-3(2t - 1) = t + t + t + 3

What is the sum of all positive integers smaller than $1000$ that can be written in the form $100\cdot 2^n$, where $n$ is an int

netineya [11]

Answer:

The sum is 1575.

Step-by-step explanation:

Consider the provided information.

It is given that positive integers smaller than 1000 and that can be written in the form $100\cdot 2^n$

Where n is integer that means the value of n can be a positive number or a negative number.

For n = 0

$100\cdot 2^{0}=100$

For n=-1

$100\cdot 2^{-1}=50$

For n=-2

$100\cdot 2^{-2}=25$

For n = -3 the obtained number is not an integer.

Now consider the positive value of n.

For n=1

$100\cdot2^1 = 200$

For n=2

$100\cdot2^2 = 400$

For n=3

$100\cdot2^3 = 800$

For n=4 the obtained number is greater than 1000.

Now add all the numbers.

$100+50+25+200+400+800=1575$

Hence, the sum is 1575.

6 0

1 year ago

What is the place value of 3 in 9. 365?

nikdorinn [45]

Answer:

It is in the tenths place

Step-by-step explanation:

In the number 9.365, 3 is in the tenths place.

8 0

1 year ago

Read 2 more answers

Wyatt’s eye-level height is 120 ft above sea level, and Shawn’s eye-level height is 270 ft above sea level. How much farther can

earnstyle [38]

Answer:

The answer is 3√5 mi.

The formula is: d = √(3h/2)

Wyatt:

h = 120 ft

d = √(3 * 120/2) = √180 = √(36 * 5) = √36 * √5 = 6√5 mi

Shawn:

h = 270 ft

d = √(3 * 270/2) = √405 = √(81 * 5) = √81 * √5 = 9√5 mi

How much farther can Shawn see to the horizon?

Shawn - Wyatt = 9√5 - 6√5 = 3√5 mi

3 0

2 years ago

A standard deck of 52 cards contains four suits: clubs, spades, hearts, and diamonds. Each deck contains an equal number of card

Artist 52 [7]

Answer:

A) The theoretical probability of choosing a heart is 1/16 greater than the experimental probability of choosing a hear

Step-by-step explanation:

7 0

1 year ago

A law school administrator was interested in whether a student's score on the entrance exam can be used to predict a student's g

frutty [35]

Answer:

The correlation coeffcient for this case was provided:

r =0.934

And this coefficient is very near to 1 the maximum possible value, so then we can interpret that the relationship between the entrace exam score and the grade point average are strongly linearly correlated .

We can also find the $r^2$ who represent the determination coefficient and we got:

$r^2 = 0.934^2= 0.872$

And the interpretation for this is that a linear model explains appproximately 87.2% of the variability between the two variables

Step-by-step explanation:

Previous concepts

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this formula:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

The correlation coeffcient for this case was provided:

r =0.934

And this coefficient is very near to 1 the maximum possible value, so then we can interpret that the relationship between the entrace exam score and the grade point average are strongly linearly correlated .

We can also find the $r^2$ who represent the determination coefficient and we got:

$r^2 = 0.934^2= 0.872$

And the interpretation for this is that a linear model explains appproximately 87.2% of the variability between the two variables

8 0

1 year ago