Answers
Notice that
13 - 9 = 4
17 - 13 = 4
so it's likely that each pair of consecutive terms in the sum differ by 4. This means the last term, 149, is equal to 9 plus some multiple of 4 :
149 = 9 + 4k
140 = 4k
k = 140/4
k = 35
This tells you there are 35 + 1 = 36 terms in the sum (since the first term is 9 plus 0 times 4, and the last term is 9 plus 35 times 4). Among the given options, only the first choice contains the same amount of terms.
Put another way, we have
[tex]\displaystyle 9 + 13 + 17 + \cdots + 149 = \sum_{k=0}^{35} (9 + 4k)[/tex]
but if we make the sum start at k = 1, we need to replace every instance of k with k - 1, and accordingly adjust the upper limit in the sum.
[tex]\displaystyle 9 + 13 + 17 + \cdots + 149 = \sum_{k-1=0}^{35+1} (9 + 4(k-1))[/tex]
[tex]\displaystyle 9 + 13 + 17 + \cdots + 149 = \sum_{k=1}^{36} (5 + 4k)[/tex]
Related Questions
The quotient of a number and negative eight is five-eighths. Find the number.
Answers
Answer:
-64/5
Step-by-step explanation:
Basically, the word "quotient" means the answer to a division problem. Therefore, its a division problem, so you have to work backwards with multiplication. -8 times a number is 5/8, so the other number is going to be negative.
The number is -64/5
Answer:
n = -5
Step-by-step explanation:
Form this quotient, representing the number by n: n / (-8) = 5/8.
Solve this equation for n by multiplying both sides by 8: -n = 5. Then n = -5
Cushman Company had $842,000 in sales, sales discounts of $12,630, sales returns and allowances of $18,945, cost of goods sold of $399,950, and $289,650 in operating expenses. Gross profit equals:
Answers
Answer: $120825
Step-by-step explanation:
Add everything up then subtract $842000 by it
1. According to the fundamental theorem of algebra, how many zeros does the function [tex]f(x) = 3x^6 - 7x^5 - 53x^3 - 43x - 34[/tex] have?
2. What are the zeros of [tex]f(x) = 6x^3 + 25x^2 - 24x + 5[/tex]
Answers
Answer:
See below for answers
Step-by-step explanation:
1) The Fundamental Theorem of Algebra states that in an nth-degree polynomial, there are n zeroes at most, including those that are complex. Therefore, there are 6 zeroes in the function since it's a 6th-degree polynomial.
2) Reduce the polynomial and use the Zero Product Property:
[tex]0=6x^3+25x^2-24x+5[/tex]
[tex]0=(6x^2-5x+1)(x+5)[/tex]
[tex]0=(3x-1)(2x-1)(x+5)[/tex]
[tex]x_1=\frac{1}{3},x_2=\frac{1}{2},x_3=-5[/tex]
Which values from the given replacement set make up the solution set of this inequality?
5m≤10; {0, 2, 4, 6}
{0, 4, 6}
{2}
{0, 2}
{2, 4, 6}
Answers
Answer:
the solution to the inequality is m[tex]\leq[/tex] 2, so the solution set can include 2 and 0 since it is less then 2. but the rest do not work. so the answer is {0,2}
Step-by-step explanation:
5m[tex]\leq[/tex]10
divide by 5 on both sides and you are left with
m[tex]\leq[/tex]2
only 2 and 0 are less than or equal to 2
Hope this helps!
hello, please help me thanks:)
Answers
Step-by-step explanation:
2x + 5y
first add 2 and 5
and join x and y and it
answer is 2+ 5
=7 and x+y = xy
it axle answer is
= 7xy
To prepare for a wedding, Aiden bught 60 candles. He paid $0.37 for each candle. His sister bought 170 candles at a sale where she paid $0.05 less for each candle than Aiden did. How much did Aiden spend on candles, how much did his sister spend on candles, and who spent more on candles (how much more when you answer this question).
Answers
Answer:
Aiden spent $22.20. His sister spent $54.40. His sister spent $32.20 more than Aiden.
Step-by-step explanation:
A vase held flowers 1/2 is the flowers were roses and 1/4 of those flowers were red what fraction where red roses?
Answers
1/2 x 1/4 means 1/8 were red roses
Pls help I’ll brainlest and add extra points
Answers
Answer:
slope is -3
y intercept is 6
Step-by-step explanation:
The y intercept is where it crosses the y axis
It crosses the y axis at 6
We need two points to find the slope (0,6) and (2,0)
m = ( y2-y1)/(x2-x1)
= (0-6)/(2-0)
= -6/2
= -3
The slope is -3
Help with algebra class please
Answers
Answer:
t=6.8
Step-by-step explanation:
t=2.01[squareroot(L)]
L=11.56
t=2.01[squareroot(11.56)]
t=2.01(3.4)
t=6.834
(round to nearest tenth)
t=6.8
The ages of the students in a statistics class are listed below. If the 18-year-old student has a birthday and turns 19, how will it affect the mean and median ages of the class?
Ages: 14, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18
A
Both the mean age and the median age will increase.
B
The mean age will increase, and the median age will remain the same.
C
The mean age will remain the same, and the median age will increase.
D
The mean age will remain the same, and the median age will decrease.
Answers
The mean age will increase, and the median age will remain the same.
Option B is the correct answer.
What is a mean?It is the average value of the set given.
It is calculated as:
Mean = Sum of all the values of the set given / Number of values in the set
We have,
Ages:
14, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18
The mean of the ages.
= (14 + 15 + 15 + 16 + 16 + 16 + 16 + 17 + 17 + 17 + 17 + 17 + 18) / 13
= 211/13
= 16.23
The median of the ages.
= 16
Now,
18 becomes 19.
14, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 17, 19.
Mean = 212/13 = 16.3
Median = 16
Thus,
The mean age is increased.
The median is the same.
Learn more about mean here:
https://brainly.com/question/23263573
#SPJ2
A six-sided, fair number cube is rolled 100 times as part of an experiment. The frequency of the roll of the number 3 is 20. Which statement about rolling a 3 is correct?
The theoretical probability is 1/6. The experimental probability is 1/6.
The theoretical probability is 1/5. The experimental probability is 1/6.
The theoretical probability is 1/6. The experimental probability is 1/5.
The theoretical probability is 1/5. The experimental probability is 1/5.
Answers
Answer:
The theoretical probability is 1/6. The experimental probability is 1/5.
Step-by-step explanation:
Answer:
c for lazy goofy peoplee
Step-by-step explanation:
Find the volume in cubic feet of a rectangular moving van with length 14 feet, width 7 feet, and height 7 feet
Answers
Answer:
length (l) = 14 feet
breadth (b) = 7 feet
height (h) = 7 feet
so, volume of the
rectangular moving
van = l*b*h
=14feet * 7feet *7feet
= 686 cubic feet
If a < b then ka < kb
Answers
At the same time of day, a woman who is 78 inches tall casts a 63-inch shadow and her son casts a 21-inch shadow. What is the son's height? *
Answers
Answer:
26in
Step-by-step explanation:
The heights of the people in relation to their shadow lengths are proportional.
78in/63in = x/21in
The child's shadow is 1/3 the length of his mom so his height is 1/3 of hers.
78/3 = 26 in
Answer:
The son is 26 inches tall.
Step-by-step explanation:
[tex]\frac{x}{21} = \frac{78}{63}[/tex]
[tex]x= \frac{21x78}{63}[/tex]
21x78= 1638
1638÷63=26
Hope this helps
Sorry if I got it wrong!
PLEASE HELP IF YOU ANSWER BOTH I WILL GIVE
1. BRAINLIEST
2. 5 STARS
3. HEARTS
Answers
Answer:
both of your answers are b
Step-by-step explanation:
20. difference means subtract
21. assosiative property has to deal with three numbers while communitive is 2 numbers
I need Someone to help me with this problems equation and answer must be correct (100 Points)
Answers
Answer:
1) 3x+18=45 x=9
2)8-5x=-7 x=3
3)3+2x=15 x=6
4) 12million - 2 million = 10 million
Step-by-step explanation:
A survey of 600 nurses yielded the following information: 427 were health club members, 325 were smokers, and 245 of the health club members were smokers. How
many of the 600 surveyed nurses were health club members or were smokers?
Answers
The number of surveyed nurses that were health club members or were smokers is 316.
Let the total number of nurses be 600 nursesn(U) = 600Let H be health club members, n(H) = 427Let S be smokers, n(S) = 325If 245 of the health club members were smokers, then n(HnS) = 245 members.
The number of surveyed nurses that were health club members or were smokers = 600 - [(427 - 325) + (427-245)].
The number of surveyed nurses that were health club members or were smokers = 600 - (102+182) = 600 - 284.
The number of surveyed nurses that were health club members or were smokers is 316.
Learn more on set notation here: https://brainly.com/question/24462379
What type of angle of this?
Answers
Answer:
angle x is equal to 60º so its an acute angle
Step-by-step explanation:
Answer:
x = 60
Step-by-step explanation:
obtuse angle is 180 degres so you subtract the amount that you see and you will get x. This only works for questions like this contact me if you need more help with questions like these
180-120=60
In a proposed business venture, a businesswoman estimates there is a 65% chance she will make $57000 and a 35% chance she will lose $67000. Determine her expected value.
Answers
Answer:
q
Step-by-step explanation:
A triangle has vertices at A(-3, 2), B(-1, -5) and C(4, 5). The triangle is transformed using the rule ro,o . What are the coordinates of A", B', and C?
Answers
Answer:
I thinck letter c.
Step-by-step explanation:
Because C.
solve for m -7/9 m = 11/6
Answers
Answer:
19/18
Step-by-step explanation:
substitute the value of m(11/6) in m-7/9
which is equal to 11/6 -7/9 =19/18
Given that
[tex] log_{4}(y - 1) + log_{4}( \frac{x}{2} ) = z \: \: and \: log_{2}(y + 2) + log_{2}(x) = z - 1 \: show \: that \: {y}^{2} = 1 + {8}^{z} \: and \: find \: the \: values \: of \: y \: and \: x [/tex]
when z = 1
Answers
Answer:
Gracias por los puntos
Bye :v
BRAINLIEST IF CORRECT! (pls no links it rlly annoying)
Answers
looking at the picture, the region AB is where the inequality of f(x) overlaps the inequality g(x), so if we pick any point on that blue region AB, then f(x) will be TRUE and g(x) will also be TRUE, lemme narrow it down some, let's pick the point on AB of say (0,0), namely x = 0 and y = 0
let's try the 1st set
0 ⩽ - 2(0) + 3
0 ⩽ 3 <--- is that true? well yes, zero is less or equals, actually less than 3
0 ⩽ 0 + 3
0 ⩽ 3 <--- is that true? yes it's
let's try the 2nd inequalities set with the same values for "x" and "y"
0 ⩾ -2(0) + 3
0 ⩾ 3 <--- is that true? nope, no dice
let's not bother checking the other, since it already gave FALSE
let's try the 3rd inequalities set, same values
0 ⩽ -3(0) + 2
0 ⩽ 2 <--- is that true? yeap
0 ⩽ -(0) + 2
0 ⩽ 2 <---- is that true? yeap
not to bother you with the 4th set one, the 4th one fails and gives FALSE
so we know the 1st and 3rd one give TRUE on for f(x) and g(x), so which one is it?
take a peek at the picture below, notice the rise and run and therefore the slopes for each, g(x) has a slope of 2/2 = 1, and f(x) has a slope of 3/1 = 3, both going downwards, so both are negative, namely -1 and -3.
that means that g(x) will look like -1x + something, or -x + something.
and means that f(x) will look like -3x + something.
so that means the only set with those slopes will be [tex]\begin{cases} y\leqslant -3x + 2\\ y \leqslant -x + 2 \end{cases}[/tex]
Pls help. I'll mark you as brainliest.
The test scores of randomly selected students are listed: 30, 35, 43, 44, 47, 48, 54, 55, 57, 59, 62, 63, 65, 66, 68, 69, 71, 72, 73, 74, 76, 77, 77, 78, 79, 80, 81, 81, 82, 83, 85, 89, 92,93,94,97,98 Find the median.
Answers
Answer:
the median is 73 because 73 is the middle number
Please help meee! I will give brainlist to quickest answer !!!
What is the equation of this graphed line?
Answers
Answer:
You said quick so here it is
[tex]y-6=2(x-2)[/tex]
On a bird-watching trip, Mei and Jackie counted 68 birds.
Of these, 45 of the birds were sparrows. Which value is a
reasonable estimate of the percent of sparrows in the
birds Mei and Jackie counted?
1. 175%
2.140%
3. 70%
4. 90%
Answers
Answer:
The answer is 70% if you round it.
Step-by-step explanation:
45 out of 68 is 66 but if you're rounding it the answer is 70%.
Can someone please help me on these? Please explain. Thank you.
Answers
Answer:
It might be 109 degrees
Step-by-step explanation:
Point J: 48 degrees
Point H: 23 degrees
Point F: 109 degrees
109 + 48 + 23 = 108 degrees
I WILL GIVE BRAINLEST HURRY PLEASE ITS DUE RIGHT NOW HURRY PLEASE plssss help me if your good at finding area in shapes plsss
Answers
in Emma's supply box a pencil weighs 3ounces.her scissors weigh 3 ounces more than the pencil and a bottle of glue weigh three times as the scissors how much those the bottle of the glue weigh in pounds and ounces.
Answers
Answer:
18 Ounces which is equal to 1 pound and 2 ounces
Step-by-step explanation:
pencil weighs 3 ounces
scissors weighs =pencil+3 ounces =6 ounces
bottle of glue=3*scissors which is equal to 18 Ounces simple 16 ounces = 1 pound
Thanks
Britney is trying out for the track team along with 24 other people nine people were running distance seven people were there to sprint three people are in the competition to throw Shotput and six people were there to polevault Britney was able to run a half a mile in six minutes and she finish seventh Place in the 100 m dash which of these pieces of data is discreet and which one is continuous
Answers
Answer:
The 6-minute half-mile time is continuous data; the number of people trying out for the team is discrete data.
Step-by-step explanation:
