26 = -11

Therefore, the 94th term will be:

= a + (n - 1)d

= -26 + (94 - 1) × -11

= -26 + (93 × -11)

= -26 - 1023

= -1049

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The price of Mira's breakfast before tip was $1.50. We know that she left a 20% tip on top of the price of the breakfast. This means that the tip she left was 0.20x dollars.

An equation is a mathematical statement that proves the equality of two expressions. It has two sides, one on the left and one on the right, separated by an equal sign (=). The expressions on both sides of the equal sign are called the terms of the equation.

Equations are used to represent and solve mathematical relationships. They can involve numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. Equations can be simple or complex, and they can have one or more variables.

Let the price of Mira's breakfast before tip be x dollars.

The tip she left was 0.20x dollars.

We also know that the total amount she paid, including the tip, was $1.80 more than the price of the breakfast. As a result, we can construct the following equation:

x + 0.20x + 1.80 = total amount paid

Simplifying the equation, we get:

1.20x + 1.80 = total amount paid

We can now solve for x, which is the price of Mira's breakfast before tip:

1.20x = total amount paid - 1.80

1.20x = total amount paid - 1.80

x = (total amount paid - 1.80) / 1.20

We know that the tip Mira left was $1.80, so the total amount paid was:

total amount paid = x + 0.20x + 1.80 = 1.20x + 1.80

By substituting this value for x in the equation, we get:

x = (1.20x + 1.80 - 1.80) / 1.20

x = 1.50

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Since the limit evaluates to different values along different paths, we conclude that the limit does not exist at (0,0).

A straight line is a geometrical concept that represents a set of points that extend infinitely in both directions without any curvature or deviation. It is the shortest distance between two points in Euclidean geometry and is defined by two points on the line. Any two distinct points in a plane can be connected by a unique straight line. Straight lines are fundamental in mathematics, physics, and engineering, and are used to represent many concepts, including trajectories, vectors, and functions.

To show that the limit does not exist, we need to find another path where the limit evaluates to a different value or does not exist.

Let's consider the path y = mx, where m is any constant. Then, as (x, y) approaches (0, 0) along this path, we have:

\(lim (x,y)\) → \((0,0) -5x^3y / (-4x^6 + 7y^2)\)

\(= lim x\) → \(0 -5x^3(mx) / (-4x^6 + 7(mx)^2)\) [substituting y = mx]

\(= lim x\) → \(0 -5m x^4 / (-4x^6 + 7m^2x^2)\)

\(= lim x\) → \(0 (-5m / x^2) / (-4x^4 + 7m^2)\)

\(= lim x\) → \(0 5m / (4x^2 - 7m^2)\)

Now, the limit will not exist if this expression evaluates to different values for different choices of m.

If m = 0, then the expression becomes 0/0, which is an indeterminate form. We can use L Hsopital's rule to evaluate this limit:

\(Lim x\) → \(0 5m / (4x^2 - 7m^2)\)= \(lim x\) → \(0 (d/dx)(5m) / (d/dx)(4x^2 - 7m^2)\)

= \(Lim x\) →\(0 0 / (8x) = 0\)

If m ≠ 0, then the denominator \(4x^2 - 7m^2\)will be nonzero as x approaches 0. Therefore, the limit will be:

\(lim x\) →\(0 5m / (4x^2 - 7m^2)\)= ±∞, depending on the sign of 5m and \(4x^2\) - \(7m^2.\)

Since the limit evaluates to different values along different paths, we conclude that the limit does not exist at (0,0).

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Answer:

A lower price and quantity would result.

Answer:

not equivalent to meteorologists ratio

Step-by-step explanation:

meteorologists ratio is

rainy days : sunny days = 2 : 5

last months weather is

rainy days : sunny days

= 10 : 20 ( divide both parts by LCM of 10 )

= 1 : 2 ← not equivalent to 2 : 5

The value of z is determined by capital-to-labor ratio and it is greater than 1.

The value of z is determined by the capital-to-labor ratio of each firm, specifically the ratio between the capital used (K) and the labor employed (L). To find the value of z, we need to compare the capital-to-labor ratios of Tom's firm (Kt/Lt) and Dana's firm (Kd/Ld).

Comparing the production functions, we can see that Tom's firm has a capital exponent of 0.7, while Dana's firm has a capital exponent of 0.3. Similarly, Tom's firm has a labor exponent of 0.3, while Dana's firm has a labor exponent of 0.8.

Since the capital exponent in Tom's firm (0.7) is greater than the capital exponent in Dana's firm (0.3), Tom's firm has a larger capital-to-labor ratio. This implies that Tom's firm uses relatively more capital compared to labor in the production process.

Therefore, z, which represents the ratio of Dana's firm's capital-to-labor ratio to Tom's firm's capital-to-labor ratio, will be less than 1. This means that Dana's firm uses relatively less capital compared to labor.

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In trigonometry, cos B represents the ratio of the adjacent side to the hypotenuse of a right-angled triangle where angle B is one of the acute angles.

The formula for cos B is given as:cos B = adjacent/hypotenuse Now, let's say we have a right-angled triangle ABC where angle B is the acute angle. The side opposite angle B is BC, the side adjacent to angle B is AB and the hypotenuse is AC. To find the value of cos B, we need to know the values of AB and AC. Once we have these values, we can substitute them in the formula for cos B and calculate the value.

To calculate the value of cos B in degrees, we use a calculator or a trigonometric table. If we have the value of cos B in decimal form, we can use the inverse cos function to find the value of B in degrees. For example, if cos B = 0.6, then B = cos-1 (0.6) = 53.13 degrees.To summarize, to find the value of cos B, we need to know the adjacent and hypotenuse sides of a right-angled triangle where angle B is one of the acute angles.

We can then substitute these values in the formula for cos B and calculate the value. If we have the value of cos B in decimal form, we can use a calculator or the inverse cos function to find the value of B in degrees.

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