Write the related series for the finite sequence –7, –10, –13, . . ., –22. then find the sum.–7 + (–10) + (–13) + (–16) + (–19) + (–22) = –87
–7 + (–10) + (–13) + (–15) + (–18) + (–22) = –85
–7 + (–10) + (–13) + (–14) + (–18) + (–22) = –84
–7 + (–10) + (–13) + (–17) + (–20) + (–22) = –89
Answer: [tex]-7+(-10)+(-13)+(-16)+(-19)+(-22)=-87[/tex]
Step-by-step explanation:
Given finite sequence : -7, -10, -13, . . ., -22.
Difference between first and second term=[tex]-10-(-7)=-10+7=-3[/tex]
Difference between second and third term =[tex]-13-(-10)=-13+10=-3[/tex]
Hence, the common difference = -3
The next term after -13 =[tex]-13+(-3)=-13-3=-16[/tex]
The next term after -16 =[tex]-16+(-3)=-16-3=-19[/tex]
The next term after -19 =[tex]-19+(-3)=-19-3=-22[/tex].........which is the last term of the sequence.
Now, the sum of the given sequence =[tex]-7+(-10)+ (-13) + (-16) + (-19) + (-22) [/tex]
[tex]=-7-10-13-16-19-22= -87[/tex]
Volume and Surface Area
Math help 100 points
Answer:
1 - V = Smaller solid=512 cm³
V = Larger solid=2197 cm³
2- 1.625² = 2.64
3 - SA of big solid is found 2535 cm²
Jason wants to choose 9 players for his track team. There are 12 players to choose from. How many different teams can Jason make?
Jason wants to form a team of 9 players out of total 12 players.
Here the order of selection does not matter because there is no particular post for any player. So we need to use Combinations and choose 9 players out of 12 players.
We know the formula for Combinations is given as follows :-
[tex]nCr=\frac{n!}{r!*(n-r)!} \\\\ Choosing \;9 \;out \;of \;12 \\\\ 12C9 = \frac{12!}{9!*(12-9)!} =\frac{12!}{9!*3!} =\frac{12*11*10*9*8*7*6*5*4*3*2*1}{(9*8*7*6*5*4*3*2*1)*(3*2*1)} \\\\ 12C9 = \frac{12*11*10}{3*2*1} =\frac{1320}{6} =220 \;combinations[/tex]
Hence, all the possible number of different teams = 220 combinations.
What are the zeroes of y = x^2 – 4x – 5?
Answer:
x=5 or x=-1
Step-by-step explanation:
The zeroes of the equation is when the x values when y=0.
We can determine this using a method that when we times out the brackets of our simplification we arrive at the original equation. We know that we must get -5 and -4x and x^2:
We can write:
[tex]y=x^2-4*x-5=0[/tex]
[tex](x-5)*(x+1)=0[/tex]
If we use the rules of algebra and multiply each term with each other:
[tex]x*x+x*1-5*x-5*1=0[/tex]
We can simplify:
[tex]x^2-4*x-5=0[/tex]
We end up with the original equation:
Therefore the zeros of the equation is when:
[tex](x-5)*(x+1)=0[/tex]
[tex]x-5=0[/tex] and [tex]x+1=0[/tex]
[tex]x=5[/tex]
[tex]x=-1[/tex[
x=5 or x=-1
The balance on a car loan after 4 years is $8,996.32. The interest rate is 5.6% compounding annually. What was the initial value of the loan?
What is a potential source of bias if an) if you are surveying students to find out their opinion of a new teacher with the following question: Is Mr Wilson a terrible teacher?
No source of bias.
Not specific Enough.
Implies that Mr. Wilson is a bad teacher.
Names the teacher.
Answer:
pronoun-antecedent number agreement error.
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A book club offers a choice of 8 books from a list of 40. In how many can a member make a collection?
This is a math combination problem. The number of ways a member can choose 8 books from a list of 40 is 76,904,685 ways.
Explanation:This is a combinatorics problem, specifically a combination problem. A combination is a selection of items from a larger set where the order does not matter. In this case, we have a set of 40 books and want to know how many ways one can select 8 books from those 40. The formula for calculating combinations is nCr = n! / [(n - r)! * r!] where 'n' represents the total number of items, 'r' represents the number of items to choose, 'nCr' represents the number of combinations of n items taken r at a time, and '!' denotes factorial, the product of all positive integers up to that number.
Applying the combination formula, a member can make the choice of 8 books from a list of 40 in:
40C8 = 40! / [(40 - 8)! * 8!] = 76,904,685 ways
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An item is called "price elastic" if you drop the price and revenue goes up. Last week you sold 10 sodas for $2 each; this week you sold 30 sodas for $1 each. Is soda price elastic?
Final answer:
Soda is price elastic because lowering the price from $2 to $1 resulted in an increase in total revenue from $20 to $30, indicating that a decrease in price caused a larger increase in quantity sold.
Explanation:
When determining whether an item is price elastic or not, we look at the effect that changing the price has on the total revenue. If a decrease in price leads to an increase in total revenue, the demand for the product is considered price elastic. In the example given, soda was sold at different prices and quantities: 10 sodas at $2 each last week, and 30 sodas at $1 this week. We use these numbers to calculate the total revenue for each week:
Last week: 10 sodas × $2/soda = $20
This week: 30 sodas × $1/soda = $30
Since the total revenue increased from $20 to $30 when the price was lowered from $2 to $1, we can see that the revenue increased as a result of the price drop, indicating that the demand for soda is indeed price elastic.
algebra 2 chapter 7
1-15 !!!
A beach ball has a diameter of 12 inches.what is the volume to the nearest tenth
The volume of a beach ball with a diameter of 12 inches is approximately 904.3 cubic inches.
To find the volume of a beach ball with a diameter of 12 inches, we first need to find the radius. The radius is half of the diameter, so the radius is 6 inches.
The formula for the volume of a sphere is:
V = (4/3)πr³
Where V is the volume and r is the radius. Plugging in our radius:
V = (4/3)π(6)³
V ≈ (4/3)π(216)
V ≈ (4/3)(678.24)
V ≈ 904.32 cubic inches
To the nearest tenth, the volume of the beach ball is approximately 904.3 cubic inches.
If Teresa counts 9 leaves on September 1, how will the number of leaves change from may 1 to September 1
Can someone please answer all these please?
a) When Lucia buys olives at the deli, the scale shows 0.325 kg at $18.88 per kg. How much should she pay?
b) John’s weekly wage is $1510.99 and he pays 2/3 of his weekly income in rent. How much rent does he pay each week?
c) A farmer owns 780 hectares of land. During a bushfire, 195 hectares are burnt. What percentage of his land was burnt?
d) Candles are $14.95 each. Estimate how much I need if I want to buy 17 of them.
Show your working.
e) Decrease 5000 by 13 %.
f) Ray bought a computer for $1600 and then a year later sold it for $1200.
Calculate his loss =
Calculate his loss as a percentage of the original price of the computer =
g) John spent $80 on dinner last Friday night. If this $80 is equal to 40% of his weekly income, calculate his weekly income.
h) Mr Jenkins invested $7500 at his local bank at 6.5% Simple Interest per annum.
What was his investment worth at the end of the first year?
Question 5
a) Express this ratio in lowest terms: 50 minutes : 2 ½ hours
b) Divide $120 in the ratio 5:7
c) Jane and Ben share in their lottery win in the ratio of 7: 3.
If Jane’s share of the money is $5600, how much does Ben receive?
The function P(x) = 3,113(1.2795)^x models the population, in millions, of California since 1990. Use the function to complete the following.
The number 3.113 represents
(a) The current population, in millions, of California.
(b) The population, in millions, of California in 1990
(c) The amount, in millions, that the population increases each year
The number 1.2795 represents
(a) The population, in millions, of California in 1990.
(b) The amount, in millions, that the population increases each year.
(c) The rate the population of California is increasing each year.
PLZ HELP ASAP INSCRIBED QUADRILATERALS
1. You can afford a monthly mortgage payment of $1,650 and can get a 15-year 5.625% loan. What is the maximum loan you can get so your payment does not exceed $1,650?
2. You apply for a home equity loan. The lender gets an appraisal on your home, showing a value of $183,500. You have a first mortgage with a current balance of $87,435. Based on a 75% LTV ratio, what is the maximum line of credit you can get?
A pair of dice are rolled. What is the probability of rolling 4 or greater?
A: 5/36
B: 1/18
C: 1/36
D: 11/12
Using the law of cosines, a=_ rounded to the nearest tenth.
Answer: a = 2.2
Given that: b = 4.0, c = 3.7, A=33.
The law of cosine is:
[tex]a^2=b^2+c^2-2bccosA\\a^2=4.0^2+3.7^2-2(4.0)(3.7)cos(33)\\a^2=4.86535118882\\a=\sqrt{4.86535118882}\\a=2.20575410888\\a=2.2[/tex]
So a = 2.2
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Which value of r indicates a stronger correlation: requals0.811 or requalsnegative 0.861? explain your reasoning?
10) Given that two tangent lines are constructed from the shared point A outside a circle with the center O and points of tangency B and C, what is the relationship between ∠OAB and ∠OAC?
Calculate the surface area of the portion of the surface z=x^2 + y that lies above the triangular region t wth vertices 0,0 4,0 and 4,2
Which is equivalent to sin^-1(tan(pi/4)) ? Give your answer in radians.
Answer:
the answer is b
Step-by-step explanation:
Assume the least squares equation is ŷ = 10 + 20x. what does the value of 10 in the equation indicate? when x = 0, y = 10. x increases by 10 for each unit increase in y. y increases by 10 for each unit increase in x. it is the error of estimation.
The value of 10 in the equation ŷ = 10 + 20x represents the y-intercept, which is the value of y when x equals zero.
Explanation:The value of 10 in the equation ŷ = 10 + 20x represents the y-intercept. In the context of the least squares equation, the y-intercept is the value of y when x equals zero. So when x = 0, y = 10, indicating that the initial value of y is 10.
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A lunch counter sells two types of sandwiches, roast beef and chicken salad. The profit on the sandwiches is $2 for chicken salad and $3 for roast beef. The amount of bread available is enough for 30 sandwiches. There are 2 hours available to prepare sandwiches. If chicken salad sandwiches take 3 minutes to prepare and roast beef sandwiches take 5 minutes, how many of each type of sandwich should be prepared to maximize the profit? Assume all sandwiches get sold
sqrt= Square Root
A student is attempting to calculate the square root of 18. His work is shown below. Which statement below best applies to his mathematical reasoning?
Givin sqrt 18 I observe that 18 is not a perfect square. I notice the perfect squares closest to 18 are 16 and 25, so I estimate the answer to fall somewhere between those numbers. Since 18 is closer to 16, I estimate that sqrt 18= 17
A.
18 is a perfect square, and the radical could have been evaluated directly.
B.
16 and 25 are not perfect squares, and therefore the student should not have chosen those numbers to estimate sqrt 18
C.
The student did not evaluate sqrt 16 and sqrt 25 before estimating sqrt 18
D.
The student has made no error. sqrt 18= 17
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Hakim invests $700 in a bank that pays 5% simple interest annually. After one year he uses the money in his account to buy a computer. The original cost of the computer is $750.00 . The computer is on sale for a 20% discount off of the original cost. The sales tax is 4% of the sale price.
After purchasing the computer, how much does Hakim have left in his bank account? Show your work.
A fluorite crystal is shaped like a regular octahedron with edges that are 2.1 inches. Which of these is the volume of the fluorite crystal in cubic inches? Round to the nearest hundredth
To find the volume of the fluorite crystal, you can use the formula for the volume of an octahedron with the given edge length of 2.1 inches, rounded to the nearest hundredth to be approximately 7.69 cubic inches.
The volume of the fluorite crystal can be calculated as follows:
Identify the formula for the volume of an octahedron: V = (1/3) × [tex]\sqrt{2}[/tex] × a³, where 'a' is the edge length.
Substitute the given edge length: V = (1/3) × [tex]\sqrt{2}[/tex] × 2.1³.
Calculate the volume: V = 7.69 cubic inches (rounded to the nearest hundredth).
Determine the values of the constants b and c so that the function given below is differentiable. f(x)={2xbx2+cxx≤1x>1
To make the function differentiable, we need to make it continuous at x = 1 by ensuring that both sides of the function have the same value. The values of the constants b and c are b = 1 - c, where c is any real number.
Explanation:The function given is:
f(x)={2xbx2+cxx ≤ 1 x > 1
To determine the values of the constants b and c such that the function is differentiable, we need to make sure that the function is continuous at x = 1 and both sides of the function have the same derivative at x = 1.
To do this, we need to find the limits of the function as x approaches 1 from both the left and the right sides.
From the given function, we can see that when x ≤ 1, the function is a polynomial and is differentiable for any value of b and c.
However, when x > 1, the function is not differentiable unless we choose the values of b and c such that the function becomes continuous at x = 1.
To make the function continuous, we need to make sure that both sides of the function have the same value at x = 1.
Substituting x = 1 into the given function, we have 2b(1)(1) + c(1) = b + c = 1 (since the function should be continuous at x = 1).
Therefore, the values of the constants b and c that make the function differentiable are b = 1 - c, where c is any real number.
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