Find the amount of money (Future Value) in an account where $5,100 is deposited (Present Value) at an interest rate of 8% per year compounded continuously and the money is left in the account for 13 years.
round to 2 decimal places.

Answer:

x=5

Step-by-step explanation

4x=x+15

x=5

Answer:

Since ABCD is a kite, AB=AD and BC=CD

Given:

AB = 4x

AD = x + 15

equating both sides;

4x = x + 15

4x - x = 15

3x = 15

x = 15/3

x = 5

There is 1 way to obtain at least two tails when you toss 9 fair coins.

What is the probability?

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

If you toss 9 fair coins, there are 2⁹ = 512 possible outcomes.

The number of ways to obtain zero or one tail is equal to the number of ways to obtain all heads or one head and the rest of tails, which is 2⁹ - 1 = 511.

Therefore, the number of ways to obtain at least two tails is the complement of the number of ways to obtain zero or one tail, which is 512 - 511 = 1.

Therefore, there is 1 way to obtain at least two tails when you toss 9 fair coins.

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The area of the wall is 275 ft square

The number of gallon to cover the wall approximately is 3

the price of the paint is $73.5

1. The area of the wall is given as l * w

this is the value that is used to solve for the area of a rectangle

the length is given as 10 ft

the width is given as 22 ft

the area would be 10 * 22

= 220 ft square

find the area of the triangle = rectangular part is given as height = 15 ft - 10 ft = 5 ft

base = 22 ft

area = 1/2 b h

= 0.5 * 22 * 5

= 55

total area = 220 + 55 = 275 ft square

2. If 1 gallon of paint covers 105 ft

the amount that would cover 275 ft would be gotten when we cross multiply

1 = 105 ft

x  = 275 ft

275 ft = 105 x

x = 275 / 105

x = 2.619

x ~ 3 gallons of paint

3. If one gallon is 24.5 dollars, the total amount that you would purchase is 3 * 24.5

= $73.5

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The statement that is true is: B. A piece of copy paper is approximately four times thicker than a human hair.

Scientific notation is a system of expressing extremely large figures in a standard form.

Considering the figures given in the question,

Thickness of copy paper = 4 × 10^-3 in

Thickness of human hair = 1 × 10^-3 in

So that;

Thickness of copy paper/ Thickness of human hair = 4 × 10^-3/ 1 × 10^-3

                                                    = 4 × 10^-3 * 10^3

                                                    = 4

Thus it can be concluded that the copy paper is approximately four times thicker than a human hair. Thus option B.

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The 'L' shape is reflected over the y axis is shown by figure B.

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given:

As, we have to reflect the image over the y axis.

That means that the image gets flipped across the y-axis.

So, the rule reflect over y axis is  (x, y) -> (-x, y).

Then, among all the option the figure that satisfies the rule is Figure B.

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Answer:

-2

Step-by-step explanation:

6y + 14 = -5y - 8

6y + 5y = -8 -14

11y = -22

y = -22/11

y = -2

The final inequality is x > - 1.

Option D is the correct answer.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

√(x + 2) > -1

Squaring both sides.

x + 2 > (-1)²

x + 2 > 1

Subtracting 2 on both sides.

x > 1 - 2

x > -1

Thus,

x > - 1 is the final inequality.

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The relations that represent functions are given as follows:

A relation represents a function when each input value is mapped to a single output value.

Hence the two items that are not functions in this problem are given as follows:

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The probability that a randomly selected cat has no treatment and no fleas is 43/87.

It is a branch of mathematics that deals with the occurrence of a random event.

Total number of cats = (cats sprayed with flea deterrent + cats with no treatment)

= (33+6 + 43+5)

=87

we need to find the number of cats with no treatment and no fleas, and divide it by the total number of cats.

Now we can see that the number of cats with no treatment and no fleas is 43.

Therefore, the probability that a randomly selected cat has no treatment and no fleas is:

P(no treatment and no fleas) = number of cats with no treatment and no fleas / total number of cats

= 43 / 87

Hence, the probability that a randomly selected cat has no treatment and no fleas is 43/87.

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The solution to each of the exponent problems are;

a) 10¹¹

b) 10²

c) 10⁴

d) 10¹²

The seven laws of exponents are;

1) Product of powers rule.

2) Quotient of powers rule.

3) Power of a power rule.

4) Power of a product rule.

5) Power of a quotient rule.

6) Zero power rule.

7) Negative exponent rule.

The given expressions are;

a) 10⁵ × 10⁶

= 10⁵⁺⁶

= 10¹¹

b) 10⁴ × 10⁻²

= 10⁴⁻²

= 10²

c) 10⁸/10⁴

= 10⁸⁻⁴

= 10⁴

d) 10⁹/10⁻³

= 10⁹⁻⁽⁻³⁾

= 10⁹⁺³

= 10¹²

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X = -3 and its substitution into the first equation results in 3y = 9, which can be written as y = 3. As a result, the system of equations' solution's y-coordinate is 6.

Equation is a mathematical and physical statement that describes physical phenomena and the relationship between various physical quantities.

It usually consists of a simple variable that presents the physical quantity, followed by a personal variable that may be a personal variable that is focused on the energy.

The system of equations has a solution, and its y-coordinate is 6. This is obtained by solving for x and then putting the specified y-value (2/3) into the equation -x+3y=9. In particular, -x+3(2/3) = 9 becomes -x = 3 when -x+3(2/3) = 9.

Therefore, The system of equations has a solution, and its y-coordinate is 6.

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Answer:

(4, -1) and (-6, 9).

Step-by-step explanation:

To find the fourth vertex of a parallelogram, we need to find the vector that represents the displacement from one of the given vertices to another, and then add that vector to the third given vertex. Since parallelograms have opposite sides that are equal in length and parallel, adding the same displacement vector to two of the given vertices will give us the coordinates of the other two vertices.

One possible displacement vector is the difference between the first and second given vertices, or (1 - (-4), -2 - 3) = (5, -5). Adding this vector to the third given vertex, (-1, 4), gives us the fourth vertex at (4, -1).

Another possible displacement vector is the difference between the second and third given vertices, or (-1 - 1, 4 - (-2)) = (-2, 6). Adding this vector to the first given vertex, (-4, 3), gives us the fourth vertex at (-6, 9).

So the two possible locations of the fourth vertex are (4, -1) and (-6, 9).

Two ratios from the image that are equivalent to each other are the oranges shapes and the two smaller green shapes.

When we compare two ratios, they are said to be equivalent. To determine whether two or more ratios are equivalent, they can be compared to one another. For instance, the ratios 1: 3 and 2: 6 are equivalent.

In this case, the two orange shapes are equivalent because they are the same size seeing as they both occupied the same portions of the green and white shapes. The smaller green shapes are also equivalent as they have the same length and width.

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Answer:

P=10x^2+38y

Step-by-step explanation:

its the answer

Answer: This data can be proven to be incorrect using the Principle of Inclusion-Exclusion.

The Principle of Inclusion-Exclusion states that for two events A and B, the number of elements in the union of A and B is equal to the sum of the number of elements in A and the number of elements in B minus the number of elements in their intersection.

Let's denote the number of students who failed in Maths as M, Accounts as A, and Costing as C.

From the information given, we have the following relationships:

M = 750

A = 600

C = 600

A ∩ C = 150

M ∩ A = 450

M ∩ C = 400

M ∩ A ∩ C = 75

Applying the Principle of Inclusion-Exclusion, the number of students who failed in at least one subject is:

M + A + C - (A ∩ C) - (M ∩ A) - (M ∩ C) + (M ∩ A ∩ C) = 750 + 600 + 600 - 150 - 450 - 400 + 75 = 925

However, the number of students who appeared for the exams is 1000, which means that the number of students who passed in all subjects should be 1000 - 925 = 75.

But we have already determined that the number of students who failed in all subjects is 75, which means that there are 75 students who are counted twice. This leads to a contradiction, and therefore the data given cannot be correct.

Step-by-step explanation:

Answer: Exact Form:

11/72

Decimal Form:

0.1527 repeating

Step-by-step explanation:

6 x 12 and 1 x 11

The volume of the pyramid is 400 cubic cm and the surface area is

340 sq cm.

A three-dimensional figure is a pyramid. Its base is a flat polygon. The remaining faces are all triangles and are referred to as lateral faces.

The number of sides on its base is equal to the number of lateral faces. The line segments that two faces intersect to form its edges. The intersection of three or more edges forms a vertex.

The volume of a pyramid is = (1/3)×l×w×h and the surface area of a pyramid is (1/2)×PL + B, where P = perimeter of the base, L = height, and

B = area of the base.

Therefore, The volume is =  (1/3)×10×10×12 cubic cm.

= 1200/3 cubic cm.

= 400 cubic cm

And, The total surface area is,

= (1/2)[2(10 + 10)×12 + (10×10) sq cm.

= 240 + 100 sq cm.

= 340 sq cm.

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Answer:

Let's call angle d₁ "θ". To find θ, we can use the Pythagorean theorem. The segment AO is the hypotenuse of a right triangle with sides BC/2 and AC/2 (since the rhombus is a parallelogram, opposite sides are equal).

AC/2 = (BC/2) / tan(θ)

So:

tan(θ) = AC/2 / (BC/2)

Plugging in the values we have:

tan(θ) = 3.8 / (5/2) = 3.8 / 2.5 = 1.52

Therefore,

θ = tan^(-1)(1.52) = 55.23°

The tangent ratio of angle c₂ is simply the tangent of the angle:

tan(c₂) = tan(90° - θ) = tan(90° - 55.23°) = tan(34.77°) = 1.52

So the tangent ratio of angle c₂ is 1.52.

Step-by-step explanation:

[tex]\lim_{p \to \(-8}[/tex]  = -59

What is a Limit?

Limit is the values that a function approaches the output for the given input values.

How to calculate this

[tex]\lim_{p \to \(-8}[/tex] ( -[tex]p^{2}[/tex] - p -3)

when p = -8

By inserting the value of p

[tex]\lim_{p \to \(-8}[/tex] = {-(-8)^2 - (-8) - 3 }

open the bracket

[tex]\lim_{p \to \(-8}[/tex] = (-64 + 8 - 3 )

[tex]\lim_{p \to \(-8}[/tex] = ( - 59 )

So, [tex]\lim_{p \to \(-8}[/tex]  =-59

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Answer: a) The probability that the system will fail during a 3-month period can be calculated as the sum of the probabilities of subsystem A and subsystem B failing, since the system fails if either one fails. The probability of subsystem A failing in 3 months is given by P(A) = 1 - e^(-0.2 * 3) * (1 + 0.2 * 3 + (0.2 * 3)^2 / 2!) = 0.0664. The probability of subsystem B failing in 3 months is given by P(B) = 1 - e^(-1.2 * 3) * (1 + 0.2 * 3 + (0.2 * 3)^2 / 2!) = 0.36. Therefore, the probability that the system will fail in 3 months is P(system) = P(A) + P(B) = 0.0664 + 0.36 = 0.4264.

b) To find the probability that there will be no more than two failures of the system during a 6-month period, we need to use the cumulative distribution function (CDF) of the Poisson distribution. Let X be the number of failures of the system in 6 months. The CDF is given by F(x) = P(X <= x) = 1 - P(X > x), where P(X > x) is the probability that there will be more than x failures. Therefore, the probability that there will be no more than two failures of the system during a 6-month period is given by F(2) = 1 - P(X > 2). We can use the formula for the Poisson distribution to find P(X > 2), which is P(X > 2) = e^(-6 * (P(A) + P(B))) * ((6 * (P(A) + P(B)))^3 / 3! + (6 * (P(A) + P(B)))^2 / 2! + 6 * (P(A) + P(B)) / 1! + 1). Plugging in the values for P(A) and P(B) from part (a), we get F(2) = 1 - e^(-6 * 0.4264) * ((6 * 0.4264)^3 / 3! + (6 * 0.4264)^2 / 2! + 6 * 0.4264 / 1! + 1) = 1 - 0.2079 = 0.7921.

c) To find the probability that the next system failure will occur within a year, we need to find the cumulative distribution function (CDF) of the time between failures, which is the sum of the time between failures of subsystem A and subsystem B. Let X be the time between failures of subsystem A, which follows an exponential distribution with rate 0.2 per month. Let Y be the time between failures of subsystem B, which also follows an exponential distribution with rate 1.2 * 0.2 = 0.24 per month. Then the CDF of the time between failures is given by F(t) = P(X + Y <= t) = 1 - P(X + Y > t0.2 * 12) * e^(-0.24 * 12) = 1 - 0.17 = 0.83. Therefore, the probability that the next system failure will occur within a year is 0.83.

Step-by-step explanation:

Answer:

p = 23

Step-by-step explanation:

using the rules of exponents

• [tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]

• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]

then

[tex](x^3)^{5}[/tex] ([tex]x^{8}[/tex] )

= [tex]x^{3(5)}[/tex] × [tex]x^{8}[/tex]

= [tex]x^{15}[/tex] × [tex]x^{8}[/tex]

= [tex]x^{(15+8)}[/tex]

= [tex]x^{23}[/tex]

= [tex]x^{p}[/tex] ← with p = 23

Answer:

The statement "x = -2" is correct. Marisa correctly solved the equation -3 = 6x by dividing both sides by 6 to find that x = -2.

Step-by-step explanation:

An equation in point-slope form for this line is y=6x+5.

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Which is the required equation of a line in a point-slope form.

Given that;

Point on a line (-1,-1)

Slope of the line 6

Now, substituting the values in the general formula of line

y+1=6(x+1)

y+1=6x+6

y=6x+5

Therefore, the equation with the given slope will be y=6x+5.

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Let's represent the number of dimes in the coin purse as d. Then, the number of nickels in the coin purse can be represented as 5d - 2.

The total value of the coins can be expressed as:

0.05 * (5d - 2) + 0.10 * d = 0.95

Expanding and simplifying the equation, we get:

0.05 * 5d - 0.05 * 2 + 0.10 * d = 0.95

0.50d - 0.10 = 0.95

0.50d = 1.05

d = 2.10

Since the number of dimes must be a whole number, we round d down to 2. So, there are 2 dimes in the coin purse and 5 * 2 - 2 = 6 nickels in the coin purse.

Answer:

The solution is C. (x+8)² + (y-11)² = 4

Step-by-step explanation:

(x - h)² + (y - k)² = r²

h = -8

k = 11

r = 2

(x + 8)² + (y - 11)² = 2²

(x + 8)² + (y - 11)² = 4

The answer is C. (x+8)² + (y-11)² = 4

The maximum height the rock reaches 3.15 feet and the rock will be above the surface for 2.6 seconds

An equation is an expression that shows the relationship between two or more variables and numbers.

here, we have,

From the graph of the function h(t) = 1 + 4t - 1.86t²:

The maximum height the rock reaches 3.15 feet.

Time spent on air

= 2.38 - (-0)

= 2.38 seconds

The maximum height the rock reaches 3.15 feet and the rock will be above the surface for 2.6 seconds.

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1) The length of the missing side of the right triangle is 34.

2) The values of the six trigonometric functions of θ are:

sin θ = sin A = 8/17

cos θ = cos A = 15/17

tan θ = tan A = 8/15

csc θ = csc A = 17/8

sec θ = sec A = 17/15

cot θ = cot A = 15/8

What is Pythagorean Theorem?

Pythagoras Theorem is a method for calculating the missing length of a right-angled triangle. The triangle has three sides: the hypotenuse (which is usually the longest), the opposite (which does not touch the hypotenuse), and the adjacent (which is always the shortest) (which is between the opposite and the hypotenuse).

Part 1

To find the length of the missing side (c) of the right triangle, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, we have:

a² + b² = c²

Substituting the given values, we get:

16² + 30² = c²

Simplifying, we get:

256 + 900 = c²

1156 = c²

Taking the square root of both sides, we get:

c = sqrt(1156) = 34

Therefore, the length of the missing side of the right triangle is 34.

Part 2

To find the values of the six trigonometric functions of θ, we need to know one of the acute angles of the triangle. Let's call the acute angle opposite side a as angle A. Using the given values, we can find the sine, cosine, tangent, cosecant, secant, and cotangent of angle A as follows:

sin A = a/c = 16/34 = 8/17

cos A = b/c = 30/34 = 15/17

tan A = a/b = 16/30 = 8/15

csc A = 1/sin A = 17/8

sec A = 1/cos A = 17/15

cot A = 1/tan A = 15/8

Therefore, the values of the six trigonometric functions of θ are:

sin θ = sin A = 8/17

cos θ = cos A = 15/17

tan θ = tan A = 8/15

csc θ = csc A = 17/8

sec θ = sec A = 17/15

cot θ = cot A = 15/8

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Answer: A) No values of k are the expressions 12d + 8 and 4(3d + 5) - 8 equivalent.

They are the same if one amount or value has the same value as another.

We need to set the formulae 12d + 8 and 4(3d + 5) - 8 equal to one another and solve for k to get the values of k for which they are equivalent:

12d + 8 = 4(3d + 5) - 8

When we simplify this equation, we obtain:

12d + 8 = 12d + 12

When we take away 12d from both sides, we obtain:

8 = 12

There are no variables of k for which the expressions are similar because this equation is false for all values of d.

As a result, the response is A) No values.

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The statistical measures relative to each definition are given as follows:

The sentences are completed using four statistical measures, and their definitions, as follows:

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