3500 dollars is placed in an account with an annual interest rate of 8.75%. to the nearest tenth of a year, how long will it take for the account value to reach 36700 dollars?

Answer:

1

Step-by-step explanation:

According to the definition of distance, the distance between the points (10, 13) and (20, 13) is 10.

The distance between two points is equal to the length of the segment that joins them.

Given the coordinates of two different points (x₁, y₁) and (x₂,y₂), the expression that allows calculating the distance "d" between two different points on the Cartesian plane is:

d= √[(x₂ - x₁)² + (y₂ - y₁)²]

In this case, you know:

Substituting in the definition of distance:

d= √[(20 -10)² + (13 -13)²]

Solving:

d= √[10² + 0²]

d= √10²

d= √100

d= 10

Finally, the distance is 10.

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Answer: $18,000.

Step-by-step explanation:

Let X be the number of adult tickets sold and Y be the number of youth tickets sold.

We can set up the following system of equations to represent this situation:

X * 25 + Y * 12.50 = 15000

X + Y <= 1000

The first equation represents the total ticket sales, and the second equation represents the maximum capacity of the theater.

To solve this system of equations, we can use a method such as graphing, substitution, or elimination.

Using the substitution method, we can solve for one variable in terms of the other and substitute it into the other equation. For example, we can solve the first equation for X:

X = (15000 - Y * 12.50) / 25

Then, we can substitute this expression for X into the second equation:

(15000 - Y * 12.50) / 25 + Y <= 1000

Solving this equation for Y gives us the number of youth tickets that can be sold:

Y <= 600

This means that the theater can sell a maximum of 600 youth tickets. We can then use this value to find the maximum number of adult tickets that can be sold by substituting it into the expression for X that we derived earlier:

X = (15000 - 600 * 12.50) / 25

Solving this equation gives us a maximum of 240 adult tickets that can be sold.

Therefore, the theater can sell a maximum of 600 youth tickets and 240 adult tickets for a total of 840 tickets. The total ticket sales for this scenario would be 600 * $12.50 + 240 * $25 = $18,000.

Answer:

6,340

Step-by-step explanation:

Follow the steps in the image.

-Hope this helped

Answer: A)

FCE and CAB are congruent angles they are formed by the same line FA and two parallel lines between them

FEC and EDB are congruent angles for the same reason

B)we will write the measure of each angle based on the statement

The line AD contains the angles ABC,CBE and EBD if we sum all angles we make the line and the measure of a line is 180 degrees so

the CBE is 72°

C)

congruent triangles are those that have all their angles equal,Since all the triangles are copies of triangle ABC, they are all congruent since they all measure the same but are located in different ways

so a triangle congruent to triangle CBE can be any for example :ABC,BED or FCE

The value of expression  (√3+1)(1-2√3)​ is -5-√3

An expression is combination of variables, numbers and operators.

The given expression is (√3+1)(1-2√3)​

Square root three plus one times of one minus two root three.

(√3+1)(1-2√3)​

Now distribute each terms

√3-2√3√3+1-2√3

√3-2(3)+1-2√3

Add the like terms

√3-6+1-2√3

√3-5-2√3

-5-√3

Hence, the value of expression  (√3+1)(1-2√3)​ is -5-√3

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Answer:

answer is d

Step-by-step explanation:

The slope of a line in the form "y = mx + b" is given by the coefficient "m" of the x term.

For the first equation, x - 2y = -1/2, we can rearrange the terms to get y = (1/2)x - 1/2. The coefficient of the x term is 1/2, so the slope of the line is 1/2.

For the second equation, -4x - 8y = 2, we can rearrange the terms to get y = -(1/2)x - 1/4. The coefficient of the x term is -1/2, so the slope of the line is -1/2.

The value of cos⁻¹(1/2) on the unit circle is 60°.

A circle with a radius of one unit is referred to as a unit circle. In the Cartesian coordinate plane, the unit circle is typically depicted. The second-degree equation with the variables x and y is used to algebraically represent the unit circle.

Given:

cos⁻¹(1/2)

As we know that for the unit circle, the value of the radius is 1,

Calculate the value of cos x as shown below,

cos x = radius of the circle / √(r² + p²)

cos x = 1 / √(1² + 1²)

cos x = 1 / √2

x = cos⁻ (1 / √2)

x = 45°

Thus, cos⁻¹(1/2) = 60°

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Answer:

19.8x-11.1y

Step-by-step explanation:

1) We can rephrase the equation as:

25x+0.9y-12y-5.2x

2) Simplify:

19.8x-0.9y-12y

3) Solve: 0.9y-12y= -11.1y

And the just put that next to 19.8 and you are done

The value of x after the statements execute is 46, as the value at the memory address of x was changed to 46.

Step 1: int x = 25;

Step 2: int *p;

Step 3: p = &x;

Step 4: *p = 46;

Step 5: x = 46;

The value of x after the statements execute is 46. This is because the statement int x = 25 sets the variable x to the value of 25. The statement int *p; creates a pointer variable p, which is a variable that stores the memory address of another variable. The statement p = &x; sets the pointer variable p to the memory address of x, so that it points to x. The statement *p = 46; changes the value of the variable that p points to, which is x, to 46. So, the value at the memory address of x was changed to 46, and thus the value of x is now 46.

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Answer:

--12°

Step-by-step explanation:

12 below can be written as the negative number -12

Answer:

i don't know if this is right but i think it may be 5n-23y or -23y+5n

Step-by-step explanation:

The amount of interest for the year was 3,770 cents, and the regular price of the electric drill that Pamela bought before the discount was 21,927 cents

Interest = P x R x T.

Where:

P = Principal amount (the beginning balance).

R = Interest rate

T = Number of time periods

In this case, we are given that;

Principal amount (P) = $580

Interest rate (R) = 6,5 %

Time = 1 year

Hence, The amount of the interest = 6,5% of $580

                                                     = 0.065 × $580

                                                     = $37.7

1 dollar = 100 cents

Hence, $37.7 = 37.7 × 100 cents equal to 3,770 cents

P = (1 – d) x

Where,

P = Price after discount

D = discount rate

X = regular price

In this case, we are given that:

P = $32.89

D = 85% = 0,85

Hence, the regular price:

P = (1 – D) x

32.89 = (1 – 0.85) X

32.89 = 0.15X

X = 32.89/0.15

X= 219.27

1 dollar = 100 cents

Hence, $219.27 = 219.27 × 100 cents equal to 21,927 cents

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Answer:

[tex]x = \frac{1 +\sqrt{359}i }{20} , x = \frac{1 -\sqrt{359}i }{20}[/tex]

Step-by-step explanation:

Given equation is

          [tex]10x^2 - x + 9 = 0[/tex]

The standard Solution of a quadratic equation is:

         [tex]x = \frac{-b +- \sqrt{b^2 - 4ac} }{2a}[/tex]

given a = 10, b = -1, c = 9, so

        [tex]x = \frac{1 +- \sqrt{(-1)^2 - 4*10*9} }{20}\\x = \frac{1 +- \sqrt{1 - 360} }{20}\\x = \frac{1 +- \sqrt{-359} }{20}[/tex]

So roots are:

[tex]x = \frac{1 +\sqrt{359}i }{20} , x = \frac{1 -\sqrt{359}i }{20}[/tex]

The height of a player at 18 points average is 78 and the points per game a player averages if he is 70 inches tall is 7

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

height (in) 84 80 79 82 74 72 86 76

points per game 22 21 21 26 12 8 28 15

Using a graphing calculator, we have the following calculation summary

The regression equation is represented as

p = bh + a

Where

b = SP/SSX = 224.88/166.88 = 1.35

a = MY - bMX = 19.13 - (1.35*79.13) = -87.5

So, we have

p = 1.35h - 87.5

At a point of 18, we have

1.35h - 87.5 = 18

So, we have

1.35h = 105.5

Divide by 1.35

h = 78

This means that

h = 70

So, we have

p = 1.35 * 70 - 87.5

Evaluate

p = 7

Hence, the point is 7

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Answer: 4.68555772

Step-by-step explanation:

The expression that represents the total cost of games after w weeks is 1000w + 2000wg.

The cost, in dollars, for a video game developer to code g games can be represented by the function v(g) = 500 + 1000g. The number of games produced in w weeks is given by the function g(w) = 2w.

The expression that represents the total cost of games after w weeks can be represented as follows;

Therefore,

v(g) = 500 + 1000g

g(w) = 2w.

total cost = v(g) × g(w)

total cost = (500 + 1000g)2w

Therefore,

total cost = 1000w + 2000gw

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Depends on the specific values of x, y, and the step size h used in the approximation.

What is differentiation ?

Differentiation is a concept in calculus that involves finding the rate of change of a function with respect to one of its variables. It is represented by the symbol ∂/∂x or ∂/∂y or ∂/∂t (where x, y and t are the variables of the function). The process of differentiation allows us to find the slope of a curve, the instantaneous rate of change, and the maximum or minimum points of a function.

The difference between dy and δy can be determined by subtracting dy from δy. The accuracy of dy in approximating δy depends on the specific values of x, y, and the step size h used in the approximation.

For example, if we consider dy = (f(x+h, y+k)-f(x,y))/h, and δy= f'(x)*δx.

Where f(x,y) is the given function for the system of differential equations and f'(x) is the derivative of the function f(x,y) with respect to x.

so the difference between dy and δy is δy-dy= f'(x)*δx - (f(x+h, y+k)-f(x,y))/h.

The accuracy of dy in approximating δy can be determined by taking the limit of the difference as h approaches 0.

In the end, it all depends on the specific problem and desired level of accuracy.

Depends on the specific values of x, y, and the step size h used in the approximation.

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The solution is Option B.

An investment of $300 gaining compound interest at a rate of 4% can be modeled by the equation B = 300 x ( 1.04 )ⁿ , where n = t

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

Let the amount to be invested be represented as P

The value of P = $ 300

Let the final amount be represented as A

Let the time period be = n = t

Let the rate of interest be represented as r = 4 %

r = 4/100

The value of r = 0.04

Now , the compound interest is calculated by the equation ,

A = P ( 1 + r/n )ⁿᵇ

Substituting the values in the equation , we get

A = 300 ( 1 + 0.04 )ⁿ

On simplifying the equation , we get

A = 300 ( 1.04 )ⁿ

where n = t = number of years

Hence , the equation is 300 x 1.04^t

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The statements that complete the blanks are underlined as follows

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

The graph

The given graph is a quadratic graph

All quadratic graphs are functions

So, the relation is a function

This statement is false,

This is so because one y value points to two different x values, as evident on the graph

As a general rule, the inverse of a quadratic function is not a function

This means that the inverse of the given relation is not a function

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Triangles that do not have the same angles or side lengths as triangle ABC cannot be similar to triangle ABC.

Similar triangles are triangles that have the same angles and side lengths. Therefore, any triangle that does not have the same angles and side lengths as triangle ABC cannot be similar to triangle ABC.

Similar triangles are triangles that have the same angles and side lengths. Therefore, any triangle that does not have the same angles or side lengths as triangle ABC cannot be similar to triangle ABC. For example, if triangle ABC has an angle of B which is a right angle and sides of length 15 cm, 8 cm, and 17 cm respectively, then a triangle with an angle of B which is not a right angle, or with side lengths that are not the same as triangle ABC's, cannot be similar to triangle ABC. This is because the angles and side lengths of both triangles must match in order for them to be similar. Therefore, any triangle that does not have the same angles and side lengths as triangle ABC cannot be similar to triangle ABC.

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Triangles which are not right angled triangles are not similar to triangle ABC.

As given in the question,

Triangle ABC is right angled triangle.

Angle B of triangle ABC is right angle.

Side length of AB = 15 cm

Side length of BC = 8 cm

Side length of AC = 17 cm

If the other triangles apart from ABC , is not a right angled triangle and its side are not in proportion .

Then the triangles are not similar to the given triangle ABC .

Therefore, triangles which are not right angled triangle are not similar to the given triangle ABC.

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Answer:

4[tex]\sqrt{\frac{1}{15} }[/tex]

Step-by-step explanation:

Answer:

x = 15

Step-by-step explanation:

since the triangles are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{MP}{XZ}[/tex] = [tex]\frac{NP}{YZ}[/tex] ( substitute values )

[tex]\frac{x+5}{30}[/tex] = [tex]\frac{4x-10}{75}[/tex] ( cross- multiply )

30(4x - 10) = 75(x + 5) ← distribute parenthesis on both sides

120x - 300 = 75x + 375 ( subtract 75x from both sides )

45x - 300 = 375 ( add 300 to both sides )

45x = 675 ( divide both sides by 45 )

x = 15

The equation y - 1 = 2 · (x - 2)² is the vertex form of the parabola y = 2 · x² - 4 · x + 9.

Parabolae are represented by quadratic equations of the form:

y = A · x² + B · x + C

Where A, B, C are real coefficients. This form is known as standard form and whose equivalent vertex form can be found by completing the square, that is, an application of algebra properties to modify part of the polynomial. Vertex form is described below:

y - k = C · (x - h)²

Where:

Now we proceed to modify the expression:

y = 2 · x² - 4 · x + 9

y = 2 · (x² - 2 · x + 9 / 2)

y = 2 · (x² - 2 · x + 4) + 1

y - 1 = 2 · (x - 2)²

The vertex form of the parabola is y - 1 = 2 · (x - 2)².

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Answer:

4

Step-by-step explanation:

This is a right triangle.

We can find the value of the missing side, hypotenuse, using Pythagoras theorem:

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

[tex] {2}^{2} + ({2 \sqrt{3} )}^{2} = {c}^{2} [/tex]

[tex]4 + 12 = {c}^{2} [/tex]

[tex]16 = {c}^{2} [/tex]

4 = c

Can you please re-post a clear image to get the correct and instant answer?

The domain of the logarithmic function f(x)=log(x) is all real numbers x>0. The range of the logarithmic function is all real numbers y>-∞.

The domain of a logarithmic function f(x)=log(x) is all real numbers x>0. This is because the logarithm function is not defined for x ≤ 0, as log(x) is undefined for x ≤ 0.

The range of the logarithmic function is all real numbers y>-∞. This is because the logarithm of a real number is always negative and approaches negative infinity as x approaches 0. Therefore, the range of a logarithmic function is all real numbers y>-∞.

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