A person invested $8, 700 in an account growing at a rate allowing the money to
double every 15 years. How long, to the nearest tenth of a year would it take for the
value of the account to reach $23, 100?

Answer:587

Step-by-step explanation:

Ok so it’s 587 I’m jp

Part A:

Complete table becomes:
Age (x)               Probability (p)                (x × p)

15                          9/40 = 0.225              3.375

16                         12/40=0.30                     4.8

17                         8/40=0.20                      3.4

18                         11/40=0.275                   4.95

....................................................................................................

Total                     1.00                    16.525

Part B:

Mean becomes: 16.525

The area of mathematics known as probability deals with numerical representations of how likely it is for an event to happen or for a claim to be true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty. Fundamentally, probability is a discipline of mathematics that uses computations to foretell the potential outcomes of a certain occurrence. It provides you the power to forecast the outcomes of future occurrences, which makes it seem cool.

Part A:

Age (x)               Probability (p)                (x × p)

15                          9/40 = 0.225              3.375

16                         12/40=0.30                     4.8

17                         8/40=0.20                      3.4

18                         11/40=0.275                   4.95

....................................................................................................

Total                     1.00                    16.525

Part B:

mean (μ) = ∑⁴(i = 1) xi pi

mean (μ) = 16.525

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Answer:

60%

Step-by-step explanation:

9/15 converted = 0.6 = 60%

On solving the provided question, we can say that the area of the rectangle  polygon is 474 ft².

A rectangle in Euclidean geometry is a parallelogram with four slight angle. It may alternatively be described as a hexagon that is basic rule, or one in which all of the angles are equal. A straight angle is another another option for the parallelogram. In a square, four of the vertices are the same length. A quadrilateral with a rectangle-shaped cross section has four 90 ° angle vertices + equal parallel sides. As a result, it is sometimes referred to as a "equirectangular rectangle". Due to such equal and parallel dimensions of its two sides, a rectangle is occasionally referred to as parallelogram.

The left rectangle has a height of 18 ft and a width of 21 ft, so its area is:

[tex]18 ft x 21 ft = 378[/tex] ft²

The right rectangle has a height of 12 ft and a width of 8 ft, so its area is:

[tex]12 ft x 8 ft = 96[/tex] ft²

Therefore, the total area of the polygon is:

378 ft² + 96 ft² = 474 ft²

So the area of the polygon is 474 ft².

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Answer: 8

Step-by-step explanation:

Answer:

P(AA) = 0.41

P(PM) = 0.38

P(AA and PM) = 0.05

As you are finding P(AA or PM), you can apply the formula:

P(A U B) = P(A) + P(B) - P( A ∩ B)

U = Union  P( A U B) = P (A or B)

∩ = And

From the formula, you can find out the answer:

P(AA or PM) = P(AA) + P(PM) - P(AA and PM)

                     = 0.41+0.38-0.05

                     = 0.74

hope this helps!!!!

Answer:

90°

Step-by-step explanation:

they are forming a right angle (90°).

The length and the width of the fencing are 85 feet and 30 feet respectively.

The whole distance that a rectangle's borders, or its sides, the cover is known as its perimeter. Given that a rectangle has four sides, the perimeter of the rectangle will be equal to the total of its four sides.

Given:

Darrin is hanging 200 feet of Christmas garland on the three sides of fencing that encloses his rectangular front yard.

The length is five feet less than three times the width.

Let w be the width.

Then, 3w - 5 is the length.

So, the perimeter of the rectangular fence = 200 + w.

Now, 2(3w - 5 + w) = 200 + w

6w - 10 + 2w = 200 + w

7w = 210

w = 30

Then length = 85

Therefore, length = 85 feet and width = 30 feet.

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Answer:

[tex]\frac{6}{15} - \frac{5}{15} = \frac{1}{15}[/tex]

Step-by-step explanation:

The expression for the time of the number of games remaining for shoes will be T = 225 - 2W.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Jacob just bought a new pair of basketball shoes. He expects the shoes to last for two hundred twenty-five games. He plays two games a week.

The expression for the life of the shoes will be written as:-

T = 225 - 2W

Here, T is the time and W is the number of weeks.

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A uniform random variable's density function is f(y) = 1 for y 1 and 0 otherwise. F(y) = 0 for y 0, F(y) = y for 0 y 1, and F(y) = 1 for y > 1 define the distribution function.

A uniform random variable's density function is f(y) = 1 for y 1 and 0 otherwise. Accordingly, the likelihood of any specific outcome of y is the same, and the likelihood of any range of outcomes is equal to the length of the range. F(y) = 0 for y 0, F(y) = y for 0 y 1, and F(y) = 1 for y > 1 define the distribution function. Accordingly, the length of the range multiplied by the likelihood of any specific occurrence yields the cumulative probability of any range of outcomes. Since the likelihood of any specific result in that range is 1 and the range's length is 0.5, for instance, the cumulative probability of 0 y 0.5 is 0.5. Since the likelihood of any given result within that range is still 1, but the range's length is 0.5, the cumulative probability of 0.5 y 1 is 0.75. The chance of any range of outcomes for y1 and y2 if they are independent random variables both having the uniform(0,1) distribution is just the sum of their respective cumulative probabilities.

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The profit was maximum when the current price raised by $2 then the profit falls in further increase of price.

The axis graph displays the point where two real number lines—one vertical and one horizontal (X axis)—intersect (Y axis). The X axis is referred to as the data set's independent variable, while the Y axis is referred to as the data set's dependent variable.

Given:

We have the Graph in which X- axis shows increase in price over the current value of Milkshake and, Y- axis shows Weekly profit Earned.

From the graph we can see that when the amount increased by $2 that gave the maximum profit.

After that it rising the money in prices leads to falls in profit.

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Answer:

Step-by-step explanation:

75

Answer: B

Step-by-step explanation:

1825/25=73

73*2=146

146

The surd is rationalized to give √6 - 5√3 + 5√2 - 25/2  + 25

It is important to note that fractions are a part of whole number or element.

The different types of fraction includes;

Given the expression;

√3 - 5/√2 + 5

√3 - 5/ √2 + 5 ×√2 - 5/√2 - 5

Multiply the values

√6 - 5√3 + 5√2 - 25/√4 - 5√2 + 5√2 + 25

Add the like surds and find the square roots, we get

√6 - 5√3 + 5√2 - 25/2  + 25

Hence, the expression is √6 - 5√3 + 5√2 - 25/2  + 25

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The distance from the school to Cristian home is least which is 1.375 miles.

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.

Paula lives 1 ⁹/₁₀ from school. Nate lives 1 ³/₄ miles from school. Cristian lives 11/8 miles from school.

Convert the mixed fraction and fraction number into a decimal number. Then we have

1 ⁹/₁₀ = 1.90 miles

1 ³/₄ = 1.75 miles

11/8 = 1.375 mies

The distance from the school to Cristian home is least which is 1.375 miles.

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Answer: Let's call the number of cookies Trey has "x".

Gerald has 8 less cookies than Trey, so he has x - 8 cookies.

Trey bought five times the number of cookies as Gerald, so he has 5 * (x - 8) = 5x - 40 cookies.

Combining these two equations, we have:

x + (x - 8) = 5x - 40

Simplifying, we get:

2x - 8 = 5x - 40

Solving for x, we find:

3x = 32

And finally, x = 10.

So Trey has 10 cookies and Gerald has 2 cookies.

Step-by-step explanation:

The table of linear function shows that f(1) is equal to -3

A linear function is a mathematical function of the form f(x) = mx + b, where m and b are constants and x is the input variable. This function produces a straight line on a graph, with a constant slope (m) and a y-intercept (b) where the line intersects the y-axis.

The slope (m) of a linear function represents the rate of change of the function, or the steepness of the line, while the y-intercept (b) represents the value of the function when x=0.

In the function table given, we can find f(1) when we look at the table.

This shows that f(1) is equal to -3

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Answer:

D=5=14 I hope this helps

Step-by-step explanation:

The second object is approximately 4.4 * 10^9 times bigger than the first object.

The division of the value of the second scientific notation from the first scientific notation is the precise and accurate way with which we can determine many many times bigger is the second object compared to the first object.

To do so, group coefficients together and exponents together to divide numbers in scientific notation. i.e.

= (3.7/8.5) * ((10^6)/(10^−4))

= 0.43529411 ×  ((10^6)/(10^−4))

Subtract the exponent from the denominator from the exponent of the numerator for the same base 0.43529411 ⋅ 10^(6 −4*−1)

= 0.43529411 × ((10^6+4)

= 0.43529411 × 10^10

= 4.3529411 × 10^9

≅ 4.4 × 10^9

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Answer:

y= -4/5x -3

Step-by-step explanation:

Step-by-step explanation:

75.00 - 25.00 = 50.00

50.00 / 20.00 = 2.50

So, she needs to mow 2.5 lawns or more to have enough money to buy the skateboard.

The inequality can be expressed as:

20.00 * x >= 50.00

x >= 2.50

So, the inequality "x >= 2.50" can be used to determine the number of lawns she needs to mow to have enough money to buy the skateboard.

The weighted average length of the nails in the drawer is given as follows:

D. 3.50 cm.

The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations.

For the weighted mean, each observation is multiplied by it's weight.

Considering the percentages as the weights, the weighted average length of the nails in the drawer is obtained as follows:

0.705 x 2.5 + 0.19 x 5 + 0.105 x 7.5 = 3.5.

Meaning that option D is the correct option for this problem.

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As per the given triangles given in the question, the corresponding names are mentioned accordingly in the answer.

A triangle is a basic polygonal geometry with three sides and three interior angles. This is a fundamental geometric shape that is particularly related. Its three vertices are joined together. Depending on their sides and angles, triangles can be classified into a wide range of groups.

In geometry, there are six different kinds of triangles. There are two categories into which they can be divided. The three triangles are categorized as equilateral triangles, isosceles triangles, and scalene triangles based on their sides. Triangles can be classified as acute, obtuse, or right-angled depending on the angle at which they are formed. There are so six different kinds of triangles in geometry.

As per the given information in the question,

a. 1, 2

b. 1

c. 2

d. 6

e. 5, 6, 7

f. 7

g. 6

h. 6

i. 4, 6

j. 4, 6

k. 4, 8

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Complete question -

The man should pull rope A to lift the load more easily

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

The diagram

To determine the rope to pull, we calculate the moment at the point

This is calculated as

Moment = Force * Perpendiculat Distance

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

Point A = F * (6 + 2)

Point B = F * (3 + 1)

Evaluate

A = 8F

B = 4F

8F is greater than 4F

Hence, the man should pull from point A

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Answer:

B) Linear Pair

D) Adjacent

E) Supplementary

Step-by-step explanation:

Because the sum of the two angles is 180°, we conclude that the correct options are:

B, D, and E.

We want to find the relationship between angles a and b.

Notice that if we would add these two angles, we would get a plane angle, then we could write:

∠a + ∠b = 180°.

That means 3 things:

The angles are adjacent because share a vertex and a common side, and the angles are supplementary because their sum is equal to 180°, and also are a linear pair, because their sum is equal to 180°.

Then the correct options are:

B, D, and E.

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The two equations for f(x) are not equal at x = 1 and f(x) is therefore discontinuous at this point

f(x) is discontinuous at x = 1 because when x = 1, the two separate equations for f(x) do not have the same output. For x < 1, [tex]f(x) = x^2 + 4[/tex], so when x = 1, [tex]f(1) = 1^2 + 4 = 5. For x > 1, f(x) = x + 4[/tex] , so when x = 1, f(1) = 1 + 4 = 5. The output of f(1) is different on each side of the discontinuity. This can be seen in the following calculation:

For x < 1,

[tex]f(x) = x^2 + 4f(1) = 1^2 + 4 = 5For x > 1,f(x) = x + 4f(1) = 1 + 4 = 5[/tex]

Since f(1) is 5 for x < 1 and f(1) is also 5 for x > 1, the two equations for f(x) are not equal at x = 1 and f(x) is therefore discontinuous at this point.

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Using newton's method to find all real roots of the equation, 4x = 1+ x³ is

x1 = -2.11491, x2 = 0.2541, x3 = 1.86081.

We have the equation,

4x = 1+ x³

To find the real roots of equation we have,

x1 = -2.11491, x2 = 0.2541, x3 = 1.86081.

The cubic equation formula in mathematics is how the cubic equation is represented. An equation with degree three is said to be cubic. In nature, the roots of all cubic equations are either one real root and two real roots or three real roots. Cubic polynomials are the name given to three-degree polynomials.

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Based on the given triangle, we can find that:

First, we will focus on the triangle NLP. NLP is a right triangle, then we can use the formula of sinus to find the length of NP, where:

Sin ∠NLP = NP / LP

Sin 35° = NP / 20

0.57 = NP / 20

NP = 11.47

NP ≈ 11

Next, we will focus on triangle GLP. GLP is a right triangle with hypotenuse of 52 and the base of 20. Using the Phytagoras theorem we can try to find the triangle's height.

GL² = GP² + LP²

52² = GP² + 20²

2704 = GP² + 400

GP² = 2304

GP = 48

GP = GN + NP

48 = GN + 11

GN = 37

To find the size of angle ∠GLN, we have to find the size of angle ∠PGN first. We will use the Sines Law:

LP / sin ∠PGN = GL / sin ∠GPN

20 / sin ∠PGN = 52 / 1

sin ∠PGN = 20/52

∠PGN = 22.5°

∠PGN ≈ 23°

∠GLP + ∠GPL + ∠PGN = 180°

∠GLP + 90° + 23° = 180°

∠GLP = 67°

∠GLP = ∠GLN + ∠NLP

67° = ∠GLN + 35°

∠GLN = 32°

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Answer:

Step-by-step explanation:

Quadratic X €

Evaluate -20

Answer:

[tex]x=\frac{1}{2} \pm \frac{i\sqrt{5}}{2}[/tex]

Step-by-step explanation:

Lets solve for [tex]x[/tex] in

[tex]-2^2-2x^2+2x+1=0[/tex]

Evaluate [tex]2^2[/tex]

[tex]-4-2x^2+2x+1=0[/tex]

Add [tex]-4[/tex] and [tex]1[/tex].

[tex]-2x^2+2x-3=0[/tex]

Divide both sides of the equation by [tex]-2[/tex].

[tex]x^2-x+\frac{3}{2}=0[/tex]

Now the equation is in standard form.

[tex]ax^2+bx+c=0[/tex]

We can solve this quadratic by completing the square.

Subtract [tex]\frac{3}{2}[/tex] from both sides of the equation.

[tex]x^2-x=-\frac{3}{2}[/tex]

Take one half of the coefficient of [tex]x[/tex] and square it, then add it to both sides.

Add [tex]\frac{1}{4}[/tex] to both sides.

[tex]x^2-x+\frac{1}{4} =-\frac{3}{2}+\frac{1}{4}[/tex]

[tex]x^2-x+\frac{1}{4} =-\frac{5}{4}[/tex]

The left hand side is a perfect trinomial square.

Factor the left hand side by writing it as a square.

[tex]\left(x-\frac{1}{2}\right)^2 =-\frac{5}{4}[/tex]

Take the square root of both sides to eliminate the exponent.

[tex]x-\frac{1}{2} =\pm\sqrt{-\frac{5}{4}}[/tex]

Rewrite [tex]\frac{5}{4}[/tex] as [tex]\left(\frac{i}{2} \right)^2 *5[/tex]

[tex]x-\frac{1}{2} =\pm\sqrt{\left(\frac{i}{2} \right)^2 *5}[/tex]

Pull terms out from under the radical.

[tex]x-\frac{1}{2} =\pm \frac{i}{2} \sqrt{5}[/tex]

Combine [tex]\frac{i}{2}[/tex] and [tex]\sqrt5[/tex].

[tex]x-\frac{1}{2} =\pm \frac{i\sqrt{5}}{2}[/tex]

Add [tex]\frac{1}{2}[/tex] to both sides of the equation.

[tex]x=\frac{1}{2} \pm \frac{i\sqrt{5}}{2}[/tex]

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