Geometric series means
|r|<1Lets spot out common ratio
36/48=3/427/36=3/4Its less than 1
Hence series converges
Sum:-
a/1-r48/(1-3/4)48/1/4192Answer:
Series converges
Sum = 192
Step-by-step explanation:
General form of geometric series: [tex]a_n=ar^{n-1}[/tex]
where:
a is the initial termr is the common ratioGiven series: 48, 36, 27, 81/4, ...
[tex]\implies a = 48[/tex]
[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{36}{48}=\dfrac34[/tex]
Geometric series converges when |r| < 1
Geometric series diverges when |r| ≥ 1
[tex]\textsf{As }r=\dfrac34\ \implies|\dfrac34| < 1\:\implies\:\textsf{series converges}[/tex]
Sum of an infinite geometric series:
[tex]S_\infty=\dfrac{a}{1-r}\quad\textsf{for}\:|r| < 1[/tex]
Substituting values of a and r:
[tex]\implies S_\infty=\dfrac{48}{1-\frac34}=192[/tex]
The equation d = 11 cosine (startfraction 8 pi over 5 endfraction t) models the horizontal distance, d, in inches of the pendulum of a grandfather clock from the center as it swings from right to left and left to right as a function of time, t, in seconds. according to the model, how long does it take for the pendulum to swing from its rightmost position to its leftmost position and back again? assume that right of center is a positive distance and left of center is a negative distance. 0.625 seconds 0.8 seconds 1.25 seconds 1.6 seconds
The time it take for the pendulum to swing from its rightmost position to its leftmost position and back again is 1.25 seconds.
What is time period of pendulum?Pendulum is the body which is pivoted a point and perform back and forth motion around that point by swinging due to the influence of gravity.
The time period of pendulum is time taken by it to complete one cycle of swing left to right and right to left.
The equation models the horizontal distance of the pendulum of a grandfather clock from the center as it swings from right to left and left to right as a function of time, t, is given as,
[tex]d = 11 \cos\left( \dfrac{8\pi}{5}t\right)[/tex]
At the maximum position, the time period is zero. Thus,
[tex]\dfrac{8\pi}{5}t=0\\t=0[/tex]
At the minimum position, the period equal to the π. Thus,
[tex]\dfrac{8\pi}{5}t=\pi\\t=\dfrac{5}{8}\\t=0.625[/tex]
This time is for one side of motion. The time for swing from its rightmost position to its leftmost position and back again is,
[tex]t=0.625+0.625\\t=1.25\rm\; s[/tex]
Thus, the time it take for the pendulum to swing from its rightmost position to its leftmost position and back again is 1.25 seconds.
Learn more about the time period of pendulum here;
https://brainly.com/question/3551146
Answer:
C:1.25
Step-by-step explanation:
Find the volume of a cone with a base diameter of 10 m and a height of 8 m. Write the exact volume in terms of , and be sure to include the correct unit in your answer.
Answer:
The answer is given in the picture
Step-by-step explanation:
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT
help please
i’ll give good rating
Answer:
closed circle means 10 is a possible answer
m is greater or equal to 10
it's the 1st and 4th options
Step-by-step explanation:
Answer:
m ≥ 10 and it's a closed circle that is a possible answer.
Step-by-step explanation:
Rules:
Open circle: < (going left) or > (going right)
Closed circle: ≤ (going left) or ≥ (going right)
Here, we have a closed circle at 10, going right (≥).
Therefore, the correct answers are: m ≥ 10 and it's a closed circle that is a possible answer.
This means that m is equal to 10, or any value that is greater than 10.
Hope this helps!
find the range of the given data 8,9,7,11,18,13
Answer:
range = 11
Step-by-step explanation:
the range is the difference between the largest and smallest value in the data set.
largest value = 18 , smallest value = 7 , then
range = 18 - 7 = 11
11 is the range of the data 8,9,7,11,18,13
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
The given data is 8,9,7,11,18,13
Eight comma nine comma seven comma eleven comma eighteen comma thirteen.
The range in statistics for a given data set is the difference between the highest and lowest values.
Largest value is 18
Lowest value is 7
Range=Largest value-Lowest value
=18-7
=11
Hence, 11 is the range of the data 8,9,7,11,18,13
To learn more on Statistics click:
https://brainly.com/question/29093686
#SPJ2
what is the correct answers NEED ANSWERS FOR BOTH ASAP
Answer:
group like terms and solve
somebody help me this is hard for me
Answer:
[tex]\huge\boxed{\bf\: \frac{1}{3}\rightarrow probability}[/tex]
Step-by-step explanation:
Given,
Total number of marbles = 6Number of blue marbles = 2Number of yellow marbles = 1Number of red marbles = 3We are asked to find the probability of choosing a blue marble if they are randomly chosen. Then,
Probabilty of a blue marble
= Number of blue marbles / Total number of marbles
= 2/6
= 1/3
[tex]\rule{150pt}{2pt}[/tex]
. It took Erin the same time to drive 21 miles as it took Brent to drive 15 miles. Erin's speed was 10 mph
faster than Brent's speed. How fast did Erin drive?
The speed at which Erin drove from the given parameters was calculated as; 35 mph
How to work with speed rates?
Let Erin's speed rate be X. Now, since it took erin 21 miles, then;
Erin's time = 21/X
Now, erin's speed was 10 mph faster than Brent's speed. Thus;
Brent's speed = (X - 10) mph
Thus, Brents time = 15/(x - 10)
Now, since they took the same time, then we know that;
21/x = 15/(x - 10)
15x = 21x - 210
6x = 210
x = 210/6
x = 35
Thus, Erins speed = 35 mph
Read more about rates at; https://brainly.com/question/12242745
Which equation represents the line shown in the graph below
Answer:
b: y = 2x + 5
Step-by-step explanation:
you can find this out by first looking at what the slope is
the slope is rise over run which is 2
then you can see that the y intercept is 5
y = 2x + 5
what the answer to 24/3/7/5=
Answer:24/3/7/5 = 8/ 35 ≅ 0.2285714
Step-by-step explanation:
Divide: 24/3: 7 = 24/3· 1/7
= 24 · 1/3 · 7
= 24/21
= 3 · 8/3 · 7= 8/7
Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 7/1 is 1/7) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 3 gives 8/
7
.
In other words - twenty-four thirds divided by seven = eight sevenths.
Divide: the result of step No. 1 : 5 = 8/7 : 5 = 8/7 · 1/5
= 8 · 1/7 · 5
= 8/35
Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 5/1
is 1/5
) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - eight-sevenths divided by five = eight thirty-fifths.
SOMEONE HELP!!!!!!!
Answer:
115.395 min
Step-by-step explanation:
First we find the volume of 6 cm of water. We use the formula:
[tex]\pi *radius^2 *height[/tex]
[tex]\pi *35^2*6 = 23,079 cm^3[/tex]
1 L/min = 1000 cm^3 / min
0.2 L/min = 200 cm^3 /min
[tex]\frac{23,079}{200} = 115.395 min[/tex]
Hailey has $9 worth of nickels.how many nickels does hailey have?
Answer:
180
Step-by-step explanation:
The answer is 180 because 20 nickels make a dollar and you do 20x9 and that equals to 180
Answer:
$180 nickels
Step-by-step explanation:
9x 20= 180
Please answer the question correctly and with a good explanation. Please and thank you
Answer:
48
Step-by-step explanation:
To calculate the area of a composite shape you must divide the shape into rectangles, triangles, or other shapes you can find the area of and then add the areas back together. You may have to calculate missing lengths before finding the area of some of the shapes.
I split it into a square and a trapezoid
The area of the square is 6x5 = 30
The area of the trapezoid is
A=a+b
2h=3+6
2·4=18
So add the area together
30+18= 48
Taharka, Lamari and Keyon are sharing the cost of a football. Taharka will pay 0.15 of the cost. Lamari
will pay 12 of the cost. Keyon will pay the rest. If the football costs $16, how much will they each pay?
Answer:
the answer should be 3.85 that they pay each
Step-by-step explanation:
Because if you add 12.15 (Taharka + Lamari) and 3.85, it equals 16. The 3.85 comes from 16.00 - 12.15
A scale model of a ramp is a right triangular prism as given in this figure. In the actual ramp, the triangular base has a height of 0.5 yards.
What is the surface area of the actual ramp, including the underside?
Enter your answer as a decimal in the box.
The answer is 7.2 I just didnt see anyone ask this
The surface area of the figure is 720 square inches
How to calculate the surface area of a ramp?The surface area of a figure is the sum of all the area of its faces.
For the given diagram, it consists of 2 triangular faces and 3 rectangular faces
Surface area= (5 * 24) + 2(13*12) + 24 * 12
Surfacee area = 120 + 312 + 288
Surface area = 720 square inches
Hence the surface area of the figure is 720 square inches
Learn more on surface area here: https://brainly.com/question/76387
A rectangle's length is 3 times its width. If the perimeter is 32, what is the area?
The area of a rectangle is 56 cm. The length is 2 cm more then x and the width is 5 cm less than twice x. Solve for x. ROund to the nearest whole number.
Answer:
x^{2} -3x=46
Step-by-step explanation:
First, we know that the area of the rectangle is L x W.
[tex]L= x+2\\W= x-5\\(x+2) * (x-5)=56[/tex]
So, we would get [tex]x^{2} -5x+2x-10[/tex]=56
[tex]x^{2} -3x=46[/tex]
Consider the number 9,953.
Is this number divisible by 2, 3, 4, 5, 9, or 10? Provide justification for
each number without using a calculator.
Hint: If a number is not divisible by 2, then what other numbers is it
also not divisible by?
Write your answer in complete sentences.
Answer:
No for all of them
Step-by-step explanation:
2 --> not even
3 --> of the sum of the numbers are not divisible by three
4 --> the last two digits are not equal to a multiple of four
5 --> the last digit is not ending with 0 or 5
9 --> the sum of the digits is not equal to a multiple of nine
10 --> the last number is not zero
Solve the math problem
Answer:
Explanatory variable (independent variable)
The variable that affects the other variable.Drawn along the horizontal axis.Response variable (dependent variable)
The variable that is being affected. Drawn up the vertical axis.(a) As the class wondered if they could predict the father's height, when they know the son's height
Explanatory variable = son's height
Response variable = father's height
(even though this is contrary to real-life, where the father's height would be used to predict the son's height)
(b) **see first attachment**
(c) The association is positive since the father's height increases as the son's height increases.
(d) **see second attachment**
Outlier = Paul (64.5, 73)
This point is far away from the majority of points on the scatter plot.
If we add a regression line to the scatter plot, we can see that this data point is the farthest from the regression line.
5. A rectangle is shown with dimensions in inches
(in.).
3/4 in.
1/3 in.
CAN
What is the area of the rectangle in square inches?
square in.
Answer:
1/4 or 0.25in
Step-by-step explanation:
If you mean that 3/4 and 1/3 is lenght and width then:
3/4 x 1/3=1/4
1/4=0.25
1/4in^2
find the value of X to the nearest tenth
Answer:
x = 22.6 degrees
Step-by-step explanation:
The triangle is a right triangle which means that you can use trigonometry to find the values for each angle.
cos(x) = opposite / hypotenouse.
So cos(x) = 12/13.
You can then solve using a calculator and find that the angle is 22.6 degrees.
Angle Terminology with Equations
(Please Full Explanation)
Delta Math:
Supplementary angles are angles that sum up to 180 degrees
∠A and ∠B are supplementary angles
∠A + ∠B = 180°2(x) - 24 + 5(x) - 27° = 180°7(x) -51° = 180°7(x) = 180° + 51°7(x) = 231°x = 33°Find ∠B
5(x) - 27°5(33) - 27°165° - 27138°Therefore ∠B is 138 degrees
Answer:
∠B = 138
Step-by-step explanation:
Suplementary means = 180 soooo
180=(2x-24)+(5x-27)
180=7x-51
231=7x
x=33
B=5x-27
5(33)-27= 138
a listing for a home for sale is shown as follows: “3/2/1 house for sale. price 140000” what does “3/2/1” mean
Answer:
A
Step-by-step explanation:
Usually when purchasing a house you refer to the bedroom then the bathroom then potentially your garden width/height or you garage
Find the measure ments of angels 2, 3, and 4
Answer:
3-is 85
2- is 95
4-95
Step-by-step explanation:
for 1 is 85
85-180=95
3800 millimetres expressed in metres is
Answer:
3.8 meters
Step-by-step explanation:
1000 mm=1m
3000mm = 3m
500mm=.5
100mm= .1
800mm=.8m
3800mm=3.8
HELP ASAP!!!!!!!!!!!!!!!!!!!!
Answer:
0.36
Step-by-step explanation:
0.67 - 0.31 = B
B = 0.36
I hope this helps!
Am I correct?!? Please tell me!
Answer:
B
Step-by-step explanation:
Standard form of a polynomial is when the terms are order from highest exponential power to lowest exponential power. The choice you chose has the highest exponential power of 1, and a leading coefficient of 1. You are incorrect. The correct answer would be the second choice of:
[tex]5 {x}^{2} + 6x - 7[/tex]
This polynomial is in standard form, and has a leading coefficient of positive 5.
Can anyone help me with this problem?
Answer:
C
Step-by-step explanation:
pls tell me if im wrong
Please do number 5 thank you
Answer:
No, the mayor cannot conclude that 90% of residents favor the expansion.
Step-by-step explanation:
The sample taken is from the employees that will work on the highway, but we need to know the resident's opinion. The workers will have a different opinion than the average person, so this is not an accurate conclusion.
describe how to simplify the he expression 3^-6/3^-4
Answer:
by using bodmas rule
to solve this problem
Step-by-step explanation:
=3^-6/3^-4
=3-2-4
=-3
I need help please thanks
Answer:
5[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
Glass: [tex]\frac{2}{3}[/tex] × 10
Hours: 1[tex]\frac{1}{4}[/tex]
1) Find the real value. He drinks [tex]\frac{20}{3}[/tex] glasses of water in 1[tex]\frac{1}{4}[/tex] hours. 1[tex]\frac{1}{4}[/tex] × [tex]60[/tex] gives us the minutes because 1 hour is 60 minutes.
Glass : Minutes:
[tex]\frac{20}{3}[/tex] : [tex]75[/tex]
2) Use ratio to find the value of one. 60 ÷ 75 gives us 0.8. Multiply [tex]\frac{20}{3}[/tex] by 0.8 or [tex]\frac{8}{10}[/tex].
Glass : Minutes
[tex]\frac{16}{3}[/tex] : 60
3) Convert [tex]\frac{16}{3}[/tex] into a mixed number.
= 5[tex]\frac{1}{3}[/tex]