MATHEMATICS COLLEGE

Find the smallest number by which 240 must be multiplied so that the product is a perfect square. *

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

$240 = 2 * 2 * 2 * 2 * 3 * 5 \n = {2}^(4) * 15 \n$

Here, 15 is not a square number so, 240 should be multiplied by 15 to make 240 as perfect square.

240* 15 = 3600

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the volume of a 15oz cereal box is 180.4in cube. the length of the box is 3.2 in. less than the height and the width is 2.3 in. find the height and length of the box to the nearest tenth.
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The ordered pair (x,y)=(2,-3) is a solution to which of the following systems of equation

Answers

Answer:

Y=2x-7

Step-by-step explanation:

You can use both the t statistic and the z statistic to test hypotheses about the mean of population. The test that uses the t statistic is typically referred to as a t test, while the test that uses z statistic is commonly called a z test. Which of the following statements are true of the t statistic? Check all that apply. The t statistic uses the same formula as the z statistic except that the t statistic uses the estimated standard error in the denominator. The t statistic provides an excellent estimate of z, particularly with small sample sizes. The formula for the t statistic is t = (M – μ) / σM. The t statistic does not require any knowledge of the population standard deviation.

Answers

Using the concepts of the t-statistic and the z-statistic, it is found that the correct option is:

The t-statistic does not require any knowledge of the population standard deviation.

The z-statistic is given by:

$z = (X - \mu)/((\sigma)/(√(n)))$

In which:

X is the sample mean.
$\mu$ is the population mean.
$\sigma$ is the population standard deviation.
n is the sample size.

The standard error is $S_e = (\sigma)/(√(n))$ .

The t-statistic is similar to the z-statistic, the difference is that the sample standard deviation is used, not the population. Thus:

$t = (X - \mu)/((s)/(√(n)))$

In which:

X is the sample mean.
$\mu$ is the population mean.
$s$ is the sample standard deviation.
n is the sample size.
The standard error is $S_e = (s)/(√(n))$ .

For large sample sizes, the sample and population standard deviations are close, thus t is a good estimate of z.

Thus, the correct option is:

The t-statistic does not require any knowledge of the population standard deviation.

A similar problem is given at brainly.com/question/16194574

Answer:

Detailed elaborated answer is given below:

QuestionThe area of a triangular painting is 50 square inches. The base is 20 inches. What is the height?
Provide your answer below:
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The area of a triangular painting is 50 in.² the base is 20 inches what is the height

Answers

The height of the triangle is 5 inches.

Area of the triangle:

The region occupied by a triangle within its sides is known as the area of the triangle. The area of a triangle can be calculated by the calculating product of the base and height of the triangle with a half i.e 1/2. The formula for the area of the triangle is given by

Area of triangle = (1/2) × base × height

Here we have

Area of the triangle = 50 in²

The base of the triangle, b = 20 inches

As we know,

Area of the triangle = 1/2 (base × height)

From the given data,

=> 50 = 1/2 (20 × height)

Multiply by 2 on both sides

=> 100 = (20 × height)

Divided by 20 into both sides

=> 100/20 = (20 × height)/20

=> 5 = height

=> height = 5 in

Therefore,

The height of the triangle is 5 inches.

Learn more about Triangles at

brainly.com/question/28977020

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which of the following is a Quadrilateral which must contain diagonals that are always congruent and must always have 90° angles?

Answers

Answer: B

Step-by-step explanation:

Which expressions are equivalent to the one below? Check all that apply.25^x
A. 5^x•5^x B. 5•5^x
C. 5^2•5^x
D. 5^2x
E. 5•5^2x F. (5•5)^x

Answers

Answer:

A. 5^x•5^x

D. 5^(2x)

F. (5•5)^x

Step-by-step explanation:

25^x = (5•5)^x = (5^2)^x = 5^(2x) = (5^x)^2 = (5^x)•(5^x)

The applicable rules of exponents are ...

(a^b)^c = a^(bc)

a•a = a^2

The length of a side of a triangle is 36. A line parallel to that side divides the triangle into two parts of equal area. Find the length of the segment determined by the points of intersection between the line and the other two sides of the triangle

Answers

Answer:

18√2

Step-by-step explanation:

The area of the smaller triangle is 1/2 that of the larger one. Since the triangles are similar, the dimensions of the smaller triangle are √(1/2) those of the larger one.

36 · √(1/2) = 36 · (√2)/2 = 18√2 . . . . length of line dividing the triangle

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25% of 56. We are practicing finding the percent of each number

Consider the diagram and the proof below.Given: In △ABC, AD ⊥ BCProve: StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFractionTriangle A B C is shown. A perpendicular bisector is drawn from point A to point D on side C B forming a right angle. The length of A D is h, the length of C B is a, the length of C A is b, and the length of A B is c.A 2-column table has 7 rows. The first column is labeled Statement with entries In triangle A B C line segment A D is perpendicular to line segment B C, In triangle A D B sine (uppercase B) = StartFraction h Over c EndFraction, c sine (uppercase B) = h, In triangle A C D, sine (uppercase C) = StartFraction h Over b EndFraction, b sine (uppercase C) = h, question mark, StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction. The second column is labeled Reason with entries given, definition of sine, multiplication property of equality, definition of sine, multiplication property of equality, substitution, and division property of equality.What is the missing statement in Step 6?b = cStartFraction h Over b EndFraction = StartFraction h Over c EndFractioncsin(B) = bsin(C)bsin(B) = csin(C)

These two trapeziums are similar.Calculate the area of trapezium G. If your answer is a decimal, give it to 1 d.p.