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antiseptic1488 [7]
3 years ago
12

The sequence 2, 3, 5, 6, 7, 10, ... consists of all natural numbers which are neither perfect squares nor perfect cubes. Find th

e 75th term of this sequence.

Mathematics
1 answer:
BartSMP [9]3 years ago
7 0

Answer: The 75th term is 86

Step-by-step explanation:

Since the sequence consists of all natural numbers which are neither perfect squares nor perfect cubes, we can write out the next ninety numbers starting from 2, and then ruling out the squares and cubes. We then count to the 75th number to the desired term. This is shown in the attachment below.

We can as well sum the number of squares and cubes in the range with the number of the number of the desired term i.e

Number of squares = 8 ( 4,9,16,25,36,49,64,81)

Number of cubes = 2 (8 and 27; excluding 64 which is as well a square)

Desired term = 75

So, 8+2+75 = 85.

Therefore, the 85th term counting from 2 ( i.e 86) is the 75th term of the sequence.

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The hypotenuse of a right triangle is 8 cm longer than the longer leg. The shorter leg is 17 cm shorter than the longer leg. Fin
balu736 [363]

Answer:

  45 cm

Step-by-step explanation:

Let x represent the length of the longer leg. Then the hypotenuse is x+8 and the shorter leg is x-17. The Pythagorean theorem gives the relation between these values as ...

  (x +8)^2 = x^2 +(x -17)^2

  x^2 +16x +64 = 2x^2 -34x +289 . . . . eliminate parentheses

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  0 = (x -45)(x -5) . . . . . . . . factor

Solutions to this equation are x=5 and x=45. The value of x must be greater than 17, so the useful solution is x=45.

The length of the longer leg of the triangle is 45 cm.

5 0
3 years ago
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Escribe el nombre de algún tipo de ángulo que se forma "Entre Dos rectas Paralelas y una Secante"
blsea [12.9K]

Answer:

We see that opposite angles are two angles between two secant lines (“secant lines” simply means two lines that cross each other) that share a vertex (that is why they are called “vertical” angles). We see also that they are not adjacent (which means next to each other) but opposite each other.

Step-by-step explanation:

Vemos que los ángulos opuestos son dos ángulos entre dos líneas secantes (“líneas secantes” simplemente significa dos líneas que se cruzan) que comparten un vértice (por eso se llaman ángulos “verticales”). También vemos que no son adyacentes (lo que significa uno al lado del otro) sino uno frente al otro.

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3 years ago
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Answer:

Correct option:

"The distribution of the statistic in all possible samples of size <em>n</em> from a given population."

Step-by-step explanation:

The sampling distribution is a probability distribution of a sample statistic.

A sample statistic is a numerical value representing a characteristic of a sample. For example, the sample mean represents the mean value of the sample, the sample variance represent the variance of the sample. Both of these values are sample statistic.

A statistic is an unbiased estimator of the parameter value.

That is, the sample mean value can be used to estimate the value of population mean.

If various large samples are taken from a population and the sample statistic value is computed for each of these samples, then the probability distribution of theses sample statistic is known as the sampling distribution.

The mean of the sampling distribution is same as the population mean and the standard deviation of the sampling distribution is known as the standard error.

The correct option is:

"The distribution of the statistic in all possible samples of size <em>n</em> from a given population."

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3 years ago
Find the surface area of the rectangular prism.
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Answer:

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(-7-1)/(2-5) = -8/-3 = 8/3
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