Let a be the first term in the arithmetic progression. Then each successive term differs from a by a fixed number c, so that
• first term = a
• second term = a + c
• third term = (a + c) + c = a + 2c
• fourth term = (a + 2c) + c = a + 3c
and so on. In general, the n-th term in the AP is a + (n - 1) c.
The sum of the 3rd and 7th terms is 38, so that
(a + 2c) + (a + 6c) = 38
==> 2a + 8c = 38
==> a + 4c = 19 … … … [1]
The 9th term is 37, so
a + 8c = 37 … … … [2]
Subtracting [1] from [2] eliminates a and lets you solve for c :
(a + 8c) - (a + 4c) = 37 - 19
4c = 18
c = 18/4 = 9/2
Solve for a using either equations [1] or [2] :
a + 8 (9/2) = 37
a + 36 = 37
a = 1
Then the n-th term in the AP is 1 + 9/2 (n - 1) or 9/2 n - 7/2, where n ≥ 1.
3(8a - 5b) – 2(a + b); use a = 3 and b = 2
Answer:
32
Step-by-step explanation:
3(8(3)-5(2))-2((3)+(2))
3(24-10) -2(5)
3(14) -10
42-10
32
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{3(8a - 5b) - 2(a + b)}\\\\\huge\textsf{= 3(8(3) - 5(2)) - 2(3 + 2)}\\\\\huge\textsf{= 3(24 - 10) - 2(3 + 2)}\\\\\huge\textsf{= (3)(14) - 2(3 + 2)}\\\\\huge\textsf{= 42 - 2(3 + 2)}\\\\\huge\textsf{= 42 - 2(5)}\\\\\huge\textsf{= 42 - 10}\\\\\huge\textsf{= 32}}[/tex]
[tex]\huge\boxed{\textsf{Answer: 32}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]
If f(x) = 5x squared -3 and g(x) = x squared - 4x -8, find (f-g)(x)
Answer:
[tex]4x^2+4x+5[/tex]
Step-by-step explanation:
[tex]f(x)=5x^2-3\\g(x)=x^2-4x-8[/tex]
Set up an expression.
[tex]5x^2-3-(x^2-4x-8)[/tex]
Distribute the negative (-1)
[tex]5x^2-3-x^2+4x+8[/tex]
Solve / Simplify
[tex]4x^2+4x+5[/tex]
I'm late, but I hope this helps!
Help !!!!!!!!!!!!!!!
Answer:
9/4 = 2 1/4
Hope this Helps!?
In a lottery game, a single ball is drawn at random from a container that contains 25 identical balls numbered from 1 through 25. Use the equation P(AUB)=P(A) + P(B) - P(ANB), where A and B are any events, to compute the probability that the number drawn is prime or greater than 12.
The probability that the number drawn is prime or greater than 12 is : ___________
Answer:
17/25
Step-by-step explanation:
The equation for the probability of two events that are not mutually exclusive is:
p(A ∨ B) = p(A) + p(B) - p(A ∧ B)
A = the number is prime
B = the number is prime
The numbers are:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25
Here are the 8 prime numbers that satisfy event A:
3, 5, 7, 11, 13, 17, 19, 23
p(A) = 8/25
Here are the 13 numbers that are greater than 12 that satisfy event B:
13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25
p(B) = 13/25
Here are the 4 numbers that satisfy both event A and event B:
13, 17, 19, 23
p(A ∧ B) = 4/25
p(A ∨ B) = p(A) + p(B) - p(A ∧ B)
p(A ∨ B) = 8/25 + 13/25 - 4/25
p(A ∨ B) = 17/25
The probability that the number drawn is prime or greater than 12 = [tex]\frac{18}{25}[/tex]
What is probability?"Probability is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."
Formula of the probability of an event A is:P(A) = n(A)/n(S)
where, n(A) is the number of favorable outcomes, n(S) is the total number of events in the sample space.
For given question,
In a lottery game, a single ball is drawn at random from a container that contains 25 identical balls numbered from 1 through 25.
n(S) = 25
Let event A: the number drawn is prime
The prime numbers from 1 to 25 are:
2, 3, 5, 7, 11, 13, 17, 19, 23
So, n(A) = 9
The probability that the number drawn is prime,
[tex]P(A)=\frac{n(A)}{n(S)}\\\\ P(A)=\frac{9}{25}[/tex]
Let event B: the number drawn is greater than 12
So, n(B) = 13
The probability that the number drawn is greater than 12,
[tex]P(B)=\frac{n(B)}{n(S)}\\\\ P(B)=\frac{13}{25}[/tex]
The number drawn is prime as well as greater than 12.
Such numbers are : 13, 17, 19, 23
n(A ∩ B) = 4
So, the probability that the number drawn is prime as well as greater than 12,
[tex]P(A\cap B)=\frac{n(A\cap B)}{n(s)}\\\\ P(A\cap B)=\frac{4}{25}[/tex]
Using the equation P(AUB) = P(A) + P(B) - P(A ∩ B) to find the probability that the number drawn is prime or greater than 12,
[tex]\Rightarrow P(A\cup B)=P(A)+P(B)-P(A\cap B)\\\\\Rightarrow P(A\cup B)=\frac{9}{25}+ \frac{13}{25} -\frac{4}{25} \\\\\Rightarrow P(A\cup B)=\frac{9+13-4}{25}\\\\ \Rightarrow P(A\cup B)=\frac{18}{25}[/tex]
Therefore, the probability that the number drawn is prime or greater than 12 = [tex]\frac{18}{25}[/tex]
Learn more about probability here:
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trigonometric identities
Without knowing what Juan's exact steps were, it's hard to say what he did wrong. The least you could say is that his solution is simply not correct.
4 sin²(θ) - 1 = 0
==> sin²(θ) = 1/4
==> sin(θ) = ±1/√2
==> θ = π/4, 3π/4, 5π/4, 7π/4
Does the point (7,34) satisfy the equation y = 2x + 8
Answer:
no
Step-by-step explanation:
Substitute the point into the equation and see if it is true
34 = 2(7) +8
34 = 14+8
34 = 22
Since this is not true, the point does not satisfy the equation
Answer:
No
Step-by-step explanation:
because 7 is X and 34 is Y
So its 2 *7 +8=22
so no
Simplify the following by removing parentheses and combining terms
- (2x + 8) + 3(2x + 8) - 2x
Answer:
2x+16
Step-by-step explanation:
PEMDAS
In how many different ways can the letter of word
CORPORATION" be
arranged. So that the vowel always
come together"
Answer:
= 6 ways = Required number of ways = (120×6)=720
Find the product and simplify your answer 6w(5w^2-5w+5)
Suppose the following data represent the ratings (on a scale from 1 to 5) for a certain smart phone game, with 1 representing a poor rating. The discrete probability distribution for the random variable x is given below:
Star Frequency
1 2140
2 2853
3 4734
4 4880
5 10,715
Required:
Construct a discrete probability distribution for the random variable X
Answer:
[tex]\begin{array}{cc}{Status} & {Probability} & {1} & {0.0845} & {2} & {0.1127} & {3} & {0.1870} & {4} & {0.1927}& {5} & {0.4231} \ \end{array}[/tex]
Step-by-step explanation:
Given
The above table
Required
The discrete probability distribution
The probability of each is calculated as:
[tex]Pr = \frac{Frequency}{Total}[/tex]
Where:
[tex]Total = 2140+ 2853 + 4734 + 4880 + 10715[/tex]
[tex]Total = 25322[/tex]
So, we have:
[tex]P(1) = \frac{2140}{25322} = 0.0845[/tex]
[tex]P(2) = \frac{2853}{25322} = 0.1127[/tex]
[tex]P(3) = \frac{4734}{25322} = 0.1870[/tex]
[tex]P(4) = \frac{4880}{25322} = 0.1927[/tex]
[tex]P(5) = \frac{10715}{25322} = 0.4231[/tex]
So, the discrete probability distribution is:
[tex]\begin{array}{cc}{Status} & {Probability} & {1} & {0.0845} & {2} & {0.1127} & {3} & {0.1870} & {4} & {0.1927}& {5} & {0.4231} \ \end{array}[/tex]
2065 Q.No. 2 a A firm produced 100 calculator sets during its first year. The total number of calculator sets produced at the end of five years is 4,500. Assume that the production increases uniformly each year. Estimate the increase in production each year. [3] Ans: 400
Answer:
400
Step-by-step explanation:
First, the firm produces 100 sets its first year. This means that our equation starts at 100. Next, the total number of calculator sets in 5 years is 4500. With y₁ representing the amount of calculator sets produced during year 1, y₂ representing the amount of sets during year 2, and so on, we can say that
y₁+y₂+y₃+y₄+y₅ = 4500
100 + y₂+y₃+y₄+y₅ = 4500
Next, we are given that the production increases uniformly by an amount each year. Representing that amount as a, we can say that
y₁+a = y₂
y₂+a = y₃
y₁+a+a = y₃
y₁+ 2 * a = y₃
and so on, so we have
100 + y₂+y₃+y₄+y₅ = 4500
100 + (100+a) + (100+2a) + (100+3a) + (100+4a) = 4500
500 + 10a = 4500
subtract 500 from both sides to isolate the a and its coefficient
4000 = 10a
divide both sides by 15 to isolate a
a = 400
Please help——- Geometry problem
Thank you.
Answer:
b
Step-by-step explanation:
sinA = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{BC}{AB}[/tex] = [tex]\frac{s\sqrt{3} }{2s}[/tex] ( cancel s on numerator/ denominator ), then
sinA = [tex]\frac{\sqrt{3} }{2}[/tex] → b
An empty freight train traveled 60 miles from an auto assembly plant to an oil refinery. There, its tank cars were filled with petroleum products, and it returned on the same route to the plant. The total travel time for the train was 4 1 2 hours. If the train traveled 20 mph slower with the tank cars full, how fast did the train travel in each direction
Answer:
On the way out the train traveled at about 40 mph, while on the return it did so at 20 mph.
Step-by-step explanation:
Since an empty freight train traveled 60 miles from an auto assembly plant to an oil refinery, and there, its tank cars were filled with petroleum products, and it returned on the same route to the plant, and the total travel time for the train was 4.5 hours, if the train traveled 20 mph slower with the tank cars full, to determine how fast did the train travel in each direction the following calculation must be performed:
60/20 = 3
60/40 = 1.5
60/20 = 3
3 + 1.5 = 4.5
Therefore, on the way out the train traveled at about 40 mph, while on the return it did so at 20 mph.
Four fifths of Ali's elephants have long tusks. If Ali has 10 elephants, how many elephants have short tusks?
Cuatro quintas partes de los elefantes de Ali tienen colmillos largos. Si Ali tiene 10 elefantes, ¿cuántos elefantes tienen colmillos cortos?
Answer:
2 elephants have short tusks.
Step-by-step explanation:
Long tusks: 4/5
Short tusks: 1/5
1/5 = x/10
x = 2
If my savings of $x grows 10 percent each year, how much will i have in 2 years?
Answer:
20 percent
Step-by-step explanation:
Each year is 10 percent so 10x2 or 10+10 will equal 20
In Example 9.2 (p. 214), if you instead carried the suitcase by the handle so that the suitcase was hanging directly at your side, how much work would you do on the suitcase as you carried it forward at a constant walking speed
9514 1404 393
Answer:
none
Step-by-step explanation:
No work is required to maintain an object at a constant speed with no change in direction. Work is only done when an object is accelerated, or moved some distance in the direction of the net force applied.
you would do no work
Answer is D , others say it’s 64 but I got it wrong
Answer:
Oh no I am sorry! If you want answers to be done the real way let me know
Answer:I'm so sorry for you but congrats you did get the answer right it's just the test I guess
Step-by-step explanation:
Assume you are selling pizzas at $ 8 per pizza. Your fixed costs (rent, salaries, and utilities) are $4,438/month. The food costs and other variable costs are 40 percent of the selling price. What is your break-even point in units if you need to make 25% target return on the sales revenue? (enter only the value)
A company breaks even for a given period when sales revenue and costs incurred during that period are equal. Thus the break-even point is that level of operations at which a company realizes no net income or loss.
A company may express a break-even point in dollars of sales revenue or number of units produced or sold. No matter how a company expresses its break-even point, it is still the point of zero income or loss.
In order to grasp the concept of breakeven, it’s important to understand that all costs are not created equal: Some are fixed, and some are variable. Fixed Costs are expenses that are not dependent on the amount of goods or services produced by the business. They are things such as salaries or rents paid per month. If you own a car, then your car payment and insurance premiums are fixed costs because you pay them every month whether you drive your car or not. Variable Costs are volume related and are paid per quantity or unit produced. For your car, your variable costs are things like gas, maintenance, or tires because you only incur these costs when you drive your car. The more miles you drive, the more your gas expenses go up—such costs vary with the level of activity.
Before we turn to the calculation of the break-even point, it’s also important to understand contribution margin.
solve this set of equation, using elimination or substitution method.
Answer:
X =224
Y= -10
Step-by-step explanation:
To solve this question it's better to convert the fractions to decimals this way it will be easy to solve.
0.25x+0.6y= -4
0.2x+0.25y=-0.9
0.2(0.25x+0.6y=-4)
0.25(0.2x+0.25y=-0.9)
0.05x+0.12y=-0.8
0.05x+0.06y=-0.225
0.0575y/0.0575=-0.575/0.0575
Y=-10
To find x you replace the value of y in any of the equations
0.25x+0.6y=-4
0.25x+0.6(-10)=-4
0.25x=-4+60
0.25x/0.25=56/0.25
X=224
I hope this helps and sorry if it's wrong
Solve by elimination.
16x – 8y = 16
8x – 4y = 8
A. infinite number of solutions
B. (-2,-5)
c. (-20, -4)
R. (2,0)
Answer:
Step-by-step explanation:
16x-8y = 16 ⇒ 8x - 4y = 8, which is identical to the second equation.
The equations are equivalent, so there are an infinite number of solutions.
Geometry please help me!!!!
Answer:
Step-by-step explanation:
Find first derivative of f(x)=(x+1)(2x-1)
Answer:
[tex]4x-1[/tex]
Step-by-step explanation:
Can somebody help me
Answer:
The x interceprs are (-3,0) and (2,0)
Step-by-step explanation:
The reason is that when you plug in a -3 in the left parentheses it would become 0, and any number times 0 would be zero, making the equation equal to zero. The same would be true for the terms in the right parentheses, plugging in a two would make it equal to zero. This would make the entire equation equal to zero, finding you the x intercepts.
The Cinci Company issues $100,000, 10% bonds at 103 on October 1, 2020. The bonds are
dated January 1, 2020 and mature eight years from that date. Straight-line amortization is used.
Interest is paid annually each December 31. Compute the bond carrying value as of December
31, 2024.
According to the given values in the question:
The Amortization period is:
= [tex]8 \ years\times 12 \ months[/tex]
= [tex]96 \ months[/tex]
Number of months of Amortization is:
= [tex]3 \ months \ in \ 2020+(4 \ years\times 12 \ months)[/tex]
= [tex]3+48[/tex]
= [tex]51 \ months[/tex]
Now,
On bonds payable, the premium will be:
= [tex]Issue \ price - Face \ value[/tex]
= [tex](100000\times 103 \ percent)- 100000[/tex]
= [tex]103000-100000[/tex]
= [tex]3000[/tex] ($)
The Unamortized premium will be:
= [tex]Premium - Unamortized \ premium[/tex]
= [tex]3000-(3000\times \frac{51}{96} )[/tex]
= [tex]3000-1593.75[/tex]
= [tex]1406.25[/tex] ($)
hence,
The carrying value as of December 31, 2024 will be:
= [tex]100000+1406.25[/tex]
= [tex]101406.25[/tex] ($)
Learn more about the bond carrying value here:
https://brainly.com/question/20630991
Integrate[Exp[Power[sinx,2]]sin2x,x]
Answer:
e^{sin²x}+c
Step-by-step explanation:
[tex]\int e^{sin^2x} sin 2x dx=?[/tex]
is this statement?
if so
then
[tex]put~sin^2x=t\\differentiate\\2 sin ~x~cos~x~dx=dt\\sin~2x ~dx=dt\\\int e^t~dt=e^t+c\\=e^{sin^2x}+c[/tex]
Need tha answer explained
Answer:
Bri what do you mean explanation your answer is correct
Please mark me brainliest thanks
Answer:
It is 77.2, so your anwer is correct.
Step-by-step explanation:
Finding decimal divided by decimal too hard? Don't worry, I've got your back! To do division, you can do it the hard way by just dividing it, but there's something more simple.
Move the dividend's decimal point to the right until it's not a decimal. Do the same with the divisor, but it depends on how many decimal places on the dividend was moved by. So in this case, you move it by 2 decimal places for BOTH! Then you just simply divide it. It gives you the same answer.
BTW if I didn't make my explanation clear, please comment.
An education researcher would like to test whether 2nd graders retain or lose knowledge during the summer when they are presumably not in school. She asks nine 2nd graders to take a comprehension exam at the end of the school year (May), and then asks those same students to come back after the summer (late August) to retake a different but equivalent exam, to see if their level of comprehension has changed. Using the data below, test this hypothesis using an (alpha level of 0.05.)
May August
95 100
72 80
78 95
50 65
89 85
92 98
75 70
90 96
65 87
Required:
What is the appropirate test?
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data:
May August
95 100
72 80
78 95
50 65
89 85
92 98
75 70
90 96
65 87
The appropriate test is a paired t test :
d = difference between May and August
d = (-5, -8, -17, -15, 4, -6, 5, -6, -22)
The hypothesis :
H0 : μd = 0
H1 : μd ≠ 0
The test statistic :
T = dbar / (Sdbar/√n)
Where, dbar and Sdbar are the mean and standard deviation of 'd' respectively.
Using calculator :
dbar = - 7.777 ; Sdbar = 9.052
Test statistic = - 7.777 / (9.052 /√9)
Test statistic = - 2.577
The Pvalue, df = n - 1 = 9 - 1 = 8
Pvalue(-2.577, 8) = 0.0327
At α = 0.05
Pvalue < α ; WE reject the H0 ; and conclude that there has been a change in score
¿How you solve?
A pool is 8 m long, 6 m wide and 1.5 m deep. It is painted at $6 per square meter.
a) How much will it cost to paint it?
b) How many litres of water will be needed to fill it?
9514 1404 393
Answer:
a) $540 cost to paint
b) 72000 liters to fill
Step-by-step explanation:
Relevant formulas are ...
P = 2(L +W) . . . . perimeter of a rectangle of length L and width W
A = LW . . . . . . area of a rectangle of length L and width W
V = LWH . . . volume of a cuboid of length L, width W, and height H
__
a) The total painted area is the area of the pool walls plus the area of the pool bottom. The wall area is the product of pool perimeter and wall height. The bottom area is the product of pool length and width.
A = PH + LW = 2(L +W)H +LW
A = 2(8 m +6 m)(1.5 m) + (8 m)(6 m) = 42 m² +48 m² = 90 m²
At $6 per square meter, the cost of painting the pool is ...
($6 /m²)(90 m²) = $540 . . . . cost to paint the pool
__
b) The volume in liters is best figured using the dimensions in decimeters.
V = (80 dm)(60 dm)(15 dm) = 72000 dm³ = 72000 L
72000 liters will be needed to fill the pool.
Change the following to percentages:
a) 83 out of 100
b) 24 out of 50
c) 9 out of 25
d) 7 out of 20
e) 6 out of 10
f)72 out of 200
g)12 out of 40
h)36 out of 60
Answer:
a.83%
b. 48%
c.36%
d.35%
e.69%
f.36%
g.30%
h.69%
A truck can be rented from Company A for $120 a day plus $0.80 per mile. Company B charges $50 a day plus $0.90 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.
Answer:
700 miles driven in a day
Step-by-step explanation:
Create an equation to represent the situation, where x is the number of miles.
0.8x + 120 = 0.9x + 50
Solve for x:
120 = 0.1x + 50
70 = 0.1x
700 = x
So, the rental costs will be the same at 700 miles driven in a day.
