Please help me on this question it’s question 8

Mathematics

2 answers:

kotegsom [21]2 years ago

7 0

9514 1404 393

Answer:

D. √2

Step-by-step explanation:

Any finite-length decimal number, positive or negative, is rational. The square root of a perfect square, such as √4 = √(2²) = 2, is also a rational number.

The number 2 is not a perfect square, so its square root is irrational.

The only irrational number on the list is √2, choice D.

_____

Additional comment

Your calculator can help you identify square roots (and other roots) that are irrational. If the square root has more digits in its decimal fraction than the original number does, then it is irrational.

Examples:

√6.25 = 2.5 . . . . root has 1 decimal digit, original number has 2. This number is rational.

√6.24 ≈ 2.49799919936 . . . . root has an infinite number of decimal digits. The number shown is limited by the available calculator display. It is more digits than the original number has. This number is irrational.

If a number with a decimal fraction is a perfect square, the number of fractional digits in its square root will be half as many as in the original number. Above, 6.25 has 2 fractional digits; its root 2.5 has 1 fractional digit--half as many. (A rational cube root will have 1/3 as many fractional digits.)

Aloiza [94]2 years ago

5 0

The answer is a d there both irrational

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Find the two Z-scores that separate the middle 73.72% on the Standard Normal Curve.

leonid [27]

Answer:

+1.12 and -1.12

Step-by-step explanation:

Let the two z scores be $-z_1and+z_1$ .

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$P(-z_1$

From the z table of the normal distribution, z₁ = 1.12. That is a z score of 1.12 gives 0.8686.

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4 0

3 years ago

Please help me with this question

Vinvika [58]

Tan(angle) = opposite/adjacent
tan(x) = 90/51
x = arctan(90/51)
x = 60.461217740442
which rounds to 60 when rounding to the nearest whole number

Answer: 60

3 0

3 years ago

An hourglass consists of two sets of congruent composite figures on either end. Each composite figure is made up of a cone and a

belka [17]

Answer: third option 268.8

Explanation:

For this kind of proble it is very important that you attach the figure because it contains important information to understand the question.

I have attached the figure for better understanding.

1) The top portion (and the bottom is congruent but rotated 180°) of the hourglass is a figure equivalent to a cylinder on top and a cone on bottom.

So the total volume contained in the top portion is the volume of a cylinder + the volume of a cone.

This is how you calculate the volume of the top portion:

1) The height of the cylinder is 54 mm - 18 mm = 36 mm

2) The formula for the volume of a cylinder is V = π (radius)^2 * height

radius = 8 mm
height = 36 mm

=> V = π(8mm)^2 * 36 mm = 2304π (mm)^3

3) The formula for the volume of a cone is V = (1/3)π(radius)^2 * height

radius = 8 mm
height = 18 mm

V = (1/3)π(8mm)^2 * 18 mm = 384π (mm)^3

4) The total volume of the top portion is volumen of the cylindrical part + voume of the cone:

Total voluem = 2304π (mm)^3 + 384π (mm)^3 = 2688π (mm)^3

5) To find the number of seconds it take until all of the sand has dripped to the bottom of the hourglass you have to divide the total volumen of sand by the rate:

time in seconds = total volume of sand / rate of dripping

time in seconds = [2688 π (mm)^3 ] / [10π (mm)^3 / s] = 268.8 s

That is the answer: 268.8 s