Ask question

Ask question

All categories

2 years ago

10

Dion’s grandmother is making a quilt using four small squares put together to form one large square block. How many different bl

ocks can she make using one each of red, green, blue, and yellow small squares? Show the possible arrangements.

1 answer:

Anon25 [30]2 years ago

6 0

Answer:

6 different arrangements

Step-by-step exp

Wish this help

You might be interested in

Luke invited 20 more boys than girls to his birthday party. However, only ¾ of the boys and ⅔ of the girls came. Exactly 19 of L

sveta [45]

Answer:

68

Step-by-step explanation:

Let:

Number of girls invited = x

Number of boys = x +20

3/4 of boy showed up

2/3 of girls showed up

Exactly 19 did not show up

Therefore, we could say:

Fraction of boys that didn't show up = 1 - 3/4 = 1/4

Fraction of girls that didn't show up = 1 - 2/3 = 1/3

That is,

[1/4 *(x + 20)] + [1/3*x] = 19

[(x + 20) / 4] + x /3 = 19

(3(x + 20) + 4x) / 12 = 19

3x + 60 + 4x = 228

7x = 228 - 60

7x = 168

x = 168 / 7

x = 24

Number of girls, x = 24

Number of boys, x + 20 = 24 + 20 = 44

Total friends invited = (24 + 44) = 68

8 0

2 years ago

On a map if 1/2 inch equals 5 miles how long would 180 miles be on the map

anzhelika [568]

18 inches would be the answer

5 0

2 years ago

An average human heart beats 60 times per minute. If an average person lives to the age of 75, how many times does the average h

boyakko [2]

Answer:

The average number of beats in a lifetime would be 2,365,200,000

Step-by-step explanation:

To find the amount we need to take basic steps. The first step is multiplying the number of beats to find out how many are in an hour. Since there are 60 in a minute and 60 minutes in an hour, multiply the two.

60 beats * 60 minutes = 3,600 beats per hour.

Now multiply the amount of beats in an hour by the number of hours in a day.

3,600 * 24 hours = 86,400 beats per day

Now multiply the number of days in a year. Technically there is 365 1/4 in a year, but we'll use the flat rate of 365 since that is generally the accepted answer.

86,400 * 365 days = 31,536,000 beats per year

And now we take that number and multiply by the number of years that he lines

31,536,000 * 75 years = 2,365,200,00 beats in a lifetime

5 0

3 years ago

Read 2 more answers

Please help me with these?!

Illusion [34]

1. We have the formula for the volume of sphere: $V= \frac{4 \pi }{3}r^3$
where
$V$ is the volume
$r$ is the radius
We know from our problem that the volume of our spherical balloon is $100in^3$ , so $V=100in^3$ . Lets replace that value in our formula and solve for $r$ :
$100in^3= \frac{4 \pi }{3}r^3$
$3(100in^3)=4 \pi r^3$
$300in^3=4 \pi r^3$
$r^3= \frac{300in^3}{4 \pi }$
$r= \sqrt[3]{\frac{300in^3}{4 \pi } }$
$r=2.879in$

We can conclude that the radius of our spherical balloon is approximately 3 inches long. Therefore, the correct answer is A. 3 in.

2. Lets simplify each one of the expressions first:
F. $\sqrt{x^2}$ since the radicand is elevated to the same number as the index of the radical, we can cancel the radical and the exponent:
$\sqrt{x^2} =x$
Since $x\ \textgreater \ 0$ , this expression is equal to $x$ .
G. $\frac{1}{2} \sqrt[3]{8x^3}$ 8 can be expressed as $8=2*2*2=2^3$ , so we can rewrite our radicand:
$\frac{1}{2} \sqrt[3]{8x^3} =\frac{1}{2} \sqrt[3]{2^3x^3} = \frac{1}{2} \sqrt[3]{(2x)^3}$
Since the radicand is elevated to the same number as the index of the radical, we can cancel the radical and the exponent:
$\frac{1}{2} \sqrt[3]{(2x)^3}= \frac{1}{2} (2x)$
Now, we can cancel the 2 in the denominator with the one in the numerator:
$\frac{1}{2} (2x)=x$
Since $x\ \textgreater \ 0$ , this expression is equal to $x$ .
H. $\sqrt[3]{-x^3}$ The radicand is elevated to the same number as the index of the radical, so we can cancel the radical and the exponent:
$\sqrt[3]{-x^3}=-x$
Since $x\ \textgreater \ 0$ , this expression is NOT equal to $x$ .

We can conclude that the correct answer is H. $\sqrt[3]{-x^3}$ .

3. The fourth root of $- \frac{16}{81}$ is $\sqrt[4]{ -\frac{16}{81} }$ . Remember that negative numbers don't have real even roots since a number raised to an even exponent is either positive or 0. Since 4 is even and $- \frac{16}{81}$ is negative, we can conclude that $- \frac{16}{81}$ has not a real fourth root.

The correct answer is D. no real root found.

4. This time we are going to take a different approach. We are going to simplify $\sqrt{a^2(x+a^2)}$ first, and then, we are going to compare the result with our given options:
$\sqrt{a^2(x+a^2)}$
Lets apply the product rule for a radical $\sqrt[n]{ab} = \sqrt[n]{a} \sqrt[n]{b}$ :
$\sqrt{a^2(x+a^2)} = \sqrt{a^2} \sqrt{x+a^2}$
Notice that in our first product the radicand is raised to the same number as the index, so we can cancel the radical and the exponent:
$\sqrt{a^2} \sqrt{x+a^2}=a \sqrt{x+a^2}$

We can conclude that the correct answer is F. $a \sqrt{x+a^2}$

5. Just like before, we are going to simplify $\sqrt{4x^2y^4}$ firts, and then, we are going to compare the result with our given options. To simplify our radical expression we are going to use some laws of radicals:
$\sqrt{4x^2y^4}$
Applying product rule for a radical $\sqrt[n]{ab} = \sqrt[n]{a} \sqrt[n]{b}$ :
$\sqrt{4x^2y^4} = \sqrt{4} \sqrt{x^2} \sqrt{y^4}$
Notice that $\sqrt{4} =2$ , so:
$\sqrt{4} \sqrt{x^2} \sqrt{y^4} =2 \sqrt{x^2} \sqrt{y^4}$
Notice that $y^4=(y^2)^2$ , so we can rewrite our expression:
$2 \sqrt{x^2} \sqrt{y^4}=2 \sqrt{x^2} \sqrt{(y^2)^2}$
Applying the radical rule $\sqrt[n]{a^n} =a$ :
$2 \sqrt{x^2} \sqrt{(y^2)^2} =2xy^2$

We can conclude that the correct answer is A. $2xy^2$ .

5. Lets check our statements:
F. $x$ is always greater than $\sqrt{x}$ .
If $x=0$ , $\sqrt{x} =0$ . Therefore, this statement is FALSE.
G. $x= \sqrt{x}$ only if $x=0$ . For a number bigger than zero the square root of that number will be always less than the number; therefore, this statement is TRUE.
H. Using a calculator we can check that $\sqrt{ \frac{1}{2} } =0.7071$ and $\frac{1}{2} =0.5$ . Since $0.7071\ \textgreater \ 0.5$ , we can conclude that $\sqrt{ \frac{1}{2} } \ \textgreater \ \frac{1}{2}$ .
We can conclude that this statement is TRUE.
J. $x^4$ is always bigger than $x^2$ .
If $x= \frac{a}{b}$ and $b\ \textgreater \ a$ , $x^4$ will always be smaller than $x^2$ . Therefore, we can conclude that this statement is FALSE.

6. We know that the formula for the volume of cube is $V=s^3$
where
$V$ is the volume
$s$ is the side
We know for our problem that a cubical storage bin has a volume of 5832 cubic inches, so $V=5832in^3$ . Lets replace that value in our formula and solve for $s$ :
$5832in^3=s^3$
$s^3=5832in^3$
$s= \sqrt[3]{5832in^3}$
$s=18in$

We can conclude that the length of the side of the cubical storage bin is 18 inches.

8 0

3 years ago

The sum of two numbers is 20. The difference between three times the first number and twice the second is 40. Find the two numbe

KiRa [710]

Their sum can be written as : a+b=20. this means that b=20-a

and the phrase: The difference between three times the first number and twice the second is 40 like this:

3a-2b=40

and we can substitute:
3a-2b=40
3a-2(20-a)=40
3a-40+2a=40

5a=40+40
5a=80

a=16
so b must be 4!

let's check:

3*16-2*4=48-8=40 correct!

4 0

2 years ago