An initial amount of money is placed in an account at an interest rate of 4% per year, compounded continuously. After four years, there is $1255.66 in the account. Find the initial amount placed in the account. Round your answer to the nearest cent.

Answer:

the function is decreasing.

the slope is -3/4 and the y-intercept is 7.

the function is linear and continuous.

y = -3/4 x + 7 3 this function.

Step-by-step explanation:

"the function is linear and discrete" is false. there are no interruptions or steps in the curve. it is a continuous curve.

the usual function form of a line is

y = ax + b

"a" being the slope, "b" being the y-intercept.

that is why the other statements are false.

Answer:

7034529

Step-by-step explanation:

Assuming you mean to multiply 0.75 by 9379372, the result would be:

0.75 x 9379372 = 7034529

The square root can be simplified as 7√2

Irrational numbers are numbers in the form of square roots, which when evaluated cannot be expressed in the form a/b e.g. √7, π, 2/√5, 3√11, etc. They are also called surd.

The opposite of an irrational number is called rational number. A rational number is a number that can be written in the form of a/b, where a and b are integers, and b is not equal to 0. e.g. 1/3, 2/3, √4 = 4/1, etc.

The square root can be simplified as follow:

√98 = √(49 * 2)

        = √49 * √2

        = 7 * √2

        = 7√2

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Required purchase price is $120 and advertised price is $300.

How much did Danielle purchase the antique dresser for?

Let's assume that Danielle purchased the antique dresser for $x.

According to the problem, she advertised it for 250% of her purchase price, which means she advertised it for,

250% of x = 2.5x

She sold the dresser for 15% less than the advertised price of 2.5x, so she sold it for,

(1 - 0.15) × 2.5x = 2.125x

We know that the selling price was $255, so we can set up the equation,

2.125x = 255

Solving for x,

x = 120

Therefore, Danielle purchased the antique dresser for $120.

What was her initial advertised price?

To find the initial advertised price, we can plug x = 120 into the expression 2.5x,

2.5x = 2.5 × 120 = 300

So, the initial advertised price was $300.

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Answer:

-tan(x)/sin^2(x).

Step-by-step explanation:

To simplify the expression:

sec(x)sin(-x) + tan(-x)

1 + sec(-x)

We can use the fact that sin(-x) = -sin(x), cos(-x) = cos(x), and tan(-x) = -tan(x) to rewrite the expression as:

-sec(x)sin(x) - tan(x)

1 + sec(x)

Next, we can multiply both the numerator and denominator by the conjugate of the denominator, 1 - sec(x), to eliminate the square root in the denominator. This gives:

(-sec(x)sin(x) - tan(x))(1 - sec(x))

(1 + sec(x))(1 - sec(x))

Simplifying the numerator by distributing and combining like terms, we get:

-sec(x)sin(x) + sec(x)tan(x) + tan(x) - sec(x)tan(x)

1 - sec^2(x)

Simplifying further by canceling out the sec(x)tan(x) terms in the numerator, we get:

-tan(x)

1 - sec^2(x)

Finally, we can use the identity 1 - sec^2(x) = sin^2(x) to rewrite the denominator and simplify further:

-tan(x)

sin^2(x)

Therefore, the simplified expression is -tan(x)/sin^2(x).

The machine's book value at the end of year three is $164,000.

The total amount of hours used by the machine in the first three years is: 2,000 + 4,000 + 8,000 = 14,000 hours

To calculate the annual depreciation expense, we must first establish the depreciation rate per machine hour. The following is how the depreciation rate per machine hour is calculated:

Depreciation rate per machine hour = (machine cost - estimated residual value) / total number of machine hours estimated

Rate of depreciation per machine hour = ($500,000 - $20,000) / 20,000 machine hours

Depreciation per machine hour = $480,000 divided by 20,000 machine hours

Rate of depreciation per machine hour = $24 per machine hour

We may compute the depreciation expense for each year by using the depreciation rate per machine hour:

Depreciation expense in year one = depreciation rate per machine hour x hours used in the first year

Depreciation expense in year one = $24 x 2,000 hours

Depreciation expense for the first year = $48,000

Year 2 depreciation expense = Depreciation rate per machine hour multiplied by the number of hours consumed in year 2.

Depreciation expense for year 2 = $24 x 4,000 hours

Depreciation expense for year two = $96,000

Depreciation expense in year three = depreciation rate per machine hour x hours used in year three

Depreciation expense in year three = $24 x 8,000 hours

Depreciation expense during the third year = $192,000

The accumulated depreciation for the first three years is the sum of the following depreciation expenses:

Accumulated depreciation equals the sum of year one depreciation expense, year two depreciation expense, and year three depreciation expense.

Depreciation accumulated = $48,000 + $96,000 + $192,000

Depreciation accumulated = $336,000

To compute the machine's book value at the end of the year 3. We deduct the accumulated depreciation from the machine's cost:

Machine book value = machine cost minus accumulated depreciation

The machine's book value is $500,000 minus $336,000

The machine's book value is $164,000

As a result, the machine's book value at the end of year three is $164,000.

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The equation of the tangent line to the graph of y = g(x) at x = 2 is y = 6x - 17.

The point-slope form of the equation of a line can be used to find the equation of the tangent line to the graph of y = g(x) at x = 2.

y - y1 = m(x - x1)

where m is the tangent line's slope and (x1, y1) is the point on the g(x) graph at x = 2.

Given that g(2) = -5, the point on the g(x) graph at x = 2 is (2, -5).

We are told that g'(2) = 6, which is the slope of the tangent line at x = 2.

As a result, the tangent line equation is: y - (-5) = 6(x - 2)

We get the following after simplifying and rearranging:

y + 5 = 6x - 12 y = 6x - 17

Hence, the equation of the tangent line to the graph of y = g(x) at x = 2 is y = 6x - 17.

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The solutions to the equations are marked and matched

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

4 + x = -8x - 5

Adding 8x on both sides , we get

9x + 4 = -5

Subtracting 4 on both sides , we get

9x = -9

Divide by 9 on both sides , we get

x = -1

b)

2 ( 5x + 2 ) = 10x - 4

On simplifying the equation , we get

10x + 4 = 10x - 4

Subtracting 10x on both sides , we get

4 ≠ 4

So , it has no solution

c)

7 + 2x = 2x - 7

Subtracting 2x on both sides , we get

7 ≠ -7

So , it has no solution

d)

-3x + 3 = 3 ( 1 - x )

-3x + 3 = 3 - 3x

x = all real numbers

Hence , the equations are solved

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Answer:

B, C, E

Step-by-step explanation:

B:

[tex](\frac{3}{4})^2-\frac{6}{16} \\= \frac{9}{16} - \frac{6}{16} = \frac{3}{16}[/tex]

C:

[tex](\frac{3}{8})^2 / \frac{3}{4} \\= \frac{9}{64} / \frac{3}{4} = \frac{9}{64} *\frac{4}{3} = \frac{3}{16}[/tex]

E:

[tex]2*\frac{3}{4} - (\frac{3}{4})^2 - \frac{3}{4} \\= \frac{6}{4} - \frac{9}{16} - \frac{3}{4} = \frac{3}{4} - \frac{9}{16} = \frac{12}{16} - \frac{9}{16} = \frac{3}{16}[/tex]

Answer:

B, C, E

Step-by-step explanation:

B:

[tex](\frac{3}{4})^2-\frac{6}{16} \\= \frac{9}{16} - \frac{6}{16} = \frac{3}{16}[/tex]

C:

[tex](\frac{3}{8})^2 / \frac{3}{4} \\= \frac{9}{64} / \frac{3}{4} = \frac{9}{64} *\frac{4}{3} = \frac{3}{16}[/tex]

E:

[tex]2*\frac{3}{4} - (\frac{3}{4})^2 - \frac{3}{4} \\= \frac{6}{4} - \frac{9}{16} - \frac{3}{4} = \frac{3}{4} - \frac{9}{16} = \frac{12}{16} - \frac{9}{16} = \frac{3}{16}[/tex]

a) The 95% confidence interval for a sample size of 34 is given as follows: (17.26, 20.34).

b) The 95% confidence interval for a sample size of 61 is given as follows: (17.67, 19.63).

c) Increasing the sample size, the margin of error decreases.

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are presented as follows:

The margin of error is defined as follows:

[tex]M = t\frac{s}{\sqrt{n}}[/tex]

From this we get that it is inversely proportional to the square root of the sample size, hence if we increasing the sample size, the margin of error will decrease.

The mean and the standard error are given as follows:

[tex]\mu = 18.8, s = 4.4[/tex]

For a sample size of 34, we have 33 degrees of freedom, hence, using a t-table, the critical value is given as follows: 2.0345.

Hence the bounds of the interval are given as follows:

For a sample size of 61, we have 60 degrees of freedom, hence, using a t-table, the critical value is given as follows: t= 2.

Hence the bounds of the interval are given as follows:

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Answer:  2/4 or 1/2

Step-by-step explanation: Based on the spinner shown, there are 5 equal sections, 1 of which is yellow and 2 of which are blue. If the spinner does not land on yellow, it will land on one of the 4 other sections, 2 of which are blue.

Therefore, the probability of landing on blue given that it does not land on yellow is 2/4 or 1/2.

Solution:

Notice that for each function, they are simply in the form [tex]f(k(x))[/tex], where [tex]k(x)[/tex] is some function of [tex]x.[/tex] More specifically,[tex]g(x)=f(x-2), h(x)=f(2x), \text{ and } j(x) = f(x^2).[/tex]

Thus, because the Interval of Convergence of [tex]f(x)[/tex] is [tex]-3 < x < 3,[/tex] the Interval of Convergence of [tex]g(x)[/tex] should be [tex]-3 < x-2 < 3 \implies -1 < x < 5.[/tex]

Similarly, the Interval of Convergence of [tex]h(x)[/tex] is [tex]-3 < 2x < 3 \implies -\frac32 < x < \frac32.[/tex]

Finally, the Interval of Convergence of [tex]j(x)[/tex] should be [tex]-3 < x^2 < 3 \implies 0 < x < \sqrt{3}.[/tex]

Yes, The statement given in the problem is correct.As, <a> satisfies all three conditions- identify, Closure and inverse, it is a subgroup of G.

A subgroup in mathematics is a subset of a group that, with regard to the same operation, is also a group. To put it another way, a subgroup is a smaller group that is a part of a bigger group.

Technically, let H be a subset of G and let G be a group that is subject to some operation (such as addition, multiplication, or composition). H is referred to be a subgroup of G if it forms a group on its own with regard to the same operation.

For given statement,

Let G is a group, and let a is the element of G. The set of all powers of a, denoted as<a>, is a subgroup of G, and it is the subgroup generated by a.

To show that <a> is a subgroup of G, we need to verify that it satisfies three conditions:

As, All the three conditions were satisfied by <a> , it is a subgroup of G

Moreover, it is the subgroup generated by a , as it is the smallest subgroup of G that contains a. This means that < a > includes all the powers of a, as well as their products and inverses, and nothing more.

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X + 1 = 0, so x = -1, and x - 24 = 0, so x = 24. Consequently, the two answers to the equation are x = -1 and x = 24.

It is a method for illustrating a notion, a connection, or a behaviour that often involves two or more variables. Equations can be used to explain several events, including economic models and physical principles. They can also be applied to problem-solving and forecasting. Symbols, integers, and mathematical operations like addition, subtraction, multiplication, and division are used to create equations.

An essential tool for factoring quadratic equations is the Zero Factor Property. Finding two terms, one of which is a factor of the constant term and the other of which is a factor of the coefficient of the squared term, whose product is equal to the constant term, is the fundamental principle behind the Zero Factor Property. With this knowledge, the given quadratic equation can be factored into two parts that equal zero.

One must first factor a quadratic equation into two factors that are equal to zero in order to solve it using the zero factor property. To do this, one needs determine the constant term's factors as well as the coefficient of the squared term's factors. The coefficient of the squared term is always obtained by multiplying the factors, which are always different integers.

The constant term's factors are always sums of numbers that result in the constant term. Once the elements are known, the equation can be factored into two factors that are equal to zero each.

Consider the equation [tex]x^2+5x-24=0[/tex], for instance. The factors of the constant term are -1 and 24, while the factors of the squared term's coefficient are 1 and 5. The equation then reads as (x + 1)(x - 24) = 0.

At this stage, the Zero Factor Property can be used to find x. Since all factors must be equal to zero, x can be solved for by setting all factors to zero. Thus, x + 1 = 0, resulting in x = -1, and x – 24 = 0, resulting in x = 24. Thus, x = -1 and x = 24 are the two answers to the problem.

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Complete questions as follows-

How do I use the zero factor property when solving a quadratic equation by factoring?

We can eulerize this graph in the most efficient way possible by making these vertices have even degree through  adding  an edge between them.

We can eulerize a graph by ensuring  to add edges to the graph in a way that preserves its connectivity while ensuring that all vertices have even degree.

A good method to do this is by  adding  edges between pairs of vertices that have odd degree until all vertices have even degree.

In the scenario above,  we can see that all vertices have odd degree except for the last vertex.

Hence , in order to make this vertex have even degree, we can add an edge from it to any other vertex with odd degree.

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The entries in both columns when matched are

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

The graph

When the line of best fit is drawn, we have

(8, 0) and (0, 8)

The equation is calculated as

y = mx + c

So, we have

8 = 0 * m + c

0 = 8 * m + c

This gives

c = 8

0 = 8 * m + 8

So, we have

m = -1

This means that the equation is

y = -x + 8

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

Equation of line of best fit: y = -x + 8

Slope = -1

y-intercept = 8

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The box plot that represents the data is given as follows:

Bottom plot.

A box and whisker plots shows these five features from a data-set, listed as follows:

The ordered data-set for this problem is given as follows:

2, 2, 4, 7, 7, 14, 16, 18.

The minimum and maximum values are given as follows:

The data-set has an even cardinality, hence the median is given by the mean of the two middle elements as follows:

Median = (7 + 7)/2 = 7.

(which removes the top two options).

The quartiles are given as follows:

Meaning that the last plot is correct. (the one that is already marked).

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Answer:

The correct answer is B.

Approximately 200 students received a test score between 70.5 and 80.

4. The Federal Reserve System

5. about 10 percent

The Fed is the renowned central bank of the United States, famous for their diverse and crucial functions which includes:

Providing short-term loans to banks: The Federal Reserve serves as a lender during critical times, acting seamlessly to help out other financial institutions in order meet the necessities required to stabilize within our economic system.

Govern through banking services provided: The account management of U.S government lies on this exceptional institution. It proficiently sponsors numerous activities such as payment processing and providing governmental services amongst others.

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Answer: D

Step-by-step explanation:

It's not A because the 4 is a constant, not a factor.

It's not B because the 11 is not constant because its a negative, therefore being subtracted.

It's not C because 3 is not an exponent, it is simply a term.

The answer is D because 2 is a coefficient, because it is a number infront of a variable.

The pair made the following investments: The combined interest for the first year was $477 from a $2550 savings account earning 6% simple interest annually and a $3600 development plan earning 9% simple interest annually.

Borrowers are required to pay the lender's basic interest as a fee in exchange for a loan.

Compound interest is not taken into account in the calculation; just the initial principal is taken into account.

Simple interest applies to all loans, not just specific ones.

Also highlighted is the type of interest that banks provide their customers on their savings accounts.

So, we presumptively have $x invested in the savings account.

Consequently, $ was invested in the development plan.(6150 - x).

S.I. = (Prt)/100 is the formula for simple interest on a sum of money (P), compounded at a rate (r), over a time period (t).

We figure out the interest on both investments:

Contribution to a savings account:

Amount invested (P) = $x.

Rate of interest (r) = 6%.

Time for investment (t) = 1 year.

As a result, interest was received= (Prt)/100 = $(x*6*1)/100 = $ (6x)/100

We are aware that $477 in interest has been paid in total.

Thus, we can write the following equation using the interest from both investments added:

(6x)/100 + {9(6150 - x)}/100 = 477

or, 6x + 55350 - 9x = 47700,

or, 55350 - 47700 = 3x,

or, 3x = 7650,

or x = 7650/3 = 2550.

As a result, investments in:

Savings account = $x = $2550.

Development plan = $(6150 - x) = $(6150 - 2550) = $3600.

Therefore, the pair made the following investments: The combined interest for the first year was $477 from a $2550 savings account earning 6% simple interest annually and a $3600 development plan earning 9% simple interest annually.

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Correct question:

In investing $6,150 of a couple's money, a financial planner put some of it into a savings account paying 6% annual simple interest. The rest was invested in a riskier mini-mall development plan paying 9% annual simple interest. The combined interest earned for the first year was $477. How much money was invested at each rate?

The correct answer is:

[tex]h1(t) = -16t^2 + 121[/tex] is a vertical translation of [tex]h2(t) = -16t^2 + 225.[/tex]

The y-intercept of h1 is 104 ft less than that of h2.

What is a y-intercept?

A function or relationship's graph meets the y-axis of the coordinate system at a point known as a y-intercept, sometimes known as a vertical intercept.

The height function for an object dropped from a height of h0 is given by:

[tex]h(t) = -16t^2 + h0\\\\h1(t) = -16t^2 + 121\\\\h2(t) = -16t^2 + 225[/tex]

To find the y-intercept of h1, we set t = 0 in the equation[tex]h1(t) = -16t^2 + 121:[/tex]

[tex]h1(0) = -16(0)^2 + 121 = 121[/tex]

Therefore, the y-intercept of h1 is 121 feet.

To find the y-intercept of h2, we set t = 0 in the equation [tex]h2(t) = -16t^2 + 225:\\\\h2(0) = -16(0)^2 + 225 = 225[/tex]

Therefore, the y-intercept of h2 is 225 feet.

The difference in their y-intercepts is:

225 - 121 = 104

Therefore, the y-intercept of h1 is 104 feet less than that of h2.

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A way to find 2/7 of a number is by Multiply by 7/2. The correct answer is D).

To find 2/7 of a number, we need to multiply the number by the fraction 2/7. Therefore, the correct answer is to multiply the number by 2/7, which is equivalent to option D: Multiply by 7/2.

Dividing by 2 and 7 or multiplying by 7 and dividing by 2 will not give us the correct answer because 2/7 is not equal to either 1/2 or 7/2. Therefore, we need to use the fraction 2/7 to calculate the desired amount.

To find 2/7 of a number, we can multiply the number by 2/7.

For example, let's say we want to find 2/7 of 42. We can multiply 42 by 2/7

2/7 x 42 = (2 x 42)/7 = 84/7 = 12

Therefore, 2/7 of 42 is 12.

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The best description of the equation is no real solutions. Option C

To solve the equation 3(x + 12) + 5x = 8x - 36, we can simplify the left-hand side by distributing the 3, and then combine like terms:

3x + 36 + 5x = 8x - 36

8x + 36 = 8x - 36

36 = -36

This equation is a contradiction, since there is no value of x that will make 36 equal to -36. Therefore, there are no real solutions to this equation.

The answer is (C) no real solutions.

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The total number of zero pairs in the expression (-5) + (-8) is 2.

We must pair the negative numbers so that their sum is equal to zero in order to determine the number of zero pairs in this expression. To put it another way, we need to find pairs of numbers whose sum is the same as their additive inverse.

We are combining two negative numbers in the expression (-5) + (-8).

In this case, we can pair the (-5) with a (+5), since (-5) + (+5) = 0, and we can also pair the (-8) with a (+8), since (-8) + (+8) = 0.

As a result, the expression (-5) + (-8) contains two zero pairs: one for (-5) and (+5) and one for (-8) and (+8).

Therefore, there are a total of 2 zero-pairs in the expression (-5) + (-8).

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For statement 5/3 = slope, the reason is Definition of slope and for statement 5/3 = 15/9 , the reason is Triangle A is similar to triangle B.

If slope of triangles are equal than Triangle A is similar to triangle Therefore, in statement 5/3 = 15/9 when we simplify

we get 5/3 = 5/3.

Then the reason for this statement is "If slope of triangles are equal" and the definition of slope in general is m = y/x.

Therefore, for the statement 5/3 = slope, the reason is Definition of slope.

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The range of [tex]f(x) = \frac{1}{3x+4}[/tex] is all real numbers except for 0 i.e. {y ∈ R, y ≠ 0} and there is no x-intercept in f(x) = 1/(3x - 4)

The range of [tex]f(x) = \frac{1}{3x+4}[/tex] is all real numbers except for 0.

To see this, note that the denominator of [tex]f(x) = \frac{1}{3x+4}[/tex], can take any real value except -4/3, since division by zero is undefined.

Therefore, f(x) can take any value except 0, which means the range of f(x) is {y ∈ R, y ≠ 0}

The reciprocal of a is 1/a

From the list of options, we have

f(x) = 1/(x + 3)

The reciprocal is x + 3 and this is a linear function

So, the reciprocal of a function that is linear is f(x) = 1/(x + 3)

The reciprocal function of the form f(x) = 1/x has a vertical asymptote at x = 0.

Similarly, the reciprocal function of the form f(x) = 1/(ax + b) has a vertical asymptote at x = -b/a.

Comparing the given functions with the above form, we can see that:

f(x) = 1/(x + (5/2)) is of the required form with a = 1 and b = 5/2.

So, it has a vertical asymptote at x = -(5/2)/1 = -5/2.

Therefore, the function with a vertical asymptote at x = -5/2 is option (a), f(x) = 1/(x + (5/2)).

The correct answer is (d) All of the above, as all functions a, b and c have a horizontal asymptote at y = 0, when solved by graphs

As x approaches (5/3)^+ (from the right-hand side), the function f(x) approaches positive infinity.

So, the true statement is (b) f(x) -> oo

Given that

f(x) = 1/(3x - 4)

So, we have

1/(3x - 4) = 0

This gives

1 = 0

This means that there is no x-intercept.

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The area of the right triangle is 1702 sq units and the area of the isosceles triangle is 539.39 sq units

The area of the right triangle is calculated as

Area = 1/2 * Base * Height

So, we have

Area = 1/2 * 37 * 92

Area = 1702

The area of the isosceles triangle is calculated as

Area = 1/2s²sin(c)

So, we have

Area = 1/2 * 37² * sin(52)

Evaluate

Area = 539.39

Hence, the value of the area is 539.39 sq units

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