Mathematics High School

Dominic invested $520 in an account in the year 1995, and the value has been growing exponentially at a constant rate. The value of the account reached $770 in the year 2001. determine the value of the account, to the nearest dollar, in the year 2005

Answers

Answer 1

Answer:

I believe the answer is $936.64

Step-by-step explanation:

I hope this helps!

Dominic Invested $520 In An Account In The Year 1995, And The Value Has Been Growing Exponentially At

Related Questions

Use propositional logic to prove that the argument is valid. Do not use truth tables (A + B) ^ (C V -B) ^(-D-->C) ^ A D Please use the following substitute operators during your quiz: ^: &
v: I
¬: !
-->: ->

Answers

To prove that the argument is valid using propositional logic, we can apply logical rules and deductions. Let's break down the argument step by step:

(A + B) ^ (C V -B) ^ (-D --> C) ^ A ^ D

We will represent the proposition as follows:

P: (A + B)

Q: (C V -B)

R: (-D --> C)

S: A

T: D

From the given premises, we can deduce the following:

P ^ Q (Conjunction Elimination)

P (Simplification)

Now, let's apply the rules of disjunction elimination:

P (S)

A + B (Simplification)

Next, let's apply the rule of disjunction introduction:

C V -B (S ^ Q)

Using disjunction elimination again, we have:

C (S ^ Q ^ R)

Finally, let's apply the rule of modus ponens:

-D (S ^ Q ^ R)

C (S ^ Q ^ R)

Since we have derived the conclusion C using valid logical rules and deductions, we can conclude that the argument is valid.

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what is y divided by x

Answers

Answer:

yes

Step-by-step explanation: i think its correct

Nancy buys 15 m of ribbon. Her sister buys 6 m less ribbon but pays twice as much per metre. Together they pay R66. What is the price per metre of each type of ribbon?

Answers

Answer: 44/9 ----> 22/9

I hope this helps you

Number 13 please.it’s the answe.r

Answers

The answer is there what u need help with?

in the 3rd century bc the egyptians used their body parts to measure things.Why do you think peoplebinvented measurement system if body parts can be used to measure?

PLEASE ANSWER IT I REALLY NEED THANKYOU

Answers

In order to have an accurate measurement system, humans would’ve had to have created one. Although body parts could be used to measure things, the lengths would’ve been different everytime. This is because no human’s body part is the exact same length as another’s. Everybody’s bone structure is different so in order to create a universally correct measurement system, humans had to invent a new one.

A radioactive substance has an initial mass of 475 grams and a half-life of 20 days. What equation is used to determine the number of days, x, required for the substance to decay to 63 grams?

Answers

The equation used to determine the number of days, x, required for the substance to decay to 63 grams is: x ≈ 83.60

To determine the number of days, x, required for a radioactive substance to decay to 63 grams, we can use the exponential decay formula. The equation that represents the decay of a radioactive substance over time is:

N(t) = N₀ * (1/2)^(t/h)

Where:

N(t) is the remaining mass of the substance at time t

N₀ is the initial mass of the substance

t is the time elapsed

h is the half-life of the substance

In this case, we have an initial mass of 475 grams, and we want to find the number of days required for the substance to decay to 63 grams. We can set up the equation as follows:

63 = 475 * (1/2)^(x/20)

To solve for x, we can isolate the exponential term on one side of the equation:

(1/2)^(x/20) = 63/475

Next, we can take the logarithm (base 1/2) of both sides to eliminate the exponential term:

log(base 1/2) [(1/2)^(x/20)] = log(base 1/2) (63/475)

By applying the logarithmic property log(base b) (b^x) = x, the equation simplifies to:

x/20 = log(base 1/2) (63/475)

Finally, we can solve for x by multiplying both sides of the equation by 20:

x = 20 * log(base 1/2) (63/475)

Using a calculator to evaluate log(base 1/2) (63/475) ≈ 4.1802, we find:

x ≈ 20 * 4.1802

x ≈ 83.60

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X+Y=17 and XY=164 find the vale of X and Y

Answers

There are no real values for X and Y that satisfy the given equations X + Y = 17 and XY = 164.

To find the values of X and Y in the given equations, we can use a system of equations approach.

Let's start by solving the first equation, X + Y = 17, for one variable in terms of the other. We can choose to solve for X:

X = 17 - Y

Now, substitute this expression for X in the second equation, XY = 164:

(17 - Y)Y = 164

Expanding the equation gives us:

17Y - Y^2 = 164

Rearranging the equation to a quadratic form, we have:

Y^2 - 17Y + 164 = 0

To solve this quadratic equation, we can use factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:

Y = (-(-17) ± √((-17)^2 - 4(1)(164))) / (2(1))

Simplifying further:

Y = (17 ± √(289 - 656)) / 2

Y = (17 ± √(-367)) / 2

Since the expression under the square root is negative, there are no real solutions for Y. This means that there are no real values for X and Y that satisfy both equations simultaneously.

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Plz hurry help!!!!:) What is the length of AD? Round your answer to the nearest hundredth.
34
3 units
310
D

Answers

Step-by-step explanation:

since theta is opposite divided by hypotenuse.

so sine 31=3÷AD

Therefore AD=3÷sine 31

thus AD=5.8248

in nearest hundredth, it will be 5.82 units

The length of AD to the nearest hundredth is 5.82 units.

What are trigonometric ratios?

Trigonometric ratios are particular measurements of a right triangle, which is a triangle having a 90° angle. The legs are the two sides that make up the right angle in a right triangle, while the hypotenuse is the third side that is across from the right angle.

Types of trigonometric ratios:

The six trigonometric ratios are

sine (sin),cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

Calculation for the side AD:

In triangle ACD,

Angle CAB = 34 degrees

Angle ADC = 31 degrees

Side AB = 3 units

Now, consider triangle ABD.

Sin (31) = AB/AD

AD = AB/sin 31

AD = 3/sin 31

AD = 5.82

Therefore, the length of the side AD is 5.82 units.

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Theres a story behind a box math
Can someone answer this for me need it asap

Answers

Answer:

1. x

2. 8-2x

3. width times 8-2x times x

4. Don't understand.

5. I don't know?

6. The volume is (6 - (2x))(8 - (2x))(x).

Step-by-step explanation:

A family went to a restaurant for dinner. The bill before tax and tip was $52.78. The sales tax is
6.5%, and the family wants to tip 18%. The tip is on the cost of the food plus tax.
What was the total cost of the meal, including tax and tip?
A
$66.33
B
$65.71
С
$62.28
D
$56.21

Answers

Answer:

Step-by-step explanation:

52.78×6.5%=3.43

52.78×18%=9.50

52.78+3.43+9.50=65.71

"Assuming that all else remains constant, the length of a confidence interval for a population mean increases when the sample size increase." Is this statement true or false?

Answers

This statement is false.

Why the statement is false?

A confidence interval is a range of values that is likely to contain the true population parameter with a certain level of confidence. The length of the confidence interval is determined by the sample size, the level of confidence, and the variability of the data.

When the sample size increases, the standard error of the mean decreases, which means that the estimate of the population mean becomes more precise. This increased precision results in a narrower confidence interval. Conversely, when the sample size decreases, the standard error of the mean increases, which leads to a wider confidence interval.

Therefore, the statement is false and it is important to recognize that increasing the sample size generally leads to a narrower confidence interval for the population mean.

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solve the equation using the quadratic formulax^2+6x-2=0x=?

Answers

$x^2\text{ + 6x - 2 = 0}$

a = 1, b = 6, c = -1

Using the quadratic formula:

$x\text{ = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}=\frac{-6\pm\sqrt[]{6^2-4\cdot1\cdot(-2)_{}}}{2\cdot1}=\frac{-6\pm\sqrt[]{36+8}}{2}=\frac{-6\pm\sqrt[]{44}}{2}=\frac{-6\pm6.6332}{2}$$x_1=\frac{-6+6.6332}{2}=\frac{0.6332}{2}=0.3166$$x_2=\frac{-6-6.6332}{2}_{}_{}=\frac{-12.6332}{2}=-6.3166$

Answer:

x1 = 0.3166

x2 = -6.3166

Which of the following functions are solutions of the differential equation y'' + y = 3 sin(x)? (Select all that apply.)
a. y = 3 sin(x)
b. y = 3/2x sin(x)
c. y = 3x sin(x)-4x cos(x)
d. y = 3 cos(x) e. y = -3/2x cos(x)

Answers

To determine which functions are solutions of the given differential equation y'' + y = 3 sin(x), we need to check if plugging each function into the differential equation satisfies the equation. We will examine each option and identify the functions that satisfy the equation.

The differential equation y'' + y = 3 sin(x) represents a second-order linear homogeneous differential equation with a particular non-homogeneous term.
(a) Plugging y = 3 sin(x) into the differential equation gives 0 + 3 sin(x) ≠ 3 sin(x). Therefore, y = 3 sin(x) is not a solution.
(b) Plugging y = (3/2)x sin(x) into the differential equation gives (3/2) sin(x) + (3/2)x sin(x) = (3/2)(1 + x) sin(x), which is not equal to 3 sin(x). Therefore, y = (3/2)x sin(x) is not a solution.
c) Plugging y = 3x sin(x) - 4x cos(x) into the differential equation gives 6 cos(x) - 4 sin(x) + 3x sin(x) - 3x cos(x) = 3 sin(x), which satisfies the equation. Therefore, y = 3x sin(x) - 4x cos(x) is a solution.
(d) Plugging y = 3 cos(x) into the differential equation gives -3 sin(x) + 3 cos(x) = 3 sin(x), which is not equal to 3 sin(x). Therefore, y = 3 cos(x) is not a solution.
(e) Plugging y = (-3/2)x cos(x) into the differential equation gives (3/2) sin(x) - (3/2)x cos(x) = (-3/2)(x cos(x) - sin(x)), which is not equal to 3 sin(x). Therefore, y = (-3/2)x cos(x) is not a solution.
Based on the analysis, the only function that is a solution to the given differential equation is y = 3x sin(x) - 4x cos(x) (option c).

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solve this algebraic expression
$16a {}^{4} - 4a {}^{2} - 4a - 1$

$solve this algebraic expression [tex]16a {}^{4} - 4a {}^{2} - 4a - 1[/tex]$

Answers

(40'+ 227) (46 -301)
SOLVING STEPS
Tat-42-40-1
= baT.
(40'740#1)
=16a4 - pati)? = (a'+ zaHi) (42°- 20-1) a'+ sabtb"= atbs
a-B'= (ath) (0-1)

$solve this algebraic expression [tex]16a {}^{4} - 4a {}^{2} - 4a - 1[/tex]$

Answer:

The factored form is,

$(4a^2+2a+1)(4a^2-2a-1)$

Step-by-step explanation:

We have,

$16a^4-4a^2-4a-1\\factoring,\\We\ can \ write \ 16a^4 \ as \ (4a^2)^2\\Also,\\then we have,\\(4a^2)^2-(4a^2+4a+1)\\Now, 4a^2 + 4a + 1 \ is \ a \ perfect \ square,\\4a^2 + 4a + 1 = (2a)^2 + 2(2a) + 1\\= (2a + 1)^2\\so, we \ have,\\(4a^2)^2 - (2a + 1)^2\\$

Using the difference of square formula,

$x^2 - y^2 = (x+y)(x-y)\\with,\\x = 4a^2,\\y = 2a+1,\\we \ get,\\(4a^2+2a+1)(4a^2-2a-1)$

Which is the factored form,

each package of M&M’s should contain 24% blue, 13% brown, 15% green, 28% orange, 12% red, and 18% yellow M&M’s on average. If you chose a random M&M, what is the probability that it would be red or blue?If you chose a random M&M, what is the probability that it wouldn’t be yellow?If you chose 2 M&M’s, what is the probability that they would both be orange?

Answers

Solution

Blue = 21%

Brown = 14 %

green = 18%

orange =21 %

red = 11%

yellow = 15%

Total = 100 %

(1)

The probability that it would be red or blue?

$\begin{gathered} Pr(RorB)=\frac{11}{100}+\frac{21}{100} \\ =\frac{32}{100} \\ =\frac{8}{25} \end{gathered}$

(2) The probability that it wouldn’t be yellow?

$\begin{gathered} 1-Pr(yellow) \\ =1-\frac{15}{100} \\ =\frac{85}{100} \\ =\frac{17}{25} \end{gathered}$

(3) The probability that they would both be orange

$\begin{gathered} Pr(YY)=\frac{21}{100}\times\frac{21}{100} \\ =\frac{441}{10000} \end{gathered}$

all employees work less than 40 hours

Answers

Nice..................

find the total differential of the function w = e y cos(x) z^2 .

Answers

To find the total differential of the function w = e^y * cos(x) * z^2, we can take the partial derivatives with respect to each variable (x, y, and z) and multiply them by the corresponding differentials (dx, dy, and dz).

The total differential can be expressed as:

dw = (∂w/∂x) dx + (∂w/∂y) dy + (∂w/∂z) dz

Let's calculate the partial derivatives:

∂w/∂x = $-e^{y} * sin(x) * z^{2}$

∂w/∂y = $e^{y} * cos(x) * z^{2}$

∂w/∂z = $2e^{y} *cos (x)* z$

Now, let's substitute these partial derivatives into the total differential expression:

$dw = (-e^{y} * sin(x) * z^{2} ) dx + (e^{y}* cos(x) * z^{2} ) dy + 2e^{y} *cos (x)*z) dz$

Therefore, the total differential of the function w = e^y * cos(x) * z^2 is given by:

$dw = (-e^{y} * sin(x) * z^{2} ) dx + (e^{y} * cos(x) * z^{2} ) dy + ( 2e^{y} * cos(x) * z) dz$

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Integral sec y dy from zero to one-sixth of pi is log to base e srt 3 times the 64th power of what

Answers

The integral of sec(y) dy from zero to one-sixth of pi is equal to the natural logarithm of the square root of 3 times 64 raised to a certain power.

To evaluate the integral ∫ sec(y) dy from zero to one-sixth of pi, we can use the trigonometric identity that the integral of sec(y) dy is equal to the natural logarithm of the absolute value of the secant of y plus the tangent of y.

Integrating sec(y) dy gives us ln|sec(y) + tan(y)|. Evaluating the integral from zero to one-sixth of pi, we substitute the upper and lower limits of integration into the expression and subtract the result at the lower limit from the result at the upper limit.

ln|sec(π/6) + tan(π/6)| - ln|sec(0) + tan(0)|

Simplifying this expression, we know that sec(π/6) = √3/2 and tan(π/6) = 1/√3. Additionally, sec(0) = 1 and tan(0) = 0.

ln|√3/2 + 1/√3| - ln|1 + 0|

ln|√3 + 1| - ln|1|

ln|√3 + 1|

Therefore, the integral ∫ sec(y) dy from zero to one-sixth of pi is equal to the natural logarithm of the square root of 3 plus 1, or ln(√3 + 1).

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is my answer correct or nah if not pls fix I have 4 min

Answers

Answer:

It seems correct to me when i put it in my calculator, of course i could be wrong

Step-by-step explanation:

Malik has $575 in the bank and each week he withdraws $25 out of his
account. How much money will he have after 8 weeks?

Answers

Answer:

375$

Step-by-step explanation:

25*8 is 200, 575-200 is 375

View image trig maths

Answers

The value cosθ is 0.707.

The value angle z is -45⁰, and 45⁰.

The value of angle θ is 45⁰ and 315⁰.

What is the cosθ?

The value cosθ, and angle Z is calculated by applying trigonometry ratio as follows;

for question 6,

tan θ = opposite side/adjacent

tan θ = 5/5

tan θ = 1

θ = 45⁰ = z

cos θ = 0.707

for question 7;

tan z = opp/adjacent

tan z = -5/5

tan z = -1

z = arc tan (-1)

z = -45⁰ =

The value of θ is calculated as;

θ = 360 - 45

θ = 315

cos (315) = 0.707

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what does 14.53.48 + 12.12.42 + 13.53.48 + 13.28.6 + 20.17.3 + 19.43.8 + 28 equal?

Answers

Answer: $76.1222$

Step-by-step explanation:

$Simplify$ $the$ $expression$$.$

$14.53.48 + 12.12.42 + 13.53.48 + 13.28.6 + 20.17.3 + 19.43.8 + 28$

The degree is the largest exponent on the variable.

$0$

Solve the rational equation by combining expressions and isolating the variable.

No solution

multiply each sides by what?
-8x(_)=-3(_)

Answers

Answer:

-8 × 3 = - 3 × ( 8)

or -21 = -21

Answer:

-21

Step-by-step explanation:

Which are examples of non-statistical questions?

Questions
Question 1 What is Sasha’s favorite movie?
Question 2 What is Stacey’s favorite book?
Question 3 What is your favorite movie?
Question 4 What is your favorite book?
questions 1 and 2
questions 1 and 3
questions 2 and 4
questions 2 and 3

Answers

i think it’s questions 1 and 2

Answer:

A 1 and 2

Step-by-step explanation:

Can someone solve this please I really need the answer and your help

Answers

The cost of Adult ticket is $ 4 and Cost of Children ticket is $ 3.

What is System of Linear Equation ?

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, whereas B is a constant. A linear equation with two variables has the standard form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

A linear equation is an algebraic equation in which each term has an exponent of 1, and which, when plotted on a graph, always yields a straight line. It is called a "linear equation" for this reason.

The cost of adult ticket be x and child ticket be y respectively.

Now as per sum ,

(i) 5x + 13y = 59 and,

(ii) 5x + 9y = 47

Subtracting equation (ii) from (i) we get,

13y - 9y = 59 - 47

⇒ 4y = 12

⇒ y = 3

putting y = 3 in equation (ii) we get

5x + 9*3 = 47 ⇒ x = 20/5 = 4

The cost of Adult ticket is $ 4 and Cost of Children ticket is $ 3.

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Find the product. 4x3y(-2x2y) 2x 5y 2 -8x 5y 2 -8x 6y -8x 5y

Answers

The calculated value of the product of the expression 4x³y(-2x²y) is -8x⁵6y²

How to determine the value of the expression

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

4x³y(-2x²y)

We need to know that algebraic expressions are described as expressions that are composed of variables, their coefficients, terms, factors and constants.

These expressions are also made up of arithmetic or mathematical operations.

These mathematical operations are;

AdditionBracket and ParenthesesSubtractionMultiplicationDivision

From the information given, we have that

4x³y(-2x²y)

Expanding the bracket, we have;

4x³y(-2x²y) = -8x⁵6y²

Hence, the solution of the product expression is -8x⁵6y²

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The volume of the box is modeled by the function V (x) = 5x^2 + 5x. What is the volume when x= 4?
А-120 cubic units
B-30 cubic units
C-100 cubic units
D-45 cubic units

The volume of the box is modeled by the function V (x) = 5x^2 + 5x. What is the volume when x= 4?-120

Answers

V= 5 x 4^2 + 5 x 4
V= 5 x 16 + 20
V= 80+ 20
V= 100
Answer is C 100 cubic units

The volume of box at x = 4 is, 100 cubic units

What is mean by Cuboid?

A cuboid is the solid shape or three-dimensional shape. A convex polyhedron which is bounded by six rectangular faces with eight vertices and twelve edges is called cuboid.

We have to given that;

The volume of the box is modeled by the function,

⇒ V (x) = 5x² + 5x

Now, At x = 4;

The volume of the box is,

⇒ V (x) = 5x² + 5x

⇒ V (4) = 5 × 4² + 5 × 4

⇒ V (4) = 5 × 16 + 20

⇒ V (4) = 80 + 20

⇒ V (4) = 100 cubic units

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The equation c = 45 + 0.04m represents the

total charges for renting a car driving m miles.

Which table contains values that represent this

relationship?

(If you show your work I will give you brainliest) (Also look at picture)

Answers

the table that contains values that represent the relationship between the total charges for renting a car and driving m miles is:

| Miles driven (m) | Total charges (c) |
|------------------|-------------------|
| 0 | 45 |
| 50 | 47 |
| 100 | 49 |
| 150 | 51 |
| 200 | 53 |.

To create a table that represents the relationship between the total charges and the miles driven, we can substitute different values of m (miles driven) into the equation and solve for c (total charges).

For example, when m = 0, we have:

c = 45 + 0.04(0)
c = 45 + 0
c = 45

This means that if you don't drive the car at all (m = 0), the total charges will be $45.

Similarly, when m = 100, we have:

c = 45 + 0.04(100)
c = 45 + 4
c = 49

This means that if you drive the car for 100 miles, the total charges will be $49.

Using this method, we can create the following table:

| Miles driven (m) | Total charges (c) |
|------------------|-------------------|
| 0 | 45 |
| 50 | 47 |
| 100 | 49 |
| 150 | 51 |
| 200 | 53 |

And so on, with the total charges increasing by $0.04 for each additional mile driven.

Therefore, the table that contains values that represent the relationship between the total charges for renting a car and driving m miles is:

| Miles driven (m) | Total charges (c) |
|------------------|-------------------|
| 0 | 45 |
| 50 | 47 |
| 100 | 49 |
| 150 | 51 |
| 200 | 53 |

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I need help to solve this please help me...

Answers

Your question has been heard loud and clear/

we know,

4cos³x = 3cosx + cos3x

put here, x = 20°

then, 4cos³20° = 3cos20° + cos3 × 20°

= 3cos20° + cos60°

cos³20° = (3cos20° + cos60°)/4 -------(1)

similarly ,

4sin³x = 3sinx - sin3x

put here, x = 10°

4sin³10° = 3sin10° - sin30°

sin³10° = (3sin10° - sin30°)/4 -----------(2)

now,

LHS = cos³20° + sin³10°

put equations (1) and (2)

= 1/4(3cos20° + cos60°) + 1/4 ( 3sin10° - sin30°)

= 1/4( 3cos20° + cos60° + 3sin10° - sin30°)

we know,

cos60° = sin30° = 1/2

= 1/4 ( 3cos20° + 3sin10°)

= 3/4(cos20° + sin10°) = RHS

hence proved

Thank you

Answer: see proof below

Step-by-step explanation:

Use the following identities & Unit Circle calculations:

4cos³x = 3cos x + cos 3x

--> cos³x = (1/4)[3cos x + cos 3x]

4sin³x = 3sin x - sin 3x

--> sin³x = (1/4)[3sin x - sin 3x]

cos 60° = sin 30° = (1/2)

Proof: LHS → RHS

Given: cos³ 20° + sin³ 10°

Triple Angle Identity: (1/4)[3cos 20° + cos 3·20°] + (1/4)[3sin 10° - sin 3·10°]

Simplify: (1/4)[3cos 20° + cos 60° + 3sin 10° - sin 30°]

(1/4)[3cos 20° + (1/2) + 3sin 10° - (1/2)]

(1/4)[3cos 20° + 3sin 10°]

Factor: (3/4)[cos 20° + sin 10°]

Proven: (3/4)[cos 20° + sin 10°] = (3/4)[cos 20° + sin 10°] $\checkmark$

DEF Company's current share price is $16 and it is expected to pay a $0.55 dividend per share next year. After that, the firm's dividends are expected to grow at a rate of 3.7% per year. What is an estimate of DEF Company's cost of equity? Enter your answer as a percentage and rounded to 2 DECIMAL PLACES. Do not include a percent sign in your answer. Enter your response below. -7.1375 正确应答: 7.14±0.01 Click "Verify" to proceed to the next part of the question.
DEF Company also has preferred stock outstanding that pays a $1.8 per share fixed dividend. If this stock is currently priced at $27.6 per share, what is DEF Company's cost of preferred stock? Enter your answer as a percentage and rounded to 2 DECIMAL PLACES. Do not include a percent sign in your answer. Enter your response below.

Answers

An estimate of DEF Company's cost of equity is 7.14%.

What is the estimate of DEF Company's cost of equity?

To estimate the cost of equity, we can use the dividend growth model. The formula for the cost of equity (Ke) is: Ke = (Dividend per share / Current share price) + Growth rate

Given data:

The dividend per share is $0.55, the current share price is $16, and the growth rate is 3.7%.

The cost of equity iss:

Ke = ($0.55 / $16) + 0.037

Ke ≈ 0.034375 + 0.037

Ke ≈ 0.071375.