Given:
The geometric sequence is:
25.5, 5.1, 1.02, 0.204, ...
To find:
The explicit rule for the given geometric sequence.
Solution:
We have,
25.5, 5.1, 1.02, 0.204, ...
Here, the first term is 25.5 and the common ratio is:
[tex]r=\dfrac{a_2}{a_1}[/tex]
[tex]r=\dfrac{5.1}{25.5}[/tex]
[tex]r=\dfrac{1}{5}[/tex]
The explicit rule for a geometric sequence is:
[tex]a_n=ar^{n-1}[/tex]
Where, a is the first term and r is the common ratio.
Putting [tex]a=25.5,\ r=\dfrac{1}{5}[/tex] in the above formula, we get
[tex]a_n=25.5(\dfrac{1}{5})^{n-1}[/tex]
Therefore, the correct option is B.
Consider the circle.
If points W and X are the endpoints of a diameter on the circle, what is the value of x?
Answer:
x = 18Step-by-step explanation:
Find the diagram attached
If W and X are the endpoints of a diameter on the circle, this means that arc WX is 180degres
Since the angle at the vertex is half the angle at the intercepted arcs.
<V = 1/2(arcWX)
4x+18 = 1/2*180
4x+18 = 90
4x = 90-18
4x = 72
x = 72/4
x = 18
Hence the value of x is 18
Several years ago, 39% of parents who had children in grades K-12 were satisfied with the quality of education the students receive. A recent poll asked 1,045 parents who have children in grades K-12 if they were satisfied with the quality of education the students receive. Of the 1,045 surveyed, 471 indicated that they were satisfied. Construct a 99% confidence interval to assess whether this represents evidence that parents' attitudes toward the quality of education have changed.
Answer:
let p be the population proportion of parents who had children in grades k-12 were satisfied with the quality of education the students receive.
Step-by-step explanation:
7 x [(26 - 5) - (5 + 6)]
Answer:70x
Step-by-step explanation: FIND BY OWN
Convert 10π/6 radians into degrees.
We know that ,
[tex]\pi rad = 180^o[/tex]
SOLUTION :Using Unitary Method ,
[tex]\implies 1 \ rad = \dfrac{180^o}{\pi } [/tex]
Therefore ,
[tex]\implies \dfrac{10\pi}{6} rad = \dfrac{10\pi}{6} * \dfrac{180^o}{\pi } [/tex]
[tex]= \boxed{\red{ 300^o }}[/tex]
Required answer !
Of 60 randomly chosen students from a school surveyed,16 chose aquarium as their favorite fiel trip.There are 720 students in the school.predict the number of student in the school who chose aquarium
Answer:
192 students
Step-by-step explanation:
60 randomly students surveyed
16 chose aquarium as their favorite field trip.
720 students in total.
[tex]\frac{16}{60}[/tex] = [tex]\frac{?}{720}[/tex] =
720 × 16 ÷ 60 =
192 students
Kamal invested $1200 in a savings acc paying 1.8% per yr compound interest.
he left the money in the acc for 5 yrs.
what is the amount of money in the acc at the end of 5 yrs???
give the ans with working and to the nearest cent
Answer:
A = $1311 and 96cents
Step-by-step explanation:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
P = $1200
r = 1.8% = 0.018
n = 1 (compounded yearly)
t = 5
[tex]A = 1200(1 + 0.018)^5 = 1200 \times(1.018)^5 = 1311. 96[/tex]
PLEASE HELP I WILL GIVE BRAINILEST which question shows The function Y equals 2^X translated four units left and two units down a y-2=2^x-4. b y+4=2^x-2. c y-4=2^x +2. d y+2 =2^x+4
Simplify the following expression:
(3i+ 4) -i + 4(6 +2i)
A. 14+8i
B. 27 + 11i
C. 14+41i
D. 28 + 10i
9514 1404 393
Answer:
D. 28 +10i
Step-by-step explanation:
As with any "collect terms" problem, you first identify the like terms, then add their coefficients. You can start with either the real or the imaginary terms to obtain a result that will point you to the correct answer choice. Of course, the distributive property works in the usual way.
(3i+ 4) -i + 4(6 +2i) = 3i +4 -i +24 +8i . . . . eliminate parentheses
= (4 +24) +(3 -1 +8)i . . . . . . . group like terms
= 28 +10i
Eight trials are simulated. The results are shown in the table.
Simulation
109 105 112 110
115 106 108 109
What is the estimated margin of error, using standard deviation?
Answer:
3.33
Step-by-step explanation:
I just took the test! :D
The estimated margin of error, using standard deviation is 3.33.
What is the estimated margin of error, using standard deviation?The margin of error shows an estimated percentage, or that surrounds a guess related to the real value of the population. For example, a confidence interval that has a margin of error tells you that your findings will be within the real population value of the time.
Typically, the higher the standard deviation, the more dispersed the data is. Understanding standard deviation is an essential part of calculating the margin of error for your data. If you do not have the value for your sample data proportion.
Standard deviation describes variability within a single sample, while standard error describes variability across multiple samples of a population. Standard deviation is a descriptive statistic that can be calculated from sample data, while standard error is an inferential statistic that can only be estimated.
Learn more about errors here:-https://brainly.com/question/11472659
#SPJ2
I need help with this, please
none of the above
Step-by-step explanation:
SSS - only two legs are defined so this doesn't apply
SAS - the two legs of one triangle are not proportional to the legs of the other triangle.
AA - only one angle is defined to be congruent to the other (the rule requires two)
Where would (2,-4) be on the coordinate plane?
Answer:
fourth quadrant
Step-by-step explanation:
express 30kmph in M/S
Step-by-step explanation:
30×5/18
25/3
=8.33 m/s
!!!!!!!!!
Answer:
I think the answer is 8.33 (rounded to 2 decimal points)
I need help with this asap thank you so much
Answer:
C
Step-by-step explanation:
Cant really put it in here so look at photo Ö
Answer:
42
Step-by-step explanation:
I am preety sure !
A rectangle has a length of (x+6) units and a width of (x - 5) units.
What is the area of the rectangle in terms of x?
A (x^2 – 30) square units
B (x^2 +30) square units
C (x^2– x+30) square units
D (x^2+– 30) square units
Answer:
x² +x -30
Step-by-step explanation:
A = length * width = (x+6)(x-5) = x² -5x+6x-30= x²+x -30
Which equation shows a y- intercept of -5
Hi there!
»»————- ★ ————-««
I believe your answer is:
Option B) [tex]y=x-5[/tex]
»»————- ★ ————-««
Here’s why:
Most options (Second, Third, and Fourth) are in slope intercept form.⸻⸻⸻⸻
[tex]\boxed{\text{Slope-Intercept Form}}\\\\y=mx + b\\\\\boxed{\text{Key:}}\\\\m - \text{The Slope}\\\\b- \text{The Y-Intercept}[/tex]
⸻⸻⸻⸻
We are looking for the equation where '-5' is in b's place.⸻⸻⸻⸻
[tex]\boxed{\text{Which equation shows a y-intercept of -5?}}\\\\---------\\\text{A}) -5y = x\\\\\text{This equation in slope-intercept form is }y=\frac{1}{5}x.\\\\\text{The 'b' part is not shown. This means that the line passes through the}\\\text{origin.}\\\\---------\\\\\text{B})\text{ }y = x-5\\\\\text{This option shows a slope of one and a y-intercept of -5.} \\\\\text{Therefore, \boxed{\text{option B is the correct answer.}}}\\\\----------\\\text{Option C has a y-intercept of 5, and Option D has a}\\[/tex]
[tex]\text{y-intercept of 1.}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Select the correct answer.
Which graph models the function f(x) = 2(x – 4)^2 + 3
Answer:
the graph is going to be facing up not down
An investment of $8500 increases in value by 4.5% every year. How long until the investment
reaches about $17,323. Round to the nearest whole year
Answer:
At an interest rate of 4.5% compounded annually, it will take 16.17 years to reach $17,323.-
Step-by-step explanation:
Giving the following information:
Present Value (PV)= $8,500
Future value (FV)= $17,323
Interest rate (i)= 4.5%
To calculate the time required for the investment to reach the objective, we need to use the following formula:
n= ln(FV/PV) / ln(1+i)
n= ln(17,323/8,500) / ln(1.045)
n= 16.17 years
At an interest rate of 4.5% compounded annually, it will take 16.17 years to reach $17,323.-
Find the length of the arc in terms of pi A 144° 10 AB = [?]
Answer:
Arc AB = 8π
Step-by-step explanation:
Length of arc = central angle/360 × 2πr
Where,
Central angle = measure of arc AB = 144° (central angle theorem)
r = radius = 10
Length of arc AB = 144/360 × 2 × π × 10
= 8π
Can someone help please? 3 |x+1|>5
Answer:
The Answer as you see
Step-by-step explanation:
Have a good luck with ur Exam
Which graph represents the equation (x – 3)2 + y2 = 16?
Answer:
It is B on edge
Step-by-step explanation:
Verne has 5 math books to line up on a shelf. Jenny has 4 English books to line up on a shelf. In how many more orders can Verne line up his books than Jenny
Answer: 96
Step-by-step explanation:
Given
Verne has 5 math books to line up on a shelf
Jenny has 4 english books to line up on a shelf
No of ways Verne can arrange the books are [tex]5![/tex]
No of ways Jenny can arrange the books are [tex]4![/tex]
Difference between them
[tex]=5!-4!\\=120-24\\=96[/tex]
Thus, Verne can line up 96 more orders than Jenny
Question
Raymond wants to estimate the percentage of parents who use cloth diapers. He asks a randomly selected group of 200
parents whether or not they use cloth diapers. What is the data?
Answer:
Step-by-step explanation:
Given : Raymond wants to estimate the percentage of parents that use cloth diapers. He asks a randomly selected group of 200 parents whether or not they use cloth diapers.
The parameter are the number which are used to represents the quantity of a particular characteristic in entire population.
We know that to estimate the percentage of success we use the proportion of success parameter "p".
Hence, the parameter here is "p" , the proportion of parents that use cloth diapers.
Answer:
specific "yes" or "no" responses to the survey
Step-by-step explanation:
Got it right
Fill in the blanks. Suppose the probability at a light bulb factory of a bulb being defective is 0.11. If a shipment of 133 bulbs is sent out, the number of defective bulbs in the shipment should be around __________, give or take __________. Assume each bulb is independent.
Answer:
The number of defective bulbs in the shipment should be around 15, give or take 4.
Step-by-step explanation:
For each bulb, there are only two possible outcomes. Either it is defective, or it is not. The probability of a bulb being defective is independent of any other bulb. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Suppose the probability at a light bulb factory of a bulb being defective is 0.11
This means that [tex]p = 0.11[/tex]
Shipment of 133 bulbs:
This means that [tex]n = 133[/tex]
Mean and standard deviation:
[tex]E(X) = np = 133*0.11 = 14.63[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{133*0.11*0.89} = 3.61[/tex]
Rounding to the nearest integers:
The number of defective bulbs in the shipment should be around 15, give or take 4.
One bag contains 6 red, 2 blue, and 3 yellow balls. A second bag contains 2 red, 4 blue, and 5 yellow balls. A third bag contains 3 red, 7 blue, and 1 yellow ball. One bag is selected at random. If 1 ball is drawn from the selected bag, what is the probability that the ball drawn is yellow?
Answer:
2 is the probability
Step-by-step explanation:
Which expression is positive
Answer:
I would say none of the above
Step-by-step explanation:
When you evaluate A & B they both give you negatives So C
Good luck on Khan academy ;)
Answer:
the answer should be C
Step-by-step explanation:
the first two questions both come out to negative numbers so the only option would be the third.
Assume that we want to estimate the mean IQ score for the population of statistics students. How many statistics students must be randomly selected for IQ tests if we want 95% confidence that the sample mean is within 3 IQ points of the population mean? The Standard Deviation is 15.
Answer:
97 students must be randomly selected for IQ tests.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
The Standard Deviation is 15.
This means that [tex]\sigma = 15[/tex]
How many statistics students must be randomly selected for IQ tests if we want 95% confidence that the sample mean is within 3 IQ points of the population mean?
This is n for which M = 3. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]3 = 1.96\frac{15}{\sqrt{n}}[/tex]
[tex]3\sqrt{n} = 1.96*15[/tex]
Simplifying both sides by 3
[tex]\sqrt{n} = 1.96*5[/tex]
[tex](\sqrt{n})^2 = (1.96*5)^2[/tex]
[tex]n = 96.04[/tex]
Rounding up(as with a sample size of 96 the margin of error will be slightly above 3):
97 students must be randomly selected for IQ tests.
Plz help me ..?????a........
Answer:
Hope it's correct
Step-by-step explanation:
I believe it's week 2.
Help!!!!!!Solve for X. Round to the nearest tenth of a degree, if necessary.
An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below.
Under Age of 18 Over Age of 18
n1 = 500 n2 = 600
Number of accidents = 180 Number of accidents = 150
We are interested in determining if the accident proportions differ between the two age groups.
Q1. Let P, represent the proportion under and p, the proportion over the age of 18. The null hypothesis is:_____.
a. pu - po < 0.
b. pu - po > 0.
c. pu - P ≠ 70.
d. Pu - Po = 0.
Q2. The 95% confidence interval for the difference between the two proportions is:____.
a. (150, 180).
b. (0.25, 0.36).
c. (0.055, 0.165).
d. (0.045, 0.175).
Answer:
Q1 z(s) is in the rejection region for H₀ ; we reject H₀. We can´t support the that means have no difference
Q2 CI 95 % = ( 0,056 ; 0,164 )
Step-by-step explanation:
Sample information for people under 18
n₁ = 500
x₁ = 180
p₁ = 180/ 500 p₁ = 0,36 then q₁ = 1 - p₁ q₁ = 0,64
Sample information for people over 18
n₂ = 600
x₂ = 150
p₂ = 150 / 600 p₂ = 0,25 then q₂ = 1 - p₂ q₂ = 1 - 0,25 q₂ = 0,75
Hypothesis Test
Null hypothesis H₀ p₁ = p₂
Alternative Hypothesis Hₐ p₁ ≠ p₂
The alternative hypothesis indicates that the test is a two-tail test.
We will use the approximation to normal distribution of the binomial distribution according to the sizes of both samples.
Testin at CI = 95 % significance level is α = 5 % α = 0,05 and
α/ 2 = 0,025 z (c) for that α is from z-table:
z(c) = 1,96
To calculate z(s)
z(s) = ( p₁ - p₂ ) / EED
EED = √(p₁*q₁)n₁ + (p₂*q₂)/n₂
EED = √( 0,36*0.64)/500 + (0,25*0,75)/600
EED = √0,00046 + 0,0003125
EED = 0,028
( p₁ - p₂ ) = 0,36 - 0,25 = 0,11
Then
z(s) = 0,11 / 0,028
z(s) = 3,93
Comparing z(s) and z (c) z(s) > z(c)
z(s) is in the rejection region for H₀ ; we reject H₀. We can´t support the idea of equals means
Q2 CI 95 % = ( p₁ - p₂ ) ± z(c) * EED
CI 95% = ( 0,11 ± 1,96 * 0,028 )
CI 95% = ( 0,11 ± 0,054 )
CI 95 % = ( 0,056 ; 0,164 )