Answers
The sum is 184.
_____
The terms being summed are ...
2·3² +3 = 2·9 +3 = 18 +3 = 21
2·4² +3 = 35
2·5² +3 = 53
2·6² +3 = 75
Their total is
21 +35 +53 +75 = 184
Related Questions
Please help with geometry
Answers
[tex]\dfrac{60^o}{360^o}=\dfrac{1}{6}[/tex]
The sector is 1/6 of the circle, therefore the area of the sector is 1/6 of area of the circle.
The formula of an area of the circle: [tex]A_O=\pi r^2[/tex]
The area of the sector:
[tex]A_s=\dfrac{1}{6}\cdot\pi\cdot12^2=\dfrac{1}{6}\pi\cdot144=24\pi\ m^2[/tex]
The formula of an area of the equilateral triangle: [tex]A_\Delta=\dfrac{a^2\sqrt3}{4}[/tex]
[tex]A_\Delta=\dfrac{12^2\sqrt3}{4}=\dfrac{144\sqrt3}{4}=36\sqrt3\ m^2[/tex]
The area of the segment:
[tex]A_{sg}=A_s-A_\Delta\to A_{sg}=(24\pi-36\sqrt3)m^2[/tex]
The area of the shaded region:
[tex]A=A_O-A_{sg}\to A=144\pi-(24\pi-36\sqrt3)=144\pi-24\pi+36\sqrt3\\\\=\boxed{A=(120\pi+36\sqrt3)m^2}[/tex]
The perimeter of a square window is 360 cm find the length of one side
Answers
To find the length of one side of a square window with a perimeter of 360 cm, we use the formula for the perimeter of a square, resulting in each side being 90 cm long.
Explanation:To find the length of one side of a square window when the perimeter is 360 cm, we can use the formula for the perimeter of a square, which is P = 4s, where P represents the perimeter and s represents the length of one side. Given that the perimeter is 360 cm, we can set up the equation 360 = 4s. Dividing both sides of the equation by 4 gives us s = 90 cm.
Therefore, the length of one side of the square window is 90 cm.
which of the points satisfy the linear inequality graphed here?
a)(0,0)
b)(10,0)
c)(-10,0)
d)(10,10)
Answers
The shaded region represents the set of points that satisfy the inequality.
We note that the point (-10, 0) is within the shaded region.
Therefore, this point satisfies the inequality.
Answer:
c)(-10,0)
The coordinate values of the vertices of △klm are integers. triangle klm has vertices located at (1, 1), (5, 4) and (5, 1). which set of coordinate pairs could represent the vertices of a triangle congruent to △klm?
Answers
A) (-1, 1), (-1, 4), (2, 1)
B) (0, 0), (3, 4), (0, 5)
C) (-1, 1), (-4, 5), (-1, 5)
D) (0, 0), (-5, 0), (0, 4)
==============================
The distance
between two points (x₁,y₁),(x₂,y₂) = d
[tex]d = \sqrt{ (x2-x1)^{2} + (y2-y1)^{2} } [/tex]
we have K(1, 1), L(5, 4) and M(5, 1)
we will find the length between each two points.
KL = [tex]d = \sqrt{ (5-1)^{2} + (4-1)^{2} } [/tex] = 5
LM = [tex]d = \sqrt{ (5-5)^{2} + (1-4)^{2} } [/tex] = 3
KM = [tex]d = \sqrt{ (5-1)^{2} + (1-1)^{2} } [/tex] = 4
now check each group from the choices
the group that will give the same result will be the correct choice.
The correct choice is C
C) (-1, 1), (-4, 5), (-1, 5)
check the answer;
K'(-1, 1), L'(-4, 5), M'(-1, 5)
K'L' = [tex]d = \sqrt{ (-4+1)^{2} + (5-1)^{2} } [/tex] = 5
L'M' = [tex]d = \sqrt{ (-1+4)^{2} + (5-5)^{2} } [/tex] = 3
K'M' = [tex]d = \sqrt{ (-1+1)^{2} + (5-1)^{2} } [/tex] = 4
Iridium -192 has a half life of 74 days after 148 days, how many milligrams of 900 mg sample will remain?
Answers
The amount that remained out of the 900 mg sample after 148 days is 225 milligrams.
Given,
Iridium -192 has a half-life of 74 days.
We need to find out after 148 days how many milligrams of the 900 mg sample will remain.
Here the initial amount is 900mg.
What is half life?It is the time at which the initial amount of a substance is reduced to half its amount.
The formula used with half-life:
[tex]N_{t} =N_{0} (\frac{1}{2})^\frac{t}{t_\frac{1}{2} }[/tex]
Where
N_t = Amount after time t
N_0 = initial amount
t_1/2 = half-life value of the substance.
t = time.
We have,
N_0 = 900 mg
t_1/2 = 74 days.
t = 148 days.
Substituting the values in the formula,
We get,
N_t = 900 ( 1/2 ) ^148/74
N_t = 900 ( 1/2 )^2
N_t = 900/4
N_t = 225 mg
We see that the amount that remains after 148 days is 225 milligrams.
Thus the amount that remained out of the 900 mg sample after 148 days is 225 milligrams.
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Which story problems could be solved using the given equation? 6 divided by 1/2 = ? Choose exactly two answers that are correct.
A.
Mike spends a hour reading every night before bed. How many hours does Mike spend reading before bed in 6 days?
B.
Alice has 6 yards of ribbon. She uses yard of ribbon for each package she’s wrapping. How many packages can Alice wrap?
C.
A cup of milk is used for every serving in a recipe. How many servings can be made with 6 cups of milk?
D.
Charlie spent of his savings on 6 equally priced admission tickets to the zoo. What fraction of his savings did Charlie spend on each ticket?
Answers
A local company manufactures netbook computers. Their profit function is given by this equation: y equal minus x to the power of 2 plus 120 x plus 3000 where x is the number of netbooks produced in one day and y is the profit (in dollars) the company makes that day. What is the maximum profit that the company can make? (Hint: Find the vertex of the parabola.)
Answers
The equation described above can also be written as, y = -x² + 100x + 4000To get the number of notebooks that will give them the maximum profit, we derive the equation and equate to zero. dy/dx = -2x + 100 = 0The value of x from the equation is 50. Then, we substitute 50 to the original equation to get the profit. y = -(50^2) + 100(50) + 4000 = 6500Thus, the maximum profit that the company makes is $6,500/day.
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Answer: $6,600
Step-by-step explanation:
Given: The profit function is given by the equation:
[tex]y=-x^2+120x+3000[/tex],where x is the number of netbooks produced in one day and y is the profit (in dollars) the company makes that day.
To find the maximum profit, first we need to find critical point of the function.
For that, first differentiate the above function w.r.t. x, we get
[tex]y'=-2x+120[/tex]
Now, Put [tex]y'=0[/tex], we get
[tex]-2x+120=0\\\\\Rightarrow\ x=60[/tex]
Again differentiate the above function w.r.t. x, we get
[tex]y"=-2<0[/tex]
By second derivative test, at x=60 , attains its maximum value.
Now, the Maximum profit will be :
[tex]y=-(60)^2+120(60)+3,000=6,600[/tex]
Hence, the maximum profit that the company can make = $6,600
What is the best way to randomly choose these 500 members?
Answers
The last choice is the correct answer
Please help me with a simple math problem.
What is the value of b?
A. 1.5
B. 3
C. 3.75
D. 4.5
Answers
According to Newton's Law of Cooling, if a body with temperature T 1 is placed in surroundings with temperature T 0, different from that of T 1, the body will either cool or warm to temperature T(t) after t minutes, where: T(t) = T 0 + (T 1 - T 0)e kt and k is a constant. A cup of coffee with temperature 140°F is placed in a freezer with temperature 0°F. The constant k ≈ -0.0815. Use Newton's Law of Cooling to find the coffee's temperature, to the nearest degree Fahrenheit, after 15 minutes. The temperature is about a0degrees Fahrenheit.
Answers
T = 0 + (140 - 0)e^(-0.0815*15) = 140e^(-1.2225) = 41.23°F
Using Newton's Law of Cooling, the coffee's temperature after 15 minutes when placed in a freezer with a temperature of 0°F is approximately 76°F.
Explanation:According to Newton's Law of Cooling, the temperature of an object changes at a rate proportional to the difference between its temperature and the temperature of its surroundings. In the given problem, we have a cup of coffee initially at 140°F placed in a freezer at 0°F, aimed to find the coffee's temperature after 15 minutes. The constant k is given as -0.0815.
We can plug these values into the equation T(t) = T0 + (T1 - T0)ekt. Therefore, the temperature of the coffee after 15 minutes can be calculated as T(15) = 0 + (140 - 0)e-0.0815*15.
Computing this gives us a value of approximately 76°F. Thus, after 15 minutes, the coffee's temperature, to the nearest degree Fahrenheit, is 76°F when placed in a freezer with a temperature of 0°F according to Newton's Law of Cooling.
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A circle has a circumference of 144\pi144π144, pi. what is the radius of the circle?
Answers
C = 2πR
Where,
R: radius of the circle.
Substituting values we have:
144π = 2πR
By clearing R we have:
R = 144/2
R = 72 units
Answer:
The radius of the circle is:
R = 72 units
Compute the area of a triangle with sides. 15 × 15 × 18
Answers
A=√(s(s-a)(s-b)(s-c)),
where a,b,c are sides of the triangle,
and s=(a+b+c)/2 - half perimeter of a triangle.
a=15,
b=15
c=18
s=(15+15+18)/2=48/2=24
s=24
s-a=24-15=9
s-b=24-15=9
s-c=24-18=6
A=√(24*9*9*6)=√(4*6*6*9*9) = 2*6*9=108
A=108
The radius of a circular clock face is 13 centimeters. how do i find the circumfrence
Answers
Hence, the circumfrence is [tex]81.64[/tex].
What is the circumference?
Circumference is the distance around a circle. We can find the circumference using either the diameter or radius of a circle. For shapes made of straight lines, we say they have a perimeter.
Here given that,
The radius of a circular clock face is [tex]13[/tex] centimeters.
The general formula of circumference of a circle is [tex]2\pi r[/tex].
As, [tex]r=13cm[/tex]
Substitue these values in the general formula then,
[tex]2\pi r=2(3.14)(13)\\\\=81.64[/tex]
Hence, the circumfrence is [tex]81.64[/tex].
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can someone please help ill try to add the picture
Answers
the lateral area, namely the area of the sides, is just the area of 4 rectangles.
left and right, 4x3 rectangles,
front and back, 15x3 rectangles,
so the lateral area of the box is just the sum of those areas,
[tex]\bf \stackrel{\textit{left and right}}{(4\cdot 3)}~~~~+~~~~\stackrel{\textit{front and back}}{(15\cdot 3)}[/tex]
Elly buys 75 shares of stock in a mutual fund for a total investment of $450. She sells 50 shares of her stock for total proceeds of $400. Determine if Elly made a profit or loss, and how much per share.
a.
loss of $0.67 per share
b.
loss of $2 per share
c.
profit of $0.67 per share
d.
profit of $2 per share
Answers
We have been given that Elly buys 75 shares of stock in a mutual fund for a total investment of $450.
It means the cost of 1 share is given by
[tex]\frac{450}{75}\\ \\ =\$6[/tex]
Now, we have been given that she sells 50 shares of her stock for total proceeds of $400.
It means the cost of 1 share is given by
[tex]\frac{400}{50} \\ \\ \$8[/tex]
She purchased per share at $6 and sold per share at $8.
It means that she made a profit of [tex]8-6=\$2[/tex] per share.
Therefore, d is the correct option.
(d) profit of $2 per share
Elly made a profit of $2 per share.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
First, we can determine the average cost per share of the 75 shares of stock that Elly bought:
Average cost per share = Total investment / Number of shares
= $450 / 75 shares
= $6 per share
Next, we can determine the total proceeds from the sale of 50 shares:
Total proceeds = Number of shares sold x Price per share
= 50 shares x ($400 / 50 shares)
= $400
Elly paid $6 per share for the 75 shares she bought, and she sold 50 shares for $8 per share.
The difference between these prices will determine whether she made a profit or loss per share:
Profit or loss per share = Selling price per share - Average cost per share
= $8 per share - $6 per share
= $2 per share
Since the profit per share is positive, Elly made a profit.
Therefore,
Elly made a profit of $2 per share.
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I need your help here! 15 pointa and brainliest. If you cant do it, at least give me the formula to this so I can solve it.
Answers
Answer:
0.40 formula x3.9 standardwise. Sorry if this doesnt help. I tried.
Step-by-step explanation:
giving away all these points to the lucky person who can explain how to get the answer (Law of Cosines) !!!
Answers
Here, (missing side length)^2 = 9^2 + 6^2 - 2(9)(6) cos (37 deg)
Just evaluate this to find the missing side length.
Three numbers are in the ratio of 6:5:1. What are the numbers if the difference between the smallest and largest is 30?
a.48, 40, 18B.36, 30, 6
c.24, 20, 4D.180, 150, 30
Answers
difference in ratio between large and smallest number is:
6-5=5
thus:
largest number=6/5*30=36
medium number=5/5*30=30
smallest number=1/5*30=6
Answer: B.36, 30, 6
What is the y-intercept of the equation 5x - 6y = 18?
A.-6
B. -3
C .5
D. 18
Answers
The y-intercept is for x = 0.
Put the value of x = 0 to the equation 5x - 6y = 18:
5(0) - 6y = 18
0 - 6y = 18
-6y = 18 divide both sides by (-6)
y = -3 → B.PLEASE HELP: 22 points//And brainliest answer.
Picture is above
Answers
Find the point on the curve y = √ 2 x + 4 which is closest to the point ( 3 , 0 ) .
Answers
The distance between (3,0) and (x, sqrt(2)*x + 4) is given by the distance formula:
distance: sqrt [ (3+x)^2 + (sqrt(2)*x + 4)^2 ]
Differentiate this, and then set the resulting derivative = to 0. Solve for x. Test your results to ensure that the distance d is actually the SMALLEST, given the root(s) x that you've found.
Write the coordinates of this point on the curve as ( x, f(x) ).
(Financial Algebra workbook 10-3)
Under his "Household expenses" Budget category, Mark has allocated $60 per month for pet food. He can purchase "wet food" for $1.50 per can or "dry food" for $3 per bag.
E). Name a combination of bags and cans that will cause him to be over budget.
Answers
please help asap 50 pts
Answers
Answer: The answer is B
Step-by-step explanation:
The smaller the coefficient, the wider the graph would be. So the smallest number, if positive, 1/5 is the widest and the largest 7 is the narrowest.
Answer:
b is ur answer
Step-by-step explanation:
What is the equation of the line that passes through the points (–12, –8) and (–17, –16)?
A.
-17=-8/5(x-16)
B.
-16=8/5(x-17)
C.
+16=-4/5(x+10)
D.
y+16=8/5(x+17)
Answers
happy to help :)_
Explain how the discriminant b squared minus 4 ac can be used to determine the number of solutions to a quadratic equation
Answers
CDs and DVDs Solve by setting up a system of linear equations with 2 variables and 2 unknowns. CDs cost $5.96 more than DVDs at All Bets Are Off Electronics. How much would 6 CDs and 2 DVDs cost if 5 CDs and 2 DVDs cost $127.73?
Answers
Let c be the cost of a CD and d be the cost of a DVD.
We know that c = d+5.96.
We also know that 5c+2d = 127.73.
Substituting our value of c from the first equation into the second one, we have
5(d+5.96)+2d = 127.73
Using the distributive property,
5*d+5*5.96+2d = 127.73
5d+29.80+2d = 127.73
Combining like terms,
7d+29.80 = 127.73
Subtract 29.80 from both sides:
7d+29.80-29.80=127.73-29.80
7d = 97.93
Divide both sides by 7:
7d/7 = 97.93/7
d = 13.99
c = d + 5.96 = 13.99+5.96 = 19.95
6 CDs and 2 DVDs would be
6(19.95)+2(13.99) = 147.68
The relationship between the total cost and the costs of CDs and DVDs are represented by a linear function.
The cost of 6 CDs and 2 DVDs is $147.68
Let:
[tex]C \to CDs[/tex]
[tex]D \to DVDs[/tex]
From the question, we have:
[tex]C = D + 5.96[/tex]
[tex]5C + 2D = 127.73[/tex]
Substitute [tex]C = D + 5.96[/tex] in [tex]5C + 2D = 127.73[/tex]
[tex]5 \times (D + 5.96) + 2D = 127.73[/tex]
[tex]5D + 29.8 + 2D = 127.73[/tex]
Collect like terms
[tex]5D + 2D = 127.73 - 29.8[/tex]
[tex]7D = 97.93[/tex]
Divide both sides by 7
[tex]D = 13.99[/tex]
Substitute [tex]D = 13.99[/tex] in [tex]C = D + 5.96[/tex]
[tex]C = 13.99 + 5.96[/tex]
[tex]C = 19.95[/tex]
The cost of 6 CDs & 2 DVDs is represented as:
[tex]Cost =6C + 2D[/tex]
So, we have:
[tex]Cost =6 \times 19.95 + 2 \times 13.99[/tex]
[tex]Cost =147.68[/tex]
Hence, the cost of 6 CDs & 2 DVDs is $147.68
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Which points in the scatter plot are outliers?
Select EACH CORRECT ANSWER
point A
point F
point H
point K
point M
Answers
The local grocery store wants to know if the shoppers prefer Crest or Colgate toothpaste. The store gives all of its shoppers a value saver card, then uses a random number generator to select 30 card numbers and surveys those shoppers. Is this sampling method representative of the entire population and explain?
A. No, some shoppers may not buy toothpaste there.
B. Yes, all shoppers have a value card and the shoppers interviewed were chosen by a random number generator.
C. No, need a bigger sample.
D. No, the store should only ask women.
Answers
No, some shoppers may not buy toothpaste there.
The answer is option A.
What is an example of a word problem?Word problems normally include mathematical modeling questions, where records and information approximately a positive machine is given and a student is needed to expand a model. For example, Jane had $5.00, then spent $2.00. How much does she have now?
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A 15 sector in a circle has an area of 11.9 m2 What is the area of the circle?
Answers
(Total measure in degrees of the circle)/(measure in degrees of the secant)*(area of secant)
=360/15*11.9
=24*11.9
=285.6 m^2
Answer: 285.6 m^2
The exchange rate between non-fixed currencies continuously fluctuates. The following table shows the exchange rate of pounds sterling to Israeli new shekel (plural shekalim) over a period of six days.
Days / £:INS
Monday: 1:6.0333
Tuesday: 1:5.8594
Wednesday: 1:5.7012
Thursday: 1:5.9462
Friday: 1:6.1715
Saturday: 1:6.0896
nate had 88.65 to convert into shekalim. the currency exchange he is using charges an 8% surcharge when converting currency. about how many more shekalim will nate recieve if he makes his trade on the day with the most favorable exchange rate than if he makes his trade on yhe day with the least favorable exchange rate?
Possible Answers
A. INS 41.69
B. INS 38.35
C. INS 31.68
D. INS 6.67
Answers
The correct answer is:
B) INS 38.35
Explanation:
The day with the best exchange rate is Friday; the rate is 1:6.1715. Converting 88.65£ with this rate, we have:
88.65(6.1715) = 547.103475.
Since he is charged an 8% surcharge, he gets to keep 100%-8% = 92% = 92/100 = 0.92 of this:
0.92(547.103475) = 503.335197
The day with the worst exchange rate is Wednesday, with a rate of 1:5.7012. Converting 88.65£ at this rate,
88.65(5.7012) = 505.41138. 4
0.92(505.41138) = 464.9784696
The difference between Friday and Wednesday is:
503.335197-464.9784696 = 38.3567274, or 38.35.
Nate would receive about 38.35 more shekalim if he made his trade on the day with the most favorable exchange rate than if he made his trade on the day with the least favorable exchange rate.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
The day with the best exchange rate is Friday; the rate is 1:6.1715. Converting 88.65£ with this rate, we have:
88.65(6.1715) = 547.103475.
Since he is charged an 8% surcharge, he gets to keep 100%-8% = 92% = 92/100 = 0.92 of this:
0.92(547.103475) = 503.335197
The day with the worst exchange rate is Wednesday, with a rate of 1:5.7012.
Converting 88.65£ at this rate,
88.65(5.7012) = 505.41138. 4
0.92(505.41138) = 464.9784696
The difference between Friday and Wednesday is:
503.335197-464.9784696 = 38.3567274, or 38.35.
Hence, Nate would receive about 38.35 more shekalim if he made his trade on the day with the most favorable exchange rate than if he made his trade on the day with the least favorable exchange rate.
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