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2 years ago

7

An element with mass 140 grams decays by 21.6% per minute. How much of the element is remaining after 20 minutes, to the nearest

10th of a gram?

2 answers:

balandron [24]2 years ago

8 0

The answer to this question is 1.1 grams

Salsk061 [2.6K]2 years ago

3 0

Answer:The mass of the remaining element = 1.1 grams .

Step-by-step explanation:

Exponential equation of decay : $y=A(1-r)^x$ ... (i), where A = initial value , r= rate of decay in decimal , x= time.

As per given : Initial mass : A= 140 grams

Rate of decay : r= 21.6% per minute= 0.216 per minute.

x= 20 minutes

Substitute values in (i) , we get

$y=140(1-0.216)^{20}\\\\=140(0.784)^{20}=1.0775794222\approx1.1\text{ gram}$

Hence, the mass of the remaining element = 1.1 grams .

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Mr. Snow bought 90 grams of Christmas candy for each of his 14 grandchildren. How many total kilograms of candy did he buy?

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Answer:

1.26 kg.

Step-by-step explanation:

We have been given that Mr. Snow bought 90 grams of Christmas candy for each of his 14 grandchildren. We are asked to find the amount of candy bought by Mr. Snow in kilograms.

First of all, we will find the amount of candy in grams by multiplying 90 grams by 14 as:

$\text{Amount of candy bought in grams}=14\times 90$

$\text{Amount of candy bought in grams}=1260$

We know that 1 kilogram is equal to 1000 grams. To convert 1260 grams into kg, we will divide 1260 by 1000 as:

$\text{Amount of candy bought in kilograms}=\frac{1260}{1000}$

$\text{Amount of candy bought in kilograms}=1.26$

Therefore, Mr. Snow bought 1.26 kilograms of candy.

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2 years ago

A randomly chosen subject arrives for a study of exercise and fitness and begins walking on a treadmill at a brisk pace. which o

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A discrete variable is a type of variable which contains a finite number of values. It usually takes its values from the set of whole numbers.

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2 years ago

1. Darnell reads at a constant rate

JulsSmile [24]

Answer:

Darnell can read 1,715 words in 7 minutes

Step by step Explanation:

1. I need to find out how many words he reads in 1 minute. Divide 735 by 3, my answer is 245

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2. multiply 735 by 2 cause he reads 735 words in 3 minutes and we are tryna find out how many words he reads in 7 minutes. 3×2=6, so 735+735 (735×2) equals 1470

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2 years ago

The area of the rectangle is 64.8 square centimeters. What is the perimeter of the rectangle? One group of ten tenths and one gr

9966 [12]

Answer:

(a) $Perimeter = 32.2\ cm$

(b) 100

Step-by-step explanation:

Solving (a):

Given

Shape: Rectangle

$Area = 64.8$

Required

Calculate the perimeter.

Area is calculated as:

$Area = L * W$

Where

$L = Length$ and $W = Width$

Substitute 64.8 for Area

$64.8 = L * W$

Make L the subject:

$L = \frac{64.8}{W}$

Perimeter is calculated as:

$P = 2 * (L + W)$

Substitute 64.8/W for L

$P = 2 * (\frac{64.8}{W} + W)$

$P = \frac{129.6}{W} + 2W$

To solve further, we take the derivative of P and set it to 0, afterwards.

$dP = -\frac{129.6}{W^2} + 2$

Set to 0

$0 = -\frac{129.6}{W^2} + 2$

Collect Like Terms

$\frac{129.6}{W^2} = 2$

Cross Multiply:

$2W^2= 129.6$

Divide through by 2

$W^2 = 64.8$

Take square roots

$W = \sqrt{64.8$

$W = 8.05$

Recall that:

$L = \frac{64.8}{W}$

So:

$L= \frac{64.8}{8.05}\\$

$L= 8.05$

The perimeter is:

$Perimeter = 2 * (8.05 + 8.05)$

$Perimeter = 2 * (16.10)$

$Perimeter = 32.2\ cm$

Solving (b):

Given

((1 Group of 10 tenths) and (1 group of 8 tenths))/(6 groups of 3 tenths)

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Solve

$Tenths = \frac{1}{10}$

So, the expression becomes:

((1 Group of $10 * \frac{1}{10}$ ) and (1 group of $8 * \frac{1}{10}$ ))/(6 groups of $3 * \frac{1}{10}$ )

This gives:

((1 Group of $\frac{10}{10}$ ) and (1 group of $\frac{8}{10}$ ))/(6 groups of $\frac{3}{10}$ )

Group means product, so the expression becomes:

$\frac{(1 * \frac{10}{10} \ and\ 1 * \frac{8}{10})}{6 * \frac{3}{10}}$

And, as used here means addition

$\frac{(1 * \frac{10}{10} + 1 * \frac{8}{10})}{6 * \frac{3}{10}}$

Simplify:

$\frac{(1 * 1 + 1 * 0.80)}{6 *0.30}$

$\frac{(1 + 0.80)}{1.80}$

$\frac{1.80}{1.80}$

$= 1.00$

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2 years ago

Write a expression that shows 3 times the sixth power of 10

user100 [1]

(10 raised to the power of 6)×3

(10*6) ×3

8 0

2 years ago