The expression x²-10x-21 is wrong since the product of two negative signs is equal to positive.
Simplifying factorsQuadratic equations are equations that has a leading degree of 2. The standard quadratic equation is given as;
f(x) = ax^2+bx+c
Given the product of the expression below;
f(x) = (x-3)(x-7)
Expand
f(x) = x(x) - 7x - 3x -3(-7)
f(x) = x^2 - 7x - 3x + 21
f(x) = x^2 - 10x + 21
Hence the expression x²-10x-21 is wrong since the product of two negative signs is equal to positive.
Learn more on factoring here: https://brainly.com/question/25829061
#SPJ1
IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
If the radius of the circle is 5 m and angle subtended by arc LKM is 70° then the length of the arc LNM is 25.29 m.
Given that the radius of the circle is 5 m and angle subtended by arc LKM is 70°.
From the figure given we can estimate that the length of arc LNM can be circumference of circle subtracted by length of arc LKM.
Circulference of the circle is basically the length of whole arc of the circle. It is also know as perimeter of the circle. The formula of calculating circumference of a circle is 2πr in which r is the radius.
So,
length of arc LNM=Circumference of circle-length of arc LKM.
We know that length of an arc =Θr
in which Θ is the angle in radian.
length of arc=70*π[tex]/180*5[/tex]
=70π[tex]/36[/tex]
Circumference of circle=2π*5
=10π
Length of arc LNM=10π-70π[tex]/36[/tex]
=(360π-70π)[tex]/36[/tex]
=290π[tex]/36[/tex]
Put π=3.14
=290*3.14[tex]/36[/tex]
=910.6[tex]/36[/tex]
=25.29m
Hence the length of arc LNM is 25.29 m.
Learn more about arc at https://brainly.com/question/2005046
#SPJ1
I need help with this slope
Answer:
B, C
Step-by-step explanation:
Look at the lower blue point.
Its coordinates are (4, 3).
The x-coordinate, 4, stands for minutes.
The y-coordinate, 3, stands for number of boxes.
This is a slope of 3/4, corresponding to 0.75 boxes per minute, or 3 boxes every 4 minutes.
Answer: B, C
Answer:
3 boxes are filled every 4 minutes.
Step-by-step explanation:
Look at the graph; at the bottom of the graph, it is shown that every __ minutes, __ boxes are filled. If you look at the first shown blue point on the left of the graph, it shows that on the fourth minute, three boxes are filled, as from the axis, you go right four and up three.
Find and sketch the domain of f(X,y) = 1/√x^2-y
Answer:
Step-by-step explanation:
The definition of a Domain in math is all the possible input values that go into the function, so we will have to find all the valid values that can go into the function
The function given is [tex]F(x, y)=\frac{1}{\sqrt{x^2-y} }[/tex] , the denominator cannot be 0.
So we set up the equation
[tex]\sqrt{x^2-y} \neq 0[/tex]
[tex]\sqrt{x^2-y}^{2} \neq 0x^2-y\neq 0x^2\neq y[/tex]
And that the the square root needs to be more than 0.
[tex]\sqrt{x^2-y}\geq 0[/tex]
[tex]x^2-y\geq 0[/tex]
[tex]x^2\geq y[/tex]
So we can conclude that all values of [tex]x^{2}[/tex] must be greater y
That means that our domain is all X values greater than[tex]\sqrt{y}[/tex]
How long do you need to invest your money in an account earning an annual interest rate of 4.252% compounded monthly so that your investment grows from $1,018.40 to $10,413.00 over that period of time?
The time needed for the investment to become $10,413 is 54.7 years
How long before $1,018.40 grows to $10,413.00?Number of years = (In FV / PV) / r
FV = future valuePV = present valuer = interest rater = 4.252/12 = 0.354%
(In 10, 413 / 1,018.40) / 0.00354 = 656.73 months = 54.7 years
To learn more about how to determine the number of years an investment would be equal to a certain value, please check: https://brainly.com/question/21841217
#SPJ1
Which equation is represented by the graph below?
A. Y= 1/8e^x
B. Y= 1/2e^x
c. Y=2e^x
D. Y= 8e^x
#49
Answer:
B
Step-by-step explanation:
When x = 1, it appears y is in between 1 and 2.
The only choice that satisfies this is B.
Answer:
The equation that represents the graph is y=2e^x
Step-by-step explanation:
plug in geogebra and confirm:D
Use the following regression equation regarding airline tickets to answer the question.
Price = 49 + 0.137 · (Distance)
Note that Distance is the amount of kilometres between the departure and arrival cities, and Price is the cost of an airline
ticket.
Interpret the slope of the regression equation in the context of the data.
The interpretation of the slope is the price of an airline ticker per kilometer is 0.137
How to interpret the slope?The regression equation is given as:
Price = 49 + 0.137 · (Distance)
A regression equation is represented as
y = b + mx
Where m represents the slope
By comparison, we have
m = 0.137
Slopes are used to represent average rates
This means that the interpretation of the slope is the price of an airline ticker per kilometer is 0.137
Read more about regression equation at:
https://brainly.com/question/14184702
#SPJ1
PLEASE HELP!
A game board with 17 spaces. Start, green, green, star, quesiton mark, question mark, star, question mark, green, cat town, green, green, star, question mark, green, green, star, green, end.
You are playing a board game and your playing piece begins the game at START. You roll a single number cube numbered 1 to 6 to find out how many spaces you can move.
What is the theoretical probability of landing on a question mark space on your first roll.
A 1/6
B 1/4
C 1/3
D 1/2
Answer:
C 1/3
Step-by-step explanation:
out of the 6 possible moves you have the possibility of landing on question mark twice. 2/6 -> 1/3
A tank originally contains 100 gallon of fresh water. Then water containing 0.5 Lb of salt per gallon is pourd into the tank at a rate of 2 gal/minute, and the mixture is allowed to leave at the same rate. After 10 minute the process is stopped, and fresh water is poured into the tank at a rate of 2 gal/min, with the mixture again leaving at the same rate. Find the amount of salt in the tank at end of an additional 10 minutes.
Let [tex]S(t)[/tex] denote the amount of salt (in lbs) in the tank at time [tex]t[/tex] min up to the 10th minute. The tank starts with 100 gal of fresh water, so [tex]S(0)=0[/tex].
Salt flows into the tank at a rate of
[tex]\left(0.5\dfrac{\rm lb}{\rm gal}\right) \left(2\dfrac{\rm gal}{\rm min}\right) = 1\dfrac{\rm lb}{\rm min}[/tex]
and flows out with rate
[tex]\left(\dfrac{S(t)\,\rm lb}{100\,\mathrm{gal} + \left(2\frac{\rm gal}{\rm min} - 2\frac{\rm gal}{\rm min}\right)t}\right) \left(2\dfrac{\rm gal}{\rm min}\right) = \dfrac{S(t)}{50} \dfrac{\rm lb}{\rm min}[/tex]
Then the net rate of change in the salt content of the mixture is governed by the linear differential equation
[tex]\dfrac{dS}{dt} = 1 - \dfrac S{50}[/tex]
Solving with an integrating factor, we have
[tex]\dfrac{dS}{dt} + \dfrac S{50} = 1[/tex]
[tex]\dfrac{dS}{dt} e^{t/50}+ \dfrac1{50}Se^{t/50} = e^{t/50}[/tex]
[tex]\dfrac{d}{dt} \left(S e^{t/50}\right) = e^{t/50}[/tex]
By the fundamental theorem of calculus, integrating both sides yields
[tex]\displaystyle S e^{t/50} = Se^{t/50}\bigg|_{t=0} + \int_0^t e^{u/50}\, du[/tex]
[tex]S e^{t/50} = S(0) + 50(e^{t/50} - 1)[/tex]
[tex]S = 50 - 50e^{-t/50}[/tex]
After 10 min, the tank contains
[tex]S(10) = 50 - 50e^{-10/50} = 50 \dfrac{e^{1/5}-1}{e^{1/5}} \approx 9.063 \,\rm lb[/tex]
of salt.
Now let [tex]\hat S(t)[/tex] denote the amount of salt in the tank at time [tex]t[/tex] min after the first 10 minutes have elapsed, with initial value [tex]\hat S(0)=S(10)[/tex].
Fresh water is poured into the tank, so there is no salt inflow. The salt that remains in the tank flows out at a rate of
[tex]\left(\dfrac{\hat S(t)\,\rm lb}{100\,\mathrm{gal}+\left(2\frac{\rm gal}{\rm min}-2\frac{\rm gal}{\rm min}\right)t}\right) \left(2\dfrac{\rm gal}{\rm min}\right) = \dfrac{\hat S(t)}{50} \dfrac{\rm lb}{\rm min}[/tex]
so that [tex]\hat S[/tex] is given by the differential equation
[tex]\dfrac{d\hat S}{dt} = -\dfrac{\hat S}{50}[/tex]
We solve this equation in exactly the same way.
[tex]\dfrac{d\hat S}{dt} + \dfrac{\hat S}{50} = 0[/tex]
[tex]\dfrac{d\hat S}{dt} e^{t/50} + \dfrac1{50}\hat S e^{t/50} = 0[/tex]
[tex]\dfrac{d}{dt} \left(\hat S e^{t/50}\right) = 0[/tex]
[tex]\hat S e^{t/50} = \hat S(0)[/tex]
[tex]\hat S = 50 \dfrac{e^{1/5}-1}{e^{1/5}} e^{-t/50}[/tex]
After another 10 min, the tank has
[tex]\hat S(10) = 50 \dfrac{e^{1/5}-1}{e^{1/5}} e^{-1/5} = 50 \dfrac{e^{1/5}-1}{e^{2/5}} \approx \boxed{7.421}[/tex]
lb of salt.
The Royal Fruit Company produces two types of fruit drinks. The first type is 55% pure fruit juice, and the second type is 80% pure fruit juice. The company is attempting to produce a fruit drink that contains 70% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 140 pints of a mixture that is 70% pure fruit juice?
We need 56 pints of the 55 % pure fruit juice and 84 pints of the 80 % pure fruit juice to prepare 140 pints of 70 % pure fruit juice.
How to use weighted averages to find the correct juice concentration
In this problem we have to use two kinds of juice with different concentrations. To get a certain concentration, we must adjust quantities of each kind and weighted averages offers a method that is easy to apply:
70 · 140 = 55 · x + 80 · (140 - x)
70 · 140 = 80 · 140 - 25 · x
25 · x = 10 · 140
x = 56
We need 56 pints of the 55 % pure fruit juice and 84 pints of the 80 % pure fruit juice to prepare 140 pints of 70 % pure fruit juice.
To learn more on weighted averages: https://brainly.com/question/28042295
#SPJ1
PLEASE PLEASE PLEASE answer this question!!! FROM KHAN ACADAMY PRE ALGEBRA
Answer:
B
Step-by-step explanation:
Hope this helps:)
Answer:
B & D
Step-by-step explanation:
A The variable "x" is canceled does not apply
B One solution
C does not apply
D One solution
Hope this helps
A truack Cars a load of 50 boxes 50 men are 20kg boxes and the rest and 25 ка Boxes. Is the Total weight of all Boxes is 1175 kg. How many of each type are there? X = 50kg Y=20kg 2= 25kg then sum of that is 1175 kg
The number of boxes with 20kg = 15
The number of boxes with 25 kg = 35.
How to estimate the value of X and Y?
To estimate the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to estimate the result.
Total weight of all boxes = 1175kg
Total number of boxes = 50
X + Y = 50........................(1)
20X + 25Y = 1175 .............(2)
(1) [tex]\times[/tex] 20
20 (X + Y = 50)
20X + 20Y = 1000 .............(3)
Subtracting (3) from (2), we get
20X + 25Y = 1175 -
20X + 20Y = 1000
--------------------
5Y = 175
Y = 175/5
Y = 35
Substitute the value of y in (1), then we get
X + Y = 50
X + 35 = 50
X = 50 - 35
X = 15
The value of X = 15 and Y = 35
Number of boxes with 20kg = 15
Number of boxes with 25 kg = 35.
To learn more about the value of x and y refer to:
https://brainly.com/question/25476188
#SPJ9
Blossom company , a machinery dealer leased manufacturer equipment to Mays corporation on January 1, 2017. The lease is a 7 year period and requires equal annual payments of $26143 at the beginning of each year . The first payment is received on January 1, 2017 . Blossom had purchased the machine during 2016 for $75000 collectibility of lease payments is reasonable predictable, and no important uncertainties surround the amount of cost yet to be incurred by blossom se the annual rentel to ensure a 8% rate of return . The machine has an economic life of 8 years with no resiidaul value and reverts to blossom at the termination of the lease.A. Compute the amount of the lease receivable
The amount of the lease receivable will be $146999.
What are lease receivable?It should be noted that lease receivables means all the payments under the operative documents in respect of:
(i) the Purchaser Basic Rent,
(ii) the Maximum recourse amount,
(iii) the Purchaser Balance and
(iv) any purchase by the Lessee of the Properly up to the amount of the Capital then outstanding.
In this case, the lease is a 7 year period and requires equal annual payments of $26143 at the beginning of each year and the first payment is received on January 1, 2017.
The lease receivable will be:
= PVAD8%,7 × Lease payment
= 5.62288 × 26143
= $146999
In conclusion, the lease receivable is $146999.
Learn more about lease receivable on:
https://brainly.com/question/25760475
#SPJ1
Country A has an exponential growth rate of 3.8% per year. The population is currently ,000, and the land area of Country A is 35,000,000,000 square yards. Assuming this growth rate continues and is exponential, after how long will there be one person for every square yard of land?
The number of years it would it take for there to be one person for every square yard is 93.6 years.
How many years would it take for there to be one person for every square yard?When there is one person for every square yard, it means that the population and land area are equal in value.
Number of years = (In FV / PV) / r
FV = future population PV = present population r = rate of growth(In 35 billion / 1 billion) / 0.038 = 93.6 years
Here is the complete question:
Country A has an exponential growth rate of 3.8% per year. The population is currently 1,000,000 ,000 and the land area of Country A is 35,000,000,000 square yards. Assuming this growth rate continues and is exponential, after how long will there be one person for every square yard of land?
To learn more about exponential functions, please check: https://brainly.com/question/26331578
#SPJ1
The terminal side of Ø is in quadrant II and cos ø = -5/13 What is sin ø?
the value of sin ∅ is 12/ 13
Quadrants and the "cast" Rule:In the first quadrant, the values for sin, cos, and tan are positive.In the second quadrant, the values for sin are positive only.In the third quadrant, the values for tan are positive only.In the fourth quadrant, the values for cos are positive only.From the given question,
We have, cos ∅= 5/13
From the trigonometric identities, we have that
[tex]sin^2\alpha + cos^2\alpha = 1[/tex]
Then , let's substitute the value of cos ∅
[tex]sin^2\alpha +(\frac{-5}{13} )^2 = 1[/tex]
Let make sin the subject of formula and find the squares of the fraction
sin²∅ = [tex]1 - \frac{25}{169}[/tex]
Find the LCM
sin²∅ = [tex]\frac{169 - 25}{169}[/tex]
Find the difference
sin²∅ = [tex]\frac{144}{169}[/tex]
Find the square root
sin∅ = [tex]\sqrt{\frac{144}{159} }[/tex]
sin∅ = [tex]\frac{12}{13}[/tex]
In quadrant II , sin is positive, so we have
sin ∅ = 12/ 13
Thus, the value of sin ∅ is 12/ 13
Learn more about quadrant here:
https://brainly.com/question/863849
#SPJ1
If f(x) = 3x4 + 2x3 - x + 15,
what would be the list of
possible rational roots?
Answer: A. ± [tex]\frac{1}{3} ,\frac{5}{3} ,1,3,5,15[/tex]
Step-by-step explanation:
± [tex]\frac{1, 3, 5, 15}{1, 3}[/tex]
= ± [tex]1, 3, 5, 15, 1/3, 5/3, 5[/tex]
Rearranging, we get:
= ± [tex]\frac{1}{3} ,\frac{5}{3} ,1,3,5,15[/tex]
A compression wave is moving away from an explosion at 100 ft/sec. How fast is the volume within the spherical compression wave increasing in t = 4 seconds? You will need the formula for the volume of a sphere! *Leave π in your answer do not convert to a decimal!
The volume within the spherical compression wave increasing in t = 4 seconds is:64000000π cubic ft/sec.
Volume of a sphereGiven:
dr/dt=100 ft/sec
When: t=4 seconds, radius(r)=400ft
Hence:
Volume of a sphere (V)=4/3πr³
dv/dt=4/3π.3r² dr/dt
dv/dt=4πr²dt/dr
When t=4 seconds
dv/dt=4π×(100×4)²×100 cubic ft/sec
dv/dt=4π×(400)²×100 cubic ft/sec
dv/dt=64000000π cubic ft/sec
Therefore the volume within the spherical compression wave increasing in t = 4 seconds is:64000000π cubic ft/sec.
Learn more about Volume of a sphere here:https://brainly.com/question/22807400
#SPJ1
Solution for the attached question below
The solution to the question is 265.
What is the logarithm of a number?Logarithm of a number A is the exponent or power or index n, a given number called the base B would be raised to give the number A.
So n is the logarithm of A to base B.
Analysis:
log 2( log2(x-9)) = 3
log2(x-9) = [tex]2^{3}[/tex]
log2(x-9) = 8
x-9 = [tex]2^{8}[/tex]
x-9 = 256
x = 256 + 9
x = 265
Learn more about logarithm: brainly.com/question/25710806
#SPJ1
Two cars start at the same time, but travel in opposite directions. One car's average speed is 80 miles per hour (mph). At the end of 2 hours, the two cars are 220 miles apart. Find the average speed in mph of the other car.
The speed of an object is the relationship between the distance covered by the object and the time taken. Thus, the average speed of the other car is 30 mph.
The speed of an object is the relationship between the distance covered by the object and the time taken. The expression for speed is given as;
speed = [tex]\frac{distance covered}{time taken}[/tex]
⇒ distance = speed x time taken
In the given question, the distance of the first car after 2 hours can be determined as:
distance = 80 mph x 2 h
= 160 miles
The distance covered by the first car after 2 hours is 160 miles.
Thus, since the total distance between the two cars after 2 hours is 220 miles, then;
distance covered by the second car = 220 miles - 160 miles
= 60 miles
The distance covered by the second car is 60 miles.
So that the average speed of the other car is;
speed = [tex]\frac{60}{2}[/tex]
= 30 mph
The average speed is 30 miles per hour (mph).
For more clarifications on the speed of an object, visit: https://brainly.com/question/24749487
#SPJ1
What kind of multi step do I have to do to prove a is parallel to b and m parallel to n.
The proof that line n is perpendicular to both a and b is proved below using definition of right angle and perpendicular transversal theorem.
How to prove Perpendicular and Parallel Lines?
We are given that;
Line a is parallel to line b
Line m is parallel to line n.
A) We want to prove that line a is perpendicular to n.
From the image, we see that there is a right angle sign on the opposite side of ∠1 facing m.
Now, we know that by definition of a right angle that ∠1 will also be a right angle.
Since angle 1 is a right angle, then we can say the line transversal a is perpendicular to line m.
B) We want to prove that line b is perpendicular to n.
The definition of the perpendicular transversal theorem, states that if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.
Thus, b will be perpendicular to n.
Read more about Perpendicular and parallel lines at; https://brainly.com/question/13657035
#SPJ1
Which of the following is NOT a criterion for making a decision in a hypothesis test?
Choose the correct answer below.
OA. If P-values a, the decision is to reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
OB. If the test statistic falls within the critical region, the decision is to reject the null hypothesis.
OC. If a confidence interval does not include a claimed value of a population parameter, the decision is to reject
the Inull hypothesis.
OD. If the P-value is less than 0.05, the decision is to reject the null hypothesis. Otherwise, we fail to reject the null
hypothesis.
If the p-value less than 0.05, the decision is to reject the Null hypothesis.
What is hypothesis testing?Hypothesis testing is statistical reasoning using information from a sample to draw conclusions about a population parameter or population probability distribution. The parameter or distribution is initially bestguessed. Because it is the underlying assumption, the null hypothesis is often referred to as H0.For instance, you might explore and find that a specific drug effectively manages headaches. But nobody will believe what you find if you can't do that experiment again.A hypothesis seeks to provide an answer to a question. We will be forced to think about the results an experiment should try to achieve by a formulated hypothesis.The independent variable is the first variable. Results with seriousness.The following should NOT be used as a decision-making standard in a hypothesis test.
If the p-value less than 0.05, the decision is to reject the Null hypothesis.
To learn more about the hypothesis, refer to:
https://brainly.com/question/606806
#SPJ9
18. Sam retires in 1996. He has an amount of R350 000 available to invest. He decides to buy a second house for 50% of the money, which he lets at an amount of R2000 per month. He increases the rent every year by an amount of R300. The balance of R175 000 he invests in the bank at a rate of 12%. He uses the interest every month to supplement his income, so the interest is not compounded. He also gets a pension of R3000 per month, which is increased by R300 per month every year. What was his monthly income in 1996? (1)
If Sam had Rs. 350000 and invested Rs.175000 in house, in bank Rs.175000 and getting 3000 pension then the monthly income was Rs. 6750.
Given that Sam had Rs.350000,investment in house Rs.175000 at a rent of Rs.2000 per month and Rs.175000 in bank at rate of 12%, getting pension of Rs.3000 per month.
We are required to find the monthly income in 1996.
We have assumed that Sam was retired on 1st January, 1996 so the amount of rent, investment in bank and pension did not increase because they had to be increase in a year and we have to calculate the monthly income in which he was retired.
Monthly income=Rent of 1 month+Simple interest of 1 month+Pension per month
=2000+175000*1/100+3000
=2000+1750+3000
=Rs.6750
Hence if Sam had Rs. 350000 and invested Rs.175000 in house, in bank Rs.175000 and getting 3000 pension then the monthly income was Rs. 6750.
Learn more about simple interest at https://brainly.com/question/25793394
#SPJ1
The terms 1/64, 1/32, 1/16 form a geometric progression (GP) If the sum of the GP is (2^36 – 2^-6), find the number of terms
If [tex]a[/tex] is the first term and [tex]r[/tex] is the common ratio of the series, then the sum of the first [tex]n[/tex] terms is
[tex]S_n = a + ar + ar^2 + \cdots + ar^n[/tex]
Multiply by [tex]r[/tex] on both sides, then subtract that from and solve for [tex]S_n[/tex].
[tex]rS_n = ar + ar^2 + ar^3 + \cdots + ar^{n+1}[/tex]
[tex](1-r)S_n = a - ar^{n+1}[/tex]
[tex]S_n = \dfrac{a(1-r^{n+1})}{1-r}[/tex]
Use the given first and second terms of the sequence to find [tex]a[/tex] and [tex]r[/tex].
[tex]a = \dfrac1{64}[/tex]
[tex]ar = \dfrac1{32} \implies \dfrac r{64} = \dfrac1{32} \implies r = \dfrac{64}{32}=2[/tex]
Solve for [tex]n[/tex].
[tex]S_n = \dfrac{1-2^{n+1}}{64(1-2)} = 2^{36} - 2^{-6}[/tex]
[tex]\dfrac{2^{n+1} - 1}{2^6} = 2^{36} - 2^{-6}[/tex]
[tex]2^{n-5} - 2^{-6} = 2^{36} - 2^{-6}[/tex]
[tex]\implies n-5 = 36 \implies \boxed{n = 41}[/tex]
I have the question shown in the screenshot
The width and height of the rectangle inscribed in the right triangle have a measure of 3.529 units.
How to find the dimensions of the rectangle of maximum area by optimization
In this problem we must use critical values and algebraic methods to determine to determine the dimensions of the rectangle such that the area is a maximum. The equation of the quadrilateral is formed by definition of the area of a rectangle:
A = w · h (1)
Where:
w - Width of the rectangle.h - Height of the rectangle.And the area of the entire triangle is:
0.5 · (5) · (12) = w · h + 0.5 · w · (12 - h) + 0.5 · (5 - w) · h
30 = w · h + 6 · w - 0.5 · w · h + 2.5 · h - 0.5 · w · h
30 = 6 · w + 2.5 · h
2.5 · h = 30 - 6 · w
h = 12 - 2.4 · w (2)
The quadrilateral of maximum area is always a square, then we must solve for w = h:
w = 12 - 2.4 · w
3.4 · w = 12
w = 3.529
Then, the width and height of the rectangle inscribed in the right triangle have a measure of 3.529 units.
To learn more on optimizations: https://brainly.com/question/15319802
#SPJ1
Emily purchased a bond valued at $20,000 for highway construction for $10,460. If the bond pays 7.2%
annual interest compounded monthly, how long must she hold it until it reaches its full face value?
...
Answer:
26.556192
Step-by-step explanation:
7.2×10460÷100
20000÷(7.2×10460÷100)
A jar has 16 marbles, 10 green, 2 blue, 4 red. what is the probability of randomly choosing a red marble then without putting it back, choosing a green marble?
The probability of drawing a red marble and then a green marble is:
P = 1/6.
How to find the probability?In the jar we have a total of 16 marbles, such that:
10 are green.2 are blue4 are red.First, the probability of getting a red marble is give by the quotient between the number of red marbles and the total number of marbles:
p = 4/16 = 1/4
Now we need to draw a green one, the probability is computed in the same way, but this time there are 15 marbles, because we already took one.
q = 10/15
The joint probability (first drawing red, then green) is given by the product between the individual probabilities:
P = p*q = (1/4)*(10/15) = 10/60 = 1/6
If you want to learn more about probability:
https://brainly.com/question/25870256
#SPJ1
101 101 Suppose that Σ ai = -12 and Σ bi = -19. i=1 i=1 Compute the sum. 101 Σ( – 5ai – 12bi) i=1
Distribute the summation over the sum.
[tex]\displaystyle \sum_{i=1}^{101} (-5a_i - 12b_i) = -5 \sum_{i=1}^{101} a_i - 12 \sum_{i=1}^{101} b_i[/tex]
Now plug in the known sums and simplify.
[tex]\displaystyle \sum_{i=1}^{101} (-5a_i - 12b_i) = -5(-12) - 12(-19) = \boxed{288}[/tex]
-11r is greater than or less than -20
Evaluate the expression.
n =
If P(n, 5) = 2520, find n.
The value of n in the permutation equation P(n, 5) = 2520 is 7
How to evaluate the permutation expression?The expression is given as:
P(n, 5) = 2520
The above expression is a permutation expression.
The permutation expression is different from the combination expression, and the permutation expression is calculated using the following permutation formula
P(n,r) = n!/(n - r)!
Substitute 5 for r in the above equation
P(n,5) = n!/(n - 5)!
Substitute the given values in the above equation
n!/(n - 5)! = 2520
Expand the above equation
n(n-1)(n - 2)(n - 3)(n - 4)(n - 5)!/(n - 5)! = 2520
Evaluate the quotient in the above equation
n(n-1)(n - 2)(n - 3)(n - 4) = 2520
Express 2520 as 7 * 6 * 5 * 4 * 3
n(n-1)(n - 2)(n - 3)(n - 4) = 7 * 6 * 5 * 4 * 3
By comparing the equation, we have
n = 7
Hence, the value of n in the permutation equation P(n, 5) = 2520 is 7
Read more about permutation at:
https://brainly.com/question/11732255
#SPJ1
f(x)=2x. If g(x) is a vertical stretch, compression, and or reflection of f(x) followed by a, what is the equation of g(x)?
The function g(x) is g(x)= (3x)^2
How to solve for g(x)?
The complete question is in the image
From the graph in the image, we have:
f(x) = x^2
The function f(x) is stretched by a factor of 3 to form g(x).
This means that:
g(x) = f(3x)
So, we have:
g(x)= (3x)^2
Hence, the function g(x) is g(x)= (3x)^2
Read more about function transformation at:
brainly.com/question/10222182
#SPJ1
Math man fell from the top of a 500 meter building. The equation d = t squared * 0.25 describes math man's distance from the ground as he falls. How long does math man spend falling if he falls all the way from the top of the building to the ground? Round your answer to the nearest tenth.
Based on the equation of the function of the height of the building, it takes the man 44.7 seconds to fall from the top
How to determine how long it takes the math man to fall?The function of the height where the man falls is a quadratic function, and the equation of the function is given as:
d = t^2 * 0.25
The height of the building is 500
This means that the value of d is 500.
So, we have;
d = 500
Substitute 500 for d in the equation d = t^2 * 0.25
500 = t^2 * 0.25
Divide both sides of the above equation by 0.25
500/0.25 = t^2 * 0.25/0.25
Evaluate the quotient in the above equation
t^2 = 2000
Take the square root of both sides in the above equation
√t^2 = √2000
Evaluate the exponent
t = 44.7
Hence, it takes the man 44.7 seconds to fall
Read more about quadratic functions at:
https://brainly.com/question/12446886
#SPJ1