Answer:
It would take around 152 hours or 468 miles.Step-by-step explanation:
If you walk from Tucson Arizona (Saguaro National Park) to San Clemente California (Dana point), it would take around 152 hours, or 468 miles, if you walking speed is as the average person which is 3 to 4 miles per hour.
You take one ball randomly from a bag with 10 yellow, 5 orange and 5 green balls. What is the probability that you take a yellow ball.
1
1/4
10/15
1/2
Answer:
1/2
Step-by-step explanation:
The probability of taking a yellow ball can be found by dividing the number of yellow balls over the total number of balls.
P(yellow ball)= yellow balls / total balls
There are 10 yellow balls. There are a total of 20 balls. There are 20 because there are 10 yellow, 5 orange, and 5 green. When 10, 5, and 5 are added, the result is 20.
yellow balls = 10
total balls= 20
P(yellow ball)= yellow balls / total balls
P(yellow ball)= 10/20
The fraction 10/20 can be simplified. Both the numerator( top number) and denominator (bottom number) can be evenly divided by 10.
P(yellow ball)= (10/10) / (20/10)
P(yellow ball)= 1/(20/10)
P(yellow ball)= 1/2
The probability of taking a yellow ball is 1/2.
A web page is accessed at an average of 20 times an hour. Assume that waiting time until the next hit has an exponential distribution. (a.) Determine the rate parameter λ of the distribution of the time until the first hit? (b.) What is the expected time between hits? (c.) What is the probability that t
Answer:
Step-by-step explanation:
Given that :
A web page is accessed at an average of 20 times an hour.
Therefore:
a. he rate parameter λ of the distribution of the time until the first hit = 20
b. What is the expected time between hits?
Let consider E(Y) to be the expected time between the hits; Then :
E(Y) = 1/λ
E(Y) = 1/20
E(Y) = 0.05 hours
E(Y) = 3 minutes
(c.) What is the probability that there will be less than 5 hits in the first hour?
Let consider X which follows Poisson Distribution; Then,
P(X<5) [tex]\sim[/tex] G(∝=5, λ = 20)
For 5 hits ; the expected time will be :
Let 5 hits be X
E(X) = ∝/λ
E(X) = 5/20
E(X) =1/4
E(X) = 0.25 hour
E(X) = 15 minutes
From above ; we will see that it took 15 minutes to get 5 hits; then
[tex]P(\tau \geq 0.25) = \int\limits^{\alpha}_{0.25} \dfrac{\lambda^{\alpha}}{\ulcorner^{\alpha}} t^{a\pha-1} \ e^{-\lambda t} \, dt[/tex]
[tex]P(\tau \geq 0.25) = \int\limits^{5}_{0.25} \dfrac{20^{5}}{\ulcorner^{5}} t^{5-1} \ e^{-20 t} \, dt[/tex]
[tex]\mathbf{P(\tau \geq 0.25) =0.4405}[/tex]
W varies inversely as the square root of x when x=4 w=4 find when x=25
Answer:
8/5
Step-by-step explanation:
w = k / √x
4 = k / √4
k = 8
w = 8 / √x
w = 8 / √25
w = 8/5
Explain how the interquartile range of a data set can be used to identify outliers. The interquartile range (IQR) of a data set can be used to identify outliers because data values that are ▼ less than equal to greater than ▼ IQR Upper Q 3 minus 1.5 (IQR )Upper Q 3 plus IQR Upper Q 3 plus 1.5 (IQR )or ▼ less than equal to greater than ▼ IQR Upper Q 1 plus 1.5 (IQR )Upper Q 1 minus IQR Upper Q 1 minus 1.5 (IQR )are considered outliers.
Answer:
- greater than Upper Q 3 plus 1.5 (IQR)
- less than Upper Q 1 minus 1.5 (IQR)
Step-by-step explanation:
To identify outliers the interquartile range of the dataset can be used
Outliers can be identified as data values that are
- greater than Upper Q 3 plus 1.5 (IQR)
- less than Upper Q 1 minus 1.5 (IQR)
Using the interquartile range concept, it is found that:
The interquartile range (IQR) of a data set can be used to identify outliers because data values that are 1.5IQR less than Q1 and 1.5IQR more than Q3 and considered outliers.
----------------------------
The interquartile range of a data-set is composed by values between the 25th percentile(Q1) and the 75th percentile(Q3).It's length is: [tex]IQR = Q3 - Q1[/tex]Values that are more than 1.5IQR from the quartiles are considered outliers, that is:[tex]v < Q1 - 1.5IQR[/tex] or [tex]v > Q3 + 1.5IQR[/tex]
Thus:
The interquartile range (IQR) of a data set can be used to identify outliers because data values that are 1.5IQR less than Q1 and 1.5IQR more than Q3 and considered outliers.
A similar problem is given at https://brainly.com/question/14683936
the average temperature for one week in Alaska are as follows: 10, 6, 9, 2, 0,3. what is the mean of these tempartures ? show all work.
Answer:
5
Step-by-step explanation:
We know that we have to add all numbers then divide it by how many numbers there are. So, 10 + 6 + 9 + 2 + 0 + 3 = 30. 30/6 = 5.
PLEASE EXPLAIN IN DETAILS HOW TO SOLVE LINEAR INEQUALITIES. Heres an example problem. Please solve and show your steps/explain.
6(x+8) ≥ ‒43+4x
Answer:
[tex]x \geq -91/2[/tex]
Step-by-step explanation:
[tex]6(x+8) \geq -43 + 4x[/tex]
Resolving Parenthesis
[tex]6x+48 \geq -43 + 4x[/tex]
Collecting like terms
[tex]6x - 4 x \geq -43-48[/tex]
[tex]2x \geq -91[/tex]
Dividing both sides by 2
[tex]x \geq -91/2[/tex]
Answer:
x ≥ - 91 / 2
Step-by-step explanation:
In this sample problem, the first thing we want to do is expand the part in parenthesis through the distributive property. This will make the simplification process easier. Another approach would be to divide either side by x + 8, but let's try the first.
Approach 1 : [tex]6(x+8) = 6x + 6 8 = 6x + 48[/tex]
[tex]6x + 48 \geq - 43+4x[/tex] - so we have this simplified expression. We now want to isolate x, so let's combine common terms here. Start by subtracting 6x from either side,
[tex]48 \geq - 43-2x[/tex] - now add 43 to either side,
[tex]91\geq -2x[/tex] - remember that dividing or multiplying a negative value changed the inequality sign. Dividing - 2 on either side, the sign changes to greater than or equal to, with respect to x,
[tex]- 91 / 2 \leq x[/tex], or in other words [tex]x \geq - 91 / 2[/tex]. This is our solution.
your marksmanship score are 6 and 10 on two test . if you want average 9 on the tests , waht must your third score be?
Answer:
11
Step-by-step explanation:
To do this you would just multiply 9 by 3 so you get 27 and subtract 6+10 which is 16 from it and then you will get 11 and that is what you will need for your third score
The third score which must be added is 11.
What are average?The average can be calculated by dividing the sum of observations by the number of observations.
Average = Sum of observations/the number of observations
Given; count = 3 (there are three trials)
average = 9
9 = sum / 3
The sum = first score + second score + third score
The sum = 6 + 10 + third score
9 = (6+10+third score)/3
Then multiply both sides by 3 to remove the denominator
27 = 6 + 10 + third score
27 = 16 + third score
Now, subtract 16 from both sides to isolate the third score
11 = third score
Hence, the third score which must be added is 11.
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Use Newton's method with initial approximation x1 = −1 to find x2, the second approximation to the root of the equation x3 + x + 8 = 0. (Round your answer to four decimal places.) x2 =
Answer:
The second approximation to the root of the equation [tex]x^{3}+x+8 = 0[/tex] is -1.5000.
Step-by-step explanation:
The Newton's method is a numerical method by approximation that help find roots of a equation of the form [tex]f(x) = 0[/tex] with the help of the equation itself and its first derivative. The Newton's formula is:
[tex]x_{i+1} = x_{i} - \frac{f(x_{i})}{f'(x_{i})}[/tex]
Where:
[tex]x_{i}[/tex] - i-th approximation, dimensionless.
[tex]x_{i+1}[/tex] - (i+1)-th approximation, dimensionless.
[tex]f(x_{i})[/tex] - Function evaluated at the i-th approximation, dimensionless.
[tex]f'(x_{i})[/tex] - First derivative of the function evaluated at the i-th approximation, dimensionless.
The function and its first derivative are [tex]f(x) = x^{3}+x+8[/tex] and [tex]f'(x) = 3\cdot x^{2}+1[/tex], respectively. Now, the Newton's formula is expanded:
[tex]x_{i+1} = x_{i}-\frac{x_{i}^{3}+x_{i}+8}{3\cdot x_{i}^{2}+1}[/tex]
If [tex]x_{1} = -1[/tex], the value of [tex]x_{2}[/tex] is:
[tex]x_{2} = -1 - \frac{(-1)^{3}+(-1)+8}{3\cdot (-1)^{2}+1}[/tex]
[tex]x_{2} = -1.5000[/tex]
The second approximation to the root of the equation [tex]x^{3}+x+8 = 0[/tex] is -1.5000.
Answer:
-2.5000
Step-by-step explanation:
Which of the following is the standard form of y =3/7 x-1 a)3/7x-y=1 b) y-3/7x= - 1 c) 7y-3x= -7 d) 3x - 7y= 7
Answer:
d)
Step-by-step explanation:
the general form is ax + by = c
For the claim that is given symbolically below, determine whether it is part of a left-tailed, right-tailed, or two-tailed hypothesis test.
p > 0.50
a. a right-tailed hypothesis test
b. a two-tailed hypothesis test
c. impossible to determine from the information given
d. a left-tailed hypothesis test
Answer:
Option A a right tailed hypothesis test
Step-by-step explanation:
A claim given symbolically is most of the time derived from the alternative hypothesis usually tested against the null hypothesis.
A symbolic claim with the option of a less than indicates a left tailed test, while one with the option of greatest than indicate a right tail test and one with the option of both (not equal to; either less or greater) indicates a two tailed test.
In this case study, the sample proportion for the claim was greater than 0.50 thus, the test is a right tailed hypothesis test
Click on the solution set below until the correct one is displayed.
Answer:
{ } or empty set.
Step-by-step explanation:
The solutions should be where the two lines intersect, but in this case, the parallel lines never intersect. That means that they have no solutions.
Hope this helps!
Answer:
{ } or empty set
Step-by-step explanation:
It's because these lines are parallel so they don't intersect to give you a coordinate.
When the input is 4, the output of f(x) = x + 21 is
Answer:
25Step-by-step explanation:
When the input is 4, the output of f(x) = x + 21 is f(4).
Substitute x = 4 to f(x):
f(4) = 4 + 21 = 25
Answer:
25
Step-by-step explanation:
We can find the output by plugging in 4 as x into the function:
f(x) = x + 21
f(4) = 4 + 21
f(4) = 25
Whats the input value of f(x)=2x+5
Answer:
x
Step-by-step explanation:
f(x)=2x+5
Input: x
Output: f(x)
For i.e:
Input: 1
Output: f(1) = 2(1) + 5 = 2 + 5 = 7
The same bedroom furniture set costs $1,500 in both Florida and Alabama. The table gives a breakdown of the taxes someone would pay when purchasing the furniture set in either state. Alabama Florida State of Alabama: 4.225% County Tax: 1.375% City Tax: 3.0% State of Florida: 6.5% County Tax: 1% City Tax: 1.625% Which statement is true? A. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by about $8. B. The furniture set is cheaper in Florida, because the amount of sales tax will be lower by about $10. C. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by $10. D. The furniture set costs the same in either state, because the amount of sales tax will be the same for the two locations.
Answer:
A: True
B, C and D: False
Step-by-step explanation:
We have a total sales tax for Alabama that is:
[tex]T_A=4.225+1.375+3=8.6[/tex]
The total sales tax for Florida is:
[tex]T_F=6.5+1+1.625=9.125[/tex]
The total sales tax is greater in Florida than in Alabama.
A. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by about $8. TRUE
The sales tax difference in this purchase can be calculated as:
[tex]1500(T_F-T_A)=1500\left(\dfrac{9.125-8.6}{100}\right)=1500\cdot 0.00525=7.875\approx 8[/tex]
B. The furniture set is cheaper in Florida, because the amount of sales tax will be lower by about $10. FALSE (it is cheaper in Alabama)
C. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by $10. FALSE (the sale tax in Alabama is $129)
The amount of sales tax in Alabama is:
[tex]ST_A=1500\cdot T_A=1500\cdot 0.086=129[/tex]
D. The furniture set costs the same in either state, because the amount of sales tax will be the same for the two locations. FALSE (it is not the same in both states).
Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of integration.) x4 18x2 4 x5 30x3 20x dx
Your integrand is missing some symbols. My best interpretation is the following integral:
[tex]I=\displaystyle\int\frac{x^4+18x^2+4}{x^5+30x^3+20x}\,\mathrm dx[/tex]
Decompose into partial fractions; we're looking for an expansion of the form
[tex]\dfrac{x^4+18x^2+4}{x^5+30x^3+20x}=\dfrac ax+\dfrac{bx^3+cx^2+dx+e}{x^4+30x^2+20}[/tex]
Now:
[tex]x^4+18x^2+4=a(x^4+30x^2+20)+(bx^3+cx^2+dx+e)x[/tex]
[tex]=(a+b)x^4+cx^3+(30a+d)x^2+ex+20a[/tex]
Matching up coefficients tells us that
[tex]\begin{cases}a+b=1\\c=0\\30a+d=18\\e=0\\20a=4\end{cases}\implies a=\dfrac15,b=\dfrac45,d=12[/tex]
so that
[tex]I=\displaystyle\frac15\int\frac{\mathrm dx}x+\frac45\int\frac{x^3+15x}{x^4+30x^2+20}\,\mathrm dx[/tex]
The integral is trivial:
[tex]\displaystyle\frac15\int\frac{\mathrm dx}x=\frac15\ln|x|+C[/tex]
For the second integral, notice that
[tex]\mathrm d(x^4+30x^2+20)=(4x^3+60x)\,\mathrm dx[/tex]
Distribute the 4 over the numerator, then substitute [tex]u=x^4+30x^2+20[/tex] and [tex]\mathrm du=(4x^3+60x)\,\mathrm dx[/tex]:
[tex]\displaystyle\frac15\int\frac{4x^3+60x}{x^4+30x^2+20}\,\mathrm dx=\frac15\int\frac{\mathrm du}u=\frac15\ln|u|+C=\frac15\ln(x^4+30x^2+20)+C[/tex]
So we have
[tex]I=\dfrac15\ln|x|+\dfrac15\ln(x^4+30x^2+20)+C[/tex]
and with some simplification,
[tex]I=\boxed{\ln\sqrt[5]{|x^5+30x^3+20x|}+C}[/tex]
In △ABC,a=11 , b=20 , and c=28 . Find m∠A .
Answer:
18.4°
Step-by-step explanation:
Use law of cosine.
a² = b² + c² − 2bc cos A
11² = 20² + 28² − 2(20)(28) cos A
121 = 1184 − 1120 cos A
cos A = 0.949
A = 18.4°
Part F
I NEED HELP!
What is the geometric mean of the measures of the line segments A Dand DC? Show your work.
Answer:
AC2 = AB2 + BC2 ---> AC2 = 122 + 52 ---> AC = 13
AD / AB = AB / AC ---> AD / 12 = 12 / 13 ---> AD = 144/13
DC = AC - AD ---> DC = 13 - 144/13 ---> DC = 25/13
AD / DB = DB / DC ---> DB2 = AD · DC ---> DB2 = (144/13) · (25/13) ---> DB = 60/13
DB is the geometric mean of AD and DC.
Step-by-step explanation:
help plsssssssssssss
Answer:
[tex]z = \frac{x}{y} [/tex]
Step-by-step explanation:
Let x be the price of carton of ice cream
Let y be the number of grams in carton
Let z be price per gram.
[tex]z = \frac{x}{y} [/tex]
Which means price of carton of ice cream divided by the number of grams in carton equals price per gram.
Hope this helps ;) ❤❤❤
The side length of the cube is s. Find the domain of the volume of the cube.
Answer:
-∞<x<∞
Step-by-step explanation:
volume of a cube=s^3
the domain is (-∞,∞) the domain is all the real number of s
Enter your answer in the box
____
Answer:
[tex]\boxed{2144}[/tex]
Step-by-step explanation:
The sum can be found by adding the parts:
[tex]\sum\limits_{n=1}^{32}{(4n+1)}=4\sum\limits_{n=1}^{32}{n}+\sum\limits_{n=1}^{32}{1}=4\cdot\dfrac{32\cdot 33}{2}+32\\\\= 2112+32=\boxed{2144}[/tex]
__
The sum of numbers 1 to n is n(n+1)/2.
Price of an item is reduced by 40% of its original price. A week later it’s reduced 20% of the reduced price. What’s the actual % of the reduction from the original price
Answer: 52%
Step-by-step explanation:
Let the original price be 100.
After 40% reduction, price will be 100 - 40% = 60
After further 20% reduction, price will be 60 - 20% = 48
%age = (cur val - orig. val ) / orig val x 100
= (48 - 100) / 100 x 100%
= -52
The actual percentage of reduction is 52%
The first reduction is given as:
[tex]r_1 = 40\%[/tex]
The second reduction is given as:
[tex]r_2 = 20\%[/tex]
Assume that the original price of the item is x.
After the first reduction of 40%, the new price would be:
[tex]New = x\times (1 -r_1)[/tex]
So, we have:
[tex]New = x\times (1 -40\%)[/tex]
[tex]New = x\times 0.6[/tex]
[tex]New = 0.6x[/tex]
After the second reduction of 20% on the reduced price, the new price would be:
[tex]New = 0.6x\times (1 -r_2)[/tex]
So, we have:
[tex]New = 0.6x\times (1 -20\%)[/tex]
[tex]New = 0.6x\times 0.8[/tex]
[tex]New = 0.48x[/tex]
Recall that the original price is x.
So, the actual reduction is:
[tex]Actual = \frac{x - 0.48x}{x}[/tex]
[tex]Actual = \frac{0.52x}{x}[/tex]
Divide
[tex]Actual = 0.52[/tex]
Express as percentage
[tex]Actual = 52\%[/tex]
Hence, the actual percentage of reduction is 52%
Read more about percentage change at:
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The organizer of a conference is selecting workshops to include. She will select from 9 workshops about anthropology and 5 workshops about psychology. In
how many ways can she select 7 workshops if more than 4 must be about anthropology?
Answer: She can select 7 workshops if more than 4 must be about anthropology in 1716 ways.
Step-by-step explanation:
Given, The organizer of a conference is selecting workshops to include. She will select from 9 workshops about anthropology and 5 workshops about psychology.
If he select 7 workshops if more than 4 must be about anthropology, the possible combinations = (5 anthropology, 2 psychology), ( 6 anthropology, 1 psychology), (7 anthropology, 0 psychology)
Number of possible combinations = [tex]^9C_5\times ^5C_2+^9C_6\times ^5C_1+^9C_7\times ^5C_0[/tex]
[tex]=\dfrac{9!}{5!4!}\times\dfrac{5!}{2!3!}+\dfrac{9!}{6!3!}\times(5)+\dfrac{9!}{7!2!}\times (1)\\\\=\dfrac{9\times8\times7\times6}{4\times3\times2\times1}\times\dfrac{5\times4}{2}+\dfrac{9\times8\times7}{3\times2\times1}\times5+\dfrac{9\times8}{2}\\\\=1260+420+36\\\\=1716[/tex] [using formula for combinations [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]]
Hence, she can select 7 workshops if more than 4 must be about anthropology in 1716 ways.
please answer asap. there are two pics :)
Answer:
[tex]\boxed{\sf A. \ 0.34}[/tex]
Step-by-step explanation:
The first triangle is a right triangle and it has one acute angle of 70 degrees.
We can approximate [tex]\sf \frac{WY}{WX}[/tex] from right triangle 1.
The side adjacent to 70 degrees is WY. The side or hypotenuse is WX.
The side adjacent to 70 degrees in right triangle 1 is 3.4. The side or hypotenuse is 10.
[tex]\sf \frac{3.4}{10} =0.34[/tex]
According to genetic theory, there is a very close to even chance that both children in a two child family will be of the same gender. Here are two possibilities.
(i). 24 couples have two children. In 16 or more of these families, it will turn out that both children are of the same gender.
(ii). 12 couples have two children. In 8 or more of these families, it will turn out that both children are of the same gender. Which possibility is more likely and why?
Answer:
Therefore scenario (ii) is more likely to occur than scenario (i), and by almost 3 times.
Step-by-step explanation:
(i) probability with 16 success out of 24 = 16/24 = 2/3
(ii) (i) probability with 8 success out of 12 = 8/12 = 2/3
Since the two experiments have the same probability, the observed probabilities are the same.
HOWEVER, since the theoretically probability is 1/2, 16.7% less than the experimental results, the number N of trials comes into play.
Using the binomial distribution,
(i)
p = 1/2
N = 24
x = 16 (number of successes)
P(16,24) = C(24,16) p^16* (1-p)^8
= 735471* (1/65536)*(1/256)
= 0.0438
(ii)
p = 1/2
N = 12
x = 8 (number of successes)
P(8,12) = C(12,8) p^8* (1-p)^4
= 495*1/256*1/16
= 0.1208
Therefore scenario (ii) is more likely to occur than scenario (i), and by almost 3 times.
Note: It would help to mention the topic you're on so answers will correspond to what is expected. Here we cover probability and binomial distribution.
A hotel rents 210 rooms at a rate of $ 60 per day. For each $ 2 increase in the rate, three fewer rooms are rented. Find the room rate that maximizes daily revenue.
Answer:
r=$14,400
The hotel should charge $120
Step-by-step explanation:
Revenue (r)= p * n
where,
p = price per item
n = number of items sold
A change in price leads to a change in number sold
A variable to measure the change in p and n needs to be introduced
Let the variable=x
Such that
p + x means a one dollar price increase
p - x means a one dollar price decrease
n + x means a one item number-sold increase
n - x means a one item number-sold decrease
for each $2 price increase (p + 2x) there are 3 fewer rooms are rented (n-3x)
know that at $60 per room, the hotel rents 210 rooms
r = (60 + 2x) * (210 - 3x)
=12,600-180x+420x-6x^2
=12,600+240x-6x^2
r=2100+40x-x^2
= -x^2 +40x+2100=0
Solve the quadratic equation
x= -b +or- √b^2-4ac / 2a
a= -1
b=40
c=2100
x= -b +or- √b^2-4ac / 2a
= -40 +or- √(40)^2 - (4)(-1)(2100) / (2)(-1)
= -40 +or- √1600-(-8400) / -2
= -40 +or- √ 1600+8400 / -2
= -40 +or- √10,000 / -2
= -40 +or- 100 / -2
x= -40+100/-2 OR -40-100/-2
=60/-2 OR -140/-2
= -30 OR 70
x=70
The quadratic equation has a maximum at x=70
p+2x
=60+2(30)
=60+60
=$120
r= (60 + 2x) * (210 - 3x)
={60+2(30)}*{(210-3(30)}
r=(60+60)*(210-90)
=120*120
=$14,400
Find exact value of cos
Work Shown:
[tex]\sin^2 \theta + \cos^2 \theta = 1\\\\\left(\frac{3}{10}\right)^2 + \cos^2 \theta = 1\\\\\frac{9}{100} + \cos^2 \theta = 1\\\\\cos^2 \theta = 1 - \frac{9}{100}\\\\\cos^2 \theta = \frac{100}{100}-\frac{9}{100}\\\\\cos^2 \theta = \frac{91}{100}\\\\\cos \theta = \sqrt{\frac{91}{100}} \ \text{ cosine positive in Q1}\\\\\cos \theta = \frac{\sqrt{91}}{\sqrt{100}}\\\\\cos \theta = \frac{\sqrt{91}}{10}\\\\[/tex]
Answer:
√91/10
Step-by-step explanation:
sin 0.3 is equal to 18(approximate value)
cos18°=0.951
which is √91/10
A deep-sea diver is in search of coral reefs.he finds a beautiful one at an elevation of -120 4/7feet. While taking pictures of the reef he catches sight of a manta ray. He swims up 25 3/7feet to check it out.what is the diver's new elevation?
Answer:-95 1/7 feet
Step-by-step explanation:
-120 4/7+25 3/7=-95 1/7 feet
Why should you find the least common denominator when adding or subtracting rational expressions?
Answer:
It is necessary to look for the least common denominator when one is trying to add or subtract rational expressions that do not have the same denominator.
Step-by-step explanation:
for example the denominator of the two addends are not the same. One has (x+2), the other (x-2).
6th grade math help me, please. :)
Step-by-step explanation:
Hello there!!
no need to be panic we will help you, alright.
look solution in picture ok...
sorry for cutting in middle.
Hope it helps...
For each of the finite geometric series given below, indicate the number of terms in the sum and find the sum. For the value of the sum, enter an expression that gives the exact value, rather than entering an approximation.
3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} + \cdots + 3 (0.5)^{13}
(1) Number of terms
(2) Value of Sum
Answer:
Number of term N = 9
Value of Sum = 0.186
Step-by-step explanation:
From the given information:
Number of term N = [tex]3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} + \cdots + 3 (0.5)^{13}[/tex]
Number of term N = [tex]3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} +3 (0.5)^{8}+3 (0.5)^{9} +3 (0.5)^{10} +3 (0.5)^{11}+3 (0.5)^{12}+ 3 (0.5)^{13}[/tex]
Number of term N = 9
The Value of the sum can be determined by using the expression for geometric series:
[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{a(r^m-r^{n+1})}{1-r}[/tex]
here;
m = 5
n = 9
r = 0.5
Then:
[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{3(0.5^5-0.5^{9+1})}{1-0.5}[/tex]
[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{3(0.03125-0.5^{10})}{0.5}[/tex]
[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{(0.09375-9.765625*10^{-4})}{0.5}[/tex]
[tex]\sum \limits ^n_{k=m}ar^k =0.186[/tex]
For the given the geometric series, 3·0.5⁵ + 3·0.5⁶ + 3·0.5⁷ + ...+ 3·(0.5)¹³,
the responses are;
(1) The number of terms are 9
(2) The value of the sum is approximately 0.374
How can the geometric series be evaluated?The given geometric series is presented as follows;
3·0.5⁵ + 3·0.5⁶ + 3·0.5⁷ + ...+ 3·(0.5)¹³
(1) The number of terms in the series = 13 - 4 = 9
Therefore;
The number of terms in the series = 9 terms(2) The value of the sum can be found as follows;
The common ratio, r = 0.5
The sum of the first n terms of a geometric progression is presented as follows;
[tex]S_n = \mathbf{\dfrac{a \cdot (r^n - 1)}{r - 1}}[/tex]
The sum of the first 4 terms are therefore;
[tex]S_4 = \dfrac{3 \times (0.5^4 - 1)}{0.5 - 1} = \mathbf{ 5.625}[/tex]
The sum of the first 13 terms is found as follows;
[tex]S_{13} = \dfrac{3 \times (0.5^{13} - 1)}{0.5 - 1} = \mathbf{ \dfrac{24573}{4096}}[/tex]
Which gives;
The sum of the 5th to the 13th term = S₁₃ - S₄
Therefore;
[tex]The \ sum \ of \ the \ 5th \ to \ the \ 13th \ term =\dfrac{24573}{4096} - \dfrac{45}{3} = \dfrac{1533}{4096} \approx \mathbf{0.374}[/tex]
The value of the sum of the terms of the series is approximately 0.374Learn more about geometric series here:
https://brainly.com/question/12471913