Answers
By applying the concept of finite sum and the properties of the series, we conclude that the finite sum [tex]p = \sum \limit_{x=1}^{3} 2^{x}+ 2[/tex] is equal to the value of 34.
How to find the result of finite sum
Let be a sum of the form [tex]p = \sum\limits_{i= 1}^{n} a_{i}[/tex], where n represents an integer. This kind of sum represents a finite sum, whose expanded form is presented below:
p = a₁ + (a₁ + a₂) + (a₁ + a₂ + a₃) + ... + (a₁ + a₂ + a₃ + ... + aₙ₋₁ + aₙ) (1)
If we know that [tex]p = \sum \limit_{x=1}^{3} 2^{x}+ 2[/tex], then the result of the finite sum is:
p = (2 + 2¹) + (2 · 2 + 2¹ + 2²) + (3 · 2 + 2¹ + 2² + 2³)
p = 4 + (4 + 6) + (6 + 14)
p = 4 + 10 + 20
p = 34
By applying the concept of finite sum and the properties of the series, we conclude that the finite sum [tex]p = \sum \limit_{x=1}^{3} 2^{x}+ 2[/tex] is equal to the value of 34.
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Related Questions
Find the volume of each solid. Round to the nearest hundredth. Show your work
Answers
Volume of a cube is length x width x height
So 8 x 8 x 8 = 512
O is the centre of the circle shown below. Line DHG is a tangent to the circle.
Work out the size of angle a.
Justify your answer.
Answers
[tex]\angle EHF=90^{\circ}[/tex] (an angle inscribed in a semicircle is a right angle)
[tex]\angle HEF=38^{\circ}[/tex] (alternate segment theorem)
[tex]a=52^{\circ}[/tex] (angles in a triangle add to 180 degrees)
A large tank of sterile water holds 200 gallons . It is leaking at an unknown rate. At 4:30 pm the tank had 137 gallons and at 7:00 pm the tank had 115 gallons. Assuming the tank was full when the leak began , write a function to estimate how much water is in the tank. now find the time at which the tank began leaking and the time at which the tank will be empty.
Answers
Answer:
1. 8.8 gallons per hour
2. 9:20 am
3. 8:04 am
Step-by-step explanation:
The tank lost 22 gallons of water in 150 minutes (2.5 hours)
This is a rate of 0.14666 gallons per minute or 8.8 gallons per hour
The function: 200 - 0.147(x)
So at 4:30 pm, the tank lost 63 gallons. So at a rate of 8.8 gallons per hour, that means it has been leaking for 7.16 (.16 hours = 9.6 minutes) hours.
So it has been leaking since 9:20 am.
In order for it to completely empty, it needs to drain 115 gallons of water.
At a rate of 8.8 gallons per hour, that means it needs 13.068 hours or 13 hours and 4 minutes.
So it will be empty at 8:04 am.
AREA UNDER A CURVE
please explain too ty <3
Answers
sin x = 15/2
COS X =
√95
12
Answers
Answer:
[tex]\sqrt{95}/5[/tex]
In the diagram, the area of
the shaded region is
Answers
Area of shaded region is 42sq.cm
I hope this helps u.
Triangle A B C has centroid G. Lines are drawn from each point to the midpoint of the opposite side to form line segments A D, B E, C F.
[Figure may not be drawn to scale]
In triangle ABC, BG = 24 mm. What is the length of segment GE?
12 mm
24 mm
36 mm
48 mm
Answers
Medians are concurrent and cut each other in the ratio of 2:1 from the vertex
BG:GE = 2:1 = 24:12
Which of the following functions shows the linear parent function, F(x) = x,
shifted right?
OA. G(x) = 4x
OB. G(x) = x + 2
OC. G(x) = x-9
OD. G(x) = -x
Answers
Answer: C
Step-by-step explanation:
See attached image.
Pls help 20 points :)
Answers
Answer:
49 cm²
Step-by-step explanation:
Half circle: 1/2 π r² ≈ 1/2 * 3.14 * 16 = 25.12
Rectangle: 3*8 = 24
Add them: 25.12 + 24 ≈ 49
37 The diameter of circle X is 15 centimeters. The diameter of circle Y is 20 centimeters.
Which measurement is closest to the difference between the circumference of circle X and the
circumference of circle Y in centimeters?
A 15.7 cm
B 7,85 cm
C 137 cm
D 31.4 cm
Answers
Answer:
A
Step-by-step explanation:
this can be done without any calculator, which I did and explain below :
the circumference of a circle is always
2×pi×r
with r being the radius, which is always half of the diameter.
so, the circle X circumference is
pi×15
circle Y
pi×20
the difference is
20×pi - 15×pi = 5×pi
5×pi is half of 10×pi, which would be 10×3.1415... = 31.415...
half of that is about 15.7.
so, A is the correct answer
Answer:
cual es la respuesta de esta pregunta
When David was asked how old he was, he said " I'm three times younger than my dad, but twice as old as Rebecca. " Then little Rebecca ran up to him and declared "i am 30 years younger than my dad". How old is David
Answers
Using a system of equations, it is found that David is 12 years old.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
The variables are given as follows:
Variable x: David's age.Variable y: Dad's age.Variable z: Rebecca's age.David is three times younger than the dad and twice as old as Rebecca, then:
x = y/3 -> y = 3x.x = 2z.Rebecca is 30 years younger than the dad, hence:
z = y - 30.
Then, since x = 2z and z = y - 30 and y = 3x, we solve for x to find David's age.
x = 2(y - 30)
x = 2(3x - 30)
x = 6x - 60
5x = 60
x = 60/5
x = 12.
David is 12 years old.
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The second term in a geometric system is 12. the fourth term in the same sequence is 4/3. what is the common ratio in the sequence.
Answers
Answer:
36/43 I think.
Step-by-step explanation:
Wyzant
5 2/8 minus 1 3/8 (show work)
Answers
Answer:
[tex]\frac{31}{8} or 3\frac{7}{8}[/tex]
Step-by-step explanation:
First, these 2 fractions are proper fractions, we will convert them into improper ones.
[tex]5\frac{2}{8} = \frac{42}{8}[/tex]
[tex]1\frac{3}{8} =\frac{11}{8}[/tex]
Now to subtract fractions, we must ensure the denominators are the same, which in this case is already the same, so we can subtract straightaway.
[tex]\frac{42}{8} - \frac{11}{8} \\=\frac{31}{8} or 3\frac{7}{8}[/tex]
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{5 \dfrac{2}{8} - 1 \dfrac{3}{8}}[/tex]
[tex]\mathsf{= \dfrac{5 \times 8 + 2}{8} - \dfrac{1 \times 8 + 3}{8}}[/tex]
[tex]\mathsf{= \dfrac{40 + 2}{8} - \dfrac{8 + 3}{8}}[/tex]
[tex]\mathsf{= \dfrac{42}{8} - \dfrac{11}{8}}[/tex]
[tex]\mathsf{= \dfrac{42 - 11}{8 - 0}}[/tex]
[tex]\mathsf{= \dfrac{42 - 11}{8}}[/tex]
[tex]\mathsf{= \dfrac{31}{8}}[/tex]
[tex]\mathsf{\approx 3 \dfrac{7}{8}}[/tex]
[tex]\huge\textsf{Therefore, your answer should be: \boxed{\mathsf{3 \dfrac{7}{8}}}}\huge\checkmark[/tex]
[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040}[/tex]
If three farmers share some bags of fertilizers in the ratio 3:4:5.if the smallest share is 18 bags.what is the largest share
Answers
Answer:
30
Step-by-step explanation:
Sum of the ratios = 3 + 4 + 5 = 12
Smallest share = 18 bags
Ratio of the smallest share = 3
Let the largest share = x
From the question
18 ------------ 3
x --------------5
Cross multiply
3x = 18 × 5
Dividing bothsides by 3
X = 18 × 5/ 3
X = 90 / 3
X = 30
Therefore.
The largest share = 30
Over the weekend, Kari drank 5/6 of a bottle of soda and Aisha drank 1/6 of a bottle.
How much more soda did Kari drink than Aisha?
Write your answer as a fraction or as a whole or mixed number.
bottles
Answers
Answer:
4/6= 2/3
Step-by-step explanation:
5/6 - 1/6 = 4/6
lowest form : 2/3
Answer:
Hello! The answer to your question is 2/3.
Step-by-step explanation:
In this problem, you have to find how much more soda Kari drank than Aisha. To find how much more, you will have to use subtraction:
[tex]\frac{5}{6}- \frac{1}{6} \\= \frac{4}{6}[/tex]
4/6 can be simplified by dividing the numerator and denominator by 2:
4/2 = 2
6/2 = 3
Therefore, your answer is:
[tex]\frac{2}{3}[/tex]
a sweet factory produces 5 different chocolate bars. the different flavors are always produced in the same proportions, for every 4 coconut flavored bars 5 honeycomb 6 orange and 4 strawberry
what is the total number of chocolate bars if there are:
a) 280 orange flavored bars?
b) 960 coconut flavored bars?
c) 79 coffee flavored bars?
Answers
a. There are 933 chocolate bars
b. There are 1200 chocolate bars
c. There are 1580 chocolate bars
How to calculate the number of chocolate barsSince there are 5 different flavors,
let
x = orange flavored bars, y = coconut flavored bars, z = coffee flavored bars, a = strawberry flavored bars and b = honeycomb flavored bars and X = total number of barsSince the different flavors are always produced in the same proportions, for every 4 coconut flavored bars 5 honeycomb 6 orange 1 coffee and 4 strawberry
So, the ratio of their proportions are x:y:z:a:b = 6:4:2:1:5
So, the total ratio is T = 6 + 4 + 1 + 4 + 5 = 20
a. What is the total number of chocolate bars if there are 280 orange flavored bars?Since we have 6 orange flavored bars, the ratio of orange flavored bars to total is 6/20
So, the amount of orange flavored bars is x = 6/20 × X
Making X subject of the formula, we have
X = 20x/6
So, if there are 280 orange bars, there will be
X = 20x/6
X = 20 × 280/6
X = 5600/6
X = 933.33
X ≅ 933 chocolate bars
So, there are 933 chocolate bars
b. What is the total number of chocolate bars if there are 960 coconut flavored bars?Since we have 4 coconut flavored bars, the ratio of coconut flavored bars to total is 4/20
So, the amount of coconut flavored bars is y = 4/20 × X
Making X subject of the formula, we have
X = 20y/4
So, if there are 960 coconut flavored bars, there will be
X = 20y/6
X = 20 × 960/4
X = 5 × 240
X = 1200 chocolate bars
So, there are 1200 chocolate bars
c. What is the total number of chocolate bars if there are 79 coffee flavored bars?Since we have 1 coffee flavored bars, the ratio of coffee flavored bars to total is 1/20
So, the amount of coconut flavored bars is z = 1/20 × X
Making X subject of the formula, we have
X = 20z
So, if there are 79 coffee flavored bars, there will be
X = 20z
X = 20 × 79
X = 1580 chocolate bars
So, there are 1580 chocolate bars
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Question 1 (Multiple Choice Worth 5 points) (04.03 MC) The ratio of sugar to flour used in a pudding recipe is 1:3. Which figure shows equivalent ratios?
Answers
The figure that shows equivalent ratios for the ratio of sugar to flour would be Figure 2.
What figure has equivalent ratios?The ratio os sugar to flour is 1:3. An equivalent ratio would be one that is 1:3 or 3:1.
Figure 2's ratios are:
6 :2
9:3
12:4
When all of these are taken to their simplest form, we get:
3 : 1
Figure 2 is therefore an equivalent ratio.
Rest of the question is:
he ratio of sugar to flour used in a pudding recipe is 1:3. Which figure shows equivalent ratios? #1: 3,1. 9,2. 3,15 #2: 6,2. 9,3. 12,4 #3: 9,5. 6,3. 13,1 #4: 9,4. 6,3. 3,2
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Given that a function, g, has a domain of -1 ≤ x ≤ 4 and a range of 0 ≤ g(x) ≤ 18 and that g(-1) = 2 and g(2) = 8, select the statement that could be true for g.
g(1) = -2
g(5) = 12
g(3) = 18
g(2) = 4
Answers
A function assigns the value of each element of one set to the other specific element of another set. The correct option is C.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given that a function, g, has a domain of -1 ≤ x ≤ 4 and a range of 0 ≤ g(x) ≤ 18 and that g(-1) = 2 and g(2) = 8.
1.) g(1) = -2
Since the range is from 0 to 18. Therefore, this is not the correct option.
2.) g(5) = 12
Since the domain is from -1 to 4. Therefore, this is not the correct option.
3.) g(3) = 18
This is the only option that is feasible. Thus, this is the correct option.
4.) g(2) = 4
Since the value of g(2) is 8. Therefore, this is not the correct option.
Hence, the correct option is C.
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A binary operation∆is defined on the set of real number R by x∆y=x²+y-2xy. evaluate (2∆½)
Answers
Answer:2.5
Step-by-step explanation:
4+1/2-2=2 1/2 according to the formula
Graph the exponential model
y = 3(6)^x Which point lies on the graph?
(-9 2)
(2, 9)
(- 1, - 18)
(1, 18)
Answers
Answer: (1, 18)
Step-by-step explanation:
Test each x, y pair.
Getting to the last one, plug in 1 for the x value.
y = 3 * (6 ^ x)
y = 3 * (6 ^ 1)
y = 3 * 6
y = 18
This matches with (1, 18) so it must lie on the graph.
5. a number from 1-50 is chosen at random.
what is the probability that it is a perfect
square or a multiple of 4?
8/25
3/50
2/5
9/50
Answers
Answer:3/
Step-by-step explanation:
URGENT PLEASE!
Find the values of x, y, and z.
Answers
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The value of x,y, and z is √38, (5√38)/3, and √80.556, respectively.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
The measure of Y is,
y² = 5² + 3²
y = √38
The measure of ∠C,
Tan(∠C) = 5/3 = z/√38
z = (5√38)/3
The measure of z is,
z² = 5² + x²
x = √80.556
Hence, the value of x,y, and z are √38, (5√38)/3, and √80.556, respectively.
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The average height of American women (in 2016) is 5 ft. 4 inches (64 inches) with a standard deviation of 3 inches. What is the probability that the average height of a random group of nine American women would be less than five feet three inches
Answers
Probability of average height of women is 0.1379
First check to see if the Central Limit Theorem applies. Since n > 30, it does. Next we need to calculate the standard error. To do that we divide the population standard deviation by the square-root of n, which gives us a standard error of 0.646. Next, we calculate a z-score using our z-score formula:
Z=(X−μ)/S.E.
S.E = σn/√n
S.E =3/√ 9
S.E=1
Plugging in gives us:
(64−63)/1 = 1
Finally, we look up our z-score in our z-score table to get a p-value.
The table gives us a p-value of,
P(z<1.0)=1−P(z>1.0)
P(z<1.0)=1−0.8621
P(z<1.0)=0.1379
So, Probability of average height of women is 0.1379
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A company's prospectus includes:
A) The company's investment options.
B) The company's guaranteed return strategy.
C) The company's revenue and net worth.
D) The company's research
Answers
A company's prospectus includes: A) The company's investment options.
What is a company's prospectus?Company's prospectus can be defined as the document that entails detail information of a company investment option that are available for sales to potentials buyers or investors.
Examples of the investment options are:
BondsStocksMutual Funds etcTherefore the correct option is A.
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A company's prospectus is a formal legal document designed to provide information and full details about an investment offering for sale to the public.
pls help I’m losing my mind
Answers
Answer:
1) x+45=180
x=180-45
x=135
ans.=135
2) (2x-30)+y= 180
28xy=180
xy= 180-28
y=152
On a coordinate plane, 2 triangles are shown. Triangle L M N has points (negative 1, 3), (3, 1), and (negative 1, 1). Triangle L prime M prime N prime has points (negative 2, negative 1), (6, negative 5), and (negative 2, negative 5).
Which composition of similarity transformations maps TriangleLMN to TriangleL'M'N'?
a dilation with a scale factor less than 1 and then a reflection
a dilation with a scale factor less than 1 and then a translation
a dilation with a scale factor greater than 1 and then a reflection
a dilation with a scale factor greater than 1 and then a translation
Answers
The composition of similarity transformations that maps Triangle LMN to TriangleL'M'N is a dilation with a scale factor less than 1 and then a reflection. Opion A. This is further explained below.
Which composition of similarity transformations maps TriangleLMN to TriangleL'M'N'?Generally, In the case of a reflection across the y-axis, the y-coordinate of a point stays the same but the x-coordinate is changed into its inverse.
Triangle LMN has the coordinates (2, 1), (1, 1), and (1, 3).
(-4,-4) (-3,-4) (-3,-2).
In conclusion, Assuming that the coordinates (2, 1), (1, 1), and (1, 3) of Triangle LMN. This is the translation 5 units down (x,y-5): Two units to the right (x+2, y-5) of the coordinates (2,-4), (1,-4), and (1,-2): (4, -4), (3, -4), (3, -2)
It is a reflection along the y-axis, with coordinates of (-4,-4) and (-3,-4) (-3,-2)
Therefore, Triangle L'M'N' is the result of the transformation sequence in Option A.
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Answer: a
Step-by-step explanation:
i got it right on the test
A rectangle has a length of 6x-5y+1. If the perimeter of the rectangle is 16x-4y-4, determine an expression for its width
Answers
Answer:
2x +3y -3
Step-by-step explanation:
The perimeter of a rectangle is the sum of the lengths of all its sides.
Perimeter of a rectangle= 2 length +2 width
16x -4y -4= 2(6x -5y +1) +2(width)
Expand:
16x -4y -4= 12x -10y +2 +2(width)
2(width)
= 16x -4y -4 -(12x -10y +2)
= 16x -4y -4 -12x +10y -2
= 4x +6y -6
2(width)= 2(2x +3y -3)
Divide both sides by 2:
width= 2x +3y -3
help!!!!
Which of the following graphs shows the
solution set to x ≥
-3 and x < 3?
Answers
Answer:
C. or third choice.
Step-by-step explanation:
For x ≥ -3 you will need a colored in circle because it has a greater than or equal to sign, and it is shaded to the right.
For x < 3 you will need a circle that is not colored in because it is a less than sign, and it is shaded to the left.
Hope this helps!
If not, I am sorry.
A box contains 2 green, 5 blue, and 8 yellow chips. If two chips are drawn at random one after the other with replacement.
find the probability that both the chips are green.
Answers
The probability that both the chips are green is: 4/225
How to determine the probability?The given parameters are:
Green = 2
Blue = 5
Yellow = 8
Total = 15
The probability that both the chips are green is:
P = P(green) * P(green)
This gives
P = 2/15 * 2/15
Evaluate
P = 4/225
Hence, the probability that both the chips are green is: 4/225
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: Enter your answer and show all the steps that you use to solve this problem in the space provided.
What other information do you need in order to prove the triangles congruent using the SAS Postulate?
Answers
Answer: [tex]\angle BCA \cong \angle ACD[/tex]
Step-by-step explanation:
By the reflexive property, [tex]\overline{AC} \cong \overline{AC}[/tex]. So, we just need the pair of angles between these corresponding sides to be congruent.