Ready
How do you find the distance between
the points shown?
Add the distance between
each point and the y-axis.
What is the distance between
point A and point B?
units
A(-8,-4)
B (2,-4)

The maximum rate of change of f(x,y,z)=x+y/z at the point (5,-3,5) can be found using the directional derivative.

The directional derivative of f(x,y,z) in the direction (u,v,w) is given by:

Df(x,y,z) = u∂f/∂x + v∂f/∂y + w∂f/∂z

Since f(x,y,z)=x+y/z, the partial derivatives of f(x,y,z) are ∂f/∂x=1, ∂f/∂y=1/z and ∂f/∂z=-y/z^2. Substituting these values into the above directional derivative equation, we get:

Df(x,y,z) = u + v/z - wy/z^2

At the point (5,-3,5), we get Df(5,-3,5) = u + (-3/5) - (5w)(-3/25)

Simplifying this expression gives us Df(5,-3,5) = u + 0.6w

Therefore, the maximum rate of change of f(x,y,z) at the point (5,-3,5) occurs in the direction (u,0,w) and has a value of 0.6w.

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The value of C in the table will be 24.

the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in the destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.

Given, a table of proportional data below,

Part      8    B    D

Part     10   15   45

Whole  A    C    72

Since the two-part will be proportional to the whole.

thus,

=> c /72 = 15/45

=> C = 72/3

=> C = 24

Therefore, the value of C  in the given table will be 24 as pe the proportionality.

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For the system of equations, there are infinitely many solutions exist.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The system of equations are,

⇒ - 2x + 2y = 10  .. (i)

⇒ y = x + 5  .. (ii)

Here, From (i) equation,

⇒ - 2x + 2y = 10

Take 2 as common,

⇒ 2 (- x + y) = 10

⇒ - x + y = 5

⇒ y = x + 5

Which is same as equation (ii).

Hence, There are infinitely many solutions exist.

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The value of the probability of event C is 0.30.

The law of total probability states that

P(A U B U C) = P(A) + P(B) + P(C) - P(A n B) - P(A n C) - P(B n C) + P(A n B n C).

Substitute the known values in the above equation, so, we have the following representation

P(A U B U C) = 0.24 + 0.26 + P(C) - 0.05 - 0.05 - 0.05 + 0.02.

Also are given:

P(A U B U C)' = 0.33,

This implies that

P(A U B U C) = 1 - 0.33 = 0.67.

Substituting the values, we get:

0.67 = 0.24 + 0.26 + P(C) - 0.05 - 0.05 - 0.05 + 0.02

0.67 = 0.24 + 0.26 + P(C) - 0.15 + 0.02

0.67 = 0.50 + P(C) - 0.13

0.80 = 0.50 + P(C)

P(C) = 0.80 - 0.50 = 0.30.

Hence, the probability is 0.30

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The value of K in the given equations 6x+4y=7 and Kx+8y=7 is k=(-4y/x)+6.

Two things are equal, according to an equation.

It will be written with the equals sign "=" as in x+2=6.

What is on the left (x + 2) is equal to what is on the right ((6)), according to that equation.

A remark like "this equals that" can be compared to an equation.

So, we have the equations:

6x + 4y = 7

Kx + 8y = 7

Now, we know that both equations are equal to 7. so, we can write it as:

6x + 4y = Kx + 8y

Solve with subject K as follows:

6x + 4y = Kx + 8y

Kx - 6x  = 4y - 8y

(K-6)x = -4y

k-6 = -4y/x

k = (-4y/x) + 6

Therefore, the value of K in the given equations 6x+4y=7 and Kx+8y=7 is k=(-4y/x)+6.

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The reference angles are given as -

The radian is the unit of angle in the International System of Units and is the standard unit of angular measure used in many areas of mathematics

Given are the angles as shown in the figure.

We can write the reference angles as -

- 34π/3 → -34 x π/3 → π/3

- 34π/3 → π/3

- 5π/12 → -5x π/12 → π/12

- 5π/12 → π/12

17π/6 → 17 x π/6 → π/6

17π/6 → π/6

Therefore, the reference angles are given as -

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The chain rule tells us where to search the derivative of a composite function.

d/dx[f(g(x))] =f'[f[g(x)g'(x).

A function is composite if you can write it as f(g(x)) In other words, it is a function within a function, or a function of a function.

Following steps should be followed to find chain rule:

1: Recognize the chain rule: The function needs to be a composite function, which implies one function is nested over the other one.

2: Know the inner function and the outer function respectively.

3: Determine the derivative of the outer function, dropping the inner function

4: Obtain the derivative of the inner function Step

5: Multiply the outcomes from step 4 and step 5 respectively.

6: Simplify the obtained chain rule derivative.

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Answer:

C' U (A U B')

Step-by-step explanation:

Using  DeMorgan's laws

(C ∪ A' ∩ B)' = C' U (A' ∩ B)'

(A' ∩ B)' = (A')' U B' = A U B'

So (C ∪ A' ∩ B)' = C' U (A U B')

To ascertain an element's molar mass, use the periodic table. Calculate the quantity of moles by dividing the supplied mass in grammes by the molar mass.

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Answer: a. The value of the firm the instant before it pays out current profits as dividends can be calculated using the Gordon Growth Model, which is given by the formula:

Value = Dividends / (Cost of Equity - Growth Rate)

Where Dividends = Current Profits, Cost of Equity = Opportunity Cost of Funds, and Growth Rate = Constant Annual Growth Rate.

Substituting the given values into the formula, we get:

Value = 900,000 / (0.04 - 0.02) = 900,000 / 0.02 = 45,000,000

b. The instant after it pays out current profits as dividends, the firm's value will be reduced by the amount of the dividends paid out. So, the value of the firm after paying out the dividends will be:

Value = 45,000,000 - 900,000 = 44,100,000

Step-by-step explanation:

Answer:

Step-by-step explanation:

x-​4/​5+​9

The x-intercepts will be at x = 0 , -2 A line crosses the x-axis at the x-intercept, and the y-intercept is where the line crosses the y-axis.

Given

f(x) = x²(x+2)

To find the x-intercepts ⇒ f(x) = 0

∴ x²(x+2) = 0

∴ x² = 0  OR   x+ 2 = 0

∴ x = 0  or   x = -2

So, the x-intercepts will be at x = 0 , -2

We must graph the function f in order to determine whether the graph crosses the x-axis, hits the x-axis, and then reverses at each intercept (x)

The attached figure represents the graph of f(x)

As shown in the figure:

1)  The graph crosses the x-axis at x = -2

2) The graph touches the x-axis and turns around at x = 0

The complete question is,

Find the x-intercepts. State whether the graph crosses the x-axis or touches the x-axis and turns around at each intercept. Show your work.

f(x) = x2(x + 2)

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Hassan earns $2.6 per hour more than Caleb. Because the rate of Hassan is more than Celeb.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

Two friends, Caleb and Hassan, took summer jobs. The equation y = 21.5x represents Hassan's earnings in dollars and cents, y, for working x hours. Caleb earned $819.40 in 34 hours.

The rate of Caleb is given as,

Celeb's rate = $21.5 per hour

The rate of Hassan is given as,

Hassan's rate = $819.40 / 34

Hassan's rate = $24.1 per hour

The difference is given as,

⇒ $24.1 - $21.5

⇒ $2.6

Hassan earns $2.6 per hour more than Caleb. Because the rate of Hassan is more than Celeb.

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PPF is bowed outward, so that as the quantity of pizza and pasta produced increases, it becomes more costly to produce another unit of pizza.

The PPF is a boundary between the attainable and unattainable combinations of pizza and pasta.

Points inside the PPF and on the PPF are attainable and points outside the PPF are unattainable.

Unattainable points are outside the PPF.

Because the PPF shows the limits to production, it separates attainable combinations from unattainable ones.

PPF is bowed outward, so that as the quantity of pizza and pasta produced increases, it becomes more costly to produce another unit of pizza.

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It is a rectangle, TUVW. A parallelogram has diagonals that are perpendicular and angles that are all 90 degrees.

No, a parallelogram is not always a rectangle. In a rectangle, all angles must be equal to 90°. But for a parallelogram, no angles need to be equal to 90°. In a rectangle the diagonals are equal but in a parallelogram, diagonals are not equal.

Parallelogram has opposite sides equal and parallel. Rectangle also has opposite sides equal and parallel. The difference between the two is that sides of rectangles form 90 degree while that of parallelogram don't.

A square is a parallelogram. This is always true. Squares are quadrilaterals with 4 congruent sides and 4 right angles, and they also have two sets of parallel sides. Parallelograms are quadrilaterals with two sets of parallel sides.

It is a rectangle, TUVW. A parallelogram has diagonals that are perpendicular and angles that are all 90 degrees.

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Answer:

y = - 2x + 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given m = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute (4, - 1 ) into the partial equation

- 1 = - 2(4) + c = - 8 + c ( add 8 to both sides )

7 = c

y = - 2x + 7 ← equation of line

Mathematical induction, .∴ Pn+1 follows if Pn is true. For all positive integers of n, Pn holds true because P1 is true.

Assume that Pn is 4 + 9 + 14 +... + (n/2)(5n + 3)=(5n -1).

First, establish that P1 is accurate when n equals 1.

LHS= 4

RHS

= 1/2(5 + 3)

= 1/2(8)

= 4

= LHS

Is P1 true.

2) Assume Pn to be accurate, i.e., 4 + 9 + 14 +... + ( 5n -1)= (n/2)(5n +3)

3) Establish Pn+1 as true in the induction stage.

Replace (n+1) on both sides of n to obtain Pn+1.

Pₙ₊₁: 4 +9 +14 +...+(5n -1)+ [5(n+1) -1]=

Establish the RHS and LHS's parity.

LHS = 4 +9 +14 +...+(5n -1)+ [5n +5-1]

Bold expression in (2) should be replaced with the value of Pn:

.∴ Pn+1 follows if Pn is true. For all positive integers of n, Pn holds true because P1 is true.

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Integers higher than or equal to -3 and less than or equal to 0 make up the set of numbers (-3 , -2 , -1, 0)

The collection of whole numbers and negative numbers is known as an integer in mathematics. Integers, like whole numbers, do not include the fractional portion. Integers can therefore be defined as numbers that can be positive, negative, or zero but not as fractions.

The formal definition of the set Z of integers is as follows: Z = {..., -3, -2, -1, 0, 1, 2, 3, ...} Unknown or unidentified integers are denoted in mathematical equations by lowercase, italicised letters from the "late middle" of the alphabet. P, q, r, and s are the most prevalent.

The category of whole numbers and the negative of natural numbers is known as integers. Thus, integers can be either positive or negative, including 0.

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An experimental design involves changing an independent variable and observing the impact on a dependent variable. The results are unaffected by other variables because they are controlled.

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The area under the curve over the given interval [-5, 3] can be approximated using 4 left endpoint rectangles.

The formula for this is A = ∑f(xi)∆x. Where A is the area, f(x) is the function, xi is the left rectangles. of the interval, and ∆x is the width of the interval. For this problem, the function is f(x) = (x^2/2) + x + 2 and the given interval is [-5, 3]. So, the left endpoints of the intervals are x1 = -5, x2 = -1, x3 = 3, and x4 = 7 and the width of each interval is ∆x = 4. Plugging these values into the formula, A = (f(-5)∆x) + (f(-1)∆x) + (f(3)∆x) + (f(7)∆x). Simplifying, A = (9*4) + (6*4) + (12*4) + (26*4). Thus, the area under the curve over the given interval is A = 360.

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The total cost of the nuts that Chris and Emily buy can be found using the expression: (1.6a) + (2.8c) + (0.7a) + (1.5c) You can also use the expression (10.6a) + (2.8c) for the total cost of nuts that Chris buy.

pound, unit of avoirdupois weight, equal to 16 ounces, 7,000 grains, or 0.45359237 kg, and of troy and apothecaries’ weight, equal to 12 ounces, 5,760 grains, or 0.3732417216 kg. The Roman ancestor of the modern pound, the libra, is the source of the abbreviation lb. In medieval England several derivations of the libra vied for general acceptance.

Among the earliest of these, the Tower pound, so called because its standard was kept in the Royal Mint in the Tower of London, was applied to precious metals and drugs and contained 5,400 grains, or 0.350 kg, whereas the mercantile pound contained 6,750 grains, or 0.437 kg. The troy pound, believed to have originated in Troyes, France, superseded the lighter Tower pound in 1527 as the gold and silver standard. Increased trade with France led also to the adoption of the 16-ounce avoirdupois pound in the 16th century to replace the mercantile pound.

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You want to know the opinions of American school teachers about establishing a national test for high school graduation then correct option is  D) all American school teachers.

In statistics,  A population is a very large set of individuals or values that belong to a specified group established by researcher.

A sample is a subset of population that represents the entire population in research.

Given : We want to know the opinions of American school teachers about establishing a national test for high school graduation.

Clearly , by the above definition

Population =   all American school teachers.

You obtain a list of the members of the National Education Association and mail a questionnaire to 2500 teachers chosen at random from this list.

sample = 2500 teachers chosen at random from this list.

Hence, the intended population is all American school teachers.

Thus , the correct answer is D) all American school teachers.

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The function is decreasing on the interval (0, [infinity])

The function h of x equals negative 2 times the square root of x is a decreasing function on the interval (0, ∞). This means that as the value of x increases, the value of h(x) decreases. On the interval (-∞, 0), the function is increasing. This means that as the value of x decreases, the value of h(x) increases. The graph of the function looks like a parabola that opens downward and is symmetric around the y-axis. The graph is a concave down curve, and the y-intercept is at (0, 0). As the value of x gets closer to 0, h(x) approaches negative infinity. As x approaches infinity, h(x) approaches 0. This means that the range of h(x) is (-∞, 0].In order to determine if the function is increasing or decreasing on a given interval, we need to look at the sign of the derivative of the function on the interval.

The derivative of h(x) is -2/sqrt(x).

For the interval (0, [infinity]), the derivative of h(x) is negative, indicating that the function is decreasing.

For the interval (–[infinity], 0), the derivative of h(x) is positive, indicating that the function is increasing.

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Using Subtraction, The Sun was out for 7 1/30 hours more than Monday.

To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference.

Finding the difference between two numbers is what it entails. The icon is as follows: (minus). We take a number and divide it by a smaller number in this operation.

On monday the sun was out for 3 3/10 hours.

On tuesday the sun was out for 6 1/5 hours.

the sun out on tuesday than monday =

Using Subtraction,

⇒ 31/ 3 - 33/10

⇒  310 - 99/30

⇒  211/30

⇒ 7 1/30 hours

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Answer:

-2.43, -2, 5/9, 2/3, 2, 2.045

Step-by-step explanation:

Negative numbers are less than positive numbers, and we can go in numerical order from 1, 2, 3 to find which number is greater than the other

Answer:

Perimeter = 8π cm

Area = (32π - 64) cm²

Step-by-step explanation:

ABCD is a square.

Therefore:

The perimeter of the shaded part is the sum of two congruent quarter circles, i.e. half the length of the circumference.

The arcs AC are quarter circles of a circle with radius 8 cm.

Therefore the perimeter of the shaded area is:

[tex]\implies \sf Perimeter=Half\;circumference=\dfrac{1}{2} \cdot 2\pi r=\pi r=8\pi\;cm[/tex]

To find the area of the shaded area, subtract the two unshaded areas from the area of the square.

As the two unshaded areas are congruent we only need to find the area of one unshaded area.

The area of one unshaded area is the area of the square minus the area of the sector ADC (which is a quarter of a circle with radius 8 cm).

[tex]\begin{aligned}\implies \textsf{Area of one unshaded area}&=\textsf{Area of square}-\textsf{Area of $\frac{1}{4}$ circle}\\&=64-\dfrac{1}{4} \pi r^2\\&=64-\dfrac{1}{4} \pi \cdot 8^2\\&=64-\dfrac{1}{4} \pi \cdot 64\\&=(64-16 \pi)\; \sf cm^2\end{aligned}[/tex]

Now we have found the area of one unshaded area, to calculate the area of the shaded area simply subtract two unshaded areas from the area of the square:

[tex]\begin{aligned}\implies \textsf{Shaded area}&=64-2(64-16\pi)\\&=64-128+32\pi\\&=(32\pi-64)\; \sf cm^2 \end{aligned}[/tex]

The number of students in the population would be:

The sample is directly related to the population of students so parts of the students can be found using the sample.

Students in population who wear glasses :

= Sample who wear glasses / Total sample x Total population

= 11 / 50 x 750

= 165 students

Students who wear contacts:

= 4 / 50 x 750

= 60 students

Students with no vision problems :

= 35 / 50 x 750

= 525 students

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The primitive data type number has the entry 1, or 1, in the database dictionary.

The database dictionary's entry for the number data type, which is a primitive data type, is 1, or 1. It is possible for a number to be a whole number, a positive or negative number, or a floating point number, and it can also denote an amount.

Numbers are stored as numeric data types in database columns. Exact numeric kinds, values where the precision and scale need to be retained, are normally the categories into which these data types are grouped. There are six distinct sorts of numbers: INTEGER, BIGINT, DECIMAL, NUMERIC, NUMBER, and MONEY.

Integral, Floating Point, Character, Character String, and Composite types are the five fundamental categories of data types recognized by the majority of current computer languages. Within each of these broad categories, numerous particular subtypes are established.

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Answer: y =1x-5

Step-by-step explanation:

The question asks for the slope form y =mx+b, where m is the slope and b is the y-intercept. The y-intercept is the y value when x = 0, also known as when the line intercepts the verticle origin line. On your graph, this point is (0, -5). So, b = -5. Now, we need to pick two points to find the slope using the equation (y2-y1)/(x2-x1). Any two points on the line will work, so even if you do not pick the same points as me, you should still get the same answer.

point one: (0,-5)

point two: (4,-1)

m = (-1 - -5) / (4 - 0) = (-1+5)/(4) = 4/4 = 1

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