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13 days ago

What is the value of the sum 5 + 10 + 15 + ... + 95 + 100? ...?

2 answers:

3 0

The series is 5 + 10 + 15 + 20 +... + 100
can be simplified as 5(1+2+3+...+20)
which further equals 5{20(20+1)/2}. Using the formula for the sum of the first n natural numbers = n(n+1)/2, we find the sum to be 5{210}
resulting in a total of 1050
.

AnnZ [9K]13 days ago

3 0

Initially, we consider the number of natural numbers up to 100. Using the formula for the sum to n = (n(n+1))/2, with n = 100, we find that (100x101)/2 equals 5050, which will be denoted as value 'x'. Next, we look at the numbers divisible by 5, which include: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, and 100. Summing these yields 1050, which will serve as value 'y'. Subtracting x from y results in 5050 - 1050 = 4000. I hope this information is helpful.

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the shorter sides of an acute triangle are x cm and 2x cm. the longest side of the trinalge is 15 cm. what is the smallest possi

Leona [9271]

The smallest whole-number value for x that works is 7. The triangle’s sides can be defined as: a = x, b = 2x, and c = 15. Recognizing c as the longest side leads us to the condition for an acute triangle: c^2 must be less than a^2 + b^2. Inputting the known values, we solve for x and find that x must exceed 6.708. As a result, the least integer that satisfies this requirement is 7.

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22 hours ago

What is 2 hundreds + 15 tens + 6 ones

tester [8842]

Two hundreds total 200.
Fifteen tens together make 150.
Six ones equals the same.
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24 days ago

Read 2 more answers

if you are adding two fractions that are both greater than 1/2 what must be true about the sum? Give three examples to support y

lawyer [9240]

Response:

When combining two fractions that each exceeds 1/2, their sum will invariably exceed 1.

Detailed breakdown: 1/2 + 1/2 = 1

Since both fractions exceed this amount, it is evident that the sum must as well.

Examples: 2/3+3/4= 1 5/12 4/6+6/9= 1 1/3

Hope this adds clarity

6 0

14 days ago

Mai wants to make an open top box by cutting out corners of a square piece of cardboard and folding up the sides. The cardboard

Inessa [9000]

Answer:

$V(x)=(4x^{3}-40x^{2}+100x)\ cm^3$

The variable x lies within the interval of all positive real numbers less than 5 cm.

Detailed solution:

Problem statement:

Determine the volume of the open-topped box as a function of the side length x (in centimeters) of the square cutouts.

Refer to the provided diagram for clarity.

Define:

x → length in centimeters of each square cutout side

The volume of the box with open top can be written as:

$V=LWH$

Given this, we have:

$L=(10-2x)\ cm$

$W=(10-2x)\ cm$

$H=x)\ cm$

By substitution:

$V(x)=(10-2x)(10-2x)x\\\\V(x)=(100-40x+4x^{2})x\\\\V(x)=(4x^{3}-40x^{2}+100x)\ cm^3$

Determine the domain of x:

Because:

$(10-2x) > 0\\10> 2x\\ 5 > x\\x < 5\ cm$

Therefore:

Domain is the interval (0,5)

That means all real numbers strictly greater than zero and less than 5 cm are valid for x.

Hence, the volume V as a function of x is:

$V(x)=(4x^{3}-40x^{2}+100x)\ cm^3$

5 0

1 month ago

when joe bowls he can get a strike 60% of the time, what is the probability jow will get at least 3 strikes out of 4 tries?

Leona [9271]

34.56%. This is a binomial probability that can efficiently be calculated using the following formula: Here, n signifies the total number of trials (in this case, 4), x denotes the number of "successes" (which is 3), p is the success probability (60% or 0.6), and q indicates the failure rate (1 - p, thus 0.4). Plugging these values into the formula yields the solution: in percentage form, the probability is found to be 34.56%.

8 0

14 days ago