Answer:
- L < 1, so by series ratio test, It is convergent
- sum of the convergent series is 49
Step-by-step explanation:
Given the data in the question;
series = 7 + 6 + 36/7 + 216/49 + .........
⇒ 7 + 7 × 6/7 + 7 × 36/49 + 7 × 216/343 +........
⇒ 7 + 7 × 6/7 + 7 × 6²/7² + 7 × 6³/7³ .....
⇒ 7( 1 + 6/7 + 6²/7² + 6³/7³ + ..... )
⇒ 7 ∞∑_[tex]_{n=0[/tex] [tex]([/tex] 6/7 [tex])^n[/tex]
⇒ ∞∑_[tex]_{n=0[/tex] ( [tex]6^n[/tex]/[tex]7^{n-1[/tex] )
So, L = [tex]\lim_{n \to \infty} | \frac{a_{n} + 1}{a_n} |[/tex]
= [tex]\lim_{n \to \infty} | \frac{\frac{6^n+1}{7n} }{\frac{6^n}{7^n-1} } |[/tex]
= [tex]\lim_{n \to \infty} | \frac{6}{7} |[/tex]
= 6 /7
L < 1
so by series ratio test,
It is convergent
So we find the sun;
Sum of infinite geometric series is;
⇒ a / (1-r)
here, a = first number and r = common ratio
∑ = 7( 1 + 6/7 + 6²/7² + 6³/7³ + ..... )
a = 1 and r = 6/7
so
∑ = 7( [tex]\frac{1}{1 - \frac{6}{7} }[/tex] )
= 7( [tex]\frac{1}{\frac{7-6}{7} }[/tex] )
= 7( [tex]\frac{1}{\frac{1}{7} }[/tex] )
= 7( 7 )
= 49
Therefore, sum of the convergent series is 49
need help asap WILL GIVE BRAINLIEST
A researcher reported the results from a particular experiment to the scientist who conducted it. The report states that on one specific part of the experiment, a statistical test result yielded a p-value of 0.18. Based on this p-value, what should the scientist conclude?
The test was not statistically significant because 2 × 0.18 = 0.36, which is less than 0.5.
The test was not statistically significant because if the null hypothesis is true, one could expect to get a test statistic at least as extreme as that observed 18% of the time.
The test was not statistically significant because if the null hypothesis is true, one could expect to get a test statistic at least as extreme as that observed 82% of the time.
The test was statistically significant because a p-value of 0.18 is greater than a significance level of 0.05.
The test was statistically significant because p = 1 − 0.18 = 0.82, which is greater than a significance level of 0.05.
Answer:
B
Step-by-step explanation:
I got it wrong but it showed me the right answer so, yea
What is the volume of the shaded portion of the
composite figure? Express your answer in terms of ..
15
12
5197 units
O 6812 units
O (6003 - 81) units
(600 – 817) units
10
Answer:
d. (600 - 81π) units ³
Step-by-step explanation:
Volume of the shaded portion = volume of triangular pyramid - volume of cone
= ⅓*A*h - ⅓πr²h
Where,
A = 15*10 = 150 units²
r = ½(9) = 4.5 units
h = 12
Plug in the values
Volume of the shaded portion = ⅓*150*12 - ⅓*π*4.5²*12
= (600 - 81π) units³
Find the Area of the Triangle
Answer:
50 squared m
Step-by-step explanation:
Volume for triangles is base x hight / 2
10 x 10 = 100 / 2 = 50
A shipment of sugar fills 6 containers. If each container holds 3 3/4
tons of sugar, what is the amount of sugar in the entire shipment?
Write your answer as a mixed number in simplest form.
Answer:
Step-by-step explanation:
Firstly, change the mixed fraction into improper fraction.
Secondly, multipy 6 containers by 15/4 to get total tons of sugar.
Thus 6*15/4=22.5
A standard american eskimo dog has a mean weight of 30 lbs with a standard deviation of 2 pounds. What is the range of weights would 99.7% of the dogs have?
Answer:
A and B ( page 12 and page 20 )
Step-by-step explanation:
1/4 of an hour he read 9 pages ( 15 mins ) ( 60 / 1 hour divided by 4 = 15 ) In other words 9 pages in 15 mins. To get to an hour u gotta multiply by 4. 15x4=60 9x4=36 ( 1 hour of reading is 36 pages read )
60 divided by 3 = 20
36 divided by 3 = 12 for sure it’s A and B
What is P(Foreign Language n Sport)?
Answer:
[tex]P(Foreign\ Language\ n\ Sport) = \frac{7}{25}[/tex]
Step-by-step explanation:
Given
See attachment for Venn diagram
Required
Determine [tex]P(Foreign\ Language\ n\ Sport)[/tex]
First, we calculate the population of the set.
This is calculated as:
[tex]Total = Sport + Foreign\ Language + None + Both[/tex]
This gives
[tex]Total = 23 + 10 + 3+14[/tex]
[tex]Total = 50[/tex]
So, the required probability is:
[tex]P(Foreign\ Language\ n\ Sport) = \frac{n(Foreign\ Language\ n\ Sport)}{Total}[/tex]
[tex]P(Foreign\ Language\ n\ Sport) = \frac{14}{50}[/tex]
14 represents the intersection between Foreign and Sport i.e. n(Foreign n Sport)
So, we have:
[tex]P(Foreign\ Language\ n\ Sport) = \frac{7}{25}[/tex]
The scale drawing of a room to be 3 inches by 4 1/2 inches. carpet, which is $15.00 per square yard, is to be installed in the room
Answer:
$202.5
Step-by-step explanation:
13.5 sqyd area
13.5 x 15= $202.5
Wanda Earned $350 babysitting over the months of July and August. She earned $90 more in August than in July. How much did she earn babysitting in July? In August?
Answer:
85
Step-by-step explanation:
350/2= 175
175+90= 265
350-265=85
Which one is correct?
Answer:
The first one (A) is the answer I got!
Step-by-step explanation:
Answer:
B = 706.5
Step-by-step explanation:
here you are given the diameter you need to First find a radius and radius is half of the diameter which is equal to 30 /2 = 15
Area of the circle is
[tex]\pi \: r { }^{2} [/tex]
3.14× 15×15 = 706.5
Need help ASAP it’s due tonight and I don’t understand
Answer:
13 of August,
Step-by-step explanation:
All of them worked together at day number zero (August 1).
We know that Elvis works every 3rd day
So he will work at:
day 3, day 6, day 9, etc.
We know that Izzy works every 4th day, then she will work at:
day 4, day 8, day 12, etc.
We know that Janaisa works every 6th day, so she will work at:
day 6, day 12, etc.
We just need to find a day where the 3 of them work, this is equivalent to finding a common multiple of the numbers: 3, 4 and 6.
To do it, we can just write the multiples of each one of these numbers and see which one is the first common multiple:
3)
3*1 = 3
3*2 = 6
3*3 = 9
3*4 = 12
3*5 = 15
...
4)
4*1 = 4
4*2 = 8
4*3 = 12
4*4 = 16
...
6)
6*1 = 6
6*2 = 12
So we can see that 12 is a common multiple of the 3 numbers.
Then they will work together 12 days after August 1th.
That would be the 13 of August,
SUSHMA BOUGHT A SAREE FROM THE MALL. SHE PAID RUPEES 2640 FOR IT. WHEN SHE CAME HOME SHE MEASURED THE LENGTH OF THE SAREE AND FOUND THAT THE SAREE WAS HALF METRE LESS IN LENGTH THAN THE SHOPKEEPER HAD TOLD HER. SHE FOUND THAT SHE IS AT LOSS OF RUPEES 220 BECAUSE OF THIS. WHAT IS THE LENGTH OF THE SAREE WHEN AHE CAME HOME???
This is the question. please do with statements and working. will mark you brainliest.
Answer:
Let the length of the sari be xm
cost of
2
1
=Rs 220
then cost of 1m=2(Rs220)=Rs440
Cost of the sari =x(Rs440)=Rs440x
But given that the cost of sari =Rs2640
Implies that
440x = 2640
Implies that
x=
440
2640
x=6
Please help me with the two questions!
Answer:
[tex]3)\ x = 8[/tex]
[tex]4)\ x = 12[/tex]
Step-by-step explanation:
Given
The similar triangles
Required
Solve for x
TUV to TLM implies that, the corresponding sides are:
[tex]TU \to TL[/tex]
[tex]TV \to TM[/tex]
[tex]UV \to LM[/tex]
To solve for x, we use the following equivalent ratios
[tex]TV : TM =TU:TL[/tex]
This gives:
[tex]24 : x + 8=36 : 24[/tex]
Express as fraction
[tex]\frac{24 }{ x + 8} =\frac{36 }{ 24}[/tex]
Cross Multiply
[tex]36(x + 8) =576[/tex]
Divide both sides by 36
[tex]x + 8 =16[/tex]
Subtract 8 from both sides
[tex]x = 8[/tex]
FGH to WVU implies that, the corresponding sides are:
[tex]FG \to WV[/tex]
[tex]FH \to WU[/tex]
[tex]GH \to VU[/tex]
To solve for x, we use the following equivalent ratios
[tex]FH : WU =FG:WV[/tex]
This gives:
[tex]x + 3 : 5 = 27 : 9[/tex]
Express as fraction
[tex]\frac{x + 3 }{ 5 }= \frac{27 }{ 9}[/tex]
[tex]\frac{x + 3 }{ 5 }= 3[/tex]
Cross Multiply
[tex]x + 3 = 3 * 5[/tex]
[tex]x + 3 = 15[/tex]
Subtract 3 from both sides
[tex]x = 12[/tex]
You earned $1600 in interest in your savings account over 10 years at a rate of 8%. How much money did you originally deposit into your savings account?
A = p(1+r)^t
1600 = p(1+0.08)¹⁰
P = 1600/2.1589
P= 741.12
741.12 dollar money did you originally deposit into your savings account!
What is the period of f(x) = sin(x)?
Answer:
2π!
Step-by-step explanation:
edge :)
Solve the following equation by elimination method
2x + y = 25
3x – 2y = 20
Answer:
First multiply the first equation by 2
2(2x + y = 25)
You'll have
4x + 2y = 50
Rewrite both equations
4x + 2y = 50
3x - 2y= 20
Add from the first equation you'll get
7x = 70... X = 10
Substitute x in one of the equations:
3(10) - 2y = 20
30 - 2y = 20
-2y = -10
y = 5
for triangle ABC find the measure of angle A.
Answer:
A= 63
Step-by-step explanation:
the both sides are equal so it will be 63 and 63
angle c would be 54
Adding all the sides would give 180 as all sides equal 180
An ice cream shop sold 56 vanilla milkshakes in a day, which was 25% of the total number of milkshakes sold that day. what was the total number of milkshakes that the ice cream shop sold that day?
Answer:
224
Step-by-step explanation:
Kayla read 12 1/2 pages on Friday. she did 3/4 of her reading before dinner. how many pages did she read before dinner (equation)
Answer:
Number of pages Kayla read before dinner = [tex]9\frac{3}{8}[/tex] pages
Step-by-step explanation:
Given:
Total number of pages Kayla read on Friday = [tex]12\frac{1}{2}[/tex] = 25/2 pages
Number of pages Kayla read before dinner = [3/4][Total pages she read]
Find:
Number of pages Kayla read before dinner
Computation:
Number of pages Kayla read before dinner = [3/4][Total pages she read]
Number of pages Kayla read before dinner = [3/4][Number of pages Kayla read before dinner]
Number of pages Kayla read before dinner = [3/4][25/2]
Number of pages Kayla read before dinner = 75/8
Number of pages Kayla read before dinner = [tex]9\frac{3}{8}[/tex] pages
ΔCDE is reflected over the y-axis. What are the vertices of ΔC'D'E' ?
Answer:
The y coordinates will remain the same. Meanwhile, the x coordinates will be the opposite.
Step-by-step explanation:
Here's an example, because no picture was included. If point C was located at (3, 5), point C' would be at (-3, 5).
Hope this helps!! :)
1. Yolanda está construyendo un patio en la parte trasera de su casa. Ella quiere usar
ladrillo y madera para el suelo del patio. A continuación se muestra el plano que ella
ha diseñado para el patio. Todas las medidas están expresadas en pies.
Usa la propiedad distributiva y la forma factorizada para mostrar dos
expresiones equivalentes que representen el área del patio.
3
X
12.5
ladrillo
madera
ahhhhhhhhhhhhhhhhhhhhhhh
Answer:
Its 9
Step-by-step explanation:
I did this in 5th grade... All you gotta do is count and there's 4 in the bottom aka 2 rows of 4 and there's 1 block on the top its 9
4+4+1=9
4+4=8
Add a 1 etc.
PLEASE HELP ASAP!!!!!!
The table below shows the lowest temperature, in degrees fahrenheit, on each of 5 days. What is is mean lowest temperature, in degrees fahrenheit, in the city for those 5 days?
-36
-25
12
-3
18
Answer: -6.8
Step-by-step explanation:
First you have to find the mean of all the #’s so to do that you will have to add all the #’s up including the negatives and you would get -34, after you do that you will have to divide by 5 and get -6.8
Find the exact values of the six trigonometric functions of the given angle. If any are not defined, say "not defined." Do not use a calculator. -135^{\circ}−135
Answer:
Step-by-step explanation:
Let's take a look at the given angle 135°
The sketch of the angle which corresponds to [tex]-\dfrac{3\pi}{4}[/tex] unit circle and can be seen in the attached image below;
The trigonometric ratios are as follows for an angle θ on the unit circle:
Trigonometric ratio related ratio on coordinate axes
sin θ [tex]\dfrac{y}{1}[/tex]
cos θ [tex]\dfrac{x}{1}[/tex]
tan θ [tex]\dfrac{y}{x}[/tex]
csc θ [tex]\dfrac{1}{y}[/tex]
sec θ [tex]\dfrac{1}{x}[/tex]
cot θ [tex]\dfrac{x}{y}[/tex]
From the sketch of the image attached below;
The six trigonometric ratio for 135° can be expressed as follows:
[tex]sin (-\dfrac{3\pi}{4})= \dfrac{y}{1}[/tex]
[tex]sin (-\dfrac{3\pi}{4})=- \dfrac{\sqrt{2}}{2}[/tex]
[tex]cos (-\dfrac{3\pi}{4})= \dfrac{x}{1}[/tex]
[tex]cos (-\dfrac{3\pi}{4})= -\dfrac{\sqrt{2}}{2}[/tex]
[tex]tan (-\dfrac{3\pi}{4})= \dfrac{y}{x}[/tex]
[tex]tan (-\dfrac{3\pi}{4})= \dfrac{-\dfrac{\sqrt{2}}{2}}{-\dfrac{\sqrt{2}}{2}}[/tex]
[tex]tan (-\dfrac{3\pi}{4})= -\dfrac{\sqrt{2}}{2}} \times {-\dfrac{2}{\sqrt{2}}[/tex]
[tex]tan (-\dfrac{3\pi}{4})= 1[/tex]
[tex]csc (-\dfrac{3\pi}{4})= \dfrac{1}{y} \\ \\ csc (-\dfrac{3\pi}{4})=\dfrac{1}{-\dfrac{\sqrt{2}}{2}} \\ \\ csc=1 \times -\dfrac{2}{\sqrt{2}} \\ \\csc =-\sqrt{2}[/tex]
[tex]sec (-\dfrac{3 \pi}{4})=\dfrac{1}{x} \\ \\ sec = \dfrac{1}{(-\dfrac{\sqrt{2}}{2})} \\ \\ sec = 1 \times -\dfrac{2}{\sqrt{2}} \\ \\ sec = - \sqrt{2}[/tex]
[tex]cot(-\dfrac{3 \pi}{4}) = \dfrac{x}{y} \\ \\ cot(-\dfrac{3 \pi}{4}) = \dfrac{-\dfrac{\sqrt{2}}{2} }{-\dfrac{\sqrt{2}}{2}} \\ \\ cot(-\dfrac{3 \pi}{4})= -\dfrac{\sqrt{2}}{2} } \times {-\dfrac{2}{\sqrt{2}}} \\ \\ cot (-\dfrac{3 \pi}{4}) = 1[/tex]
A rectangular parking lot has a perimeter of 88 meters. The length of the parking lot is three times the width. Find the length and the width.
Answer:
Length = 33 m
Width = 11 m
Step-by-step explanation:
l = 3w
2l + 2w = 88
l + w =44
Subsitiute for l
3w + w = 44
4w = 44
w = 11
l = 3(11)
l = 33
4. Two cylinders have dimensions in the ratio of 2:3. The smaller cylinder has a surface area of 16 cm.
What is the surface area of the larger cylinder?
Answer:
(cross multiply)
2:3
16:X
2X=16×3
2x=48
x=48÷2
x=24
Tail-feather length in birds is sometimes a sexually dimorphic trait. That is, the trait differs substantially for males and for females. Researchers studied the relationship between weight (x) and tail-feather length (y) in a sample of five wild male longtailed finches. Here are the data:
Weight Tail Length
20.5 82.5
19.1 82.5
15.9 67
16.7 70.5
15.7 73.5
The value of the linear correlation coefficient between weight and tail feather length is approximately : _________
Answer:
Step-by-step explanation:
it's about 18, as per the graph
What is the value of (−2)3 ?
Group of answer choices
-5
-6
-8
8
9514 1404 393
Answer:
-6 or -8, depending on what you mean
Step-by-step explanation:
(-2)3 = -(2)(3) = -6
__
(-2)^3 = (-2)(-2)(-2) = -(2)(2)(2) = -8
Brainliest☻
Which relation symbol makes this number sentence true?
4/5 ___ 9/12
=
≠
Answer:
≠
Step-by-step explanation:
4/5 ≠ 9/12
≠ is the answer.
Answer:
≠
Step-by-step explanation:
First, find a common denominator
Let's use 60
Convert each fraction to a fraction with a denominator of 60
4/5 = 48/60
9/12 = 45/60
48/60 ≠ 45/60 so 4/5 ≠ 9/12
A bag of M&Ms contains 7 blue, 4 brown, 4 orange, 2 yellow, 3 red, and 3
green. Reaching into the bag, a person grabs 5 M&Ms.
What is the probability of getting 3 blues?
Answer:
0.1248 = 12.48% probability of getting 3 blues.
Step-by-step explanation:
The M&Ms are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
7 + 4 + 4 + 2 + 3 + 3 = 23 total M&Ms, which means that [tex]N = 23[/tex]
Sample of 5 means that [tex]n = 5[/tex]
7 blue means that [tex]k = 7[/tex]
What is the probability of getting 3 blues?
This is P(X = 3).
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 3) = h(3,23,5,7) = \frac{C_{7,3}*C_{16,2}}{C_{23,5}} = 0.1248[/tex]
0.1248 = 12.48% probability of getting 3 blues.
please help me asap !!!!!!
Answer:
D
Step-by-step explanation:
Pretty sure its D