Complete the process of solving the equation.
Fill in the missing term on each line. Simplify any fractions.
11w + 3 = 14
11w =
W =
Subtract 3 from both sides
Divide both sides by 11

The negative of the gradient (-grad f(x)) points in the direction of the maximum decrease of f from x.

The gradient of a scalar-valued function is a vector that points in the direction of the maximum increase of the function.

In other words, if we consider a point in the domain of the function and take the gradient at that point, the direction of the gradient vector indicates the order in which the function increases the most from that point. Conversely, the negative gradient points in the direction of the maximum decrease of the function.

Specifically, let f be a scalar-valued function of n variables [tex](f: R^n - > R),[/tex]and let x be a point in the domain of f. The gradient of f at x is defined as the vector:

[tex]grad f(x) = (∂f/∂x1, ∂f/∂x2, ..., ∂f/∂xn)[/tex]

where ∂f/∂xi denotes the partial derivative of f with respect to xi evaluated at x, the direction of the gradient vector grad f(x) at x is the direction in which f increases the most from x, and the magnitude of the gradient vector is the rate of change of f at x in that direction.

The negative of the gradient (-grad f(x)) points in the direction of the maximum decrease of f from x.

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A replacement value is a value that can be substituted for a variable in an equation or expression in order to solve for that variable or simplify the expression.

An expression is a combination of numbers, variables, and/or operators that represents a mathematical relationship or calculation. An expression can be as simple as a single number or variable, or it can be more complex and involve multiple operations and variables.

A variable is a symbol or letter that represents a quantity or value that can change or vary in different contexts.

In the given question,

A replacement value is a value that can be substituted for a variable in an equation or expression in order to solve for that variable or simplify the expression.

For example, suppose you have the equation 2x + 3 = 7, and you want to solve for x.

To do so, you can use a replacement value.

You can subtract 3 from both sides of the equation to isolate the term with x, which gives you:

2x = 4

Now, you can divide both sides of the equation by 2 to solve for x:

x = 2

In this case, the replacement value was the number 2, which was substituted for the variable x in the equation in order to solve for x.

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The number of words formed with letters of the word 'PROBLEM' which neither start with O nor end with E is 3600.

The word PROBLEM has 7 letters, which can be arranged in 7! (factorial) ways, i.e. [tex]7*6*5*4*3*2*1 = 5040.[/tex]

Now to calculate the number of words formed with letters of the word 'PROBLEM' which neither start with O nor end with E, we can first calculate the number of words which start with O or end with E.

For words starting with O, there are 6 letters left and these can be arranged in 6! ways, i.e.[tex]6*5*4*3*2*1 = 720.[/tex]

For words ending with E, there are again 6 letters left and these can be arranged in 6! ways, i.e. [tex]6*5*4*3*2*1 = 720[/tex].

Now the total number of words which start with O or end with E will be the sum of two, i.e. 720 + 720 = 1440.

Therefore, the number of words formed with letters of the word 'PROBLEM' which neither start with O nor end with E will be the total number of words minus the total number of words which start with O or end with E, i.e. 5040 - 1440 = 3600.

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The minors and cofactors of the given matrix are:

|882 270 -72| |-490 194 198| |78 -44 -72|

To find the minors and cofactors of the given matrix, we first need to understand what a minor and a cofactor are.

The minor of an element a_ij is the determinant of the submatrix obtained by deleting the i-th row and j-th column of the original matrix.

The cofactor of an element a_ij is the minor of a_ij multiplied by (-1)^(i+j).

Using this definition, we can find the minors and cofactors of the given matrix as follows:

Minor of a_11:

|-7 9 5 -1|

|-5 -9 -7 9|

|-6 -3 -7 9|

Minor = (-7)(-9)(-7) + (9)(-7)(-6) + (5)(-5)(-3) + (-1)(-6)(9) = 882

Cofactor of a_11:

Cofactor = (-1)^(1+1) * 882 = 882

Minor of a_12:

|-6 -3 -7 9|

|-5 -9 -7 9|

|-5 -1 -9 5|

Minor = (-6)(-9)(-9) + (-3)(-7)(5) + (-7)(-5)(-1) + (9)(-5)(-5) = -270

Cofactor of a_12:

Cofactor = (-1)^(1+2) * (-270) = 270

Minor of a_13:

|-6 -6 -3|

|-5 -9 -7|

|-5 -1 -9|

Minor = (-6)(-9)(-9) + (-6)(-7)(-1) + (-3)(-5)(-1) + (-9)(-5)(-6) = -72

Cofactor of a_13:

Cofactor = (-1)^(1+3) * (-72) = 72

Minor of a_21:

|-5 -9 -7 9|

|-6 -3 -7 9|

|-5 -1 -9 5|

Minor = (-5)(-7)(-9) + (-9)(-5)(-5) + (-7)(-5)(-1) + (9)(-1)(-5) = 490

Cofactor of a_21:

Cofactor = (-1)^(2+1) * 490 = -490

Minor of a_22:

|-6 -6 -3|

|-5 -1 -9|

|-5 -1 -9|

Minor = (-6)(-9)(-1) + (-6)(-1)(-5) + (-3)(-5)(-1) + (-9)(-5)(-5) = 194

Cofactor of a_22

Cofactor = (-1)^(2+2) * 194 = 194

Minor of a_23:

|-6 -6 -3|

|-5 -9 -7|

|-5 -1 -9|

Minor = (-6)(-9)(-7) + (-6)(-7)(-1) + (-3)(-5)(-1) + (-7)(-5)(-6) = 198

Cofactor of a_23:

Cofactor = (-1)^(2+3) * (-198) = 198

Minor of a_31:

|-5 -9 -7|

|-6 -3 -7|

|-5 -1 -9|

Minor = (-5)(-3)(-9) + (-9)(-5)(-1) + (-7)(-6)(-1) + (-6)(-1)(-7) = -78

Cofactor of a_31:

Cofactor = (-1)^(3+1) * (-78) = 78

Minor of a_32:

|-6 -6 -3|

|-5 -1 -9|

|-5 -1 -9|

Minor = (-6)(-9)(-1) + (-6)(-1)(-5) + (-3)(-5)(-1) + (-1)(-5)(-5) = 44

Cofactor of a_32:

Cofactor = (-1)^(3+2) * 44 = -44

Minor of a_33:

|-6 -6 -3|

|-5 -9 -7|

|-6 -3 -7|

Minor = (-6)(-9)(-7) + (-6)(-7)(-3) + (-3)(-6)(-1) + (-7)(-5)(-6) = -72

Cofactor of a_33:

Cofactor = (-1)^(3+3) * (-72) = -72

Therefore, the minors and cofactors are:

|882 270 -72| |-490 194 198| |78 -44 -72|

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The marginal probability function E(Y1) = 2/3, variance of a binomial distribution is V(Y1) = 4/9, and E(Y1-Y2) = 0, using the joint probability function for Y1 and Y2 and the fact that they have binomial distributions with n=2 and p=1/3.

The marginal probability function of Y1 is binomial with n=2 and p=1/3, as given in Exercise 5.19. Therefore, we have:

E(Y1) = np = 2(1/3) = 2/3.

The variance of a binomial distribution with parameters n and p is given by np(1-p), so we have:

V(Y1) = np(1-p) = 2(1/3)(2/3) = 4/9.

We can use the linearity of expectation to find E(Y1-Y2):

E(Y1 - Y2) = E(Y1) - E(Y2)

We know that E(Y1) = 2/3 from part (a), but we need to find E(Y2). Using the same reasoning as in part (a), we find that the marginal probability function of Y2 is also binomial with n=2 and p=1/3. Therefore, we have:

E(Y2) = np = 2(1/3) = 2/3.

Substituting these values into the expression for E(Y1-Y2), we get:

E(Y1 - Y2) = 2/3 - 2/3 = 0.

Therefore, E(Y1-Y2) is equal to 0.

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Answer:

the two numbers are 15 and 35, and their ratio is 3:7, and their difference is 20.

Step-by-step explanation:

The probability of spinning a slice that is not yellow is equal to the total number of non-yellow slices divided by the total number of slices.

Total number of non-yellow slices = 9 (3 red + 5 blue)

Total number of slices = 12

Therefore, the probability of spinning a slice that is not yellow is 9/12 or 75%.

Answer:

Step-by-step explanation:

Answer:

x=12

Step-by-step explanation:

2x-y=15

y=9

2x-9=15

2x=24

x=12

Answer:

B

Step-by-step explanation:

It's like a piece of paper, fold it in half

Answer:157

Step-by-step explanation:

it just is =]

10.5% is better because 20 dollers is good but it not gonna increase like 10.5%

To solve this equation, begin by expanding the parentheses.

y = 4x² + 40x + 100 + 16

Then, collect like terms on the left hand side.

y = 4x² + 40x + 116

Finally, rearrange the equation to get y on the left side.

4x² + 40x - (y - 116) = 0

The final answer will be a quadratic equation.

The measure of angle BAC is 55°, which is closest to option B (50°).

The ratio of the length of the side directly opposite an acute angle to the side directly adjacent to the angle is known as the tangent in trigonometry. Only triangles with straight angles can have this.

Let's give the angles shown in the diagram the following labels:

Angle ACD = 55°

Angle ABD = 35°

Angle BCD = 90°

To determine the size of angle ABC, we can use the knowledge that a triangle's total angles equal 180°. Because the straight line formed by angles ABD and BCD, we have:

[tex]Angle ABC = 180° - Angles ABD and BCD.[/tex]

[tex]Angle ABC = 180° - 35° - 90°Angle ABC = 55°[/tex]

Given that triangle ABC has two angles, we can use the knowledge that a triangle's total of angles equals 180° to determine the size of angle BAC:

[tex]Angle BAC = 180° - Angle ABC - Angle ACBAngle BAC = 180° - 55° - 70°Angle BAC = 55°[/tex]

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It is most similar to option B (50°) when the angle BAC is 55°.

What is a tangent angle?

The tangent in trigonometry is the length of the side directly opposite an acute angle divided by the length of the side directly next to the angle.

This property can only be found in triangles with straight angles.

Let's give the angles shown in the diagram the following labels:

Angle ACD = 55°

Angle ABD = 35°

Angle BCD = 90°

We can use the fact that a triangle's total number of angles is 180° to calculate the size of angle ABC. due to the fact that the straight line created by angles ABD and BCD

Triangle ABC has two angles, so we can use the fact that a triangle's sum of angles is 180° to calculate the size of angle BAC.

Therefore, the BAC measurement is 55°, which is closest to option B's 50°.C is 55°, which is closest to option B (50°).

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Answer: 1979.2 meters

Step-by-step explanation:

Diameter of wheel is 63 cm. Circumference is 63π = 197.92 cm. 1000 revolutions of 197.92 = 197920 cm = 1979.2 meters.

let's reword it

what is the arc of a circle whose central angle is 100 revolutions and has a radius of 63÷2?

let's keep in mind that radius is half the diameter, and a revolution is 2π radians or 360°, so hmmm 100 revolutions will just be 360*100 = 36000°.

[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ \theta =36000\\ r=\frac{63}{2} \end{cases}\implies s=\cfrac{(36000)\pi (\frac{63}{2})}{180}\implies s=\cfrac{(36000)(\frac{22}{7}) (\frac{63}{2})}{180} \\\\\\ s=200(\frac{22}{7}) (\frac{63}{2})\implies s=(200)(99)\implies \boxed{s=19800}~metres[/tex]

The fixed price of the land is 296257.50.

What is discount?

Discount is the state of having a bond's price lower than its face value. The difference between the purchase price and the item's par value is the discount.

Discounts are different types of price reductions or deductions from a product's cost. It is frequently employed in consumer transactions when consumers receive discounts on a range of goods. The % discount rate is provided.

Here the discount on the fixed price = 10%

Commission for the broker = 5%

If total amount = 100%+10% = 110%

Then received amount = [tex]\frac{110}{100}\times256500[/tex]

=> Received amount =  282150

Now 5% commission then,

=> [tex]\frac{105}{100}\times 282150[/tex] = 296257.50.

Hence the fixed amount of the land before discount is 296257.50.

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The best description of the research design for this study is a controlled experiment.

What is a controlled experiment?

A controlled experiment is a type of scientific investigation in which an independent variable is manipulated and the dependent variable is measured while controlling for other variables that may affect the outcome.

Finding the best description of the research design for this study :

In this research study, the researchers are manipulating the environment in which the dogs are kept. Two dogs are kept away from human beings during the day and freed at night, while the other two dogs are kept in an environment where they regularly engage with human beings at both the day and the evening. By doing this, the researchers can observe and measure the behavior of the dogs in both groups and determine if there is a difference in their behavior towards trespassers.

This research design is a controlled experiment because the researchers are manipulating one variable, which is the environment in which the dogs are kept, while keeping other variables constant. This allows them to establish cause-and-effect relationships between the independent variable (environment) and the dependent variable (dog behavior).

In conclusion, the research design for this study is a controlled experiment because it involves manipulating the environment in which the dogs are kept and measuring their behavior while controlling for other variables that may affect the outcome.

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Answer:

this is when you want to draw a sketch of a building

Answer:

80 %

Step-by-step explanation:

FRACTIONS

X/100 = 25,390/32,000

CROSS MULTIPLICATION

X * 32,000 = 32,000X

25,390*100 = 2,539,000

DIVIDE

2,539,000/32,000 = 32000X/32000- CANCEL

X = 79.34375 % Round - X = 80%

If there are 95 families to feed then each family will receive 11 cans of assorted tins.

Assorted tins typically refer to cans or containers of food items that come in different varieties or flavors.

To calculate the number of cans each family will receive, we need to first determine the total number of cans in the 19 boxes.

19 boxes × 55 cans per box = 1045 cans

Now we can divide the total number of cans by the number of families to determine the number of cans each family will receive:

1045 cans ÷ 95 families = 11 cans per family (rounded to the nearest whole number)

Therefore, each family will receive 11 cans of assorted tins.

For example, a box of assorted tins may contain cans of different types of vegetables, fruits, soups, or other food items. The specific assortment may vary depending on the context and the supplier. In the context of the given question, the 19 boxes of assorted tins likely contain cans of different types of food that will be packed into food parcels for the poor.

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Mathematicians divide the world of numbers into seven subsets, namely natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, and complex numbers.

Natural numbers: These are the counting numbers, starting from 1 and continuing indefinitely. They can also be denoted as "N" or "ℕ".

Whole numbers: These are the natural numbers, as well as zero. They can also be denoted as "W" or "ℤ⁺⁰".

Integers: These are the whole numbers, as well as their negative counterparts. They can also be denoted as "Z" or "ℤ".

Rational numbers: These are numbers that can be expressed as a fraction, where the numerator and denominator are integers (and the denominator is not zero). They can also be denoted as "Q" or "ℚ".

Irrational numbers: These are numbers that cannot be expressed as a fraction of two integers. They are often represented by decimal expansions that neither terminate nor repeat. Examples include π and the square root of 2.

Real numbers: These are all the rational and irrational numbers, taken together. They can also be thought of as numbers that can be located on a number line. They are often denoted as "R" or "ℝ".

Complex numbers: These are numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit (defined as the square root of -1). Complex numbers can be added, subtracted, multiplied, and divided, just like real numbers. They are often denoted as "C" or "ℂ".

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Answer:

The original price of petrol is R12.58 per litre and the new price is R13.28 per litre. To find the percentage increase in the price, we can use the following formula:

Percentage increase = ((new price - old price) / old price) x 100%

Substituting the values, we get:

Percentage increase = ((13.28 - 12.58) / 12.58) x 100%

Percentage increase = (0.70 / 12.58) x 100%

Percentage increase = 0.0557 x 100%

Percentage increase = 5.57%

Therefore, the percentage increase in the price of petrol is 5.57%.

Step-by-step explanation:

Answer: June uses 192 jellybeans for every dozen (12) plastic eggs she fills, which means she uses 192/12 = <<192/12=16>>16 jellybeans per plastic egg.

To find how many plastic eggs can be filled with 1,152 jellybeans, we can divide 1,152 by the number of jellybeans per egg:

Number of eggs = 1,152 ÷ 16 = <<1152/16=72>>72

Therefore, June can fill 72 plastic eggs with 1,152 jellybeans.

Step-by-step explanation:

The required simplified forms are 3x - 1, 6x , 2x² - 10x , a + 2b , 15x - 8 , x² + 2x + 6 , x² - y² , 6x² - 22x.

the definition of an equation is a mathematical statement that demonstrates that two mathematical expressions are equal. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' symbol.

Simplified forms of the equation are

[tex]$c: 3(x-2)+5=3x-6+5=3x-1$[/tex]

[tex]$f: 2x(3-x)+x^2=6x-x^2+x^2=6x$[/tex]

[tex]$i: 7x^2-5x(x+2)=7x^2-5x^2-10x=2x^2-10x$[/tex]

[tex]$c: 2a-(a-2b)=2a-a+2b=a+2b$[/tex]

f: [tex]$3x-4(2-3x)=3x-8+12x=15x-8$[/tex]

[tex]$x(x+4)-2(x-3)=x^2+4x-2x+6=x^2+2x+6$[/tex]

[tex]$x(x+y)-y(x+y)=(x-y)(x+y)=x^2-y^2$[/tex]

[tex]$o: 4x(x-3)-2x(5-x)=4x^2-12x-10x+2x^2=6x^2-22x$[/tex]

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If we total up the dots plot for 3, 4, and 5 pets, we find that 3 people have 2 pets at home, 10 individuals have at least 3 pets at home.

The fact that dogs are the most common pet in the world shouldn't be shocking. There is a reason why there are tens of millions of dogs living in the United States alone, which is why some people say that dogs are a man's greatest friend. Around the world, at least one dog is kept in one-third of all households.

A fully domesticated animal kept constitutes a "household pet." a pet kept by you for personal company, like a dog, cat, reptile, bird, or mouse. Any kind of horse, cow, pig, sheep, goat, chicken, turkey, other captive fur-bearing animal is not considered a household pet, nor is any animal that is typically kept for food or profit.

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The total number of people with pets at home is 11, which is the sum of the heights of the columns.

What is equation?

A math equation is a method that links two claims and represents equivalence using the equals sign (=). An equation is a mathematical statement that establishes the equivalence of two mathematical expressions in algebra.

Based on the given dot plot, we can answer the following questions:

How many people have 2 pets at home?

Answer: Two people have 2 pets at home, as indicated by the two dots in the second column.

How many people have at least 3 pets at home?

Answer: Six people have at least 3 pets at home, as indicated by the dots in the third column and beyond.

How many more people have 2 pets than 5 pets?

Answer: There are no dots in the last column, which represents 5 pets. Therefore, the difference between the number of people with 2 pets and those with 5 pets is 2 - 0 = 2.

How many people have less than 3 pets at home?

Answer: Three people have less than 3 pets at home, as indicated by the dots in the first two columns.

Therefore, the total number of people with pets at home is 11, which is the sum of the heights of the columns.

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Answer:

21 years old

Step-by-step explanation:

Set Alan's age as x, Bernice's age as y

2x=y

x-4+y-4=55

x+y=63

3y=63

x=21

y=42

[tex]\bold{Solution:}[/tex]

[tex]\Delta[/tex][tex]DE[/tex][tex]F[/tex] congruent to [tex]\Delta[/tex][tex]JKI[/tex]

[tex]\bold{FD=JI} \text{(corresponding angles of congruent triangles)}[/tex]

[tex]z + 22 = 3z[/tex]

[tex]\text{or,} \ z-3 z= -22[/tex]

[tex]\text{or,} \ -2z = -22[/tex]

[tex]\text{or,} \ z = \bold{11}[/tex]

[tex]\bold{EF=KI} \text{(corresponding angles of congruent triangles)}[/tex]

[tex]5y+13=6y[/tex]

[tex]\bold{y=13}[/tex]