Answer:
a = 2/27
b = 13/27
Step-by-step explanation:
The given polynomial is presented as follows;
f(x) = a·x³ + b·x² + x + 2/3
Given that x + 3 is a factor, we have;
f(-3) = 0 = a·(-3)³ + b·(-3)² - 3 +2/3 = 0
-27·a + 9·b - 3 + 2/3 = 0
-27·a + 9·b = 7/3........(1)
Also we have
(a·x³ + b·x² + x + 2/3) ÷ (x + 2) the remainder = 5
Therefore;
a·(-2)³ + b·(-2)² + (-2) + 2/3 = 5
-8·a + 4·b - 2 + 2/3 = 5
-8·a + 4·b = 2 - 2/3 = 4/3........(2)
Multiplying equation (1) by 4/9 and subtracting it from equation (2), we have;
-8·a + 4·b - 4/9×(-27·a + 9·b) = 4/3 - 4/9 × 7/3
-8·a + 12·a = 8/27
4·a = 8/27
a = 2/27 ≈ 0.0741
imputing the a value in equation (1) gives;
-27×2/27 + 9·b = 7/3
-2 + 9·b = 7/3
9·b = 7/3 + 2 = 13/3
b = 13/27 ≈ 0.481.
The admission fee at an amusement park is $20 for children and $35 for adults. On a certain day, 390 people entered the park, and the admission fees collected totaled $10650. How many children and how many adults were admitted? NUMBER OF CHILDREN= ? NUMBER OF ADULTS= ?
Answer:
Children = 200
Adults = 190
Step-by-step explanation:
Children = x
Adults = y
x + y = 390
x = 390 - y..............(1)
20x + 35y = 10650
Substituting
20(390-y) + 35y = 10650
y = 190
x = 390 - 190 = 200
Answer:
Step-by-step explanation:
Number of children = c
Number of adults = a
Total people = 390
a + c = 390 ------------------ (I)
Admission fee for 'c' children = 20 * c = 20c
Admission fee for 'a' adult = 35 * a = 35a
Total amount = $ 10650
35a + 20c = 10650 -------------(II)
Multiply equation (I) by (-20)
(I)*(-20) -20a - 20c = - 7800
(II) 35a + 20c = 10650 { Now add and so 'c' will be eliminated}
15a = 2850
a = 2850/15
a = 190
Plug in a = 190 in equation (I)
190 + c = 390
c = 390 - 190
c = 200
Number of children = 200
Number of adults = 190
Work out angle x Triangles are not drawn to scale
Answer:
1) x = 71°, 2) x = 27°, 3) x= 32°
Step-by-step explanation:
1) Rectangle ABCD.
∠D = 90°
From ΔABE.
∠EAB +∠ABE + ∠BEA = 180°
45 + 90 +∠BEA = 180
∠BEA = 45
∠BEA + ∠AED +∠DEC = 180 °, because ∠BEC is a straight angle
45 + x + 64 = 180
x = 71°
2) Δ XYZ is equilateral, all angles = 60°.
∠YZX = 60°.
∠YZW = 180°, because it is a straight angle.
∠YZX + ∠XZW= 180
60 + ∠XZW= 180
∠XZW = 120.
From ΔXZW
∠ZXW + ∠XWZ + WZX = 180
x + 33 + 120 = 180
x = 27°
3) In ΔPQR,
PQ = PR, so ∠PQR = ∠PRQ = 69°
∠PRQ + ∠PRS = 180, because ∠QRS = 180° as straight angle.
∠PRQ + ∠PRS = 180
69 + ∠PRS = 180
∠PRS = 111°.
From ΔPRS
∠PRS + ∠RSP + ∠SPR = 180
111 + 37 + ∠SPR = 180
111 + 37 + x= 180
x = 32
On Friday, Mica has $22.50 in her bank account. Mica goes to the market to get groceries for the week and ends up spending more than planned. When Mica checks her account, she now has a balance of $-48.15. How much money did Mica spend at the market?
Answer: $70.65
Step-by-step explanation:
From the question, we are informed that Mica has $22.50 in her bank account and then she goes to the market to get groceries for the week and ends up spending more than planned. She later checks her account and found out that she now has a balance of $-48.15.
To get the amount of money that Mica spent at the market, we subtract her balance from the opening balance she had in her bank account. This will be:
= $22.50 - (-$48.15)
= $22.50 + $48.15
= $70.65
Mics spent $70.65 at the market.
If two lines meet at a right angle they are said to be _________ to each other.
Answer: perpendicular
Answer:
perpendicular
Step-by-step explanation:
If two lines meet at a right angle they are said to be perpendicular to each other.
Two lines are perpendicular when they intersect at a right angle.
Which represents the reflection of f(x) = x over the y-axis?
х
-1
0
1
4
f(x)
undefined
0
1
2
f(x)
х
-1
0
1
1
0
-1
-2
4
Answer:
Graph having x ≤ 0
Step-by-step explanation:
f(x) = [tex]\sqrt{(-x)}[/tex]
Given function 'f' when reflected across the y--axis,
Translated form of the parent function will be,
g(x) = [tex]\sqrt{(-x)}[/tex]
Table for the input-output values for this function will be,
x g(x)
-1 1
0 0
1 undefined
4 undefined
Table shows that the given function is undefined for x > 0
Domain of g(x) will be (-∞, 0],
Therefore, graph having values of x ≤ 0 will be the answer.
Answer:
I think its D on edge!
Step-by-step explanation:
solved in addition and use multiplication!! PLEASE HELP ASAP!
Answer:
First by 3, second by -2.
Step-by-step explanation:
You need to get the x-factor to the smallest common multiple of 4 and 6, which is 12.
But also, if you add both, they should cancel out the x term, i.e.,:
-12x + 12x = 0
You get that by multiplying by 3 and -2, respectively.
The nth term of a sequence is n(n - 1).
What are the first four terms?
What is the 50th term?
Is 59 a term in the sequence?
Which term is 182?
The ______ th term
Answer:
T1=0
T2=2
T3=6
T4=12
T50=2450
59 is not a term in the sequence
Step-by-step explanation:
Tn=n(n-1)
182=n2 - n
0=n2 - n - 182
0=n2-14n+13n-182
0=n(n-14)+13(n-14)
0=(n-14) (n+13)
Since n cannot be negative n is not equal to -13
Therefore,
n=14
Five thousand tickets are sold atâ $1 each for a charity raffle. tickets are to be drawn at random and monetary prizes awarded asâ follows: 1 prize of â$500â, 3 prizes of â$300â, 5 prizes of â$30â, and 20 prizes ofâ $5. what is the expected value of this raffle if you buy 1â ticket?
Answer:
-$0.67
Step-by-step explanation:
If you buy one ticket, the possible outcomes are:
100% chance of spending $1 (buying the ticket)
1 in 5,000 chance of winning $500
3 in 5,000 chance of winning $300
5 in 5,000 chance of winning $30
20 in 5,000 chance of winning $5.
The expected value of the raffle is determined by:
[tex]E(X)=-1+\frac{1}{5,000}*500+\frac{3}{5,000}*300+\frac{5}{5,000}*30+\frac{20}{5,000}*5\\E(X)=-\$0.67[/tex]
The expected value of this raffle if you buy 1 ticket is -$0.67.
Imagine a player getting ready for a tournament. He has 4 games to play during the day: 9:00 a.M., 11:00 a.M., 1:00 p.M., and 3:30 p.M. He refuses to wear shorts until temperature rises to at least +5 degrees. Based on a starting temperature of -9 degrees at 6am and an increase in temperature of 2 degrees an hour, when might he be able to change from his pants to shorts? Provide explanations why he can/can't put his shorts on for Game 1, Game 2, Game 3 and Game 4.
Answer:
by game 3(at 1:00 p.m.)
temperature increases to 5 degrees at 1:00 p.m
The probability that Paul wins a raffle is given by the expression n/n + 6 . What is the expression, in the form of a combined single fraction, for the probability that Paul does not win.
Answer:
The probability that he doesn’t win is 6/(n + 6)
Step-by-step explanation:
Mathematically, the probability that an event occur is 1 minus the probability that the event doe not occur.
Thus, what we are saying here is that the sum of the probabilities that Paul wins the raffle draw and he doesn’t win the raffle draw is 1
This can be mathematically expressed as;
probability that he doesn’t win = 1 - probability that he wins
Thus we have;
1- n/(n+ 6)
= [(n+ 6) -(n)]/(n+6) = 6/n+ 6
A $3,000 bond has coupons at a rate 12% paid semi-annually and matures on December 1st, 2025 at $3,200. Find the practical clean and dirty book values of this bond on October 15th, 2020 to yield 6% convertible semi-annually.
Answer:
Clean price is $3,977.22
Dirty price = $4110.99
Step-by-step explanation:
We proceed as follows;
Semiannual coupon payments = $3000* 12%/2 = 6% * 3,000 = 6/100 * 3,000 = $180
Coupons are paid on 1st June and 1st December every year(semi-annually means twice a year, every 6 months)
No. of payments remaining = 11 (1 payment in 2020 on 1st December,2020 and 2 in each of the following 5 years)
Semiannual Yield = 6%/2 =3%
The clean price of the bond is given by
P = 180/1.03+ 180/1.03^2+.....+180/1.03^11+ 3200/1.03^11
=180/0.03*(1-1/1.03^11)+3200/1.03^11
=$3977.22
Dirty price = clean price +accrued interest
Accrued Interest = Interest from 1st June , 2020 to 1st December,2020
= no of days from 1st June to 15th October/no of days from 1st June to 1st December * $180
= 136/183*$180
=$133.77
So, Dirty price = $3977.22+$133.22 = $4110.99
A pack of cards is numbered 1 to 24. A card is chosen at random. Find the probability that the number on the card is divisible by 2 or 3
Answer:
Step-by-step explanation:
It's simple. So the only cards which are divisible by 2 or 3 are: 2,3,4,6,8,9,10,12,14,15,16,18,20,21,22,24. The formula of probability is P= m/n. Where m-Number of ways it can happen and n- Total number of outcomes.
Our answer is P= 16/24=2/3=66,66%
Can someone help me
Answer:
y=22cm
Step-by-step explanation:
using L×B=A where y is L
308=14y
y=308/14
y=22cm
Plzzz helpppp urgenly❤️
Answer:
[tex]\mathrm{D.} \: (\frac{5}{4} )^{\frac{7}{2}[/tex]
Step-by-step explanation:
[tex]\sqrt{(\frac{5}{4})^7 }[/tex]
Apply rule : [tex]\sqrt{a} =a^{\frac{1}{2} }[/tex]
[tex]((\frac{5}{4})^7 )^{\frac{1}{2} }[/tex]
Apply rule : [tex](a^b)^c=a^{bc}[/tex]
[tex](\frac{5}{4} )^{7 \times \frac{1}{2} }[/tex]
[tex](\frac{5}{4} )^{\frac{7}{2}[/tex]
Kevin cuts lawns during the summer months. He charges $10 plus $5 per hour. The algebraic model is C = 5h + 10, where C represents the total cost and h represents the hours worked. Use pencil and paper to create a table of values for hours worked from 1 to 5, incrementing h by 1 in each row.
Answer:
1 hour : 15 dollars
2 hours: 20 dollars
3 hours: 25 dollars
4 hours: 30 dollars
5 hours: 35 dollars
Step-by-step explanation:
Substitute the hour number in for h and solve. for example, if you were trying to find 5 hours, you would produce the equation c = 5(5) + 10. once you solve that you get c = 25 + 10 which is also c = 35.
Which of the following equations is graphed below?
Answer: 3rd answer choice
Step-by-step explanation:
Answer: 4th answer choice
Step-by-step explanation:
Suppose you invest $2250 in a D that earns 3% APR and is compounded monthly. The Cd matures in 2 years. How much will this CD be worth at maturity?
Answer:
$2388.95
Step-by-step explanation:
Principal, P= $2250Annual Interest Rate, r= 3% =0.03Time, n= 2 yearsSince it is compounded monthly, Period, k= 12 MonthsThe worth of a compound deposit after a period of n years is calculated using the formula:
[tex]A(n)=P(1+\frac{r}{k})^{nk}[/tex]
[tex]A(2)=2250(1+\frac{0.03}{12})^{12 \times 2}\\\\=2250(1+0.0025)^{24}\\=2250(1.0025)^{24}\\=\$2388.95[/tex]
At maturity, the deposit will be worth $2388.95.
PLZ HELP 10POINTS EASY HELP!!!!!!!!!!
Answer:
2nd no is corret
Step-by-step explanation:
as altitude is defined as a st. line meeting its base forming 90degree angle.
Answer:
I think the second answer, JH is an altitude of GJI, is the correct answer.
Step-by-step explanation:
Having JH be an altitude of GJI means that it makes a 90 degree angle. And to prove that it's a 90 degree angle we look at where it has the little squares. The squares represent 90 degrees.
Hope this helps!
Em determinada loja, o lucro obtido pela venda de x fones de ouvido, em reais, pode ser representado pela expressão algébrica 7x-17. Qual será o lucro obtido por essa loja se forem vendidos 13 fones de ouvido?
Answer:
74 reais
Step-by-step explanation:
Em uma determinada loja, o lucro obtido com a venda de fones de ouvido x, em reais, pode ser representado pela expressão algébrica 7x-17. Quanto lucro esta loja terá se vender 13 fones de ouvido?
O lucro é representado como 7x - 17
onde x = número de fones de ouvido vendidos
Se 13 fones de ouvido foram vendidos, o lucro será:
(7 * 13) - 17
= 91 - 17
= 74 reais
Yuri measures the height of the water in an aquarium in one metric unit. He then moves the decimal point three units to the left. Which pair of measurements might he be converting? Use the metric table to help answer the question.
Answer:the answer A( kiloliters to liters)
Answer:
Millimeter to Meter
Step-by-step explanation:
Pleaseeeeeee. Helpppppppppppp meeeeeeeeeeee
Answer:
first tower needs 4
second needs 3
third needs 2
and the fourth needs 1
Total needed triangles for all is 10
Step-by-step explanation:
What is the appropriate symbol? 1.42 _____ 1.420 = < >
Answer:
=
Step-by-step explanation:
1.42 is equal to 1.420. The 0 adds no value since it is after the decimal point so 1.420 is just 1.42, which is equal to itself, 1.42.
Answer:
=
Step-by-step explanation:
When you are looking at decimals, specifically on the right side of the decimal point, the amount of 0's after the last given non-0 digit can be disregarded.
1.420 is the same as 1.42
With this given information:
1.42 ____ 1.420
1.42 ____ 1.42
1.42 = 1.42
= would be your sign.
~
Explain the significance of the equation 100x -2y+ 400 = 0 which represents the hourly cost of a car repair.
Answer: The significance is that it is how much you will pay for the total repair which will help you know how much money you will spend.
Step-by-step explanation:
What is the measure of Angle c? 3 lines intersect to form 5 angles. Clockwise, from top left, the angles are b, 90 degrees, c, 124 degrees, a.
Answer:
c
Step-by-step explanation:
Answer:the answer is 90
Step-by-step explanation:
solve (-t-5)/3= (t-3)/5
Answer & Step-by-step explanation:
[tex]\frac{-t-5}{3}=\frac{t-3}{5}[/tex]
Cross multiply.
[tex]-5t-25=3t-9[/tex]
Subtract -3 on both sides.
[tex]-8t-25=-9[/tex]
Add 25 on both sides.
[tex]-8t=16[/tex]
Divide -8 on both sides.
[tex]t=-2[/tex]
The volume of a cone with a height of 6 cm is 8 pi cubic centimeters. Which expression can be used to find r, the radius of the base of the cone? 6 = one-third pi (r squared) (8 pi) 8 pi = one-third pi (r) (6 squared) 6 = one-third (pi r)(8 pi) 8 pi = one-third pi (r squared) (6)
Answer:
last option is correct
Step-by-step explanation:
Mathematically, we can write the volume of a cone as;
V = 1/3 * pi * r^2 * h
From the question, V is 8 pi cm^3 while h is 6cm
Thus, substituting these values into the equation, we have;
8pi = 1/3 * pi * r^2 * 6
The last option is the correct answer that tallies with the above
Answer:
8 pi = one-third pi (r squared) (6)
its d
Step-by-step explanation:
How is the graph of the cosine function different from the graph of the sine function? How is it the same?
Answer:
Similarity:
In Both cosine and sine graphs, a positive and negative number vertically flips the graph and tells whether the graph starts at maximum (positive) or minimum (negative).
Difference:
The difference between the sine and the cosine graph is the point where they start.
The graph of positive cosine starts at the maximum while that of the negative cosine starts at the minimum.
The graph of a positive sine starts at the middle, goes up and then down while that of the negative sine starts at the middle goes down and then up.
Please answer this question fast in 2 minutes
Answer:
<5solution,
<3+<4=180°( linear pair)----> equation (i)
<4+<5=180°( linear pair)------>equation (ii)
From equation (i) and (ii)
<3+<4=<4+<5
<3=<5 (vertically opposite angles)
hope this helps...
Good luck on your assignment
. Una persona desea realizar una pintura para su próxima exposición en donde esta tenga tres colores fluorescentes y dos colores pastel, al realizar la revisión de su paleta de pintura, este artista cuenta con siete colores fluorescentes y cinco colores pastel. De lo anterior se puede indicar que la cantidad de maneras en que puede realizar la pintura como lo desea es *
A. 305.
B. 350.
C. 405.
D. 450
Answer: B. 350.
Step-by-step explanation:
Given: Total number of fluorescent colors = 7
Total number of pastel colors = 5
Since , he want three fluorescent colors and two pastel colors.
Number of ways to select r things out of n things = [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
Number of ways to choose colors = [tex]^7C_3\times\ ^5C_2[/tex]
[tex]=\dfrac{7!}{3!4!}\times\dfrac{5!}{2!3!}\\\\=\dfrac{7\times6\times5\times4!}{3\times2\times1\times4!}\times\dfrac{5\times4\times3!}{2\times3!}\\\\=350[/tex]
Hence, the correct option is B. 350.
I need help with this question please help