The correct option is c. 7
The summation of the expression [tex]\sum_{i=1}^{3}\left(4\left(\frac{1}{2}\right)^{i-1}\right)[/tex] is 7.
What is summation (∑)?The sum of terms that follow a pattern is denoted by the symbol '∑' "summation," which also serves as a shorthand notation.
A sum of several terms is typically represented by the symbol "∑" This symbol is typically accompanied with a variable index that includes all terms that must be taken into account when calculating the total.
The given expression is;
[tex]\sum_{i=1}^{3}\left(4\left(\frac{1}{2}\right)^{i-1}\right)[/tex]
The the property of summation, expand the values.
[tex]\sum_{i=1}^{3}\left(4\left(\frac{1}{2}\right)^{i-1}\right)=4\left(\frac{1}{2}\right)^{1-1}+4\left(\frac{1}{2}\right)^{2-1}+4\left(\frac{1}{2}\right)^{3-1}[/tex]
[tex]\sum_{i=1}^{3}\left(4\left(\frac{1}{2}\right)^{i-1}\right)=4\left(\frac{1}{2}\right)^{0}+4\left(\frac{1}{2}\right)^{1}+4\left(\frac{1}{2}\right)^{2}[/tex]
[tex]\sum_{i=1}^{3}\left(4\left(\frac{1}{2}\right)^{i-1}\right)=4\left(\frac{1}{1}\right)+4\left(\frac{1}{2}\right)+4\left(\frac{1}{4}\right)[/tex]
[tex]\sum_{i=1}^{3}\left(4\left(\frac{1}{2}\right)^{i-1}\right)=4+2+1\\[/tex]
[tex]\sum_{i=1}^{3}\left(4\left(\frac{1}{2}\right)^{i-1}\right)=7\\[/tex]
Therefore the solution of the given equation is 7.
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The correct question is;
What is the value of [tex]\sum_{i=1}^{3}\left(4\left(\frac{1}{2}\right)^{i-1}\right)[/tex] ?
a.7/8
b.8
c.7/2
d.7
This Stem-and-Leaf Plot represents test scores of students in a math class. If two test scores, 68 and 75, are added to the data, which statement will be true?
A. The median will change; the mode will stay the same.
B. The mode will change; the median will stay the same.
C. The median and the mode will both change.
D. The median and the mode will stay the same.
The median will change; the mode will stay the same.
Will the median and mode change?The median is the number that is at the center of a data set when the data are arranged either in ascending or descending order.
Median = 23
When 68 and 75 are added, the median would change.
Mode refers to a value that appears most frequently in a data set.
The mode = 75
So, when 75 is added, the mode does not change.
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Sarah bought two t-shirts and one sweatshirt. The t-shirts cost $\$15.22$ each. If Sarah spent a total of $\$67.94,$ how many dollars did the sweatshirt cost
Answer: $37.50
Step-by-step explanation:
The measures of the angles of a triangle
are shown in the figure below. Solve for x.
33°
(3x-12)°
Answer:22
Step-by-step explanation:22
The triangles are similar. Find the value of the variable.
assuming the pattern continues, what is s12 for the series -5-14-23-32-...?
Answer:
S₁₂ = - 654
Step-by-step explanation:
there is a common difference between consecutive terms , that is
- 14 - (- 5) = - 23 - (- 14) = - 32 - (- 23) = - 9
this indicates the series is arithmetic with sum to n terms
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
here a₁ = - 5 and d = - 9 , then
S₁₂ = [tex]\frac{12}{2}[/tex] [ (2 × - 5) + (11 × - 9) ]
= 6(- 10 - 99 )
= 6 × - 109
= - 654
What is the volume, in cubic centimeters, of a cube whose side measures 4 centimeters ?
Fill in the blank by entering only a number as your answer.
The formula for the volume of a cube is-side length^3.
For your problem, side length=4, so the answer is 4^3=64
ANSWER: 64 CUBIC CENTIMETERS hope this helped you
(T-Tb)
Write each expression in the correct column to show whether the quotient is less than, greater than, or equal to 1
The expressions based on the information given are illustrated below
How to calculate the expression?3/4 ÷ 1/2 = 1.5 = quotient is grater than 1
1/2 ÷ 3/4 = 2/3 = quotient is less than 1
2/9 ÷ 1/27 = 6 = quotient is grater than 1
5/3 ÷ 20/6 = 1/2 = quotient is less than 1
4/3 ÷ 3/5 = 20/9 = quotient is grater than 1
19/8 ÷ 2 3/8 = 1 = quotient is equal to 1.
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Could someone please draw the triangle based off of this description
The altitudes of equal length, BE and CF gives AB = AC, from which we have;
∆ABC is an isosceles triangleHow can the RHS rule be used to indicate an isosceles triangle?From the given description, we have;
BE = CF
<CFB = <BEC = 90° All right angles are congruent
BC = BC by reflexive property of congruency
BC = The hypotenuse side of triangles ∆BFC and ∆CEB
Therefore;
∆BFC is congruent to ∆CEB by Right angle Hypotenuse Side, RHS, rule of congruency.
Therefore;
BF = CE by Corresponding Parts of Congruent Triangles are Congruent, CPCTC
Similarly, we have;
∆AEB is congruent to ∆AFC, by Side-Angle-Angle, SAA, rule of congruency
Which gives;
FA = AE by CPCTC
BF + FA = CE + AE, by substitution property of equality
BF + FA = AB
CE + AE = AC
Therefore;
AB = ACTherefore;
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What is the solution to the system of equations? (7, 4) (7, startfraction 13 over 3 endfraction) (8, startfraction 14 over 3 endfraction) (9, 7)
The points are (7, 13/3).
Lets simplify the equation,
The equation of first line: y = 1/3 x + 2
the equation of second line: y= 4/3x - 5
Solve the system of equations by elimination,
Multiply equation A by -4 both sides
-4y = -4(1/3x +2)
-4y = -4/3x-8
After eliminating the equation we get,
y = 13/3
So now have to find x
13/3 = 1/3x + 2
Lets multiply above by 3
x = 13-6
x = 7.
Hence the points are (7, 13/3)
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Answer:
B
Step-by-step explanation:
What is the solution to the system of equations?
(7, 4)
(7, StartFraction 13 over 3 EndFraction)
(8, StartFraction 14 over 3 EndFraction)
(9, 7)
Question 6 (1 point)
Find m/RST.
(4x-24)
U
S/(3x)*
O a m/RST = 72°
Ob
mZRST 108⁰
Oc
mZRST = 156°
Od mZRST = 24°
Answer:
72°
Step-by-step explanation:
3x = 4x - 24 (alternate exterior angles theorem)
x = 24
So, angle RST measures 72°.
If three different orders are selected, find the probability that they are all from Restaurant B
If three different orders are selected, find the probability that they are all from Restaurant B is; 0.026
How to find the probability?Total orders both accurate and not accurate = 1131
Total orders from restaurant B (both accurate and not accurate) = 337
Probability of first order from B = 337/1131
Probability of second order from B = 336/1130
Probability of third order from B = 335/1129
Probability of the first three orders from B = 337/1131 × 336/1130 × 335/1129
Probability of the first three orders from B = 0.026
Complete question is;
Use the data in the following table , which lists drive - thru order accuracy at popular fast food chains Assume that orders are randomly selected from those included in the table Drive thru Restaurant A B C D Order Accurate 312 277 250 144 Order Not Accurate 32 60 37 19 If three different orders are selected , find the probability that they are all from restaurant A
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which function is greater at the given value y=3^x or y=x^3 at x=2
Answer:
[tex] {3}^{x} [/tex]
Step-by-step explanation:
[tex] {x}^{3} = 8[/tex]
[tex] {3}^{x} = 9[/tex]
WILL GIVE BRAINLEST!!!
I. The diagonals in a trapezoid are always equal in length.
II. The diagonals in a trapezoid always bisect each other.
III. The diagonals in a trapezoid always intersect at the median.
Which of the above statements are NOT true for all trapezoids?
I only
I, II, and III
I and III
I and II only
Answer:
I and II only
Find the volume of the composite figure. Round to the nearest tenth if necessary.
The volume of the composite figure is of 425 m³.
What is the volume of a prism?The volume of a prism is given by the base area multiplied by the height.
In this problem:
For the top figure, the base is a square with 5m, with height of 13m.For the bottom figure, the base is a square with 5m, with height of 4m.Hence the volume in m³ is:
V = 5² x 13 + 5² x 4 = 25 x 17 = 425 m³.
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which of the following rational functions is graphed below?
Answer: C
Step-by-step explanation:
There is a vertical asymptote at x=3, so the denominator should have a factor of (x-3).
This eliminates everything except for C.
Margo spends a quarter of her paycheck on a new dress, one-eighthof her paycheck on shoes, and $24 on a birthday present. if she spent $60 altogether, how much was margo’s paycheck?
Solving a linear equation, we conclude that Margo's paycheck is of 96 dollars.
How much was Margo's paycheck?
We know that she spends one quarter on a dress, one eight on shoes, and $24 on a birthday present.
We also know that she spent a total of $60.
If we define P as Margo's paycheck, then we know that:
(1/4)*P + (1/8)*P + $24 = $60
Now we just need to solve that linear equation for P, we will get:
(2/8)*P + (1/8)*P = $60 - $24 = $36
(3/8)*P = $36
P = (8/3)*$36 = $96
In this way, we conclude that Margo's paycheck is of 96 dollars.
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A company designs microphones for use in conference rooms. a new microphone needs to focus on the person speaking and not the voices of other people in the room. which polar equation would best match the desired audible range of the microphone?
r = 3 + 3cos(θ) polar equation would best match the desired audible range of the microphone.
How do you know if an equation is polar?Determine the kind of polar equation. The polar equation has the shape of a limaçon, and is written as r = a - b cos. We just need to assess the equation throughout the range [0, 1] and then reflect the graph about the polar axis because the equation passes the condition for symmetry to the polar axis.What is a polar in math?The polar coordinate system in mathematics is a two-dimensional coordinate system in which the distance from a reference point and the angle from a reference direction are used to identify each point's location on a plane.What is the meaning of polar form?In addition to the rectangular form, a complex number can also be represented in polar form. Typically, we write complex numbers as z = x + iy, where I is an imaginary integer. However, in polar form, complex numbers are modeled as a union of argument and modulus.Learn more about polar form here:
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Answer:
D
Step-by-step explanation:
determine the slope of the line
Answer: -1/2
Step-by-step explanation:
The slope of a line tells you how steep the line is, and what direction it is going in. We can calculate the slope by seeing how much the line moves horizontally and vertically.
We can calculate the slope using [tex]\frac{rise}{run}[/tex], which is how much a point rises (goes up or down) and runs (goes left or right) to go to the next point.
Let's take two points on the graph: (-2, 0) and (0, -4). The rise will be the difference of the y-values, and the run will be the difference of the x-values.
[tex]\frac{-2-0}{0-(-4)}=\frac{-2}{4}=\frac{-1}{2}[/tex]
Hence, the slope of this line is [tex]\frac{-1}{2}[/tex]
A rectangular corral is to be built using 70m of fencing. If the fencing has to enclose
all four sides of the corral, what would be the dimensions to produce the maximum
possible area and what would the area of the corral be? Include a complete solution
Answer:
306 square meters
Step-by-step explanation:
The maximum area is when the length and width are the closest together.
70/2=35 we divide because there are 2 lengths and 2 widths in a rectangle
35/2=17.5, find the 2 closest integers, they are 17 and 18
17*18=306
Find the volume of the composite solid.
The volume of the composite solid shown in the diagram is: 80 ft.³.
What is the Volume of Composite Solid?Volume of the composite solid = volume of triangular prism + volume of triangular pyramid.
Volume = 0.5 × base of triangle × height of triangle × length of prism + 1/3 × Base area × Height = 0.5 × 8 × 5 × 3 + 1/3 × 0.5 × 8 × 5 × 3
Volume = 60 + 20
Volume of the composite solid = 80 ft.³.
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Bill and his classmates completed 14 activities in 4 hours. what is the unit rate at which they ocompleted the activities
Step-by-step explanation:
we first divide fourteen by four
14/4= 3.5
then we change 0.5 to hours by multiplying by 60
0.5 * 60 = 30
so in conclusion it would take 3hrs 30mins to finish each activity
help!!!!!!!!!!!! >>>>>Which number set contains all rational
numbers?
The only set that only has rational numbers is the first one:
{1/3, -3.45, √9}
Which of the given sets contains only rational numbers?
A rational number is a number that can be written as the quotient of two integers.
If we look at the first set, the elements are:
1/3 which is a rational number.-3.45 = -345/100 which is a rational number√9 = 3 = 3/1 which is a rational number.In the other sets we can see elements like:
√37, √44, or √2 which are all irrational numbers, then the only correct option is the first one.
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please help me it is an easy question
Answer:
200 yd²
Step-by-step explanation:
A = 17 yd
B = 15 yd
C = 2 yd
D = 8 yd
b) Area of rectangle = length * width
[tex]\sf Area \ of \ 2 \ triangle = 2* \dfrac{1}{2}* base * height = base* height\\\\[/tex]
Area of right triangular prism = Areas of two triangle + area of the upper rectangle + area of middle rectangle + area of below rectangle
= 8 * 15 + 17 * 2 + 15 *2 + 8*2
= 120 + 34 + 30 + 16
= 200 yd²
HELP !! Which of the following points lies on the graph of this equation? y =2x -2
Answer:
A.
Step-by-step explanation:
i'm 99% sure!
Answer:
B
Step-by-step explanation:
Plug in the coordinates.
8. A spinner is divided into 6 equal sections o
numbered 1 through 6. What is the probability
that the arrow will land on a multiple of 3?
(A) =
(B)
116113-1
(C) 1/12
(D) 1
8 (0)
81(0)
Cla
brosse und Ato mondo Fran
S(A)
(80)
Answer:
1/3
Step-by-step explanation:
The numbers are 1, 2, 3, 4, 5, and 6.
Both 3 and 6 are multiples of 3.
So, 2/6 is the probability since there is an equal change that the arrow will land on each section.
This simplifies to 1/3.
Brainliest, please :)
Answer:
P (multiple of 3) = [tex]\bf \frac{1}{3}[/tex]
Step-by-step explanation:
Numbers on the spinner, ξ = {1, 2, 3, 4, 5, 6} (6 elements)
Multiples of 3 = {3, 6} (2 elements)
P (multiple of 3) = no. of multiples of 3 / total no. of numbers on spinner
= [tex]\frac{2}{6}[/tex]
= [tex]\bf \frac{1}{3}[/tex]
2. Which of the following expressions is equivalent to 322?
01
08.1/1
032.2
08-2
Answer:
C. (32/4)*2
Step-by-step explanation:
C is the correct answer because when we divide 4/2 it equals 2.
Hope this helps!
Answer:
D
Step-by-step explanation:
Given expression:
[tex] \dfrac{32}{4} \times \dfrac{4}{2} \times 2 [/tex]
Evaluation of the given expression:
[tex] = 8 \times 2 \times 2 [/tex]
[tex] = 32 [/tex]
A. [tex] \dfrac{32}{\frac{16}{4}} = \dfrac{32}{4} = 8 [/tex]
B. [tex] 8 \times \dfrac{4}{2} = 8 \times 2 = 16 [/tex]
C. [tex] \dfrac{32}{4} \times 2 = 8 \times 2 = 16 [/tex]
D. [tex]8 \times \dfrac{4}{2} \times 2 = 8 \times 2 \times 2 = 32[/tex]
Only expression D evaluates to the same value as the given expression.
Answer: D
Please answer the question below..
The value of x that makes the unshaded area equal to the shaded area is 7.07 inches.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The area of big sector = (60/360) * π(10)² = (50π /3) cm²
Area of small sector = (60/360) * π(x)² = (x²π /6) cm²
Unshaded area = (x²π /6) cm²
Shaded area = (50π /3) - (x²π /6) = (100π - x²π) /6
Shaded area = unshaded area
(100π - x²π) /6 = (x²π /6) cm²
x = 7.07
The value of x that makes the unshaded area equal to the shaded area is 7.07 inches.
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The length of x in the sector is 7.08 cm.
How to find area of a sector?area of a sector = ∅ / 360 × πr²
where
r = radiusTherefore,
area of a sector = 60 / 360 × π × 10²
area of a sector = 60 / 360 × π × 100
area of a sector = 6000 / 360 π
Hence,
area of the unshaded portion = 6000 / 360 π ÷ 2 = 6000π / 720 = 26.1666666667 = 26.2 cm
Hence,
26.2 = 60 / 360 × 3.14 × x²
x² = 26.2 / 0.52333333333
x = √50.0637261552
x = 7.07557064836
x = 7.08 cm
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Evaluate if a = - 3 and c = 5
- Зас
7
Answer:
315
Step-by-step explanation:
-3ac7
-3x-3=9x5=45x7=315
❄ Hi there,
evaluate this expression by using substitution:
If
a=-3c=5then
-3ac= (see below)[tex]\sf{-3(-3)(5)}[/tex]
[tex]\sf{9\times5}[/tex]
[tex]\triangleright \ \sf{45}[/tex]
That's it!
❄
The constant of 2/3 cupcakes per minute means that in a minute, 2/3 of a cupcake is made.
Given the graph of w(x), w(2) = ?
(the graph is below)
Based on the graph of the cupcakes done, we find that w(2) = 5.
How many cupcakes are made by the cooker?
Herein we have an application of linear equations to the production of cupcakes. In accordance with the graph, the horizontal axis is for the preparation time (x) and the vertical axis is for the quantity of cupcakes done (w). Based on the graph, we find that w(2) = 5.
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Use a triple integral to find the volume of the wedge bounded by the parabolic cylinder yx and the planes zy and z0.
By using the triple integral, the wedge's volume is 4/15.
What is parabolic cylinder?A parabolic cylinder is a three-dimensional quadratic surface (sometimes known as a quadric surface) in mathematics, specifically analytical geometry, and is defined by the equation x 2 + 2 a y = 0 x2+2ay=0. A parabola serves as the directrix of a parabolic cylinder, to put it another way.
According to the assertion:The wedge's volume, which the parabolic cylinder encloses, must be determined.
Consequently, as a result of the z=y form,
In addition to the specified boundary, the plane y=0 x = 0, z = 0.
For all of this, we are therefore in the first octant. additionally, the plane
x + y = 1 is a constraint.
Triple integrals are three independent integrations that are done one after the other to calculate a volume or to integrate across three independent dimensions in a fourth dimension.
The following would be written as a triple integral:
∫x=0 ∫y=0
∫z=0 dy dz dx
Once the values have been entered and the problem has been solved, we obtain the
[−4/15(1−x)^5/2] at x=0
The answer will then change to 4/15.
As a result, using the triple integral, the wedge's volume comes out to 4/15.
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