“Financial statements are a vital communication tool for key stakeholders”. Discuss this statement considering
the role of financial record keeping in the survival and growth of small businesses.
Financial statements can help small businesses pinpoint their weak points, plan for expansion, and find new partners or investors.
The roles of financial recordsFinancial statements are an essential tool for communicating with important parties, such as lenders, suppliers, and investors. Maintaining accurate financial records is essential to the survival and expansion of small businesses.
The financial health, performance, and profitability of the organization are shown by accurate and trustworthy financial accounts. Stakeholders can use them to make well-informed decisions on the business's creditworthiness, investment prospects, and loan repayment capacity.
Financial statements can help small businesses pinpoint their weak points, plan for expansion, and find new partners or investors.
Small firms may find it difficult to win the trust and support of stakeholders without appropriate financial record keeping and transparent statements, which will impede their chances of survival and expansion.
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PLEASE HURRY 20 POINTS PLEASEEEEE>Which graph shows the solution to the system of linear equations? y equals negative three fourths times x plus 2 y equals negative one half times x minus 1 a coordinate grid with one line that passes through the points 0 comma 2 and 4 comma negative 1 and another line that passes through the points 0 comma negative 1 and 1 comma negative 3 a coordinate grid with one line that passes through the points 0 comma 2 and 3 comma negative 2 and another line that passes through the points 0 comma negative 1 and negative 1 comma 1 a coordinate grid with one line that passes through the points 0 comma 2 and 3 comma negative 2 and another line that passes through the points 0 comma negative 1 and 2 comma negative 2 a coordinate grid with one line that passes through the points 0 comma 2 and 4 comma negative 1 and another line that passes through the points 0 comma negative 1 and 2 comma negative 2
The correct graph is A.
The first equation is y = -3/4x + 2. This can be rewritten as y - 2 = -3/4x. Solving for x, we get x = (4/3)(y - 2).
The second equation is y = -1/2x - 1. This can be rewritten as y + 1 = -1/2x. Solving for x, we get x = -2(y + 1).
The two lines intersect at the point (0, 2). Plugging in x = 0 into both equations, we get y = 2 for both equations. Therefore, the two lines must intersect at the point (0, 2).
The slope of the first line is -3/4. The slope of the second line is -1/2. The slopes are negative inverses of each other. Therefore, the two lines are perpendicular.
A coordinate grid with one line that passes through the points 0 comma 2 and 4 comma negative 1 and another line that passes through the points 0 comma negative 1 and 1 comma negative 3 is incorrect because the two lines are not perpendicular.
A coordinate grid with one line that passes through the points 0 comma 2 and 3 comma negative 2 and another line that passes through the points 0 comma negative 1 and negative 1 comma 1 is incorrect because the two lines intersect at the point (0, 2).
A coordinate grid with one line that passes through the points 0 comma 2 and 3 comma negative 2 and another line that passes through the points 0 comma negative 1 and 2 comma negative 2 is incorrect because the two lines are not perpendicular.
15% will last how long when the battery discharge rate is 0.12% in 30 seconds
37.5 seconds is equivalent to 0.625 minutes for the battery to discharge from 15% to 0% with a discharge rate of 0.12% every 30 seconds.
To calculate how long a battery will last when it discharges at a rate of 0.12% per 30 seconds, we can set up a proportion based on the given information.
Let's assume the battery has a total charge of 100%. We want to find out how long it takes for the battery to discharge from 15% to 0%, given a discharge rate of 0.12% every 30 seconds.
First, let's determine the proportion:
(0.12% / 30 seconds) = (15% / x sec
To solve for x (the time it takes for the battery to discharge from 15% to 0%), we can cross-multiply:
0.12% × x = 30 seconds × 15%
Now, let's solve for x:
0.0012 × x = 0.3 × 15%
0.0012 × x = 0.045
Divide both sides by 0.0012:
x = 0.045 / 0.0012
x ≈ 37.5
Therefore, it would take approximately 37.5 seconds for the battery to discharge from 15% to 0% with a discharge rate of 0.12% every 30 seconds.
To convert 37.5 seconds into minutes, we divide the number of seconds by 60 (since there are 60 seconds in a minute).
37.5 seconds / 60 = 0.625 minutes
Therefore, 37.5 seconds is equivalent to 0.625 minutes.
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(question 8) Find the critical points of the function
Answer:
[tex]\textsf{A.} \quad \dfrac{-3}{2}[/tex]
Step-by-step explanation:
The critical points of a function are the points where the derivative of the function is either zero or undefined.
We can find the derivative of the given function using the product rule.
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}[/tex]
Given function:
[tex]f(x)=(2x+1)e^x[/tex]
[tex]\textsf{Let}\; u=2x+1 \implies \dfrac{\text{d}u}{\text{d}x}=2[/tex]
[tex]\textsf{Let}\; v=e^x \implies \dfrac{\text{d}v}{\text{d}x}=e^x[/tex]
Apply the product rule:
[tex]\begin{aligned}f'(x)&=(2x+1)e^x+e^x(2)\\&=(2x+1)e^x+2e^x\\&=e^x(2x+1+2)\\&=e^x(2x+3)\end{aligned}[/tex]
Set the derivative equal to zero and solve for x:
[tex]\begin{aligned}f'(x)&=0\\e^x(2x+3)&=0\\2x+3&=0\\2x&=-3\\x&=-\dfrac{3}{2}\end{aligned}[/tex]
Therefore, the critical point of the function f(x) is when x = -3/2.
1.
Find the surface area of the right cone.
Round your answer to the nearest
hundredth.
22 ft
8 ft
Answer:
789.40 square feet (to nearest hundredth)
Step-by-step explanation:
surface area = area of circular base + curved surface area
= πr² + πrL, where L is length of sloped edge.
using Pythagoras' Theorem, L² = 22² + 8² = 548.
L = 2√137 (do not round the answer yet, keep it in this form).
surface area = πr² + πrL
= π(8)² + π(8)(2√137)
= 789.40 square feet (to nearest hundredth)
color blindness occurs in 4% of the male population. design a simulation that can be used to estimate the probablitiy that a randomly chose male will be color blind
To design a simulation to estimate the probability that a randomly chosen male will be color blind, you can follow these steps:
Set up the simulation: Determine the number of males to include in your simulation. Let's say you choose to simulate 10,000 males.
Generate random color blindness: Use a random number generator to assign color blindness status to each simulated male. Since color blindness occurs in 4% of the male population, you can randomly assign color blindness to approximately 4% of the males in your simulation.
Count the number of color-blind males: Iterate through the simulated males and count the number of males who are color blind.
Calculate the probability: Divide the count of color-blind males by the total number of males in the simulation to obtain the estimated probability. Multiply the result by 100 to express it as a percentage.
Here's a Python code snippet to illustrate this simulation:
import random
num_simulated_males = 10000
num_color_blind_males = 0
for _ in range(num_simulated_males):
if random.random() <= 0.04: # Probability of being color blind
num_color_blind_males += 1
probability_color_blind = (num_color_blind_males / num_simulated_males) * 100
print(f"Estimated probability of a randomly chosen male being color blind: {probability_color_blind:.2f}%")
Keep in mind that this simulation provides an estimate based on the assumed probability of 4% for color blindness in the male population. The actual probability may vary slightly, but running the simulation with a large number of simulated males should yield a reasonably accurate estimate.
The formula for continuously compounded interest is given by
, where
is the account balance,
is the principal,
is the annual interest rate (expressed as a decimal), and
is the time in years.
If $5000 is deposited into an account earning an annual interest rate of 2.5%, compounded continuously, then what is the account balance after 12 years?
Round your answer to the nearest dollar and do not include the $ symbol in your answer.
The balance of the account after 12 years is given as follows:
$9,111.
How to obtain the balance of the account?The balance of an account after t years, using continuous compounding, is given by the exponential equation presented as follows:
[tex]A(t) = A(0)e^{kt}[/tex]
In which the parameters are given as follows:
A(0) is the initial deposit.k is the interest rate, as a decimal.The parameter values for this problem are given as follows:
A(0) = 5000, k = 0.025, t = 12.
Hence the balance of the account after 12 years is given as follows:
[tex]A(t) = A(0)e^{kt}[/tex]
[tex]A(12) = 5000e^{0.025 \times 24}[/tex]
A(12) = $9,111.
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Write the expression for the following statement without
any spaces: the quantity 5 plus 3z, to the 8th
power less than 9b divided by 7
can be expressed as
The inequality expression for the sentence in this problem is given as follows:
[tex](5+3z)^8 < \frac{9b}{7}[/tex]
How to represent the sentence?The sentence in the context of this problem is defined as follows:
"quantity 5 plus 3z, to the 8th power less than 9b divided by 7"
The first quantity, 5 plus 3z, to the 8th power, is expressed as follows:
[tex](5 + 3z)^8[/tex]
The second quantity, 9b divided by 7, is given as follows:
9b/7.
The inequality symbol for the word less is given as follows:
<.
Hence the inequality is given as follows:
[tex](5+3z)^8 < \frac{9b}{7}[/tex]
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Why is a bank eligible to ask a service fee
A bank is eligible to ask for a service fee because it provides various services to its customers that incur costs.
Banks are financial institutions that offer a range of services such as deposit accounts, loans, credit cards, money transfers, and investment options. These services require infrastructure, technology, staff, and administrative costs to operate effectively.
The service fee charged by a bank helps cover these operational expenses and ensures the bank can continue providing quality services to its customers. Additionally, banks may also charge fees to generate revenue and earn profits. Banks are businesses that need to maintain financial sustainability, and service fees contribute to their overall revenue stream.
Banks typically outline their fee structure and disclose the applicable charges in their terms and conditions or fee schedules. Common examples of service fees include monthly maintenance fees for deposit accounts, transaction fees for certain types of transactions, overdraft fees, wire transfer fees, and fees for additional banking services.
It's important for banks to be transparent about their fee structure and provide clear information to customers regarding the charges. Customers can then make informed decisions about which services to use and understand the costs associated with those services.
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Explain the difference between an indefinite integral and a definite integral.
A) An indefinite integral, after evaluating it at the limits of integration, results in a particular number. A definite integral results in a set of functions that share the same derivative and uses an arbitrary constant of integration.
B) A definite integral, after evaluating it at the limits of integration, results in a particular number. An indefinite integral results in a set of functions that share the same derivative and uses an arbitrary constant of integration.
C) An indefinte integral cannot always be integrated analytically and may require numeric integration, while it is always possible to integrate a definite integral. Definite integrals always return a real number after evaluation at its limits of integration.
D) A definite integral is defined and continuous over the interval of integration and has finite limits of integration. An indefinite integral is also defined and continuous over the interval of integration, but may have as a limit of integration.
The answer is A.
An indefinite integral is a function that, when differentiated, equals the original function. It is denoted by ∫f(x)dx, where f(x) is the function to be integrated. An indefinite integral always has an arbitrary constant of integration, which is denoted by C. This is because the derivative of any constant is zero, so the derivative of ∫f(x)dx+C is still equal to f(x).
A definite integral is the limit of a Riemann sum as the number of terms tends to infinity. It is denoted by ∫
a
b
f(x)dx, where a and b are the limits of integration. A definite integral does not have an arbitrary constant of integration, because the limits of integration specify a unique value for the integral.
In other words, an indefinite integral is a family of functions that share the same derivative, while a definite integral is a single number.
Please help !!!!!!!!!!!!!!!
Okay!
In the given diagram, we have two intersecting lines. To determine the relationship between the angles and solve for x, we can use the properties of angles formed by intersecting lines.
From the diagram, we can see that angle K is vertically opposite to the angle (4x-10)°. In a case of intersecting lines, vertically opposite angles are equal.
So, we can write:
K = (4x-10)°
To solve for x, we need more information or another equation involving x. Without any additional equations or information, we cannot determine the value of x.
If you have any additional equations or information related to the problem, please provide them, and I'll be happy to assist you further in solving for x.
ahmed throws a ball to john. The ball travels 10m in x m/s.
a) write an expression in terms of x for the time taken for the ball to reach john
john throws the ball to pierre over a distanxce of 15m in 0.5 m/s less than the timw taken for the ball to reach john from ahmed.
b) write an expression in terms of x for the time taken for the ball to go from john to pierre.
the time taken between john catching the ball and then throwing it to pierre is 2 seconds . the total time taken from ahmed to pierre in 7 seconds. write an equation to show that it simplifies to 2x^2-9x-2=0
Answer:
a) The time taken for the ball to reach John is: 10/x seconds.
b) The time taken for the ball to go from John to Pierre is: 15/(x - 0.5) seconds.
c) The equation that shows the total time taken from Ahmed to Pierre simplifies to 2x^2 - 9x - 2 = 0.
Step-by-step explanation:
a) The time taken for the ball to reach John can be calculated using the formula:
time = distance / speed
Since the distance traveled by the ball is 10m and the speed is x m/s, the time taken can be expressed as:
time = 10 / x seconds
b) The time taken for the ball to go from John to Pierre can be expressed as:
time = distance / speed
Since the distance traveled by the ball is 15m and the speed is 0.5 m/s less than the speed at which the ball traveled from Ahmed to John (i.e. x - 0.5 m/s), the time taken can be expressed as:
time = 15 / (x - 0.5) seconds
c) Let's use the information given to write an equation for the total time taken from Ahmed to Pierre. We know that the time taken for the ball to travel from Ahmed to John is 10/x seconds, the time taken for the ball to travel from John to Pierre is 15/(x-0.5) seconds, and the time taken between John catching the ball and throwing it to Pierre is 2 seconds. Therefore, the total time taken can be expressed as:
10/x + 15/(x-0.5) + 2 = 7
Multiplying both sides by x(x-0.5) to get rid of the denominators, we get:
10(x-0.5) + 15x + 2x(x-0.5) = 7x(x-0.5)
Simplifying and rearranging, we get:
2x^2 - 9x - 2 = 0
Therefore, the equation simplifies to 2x^2 - 9x - 2 = 0.
use parenthesis to makeveach equation true 8×9-2-3
Using the parentheses to rewrite the equation 8×9-2-3 gives 67.
How to use parenthesis to make equation true?
In mathematics, the order of operations are the rules that tell the sequence in which the multiple operations in an expression should be solved.
A way to remember the order of the operations is PEMDAS, where each letter stands for a mathematical operation. There is also another version called BODMAS but the principles are the same
Parenthesis ( )
Exponent a⁷
Multiplication ×
Division ÷
Addition +
Subtraction -
Given: 8×9-2-3
We can rewrite the equation using parenthesis using PEMDAS:
Multiplication first, then followed by addition/subtraction:
8×9-2-3 = (8 × 9) - 2 - 3
= 72 - 2 - 3
= 67
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sovle this this an hard one
Answer:
B, line B
Step-by-step explanation:
Line B closest fits the plotted points (dots). That's the best fit.
16) In the given picture, line / is parallel to line m. if m<1 = 35°
(A) Find m<3
(B) Find m<7
(C) Find m<8
(D) Find m<5
Answer:
∠ 3 = 35° , ∠ 7 = 145° , ∠ 8 = 35° , ∠ 5 = 145°
Step-by-step explanation:
∠ 3 and ∠ 1 are vertically opposite angles and are congruent , then
∠ 3 = 35°
-----------------
∠ 3 and ∠ 5 are same- side interior angles and sum to 180°, that is
∠ 5 + ∠ 3 = 180°
∠ 5 + 35° = 180° ( subtract 35° from both sides )
∠ 5 = 145°
------------------
∠ 5 and ∠ 7 are vertically opposite angles and are congruent , then
∠ 7 = 145°
--------------
∠ 1 and ∠ 8 are corresponding angles and are congruent , then
∠ 8 = 35°
---------------
Issa puts
dollars into an investment with an interest rate of 4 percent per year and
dollars into an investment with an interest rate of 10 percent per year. She invests a total of $5900, and her interest earnings after one year are $434. From this information, we can create two equations: one for the total investment and one for the interest earned. State both equations, and then solve the system to determine how much Issa invested in each.
The equation that describes the total investment is
The equation that describes the interest earned is
Amount invested at 4 percent interest is $
Amount invested at 10 percent interest is $
Issa invested $2600 at a 4 percent interest rate and $3300 at a 10 percent interest rate.
Let's assume Issa invests x dollars at a 4 percent interest rate and y dollars at a 10 percent interest rate.
The equation that describes the total investment is:
x + y = 5900
The equation that describes the interest earned is:
0.04x + 0.1y = 434
To solve this system of equations, we can use substitution or elimination method. Here, we'll use the substitution method.
From the first equation, we can express x in terms of y:
x = 5900 - y
Substituting this value of x into the second equation, we have:
0.04(5900 - y) + 0.1y = 434
Now, let's solve this equation to find the value of y:
0.04(5900 - y) + 0.1y = 434
236 - 0.04y + 0.1y = 434
0.06y = 198
y = 198 / 0.06
y = 3300
Now that we have the value of y, we can substitute it back into the first equation to find x:
x + 3300 = 5900
x = 5900 - 3300
x = 2600
Therefore, Issa invested $2600 at a 4 percent interest rate and $3300 at a 10 percent interest rate.
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
mentum. All rights reserved.
The slope of a line is positive with a value of 3/2 or 1.5.
What is the slope of the line?The slope of the line is the ratio of the rise to the run, or rise divided by the run.
The slope of a line is used to describe the steepness and direction of the line.
Mathematically, the formula for the slope of a line is given as;
slope = Δy / Δx
where;
Δy is the change in the y valuesΔx is the change in x valuesThe slope equation is expanded as follows;
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
From the graph, the values of x and y is determined as;
( x₁, y₁ ) = ( - 2, 0 )
( x₂, y₂) = ( 0, 3 )
The slope of the line is calculated as follows;
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
m = ( 3 - 0 ) / ( 0 - - 2)
m = 3 / 2
m = 1.5
Thus, the line has a positive slope.
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The complete question is below:
What is the slope of the line? type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
_m 6. A sphere has a volume of 123 cm³. Find its radius to the nearest cm. (Use m = 3.14) (1 mark) Answer:
Step-by-step explanation:
Formula for sphere volume = 4/3 pi r^3
V = 4/3 pi r^3 solve for 'r'
r = cubrt ( 3/4 v / pi ) = cubrt ( 3/4 * 123 / 3.14) = 3 cm
There are 140 students in the seventh grade, and 20% are in the Environmental Club. How many students are in the Environmental Club?
Answer:
28
Step-by-step explanation:
You want to know what 20% of 140 is.
PercentThe % symbol can be considered to mean "/100". This means ...
20% = 20/100
and 20% of 140 is ...
20% × 140 = 20/100 × 140 = 2800/100 = 28
There are 28 students in the Environmental Club.
__
Additional comment
You know that 10% is 1/10. This fraction can of 140 can be found by moving the decimal point one place left:
10% of 140. = 14.0
Of course, 20% is twice as much, so ...
20% of 140 = 2 × (10% of 140) = 2 × 14 = 28
In this context, "of" means "times": 20% of 140 means 20% × 140.
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Can someone help me please
In the given diagram, we have a triangle with two angles labeled as (3x + 10)° and (4x - 30)°. We need to solve for the value of x.
To find the value of x, we can use the property that the sum of the interior angles of a triangle is always 180 degrees. Therefore, we can set up the equation:
(3x + 10) + (4x - 30) + 90 = 180
Let's simplify the equation step by step:
Combine like terms:
3x + 4x + 10 - 30 + 90 = 180
7x + 70 = 180
Next, isolate the variable term by subtracting 70 from both sides:
7x + 70 - 70 = 180 - 70
7x = 110
To solve for x, divide both sides of the equation by 7:
(7x)/7 = 110/7
x = 15.71
Therefore, the value of x is approximately 15.71.
Please note that this solution assumes the given diagram accurately represents the angle measurements, and the calculations provided are based on that assumption.
Carlos has a collection of old vinyl records. To play some of the records, the turntable rotates through an angle of 3/2pi radians in 1 second. How many revolutions does the record make in one minute?
A. 33 1/3 revolutions per minute
B. 45 revolutions per minute
C. 78 revolutions per minute
D. 16 2/3 revolutions per minute
Step-by-step explanation:
We know that the turntable rotates through an angle of 3/2pi radians in 1 second.
To find the number of revolutions in one minute, we need to convert the angle to revolutions per minute.
There are 2π radians in one revolution, so we can set up a proportion:
(3/2π radians) / (1 second) = (x revolutions) / (1 minute)
To solve for x, we can cross-multiply and simplify:
(3/2π) * (1 minute) = x * (1 second) * (2π)
x = (3/2π) * (60/1)
x = 45 revolutions per minute
Therefore, the answer is B. 45 revolutions per minute.
I hope it helps!!
someone give me answers please!
Answer:
Area is 140
Step-by-step explanation:
This might be hard at first, but if you can figure out that the triangle on the left can be moved to the right, it forms a rectangle!
So, 10 x 14 = 140 Square units
Triangles MNO and JKL below are congruent. If m<M =40c, m<N =120c, and m<O =20c, whats m<L? a. 120° b. 20° c. 40° d. 70°
Answer: b, 20°
Step-by-step explanation: Since triangles MNO and JKL are congruent, we know that all of their corresponding angles are congruent. This means that m<L = m<O = 20°
Pls help due tomorrow
Your keys drop from the top of the tower and fall straight to the ground. You want to know how far from the base of the tower the keys landed. Draw a right triangle that will help you solve the problem. label each triangle with the information you know. (the tower is 150 meters tall with a 72-degree angle )
2. using the known angle, what side is known? What side is unknown? Use opposite, adjacent, or hypotenuse in your answer.
known side ___
unknown side ___
3. What trigonometric ratio would you use to find the distance from the base of the tower to your keys? identify your choice, and then calculate the distance.
Trigonometric ratio (name) ___
Calculation (Show your work): ___
4. While you're at the top of the tower, you see an ant walking along the edge of the building. if the ant were to walk straight down the side of the tower until it reached the ground, how far would the ant travel? Which trigonometric ratio would you use to find this distance? use the ratio to find the measurement.
5. confirm that your answer to question 5 is correct using the Pythagorean theorem instead of trigonometric ratios.
6. The leaning tower of Niles, in Illinois, is a replica of the famous Leaning tower of Pisa. it was completed in 1934. the tower of Niles is 94 feet high and makes an angle of 85.5 degrees from the ground to the top of the tower. if you drop your keys from the top of this tower, how far from the base of the tower would they land?
Answer:
know side: 3
Unknown side: 5
Answer: The trigonometric ratio that I would use to find the distance from the base of the tower to the keys is the tangent; tan (86°) = height / distance.
Explanation and calculation:
You can draw a right triangle with angle 86°, opposite leg equal to the height (50 meter) and adjacent leg equal to the distance from the base of the tower to the keys: tan (86°) = 50 m / x
=> x = 50 m / tan(86°)
x = 50 m / 14.30 = 0.98 m
Answer: 0.98 m
Find u if a normal distribution has a standard deviation of 3.5 with a z-score of -0.74 for a value of 6.2
Answer:
8.79-------------------
Use the formula for z-score
z = (x - μ) / σSubstituting the given values, we get:
-0.74 = (6.2 - μ) / 3.5Solve it for mean μ:
-0.74 * 3.5 = 6.2 - μ -2.59 = 6.2 - μ μ = 6.2 - (-2.59) μ = 8.79Therefore, the mean of the normal distribution is 8.79.
Andrei, Amit and Andrew were each asked to factor the term 20x^620x
6
20, x, start superscript, 6, end superscript as the product of two monomials. Their responses are shown below.
Andrei Amit Andrew
20x^6=(2x)(10x^5)20x
6
=(2x)(10x
5
)20, x, start superscript, 6, end superscript, equals, left parenthesis, 2, x, right parenthesis, left parenthesis, 10, x, start superscript, 5, end superscript, right parenthesis 20x^6=(4x^3)(5x^3)20x
6
=(4x
3
)(5x
3
)20, x, start superscript, 6, end superscript, equals, left parenthesis, 4, x, cubed, right parenthesis, left parenthesis, 5, x, cubed, right parenthesis 20x^6=(20x^2)(x^3)20x
6
=(20x
2
)(x
3
)20, x, start superscript, 6, end superscript, equals, left parenthesis, 20, x, squared, right parenthesis, left parenthesis, x, cubed, right parenthesis
1) Which of the students factored 20x^620x
6
20, x, start superscript, 6, end superscript correctly?
Choose all answers that apply:
Choose all answers that apply:
(Choice A) Andrei
A
Andrei
(Choice B) Amit
B
Amit
(Choice C) Andrew
C
Andrew
(Choice D) None of the above
D
None of the above
Based on the given responses, the student who factored 20x^6 = (2x)(10x^5) correctly is Andrei. Therefore, the correct answer is (Choice A) Andrei.
Among the given responses, the student who factored 20x^6 = 20, x to the power of 6 correctly is Andrei. Andrei's factorization is (2x)(10x^5), which correctly represents the original term 20x^6. Therefore, the correct answer is (Choice A) Andrei.
Amit's factorization is (4x^3)(5x^3), which is incorrect because it breaks down the term into two factors with the same exponent, while the original term has an exponent of 6.
Andrew's factorization is (20x^2)(x^3), which is also incorrect as it does not accurately represent the original term 20x^6.
Hence, the only student who correctly factored 20x^6 = 20, x to the power of 6 is Andrei.
The right answer is A. Andrei who factored 20x^6 = (2x)(10x^5) correctly.
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Question 6
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Suppose you want to have $300,000.00 for retirement in 35 years. You plan to make regular quarterly
deposits into an account earning 8% interest compounded quarterly.
How much would you need to deposit in the account each quarter?
You need to deposit
each quarter.
Submit Question
How much money will you have put into the account? Hint
You will have put
How much interest will you have earned? Hint
You will have earned
into the acou
in interest.
over the 35 years.
you will have put approximately $1,014,706.40 into the account over the 35 years. The interest will you have earned is -$714,706.40.
To calculate the amount you need to deposit each quarter, we can use the formula for the future value of a series of regular deposits:
FV = P * ((1 + r)^n - 1) / r
Where:
FV is the future value (target amount) you want to achieve ($300,000.00)
P is the deposit amount per quarter (what we need to find)
r is the interest rate per quarter (8% or 0.08)
n is the number of quarters (35 years * 4 quarters per year = 140 quarters)
Now, let's substitute the values into the formula and solve for P:
$300,000.00 = P * ((1 + 0.08)^140 - 1) / 0.08
$300,000.00 * 0.08 = P * ((1.08)^140 - 1)
$24,000.00 = P * (4.31793257 - 1)
$24,000.00 = P * 3.31793257
P = $24,000.00 / 3.31793257
P ≈ $7,243.21
Therefore, you would need to deposit approximately $7,243.21 into the account each quarter to accumulate $300,000.00 for retirement in 35 years.
To calculate the total amount of money you will have put into the account over the 35 years, you can multiply the deposit amount per quarter by the number of quarters:
Total deposit = P * n = $7,243.21 * 140 = $1,014,706.40
Therefore, you will have put approximately $1,014,706.40 into the account over the 35 years.
To calculate the interest earned, you can subtract the total deposit amount from the target amount:
Interest earned = Future value - Total deposit = $300,000.00 - $1,014,706.40 = -$714,706.40
The negative value indicates that the interest earned is negative, meaning that you will have fallen short of your target amount by $714,706.40 due to the interest earned being less than the total deposit made.
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Use the Intermediate Value Theorem to show that the given function has a zero in the interval [0, 2].
Answer:
See below for answer and explanation
Step-by-step explanation:
The Intermediate Value Theorem (IVT) states that there is a value [tex]c[/tex] in [tex][a,b][/tex] such that [tex]f(c)=0[/tex]. Because [tex]f(0)=0^2+5(0)-4=-4[/tex] and [tex]f(2)=2^2+5(2)-4=10[/tex], this must mean that 0 is in between -4 and 10, which concludes that there is a zero over the interval [0,2] for the given function by IVT.
PLEASE HELP!!!
The inside of the cylindrical swimming pool shown must be covered with a vinyl liner. The liner must cover the side and bottom of the swimming pool.
The diameter of the pool is 20 feet and the height is 3 feet, as shown.
What is closest to the minimum amount of vinyl needed for the liner?
O 1320 sq ft
O 817 sq ft
O 503 sq ft
O 126 sq ft
The minimum amount of vinyl needed for the liner is 502.4 sq. feet.
We have,
An open cylinder is a type of cylinder in which one of its circular surfaces has been removed.
Thus its area can be determined as:
area of an open cylinder = πr² + 2πrh
where r is the radius, and h is the height.
The area of the swimming pool that will be covered by vinyl liner resembles an open cylinder. So that;
area of the open swimming pool = πr² + 2πrh
= πr(r + 2h)
we have,
r = diameter/ 2
= 20/ 2
r = 10 feet
area of the open swimming pool = 3.14×10(10 + 2×3)
= 31.4×16
= 502.4
The minimum amount of vinyl needed for the liner is 502.4 sq. feet.
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Pleaseeeeee help with these two questions:
A car accelerates for 4.5 seconds at a rate of 2 m/s^2. If the car was driving at 10 m/s initially, what is it's final velocity? The car is moving on a straight path.
12.25 m/s
22.5 m/s
4.44 m/s
19 m/s
QUESTION 2
If a 5000 kg car hits a 500 kg motorcycle, which of the following is true? Assume they collide and cleanly bounce off of each other.
-The motorcycle will have a greater acceleration after the collision due to the greater force exerted by the car on
impact.
-The forces are equal and opposite so both vehicles will have the same acceleration after the impact.
-The motorcycle will have a greater acceleration after the collision due to its lower inertia.