If an infinite series will__ it does not converge?

aalyn [17]

The answer of the question is B

8 0

3 years ago

The width of a rectangle is 6 cm less than its length. If its perimeter is 80 cm then its lengths (in cm) and area (in cm²) are

mr_godi [17]

Start by stating the given info as mathematical expressions:

1. "The width of a rectangle is 6 cm less than its length."
$w=l-6$

2. "Its perimeter is 80 cm."
$P=80$

Using the formula for perimeter ( $P=2l+2w$ ) we can show:
$80=2l+2w$ .

We now have 2 equations in 2 unknowns and can solve by substitution:
 $80=2l+2w$
$80=2l+2(l-6)$
$80=2l+2l-12)$
$92=4l$
$l=23$

The length is 23cm.

Having the length w can then find the width:
$w=l-6$
$w=23-6$
$w=17$

The width is 17cm.

And finally the area:
$A=lw$
$A=(23)(17)$
$A=391$

The area is $391cm^{2}$ .

As a check we can use the known perimeter:
$80=2l+2w$
$80=2(23)+2(17)$
$80=46+34$
$80=80$ Checks true.

5 0

4 years ago

A TV has a listed price of $647.99 before tax. If the sales tax rate is 9.75%, find the total costs of the TV with the sales tax

Lena [83]

Answer:

$647.99

Step-by-step explanation:

Divide the tax rate (9.750%) by 100 to get a decimal rate of 0.09750.

Add 1 to the decimal rate to get 1.09750.

Divide that tax-included price ($647.99) by 1.09750 price to get a pretax price of $590.42.

Subtract the pretax price from $647.99 to get the sales tax amount of $57.57.

6 0

3 years ago

Heavy football players: Following are the weights, in pounds, for offensive and defensive linemen on a professional football tea

Vaselesa [24]

Answer:

a) Mean = 302.25, Median = 309.5

b) Mean = 276.08, Median = 272

c) Offensive linemen tends to be heavier.

Step-by-step explanation:

We are given the following in the question:

Offense: 325, 292, 316, 308, 325, 263, 302, 311, 265, 329, 267, 324

Defense: 265, 276, 255, 306, 317, 281, 268, 282, 260, 261, 256, 286

a) mean and median weight for the offensive linemen

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{3627}{12} = 302.25$

$Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}$

Sorted Data: 263, 265, 267, 292, 302, 308, 311, 316, 324, 325, 325, 329

$\text{Median} = \dfrac{6^{th}+7^{th}}{2}=\dfrac{308+311}{2} = 309.5$

b) mean and median weight for the defensive linemen

$Mean =\displaystyle\frac{3313}{12} = 276.08$

Sorted Data: 255, 256, 260, 261, 265, 268, 276, 281, 282, 286, 306, 317

$\text{Median} = \dfrac{6^{th}+7^{th}}{2}=\dfrac{268+276}{2} = 272$

c) Comparison

On comparing the mean and median of offensive and defensive linemen, offensive tends to be heavier

4 0

3 years ago

M squared - 10 squared

LUCKY_DIMON [66]

That would be m squared- 100. I don't exactly know where to go from here. There isn't really enough info for me to go on. Hopefully this helps a little.

5 0

3 years ago