a. 68 % between $147,700 and $152,300 if the standard deviation is $2300
b. 2.5 % more than $154,800 if the standard deviation is $2400
Given that:
Prices of a certain model of a new home are normally distributed with a mean of $150,000.
Using the 68-95-99.7 rule , find the percentage of buyers who paid between $147,700 and $152,300 if the standard deviation is $2300.
Let X = prices of a certain model of a new home
SO, X ~ Normal ( μ = 150,000 , σ = 2,300 )
z score probability distribution for normal distribution
Z = X - μ / σ
where μ population mean price = $150,000
σ standard deviation = $2,300
According to 68-95-99.7 rule;
Around 68% of the values in a normal distribution lies between μ - σ and μ +σ .
Around 95% of the values occur between μ - 2σ and μ + 2σ .
Around 99.7% of the values occur between μ - 3σ and μ + 3σ.
Find the z scores for both given values
Z = X - μ / σ
= [tex]\frac{147,700 - 150,000}{2,300}\\ \\ \\[/tex]
= -1
Z = X - μ / σ
= [tex]\frac{152,300 - 150,000}{2,300}[/tex]
= -1
The z score indicates that the category of between μ - σ and μ +σ .
Therefore , this represents that percentage of buyers who paid between $147,700 and $152,300 is 68%.
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a vehicle purchased for $25,000 depreciates at a constant rate of 5%. determine the approximate value of the vehicle 12 years after purchase. round to the nearest whole dollar.
The value of the vehicle after 12 years of purchase will be $13,500.
Here, we are given that a vehicle purchased for $25,000 depreciates at a constant rate of 5%.
Therefore, the value of the vehicle after 1 year will reduce by-
25,000 × 5/100
= 250 × 5
= 1250
Thus, the value after 1 year will become = 25,000 - 1250 = 23750
In the same manner, the value will keep on reducing every year. Thus, the value after 12 years will become-
25,000 [tex](1- 5/100)^{12}[/tex]
= 25,000 [tex](1 - 0.05)^{12}[/tex]
= 25,000 [tex](0.95)^{12}[/tex]
= 25,000 × 0.54
= 250 × 54
= 13,500
Thus, the value of the vehicle after 12 years of purchase will be $13,500.
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Write the following inequality in slope-intercept form.
14x + y ≤ 18
Choose a correct sentence
a) I don’t go to work tomorrow unless I feel better
b) I will buy this car if I’ll like it
c) I’ll tell when I hear from him
d) I’m not usually attending such par
Answer: D
Step-by-step explanation: It is D because the: "'m" in: "i'm" means: I am. The: 'I'm" is referring to you.
in C, the: "i'll" means: I will. After the: "tell", it doesn't make sense because it's not referring to someone. In between the: "tell" and "I", you should include: you. Overall, it should've sounded like: I'll tell you when I hear from him.
In B, the: "i'll" means I will. If you say in starting at this POS, It would sound: I will buy this car if I will like it. this does not make sense because instead of: i'll, you should replace it with: I.
In A, the: "don't" doesn't make sense because saying starting at a POS: I don't go to work tomorrow unless I feel better. You should replace the: "don't" with: won't.
Overall, D is the most acceptable answer.
Two pounds of grapes cost 6 dollars how many pounds can you buy with 1 dollar?
Step-by-step explanation:
If €2 of grapes cost $6
$1 =2/6
=€0.3
verify that (0,0) is a critical point, show that the system is locally linear, and discuss the type and stability of the critical point (0,0) by examining the corresponding linear system.
dx/dt=(1+x)siny
dy/dt=1-x-cosy
Based on the information given in the question the (0, 2kπ) maybe the spiral point or center point of the nonlinear system. The stability of (0, 2kπ) is indeterminate.
what is differential equations?An equation comprising one or more functions and their derivatives is known as a differential equation in mathematics. A function's derivative expresses the rate of change of the function at a specific moment. It is mostly employed in the sciences of physics, engineering, and biology.
F = (1 + x) sin y = 0
G = 1 − x − cos y = 0
we know that all the critical points are (0, 2kπ), (2,(2k + 1)π). Since the F, G are
continuous differentiable, the system is almost linear near the critical points.
µ
Fx Fy Gx Gy=µsin y (1 + x) cos y−1 sin y
The linear system near critical point (2,(2k + 1)π) is
du/dt = −3v, dv/dt = −u
where u = 2 + x, v = (2k + 1)π + y. The eigenvalues of the linear system are −√3,√3,hence the critical point (2,(2k + 1)π) is saddle point and unstable. The linear system
near critical point (0, 2kπ) is
du/dt = v
dv/dt = −u, where u = x, v = 2kπ + y. The eigenvalues of the linear system are −i, i, hence the
critical point (0, 2kπ) is center point and stable of the corresponding linear system. Then (0, 2kπ) maybe the spiral point or center point of the nonlinear system. The stability of (0, 2kπ) is indeterminate.
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Determine the most conservative sample size for the estimation of the population proportion for the following: E = 0.029, confidence level 95% Round your answer up to the nearest whole number. the absolute tolerance is +/-1
the most conservative sample size for the estimation of the population proportion is 4471, rounded up to the nearest whole number.
Using the formula n = (Zα/2)^2(p*(1-p))/E^2, where:
n = sample size
Zα/2 = z-score for 0.025 (α/2) = 1.96
p = 0.5 (assumed to be the estimated proportion of the population)
E = 0.029 (specified absolute tolerance)
n = (1.96^2)*(0.5(1-0.5))/0.029^2 = 4471
Therefore, the most conservative sample size for the estimation of the population proportion is 4471, rounded up to the nearest whole number.
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a family is thinking about buying a house costing 350,000. they will pay 20% down, and the rest to be amoritized over 30 years
The family monthly payment on annual interest is 1691.
What is annual interest rate?
The annual interest produced by a sum that is paid to investors or charged to borrowers is referred to as the annual percentage rate (APR). APR is a percentage that expresses the actual annual cost of borrowing money throughout the course of a loan or the revenue from an investment.APR stands for annual percentage rate, which takes fees into account. The APR is stated as a percentage, just like an interest rate. It does, however, contain other costs or fees such mortgage insurance, the majority of closing costs, discount points, and loan origination fees, unlike an interest rate.Calculation of amount payable to the bank
Cost of House - 350000
Down payment 10% - 35000
Amount payable - 315000
]5% Annual interest rate and compounded monthly is 186.28030751
A) family monthly payment= Amount payable/Annuity factor =315000/186.28030751 =1691
B)Total interest paid on loan =293756.40
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The sum of the kinetic and potential energy of the particles in an object is the ______ of the object.
a.Heat. b.state c.temperature. d.thermal energy
Answer: Thermal energy
Step-by-step explanation:
Thermal energy is the sum of the kinetic and potential energy of all the particles in an object.
Question 4(Multiple Choice Worth 5 points)
(Pythagorean Theorem LC)
Can a triangle be formed with side lengths 3, 9, 17? Explain.
O No, because 3+9 <17
O Yes, because 3 +9> 17
O No, because 17-3<9
O Yes, because 17-9<3
Answer:
O No, because 3²+9² <17²
Step-by-step explanation:
O No, because 3²+9² <17²
. If Total assets = $34,500 and Total liabilities = $28,000, Owner's equity =
A. $5,600
OB. $65,200
O C. $6,500
O D. $62,500
Answer:
C. $6,500
Step-by-step explanation:
Owner's equity is the amount of the business's assets that are owned by the owner or shareholders. It is calculated by subtracting the total liabilities from the total assets.
Given that Total assets = $34,500 and Total liabilities = $28,000, the owner's equity is:
Owner's equity = Total assets - Total liabilities
= $34,500 - $28,000
= $6,500
Therefore, the correct answer is C. $6,500.
Valeria invested $770 in an account paying an interest rate of 53% compounded
monthly. Zoey invested $770 in an account paying an interest rate of 5%
compounded continuously. To the nearest dollar, how much money would Zoey have
in her account when Valeria's money has tripled in value?
4
Answer:
[tex]\$856.03[/tex]
Step-by-step explanation:
Continuous Compound Interest Formula:The Continuous Compound Interest Formula is derived from the Compound Interest Formula: [tex]A = P(1 + \frac{r}{n})^{nt}[/tex], as the number of times interest is applied, goes to infinity. Through some simple algebraic manipulation, we get the formula: [tex]A = Pe^{rt}[/tex] (e is known as Euler's Number and is notation for a constant value like [tex]\pi[/tex])
Calculating Time:Since Valeria invested 770 in an account with an interest of 53% paying monthly, we want to find how much time it takes to triple her money, and then plug that into Zoey's equation.
So let's generally solve for time in the equation:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
First divide by P
[tex]\frac{A}{P} = (1 + \frac{r}{n})^{nt}[/tex]
From here, it helps to take the base 10 log of both sides, so we can apply logarithmic properties, in this case we want to bring the exponent down.
[tex]log(\frac{A}{P}) = nt * log(1 + \frac{r}{n})[/tex]
Now from here' lets divide both sides by the log (the one on the right side) and "n" to give us:
[tex]\frac{log(\frac{A}{P})}{n * log(1 + \frac{r}{n})} = t[/tex]
Now whenever we need to calculate time, we simply need to plug in these values. We're given the following information from the problem:
[tex]P = 770\\r = 0.53\\n = 12\text{ compound monthly means 12 per year}\\A= 2,310 \text{ this is just 770 * 3, since we're looking for when Valeria's money triples}[/tex]
Plugging in the values we get:
[tex]\frac{log(\frac{2310}{770})}{12*log(1+\frac{0.53}{12}}=t[/tex]
Plugging this into a calculator, gives an approximate value of:
[tex]2.1183\approx t[/tex]
Calculating Zoey's Balance:From here we simply need to plug values into the continuous compound interest formula: [tex]A=Pe^{rt}[/tex]
We're given the following information:
[tex]A = 770\\r= 0.03\\[/tex]
and we know that:
[tex]t\approx 2.1183[/tex]
since we solved for that.
So now let's just plug values into the equation!
[tex]A\approx 770 * e^{0.05 * 2.1183}\\A \approx 856.03[/tex]
So now we have our solution!
Which math expression means "52 more than an unknown number"?
A. x + 52
B. X÷52
C. 52.x
D. x - 52
← PREVIOUS
SUBMIT
As per the statement in the question, the expression will be x + 52.
What are arithmetic operations?The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.
They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.
As per given information in the question,
Let the unknown number is x.
The statement says that the number is more than 52.
Then, the expression according to the statement will be,
= x + 52
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El tercer término de una progresión
geométrica vale 80, y la razón es 4. Calcula la
suma de los cinco primeros términos
Answer:
Suma= 80 + (4 × 40) + (4 × 20) + (4 × 10) + (4 × 5)
Suma= 80 + 160 + 80 + 40 + 20
Suma= 400
Step-by-step explanation:
The sum of the first five terms of the geometric progression is 1705.
To calculate the sum of the first five terms of a geometric progression, we need to determine the first term and the common ratio. Given that the third term is 80 and the ratio is 4, we can find these values.
In a geometric progression, each term is obtained by multiplying the previous term by the common ratio. Let's denote the first term as "a" and the common ratio as "r."
Given that the third term is 80, we can write the equation:
a * r² = 80
We are also given that the ratio is 4, so we have:
r = 4
Substituting this value of r into the equation, we get:
a * (4)² = 80
a * 16 = 80
16a = 80
a = 5
Now that we have determined the first term (a = 5) and the common ratio (r = 4), we can calculate the sum of the first five terms using the formula for the sum of a geometric series:
Sum = a * (1 - rⁿ) / (1 - r)
Plugging in the values, we have:
Sum = 5 * (1 - 4⁵) / (1 - 4)
Simplifying the calculation:
Sum = 5 * (-1023) / (-3)
Sum = 1705
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A city council consists of 10 members. Four are Republicans, three are Democrats, and three are Independents. If a committee of three is to be selected, find the probability of selection..
1. All Republicans. Round your answer to five decimal places. ??
2. All Democrats. Round your answer to five decimal places. ??
3. One of each party. Round your answer to five decimal places. ??
4. Two Democrats and one Independent. Round your answer to five decimal places. ??
5. One Independent and two Republicans. Round your answer to five decimal places.??
HELP ASAP AND THANKS! :)
The expression for the interest earned on each account and the balance after 3 years are;
1) Interest = P(1 + 0.039t)
Balance = $485.90
2) Interest = P(1.039)^(t)
Balance = $487.91
3) Interest = P(1.039)^(t)
Balance = $487.91
4) Interest = 435e^(0.039t)
Balance = $488.99
How to calculate the simple interest?We are given different formulas for interest and we are told to find the balance of each option after 3 years. Thus, we have;
1) P(1 + rt)
Where;
P is principal = $435
r is rate = 0.039
t is time = 3 years
We have;
Balance = 435(1 + (0.039 * 3))
Balance = $485.90
2) P(1 + (r/n))^(nt)
Where;
P is principal = $435
r is rate = 0.039
t is time = 3 years
n is number of times interest is compounded per year = 1 (because it is yearly)
Thus;
A = 435(1 + (0.039/1))^(3 * 1)
A = $487.91
3) Same as 2 above
4) P₀e^(rt)
where;
P₀ is principal = $435
r is rate = 0.039
t is time = 3 years
Thus;
A = 435(e^(0.039 * 3)
A = $488.99
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Use ΔABC, shown to the right, to answer the following question.
If AK=31. What is KP??
The intersection of the two medians results in a 1:2 division. Consequently, the KP value is 15.5.
Given,
Triangle ABC is shown;
Triangle;-
A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.
Here,
If AK = 31 and we are aware that the two medians coincide, then the division is 1:2.
Then,
KP/AK = 1/2
KP = AK / 2
KP = 31/2
KP = 15.5
Therefore,
The value of KP is 15.5 units.
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Rick deposits $3 into his bank account. The following week, he deposits 3 times that amount. Each week after that, he deposits 3 times the amount he did the previous week. How much does he deposit in all during the first 3 weeks?
Answer:
Step-by-step explanation:
Rick desposits 3$ into his account:
b=Rick's bank balance
b+3
The following week, he deposits 3 times that amount:
3*3=9
2nd week= b+9
Each ewek after that, he deposits 3 times the amount he did the previous week:
3rd week = b+9x3
3rd week = b+27
How much does it deposit in all during the first 3 weeks?
1st week = $3
2nd week = $9
3rd week = $27
3+9+27=39
ANSWER:Rick deposits $39 in the first 3 weeks
Answer for second question:
d=dollars
w=weeks
d=[tex]d=3^2[/tex]
"One who performs his duty without attachment, surrendering the results unto the Supreme Lord, is unaffected by sinful action, as the lotus leaf is untouched by water." - Krishna, Bhagavad Gita 5.10
Thanks, I hope I could help
Miraculous21
Shown following are several times in the history of the universe. Rank these times from left to right based on the peak wavelength in the spectrum of the cosmic microwave background, from shortest to longest.
100 million years after the Big Bang
1.5 billion years after the Big Bang
500,000 years after the Big Bang
1 million years after the Big Bang
today
Based on the highest wavelength in the cosmic microwave background spectrum, rank these eras from left to right, from shortest to longest, 500,000 years after the Big Bang.
What is the wavelength's peak?Peak Wavelength - The maximum wavelength at which a light source's radiometric emission spectrum is observed is referred to as the peak wavelength. Simply put, it represents photo-detectors rather than the human eye's perception of any emission from the light source.
What can we infer from the peak wavelength?The temperature can be calculated using the Wien displacement law and the peak wavelength. On a chromaticity diagram, the variation in apparent hue of stars at various temperatures can be traced.
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Assume that all intersecting sides meet at right angles. Be sure to include the correct unit in your answer.
One of the four fundamental mathematical operations is addition. The length of the missing side is 6 yd.
What exactly is addition?
Addition is one of the four basic mathematical operations, along with subtraction, multiplication, and division. The total quantity or sum of two whole numbers is obtained by adding them together.
According to the question,
All the line intersecting at right angles . So,
The lines AB, CD, and EF are parallel in the diagram, we can write the length of AB as,
AB length = EF length - CD length
= 14yd - 8yd
= 6yd
As a result, the missing side length is 6yd
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Which of the points below does not lie on the curve y = x² ?
A: (3/2, 9/2) B: (-1,1) C: (4,16) D: (1/2,1/4)
Answer:
Point A does not lie on the curve y = x²
Step-by-step explanation:
Given points:
[tex]\sf A: \left(\dfrac{3}{2}, \dfrac{9}{2}\right)[/tex]
[tex]\sf B: \left(-1,1 \right)[/tex]
[tex]\sf C: \left(4,16 \right)[/tex]
[tex]\sf D: \left(\dfrac{1}{2}, \dfrac{1}{4}\right)[/tex]
To determine if the given points lie on the curve y = x², simply substitute the x-value of each point into the equation and compare y-values.
Point A
[tex]\boxed{\begin{aligned}x=\dfrac{3}{2} \implies y&=\left(\dfrac{3}{2} \right)^2\\\\y&=\dfrac{3^2}{2^2}\\\\y&=\dfrac{9}{4}\end{aligned}}[/tex]
As 9/4 ≠ 9/2, point A does not lie on the curve.
Point B
[tex]\boxed{\begin{aligned}x= -1\implies y&=\left(-1 \right)^2\\y&=1\end{aligned}}[/tex]
As 1 = 1, point B does lie on the curve.
Point C
[tex]\boxed{\begin{aligned}x=4 \implies y&=\left( 4\right)^2\\y&=16\end{aligned}}[/tex]
As 16 = 16, point C does lie on the curve.
Point D
[tex]\boxed{\begin{aligned}x=\dfrac{1}{2} \implies y&=\left(\dfrac{1}{2} \right)^2\\\\y&=\dfrac{1^2}{2^2}\\\\y&=\dfrac{1}{4}\end{aligned}}[/tex]
As 1/4 = 1/4, point D does lie on the curve.
Let a ⇑ b = a² + b². What is the value of [(3 ⇑ 1) ⇑ 2] − [3 ⇑ (1 ⇑ 2)]?
The numeric value of the expression [(3 ⇑ 1) ⇑ 2] − [3 ⇑ (1 ⇑ 2)] is given as follows:
70.
How to obtain the numeric value of the expression?The operator for this problem is given as follows:
a ⇑ b = a² + b².
Then the operations are made following the precedence of operations, due to the parenthesis, as follows:
(3 ⇑ 1) = 3² + 1² = 9 + 1 = 10.(1 ⇑ 2) = 1¹ + 2² = 1 + 4 = 5.Then the expression can be written as follows:
[(3 ⇑ 1) ⇑ 2] − [3 ⇑ (1 ⇑ 2)] = [10 ⇑ 2] − [3 ⇑ 5].
Then the operators are calculated as follows:
10 ⇑ 2 = 10² + 2² = 100 + 4 = 104.3 ⇑ 5 = 3² + 5² = 9 + 25 = 34.Finally, the subtraction is applied between these two results to obtain the numeric value of the expression, as follows:
104 - 34 = 70.
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our new magazine initially sells 400 copies per month. research indicates that a vigorous advertising campaign could increase sales by 30% each month if our market were unlimited. but research also indicates that magazine sales in our area are unlikely to exceed 2000 per month. make a logistic model of projected magazine sales. (use t as your variable. round b to three decimal places.)
The logistic model of the projected magazine sales is P = e¹⁰⁰⁰/1+e¹⁰⁰⁰
What is meant by logistic model?
In math, logistic model refers a statistical analysis method to predict a binary outcome, such as yes or no, based on prior observations of a data set.
Here we have given that our new magazine initially sells 400 copies per month. research indicates that a vigorous advertising campaign could increase sales by 30% each month if our market were unlimited. but research also indicates that magazine sales in our area are unlikely to exceed 2000 per month.
Here we need to make a logistic model of projected magazine sales.
As per the formula of logistic model, while we looking into the given question, we identified the values,
a = 400
x = 30% => 0.3
b = 2000
Then the logistic model of the given situation is written as,
=> P = e⁴⁰⁰⁺⁰°³ˣ²⁰⁰⁰/ 1 + e⁴⁰⁰⁺⁰°³ˣ²⁰⁰⁰
=> P = e¹⁰⁰⁰/1+e¹⁰⁰⁰
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A motorboat travels 192 kilometers in 3 hours going upstream and 360 kilometers in 4 hours going downstream. What is the rate in still water and the rate of the current
To find the rate in still water, we need to find the average speed of the boat. The total distance traveled by the boat is 192 + 360 = 552 kilometers. The total time taken is 3 + 4 = 7 hours.
So, the average speed of the boat is 552/7 = 78.857 km/hr.
To find the rate of the current, we need to find the difference in speed between the upstream and downstream journeys. The difference in speed is 360/4 - 192/3 = 90 - 64 = 26 km/hr.
So, the rate of the current is 26 km/hr.
Therefore, the rate in still water is 78.857 km/hr and the rate of the current is 26 km/hr.
Is it true m ⊥ p? Your response should be at least 3 complete sentences. Be sure to include any relevant measurements and calculations.
No, the lines are not perpendicular because Line m has a slope of 2/3 and line p has a slope of -5/3.
What is the slope of a line which passes through points ( p,q) and (x,y)?Its slope would be:
[tex]m = \dfrac{y-q}{x-p}[/tex]
Slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.
For two lines to be perpendicular then the slopes are reciprocal of each other.
Line m: (-3,2) (3,6)
line m: 2/3
Line p: (3,-4) (-3,6)
x₁=3 x₂=-3 y₁=-4 y₂=6
p = -5/3
Therefore,
m ⊥ p is False.
The slopes are not negative reciprocal of each other. therefore the lines are not perpendicular.
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PLEASE HELP ME ILL WHOEVER ANSWER BRAINLIEST PLEASE ACTUALY ANSWER THE QUESTION NEED RIGHT ANSWER Solve. 4 1/4−1/3x=−3/4 Enter your answer in the box. x =
Answer:
-9/47
Step-by-step explanation:
[tex]4 \frac{1}{4}x-\frac{1}{3}x=-\frac{3}{4} \\ \\ \frac{17}{4}x-\frac{1}{3}x=-\frac{3}{4} \\ \\ 51x-4x=-9 \\ \\ 47x=-9 \\ \\ x=-\frac{9}{47}[/tex]
Answer:
Step-by-step explanation:
- 5/12
i did the test lol
What is the slope of the graph of y = -3x? need answer now asap
-3
3
-1/3
1/3
Answer:
Step-by-step explanation:
The slope of the graph of y = -3x is -3. The slope of a line is the amount that the line rises or falls for every unit it moves horizontally. In this case, the line rises by -3 units for every 1 unit it moves horizontally. This means that the slope of the line is -3.
The points (-7, r) and (-3, 14) lie on a line with slope 3. Find the missing coordinate r.
The value of the missing coordinate, r as required to be determined from the given information is; r = 2.
What is the value of the missing coordinate, r?It follows from the task content that the value of the missing coordinate, r is to be determined from the task content.
On this note, since the given points are; (-7, r) and (-3, 14) and the slope of the line through them is; 3.
It follows from the slope formula;
m = (y₂ - y₁) / (x₂ - x₁) that;
3 = ( 14 - r ) / ( -3 -(-7) )
-9 + 21 = 14 - r
r = 14 + 9 - 21
r = 2.
On this note, the required value of the missing coordinate, r is; 2.
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URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
The two figures would be similar if the value of x is 31 mm. Thus option D.
On comparison of two or more shapes, they will only be similar if they all have a set of common corresponding properties. These properties may be due to their corresponding length of sides, or measure of internal or external angles.
To determine the value of x that would make the shapes to be similar, compare the corresponding sides of the shapes.
So that we have;
[tex]\frac{14.5}{29}[/tex] = [tex]\frac{15.5}{x}[/tex]
make x the subject of the formula
x = [tex]\frac{29*15.5}{14.5}[/tex]
= 31
x = 31 mm
The value of x that would make the two figures similar is 31 mm.
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Each page of a top-secret report on aliens requires 2 KB of space in digital format. What is the maximum number of pages the report can have so that it can be completely stored on a USB drive that holds 4*10^6 KB?
Write your answer in scientific notation, and round to one decimal place. ______ pages
The maximum number of pages the report can have in scientific notation is equal to 2.0×10⁶ pages.
Scientific Notation is the expression in which numbers are written in the powers of 10 so that their expression can be used in calculation and also it makes calculation easy. To find the maximum number of pages the report can have, we need to divide the size of the USB drive, which is 4×10⁶ KB, by the size of each page, which is 2 KB/page. Doing this gives us:
4×10⁶ KB / 2 KB/page = 2×10⁶ pages
Rounding to one decimal place gives us: 2,000,000.0 pages
So, the maximum number of pages the report can have is 2,000,000.0 pages. In scientific notation, this is: 2.0×10⁶ pages.
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Find an equation for the conic that satisfies the given conditions. parabola, focus (2, −1), vertex (2, 5)
The equation of the parabola with focus (2, -1) and vertex (2, 5) is
[tex](x-2)^2[/tex]= -24(y - 5).
An equation of a parabola with focus ( 0, p ) and directrix y = − p is
[tex]x^2[/tex] = 4py, p < 0
Here, we have the focus = (2, -1) and vertex = (2, 5)
substituting the values in the above equation we get,
p = -1 - 5 = -6
hence, p = -6
now let us find the equation of the parabola as follows-
[tex](x-2)^2[/tex]= 4p(y - 5)
[tex](x-2)^2[/tex]= 4 (-6) (y - 5)
[tex](x-2)^2[/tex]= -24(y - 5)
Hence, the equation of the parabola with focus (2, -1) and vertex (2, 5) is
[tex](x-2)^2[/tex]= -24(y - 5).
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