determine the 2nd and 3rd terms of a geometric sequence of which T1 =5 and T4=40
Answers
Answer:
Second term of this sequence: [tex]10[/tex].
Third term of this sequence: [tex]20[/tex].
Step-by-step explanation:
The first step is to find the common ratio of this sequence.
In a geometric sequence, multiply one term by the common ratio to find an expression for the next term. Let [tex]r[/tex] denote the common ratio of this sequence. For this sequence:
The first term of this sequence is [tex]5[/tex]. Multiply the first term by the common ratio to find an expression for the third term: [tex]5\, r[/tex].Multiply the second term by the common ratio to find an expression for the fourth term: [tex]5\, r^{2}[/tex].Similarly, an expression for the the fourth term would be: [tex]5\, r^{3}[/tex].However, the question states that the value of the fourth term is [tex]40[/tex]. In other words, [tex]5\, r^{3} = 40[/tex].
Solve this equation for [tex]r[/tex]:
[tex]r^{3} = 8[/tex].
[tex]r = 2[/tex].
(Since the power of [tex]r[/tex] is non-even in the equation, there's no need to consider the sign of [tex]r\![/tex] when taking the cube root.)
Substitute [tex]r = 2[/tex] into the expression for the second term and the third term to find their values:
Second term: [tex]5\, r = 10[/tex].Third term: [tex]5\, r^{2} = 20[/tex].Related Questions
A telephone exchange operator assumes that 7% of the phone calls are wrong numbers. If the operator is accurate, what is the probability that the proportion of wrong numbers in a sample of 459 phone calls would differ from the population proportion by more than 3%
Answers
Answer:
0.0118 = 1.18% probability that the proportion of wrong numbers in a sample of 459 phone calls would differ from the population proportion by more than 3%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
A telephone exchange operator assumes that 7% of the phone calls are wrong numbers.
This means that [tex]p = 0.07[/tex]
Sample of 459 phone calls:
This means that [tex]n = 459[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.07[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\sqrt{\frac{0.07*0.93}{459}}} = 0.0119[/tex]
What is the probability that the proportion of wrong numbers in a sample of 459 phone calls would differ from the population proportion by more than 3%?
Proportion below 0.07 - 0.03 = 0.04 or above 0.07 + 0.03 = 0.1. Since the normal distribution is symmetric, these probabilities are the same, which means that we find one of them and multiply by 2.
Probability the proportion is below 0.04.
p-value of Z when X = 0.04. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.04 - 0.07}{0.0119}[/tex]
[tex]Z = -2.52[/tex]
[tex]Z = -2.52[/tex] has a p-value of 0.0059
2*0.0059 = 0.0118
0.0118 = 1.18% probability that the proportion of wrong numbers in a sample of 459 phone calls would differ from the population proportion by more than 3%
If 3x^2+2x-8=(3x-4)(x+2), which equations should be solved to find the roots of 3x^2+2x-8=0
Answers
9514 1404 393
Answer:
C, E
Step-by-step explanation:
The solutions are found by setting each of the factors to zero:
3x -4 = 0 . . . . . matches C
x +2 = 0 . . . . . matches E
log4(x^2+1)=log4(-2x)
Answers
Answer:
x = − 1
Step-by-step explanation:
Please help with this question!?
Answers
Answer:
7
Step-by-step explanation:
Substitute 2 for x.
[tex] {2}^{2} + 3 = 7[/tex]
use the discriminant to determine the number of solutions to the quadratic equation −6z2−10z−3=0. What are the real solutions and complex solutions?
Answers
Answer:
Step-by-step explanation:
-6z²-10z-3=0
multiply by -1
6z²+10z+3=0
disc .=b²-4ac=10²-4×6×3=100-72=28≥0
also it is not a perfect square.
so roots are real,irrational and different.
[tex]z=\frac{-6 \pm\sqrt{28} }{2 \times 6} \\=\frac{-6 \pm 2 \sqrt{7}}{12} \\=\frac{-3 \pm\sqrt{7} }{6}[/tex]
What transformation to the linear parent function, f(x) = x, gives the function
g(x) = x + 7?
A. Shift 7 units left.
B. Shift 7 units right.
C. Vertically stretch by a factor of 7
D. Shift 7 units down
Answers
Answer:
I think A
Step-by-step explanation:
Lightbulbs. A company produces lightbulbs. We know that the lifetimes (in hours) of lightbulbs follow a bell-shaped (symmetric and unimodal) distribution with a mean of 7,161 hours and a standard deviation of 564 hours. Use the Empirical Rule (68-95-99.7 rule) to answer the following question: The shortest lived 2.5% of the lightbulbs burn out before how many hours
Answers
Answer:
Please find the complete question and its solution in the attached file.
Step-by-step explanation:
Shortest had survived after 6741 hours [tex]2.5\%[/tex] of the lights burnt.
[tex]\to 0.15\% + 2.35\% = 2.50\%[/tex]
What is the lateral area of a cone with radius 19 cm and slant height 11 cm?
a. 19[tex]\pi[/tex] cm²
b. 30[tex]\pi[/tex] cm²
c. 200[tex]\pi[/tex] cm²
d. 209[tex]\pi[/tex] cm²
Answers
Answer:
The answer is 209 pi cm^2
L.A.(Lateral Area) = π19×11 = 209 π
The lateral area of the given cone with a raidus of 19 cm and a slant height of 11 cm is: D. 209π cm²
What is the Lateral Area of a Cone?Lateral area of a cone = πrL, where r is the radius and L is the slant height of the cone.
Given the following:
Slant height (L) = 11 cmRadius (r) = 19 cmLateral area of a cone = π(19)(11)
Lateral area of a cone = 209π cm²
Learn more about lateral area of a cone on:
https://brainly.com/question/61056
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Please help me i will give Brainly
Answers
Answer:
Step-by-step explanation:
[tex]\frac{3x + 5}{2x + 7}[/tex] = 5
do cross multiplication
3x + 5 = 5(2x + 7)
3x + 5 = 10x + 35
5 - 35 = 10x - 3x
-30 = 7x
-30/7 = x
20 A
since there are 7 angles given it means that the polygon is heptagon as heptagon has 7 sides.
sum of interior angle of heptagon = (n-2)*180
(7-2)*180
5*180
900
Now ,
110 + 90 + 150 + 102 + 110 + 170 + x = 900
732 + x = 900
x = 900 - 732
x = 168 degree
20 B
since 5 angles are given it means that the polygon is pentagon as pentagon has 5 sides.
sum of interior angles of a pentagon = (n-2)*180
(5-2)*180
3*180
540 degree
Now ,
110 + 95 + 120 + 114 + x = 540
465 + x = 540
x = 540 - 465
x = 75 degree
21
let one rational number be x
according to the question,
1/7 * x = 2
x/7 = 2
do cross multiplication
x = 14
Which best describes what forms in nuclea fission?
O two smaller, more stable nuclei
O two larger, less stable nuclei
• one smaller, less stable nucleus
one larger, more stable nucleus
Answers
Answer:
One larger, more stable nucleus
Roger has found a home to be purchase for $120,372 and has agreed to pay 28% down. Find the amount of Roger's down payment. Find the amount of money that Roger would need to borrow through a mortgage in order to purchase the home.
If Roger found a 30 year mortgage with a 5.9% APR. Find Roger's monthly payment. Using the monthly payment how much did Roger pay over the life of the mortgage?
Round your answer to the nearest cent.
Answers
Answer:
He needs to borrow: 86667.84
His monthly payment would be: 514.06
He would pay a total of: 185061.6 over the life of the loan
Step-by-step explanation:
roger would need to borrow .72*120372= 86667.84
2.)
calculate the effective rate .059/12= .004916667
[tex]86667.84=x\frac{1-(1+.004916667)^{-30*12}}{.004916667}\\x=514.0585984[/tex]
which we round to 514.06
3.) he is going to pay a total of 514.06*30*12= 185061.6 over the life of the loan
What is 75% as a fraction
Answers
Answer:
[tex]\frac{75}{100}[/tex]
Step-by-step explanation:
75 percent is 3/4 of 100 percent.
Please help on my hw, I'm not feeling good, and can't concentrate
Answers
Answer:
Solution given:
f(x)=x²
g(x)=x+5
h(x)=4x-6
now
23:
(fog)(x)=f(g(x))=f(x+5)=(x+5)²=x²+10x+25
24:
(gof)(x)=g(f(x))=g(x²)=x²+5
25:
(foh)(x)=f(h(x))=f(4x-6)=(4x-6)²=16x²-48x+36
26:
(hof)(x)=h(f(x))=h(x²)=4x²-6
27;
(goh)(x)=g(h(x))=g(4x-6)=4x-6+5=4x-1
28:
(hog)(x)=h(g(x))=h(x+5)=4(x+5)-6=4x+20-6=4x-14
A small insurance company has determined that on average it receives 6 property damage claims per day. P left parenthesis X equals k right parenthesis space equals space fraction numerator lambda to the power of k e to the power of negative lambda end exponent over denominator k factorial end fraction k space i s space t h e space g i v e n space n u m b e r space o f space e v e n t space o c c u r r e n c e s lambda space i s space t h e space a v e r a g e space r a t e space o f space e v e n t space o c c u r r e n c e s What is the probability that the company will receive 7 property damage claims on a randomly selected day? Answer choices are rounded to the hundredths place.
Answers
Answer:
The probability that the company will receive 7 property damage claims on a randomly selected day is 0.137
Step-by-step explanation:
Given,
[tex]\lambda=6[/tex],
The probability mass function of Poisson distribution is used for evaluating the probability of the company will receive 7 property damages claims on any selected day is,
[tex]\begin{aligned}P(X=K)&=e^{-6} \times \dfrac{6^7}{7!}\\&=0.002478\times\dfrac{279936}{5040}\\&=\dfrac{693.89136}{5040}\\P(X=7)&=0.1365927874\\P(X=7)&=0.137\; (\rm{rounded \;off})\end{aligned}[/tex]
To learn more about this, please refer to the below link:
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If Camillo goes with the better buy, how much will he pay for the 25 loaves of bread that he needs for the gourmet peanut butter and jelly sandwiches? Enter your answer to the nearest cent.
Answers
Answer:
$49.5
Step-by-step explanation:
* means multiply
at $1.98 per loaf
25 * 1.98 =
49.5
Answer:
48.75
Step-by-step explanation:
It would be the cheapest option
Write an equation for staying in Paris, France.
Answers
Answer:
[tex]y = 125.00x + 591.00[/tex]
Step-by-step explanation:
Given
See attachment for table
Required
Equation for Paris
From the table, we have:
[tex]flight = 591.00[/tex]
[tex]hotel = 125.00[/tex]
Let the number of nights be x.
So, the equation for the total amount (y) is:
[tex]y = flight + hotel * x[/tex]
[tex]y = 591.00 + 125.00 * x[/tex]
[tex]y = 125.00x + 591.00[/tex]
Measurement error that is normally distributed with a mean of 0 and a standard deviation of 0.5 gram is added to the true weight of a sample. Then the measurement is rounded to the nearest gram. Suppose that the true weight of a sample is 166.0 grams.
(a) What is the probability that the rounded result is 167 grams?
(b) What is the probability that the rounded result is 167 grams or more?
Answers
Answer:
(a)[tex]0.15731[/tex]
(b)0.02275
Step-by-step explanation:
We are given that
Mean=0
Standard deviation=0.5 g
True weight of a sample=166 g
Let X denote the normal random variable with mean =166+0=166
(a)
P(166.5<X<167.5)
=[tex]P(\frac{166.5-166}{0.5}<\frac{X-\mu}{\sigma}<\frac{167.5-166}{0.5})[/tex]
=[tex]P(1<Z<3)[/tex]
=[tex]P(Z<3)-P(Z<1)[/tex]
[tex]=0.99865-0.84134[/tex]
[tex]=0.15731[/tex]
(b)
[tex]P(X>167)=P(Z>\frac{167-166}{0.5})[/tex]
[tex]=P(Z>2)[/tex]
[tex]=1-P(Z<2)[/tex]
[tex]=1-0.97725[/tex]
[tex]=0.02275[/tex]
Evaluate:
11x - 8(x - y)
Answers
Answer:
11x-8x+8y
3x+8y SEEESH IN DEEZ NU TS
Step-by-step explanation:
In preparing for the upcoming holiday season, Fresh Toy Company (FTC) designed a new doll called The Dougie that teaches children how to dance. The fixed cost to produce the doll is $100,000. The variable cost, which includes material, labor, and shipping costs, is $34 per doll. During the holiday selling season, FTC will sell the dolls for $42 each. If FTC overproduces the dolls, the excess dolls will be sold in January through a distributor who has agreed to pay FTC $10 per doll. Demand for new toys during the holiday selling season is extremely uncertain. Forecasts are for expected sales of 60,000 dolls with a standard deviation of 15,000. The normal probability distribution is assumed to be a good description of the demand. FTC has tentatively decided to produce 60,000 units (the same as average demand), but it wants to conduct an analysis regarding this production quantity before finalizing the decision.
(a) Create a what-if spreadsheet model using formulas that relate the values of production quantity, demand, sales, revenue from sales, amount of surplus, revenue from sales of surplus, total cost, and net profit. What is the profit corresponding to average demand (60,000 units)? $
(b) Modeling demand as a normal random variable with a mean of 60,000 and a standard deviation of 15,000, simulate the sales of The Dougie doll using a production quantity of 60,000 units. What is the estimate of the average profit associated with the production quantity of 60,000 dolls? $ How does this compare to the profit corresponding to the average demand (as computed in part a)? The input in the box below will not be graded, but may be reviewed and considered by your instructor
(c) Before making a final decision on the production quantity, management wants an analysis of a more aggressive 70,000-unit production quantity and a more conservative 50,000-unit production quantity. Run your simulation with these two production quantities. What is the mean profit associated with each? When ordering 50,000 units, the average profit is approximately $. When ordering 70,000 units, the average profit is approximately $.
(d) Besides mean profit, what other factors should FTC consider in determining a production quantity? Compare the four production quantities (40,000; 50,000; 60,000; and 70,000) using all these factors. What trade-offs occur? If required, round Probability of a Loss to three decimal places and Probability of a Shortage to two decimal places. What is your recommendation? The input in the box below will not be graded, but may be reviewed and considered by your instructor.
Answers
write the following numbers in scientific notation. 0.0009. 12. 1000. 0.03. 1.12. 120
Answers
Answer:
Step-by-step explanation:
Take the first real number and keep a decimal point to the right of it. Write the number after it.
Put a multiplication symbol and then 10.
Now count the number places to the right of the first real number and the number of place will be the power of 10.
If , number of place are before the first real number, then the power of 10 will be negative.
0.0009 = 9 * 10⁻⁴
12 = 1.2 *10
1000 = 1* 10³
0.03 = 3 *10⁻²
120 = 1.2 * 10²
1.12 = 1.12 *10⁰
Please help I don’t understand at all
Answers
Answer:
a
Step-by-step explanation:
1. Reduce the index of the radical and exponent with 2
√(a^2) = a
Basically square root is also can be represent as power of 1/2. Which is (a^2)^1/2. Then you can multiply both power. So you will get a^(2/2). solve it hence the solution is a^1 which is a. Hopefully this will help
rationalize the denominator of √3+√2\ 5+√2
Answers
Answer:
[tex]\frac{ 5 \sqrt3 \ + \ 5 \sqrt2 \ - \ \sqrt6 \ - \ 2}{23}[/tex]
Step-by-step explanation:
[tex]\frac{\sqrt3 \ + \ \sqrt2 }{5 \ + \ \sqrt2 } \\\\=\frac{\sqrt3 \ + \ \sqrt2 }{5 \ + \ \sqrt2 } \times \frac{5 \ - \ \sqrt2 }{5 \ - \ \sqrt2 } \\\\=\frac{( \sqrt3 \ + \ \sqrt2)(5 \ - \ \sqrt2)}{(5 \ + \ \sqrt2)( 5 \ - \ \sqrt 2 )}\\\\=\frac{( \sqrt3 \ + \ \sqrt2)(5 \ - \ \sqrt2)}{(5 \ + \ \sqrt2)( 5 \ - \ \sqrt 2 )}\\\\=\frac{5 \sqrt3 \ + \ 5\sqrt 2 \ - \ \sqrt{ 3\times 2 } \ - \ \sqrt{2 \times 2}}{(5)^2 \ - \ (\sqrt2)^2}\\\\= \frac{ 5 \sqrt3 \ + \ 5 \sqrt2 \ - \ \sqrt6 \ - \ 2}{25 - 2}\\\\[/tex]
[tex]= \frac{ 5 \sqrt3 \ + \ 5 \sqrt2 \ - \ \sqrt6 \ - \ 2}{23}[/tex]
check all that apply. sec theta is undefinded for theta = ____ . A. pi/2
B.0 C. pi D.3pi/2
Answers
Answer:
Step-by-step explanation:
secθ = 1/cosθ
cosθ = 0 for π/2, 3π/2
secθ is undefined for θ = π/2, 3π/2
the amount of mil available per child in a day care centrr is given by the function m(x) =25/x, where x is the number of children and m is the quantity of available milk in liters. if 50 children are present on a day how much milk is available per child
Answers
Answer:
0.5 liters of milk are available per child.
Step-by-step explanation:
Amount of milk available per children:
The amount of milk, in liters, available for x children is given by:
[tex]m(x) = \frac{25}{x}[/tex]
50 children are present on a day
This means that [tex]x = 50[/tex]
How much milk is available per child?
This is m(50). So
[tex]m(50) = \frac{25}{50} = 0.5[/tex]
0.5 liters of milk are available per child.
Let f(x) = -2x + 7 and g(x) = -6x + 3. Find f.g and state its domain.
-14x^2 + 36x - 18; all real numbers
12x^2 - 48x + 21; all real numbers
-14x^2 + 36x - 18; all real numbers except x = 7
12x^2 - 48x + 21; all real numbers except x = 1
Answers
Answer:
Not sure if this is right, but I hope it helps. Please see attached pic
Step-by-step explanation:
When you compute with decimals you should always check your answer is reasonable why
Answers
Answer:
Ang pangit mo
Kamuka mo Yong clown
HELP PLEASE!!!
Can someone tell me what a constant of proportionality is?
Please add an example if you can!
Thanks!
Answers
Answer:
A number or number sentence that doesn't change
Step-by-step explanation:
Answer:
the constant of proportionality k, is the constant value of the ratio of two proportional quantities y and x
Step-by-step explanation:
k = y/x or y= kx
example : the cost of 20 books is rs. 180 how much will 15 books cost ?
a. rs. 125
b. rs. 130
c. rs. 135
d. rs. 140
answer is c. rs. 135
The sum of 7/3 and four times a number is equal to 2/3 subtracted from five times the number?
Answers
Answer:
-3
Step-by-step explanation:
You have some money to invest in one of two accounts. The first account pays
5% simple interest, and the second pays 4% compound interest. How would
you decide which account to use? Discuss your answer.
Answers
Answer:
compound interest
Step-by-step explanation:
compound interest yields higher profit than simple interest
Answer:
the simple interest function will be greater in the beginning, but the
compound interest equation will overtake the simple after a while.
it appears that the 4% compound equation will overtake the simple at about 10 years
Step-by-step explanation:
[tex]1 + .05t = 1(1.04)^t[/tex]
4. Bonus: A computer programmer was told
that he would be given a bonus of 5% of any
money his programs could save the company.
How much would he have to save the company
to earn a bonus of $500?
Answers
Answer:
$10,000
Step-by-step explanation:
.05 x = 500
x = 500/.05
x = $10,000
