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3 years ago

7

Spencer made a quilt for his cousin's doll. The quilt had a 7x7 array of different color square patches. If each patch is 1 3/4

in long, what is the area of the whole quilt?

1 answer:

Damm [24]3 years ago

3 0

Answer:

$\frac{2401}{16}$ square inches

Step-by-step explanation:

Given:

The quilt made by Spencer had a 7×7 array of different color square patches such that each patch is $1\frac{3}{4}$ in long.

To find: the area of the whole quilt

Solution:

Side of each quilt = $7(\frac{3}{4})=7(\frac{7}{4})=\frac{49}{4}$

Quilt is in the form of a square such that area of square is given by $(side)^2$

Therefore, area of quilt = $(side)^2=(\frac{49}{4})^2 =\frac{2401}{16}$ square inches

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A huge ice glacier in the Himalayas initially covered an area of 454545 square kilometers. Because of changing weather patterns,

guajiro [1.7K]

We have been given that a huge ice glacier in the Himalayas initially covered an area of 45 square kilo-meters. The relationship between A, the area of the glacier in square kilo-meters, and t, the number of years the glacier has been melting, is modeled by the equation $A=45e^{-0.05t}$ .

To find the time it will take for the area of the glacier to decrease to 15 square kilo-meters, we will equate $A=15$ and solve for t as:

$15=45e^{-0.05t}$

$\frac{15}{45}=\frac{45e^{-0.05t}}{45}$

$\frac{1}{3}=e^{-0.05t}$

Now we will switch sides:

$e^{-0.05t}=\frac{1}{3}$

Let us take natural log on both sides of equation.

$\text{ln}(e^{-0.05t})=\text{ln}(\frac{1}{3})$

Using natural log property $\text{ln}(a^b)=b\cdot \text{ln}(a)$ , we will get:

$-0.05t\cdot \text{ln}(e)=\text{ln}(\frac{1}{3})$

$-0.05t\cdot (1)=\text{ln}(\frac{1}{3})$

$-0.05t=\text{ln}(\frac{1}{3})$

$t=\frac{\text{ln}(\frac{1}{3})}{-0.05}$

$t=\frac{\text{ln}(\frac{1}{3})\cdot 100}{-0.05\cdot 100}$

$t=\frac{\text{ln}(\frac{1}{3})\cdot 100}{-5}$

$t=-\text{ln}(\frac{1}{3})\cdot 20$

$t=-(\text{ln}(1)-\text{ln}(3))\cdot 20$

$t=-(0-\text{ln}(3))\cdot 20$

$t=20\text{ln}(3)$

Therefore, it will take $20\text{ln}(3)$ years for area of the glacier to decrease to 15 square kilo-meters.

6 0

3 years ago

Mary has 12 video games. She purchases five new video games each month as part of a video game club.

Oxana [17]

Answer:

The answer to your question is: V = 12 + 5n

Step-by-step explanation:

Data

Video games right now = 12

She purchases 5 video games each month

Equation = ?

# of video games in n month = V

Process

- Consider the initial amount of video games

V = 12

- Now, consider the number of video games the buys each month and the months

5n

- Finally, join both terms

V = 12 + 5n

8 0

3 years ago

I would like to have equal fish tanks for my fish. I have 12 angel fish and 24 sword fish and 30 guppies .How many tanks will I

velikii [3]

I would find the common factors between all of them, and settle with the factor 3.

If I have 3 tanks:

12/3 = 4

24/3 = 8

30/3 = 10

In each of the 3 tanks, there will be 4 angel fish, 8 sword fish, and 10 guppies.

I hope I helped :)

(I hope I didn't misunderstand the question, so if I did, I'm really sorry about that.)

7 0

3 years ago

What is the common ratio of the geometric sequence below?

Lilit [14]

Answer:

The correct answer is A -3.

Step-by-step explanation:

18/(-3)=-6

To get to -6 from 18 you need to divide by -3.

To get to 2 from -6 you will divide by -3.

5 0

3 years ago

(HELP! I HAVE NO TIME) At 2pm, a store had sold 15 packs of toilet paper. By 5pm, the store had sold 57 packs of toilet paper. W

Novay_Z [31]

$\mathrm {Hey, there!}$

Let's solve your problem:

The answer would be 280%.

We know the following information:

2pm - 15 toilet paper rolls

5pm - 57 toilet paper rolls

We have to find the <u>percent rate of change.</u>

Here is how we will do this problem:

<h3><u>First, Set up a ratio:</u></h3>

Change in the quantity [15 - 57]

-------------------------------------

Original quantity [15]

57 - 15 = 42

<h3><u>Next, we will divide. the ratio.</u></h3>

Given quantity - 42

Number of packs sold at 2pm - 15

Fraction - 42/15

<h3><u>Convert the fraction to a decimal.</u></h3>

Fraction - 42/15

Decimal - 2.8

<h3><u>Make the decimal to a percent.</u></h3>

Decimal - 2.8

Percent - 28%

<u>Add a zero to the 28.</u>

<h2><u>Our answer is 280%</u></h2>

<h3></h3>

4 0

3 years ago

Read 2 more answers