Answer:
54
Step-by-step explanation:
Tn = an²+bn
T2 = a2²+2b
2 = 4a +2b
Multiply all through by 2
4 = 8a +4b
4b = 4-8a
T4 = a4² + 4b
20 = 16a +4b
4b = 20-16a
4-8a = 20-16a
16a -8a = 20-4
8a = 16
a = 16/8 = 2
4b = 4-8a = 4-8(2) = 4-16 = -12
b = -12/4 = -3
T6 = a6² + 6b
T6 = 2(36) + 6(-3) = 72 -18 = 54
Answer:
54
Step-by-step explanation:
Dagny Taggart has just purchased a home and taken out a $300,000 mortgage. The mortgage has a 25 year term with monthly payments and has an APR of 6% (monthly compounding). The total amount of interest that Dagny will pay during the first month of her mortgage is closest to:
a.
1923.24
b.
1816.93
c.
1500
d.
1485
Answer:
c.
1500
Step-by-step explanation:
The computation of the total amount of interest in first month is shown below:
Interest for first month is
= Mortgage amount × interest rate ÷ total number of months in a year
= $300,000 × 6% ÷ 12
= $1,500
Hence, the interest in the first month is $1,500
Therefore the c option is correct
An underground aquifer near Seiling, Oklahoma, sits on an impermeable layer of limestone. West of Seiling the limestone layer is thought to slope downward in a straight line. In order to map the limestone layer, hydrologists started at Seiling heading west and drilled sample wells. Two miles west of Seiling the limestone layer was found at a depth of 220 feet. Three miles west of Seiling the limestone layer was found at a depth of 270 feet
(a) What would you expect to be the depth of the limestone layer 5 miles west of Seiling
(b) You want to drill a well down to the limestone layer as far west from Seiling as you can. Your budget will allow you to drill a well that is 275 feet deep. How far west of Seiling can you go to drill the well? (Round your answer to one decimal place.)
Answer:
(A) 490ft.
(B) 2.8 miles
Step-by-step explanation:
Important points to note:
- The limestone layer is thought or assumed to slope downward in a straight line.
- 2 miles west of Seiling, the limestone layer was found at a depth of 220ft.
- 3 miles west of Seiling, the limestone layer was found at a depth of 270ft.
(A) What would you expect to be the depth of the limestone layer, 5 miles west of Seiling?
The expected depth of the limestone layer is:
2 miles + 3 miles = 5 miles
220ft + 270ft = 490ft
(B) Your budget will allow you drill a well that is 275ft deep. How far west of Seiling (in miles) can you go, to drill the well?
If 490ft ~ 5 miles
then 275ft ~ K miles
K = [275 x 5] / 490 = 2.80612245 miles
Rounding to 1 decimal place, the distance is 2.8 miles.
(SAT Prep) Find the value of x.
Answer:
x = 155
Step-by-step explanation:
First find the missing angle in the smaller triangle.
We know that the sum of the angles in a triangle is 180 so 35 + 90 + the missing angle = 180 so 180 - (35+90) = 180 - 125 = 55
Since the line above is a straight line, the sum of the angles must equal 180 so 55 + 60 + ? = 180. So 180 - 115 = 65.
The triangle is a right triangle so that means on of the angles is 90. So 65 + 90 = 155, so we have 180 - 155 = 25.
The angle that x is on is also a straight line so that means the angles must add up to 180 so 180 - 25 = 155.
The Sunny Days Apartment building has a cylindrical, above ground pool in the yard. The radius of the pool is 2 times its height, and the volume is 3000 cubic feet. How deep is the pool? In other words, what is the height of the pool?
9514 1404 393
Answer:
6.2 ft
Step-by-step explanation:
The volume of a cylinder is given by ...
V = πr²h
Here, we have r=2h and V=3000 ft³. Putting these numbers into the formula and solving for h, we get ...
3000 ft³ = π(2h)²h
(3000 ft³)/(4π) = h³ . . . . . divide by the coefficient of h³
h = ∛(750/π) ft ≈ 6.2 ft
The pool is about 6.2 feet deep.
An accounting firm has recently recruited six graduates: three men and three women. Three of the graduates are to be selected at random to work in the firm’s suburban office. Construct the probability tree. What is the probability that at least two women will be selected? Round your answer to three decimal places.
Answer:
a) The probability tree is constructed below
b) the probability that at least two women will be selected is 0.500
Step-by-step explanation:
Given the data in the question;
a) The probability tree is as follows;
3 men, 3 women
↓
_______________________|________________________
↓ ↓ ↓ ↓
3 men 2 men 1 man 0 men
0 women 1 woman 2 woman 3 women
b) the probability that at least two women will be selected
p( at least two women would be selected) = P( there are 2 women out of 3 ) + P( there 3 women out of 3
so
p( at least two women would be selected) = C
³C₂ × ³C₁ / ⁶C₃ + ³C₃³C₀ / ⁶C₃
= 3!/(2!(3-2)!) × 3!/(1!(3-1)!) / 6!/(3!(6-3)!) + 3!/(3!(3-3)!) × 3!/(0!(3-0)!) / 6!/3!(6-3)!)
= 3 × 3 / 20 + 1 × 1 / 20
= 9/20 + 1/20
= 0.45 + 0.05
p( at least two women would be selected) = 0.500
Therefore, the probability that at least two women will be selected is 0.500
There is a line who slope is 3 and who’s Y intercept is -10. Right it’s equation in slope intercept form
Step-by-step explanation:
substitute the given value in the standard form equation. it will give you the slope intercept form
Write the exact value of the side length of a square with an area of
95 square units
The side length of the square is a = 9.75 units
What is the area of a square?A square is a four sided quadrilateral with all of the side having equal lengths. The total internal angle of a square is 360° with each side perpendicular to each other.
A square is a 4 sided polygon where all the sides are of equal length.
The area of the square is the square of any one of its side
Let a be the side of the square
Area of the square = a²
Given data ,
Let the area of the square be represented as A
Now , the value of A is
Area of the square = a²
The exact value of the side length of a square with an area of 95 square units can be found by taking the square root of 95.
√95 ≈ 9.74679434481 (approximate value)
Hence , the exact value of the side length of the square is approximately 9.74679434481 units
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When 2 times a number is increased by 9, the answer is the same as
when 30 is decreased by the number. Find the number. HELP ME
Answer:
its 7
Step-by-step explanation:
why did u delete my answer if its right?
A trader makes a loss of 10% when he sells a watch for 15,300
what did it cost?
Answer:
CP = 17000
Step-by-step explanation:
Given that,
Loss = 10%
Selling price of the watch, SP = $15,300
We need to find the cost price of the watch.
[tex]CP=\dfrac{100}{100-L\%}\times SP\\\\CP=\dfrac{100}{100-10}\times 15300\\\\CP=17000[/tex]
So, the cost price of the watch is 17000.
please help me get this answer
Answer:
Step-by-step explanation:
Due to similarity in Tri ABC and ADE so,
[tex]\frac{AD}{AB} =\frac{DE}{BC} =\frac{AE}{AC}[/tex]
[tex]AE=28.2*\frac{20}{24} =23.5cm[/tex]
[tex]EC=AC-AE =28.2-23.5=4.7cm[/tex]
Starbucks opened two new locations. Location A costed $800 to open but makes $100 a month. Location B costed $1200 to open but makes $200 a month. Determine how long it will take for the locations to have made the same amount after paying off their costs and how much that amount is. *
Answer:
I think it is A that will take longer but im not 100 percent sure
Step-by-step explanation:
First write an equation:
Location A- 800+100x
Location B- 1200+200x
Then you need to plug numbers in for x
Consider a bag with 5 green marbles, 3 blue marbles, and 2 red marbles. If two marbles are drawn without replacement what is the probability that they are both blue?
A) .055556
B) .066667
C) .077778
D) .088889
Can someone help me with a two step equatio that is x=2
Simplify -3a + 5b - c given a = 2, b = -1 and c= 10
Answer:
-21
Step-by-step explanation:
-3a + 5b - c
-3(2)+5(-1)-(10)=-21
find the area of ABC
Answer:
area of ABC=1/2 b×h=1/2×20×6=30m²
Answer:
60 m^2
Step-by-step explanation:
( Base * Hight / 2 = Area)
20 * 6 = 120
120 / 2 = 60
Simplify to a single power of 5
Answer:
7
Step-by-step explanation:
multiplying exponents adds them together... 5+2=7
Find the unit rate. Enter your answer as a mixed number. A fertilizer covers 5/6 square foot in 1/2 hour
Answer:
1.67square foot/hr
Step-by-step explanation:
If a fertilizer covers 5/6 square foot in 1/2 hour, then;
5/6 square foot = 1/2 hour
To determine the unit rate, we will say;
x square foot = 1 hr
Divide both expressions
5/6x = 1/2
5 * 2 = 6x
10 = 6x
x = 10/6
x = 1.67square foot/hr
Hence the unit rate is 1.67square foot/hr
Please help for instant brainliest.
Here again are the results of a survey that students conducted at a mall. The students conducted this survey as part of a statistics project to determine if younger adults are more likely to have tattoos. At least one tattoo No tattoo Row Totals Age 18 - 29 170 320 490 Age 30 - 50 60 445 505 Column Totals 230 765 995 Which proportions are most useful in analyzing the relationship between age and tattoos? Group of answer choices 170 / 230 and 60 / 230
Answer:
1. 170/490 and 60/505
2. 320/490 and 445/505
Step-by-step explanation:
No options were given, but the question can still be answered
Given
[tex]\begin{array}{cccc}{} & {\ge 1\ tattoo} & {0\ tattoo} & {Row\ Total} & {18 -29} & {170} & {320} & {490} & {30 - 50} & {60} & {445} & {505} & {Column\ Total} & {230} & {765} & {995}\ \end{array}[/tex]
Required
Which proportion best compares age and tattoos?
The row data represents the age range of each group while the column data represents the amount of tattoo by each group.
So, to make comparison:
You simply pick a cell data and compare it to the row total.
Take for instance
For those who have at least 1 tattoo. The proportion to use are:
170/490 --- For age range: 18 - 29
60/505 --- For age range: 30 - 29
For those without tattoo. The proportion to use are:
320/490 --- For age range: 18 - 29
445/505 --- For age range: 30 - 29
Sadie swam x laps in the pool. Eric swam 3/5 more than that. Write an expression for the number of laps Eric swam
Answer:
y = 3/5 + x
'y' = # laps Eric swam
Step-by-step explanation:
Answer:
.
Step-by-step explanation:
.
A. 2 sqrt 3
B. 4
C. 8
D. 4 sqrt 6
E. 12
Please help
Answer:
Option B. 4
Step-by-step explanation:
From the question given above, the following data were obtained:
Angle θ = 60 °
Opposite (Fe) = 4√3
Adjacent (DE) = x
The value of x can be obtained by using the Tan ratio as illustrated below:
Tan θ = Opposite / Adjacent
Tan 60 = 4√3 / x
√3 = 4√3 / x
Cross multiply
√3 × x = 4√3
Divide both side by √3
x = 4√3 /√3
x = 4
Thus, the length of DE is 4
What is 730 divided by 30
Answer:
24 1/3
Step-by-step explanation:
long division
at a garage sale a large bin full of DVDs and CDs are being sold.all the DVDs and all the CDs are the same price. Aaliyah bought two DVDs for six dollars and the four CDs for eight dollars. Her friend lynn wants to buy four DVDs and two CDs. How much will Lynn have to pay Aaliyah‘s brother Pierre wants to spend $20 on DVDs and CDs what combination of DVDs and CDs could he buy
Answer:
Step-by-step explanation:
$6/(2 DVDs) = $3/DVD, and $8/(4 CDs) = $2/CD
a DVD costs $3
a CD costs $2
Lynn bought 4 DVDs and 2 CDs for 4×$3 + 2×$2 = $16.
Pierre bought d DVDs and c CDs for $20.
d is 0, 2, 4, or 6
c = (20-3d)/2
(d,c) = (0,10), (2,7), (4,4), or (6,1)
Can anyone help with condensing this?
Answer:
log 16x^7.
Step-by-step explanation:
log 4 + 2 log 2 + 7 log x
= log4 + log 2^2 + log x^7
= log (4*4*x^7)
= log 16x^7.
What is the percent of change from 400 to 600
Answer:
I dont speak english so i dont know whats is your question
which algebraic expression represents "the difference of fofty-four and seven times a number
Answer:
44-7x
Step-by-step explanation:
A random sample of 250 juniors majoring in psychology or communication at a large university is selected. These students are asked whether or not they are happy with their majors. Assume that none of these 250 students is majoring in both areas. There are a total of 100 majoring in psychology and only 80 of those majoring in psychology are happy while 35 students majoring in communication are unhappy.
If one student is selected at random from this group, find the probability that this student is:________
i. happy with the choice of major
ii. a psychology major
iii. a communication major given that the student is happy with the choice of major
iv. unhappy with the choice of major given that
Solution :
It is given that :
Number of students in a random sample majoring in communication or psychology at an university = 250
Total number of students majoring in psychology = 100
Number of students majoring in psychology those who are happy = 80
So number of students majoring in psychology those who are not happy = 20
Total number of students majoring in communication = 250 - 100 = 150
Number of students majoring in communication those who are happy = 115
So number of students majoring in psychology those who are not happy = 35
a). Probability of the students happy with their major choices are
[tex]$=\frac{80+115}{250}$[/tex]
= 0.78
b). Psychology major [tex]$=\frac{80+20}{250}$[/tex]
= 0.4
c). Probability of the students who are happy with the communication as the choice of major = [tex]$\frac{115}{250}$[/tex] = 0.46
d). Students unhappy with their choice of major given that the student is psychology major = [tex]$\frac{20}{250}$[/tex] = 0.018
a) Probability of the students happy with their major choices is 0.78.
b) Probability of Psychology major is 0.4
c) Probability of the students who are happy with the communication as the choice of major is 0.46.
d) Students unhappy with their choice of major given that the student is psychology major is 0.018
Given:
Number of students in a random sample majoring in communication or psychology at an university = 250
Total number of students majoring in psychology = 100
Number of students majoring in psychology those who are happy = 80
So, number of students majoring in psychology those who are not happy = 20
Total number of students majoring in communication = 250 - 100 = 150
Number of students majoring in communication those who are happy = 115
So, number of students majoring in psychology those who are not happy = 35
a). Probability of the students happy with their major choices are
[tex]=\frac{80+115}{250} =0.78[/tex]
b). Psychology major
[tex]\frac{80+20}{250} =0.4[/tex]
c). Probability of the students who are happy with the communication as the choice of major =[tex]\frac{115}{250} =0.46[/tex]
d). Students unhappy with their choice of major given that the student is psychology major =[tex]\frac{20}{250} =0.018[/tex]
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n is an integer.
Write the values of n such that -15 < 3n <6
I need know please
Answer:
-5<n≤2
Step-by-step explanation:
Divide 3 by -15 nad 6 since we need to find the "n" we need to divide on all sides, so -15 divided by 3 is -5 so replace -15 with -5 and 6 divided by 3 is 2 so replace 6 with 2
To get to the baseball game, Todd drove 2 hours and 10 minutes, stopped for 15 minutes, then drove 1 hour 15 minutes more to get to the game. If he arrived at 6:10, what time did he leave?
Question #4
The radius of a circle is 12 inches.
Enter the circumference of the circle, in inches. Round your answer
to the nearest hundredth.
Answer:
80.11 inches
Step-by-step explanation:
The formula to finding the circumference of a circle is:
C = 2πr (C = circumference, π = pi, r = radius)
Replace r with the radius:
C = 2π(12.75)
Now, multiply 2 times pi, then multiply that by 12.75, and the answer rounded
to the nearest hundredth is 80.11