Eva is going to invest in an account paying an interest rate of 6.1% compounded continuously. How much would Eva need to invest, to the nearest ten dollars, for the value of the account to reach $71,000 in 7 years?

The answer is 46320

The value of AB after solving the triangle is 10√3.

Since angle C is the right angle in triangle ABC, we know that angle A = 90 - m2C = 90 - 30 = 60. And since triangle ABC is a right triangle, we can use the Pythagorean Theorem to find the length of the hypotenuse, AB.

The Pythagorean Theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. So in this case,

We know that angle A is 60, so we can use the trigonometric function sine to find the value of BC/AB. We know that

We can then square both sides of this equation to get

Since we know that BC/AB = 3/4, we can substitute this value into the equation

AB^2 = 100 + BC^2 to get

AB^2 = 100 + (BC^2) = 100 + (3/4)AB^2.

Solving this equation for AB, we get AB = 10√3

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A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.

When a linear equation is graphed, it always produces a straight line since each term in the equation has an exponent of 1 or 0. A linear equation is an algebraic equation. If an equation has the formula y=mx+b, with m representing the slope and b the y-intercept, it is said to be linear.

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

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Answer:

25

Step-by-step explanation:

so molly and liza are exercising right?.so 10 push-ups at the same time wich means they do 10 push-ups together and liza push-ups 15 and molly does 40 pushups so. its addition so 10+15=25 so thats the answer.

Therefore, N2 and 2N are not equal, they are different mathematical expressions.

A finite collection of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.

A mark, sign, or term that denotes, denotes, or is taken to denote a concept, an item, or a connection is known as a symbol. By connecting seemingly unrelated ideas and events, symbols let individuals look beyond the known and the visible.

No, N2 and 2N are not the same.

N2 is the square of N, which means it is N multiplied by itself. For example, if N = 5, then N2 = 5*5 = 25.

2N, on the other hand, is N multiplied by 2. For example, if N = 5, then 2N = 5*2 = 10.

So, N2 and 2N are not equal, they are different mathematical expressions.

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Volume of the triangle is 1420m³ given in the question.

There are various volumes for various geometric shapes. Cubes, cuboids, spheres, cylinders, cones, etc. are examples of common 3D shapes that we encounter on a daily basis.

Finding the volume is simple when dealing with shapes with a flat surface, like a cube or a cuboid. Cones, cylinders, and spheres are examples of curved shapes, and it is necessary to take into account both their curved surfaces' dimensions and their overall curvature. Possibly their diameters or radii

The term "irregular solids" refers to solids that lack precise measurements or shapes. A fixed formula that can be used to calculate the volumes of such solids is typically absent. It is possible to obtain these volumes in a variety of ways, one of which is the liquid displacement method, which is based on the Archimedes Principle.

Now volume triangle = area × height

⇒ 1/2 × 20 × 14.2 × 10

= 1420m³

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Answer:

6.3

Step-by-step explanation:

This is a right triangle, so in order to solve you can use the Pythagorean theorem; which is a² + b² = c² (The hypotenuse, or the longest side, equals C.  A and B equal the legs, or the shorter sides.)  So once you plug in the values, your equation should look like this:

3² + b² = 7²

Square each side, or in other words multiply it by itself.  

9 + b² = 49

Subtract 9 from both sides.  

b² = 40

Take the square root of 40 and your done!

b = 6.3

I hope this helped you!  :)

2.25×10 times greater is the weight of the elephant than the weight of the lion.

Two or more expressions with an Equal sign is called as Equation.

Given that a zookeeper  weighted an African elephant to be 9 x 10³ pounds.

An African lion to be 4 x 10² pounds

We need to find how many times greater is the weight of the elephant than the weight of the lion

Now, Divide the weighed an African elephant with weighed an African lion to determine times greater is the weight of the elephant than the weight of the lion,

N=9×10³/4×10²

=2.25×10

Hence, 2.25×10 times greater is the weight of the elephant than the weight of the lion.

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%, a relative figure signifying hundredths of any amount. Before the raise, I was making $45,000.

A percentage that represents a tenth of a quantity. In essence, percentages are fractions with a denominator of 100. The percent symbol (%) is placed next to a number to indicate that it is a percentage. For instance, you would have received a 75% on the examination if you correctly answered 75 out of 100 questions (75/100).

Calculating a percentage involves dividing an item by its sum and multiplying the result by 100.

Considering the query

It was $52,200 after a 16% raise in my pay.

In light of the conditions stated, come up with

[tex]$=\frac{52200}{1+16 \%}$$=\frac{52200}{1+0.16}$$=\frac{52200}{1.16}$$=\frac{5220000}{116}$[/tex]

= $45000

Before the raise, I was making $45,000.

Therefore, the answer is $45,000.

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The value of the expressions (2.3 × 10⁴) × (1.5 × 10⁻²) and (3.6 × 10⁻⁵) ÷ (1.8 × 10²) will be 345 and 2 × 10⁻⁷, respectively.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expressions are given below.

(2.3 × 10⁴) × (1.5 × 10⁻²) and (3.6 × 10⁻⁵) ÷ (1.8 × 10²)

Simplify the expression (2.3 × 10⁴) × (1.5 × 10⁻²), then the value of the expression will be given as,

⇒ (2.3 × 10⁴) × (1.5 × 10⁻²)

⇒ 345

Simplify the expression (3.6 × 10⁻⁵) ÷ (1.8 × 10²), then the value of the expression will be given as,

⇒ (3.6 × 10⁻⁵) ÷ (1.8 × 10²)

⇒ 2 × 10⁻⁷

The value of the expressions (2.3 × 10⁴) × (1.5 × 10⁻²) and (3.6 × 10⁻⁵) ÷ (1.8 × 10²) will be 345 and 2 × 10⁻⁷, respectively.

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The value of 5 1/7 minus 2 5/21 will be 2 19 / 21.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Based on the information, the value of 5 1/7 minus 2 5/21 will be:

= 5 1/7 - 2 5 / 21

= 5 3/21 - 2 5 / 21

= 2 19 / 21

The value is 2 19/21.

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Hello there!

Answer:

33 days

Step-by-step explanation:

Every day you give 5 ml of medicine to 6 donkeys. So you spent 5 ml * 6 = 30 ml per day

1 L = 1000 ml

To find the answer you should volume of bottle divide by 30 ml per day:

1000 ml / 30  = 33.333...

It means that if will be possible to use the bottle 33 days but then it will be left

An arithmetic sequence is a sequence of numbers in which the difference between any two successive members of the sequence is a constant value. The general form of an arithmetic sequence is:

a, a + d, a + 2d, a + 3d, ...

where "a" is the first term of the sequence, and "d" is the common difference between successive terms.

Given the function f(n) = 2n - 1, we can see that the function outputs a sequence of integers, with a common difference of 2. So f(n) is not an arithmetic sequence.

Arithmetic sequence is a list of numbers in which each number is the sum of the previous number and a constant number.

Example: 1,3,5,7,9 is an arithmetic sequence because the constant difference is 2.

If you have any other question feel free to ask.

Answer:

[tex]\frac{d}{c}[/tex]

Step-by-step explanation:

[tex]\frac{cxcxdxdxd}{cxcxcxdxd}[/tex]  You can cross out 2 c's from the top and the bottom and 2 d's from the top and the bottom.  It now looks like this

[tex]\frac{d}{c}[/tex]

To find the inverse of a function, you can follow these steps:

Swap the variables x and y in the original function. For example, if the original function is y = √x + 8, you would swap the variables to get x = √y + 8.

Solve the equation for y. In this case, you would get:

x = √y + 8

y = x - 8

Replace y with f^-1(x) to denote the inverse function. The inverse function is defined as f^-1(x) = y, so you would get:

f^-1(x) = x - 8

This is the inverse function of y = √x + 8.

Note that the inverse function is only defined for values of x such that y ≥ 8. This is because the original function y = √x + 8 is only defined for y ≥ 8.

The solution to the system of linear equations 3x + 2y = 14 and 5x + y = 32 is (x, y) = (6, 10).

3x + 2y = 14

5x + y = 32

Subtracting 3x from both sides of the first equation:

2y = 14 - 3x

Substituting this into the second equation:

5x + (14 - 3x) = 32

Simplifying:

8x = 18

x = 18/8

x = 2.25

This x value is substituted into the first equation.:

2y = 14 - 3(2.25)

2y = 14 - 6.75y

= 7.25

The solution is (x, y) = (2.25, 7.25)

The solution to the system of linear equations 3x + 2y = 14 and 5x + y = 32 is (x, y) = (2.25, 7.25). To solve the system, we first subtracted 3x from both sides of the first equation and then substituted this into the second equation. After simplifying, we obtained a value of x, which we then substituted into the first equation to obtain a value of y. This gave us the solution (x, y) = (2.25, 7.25).

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The function that will define the situation is y = 10x

The domain:  {0, ∞)

The range: {0, ∞)

The function that will define the situation is a linear function of the form

y = mx + c

definition of variable to suit the problem

y = output variable

m = slope

x = input variable

c = y intercept

The equation as described in the problem is represented using linear function as as follows

c = there is no condition defined here hence = 0

m = cost of per hour = $2.50

x = time in hours

y =  amount paid in hours

y = 10x

The domain in this case is time from 0 to infinity {0, ∞)

The range is also {0, ∞)

there are no limitations to hep set the range and domain

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Answer:

u = 8

Step-by-step explanation:

calculate the slope of the line passing through the 2 give points using the slope formula, then equate to the given slope.

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

with (x₁, y₁ ) = (- 5, 5 ) and (x₂, y₂ ) = (5, u )

m = [tex]\frac{u-5}{5-(-5)}[/tex] = [tex]\frac{u-5}{5+5}[/tex] = [tex]\frac{u-5}{10}[/tex] , then equating the 2 expressions gives

[tex]\frac{u-5}{10}[/tex] = [tex]\frac{3}{10}[/tex] ( cross- multiply )

10(u - 5) = 30 ( divide both sides by 10 )

u - 5 = 3 ( add 5 to both sides )

u = 8

Step-by-step explanation:

(u - 5)/(5 + 5)= 3/10

(u - 5)/10= 3/10

10u - 50 = 30

10u = 80

u = 8

The terminal point of vector cu lies in quadrant III.

Option B is the correct answer.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

p = (0, 0) and Q = (9, 12)

u = PQ = (9 - 0, 12 - 0) = (9 , 12)

Now,

cu = (9c, 12c)

where c < 0

If c = -1

cu = (-9, -12)

The coordinates (-x, -y) lie in quadrant III.

(-9, -12) is in quadrant III.

Thus,

Vector cu lies in quadrant III.

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The length of f = 66 centimeters

It is a law that express a relationship between side length of triangle and their opposite angles.

If ABC is triangle, then sine rule can be expressed as

BC/ sin A = AB /sin C = AC /sin B

Given, a triangle fgh where angle ∠ f = 131° and ∠g = 47°

also, side length, g = 64 cm

the remaining angle ∠ h = 180° - (131°+47°)

∠h = 2°

this is because angle sum of three angle for a triangle is 180 degrees.

what is the length of f?

we know that Δf g h has three side f g, g h and f h.

we denote the side f g = h, side g h = f and side f h = g

according to the sine rule for a triangle

h/ sin h = f /sin f = g /sin g

f/ sin f = g/ sin g

f / sin 131° = 64 / sin 47°

f = (64 × sin 131°) / sin 47°

f = 66 cm

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The number of real solutions of a quadratic equation depends on the sign of the discriminant.We can find discriminant by using discriminant formula.

A real solution in algebra is simply a solution to an equation that is a real number. there can be 0, 1, or 2 solutions to a quadratic equation depending on whether the expression inside the square root sign (b2 - 4ac), is positive, negative, or zero.

When the discriminant value is positive we get two real solutions. When the discriminant value is zero we get one real solution. When the discriminant value is negative we get a pair of complex solutions.

So that we can find real solution of quadratic equation by finding discriminant of given equation.

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The solution is Option C and Option D.

The exponential function is given by f ( x ) = 2 ( 3 )ˣ

The exponential function is given by f ( x ) = 800 / 4ˣ

What are the laws of exponents?

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

Let the x values be x = { 0 , 1 , 2 , 3 }

Let the y values be y = { 7 , 19 , 31 , 43 }

The equation of line is y = 12x + 7

This is a linear equation

b)

Let the x values be x = { 0 , 1 , 2 , 3 }

Let the y values be y = { 5 , 10 , 15 , 30 }

The equation is a quadratic equation

c)

Let the x values be x = { 0 , 1 , 2 , 3 }

Let the y values be y = { 2 , 6 , 18 , 54 }

The equation is y = 2 ( 3 )ˣ

This is an exponential function

d)

Let the x values be x = { 0 , 1 , 2 , 3 }

Let the y values be y = { 800 , 200 , 50 , 12.5 }

The equation is f ( x ) = ( 800 / 4ˣ )

This is an exponential function

Hence , the exponential equations are solved

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The number of seeds per square foot is the variable that explains the variation in the yield of the crop in pounds per square foot.

The explanatory variable for this relationship is the number of seeds per square foot. The number of seeds per square foot is the variable that is being manipulated or changed by the farmers in order to observe the effect on the yield of the crop in pounds per square foot.

The farmers observed that the yields were the smallest when the number of seeds per square foot was either very small or very large, this means that there is an optimal number of seeds per square foot that yields the highest crop.

So, the number of seeds per square foot is the variable that explains the variation in the yield of the crop in pounds per square foot.

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Answer:

29

Step-by-step explanation:

The correct answer is A representative, random sample of individuals are questioned regarding their attitudes or behaviours. (Option B)
A) "Individuals are carefully observed in their natural environments" is a description of participant observation, which is a type of qualitative research method. In this method, researchers observe and interact with individuals in their natural environments in order to understand their behaviours and attitudes in context. This method is often used in fields such as anthropology, sociology, and psychology.

B) "A representative, random sample of individuals are questioned regarding their attitudes or behaviours" describes a survey, which is a quantitative research method. Surveys are used to gather information from a representative sample of individuals in order to make inferences about a larger population. Surveys can be conducted in various ways, such as through phone calls, mail or online and can be used to study the attitudes, behaviours, and characteristics of a population.

C) "An individual is studied in great depth" is a description of a case study, which is a qualitative research method. In this method, a researcher closely examines an individual or a small group of individuals in order to gain a detailed understanding of their experiences, behaviours, and attitudes. Case studies are often used in fields such as psychology, sociology, and anthropology.

D) "An investigator determines the extent to which two variables influence each other" is a description of a correlation study, which is a quantitative research method. In this method, the researcher examines the relationship between two or more variables. The researcher measures the values of the variables for a sample of individuals, and then uses statistical methods to determine the degree of association between the variables, and if there is a causal relationship or not.

Thus, The correct answer is A representative, random sample of individuals are questioned regarding their attitudes or behaviours. (Option B)

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Step-by-step explanation:

one side : 2x - 1

so, 5 sides (the perimeter is the sum of all sides) :

5 × (2x - 1) = 10x - 5

An equation that can be used to find the value of,x=$700.0 - $176.95.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

The statement is not an equation if there is no "equal to" sign in it.

According to our question-

x= $700.0 - $176.95

523.05

Hence, An equation that can be used to find the value of,x=$700.0 - $176.95.

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The number of possible combinations of 4 digit codes would be 72.

A permutation is an arrangement of things where order matters, AB and BA are two different permutations.

The combination is a selection of things where order does not matter, AB and BA are the same combinations.

Given, I am creating a 4 digit code with the numbers 1 to 10.

Now, From 1 to 10 there are (10 - 1 + 1 ) = 10 and we are taking 4 numbers at a time.

Therefore the number of combinations of 4 digit codes would be,

[tex]^9C_4\times2![/tex]. As the number consists of two digits.

= [9!/(9 -2)!×2!]×2!.

= 9!/7!.

= 72 possible ways.

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The answer to the Linear expression 7(3n + 2) - 3n - 5 is 18n + 11

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.

From the expression 7(3n + 2) - 3n - 5

By expanding the bracket, we have

21n + 14 - 3n - 5

By collecting like terms, we have

21n - 3n + 14 - 3

18n + 11

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The number of students expected to prefer cheese pizza from the 340 students is 200 stduents.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

Cheese pizza = 40 students

Pepperoni pizza = 28

The ratio of cheese and Pepperoni pizzas.

= 40:28

= 10:7

Now,

Cheese pizza = 10x

Pepperoni pizza = 7x

The number of expected students who prefer cheese pizza.

= (10x)/(17x) x 340

= 10/17 x 340

= 10 x 20

= 200

Thus,

The number of expected students preferring cheese pizza is 200.

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