What is -14 squared + 5675843


Answer 1



Step-by-step explanation:

-14² + 5675843

Solve for exponent.

196 + 56758

Add the numbers.

= 5676039

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Write the expanded form 0.45 in this way using fractions and using decimals


Using fractions, 0.45 can be written as (3)/(10)+ (3)/(20). Using decimals, 0.45 can be written in the form as 0.30 + 0.15.

What is Decimal Numbers?

Decimal number system is applicable for both integers as well as non integers. Decimal number include a whole number part and a decimal part separated using decimal point.

Fractions are the numbers which are part of a whole.

All decimal numbers can be written as fractions and fractions can be written in the form of decimal numbers.

The given number is 0.45.

0.45 can be written as (45)/(100).

(45)/(100) can be expanded in various ways like (40 + 5)/100, (42 + 3)/100 and so on.

(45)/(100) can be written in one of the form as (30)/(100) + (15)/(100).

When simplified, (30)/(100)simplified to (3)/(10)and (15)/(100) simplified to (3)/(20).

So 0.45 = (3)/(10)+ (3)/(20).

Now, in the decimal form, (3)/(10)= 0.3 and (3)/(20)= 0.15

So, 0.45 = 0.3 + 0.15

Hence 0.45 can be expanded in the fractional form as  (3)/(10)+ (3)/(20)and in the decimal form as 0.3 + 0.15.

To learn more about Decimals, click :




0.4 + 0.05= 0.45


4/10+ 5/100= 0.45

Step-by-step explanation:

Hope this helps!! Tell me if I'm wrong! :)

Find the area of the shape



The area is 91 cm²

Step-by-step explanation:

The shape is a kite.

area of a kite = ½(p*q)

Where, p and q are the diagonals of the kite.

p = 13 cm

q = 7 + 7 = 14 cm

The area of the kite = ½(13 * 14)

= ½(182)

Area = 91 cm²

Find the length of the missing triangle



The pythagoras's theorem is the relation between the sides of a right-angles triangle, it shows that the square of the hypotenuse of the triangle will be equal to the sum of squares of the remaining sides

hypotenuse² = perpendicular² + base²

replacing the variables with the sides of the given triangle:

x² = 15² + 8²

x² = 225 + 64

x² = 289

x = √289

x = 17 mi

Use the method of variation of parameters to find a particular solution of the given differential equation. Then check your answer by using the method of undetermined coefficients.y'' − y' − 2y = 5e−t



y = C₂ e²ᵗ + e⁻ᵗ [C₁ - (5t/3)]

Step-by-step explanation:

y" - y' - 2y = 5e⁻ᵗ

The total solution of this differential equation will be a sum of its complimentary and particular solutions.

y = y꜀ + yₚ

The complimentary or homogenous solution is a solution of

y" - y' - 2y = 0

y꜀ = Ay₁ + By₂

Solving this part in the attached image, we obtain

y₁ = e⁻ᵗ and y₂ = e²ᵗ

The particular solution can be obtained using the method of variation of parameters and the method of undetermined coefficients.

The method of variation of parameters is used and explained in the page 1, 2 and page 3 of the attached images.

The method of undetermined coefficients is then used to check if the solution obtained is correct.

With y = C₂ e²ᵗ + e⁻ᵗ [C₁ - (5t/3)],

y' and y'' were obtained and put in the equation, and the answer obtained was 5e⁻ᵗ.

So, Proved!

y = C₂ e²ᵗ + e⁻ᵗ [C₁ - (5t/3)]

Hope this helps!!!

Square root of 20 is it rational or irrational ?square root of 24 is it rational or irrational ?
square root of 61 is it rational or irrational ?
square root of 62 is it rational or irrational ?
square root of 101 is it rational or irrational ?
square root of 105 is it rational or irrational ?


Each square root of a number that does not generated as a square of an integer is irrational. This means that none of the given numbers is rational, that is,  they are all irrational.

Good luck!!!!

In a large university, 20% of the students are business majors. A random sample of 100 students is selected, and their majors are recorded. a) Compute the standard error of the proportion. b) What is the probability that the sample contains at least 12 business majors



a. 0.04

b. 0.9772

Step-by-step explanation:

Please check attachment for complete solution and step by step explanation

Final answer:

The standard error of the proportion is 0.04. The probability of having at least 12 business students in a sample of 100 can be found by using the binomial distribution formula, though precise calculation would require the use of statistical software.


In a large university, 20% of students are business majors. The question is asking about the standard error and the probability of having at least 12 business students in a random sample of 100 students.

a) The standard error (SE) of the proportion is calculated as the square root of [p(1-p)/n], where 'p' is the proportion of business majors (0.2 in this case)and 'n' is the sample size (100 in this case). So, the SE = sqrt[(0.2)(0.8)/100] = sqrt[0.0016] = 0.04.

b) In order to calculate the probability that there are at least 12 business students, we would use the binomial distribution. Using the binomial distribution formula P(X >= x) = 1 - P(X < x), where 'X' is a random variable representing the number of business majors, and 'x' is 12. Since the calculation is tedious, one would use statistical software or a calculator to find this probability. Typically, the result would be greater than 0.

Learn more about Probability and Standard Error here: