Answer:
1 < x ≤4
Step-by-step explanation:
3 < 2x + 1 ≤9
Solve for x
Subtract 1 from all sides
3-1 < 2x + 1-1 ≤9-1
2 < 2x ≤8
Divide by 2
2/2 < 2x/2 ≤8/2
1 < x ≤4
help I'm practicing
Answer:
The total surface area is;
[tex]336\text{ }ft^2[/tex]Explanation:
Given the square pyramid as show in the attached image.
The total surface area is the sum of the area of the base square and the area of the four triangles.
[tex]A=l^2+4(\frac{1}{2}lh)[/tex]Given;
[tex]\begin{gathered} l=12\text{ ft} \\ h=8\text{ ft} \end{gathered}[/tex]substituting the given values;
[tex]\begin{gathered} A=l^2+4(\frac{1}{2}lh) \\ A=12^2+4(\frac{1}{2}\times12\times8) \\ A=144+192 \\ A=336\text{ ft}^2 \end{gathered}[/tex]Therefore, the total surface area is;
[tex]336\text{ }ft^2[/tex]A random sample of n = 50 teachers was selected from a Local Government and it has been established that 30% of the entire teachers are ghost workers and 70% are real workers. Determine the expected number of the real workers in any sample of size 50?
The expected number of the real number in any sample size is 150.
What is sample size?
In statistics, the sample size refers to the group of people whose data is analyzed during calculation. Depending upon the constraints, the data is analyzed for the measurement. The analysis of samples is perform with the help of Binomial distribution.
According to the question, the given random sample can be solved with the help of Binomial distribution:
The sample size of teachers: n = 50
Percentage of ghost workers: 30%
Percentage of real workers: 70%
For ghost workers: n = 50 and p = 0.31 and q = 1 - p = 1 - 0.31 = 0.69
Now, to calculate the expected number of the real workers as per given samples:
For real workers: n = 50 and p = 0.70 and q = 1 - p = 1 - 0.70 = 0.30
Expected number is: (n)(q) = (50)(0.30) = 150
Hence, the expected number of the real number in any sample size is 150.
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8. A car costs $10,500, and you're offered a loan that requires $800 down and a monthly payment of $187.53 for 60 months, how much will you pay in interest? Round your answer to the nearest dollar.$
The Solution:
Given that a car that cost $10500 was offered as a loan with a down payment of $800.
This means the loan balance will now be:
[tex]\text{Loan baleance=10500-800= \$9700}[/tex]The loan payment plan is a monthly payment of $187.53 for 60 months.
[tex]\text{Total Payment=187.53}\times60=\text{ \$11251.80}[/tex]We are required to find how much was paid in interest.
We shall take the difference between the total payment and the loan balance.
[tex]\begin{gathered} \text{Interest paid=Total payment-Loan balance} \\ \text{Interest paid=11251.80-9700= \$1551.80}\approx\text{ \$1552} \end{gathered}[/tex]Therefore, the correct answer is $1552
Convert each slope-intercept or point slope equation into standard form.
y - 3 = 1/5(x + 6)
The Standard form of the equation will be;
⇒ x - 5y = -21
What is Standard form of equation?
The standard form of the equation is defined as;
Ax + By = C
Where, A, B and C are integers.
Given that;
The equation in slope - intercept form as;
⇒ y - 3 = 1/5 (x + 6)
Now,
We convert the equation in standard form as;
Since, The equation in slope - intercept form as;
⇒ y - 3 = 1/5 (x + 6)
Change into standard form as;
⇒ y - 3 = 1/5 (x + 6)
Multiply by 5 both side, we get;
⇒ 5( y - 3) = (x + 6)
⇒ 5y - 15 = x + 6
Add 15 both side, we get;
⇒ 5y - 15 + 15 = x + 6 + 15
⇒ 5y = x + 21
Subtract 21 both side, we get;
⇒ 5y - 21 = x + 21 - 21
⇒ 5y - 21 = x
Subtract 5y both side, we get;
⇒ 5y - 21 - 5y = x - 5y
⇒ - 21 = x - 5y
⇒ x - 5y = -21
Therefore,
The Standard form of the equation will be;
⇒ x - 5y = -21
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How can you use the Power of a Quotient, Quotient of Powers, Zero Exponent Laws Identity Exponent and to evaluate numerical expressions with whole-number exponents?
Whereas working with laws of exponents, when splitting the exponential equations with the same base, the exponents ought to be subtracted.
Basically, the Quotient of Powers rules is used to decrease the number of terms when parts like terms with exponents. In order to get the solution, just remove the exponents while dividing the terms with the same base, it is applicable to exponents with the same bases. when powers are multiplied, for two whole numbers of the same bases the exponents are added, whereas when powers are divided for two whole numbers of the same bases, exponents are subtracted. The zero exponent rule basically states that when any number is raised to the power of zero it results in 1.
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41 points 3 games how many points 11 games
Answer:
33by 11
Step-by-step explanation:
in 41 3 games firstly we find 1 point it is 3by41
fill in the missing numbers along the sides of the triangle so that it contains each of the numbers from 4 through 12 exactly once. furthermore each side of the triangle should contain four numbers whose sum is 32the pair of numbers that can be used for A and B is ___. the pair of numbers that can be used for C and D is ____. and the pair of numbers that can be used for E and F is___.
Answer:
For A and B, we have (10, 6)
For C and D, we have (12, 8)
For E and F, we have (12, 8)
Explanation:
To determine the missing numbers along each side of the triangle, we have to
*Add the two numbers at the vertex
*Subtract it from 32
*Divide it by 2
*Add 2 to it to have the 1st number
*Subtract 2 from it to have the 2nd number
So to find the pair of numbers that can be used for A and B, we'll have;
[tex]\begin{gathered} 12+4=16 \\ 32-16=16 \\ \frac{16}{2}=8 \\ 8+2=10 \\ 8-2=6 \end{gathered}[/tex]Therefore the missing numbers for A and B are 10 and 6.
So to find the pair of numbers that can be used for C and D, we'll have;
[tex]\begin{gathered} 4+8=12 \\ 32-12=20 \\ \frac{20}{2}=10 \\ 10+2=12 \\ 10-2=8 \end{gathered}[/tex]Therefore the missing numbers for C and D are 12 and 8.
So to find the pair of numbers that can be used for E and F, we'll have;
[tex]\begin{gathered} 12+8=20 \\ 32-20=12 \\ \frac{12}{2}=6 \\ 6+1=7 \\ 6-1=5 \end{gathered}[/tex]So to avoid repetition of any of the numbers between 4 and 12, we have to add and subtract 1 instead of 2.
Write the quadratic function in vertex form. Then identify the vertex.
g(x)=x^2+12x+37
The vertex form is y= (x+ 6)²+1.
What is Vertex form?The vertex form of a quadratic equation is y = a (x- h)² + k as opposed to the regular quadratic form, which is an x² + bx + c = y. In both cases, the variables that indicate whether the parabola is facing up (+ a) or down ( a) are y, the y-coordinate, x, and a.
a=1
b=12
c=37
Consider the vertex form of a parabola.
a(x+ d)²+e
Now, d= b/2a
d=12/ 2
d=6
and, e= c-b²-4a
e= 37 - (12)²/4x1
e= 37 - 36
e= 1
Then, the vertex form is
y = a(x+ d)²+e
y= 1(x+ 6)²+1
y= (x+ 6)²+1
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Select the GCF of these numbers. 2^5 · 5· 11 and 2^3· 5^2 · 7
The greatest common factors of 2^5 · 5· 11 and 2^3· 5^2 · 7 is equivalent to 2^3 * 5
What are greatest common factors?The largest positive integer that divides each of two or more non-zero integers is known as the greatest common divisor.
This factor must be able to divide all the terms of the expression withour remainder.
Given the numbers 2^5 · 5· 11 and 2^3· 5^2 · 7. Find the factors;
2^5 · 5· 11 = 2^3 * 2^2 * 5 * 11
2^3· 5^2 · 7= 2^3 * 5 * 5 * 7
Since the number 2^3 * 5 is common to both factors, hence the GCF of these numbers 2^5 · 5· 11 and 2^3· 5^2 · 7 is 2^3 * 5
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Write the given expression as an algebraic expression in x.
cos(2 taninverse (x))
Writing the given trigonometry expression: cos(2 tan inverse (x)) as algebraic expression gives
How to write given expression: cos(2 tan inverse (x)) as algebraic expressionData given in the question are as follows:
cos(2 tan inverse (x))
Using trigonometry (double angle formula)
cos 2x = 1 - 2sin² x
when x = tan inverse (x)
cos(2 tan inverse (x)) = 1 - 2sin² tan inverse (x) (1)
cos² x + sin² x = 1
cos² x = 1 - sin² x
cos x = √(1 - sin x)
tan x = sin x / cos x
[tex]tan x = \frac{sinx }{\sqrt{1-sin^{2}x } }[/tex]
squaring all parts of the trigonometry expression and clearing the fraction
[tex]tan^{2}x = \frac{sin^{2} x }{1-sin^{2}x }[/tex]
[tex](tan^{2}x) (1-sin^2x) = sin^2x[/tex]
[tex]tan^{2}x-tan^{2}xsin^2x = sin^2x[/tex]
[tex]tan^{2}x = sin^2x+tan^{2}xsin^2x[/tex]
[tex]tan^{2}x = sin^2x(1+tan^{2}x)[/tex]
[tex]sin^2x = \frac{tan^{2}x}{(1+tan^{2}x)}[/tex]
since tan (tan inverse) (x) = x
[tex]1 - 2sin^2 tan^{-1} (x) = 1 - 2x^2 / (1 + x^2)[/tex]
[tex]=\frac{ 1 + x^2 -2x^2}{1+x^2}[/tex]
[tex]=\frac{ 1 -x^2}{1+x^2}[/tex]
Therefore trigonometry expression cos(2 tan inverse (x)) gives an algebraic expression in the form (1-x²) / (1+x²)
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Two trains leave the same station at the same time, one traveling west at a constant speed of 60 miles per hour, the other traveling south at a constant speed of 80 miles per hour. After how long are the two trains exactly 300 miles apart?
After 2.14 hours the trains are exactly 300 miles apart.
How to find the time the trains travel 300 miles apart?Two trains leave the same station at the same time, one traveling west at a constant speed of 60 miles per hour, the other traveling south at a constant speed of 80 miles per hour.
The time both of them will travel 300 miles can be calculated as follows:
Therefore,
speed = distance / time
distance = speed × time
The train that travel west:
let
t = time of the train that travel west
distance = 60t
The train that travel south:
distance = 80t
Therefore,
total distance = 60t + 80t
300 = 140t
t = 300 / 140
t = 2.14285714286
t = 2.14 hours
Therefore,
time taken = 2.14 hours
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I have watched 32% of the episodes of my favorite show. I have watched 8 episodes. How many episodes are there?
Answer:
There are 35 episodes in the show
Whats a ratio for 5ml and 120ml
Step 1:
The ratio for 5ml to 120ml
Step 2:
The symbol of ratio is :
Therefore,
[tex]\begin{gathered} 5ml\text{ ratio 120ml} \\ =\text{ 5 : 120} \\ =\text{ }\frac{5}{120} \\ =\text{ }\frac{1}{24} \\ =\text{ 1 : }24 \end{gathered}[/tex]Step 3
Final answer
1 : 24
Geometry ?Use the photo to help me solveTriangle DEF is shown. What is the coordinate of D if triangle D E F is created by dilating DEF with a scale of 0.5 about the origin
Since the scaling factor of the dilation (0.5) is fewer than 1, it shrinks (make smaller) the triangle around the origin (zero). Intuitively, the dilation is getting the points of the triangle closer to zero (in a way that preserves the shape of the triangle).
Formally, to know the coordinates of a point of the triangle after the dilation, we just need to multiply the original coordinates of the point by the scaling factor (this works for the dilation is around zero).
The original coordinates of D are
[tex](3,0)\text{.}[/tex]Multiplying them by the scale factor, we get
[tex]0.5\cdot(3,0)=(0.5\cdot3,0.5\cdot0)=(1.5,0)\text{.}[/tex]AnswerThe coordinates of D after the given dilation is
[tex](1.5,0)\text{.}[/tex]Write the equation of the line with the given information in point-slope form. (-5, 11) and (-2, 1)
Answer
The equation in point-slope form is
y - 1 = (-10/3) (x + 2)
We can then simplify this by multiplying through by 3 to obtain
3y - 3 = (-10) (x + 2)
3y - 3 = 10x - 20
3y = 10x - 20 + 3
3y = 10x - 17
Explanation
The general form of the equation in point-slope form is
y - y₁ = m (x - x₁)
where
y = y-coordinate of a point on the line.
y₁ = This refers to the y-coordinate of a given point on the line
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
x₁ = x-coordinate of the given point on the line
We can calculate the slope of the line and then use any of the two points given to serve as the point (x₁, y₁) in the equation
For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]For this question,
(x₁, y₁) and (x₂, y₂) are (-5, 11) and (-2, 1)
x₁ = -5
y₁ = 11
x₂ = -2
y₂ = 1
[tex]\text{Slope = }\frac{1-11}{-2-(-5)}=\frac{-10}{-2+5}=\frac{-10}{3}[/tex]Slope = m = (-10/3)
Using the point (-2, 1) as (x₁, y₁), we can write the equation of the line
y - y₁ = m (x - x₁)
y - 1 = (-10/3) (x - (-2))
y - 1 = (-10/3) (x + 2)
We can then simplify this by multiplying through by 3 to obtain
3y - 3 = (-10) (x + 2)
3y - 3 = 10x - 20
3y = 10x - 20 + 3
3y = 10x - 17
Hope this Helps!!!
The half-life of a radioactive kind of copper is 3 hours. if you start with 2,352 grams of it, how much will be left after 9 hours??
Answer:
294 grams
Explanation:
The amount of radioactive material left after t hours given that the half-life is to hours is
[tex]A=P(0.5)^{\frac{t}{t_0}}[/tex]Now, in our case t0 = 3, t = 9 and P = 2352 g; therefore, the above equation gives
[tex]A=2352(0.5)^{9/3}[/tex][tex]A=294g[/tex]which is our answer!
Hence, the amount of radioactive copper left after 9 hours is 294 grams.
help meeeeeeeeeeeeeeeeeee pleaseeeeeeeee!!!
Answer:
I think it is y
Step-by-step explanation:
Kali just started a new sales floor job to save for college. She earns 15.75 plus a flat fee of 50 . She wants to earn between 200 and 400 . The following inequality represents her earning potential
200 ≤ 15.75x + 50 ≤ 400 Solve the inequality PLEASE HELP ASAP
!!
The given inequality has the following solution set
9.52 ≤ x ≤ 22.22
If we express this as an interval, we get [9.52, 22.22].
Here is the inequality which is Kali's earning potential
200 ≤ 15.75x + 50 ≤ 400
To solve the inequality, we must isolate the variable in the center; if we remove 50 from each of the three sides, we get:
200 - 50 ≤ 15.75x + 50 - 50 ≤ 400 - 50
150 ≤ 15.75x ≤ 350
Now we must divide both totals by 15.75, yielding:
150/15.75 ≤ 15.75x/15.75 ≤ 350/15.75
9.52 ≤ x ≤ 22.22
This is the inequality's solution; the solution set expressed as an interval will be [9.52, 22] or 9.52 ≤ x ≤ 22.22
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find an equation of the circle that has center (1,-5) and passes through (2,1)
1) Since the equation of the circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]And we've been told the Center (1,-5) and one point located at the circumference, (2,1). So let's find the radius, i.e. the distance from the center to any point to the circumference.
2) Let's use the Formula for the distance between (1,-5) and (2,1), derived from the Pythagorean Theorem:
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ d=\sqrt[]{(2-1)^2+(1_{}+5)^2} \\ d=\sqrt[]{37} \end{gathered}[/tex]3) So d = radius, and now we can plug those pieces of information into the formula of the circle:
[tex]\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ (x-1)^2+(y+5)^2=(\sqrt[]{37})^2 \\ (x-1)^2+(y+5)^2=37 \end{gathered}[/tex]So we now have the formula for that circle.
Answer:
Radius (R) is equal to the distance between the points (-2,1) and (3,1)
R² = (1 - 5)² + (1 - 1)² = (-24)² + 0 = 579
R = 23.16
what is the product of [tex] ( - \frac{3}{4} ) \times ( - \frac{7}{8} )[/tex]
What is the product of
In the multiplication of fractions, you multiply the numerators with each other and the denominators with each other
( - 3/5) *(-7/8)
= -3*-7 / (5*8) = (positive)
= 21/40
_____________________
Answer
= 21/40
_____________________
Do you have any questions regarding the solution?
A. The printer prints the entire report in 152 minutes
B.The printer prints 3 more pages per minutes in colored ink than black ink.
C.The printer prints 3 fewer pages per minute in colored ink than black ink.
D.The printer prints the same number of pages per minute in either type of ink.
Answer:
C
Step-by-step explanation:
the function calculates the number of pages left to print. that means for every minute it subtracts a number of pages from the total of pages (that total being 152 pages).
the colored print only manages 30 pages per minute, while the pure black ink printing manages 33 pages per minute.
what is the value of a in the equation 5a – 10b = 45, when b =3?a)3b)15c)21d)39
SOLUTION
Given the question, the following are the solution steps to answer the question.
STEP 1: Write the given equation
[tex]5a-10b=45[/tex]STEP 2: Substitute 3 for b in the equation
[tex]5a-10(3)=45[/tex]STEP 3: Simplify the equation to solve for a
[tex]\begin{gathered} 5a-30=45 \\ 5a=45+30 \\ 5a=75 \\ a=\frac{75}{5} \\ a=15 \end{gathered}[/tex]Hence, the value of a is 15
One month Tony rented 5 movies and 3 video games for a total of $32. The next month he rented 2 movies and 12 video games for a total of $83. Find therental cost for each movie and each video game.Rental cost for each movie:Rental cost for each video game:
Let x represent the rental cost for each movie.
Let y represent the rental cost for each video game.
We were told that One month Tony rented 5 movies and 3 video games for a total of 532. This means that
5x + 3y = 32
Also, the month, he rented 2 movies and 12 video games for a total of $83. This means that
2x + 12y = 83
Dividing through by 2, we have
x + 6y = 41.5
x = 41.5 - 6y
Substituting x = 41.5 - 6y into 5x + 3y = 532, we have
5(41.5 - 6y) + 3y = 32
207.5 - 30y + 3y = 32
- 30y + 3y = 32 - 207.5
- 27y = - 175.5
y = - 175.5/- 27
y = 6.5
x = 41.5 - 6(6.5) = 41.5 - 39
x = 2.5
Rental cost for each movie = $2.5
Rental cost for each video game = $6.5
Yesterday, grace drove 28 1/2 miles. She used 1 1/4 gallons of gasoline. What is the unit rate for miles per gallon?
Answer: 22.8 miles or 22 4/5
Step-by-step explanation:
To find the unit rate you do
28.5 ÷ 1.25 = 22.8
I’m confused on this drag and drop assignment can someone please help me out? I’ll give brainliest
The most appropriate choice for the similarity of figures will be given by:
(A) ZY = 20(B) x = 12(C) 22.5 cm on the drawing represented 9 miles on the ground.What is the similarity of the figures?Two figures are said to be similar if the corresponding angles are equal and the corresponding sides are in the same ratio.So,
(A) HIJK∼WXYZ [Given].
HJ/WX = KJ/ZY6/5 = 24/ZY6 × ZY = 24 × 5ZY = 24×5/6ZY = 20(B) The two triangles are similar [Given].
2/2+4.5 = x/396.5x = 39×2x = 39×2/6.5x = 12(C) 5cm on the drawing represented 2 miles on the ground.
Let 22.5 cm on the drawing represent x miles on the ground.
The problem:
5/22.5 = 2/x5x = 22.5 × 25x = 45x = 45/5x = 9 miles22.5 cm on the drawing represented 9 miles on the ground.
Therefore, the most appropriate choice for the similarity of figures will be given by:
(A) ZY = 20(B) x = 12(C) 22.5 cm on the drawing represented 9 miles on the ground.To learn more about the similarity of figures, refer to the link:
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Which expression evaluates to 2048?
A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.
The expression [tex]$&\left(\frac{\left(\frac{1}{2}\right)^{-1}}{\left(\frac{1}{2}\right)^2}\right)^3\left(\frac{1}{2^{-1}}\right)^2 \\[/tex], we get 2048.
What is meant by exponent rule?Exponent rules include: Rule of the product of powers: When multiplying like bases, add the powers together. Rule of the quotient of powers: When splitting like bases, take the powers out. Power of powers rule: When increasing a power by another exponent, multiply all the powers together.
A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.
Let the value be 2048
[tex]$&\left(\frac{\left(\frac{1}{2}\right)^{-1}}{\left(\frac{1}{2}\right)^2}\right)^3\left(\frac{1}{2^{-1}}\right)^2 \\[/tex]
simplifying the above expression we get
[tex]$&\left(\frac{\left(\frac{1}{2}\right)^{-1}}{\left(\frac{1}{2}\right)^2}\right)^3=512 \\[/tex]
[tex]$&=512\left(\frac{1}{2^{-1}}\right)^2[/tex]
By using exponent rule, we get
[tex]$&\left(\frac{1}{2^{-1}}\right)^2=\frac{1^2}{\left(2^{-1}\right)^2} \\[/tex]
[tex]$&=512 \cdot \frac{1^2}{\left(2^{-1}\right)^2}[/tex]
1² = 1
[tex]$&=512 \cdot \frac{1}{\left(2^{-1}\right)^2}[/tex]
[tex]$\left(2^{-1}\right)^2=\frac{1}{4}$$[/tex]
[tex]$=512 \cdot \frac{1}{\frac{1}{4}}$$[/tex]
[tex]$\left(2^{-1}\right)^2=\frac{1}{4}$$[/tex]
[tex]$=512 \cdot \frac{1}{\frac{1}{4}}[/tex]
[tex]$&\frac{1}{\frac{1}{4}}=4 \\\pi[/tex]
= 512 × 4
= 2048
By simplifying the expression [tex]$&\left(\frac{\left(\frac{1}{2}\right)^{-1}}{\left(\frac{1}{2}\right)^2}\right)^3\left(\frac{1}{2^{-1}}\right)^2 \\[/tex], we get 2048.
Therefore, the correct answer is option (b).
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Need help with absolute value please
Answer:
let's say you need to find the absolute value of -5 the answer would be 5.
Step-by-step explanation:
Since the distance between -5 and 0 in a number line is 5. This would also be applied If you you were trying to find the absolute value of 5. it would also be 5.
When in math, I figured out negative number's absolute value will always be positive. absolute value numbers of positive numbers will stay the same.
a firm uses a trend projection and a seasonal factor to simulate sales for a given time period. it assigns 0 if sales fall 1 if sales are steady 2 if sales rise moderately and 3 if sales rise a lot. the simulator generates the following output
0102000103200002123120203002101
estimate the probability that sales will remain steady. express as a fraction and as a decimal
The probability that the sales will will remain steady is; 7/30 or 0.233
What is the probability of occurrence?We are given the numbers generated by the simulator for the sales as;
0, 1, 0, 2, 0, 0, 0, 1, 0, 3, 2, 0, 0, 0, 0, 2, 1, 2, 3, 1, 2, 0, 2, 0, 3, 0, 0, 2, 1, 0, 1
Now, we are given the following implications of the simulator as;
If it assigns 0, then it means that sales fall.If it assigns 1, then it means that sales are steady.If it assigns 2, it means that sales rise moderately.If it assigns 3, it means that sales rise a lot.Now, we want to find the probability that the sales will will remain steady which is the point at which it assigns 1 from the 30 numbers generated. Thus;
P(sales will remain steady) = 7/30 = 0.233
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If z varies inversely as w, and z=20 when w=6, find z when w=3.
Z=
What is the value of the following sum: 1+2+3+…+397+398+399+400?
Answer:
80,200
Step-by-step explanation:
There is a formula for the sum of a series of numbers from a_1 to a_n.
S = (a_n * a_n+1)/2
This formula means: multiply the last number of the series by what would be the next number, and divide by 2.
The last number you have is 400. The next number would be 401.
Multiply 400 by 401 and divide by 2. That is the sum of the 400 numbers.
S = (401 * 402)/2
S = 160400/2
S = 80200
Answer: The sum is 80,200
Here's a way to understand the formula.
You are adding 400 numbers, from 1 to 400.
Write the first 200 numbers on a line:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ... 198 199 200
Now write the next 200 numbers, from 201 to 400 under these numbers, but start from 400 and go down 1 each number to the right.
You end up with these two lines:
1 2 3 4 5 6 7 8 9 ... 198 199 200
400 399 398 397 396 395 394 393 392 ... 203 202 201
Now add every two numbers in the same column.
1 2 3 4 5 6 7 8 9 ... 198 199 200
400 399 398 397 396 395 394 393 392 ... 203 202 201
------------------------------------------------------------------------------------------------------
401 401 401 401 401 401 401 401 401 ... 401 401 401
Now you have 200 times the number 401.
200 * 401 = 80,200