Answers
[tex]\displaystyle=2\left(\sum_{i=1}^{10}i-\sum_{i=1}^2i\right)-9\left(\sum_{i=1}^{10}-\sum_{i=1}^21\right)[/tex]
Recall that
[tex]\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2[/tex]
[tex]\displaystyle\sum_{i=1}^n1=n[/tex]
so the above reduces to
[tex]2\left(\dfrac{10\cdot11}2-\dfrac{2\cdot3}2\right)-9\left(10-2\right)=32[/tex]
Related Questions
A 9 cm tall cone shaped paper cup can hold up to 58.9 cm cubed of water. What is the minimum amount of paper needed to make the paper cup, assuming no overlap in the paper? Use 3.14 for π.
Answers
To calculate the cone area we need to know the radius.
We do not have the radio, but we have the volume.
So:
r = √(3×V) / h
r = 4,431cm
Now we calculate the generatrix g.
If we make a lateral projection of the cone, we have a triangle whose height is h = 9cm. The base is the radius r = 4,431cm and the hypotenuse is the generatrix g.
So:
g = √(r ²+ h²)
g = 10.03cm
Finally the area of a cone is given by the formula:
A = pi × r ×(g + r)
A = 201.30 cm²
A rectangular floor space in a community center is 40 ft long and 32 ft wide. A volunteer is setting up chairs on the floor space. Each chair needs an area of approximately 4 ft by 5 ft.
Which estimate best approximates the number of chairs that can be set up on the floor space?
A. 20
B. 60
C. 260
D. 320
Answers
Answer:
60
Step-by-step explanation:
Just confirming for the K12 students ;)
I keep getting 70 but that's not an answer??
Betty's bite size candies are packaged in bags the number of candies per bag is normally distributed with a mean of 50 candies and a standard deviation of 3. At a quality control checkpoint a sample of bags is checked and 12 bags contain fewer than 47 candies how many bags were probably taken as samples?
a) 15
b) 75
c) 36
d) 24
Answers
A normal distribution, 68% of the sample falls within 1 standard deviation, which means 100-68 = 32 is out side the mean. Half of that, 32 / 2 = 16% is above and the other half (16%) would be below.
12 bags were below, so we would do a ratio, with the percentages as a whole number, so 16% = 16 and 100% = 100:
12/16 = X/100
Cross multiply: 16x = 1200
Divide both sides by 16:
X = 1200/16
X = 75
The answer is 75 bags were tested.
The Big Dipper ice cream store charges 25 cents for a cone and 75 cents for each scoop of ice cream added to the cone. What will a customer pay for a double dip ice cream cone?
Answers
Answer: $1.75
He wants technically 2 scoops of ice cream which is 0.75 + 0.75 = $1.50
He only wants 1 cone so thats $0.25
Final Total:
1.50 + 0.25 = $1.75
He will pay $1.75 for a Double Dip Ice Cream Cone!
Express the fraction in simplest form.
9/12
a.2/3
b.3/4
c.12/16
d.10/13
Answers
[tex]Answer:\ \boxed{b.\ \dfrac{3}{4}}[/tex]
Select the objects that hold the same amount of liquid as a 98 fluid ounce jug
Answers
1 cup = 8 fl oz
2 cups = 16 fl oz
1 pint = 2 cups, so 1 pint also equals 16 fl oz.
2 pints equal 1 quart, so 16 x 2 = 32 oz (the number of fluid ounces in a quart)
1 pint - 16 fl oz
1 quart = 32 fl oz
Choice A: 3 quarts x 32 =96 fl oz.
Choice B: 2 quarts x 32 = 64 fl oz
Choice C: 2 quarts x 32 + 2 pints x 16 = 64 + 32 (96 fl oz)
Choice D: 1 quart x 32 + 8 cups x 8 = 32 + 64 (96 fl oz)
Choice E: 2 cups x 8 + 2 pints x 16 = 16 + 32 (48 fl oz)
A recipe calls for 5 8 pound of cheese per batch. Assuming you have enough of the other ingredients, how many batches of the recipe can you make with 5 pounds of cheese?
Answers
Gary number has 6 in thousands and a7 in hundred and a 5 in ones. when rounded to the nearest ten, the number is 6760. what is gary's number
Answers
If a number is 5 or more, round up.
If a number is 4 or less, round down.
I hope this helps!
The Comegna family wants to build a human pyramid when they go to the beach this summer. They will put one person on top and add 2 more people for each descending row.
a. How many people will be in the seventh row?
PLEASE HELP!! the rest are in the attachment
Answers
a. Number of people in the seventh row will be as follows:
d=2
a1=1
n=7
thus the number of people in the 7th row will be obtained using the explicit formula:
an=a1+(n-1)d
a7=1+(7-1)2
a1=1+12
a1=13
b. Total number of people in 7 rows will be calculated using the formula:
sn=n/2(a1+an)
plugging in the values:
s7=7/2(1+13)
s7=7/2(14)
s7=49
c. Total number of people required to make 10 rows will be:
n=10
a1=1
a10=1+(10-1)2
a10=1+18
a10=19
thus
s10=10/2(1+19)
s10=100
It will take 100 children
d. To get the number of rows the Simpsons Pyramid had we shall use the explicit formula:
an=a+(n-1)d
d=4
a1=1
an=37
plugging in the values we get:
37=1+(n-1)4
solving for n:
36=4n-4
40=4n
n=10
thus the number of rows would be 10
e. Total number of people will be:
d=4
n=10
a1=1
Sn=n/2(a1+an)
Sn=10/2(1+37)
Sn=190
PART 2: Geometric sequence and series
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A radio station wants to determine whether its audience would like to listen to more rap music. It asks its listeners to call in and participate in a survey. Each listener is asked: “Do you want us to play more rap music or less rap music?” One hundred fifty listeners call in, and their responses are recorded.
What is the focus of the study?
The type of music listeners want to hear.
The playing of rap music.
The number of listeners who respond.
The response of the listeners.
Answers
A radio station made a survey of their listeners to determine whether the audience would like to listen to more rap music. They asked the question “Do you want us to play more rap music or less rap music?” The station recorded one hundred fifty listeners who call in.
The focus of the study is about the playing of the rap music because it is what the question is about. Not the type of music listeners want to hear, nor the number of listeners who respond nor the response of listeners.the response of listeners to give opinion on to play more or less rap music
Ed and Marge were candidates for the city council. Marge won with 93 more votes than Ed. The total number of votes cast in the election was 587. Find the number of votes received by each candidate.
Answers
so ed had 494 votes
I think it would be 494/2=247 votes
If y varies directly as x and y=12 when x=72, find x when y=9
Answers
648 ÷ 12 = 54
x = 54
Hope this helps :)
Change -40° to radians.
A). 2π/9
B). -2π/9
C). 4π/9
D). -4π/9
Answers
(-40°)[tex] (\frac{ \pi }{180} )= -\frac{2 \pi }{9} [/tex]
We can conclude that the correct answer is: B). -2π/9
if a crate contains 25,500 oz of rice , about how many kg does it contains ? 1 pound equals 16 oz & 1 pound equals 0.454 kg
351 kg
724 kg
25500 kg
185000 kg
Answers
Your problem statement tells you that both 0.454 kg and 16 oz are equal to a pound, so they are also equal to each other. Their ratio (with kg on top and oz on the bottom) is a suitable conversion factor.
[tex]25,500\,oz \times \dfrac{0.454\,kg}{16\,oz}=723.5625\,kg[/tex]
The best choice is ...
724 kg
To find the mass of 25,500 ounces of rice in kilograms, one needs to convert ounces to pounds, then pounds to kilograms. After the conversions, the crate contains approximately 724 kg of rice.
Explanation:To calculate the mass of 25,500 ounces of rice in kilograms, we first convert ounces to pounds and then pounds to kilograms using the conversion rates provided.
First, we need to find out how many pounds are equivalent to 25,500 ounces. We use the proportion 1 pound = 16 ounces.Divide the total number of ounces by 16 to find the number of pounds:Now, we'll convert pounds to kilograms: 1 pound = 0.454 kg.Multiply the number of pounds by the kilogram equivalent:When we round this number to the nearest whole number, we get 724 kg, which is the approximate mass of the rice in the crate.
what is the solution to the following system of equations (3x-4y=-25)( 3x+ 4y=5)? PLEASE HURRY!!!!!!!!!!!
Answers
substract the value of x to the second equation:
[tex]3\cdot\left(-\dfrac{10}{3}\right)+4y=5\\\\-10+4y=5\ \ \ |+10\\\\4y=15\ \ \ \ |:4\\\\y=\dfrac{15}{4}[/tex]
[tex]\left\{\begin{array}{ccc}x=-\dfrac{10}{3}\\\\y=\dfrac{15}{4}\end{array}\right[/tex]
Find the length of the third side of a right triangle with a hypotenuse of 17 and a leg of 10.
Answers
You need to use the Pythagorean theorem.
[tex]{a}^{2} + {b}^{2} = {c}^{2} [/tex]
The hypotenuse is "c" and each leg is either "a" or "b".
[tex] {10}^{2} + { x}^{2} = {17}^{2} [/tex]
[tex]100 + {x}^{2} = 289 \\ {x}^{2} = 189 \\ x = 13.7477270849[/tex]
A park in a subdivision has a triangular shape. Two adjacent sides of the park are 533 feet and 525 feet. The angle between the sides is 53 degrees. Find the area of the park to the nearest square foot.
Answers
Answer:
The area of the park is 1,11,739 square feet.
Step-by-step explanation:
Since, the area of a triangle is,
[tex]A=\frac{1}{2}\times s_1\times s_2\times sin\theta[/tex]
Where, [tex]s_1[/tex] and [tex]s_2[/tex] are the adjacent sides and [tex]\theta[/tex] is the included angle of these sides,
Here, the two adjacent sides of the park are 533 feet and 525 feet, while, the angle included by these sides is 53°.
That is, [tex]s_1[/tex] = 533 ft, [tex]s_2[/tex] = 525 ft and [tex]\theta[/tex] = 53°,
Hence, the area of the park is,
[tex]A=\frac{1}{2}\times 533\times 525\times sin 53^{\circ}[/tex]
[tex]=\frac{279825\times 0.79863551004}{2}[/tex]
[tex]=\frac{223478.181599}{2}=111739.090799\approx 111739\text{ square ft}[/tex]
what percentage does the third quartile represent?
Answers
HELP WHOEVER ANSWERS CORRECTLY WILL BE BRAINLIEST!!!!
Answers
7.25 x 9.5 x 2 = 137.75 gets the surface area of the two rectangle sides.
To get the bottom rectangle, do 8 x 9.5 = 76
To find the two triangles, do 6 x 8 x 0.5 x 2 = 48
Now add them all together: 137.75+76+48=261.75
So, the answer is 261.75 square feet of material.
Dylan opened a credit card account with $675.00 of available credit. Now that he has made some purchases, Dylan's account only has $384.75 of available credit. What is the percentage decrease of the amount of available credit in Dylan's account?
Answers
675-384.75=290.25
290.25/675=.43*100%=43%
Which expression is equal to sin 75°? sin 135° cos 60° – cos 135° sin 60° cos 135° cos 60° + sin 135° sin 60° sin 135° cos 60° + cos 135° sin 60° cos 135° cos 60° – cos 135° cos 60°?
Answers
Answer:
The answer is A
Maya is trying to break or tie the league record for home runs in her softball league. She solved the inequality mc019-1.jpg to find the minimum number of home runs she must average per week over the five remaining weeks of the season to break or tie the record. What error did Maya make when she chose this inequality to model the situation?
She chose the incorrect relation and should have solved 5x<30
She modeled “average” incorrectly and should have solved x/5<_30
She chose the incorrect relation and should have solved 5x_>30
She modeled “average” incorrectly and should have solved x+5<_30
Answers
Maya made an error in her chosen inequality by focusing on a minimum rather than the goal of breaking or tying the record. Assuming the record is 30, she should have used the inequality 5x >= 30, where x is the average number of home runs needed per week.
Explanation:It appears that Maya has made an error when she chose the inequality to model the situation. Since Maya is trying to break or tie the league record for home runs, she should be considering how many home runs she needs to hit in order to exceed or equal the current record, rather than considering a minimum. Her inequality should reflect the desired goal. If the league record is 30 home runs, for example, and there are 5 weeks left in the season, Maya might want to know how many home runs she must hit on average each week to break the record. Therefore, she should have solved the inequality 5x >= 30, where x represents the number of home runs she needs to hit on average each week.
Learn more about Mathematical modeling here:https://brainly.com/question/33446037
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if a train travels 25 miles in 2 hours and 15 minutes, what is it's average speed in miles per hour?
• 10 mph
• 11.1 mph
• 12.5 mph
• 9.1 mph
Answers
2 1/4 hours = 25 miles
1 hour = 25 ÷ 2 1/4 = 25 ÷ 9/4 = 25 x 4/9 = 11.1 miles
Answer: 11.1 mph
2. The robot was initially placed at position (6,9), and at = 2 seconds, its position is (10,15).
a. How far did the robot travel in 2 seconds?
b. What is the speed of the robot?
Could you work it out
Answers
what's its speed? well, it traveled √(52) in 2 seconds, so is simply √(52)/2, which is about 3.6 units per second.
GEOMETRY HELP 70 POINTS FAST!!!!!!!
FIND SURFACE AREA. IT’S OKAY IF YOU DID ONE BUT I WOULD PREFER IF YOU DID BOTH THANKS
Answers
9) Surface area = PI x 3 x (3+8.5) = 108.38 yd^2
Because you already have your radius but you need to find your hight. You use a triangle and do a^2+b^2=c^2 and that gives you 9.75. Then plug those two numbers into the surface area of a cone equation.
8)C
Because you need to find something the radius by dividing 18 by 2 which gives you 9. Then you need to find the hight which you make a triangle and do a^2+b^2=c^2 and that gives you 19.98. And plug those numbers into the surface area of a cone formula
The frequency of A4 is 440.00 Hz. What is the frequency of A6, which is two octaves above A4?
A) 110.00 Hz
B) 220.00 Hz
C) 880.00 Hz
D) 1760.00 Hz
Answers
Explanation:
The formula to find the unknown frequency is:
(2^n)*f
Where n = Number of octaves above to the known frequency (A4) = 2
f = Known frequency (of A4) = 440 Hz
Hence
(2^2)*(440)
1760 Hz (of A6)
Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain. Given XY = WZ and XW = YZ
a.
No; you cannot determine that the quadrilateral is a parallelogram.
b.
Yes; two opposite sides are both parallel and congruent.
c.
Yes; opposite sides are congruent.
d.
Yes; diagonals of a parallelogram bisect each other.
Answers
If both pairs of opposite sides of a quadrilateral are congruent, then you'll always have two opposite pairs of parallel sides. Congruent means that they measure the same. Since two congruent sides separating the other pair of opposite sides must always keep those opposite lines the same distance apart, then, the opposite sides are also parallel.
From the information provided a. No; you cannot determine that the quadrilateral is a parallelogram.
A parallelogram is a quadrilateral (has four sides and four angles) in which opposite sides are parallel and congruent to each other. The diagonals of a parallelogram bisect each other.
Given XY = WZ and XW = YZ, this means that the opposite sides are congruent.
Just from the information provides, we cannot determine that the quadrilateral is a parallelogram.
Find out more at: https://brainly.com/question/555469
what is the image of point (3,4) for mapping (x.y) , (x+4, y+6)
Answers
The total cost of a jacket and a pair of shoes was $99.15. if the price of the jacket was $5.81 less than the pair of shoes, what was the price of the jacket? express your answer as a simplified fraction or a decimal rounded to two places.
Answers
Then price of jacket would be x - 5.81
Combining the two would give you
x + x - 5.81 = 99.15
combining like terms simplifies to 2x - 5.81 = 99.15;
now adding 5.81 to both sides of the equal sign leaves
2x = 104.96
and finally, dividing both sides by 2, gives x = $52.48; which is the cost of the shoes. Recall, the cost of the jacket is 5.81 less than the cost of the shoes.
so, COST OF THE JACKET is 52.48 - 5.81 = $46.67
Final answer:
To find the price of the jacket, set up a system of equations with the given information and solve for the jacket's price. The final calculated price of the jacket is $46.67.
Explanation:
The total cost of a jacket and a pair of shoes was $99.15. The price of the jacket was $5.81 less than the pair of shoes. Let's denote the price of the jacket as j and the price of the shoes as s. The problem gives us the following system of equations:
1) j + s = $99.15
2) s = j + $5.81
By substituting equation 2 in equation 1, we get:
3) j + (j + $5.81) = $99.15
Simplify and solve for j:
4) 2j + $5.81 = $99.15
5) 2j = $93.34
6) j = $46.67
Therefore, the price of the jacket is $46.67, which is the answer rounded to two decimal places as the student requested.
Which choice is similar to the figure shown?
Answers
Take 45/30, you get 1.5. 1.5 x 20 = 30.
Hope I helped!