Given:
The sum of the first three terms = 12
The sum of the first six terms = (−84).
To find:
The third term of a geometric progression.
Solution:
The sum of first n term of a geometric progression is:
[tex]S_n=\dfrac{a(r^n-1)}{r-1}[/tex]
Where, a is the first term and r is the common ratio.
The sum of the first three terms is equal to 12, and the sum of the first six terms is equal to (−84).
[tex]\dfrac{a(r^3-1)}{r-1}=12[/tex] ...(i)
[tex]\dfrac{a(r^6-1)}{r-1}=-84[/tex] ...(ii)
Divide (ii) by (i), we get
[tex]\dfrac{r^6-1}{r^3-1}=\dfrac{-84}{12}[/tex]
[tex]\dfrac{(r^3-1)(r^3+1)}{r^3-1}=-7[/tex]
[tex]r^3+1=-7[/tex]
[tex]r^3=-7-1[/tex]
[tex]r^3=-8[/tex]
Taking cube root on both sides, we get
[tex]r=-2[/tex]
Putting [tex]r=-2[/tex] in (i), we get
[tex]\dfrac{a((-2)^3-1)}{(-2)-1}=12[/tex]
[tex]\dfrac{a(-8-1)}{-3}=12[/tex]
[tex]\dfrac{-9a}{-3}=12[/tex]
[tex]3a=12[/tex]
Divide both sides by 3.
[tex]a=4[/tex]
The nth term of a geometric progression is:
[tex]a_n=ar^{n-1}[/tex]
Where, a is the first term and r is the common ratio.
Putting [tex]n=3,a=4,r=-2[/tex] in the above formula, we get
[tex]a_3=4(-2)^{3-1}[/tex]
[tex]a_3=4(-2)^{2}[/tex]
[tex]a_3=4(4)[/tex]
[tex]a_3=16[/tex]
Therefore, the third term of the geometric progression is 16.
Compute ????×????, where ????=????−2????+5????, ????=2????+????+3????. (Write your solution using the standard basis vectors ????, ????, and ????. Use symbolic notation and fractions where needed.)
Given: ????=????−2????+5????
and ????=2????+????+3????
To find: We need to find the value of ????×????
Solution: Here given,
????=????−2????+5????
and ????=2????+????+3????
Therefore, solving these two we have, ????=0
So,????×????=0
Allie rode her bike up a hill at an average speed of 12 feet/second. She then rode back down the hill at an average speed of 60 feet/second. The entire trip took her 2 minutes. What is the total distance she traveled. [Hint: use t = time traveling down the hill]
Answer:
The total distance Allie traveled was 0.81 miles.
Step-by-step explanation:
Since Allie rode her bike up a hill at an average speed of 12 feet / second, and she then rode back down the hill at an average speed of 60 feet / second, and the entire trip took her 2 minutes, to determine what is the total distance she traveled, the following calculation must be performed:
12 + 60 = 72
72 x 60 = 4320
1000 feet = 0.189394 miles
4320 feet = 0.8181818 miles
Therefore, the total distance Allie traveled was 0.81 miles.
A certain list of movies were chosen from lists of recent Academy Award Best Picture winners, highest grossing movies, series movies (e.g. the Harry Potter series, the Spiderman series), and from the Sundance Film Festival and are being analyzed. The mean box office gross was $138.64 million with a standard deviation of $11.2526 million. Given this information, 98.49% of movies grossed greater than how much money (in millions)
Help please. I'm stuck
Answer:
The numbers are 65, 67, and 69
Step-by-step explanation:
Hi there!
We need to find 3 consecutive odd integers.
Consecutive numbers are numbers that follow each other (ex. 1, 2, 3, 4)
We're given that 5 times the first number + 4 times the second + 3 times the third = 800
Let's make the first number x
Since the second number is consecutive to the first and odd, it will be x+2 (Why? Well, let's say x is 5. In that case, x+1=6, which is even. However, x+2=7)
Therefore, the third number is x+4 (once again, if x is 5, x+3=8, but x+4=9)
5 times the first number is 5x
4 times the second is 4(x+2)
3 times the third is 3(x+4)
And of course, that equals 800
As an equation, it'll be:
5x+4(x+2)+3(x+4)=800
open the parenthesis
5x+4x+8+3x+12=800
combine like terms
12x+20=800
Subtract 20 from both sides
12x=780
Divide by 12 on both sides
x=65
The first number is x, so the first number is 65
The second number is x+2, or 65+2=67
The third number is x+4, or 65+4=69
Hope this helps!
Use the coordinates of the labeled point to find a point-slope equation of the
line.
5
5
(-2,-5) 6.5
>
O A. y- 5 = -2(x - 2)
O B. y + 5 = 2(x + 2)
O C. y + 5 = -2(x + 2)
OD. y- 5 = 2(x - 2)
Answer:
B. [tex] y + 5 = 2(x + 2) [/tex]
Step-by-step explanation:
Point-slope equation is given as [tex] y - b = m(x - a) [/tex], where,
(a, b) = (-2, -5)
[tex] m = slope = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Using two points on the line (-2, -5) and (0, -1),
Slope (m) = (-1 -(-5))/(0 -(-2)) = 4/2
m = 2
✔️To write the equation in point-slope form, substitute a = -2, b = -5, and m = 2 into [tex] y - b = m(x - a) [/tex]
Thus:
[tex] y - (-5) = 2(x - (-2)) [/tex]
[tex] y + 5 = 2(x + 2) [/tex]
Find the value of x in each case
The answer is 36 degrees
Step 1
Angle GEH=180-2x (angles on a a straight line are supplementary)
Step 2
4x= G^+GE^H(sum of exterior angle)
4x=x+(180-2x)
4x=180-x
4x+x=180
5x=180
x=36 degrees
You paid $6.99 for a shirt that was 70% of what was the original price of the shirt?
Answer:
$23.3
Step-by-step explanation:
you can use ratios to solve this:
$6.99/x=0.30/0.100 then cross multiply to get 0.3x=6.99
So, 6.99 divided by 0.3 = 23.3
so the original price is $23.3
Sarah ordered 39 shirts that cost $8 each. She can sell each shirt for $16.19. She sold 32 shirts to customers. She had to return 7 shirts and pay a $1.4 charge for each returned shirt. Find Sarah's profit.
Answer:
$196.28
Step-by-step explanation:
Original cost: 39 × $8 = $312
Revenue: 32 × $16.19 = $518.08
Return charge: 7 × $1.4 = $9.8
$312 + $9.8 = total cost, which is $321.8
$518.08 - $321.8 = profit
Profit = $196.28
please help i am stuck on this assignment
Answer:
answer
x = -13/ 15, 0
Step-by-step explanation:
15x^2 + 13 x = 0
or, x(15x + 13) = 0
either, x = 0
or, 15x + 13 = 0
x = -13/15
Answer:
The answer should be C...............
imma sorry if I'm wrong
How to solve and what is the answer
Answer:
5
Step-by-step explanation:
Look at photo help please I will give brainliest
Answer:
3x² + 13x + 4
Step-by-step explanation:
I did the steps in my book
Donald and Sara are surveying their neighbors about the community playground. Their questions, written on the survey, are below:
Donald: How many times do you visit the playground in a month?
Sara: Did you visit the playground this month?
Who wrote a statistical question and why?
Sara, because there will be variability in the responses collected
Donald, because every neighbor can give a different answer
Sara, because there can be only one answer to the question
Donald, because every neighbor will give the same answer
Answer:
B
Step-by-step explanation: Because Donald asks a more broad and open question which people could give different answers too
Jonas builds a snow fort. He tells his friends it is 0.8 meters tall inside, but he rounded the height to the nearest tenth.
Which could be the height of the snow fort before Jonas rounded it?
2 answers
A. 0.85
B. 0.82
C. 077
Answer:
B. 0.82
C. 077
Step-by-step explanation:
Given
[tex]Number = 0.8[/tex] -- approximated
Required
The possible value of Number
Since [tex]Number = 0.8[/tex] is approximated, then the possible values of Number that can be gotten from the preparation
The approximated value 0.8 has the following range: 0.75 to 0.84
Options B and C are in this category.
Candice is preparing for her final exam in Statistics. She knows she needs an 74 out of 100 to earn an A overall in the course. Her instructor provided the following information to the students. On the final, 200 students have taken it with a mean score of 68 and a standard deviation of 4. Assume the distribution of scores is bell-shaped. Calculate to see if a score of 74 is within one standard deviation of the mean.
a) Yes, 74 is the upper limit of one standard deviation from the mean.
b) Yes, the upper level of one standard deviation is 72.
c) Yes, 74 is greater than the 64, one standard deviation below the mean.
d) No, 74 is greater than the mean of 68.
Answer:
Hence the correct option is option b) Yes, the upper level of one standard deviation is 72.
A score of 74 is not within one standard deviation of the mean.
Step-by-step explanation:
Here the given details are,
Mean = 68
SD = 4
Distribution is normal.
Z-score for x = 74 is given as below:
[tex]Z = (X - mean)/SD\\Z = (74 - 68)/4\\Z = 1.5[/tex]
So, the score of 74 is 1.5 standard deviations from the mean.
[tex]Mean + 1\timesSD = 68 + 1\times4 = 72Mean - 1\timesSD = 68 - 1\times4 = 64[/tex]
Therefore the score is not lies between 64 and 72.
Yes, the upper level of one standard deviation is 72.
g At a certain gas station, 30% of all customers use the restroom. What is the probability that, out of the next 10 customers, (a) exactly 4 will use the restroom
Answer:
[tex]P(x=4) = 0.200[/tex]
Step-by-step explanation:
Given
[tex]n=10[/tex] --- selected customers
[tex]x = 4[/tex] --- those that are expected to use the restroom
[tex]p =30\% = 0.30[/tex] --- proportion that uses the restroom
Required
[tex]P(x = 4)[/tex]
The question illustrates binomial probability and the formula is:
[tex]P(x) = ^nC_x * p^x * (1 - p)^{n - x}[/tex]
So, we have:
[tex]P(x=4) = ^{10}C_4 * (0.30)^4 * (1 - 0.30)^{10 - 4}[/tex]
[tex]P(x=4) = ^{10}C_4 * (0.30)^4 * (0.70)^6[/tex]
[tex]P(x=4) = 210* (0.30)^4 * (0.70)^6[/tex]
[tex]P(x=4) = 0.200[/tex]
Uma pizzaria oferece em seu cardápio 12 sabores de pizza. Se um cliente pretende pedir 3 pizzas, então o número de maneiras que ele pode realizar esse pedido é;
•364
•220
•440
•1320
Answer:
Step-by-step explanation:
Partindo do pressuposto de que você pode ter coberturas duplas e triplas do mesmo item, o cálculo é relativamente simples. Para calcular as combinações possíveis; deve-se multiplicar as coberturas disponíveis pelo número total de coberturas permitidas. Este cálculo é semelhante a como olhamos para diferentes sistemas de contagem de base. Normalmente contamos com decimais (base 10), portanto, o número de combinações, se usar 3 dígitos, seria calculado por 10 x 10 x 10.
10x10 = 100
100x10 = 1000 combinações (0 a 999)
Sua pergunta sobre coberturas de pizza é a mesma, mas assumindo um sistema de numeração de base 12, então 12x12x12 ou 12³
Portanto, 1.728 combinações incluindo 0 (sem coberturas?) E também incluindo 12 ocasiões em que todas as 3 coberturas seriam iguais. Se esses cenários de pessoas forem restritos de modo que você só possa ter coberturas duplas máximas, etc., então essas combinações devem ser removidas (subtraídas do total de combinações permitidas).
Espero ter ajudado você a entender os princípios, então você deve ser capaz de trabalhar a partir disso, de muitas outras soluções semelhantes
Find the solution set.
The solution set for 5v2 – 125 = 0
the complement of guessing 5 correct answers on a 5 question true or false examination is
Answer:
Guessing at least one incorrect answer
Step-by-step explanation:
The complement of guessing 5 correct answers on a 5-question true/false exam is-
Guessing at least one incorrect answer because, when 1 or more questions are incorrectly guessed, the event of 5 correct answers can not occur.
g A. (Points: 7) Compute (without using a calculator) 241^257 mod 12 B. (Points: 3) Compute Z*20 C. (Points: 6) Find the multiplicative inverse of 7 in Z19
Answer:
[tex]241^{257}\ mod\ 12 =1[/tex]
[tex]7 * 20 = 140[/tex]
[tex]\frac{1}{700}[/tex]
Step-by-step explanation:
Solving (a): 241^257 mod 12
To do this, we simply calculate [tex]241\ mod\ 12[/tex]
Because [tex]a\ mod\ b = a^n\ mod\ b[/tex]
The highest number less than or equal to 241 that is divisible by 12 is 240; So:
[tex]241\ mod\ 12 = 241- 240[/tex]
[tex]241\ mod\ 12 =1[/tex]
Hence:
[tex]241^{257}\ mod\ 12 =1[/tex]
Solving (b): 7 * 20
[tex]7 * 20 = 140[/tex]
Solving (c): Multiplicative inverse of 7 in 719
The position of 7 in 719 is 700
So, the required inverse is 1/700 ---- i.e. we simply divide 1 by the number
There are 200 blue balls and 10 red balls in an urn. Suppose that 10 balls are taken random;ly from the urn and let X denote the number of red balls selected.
a) The distribution of the random variable X is___.
i) Binomial.
ii) Hypergeometric.
iii) Poisson.
iv) Normal.
v) Exponential.
vi) Uniform
b) Find P(all 10 balls are red).
c) Which distribution from those listed in part (a) can be used as an approximation to the distribution of X? With this approximation find P(X = 10).
Answer:
Hypergeometric
Kindly check explanation
Step-by-step explanation:
For a hypergeometric distribution, the following conditions must be met :
1.) The total number of samples must be fixed.
2.) Sample size will be a portion of the population
3.) The probability of success changes per trial. This is because sampling is done without replacement
The above scenario meets the condition described:
Total number of samples = 210
Sample size, n = 10
Blue balls = 200 ; red balls = 10
P(10 red balls)
Using the hypergeometric distribution function and the calculator :
X ~ H(n, N, M)
X ~ (10, 200, 210) = 0.6072
The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with mean of 1262 and a standard deviation of 118. Determine the 26th percentile for the number of chocolate chips in a bag. (b) Determine the number of chocolate chips in a bag that make up the middle 95% of bags. (c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip cookies?
Answer:
a) 1186
b) Between 1031 and 1493.
c) 160
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normally distributed with mean of 1262 and a standard deviation of 118.
This means that [tex]\mu = 1262, \sigma = 118[/tex]
a) Determine the 26th percentile for the number of chocolate chips in a bag.
This is X when Z has a p-value of 0.26, so X when Z = -0.643.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.643 = \frac{X - 1262}{118}[/tex]
[tex]X - 1262 = -0.643*118[/tex]
[tex]X = 1186[/tex]
(b) Determine the number of chocolate chips in a bag that make up the middle 95% of bags.
Between the 50 - (95/2) = 2.5th percentile and the 50 + (95/2) = 97.5th percentile.
2.5th percentile:
X when Z has a p-value of 0.025, so X when Z = -1.96.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.96 = \frac{X - 1262}{118}[/tex]
[tex]X - 1262 = -1.96*118[/tex]
[tex]X = 1031[/tex]
97.5th percentile:
X when Z has a p-value of 0.975, so X when Z = 1.96.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.96 = \frac{X - 1262}{118}[/tex]
[tex]X - 1262 = 1.96*118[/tex]
[tex]X = 1493[/tex]
Between 1031 and 1493.
(c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip cookies?
Difference between the 75th percentile and the 25th percentile.
25th percentile:
X when Z has a p-value of 0.25, so X when Z = -0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.675 = \frac{X - 1262}{118}[/tex]
[tex]X - 1262 = -0.675*118[/tex]
[tex]X = 1182[/tex]
75th percentile:
X when Z has a p-value of 0.75, so X when Z = 0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.675 = \frac{X - 1262}{118}[/tex]
[tex]X - 1262 = 0.675*118[/tex]
[tex]X = 1342[/tex]
IQR:
1342 - 1182 = 160
what graph shows the solution to the equation below log3(x+2)=1
Answer:
The solution to the equation log3(x+2)=1 is given by x=1
Step-by-step explanation:
We are given that
[tex]log_3(x+2)=1[/tex]
We have to find the graph which shows the solution to the equation log3(x+2)=1.
[tex]log_3(x+2)=1[/tex]
[tex]x+2=3^1[/tex]
Using the formula
[tex]lnx=y\implies x=e^y[/tex]
[tex]x+2=3[/tex]
[tex]x=3-2[/tex]
[tex]x=1[/tex]
it's tooooo easy who wants brain list
Answer:
1) Isosceles
2) Acute
3) Right angled
4( Obtuse
5) Equilateral
One number is 1/4 of another number. The sum of the two numbers is 5. Find the two numbers. Use a comma to separate your answer
Answer: 1, 4
Step-by-step explanation:
Number #1 = xNumber #2 = [tex]\frac{1}{4} x[/tex][tex]\frac{1}{4} x+x=5\\\\\frac{1}{4} x+\frac{4}{4} x=5\\\\\frac{5}{4} x=5\\\\5x=4*5\\5x=20\\x=4[/tex]
Number #1 = x = 4Number #2 = [tex]\frac{1}{4} x[/tex] = [tex]\frac{1}{4} *4=\frac{4}{4} =1[/tex]Find the volume (in cubic inches) of an exercise ball with a radius of 14 inches. (Round your answer to one decimal place.)
Answer:
11,494.0³
Step-by-step explanation:
Volume of a sphere= (4/3) × pi × radius³
4÷3 × 3.14 ×14³
= 11,494.0³
Yuki bought a drop–leaf kitchen table. The rectangular part of the table is a 2–by–3–foot rectangle with a semicircle at each end, as shown.
Answer:
[tex](a)\ Area = 13.0695[/tex]
[tex](b)\ Area = 26.139[/tex]
Step-by-step explanation:
Given
The attached image
Solving (a): The area (one side up)
This is calculated as:
Area= Area of semicircle + Area of rectangle
So, we have:
[tex]Area = \pi r^2 + l *w[/tex]
Where:
[tex]l,w =2,3[/tex] --- the rectangle dimension
[tex]d = 3[/tex] --- the diameter of the semicircle
So, we have:
[tex]Area = \pi * (3/2)^2 + 2 * 3[/tex]
[tex]Area = \pi * 2.25 + 6[/tex]
[tex]Area = 2.25\pi + 6[/tex]
[tex]Area = 2.25*3.142 + 6[/tex]
[tex]Area = 13.0695[/tex]
Solving (b): Area when both leaves are up.
Simply multiply the area in (a) by 2
[tex]Area = 2 * 13.0695[/tex]
[tex]Area = 26.139[/tex]
What is the domain of the given
set of ordered pairs?
(2, 4), (5,5), (8, 6), (11, 7)
Answer:
2, 5, 8, 11
Step-by-step explanation:
The domian is the x axis points thingy
Land costing $140,000 was sold for $173,000 cash. The gain on the sale was reported on the income statement as other income. On the statement of cash flows, what amount should be reported as an investing activity from the sale of land?
Answer:
Amount should be reported in investing activities = $173,000
Step-by-step explanation:
Given:
Amount of land costing = $140,000
Sold amount of land = $173,000
Find:
Amount should be reported in investing activities
Computation:
Amount should be reported in investing activities = $173,000
The cash flow statement shows how much money is coming in and going out. The whole amount of cash received, which is 173,000 dollars, will be recorded as proceeds from the sale of land in the investment activity. As a result, the right answer is 173,000.
A party supply company makes cone shaped party hats for children using thin cardboard. To the nearest square centimeter, how much cardboard is required to make the party hate use pie = 3.14.
Answer:
A. 754 cm²
Step-by-step explanation:
Amount of cardboard needed = surface area of the cone
Curved surface area of the cone = πrl
Where,
π = 3.14
r = ½(20) = 10 cm
l = 24 cm
Plug in the values into the formula
Curved surface area = 3.14 × 10 × 24 = 753.6 ≈ 754 cm²
At the 6th grade school dance, there are 132 boys, 89 girls, and 14 adults. What is the ratio of adults to boys at the school dance?
Answer:
14 to 132
Step-by-step explanation:
We are given that there are 132 boys and 14 adults. Since the question is only asking for the ratio of adults to boys, we don't have to worry about the number of girls in this question. From here, we see that the question is asking for the ratio of adults to boys, so we put it in that exact order. Our answer is 14 to 132. I hope this helps and please don't hesitate to reach out with more questions!
