Answer:
The first term of the sequence is -8.95 with a common difference of 2.1.
The sequence is:
-8.95, -6.85, -4.75, -2.65...
Step-by-step explanation:
We are given that the sum of the first ten terms of a linear sequence is 5, and the sum of the next ten terms is 215.
And we want to find the sequence.
Recall that the sum of an A.P. is given by:
S = k / 2 ( a + xk)
Where a is the first term, k is the number of terms, and x_k is the last term.
We can represent our term values with the direct formula:
Xn = a + d (n-1)
Where the first term, x₁ = a.
The sum of the first ten terms is 5. Hence, S = 5, k = 10, a = x₁ and x_k = x₁₀:
(5) = 10/2 (a+xk)
5 = 5(a+(a+9d))
2a + 9d = 1
The sum of the next ten terms (that is, from x₁₁ to x₂₀) is 215. Hence, S = 215 when k = 10, a = x₁₁, and x_k = x₂₀:
(215) = (10)/2 (a + xk)
215 = 5((a+d(11-1))+(a+d(20-1)))
2a + 29d = 43
This yields a system of equations:
[tex]\left \{ {{2a+9d=1} \atop {2a+29d=43}} \right.[/tex]
Solve:
(2a + 9d) + (-2a - 29d) = (1) + (-43)
-20d = -42
d = 2.1
Consequently:
a = 1/2(1-9d)
= 1/2(1-9(2.1))
= -8.95
In conclusion, the first term of the sequence is -8.95 with a common difference of 2.1.
The sequence is:
-8.95, -6.85, -4.75, -2.65...
what is the common denominator 4/15 and 1/3? Need answers ASAP
Answer:
15
Step-by-step explanation:
To find the common denominator we look for the LCM
15: 15,30,45,60
3: 3,6,9,12,15
Our LCM is 15
Meaning our LCD is 15
Brainliest please :)
ASAPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
the answer is 1/10 :))))))))
Why does the slope intercept forumla use m and b.
Answer:
y=mx+b
Step-by-step explanation:
m=slope
b= y-intercept
Question 1 (3 points) What value of p makes this equation true? 3p - 8 = -23 . O p = -6 Op = -5 Op = 5 p = 6
The value of p that makes the given equation true is equal to: B. p = -5
Given the following equation:
[tex]3p - 8 = -23[/tex]To find a value of p that makes the given equation true:
In this exercise, you're required to determine a value of p that satisfies the given equation true such that when substituted into the equation, it has a true result or outcome.
Rearranging the equation by collecting like terms, we have:
[tex]3p - 8 = -23\\\\3p=-23+8\\\\3p=-15\\\\p=\frac{-15}{3}[/tex]
p = -5
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Joe was looking through a numeric puzzle
book and found the following puzzle. The
sum of two numbers is two. The difference
of the two numbers is also two. What are
the two numbers?
0 and 2
Step-by-step explanation:
If you subtract 2 by 0 then it will equal 2 and if you add 2 to 0, you also have 2.
How do u solve this? pls LOL
Answer:
8
Step-by-step explanation:
HF and DE are parallel to each other ( since corresponding angles are equal = 90°) .
Hence the smaller and the larger triangle will be similar to each other.
Also we know the corresponding sides of similar triangles are proportional .
=> 10 / z = 10+5/12
=> 10/z = 15/12
=> z = 10 *12/15
=> z = 8 yards
Answer:
8
Step-by-step explanation:
What is 121 divided by 18?
Answer:
6.7222222222
Step-by-step explanation:
This Maths Is Easy, Y Did You Post It?
Answer:
=6.7222222222
Step-by-step explanation:
Easy peesy lemon squezy!
Hi I was wondering if I could get some help with this question please 26POINTS!!
PLEASE HELP
given the parent function f(x)=√x and a new function g(x)=√x+6+3. Select from the drop-down menus to correctly describe the changes on the graph from f(x) to g(x).
The graph will shift 6 unit______and 3 units______.
choices:up up
down down
left left
right right
Answer:
The graph will shift 6 unit left and 3 units left
Step-by-step explanation:
[tex]g(x) = \sqrt{x+6+3}[/tex]
How long does it take to get sat results.
Suppose $22,825 is deposited into a savings account with a simple interest rate of 4.03%. Find the account balance after 5 years and 3 months.
Answer:
80,775
Step-by-step explanation:
I= (22,825) (0.0403) (63)
I= 57,950
P+I=A
I= A+P
I= 22,825 + 57,950
I= 80,775
The store owner purchased 26 shirts for $810.68. How much did each shirt cost?
Answer:
$31.18
Step-by-step explanation:
810.68/26=31.18
Answer:
$31.18 e/a
Step-by-step explanation:
e^ln(5x) =
5x
ln(5)
5ln(x)
ln(x)
Answer:
5x
Step-by-step explanation:
The natural log of 5x is the exponent to give e to get 5x as a result. You are simply applying the definition of logarithm
The expression [tex]e^{ln(5x)[/tex] evaluates to 5x after simplification.
Option: A is correct.
Here, we have,
The expression [tex]e^{ln(5x)[/tex] involves two important mathematical properties:
[tex]e^{ln(x)} = x[/tex]:
This is a fundamental property of the natural logarithm and the base of the natural exponential function, e.
When the natural logarithm (ln) and the natural exponential function [tex](e^x)[/tex] are composed, they "cancel out," and the result is the argument inside the ln function (x).
[tex]e^0 = 1[/tex]:
The natural exponential function raised to the power of 0 is equal to 1.
Now, let's simplify the expression step by step:
[tex]e^{ln(5x)[/tex]
Using property 1,[tex]e^{ln(5x)[/tex] simplifies to:
5x
Therefore, the correct option is "5x."
The expression [tex]e^{ln(5x)[/tex] evaluates to 5x after simplification.
Option: A is correct.
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Simplify the following expression. (0.5x – 3)(0.5x + 3)
Answer:
0.25x^2-9
Step-by-step explanation:
Difference of squares converse:
0.25x^2-9
Answer:
0.25x^2-9
Step-by-step explanation:
multiply 0.5x with 0.5x which is 0.25x^2. then multiply 0.5x with 3 which is 1.5x. then multiply -3 with 0.5x which is -1.5x. then multiply -3 with 3 which is 9. so you will have 0.25x^2+1.5x-1.5x-9.
1.5x and -1.5x is 0. so you are left with 0.25x^2-9
help me with this plsssss
Answer:
y=1/2x+-5 is A
y=-2/3x+1 is B
y=4x+3 is C
y=2x+6 is D
Given the sequence 3, 1,-1, -3, ... use the arithmetic sequence formula to write an equation.
Then, find a32.
Answer:
a₃₂ = - 59
Step-by-step explanation:
The nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 3 and d = a₂ - a₁ = 1 - 3 = - 2 , then
[tex]a_{n}[/tex] = 3 - 2(n - 1) = 3 - 2n + 2 = - 2n + 5
Then
a₃₂ = - 2(32) + 5 = - 64 + 5 = - 59
The Roosevelts and the Jaspers live in the same city and pay the same sales
Roosevelts made $91,000 and the Jaspers made $37,000 last year, is the
sales tax in their city an example of a regressive tax?
tax rate, and both families made $16,000 in taxable purchases last year. If the If
Answer:
Yes, the sales tax in their city is an example of regressive tax
Step-by-step explanation:
Firstly, we need to understand what is meant by the term regressive tax.
What is meant by a regressive tax system is a system of taxation in which there is a decrease in tax rate as there is an increase in amount subjected to tax.
Now, the key to knowing if what we have in the question is a regressive taxation is by calculating the percentage of the tax that was paid.
For the Roosevelt’s , the percentage of tax paid would be 16,000/91,000 * 100% = 17.6%
For the Jasper’s, the percentage of tax paid would be 16,000/37,000 * 100% = 43.24%
We can see that at a lower amount subjected to tax, the Jasper’s paid more and thus we can conclude irrevocably that sales tax in their city is an example of a regressive tax
Combine the like terms to create an equivalent expression:
-12-6p-(-2)
Answer:-2(5+3p)
Step-by-step explanation:
Pls help, I need (c) of the problem 3-106
Answer:
Negative x minus two
Step-by-step explanation:
3 - (x + 5)
Distribute the negative sign:
3 - x - 5
Simplify:
-x - 2
In words:
Negative x minus two
Molly walked 3.45 miles on a hike. Her sister walked 1.23 miles. Her brother walked 0.85 miles.
How much farther did Molly walk than her brother and sister combined?
O 0.38 miles
1.37 miles
O 2.22 miles
O 5.53 miles
Answer:
1.37 miles
Step-by-step explanation:
First, you have to find out how far Molly's brother and sister walked combined. 1.25+0.85=2.08. Now you subtract that from Molly's distance, 3.45. 3.45-2.08-1.37 miles.
Doctors are interested in determining if the human body temperature is really 98.6 degrees. he selects 30 students and records their temperature using a digital thermometer. what type of test would they conduct to test this claim?
Answer:
I think its one mean, if it's not I'm very sorry
In order to corroborate his assertion that the average body temperature is lower than 98.6 degrees Fahrenheit, the croaker created a test statistic.
What's Test Statistic?A test statistic is a figure attained from a statistical analysis. It explains how far your observed data is from the null thesis, which states that there's no correlation between the variables or distinction between the sample groups.
Test statistics are statistics that are produced from samples to determine whether or not to accept the null thesis.
A sample is data that represents a portion of the population. In other words, it's a gauged - down interpretation of a larger group.
The croaker conducted a thesis test in order to corroborate the information that has been handed in the question. And he calculated the test statistic, or arbitrary data from the sample taken from the population data, for the thesis test.
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Please solve: 7x - 4 = 2
Write the prime factorization of 315.
315 =
Write the prime factorization of 315.
315 =
Write the prime factorization of 315.
315 =
Write the prime factorization of 315.
315 =
3 exponent 2 × 5 exponent 1 × 7 exponent 1
50 POINTS!!
Write an
equation for the circle with centre (0,0), if (12,5) lies on its circumference
Answer:
x² + y² = 169
Step-by-step explanation:
The equation of a circle centred at the origin is
x² + y² = r² ( r is the radius )
Given (12, 5 ) lies on the circumference , then the point will satisfy the equation.
Substitute (12, 5 ) into the equation
12² + 5² = r²
144 + 25 = r²
169 = r²
Then equation of circle is
x² + y² = 169
4. How many y-intercepts can the graph of an absolute value function have?
Answer: a function can only have one y-intercept.
How many whole groups can you fit into 51?
Step-by-step explanation:
in one group 17members
in second group 17members
in third group 17members
Hope it helps ohh God! please make your question a little easier so the other person can understand what you mean to say/ask when we read.
Use mental math to find the partial products 3,000 x 5=
Answer:
15,000
Step-by-step explanation:
3 times 5 is 15, just add the 3 zeros.
15,000 is the partial product of 3000*5.
What is partial products?A partial product is a product obtained when we multiply a multiplicand by one digit of a multiplier that has more than one digit.
Given that, 3000*5
3000*5 = 15000
Hence, the partial product of 3000*5 is 15000.
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Suppose that you randomly selected 22 adults. If 10% of the population smoke, a) Using the Range Rule of Thumb, what is the minimum number of usual smokers we can expect to get out of 22 adults?
Answer: 2 to 3 people who would be smoking
Step-by-step explanation:
22 divided by 10 = 2.2
and since there could be more
or less so it could be 2 or 3
The mean vitamin C level for 20 dogs was 7.6 milligrams per liter, with a standard deviation of 2.1 milligrams per liter.
One dog’s vitamin C level was not in the normal range. It was 0.9 milligrams per liter, which is a very low level of vitamin C.
If the value 0.9 is eliminated from the data set, does the mean increase or decrease?
Your answer:
I will give you 5.0 and a thanks and maybe brainliest
Answer: The mean increases.
Step-by-step explanation:
The value of 0.9 mg/L is very low compared to a means of 7.6 mg/L with a standard deviation of 2.1 mg/L. It seems as though it is an outlier that is suffiently different from the others, and probably should be dropped from the data set. That would do 2 things: 1) the stabdard deviation will likely decrease, indicating a more confident data set, and 2) the mean vitamin C level will increase.
Does anyone know this answer??
Answer:
(2, -9)
Step-by-step explanation:
2 - (-9) > 8 First, substitute the values for x and y.
2 + 9 > 8
11 > 8 The inequality is true, so (2, -9) is the correct pair.
Answer:
Answer is C
Step-by-step explanation:
basically you substitute (X,Y) in X-Y >0. so X-Y should be greater than 0. also, make sure you use the signs properly.
so in C. 3--10 > 0 so negative sigs cancel each other out so its 3+10 so 13> 0
Ill reward you a bounty of 100 points! plus brainiest if you are the first one to answer my question:
Part 1
Write your own real-world scenario where the Pythagorean Theorem can be applied to find a missing piece. You may choose to write a problem that is two- or three-dimensional in nature. Be sure that you will be able to draw a diagram of your scenario.
Write out your problem and submit it for Part 1. Be sure to end your scenario with a question.
Part 2
Draw a diagram of the scenario you created in Part 1. You may draw by hand and scan and upload your drawing or create a computer-generated drawing for submission. Be sure to label all parts and dimensions of the drawing.
Part 3
Solve the question that you posed in Part 1. Show all of your steps in answering the question.
For this option, you will need to submit all three parts for full credit—your real-world problem and question, the diagram that you created, and your work solving the problem, showing all steps.
*Please note that your instructor is looking for your own original idea. While it is acceptable to use the Internet for research and inspiration, academic integrity policies apply.
Answer:
The real-world scenario is given as: A yacht traveling 20 miles due east off a harbor is located 50 miles due north from the yacht
Recall:
Pythagorean Theorem applies to a right triangle where and c is the hypotenuse.
If we know the two of the three side lengths of a right triangle, we can find the other third length.
An example of a scenario where the Pythagorean Theorem can be applied to solve a real-world problem can be sketch in a diagram
Therefore:
The real-world scenario is given as: A yacht traveling 20 miles due east off a harbor is located 50 miles due north from the yacht
Step-by-step explanation:
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Have a good day