Simplify (s^-5)^3. Write your answer using only positive exponents.

Answer: For all three functions, the direction of fastest increase at the point (1, 1, 1) is the direction of the gradient vector of the function at that point.

For function (a), the gradient vector at (1, 1, 1) is given by the partial derivatives of the function at that point:

[2/x³, 2y, 22] = [2, 2, 22].

The direction of this gradient vector is given by the direction in which each of its components is increasing the most rapidly. In this case, all three components are increasing at the same rate, so the gradient vector points in the direction of the positive x, y, and z axes.

For function (b), the gradient vector at (1, 1, 1) is given by the partial derivatives of the function at that point:

[4y + 4z, 4x + 4z, 4x + 4y] = [4, 4, 4].

Again, all three components are increasing at the same rate, so the gradient vector points in the direction of the positive x, y, and z axes.

For function (c), the gradient vector at (1, 1, 1) is given by the partial derivatives of the function at that point:

[2x, 2y, 2z] = [2, 2, 2].

As before, all three components are increasing at the same rate, so the gradient vector points in the direction of the positive x, y, and z axes.

Therefore, for all three functions, the direction of fastest increase at (1, 1, 1) is the direction of the positive x, y, and z axes.

Step-by-step explanation:

The height in feet of its replica at this park, rounded to the nearest whole number is 14 feet.

Distance is the measurement of an object's horizontal distance from a specific location, whereas height is the measurement of an object's height in the vertical direction.

Since the heights of real buildings are 1:10 times higher than those of model buildings, this is evident. We also know that the actual height of the US Capitol is 289 feet, so we divide that figure by 20 to determine the model's height. That amounts to 14.45, rounding to 14. Thus, the duplicate is 14 feet, rounded up to the nearest whole number.

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35% in each package is red.

that means nothing else than for every M&M you pick, the probability is 35% (or 0.35) that is is red.

it also means the probability to get anything but red is 1 - 0.35 = 0.65 (65%).

if I understand you correctly, the question is for the probability that there are no more than 18 red M&Ms in a package of 52.

in other words, the probabilty that there are exactly 18, or exactly 17, or exactly 16 ... or exactly 1, or no red M&Ms.

the probability to get exactly 18 red out of 52 is

0.35¹⁸ × 0.65³⁴

for one of the combinations.

and we have C(52, 18) possible combinations :

52! / (18! × (52-18)!) = 52! / (18! × 34!)

18 red = 0.35¹⁸ × 0.65³⁴ × C(52, 18) = 0.115457378...

17 red = 0.35¹⁷ × 0.65³⁵ × C(52, 17) = 0.110273578...

16 red = 0.35¹⁶ × 0.65³⁶ × C(52, 16) = 0.096708177...

15 red = 0.35¹⁵ × 0.65³⁷ × C(52, 15) = 0.077665254...

14 red = 0.35¹⁴ × 0.65³⁸ × C(52, 14) = 0.056935055...

13 red = 0.35¹³ × 0.65³⁹ × C(52, 13) = 0.037956703...

12 red = 0.35¹² × 0.65⁴⁰ × C(52, 12) = 0.022909582...

11 red = 0.35¹¹ × 0.65⁴¹ × C(52, 11) = 0.012452595...

10 red = 0.35¹⁰ × 0.65⁴² × C(52, 10) = 0.006056874...

9 red = 0.35⁹ × 0.65⁴³ × C(52, 9) = 0.002615926...

8 red = 0.35⁸ × 0.65⁴⁴ × C(52, 8) = 0.000993712...

7 red = 0.35⁷ × 0.65⁴⁵ × C(52, 7) = 0.000328083..

6 red = 0.35⁶ × 0.65⁴⁶ × C(52, 6) = 9.271902896e-005

5 red = 0.35⁵ × 0.65⁴⁷ × C(52, 5) = 2.198201902e-005

4 red = 0.35⁴ × 0.65⁴⁸ × C(52, 4) = 4.252473918e-006

3 red = 0.35³ × 0.65⁴⁹ × C(52, 3) = 6.446899235e-007

2 red = 0.35² × 0.65⁵⁰ × C(52, 2) = 7.183687719e-008

1 red = 0.35 × 0.65⁵¹ × C (52, 1) = 5.231817386e-009

0 red = 0.35⁰ × 0.65⁵² × C(52, 0) =

= 0.65⁵² = 1.868506209e-010

the probability to have no more than 18 reds is the sum of all that :

0.540472593...

FG stands for Function Generator, which is a device that produces electrical signals with a function of frequencies and amplitudes. It is commonly used in scientific laboratories to generate signals for testing and research purposes.

A function generator is an electrical device used to generate electrical signals with a range of frequencies and amplitudes. It is commonly used in scientific laboratories to generate test signals for testing and research purposes. Function generators typically consist of an oscillator, amplifier, and waveform selector. The oscillator generates a signal of a given frequency and amplitude, while the amplifier adjusts the output voltage. The waveform selector allows the user to choose from a variety of waveforms, such as sine, square, triangle, and sawtooth. Function generators can be used to simulate various types of electrical signals, such as AC and DC signals, as well as a variety of noise signals. They are also used to test various types of electronic components, such as transistors and capacitors, and to conduct research in fields such as telecommunications and signal processing. The acronym FG stands for Function Generator.

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Answer:

52 bags and 2 extra

Step-by-step explanation:

Simply divide the no. of rolls by no. of rolls per bag

Answer:

12 bags

Step-by-step explanation:

158 rolls ÷ 13 rolls/bag = 12.15 bags

You will have 12 full bags plus about 2 extra rolls left over, which you can try to sell separately or as a "pack" of 2.  Or, you can sell one overstuffed bag with 2 extra rolls in it (for a total of 15 rolls) for a little extra on the price.

The completed blanks in the statement are underlined as follows

From the question, we have the following parameters that can be used in our computation:

A mathematical expression

The mathematical expression is given as

2x⁴ + 53x⁵ - 2 + x⁶

The standard form

To do this, we rearrange the expression from the highest power to the least

So, we have the following representation

x⁶ + 53x⁵ + 2x⁴  - 2

The degree

This is the highest power in the expression

So, the degree is 6

The leading coefficient

This is the coefficient of the term that has highest power of x

So, the leading coefficient is 1

The name of the expression

The expression has 4 terms

So, the name is a polynomial

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The solution of the pair of equations y = 0 and y = -3 is y = -3/2.

The given pair of equations is:

y = 0

y = -3

We can solve this pair of equations using elimination. To do this, we first add the two equations together, which gives us:

y + y = 0 + (-3)

2y = -3

We then divide both sides by 2 to get the solution for y:

2y/2 = -3/2

y = -3/2

Therefore, the solution of the pair of equations y = 0 and y = -3 is y = -3/2.

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The experimental probability is 30% higher than the predicted probability.

What is meant by experimental probability?

Experimental Probability: what actually occurs when the experiment is carried out. For example, the probability of getting a head if you flip a coin is ½, since only 2 things could happen (a head or a tail) and each one has an equal chance of occurring.

The spinner has 10 sections and a 10% chance of landing on the section representing rain. Therefore, the probability of rain predicted by the spinner is 0.1 or 10%.

From the simulation, the results are 3, 6, 1, 8, and 3. Out of these 5 spins, 2 of them landed on the section representing rain (1, 3). Therefore, the experimental probability of rain from the simulation is 2/5 or 40%.

The difference between the experimental probability from the simulation and the prediction is the difference between the two percentages, which is:

(experimental probability) - (predicted probability) = 40% - 10% = 30%

Hence, the experimental probability is 30% higher than the predicted probability.

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Answer:

-33

Step-by-step explanation:

Plug 9 in for c, then simplify the resulting expression.

5c - 9c + 3

5(9) - 9(9) + 3

↓ execute multiplication

45 - 81 + 3

↓ simplify by adding 81 and 3

45 - 84

↓ execute subtraction

-33

Answer:

[tex] \sf \: - 33 \: (if \: c = 9)[/tex]

Step-by-step explanation:

Given expression,

→ 5c - 9c + 3

Now we have to use,

→ c = 9

Simplifying the given expression,

→ 5c - 9c + 3

→ 5(9) - 9(9) + 3

→ 45 - 81 + 3

→ -36 + 3

→ -33 => (answer)

Hence, required answer is -33.

1)correct option is b) true

2)Which of the following expressions always evaluates to true?

 correct option is d)(x > 0) && (x == 0)

given that

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Many authors make a distinction between an expression and a formula, with the former designating a mathematical object and the latter a claim about such objects.

x = 5 and y = 7

Choose the value of the following expression: (x != 7) && (x <= y)

a. false

b. true

c. 0

d. null

(5! = 7) && (5<=7)

5 ≠ 7

correct option is b) true

Suppose that x is an int variable.

Which of the following expressions always evaluates to true?

a. (x > 0) || ( x <= 0)

b. (x > 0) && ( x <= 0)

c. (x >= 0) 11 (x == 0)

d. (x > 0) && (x == 0)

a) x = 1,2,3.... || x =0,-1,-2,-3......

b)x = 1,2,3.... && x = 0,-1,-2,-3,.....

c) x = 0,1,2,3..... 11 x = 0

d) x = 1,2,3.... && x = 0

correct option is d)(x > 0) && (x == 0)

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Answer:128 cm^2

Step-by-step explanation:

Answer:

18b^6

Step-by-step explanation:

3b⁴ x 6b²

Answer:

A = 80 cm²

Step-by-step explanation:

the area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the perpendicular height )

here b = 4 and h = 2 , then

A = 4 × 2 = 8 cm²

there are a total of 10 tiles required ( 5 black and 5 white ) , then total area is

A = 10 × 8 cm² = 80 cm²

You ran 1/8 of miles more today than yesterday.

Subtraction can be done for any numbers or algebraic expressions. It is the process of taking out certain value from a given amount of number.

Miles you ran yesterday is three fourths of a mile.

Let 1 mile be M.

Miles you ran yesterday = 3/4 M

Today you ran seven-eighths of a mile.

Miles you ran today = 7/8 M

Difference of miles = 7/8 M - 3/4 M

3/4 is same as 6/8.

Difference of miles = 7/8 M - 6/8M

                                = 1/8 M

Hence you ran 1/8 of miles more than yesterday.

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The distance and bearing of the boat from its original location are about 183.33 miles, N71.97°E

A bearing is a description of the amount by which a north or south headed line is deflected in the eastern or western direction.

The initial direction in which the boat is traveling = Due east

The distance the boat travels in the direction due east = 130 miles

The distance the boat travels in the direction N38°E = 72 miles

Therefore;

The distance the boat has traveled from its original location is found using the law of cosines as follows;

The included angle between the 130 miles distance the boat travels east and the 72 miles distance the boat travels N38°E = 90° + 38° = 128°

Let d represent the distance of the boat from its original location, we get;

d² = 130² + 72² - 2 × 130 × 72 × cos(128°) ≈ 33609.1828181

d ≈ √(33609.1828181) ≈ 183.33

The distance of the boat from its original location is about 183.33 miles

Let the angle formed by the direction of the boat to its destination and the path the boat travels east, according to the law of sines, we get;

183.33/(sin(128°) ≈ 72/(sin(B))

(sin(B)) ≈ 72 × (sin(128°))/183.33

m∠B ≈ arcsin(72 × (sin(128°))/183.33) ≈ 18.03°

The bearing of the boat from its original location is; N(90° - 18.03°)E = N71.97°E

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X²-3There are a number of ways to factor equations like x2 -3x+2=3x+2=0. If all the terms are positive: (x + ) (x + )=0,  If the center term is negative: ( (-)( x -)=0 • If the last or if both terms are negative: ( x +)(x-)=0

The following are the rulesIf, ll trinomial terms are positive, then all binomial terms will be positive.If the trinomial’s last term is negative but the middle and first terms are positive, one term of the binomial will be negative and the other will be positive.

If we can find two numbers whose product is A * C and whose sum is B, we may factor a trinomial of the type Ax2 + Bx + C. Exemplification 1. Determine if 4x2 + 8x + 3 can be factored. Solution. We want for two numbers whose product is (4)(3) = 12 and whose total is 8. (the coefficient of x).

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The domain and range of the logarithmic function is given by:

Domain= [ 0 , ∞ ) and Range = { y ∈ R }.

As given in the question,

Let y = logₐ x be the given logarithmic function.

Logarithmic function is defined for all the positive values.

Domain of the logarithmic function is given by x∈ R , x > 0.

Range of the logarithmic function is inverse of the domain of the exponential function.

x = e^y

Here y is set of all the real numbers.

Range of logarithmic function is set of all the real numbers.

Therefore, domain of the logarithmic function is set of all real number greater than zero and range of the logarithmic function is the set of all the real numbers.

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On solving the provided question we can say that - in fractions 2/3 and 2 we can do 2/3X2 = 4/3

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. 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. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

here,

in the given fractions 2/3 and 2/1,

we can do that -

2/3 X 2/1 = 4/3

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A statement which best describes the solution set of the given inequality 5n + 1.5 ≥ 4 is: C. all rational number values of n that are at least 0.5.

In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals such as the 12, 0.5, √16, etc.

Next, we would translate the word problem into algebraic inequality and then solve for the value of n as follows;

5n + 1.5 ≥ 4

Subtracting 1.5 from both sides of the algebraic inequality, we have:

5n + 1.5 - 1.5 ≥ 4 - 1.5

5n ≥ 2.5

Dividing both sides of the algebraic inequality y 5, we have:

n ≥ 2.5/5

n ≥ 0.5

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Complete Question:

Grant reads as part of his homework each week. he must read for at least 4 hours each week as part of his homework. This past weekend, he reads for 1.5 hours. Grant makes a graph of the inequality 5n +1.5 greater than or equal to 4 to determine all the numbers, n, of hours he could read on each of the 5 weekdays this week. The graph is shown.

Which describes the solution set of the inequality?

A. all whole number values of n that are at least 1

B. all whole number values of n that are greater than 1

C. all rational number values of n that are at least 0.5

D. all rational number values of n that are greater than 0.5

178 students taking a music class and 82 students taking an art class

There was no clear question, but I'm assuming you want to know how many students are enrolled in music and painting classes.

Let x= the number of children enrolled in art classes.

number of children enrolled in music classes: 2x + 14

The overall number of children will be 260, including all of these children.

x+2x+14 = 260

3x=246 x=82 pupils attend an art lesson.

To find people taking music classes, enter x to 2x+14.

2(82)+14 = 178

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The complete question would be;

There are 260 eighth-grade students at South Whitemarsh Middle School. All eighth-grade students are required to enroll in either a music class or an art class. No students take both art and music classes. The number of students taking music classes is 14 more than twice the number taking art classes.

After solving the algebraic equation, Miguel has 4 quarters, 12 dimes and 16 nickels.

What is algebra?

One of the earliest areas of mathematics that deals with number theory, geometry, and analysis is algebra. Algebra is also defined as the study of mathematical rules and symbols through the manipulation of those mathematical symbols.

The number of quarters is taken to be x, then the number of dimes will be 3x, and the number of nickels will be 3x + x = 4x

$3.00 when converted to cents is 300 cents.

The value of nickels is 5 x 4x=20x.

The value of dimes is 10 x 3x=30x.

The value of quarters is 25x.

As the total value of money Miguel has is 300 cents, then the algebraic equation will be -

20x + 30x + 25x = 300

Solve to get the value of x -

75x = 300

x = 4

Therefore, the amount of quarters is x = 4 quarters.

The amount of dimes is x = 3x = 3 x 4 = 12 dimes.

The amount of nickels is 4x = 4 x 4 = 16 nickels.

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The radius of a sphere whose surface area is  324*pi cm² is:

R = 9 cm.

We know that the surface of a sphere of radius R is given by:

S = 4*pi*R^2

Where pi = 3.14

Here we know that a sphere has a surface of 324*pi cm², then we can write the equation:

S =  324*pi cm² = 4*pi*R^2

We can divide both sides by pi, so we get:

324 cm^2 = 4*R^2

Now we can solve that equation for R, we will get:

R^2=  (324 cm^2)/4 = 81cm^2

R = √(81 cm^2)

R = 9cm

The radius of the sphere is 9cm.

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Answer:

First, you need to calculate your grade in percentages. The total answers count 70 - it's 100%, so we to get a 1% value, divide 70 by 100 to get 0.70. Next, calculate the percentage of 15: divide 15 by 1% value (0.70), and you get 21.43% - it's your percentage grade.

Step-by-step explanation:

Step-by-step explanation:

Regular decagons have two additional identifying properties: 10 exterior angles of 36° , summing to 360° 10 interior angles of 144° , summing to 1,440°

Each interior angle of a regular dodecagon is equal to 150°. Each exterior angle of a regular dodecagon is equal to 30°. 30×12= 360

Answer: -2(4*2+(1/2)2) = -18

Step-by-step explanation: In order to solve this problem, we just have to use the order of operations. This can be shortened to PEMDAS.

The first step is PARENTHESIS. There are two parenthesis within this problem, so we start from the smaller ones and then go to the bigger ones. So, 1/2. That's equal to 0.5, so now we have -2(4*2+(0.5)2).

There are no EXPONENTS within this problem, so we skip the E part of the order.

Next is MULTIPLICATION and DIVISION. There are two instances of multiplication within the parenthesis. 4*2 is equal to 8. Because 2 is right next to the parenthesis, its contents are being multiplied by it. So, 0.5*2 is equal to 1.

Next is ADDITION and SUBTRACTION. There's no subtraction, but we can add 1 and 8 to get 9. This was the final process within the parenthesis, so now we can focus on what's happening outside.

For the same reasons mentioned before, we know that 9 is being multiplied by -2. 9*-2 is equal to -18. This is because any positive number multiplied by a negative number will result in a negative product.

Thus, our final answer is -18.

Diana's savings will be 280 dollars after four weeks.

Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.

The expression is given in the question, as follows:

300 - 5x

Where x represents the number of the week.

We have to determine Diana's savings after four weeks

As per the question, we have

⇒ 300 - 5x

Substitute the value of x = 4 in the above expression

⇒ 300 - 5(4)

⇒ 300 - 20

⇒ 280

This means her savings will be 280 dollars after four weeks.

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The question seems to be incomplete the correct question would be:

Diana's savings at the end of each week can be described by the expression 300-5x where x represents the number of the week.

What is her savings after four weeks?

Some polynomials have specific names indicated by their prefix like monomial is a polynomial with exactly one term (“mono”—means one) binomial is a polynomial with exactly two terms (“bi”—means two) trinomial is a polynomial with exactly three terms (“tri”—means three).

Some polynomials have unique names that are denoted by their prefix, such as monomial, which is a polynomial with precisely one term ("mono"—means one). A binomial polynomial has precisely two terms ("bi" indicates two). A trinomial is a polynomial with three terms ("tri"—three). A polynomial is a mathematical statement made up of indeterminates and coefficients that solely includes the operations of addition, subtraction, multiplication, and positive-integer powers of variables. x2 4x + 7 is an example of a polynomial with a single indeterminate x.

Here,

Some polynomials have unique names that are denoted by their prefix, such as monomial, which is a polynomial with precisely one term ("mono"—means one). A binomial polynomial has precisely two terms ("bi" indicates two). A trinomial is a polynomial with three terms ("tri"—three).

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A solution set is the set of all variables or numbers that makes the equation true.

If solving a linear equation leads to a true statement is equal to 0 = 0 the equation is an identity. Its solution set is all real numbers.A solution set is the set of values that satisfy a given set of equations or inequalities. The feasible region of a constrained optimization problem is the solution set of the constraints.

There are three possibilities for the number of real solutions of a quadratic equation, and those are that a quadratic equation can have no real solutions, exactly one real solution, or exactly two real solutions.Zero is considered to be both a real and an imaginary number.

Now we can find solution set by solving the equation.

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The evaluation of the expression 2(b + 4) when b = 4 is 18

From the question, we have the following parameters that can be used in our computation:

Expression: 2(b + 4)

Values: b = 5

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

2(b + 4) = 2 * (5 + 4)

Evaluate the products

This gives

2(b + 4) = 10 + 8

Evaluate the like terms in the equation

So, we have the following representation

2(b + 4) = 18

Using the above as a guide, we have the following:

The solution is 18

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