Answer:
6, 2, 2/3, 2/9, 2/27, 2/81
Step-by-step explanation:
The nth term of a geometric progression is expressed as;
Tn = ar^n-1
a is the first term
n is the number of terms
r is the common ratio
Given
a = 6
r = 1/3
when n = 1
T1 = 6(1/3)^1-1
T1 = 6(1/3)^0
T1 = 6
when n = 2
T2= 6(1/3)^2-1
T2= 6(1/3)^1
T2 = 2
when n = 3
T3 = 6(1/3)^3-1
T3= 6(1/3)^2
T3= 6 * 1/9
T3 = 2/3
when n = 4
T4 = 6(1/3)^4-1
T4= 6(1/3)^3
T4= 6 * 1/27
T4 = 2/9
when n = 5
T5 = 6(1/3)^5-1
T5= 6(1/3)^4
T5= 6 * 1/81
T5 = 2/27
when n = 6
T6 = 6(1/3)^6-1
T6= 6(1/3)^5
T6= 6 * 1/243
T6 = 2/81
Hence the first six terms are 6, 2, 2/3, 2/9, 2/27, 2/81
The number of country A forces in country B decreased to approximately 34,000 in 2014 from a high of about 100,000 in 2008. The amount of country A funding for country B security forces also decreased during this period. The function f (x) = -1.330x + 5.149x +5.517 can be used to estimate the amount of country A funding for country B security forces, in billions of dollars, x years after January 2007. In what year was the amount of country A funding for country B security forces about $ 10.5 billion?
Answer:
2009
Step-by-step explanation:
The question can be interpreted as:
[tex]f(x) = -1.330x^2 + 5.149x + 5.517[/tex]
Required
Determine x when f(x) = 10.5
Substitute 10.5 for f(x) in [tex]f(x) = -1.330x^2 + 5.149x + 5.517[/tex]
[tex]10.5 = -1.330x^2 + 5.149x + 5.517[/tex]
Collect Like Terms
[tex]-1.330x^2 + 5.149x + 5.517-10.5=0[/tex]
[tex]-1.330x^2 + 5.149x -4.983=0[/tex]
Using quadratic formula
[tex]x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]
Where
[tex]a = -1.330[/tex]
[tex]b = 5.149[/tex]
[tex]c = -4.983[/tex]
[tex]x = \frac{-5.149 \± \sqrt{5.149^2 - 4*-1.330*-4.983}}{2*-1.330}[/tex]
[tex]x = \frac{-5.149 \± \sqrt{0.002641}}{-2.660}[/tex]
[tex]x = \frac{-5.149 \± 0.0514}{-2.660}[/tex]
Split:
[tex]x = \frac{-5.149 + 0.0514}{-2.660}\ or\ x = \frac{-5.149 - 0.0514}{-2.660}[/tex]
[tex]x = \frac{-5.0976}{-2.660}\ or\ x = \frac{-5.2004}{-2.660}[/tex]
[tex]x = 1.92\ or\ x = 1.96[/tex]
Both values of x approximates to 2.
So:
[tex]x = 2[/tex]
2 years after 2007 is 2009.
Hence, the funding is about $10.5 billion in 2009
if cos theta = 3/5, then tan theta =
Step-by-step explanation:
cos theta=3/5
theta=53.13°
tan theta =1.33
"What is the difference between a ratio and its related rate and unit rate?"
Answer:
Step-by-step explanation:
The ratio is the relationship of two numbers. ... A rate is a little bit different than the ratio, it is a special ratio. It is a comparison of measurements that have different units, like cents and grams. A unit rate is a rate with a denominator of 1.
The difference between ratio and unit rate is that both of them are measures of two units and are written in the form of a numerator and a denominator but the unit rate denominator must be one.
What is a ratio?It shows how many times one value is contained in another value.
The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
Ratio and unit rate
Ratio and unit rate both are written in the form of a numerator and a denominator.
The ratio is a measure of two units contained in a whole amount.
Example: 3 apples and 3 mangoes are contained in a bag
The ratio of apple and mango is 3:3 = 1:1
The unit rate is also a measure between two units but the denominator should always be one.
Example: A man can run 10 miles in 10 hours
In one hour 1 mile.
The unit ratio is 10miles per hour.
Thus,
The difference between ratio and unit rate is that both of them are measures of two units and are written in the form of a numerator and a denominator but the unit rate denominator must be one.
Learn more about ratios here:
https://brainly.com/question/2462048
#SPJ6
A company produces two types of jackets; windbreakers and rainbreakers. The company has at most 61 hours of finishing time per week and 67 hours of packaging time per week. Each windbreaker jacket takes 59 minutes of finishing time and 21 minutes of packaging time per week, whereas each rainbreaker jacket takes 58 minutes of finishing time and 34 minutes of packaging time per week. The company's profit for each windbreaker and rainbreaker jacket is 28 and 41, respectively. Let x denote the number of windbreaker jackets they should produce and y denote the number of rainbreaker jackets they should produce. The company wants to maximize profit. Set up the Linear Programming Problem for this situation.
Answer:
Max p = 28x + 41y
Subject to
59x + 58y ≤ 3660
21x + 34y ≤ 4020
x ≥ 0, y ≥ 0
Step-by-step explanation:
As given ,
Windbreakers Rain breakers Total
Finishing time 59 min 58 min 61 hr
Packaging time 21 min 34 min 68 hr
Profit 28 41
Let
The number of windbreaker jackets they should produce = x
The number of rain breaker jackets they should produce = y
As given,
The company wants to maximize profit.
⇒ Maximum Profit , p = 28x + 41 y
Now,
As 1 hour = 60 min
⇒61 hours = 61×60 = 3660 min
and 67 hours = 67×60 = 4020 min
∴ we get
The equations become
59x + 58y ≤ 3660
21x + 34y ≤ 4020
x ≥ 0, y ≥ 0
So, the Linear Programming Problem (LPP) for this problem is -
Max p = 28x + 41y
Subject to
59x + 58y ≤ 3660
21x + 34y ≤ 4020
x ≥ 0, y ≥ 0
If student D can solve 60% of multiple choice questions and Student B can solve 51% of the multiple choice questions and Student C can solve 57%. The students are unaware of each other.
a) At least one can be solved
b) Probability at most one of them can be solved
c) Probability that neither of them can be solved
d) Exactly two them can be solved
Home Depot sells an $1850 gas grill on the installment plan. The installment agreement includes a 20% down payment and 12 monthly payments of $160.
What is the total cost of the grill on the installment plan?
Answer:
Total cost of the grill installment plan = 2290
Step-by-step explanation:
370 + 1920 = 2290
By eating 1 egg, 1 cupcake, and 1 slice of pizza, a child consumes 300 mg of cholesterol. If the child eats 3 cupcakes and 4 slices of pizza, he or she takes in 86 mg of cholesterol. By eating 2 eggs and 1 cupcake, a child consumes 566 mg of cholesterol. How much cholesterol is in each item?
Answer:
cholesterol in egg= 273 mg
cholesterol in cupcake = 18 mg
cholesterol in slice of pizza = 9 mg
Step-by-step explanation:
Given data:
1 egg , 1 cupcake , 1 slice of pizza = 300mg
3 cupcakes , 4 slices of pizza = 90mg
2 eggs , 1 cupcake = 564mg
Let egg be x , let cupcake be y and let pizza be y
x + y + z = 300 (equation 1)
0x + 3y + 4z = 90 (equation 2)
2x + y + 0z = 564 (equation 3)
Using equation 1 and equation 2
x + y + z = 300 (Multiply equation by 3)
0x + 3y + 4z = 90
3x + 3y +3z =900
0x +3y +4z = 90 (Subtracting the equations)
3x - z = 810 (equation 4)
Using equation 2 and equation 3
0x + 3y + 4z = 90
2x + y + 0z = 564 (Multiply equation by 3)
0x + 3y + 4z = 90
6x +3y + 0z = 1692 (Subtracting the equations)
-6x +4z =-1602 (equation 5)
Solving equation 4 and equation 5
3x - z = 810 therefore z =3x -810
Substituting z into equation 5
-6x +4(3x - 810) =-1602
-6x + 12x - 3240 = -1602
6x = -1602+3240
6x = 1638
x = 273
Substituting x into z = 3x - 810
z = 3(273) - 810
z = 819-810
z = 9
Using equation 1 to find y
x + y + z = 300
273 + y + 9 = 300
282 + y = 300
y = 300-282
y = 18
Please help......................
18.9 or 18 9/10 or b or the second option.
Answer:
it's 18 9/10
Step-by-step explanation:
Find x. Round to the nearest tenth.
By knowing all sides of triangle and applying the formula of the law of the cosines we conclude that the missing angle X is approximately 117.9°.
How to find the missing angle
In this question we have a triangle with three known side lengths but all missing angles, we can determine the missing angle by using the law of cosines. If we know that x = 90 ft, y = 55 ft and and z = 50 ft, then the missing angle X is:
90² = 55² + 50² - 2 · 55 · 50 · cos X (1)
X ≈ 117.916°
To learn more on law of the cosines: https://brainly.com/question/17289163
#SPJ1
Find the third, fifth, and eleventh terms of the sequence described by the rule.
A(n) = - 6+ (n - 1)(6)
A(3)= ?
Answer:
A(3) = 6
A(5) = 18
A(11) = 54
PLS MARK AS BRAINLIEST
Jon borrows $8.75 from his friends to pay
for snacks, and $13.50 from his sister to go
to the movies. How much money does he
need to repay?
I need help please help me solve the the table
Answer:
cool
Step-by-step explanation:
If a card is randomly selected, what is the probability of drawing spade or club?
Suppose that c is a number for which the equation c÷c = 1 is false. What is c?
Answer:
Hope it help
Mark me as brainliest
Step-by-step explanation:
what is the additive inverse of the complex number -8+3i
Answer:
8-3i
Step-by-step explanation:
additive inverse of a+bi is -(a+bi)
so -(-8+3i) -- distribute negative through ()
8-3i
Help me find the answer to this please. And also explain how to slove these problems.
Answer:
B and C
Step-by-step explanation:
Minimum and Maximum points occur when the gradient of the function is equal to 0. Graphically this looks like a bend such that the function dips from decreasing to increasing (the gradient goes form being negative to positive) and vice versa.
A minimum point occurs where all the nearby values are higher than that of the point in question.
A maximum point occurs where all the nearby points are lower than the point in question.
By looking at the graph, there is a maximum point around (4.5, 1.5) which is consistent with B but not A (since A talks about a minimum point)
By looking at the graph, there is a minimum point around (0.5, 1.5) which is consistent with C.
I've highlighted areas of interest below so hopefully that's helpful :>
Use I = PRT to solve.
(time is in years)
1 = $270,000
P = $150,000
R = 12%
Find T.
Answer:
Time T = 15 year
Step-by-step explanation:
Given:
Interest I = $270,000
Principal P = $150,000
Rate R = 12% = 0.12
Find:
Time T
Computation:
I = PRT
270,000 = (150,000)(0.12)(T)
270,000 = (18,000)(T)
Time T = 15 year
A clock gains time at a steady rate. It is set to the correct time at
10: 00 AM. When the clock shows 2 : 00 PM, the correct time is
1: 36 PM. How many minutes fast will the clock be the next time the
correct time is 5 : 30 PM?
Answer:
The clock will be 50 minutes fast
Step-by-step explanation:
Proportions
It's known a clock gains time at a steady state, or constant rate.
At 10:00 AM the clock is set at the correct time and at 1:36 PM the clock shows 2:00 PM. This means in that period of time, it has gained 24 minutes.
From 10:00 AM to 1:36 PM there are 3 hours and 36 minutes, or equivalently, 3*60+36 = 216 minutes
Our clock gains time at a rate of 24 minutes each 216 minutes. This gives the ratio 24:216 = 1:9.
When the new correct time is 5:30 PM, there will have passed 7 hours and 30 minutes since 10:00 AM, or equivalently, 7*60+30 = 450 minutes.
Since the clock gains time at a ratio 1:9, the time gained is 450/9=50 minutes.
The clock will show 50 minutes more than the correct time of 5:30 PM, that is, 6:20 PM.
The clock will be 50 minutes fast
Find the measure of Angel 1 and 2.
Need help on this question, please help!
Answer:
I think it is 50
Step-by-step explanation:
Yoshi has a rope 30 feet long. He must cut it in pieces that are 1/4 foot long will he get more or fewer than 30 pieces
Answer:
More
Step-by-step explanation:
If we divide 30 by .25 we will get 120
Mid-Mod 3 Review
Name
1 Lisa used 5 orange juice containers, From the fust container, she poured out gallon of
orange juice. She then poured out 'h gallon from each of the four remaining containers,
a. How much orange juice did Lisa pour out in all? Show and label all your work.
en una rampa inclinada un ciclista avanza una distancia horizontal de tan solo 77 metros ¿cuál es la altura en metros de esa rampa
Answer:
English?
Step-by-step explanation:
If you score a 99, what percentage of the population scored above you?
Answer:
1%
Step-by-step explanation:
Answer:
1% pf the population scored above you
Step-by-step explanation:
make brainliest
If the turning point is lower than the nearby point it's called a
Answer:
Step-by-step explanation:
Local minimum. It would be the minimum value of the function not including the end points. If you are including the end points, its an absolute minimum
Which expression is equivalent to 2(3 - x) - 12 + 4x
1. 3x - 6
2. 3x - 7
3. 2x - 6
4. 2x - 7
a+b=10, c+d=18, a+c=12, b+d= 16. find the value of A,B,C and D?
Answer:
1
5
Quora uses cookies to improve your experience.
Read More
If a+b=8, b+c=10 and c+a=12, what is the value of a+b+c?
Answer
12
Follow
Request
More
Ad by SEMrush
What are the most effective ways to promote blogs?
There are tons of different ways to promote your blog. What you ultimately decide is best for you depends on the reasons you want
Continue reading in feed
29 Answers
Include Related Answers
Patrick Ivers, former mathematics & English instructor
Answered June 26, 2018
If a+b=8, b+c=10 and c+a=12, what is the value of a+b+c?
The puzzle is solved by defining each variable in terms of another variable & a number & then making substitutions. Begin by taking each sum to define one of the variables in terms of the other. (Different combinations are available, but I’ll follow the a,b,c order.)
a+b=8 becomes a=8-b
b+c=10 becomes b=10-c
c+a=12 becomes c=12-a
Now subtract two of the equations that contain the same variable. I’ll pick two that contain an a: c+a =12 & a+b=8. Subtracting the latter from the former eliminates the “a”s, leaving c-b=4. Adding b to both sides to isolate c gives c=b+4. From above we can take b=10-c to substitute for b in c=b+4, giving us c=(10-c) + 4). Simplify the right side to c=14-c, add c to both sides, giving 2c=14, & then divide both sides by 2 to obtain c=7.
Replace the c in b=10-c with 7 to
Continue Reading
3
1
Add a comment...
Related Answer
Paul K. Young, Former PhD candidate in Mathematics
Answered September 28, 2016
If A = B and B = C, does A = C?
In mathematics = is assumed to be a transitive relationship. Transitivity means precisely what you stated: A = B and B = C implies A = C.
While it’s possible to use = to represent a non-transitive relationship this would be considered an abuse of notation. A ~ B or R(A, B) would be a better way to express the relation in this case.
Similar assumptions are made about operators like + and *. + is generally assumed to be commutative, whereas * can be used for noncommutative operations like matrix multiplication. E.g. A * B != B * A.
Equality in programming is another story entirely.
In many languages = is the assignment operator and == is the equality operator. Assignment is not transitive - it’s not even a relation.There are cases where the equality operator doesn’t define a transitive relation.
a wildlife photographer photographs a crocodile and then paddles against a river current for 6 km. Then, hoping to photograph a hippopotamus, she paddles 15 km across a lake. She paddles across the lake for one hour longer than she paddled up the river. find the speed of the boat as she paddles the lake if the river current is 2 km/h. Pls answer. You'll get 100 points.
Answer:
5 km/h or 6 km/hStep-by-step explanation:
Let the speed of the boat be xSpeed against the current in the river is x - 2Time in the river:
6/(x - 2)Time in the lake:
15/xThe difference:
6/(x - 2) = 15/x - 1Solve for x to find the speed of the boat
Multiply both sides by x(x - 2) to clear the fraction:
6x = 15(x - 2) - x(x - 2)6x = 15x - 30 - x² + 2xx² - 11x + 30 = 0(x - 5)(x - 6) =0x -5 = 0, x - 6 = 0x = 5 km/h, x = 6 km/hAnswer:
5km/hr or 6km/hr
Step-by-step explanation:
1.Write an equation that models the following verbal statement and show/explain how you know your translation is correct.
Five less than four times a number is equal to three times the number.
2. Alejandra stayed 3 nights in a hotel for a total of $254.91. If each night was the same price, what did Alejandra pay per night? Show your thinking, use units to label your answer!
Answer:
Step-by-step explanation:
4x-5 = 3x
Which fraction is greater than 2/5? 3/10, 7/10, 2/4, 3/6
Answer:
all of them are except for 3/10
Step-by-step explanation:
Answer:
3/6
Step-by-step explanation:
plz mark as brainliest
thank you
19NBoli