Answer:
The sum of 10 terms is S₁₀ = -1023
Step-by-step explanation:
Explanation:-
Given series
3 + (-6) + 12 + (-24) + ⋯
This is geometric sequence 3 , -6 ,12 , -24 ,....
a = 3 and common ratio [tex]r = \frac{-6}{3} = -2[/tex]
Given ratio r = -2 < 1
Sum of 'n' terms of a G.P
[tex]S_{n} = \frac{a(1-r^{n} ) }{1-r} if r <1[/tex]
Sum of '10' terms of a G.P
[tex]S_{10} = \frac{3((1-(-2 )^{10} }{1-(-2)}[/tex]
[tex]S_{10} = \frac{3((1-(-2 )^{10} }{3} = 1-2^{10} = 1- 1024 = - 1023[/tex]
Conclusion:-
Sum of '10' terms of a G.P = - 1023
Verification:-
The series of first 10 terms
3+(-6)+12+(-24)+48+(-96)+192+(-384)+768+(-1536) = -1023
What is the approximate area of the shaded sector in the circle shown below?
A. 31.7 cm^2
B. 5.76cm^2
C. 2.88cm^2
D. 126.7cm^2
Answer:it’s 31.7 cm^2
Step-by-step explanation:
The approximate area of the shaded sector is 31.7 cm² (Option A).
To find the area of the shaded sector, we need to calculate the fraction of the entire circle that the sector represents and then multiply it by the area of the whole circle.
The formula to find the area of a sector is given by:
Area of sector = (θ/360) * π * r²
where θ is the central angle and r is the radius of the circle.
In this case, the radius (r) of the circle is given as 11 cm, and the central angle (θ) is given as 30 degrees.
Let's calculate the area of the shaded sector:
θ = 30 degrees
r = 11 cm
Area of sector = (30/360) * π * 11²
= (1/12) * π * 121
= π * 10.0833...
Now, we can approximate the value of π as 3.14:
Area of sector ≈ 3.14 * 10.0833...
≈ 31.7 cm²
Therefore, the approximate area of the shaded sector is 31.7 cm².
The correct option from the given choices is A. 31.7 cm².
To know more about sector, refer here:
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I need some help please!! I'll give brainliest to first answer!!!!!!!!!!!!!
Answer:
Keith; -5, -12
Step-by-step explanation:
Logic ( Subtract 12 from both sides, then factor it out)
If there are 3 classrooms that each have 25 desks and there are a total of 87 students, how many more desks need to be added to a 4th classroom, that was originally empty, so that each of the students has a desk to sit in?
Answer:
12
Step-by-step explanation:
If there are 3 classrooms that each have 25 desks and there are a total of 87 students, how many more desks need to be added to a 4th classroom, that was originally empty, so that each of the students has a desk to sit in?
25 * 3 = 75
87 - 75 = 12
Which situation describes INDEPENDENT events? A) One student is chosen from Classroom A, then a student is chosen from Classroom B. B) One card is chosen from a standard deck, it is set aside, then a second card is drawn. C) One student is chosen from Classroom A, then a second student is chosen from Classroom A. D) Tom chooses a letter of the alphabet, then Beth must choose a different letter from the alphabet.
Answer:
Step-by-step explanation:
A) One student is chosen from Classroom A, then a student is chosen from Classroom B
the sets for each probability to happen are different. what happen in first clause is unrelated to the second clause
Discussion Topic: As part of their job, meteorologists make weather predictions from data. How accurate are their predictions? What are other scenarios in which you would use data to make a prediction? How would you defend your prediction using data?
Answer: 1. Not always accurate.
2. A football game.
3. By using the data from the winning percentage against number of games played.
Step-by-step explanation:
Meteorologists are responsible for making weather predictions, but their predictions are always not accurate because they use datas and theory to predict the scenarios of the weather or what it might be. Their predictions are not accurate because of changes in weather or data being used unexpectedly.
A scenario where I would use data to make a prediction could be in a football match or game where you i have a percentage of winning, which depends on how many times the game is played.
The winning percentage gives us the data on the probability of winning the game which would help predict how many times you'll win a game by how many times the game is played.
PLEASE HELP
For a hypothesis test of H0: p = 0.35 against the alternative Ha: p > 0.35, the z test statistic is found to be 2.45. What can be said about this finding?
A. The finding is significant at α = 0.05, but not at α = 0.01.
B. The finding is significant at α = 0.01, but not at α = 0.05.
C. The finding is significant at both α = 0.05 and α = 0.01.
D. The finding is not significant at α = 0.05 and α = 0.01.
Answer:
C
Step-by-step explanation:
Is is a one-tailed test
P(z < 2.45) = 0.9929
1 - 0.9929 = 0.0071
Significant at both 0.05 and 0.01 because both are greater than 0.0071
Answer:
The finding is significant at both α = 0.05 and α = 0.01.
Please help ASAP! I will mark BRAINLIEST! Please answer CORRECTLY! No guessing!
Answer:
C. [tex]b^{27}[/tex]
Step-by-step explanation:
Assume b is a number like 3
([tex]3^{9}[/tex])³=19683³=7625597484987
[tex]3^{24}[/tex]=282429536481
B is definitely wrong. Not even going to try.
[tex]3^{27}[/tex]=7625597484987
D is definitely wrong. Not even going to try.
In a quadrilateral, the measure of two opposite angles is the same. Each of the other
two angles measures exactly two times the given angle. Find the measure of each angle
in the quadrilateral.
Answer:
the two opposite angles equal 45 and the other two who are twice the amount is 90
Step-by-step explanation:
sum of angles in a quadrilateral is 360. Lets name the two equal diagonal angles x that means the equation wil be
x+x+2x+2x=360
8x=360
x=45
so the equal diagonal ones will be 45 and the other two angles will be twice as much so 45x2=90
WILL MARK BRAINLIEST!!
The volume of a cylinder is 1,386 m3 and its radius is 7 m. What is its height to the nearest whole number?
Answer:
h = 9
Step-by-step explanation:
[tex]volume = \pi \: {r}^{2} h \\ 1,386 = \frac{22}{7} \times 7 \times 7 \times h \\ 1,386 = 154 \times h \\ h = \frac{1,386}{154} \\ h = 9[/tex]
Using a fair, six-sided die, what is P(2 or 3)?
Find the number, if...
3/8 of it is 24.
Answer:
64
Step-by-step explanation:
To get the answer, just perform the reverse operation of what the question said. In this case, you would want to multiply by the reciprocal, which is (8/3). So the answer is found by just solving 24*(8/3).
Answer:
The number is 64
Step-by-step explanation:
Let the number be x
3/8 of x = 24
x = 24 ÷ (3/8)
[tex]x=24*\frac{8}{3}\\\\x=8*8[/tex]
x = 64
Find cos x if sin x =0.82.
Answer:
cosx= 35. Use Trignometrical identity cosx = √1−sin2x . cos x = √1−1625 = √925 = 35 to be the ...
Missing: =0.82 | Must include: =0.82
Step-by-step explanation:
Solve for all values of x by factoring.
x2 + 10x + 8 = x
Answer:
x=-1,x=-8 can't factor it
Step-by-step explanation:
Step-by-step explanation:
x = -1 , x = -8
Hope its help u
Marquis wrote the linear regression equation y=1.245x-3.685 to predict the cost, y, of x songs purchased. Which is the best estimate of number of songs that marquis purchased?
The complete question is;
Marquis wrote the linear regression equation y = 1.245x - 3.685 to predict the cost, y, of x songs purchased. Marquis spent $40 on songs. Which is the best estimate of the number of songs that Marquis purchased?
Answer:
The best estimate of the number of songs that Marquis purchased = 35 songs
Step-by-step explanation:
First of all, let's make x the subject of the linear regression equation.
We are given that,
y = 1.245x - 3.685
So,
1.245x = (y + 3.685)
x = (y + 3,685) / (1,245)
We are told that Marquis spent $40 on songs.
Thus;
Substituting the value of $40 for y into the equation to get;
x = (40 +3,685)/(1,245)
x = 35.09
x ≈ 35
Thus, the best estimate of the number of songs that Marquis purchased is 35
Answer:
the number of songs that Marquis purchased is 35
Find the value of k ,if x=2 and y=3.Find the equation of 2x+3y=k
Answer:
k=13
Step-by-step explanation:
substitute x and y
4+9=k
k=13
Answer:
13
Step-by-step explanation:
Plug in the given x and y values: 2(2) + 3 (3) = k
Then multiply 4 + 9 = k
Then add 13 = k
Complete 8 for 15 points.
Answer:
756 is evenly divisible by 2, 3, 4, 6, and 9.
Step-by-step explanation:
756 is evenly distributed by the numbers (above).
756/2 = 378756/3 = 252756/4 = 189756/5 = 151.2 756/6 = 126756/8 = 94.5756/9 = 84 756/10 = 75.6 756/25 = 30.24The area of a rectangular baking sheet is 25 square inches. The base of the sheet is 10 inches. What is the height?
2 and one-half in.
3 in.
3 and one-half in.
250 in.
Answer:
2 1/2
Step-by-step explanation:
take 25 and divide it by 10 giving you 5/2 but that equals 2.5 and 2.5 equals 2 1/2
I am thinking of a number. My number is between 20 and 30 My number and 12 have only one common factor. What number could I be thinking of? Give all three possible answers.
Answer:
21, 22 and 26
Step-by-step explanation:
To answer this question first we need to know which are the factors of 12:
[tex]12= 2^2(3)[/tex]
So, now, we need 3 numbers that are between 20 and 30 and that only have one common factor with 12, in other words, they need to have just a 2 or a 3 in their factorization.
Let's take number 21:
[tex]21= (7)(3)[/tex], we can see that 21 only has a 3 and a prime so therefore it has only one common factor with 12
Now, let's take the number 22,
[tex]22=11 (2)[/tex], thus since 22 has a 2 and a prime, it has only one common factor with 12.
Now, let's take the number 26
[tex]26= 13 (2)[/tex], thus, since 26 has a 2 and a prime, it has only one common factor with 12.
Thus, the three possible answers are 21, 22 and 26
1. Calculate the slope between the two points (2,5) and (-3,-4).
To find the slope of thine that passes through these points, use the slope formula. It can be read as “slope equals the second y-coordinate minus the first y-coordinate over the second x-coordinate minus the first x-coordinate.”
So we have [tex]\frac{-4 - 5}{-3 - 2}[/tex] and this simplifies to -9/-5 or 9/5.
Remember, a negative divided by a negative is a positive.
Correct answers only!
To the nearest cent, how much will she have in 2 years?
Use the formula B = p(1 + r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Answer:
0.62
Step-by-step explanation:
A 25ft ladder is propped against a storeroom. The angle the ladder forms is 50°. How far up the storeroom does the ladder reach?
Answer:
This means the store room is 19.15ft up
Step-by-step explanation:
The set up of the question will form a right angle triangle.
The length of the ladder will be the hypotenuse of the triangle and the angle the ladder forms will be the angle of elevation. This angle of elevation will face the opposite side of the triangle which is the height of the storeroom directly.
Using the SOH CAH TOA trigonometry identity,
According to SOH;
Sin∅ = opposite/hypotenuse
∅ is the angle the ladder forms
sin50° = x/25
x = 25sin50°
x = 19.15ft
This means the store room is 19.15ft up
Which table could be used with Table A to verify that the function modeling Fahrenheit temperature, F(C), based on a given Celsius temperature, C, is the inverse of C(F)?
Answer:
Its A
Step-by-step explanation:
c=-20, -15, -5
f(c)=-4,5,23
gl with your test or quiz
Answer: its A
Step-by-step explanation:
In ΔMNO, the measure of ∠O=90°, MN = 9 feet, and OM = 4.2 feet. Find the measure of ∠N to the nearest degree.
Answer:
The measure of angle N to the nearest degree is 28 degrees
Step-by-step explanation:
To answer this question, we shall be needing a diagrammatic representation of the triangle. Please check attachment for this.
To calculate the angle N, we shall be making use of trigonometric identities. From the diagram we see that we have the hypotenuse ( the longest side and the side facing the angle 90) and also the opposite ( the side facing the angle N)
Thus, the correct trigonometric identity to use here is the Sine
Mathematically, the sine of an angle = length of the opposite/length of the hypotenuse
Our opposite here is 4.2 feet with our hypotenuse as 9 feet
Plugging these values, we have
Sin N = 4.2/9
Sin N = 0.46666667
N = arc sin (0.46666667)
N = 27.82 , to the nearest degree we have 28 degrees
Answer:
28°
Step-by-step explanation:
:)
Find the value of x in these right-angled triangle, correct two decimal places A=20 B=7
Answer:
There are two possibilities: 1) A is the hypotenuse: [tex]C \approx 18.74[/tex], 2) A is not the hypotenuse: [tex]C \approx 21.19[/tex]
Step-by-step explanation:
Let be C the remaining side of the triangle. Given that triangle is right-angled and the remaining side can be found by Pythagorean Theorem, there are two options by using the two known sides:
1) A is the hypotenuse
[tex]20^{2} = 7^{2} + C^{2}[/tex]
[tex]C^{2} = 20^{2}-7^{2}[/tex]
[tex]C = \sqrt{20^{2}-7^{2}}[/tex]
[tex]C \approx 18.74[/tex]
2) A is not the hypotenuse
[tex]C^{2} = 20^{2} + 7^{2}[/tex]
[tex]C = \sqrt{20^{2}+7^{2}}[/tex]
[tex]C \approx 21.19[/tex]
Find an equation, in slope-intercept form, that passes through the point (−4,3) with a slope of −3.
Answer:
y = -3x - 9
Step-by-step explanation:
Equation of line in point slope form is given as:
[tex]y - y_1 = m(x-x_1) \\
y - 3= - 3\{x - (-4)\}\\
y - 3 = - 3(x + 4)\\
y =- 3x - 12 +3\\
y = - 3x - 9\\ is \: the \: required \: equation \\ [/tex]
15 5 6 6 19 4 5 5 3 4 5 19 5 4 6
What is the mean? Round your answer to the nearest tenth.
PLEASEEE HELPPPP MEE WITH LINE PLOTSSS I DONT UNDERSTAND THISSSS
PLEASEE HELPPPP!!!!!!!
Answer:
Look at the lightest loaf of bread. It weighs 22 1/3 oz. The heavist loaf weighs 24 1/2. Subtract 24 1/2 and 22 1/3. Then, if the answer to that is 1 1/2 ounces then you agree. If it is not, then disagree. Then, add up all of the weights of the bread and find the answer.
What is the probability that the first marble is green a the second is red? Write fraction in simplest form.
What is the base 8 representation of the number 600?
Answer:
1130
Step-by-step explanation:
8x75=600
8÷9=72+3
8×1=8+1=9
8×1+1=9
Answer:1130^8
Step-by-step explanation:trust me bro
Which best describes the transformation that occurs from
the graph of f(x) = x² to g(x)=(x-2)²+3
Answer:
The graph changes from the original position to right 3 units and down 1 unit.
I hope this helps. If you have any more questions, please feel free to post them and someone will be able to help you, whether it's myself or others. Please leave a like, rating, and if possible, Brainliest. Have a great day!
