Lin ran 29 meters in 10 seconds she ran at a constant speed how far did lin run per second

In an experiment, a researcher manipulates one variable to see how it affects a second variable. the second variable, which is o

kherson [118]

It’s called the dependent variable.

4 0

3 years ago

Find the sum of the counting numbers from 1 to 25 inclusive. In other words, if S = 1 + 2 + 3 + ... + 24 + 25, find the value of

Anastaziya [24]

Answer:

325

Step-by-step explanation:

You must have heard about Arithmetic Progressions (AP)

Arithmetic progressions are a series of numbers such that every successive number is the sum of a constant number and the previous number.

Our very own counting numbers form AP

For example :-

2 = 1 + 1

3 = 2 + 1

4 = 3 + 1

The number in bold (1) is that constant number which is added to a number to form its successive number.

To find the sum of series forming AP, we use the formula :-

$sum = \frac{n}{2} \{ a + a _{n} \}$

here,

n is the number of terms
a is the first number of the series
an is the last number of the series

So we'll use all this information to find the sum of continuous numbers from 1 to 25 where 1 is the first term(a) and 25 is the last(an).

and n is 25

$S = \frac{25}{2}\{ 1 +25\}$

$= \frac{25 \times 26}{2}$

$= 25 \times 13$

$= 325$

So, the value of S comes out to be 325.

8 0

3 years ago

Read 2 more answers

Income Suppose income from an endowment is generated at the annual rate of $42,000 per year. Find the capital value of this endo

Mrac [35]

Answer:

Capital value after 1 year will be equal to $45150

Step-by-step explanation:

We have given principal amount P = $42000

Rate of interest r = 7.5 %

Time t = 1 year

Capital value is given by $A=P(1+\frac{r}{100})^n$

So $A=42000\times (1+\frac{7.5}{100})^1$

$A=42000\times 1.075=45150$

So capital value after 1 year will be equal to $45150

4 0

3 years ago

What is the slope of the line represented by the equation 2x+3y= –12 ? –32 –23 23 32

mr_godi [17]

Answer:

Option 2 - $m=-\frac{2}{3}$ is the slope of the equation.

Step-by-step explanation:

Given : Equation $2x+3y=-12$

To find : What is the slope of the line represented by the equation ?

Solution :

The slope form of line is $y=mx+c$

Equation $2x+3y=-12$

Take 2x to another side,

$3y=-12-2x$

Divide 3 both side,

$y=\frac{-12-2x}{3}$

$y=\frac{-2}{3}x-4$

On comparing with general equation,

$m=-\frac{2}{3}$ is the slope of the equation.

Therefore, option 2 is correct.

7 0

3 years ago

Read 2 more answers

Help Please!!!!!!! Need Help!!!

Citrus2011 [14]

Answer:

925

Step-by-step explanation:

In order to solve this summation formula, you need to first understand what it means. The summation symbol is tell you to add the terms in a sequence. Below the summation sign, there is a variable and number; the variable n is the index of summation and the number 1 is the lower limit of summation or the first value of the sequence. The number 25 above the summation sign is the upper limit (so there would be 25 terms, with the first being 1). The polynomial to the right of the summation symbol represents the explicit function for each term. For example, using this, the first term would be (3(1) - 2) and the second (3(2) - 2) and so on. This means the value of that equation is:

(3(1) - 2) + (3(2) - 2) + (3(3) - 2)... + (3(25) - 2)

One way to solve this is to write all 25 of the terms and add them, but since that's tedious, you can solve this by first doing the basic summation of 1 to 25 and then inputting that into the equation:

1 + 2 + 3... + 25 = (25 × 26)/2 (when the first number is one and the rate of change is 1, the sum of the terms in a sequence is (n*(n+1))/2)

= 325

Now, that you know what the sum of the sequence of terms 1 to 25 are, you can multiply this by the constant since if you break up the equation you would be multiplying 3 by 1 then 3 by 2 and so on until 25, or 3 × (1 + 2 + 3... + 25):

3 × 325 = 975

At this point, you just need to add (-2) × 25. You do this because since there are 25 terms, if you subtracted 2 each time, you would subtract 2 twenty-five times:

975 + ((-2) × 25)

= 975 - 50

= 925

3 0

2 years ago