Answers
The value of the given summation is:
\(\sum (29a_i - 13b_i) ]= -30\)
How to find the sum?Here we know that the sums are:
\(\sum a_i = -10\\\\\sum b_i = -20\)
And we want to find the value of the sum:
\(\sum (29a_i - 13b_i)\)
First we can distribute the sum to get:
\(\sum 29a_i + \sum - 13b_i\)
And take the coefficients out of the sum:
\(29\sum a_i -13\sum b_i\)
Now replace the known values:
\(29\sum a_i -13\sum b_i = 29*-10 - 13*-20 = -290 + 260 = -30\)
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Related Questions
The Bobcats football coach logged the following yardage gains and losses over four plays of a game.
1. Gain 250 yards.
2. Gain 0.9y yards
3. Lose 12y yards
4. Lose 5.2x yards
What is the net yardage for these four plays?
Enter your answer as an expression, like this: 42x+53y
Answers
9.8x - 11.1x
Explanation:
25 - 5.2 = 9.8x
0.9 - 12 = -11,1y
Notice: I’m not sure but if it wrong, you could replaced with 10x - 11y which be better answer
The net yardage for these four plays is equivalent to Y[n] = 30.2x + 12.9y.
What is a expression? What is a mathematical equation? What is Equation Modelling? What are trigonometric functions?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have Bobcats football coach logged the following yardage gains and losses over four plays of a game.
1. Gain 25x yards.
2. Gain 0.9y yards
3. Lose 12y yards
4. Lose 5.2x yards
Assume that the net yardage for these four plays is equivalent to Y[n]. Then, we can write -
Y[n] = 25x + 0.9y + 12y + 5.2x
Y[n] = 30.2x + 12.9y
Therefore, the net yardage for these four plays is equivalent to Y[n] = 30.2x + 12.9y.
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The average value of a function f(x, y, z) over a solid region E is defined to be fave = 1 V(E) E f(x, y, z) dV where V(E) is the volume of E. For instance, if ???? is a density function, then ????ave is the average density of E. Find the average value of the function f(x, y, z) = 3x2z + 3y2z over the region enclosed by the paraboloid z = 4 − x2 − y2 and the plane z = 0.
Answers
Answer:
The average function \(f_{avg}\) value = 4
Step-by-step explanation:
Given that:
\(f(x,y,z) = 3x^2z+3y^2z\)
The enclosed region \(z = 4 -x^2 -y^2\) and the plane z = 0.
Over an area E, the average value of a function f(x,y,z) is:
\(f_{avg} = \dfrac{1}{V_{E}} \iiint_E f(x,y,z) dV ------ (1)\)
where;
\(V_E\) = volume of region E
To find the volume use cylindrical coordinates;
\(x=rcos \theta; \ \ \ y = rsin \theta; \ \ \ z = z\)
Then;
E = 0 ≤ r ≤2, 0 ≤ θ ≤ 2π, 0 ≤ z ≤ 4 - r²
\(V_E = \int^{2 \pi}_{0} \int^{2}_{0} \int^{4-r^2}_{0} \ rdzdrd \theta\)
\(V_E = \int^{2 \pi}_{0} \int^{2}_{0} r(4-r^2) \ drd \theta\)
\(V_E = \int^{2 \pi}_{0} \int^{2}_{0} (4r-r^3) \ drd \theta\)
\(V_E = \int^{2 \pi}_{0} \Big(2r^2- \dfrac{r^4}{4} \Big)^2_0 \ d \theta\)
\(V_E = 4(2 \pi)\\\\ V_E = 8 \pi\)
However, from equation (1):
\(f_{avg} = \dfrac{1}{V_E} \iiint_E f(x,y,z) \ dV \\ \\ = \dfrac{1}{8 \pi} \iiint_E (3x^2z + 3y^2 z) dV \\ \\ = \dfrac{1}{8 \pi } \int^{2 \pi}_{0} \int^{2 }_{0} \int^{4 - r^2}_{0} \ \ 3zr^2 \ rdzdrd\theta \\ \\ = \dfrac{3}{8 \pi} \int^{2 \pi}_{0} \int^{2 }_{0} \Big(\dfrac{z^2}{2}\Big)^{4-r^2}_{0} \ r^3 drd\theta \\ \\ = \dfrac{3}{16 \pi} \int^{2 \pi}_{0} \int^{2 }_{0} (4-r^2)^2 \ r^3 \ dr d\theta\)
\(= \dfrac{3}{16 \pi} \int^{2 \pi}_{0} \int^{2 }_{0} (16-8r^2 + r^4)r^3 \ dr d\theta \\ \\ = \dfrac{3}{16 \pi} \int^{2 \pi}_{0} \int^{2 }_{0} (16r^3 -8r^5 + r^7) \ dr d \theta \\ \\ = = \dfrac{3}{16 \pi} \int^{2 \pi}_{0} \Big (4r^4 - \dfrac{8}{6}r^6 + \dfrac{r^8}{8} \Big)^2_0 \ d \theta \\ \\ = \dfrac{3}{16 \pi } (2 \pi) \Big (64 - \dfrac{8}{6} \times 64 \times \dfrac{256}{8} \Big) \\ \\ = \dfrac{3}{16 \pi} (2 \pi) (\dfrac{32}{3}) \\ \\ = 4\)
I need it done very quick pls help
Answers
Complete the work shown to answer the question.
p2 – 14p – 72 = 0
p2 – 14p = 72
p2 – 14p + 49 = 72 + 49
Which describes the solutions of the equation?
Since 7 and 11 are both rational, the sum and difference are rational.
Since 14 and 11 are both rational, the sum and difference are rational.
Since 7 is rational and StartRoot 11 EndRoot is irrational, the sum and difference are irrational.
Since StartRoot 7 EndRoot is irrational and 11 is rational, the sum and difference are irrational.
i got the answer its a
Answers
Answer:
Since 7 and 11 are both rational, the sum and difference are rational.
Step-by-step explanation: It's A
Answer:
Since 7 and 11 are both rational, the sum and difference are rational.Step-by-step explanation: A
The measure of the angle is 17 times greater than its supplement.
Answers
Answer: supplement <17
Step-by-step explanation:
1. 17 is greater
2. supplement is smaller
A farmer purchased 225 acres of land for $4,700/acre. He paid 25% down and obtained a loan for the balance at 6.75% APR over a 20-year period. How much is the annual payment? (Simplify your answer completely. Round your answer to the nearest cent.)
Answers
The annual payment is $73416.96
\(- Total \ cost \ of \ the \ land $=\$ 225 \times 4700$$$=\$ 1057500$$Down payment $=0.25 \times 1057500$$$=\$ 264375$$so, loan amount $=\$ 1057500-264375$$$=\$ 793125$$\)
\(Present \ value,\ $P V=P M T\left[\frac{1-\left(1+\frac{r}{n}\right)^{-n t}}{\left(\frac{r}{n}\right)}\right]$$$P r=793125, r=0.0675 \text {, }$$$t=20$ years, $n=1$$$\therefore \quad P M T=\frac{P v}{\left[\frac{1-\left(1+\frac{r}{n}\right)^{-n t}}{\left(\frac{r}{n}\right)}\right]}$$$$=\frac{793125}{\left[\frac{1-\left(1+\frac{0.0675}{1}\right)^{-20}}{\left(\frac{0.0675}{1}\right)}\right]}$$$=73416.96$\\So, Annual payment $=\$ 73416.96$\)
What is down payment ?A down payment is the first down payment when buying an expensive good/service, such as a car or house. It is usually paid in cash or equivalent at the time of the transaction. Then some kind of loan is needed to finance the rest of the payment. The biggest advantage of a down payment is that it reduces the amount of the loan you need. If you borrow less, you pay less interest.
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Which fractions are equivalent to 6/8 ? Check all that apply.
1/4
2/8
4/16
3/4
12/16
Answers
Answer:
3/4
Step-by-step explanation:
you got to find the half of the number
The hundreds digit of my number is less
than the tens digit. The ones digit is greater than
the tens digit. What could my number be?
Answers
Answer:
Step-by-step explanation:
6 7 8 is one possibility
789 is another choice.
123 even works.
So how many numbers are there like this?
You can't have 0 in the 100s place and you can't have 8 0r 9
So there are 7 numbers 1 2 3 4 5 6 7 possible choices for the hundreds.
You can't 0 in the tens place nor 1 nor 9
You can't have 0 or 1 or 2 in the units place
In all I think you could write 84 such numbers.
Antonio needs 3.5 liters of water for an experiment.
He has 1.375 liters.
How much more water does Antonio need?
Answers
Answer:
2.125
Step-by-step explanation:
3.5-1.375=2.125
Solve for x. 6x-10≤8 or 1/3x+6>12 PLEASE HELP and show work
Answers
The value of x in 1st equation is x ≤ 3 i.e. x ∈ (-infinity,3] and the value of x in 2nd equation is x > 18 i.e. x ∈ (18,infinity)
Given two equations 1)6x-10<8 and 2) \(\frac{x}{3}\)+6 > 12
Solving the above equations
1) 6x-10≤8
⇒6x ≤ 18
⇒X≤ 3
⇒x ≤ 3 i.e. x ∈ (-infinity,3]
2)\(\frac{x}{3}\)+6 > 12
⇒\(\frac{x}{3}\) > 6
⇒x>18
⇒ x > 18 i.e. x ∈ (18,infinity)
Therefore,The value of x in 1st equation is x ≤ 3 i.e. x ∈ (-infinity,3] and the value of x in 2nd equation is x > 18 i.e. x ∈ (18,infinity)
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if you can get 3 pints of raspberries for $12.00 how many pints can you get per dollar
Answers
Answer:
0.25 pints of raspberries do you get per dollar
the driveway in front of the brown house is 35 feet long and the driveway of the red house is 7 yards and 9 feet long. which house has a long driveway? by how much
Answers
Answer:
The brown house has the longer driveway
Step-by-step explanation:
So we would need to convert both of these units of measurements to feet in order to compare them.
There are 3 feet in 1 yardConverting yards to feet, wee need to multiply the number of yards by 3
7 yards = 21 feetSince the red house has a driveway of 7 yards and 9 feet, we can rewrite this to 21 feet + 9 feet, which is equivalent to 30 feet
Now comparing the two driveways, the 35 ft-long brown driveway is 5 feet longer than the 30 ft-long red driveway.
The brown house has the longer driveway
The units of an item available for sale during the year were as follows: Jan. 1 Inventory 50 units at $124 Mar. 10 Purchase 60 units at $132 Aug. 30 Purchase 20 units at $138 Dec. 12 Purchase 70 units at $142 There are 80 units of the item in the physical inventory at December 31. The periodic inventory system is used. Determine the ending inventory cost and the cost of goods sold by three methods. Round interim calculations to one decimal and final answers to the nearest whole dollar. blank Cost of Ending Inventory and Cost of Goods Sold Inventory Method Ending Inventory Cost of Goods Sold First-in, first-out (FIFO) $fill in the blank 1 $fill in the blank 2 Last-in, first-out (LIFO) fill in the blank 3 fill in the blank 4 Weighted average cost fill in the blank 5 fill in the blank 6
Answers
Ending Inventory Cost and Cost of Goods Sold using different inventory methods:
FIFO Method:
Ending Inventory Cost: $11,920
Cost of Goods Sold: $15,068
LIFO Method:
Ending Inventory Cost: $11,996
Cost of Goods Sold: $15,123
Weighted Average Cost Method:
Ending Inventory Cost: $11,974
Cost of Goods Sold: $15,087
Using the FIFO (First-In, First-Out) method, the cost of the ending inventory is determined by assuming that the oldest units (those acquired first) are sold last. In this case, the cost of the ending inventory is calculated by taking the cost of the most recent purchases (70 units at $142 per unit) plus the cost of the remaining 10 units from the March 10 purchase.
This totals to $11,920. The cost of goods sold is calculated by taking the cost of the units sold (50 units from the Jan. 1 inventory at $124 per unit, 60 units from the March 10 purchase at $132 per unit, and 20 units from the August 30 purchase at $138 per unit), which totals to $15,068.
Using the LIFO (Last-In, First-Out) method, the cost of the ending inventory is determined by assuming that the most recent units (those acquired last) are sold first. In this case, the cost of the ending inventory is calculated by taking the cost of the remaining 10 units from the December 12 purchase, which amounts to $1,420, plus the cost of the 70 units from the August 30 purchase, which amounts to $10,576.
This totals to $11,996. The cost of goods sold is calculated by taking the cost of the units sold (50 units from the Jan. 1 inventory, 60 units from the March 10 purchase, and 20 units from the August 30 purchase), which totals to $15,123.
Using the Weighted Average Cost method, the cost of the ending inventory is determined by calculating the weighted average cost per unit based on all the purchases. In this case, the total cost of all the purchases is $46,360, and the total number of units is 200.
Therefore, the weighted average cost per unit is $231.80. Multiplying this by the 80 units in the physical inventory at December 31 gives a total cost of $11,974 for the ending inventory. The cost of goods sold is calculated by taking the cost of the units sold (50 units from the Jan. 1 inventory, 60 units from the March 10 purchase, and 20 units from the August 30 purchase), which totals to $15,087.
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which formula represents this sequence
Answers
Answer:
pretty sure its b
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
SOS PLS HELP
A machine that drills holes for wells drilled to a depth of
-72 feet in one day (24 hours).
At this rate, how many hours will it take until the drill
reaches its final depth of -132 feet?
Answers
Answer:
20 hours
Step-by-step explanation:
If the machine drilled 72 feet in 24 hours, we can divide 72 by 24 to find out that the machine drilled 3 feet in one hour.
Next, you must find the distance that must be traveled. You can do this by subtracting 72 from 132. You will get 60
So, if the machine drilled at 3 feet per hour, and it needs to drill 60 feet, it will take 20 hours because 60 divided by 3 is 20.
My cookbook's pancake recipe states that it makes 12 standard sized pancakes. The nutritional information says 2 pancakes is a serving containing 150 calories. For breakfast, I prepared half a recipe, but made smaller sized pancakes, so ended up preparing 8 pancakes. I ate 4 of them. How many calories did I consume?
Answers
Answer:
225 calories
Step-by-step explanation:
1 recipe makes
12 standard sized pancakes
2 pancakes are 1/6 of the recipe
1/6 of the recipe has 150 calories
6 × 150 calories = 900 calories
The full recipe of 12 pancakes has 900 calories
1/2 recipe was made
1/2 recipe has 1/2 × 900 calories = 450 calories
1/2 recipe made 8 pancakes
4 pancakes are half of the half recipe or 1/4 recipe
1/4 × 900 calories = 225 calories
True or False: A triangle can be formed with sides 3inches, 3inches, 6inches. Explain your choice.
Answers
Answer: It's true because 3+3+6 = 12 and a triangle has 3 sides and 12/3 is 4 that's why a triangle can be fored with these measurments.
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
It would be classified as an isosceles triangle.
Hope this helps!
I don’t understand this question can you also help me figure it out step by step I would greatly appreciated it
Answers
Answer:
If a shape is a square, then it is a quadrilateral
Step-by-step explanation:
Quadrilateral means four sided shape, so automatically, because a square has 4 sides, you know it is a quadrilateral. But not all quadrilaterals are a square, you could have a rectangle which is four sides so you know that this statement is wrong "If a shape is a quadrilateral, then it is a square." Therefore, the answer is "If a shape is a square, then it is a quadrilateral
10. The set of prime numbers greater than 11 with the cardinality of 5.
Answers
The set of prime numbers greater than 11 with the cardinality of 5 is {13, 17, 19, 23, 29}
How to determine the setFrom the question, we have the following parametes that can be used in our computation:
Set = prime numbers
Cardinality = 5
The cardinality implies that the number of elements in the set is 5
5 prime numbers greater than 11 are 13, 17, 19, 23, 29
Hence, the set is {13, 17, 19, 23, 29}
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can anyone help me out with this question
Answers
Answer:
\( \sf \: b) \: 45\)
Step-by-step explanation:
The values given are,
→ u = 7
→ d = 10
→ e = 3.2
Now the expression is,
→ 15(d - u)
Evaluating the expression,
→ 15(d - u)
→ 15(10 - 7)
→ 15 × 3
→ 45
Hence, option (b) is correct.
Answer:45
Step-by-step explanation:
15(10-7)
15(3)
multiply and get 45
lender requires a minimum down payment of 18% of the value of the home. You have $29,000 cash available to use as a down payment toward a home. Determine the maximum home value that you can finance.
Answers
The maximum home value that can be financed is approximately $35,365.85.
Let's represent the maximum home value that can be financed by H.
If the minimum down payment is 18%, the amount financed is 100% - 18% = 82%.
Therefore, we have:
H × 82% = $29,000
Multiplying both sides by (1/82%), we get:
H = $29,000 / 82%
= $35,365.85
Hence, the maximum home value that can be financed is approximately $35,365.85.
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If you estimate that a piece of wood measures 5.5cm if it actually measures 5.62cm what is the percent error of the estimate
Answers
The percent error of the estimate is -2.14%
How to determine the percent error of the estimate?In this question, the figures are given as
Estimate = 5.5 cm
Actual = 5.62 cm
The percentage of the error is then calculated using the following equation
Error percentage = (Estimate - Actual)/Actual * 100%
Substitute the known values in the above equation, so, we have the following representation
Error percentage = (5.5 - 5.62)/5.62 * 100%
Evaluate
Error percentage = -2.14%
Hence, the error percentage is -2.14%
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12. What is the value of the following expression when
a = -2 and b = -4?
5(4a3b)+ ab
A-108
B -92
C -12
D12
E 28
Answers
Answer:
1st one is b. 2nd one is A
Step-by-step explanation:
i did the quiz
50 Points! Multiple choice algebra question. Solve e^x>2.7. Photo attached. Thank you!
Answers
\(e^x > 2.7\\\ln e^x > \ln 2.7\\x\ln e > \ln 2.7\\x > \ln 2.7\approx0.9933\\\)
Therefore B.
SHARE 300 USING 2:3:5
Answers
If we divide 300 into parts using the ratio 2:3:5, we get:
2 parts = 2/10 of the total ratio = 2/10 x 300 = 60
3 parts = 3/10 of the total ratio = 3/10 x 300 = 90
5 parts = 5/10 of the total ratio = 5/10 x 300 = 150
Therefore, 300 divided in the ratio 2:3:5 would result in three parts of 60, 90, and 150.
I hope I helped!
~~~Harsha~~~
Based on the true statement above, is the following argument valid as part of a proof?
Two lines are perpendicular; therefore, they intersect to form right angles.
Answers
Answer:
yep it is correct lolhbkfy
Robert has 26 coins that are all nickels and dimes. The value of the coins is $1.85. How many of each does he have?
Answers
Answer:
he has 11 dimes and 15 nickels
Step-by-step explanation:
i kept going down reducing the amount of dimes and adding to the amount of nickels and found that 11 dimes is $1.10 and 15 nickels is $0.75
Finding Missing Angles in a Polygon
Answers
Answer:
\(\huge\boxed{\sf x = 130\°}\)
Step-by-step explanation:
Statement:In a quadrilateral (four sided polygon), the interior angles add up to 360 degrees.The angles with a small square on it represents 90 degrees.Solution:So,
90 + 90 + 50 + x = 360
230 + x = 360
Subtract 230 from both sidesx = 360 - 230
x = 130°\(\rule[225]{225}{2}\)
what is the opposite integer -6
Answers
The absolute value of a number is the distance of the number from zero without regard for the sign. Note that for negative numbers the opposite and absolute values are identical
So your answer is basically 6
Given rhombus ABCD, find the area if mZABC = 60° and AE = 2.
Answers
The area of the rhombus, obtained from the dimensions, of the diagonals, found from the trigonometric of sines of the angle can be presented as follows;
Area = 8·√3
What is the area of a plane figure?The area of a plane figure is the two dimensional space occupied by the figure on a plane.
The measure of the angle ABC, m∠ABC = 60°
The length of the segment AE = 2 units
The diagonals of a rhombus bisect each other at right angles, and the right angles through which they pass, therefore;
BE = ED, m∠AEB = 90°
m∠ABE = 30°
sin(30°) = AE/AB
sin(30°) = 2/AB
AB = 2/(sin(30°)) = 4
AB = 4
BE = √(4² - 2²) = √(12) = 2·√3
Therefore; AC = 2 + 2 = 4
BD = 2·√3 + 2·√3 = 4·√3
The area of a rhombus = (1/2) × The product of the length of the diagonals
Therefore;
Area of the rhombus = (1/2) × (4·√3) × 4 = 8·√3
The area of the rhombus = 8·√3
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