Sasha invests $1000 that earns 18% interest compounded quarterly. How much money will she have after 7 years?

A.
$4392.69

B.
$4392.70

C.
$3429.70

D.
$3430.00

Answer: 1/6

Step-by-step explanation:

Probability of getting heads or tail is:

P (H) = P(T) = 1/2

The probability of getting any number on the die is:

P (1) = P (2) = P(3) = P (4) = P (5) = P (6) = 1/6

The probability of getting a tail on the coin and a number less than 3 on the die is:

\(P($Tails and a number less than 3$)=P($Tails$) \times P$(A number less than 3)$$\begin{aligned}&=\frac{1}{2} \times[P(1)+P(2)] \\&=\frac{1}{2} \times\left[\frac{1}{6}+\frac{1}{6}\right] \\&=\frac{1}{6}\end{aligned}$$\)

Therefore the required of getting tails and a number less than 3 is 1/6

we have that

P+0.50=0.8554

so

P=0.3554

using the tables of z-score

For P=0.3554

the value of z is

The completely factored form of the polynomial is 7x² (x + 6) (x - 4)

Given,

The polynomial ; 7x⁴ + 14x³ - 168x²

We have to find the complete factored form of this polynomial;

Polynomial;

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

Here,

The polynomial is  7x⁴ + 14x³ - 168x²

Now,

Factorize the polynomial using common factors;

That is,

7x⁴ + 14x³ - 168x²

7x² (x² + 2x - 24)

Solve x² + 2x - 24 using quadratic formula;

That is,

\(\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}\) = \(\frac{-2(+-)\sqrt{2^{2} -4*1*-24} }{2*1}\) = \(\frac{-2(+-)\sqrt{4-96} }{2}\) = -2±√-92 / 2

Now,

Solve

-2 + √-92 / 2 = 3.79 ≈ 4

Solve

-2 - √-92 / 2 = -5.79 ≈ -6

Then,

The factors will be (x - 4) and (x + 6)

So,

7x² (x + 6) (x - 4) will be the factored form of the polynomial.

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Answer:

1/8

Step-by-step explanation:

Answer:

1 3/32

Step-by-step explanation:

7/8 + 1/4(3/2 - 5/8)

= 7/8 + 1/4(7/8)

=7/8 + 7/32

=28/32 + 7/32

=35/32

=1 3/32

The Fed rule, also known as the Taylor rule, is an equation that attempts to describe how the Federal Reserve adjusts interest rates in response to changes in economic conditions.

The rule was first proposed by economist John Taylor in 1993 and has since become a widely used guide for central banks around the world.

The Fed rule is typically expressed as follows: r = p + 0.5y + 0.5(P - 2) + 2, where r is the federal funds rate, p is the target rate of inflation, y is the difference between actual output and potential output (also known as the output gap), and P is the current rate of inflation.

According to the rule, when the economy is operating below potential and inflation is low, the Fed should lower interest rates to stimulate growth.

Conversely, when the economy is growing too quickly and inflation is rising, the Fed should raise interest rates to slow down the economy and prevent inflation from getting out of control.

The Fed rule is not a perfect guide for monetary policy, as there are many other factors that can influence interest rate decisions, including global economic conditions, geopolitical events, and financial market developments.

However, it provides a useful framework for understanding the Fed's thinking about interest rates and helps to promote transparency and predictability in monetary policy.

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The percent error in the experimental value of g is option (d) 2.04%. This means that the experimental value of g deviates from the accepted value by 2.04%.

To calculate the percent error, we need to compare the experimental value of g with the accepted value.

Let's assume the experimental value of g is ge and the accepted value is ga.

The formula for percent error is:

Percent Error = |(ge - ga) / ga| * 100

Substituting the given values:

Percent Error = |(ge - 9.8) / 9.8| * 100

We are given that the accepted value of g is 9.8 m/s^2.

Suppose the experimental value of g is 9.6 m/s^2.

Percent Error = |(9.6 - 9.8) / 9.8| * 100

Percent Error = |-0.2 / 9.8| * 100

Percent Error = 0.0204 * 100

Percent Error = 2.04%

The correct option from the given choices would be (d) 4%, which is the closest value to the calculated percent error.

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well, from 1990 to 1998 is 8 years, and we know the amount went from $4800 to $6300, let's check for the rate of growth.

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6300\\ P=\textit{initial amount}\dotfill &\$4800\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{years}\dotfill &8\\ \end{cases} \\\\\\ 6300=4800(1 + \frac{r}{100})^{8} \implies \cfrac{6300}{4800}=(1 + \frac{r}{100})^8\implies \cfrac{21}{16}=(1 + \frac{r}{100})^8\)

\(\sqrt[8]{\cfrac{21}{16}}=1 + \cfrac{r}{100}\implies \sqrt[8]{\cfrac{21}{16}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[8]{\cfrac{21}{16}}=100+r\implies 100\sqrt[8]{\cfrac{21}{16}}-100=r\implies \stackrel{\%}{3.46}\approx r\)

now, with an initial amount of $4800, up to 2007, namely 17 years later, how much will that be with a 3.46% rate?

\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4800\\ r=rate\to 3.46\%\to \frac{3.46}{100}\dotfill &0.0346\\ t=years\dotfill &17\\ \end{cases} \\\\\\ A=4800(1 + 0.0346)^{17} \implies A=4800(1.0346)^{17}\implies A \approx 8558.02\)

Answer:

The answer is x > -2.5 or (-2.5,infinity)

Step-by-step explanation:

The equation for the hyperbola with foci (0,±5) and asymptotes y=± 3/4 x is:

y^2 / 25 - x^2 / a^2 = 1

where a is the distance from the center to a vertex and is related to the slope of the asymptotes by a = 5 / (3/4) = 20/3.

Thus, the equation for the hyperbola is:

y^2 / 25 - x^2 / (400/9) = 1

or

9y^2 - 400x^2 = 900

The center of the hyperbola is at the origin, since the foci have y-coordinates of ±5 and the asymptotes have y-intercepts of 0.

To graph the hyperbola, we can plot the foci at (0,±5) and draw the asymptotes y=± 3/4 x. Then, we can sketch the branches of the hyperbola by drawing a rectangle with sides of length 2a and centered at the origin. The vertices of the hyperbola will lie on the corners of this rectangle. Finally, we can sketch the hyperbola by drawing the two branches that pass through the vertices and are tangent to the asymptotes.

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\( \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star\)

\(\textsf{ \underline{\underline{Steps to solve the problem} }:}\)

Find inverse of given function :

\(\qquad❖ \: \sf \:y = \sqrt{x} + 7\)

\(\qquad❖ \: \sf \: \sqrt{x} = y - 7\)

\(\qquad❖ \: \sf \:x = (y - 7) {}^{2} \)

Next, replace x with f-¹(x) and y with x ~

\(\qquad❖ \: \sf \:f {}^{ - 1} (x) = (x - 7) {}^{2} \)

we got our inverse function.

Condition : x should be greater or equal to 7

because we will get same value of y for different x if we also include values less than 7.

\( \qquad \large \sf {Conclusion} : \)

\( \huge\mathbb{ \underline{SOLUTION :}}\)

\(\longrightarrow\bold{f(x)= \sqrt{7}}\)

To solve for the inverse of a function we begin by re-writing the function as an equation in terms of y.

\(\bold{Becomes,}\)

Next step we switch sides for x and y variables and then solve for the y variable as shown below,

\(\longrightarrow\sf{y= \sqrt{x}+7}\)

\(\bold{Then,}\)

\(\longrightarrow\sf{x= \sqrt{y}+7}\)

\(\small\bold{Solve \: for \: y \: and \: subtract \: 7 \: from \: the \: both \: }\) \(\bold{sides,}\)

\(\longrightarrow\sf{x-7= \sqrt{y}}\)

\(\small\bold{Square \: both \: sides }\)

\(\sf{(x-7)^2=(\sqrt{y})^2}\)

\(\sf{(x-7)^2=y}\)

We now re-write in function notation. Take note however that this is the inverse:

\(\bold{Where \: y}\) \(\sf{=(x-7)^2 }\)

\(\longrightarrow\sf{y= (x-7)^2 }\)

\(\huge\mathbb{ \underline{ANSWER:}}\)

\(\large\boxed{\sf A. \: \: f^{-1}(x)= (x − 7)^2 , \: for \: \underline > 7 }\)

The average size of a customer's bill at a restaurant that earns daily $3,250 for the meals that it sells to 200 customers is $16.25. Therefore, the right answer is option (c).

The average or mean is calculated by taking the ratio of the total sum of the outcomes of an event to the frequency or the number of times the event occurs.

It can be written as \(\frac{n_1+n_2+.....+n_a}{a}\).

In the given question, the sum of the customer bill is given as $3,250.

And the number of customers served is given to be 200.

Therefore, the average size of a customer's bill is calculated by \(\frac{3250}{200}\)

Which turns out to be $16.25.

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The answer is $16.25. To find the average size of a customer's bill, you would divide the total earnings by the number of customers.
$3,250 / 200 customers = $16.25 per customer.

To find the average size of a customer's bill at the restaurant, you need to divide the total daily earnings by the number of customers. Here's a step-by-step explanation:

1. The restaurant earns $3,250 daily from the meals it sells.
2. The restaurant serves 200 customers daily.

Now, calculate the average bill size:

3. Divide the total daily earnings ($3,250) by the number of customers (200).

$3,250 ÷ 200 = $16.25

The average size of a customer's bill at the restaurant is $16.25.

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The true mean study time is likely between 19.6 and 21.6 hours per week .The higher the confidence level, meaning that we can be more sure that the true mean study time is within the given range.

The margin of error is an important statistic that helps measure the accuracy of a survey. It is calculated by multiplying the standard deviation by the z-score for the given confidence level. A 90% confidence level has a z-score of 1.645, a 96% confidence level has a z-score of 1.96, and a 99% confidence level has a z-score of 2.58. Using this information, the margin of error for a survey of 225 students with a mean study time of 20.6 and a standard deviation of 2.7 is approximately 1.0. This means that the true mean study time is likely between 19.6 and 21.6 hours per week. The higher the confidence level, the higher the margin of error, meaning that we can be more sure that the true mean study time is within the given range.

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Answer:

6, 0

Step-by-step explanation:

Answer:

y= -3/4x+3

Step-by-step explanation:

The general equation is y=mx+b with m representing the slope, and b representing the y-intercept. So if you are given the slope and y-intercept, you just plug those in for m and b respectively. Hope this helps!

Answer:

4

Step-by-step explanation:

-1  0  1  2  3  

1   2    3    4

It is true that when you design an algorithm, it should be general enough to provide a solution to many problem instances, not just one or a few of them.

In mathematics, an algorithm is a process, a description of a series of steps that may be used to solve a problem; however, they are now far more prevalent than that.

Although many areas of research (and daily life) employ algorithms, long division's step-by-step process is probably the most prevalent example.

Thus, It is true that when you design an algorithm, it should be general enough to provide a solution to many problem instances, not just one or a few of them.

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Siegmeyer Corp. should accept Project A because its NPV is greater than zero, indicating positive profitability.

Siegmeyer Corp. is evaluating the financial feasibility of Project A, a new inventory system that requires an initial investment of $800,000. The company's required rate of return is 12%. To determine whether the project should be accepted or rejected, the net present value (NPV) needs to be calculated.

The NPV of a project represents the difference between the present value of its cash inflows and the present value of its cash outflows. By discounting future cash flows at the required rate of return, we can assess the profitability of the project. In this case, the expected cash flows over the next four years are $350,000, $325,000, $400,000, and $200,000.

To calculate the NPV, we discount each cash flow back to its present value and subtract the initial investment:

NPV = (Cash flow in year one / (1 + required rate of return))¹

     + (Cash flow in year two / (1 + required rate of return))²

     + (Cash flow in year three / (1 + required rate of return))³

     + (Cash flow in year four / (1 + required rate of return))⁴

     - Initial investment

By performing the calculations, the NPV of Project A can be determined. If the NPV is greater than zero, it indicates that the project is expected to generate positive returns and should be accepted.

In this case, the NPV should be compared to zero, and if it is greater, Siegmeyer Corp. should accept Project A.

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The result of the division is x³ + x² + x + 1, and there is no remainder.

To divide (x⁴ - 1) by (x - 1), we can use long division:

           x³ + x² + x + 1

     _____________________

x - 1 | x⁴ + 0x³ + 0x² + 0x - 1

         -(x⁴ - x³)

         ____________

                 x³ + 0x²

             -(x³ - x²)

             ____________

                     x² + 0x

                 -(x² - x)

                 ____________

                         x - 1

                     -(x - 1)

                     __________

                              0

The result of the division is x³ + x² + x + 1, and there is no remainder.

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Answer:

10

Step-by-step explanation:

substitute a = 2 and e = 4 into the expression

3a + e

=  3(2) + 4

= 6 + 4

= 10

Step-by-step explanation:

since we got a point and actually the slope, we can start with the point-slope form and transform.

you know that the slope-intercept form is

y = ax + b

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

we see therefore, that the slope of the given line is 1/4.

a perpendicular slope (90°) turns the slope fraction upside-down and flips the sign.

so, the perpendicular slope is -4/1 = -4.

the point-slope form is

y - y1 = a(x - x1)

"a" is again the slope (for the new line this is -4), (x1, y1) is a given point. in our case (1, 1).

so, we get

y - 1 = -4(x - 1)

we transform by simplifying :

y - 1 = -4x + 4

y = -4x + 5

y = -4x + 5

is the perpendicular line in slope-intercept form that passes through (1, 1).

Answer:

my answer is A

Step-by-step explanation:

if you work out the equation where you know that at the x intercept y=0 you will find A to be true

90 miles driving at 45 mph for 2 hours

The value of x = 63.43° and x= 243.34°.

We have given tan x = 2   0°≤x≤360°

so x=\(tan^{-1}\)2         0°≤x≤360°

so here we have 2 answer

x = 63.43 and x = 63.43

The trigonometric function 'tangent' has an inverse called inverse tan. The opposing side of the right triangle is divided by the adjacent side, and this relationship is utilized to compute the angle by using the tangent ratio of the angle. This function can be used to calculate the value of tan 1, arctan 1, tan 10, etc. All inverse trigonometric functions must be named with the prefix "arc," so inverse tangent is abbreviated as "arctan." Despite the fact that it is conventional to use tan-1, we shall utilize arctan for the duration of this tutorial.

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Answer:

Answer is 6x-13

Step-by-step explanation:

Given

XZ=8x-18 and RZ=2x+5

XR=XZ-RZ

8x-18-2x+5

8x-2x-18+5

6x-13Ans

The distance between points M(6, 16) and Z(-1, 14) is approximately 7.1 units.

We can use the distance formula to find the distance between two points in a coordinate plane. The distance formula is:

d = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) and (x2, y2) are the coordinates of the two points. Substituting the coordinates of M(6, 16) and Z(-1, 14), we get:

d = √((-1 - 6)² + (14 - 16)²) = √(49 + 4) = √53 ≈ 7.1

Therefore, the distance between points M(6, 16) and Z(-1, 14) is approximately 7.1 units.

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First Question is boolean,

Question 35 is probably floating point ,

Question 36 is probably an integer, since it shows 1, 2, 3, and 1, 2, 3 are not fractions, and integers are whole numbers.

Im not 100% sure but I hope I helped,

Have a nice day/night :)

Answer:

4

Step-by-step explanation:

18x = 12(x+2)

18x = 12x+24

18x-12x = 24

6x = 24

x = 4

The root of the graph of f(x) =(x - 5)3(x + 2)2 touches the x-axis at -2,5

(x - 5)^3 has a power of 3 which is an ODD number. An ODD power means that the graph will cross through the x-axis.

(x + 2)^2 has a power of 2 which is an EVEN number. An EVEN power means that the graph will touch the x-axis.

Given: Function f(x) is (x - 5)3(x + 2)2

If a curve touches the x-axis then f(x) = 0

⇒ (x - 5)3(x + 2)2 = 0.

But if ab = 0 ⇒ either a = 0 or b = 0 or both zero.

⇒ (x - 5)3 = 0 and (x + 2)2 = 0

⇒ (x - 5) = 0 and x + 2 = 0

⇒ x = 5 and x = - 2.

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