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3 years ago

Use the conditional statement to answer the question.

Mathematics

2 answers:

Blababa [14]3 years ago

7 0

Answer:

Here it is for you future peoples!

Step-by-step explanation:

alex41 [277]3 years ago

3 0

For a statement to be biconditional, both the statement and its inverse must be true.

The prime numbers are the numbers that can only be divided between themselves and between 1. For example: 7,19,11 .

The even numbers are those that when divided by 2, result in a whole number. If a number is not even, then it's odd .

Not all prime numbers are odd. For example, the number 2 is a prime number and is even.

The inverse of the statement is also not true. The number 9, for example, is an odd number, however, it is not a prime number, it is already divided by 3.

So both the statement and its inverse are false.

The correct answer is option D): No, because the statement and its conversation are false

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a solid consists of cylinder surmounted by a right circular cone. The height of the cone is 2h. If the volume of the solid is 3

Mademuasel [1]

Answer:

height of cylinder = 4/3 h

Step-by-step explanation:

The solid has a cylinder surmounted with a cone .Therefore, the volume of the solid is the sum of the cone and the cylinder.

volume of the solid = volume of cylinder + volume of cone

volume of the solid = πr²h + 1/3πr²h

let

height of the cylinder = H

recall

the height of the cone = 2h

volume of the solid = πr²h + 1/3πr²h

3(1/3πr²2h) = πr²H + 1/3πr²2h

2πr²h = πr²H + 2/3 πr²h

πr²(2h) = πr²(H + 2/3 h)

divide both sides by πr²

2h = H + 2/3 h

2h - 2/3h = H

H = 6h - 2h/3

H = 4/3 h

height of cylinder = 4/3 h

8 0

3 years ago

Determine the formula for the nth term of the sequence: -2,1,7,25,79,...

rodikova [14]

A plausible guess might be that the sequence is formed by a degree-4* polynomial,

$x_n = a n^4 + b n^3 + c n^2 + d n + e$

From the given known values of the sequence, we have

$\begin{cases}a+b+c+d+e = -2 \\ 16 a + 8 b + 4 c + 2 d + e = 1 \\ 81 a + 27 b + 9 c + 3 d + e = 7 \\ 256 a + 64 b + 16 c + 4 d + e = 25 \\ 625 a + 125 b + 25 c + 5 d + e = 79\end{cases}$

Solving the system yields coefficients

$a=\dfrac58, b=-\dfrac{19}4, c=\dfrac{115}8, d = -\dfrac{65}4, e=4$

so that the n-th term in the sequence might be

$\displaystyle x_n = \boxed{\frac{5 n^4}{8}-\frac{19 n^3}{4}+\frac{115 n^2}{8}-\frac{65 n}{4}+4}$

Then the next few terms in the sequence could very well be

$\{-2, 1, 7, 25, 79, 208, 466, 922, 1660, 2779, \ldots\}$

It would be much easier to confirm this had the given sequence provided just one more term...

* Why degree-4? This rests on the assumption that the higher-order forward differences of $\{x_n\}$ eventually form a constant sequence. But we only have enough information to find one term in the sequence of 4th-order differences. Denote the k-th-order forward differences of $\{x_n\}$ by $\Delta^{k}\{x_n\}$ . Then

• 1st-order differences:

$\Delta\{x_n\} = \{1-(-2), 7-1, 25-7, 79-25,\ldots\} = \{3,6,18,54,\ldots\}$

• 2nd-order differences:

$\Delta^2\{x_n\} = \{6-3,18-6,54-18,\ldots\} = \{3,12,36,\ldots\}$

• 3rd-order differences:

$\Delta^3\{x_n\} = \{12-3, 36-12,\ldots\} = \{9,24,\ldots\}$

• 4th-order differences:

$\Delta^4\{x_n\} = \{24-9,\ldots\} = \{15,\ldots\}$

From here I made the assumption that $\Delta^4\{x_n\}$ is the constant sequence {15, 15, 15, …}. This implies $\Delta^3\{x_n\}$ forms an arithmetic/linear sequence, which implies $\Delta^2\{x_n\}$ forms a quadratic sequence, and so on up $\{x_n\}$ forming a quartic sequence. Then we can use the method of undetermined coefficients to find it.

5 0

2 years ago

Helen bought notebooks and pencils for school. The number of pencils she bought is given by 6(n-3) , where n is the number of no

pychu [463]

So the number of pencils bought can be represented by an equation: $P=6(n-3)$ , where n is the number of notebooks bought. Since Helen bought 5 notebooks, simply plug 5 into n: $P=6(5-3)=6(2)=12$ . So Helen bought 12 pencils.

3 0

3 years ago

a rectangular pyramid has a volume of 190 cubic centimeters. Find two possible sets of measurements for the base area and height

DerKrebs [107]

<h3>One possible set for the base area and height of the pyramid is 570 cm and 1 cm respectively</h3><h3>Other possible set for the base area and height of the pyramid is 285 cm and 2 cm respectively</h3>

Solution:

The volume of rectangular pyramid is given as:

$Volume = \frac{1}{3} \times base\ area \times height$

Given that,

Rectangular pyramid has a volume of 190 cubic centimeters

$190= \frac{1}{3} \times base\ area \times height$

Substitute, base area = 570 and height = 1

Then we get,

$190 = \frac{1}{3} \times 570 \times 1\\\\190 = 190$

Thus one possible set for the base area and height of the pyramid is 570 cm and 1 cm respectively

Substitute, base area = 285 and height = 2

$190 = \frac{1}{3} \times 285 \times 2\\\\190 = \frac{1}{3} \times 570\\\\190 = 190$

Thus other possible set for the base area and height of the pyramid is 285 cm and 2 cm respectively

6 0

3 years ago

It is given that the straight line y = (q + 2)x + 10 is parallel to the straight line 4x + 2y = 5. Find the value of q.

solmaris [256]

Answer:

q= -4

Step-by-step explanation:

First, simplify 4x+2y=5

2y=-4x+5

y=-2x+5/2

q+2 has to equal to -2

q = -4

7 0

2 years ago