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3 years ago

Sixth grade

Mathematics

1 answer:

garri49 [273]3 years ago

6 0

Answer:

11-C

Step-by-step explanation:

Cause 11-C

equels the same amount as the one on the top of 11-C

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What is the value of cos x°

Bas_tet [7]

Answer:

15÷17

Step-by-step explanation:

C A/H....adjacent over hypotenuse

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3 years ago

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What is the answer to |x-4|<13

VARVARA [1.3K]

Answer:

<h2>The solution is -9 < x < 17.</h2>

Step-by-step explanation:

|x-4|<13.

The above equation means, whatever the actual value of x is, the value of (x - 4) must be greater than - 13 and less than 13.

Hence, -13 < x - 4 < 13 or, -9 < x < 17. The value of x will be in between -9 and 17. The value of x can not be -9 or 17.

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3 years ago

The length of a rectangle is 55 meters less than 44 times the width. if the perimeter is 150150 meters, find the length and the

MrRa [10]

They did not state exactly what the width or length is. So in this case, let's name the number of width to be x. And thus we can derive to the conclusion of,

Width : x
Length : x-44 (from the 1st sentence of question)
So, We all know that a rectangle has 2 Lengths and 2 widths. So we can derive the conclusion that,
2(x)+2(x-44)=150150
2x+2x-88=150150
4x-88= 150150
4x= 150150+88=150238
4x=150238
x= 150238÷4
=37559.5

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4 years ago

Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false:

kondaur [170]

$\text{Proof by induction:}$
$\text{Test that the statement holds or n = 1}$

$LHS = (3 - 2)^{2} = 1$
$RHS = \frac{6 - 4}{2} = \frac{2}{2} = 1 = LHS$
$\text{Thus, the statement holds for the base case.}$

$\text{Assume the statement holds for some arbitrary term, n= k}$
$1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2} = \frac{k(6k^{2} - 3k - 1)}{2}$

$\text{Prove it is true for n = k + 1}$
$RTP: 1^{2} + 4^{2} + 7^{2} + ... + [3(k + 1) - 2]^{2} = \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2} = \frac{(k + 1)[6k^{2} + 9k + 2]}{2}$

$LHS = \underbrace{1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2}}_{\frac{k(6k^{2} - 3k - 1)}{2}} + [3(k + 1) - 2]^{2}$
$= \frac{k(6k^{2} - 3k - 1)}{2} + [3(k + 1) - 2]^{2}$
$= \frac{k(6k^{2} - 3k - 1) + 2[3(k + 1) - 2]^{2}}{2}$
$= \frac{k(6k^{2} - 3k - 1) + 2(3k + 1)^{2}}{2}$
$= \frac{k(6k^{2} - 3k - 1) + 18k^{2} + 12k + 2}{2}$
$= \frac{k(6k^{2} - 3k - 1 + 18k + 12) + 2}{2}$
$= \frac{k(6k^{2} + 15k + 11) + 2}{}$
$= \frac{(k + 1)[6k^{2} + 9k + 2]}{2}$
$= \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2}$
$= RHS$

Since it is true for n = 1, n = k, and n = k + 1, by the principles of mathematical induction, it is true for all positive values of n.

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4 years ago

Find the IQR for the data set 24, 36, 42, 57, 65

Zielflug [23.3K]

Answer:

Step-by-step explanation:

The median of this data set is 42.

The 1st quadrant is the mean of 24 and 36: 30.

The 3rd quadrant is the mean of 57 and 65, or 61.

Thus, the IQR is the difference between 61 and 30: It is 31.

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3 years ago

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