There are 100 numbers in the range 100-199. Find the smallest and largest multiple of 13 in this range. We have
104 = 8•13
195 = 15•13
so there are 15 - 8 + 1 = 8 multiples of 13 between 100 and 199.
Then the sum we want is
[tex]\displaystyle \sum_{k=100}^{199} k - \sum_{\ell=8}^{15}13\ell[/tex]
or equivalently,
(100 + 101 + 102 + … + 199) - 13 (8 + 9 + … + 15)
To compute these sums, recall the following formula:
[tex]\displaystyle \sum_{i=1}^n i = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2[/tex]
Then
[tex]\displaystyle \sum_{k=100}^{199} k = \sum_{k=1}^{199} k - \sum_{k=1}^{99} k = \frac{199\cdot200}2 - \frac{99\cdot100}2 = 14,950[/tex]
and
[tex]\displaystyle \sum_{\ell=8}^{15} 13\ell = 13 \left(\sum_{\ell=1}^{15} \ell - \sum_{\ell=1}^7 \ell\right) = 13 \left(\frac{15\cdot16}2 - \frac{7\cdot8}2\right) = 1,196[/tex]
which means the sum we want is 14,950 - 1,196 = 13,754.
Describe the transformation of g(x)=4|x|
[tex]g(x) = 4 |x| = x = 0[/tex]
need help with these questions
Step-by-step explanation:
these are both quadratic curves, parabolas, and factorization means to express the 2 terms as multiplication with each other, so that the result would be the simplified function. in other words : find the two factor terms that make the whole function.
the advantage of factorization is to see the 2 solutions for y=0 right away.
the general form is
y = (x + a)(x + b)
and the y=0 solutions are then simply x = -a and x = -b.
in example 3 we have 2 different y=0 solutions, seemingly at x = 1 and x = 5.
that makes the factorization :
y = (x - 1)(x - 5)
when x becomes one of these values, the corresponding factor becomes 0 and therefore y becomes 0 too.
in example 4 we have only one y=0 solution (or so it seems; in fact there are still formally 2 solutions, they are just equal).
it is seemingly at x = -2.
since both solutions are equal, we have also two equal factors.
that makes the factorization
y = (x + 2)(x + 2) = (x + 2)²
A person is running a distance race at a constant rate. What time will they finish the race what information would you need to be able to solve the problem?
Answer:
you need the distance they're running and the pace they are running at.
The result of a division problem is the a ) divisor . b ) quotient . c ) factor . d ) remainder .
Answer:
b) quotient
Step-by-step explanation:
divisor is the number/value you are dividing with.
A remainder is a number that remains after you divide.
A factor is a number that can divide into a number or numbers without leaving a remainder
The diameter of a circle is 6.8 m. Find the circumference to the nearest tenth
Answer:
21.4m
Step-by-step explanation:
Circumference : x diameter
is approximately 3.142
3.142 x 6.8 = 21.3656
Nearest tenth = 21.4m
Can someone help me please
Answer:
40 students earned a B on this paper.
40%×80=32 people who chose action as their fav.
A company generally purchases large lots of a certain kind of electronic device. A method is used that rejects a lot if 4 or more defective units are found in a random sample of 100 units. ​(a) What is the probability of rejecting a lot that is ​3% ​defective? ​(b) What is the probability of accepting a lot that is ​4% ​defective?
Using the binomial distribution, it is found that there is a:
a) 0.3526 = 35.26% probability of rejecting a lot that is 3% defective.
b) 0.4295 = 42.95% probability of accepting a lot that is 4% defective.
For each device, there are only two possible outcomes, either it is defective, or it is not. The probability of a device being defective is independent of any other device, hence the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.In this problem, the sample has 100 units, hence [tex]n = 100[/tex].
Item a:
3% of the pieces are defective, hence [tex]p = 0.03[/tex].
The probability is:
[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]
In which:
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
Hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{100,0}.(0.03)^{0}.(0.97)^{100} = 0.0476[/tex]
[tex]P(X = 1) = C_{100,1}.(0.03)^{1}.(0.97)^{99} = 0.1471[/tex]
[tex]P(X = 2) = C_{100,2}.(0.03)^{2}.(0.97)^{98} = 0.2252[/tex]
[tex]P(X = 3) = C_{100,3}.(0.03)^{3}.(0.97)^{97} = 0.2275[/tex]
Then:
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0476 + 0.1471 + 0.2252 + 0.2275 = 0.6474[/tex]
[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.6474 = 0.3526[/tex]
0.3526 = 35.26% probability of rejecting a lot that is 3% defective.
Item b:
4% of the pieces are defective, hence [tex]p = 0.04[/tex].
Lot is accepted if less than 4 units are defective, hence:
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
[tex]P(X = 0) = C_{100,0}.(0.04)^{0}.(0.96)^{100} = 0.0169[/tex]
[tex]P(X = 1) = C_{100,1}.(0.04)^{1}.(0.96)^{99} = 0.0703[/tex]
[tex]P(X = 2) = C_{100,2}.(0.04)^{2}.(0.96)^{98} = 0.1450[/tex]
[tex]P(X = 3) = C_{100,3}.(0.04)^{3}.(0.96)^{97} = 0.1973[/tex]
Then:
[tex]P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0169 + 0.0703 + 0.1450 + 0.1973 = 0.4295[/tex]
0.4295 = 42.95% probability of accepting a lot that is 4% defective.
A similar problem is given at https://brainly.com/question/24863377
Simplify.
5x+3(x+2)+3
A. 8x + 9
B. 5x + 8
C. 8x + 5
D. 6x + 8
Answer:
A- 8x+9
Step-by-step explanation:
------------------------------------------
5x + 3 (x + 2) + 3
5x + 3x + 6 + 3
8x + 6 + 3
8x + 9
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Sally must have at least $200 in her savings account to avoid a
fee. She currently has $850 in her account, but plans to spend
$75 per week. Write an inequality to determine the number of
weeks she can spend money and avoid a penalty.
Answer:
675$
Step-by-step explanation:
got it right
An aircraft factory manufactures airplane engines. The unit C(the cost in dollars to make each airplane engine) depends on the number of engines made. If x engines are made , then the unit cost is given by the function C (x) = 0.9x^2-306x+34,590. What is the minimum unit cost?
Laws involving positive integral exponents to zero & negative integral exponents.
Paul and anthony were asked to simply a^(2)/a^(-7) . Who do you think is correct in simplifying tge given expression? Justify your answer in 3 to 5 sentences.
Answer:
Both are correctStep-by-step explanation:
Paul used the following identities:
[tex]a^{-b}=1/a^b[/tex][tex]a^b*a^c=a^{b+c}[/tex]Anthony used the identity:
[tex]a^b/a^c= a^{b-c}[/tex]Number of Bars
1
Analyze A store sells variety packs
of granola bars. The table shows
the types of bars in each pack.
Mason says that for every 7 bars in
a pack, there is 1 cinnamon bar.
Do you agree? Explain.
Type
Cinnamon:1
Honey:4
Peanut Butter:3
Answer: Disagree. 1 in 8 bars are cinnamon.
Step-by-step explanation:
There are a total of 8 bars in the pack. Cinnamon is 1 of the 8. Therefore, for every 8 bars, one is cinnamon.
Find the square of the given algebraic expression (p+9).
I mark u brainliest answer
The annual rainfall in a town has a mean of 51.84 inches and a standard deviation of 8.05 inches. Last year there was rainfall of 63 inches. How many standard deviations away from the mean is that
It is 1.39 standard devaitions away from the mean.
Since the mean x = 51.84 inches and the standard deviation, σ = 8.05 inches.
The amount of rainfall last year was X = 63 inches.
The difference between X and the mean x is d = X - x
= 63 - 51.84 in
= 11.16 in
To find the number of standard devaitions X is from the mean, n, we divide d by the standard deviation,σ.
So, n = d/σ
= 11.16 in/8.05 in
= 1.39
So, it is 1.39 standard devaitions away from the mean.
Learn more about number of standard deviations here:
https://brainly.com/question/24254824
HELP ME PLEASE!! I DONT WANT TO FAIL THIS AGAIN.
Answer:
A.
Step-by-step explanation:
You can see that the rate of change of function A is 3. because that's the slope (M) in y=mx+b
5 is slope for B because unit rate is 5 ( 1 to 3 change is +10 so unit rate is 5)
Mrs. Penn charges $10.00 an hour on top of a $5.00 flat fee for tutoring. Mrs. Smith charges $14.00 an hour with no flat fee. Write and solve an equation to find how many hours T takes for Mrs. Penn and Mrs. Smith to get paid the same amount.
Answer:
1.25 Hours (1 hour & 15 minutes)
Step-by-step explanation:
14x = 5 + 10x
Subtract 10x from both sides
4x = 5
Divide by 4 on both sides
x = 1.25
It will take 1 hour and 15 minutes (1.25 hours) for Mrs. Penn and Mrs. Smith to be paid the same amount.
Hello Good morning/evening/afternoon !
Pls Help ?!
Answer: y = 3/5x + 6
Step-by-step explanation: Slope intercept form is y = mx + b
We must convert your problem into this.
3x - 5y = -30
-5y = -30 - 3x
-5y = -3x - 30
y = (-3x - 30)/-5
y = 3/5x + 6
Would appreciate brainly <3
ABCD is a parallelogram.the length of AB is 15 what is the the length of CD
rhombus opposite sides are equal.
So, CD = 15
· Carlos ran one lap in 1 minute 3 seconds. Orlando rana one lap 5 seconds faster than Carlos. How many seconds did it take Orlando to run one lap?
Answer:
58 seconds.
Step-by-step explanation:
Since one minute equals 60 seconds, Carlos took 63 seconds.
Orlando ran in 63 seconds - 5 seconds, which is equal to 58 seconds.
What is the relationship between 2.57×104 and 2.57×10−1 ?
2.57×104 is
Choose:
100
1000
10,000
100,000
1,000,000
times
Choose:
Greater or Less
than 2.57×10−1 .
Answer:
2.57×104= 267.28
2.57×10-1= 24.7
Answer:
2.57x10^4 is 100,000 Greater that 2.57x10^-1
Step-by-step explanation:
2.57x10^4 has a power by 4 which means
10^4 = 10,000
and 2.57x10^-1 has a power by -1 which means
10^-1 = 0,1
therefore 2.57x10^4 is 100,000 Greater that 2.57x10^-1
1/5 divided by 2/3 input the answer as a fraction
Answer:
Three tenths/ 3/10
Step-by-step explanation:
1/5 divided by 2/3 is 0.3 which is equal to 3/10
What integer is equivalent to 25 3/2?
Answer:
[tex]25\frac{3}{2} =26.5[/tex]
Step-by-step explanation:
This mixed number can be separated into 25 and [tex]\frac{3}{2}[/tex]. Convert the fraction to a decimal by plugging it into a calculator, then add 25.
If you meant what whole number is equivalent, that does not exist.
HELP FAST PLS I’ll mark u brainliest
Answer:
about 20 cents
Step-by-step explanation:
#Shop A
Pack of 10pens=£2.30Pack of 70pens:-
[tex]\\ \sf\longmapsto 7(2.30)=16.10[/tex]
#2
Pack of 5=1.60£Pack of 70
[tex]\\ \sf\longmapsto 14(1.60)=20.80[/tex]
But you get half price
20.80/2=10.40Difference:-
[tex]\\ \sf\longmapsto 16.10-10.40=5.70\£[/tex]
Help help help help help help help help help help help
Answer:
A' 2,2
B' 3, -1
C' -1,0
Step-by-step explanation:
Because you're translating it by -2, 3, you're basically subtracting 2 from the x value and adding 3 to the y value.
A = 4, -1
A' = 2, 2
B = 5, -4
B' = 3, -1
C = 1, -3
C' = -1, 0
Hoping to lure more shoppers downtown, a city builds a new public parking garage in the central business district. The city plans to pay for the structure through parking fees. During a two-month period (44 weekdays), daily fees collected averaged $126, with a standard deviation of $15. a) What assumptions must you make in order to use these statistics for inference
The assumptions required for making inference about a population using sample data include ;
The 10% condition, sample size must not be more than 10% of the population size Data should be approximately normal with sample size, n being greater than 30 (n ≥ 30).The sample selection must be independent, as the outcome of a certain trial must not depend on the outcome of another.Learn more : https://brainly.com/question/25609474
work out the value of 10²-4³ give ypur answer as a power of 6
Answer: 36
Step-by-step explanation: 10^2 is 100 and 4^3 is 64, and 100-64=36
I don't know the answer to this & I don't understand how to get it.
Answer:
i thank it h
Step-by-step explanation:
Answer:
Well your answer is (F)
Step-by-step explanation:
?
Out of the 25 students in Mrs. Green's class, 15 have a pet. What percent of the students in Mrs. Green's class have a pet?
Order the numbers –0.5, 1.25, 0.75, and –1.08 from least to greatest.
Answer:
Least to greatest
0.75 , 1.25 , -1. 08 , -0. 5
Step-by-step explanation:
Hope my answer helps you
If we recall that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, which lengths make sense for possible values of b? Select two options.
Answer:
Step-by-step explanation:
the first ine make sense to me
if not right sorry
Answer:
0.5in and 2in
Step-by-step explanation:
It is the answer