Last year, Kevin had 20,000 to invest. He invested some of it in an account that paid 6% simple interest per year, and he invested the rest in an account that paid 10% simple interest per year. After one year, he received a total of $1480 in interest. How much did he invest in each account?

Factor of x ^2+7x−18 is (x−2)(x+9)

What is factorization?

In mathematics, factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.

We are given a polynomial expression in terms of variable x as:

x² - 7x + 18

x ^2+7x−18

=x ^2−2x+9x−18

=x(x−2)+9(x−2)

=(x−2)(x+9)

∴ x ^2+7x−18=(x−2)(x+9)

Hence, Factor of x ^2+7x−18 is (x−2)(x+9)

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Therefore , the solution of transformation of function is Translation shifting the graph of a function up or down, or left or right.

A transformation of a function is a new function that is derived from the original function by applying some mathematical operation. The process of creating a new function from an existing one by applying a mathematical operation is called a transformation.

Here,

There are different types of transformations that can be applied to a function, such as:

Translation: shifting the graph of a function up or down, or left or right.

Reflection: flipping the graph of a function over the x-axis, y-axis, or a line of symmetry.

Stretching or compressing: changing the scale of the graph along the x-axis or y-axis.

Rotation: rotating the graph of a function about the origin.

Function G is a transformation of function f. G(x) = x^2

A transformation of a function is a new function that is derived from the original function by applying some mathematical operation. In this case, function G is derived from function f by squaring the input value. The result is a new function that maps the input value to its square. The notation G(x)= x^2 is a common notation to represent a function and it means that G is a function that takes x as input and returns the square of x as output.

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An equivalent expression of the expression 22/- 4 is,

⇒ - 11/2

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

We have to given that;

The expression is,

⇒ 22/-4

Now, We can simplify as;

⇒ 22 / - 4

⇒ - 22/4

⇒ - 11/2

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The probability of the first name selected is yours and the second name selected is your friend's name is 1/100 or in ratio 1:100.

Probability is the branch of mathematics that studies how random events turn out. In mathematics, the term "probability" is used to describe chance or potential outcomes. It makes it clear how likely it is that a certain outcome will occur. The phrases "It will likely rain today," "He'll mostly pass the test,"

"There's not much chance of getting a storm tonight," & "The price of onions will probably go up again" are common phrases. Instead of words like possibility, uncertainty, perhaps, likely, etc., the word probability is used in each of these sentences.

Probability, in its simplest form, can be defined as the capacity to forecast an outcome based on the variety and quantity of possible outcomes or by examining historical data.

The probability of first name selected is yours is = 1/10

The probability of 2nd name selected is yours is = 1/10

The probability of selecting your name and your friend name consecutively

= 1/10 * 1/10

= 1/100

Thus, the probability of the first name selected is yours and the second name selected is your friend's name is 1/100.

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Answer:

Step-by-step explanation:

2(2x + 4) + 2(x-7) = 48

4x+8 +2x-14=48

6x-6 = 48

6x = 48+6

6x = 54

x = 54/6

x = 9

The perimeter of this figure, to the nearest unit, is 21.9 units, and the area of this figure, to the nearest square unit is 62.53 square units.

What is a square?

It is defined as a two-dimensional geometry that has four sides and four vertices. The sides of the square are equal in length. It is a regular quadrilateral.

We have a figure shown in the picture made with squares and circles.

To find the perimeter of the figure.

First, calculate the circumference of the circle portion.

The circumference of the 1/4 circle = (1/4)2πr

The radius of the circle r = 5 units

The circumference of the 1/4 circle = (1/4)2π(5)

The circumference of the 1/4 circle = 7.85 units

The perimeter of the figure = 2 + 5 +7.85 + 2+ 5

The perimeter of the figure = 21.85 units ≈ 21.9 units

The area of the figure = area of the square - an area of the square(5×5) +

area of the 1/4 circle

The area of the figure = 3×3 - 5×5 + π(5)²

The area of the figure = 9 - 25 + 78.53

The area of the figure = 62.53 square units

Hence, the perimeter of this figure, to the nearest unit is 21.9 units, and the area of this figure, to the nearest square unit is 62.53 square units.

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When she comes back to the lab the next morning at 8:00AM, the number of bacteria that will there be is 2000.

From the information, the biologist is researching a newly-discovered species of bacteria. At 8:00AM when she arrives at the lab, she puts a population of 600 bacteria into a favorable growth medium.

She measures the sample again before she goes home at 4:00PM and notes that the population is now 1300 bacteria. The difference in the population will be:

= 1300 - 600

= 700

When she comes back to the lab the next morning at 8:00AM, the number of bacteria that will there be will be:

= 1300 + 700

= 2000

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The derivative of the function F(x) =x2 et4dt is e−x4(2x)−e−x2.

The derivative of a function of a real variable in mathematics quantifies the sensitivity of the function's value (output value) to changes in its argument (input value). Calculus's core tool is the derivative.

Take the derivative to differentiate anything.

Finding the slope at any point is the same as taking the derivative of a function, so differentiating is just finding the slope.

You may be aware that is typically indicated by either

I'm assuming you mean to determine the derivative of F(x)

F(x)=∫x2xe−t2dt

Let G(x)=∫x0e−t2dt

According to the calculus fundamental theorem

F′(x)=ddx(G(x2)−G(x))

=G′(x2)(2x)−G′(x)

=e−x4(2x)−e−x2.

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This information can be entered into an Excel sheet by creating columns for each item (A-J) and entering the corresponding values in the corresponding cells.

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The right triangle having the hypotenuse has x = 17.88.

Since a right triangle's three interior angles always add up to 90 degrees and a triangle's three interior angles always add up to 180 degrees, the other two interior angles must also always add up to 90 degrees (they are complementary).

Hypotenuse refers to the side across from the right angle. The legs are the sides extending from the right angle. If applying the Pythagorean Theorem, the hypotenuse or its length is frequently denoted with a lowercase c. A and B are typically used to denote the legs' lengths.

Using trigonometry rule

Cos 33° = 15/x

x = 17.88

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Answer: The correct answer is choice A. 5.4

Step-by-step explanation:

I hope this helps! :D

Answer:

slope = - 1

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = A (0, 2 ) and (x₂, y₂ ) = B (2, 0 )

m = [tex]\frac{0-2}{2-0}[/tex]  = [tex]\frac{-2}{2}[/tex] = - 1

Frank is going to plant d vegetable seeds in one garden, and 3d + 6 vegetable seeds in another. So Frank is going to plant 4d + 6 vegetable seeds in total.

Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. Algebra is used to solve problems and to describe patterns and relationships between variables. It is a powerful tool for modeling and understanding many types of real-world situations.

In algebra, letters or other symbols are used to represent numbers or quantities that are not known. These symbols can be manipulated using mathematical operations, such as addition, subtraction, multiplication, and division. Equations and inequalities involving these symbols can be solved to find the values of the unknowns. Algebraic equations can also be graphed to visualize the relationship between the variables.

To find the total number of vegetable seeds Frank is going to plant, we can add the number of seeds he is planting in each garden:

d + (3d + 6) = d + 3d + 6 = 4d + 6

So Frank is going to plant 4d + 6 vegetable seeds in total.

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A: The differential equation can be expressed in the form f(x ,y) = g(x)h(y) = 0, indicating that it is homogeneous. Divide both sides of the equation by y to observe this, which results in  dy/dx + sin^2(x) = cos^2(x)

B: Since there is just one function y and its derivative dy/dx involved in the equation, it is an ODE.

D: Because there is only one function y and its derivative  dy/dx involved in the equation, first-order differential equations are what it is.

G: The formula for the equation is a(x)y' + b(x)y = c(x), where a(x)=1, b(x) = sin^2(x), c(x) = cos^2(x) . Given that x and the coefficients of y and dy/dx are constants, the equation is linear.

H: The equation may be written as dy / y =  (cos^2(x))dx/(1+sin^2(x)),and it is a candidate for integrating factors because we can multiply both sides by (1+sin^2(x))dx .

I: The variables x and y can be separated by integrating both sides of the equation, which can be represented as  (dy/y) = (cos^2(x))dx/(1+sin^2(x)) + (sin^2(x))dx .

J: The equation is self-sufficient; it is not dependent on any explicit function of t.

       Therefore, the differential equation  dy/dx+sin^2(x)y=cos^2(x)y .A candidate for integrating factors exists in the first-order linear, homogeneous, separable, and autonomous ODE known as y.

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For a lower-tail test, a t-statistic that is negative and far from zero would then lead us to favor the alternative hypothesis

An alternative way to conduct a hypothesis test is to again assume initially that the null hypothesis is true, but then to calculate the probability of observing a t-statistic as extreme as the one observed or even more extreme

For a lower-tail test, the p-value is the area under the curve of the t-distribution (with n−1 degrees of freedom) to the left of the observed t-statistic.

Lower-tail tests work in a similar way to upper-tail tests, but all the calculations are performed in the negative (left-hand) tail of the t-distribution density curve

A lower-tail test would result in an inconclusive result for the home prices example (since the large, positive t-statistic means that the data favor neither the null hypothesis, NH: E(Y) = 255, nor the alternative hypothesis, AH: E(Y) < 255).

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Answer: For the first number 40, one possible set of factors that have a product of 40 and a sum of 13 is (1,40) or (40,1) . Because 1*40=40 and 1+40 = 41

We can not have any other pair whose product is 40 and sum is 13 as it is not possible for any pair of factors of 40 to sum up to 13 as the only pair is (1,40) or (40,1) and their sum is 41

Step-by-step explanation:

The rearranged formulae with x as the subject is x=y-2

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here:

y=x+2

rearranging we get

x=y-2

Hence, The rearranged formulae with x as the subject is x=y-2

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Answer:

bar graph

Step-by-step explanation:

The polynomial f''(x) = 3 · (x + 10)³ + 2 · (x + 10)² - 4 · (x + 10) + 11 represents a cubic function equal to polynomial f''(x) = 3 · (x + 10)³ + 2 · (x + 10)² - 4 · (x + 10) + 11 shifted up two units and left ten units.

Cubic equations are polynomials of grade 3, whose form is shown below:

y = a · x³ + b · x² + c · x + d

Where:

In this problem we need to apply horizontal and vertical translations to modify a given cubic polynomial:

Horizontal translation

f(x) → f(x - k)

Where k > 0 for a rightward translation.

Vertical translation

f(x) → f(x) + k

Where k > 0 for a upward translation.

First, assume a given cubic function:

(a, b, c, d) = (3, 2, - 4, 9)

f(x) = 3 · x³ + 2 · x² - 4 · x + 9

Second, apply a vertical translation two units up: (k₁ = 2)

f'(x) = 3 · x³ + 2 · x² - 4 · x + 9 + 2

f'(x) = 3 · x³ + 2 · x² - 4 · x + 11

Third, apply a horizontal translation ten units left:

f''(x) = 3 · (x + 10)³ + 2 · (x + 10)² - 4 · (x + 10) + 11

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Answer:

9) 11.18 feet

10) 6.14 inches

Step-by-step explanation:

The first problem sets up a situation with a right triangle. See image. Two sides are given, so you can use Pythagorean Theorem to find the last side. See image.

The second problem also sets up a right triangle. But here only one side length is given and one angle, so you use trigonometry. Sine is the ratio of the opposite side/hypotenuse. Use sine to find the missing length. See image.

I rounded these answers to the nearest hundredth (two decimal places) Check directions if they should be rounded more or less.

The value of K so that the line passing through (-4, 1) and (k, 3) is perpendicular to 8x + 13y = 26 is solved to be

A linear function consists of functions where the variables has exponents of 1. the relationship is expressed in the slope intercept form as below.

y = mx + c

definition of variable to suit the problem

y = output variable

m = slope

x = input variable

c = y intercept

The given equation is rewritten in slope intercept form as follows

8x + 13y = 26

13y = 26 - 8x

y = 2 - 8/13 x

the slope is 8/13

For a perpendicular line the slope = -1/m

= -1/(8/13)

= -13/8

For a line to have a slope of -13/8, the points will be

-13/8 = (1 - 3) / (-4 - k)

cross multiplying

-13(-4 - k) = 8(1 - 3)

52 + 13k = -16

solving for k

13k = -16 - 52

13k = 68

k = 68/13

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Answer:

(f+6) (x)= x^3+3x^2+1 / x2

Step-by-step explanation:

To fulfill all of the orders, they must pay their employees a total of $9600 as 480 * 20 = $9600 .

This unit technique is a way of problem-solving that entails calculating the value of a specific unit, multiplying that value, and then calculating the required value. To put it simply, the unit method is used to extract a single model value from a specified multiple. One pen costs 400 rupees, thus 40 pens would cost 400 rupees. There might be a regular procedure for doing this out. merely one nation. anything containing a distinctive component. Mechanics of matrices or operators, abstract algebra, mathematical analysis, and its adjoint and reciprocal are all equivalent.

given

Each employee is paid $12 per hour for the first 40 hours,

therefore $480 must be paid to all of their employees in order to fulfill all orders (20 * 3 = 60 days for 20 automobiles

, or 5 employees working 8 hours per day).

480 * 20 = $9600

To fulfill all of the orders, they must pay their employees a total of $9600.

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The given equation is inconsistent equation.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Identity equations are those equations which are satisfied for every values of the variables.

Conditional equations are those which is only true for some values.

Inconsistent equations are those which does not have a solution.

Given equation is,

8 (x + 6) = 9 + 8x

8x + 48 = 9 + 8x

8x - 8x = 9 - 48

0 = -39

There is no solution for the variable x. So it is inconsistent equation.

Hence the equation is inconsistent.

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13.3 mg should be given to a patient who weighs 190lb.

What is the unitary method?

The unitary method determines the value of a unit and then the value of the required number of units.

Assume you go to the market to buy six apples. The shopkeeper informs you that he is selling ten apples for Rs one hundred. The apples are the units in this case, and the cost of the apples is the value. It is critical to recognise the units and values when using the unitary method to solve a problem.

Given that a patient weighs 40 lb, then he needs 2.8 mg of medication.

Now find how much medication is required for a  patient whose weight is 1 lb.

Apply unitary method:

A patient weighs 1 lb, then he needs 2.8/40 mg of medication.

Now find how much medication is required for a  patient whose weight is 190 lb.

A patient weighs 190 lb, then he needs (2.8×190)/40 mg of medication.

                                                                = 13.3mg

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Yes, Lena is correct she will use less pages if she puts 10 stickers(Square type) per page.

what are squares?

A square is a two-dimensional plane figure with four equal sides and all four angles are equal to 90 degrees. The properties of the rectangle are somewhat similar to a square, but the difference between the two is, a rectangle has only its opposite sides equal. Therefore, a rectangle is called a square only if all its four sides are of equal length.

The most important properties of a square are listed below:

Area of square=(side)²

Perimeter of square=4*side

Now

As if there is space left on page after putting 5 square type stickers then the area that is left on rectangular pages will be wasted if we do not use that space.

So, Lena is correct she will use less pages if she puts 10 stickers/page.

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333 integers,  there are 333 integers between 1 and 1,000 which are divisible by 3, by divisibility test.

The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.

here

add all the numbers,

1 + 2+ 3 + 4+ 5 = 15

and 15/3 = 5

so it is divisible by 3

not by 9

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On solving the provided question, we can say that from the graph, we have  y-intercept of f(x); f(x) = 2(3)°; f(x) = 2 = (0, 2), y-intercept of g(x) = g(x) = (0, 3) so Distance =  (3,-2)

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle

from the graphs, we have

y-intercept of f(x)

f(x) = 2(3)°

f(x) = 2

(0, 2)

y-intercept of g(x)

g(x) = (0, 3)

Distance

(3,-2)

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The value of 98,060 × 4 = 392240.

The distributive property of multiplication states that when we multiply a number by the total of two or more addends, the outcome is the same as when we multiply the number by each addend separately.

The sum and difference of two more numbers are both subject to the distributive property of multiplication.

According to the Distributive Property of Multiplication:  

                            (A + B)C = AC + BC

Here we have

98,060 × 4

As we know 98060 = (98000 + 60)  

=  (98000 + 60) × 4  

=  (98000 × 4) + (60 × 4)      [ ∵ (A + B)C = AC + BC ]

=  392000 + 240

=  392240

Therefore,

The value of 98,060 × 4 = 392240.

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The amount of Brown material: 39 gallons and Green material: 13 gallons.

A proportion is a fraction of a total amount, and in problems involving it, basic arithmetic operations such as multiplication or division are used along with the unit rates to find the equivalent measures.

On the first column of the table, the total amount is:

12.75 + 4.25 = 17 gallons.

The fractions of each material are given as follows:

Brown material: 12.75/17 = 0.75

Green material: 4.25/17 = 0.22.

Therefore, the amount of brown material needed with 52 gallons is:

0.75 x 52 = 39 gallons.

The amount of green material needed with 52 gallons is:

0.25 x 52 = 13 gallons.

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