Denote the sum by S. So
S = 5 + 11 + 17 + 23 + ... + 83
There's a constant difference of 6 between consecutive terms in S, so the 3 terms before 83 are 77, 71, and 65. So
S = 5 + 11 + 17 + 23 + ... + 65 + 71 + 77 + 83
Gauss's approach involves inverting the sum:
S = 83 + 77 + 71 + 65 + ... + 23 + 17 + 11 + 5
If we add terms in the same position in the sums, we get
2S = (5 + 83) + (11 + 77) + ... + (77 + 11) + (83 + 5)
and we notice that each grouped term on the right gives a total of 88. So the right side consists of several copies n of 88, which means
2S = 88n
and dividing both sides by 2 gives
S = 44n
Now it's a matter of determining how many copies get added. The terms in the sum form an arithmetic progression that follows the pattern
11 = 5 + 6
17 = 5 + 2*6
23 = 5 + 3*6
and so on, up to
83 = 5 + 13*6
so n = 13, which means the sum is S = 44*13 = 572.
3. Five kissing cousins met at a family reunion.
Each cousin kissed each of the other cousins
just once. How many kisses were given in all?
Answer: 20 kisses
Step-by-step explanation:
given data:
number of cousins at the family reunion = 5
each cousing kissing each other just once.
if one cousin kisses everybody round that would be
= 1 * 4
= 4 kisses.
4 kisses from each cousins * number of cousins at the family reunion.
= 4 * 5
= 20 kisses.
in total there were 20 kisses at family reunion
Using the principle of combination, the number of kisses given in all by the five cousins is 10
Number of cousins, n = 5Using the relation :
[n(n-1)] ÷ 2Substituting the values into the relation :
[n(n-1)] ÷ 2
[5(5-1)] ÷ 2
(5 × 4) ÷ 2
20 ÷ 2
= 10 kisses
Hence, the Number of kisses exchanged in all is 10.
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Solve the equation 34 - (x + 8) = 6x-2
Answer:
x = 4
Step-by-step explanation:
To solve the equation, we would have to solve for the variable x.
34 - (x + 8) = 6x - 2
Remove the parentheses.
34 - x - 8 = 6x - 2
Add 2 to both sides and combine like terms.
28 - x = 6x
Add x to both sides.
28 = 7x
Swap sides.
7x = 28
Divide both sides by 7.
x = 4
So the solution to the equation would be x = 4
I hope you find my answer and explanation to be helpful. Happy studying. :)
When x = 4, the y-coordinate is
When x = 8, the y-coordinate is
When simplified, the constant of proportionality, k, is x 2
Answer:
X2=8/4
X=1
and thats whats it equal too.
5. How can you get the variable alone in the equation x + 37 = 94?
a. Undo subtracting 37 by adding 37 to both sides
b. Undo subtracting x by adding x to both sides
c. Undo adding x by subtracting x from both sides
d. Undo adding 37 by subtracting 37 from both sides
what is the answer to 742/11?
Answer:
the answer is 67.4545454545
Step-by-step explanation:
Bernice rectangle workbook is 2/3 foot width and 5/6 foot long.what is the area of the page in her workbook.
Answer:
As a:
Fraction: 11/20
Decimal: 0.55
Percentage: 55%
Step-by-step explanation:
Where would the plane STV intersect plane Z?
Answer:
Plane Z or plane VTX.
Step-by-step explanation:
From the picture attached,
ST pierces the plane at a point T.
That means line ST is perpendicular to the horizontal plane Z or plane VTX.
Since, S is a point lying on line ST it will not lie on the vertical plane VTX Or plane Z.
Therefore, point S is not contained in the plane Z.
Week (x) 1 2 3 4 5 Number of Customers (y) 30 42 56 72 90 A new business began tracking how many customers entered the store each week. The store owner realized the relationship between the week and the number of customers was quadratic. If the trend continues, during which week will 156 customers enter the store? A) week 7
B) week 8
C) week 16
D) week 17
Answer:
b
Step-by-step explanation:
How to calculate a 15% tip?
Grades on a standardized test are known to have a mean of 1000 for students in the United States. The test is administered to 453 randomly selected students in Florida; in this sample, the mean is 1013, and the standard deviation (s) is 108. a. Construct a 95% confidence interval for the average test score for students in Florida. b. Is there statistically significant evidence that students in Florida perform differently from other students in the United States
Answer:
a
The 95% confidence interval is [tex]1003 < \mu <1023[/tex]
b
Yes there is statistically significant evidence that students in Florida perform differently from other students in the United States
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 1000[/tex]
The sample size is [tex]n = 453[/tex]
The sample mean is [tex]\= x = 1013[/tex]
The standard deviation is [tex]s = 108[/tex]
Given that the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = 100 - 95[/tex]
=> [tex]\alpha = 5\%[/tex]
=> [tex]\alpha = 0.05[/tex]
The critical value for [tex]\frac{\alpha }{2}[/tex] obtained from the normal distribution table is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{s}{\sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{108}{\sqrt{453} }[/tex]
=> [tex]E = 9.946[/tex]
Generally the 95% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
=> [tex]1013 - 9.946 < \mu < 1013 + 9.946[/tex]
=> [tex]1003 < \mu <1023[/tex]
Given that the population mean(1000) is not within the 95% confidence interval for l for the average test score for students in Florida, then it means that there is statistically significant evidence that students in Florida perform differently from other students in the United States
14. Joe has 3 more than half the number of pets his
friend does. Joe has 4 pets. He represented this
situation with the following equation: 4 = 3+x.
2
1
To figure out how many pets his friend has, Joe wants
to subtract a number from four. He will then multiply the
result by a number to determine how many pets his
friend has
What number should Joe subtract?
What number should Joe multiply by?
Answer:
He should subtract 3 from 4 and then multiply by 2.
Step-by-step explanation:
4 = 3 + 1/2x
1 = 1/2 x
2 = x
Pablo wants to get a grade of at least 95 in math this semesterSo far he has test scores of 89 98, 97 and 92. He will take his last test on Friday What is the lowest grade he can get on the test and still get a 95 this semester?
Answer:
the answer is 97 if you're rounding but 99 if you want exactly 95
Step-by-step explanation:
if you add all the previous grades up it'll add up to 376 and then when you add 97 and then divide it by 5 (the total amount of assignments) it'll add up to 94.6 which rounds up to a 95 unless you want it a 95 exactly which would probably be 99
Answer:
99
Step-by-step explanation:
Relative to his desired average, Pablo's scores are ...
-6, +3, +2, -3
In order for his average grade to be 95, the sum of all of these deviations and the one on his last test must be zero
-6 +3 +2 -3 +x = 0
x = 4
Pablo must get a 95+4 = 99 on his last test to have a 95 average.
1. Let n be the number (in thousands) of fans who attend a Foo Fighiers concert. What does n = 25 mean in this situation?
Answer: 25,000 fans attend a Foo Fighters concert
Step-by-step explanation:
25 x 1000 = 25000
(5 points) A random sample of adult drivers was obtained where 50% were men and 49% were women. Note that everyone is not classified as a man or a woman. A survey showed that 77% of the drivers rely on GPS systems. 38% of the drivers are men and use GPS while 38% of the drivers are women and use GPS. Suppose a person included in this survey is randomly selected. (0.5 pts.) a) Suppose the person selected is a man. What is the probability that he relies on a GPS system
Answer:
the probabiility that the selected man relies on a GPS system is 0.494
Step-by-step explanation:
From the given information:
Let X be the event that selected person is a man
Let Y be the event that selected person is a woman
Let Z be the event that selected relies or use GPS system.
So;
the following probabilities are:
P(X) = 0.50
P(Y) = 0.49
P(Z) = 0.77
P(X ∩ Z) = 0.38
P(Y ∩ Z) = 0.38
Now;
if the selected person is a man, the probability that he relies on a GPS system can be determined as follows:
[tex]P(Z|X) = \dfrac{P(X \cap Z)}{P(Z)}[/tex]
[tex]P(Z|X) = \dfrac{0.38}{0.77}[/tex]
[tex]\mathbf{P(Z|X) =0.494}[/tex]
Thus, the probabiility that the selected man relies on a GPS system is 0.494
Find the perimeter of the rectangle
Answer:
22 in.
Step-by-step explanation:
Perimeter = Length + Length + Breadth + Breadth
Perimeter = 7 in. + 7 in. + 4 in. + 4 in.
Perimeter = 22 in.
x-15≤-6 solve for x and simplify
Answer:
x≤9
Step-by-step explanation:
because im cool
Answer:
Step-by-step explanation:
x - 15 ≤ -6 (move the constant to the right)
x ≤ - 6 + 15 (calculate)
x ≤ 9
Put these numbers in order from least to greatest.-10, 4/25, -2/8
The answer is
-10, -2/8, 4/25
A circle has a radius of 7 inches. What is the area of the circle? Use 3.14 for p. (Area of a circle = pr2
Answer:
153.94
Step-by-step explanation:
Simplify the cube root in simplest radical form.
9x374
Please help
Answer:
D. [tex]xy\sqrt[3]{9y}[/tex]
Step-by-step explanation:
[tex]\sqrt[3]{9x^3y^4}[/tex]
[tex]\sqrt[3]{9}\sqrt[3]{x^3}\sqrt[3]{y^4}[/tex]
The [tex]\sqrt[3]{x^3}[/tex] cancels out to become x:
[tex]\sqrt[3]{9}x\sqrt[3]{y^4}[/tex]
Split the [tex]y^4=y*y^3[/tex]
[tex]\sqrt[3]{9}x\sqrt[3]{y^3}\sqrt[3]{y^1}[/tex]
[tex]\sqrt[3]{y^3} =y[/tex]
[tex]xy\sqrt[3]{9} \sqrt[3]{y}[/tex]
Put the cube root of y and cube root of 9 together:
[tex]xy\sqrt[3]{9y}[/tex]
a circle has a circumference of 6cm. find the diameter of the circle
Answer:
1.9 or 2
Step-by-step explanation:
To find diameter you do,
d= C/pi
C is circumference
so, d=6/3.14
=1.910... or 2
Hope this helps :)
Evaluate 4 |7 − n| + 5 when n = 12 .
Answer:
15
Step-by-step explanation:
4 |7 − n| + 5
Substitute n = 12
4 |7 − 12| + 5
4 |-5| + 5
Take the absolute value of -5, which is 5
4 * 5 +5
Multiply
20 -5
15
If your expression contains square roots, during which step of PEMDAS do you solve them? A parentheses B exponents C multiplication D division
Answer:
B
Step-by-step explanation:
Roots can also be represented as indicies (exponents) and thus should be treated like them. For example, square root could also be written as exponent 1/2.
When dealing with square roots in a equation, PEMDAS calls for this to be solved when you do B. Exponents
The root of a number is that number expressed exponentially by the root in inverted form. In other words, when you take something to its square root, you would be taking it to the inverse of 2 which is 1/2.
For instance:
√4 = 2 = 4¹/²
This means that you can then solve the square root when you deal with exponents which is the second step.
In conclusion, if you see an expression with square roots, PEMDAS allows you to solve it as an exponent.
Find out more at https://brainly.com/question/20687401.
Which exponential expression is equivalent to the one below?
Answer:
The answer is A.
Step-by-step explanation:
You have to elaborate it :
[tex] {(54 \times ( - 13))}^{66} [/tex]
[tex] = {(54)}^{66} \times {( - 13)}^{66} [/tex]
2. Give recursive definitions for the following sets. a. The set of all strings over {a, b} containing at least one "a". b. The set of odd-length binary strings that end with 00.
Answer:
Two definition of sets of all strings and sets of odd length binary are given
Step-by-step explanation:
A.) Suppose A is the string of contain at least one a:A = a
B will be same as it is b:B = b
Sets of the union of the AB and BA in which A followed B and corresponding B will follow A. Set = will (AB) (BA) = (*a*, *b*) (*b*, *a* )….
B.) There is the regular expression is compared with two 00 which is surrounded by the 0+1 that accepted at least two 0s.
Sep 27,
The midpoint of AB is M(-5,0). If the coordinates of A are (-8,5), what are the
coordinates of B?
Answer:
Step-by-step explanation:
(x-8)/2 = -5
x - 8 = -10
x = -2
(y+5)/2=0
y + 5 = 0
y = -5
(-2, -5)
What is the correct definition of the word bias? a. particular point of view b. a personal or unreasoned judgment c. to study in detail, or examine critically d. the capability of being believed; trustworthiness
Answer:
b. a personal or unreasoned judgment
Step-by-step explanation:
The answer is B because bias is basically something or someone that you favor over anything or anyone else. Or what you belving in your own opion.
As an example, our strong bias in favor for the idea, or a test biased towards people who are excellent at math.
Answer:
D
Step-by-step explanation:
if you don't believe me look up the definition
solve each equation 4(a+5)=10+4a
Answer:
10 = a
Step-by-step explanation:
To find this answer, first you need to distribute 4 times a and 4 times 5, since this is in parenthesis. You should get 4a + 20 = 10 + 4a. From there, you can subtract 4a from both sides of the equal sign, which will cancel out one of the 4a's. You should be left with 20 = 10 + a. Finally, you can subtract 10 from both sides of the equal sign and get 10 = a.
If g(x)=2/3(x-4)^2, find x when g(x)=8
8 = 2/3(x - 4)^2
Take the sqrt of both sides
Sqrt(8) = 2/3(x - 4)
Divide each side by 2/3
(3 * sqrt(2)) = x - 4
Add 4 to both sides
(3 * sqrt(2)) + 4 = x
Chelsea wants to buy a new iPhone that costs $324. She
has already saved $56. If she can save $20 a week, how
many weeks will it take for her to be able to purchase the
iPhone?
Answer:
14 full weeks.
Step-by-step explanation:
The phone costs $324 and she saved $56, so we subtract $56 from $324.
$324 - $56 = $268
She saves $20 each week so we divide $268 by $20 to get the number of weeks.
$268/20 = 13.4
It will take 13.4 weeks, but we have to round up because at 13 weeks she won't have enough saved. So 14 full weeks.
PLEASE HELP!
What percent of the circle is shaded?
Can you also explain how to get the answer?
Answer:
C
Step-by-step explanation:
The answer is 30% because 2/5 of the circle is shaded.
