Answer:
n = 10
Step-by-step explanation:
3n1!/(n-4)! = (n-1)!/( n-1-5)
3n(n-1)(n-2)(n-3)(n-4) / N-4 -------- case1 ( cancel ( n-4) from top and bottom)
= (n-1)(n-2)(n-3)(n-4)(n-5)(n-6) / n-6 --------- case 2 ( Cancel n-6 from top and
bottom and also cancel n-1,
n-2, n-3 with case 1)
3n = ( n-4)(n-5)
3n = n² - 5n - 4n + 20
3n = n² - 9n + 20
0 = n² - 9n - 3n + 20
0 = n² - 12n + 20
0 = (n-2)(n-10)
n = 2 ( not valid) n = 10
Therefore n = 10
Consider the following repeating decimal. 0.619
(a) Write the repeating decimal as a geometric series.
0.619 = _______ + n=0 summation infinity _______
(b) Write the sum of the series as the ratio of two integers
Answer:
a. 0.6[tex]\overline {19}[/tex] = [tex]0.6 + \ \sum \limits ^{\infty}_{n=0} \ 0.019 \ ( \dfrac{1}{100})^n[/tex]
b. 0.6[tex]\overline {19}[/tex] = [tex]\mathbf{\dfrac{613}{990}}[/tex]
Step-by-step explanation:
Consider the following repeating decimal. 0.6[tex]\overline {19}[/tex]
a) Write the repeating decimal as a geometric series.
0.6[tex]\overline {19}[/tex] is being expressed as 0.6191919...
0.6[tex]\overline {19}[/tex] = 0.6 + 0.019 + 0.00019+ 0.0000019 + ...
0.6[tex]\overline {19}[/tex] =[tex]0.6 + \dfrac{19}{1000}+ \dfrac{19}{100000}+ \dfrac{19}{10000000}+ ...[/tex]
0.6[tex]\overline {19}[/tex] = [tex]0.6+ \dfrac{19}{1000} \begin {bmatrix} 1 + \dfrac{1}{100} + \dfrac{1}{10000}+ ... \end {bmatrix}[/tex]
0.6[tex]\overline {19}[/tex] = [tex]0.6 + \ \sum \limits ^{\infty}_{n=0} \ 0.019 \ ( \dfrac{1}{100})^n[/tex]
(b) Write the sum of the series as the ratio of two integers
0.6[tex]\overline {19}[/tex] = [tex]0.6 + 0.019 ( \dfrac{1}{1-0.01})[/tex]
0.6[tex]\overline {19}[/tex] =[tex]0.6 + \dfrac{19}{1000}\times \dfrac{100}{99}[/tex]
0.6[tex]\overline {19}[/tex] = [tex]0.6 + \dfrac{19}{990}[/tex]
0.6[tex]\overline {19}[/tex] = [tex]\dfrac{594+19}{990}[/tex]
0.6[tex]\overline {19}[/tex] = [tex]\mathbf{\dfrac{613}{990}}[/tex]
If 3s = t + 5 and se = 4, then t =
Answer:
t must be 7
Step-by-step explanation:
Replace s with 4 and solve for t in the original equation:
3 s = t + 5
3 (4) = t + 5
12 = t + 5
12 - 5 = t
7 = t
So t must be 7
The weight of an organ in adult males has a bell-shaped distribution with a mean of 310 grams and a standard deviation of 40 grams. Use the empirical rule to determine the following.
a. About 95 % of organs will be between what weights?
b. What percentage of organs weighs between 270 grams and 350 grams?
c. What percentage of organs weighs less than 270 grams or more than 350 grams?
d. What percentage of organs weighs between 230 grams and 430 grams?
Answer:
Step-by-step explanation:
Given that:
The mean μ = 310
The standard deviation σ = 40
Using the empirical rule to determine the following :
a. About 95 % of organs will be between what weights?
At 95% data values lies within 2 standard deviations of mean.
Thus, the required range is :
= μ ± 2σ
= ( 310 - 2 (40) , 310 + 2(40) )
= (230, 390)
b. What percentage of organs weighs between 270 grams and 350 grams
Here:
μ ± σ = (310 - 40, 310 + 40)
μ ± σ = (270, 350)
Using empirical rule, 68% data values is in the range within 1 standard deviation of mean. This implies that 68% data values lie between (270, 350).
c. What percentage of organs weighs less than 270 grams or more than 350 grams?
The complement theorem can be use to estimate the percentage of organs that weighs less than 270 grams or more than 350 grams,
This can be illustrated as :
= 100 % - 68 %
= 32 %
d. What percentage of organs weighs between 230 grams and 430 grams?
Using the empirical rule:
The percentage of organs weighs between 230 grams and 430 grams is:
u - 2σ and u + 3σ respectively.
What is the solution set of the equation 2z+6z+2=3−1z
Note: z≠0,−2
Answer:
z = 1/9
Step-by-step explanation:
2z + 6z + 2 = 3 - 1z
2z + 6z + 1z = 3 - 2 (on rearranging)
9z = 1 (on solving)
z = 1/9
HOPE IT HELPS (✿^‿^)
How can the decimal –70.73 be written as a mixed number?
Answer:
-70[tex]\frac{73}{100}[/tex]
Hope It Help
Six-four million, one hundred eighty-six thousand, three hundred square miles in standard form
Answer:
64,186,300 square miles
I'm sorry if I misunderstood.
Good luck mate! :)
Please add Brainliest if you'd like, not that it matters.
Remember to try your best every day!
A list of the top twenty restaurants in chicago was released. Four of the restaurants specialize in seafood. If five of the restaurants are selected randomly from the list, the standard deviation for the number of restaurants specializing in seafood is_____.
Answer:
the standard deviation for the number of restaurants specializing in seafood is 0.8944
Step-by-step explanation:
Given that :
Sum total number N of top restaurants in Chicago = 20
Four of the restaurants specialize in seafood,
then , the probability that a randomly selected restaurant from the top 20 in the list will specialize in seafood will be p = 4/20
p = 0.2
sample size n = 5
Assuming X to be the random variable that follows a Binomial distribution that represent the number of restaurants specializing in seafood.
Then: [tex]X \sim Binomial (n,p)[/tex]
where;
n = 5 and p = 0.2
The standard deviation σ can be determined by using the formula:
[tex]\sigma = \sqrt{np(1-p)}[/tex]
[tex]\sigma = \sqrt{5\times 0.2(1-0.2)}[/tex]
[tex]\sigma = \sqrt{1.0(0.8)}[/tex]
[tex]\sigma = \sqrt{0.8}[/tex]
σ = 0.894427191
σ [tex]\simeq[/tex] 0.8944
Tyrion can invest in an account earning 2.5% interest compounded monthly. If he invests $5000, ow much will he have in 7 years?
Answer:
$5925.51Step-by-step explanation:
We are going to be using the compound interest formula
Given data
principal P= $5000
N is time = 7 years
rate r= 2.5%= 0.025
compounded monthly k= 112
final amount A=?
The expression for the compound interest is
[tex]A= P(1+\frac{r}{K} )^K^N[/tex]
substituting into the expression we have
[tex]A= 5000(1+\frac{0.025}{12} )^1^2^*^7\\\\ A= 5000(1.002 )^1^2^*^7\\\\ A= 5000(1.002 )^8^7\\\\A= 5010*1.18273815853 \\\\ A= 5925.51[/tex]
in seven years he will have $5925.51
Find the product. (3p–2)(2p^2–p+3)
Answer:
6p^3−7p^2+11p−6
Step-by-step explanation:
1. You would want to foil it, which means multiplying one number from each parentheses to the next parentheses, like so:
3p * 2p ^ 2 = 6p^3
3p * -p = -3p
3p * 3 = 9p
-2 * 2p^2 = -4p^2
-2 * -p = 2p
-2 * 3 = - 6
2. Now add all of the numbers we foiled together, thus getting you:
6p^3−7p^2+11p−6
I need help with the following questions. Help would be very much appreciated! :D
Step-by-step explanation:
a) 12:40 = 3: 10
b) 40:12 = 10:3
c)
[tex]1. \: \frac{non \: fiction}{graphic \: novels} [/tex]
[tex]2. \: \frac{science \: fiction}{graphic \: novels} \: \: \: \: \: \: \: 3. \frac{science \: fiction}{non \: fiction} [/tex]
d)
Fiction books is 80.
If half of a box of candy weighs 3/5 of a pound, how much would 4 full boxes weigh?
How to do ii)
Deduce A^-1 = A^2 based on A^3=I
Multiply by [tex]A^{-1}[/tex] on the right of both sides of [tex]A^3=I[/tex], then use the fact that matrix multiplication is associative.
If [tex]A^3=I[/tex], then
[tex]A^3A^{-1}=IA^{-1}[/tex]
[tex]A^2(AA^{-1})=A^{-1}[/tex]
[tex]A^2I=A^{-1}[/tex]
[tex]\implies A^2=A^{-1}[/tex]
If you roll a die 100 times, what is the approximate probability that you will roll between 9 and 16 ones, inclusive? (Round your answer to two decimal places.) HINT [See Example 4.]
Answer: 0.47
Step-by-step explanation:
Given that
n = 100, probability of rolling 1 = 1/6
binomial approximation
np = 100 ( 1/6) = 16.667
standard deviation = √ 100 × 1/6 ×5/6 = 3.7627
P ( 9 ≤ X ≤ 16 )
= P ( 8.5 < X < 16.5 )
so,
= P ((8.5 - 16.6667) / 3.7627 < Z < (16.5 - 16.6667) / 3.7627
= P ( -2.17 < Z < -0.04 )
= 0.484 - 0.015
= 0.47
Therefore the approximate probability that you will roll between 9 and 16 ones is 0.47
A manufacturer claims that the calling range (in feet) of its 900-MHz cordless telephone is greater than that of its leading competitor. A sample of 9 phones from the manufacturer had a mean range of 1260 feet with a standard deviation of 24 feet. A sample of 12 similar phones from its competitor had a mean range of 1230 feet with a standard deviation of 37 feet. Do the results support the manufacturer's claim? Let μ1 be the true mean range of the manufacturer's cordless telephone and μ2 be the true mean range of the competitor's cordless telephone. Use a significance level of α=0.1 for the test. Assume that the population variances are equal and that the two populations are normally distributed.
a. State the null and alternative hypotheses for the test.
b. Compute the value of the t test statistic. Round your answer to three decimal places.
c. Determine the decision rule for rejecting the null hypothesis H0. Round your answer to three decimal places.
d. State the test's conclusion.
Answer:
a
The null hypothesis is [tex]H_o : \mu_1 - \mu_2 \le 0[/tex]
The alternative hypothesis is [tex]H_a : \mu_1 - \mu_2 > 0[/tex] (Manufacturers claim)
b
[tex]t = 2.114[/tex]
c
Decision rule
Reject the null hypothesis
d
There is sufficient evidence to support the claim that the calling range (in feet) of Manufacturers 900-MHz cordless telephone is greater than that of its leading competitor
Step-by-step explanation:
From the question we are told that
The first sample size is [tex]n_1 = 9[/tex]
The second sample size is [tex]n_2 = 12[/tex]
The first sample mean is [tex]\= x_1 = 1260 \ feet[/tex]
The second sample mean is [tex]\= x_2 = 1230[/tex]
The first standard deviation is [tex]\sigma_1 = 24[/tex]
The second standard deviation is [tex]\sigma_2 = 37[/tex]
The significance level is [tex]\alpha = 0.10[/tex]
The null hypothesis is [tex]H_o : \mu_1 - \mu_2 \le 0[/tex]
The alternative hypothesis is [tex]H_a : \mu_1 - \mu_2 > 0[/tex] (Manufacturers claim)
Generally the degree of freedom is mathematically represented as
[tex]df = n_1 + n_2 -2[/tex]
[tex]df = 9 + 12 - 2[/tex]
[tex]df = 19[/tex]
Generally the pooled standard deviation is mathematically represented as
[tex]\sigma_p = \sqrt{ \frac{(n_1 - 1)\sigma_1^2 + (n_2-1 )\sigma_2^2 }{ (n_1 - 1 ) + (n_2 - 1 )} }[/tex]
[tex]\sigma_p = \sqrt{ \frac{(9 - 1)24^2 + (12-1 )37^2 }{ (9 - 1 ) + (12 - 1 )} }[/tex]
[tex]\sigma_p =32.17[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x_1 - \= x_2 }{\sqrt{\frac{\sigma_p^2}{n_1 } +\frac{\sigma_p^2}{n_2 } } }[/tex]
[tex]t = \frac{1260 - 1230 }{\sqrt{\frac{32.17^2}{9 } +\frac{32.17^2}{12 } } }[/tex]
[tex]t = 2.114[/tex]
Generally the p-value is obtained from the student t distribution table and the value is
[tex]p-value = P(t > 2.11) = t_{2.11 , 19} = 0.024173[/tex]
Given that the [tex]p-value < \alpha[/tex]
The null hypothesis is rejected
Hence we can conclude that there is sufficient evidence to support the claim that the calling range (in feet) of Manufacturers 900-MHz cordless telephone is greater than that of its leading competitor
pls someone help me
Answer:
C
Step-by-step explanation:
Starting at zero, it went back 2/5 to negative 2/5. Then it went forward 4/5 to positive 2/5, which is the answer.
Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from normally distributed populations. Assume that the population standard deviations are equal.
Answer:
See the attachment for formatted formulas
Step-by-step explanation:
Let X11, X12, ……,X1n and X21 , X22……., X2n be two small independent random samples from two normal populations with means u1 and u2 and the standard deviations σ1 and σ2 respectively. If σ1= σ2 (=σ) but unknown then the unbiased pooled or combined estimate of the common variance σ2 (the term variance means that each population has the same variance) is given by
Sp2 = ((n_1-1) s_(1^2 )+ (n_2-1) s_2^2)/(n_1+n_2-2)
Where
S12 = 1/(n_1- 1) ∑▒〖 (X_1i- X`_1)〗^2 and
S22 = 1/(n_2- 1) ∑▒〖 (X_2j- X`_2)〗^2
The test statistic
t = ((X_1`-X_2`)- (μ_1- μ_2))/(√(s_p&1/n_1 )+ 1/n_2 )
Has t distribution with v= n1 + n2 – 2 degrees of freedom.
It is used as a test statistic for testing hypotheses about the difference between two population means.
The procedure for testing hypothesis H0: μ_1- μ_2= ∆_0 in case of small independent samples when σ_1= σ_2 is as follows.
Formulate the null and alternative hypotheses given σ_1= σ_2= σ unknown.H0: μ_1- μ_2= ∆_0 against the appropriate alternative.
Decide the significance level α. The test statistic under H0 ist = ((X_1`-X_2`)- ∆_0 )/(√(s_p&1/n_1 )+ 1/n_2 )
Which has t distribution with v= n1 + n2 – 2 degrees of freedom.
Identify the critical region Compute the t- value from the given data Reject H0 if t falls in the critical region, accept H0 otherwise.A candy box is to be made out of a piece of cardboard that measures 8 by 12 inches. Squares of equal size will be cut out of each corner, and then the ends and sides will be folded up to form a rectangular box. What size square should be cut from each corner to obtain a maximum volume
Answer:
Length of square cut = 1.569 inches
Step-by-step explanation:
given data
Length of cardboard = 12 inches
Breadth of cardboard = 8 inches
solution
we will consider here side of the square = x
when we cutting out the square then there Length and breadth of candy box will be
Length of box = (12 - x - x)
Length of box = (12 - 2x) inches.
and
Breadth of box = (8 - x - x)
Breadth of box = (8 - 2x) inches.
and Height of candy box wil be = x inches
so
Volume of a cuboid = L × b × h .....................1
Volume of a cuboid = (12 - 2x) × (8 - 2x) × x
Volume of a cuboid = 96x - 40x² + 4x³
now we Differentiate with respect to x
V' = 96 - 80x + 12x²
and for maximum volume we put V' = 0
0 = 96 - 80x + 12x²
solve it we get
x = 5.097
x = 1.569
when x = 5.097 inches
Breadth of candy box = 8 - 10.194 = -2.194 inches
but we know breadth never be negative,
so we take
Length of square cut = 1.569 inches
Which option shows the correct hypotheses for the test that the explanatory variables jointly significantly predict engine overhaul time?
Unclear question. However, I inferred you want to know about hypotehsis test.
Step-by-step explanation:
Remember, any hypothesis test is divided into two types. They are:
the null hypothesis andthe alternate hypothesis.Using this question example, here's the hypothesis statements ma sound:
Null hypothesis; There is a significant impact by the explanatory variables on engine overhaul time.
Alternate hypotheses; There is no impact by impact by the explanatory variables on engine overhaul time.
Your friend has prepared his monthly budget and asks you if he has overlooked anything in this planning. which of the following questions points out his most serious omission?
Answer:
The best and most correct answer among the choices provided by the question is
The statement that points out his most serious omission is "What if the electric bill increases?".
Step-by-step explanation:
Amy deposited $750 in a saving account that pays 6.75% Interest compounded monthly. Calculate the total amount in the account after 10 years.
Answer:
Amount after 10 years is $1472.775
Step-by-step explanation:
Amy deposited $750 in a saving account that pays 6.75% Interest compounded monthly for 10 years.
Principal amount= $750
Rate of interest= 6.75%
Time= 10 years
Number of times compounded= 10*12
Number of times compounded= 120
A= p(1+r/n)^(nt)
A= 750(1+0.0675/120)^(120*10)
A= 750(1+0.0005625)^(1200)
A= 750(1.0005625)^(1200)
A= 750(1.9637)
A= 1472.775
Amount after 10 years is $1472.775
If 3s = t + 5 and s
= 4, then t = ?
3s=t+5
s=4
we substitute 4 for s in the equation
3*4=t+5
12=t+5
t=12-5
t=7
Answer:
Brainliest!
Step-by-step explanation:
3s = t+5
s = 4
so...
3 (4) = t+5
12 = t+5
t = 7
What is 0.000345 expressed in scientific notation?
O 3.45 x 102
O 3.45 x 10
0 3.45 x 102
0 3.45 x 10 4
Answer:
The answer is D 10 to the power of -4.
Step-by-step explanation:
When the decimal point moves left, the power of becomes negative. Therefor the answer is D.
Have a good day.
Find the value of x. Picture below
Answer:
x=6
Step-by-step explanation:
BD is bisecting of <B
x/3=8/4 the theorem of the bisecting
4*x=3*8
4x=24
x=24/4
x=6
Find the sum of the convergent series by using a well-known function. (Round your answer to four decimal places.) [infinity] (−1)n + 1 1 7nn n = 1
Answer:
Here is the full question:
Find the sum of the convergent series by using a well-known function. (Round your answer to four decimal places.) Σ_(n=1)^∞ (-1)^n+1 1/7^n n
Step-by-step explanation:
Σ_(n=1)^∞ (-1)^n+1 1/7^n n
We will use the function In (1 + x)
We will now give a power series expansion of the function while it is centered at x=0
This will give us In (1 + x) = Σ_(n=1)^∞[tex](-1)^{n+1}[/tex][tex]\frac{x^{n} }{n}[/tex]
Note that x= 1/7
Now let us equate the two equations
Σ_(n=1)^∞[tex](-1)^{n+1}[/tex][tex]\frac{1}{7^{n}n }[/tex] = ㏑(1 + x)|[tex]_{x = \frac{1}{7} }[/tex] = ㏑[tex]\frac{8}{7}[/tex]
Sum of the series will give ㏑[tex]\frac{8}{7}[/tex]
The following table shows a proportional relationship between xxx and yyy. xxx yyy 222 999 555 22.522.522, point, 5 888 363636 Write an equation to describe the relationship between xxx and yyy.
Answer:
y=4.5x
Step-by-step explanation:
I got it correct on Khan!
Hope this helps ;)
The equation that describes the proportional relationship between x and y is: y = 4.5x.
How to Write the Equation of a Proportional Relationship?To write the equation of a proportional relationship between variables x and y, find the constant of proportionality, which is k = y/x, then plug in the value of k into y = kx.
Constant of proportionality (k) = 9/2 = 22.5/5 = 36/8 = 4.5
Substitute k = 4.5 into y = kx.
y = 4.5x.
The equation is: y = 4.5x.
Learn more about the proportional relationship on:
https://brainly.com/question/15618632
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Dione has 3 rolls of pennies containing 50 coins each, 4 rolls of nickels
containing 40 coins each, 5 rolls of dimes containing 50 coins each, and 6
rolls of quarters containing 40 coins each. How much money does she have?
Answer:
$94.50
Step-by-step explanation:
3(50)=150 $1.50
4(40)=160 160(5)=800 $8.00
5(50)=250 250(10)=2500 $25.00
6(40)=240 240(25)=6000 $60.00
60+25+8+1.5=$94.50
Many smoke detectors contain:
A. Carbon-14
B. Americium-241
C. Strontium-90
D. Iodine
Answer:
Option B, Americium-241, is the right answer.
Step-by-step explanation:
A device which senses smoke usually as an indicator of fire is known as a smoke detector.The two most common types of smoke detectors are the Ionization chamber and photoelectric smoke indicators. Many of these smoke detectors comprise some amount of americium-241, which is a radioactive substance. These smoke detectors respond immediately to fires that give off some smoke.A candle is in the shape of a cylinder with a diameter of 3.5 in and height of 8.5 in. The weight of the candle is 1400 grams.
a. Find the density of the candle.
b. If the candle burns at a rate of 0.75in per hour, find its volume after burning for 3 hours.
c. Compare the volume and surface area of the burned candle to its beginning volume and surface area.
d. What is the weight of the candle after burning for 3 hours?
Answer:
a
Step-by-step explanation:
Let x stand for the length of an individual screw. 100 screws were sampled at a time. The population mean is 2.5 inches and the population standard deviation is 0.2 inches. What is the mean of the sampling distribution of sample means?
a) 0.2
b) 2.5
c) 0.02
d) 2.
Answer:
The correct option is b
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 100[/tex]
The population mean is [tex]\mu = 2.5[/tex]
The sample standard deviation is [tex]\sigma = 0.2[/tex]
Generally the mean of the sampling distribution of sample means is mathematically represented as
[tex]\mu_{\= x } = \mu[/tex]
=> [tex]\mu_{\= x } = 2.5[/tex]
For the diagram, calculate; the radius of the smaller section and the perimeter of the shape of the and;
Answer:
a). Radius r of the small sector= 12cm
b). Perimeter of the shape= 68 cm
c). Angle= 47.7°
Step-by-step explanation:
a). Radius of the big sector= 24 cm
Arc if the big sector= 20 cm
Arc of the small sector= 10 cm
For the radius r of the small sector
r/10 = 24/20
r=(10*24)/20
r= 24/2
r= 12 cm
Radius r of the small sector= 12cm
b). Perimeter of the shape
= Total length of the shape
Let's note that the other side of the sector is also the radius= 24 cm
Perimeter= 20+24+24
Perimeter of the shape= 68 cm
c) the angle
Length of arc = 2πr*(angle/360)
Let angle = b
Length of arc = 20cm
20= 2*3.14*24*(b/360)
(20*360)/(2*3.14*24)= b
47.7°= b
Angle= 47.7°