Leslie invests in a bank account that earns interest compounded quarterly. The expression 500(1.026)4t can be used to find the account balance in t years.

Part A
What was Leslie’s initial investment?

$

Part B
What is the quarterly interest rate the account earns?

Answer:

[tex]\circ \quad sin\left(-\dfrac{\pi}{2}\right) = -1\\\\[/tex]

[tex]\circ \quad \cos \left(-\dfrac{\pi }{2}\right)= 0\\\\[/tex]

[tex]\circ \quad \tan \left(-\dfrac{\pi }{2}\right) = -\dfrac{1}{0}[/tex]   is not defined

[tex]\circ \quad \csc\left(-\dfrac{\pi }{2}\right) =-1\\\\[/tex]

[tex]\circ \quad \sec\left(-\dfrac{\pi }{2}\right) = \dfrac {1}{0}\\[/tex]  is not defined

[tex]\circ \quad \cot\left(-\dfrac{\pi}{2}\right) =\:0[/tex]

Step-by-step explanation:

[tex]\text{Values of trig functions for $-\dfrac{\pi}{2}$ are: }\\\\[/tex]

[tex]\circ \quad sin\left(-\dfrac{\pi}{2}\right) = - sin\left(\dfrac{\pi}{2}\right) = -1\\\\[/tex]

[tex]\circ \quad \cos \left(-\dfrac{\pi }{2}\right)=\cos \left(\dfrac{\pi }{2}\right) = 0\\\\[/tex]

[tex]\circ \quad \tan \left(-\dfrac{\pi }{2}\right) = \dfrac{sin\left(-\dfrac{\pi}{2}\right)}{cos\left(-\dfrac{\pi}{2}\right) } = \dfrac{-1}{0}[/tex]
This is undefined since division by zero is undefined

[tex]\circ \quad \csc\left(-\dfrac{\pi }{2}\right) = \dfrac{1}{sin\left(-\dfrac{\pi }{2}\right)} = \dfrac{1}{-1} =-1\\\\[/tex]

[tex]\circ \quad \sec\left(-\dfrac{\pi }{2}\right) = \dfrac{1}{\cos\left(-\dfrac{\pi }{2}\right)} = \dfrac {1}{0}[/tex]
This is undefined

[tex]\circ \quad \cot\left(-\dfrac{\pi}{2}\right) = \dfrac{cos\left(-\dfrac{\pi }{2}\right)}{sin\left(-\dfrac{\pi }{2}\right)}\:=\:\dfrac{0}{-1\:}=\:0[/tex]

$3988.71 should be invested by them to be able to contribute $9000 to his education.

We can use the continuous compound interest formula:

[tex]A = Pe^{(rt)[/tex]

where A is the future value, P is the present value, r is the interest rate, and t is the time in years.

We know that A = $9000, r = 0.085 (8.5% expressed as a decimal), and t = 12.

Solving for P, we get:

[tex]P = A / e^{(rt)}\\\\P = 9000 / e^{(0.085*12)}\\\\P = \$ \ 3988.71[/tex]

Therefore, Mr. and Mrs. Tran should invest approximately $3988.71 now in order to have $9000 in twelve years, assuming continuous compound interest at a rate of 8.5% per year.

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The value of x in the equation x² = -20 is x  = 2i√5

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

x² = -20

To start with, we take the square root of both sides of the equation

So, we have

√x² = √-20

When the square roots are evaluated, we have

x  = √-20

Express -20 as 4 * -5

So, we have

x  = √4 * -5

This gives

x  = 2√-5

The expression √-5 is a complex number

So, we have

x  = 2i√5

Hence, the value of x in x² = -20 is x  = 2i√5

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Answer:

No Solution

Step-by-step explanation:

Because this solution deals with absolute value equations.

The value of the variable a in the equation is 5 from the calculation here.

We need to square of a number is described as a number that when multiplied by itself give the original number.

Also, index forms are described as those mathematical forms that are used to represent numbers that are too large or small.

From the information given, we have the equation;[tex]a^2[/tex]=25

find the square root of value of 25,

We have;25 = [tex]5^2[/tex]

Substitute the value, we get;[tex]a^2[/tex] =  [tex]5^2[/tex]

Take out the similar factor, this is their exponents.

We then have;

a = 5

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Complete question;

Find the value of a in the equation;a² = 25

It will take approximately 12.85 hours until only 1 gram of the element remains.

If after 2 hours, 36% of the initial amount remains, then the remaining amount is 0.36 times 100 grams, which is 36 grams. Let's define the amount of the element remaining after time t in hours as R(t). Since the element is decaying exponentially, we can model it with the equation R(t) = 100[tex](0.36)^t[/tex].

We want to find how many hours it will take until only 1 gram remains. We can set R(t) equal to 1 gram and solve for t:

1 = 100[tex](0.36)^t[/tex]

Taking the logarithm of both sides, we get:

ln(1) = ln(100[tex](0.36)^t[/tex])

0 = ln(100) + t*ln(0.36)

t = -ln(100)/ln(0.36)

Using a calculator, we find that t ≈ 12.85 hours.

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The slope of the lines

Line 1 = -5/2

Line 2 = -5/4

Line 3 = -5/4

Line 1 and 2 are neither

Line 1 and 3 are neither

Line 2 and 3 are parallel

Slope can be defined as the degree of steepness of a line.

The formula for calculating the slope of a line is expressed as;

Slope, m = y₂ - y₁/x₂ - x₁

Given that the line coordinates are;

(x₁, y₁)(x₂ , y₂)

For Line 1, we have;

(0, 7)(8 , -3)

Substitute the values, we get;

Slope, m = (-3 - 7)/(8 - 0)

subtract the values

Slope, m = -10/8 = -5/2

For line 2

(8, -8)(4, -3)

Substitute the values

Slope, m = -3 -(-8)/4 - 8

Slope, m = -5/-4 = 5/4

For Line 3

(-4, 3)(4, -7)

Substitute the values

Slope, m = -7 - (3)/4 -(-4)

Slope, m = -10/8 = -5/4

Note that,  lines with the same slope are parallel and if the slope of one line is the negative reciprocal of the second line, then they are perpendicular.

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Answer:

HH

HT

TH

TT

Step-by-step explanation:

Answer:

TT, TH, HT, HH

Step-by-step explanation:

Therefore, 4,000 centimeters are equivalent to 40 meters. Hence, the answer is A) 4,000 cm.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, left-hand side (LHS) and right-hand side (RHS), connected by an equal sign (=). The LHS and RHS can contain numbers, variables, operators, and functions, and the equal sign indicates that the value of the expression on the LHS is equal to the value of the expression on the RHS.

Here,

Since there are 100 centimeters in one meter, we can convert meters to centimeters by multiplying the length in meters by 100.

So, to convert 40 meters to centimeters, we can multiply 40 by 100:

40 meters = 40 x 100

= 4,000 centimeters

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The composite functions are:

a) f ∘ g = 3x² + 4, with domain of all real numbers.

b) g ∘ f = 9x² + 24x + 16, with domain of all real numbers.

c) f ∘ f = 9x + 16, with domain of all real numbers.

d) g ∘ g = x⁴, with domain of all real numbers.

To find the composite functions, we need to substitute the function g into the function f or vice versa, depending on the order of composition. The resulting composite function will have a domain that is restricted by the domains of the individual functions involved.

a) To find f ∘ g, we substitute g(x) = x² into f(x) = 3x + 4:

f(g(x)) = 3g(x) + 4 = 3x² + 4

The domain of f ∘ g is all real numbers because the domain of g(x) = x² is all real numbers.

b) To find g ∘ f, we substitute f(x) = 3x + 4 into g(x) = x²:

g(f(x)) = (3x + 4)² = 9x² + 24x + 16

The domain of g ∘ f is all real numbers because the domain of f(x) = 3x + 4 is all real numbers.

c) To find f ∘ f, we substitute f(x) = 3x + 4 into f(x) = 3x + 4:

f(f(x)) = 3f(x) + 4 = 3(3x + 4) + 4 = 9x + 16

The domain of f ∘ f is all real numbers because the domain of f(x) = 3x + 4 is all real numbers.

d) To find g ∘ g, we substitute g(x) = x² into g(x) = x²:

g(g(x)) = (x²)² = x⁴

The domain of g ∘ g is all real numbers because the domain of g(x) = x² is all real numbers.

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Answer:

12.5%

Step-by-step explanation:

We Know

A student scored 80 on a test last week and 90 on the same test this week.

What is the percent increase in the score?

We Tale

(90 ÷ 80) x 100 = 112.5%

Then we take

112.5 - 100 = 12.5%

So, the percent increase in score is 12.5%

Keyboards A and B are significantly different from one another

The F ratio has been found to be 4.30, equating to the MS between treatments divided by MS error resulting in a value of 2082/484. In order to seek out the critical value for F at an alpha level of 0.05 within degrees of freedom between treatments (2) and degrees of freedom error (3), we must consult the F-table, revealing it to be 5.14.

We reach the conclusion that rejecting the null hypothesis would not prove necessary as there appears to be no great significance when it comes down to the number of errors made with the three concerned keyboards.

Tukey's HSD signifies 2.0, indicating any distinction of means exceeding such scores is considered noteworthy. Calculating pairwise comparisons can enlighten us as to which keyboards are significant from one another:

Comparing Keyboard A versus Keyboard B: The difference was calculated using |25-6| / ✓(484/6*(1/6+1/6)) = 3.03, determining its significance surpassing Tukey's HSD (2.0).

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Answer:132.7495cm^2

Step-by-step explanation:
The formula for the area of a circle is πr^2.
We then substitute into this formula using 3.142 as π.
This leaves us with 3.142x6.5(radius is half of diameter)^2
When you type it into your calculator it should give you
132.7495cm^2

The total is $24,947.06 plus $9,647.06 in compound interest.

One way to earn or pay interest on interest is through compound interest. It denotes that interest will be charged on both the main amount and the accrued interest in the subsequent period. Savings or investments can expand over time with the aid of compound interest.

We can use the following formula to determine compound future value:

FV = P * (r/n + 1)(n*t)

where P is the principal, r is the yearly interest rate, n is the number of times interest is compounded annually, and t is the amount of time in years.

Your values have led us to:

FV = 15300 * (1 + 0.08/4)²⁴

FV = $24,947.06

The total is $24,947.06 plus $9,647.06 in interest.

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Therefore, the width of the bridge is approximately 5.9 feet. Therefore, the height of the bridge is approximately 8.4 feet. Therefore, the length of CH is approximately 36.9 feet. Therefore, the measure of angle BHC is approximately 189 degrees. Therefore, the answer to part (e) is no.

A triangle is a closed, two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry, and is formed by connecting three non-collinear points. The sum of the interior angles of a triangle is always 180 degrees, and there are several types of triangles including equilateral, isosceles, and scalene.

Here,

To solve this problem, we will use the fact that AAGC is congruent to AEGC. This means that angle ACG is equal to angle AEC, and angle AGC is equal to angle AEG.

(a) To determine the width AE of the bridge, we can use the tangent function. We have:

tan(27°) = AE/12

Solving for AE, we get:

AE = 12 tan(27°) ≈ 5.9 ft

(b) To determine the height CG of the bridge, we can use the same approach. We have:

tan(36°) = CG/12

Solving for CG, we get:

CG = 12 tan(36°) ≈ 8.4 ft

(c) To determine the length of CH, we can use the Pythagorean theorem. We have:

CH² = CG² + GH²

Substituting the values we found earlier, we get:

CH² = (8.4 ft)² + (40 ft - 5.9 ft)²

CH² = 70.56 ft² + 1288.41 ft²

CH² = 1358.97 ft²

Taking the square root, we get:

CH ≈ 36.9 ft

(d) To determine the measure of angle BHC, we can use the fact that angles AGC and AEG are congruent. We have:

angle BHC = 180° - angle AHC - angle CHB

angle AHC = angle ACG - angle HCG = 27° - 36° = -9° (note that this is a negative angle because it is measured clockwise)

angle CHB = angle CGB - angle HCG = 36° - 36° = 0°

Substituting these values, we get:

angle BHC = 180° - (-9°) - 0°

angle BHC = 189°

(e) To determine whether CH bisects angle ZACG, we need to show that angle CAH is congruent to angle CAG. We have:

angle CAH = 180° - angle HCG - angle ACG

= 180° - 36° - 27°

= 117°

angle CAG = 180° - angle ACG - angle AGC

= 180° - 27° - 27°

= 126°

Since angle CAH is not congruent to angle CAG, we can conclude that CH does not bisect angle ZACG.

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The given Mayan number which is: :|| :|| in decimal (base 10) is 42.

The Mayan number system is a base-20 system that uses three symbols: a dot (.), a horizontal bar (|), and a shell-like symbol (:). The symbol for zero is a shell-like symbol (:).

In order to obtain the decimal equivalent (base 10) of a Mayan numeral, it is imperative to comprehend the positional significance of each constituent symbol.

The numerical system employed here assigns a weight to each digit that corresponds to a certain power of 20. Specifically, the weight associated with the least significant digit is 20 raised to the exponent of 0, while the weight of the digit to its immediate left is 20 raised to the exponent of 1, and so forth.

The Mayan number given, : :|| :||, can be broken down as follows:

The leftmost position has no symbol, which represents a value of 0.

The second position from the left has two shell-like symbols (:), which represent a value of 2x20¹ = 40.

The third position from the left has two horizontal bars (||), which represent a value of 2x20⁰ = 2.

The given Mayan number in decimal (base 10) is 40 + 2 = 42.

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Answer:

2105, plug it into calculator

The measure of angle a is solved to be 22 degrees

When two secant lines intersect outside a circle the formula for the vertex angle at a is

To find the vertex angle at point A where two secant lines intersect outside a circle, you can use the following formula:

angle A = 1/2 * (measure of arc 1 - measure of arc 2)

let arc 1 = 140 degrees

arc 2  = 96 degrees

plugging in the values

angle A = 1/2 * (140 - 96)

angle A = 1/2 * 44

angle A = 22 degrees

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The conditional statement is solved and you could ask for an enrollment verification notice from the school

Given data ,

Let the statement be informally proven that you are taking courses online

And , To informally prove that you are taking courses online, you can contact the professors of the courses via email and obtain informal permission from them first.

Then you can initiate the request using the new online information system of the school to obtain an enrollment verification notice

It is a legitimate document that the school has produced that may be utilized for a number of things, including debt deferments, employment, and insurance.

Hence , the conditional statement is solved

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Answer: c=10, b=5 root 3

Step-by-step explanation:

it is a 30-60-90 triangle (use sum of angles in a triangle theorem.)

5 is the leg oppoiste to the 30 degree, so it is half of the hypotenuse, which is c, so c=10

then just use pythagorean theorem and 100-25=75 so answer is root 75 simplified to 5 root 3

To decide how the whole could look, I used the information given in the statement that Angela drew a square representing 2/2 of a whole. This tells me that Angela's square represents the entire whole.

If Angela drew a square that shows 2/2 of a whole, it means that the square represents the entire whole.

To show how the whole could look, we can draw a larger square around Angela's square. This larger square would represent the whole, and Angela's square would be a part of it.

Based on this information, I determined that the whole could be represented by a larger square that encompasses Angela's square. The size of the larger square would be such that the area of Angela's square is equal to 1 whole unit, since Angela's square represents 2/2 or 1 whole unit of the whole.

Therefore, I drew a larger square that has the same area as 1 unit and enclosed Angela's square within it. This larger square represents the entire whole, and Angela's square is a part of it. (Image attached)

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Step-by-step explanation:

Count numbers

There are six numbers that counted in

Thousands and tens

The number is 357476 which is three hundred and fifty seven thousands, four hundred and 76

To find the answer you cancel 35 and remains with 7 the other numbers 4 and 6 you turns them into zeros and remain with seven

Thousands and tens is the answer of placing a value of two sevens.

Answer:

2,090. because Sarah has long distances and wanted to go home

When expressed in symbolic form, the original claim would then be H ₀: μ = 68. 9  bpm.

One common approach to express a hypothesis in symbolic form is through the application of logical symbols including "if-then" statements. This symbolized portrayal can be instrumental in directing the design of an experiment aimed at assessing its validity.

The null hypothesis is represented as H₀, with μ describing the mean pulse rate for male adults within the population. The underlying assertion suggests that on average adult males possess a pulse rate equivalent to 68.9 bpm.

H ₀: μ = 68. 9  bpm.

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The measure of distance x, that is, the distance between a point P and the point of horizon, is equal to 284.372 miles.

In this problem we must determine the distance between a point P located about earth's circumference and the point of horizon, located on earth's circumference. Since the line between these two points is tangent to earth, then, distance x can be found by Pythagorean theorem:

x = √[(3959 mi + 10.2 mi)² - (3959 mi)²]

x = 284.372 mi

The distance x is equal to 284.372 miles.

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The equation of the tangent line to the curve [tex]x^\((2/3) + y^\((2/3)[/tex]= 10 at the point (-27, 1) is  -(1/3)(x + 27).

First step is to take the  derivative of both sides of the equation

[tex](2/3 )x ^\((-1/3) + (2/3)y ^\((-1/3)*dy/dx = 0[/tex]

Solve for dy/dx

[tex]dy / dx = -(y ^\(1/3)/x ^(1/3))[/tex]

Substitution

[tex]dy /dx = -(1 ^\((1/3)/(-27) ^ \((1/3)) = -(1/3)[/tex]

Formulate a linear equation

y - y1 = m(x - x1)

Where:

m= slope

(x1, y1)= point (-27, 1):

So,

y - 1 = -(1/3)(x + 27)

Therefore the equation is y - 1 = -(1/3)(x + 27).

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Answer:

6[tex]\sqrt{13}[/tex]

Step-by-step explanation:

a^2+b^2=c^2          c is hypotenuse, which is what we're looking for

12^2+18^2=c^2

144+324=c^2

c=[tex]\sqrt{468}[/tex]=[tex]\sqrt{36*13}[/tex]=6[tex]\sqrt{13}[/tex]