Answer:
52
Step-by-step explanation:
a(n)=-5+(n-1)3
a(20)=-5+(20-1)3
a(20)=52
The 20th term of the arithmetic sequence is 52.
What is Arithmetic sequence?An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence.
For example,
In an arithmetic sequence, the difference between consecutive terms is always the same. For example, the sequence 3, 5, 7, 9 ... is arithmetic because the difference between consecutive terms is always two.
The nth term of an arithmetic sequence is given by an = a + (n – 1)d.
Given:
a(n)=-5+(n-1)3
First term,
a(1)= -5 + 0
a(1)= -5
second, a(2)= -5 + 1*3
a(2)= -2
Third, a(3)= -5+6
a(3)= 1
d= 3
So, the 20th term
a(20)= -5+ (20-1)3
a(20)= -5 + 57
a(20)= 52
Hence, the 20th term is 52.
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(16 choose 0) + (16 choose 1) + ..... + (16 choose 16)
Please Help!
Use the binomial theorem:
[tex](1+1)^{16}=\displaystyle\sum_{k=0}^{16}\binom{16}k1^{16-k}1^k[/tex]
So
[tex]\dbinom{16}0+\dbinom{16}1+\cdots+\dbinom{16}{16}=\boxed{2^{16}}[/tex]
More generally,
[tex]\displaystyle\sum_{k=0}^n\binom nk=2^n[/tex]
Brainliest for correct awnser! What is the domain of f(x)?
Answer:
[tex]\mathrm{B.}[/tex] All real numbers except x = 2, x = 5
Step-by-step explanation:
If the denominator is equal to 0 then the function would be undefined.
Set the denominator equal to 0.
x² - 7x + 10 = 0
Factor the left side of the equation.
(x - 5)(x - 2) = 0
Set the factors equal to 0.
x - 5 = 0
x = 5
x - 2 = 0
x = 2
The domain is all real numbers except x = 2 and x = 5.
A restaurant has two different seating options: a table and a family booth. A table can seat 2 people, and a family booth can seat 6 people. The restaurant has a maximum capacity of 120 people. If the restaurant has 15 family booths, which inequality could be used to find t, the number of tables in the restaurant
Answer:
t ≤ 15
Step-by-step explanation:
Let t = tables
6 * 15 + 2* t ≤ 120
90 + 2t ≤ 120
2t ≤ 30
t ≤ 15
Without actually solving the problem, choose the correct solution by deciding which choice satisfies the given conditions.
Kesha has a total of 100 coins, all of which are either dimes or quarters. The total value of the coins is $14.50. Find the number of each type of coin.
Which choice satisfies the given conditions?
O A. 70 dimes, 30 quarters
B. 20 dimes, 80 quarters
C. 40 dimes, 42 quarters
Answer:
A. 70 dimes, 30 quarters
Step-by-step explanation:
Only options A and B create a total of 100 coins. It cannot be option B because 80 quarters by itself, is already over $14.50.
Fill in the blank. For data sets having a distribution that is approximately bell-shaped, _______ states that about 68% of all data values fall within one standard deviation from the mean
Answer:
Empirical Rule
Step-by-step explanation:
The Empirical Rule is also known as the Sigma rule or the 68-95-99.7% rule. The rule state that for a given data set, 68% of all data values will fall within the first standard deviation from the mean. The rule also states that 95% of all data values would fall within two standard deviations, while almost all the data which amounts to about 99.7% will fall within three standard deviations.
The empirical rule is used in forecasting based on the given datasets because it is a certainty that after obtaining the standard deviation, data values can be assigned to the categories they fall into, under the Empirical rule.
In a game of rock-paper-scissors, you have a 1/3 chance of winning, a 1/3 chance of losing, and a 1/3 chance of tying in any given round. What is the probability that you will win at least twice in 3 rounds, given that there aren't any tied rounds in this particular match
Answer: 1/5
Step-by-step explanation:
given data;
chances of winning = 1/3
chances of losing = 1/3
chances of tying in a given round = 1/3
solution:
probability that you would win atleast 2 in any 3 matches without a tied match is
1/3 / ( 2 - 1/3 )
= 1/3 / 5/3
= 1/5
the probability of winning 2 of 3 games without a tie is 1/5
please factor!
7x^2+27xy-4y^2
If a = i - 9k and b = j + k , find ab .
Answer:
solution
given a=1_9k and b=j+k
Now,ab=(1_9k)(j+k)
=1((j+k)-9k(j+k)
=j+k_9jk-9k^2
=k_9k^2+j_9jk
=k((1_9k)+j(1_9k)
=(1_9k)(k+k)
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If
x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this
situation.
x + y = 24
3x + 5y = 100
What does the solution of this system indicate about the questions on the test?
The test contains 4 three-point questions and 20 five-point questions.
The test contains 10 three-point questions and 14 five-point questions.
The test contains 14 three-point questions and 10 five-point questions.
The test contains 20 three-point questions and 8 five-point questions.
Mark this and retum
Save and Exit
Nexi
Submit
Answer: B) 10 three-point questions and 14 five-point questions
Step-by-step explanation:
x represents three-point questions
y represents five-point questions
3x + 5y = 100 → 1(3x + 5y = 100) = 3x + 5y = 100
x + y = 24 → -3(x + y = 24) = -3x -3y = -72
2y = 28
y = 14 (five-point questions)
x + y = 24
x + 14 = 24
x = 10 (three-point questions)
Add (7.8x10^5+(2.4x10^5)
answer: 1020000
step-by-step explanation:
(7.8*10^5+(2.4*10^5) given expression
(7.8*10^5)+(2.4*10^5) group with parenthesis
(7.8+2.4)*10^5 combine like terms
10.2*10^5 preform addition
10.2*100000 evaluate the exponent
1020000 multiply out
The local diner offers a meal combination consisting of an appetizer, a soup, a main course, and a dessert. There are three appetizers, three soups, three main courses, and three desserts. Your diet restricts you to choosing between a dessert and an appetizer. (You cannot have both.) Given this restriction, how many three-course meals are possible
Answer:
There are 2 * 32 = 64 possible ways for choosing three course meal.
Step-by-step explanation:
1-If we choose an appetizer, main course and a soup then there are 32 ways to choose this three course meal. 4 * 2 * 4 = 32 ways. There will be an appetizer, main course and a soup in the meal.
2-If we choose a soup, main course and a dessert then there are 32 ways to choose this three course meal. 4 * 2 * 4 = 32 ways. There will be a soup, main course and a dessert in the meal.
There are 2 possible ways to choose either an appetizer or dessert in a 3 course meal. There will be 64 ways in total for the three course meal.
Determine the value of x and y
Answer:
x = 28, y = 23
Step-by-step explanation:
5y - 4 and 3y are alternate exterior angles and are supplementary, thus
5y - 4 + 3y = 180
8y - 4 = 180 ( add 4 to both sides )
8y = 184 ( divide both sides by 8 )
y = 23
Thus
3y = 3 × 23 = 69
2x + 13 and 3y are corresponding angles and congruent, thus
2x + 13 = 69 ( subtract 13 from both sides )
2x = 56 ( divide both sides by 2 )
x = 28
Which interval contains a local minimum for the graphed
function?
Answer:
[2.5 ,4]
Step-by-step explanation:
The graph in this interval has a vertex while opening up wich means it's a minimum
Which of the following functions is graphed below?
O A. y - x - 61+3
O B. y - x + 61-3
O C. y = x +61+3
D. y - x - 61-3
Answer:
B
Step-by-step explanation:
Since the vertex of the function is (-6, -3), we know the equation must be y = |x + 6| - 3.
Answer:
B. |x+6|-3
Step-by-step explanation:
Well we can tell by looking at the graph that the line has a y-intercept of +3,
meaning we can cross out choices A and C.
Now we can graph B and D,
Look at the image below ↓
By looking at the graphed lines we can tell that y = |x+6|-3 is the correct answer.
Wel can also conclude that choice B is correct because of its vertex being at (-6,-3).
Thus,
answer choice B is the correct answer.
Hope this helps :)
A salesperson earns 6% commission on $25.000. How much
commission was earned?
The commission earned was $
Answer: $1500
Step-by-step explanation:
6% commission on $25,000
= 25000 x .06
= 1500
Sanjay makes souvenir pyramids by pouring liquid into a pyramid-shaped mold. The mold he uses has a square base with a side length of 10\text{ cm}10 cm10, start text, space, c, m, end text, and the height of the mold is 10\text{ cm}10 cm10, start text, space, c, m, end text. Sanjay wants to make a smaller pyramid using the same mold, so he plans to fill the mold 2\text{ cm}2 cm2, start text, space, c, m, end text from the top. What is the approximate volume of this smaller pyramid?
Answer:
170.67
Step-by-step explanation:
Answer:
171
Step-by-step explanation:
Modeling the situation
If we fill the pyramid mold 2\text{ cm}2 cm2, start text, space, c, m, end text from the top, we have a smaller pyramid that's similar to the original pyramid.
Since the pyramids are similar, we can set up a proportional equation to find the side lengths and height of the smaller pyramid, and then find its volume.
Hint #22 / 4
Base and height of smaller pyramid
The height of the smaller pyramid is 10-2=8\text{ cm}10−2=8 cm10, minus, 2, equals, 8, start text, space, c, m, end text.
We can solve for the length \blueE{\ell}ℓstart color #0c7f99, ell, end color #0c7f99 in the smaller pyramid using a proportional equation.
\begin{aligned} \dfrac{\blueE{\ell}}{10} &= \dfrac{8}{10} \\\\ \blueE{\ell} &= \blueE{8} \end{aligned}
10
ℓ
ℓ
=
10
8
=8
Hint #33 / 4
Volume of smaller pyramid
\begin{aligned} \text{volume}_{\text{pyramid}} &= \dfrac13(\text{base area})(\text{height}) \\\\ &= \dfrac13 \cdot (\blueE{\ell})^2\cdot (\text{height}) \\\\ &= \dfrac13 \cdot \blueE{8}^2\cdot(8)\\\\ &= \dfrac{512}{3}=170.\overline{6}\\\\ &\approx \purpleD{170.67} \end{aligned}
volume
pyramid
=
3
1
(base area)(height)
=
3
1
⋅(ℓ)
2
⋅(height)
=
3
1
⋅8
2
⋅(8)
=
3
512
=170.
6
≈170.67
Hint #44 / 4
To the nearest cubic centimeter, the volume of the smaller pyramid is about 171\text{ cm}^3171 cm
3
171, start text, space, c, m, end text, cubed.
Evaluate 2x^+2x+8 when x=4
If a gang of eight rob a bank, what percent of the loot belongs to three of the robbers? What percent belongs to them if two of the gang are killed? By what percent does each robber’s share increase? What percent belongs to three of them? What percent belongs to them if two of the gang are killed? Each robber's share increases by how much percent?
Answer:
(assuming all members of the gang get equal percentages)
For a gang of 8: 12.5% (100/8)
If 2 are killed: 16.67% (100/6), so percentage increases by roughly 4.2% (16.67-12.5)
Percent that belongs to 3: 12.5%*3=37.5%
Percent that belongs to 3 if 2 are killed: 16.67%*3=50.0%
Each robber's share still increases by 4.2% (50%-37.5%=12.5%, 12.5%/3=4.2%)
If you would like additional help with math or another subject, check out growthinyouth.org!
Step-by-step explanation:
matthew grew 2.7 inches last year and 4.4 inches this year. How many inches has Matthew grown over the last two years combined
Answer:
7.1 inchesStep-by-step explanation:
Total inches grown last year by matthew = 2.7inches
Total inches grown this year by Matthew = 4.4 inches
Total inches grown by Matthew over the last two years combined will be the sum of heights of matthew for both the previous year and the current year.
Total inches grown = 2.7 inches + 4.4 inches
Total inches grown over the last two years = 7.1 inches
he data represents the daily rainfall (in inches) for one month. Construct a frequency distribution beginning with a lower class limit of 0.000.00 and use a class width of 0.200.20. Does the frequency distribution appear to be roughly a normal distribution? 0.310.31 0 0 0 0.190.19 0 0.150.15 0 0.010.01 0.190.19 0.530.53 0 0
Answer:
It is not normally distributed as it has it main concentration in only one side.
Step-by-step explanation:
So, we are given that the class width is equal to 0.2. Thus we will have that the first class is 0.00 - 0.20, second class is 0.20 - 0.40 and so on(that is 0.2 difference).
So, let us begin the groupings into their different classes, shall we?
Data given:
0.31 0.31 0 0 0 0.19 0.19 0 0.150.15 0 0.01 0.01 0.19 0.19 0.53 0.53 0 0.
(1). 0.00 - 0.20: there are 15 values that falls into this category. That is 0 0 0 0.19 0.19 0 0.15 0.15 0 0.01 0.01 0.19 0.19 0 0.
(2). 0.20 - 0.40: there are 2 values that falls into this category. That is 0.31 0.31
(3). 0.4 - 0.6 : there are 2 values that falls into this category.
(4). 0.6 - 0.8: there 0 values that falls into this category. That is 0.53 0.53.
Class interval frequency.
0.00 - 0.20. 15.
0.20 - 0.40. 2.
0.4 - 0.6. 2.
Draw a pie chart for the percent of the money spent on various types of books by a library in a year.
Answer:
The pie chart representing for this question is presented in the attached image to this solution.
Step-by-step explanation:
Complete Question
Draw a pie chart for the percent of the money spent on various types of books by a library in a year.
Type of book | %
Fiction | 20%
Classics | 15%
Sports | 10%
Biography | 12.5%
Magazines | 22.5%
Others | 20%
Solution
A pie chart is a graphical representation of a set of numerical data which comes in a circular shape divided into slices, with the size of each slice corresponding to the proportion of the numerical data it represents.
Because it is a circle, the total angles in a pie chart is 360°.
The angles are divided into slices with the size of each slice corresponding to how large the data it represents is.
So, we first convert the data given into degrees.
Since the data is given in percentage, for each of the groups, the conversion from percentage will be
Angle = (Proportion) × 360°
Type of book | % | Angle
Fiction | 20% | 72°
Classics | 15% | 54°
Sports | 10% | 36°
Biography | 12.5% | 45°
Magazines | 22.5% | 81°
Others | 20% | 72°
The pie chart representing this data is presented in the attached image to this solution.
Hope this Helps!!!
Mustafa’s soccer team is planning a school dance as a fundraiser. The DJ charges $200 and decorations cost $100. The team decides to charge each student $5.00 to attend the dance. If n represents the number of students attending the dance, which equation can be used to find the number of students needed to make $1,500 in profit? A: 5n - 300 = 1,500 B: 5n + 300 = 1,500 C: 5n - 200 + 100n = 1,500 D: 5n - 100 - 200n = 1,500
Answer:
The answer should be B: 5n+300=1,500.
Step-by-step explanation:
The number of people to attend is going to vary and 300 is a set variable, so it won't change of be affected. Since the team doesn't know how many people will be able to attend in order to reach their goal, n is going to take the place for the amount of people.
If you were to solve this, the answer would be:
5n+300=1,500
5n=1,500-300
5n=1,200
n=240
So 240 people can attend the dance.
Answer:5n-300=1,500
Step-by-step explanation:
Which of the following are exponential functions? Select all correct answers.
Select all that apply:
NE1
f(x) = 10(1/7)^x
g(x) = 4(-3)^x
h(x) = 4(-13)^x
j(x) = 8(4.13)^x
k(x) = 12(8)^x
Answer:
F, J, and K
Step-by-step explanation:
The others are negative so they can't be exponential
The exponential function can't be negative or irrational, so options A, D, and E are correct.
What are exponential functions?The exponential function in mathematics is represented by the symbol eˣ (where the argument x is written as an exponent). The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to complex numbers or adapted to other mathematical objects like matrices or Lie algebras. The idea of exponentiation, or repeated multiplication, is where the exponential function got its start, but more recent definitions—there are several that are equivalent—allow it to be rigorously extended to all real arguments, including irrational values.
As we discussed above, the exponential function can't be negative or irrational so, look at the options only,
f(x) = 10(1/7)ˣ,
j(x) = 8(4.13)ˣ,
k(x) = 12(8)ˣ are the exponential functions, whereas
g(x) = 4(-3)ˣ,
h(x) = 4(-13)ˣ are negative, so they can't be exponential functions.
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what is 99/00+44(55)99
Answer:
undefined! one cannot divide by 0
Step-by-step explanation:
Answer:
undefined!
Step-by-step explanation:
The function h(t) = -4.9t² + 19.6t is used to model the height of an object projected in the air where h(t) is the height (in meters) and t is the time (in seconds). What is the domain and range? Domain:
Answer:
Step-by-step explanation:
when h(t)=0
-4.9 t²+19.6t=0
4.9t(-t+4)=0
either t=0 or t=4
so domain is 0≤t≤4
for range
h(t)=-4.9t²+19.6t
=-4.9(t²-4t+4-4)
=-4.9(t-2)²+19.6
so range is 0≤h≤19.6
Domain = 0<t<4, make sure to use less than or equal to signs not just less than signs.
Range = 0<h<19.6, again, use less than or equal to signs.
what is the standard form for these 2 quadratic equations ASAPP!!!!
Problem 3
Answer: y = x^2 - 7x + 10----------
Work Shown:
Use either the FOIL method, distributive property, or the box method to get the following
(x-2)*(x-5) = x^2 - 5x - 2x + 10 = x^2 - 7x + 10
==========================================
Problem 4
Answer: y = x^2 - x - 6----------
Work Shown:
Same idea as problem 3 above
(x-3)(x+2) = x^2+2x-3x-6 = x^2 - x - 6
Answer:
3. y = x² - 7x + 10
4. y = x² - x - 6
Step-by-step explanation:
What is the quotient? StartFraction 7 Superscript negative 4 Over 7 Superscript negative 9 EndFraction
Answer:
19
Step-by-step explanation:
7 supersricpt 8
Solve the following rational equation for x.
1/4x-3/4=7/x
Answer:
x1= -4, x2 = 7
Step-by-step explanation:
Move expression to the left-hand side:
1/4x-3/4-7/x=0
Write all the numerators above a common denominator:
x^2 - 3x - 28 /4x =0
When the quotient of expressions equal 0, the numerator has to be 0
x^2 + 4x - 7x - 28 = 0
x(x+4) - 7(x+4) =0
(x+4) × (x-7) =0
Separate into possible cases:
x+4=0
x-7=0
Answer: -9
Step-by-step explanation:
A random sample of 64 observations produced a mean value of 86 and standard deviation of 4.5. The 95% confidence interval for the population mean μ is between:_________.
Answer: (84.876, 87.124)
Step-by-step explanation:
Confidence interval for population mean if population standard deviation is unknown:
[tex]\overline{x}\pm t_{\alpha/2}(\dfrac{s}{\sqrt{n}})[/tex]
, where n= sample size
s= sample standard deviation
[tex]\overline{x}[/tex] = sample mean
[tex]\alpha=[/tex] significance level
[tex]t_{\alpha/2}[/tex] = critical-t value
Given: n= 64
Degree of freedom = n-1 = 63
s= 4.5
[tex]\overline{x}[/tex] = 86
[tex]\alpha=[/tex] 0.05
[tex]t_{\alpha/2}[/tex] = 1.9983
Now, the required 95% confidence interval would be:
[tex]86\pm (1.9983)(\dfrac{4.5}{\sqrt{64}})\\\\=86\pm (1.9983)(\dfrac{4.5}{8})\\\\=86\pm (1.9983)(0.5625)\\\\\approx86\pm 1.1240\\\\ =(86-1.1240,\ 86+1.1240)\\\\=(84.876,\ 87.124)[/tex]
The 95% confidence interval for the population mean μ is between: (84.876, 87.124)
Solve the quadratic equation 8x2 + 6x = 5 using the quadratic formula
Answer:
[tex]x=-\frac{11}{6}[/tex]
Step-by-step explanation:
8x2=6x=5
16+6x=5
6x=5-16
6x=-11
[tex]x=-\frac{11}{6}[/tex]
Answer:
See below.
Step-by-step explanation:
[tex]8x^2+6x=5[/tex]
Reformat this so the equation equals zero:
[tex]8x^2+6x-5=0[/tex]
[tex]a=8, b=6, c=-5[/tex]
[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
[tex]x=\frac{-(6)\pm\sqrt{(6)^2-4(8)(-5)} }{2(8)}[/tex]
[tex]x=\frac{-6\pm\sqrt{36+160} }{16}[/tex]
[tex]x=\frac{-6\pm\sqrt{196} }{16}[/tex]
[tex]x=\frac{-6\pm14 }{16}[/tex]
[tex]x=\frac{-6+14}{16}=8/16=1/2[/tex] or
[tex]x=\frac{-6-14}{16}=-20/16=-5/4[/tex]