Sum of first n terms of two AP's are in the ratio (3n + 8) : (7n + 15).
Find:the ratio of their 12th terms
Solution:Let the first terms and common differences of the two APs be a , d & a' , d'.
We know that,
Sum of first n terms of an AP (Sn) = n/2 * [ 2a + (n - 1)d ]
So,
⟹ n/2 * [ 2a + (n - 1)d ] : n/2 * [ 2a' + (n - 1)d' ] = 3n + 8 : 7n + 15
⟹ 2a + (n - 1)d : 2a' + (n - 1)d' = 3n + 8 : 7n + 15
Multiply numerator and denominator by 1/2 in LHS
⟹ a + (n - 1)/2 * d : a' + (n - 1)/2 * d' = 3n + 8 : 7n + 15
Now,
3n + 8 : 7n + 15 is the ratio of nth terms of the two APs.
We have to find the ratio of 12th terms.
We know that,
nth term of an AP (aₙ) = a + (n - 1)d
⟹ a₁₂ = a + (12 - 1)d
⟹ a₁₂ = a + 11d
So,
⟹ a + (n - 1)/2 * d = a + 11d
⟹ n - 1/2 = 11
⟹ n - 1 = 22
⟹ n = 23
Hence, we have to substitute n as 23 to find the ratio of their 12th terms.
⟹ a + 11d : a' + 11d' = 3(23) + 8 : 7(23) + 15
⟹ a + 11d : a' + 11d' = 77 : 176
⟹ a + 11d : a' + 11d' = 7 : 16
∴ The ratio of the 12th terms of the two APs is 7 : 16.
I hope it will help you.
Regards.
Evaluate the expression when a=-2 and b=5.
- 7b+a
Answer:
Answer
= -7×5-2
= -35-2
=-37
Answer:
i got -37
Step-by-step explanation:
=-7x5+-2
=-35-2
=-37
Natalie is planning a summer pool party and need some fresh fruit like a fruit stand has watermelons for five dollars each and strawberries for three dollars per pint Natalie purchase 13 items and spent $45 on fruit snacks how much of each fruit did she buy
Answer:Therefore Natalie bought 3 water melons and 10 strawberries
Step-by-step explanation:
Step 1
let watermelons be represented by w
and strawberries be represented by s
Step 2
5w +3s = $45.......eqn 1
w+s=13..........eqn 2
Making w subject of formulae and substituting in equation 2
w= 13-s
5(13-s) + 3s=45
65-5s+3s =45
65-45=5s-3s
20=2s
s=20/2=10
substituting s=10 in equation 2
w +10=13
w= 13-10
w=3
Therefore Natalie bought 3 water melons and 10 strawberries
A monkey sits on a limb that is 25 feet above the ground. He swings up 10 feet. Climbs up 6 feet more. Then jumps down 13 feet. How far off the ground is the monkey now?
Answer:
28 feet
Step-by-step explanation:
A monkey sits on a limb that is 25 feet above the ground
He swings up 10 feet
Climbs up 6 feet
He then jumps down 13 feet
Therefore the distance of the monkey from the ground can be calculated as follows
= 25 + 10 +6 - 13
= 41-13
= 28 feet
Can someone tell me how I solve this, like explain how I do the steps not just the answer
==================================================
Explanation:
Pick any two rows from the table to form (x,y) points
I'll select the first two rows.
(x1,y1) = (-4,-3) from row 1
(x2,y2) = (0,-2) from row 2
Plug those values into the slope formula
m = (y2-y1)/(x2-x1)
m = (-2-(-3))/(0-(-4))
m = (-2+3)/(0+4)
m = 1/4
The slope is 1/4, which is also the rate of change.
HELP! ASAP! PLEASE!
PLEASE EXPLAIN AND TRY NOT TO GET IT WRONG. I'M AT 79 AND IF I GET 80 = PASS.
Answer:
negative
Step-by-step explanation:
a posotive times a negative is a negative
Answer:
positive
Step-by-step explanation:
Based on the number line, we can assume u is -1/2 and v is 2Plug the values of u and v in: [tex]-\frac{-\frac{1}{2} }{2}[/tex] Because there are two negatives, they can cancel out to become a positive: [tex]\frac{\frac{1}{2} }{2}[/tex] [tex]\frac{\frac{1}{2} }{2}[/tex] = 1/2 ÷ 2 = 0.25Because 0.25 is positive, the answer is positiveI hope this helps!
TIMED PLZ HELP
A. y = 4x + 5
B. y = 1/4 - 2
Slope =
Slope =
y-intercept
y-intercept
11
Answer:
Step-by-step explanation:
y-intercept form: y =mx +b
Here m is slope and b is y-intercept
A) y = 4x + 5
Slope = 4
y-intercept = 5
B) y = 1/4x -2
Slope = 1/4
y-intercept = -2
For the summer reading club, Xavier is required to read 2 books every week.
What line represents this requirement?
Line a
Line b
Line c
Line d
*^^NEED WITHIN 30 MINUTES ILL GIVE YOU BRAINLIEST****
This is solving special right triangles (45, 45, 90, and 30, 60, 90) and some sides have radicals ANSWER IN RADICAL FORM
Answer:7) x= Radical 3 y=1
8)x=12 Y=6 radical 3
9) n= 4/radical 3 m=2( 4/radical 3) [you’ll have to rationalize these since you can’t have a radical in the bottom]
10) x= 7/2 radical 3. y=7/2
plz help asap or im hear my teacher complain
Answer:
hiiiii ❤
Step-by-step explanation:
A car salesperson earns 30 percent of the profit for each car sold. If a salesperson earns $300 from the sale of a car, what was the profit?
Answer:
x=$10000
Step-by-step explanation:
sorry if its wrong lol
$800 = $300 +.05(x), x being the amount that must be sold
Subtract 300 from both sides
$500= .05(x)
Divide by .05
PLEASE HELPPPPPPPPPPP a nuclear disaster at Chernobyl in April 1986, approximately 12,600 kg of radioactive iodine-131 was released into the atmosphere. Iodine-131 is know to decay by half every 8 days. How many kilograms of iodine-131 remained after 24 days?
Answer:
1575 kg
Step-by-step explanation:
Decay rate formula =
N(t) = No(1/2)^t/t½
No = Initial amount = 12600kg
N(t) = Amount after time t
t½ = half life = 8 days
t = time = 24 days
N(24) = 12600 × (1/2)^24/8
1575kg
Dede’s class has 60 students and 28 of them are girls. Which represents the ratio of boys to girls in the class?
7:15
8:15
7:8
8:7
Answer:
the answer would be 7:8 I hope this helps you :\
Step-by-step explanation:
I need help I know the answer I just need to figure out what “m” and “b” is, as in y=Mx+b
Answer: m is slope and b is y intercept
Step-by-step explanation:
M is the slope and b is the y- intercept. Hope that helps.
I have more and will give more points if you answer all of them
Answer:
Look at my photo to see where to graph this:
Do you see? your going to click - 5 and make it go horizontal
The area of rectangle is 120 m² and its breadth is 8 m. Find the perimeter of the rectangle.
• Area of rectangle = 120 m²
• Breadth = 8m
To find :• perimeter of the rectangle .
Solution:As we know that ,
• Area of rectangle = L× B
=> 120 = L × 8
=> L = 120/8
=> L = 15
Length of the rectangle is 15m .
Now ,
• perimeter of rectangle = 2 (L+B)
=> perimeter of rectangle = 2 (15+8)
=> perimeter of rectangle = 2 ( 23)
=> perimeter of rectangle = 46
Hence, the perimeter is 46 m .
I hope it will help you.
Regards.
Select all of the nets that can be folded and assembled into a triangular prism like this one
Answer:
the answer is A and D
because i did it
Step-by-step explanation:
If 5 2 = 10 and 10 = 100,
then 5 2 = 100
what is the property
Answer:
Multiplication
Step-by-step explanation:
Ik
HELP NEEDED ASAP WILL GIVE BRAINLIEST AND 5 STAR RATE
Answer:
D
Step-by-step explanation:
The reason is because A, B, C start at the origin and move constantly. D does not increase as much.
A survey found that women's heights are normally distributed with mean 64.2 in. and standard deviation 4.2 in. The survey also found that men's heights are normally distributed with mean 70.1 in. and standard deviation 4.1 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 57 in. and a maximum of 63 in. Complete parts (a) and (b) below
A survey found that women's heights are normally distributed with mean 64.2 in. and standard deviation 4.2 in. The survey also found that men's heights are normally distributed with mean 70.1 in. and standard deviation 4.1 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 57 in. and a maximum of 63 in. Complete parts (a) and (b) below
a) find the percentage of women meeting the height requirement
b) find the percentage of men meeting the height requirement
Answer:
a
P(57 < X < 63) = 34.4%
b
P(57 < X < 63) = 4.096%
Step-by-step explanation:
From the question we are told that
The mean of women's height is [tex]\mu_ 1 = 64.2[/tex]
The standard deviation is [tex]\sigma_1 = 4.2 \ in[/tex]
The mean of men' height is [tex]\mu_2 = 70.1 \ in[/tex]
The standard deviation of men's height is [tex]\sigma_2 = 4.1 \ in[/tex]
The minimum height requirement is a = 57 in
The maximum height requirement is b = 63 in
Generally the percentage of women meeting the height requirement is mathematically represented as
[tex]P(57 < X < 63) = P(\frac{ 57 - 64.2}{ 4.2} < \frac{X - \mu_1}{\sigma_1} < \frac{ 63 - 64.2}{ 4.2} )[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
So
[tex]P(57 < X < 63) = P( -1.7143 < Z <-0.2857)[/tex]
=> [tex]P(57 < X < 63) = P ( Z <-0.2857) - P(Z < -1.7143)[/tex]
Generally from the z table the probability of ( Z <-0.2857) and (Z < -1.7143) is
P( Z <-0.2857) = 0.38755
and
P(Z < -1.7143) = 0.043237
So
P(57 < X < 63) = 0.38755 - 0.043237
=> P(57 < X < 63) = 0.3443
Converting to percentage
P(57 < X < 63) = 0.3443 * 100 = 34.4%
Generally the percentage of men meeting the height requirement is mathematically represented as
[tex]P(57 < X < 63) = P(\frac{ 57 - 70.1}{ 4.1} < \frac{X - \mu_1}{\sigma_1} < \frac{ 63 - 70.1}{ 4.1} )[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
So
P(57 < X < 63) = P( -3.1951 < Z <-1.7317)
=> [tex]P(57 < X < 63) = P ( Z <-1.7317) - P(Z < -3.1951)[/tex]
Generally from the z table the probability of ( Z <-0.2857) and (Z < -1.7143) is
P( Z <-1.7317) = 0.041663
and
P(Z < -3.1951 ) = 0.00069891
So
P(57 < X < 63) = 0.041663 - 0.00069891
=> P(57 < X < 63) = 0.04096
Converting to percentage
P(57 < X < 63) = 0.04096 * 100 = 4.096%
Juana is making fruit salad. The table shows the numbers of apples and bananas needed for various amounts of fruit salad. How many apples does Juana need to make 5 bowls of fruit salad?
Bowls of fruit salad
2 4 6
Apples needed
12 24 36
Bananas needed
14 28 42
Answer:
30 apples for 5 fruit bowls
Step-by-step explanation:
if you divide 12/2, you get 6, and six is the rate of how many apples in each bowl, so 6 x 5 is 30.
the question is: 82 of 200 animals in the dog and can rescue center are cats. What percent of animals are dogs?
Answer:
59%
Step-by-step explanation:
it says there is 200 animal and 82 are cats. we're trying to find the number of dogs. So subtract 82 from 200. that equals 118/200. 118/200 is 59%
If there are 200 animals at the rescue center, the percentage of animals that are dogs is 59%.
Given the following data:
Number of cats = 82 catsTotal number of animals = 200 animalsTo find the percentage of animals that are dogs:
[tex]Total \;animals = C + D[/tex]
Where:
C is the number of cats.D is the number of dogs.Substituting the given parameters into the formula, we have;
[tex]200 = 82 + D\\\\D = 200 - 82[/tex]
Dogs, D = 118 dogs.
Now, we can find the percentage of animals that are dogs:
[tex]Percent = \frac{D}{T}\times 100\\\\Percent = \frac{118}{200}\times 100\\\\Percent = 0.59 \times 100[/tex]
Percent of dogs = 59%
Read more: https://brainly.com/question/13282374
[tex]7+4-5+21-2+4[/tex][tex]7+4-5+21-2+4[/tex]Geometry The volume of a rectangular prism is 208 cm3. If the area of one end is 16 cm2, what is the length of the prism?
Answer:
thanks for the free points don't do this to other people if you don't want it done to you.
12x-6=16+8x solve for x
Answer:
x =19Step-by-step explanation:
[tex]\frac{x+2}{6}=\frac{2x-10}{8} \\\\Cross\:Multiply\\\\8x+16=12x-60\\\\\mathrm{Subtract\:}16\mathrm{\:from\:both\:sides}\\8x+16-16=12x-60-16\\\\Simplify\\8x=12x-76\\\\\mathrm{Subtract\:}12x\mathrm{\:from\:both\:sides}\\8x-12x=12x-76-12x\\\\Simplify\\-4x=-76\\\\\mathrm{Divide\:both\:sides\:by\:}-4\\\frac{-4x}{-4}=\frac{-76}{-4}\\\\Simplify\\\\x =19[/tex]
Which shows two expressions that are equivalent to (Negative 7) (Negative 15) (Negative 5)?
-525 and (35)(-15)
Step-by-step explanation:
You can calculate the result of this expression as follows:
(-7)(-15)(-5)=(-1)³(7×15×5)=-(7×15×5)=-525
as, (-1)^n=1 if n is even and (-1)^n=-1 if n is odd.
We already saw that -525 is equivalent to the expression. Furthermore:
(-7)(-15)(-5)=(-15)(-7)(-5)=(-15)(-1)²(7×5)=(-15)(7×5)=(-15)(35).
so the second expression is also equivalent.
You can discard the third and fourth answers because 115×5=575≠525. The first one is also discarded, because (-7)(75)=525≠-525.
The value of equivalent expression are, (- 1)(525) and (35)(- 15).
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Now, We can check all the options as,
(- 7) (-15) (- 5)
= (105)(-5)
= - 525
(–7)(–75) and (–1)(525)
= 525 & - 525
Not Equal
(–1)(525) and (35)(–15)
= -525 and - 525
Both Equal to (- 7) (-15) (- 5)
(35)(–15) and (115)(–5)
= -525 and - 575
Not Equal
(–1)(525) and (115)(–5)
= -525 and - 575
Not Equal
Hence, Expressions (- 1)(525) and (35)(- 15) are equivalent to (- 7) (-15) (- 5).
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ2
The complete question is this,
Which shows two expressions that are equivalent to (Negative 7) (Negative 15) (Negative 5)? (Negative 7) (Negative 75) and (Negative 1) (525) (Negative 1) (525) and (35) (Negative 15) (35) (Negative 15) and (115) (negative 5) (Negative 1) (525) and (115) (negative 5)
ANOTHER SLOPE MATH PROBLEM I NEED HELP WITH!!
Answer:
negative
Step-by-step explanation:
When the line is going down from left to right, its slope is negative.When the line is going up from left to right, its slope is positive.When the line is vertical (parallel to the y-axis), the slope is undefined.When the slope is horizontal (parallel to the x-axis), the slope is zero.:Done
9. Andre is buying snacks for the track and field team. He buys a pounds of apricots
for $6 per pound and b pounds of dried bananas for $4 per pound. He buys a total of
5 pounds of apricots and dried bananas and spends a total of $24.50.
Which system of equations represents the constraints in this situation?
A.
6a + 4b = 5
a+b = 24.50
+
S 6a+ 4b = 24.50
B.
(a + b = 5
C.
6a = 4b
5(a + b) = 24.50
ſ 6a + b = 4
D.
5a + b = 24.50
Answer:
Option (B)
Step-by-step explanation:
Let the amount of apricots purchased = a pounds
and the amount of bananas purchased = b pounds
Since, Andre purchased total amount of apricots and bananas = 5 pounds
Equation for the total amount will be,
a + b = 5
If the cost of bananas = $4 per pounds and the cost of apricots = $6 per pound
Total amount spent = $24.50
Therefore, equation for the expense will be,
6a + 4b = 24.50
Therefore, Option (B) will be the answer.
Answer:
:)
Step-by-step explanation:
B is correct
( I got it right in class thank you other person who answered)
The cost of admission to a popular music was $162 for 12 children and 3 adults. The admission $122 for 8 childern and 3 adults in another music concert. For extra credit (10 pts), how much was the admission for each child and adult? Write the equation
Answer:
Step-by-step explanation:
let the number of children be x
and the number of adults be y
so
12x+3y=162-----1
and
8x+3y=122------2
equating both 1 and 2 we have
12x+3y=162-----1
8x+3y=122------2
subtract 2 from 1 we have
12x+3y=162-----1
- 8x+3y=122------2
4y+0=40
4y=40
y=40/4
y=10
put y=4 in eqn 1 we have
12x+3y=162-----1
12x+3*10=162-----1
12x+30=162
12x=162-30
12x=132
x=132/12
x=11
therefore a child will cost $11 and adult will cost $10
Fill in the missing boxes ratios
Answer: 35, 9, 70
Step-by-step explanation:
i raised the points up, please help!! i will mark u as brainliest too!!
Can you write a number using 20 digits after the decimal point. Explain your thinking.
