The sum of the whole numbers from 1 to 680 is 231540.
What is the sum of the whole numbers from 1 to 680?Arithmetic sequence is a list of numbers where each number is equal to the previous number, plus a constant called the common difference.
The formula for sum of first n numbers can be expressed as;
Sₙ = (n/2)( a₁ + aₙ )
Where n is the number of terms, a₁ is the first term and aₙ is the nth term.
Given that,
The numbers are whole numbers from 1 to 680
Number of terms n = 680First term a₁ = 1680th term a₆₈₀ = 680Sum S₆₈₀ = ?Plug the given values into the equation above.
Sₙ = (n/2)( a₁ + aₙ )
S₆₈₀ = (680/2)( 1 + 680 )
S₆₈₀ = 340( 681 )
S₆₈₀ = 231540
Therefore, the sum of the whole numbers from 1 to 680 is 231540.
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Victor wants to learn to snowboard. He went to Snowy Ridge Mountain and rented a snowboard for $35, then took 5 hours of group snowboarding lessons. Victor paid $175 in all.
Which equation can you use to find how much Snowy Ridge charges, x, for each hour of group snowboarding lessons?
Answer: They charge $28 per lesson the Equation is 35 + 5x = $175
Step-by-step explanation: He rented the snowboard for $35 and then took 5 hours of snowboarding lessons. Then the whole thing cost $175.
A plot of land is in the shape of a triangle
If one side is x meters, a second side is
(2x - 4) meters and a third side is
(4x - 5) meters, express the perimeter of
the lot as a simplified expression in x.
Answer:
7x-9
Step-by-step explanation:
P=x+(2x-4)+(4x-5)
P= x+2x-4+4x-5
P =x+6x-9
P =7x-9
P is perimeter
If the mean of 9 score is 4.5 what must the 10th score be for the mean of all score to be 5
The 10th score should be 9.5 for the mean to be 5.
What is mean value ?The mean value is the average value of the given data.
According to the given question the mean of 9 score is 4.5 what must the 10th score be for the mean of all score to be 5.
The total average score for 9 games is
= ( 9 × 4.5 )
= 40.5.
The total average score for the mean to be 5 in 10 games is
= ( 10 × 5 )
= 50.
∴ The 10th score must be ( 50 - 40.5 ) which is
= 9.5.
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Substitute the given values into the formula, and solve for the unknown variable. A=bh
b=10 A=70
Answer:
h = 7
Step-by-step explanation:
We are given the equation A=bh , and need to work out the unknown variable .
So we substitute the values of A and b given :
70 = (10)(h)
70 = 10 × h
Divide both sides by 10 :
70 ÷ 10 = h
h = 7
Hope this helped and have a good day
Which equation is true when c = 3?
2c + 8 = 31
35 − 5c = 32
9 − 6c = 0
4c + 8 = 20
Answer:
4c + 8 = 20
Step-by-step explanation:
To find which equation is true, we have to plug 3 into x in each equation.
2c + 8 = 31
Plug in 3 into c
2(3) + 8 = 31
6 + 8 = 31
14 = 31
Since 14 doesn't equal 31, this equation isn't true.
35 − 5c = 32
Plug in 3 into c
35 − 5(3) = 32
35 - 15 = 32
20 = 32
Since 20 doesn't equal 32, this equation isn't true.
9 − 6c = 0
Plug in 3 into c
9 − 6(3) = 0
9 − 18 = 0
-9 = 0
Since -9 doesn't equal 0, this equation isn't true.
4c + 8 = 20
Plug in 3 into c
4(3) + 8 = 20
12 + 8 = 20
20 = 20
Since 20 equals 20, this equation is true.
Have a lovely rest of your day! :)
-1+(-3) is blank units from -1 in the blank direction
-1+(-3) is 3 units from -1 in the left direction
-1+(-3) is blank units from -1 in the blank direction
-4 is 3 units from -1 in the left direction
because we know that
in the real line if we go 3 units in left from -1 we get -4
since in the real number line
the pattern is ................ - 5, -4, -3, -2, -1 ,0,1,2,3,4,5,............
thus we get
-1+(-3) is blank units from -1 in the blank direction
-4 is 3 units from -1 in the left direction
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In the figure below, m1=3x° and m2 = (x+18)°.
Find the angle measures.
L
2
m 21 =
m2 2 =
Answer: m 21=
I got it right on test!
Step-by-step explanation:
square root 147 simplified
Answer:
7√3
Step-by-step explanation:
Answer and how to solve this
Answer: Marie ran 4.5 miles on Monday.
Step-by-step explanation: 5.7
+1.2
6.9
Find the volume of the cylinder. Find the volume of a cylinder with the same radius and double the height.
The volumes of the cylinder are 565. 56 cubic inches and 1131. 12 cubic inches respectively.
How to determine the volumeThe formula for volume of a cylinder is expressed as;
Volume = πr²h
Where;
r is the radius = 6 Inh is the height = 5 InSubstitute the values
Volume = 3. 142 × 6² × 5
Volume = 3. 142 × 36 × 5
Volume = 565. 56 cubic inches
If the height is doubled, h = 2 × 5 = 10
Substitute the values
Volume = 3. 142 × 6² × 10
Volume = 3. 142 × 36 × 10
Volume = 1131. 12 cubic inches
Thus, the volumes of the cylinder are 565. 56 cubic inches and 1131. 12 cubic inches respectively.
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A rectangular piece of metal is 15 in longer than it is wide. squares with sides 3 in long are cut from the four
corners and the flaps are folded upward to form an open box. if the volume of the box is 1782 in2, what were the
original dimensions of the piece of metal?
The original dimensions of the piece of metal are 39 inch by 24 inches.
Let the breadth of the rectangular piece be b inches.
Hence, according to the data given in the question,
Length of the rectangular piece will be (b + 15) inches.
After 4 squares of 3 inches each are cut from the corners of the rectangular piece, the length and breadth of the piece becomes:-
Length = b + 15 - 3 - 3 = (b + 9) inches
Breadth = b -3 -3 = (b - 6) inches
The height of the subsequent open box made will be 3 inches.
We have,
Volume of the cuboidal open box = 1782 cubic inches.
Also, we know that,
Volume of cuboid = l*b*h
Where,
l is the length,
b is the breadth, and
h is the height
Hence,
(b+9)(b-6)(3) = 1782 cubic inches
(b+9)(b-6) = 1782/3 = 594
We can write 594 as 33*18
Hence,
(b+9)(b-6) = 33*18
b+9 = 33 or b-6 = 18
b = 33-9 = 18+6 = 24
Hence, the original dimensions are :-
b + 15 = 24 + 15 = 39 inches, and
b = 24 inches
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Classify the angle as acute , obtuse , right , or straight
Answer:
1. straight
2. right
3. obtuse
4. acute
Step-by-step explanation:
What is the value of 1/4(38-14)+3^3 divided by 9?
Answer:
9
Step-by-step explanation:
[tex]38-14\\\bold{24}\\\rightarrow 1\div \:4\cdot \:24+3^3\div \:9\\3^3\\\bold{27}\\\rightarrow 1\div \:4\cdot \:24+27\div \:9\\1\div \:4\cdot \:24\\\frac{1}{4}\cdot \:24\\\bold{6}\\\rightarrow 6+27\div \:9\\27\div \:9\\\bold{3}\\6+3\\=9[/tex]
write the following sets is roster from and set-builder form 1. set A is the set of the whole numbers less than 5. 2. set B is the set of prime numbers. 3. set C is the set of months that starts with "J". 4. set D is the set of composite numbers less than 10. 5. set E is the set of vowel letters in the word "rhythm".
Answer:
The answer are given below:
Step-by-step explanation:
1. Roaster form
A={0,1,2,3,4}
Set builder form
A={x: x⊂ w, x<5}
2.
Roaster form
B={2,3,5,7,11,13,17,.................}
Set builder form
B={x: where x is a prime number}
3.
Roaster form
C={jan ,june ,july }
Set builder form
C={x: x is month starting with "J" }
4.
Roaster form
D={4,6,8,9}
Set builder form
D={x: where x is a prime number, x<10}
5.
Roaster form
E={null}
Set builder form
E={x: x is null}
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Which is the order from least to greatest of the following: four thirds, 0.8, one fifth, thirty percent?
four thirds, 0.8, one fifth, thirty percent
thirty percent, four thirds, 0.8, one fifth
one fifth, four thirds, thirty percent, 0.8
one fifth, thirty percent, 0.8, four thirds
The order from least to greatest of the numbers will be D. one fifth, thirty percent, 0.8, four thirds.
How to calculate the value?It should be noted that 1/5 = 0.2
It should be noted that 30% = 0.3
It should be noted that 4/3 = 1.33
Therefore the order from least to greatest of the numbers will be one fifth, thirty percent, 0.8, four thirds
In conclusion, the correct option is D.
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5a + 2b = 40 solve for b
Answer:
5a-40=-2b
5a-40/-2=-2b/-2
-5a/2+20=b
The volume, in cubic centimeters, of a fish tank is represented by the polynomial model V(x)=36x^2-3.75x^3. What is the maximum volume of the fish tank?
A. 384.00 cubic centimeters
B. 333.83 cubic centimeters
C. 472.85 cubic centimeters
D. 491.52 cubic centimeters
Answer:
D. 491.52
Step-by-step explanation:
It rained a total of 10 inches in a week. the first day it rained 6 inches, then it rained 2/3 every day after that. how many more days did it rain for?
Solving the given fraction, we get that It will rain for 1 day more, that means a total of 2 days.
According to the question, first day it rained 6 inches. Then it rained 2/3 every day after that. Solving the fractions, we get that second day it will rain,
(6 × 2/3) = 4 inches as it rained 2/3 every day after that .
So, it rained a total of, 6 + 4 inches = 10 inches in a week.
We have been given that it rained a total of 10 inches in a week. While solving the fraction, we found that it rained for 10 inches in just days, 6 inches in a day and 4 inches the other day. This tells us that it will not rain for the remaining 5 ( 7 - 2 ) days.
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Polygon L is a scaled copy of Polygon K
What is the value of J ?
The value of j in the scaled copy in the polygon is: 0.03.
How to Find the Sides of a Scaled Copy?When a figure is scaled, the corresponding dimensions of the new and original figures have a ratio that is the same because they are proportional to each other.
Polygon K and polygon L are similar polygons and therefore their corresponding side lengths are proportional. The ratio below would be created:
j/0.5 = 0.18/3
Cross multiply
j = (0.5 × 0.18)/3
j = 0.09/3
j = 0.03
Therefore, the value of j in the scaled copy in the polygon is: 0.03.
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which linear inequality will have a solution of (0,0)
a. y<-2x
b. y<-3x+4
c. y>-2x+6
d. y>-3x
The linear inequality will have a solution of (0,0) is y<-2x and y>-3x.
Option (A) and (D) is correct.
What is inequality?
The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.
Given:
Linear inequalities are the expressions where any two values are compared by the inequality symbols such as, '<', '>', '≤' or '≥'. These values could be numerical or algebraic or a combination of both.
According to given question we have
a. y<-2x
To put the value of x any y (0,0) we get
=0<-2*0
=0<0
b. y<-3x+4
To put the value of x any y (0,0) we get
=0<-3*0+4
=0<0+4
=0<4
c. y>-2x+6
To put the value of x any y (0,0) we get
=0>-2*0+6
=0>0+6
=0>6
d. y>-3x
To put the value of x any y (0,0) we get
=0>-3*0
=0>0
Therefore, the linear inequality will have a solution of (0,0) is y<-2x and y>-3x.
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An ice cream factory makes 100 quarts of ice cream in 5 hours. How many quarts could be made in 36 hours?
Answer:
They can make 720 quarts in 36 hours.
Step-by-step explanation:
First we set up a ratio of 100 quarts:5 hours since that is a given ratio. Since hours was in the denominator of the ratio before, we place the 36 in the denominator of the other ratio, x quarts: 36 hours.
Setting them equal gives the following proportion:
100/5=x/36
Cross multiply to solve:
5x=3600
x=720
Answer:
720
Step-by-step explanation:
100 divided by 5 =20 and 20 times 36 is 720 hope this helped
show your work for -4x+3(2x-5)=31
Step-by-step explanation:
[tex] - 4x + 3(2x - 5) = 31 \\ - 4x + 6x - 15 = 31 \\ 2x - 15 = 31 \\ 2x = 31 + 15 \\ 2x = 46 \\ x = 46 \div 2 \\ x = 23[/tex]
I need help with example 9 please
Answer:
a reflection across the y-axis and a translation up of 4
Step-by-step explanation:
A rectangular bathroom mirror has a perimeter of 24 feet and an area of 20 square feet. What are the dimensions of the mirror?
A rectangular bathroom mirror having a perimeter of 24 feet and an area of 20 square feet, The length and breadth of rectangle are 10 feet and 2 feet respectively.
Given,
perimeter of the rectangle = 24 feet
area of rectangle = 20 sq. feet
Formula of perimeter of rectangle = 2(L + B)
where L = length of the rectangle , Breadth of the rectangle.
⇒ 24 = 2(L + b)
⇒ 12 = L + B
⇒ L = 12 - B ........(1)
Formula of area of rectangle = L × B
⇒ 20 = L × B
⇒ L = 20 / B .......(2)
From (1) and (2)
equating two equations,
12 - B = 20 / B
⇒ 12B = 20 + B²
⇒ B² - 12B + 20
On solving,
⇒ B = 10, 2
So, the Length and breadth of rectangle are 10 feet and 2 feet
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witch equation is true when x=4? A 3X+4=8 B 5X-2=18 C 2X+8=40 D 4X+4=12
Answer:
5X - 2 = 18
Step-by-step explanation:
5 x 4 = 20
20 - 2 = 18
Which length of time is between 10.55 pm and 1.20 am?
A 1h 25 min
B 2h 15 min
C 2h 25 min
D 3h 25 min
From 10:55 pm to 11:00 pm, 5 minutes have elapsed.
From 11 pm to 12:00 pm, 60 minutes have elapsed, and from 12:00 pm to 1:00 am, another 60 minutes have elapsed, from 1:00 am to 1:20 am, 20 minutes have elapsed plus.
x = 5m ➕ 60m ➕60m ➕ 20 mx = 145 minutesIn the 145 minutes, there are 2 hours and 25 minutes.
Answer: From 10:55 pm to 1:20 a.m there is a time period of 2 hours and 25 minutes. Correct alternative is "C".
Skandar
The length of a rectangle is four times its width.
If the perimeter of the rectangle is 70 yd whats the length and width
Answer:
length is 20 width is 5
Step-by-step explanation:
35
5 20
help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help help
Answer:
1. (2x + 1) (x - 4)
2. (3y +2 ) (y + 1)
3. (w - 3) (3w + 5)
4. (4s - 1) (s + 7)
5. (x + 5) (2x - 3)
Step-by-step explanation:
Lots of good articles on factoring quadratics - that is what this is called.
Answer:
1. (2x + 1) (x - 4)
2. (3y +2 ) (y + 1)
3. (w - 3) (3w + 5)
4. (4s - 1) (s + 7)
5. (x + 5) (2x - 3)
Step-by-step explanation:
the price for 15 boxes of pencils is $67. The price for 34 boxes is $143. by how much does the cost increase for each additonal box of pencils purchased?
Answer:
$0.3
Step-by-step explanation:
Cost of one box in a set,
→ 67/15
→ 4.47 = $4.5
Cost of one box in another set,
→ 143/34
→ 4.205 = $4.2
The cost increase for each extra box,
→ 4.5 - 4.2
→ $0.3
Hence, the answer is $0.3.
Use technology to c ompute the standard deviation for the following sample data. 32, 41, 36, 24, 29, 30, 40, 22, 25, 37
The standard deviation is provided by this. = 6.7528
What role does standard deviation play?Because it aids in comprehending measurements whenever the data is distributed, the standard deviation is significant. The standard deviation of the data will be higher the more evenly distributed the data is.
According to the given data:sample data = ( 32, 41, 36, 24, 29, 30, 40, 22, 25, 37)
To find mean of the given data:
Mean = Sum of items/ Count items
Mean = (32 + 41 + 36 + 24 + 29 + 30 + 40 + 22 + 25 + 37 / 10)
= 31.6
now finding the variance:
First we Add All the sample:
32 + 41 + 36 + 24 + 29 + 30 + 40 + 22 + 25 + 37 = 316
make Square of the solution:
316*316 =99856
and multiply by how many items there are. We have 10 items.
=99856/10
= 9985.6
For the time being, put this number aside.
Take your original set of numbers from Step 1 and square each one this time on its own.
32² + 41² + 36² + 24² + 29² + 30² + 40² + 22² + 25² + 37² = 10396
Subtract the sum from Step 2 from of the sum from Step 3.
10396 - 9985.6 = 410.4
The items in someone data set is reduced by 1 by.10 - 1 = 9
Divide the result of Step 4 even by result of Step 5. You get the variation from this.
410.4 / 9 = 45.6
Your response from Step 6 should be squared. The standard deviation is provided by this.
6.7528
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I understand that the question you are looming for is:
For the following sample data, compute the variance and the standard deviation. 32, 41, 36, 24, 29, 30, 40, 22, 25, 37