1. An AP has a common difference of 3. Given that the nth term is 32, and the sum of the first n terms is 185, calculate the value of n.
Answer:
The value of n is 10
Step-by-step explanation:
The formula of the nth term of the arithmetic progression is a[tex]_{n}[/tex] = a + (n - 1)d
a is the first termd is the common difference between each 2 consecutive termsn is the position of the termThe formula of the sum of nth terms is S[tex]_{n}[/tex] = [tex]\frac{n}{2}[/tex] [2a + (n - 1)d]
∵ An AP has a common difference of 3
∴ d = 3
∵ The nth term is 32
∴ a[tex]_{n}[/tex] = 32
→ Substitute them in the 1st rule above
∵ 32 = a + (n - 1)3
∴ 32 = a + 3(n) - 3(1)
∴ 32 = a + 3n - 3
→ Add 3 to both sides
∴ 35 = a + 3n
→ Switch the two sides
∴ a + 3n = 35
→ Subtract 3n from both sides
∴ a = 35 - 3n ⇒ (1)
∵ The sum of the first n terms is 185
∴ S[tex]_{n}[/tex] = 185
→ Substitute the value of S[tex]_{n}[/tex] and d in the 2nd rule above
∵ 185 = [tex]\frac{n}{2}[/tex] [ 2a + (n - 1)3]
∴ 185 = [tex]\frac{n}{2}[/tex] [2a + 3(n) - 3(1)]
∴ 185 = [tex]\frac{n}{2}[/tex] [2a + 3n - 3]
→ Multiply both sides by 2
∴ 370 = n(2a + 3n - 3)
∴ 370 = 2an + 3n² - 3n
→ Substitute a by equation (1)
∴ 370 = 2n(35 - 3n) + 3n² - 3n
∴ 370 = 70n - 6n²+ 3n² - 3n
→ Add the like terms in the right side
∵ 370 = -3n² + 67n
→ Add 3n² to both sides
∴ 3n² + 370 = 67n
→ Subtract 67 from both sides
∴ 3n² - 67n + 370 = 0
→ Use your calculator to find n
∴ n = 10 and n = 37/3
∵ n must be a positive integer ⇒ 37/3 neglecting
∴ n = 10
∴ The value of n is 10
In 5 + In x = 1
this is from my algebra 2 class and we just have to solve
Answer:
2
Step-by-step explanation:
In 5 + In x = 1
In 5 + In x = In 10 (Because In 10 = 1)
In(5x) = In 10
5x = 10
x = 10/5
x = 2
For two days, your boss decides to double the amount you make if on day 1, you make $70 dollars and on day 2, you make$80 dollars, write an expression for the total commission you earn?
Answer:
300
Step-by-step explanation:
Day 1: $70
Day 2: $80
Total commission = day 1 × 2 + day 2 × 2
= 70 × 2 + 80×2
= 140 + 160
= 300
Or
Total commission = 2(day 1 + days 2)
= 2(70 + 80)
= 2(150)
x = 300
Mrs. Davis has 54 dollars and 50 cents saved, she will save 33 dollars and twenty-five cents each week for the next 30 weeks, she will not spend any of the money, how many dollars will miss Davis have saved after 30 weeks.
Answer:
$1,053.50
Step-by-step explanation:
First you need to multiply $33.30 by 30 so you can figure out how much she'll save over the next 30 weeks. You will get $999. Then you add $54.50 and $999 together to get 1,053.50.
Topic 3 Assessment
POSSIBLE POINTS 11
Are the following functions linear or nonlinear? Function A
Function B
Function A
Function B
X3 6 9 1215
ty
9
y510152025 8
6
5
4
3
2
6
7 8 9
1
2
3 4 5 6 7 8 9
Nex
I think function A is linear and function B isnt
Step-by-step explanation:
Function A has a constant rate of change and function B looks like a curve
A rectangular prism has a length of 10ft, a height of 3ft, and a width of 4ft. What is its volume, in cubic ft?
Answer:
120
Step-by-step explanation:
deltamath
120 cubic ft is the volume of rectangular prism having a length of 10ft, a height of 3ft, and a width of 4ft
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
A rectangular prism is a 3D figure with 6 rectangular faces.
Given, rectangular prism has a length of 10ft, a height of 3ft, and a width of 4ft.
To find the volume of rectangular prism we have to multiply length, width and height.
Volume =Length×Width×Height
Put the values of length, width and height in the above formula.
=10×4×3
=120 cubic ft
Hence 120 cubic ft is the volume of rectangular prism having a length of 10ft, a height of 3ft, and a width of 4ft
To learn more on Three dimensional figure click:
https://brainly.com/question/2400003
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Cheyenne is playing a board game. Her score was −225 at the start of her turn, and at the end of her turn her score was −405. What was the change in Cheyenne's score from the start of her turn to the end of her turn?
The change was__ points
Solve:
4(-6) =
-9(5) =
-1.5(-7) =
Answer:
5
Step-by-step explanation:
if m7 = 55°, which of the following statements are true? Select all that apply.
A. m6 = 55°
B. m5 = 135°
C. m1 + m4 = 250°
B. m1 + m6 = m7 + m4
Answer:
A. m∠6 = 55°
C. m∠1 + m∠4 = 250°
D. m∠1 + m∠6 = m∠7 + m∠4
Solve the inequality:
10x+5≥25
Select one:
x≥2
x≥20
x≥30
x≥3
Answer:
x≥2
Step-by-step explanation:
Step 1: Subtract 5 from both sides.
10x+5−5≥25−5
10x≥20
Step 2: Divide both sides by 10.
10x /10 ≥ 20 /10
HOPE IT HELPS
Write a story problem to go with the multiplication problem 4 x 2/3 then solve the promblem
A possible problem for the multiplication 4 x 2/3 is
At a small restaurant, there are 4 tables each with 3 seats. Today, all tables have customers but there are only 2 customers at each tableWhat is a mathematical word problem?A mathematical word problem refers to a situation that can be understood and solved by using mathematics.
What is one possible mathematical problem for 4 x 2/3?A possible mathematical problem needs to integrate all the numbers or variables in the problem. Because of this, let's begin by determining which number corresponds to which factor.
4: Number of tables at a restaurant.2: Number of people at each table.3: Number of seats at each table.Now, let´s create the problem. At a small restaurant, there are 4 tables each with 3 seats. Today, all tables have customers but there are only 2 customers at each table. Which expression represents this situation.
Learn more about mathematics in: https://brainly.com/question/12083755
show that (X+1)(x+3)(x+5)=ax3+bx2+cx+d
Answer:
a = 1
b = 9
c = 23
d = 15
Step-by-step explanation:
Expand it out:
(x^2 + 4x + 3)(x+5)
(x^3 +4x^2 +3x + 5x^2 + 20x + 15)
=x^3 + 9x^2 + 23x +15
Help me out please an thank you
Answer:
Eg would be 10.6 because its the same length as EF
Answer:
8.6?
Step-by-step explanation:
if it's a right angle an the exact same thing on the other side, than wouldn't you just add 4.3 + 4.3?
If you roll a number cube two times, what is the probability of rolling an even on the first roll and a four on the second roll?
Answer:
1/12
Step-by-step explanation:
Probability is a ratio derived as the number of possible outcomes divided by the total outcome.
On a number cube, the even sides are 2, 4 and 6. This means that the possible outcome for rolling an even is 3 while the total outcome is 6. Hence the probability of rolling an even P(E)
= 3/6
The probability of rolling a 4 P(4)
= 1/6 (4 appears on one side)
Hence the probability of rolling an even on the first roll and a four on the second roll
P(En4) = 3/6 * 1/6
= 3/36
= 1/12
Solve for x check the picture
Answer:
x = 21
Step-by-step explanation:
2x and 42 are alternate angles and are congruent, so
2x = 42 ( divide both sides by 2 )
x = 21
Richard Brian puts $30 worth of gas in his truck. The price per gallon was $2.50. Which equation can be solved to find the number of gallons Richard Brian's purchased?
Answer: See explanation
Step-by-step explanation:
From the question, we are informed that Richard Brian puts $30 worth of gas in his truck and the price per gallon was $2.50.
The equation that can be solved to find the number of gallons Richard Brian's purchased will be the worth of gas in the truck divided by the price per gallon. This will be:
x = 30 / 2.50
where x = number of gallon.
= 12 gallons
PLEASE ANSWER ASAP FOR BRAINLIEST!!! A triangle has side lengths of 17 cm and 8 cm. Which could be the value of the third side, 28 cm or 23 cm? The value (select) v cm is the value of the third side.
Answer:
23
Step-by-step explanation:
The sum of any two sides of a triangle has to be greater than the other side
Only 23 meets this criteria
Answer:
i think it is 23
Choose the two situations that describe volume.
A. measuring the length and width of a box
B. finding the total number of cubes a box will hold
C. counting how many blocks make up a block tower
D. measuring the length of each side of a desk using cubes
E. counting the number of cubes it takes to cover the entire surface of a desk
What is it?
Answer:
B and C are volume
A = area/perimeter
D = Perimeter
E = surface area
I need help with this
The shelf life of a battery produced by a major company is known to be normally distributed, with a mean life of 4 years and a standard deviation of 0.75 years. What is the upper quartile of the battery shelf life? What range of years contains the middle 68% of all battery shelf lives?
Answer:
4.5 years ; (3.25, 4.75)
Step-by-step explanation:
Given that :
Mean , m = 4
Standard deviation, s = 0.75
The upper quartile, which is the 3rd quartile of a standard normal distribution is 0.67
Therefore, the upper quartile Q3:
Q3 = mean + 0.67 * standard deviation
Q3 = 4 + 0.67(0.75)
Q3 = 4 + 0.5025
Q3 = 4.5025
Q3 = 4.5 years
Range of values that contain the middle 68%
According to the empirical rule;
68% is within 1 standard deviation of the mean
Therefore ;
Interval will be ;
Mean ± 1 standard deviation
(4 - 0.75) ; (4 + 0.75)
(3.25, 4.75)
There are two clocks in a shop. The first clock chimes every 5 minutes. The second clock chimes every 6 minutes. If both clocks chime together at 3:15 pm, at what time will both clocks chime together again?
Colin was thinking of a number. Colin halves it and gets an answer of 5.2. What was the original number?
Answer: 10.4
Step-by-step explanation:
Let the number that Colin is thinking of be represented as x.
We are informed that Colin halves the number and gets an answer of 5.2. This can be written as:
x ÷ 1/2 = 5.2
0.5x = 5.2
Divide through by 0.5
0.5x/0.5 = 5.2/0.5
x = 10.4
The number is 10.4
A tree planter can plant 40 trees in 8 hours.
How many trees can a tree planter plant in 2
hours?
Answer:
He can plant 10 trees in 2 hours.
Step-by-step explanation:
First you need to find the number of trees he can plant in an hour.
For this purpose, we will divide 40 by 8 to get an idea about how many he can plant in an hour.
Trees planted in an hour = 40/8 = 5
Now for 2 hours = 5*2 = 10 trees.
Help please help me
Step-by-step explanation:
if you're looking for x
x=180-42-51= 87°
and if you're looking for D
D= 180-42= 138°
help plzzzzzzzzzzzzzzzzzzzzzzzzz
Answer:
x<2
Step-by-step explanation:
Answer:
43
Step-by-step explanation:
Y is a complete collection of all what the web is expected to be with the elements having atomic the
HELPPPPPPPP !!!!!!!!!
Could someone please answer:
4(y+3)+2(y+7) =
6(2w+5)+9(w+2) =
3(y-2)+4(2y+5 =
7(2g+3)-5(g+2)=
6(x-2)-4(x-8) =
2(3y-8)-5(2y-1) =
8(5+2m) +3(5-3m) =
4(w+7)-2(2w+1) =
9(1+2y)+3(3-y) =
Please answer them all I will award brainliest answer <3
Answer:
Step-by-step explanation:
4(y+3)+2(y+7) = 2(3y`=13)
6(2w+5)+9(w+2) = 3(7w+16)
3(y-2)+4(2y+5) = 11y+4
7(2g+3)-5(g+2)= 9g+11
6(x-2)-4(x-8) = 2(x+10)
2(3y-8)-5(2y-1) = -4y-11
8(5+2m) +3(5-3m) = 55+7m
4(w+7)-2(2w+1) = 26
9(1+2y)+3(3-y) = 3(6+5y)
Answer:
1.) y=4.3
2.) w=2.2
3.) y=1.2
4.)g=1.2
5.)x=-22
6.)y=2.75
7.)m=7.8
8.)w=26
9.)y=1.2
sorry i took awhile im in class rn
Step-by-step explanation:
3, 6, 11, 18, 27, … What is the 12th term of the sequence?
Answer:
Answer is 39
Step-by-step explanation:
Answer:
146
Step-by-step explanation:
hope it helps
Marking Branliest
A right rectangular pyramid is sliced horizontally (Across) at the red line by a plane paralell to the base of the pyramid. What is the shape of the cross-section ?
Answer:
Rectangle
Step-by-step explanation:
Since the base is a rectangle and the pyramid was cut horizontally that would leave the shape of the cross-section to be a rectangle as well.
hope this helped, have a great day :)
Answer:
Rectangle
Step-by-step explanation:
3 1Evaluate the expression. 8 2+ 3.8 – 10 x 2
Answer: 65.8
Step-by-step explanation:
First multiply 10 x 2=20
then you add 82 and 3.8 which is 85.8
then you subtract 20 from 85.8 and you get 65.8