MATHEMATICS HIGH SCHOOL

Find 1+2+3+4+ ... +40, the sum of the first 40 natural numbers.
The sum is

Answers

Answer 1

Answer:

Answer : 840

1 + 41 = 42

2 + 40 = 42

___________

20 pairs

20 × 42 = 840

Answer 2

Answer:

Answer:

$\bold{S_(40)=820}$

Step-by-step explanation:

$1+2+3+4+ ... +40=S_(40)\n\na_1=1\na_(40)=40\nn=40\n\nS_n=\frac{a_1+a_n}2\cdot n\n\nS_(40)=\frac{1+40}2\cdot40=41\cdot20=820$

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The perimeter of a rectangle of 150 feet. The length of the rectangle is twice the width. Find the length and width of the rectangle
Choose the polynomial written in standard form. x3y2 + 4x4y + 10x9 x4y2 + 4x4y5 + 10x2 xy2 + 4x3y8 + 10x2 x4y5 + 4x3y2 + 10x2 is it the second one?

A gallon of paint can cover 150 square feet. Find how many galloti container of paint should be beate to paint 3 coats on each wall of a rectangular room with dimension feet by 14 feet and will shar 12-feet tall.

Answers

Area of the wall = 12 ft * 14 ft = 168 ft^2

Each wall is coated thrice with the paint.

Therefore, 168ft^2 * 3 = 504 ft^2

150ft^ 2 = 1 gallon paint.

Therefore 504 ft^2 requires

= 504/150

= 3.36 gallons of paint

Answer:

Step-by-step explanation:

Wk castes

1. There are 25 students who started computer programming in elementary school and 25 students who started computer programming in middle school. The first group had a mean final project grade of 95% and the second group had a mean final project grade of 92%. The line plot shows the differences after 10 rerandomizations. Determine whether the difference in the means of the two groups is significant based on the line plot. Explain your answer.

Answers

the answer is attached below

Answer:

the difference in the means is not significant

Step-by-step explanation:

Let’s begin first by finding the difference between the means of the 2 groups.

Difference in means = 95% - 92% = 3% Now let’s look at the line plot of the 10 rerandomizations. On that plot, 4 of the randomizations have a difference of 3.

Probability of having a difference of 3 = 4 / 10 *100% = 40%

So just by mixing up the scores from both classes and finding the difference between the mean of 2 randomly defined groups, there was a difference of 3 between the 2 means in 40% of the trials.

Since this probability is so large, the difference in the means is not significant. The line plot shows that it would be very likely that the difference in the means is just due to random chance

Solve the following pair of linear equations using substitution method $x-3y = 13$

$x+2y=8$

Answers

Answer:

(10, - 1 )

Step-by-step explanation:

Given the 2 equations

x - 3y = 13 → (1)

x + 2y = 8 → (2)

Rearrange (1) making x the subject by adding 3y to both sides

x = 3y + 13 → (3)

Substitute x = 3y + 13 into (2)

3y + 13 + 2y = 8

5y + 13 = 8 ( subtract 13 from both sides )

5y = - 5 ( divide both sides by 5 )

y = - 1

Substitute y = - 1 into (3) for corresponding value of x

x = 3(- 1) + 13 = - 3 + 13 = 10

solution is (10, - 1 )

Find the volume of an object with a mass of 63 grams and a density of 9 g/cm

Answers

you have to divide it 63 divide by 9 = 7

Final answer:

To find the volume of an object, divide its mass by its density.

Explanation:

The volume of an object can be found by dividing its mass by its density. In this case, the mass is given as 63 grams and the density is given as 9 g/cm. To find the volume, divide the mass by the density: Volume = Mass / Density.

Substituting the given values, we get Volume = 63 g / 9 g/cm. Simplifying the equation, we find that the volume of the object is 7 cm³.

Learn more about Volume calculation here:

brainly.com/question/33318354

#SPJ2

Which of the following fractions is equivalent to 3/8?A.6/14
B.9/24
C.4/9
D.15/35

Answers

I'm going to suggest that we take these and "UN-simplify" them.

For each choice, divide the numerator by 3 and the denominator by 8.

Look at this:

A). 6/14

6 ÷ 3 = 2
14 ÷ 8 = 1.875 ===> 2/1.875 not interesting

B). skip B for just a second

C). 4/9

   4 ÷ 3 = 1.33
   9 ÷ 8 = 1.125 ===> 1.33/1.125    not interesting

D). 15/35

   15 ÷ 3 = 5
   35 ÷ 8 = 4.375    ===> 5/4.375 not interesting

But now look at choice-B:

B). 9/24

   9 ÷ 3 = 3
   24 ÷ 8 = 3 ===> 1/1 interesting !

-- To simplify 9/24, the top and bottom were divided by 3, giving 3/8.

-- To UN-simplify 3/8, the top and bottom were multiplied by 3, giving 9/24.

-- Choice-B is the one that's equivalent to 3/8.
______________________________________________

OK. All of that wasn't really necessary.
All you really need to do is take each choice and simplify it.

A). 6/14
   Divide top and bottom by 2 ===> 3/7

B). 9/24
   Divide top and bottom by 3 ===> 3/8

C). 4/9
   Can't be simplified. Already in simplest form.

D). 15/35
   Divide top and bottom by 5 ===> 3/7

In the equation Q – 12 = 89, what is the value of Q