A geometric sequence has a common ratio.
The formula for the nth term is
[tex]\sf{a_n =ar^{n-1} }[/tex]
where,
an = nth term of the sequence,a = first term of the sequence and r = common ratioGiven -
A geometric sequence 2, -4, 8, ...To find -
the 12th term of the given geometric sequenceSolution -
A.T.Q, a = 2 and r = -2
[tex]\rightarrow\sf{a_{12} =2(-2)^{12-1} }[/tex]
[tex]\rightarrow\sf{a_{12 }=2(-2)^{11} }[/tex]
[tex]\rightarrow\sf{a_{12} =2×(-2048) }[/tex]
[tex]\rightarrow\bf{a_{12 }=-4096 }[/tex]
Hence, the 12th term is -4096.
indicate the formula for the following conditions.
P(n,r) = ?
Answer:
P (n,r)= [tex]\frac{n!}{(n-r)!}[/tex]
Step-by-step explanation:
P (n,r)= ?
complete formula for permutation of objects in a set:
P (n,r) = [tex]\frac{n!}{(n-r)!}[/tex]
1. (03.04)
What are the zeros of f(x) = (x - 5)(x – 4)(x - 2)? (2 points)
Answer:
for x=5, x=4 , x=2
Step-by-step explanation:
zero points, the x values that make this formula to be zero.
5-5=0
4-4=0
2-2=0
these values satisfied
Sylvie needs $110 for a concert ticket. She already has $16 and she can earn the rest by working 10 hours at her job. If h represents her hourly earnings, which of the following equations can be solved to find Sylvie’s hourly earnings? Select all that apply.
A. 110 – 16 = 10h
B. 110 = 16h + 10
C. 16 = 110 – h
D. 110 = 16 + 10h
E. 110 + 16 = 10h
Answer:
The correct answers are:
A.) 110 - 16 = 10h
B.) 110 = 16h + 10
Step-by-step explanation:
Sylvie needs $110 for a concert ticket and already has $16 in her pocket. She can make up the difference by working an additional 10 hours at her job.
To earn the $110 required for the concert ticket, she'll need to work 10 hours in addition to the $16 she already has.
As a result, the following calculation can be used to calculate her hourly rate:
110 = 16 + 10h
110 - 16 = 10h
I hope this helps! ^-^
Help!!!! I need help with this one
Answer:
y=1/3x+2
Step-by-step explanation:
y=mx+b form is where m = the slop and b = the y interecept.
Y - Intercept
we can tell the y-intercept is 2 just by looking at the graph
Slope
For the slope, we can pick two points on the line, in this case, I will pick the points (0,2) and (3,3). Then, we can use the slope formula (y2-y1)/(x2-x1) to find the points, and after plugging the points in, we get 1/3, which is the slope
Plugging the numbers into slop intercept form
So we now know the slope is 1/3 and y-intercept is 2, so after plugging it into slope-intercept form (y=mx+b), we get y=1/3x+2
what is the median of the data set below? 45 57 41 67 33 43 A.41 B.44 C.54 D.67
Answer:
41
Step-by-step explanation:
The middle number is the median
The following two-way table shows the data for the students of two different grades in a school:
Member of Public Library Not Member of Public Library Total
25
3
28
Grade 6
Grade 7
Total
23
7
30
48
10
58
Based on the relative row frequency, the students of which grade are more likely to be members of the public library?
The students of both grades are equally likely to be members of the public library
No conclusion can be drawn about the chances of a student being a member of the public library
Need help with this last question
can you please help me?
Answer:
$91.30
Step-by-step explanation:
Hours worked on Monday: 8.30 hours (4.15 in the morning and 4.15 in the afternoon)
8.30 hours x $11 per hour: $91.30
what should be subtracted from 8p + 5p to get 6a - 5b ?
Answer:
8p+5p
=13p
=6a-5b procesa
PLEASE HELP MEEEEE PLEASE ASAP
. SCULPTURE An artist creates two metal sculptures in the shape of regular octagons. A side of the larger sculpture is 3.5 times longer than a side of the smaller octagon. The area of the smaller octagon is 19.28 square inches.
a. What is the area of the larger octagon?
b. The artist is going to pack the sculptures in a cylindrical box to take them to an art show. To the nearest inch, what is the diameter of the smallest box he can use? Explain your reasoning. (Hint: Find the radius of the larger octagon.)
By using what we know about octagons, we will see that:
a) The area is 244.89 in^2b) The diameter is 18.58 inWhat is the area of the larger octagon?
For an octagon of side length S, the area is:
A = 2*(1 + √2)*S^2
In this case, the area of the smaller octagon is:
19.28 in^2 = 2*(1 + √2)*S^2
Solving for S we get:
S = √( 19.28 in^2/(2*(1 + √2))) = 2.03 in
If we apply an enlargement of a factor 3.5, the new side length is:
S' = 3.5*2.03 in = 7.11 in
Then the area of the larger octagon is:
A' = 2*(1 + √2)*(7.11 in)^2 = 244.89 in^2
b) For an octagon of side length S, the radius is:
R = S*√(1 + 1/√2)
Then the radius of the larger octagon is:
R' = (7.11 in)*√(1 + 1/√2) = 9.29 in
Then the diameter of the box must be:
D = 2*R' = 2*9.29 in = 18.58 in
If you want to learn more about octagons, you can read:
https://brainly.com/question/1592456
How to solve this please
Their sum of ages is 45
So
x+x+27=452x+27=452x=18x=9Therefore
Nabil is 9years oldTala is 36 years oldStep-by-step explanation:
let the tala's age be x and nabil's be y
x+y=45(equation 1)
x=y+27
x-y=27(equation 2)
solving 1 and 2 equation
x+y=45
x-y=27
______
2x=18
x=9
therefore the talas age is 9
putting the value of x in equarion 1
9+y=45
y=45-9
y=36
Vic has 14 coins in nickels and quarters the value of this coins is 1.70 how many quarters does he have
Answer:
4 quarters
Step-by-step explanation:
4 quarters = $1
14 nickels = $0.70
Can someone please help me out with this question?
Answer:
B and B
Step-by-step explanation:
For the first problem, the range is simply the data set rearranged from smallest to largest.
For the second problem, you just have to cross multiply each variable in order to expand the equation and get an answer.
The answer for that one is [tex]12x^{3} -42x^{2} +8x+55[/tex]
How long is the arc intersected by a central angle of startfraction pi over 3 endfraction radians in a circle with a radius of 6 ft? round your answer to the nearest tenth. use 3.14 for pi. 1.0 ft 5.7 ft 6.3 ft 7.0 ft
The length of the arc which subtends a [tex]\pi/3[/tex] radians angle on a circle with 6 ft radius is given by: Option C: 6.3 feet approximately.
How to find the relation between angle subtended by the arc, the radius and the arc length?[tex]2\pi^c = 360^\circ = \text{Full circumference}[/tex]
The superscript 'c' shows angle measured is in radians.
If radius of the circle is of r units, then:
[tex]1^c \: \rm covers \: \dfrac{circumference}{2\pi} = \dfrac{2\pi r}{2\pi} = r\\\\or\\\\\theta^c \: covers \:\:\: r \times \theta \: \rm \text{units of arc}[/tex]
For this case, we have:
Radius of the circle = r = 6 ftAngle subtended by the considered arc of the circle on its center = [tex]\theta^c = \dfrac{\pi}{3}^c[/tex]Thus, if we take:
Length of the arc = L feet, then:
[tex]L =r \times \theta = 6 \times \dfrac{\pi}{3} = 2\pi \: \rm ft \approx 6.28 \approx 6.3 \: ft[/tex]
Thus, the length of the arc which subtends a [tex]\pi/3[/tex] radians angle on a circle with 6 ft radius is given by: Option C: 6.3 feet approximately.
Learn more about arc length here:
https://brainly.com/question/12058177
Answer:
c
Step-by-step explanation:
i did it and got it right
Which polynomial is a quartic trinomial?
A. -x^4-5x^2 + 1
B. x^2 + 4
C. x^3 + 2x^2 - 8x + 16
D. 3x^5 + 7x^2 - 9x^4
Answer:
A
Step-by-step explanation:
a quartic trinomial is a polynomial of degree 4 , with 3 terms
The only polynomial to fit this description is A
I forgot to do homework and its due tomorrow
Solve:
-2 3/4 ÷ (-2.5)
Answer:
It is 1.1
Step-by-step explanation:
-hope this helps.
The box plots show the number of days spent at a national park by two different groups of visitors.
Two box plots are shown together. The title is Time Spent at Park. The number line goes from zero to five by a scale of one half. For Group A, the whiskers range from one half day to five days, and the box ranges from two days to three and one half days. A line divides the box at three days. For Group B, the whiskers range from one day to four and one half days, and the box ranges from two days to four days. A line divides the box at three and one half days.
Select all the statements that are supported by the random samples.
About 75% of visitors in Group A spent 3.5 days or more at a national park.
About , 75 %, of visitors in Group A spent , 3.5, days or more at a national park.
About 50% of visitors in Group B spent 3.5 days or less at a national park.
About , 50 %, of visitors in Group B spent , 3.5, days or less at a national park.
About 25% of both Groups A and B spent 2 days or less at a national park.
About , 25 %, of both Groups A and B spent , 2, days or less at a national park.
Group A had greater variability in the number of days spent at a national park.
Group A had greater variability in the number of days spent at a national park.
Group B had a greater median and a greater spread in the number of days spent at a national park.
The answer is B i took the quiz
Do problems #4-6. Your answer choices are in a table below. Type your answer numbers the blank to move on! No spaces, no commas. Put it all together. *
I need help with 5
[tex]\frac{1}{2a}[/tex]
Step-by-step explanation:Simplify or expand
[tex](2a)^{-1}[/tex]
Simplify using negative exponent rule [tex]a^{-n}=\frac{1}{a^n}[/tex]
[tex]\frac{1}{2a}[/tex]
I hope this helps you
:)
A circular clock has a circumference of 27 inches. Find the approximate diameter of the clock. Use 3.14 for π . Round to the nearest hundredth if necessary.
Answer:
8.60 inches
Step-by-step explanation:
The equation for circumference is 2πr. So we can solve for r (radius).
27inches=2πr
divide both sides by 2π :
r=4.299
The equation for diameter is 2*r so we just multiply
4.299 *2 = 8.598
since we have to round to the hundredth place the answer would be
8.60
The approximate diameter of the circular clock is 8.60 inches.
What is Circumference of a Circle?Circumference of a circle is defined as the total length of the boundary of the circle.
The concept is same as the perimeter for straight sided figures.
Given that,
Circumference of the clock = 27 inches
The formula to find the circumference is,
C = 2πr
where r is the radius.
2r is the diameter.
2πr = 27
2r = 27 / 3.14
2r = 8.5987 ≈ 8.60
Hence the diameter of the clock is 8.60 inches.
Learn more about Circumference here :
https://brainly.com/question/17009295
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Figure #2 Volume =____ in^3
Answer:
480 in^3
Step-by-step explanation:
Multiplying the length of each of the sides together gives the volume, so [tex]12*4*10=480[/tex]
What is the value of x?
Answer:
19
Step-by-step explanation:
(5x+37)+(3x-9)=180
8x= 152
x=19
PLEASE HELP ME IN THIS QUESTION!!!
Answer:
CD = 16
Step-by-step explanation:
Segments EF and EC are tangent and secant respectively to the circle drawn from external point E.
Thus, by tangent-secant theorem:
[tex]ED\times EC= EF^2[/tex]
[tex]\implies x(x+x+7)= (15)^2[/tex]
[tex]\implies 2x^2+7x= 225[/tex]
[tex]\implies 2x^2+7x-225=0[/tex]
Comparing above quadratic equation with [tex]ax^2+bx+c=0[/tex], we find:
a = 2, b = 7, c = -225
Now, we find the value of the discriminant
[tex]\implies b^2-4ac= (7)^2-4(2)(-225)= 1849[/tex]
Now, by quadratic formula:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]\implies x=\frac{-7\pm\sqrt{1849}}{2(2)}[/tex]
[tex]\implies x=\frac{-7\pm (43)}{4}[/tex]
[tex]\implies x=\frac{-7+ 43}{4}\: or\:x=\frac{-7- 43}{4} [/tex]
[tex]\implies x=\frac{36}{4}\: or\:x=\frac{- 50}{4} [/tex]
[tex]\implies x=9\: or\:x=-12.5 [/tex]
x represents length, so it can't be negative.
[tex]\implies x\neq -12.5[/tex]
[tex]\implies x=9[/tex]
CD = x + 7
-> CD = 9 + 7
-> CD = 16
Solve for area and perimeter in each of the following problems. (2)
Step-by-step explanation:
Area =5m×11m=55m²
perimeter =(11m+5m)×2=52m
hope it helps!
Helpppppp!!!
(Show work)
Answer:
( - y - 3 , - x - 1 )
Step-by-step explanation:
( x , y ) ----> ( - y , x ) ----> ( - y - 3 , x + 1 ) ----> ( - y - 3 , - x - 1 )
find the next three terms of the sequence 2000,200,20,...and write the term to term rule.
Answer:
2, 0.2, 0.02
The first number is 2000. The term to term rule is 'divide by 10'.
Step-by-step explanation:
To calculate the next term, divide the previous term by 10:
2000 ÷ 10 = 200
200 ÷ 10 = 20
Therefore, the next three terms will be:
20 ÷ 10 = 2
2 ÷ 10 = 0.2
2 ÷ 10 = 0.02
Term to term rule
To work out the term to term rule, give the initial number of the sequence and then describe the pattern:
The first number is 2000. The term to term rule is 'divide by 10'.
Sarah and Lily mow lawns during the summer to earn money. Sarah
determined that she can earn between $6. 00 and $6. 25 per hour. Lily estimates
that she earns between $7. 50 and $8. 00 per hour. About how much more money will
Lily earn than Sarah if they each work 22 hours?
Answer:
21.75
Step-by-step explanation:
Because 6.00+6.25=12.25+7.00=19.75+8.00=27.75
two barrels filled with juice are similar in shape. the smaller barrel has a height of 2 feet. the larger barrel has a height of 5 feet. the total volume of the barrels is 532 cubic feet. what is the volume if the smaller barrel
Please help
Step-by-step explanation:
Volume of Barrel : [pi x h(r² + 2R²)] / 3
Barrel A : 2pi(r² + 2R²)]/ 3
Barrel B : 5pi(r² + 2R²)]/ 3
Barrel A + Barrel B = 532
5pi(r² + 2R²)/3 + 2pi(r² + 2R²)/3 = 532
5pi(r² + 2R²) + 2pi(r² + 2R²) = 1596
7pi(r² + 2R²) = 1596
pi(r² + 2R²) = 228
Barrel A = 2 x 228/3 = 76 ft³ SMALLER
Barrel B = 5 x 228/3 = 380 ft³
hope it's helpful, I'm not sure if (r) and (R) are the same if the two barrels has a similar shape. but if they're the same, then the answer is correct
Han earns $33.00 for babysitting 4 hours. At this rate, how much will he earn if he babysits for 7 hours? Explain your reasoning
Answer:
55.75
Step by step explain:
33.00 divided by 4 equals 8.25
then multiply 8.25 by 7 which equals 55.75
.) What is the sum? -3/4+(-3/4)
Answer:
The answer is -1.5
Step-by-step explanation:
Hope that helps.
Answer:
Step-by-step explanation:
-3/4 + (-3/4) remove parentheses
-3/4- 3/4 calculate the difference
-3/2 or - 1 1/2 or -1.5