Answers
The correct answer is option B which is Sn = -111974.
What is geometric expansion?When there is a constant between the two successive numbers in the series then it is called a geometric series.
Here we have the following data:-
[tex]\sum_{n=1}^7-2.6^{n-1}[/tex]
[tex]a_n = a_1r^{n-1}\ \ \ \ \ S_n = a_1(\dfrac{1-r^n}{1-r})[/tex]
Here we need to calculate the first term second term and common ratio to calculate the sum of the series.
a₁ = -2.(6¹⁻¹) = -2
a₂ = -2.( 6²⁻¹) = -2 (6) =-12
Common ratio:-
[tex]a_n = a_1r^{n-1}[/tex]
[tex]-12 = -2r^{2-1}[/tex]
r = 6
Put all the values in the sum formula:-
[tex]S_n = -2(\dfrac{1-6^7}{1-6})[/tex]
[tex]S_n = -2(\dfrac{279935}{5})=-2\times 55987[/tex]
[tex]S_n[/tex] = -111974
Therefore the correct answer is option B which is Sn = -111974.
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Related Questions
Select the correct answer.
The graph of function f is shown.
If g(x) = -2f(x), which graph is the graph of function g?
Answers
Answer:
Step-by-step explanation:
Note that the new function, g(x), provides a value for y that is -2 times the value returned by f(x). That means that for the same value of x, the resulting value of g(x) will be -2 times that provided by f(x).
See the attached image. The table shows how the values of y change for each value of x used in the respective function. Plot those new values to produce the graph.
Please help I can’t figure it out
Answers
Answer: -4
Step-by-step explanation: Notice that the increments in the graph do not go in 1's, but in 2's. Meaning the first line is 2, and second line is 4, and in the middle is 3. Be careful.
The range is where the line on the graph hits the y-axis (horizontal line, or line going up). The only possible place the line hits the y-axis is at -4. No other y-value. Thus, the range of the function is -4.
Can someone help me out with this problem
Answers
Answer:
[tex]\fbox {1) A}\\\fbox {2) A}[/tex]
Step-by-step explanation:
Q1
⇒ Graph A is most accurate as the situation is linear and the dots indicate per cup as you can't have any rational part (such as 0.5 cups, etc.)
Q2
⇒ A
⇒ The graph is discrete because the sellers have limited the purchaser to buy a distinct whole number of cups
How many eight-digit numbers can be formed if the leading digit cannot be a zero
and the last number cannot be 1 or 0?
Answers
Answer:
81 x 10^6
Step-by-step explanation:
x0000000
11111111x
22222222
33333333
....................
88888888
99999999
---------------------
The first digit and 8th digit column has only 9 numbers and the rest 6 column have 10 possible numbers
9 x 9 x 10^6 = 81 x 10^6
please help me on how to solve for the distances
Answers
Answer:
B
Step-by-step explanation:
For every 1 litre of water used to make a
medicine, 311ml of sucrose and 29ml of
saline solution are used. Express the amount
of water, sucrose and saline solution needed
as a ratio in its simplest form.
Answers
Step-by-step explanation:
hope you can understand
Which expression for YYY correctly outputs that x is between 50-100? if (YYY) { // Output "50, 51, ..., 99, 100" } Group of answer choices (x >= 50) || (x <= 100) 50 <= x <= 100 50 >= x <= 100 (x >= 50) && (x <= 100)
Answers
The expression for YYY is (d) (x >= 50) && (x <= 100)
How to determine the correct expression?The instruction is given as:
If (YYY) {
// Output "50, 51, ..., 99, 100"
}
The value of x is given as:
x = 50 to 100 (inclusive)
This means that:
x must be greater than or equal to 50 AND x cannot exceed 100
The keyword AND is represented as &&.
So, the condition is:
x >= 50 && x <= 100
Hence, the expression for YYY is (d) (x >= 50) && (x <= 100)
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Select the correct answer. A linear function on a coordinate plane passes through (minus 3, 2), (0, 4), and (3, 6) Which equation describes the line graphed above? A. B. C. D.
Answers
Answer:
I don't see the equation options. See below for a predicted equation.
y= (2/3)x + 4
Step-by-step explanation:
The points are (-3,2), (0,4), and (3,6). I will assume they lie in a straight line.
Find an equation of the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0).
m, the slope, is also known as the "Rise/Run."
Pick any two points. I'll use (0,4) and 3,6)
Rise = (6-4) = 2
Run = (3-0) = 3
Slope = 2/3
The equation becomes y = (2/3)x + b
B is easy in this case. Point (0,4) tells us that y = 4 when x = 0 (the definition of b).
The equation is y= (2/3)x + 4
See the attached graph.
what is the simlest form of the ratio 32:48
Answers
Answer: 2:3
Step-by-step explanation:
First list out the factors for 32 and 48
32- 1, 2, 4, 8, 16, 32
48- 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The greatest factor they have in common is 16. So, divide both numbers by 16 to get the simplest form of the ratio.
32/16=2
48/16=3
The simplest form is 2:3
Which linear inequality is represented by the graph?
Answers
Answer:
The equation of the line is y ≥ 1/3(x)-1
Step-by-step explanation:
Given
The line intersects y-axis at (0,-1). Therefore, the y-intercept is -1
The line passes through the points (0,-1) and (3,0)
The slope can be obtained as follows,
m = 0-(-1)
3-0
= 1/3
The linear equation with slope and intercept is given as follows.
y = mx + c
Substitute 1/3 for m, 3 for x and 0 for y in equation to obtain the value of
c .
0 = 1/3 *3 + c
c= -1
To check whether the equation includes origin substitute 0 for x and 0 for y in equation
Therefore, y≥ mx+c
= 1/3*x-1
Hence, Linear inequality represented is y ≥ 1/3(x) -1
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The price of a Year 7 mathematics textbook is $60. The store gives a discount of 20% on the textbook.
You have $50 to spend. Would you be able to buy the textbook? Explain.
Answers
Answer:
yes,you can buy the textbook
Step-by-step explanation:
determine discount
60 × 0.2(decimal form of 20%)
=12
apply discount
60-12
=48
50>48✓
Write an expression for the perimeter of the triangle shown below:
A triangle is shown with side lengths labeled 0.3x plus 24, 5x, and 0.2x minus 15.
10x − 9
10x − 39
5.5x − 9
5.5x + 9
Answers
Answer:
5.5x + 9
Step-by-step explanation:
0.3x plus 24, 5x, and 0.2x minus 15
Expression:
This means that,
0.3x + 24 + 5x + 0.2x - 15
We know the perimeter of the triangle is,
P = a+b+cWhere a , b , c refers to the sides of that triangle.
So Just add them up:
0.3x + 24 + 5x + 0.2x - 150.3x+5x+0.2x + 24 - 150.5x+5x + 95.5x + 9Hence,last choice is accurate.
20. a) After allowing 20% discount on the Marked Price and levying 15% VAT, an article was sold. If the discount amount is Rs.800, find the selling price of the article including VAT.
Answers
The selling price of the article including VAT will be 1000.
What is the selling price?The cost at which an article is sold is known as the selling price.
Let the market price will be x
Given data;
Discount=20 %
The amount of the discount is;
[tex]\rm Discount = x- x \times \frac{20}{100} =\frac{80x}{100}[/tex]
Applied tax is;
[tex]\rm \frac{80x}{100} +\frac{80x}{100} \times \frac{15}{100} =904 \\\\ \frac{8000x+1040 x}{10000} =904 \\\\ 9040 x = 904 \times 10000 \\\\\ x=\frac{904 \times 10000}{9040} \\\\ x=1000[/tex]
Hence, the selling price of the article including VAT will be 1000.
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Which transformations could have taken place? Select two options.
Answers
The two options are R₀ 270 , R₀ 90 , Option C and D .
The complete question is attached in the image.
What are the two types of Transformations ?There are two types of transformations namely , Rigid Transformation and Non- Rigid Transformation
The rigid transformations do not change the shape and size of the preimage .
The non Rigid transformation do not change the shape but change the size of the preimage.
The rule rotating the origin , 270 degree is
(x,y) ----> (y , -x)
as (x,y) is (0,5)
Therefore after 270 degree transformation
(y,-x) is (5 , 0)
So, the clockwise rotation is 90 degree about origin
(x,y) ----> (y , -x)
as (x,y) is (0,5)
Therefore after 90 degree transformation
(y,-x) is (5 , 0)
Therefore the two options are R₀ 270 , R₀ 90 , Option C and D .
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-1 1/3 - 1 2/3
answer in simplest form
Answers
-4/3 - 5/3 = -9/3
-9/3 = -3
final answer: -3
Answer:
-3
Step-by-step explanation:
both are negatives, so think of it as addition
at the very end make sure you add the negative symbol :)
-1 1/3 - 1 2/3
If s(x) = 2 – x² and t(x) = 3x, which value is equivalent to (sof)(-7)?
-439
-141
153
443
Answers
Answer:
- 439
Step-by-step explanation:
evaluate f(- 7) and substitute the value obtained into s(x)
f(- 7) = 3(- 7) = - 21 , then
s(- 21) = 2 - (- 21)² = 2 - 441 = - 439
Answer:
A. (s*t)(-7)=-439
Step-by-step explanation:
(s*t)(-7) is the same as s(t(-7)). First find t(-7)
t(-7)=3(-7)=-21
t(-7)=-21
Plug -21 into s(t(-7)) for t(-7).
Find s(-21).
s(-21)=2-(-21)^2=-441+2=-439
Hope this helps!
If not, I am sorry.
Rhonda gave the cashier $20 to pay for 3 pairs of socks. The cashier gave her $5.12. Each pair of socks cost the same amount. What is the cost in dollars and cents for each pair of socks?
Answers
Answer:
4.96 dollars
Step-by-step explanation:
20-5.12=14.88
14.88/3= 4.96 dollars
so each pair of socks costs 4.96$
A ferris wheel with a diameter of 214 feet was built in a city. The top of the wheel stands 223 feet above the ground. Find h if θ = 150°, 240°, and 315°. Round your answers to the nearest whole number.
The diagram in the attached image is a model of the wheel.
Answers
The height at 150°, 240°, and 315° will be 208.66 feet, 169.5 feet, and 40.34 feet, respectively.
What is a vector?The quantity which has magnitude, direction and follows the law of vector addition is called a vector.
A Ferris wheel with a diameter of 214 feet was built in a city.
The top of the wheel stands 223 feet above the ground.
Then the radius will be
r = 214 / 2
r = 107 feet
The distance between the ground and bottom of the Ferris wheel will be
d = 223 – 214
d = 9 feet
Then the height will be given as
h = r(1 – cos θ) + h
h = 107(1 – cos θ) + 9
At θ = 150°, then the height will be
h = 107(1 – cos 150°) + 9
h = 208.66 feet
At θ = 240°, then the height will be
h = 107(1 – cos 240°) + 9
h = 169.5 feet
At θ = 315°, then the height will be
h = 107(1 – cos 315°) + 9
h = 40.34 feet
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74 is the same as
radians.
Round to the nearest hundredth of a radian.
Answers
Answer:
1,29
Step-by-step explanation:
74*2pi/360
ezzzzzz
PLEASE HELP
If the perimeter of a garden is 16 yards, how many inches is it? Hint: There are 3 feet in 1 yard.
Answers
If 3 ft = 1yard
? = 16 yards?
Thats [tex]\frac{16 yards * 3ft}{1yard}[/tex]
The common values cancel each other out and you'll have 48 feet :)
Mila is preheating her oven before using it to bake. The initial temperature of the oven is 75° and the temperature will increase at a rate of 10° per minute after being turned on. What is the temperature of the oven 15 minutes after being turned on? What is the temperature of the oven t minutes after being turned on?
Temp after 15 minutes:
Temp after t minutes
need answer quickly
Answers
therefore, the temp after t minutes can be represented by the equation f(x) = 10t + 75
What else would need to be congruent to show that ABC = XYZ by ASA
Answers
Answer:
A). AC is congruent to XZGiven - angle X = angle A
angle Z = angle C
To find - criteria of congruence
Solution -
In triangle BAC and triangle YXZ
angle X = angle A
angle Z = angle C
we need one pair of side to be comgruent to show the following traingles congruent
if AC is congruent to XZ
then by angle side angle criteria of triangle both the triangles are congruent..
An Amazon delivery driver receives a bonus if he delivers a package to a customer in 20 minutes plus or minus 5 minutes. Which inequality or equation represents the drivers allotted time (x) to receive a bonus
Answers
[tex]15 \leq X \leq 25[/tex] is the equation represents the drivers allotted time (x) to receive a bonus.
What us the absolute value of inequality?An absolute value inequality is an expression with absolute functions as well as inequality signs.
According to the question:
Mathematically absolute value inequality is represented as :
|X -20|≤ 5
Solving the equation using
|z| ≤ a→ -a ≤ z ≤ a :
here, z = X- 20 and a = 5:
[tex]| X-20| \leq 5\\\\ - 5\leq X-20 \leq 5[/tex]
By Solving X adding 20 on the three sides of the inequality
[tex]-5 + 20 \leq X -20 +20 \leq 5 + 20[/tex]
By simplifying it:
[tex]15 \leq X \leq 25[/tex]
Therefore the equation or inequality which represents the drivers allotted time (x) to receive a bonus [tex]15 \leq X \leq 25[/tex]
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Suppose a household’s income increases from $2500 to $3000 and quantity demanded changes from 190 to 150. What is the income elasticity?
a.
0.6
b.
$500
c.
-1.05
d.
2.5
Answers
The income elasticity for the household is -1.05.
What is the income elasticity?Income elasticity measures how quantity demanded changes when there is a change in the income of a person / household
Income elasticity = percentage change in quantity demanded / percentage change in income
percentage change in income = (3000 / 2500) - 1 = 0.2 = 20% percentage change in quantity demanded =( 150 /190) - 1 = -0.21 = -21%Income elasticity = -21% / 20 = -1.05
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a paperweight has height 4cm and volume 38.4cm3.
a mathematically similar paperweight has height 7cm.
calculate the volume of this paperweight.
Answers
The similar paperweight has a volume of 67.2 cubic cm if the height is 7 cm.
What is volume?It is defined as a three-dimensional space enclosed by an object or thing.
As we know,
Volume = base area×height
38.4 = base area×4
base area = 38.4/4 = 9.6 square cm
A mathematically similar paperweight has a height of 7 cm.
Volume = base area×height
Volume = 9.6×7 = 67.2 cubic cm
Thus, the similar paperweight has a volume of 67.2 cubic cm if the height is 7 cm.
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Which formula can be used to describe the sequence? negative two-thirds, −4, −24, −144,...
Answers
Answer:
Step-by-step explanation:
The height of each story in a hotel is feet. The height is measured from the ceiling to the floor. The hotel has 2 underground levels that are used as banquet halls. Stephen is a waiter who works two levels below ground. At what elevation are Stephen’s feet? Assume the ground level of the hotel is at 0 feet.
A.
feet
B.
feet
C.
D.
feet
find the value of a from the following 1. tan3a=cot2a
Answers
The value of a is 14.
What is Trigonometry?
The branch of mathematics concerned with specific functions of angles and their application to calculations.
Given:
tan3a=cot2a
tan 3a= tan (90- 2a)
On comparing
3a= 90- 2a
5a= 90
a= 14
Hence, the value of a is 14.
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PLS HELP! (PRE-ALG) WILL GIVE BRAINLIEST. Thx sm
Jean transformed a point by using the rule (x,y) → (x−6.y+8). The image point is (-4, 1). Which point is the pre-image?
a. (-10, 9)
b. (2-7)
c. (-2,7)
d. (10,-9)
Answers
I believe the answer is -2, 7
A row operation a performed on a matrix as shown below what is the value of x?
Answers
The value of x in the second matrix is -1
How to determine the value of x?The operation is given as:
[tex]\left[\begin{array}{ccc}2&-1&1\\1&1&1\\4&-2&2\end{array}\right] \left[\begin{array}{c}4&11&5\end{array}\right] \to \left[\begin{array}{ccc}0&-3&x\\1&1&1\\4&-2&2\end{array}\right] \left[\begin{array}{c}-18&11&5\end{array}\right][/tex]
Let the rows be represented by R1, R2 and R3.
By observation, the row operation performed is:
[tex]R1 \to R1 - 2R2[/tex]
This means that:
The new elements of row 1 are gotten by subtracting twice the elements of row 2 from row 1.
Using the above operation, we have:
x = 1 - 2 * 1
Evaluate the difference
x = -1
Hence, the value of x is -1
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A line contains points M(1, 3) and N(5, 0). What is the slope of MN?
negative StartFraction 4 Over 3 EndFraction
negative StartFraction 3 Over 4 EndFraction
StartFraction 3 Over 4 EndFraction
StartFraction 4 Over 3 EndFraction
Answers
Answer:
-¾
Step-by-step explanation:
gradient = delta y over delta x
gradient = 0 - 3 / 5 - 1
gradient = -3 / 4
