9514 1404 393
Answer:
converges
Step-by-step explanation:
The common ratio is 20/25 = 16/20 = 4/5. The magnitude of this is less than 1, so the series converges.
If there was a system where 5 points was equivalent to $1 how many points would $43 be?
Answer:
Step-by-step explanation:
5 pts = $1
$43 × (5 pts)/$1 = 43×5 pts = 215 pts
Find the absolute extrema of the function over the region R. (In each case, R contains the boundaries.) Use a computer algebra system to confirm your results. (Order your answers from smallest to largest x, then from smallest to largest y.)
f(x, y) = x2 − 4xy + 5
R = {(x, y): 1 ≤ x ≤ 4, 0 ≤ y ≤ 2}
f(x, y) = x ² - 4xy + 5
has critical points where both partial derivatives vanish:
∂f/∂x = 2x - 4y = 0 ==> x = 2y
∂f/∂y = -4x = 0 ==> x = 0 ==> y = 0
The origin does not lie in the region R, so we can ignore this point.
Now check the boundaries:
• x = 1 ==> f (1, y) = 6 - 4y
Then
max{f (1, y) | 0 ≤ y ≤ 2} = 6 when y = 0
max{f (1, y) | 0 ≤ y ≤ 2} = -2 when y = 2
• x = 4 ==> f (4, y) = 12 - 16y
Then
max{f (4, y) | 0 ≤ y ≤ 2} = 12 when y = 0
max{f (4, y) | 0 ≤ y ≤ 2} = -4 when y = 2
• y = 0 ==> f (x, 0) = x ² + 5
Then
max{f (x, 0) | 1 ≤ x ≤ 4} = 21 when x = 4
min{f (x, 0) | 1 ≤ x ≤ 4} = 6 when x = 1
• y = 2 ==> f (x, 2) = x ² - 8x + 5 = (x - 4)² - 11
Then
max{f (x, 2) | 1 ≤ x ≤ 4} = -2 when x = 1
min{f (x, 2) | 1 ≤ x ≤ 4} = -11 when x = 4
So to summarize, we found
max{f(x, y) | 1 ≤ x ≤ 4, 0 ≤ y ≤ 2} = 21 at (x, y) = (4, 0)
min{f(x, y) | 1 ≤ x ≤ 4, 0 ≤ y ≤ 2} = -11 at (x, y) = (4, 2)
Supervisor: "I need you to increase the number of customers you talk to daily by
20%."
Employee: "I talk to an average of 8 customers per hour during an 8 hour shift so
now I'll need to talk to customers per day."
68
77
85
97
160
NEXT
Answer:
77
Step-by-step explanation:
Currently:
Talk to 8 customers per hour, work 8 hours, so:
Talk to 8*8 = 64 customers.
With the increase:
Has to increase by 20%, so 64 is multiplied by 1 + 0.2 = 1.2. Then
64*1.2 = 76.8
Rounding up, 77 is the answer.
If the nominal rate of interest is 10% per annum and there is quarterly compounding, the effective rate of interest will be: a) 10% per annum b) 10.10 per annum c) 10.25%per annum d) 10.38% per annum
9514 1404 393
Answer:
d) 10.38%
Step-by-step explanation:
The multiplier for four quarters of quarterly compounding is ...
(1 +10%/4)^4 = 1.025^4 = 1.103812890625
This is about 1 + 10.38%.
The effective rate of interest is about 10.38% per annum.
Help only #31,33, please thank you
Answer:
31) 4d + 28 33) 10 + 5
Step-by-step explanation:
31) 4 ( d + 7) = 4 x 7 = 28 = 4d + 28
33) 5 ( 2m + 1 ) = 5. 2m + 5 . 1: 10m + 5
A bag of 31 tulip bulbs contains 13 red tulip bulbs, 9 yellow tulip bulbs, and 9 purple tulip bulbs. Suppose two tulip bulbs are randomly selected without replacement from the bag. (a) What is the probability that the two randomly selected tulip bulbs are both red? (b) What is the probability that the first bulb selected is red and the second yellow? (c) What is the probability that the first bulb selected is yellow and the second red? (d) What is the probability that one bulb is red and the other yellow?
Answer:
36% on first
Step-by-step explanation:
please help me with this on the image
Answer:
we will then have to also multiply the y with three so the answer is B and that's ( ×3)
a swimming pool is 130 feet long and the length is 3 times the width plus 10 feet. Let x be the width of the pool. how wide is the pool?
Answer:Perimeter of a rectangle is 2*the length plus 2*the width
P = 2L + 2W and P = 130, so
L + W = 65
Three times the length is equal to 10 times the width, giving
3L = 10W
Substituting into the above for L = 65 – W,
3(65 – W) = 10W
195 – 3W = 10W
195 = 13W
W = 195/13 = 15
W = 15 yards,
And L = (10/3)W = (10/3)*15 = 50
L = 50 yards
Step-by-step explanation:
To host an event at a popular convention center, it costs $300 plus $45 per person attending. Step 1 of 3 : Write a rational expression that represents how much you would need to charge each attendee in order to cover the cost of hosting the event. Let x be the number of attendees.
Answer: (300 + 45x) / x
Step-by-step explanation:
Based on the information given in the question, the total cost will be the addition of the fixed cost and the variable cost which will be:
= 300 + (45 × x)
= 300 + 45x
The amount that needs to be charge for each attendee in order to cover the cost of hosting the event will be:
= (300 + 45x) / x
Please help me with this someone
9514 1404 393
Answer:
79 23/24 yards
Step-by-step explanation:
10 5/8 +24 5/6 +44 1/2 = (10 +24 +44) +(5/8 +5/6 +1/2)
= 78 +(15/24 +20/24 +12/24) = 78 +47/24 = 79 23/24 . . . yards
_____
Express the fractions over a common denominator, add, and convert back to a mixed number. Here, the fraction cannot be reduced.
47/24 = 1 23/24
Evaluate the expression 2x - (4y - 3) + 5xz, when x = -3, y = 2, and z = -1.
Answer:
4
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
Identify
2x - (4y - 3) + 5xz
x = -3
y = 2
z = -1
Step 2: Evaluate
Substitute in variables: 2(-3) - (4(2) - 3) + 5(-3)(-1)(Parenthesis) Multiply: 2(-3) - (8 - 3) + 5(-3)(-1)(Parenthesis) Subtract: 2(-3) - 5 + 5(-3)(-1)Multiply: -6 - 5 + 15Subtract: -11 + 15Add: 4convert the following decimals to a simplified fraction. showing all work
Hello.
Answer:
1/200, 667/500
I hoped this helped
A box contains 100 tickets labeled with numbers. The average of the labels is 14 and the SD of the labels is 8.2. Eighteen tickets will be drawn independently at random with replacement from the box. The chance that the absolute value of the difference between the sample sum of the labels on the tickets and 252 does not exceed 278.32 is: __________
Answer:
at most
Step-by-step explanation:
The sample drawn from the population is a relative representation not the absolute representation. The box has 100 tickets in it and sample of tickets is selected to identify difference between sample sum and 252. The at most value for the sample sum can be 278.32 and value cannot exceed beyond this.
Convert the following numbers into scientific notation. ( i did them but I feel like they wrong can y’all correct them if they are?)
Answer:
only 4 is incorrect...
1,450,000 = 1.45 x [tex]10^{6}[/tex] NOT
1,450,000 = 1.45 x [tex]10^{7\\}[/tex]
Step-by-step explanation:
Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place. Below, enter your answers so that
∠A1 is smaller than ∠A2.)
b = 129, c = 168, ∠B = 48°
Angle A1 Angle A2
Angle C1 Angle C2
side a1 side a2
Answer:
∠A1 = 27.4°, ∠A2 = 56.6°, ∠C1 =104.6°, ∠C2=75.4°, a1 = 79.9 and a2 = 144.9
Step-by-step explanation:
From Sine rule
[tex]\frac{a}{sinA}=\frac{b}{sinB} = \frac{c}{sinC}[/tex]
∴ b / sinB = c / sinC
From the question,
b = 129, c = 168 and ∠B = 48°
∴ 129 / sin48° = 168 / sinC
Then, sinC = (168×sin48)/129
sinC = 0.9678
C = sin⁻¹(0.9678)
C = 75.42
∠C2=75.4°
and
∴∠C1 = 180° - 75.4°
∠C1 =104.6°
For ∠A
∠A1 = 180° - (104.6°+48°) [sum of angles in a triangle]
∠A1 = 27.4°
and
∠A2 = 180° - (75.4° + 48°)
∠A2 = 180° - (123.4°)
∠A2 = 56.6°
For side a
a1/sinA1 = b/sinB
a1/ sin27.4° = 129/sin48
a1 = (129×sin27.4°)/sin48
a1 = 79.8845
a1 = 79.9
and
a2/sinA2 = b / sinB
a2/ sin56.6° = 129/sin48
a2 = (129×sin56.6°)/sin48
a2 = 144.9184
a2 = 144.9
Hence,
∠A1 = 27.4°, ∠A2 = 56.6°, ∠C1 =104.6°, ∠C2=75.4°, a1 = 79.9 and a2 = 144.9
Find the mean, median, and mode of the following data. If necessary, round to one more decimal place than the largest number of decimal places given in the data.
MLB Batting Averages
0.2750.275 0.3190.319 0.3140.314 0.2800.280 0.2880.288
0.3140.314 0.2950.295 0.2960.296 0.3170.317 0.2760.276
0.2740.274 0.2890.289 0.2950.295 0.2760.276 0.2750.275
0.2960.296 0.3110.311 0.2890.289 0.2830.283 0.3120.312
Answer:
0.2937 ;
0.292 ;
0.275, 0.314, 0.295, 0.296, 0.276, 0.289
Step-by-step explanation:
0.275 0.319 0.314 0.280 0.288 0.314 0.295 0.296 0.317 0.276 0.274 0.289 0.295 0.276 0.275 0.296 0.311 0.289 0.283 0.312
Reordered data :
0.274, 0.275, 0.275, 0.276, 0.276, 0.280, 0.283, 0.288, 0.289, 0.289, 0.295, 0.295, 0.296, 0.296, 0.311, 0.312, 0.314, 0.314, 0.317, 0.319
The mean : ΣX / n ; n = sample size, = 20
Mean = 5.874 / 20 = 0.2937
The median : 1/2(n+1)th term
Median = 1/2(21)th term = 10.5 th term
Median = (10th + 11th) terms / 2
Median = (0.289+0.295) / 2 = 0.292
The mode = 0.275, 0.314, 0.295, 0.296, 0.276, 0.289 (values with ten highest number of occurence.)
Which is the solution to-x/2<-4
A x<-8
B x2-8
C x <8
D x 8
Answer:
A.x<-8
Step-by-step explanation:
=1/2x<−4
=2*(1/2x)< (2)*(-4)
= x<-8
12 workers take 4 hours to complete a job. How long would it take 15 workers to complete the job?
Answer:
3.75
Step-by-step explanation:
I need to know how to find the area and to simplify it
Area of parallelogram = b × h
Base = x + 7
Height = x + 3
ATQ
Area = (x + 7) ( x + 3)
x² + 3x + 7x + 21
x² + 10x + 21
Answered by Gauthmath must click thanks and mark brainliest
properties of exponents. the answer is 1/2^12 i need help with the work
Step-by-step explanation:
Answer in attached image...
hope it helps
(2^-1 -2^-1 × 2^-4)^2
(1/2 - 1/2 × 1/2^4)^2
(1/2 - 1/2^5)^2
(1/2 - 1/32)^2
(16/32-1/32)^2
(15/32)^2
(15/2^5)^2
Must click thanks and mark brainliest
T
On Melissa's 6th birthday, she gets a $2000 CD that earns 5% interest, compounded semiannually. If the
CD matures on her 16th birthday, how much money will be available?
TE
$
(S
9514 1404 393
Answer:
$3277.23
Step-by-step explanation:
The future value of the CD with interest at rate r compounded semiannually for t years will be given by ...
A = P(1 +r/2)^(2t)
where P is the principal value.
For the given rate and time, this is ...
A = $2000(1 +0.05/2)^(2·10) = $2000(1.025^20) ≈ $3277.23
The value of the CD at maturity will be $3277.23.
Solve.
x^2-9x+3=0
x=
or
x=
Solve for x.
2(3x - 7) = 16
Simplify your answer as much as possible.
X =
Answer:
x = 5
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
2(3x - 7) = 16
Step 2: Solve for x
[Division Property of Equality] Divide 2 on both sides: 3x - 7 = 8[Addition Property of Equality] Add 7 on both sides: 3x = 15[Division Property of Equality] Divide 3 on both sides: x = 5Answer:
X=5
Step-by-step explanation:
divide by 2 on both sides first then you have
3x-7 = 8
take 7 to the other side so that you have an X factor on one side, thus
3x =15
then divide by 3 to remain with X
X = 5
The two countries with the highest cocoa production are the
Ivory Coast and Ghana. The Ivory Coast produces three times the amount of cocoa
produced in Ghana. (Source: International Cocoa Organization) Express the
amount of cocoa produced in the Ivory Coast in terms of the amount of cocoa produced in Ghana.
Answer:
38 percent of the Cocoa is produced in the ivory coast, with thousands being produced in Ghana, so Ghana is the main production rate of the cocoa, with the ivory coast producing less than half.
Step-by-step explanation:
Find formulas for X, Y, and Z in terms of A, B, and C. It may be necessary to make assumptions about the size of a matrix in order to produce a formula.
[A B C 0] [1 0 X Y] = [0 1 Z 0]
Find the formulas for X, Y, and Z. Note that I represents the identity matrix and 0 represents the zero matrix.
Answer:
Here the answer is given as follows,
A ladder leans against the side of the a house. The ladder is 19 feet long and forms an angle of elevation of 75 degree when leaned against the house. How far away from the house is the ladder? Round your answer to the nearest tenth.
Answer: 18.35259
Hope it helps!
Sammy and 4 friends went to Austin for a summer weekend. Sammy made 21 cups of lemonade. Everyone, including, Sammy, wants an equal amount of all the lemonade. How much lemonade should each person get?
Answer:
5 cups
Step-by-step explanation:
sammy + 4 friends = 5 people
21/5 = 4.2
we rounded it off to 5 cups.
Phân loại theo kiểu bố trí (cấu trúc) của mẫu sổ kế toán không gồm sổ nào trong các sổ dưới đây
Answer:
I I want everything in English
Step-by-step explanation:
it is difficult to read other languages write it in English please
A committee on community relations in a college town plans to survey local businesses about the importance of students as customers. From the 10,000 businesses listed in the telephone book, the committee chooses 150 businesses at random. Of these, 72 return the questionnaire mailed by the committee. The nonresponse rate is ______ percent. (Give your answer as a whole number.)
Answer:
The nonresponse rate is 52 percent.
Step-by-step explanation:
150 sampled:
72 returned and 150 - 72 = 78
The nonresponse rate is
Percentage that 78 is out of 150, that is:
78*100%/150 = 52%
The nonresponse rate is 52 percent.
Given: 3x+11=y, solve for x if y = 29
answer is 6
Step-by-step explanation:
3x+11=y
y=29
3x+11=29
3x=29-11
3x=18
x=18÷3
x=6
Answer:6
Step-by-step explanation:
3x+11=29
3x=29-11
3x=18
X=18/3
X=6
