The polynomial f(x) with real coefficients and the given zeros is:
f(x) = x^3 - (12 + i)x^2 + (x - 3 - 2i)x + 27x + (27 + 3i)
To form a polynomial with degree 5 and the given zeros, we can start by writing the factors corresponding to each zero.
The zero 3 gives us the factor (x - 3).
The zero -i gives us the factor (x + i) since complex zeros always come in conjugate pairs.
The zero 9+i gives us the factor (x - (9+i)).
Now, we can multiply these factors together to obtain the polynomial:
f(x) = (x - 3)(x + i)(x - (9+i))
Next, we simplify the expression:
f(x) = (x - 3)(x + i)(x - 9 - i)
Expanding the product, we have:
f(x) = (x^2 + xi - 3x - 3i)(x - 9 - i)
Multiplying further:
f(x) = (x^3 - 9x^2 - ix^2 + xi - 3x^2 + 27x + 3ix - 3xi - 27i - 3x + 27 + 3i)
Combining like terms:
f(x) = x^3 - (9 + i)x^2 - 3x^2 + (x - 3 - 3i)x + 27x + (27 + 3i)
Simplifying:
f(x) = x^3 - (12 + i)x^2 + (x - 3 - 2i)x + 27x + (27 + 3i)
The polynomial f(x) with real coefficients and the given zeros is:
f(x) = x^3 - (12 + i)x^2 + (x - 3 - 2i)x + 27x + (27 + 3i)
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(q3) Find the length of the curve described by the function
The length of the curve described by the function x = (y - 5)² where 0 ≤ y ≤ 1, is approximately A. 7.982.
How to calculate the valueSubstituting the values back into the arc length formula, we have:
L = ∫√(dx/dt)² + (dy/dt)² dt
L = ∫√(2(t - 5))² + 1² dt
L = ∫√(4(t - 5)² + 1) dt
Now, let's integrate this expression over the given range 0 ≤ y ≤ 1:
L = ∫[0,1]√(4(t - 5)² + 1) dt
Approximating the integral with the midpoint rule:
L ≈ ∑[i=0 to n-1] √(4(t_i+1 - 5)² + 1) Δt
Let's choose n = 1000 for a reasonably accurate result. Thus, Δt = (1 - 0) / 1000 = 0.001.
Calculating the sum:
L ≈ ∑[i=0 to 999] √(4(t_i+1 - 5)² + 1) * 0.001
Performing this calculation, we find that L ≈ 7.982.
Therefore, the length of the curve described by the function x = (y - 5)² where 0 ≤ y ≤ 1, is approximately 7.982.
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Dividing by a Monomial
What is (9x^3-6x^2+15x) ÷ 3x^2?
Answer:
[tex]3x-2+\frac{5}{x}[/tex]
Step-by-step explanation:
To divide the polynomial (9x^3 - 6x^2 + 15x) by the monomial 3x^2, we can write it as:
(9x^3 - 6x^2 + 15x) ÷ (3x^2)
To simplify the division, we divide each term of the polynomial by 3x^2:
(9x^3 ÷ 3x^2) - (6x^2 ÷ 3x^2) + (15x ÷ 3x^2)
To divide monomials with the same base, we subtract the exponents. So:
9x^3 ÷ 3x^2 = 9/3 * (x^3/x^2) = 3x^(3-2) = 3x
(-6x^2) ÷ (3x^2) = -6/3 * (x^2/x^2) = -2
15x ÷ 3x^2 = 15/3 * (x/x^2) = 5/x
Putting it all together, we have:
(9x^3 - 6x^2 + 15x) ÷ (3x^2) = 3x - 2 + 5/x
Therefore, the division of (9x^3 - 6x^2 + 15x) by 3x^2 is 3x - 2 + 5/x.
whicch of the follow represent y<2x-3?
The graph that represents the linear inequality y < 2x - 3 include the following: A. graph A.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + b
Where:
m represent the slope or rate of change.x and y are the points.b represent the y-intercept or initial value.Based on the information provided above, we have following the linear inequality:
y = mx + b
y < 2x - 3 (it means the dashed boundary line would be shaded below).
Since the y-intercept is equal to -3, we can reasonably infer and logically deduce that only graph A represents the linear inequality y < 2x - 3 while the y-intercept of graph B is equal to 1.
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Oliver wants to invest $15,000 in an account that pays 4.5% per year. After 3 years, if he pulls out his money, will he have enough to pay for his son’s college tuition of $20,000?
Answer:
No
Step-by-step explanation:
[tex]A=Pe^{rt}\\20000\stackrel{?}{\leq}15000e^{0.045(3)}\\20000\nleq17168.05[/tex]
Therefore, Oliver will not be able to pay for his son's college tuition of $20,000 after 3 years. He'll be short by about $3000.
The data modeled by the box plots represent the battery life, in hours, of two different brands of
batteries that Mary tested. Use this graph to answer the following 4 questions.
a) Brand X median = 13 hours
Brand Y median = 16 hours
b) It is found that Brand Y consists of batteries with better battery life compared to Brand X
What are mean and median?The mean is the average value which can be calculated by dividing the sum of observations by the number of observations
Median represents the middle value of the given data when arranged in a particular order.
a) We need to get the median value of each of the two data sets, each dataset consists of 5 distinct points. The median value is the mid-value of each of the plots as;
The third value counting from either end of the plots
For Brand X, the median value = 13 hours
For Brand Y, the median value = 16 hours
b) Secondly, to compare the median values of the data sets, the median value of the second brand (Brand Y) is bigger than the inner value of the first brand (Brand X)
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(q12) Apply Poiseuille’s Law to calculate the volume of blood that passes a cross–section per unit time
Viscosity = 0.0010
Radius = 0.030 cm
Length = 3 cm
P = 1000 dynes/square cm
The volume of blood that passes through the cross-section per unit time is approximately 0.1532 cm^3/s.
Poiseuille's Law describes the flow of fluid through a cylindrical tube. It can be used to calculate the volume of blood that passes through a cross-section per unit time. The formula for Poiseuille's Law is as follows:
Q = (π * ΔP * r^4) / (8 * η * L)
Where:
Q is the volume flow rate,
ΔP is the pressure difference across the tube,
r is the radius of the tube,
η is the viscosity of the fluid, and
L is the length of the tube.
Given information:
Viscosity (η) = 0.0010
Radius (r) = 0.030 cm
Length (L) = 3 cm
Pressure difference (ΔP) = 1000 dynes/square cm
First, we need to convert the radius and length to meters, as the SI unit system is typically used in scientific calculations:
Radius (r) = 0.030 cm = 0.030 * 0.01 m = 0.0003 m
Length (L) = 3 cm = 3 * 0.01 m = 0.03 m
Now, we can calculate the volume flow rate (Q) using Poiseuille's Law:
Q = (π * ΔP * r^4) / (8 * η * L)
= (π * 1000 * (0.0003)^4) / (8 * 0.0010 * 0.03)
= (3.1416 * 1000 * 0.000000000027) / (0.024)
= 0.0036756 / 0.024
≈ 0.1532 cm^3/s
Therefore, the volume of blood that passes through the cross-section per unit time is approximately 0.1532 cm^3/s.
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Camacho is buying a monster truck. The price of the truck is
x
xx dollars, and he also has to pay a
13
%
13%13, percent monster truck tax.
The total amount Camacho needs to pay, including the 13% monster truck tax, is 1.13x dollars.
To calculate the total amount Camacho needs to pay, including the 13% monster truck tax, we need to add the tax amount to the original price of the truck.
Let's denote the price of the truck as x dollars.
The tax amount is calculated by taking 13% of the truck's price. In mathematical terms, this can be expressed as:
Tax amount = (13/100) * x
To find the total amount Camacho needs to pay, we add the tax amount to the price of the truck:
Total amount = Price of the truck + Tax amount
= x + (13/100) * x
= x + 0.13x
= 1.13x
Therefore, the total amount Camacho needs to pay, including the 13% monster truck tax, is 1.13x dollars.
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Question
Camacho is buying a monster truck priced at xx dollars. In addition to the truck's price, he must pay a 13% monster truck tax. What is the total amount Camacho needs to pay, including the tax?
What is the meaning of "the notion of finiteness"?
The notion of finiteness refers to the idea that something has a definite limit or is not infinite. It is a concept that has been applied in various fields of study, such as mathematics, computer science, and philosophy.
In mathematics, finiteness is a fundamental concept used to define various mathematical objects and structures, such as sets, numbers, and sequences. It is also used to define the properties of functions and to study the properties of mathematical systems.
In computer science, the notion of finiteness is crucial for the design and analysis of algorithms and computer programs. Computer scientists use finite state machines, which are mathematical models that describe the behavior of a system that can be in one of a finite number of states.
This concept is essential to the development of computer programs that are efficient, reliable, and secure.
In philosophy, finiteness is a concept that is often used to reflect on the nature of human existence and the limits of human knowledge. It is also used to examine the concept of time and the nature of reality.
In general, the notion of finiteness is a fundamental concept that has many applications in various fields of study.
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Suppose we have a random sample of size n = 5 from a continuous uniform distribution on the interval [0, 1]. Find the probability that the third largest observation in the sample is less than 0.7.
Note that the probability that the third largest observation in the sample is less than 0.7 is 0.4864.
How is this so ?
The probability that the third largest observation in the sample is less than 0.7 is the probability that the first two observations are greater than 0.7.
The probability that a single observation is greater than 0.7 is 0.3.
The probability that two observations are greater than 0.7 is -
P(X1 > 0.7, X2 > 0.7)
= (0.7)²
P(X3 < 0.7) = 1 - (0.7)³
= 0.4864
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the rule for converting temperature given in degrees Celsius to degrees Fahrenheit is given as multiple degrees Celsius by 1/8 and then add 32 temperatures in °C 0 5 20 32 100 Temperatures in °F
Based on the information provided, if we convert 50° from Celcius to Fahrenheit the temperature is 122° Fahrenheit.
How to convert the temperature from Celcius to Fahrenheit?To convert the temperature from Celsius to Fahrenheit we will use the formula suggested. This can be expressed as the temperature in Celsius x 1.8 + 32. Now, let's calculate the new temperature:
t x 1.8 + 32
50 x 1.8 + 32
90 +32
122° Fahrenheit
Therefore, the temperature in Fahrenheit is 122° Fahrenheit, however, this formula can be applied to convert any temperature.
Note: This question is incomplete, here is the missing section.
Convert 50° from Celcius to Fahrenheit
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...................................................................................................
Answer:
60 in.²
Step-by-step explanation:
A = (B + b)h/2
A = (14 in. + 6 in.)(6 in.)(1/2)
A = 60 in.²
Answer:
60 in^2
Step-by-step explanation:
solution Given:
Area of the shaded region or trapezoid = Area of Rectangle ABCD - Area of triangle CDE
we have
Area of Rectangle ABCD= length* breadth =BC*AB=14*6=84 in^2
Area of Triangle CDE= 1/2* base*height=1/2*DE*CD=1/2*8*6=24 in ^2
Now
Area of the shaded region or trapezoid = Area of Rectangle ABCD - Area of triangle CDE
=84 in^2-24in^2
=60 in^2
Similarly, we have another way to calculate the area of the trapezoid;
Area = 1/2*h*(side1*side2)
=1/2*AB*(AE+BC)
=1/2*6*(6+14)
=60 in^2
Find the volume of the cylinder to the nearest cubic foot. Use a calculator. A. 236 ft3 B. 942 ft3 C. 251 ft3 D. 75 ft3
[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=5\\ h=3 \end{cases}\implies V=\pi (5)^2(3)\implies V\approx 236~ft^3[/tex]
Answer:
236 ft^3
Step-by-step explanation:
Base radius = 5 ft
Height = 3 ft
Volume = πr^2h
= π × 5^2 × 3
= 75π
= 235.61944901923 feet^3
Nearest Cubic Foot = 236 ft^3
Nearest Cubic Foot:
Hence Answer is:
236 ft^3
Hope this helps!
What amount must be remitted if the following invoices, all with terms 5/10, 2/30, n/60, are paid together on December 8?
Invoice No. 312 dated November 2 for $923.00
Invoice No. 429 dated November 14 for $784.00
Invoice No. 563 dated November 30 for $873.00
Question content area bottom
Part 1
The amount remitted is $
The amount to be remitted when paying the invoices together on December 8 is $2,477.19.
To calculate the amount that must be remitted when paying the invoices together on December 8, we need to consider the available discount periods and the due date.
Let's break down the information provided:
Invoice No. 312 dated November 2 for $923.00
Invoice No. 429 dated November 14 for $784.00
Invoice No. 563 dated November 30 for $873.00
Given the terms 5/10, 2/30, n/60, this means that a 5% discount is offered if payment is made within 10 days, a 2% discount is offered if payment is made within 30 days, and the net amount is due within 60 days.
To calculate the amount to be remitted, we need to consider the applicable discount periods. For payments made on or before December 8, the following discounts apply:
Invoice No. 312: 5% discount if paid within 10 days
Invoice No. 429: 5% discount if paid within 10 days
Invoice No. 563: 2% discount if paid within 30 days
To calculate the remitted amount, we subtract the applicable discount from each invoice amount and sum them up:
Invoice No. 312: $923.00 - (5% of $923.00) = $923.00 - ($46.15) = $876.85
Invoice No. 429: $784.00 - (5% of $784.00) = $784.00 - ($39.20) = $744.80
Invoice No. 563: $873.00 - (2% of $873.00) = $873.00 - ($17.46) = $855.54
Total amount to be remitted = $876.85 + $744.80 + $855.54 = $2,477.19
Therefore, the amount to be remitted when paying the invoices together on December 8 is $2,477.19.
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Brenda wants to invest $15,000 in an account that pays 4.5%. After 10 years will she be able to afford a $20,000 car?
Answer:
Brenda will be able to afford the $20,000 car after 10 years.
Step-by-step explanation:
To determine whether Brenda will be able to afford a $20,000 car after 10 years, we need to calculate the future value of her investment with an interest rate of 4.5%.
The formula for calculating the future value of an investment is:
FV = PV * (1 + r)^n
Where:
FV = Future Value
PV = Present Value (initial investment)
r = Interest rate
n = Number of periods
In this case, Brenda's initial investment (PV) is $15,000, the interest rate (r) is 4.5% (or 0.045 as a decimal), and the number of periods (n) is 10 years.
Let's calculate the future value of Brenda's investment:
FV = $15,000 * (1 + 0.045)^10
FV = $15,000 * (1.045)^10
FV ≈ $22,292.26
After 10 years, Brenda's investment will grow to approximately $22,292.26.
Since the future value of her investment is greater than the cost of the car ($20,000), Brenda will be able to afford the $20,000 car after 10 years.
HELP! FAST! I NEED HELP REAALLYY FAST!!! IF UR SMART HELP!
Step-by-step explanation:
multiple the given number and you can get the answer :)
A hospital patient needs 500 mg of dextrose. You have a 250 mL bag containing a 5 % by mass solution of dextrose in water. How many mL of solution should you give the patient? (Assume that the density of the dextrose solution = 1.0 g/mL).
The patient needs to be given 0.04 mL of solution.
Given data:
Mass of dextrose = 500mg;
Volume of solution = 250mL;
Percentage by mass = 5%;
Density of solution = 1.0 g/mL
We need to calculate how many mL of solution should be given to the patient. We can start the calculation by finding the mass of the solution.
We know that 5% by mass solution contains 5g dextrose in 100g solution.
Therefore, in 250mL (or 250g) solution,
the mass of dextrose = 5/100 × 250 = 12.5g
Now, we have the mass of dextrose in the solution as 12.5g and we need to give 500mg to the patient.
So, the volume of solution required to get 500mg dextrose = (500/1000)/12.5 = 0.04 mL
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For the transformed equation y=-2sin(x)-3, find and explain in detail how to find:
The amplitude of a sine function is the absolute value of the coefficient multiplying the sin(x) term.
How to explain the informationIn this case, the coefficient is -2. Since the amplitude is always positive, we take the absolute value of -2, which gives us an amplitude of 2.
The period of a sine function is given by the formula 2π/b, where b is the coefficient multiplying the x variable. In our equation, the coefficient is 1 (since sin(x) has an implied coefficient of 1), so the period is 2π/1 = 2π.
The phase shift of a sine function is determined by the value inside the parentheses. In this case, there is no value inside the parentheses, so there is no phase shift. The function remains centered around the origin (x = 0).
The vertical shift of a function is the constant term added or subtracted from the trigonometric function. In this equation, the constant term is -3, which means the graph is shifted downward by 3 units.
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The curve through the ordered pairs (0, 10), (1, 5), and (2, 2.5) can be represented by the function f(x) = 10(0.5)*.
What is the multiplicative rate of change of the function?
O 0.5
02
2.5
5
Mark this and return
Save and Exit
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Submit
The multiplicative rate of change of the function is,
⇒ 0.5
We have to given that,
The curve through the ordered pairs (0, 10), (1, 5), and (2, 2.5) can be represented by the function,
⇒ f(x) = 10(0.5)ˣ
Now, For the multiplicative rate of change of the function,
Let two values, of points are x = 1 and x = 0
Put x = 1 in function,
⇒ f(1) = 10(0.5)¹
⇒ f(1) = 10(0.5)
⇒ f(1) = 5
Put x = 0;
⇒ f(0) = 10(0.5)⁰
⇒ f(0) = 10
Hence, The ratio is,
⇒ f (1)) / f (0)
⇒ 5 / 10
⇒ 0.5
Thus, the multiplicative rate of change of the function is,
⇒ 0.5
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the set of integers that are multiple of 5
use set notation
Answer:
Step-by-step explanation:
\[y={5x,x \n I\]
={...,-10,-5,0,5,10,...}
[tex]{\Large \begin{array}{llll} y=\{5x; ~~ x\in \mathbb{Z}\} \end{array}} \qquad \textit{integers multiples of 5}[/tex]
A life insurance company has determined that each week an average of seven claims is filed .what is the probability that during the next week exactly sevent claims will be filled?
The probability that exactly seven claims will be filed during the next week is approximately 0.1038 or 10.38%.
To determine the probability of exactly seven claims being filed during the next week, we need to use the Poisson distribution. The Poisson distribution is commonly used to model the number of events occurring in a fixed interval of time or space when the events occur with a known average rate and independently of the time since the last event.
In this case, we are given that the average number of claims filed per week is seven. This average rate is also the parameter λ (lambda) of the Poisson distribution.
The probability mass function (PMF) of the Poisson distribution is given by:
P(X = k) = (e^(-λ) * λ^k) / k!
Where X is the random variable representing the number of claims filed, k is the specific number of claims we are interested in (in this case, k = 7), e is the base of the natural logarithm (approximately 2.71828), and k! represents the factorial of k.
Substituting the given average rate of seven claims per week into the equation, we have:
P(X = 7) = (e^(-7) * 7^7) / 7!
Calculating this expression will give us the probability of exactly seven claims being filed during the next week.
P(X = 7) ≈ 0.1038
Therefore, the probability that exactly seven claims will be filed during the next week is approximately 0.1038 or 10.38%.
This means that, on average, we can expect approximately 10.38% of weeks to have exactly seven claims filed based on the given average rate of seven claims per week.
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H0 : μ1 = μ2 H1 : μ1 ≠ μ2 A random sample of 10 observations from one population revealed a sample mean of 22 and a sample standard deviation of 3.7. A random sample of 7 observations from another population revealed a sample mean of 26 and a sample standard deviation of 5.0. The population standard deviations are unknown but assumed to be equal. At the 0.10 significance level, is there a difference between the population means? Required: a. State the decision rule. (Negative amounts should be indicated by a minus sign. Round your answer to 3 decimal places.) b. Compute the pooled estimate of the population variance. (Round your answer to 3 decimal places.) c. Compute the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) d. State your decision about the null hypothesis. multiple choice 1 Reject H0. Do not reject H0. e. The p-value is multiple choice 2 between 0.1 and 0.05. less than 0.001. between 0.02 and 0.05. between 0.001 and 0.01. between 0.1 and 0.2.
Answer:
(a) Decision rule: reject null hypothesis if [tex]t < -1.753[/tex] or [tex]t > 1.753[/tex], and fail to reject null hypothesis if [tex]-1.753\leq t\leq 1.753[/tex]
(b) [tex]s_{p}^{2}=18.214[/tex]
(c) [tex]t=-1.902[/tex]
(d) Reject [tex]H_{0}[/tex]
(e) The p-value is between 0.1 and 0.05
Step-by-step explanation:
The explanation is attached below.
Find the measure of ∠AED for m∠BEC = 36.
Hello!
∠AED and ∠BEC are opposite angles
so ∠AED = ∠BEC = 36°.
∠AED = 36°Can someone please help me with this?
Answer:
[tex]\displaystyle \sin\theta=\frac{\sqrt{7}}{4}[/tex]
Step-by-step explanation:
[tex]\displaystyle \cos^2\theta+\sin^2\theta=1\\\\\biggr(\frac{3}{4}\biggr)^2+\sin^2\theta=1\\\\\frac{9}{16}+\sin^2\theta=1\\\\\sin^2\theta=\frac{7}{16}\\\\\sin\theta=\frac{\sqrt{7}}{4}[/tex]
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Please mark brainliest ❣️
Thanks
Step-by-step explanation:
Cos ∅ = 3/4
SOHCAHTOA
Sin∅ = opp/ hyp
Cos ∅ = adj/ hyp •°• adj = 3 hyp = 4
Using Pythagorean theorem
hyp² = adj² + opp²
4² = 3² + opp²
•°• opp = √ 7
sin ∅ = √7 /4
Concept Check
Complete the problem. (From Example 1)
1. Liz Reynolds deposited $2,000 into a savings account that pays 8% compounded quarterly, Complete the
table to compute the amount in the account after 1 year.
Original Principal
Interest for First Quarter
Amount at End of First Quarter
Interest for Second Quarter
Amount at End of Second Quarter
Interest for Third Quarter
Amount at End of Third Quarter
Interest for Fourth Quarter
Amount at End of Fourth Quarter
$2,000.00 x 8%*%=
$2,000.00+ $40,00-
$2,040.00 x 8% x = b.
e.
$40.00
h.
F
4
m
a.
+C.
d.
+1.
W
98 +1.
$2,000,00
$40.00
Liz table that shows her compounded interest should be completed the following way;
Original Principal $2,000
Interest for First Quarter $2,000.00 x 8% ×1/4 = $40 = + $ 40
Amount/End of First Quarter $2,000.00+ $40.00 = $2040 = + $ 2040
Interest for Second Quarter $ 2040 × 8% ×1/4 = $ 40.8 = + $ $ 40.8
Amount/End of Second Quarter 2040 + 40.8 = $ 2080.8 = + $ 2080.8
Interest for Third Quarter 2080.8 × 8% ×1/4 = $ 41.616 = + $ 41.616
Amount/End Third Quarter 2080.8+41.616 = $2122.416 = + $ 2122.416
Interest/Fourth Quarter 2122.416 × 8% ×1/4 = $ 42.4483 = + 42.4483
Amount/ End of Fourth Quarter $2122.416 + $42.4483 = 2164.8643
What is meant by quarterly compound interest?Quarterly compound interest is a type of interest that is calculated and paid out four times in a year. This means that the interest earned in one quarter is added to the principal amount, and then interest is calculated on the new, larger principal amount in the next quarter.
Quarterly compound interest is more profitable than annual compound interest in many cases, however, it depends on the percentage increase.
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(q19) The scores of a mid term exam are distributed normally with mean 70 and standard deviation 15. What percentage of students would have the score between 60 and 75?
This means that approximately 51.57% of the students would have scores between 60 and 75.
The problem is asking for the percentage of students that would have scores between 60 and 75 in a normally distributed test with a mean score of 70 and a standard deviation of 15.
To solve the problem, first we need to standardize the scores by using the formula:
z = (x - μ) / σ where z = the standardized score x = the raw score μ = the mean score σ = the standard deviation Then,
we can find the area between the z-scores corresponding to 60 and 75 using a standard normal distribution table or calculator.
The area represents the percentage of students who scored between 60 and 75.
To find the z-score corresponding to 60:x = 60μ = 70σ = 15z = (60 - 70) / 15 = -0.67
To find the z-score corresponding to 75:x = 75μ = 70σ = 15z = (75 - 70) / 15 = 0.33
Now, we can find the area between -0.67 and 0.33 using a standard normal distribution table or calculator.Using a calculator, we can use the normalcdf function to find the area:normalcdf(-0.67, 0.33) = 0.5157
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An equation is shown below: 5(2x − 3) = 15 Part A: How many solutions does this equation have? Part B: What are the solutions to this equation? Show your work.
Answer:
It has one solution
Step-by-step explanation:
5(2x-3)=15
10x-15=15
10x=15+15
10x=30
divide both sides by 10
10x/10=30/10
x=3
Answer:
Part A: This equation has only one solution.
Part B: The solution to the equation is x = 3.
Step-by-step explanation:
To solve the equation 5(2x - 3) = 15, we can follow these steps:
Part A: Determining the number of solutions
Since this is a linear equation with one variable, it can have either one solution, infinitely many solutions, or no solution.
Part B: Solving the equation
Let's solve the equation step by step:
Distribute the 5 on the left side of the equation:
5 * 2x - 5 * 3 = 15
10x - 15 = 15
Add 15 to both sides of the equation to isolate the variable term:
10x - 15 + 15 = 15 + 15
10x = 30
Divide both sides of the equation by 10 to solve for x:
(10x) / 10 = 30 / 10
x = 3
Therefore, the solution to the equation 5(2x - 3) = 15 is x = 3.
To summarize:
Part A: This equation has only one solution.
Part B: The solution to the equation is x = 3.
Determine the missing side lengths and angles for the similar triangles in the picture below.
∠C =
∠F =
AB =
DF =
NO LINKS!
Answer:
∡C=53°
∡F=102°
AB=11
DF=27
Step-by-step explanation:
Similar triangles have the same shape but not necessarily the same size. If two triangles are similar, their corresponding angles are equal and their corresponding sides are proportional.
Some of the properties of similar triangles:
The ratio of any two corresponding sides of similar triangles is the same.The ratio of the areas of two similar triangles is the square of the ratio of any two corresponding sides.°ZThe ratio of the perimeters of two similar triangles is the same as the ratio of any two corresponding sides.The heights and medians of similar triangles are proportional to the corresponding sides of the triangles.For the question:
In ΔABC and ΔEFD
Since the respective corresponding angles are equal.
so,
∡A=∡E=25°
∡B=∡F=102°
∡C=∡D=53°
so, ΔABC [tex]\sim[/tex] ΔEFD
Again
Since their corresponding sides are proportional.
First, we need to find the ratio of their respective side:
DE: CA=63:14=9:2 when compared to big triangle to small triangle.
CA: DE=14:63=2:9 when compared to big triangle to small triangle.
AB=2/9*EF=2/9*49.5=11
DF=9/2*CB=9/2*6=27
Write the polynomial inn standard form: f(x) = f(x) -2[tex]x^{4}[/tex] - [tex]x^{6}[/tex] - 4 + 5x
The polynomial in standard form is - x⁶ -2x⁴ + 5x - 4 = 0.
The polynomial expression you provided is indeed valid, and we can write it in standard form by rearranging the terms:
f(x) = f(x) - 2x⁴ - x⁶ - 4 + 5x
f(x) - f(x) = -x⁶ - 2x⁴ + 5x - 4
The term "f(x)" appears on both sides of the equation, so we can subtract it from both sides:
0 = - x⁶ -2x⁴ + 5x - 4
Now, we have the polynomial equation in standard form:
- x⁶ -2x⁴ + 5x - 4 = 0
In this form, the polynomial is written with the terms arranged in descending order of the exponents (from highest to lowest), and the constant term is on the right side of the equation.
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In the diagram a || b. Use the diagram to answer the question. Name the alternate interior angle to <2
The angle 7 is the alternative interior angle to angle 2.
Given that,In the diagram a || bWe need to find the alternate interior angle to <2 .Alternate interior angles are the angles that are formed when a transversal crosses two parallel lines.
They are the angles that are on opposite sides of the transversal and inside the two parallel lines.
Thus, in the given diagram, the angle that is opposite to angle <2 and is inside the two parallel lines a and b is the alternate interior angle to angle <2.
We can see that the alternate interior angle to angle <2 is <7. Therefore, the alternate interior angle to angle <2 is <7.
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A line passes through the point 3, 3) and has a slope of 3. Write an equation in slope-intercept form for this line.
The equation of the line in slope-intercept form is y = 3x - 6.To write the equation of a line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we can use the given information.
To find the equation of a line in slope-intercept form (y = mx + b), we need to determine the y-intercept (b). Given that the line passes through the point (3, 3) and has a slope of 3, we can substitute these values into the equation
Given that the line passes through the point (3, 3) and has a slope of 3, we can substitute these values into the equation.
The slope-intercept form equation becomes y = 3x + b.
To find the value of b, we substitute the coordinates (3, 3) into the equation:
3 = 3(3) + b
3 = 9 + b
b = -6
In this equation, the slope (m) is 3, indicating that for every increase of 1 in the x-coordinate, the y-coordinate increases by 3. The y-intercept (b) is -6, indicating that the line crosses the y-axis at the point (0, -6).
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