Answer: ![7\times10^{19} buckets](https://tex.z-dn.net/?f=7%5Ctimes10%5E%7B19%7D%20buckets)
Step-by-step explanation:
Given: A cubic kilometer=
cubic centimeters
The volume of world’s oceans=
cubic kilometers of water.
⇒ The volume of world’s oceans=
cubic centimeters of water.
Volume of a bucket = 20,000 cubic centimeters of water.
The number of bucket-loads would it take to bucket out the world’s oceans
![n=\frac{\text{volume of ocean}}{\text{volume of bucket}}=\frac{1.4\times10^{9}\times10^{15}}{20000}](https://tex.z-dn.net/?f=n%3D%5Cfrac%7B%5Ctext%7Bvolume%20of%20ocean%7D%7D%7B%5Ctext%7Bvolume%20of%20bucket%7D%7D%3D%5Cfrac%7B1.4%5Ctimes10%5E%7B9%7D%5Ctimes10%5E%7B15%7D%7D%7B20000%7D)
![\Rightarrow\ n=\frac{1.4\times10^{9+15}}{0.2\times10^5}......[a^n\times a^m=a^{m+n}]\\\Rightarrow\ n=7\times10^{24-5}.....[\frac{a^m}{a^n}=a^{m-n}]\\\Rightyarrow\ n=7\times10^{19}](https://tex.z-dn.net/?f=%5CRightarrow%5C%20n%3D%5Cfrac%7B1.4%5Ctimes10%5E%7B9%2B15%7D%7D%7B0.2%5Ctimes10%5E5%7D......%5Ba%5En%5Ctimes%20a%5Em%3Da%5E%7Bm%2Bn%7D%5D%5C%5C%5CRightarrow%5C%20n%3D7%5Ctimes10%5E%7B24-5%7D.....%5B%5Cfrac%7Ba%5Em%7D%7Ba%5En%7D%3Da%5E%7Bm-n%7D%5D%5C%5C%5CRightyarrow%5C%20n%3D7%5Ctimes10%5E%7B19%7D)
hence,
bucketloads would it take to bucket out the world’s oceans.
Answer:
Teachers in his school district have less than 5 yearſ of experience on average is true.
Step-by-step explanation:
Sample mean = ![\bar{x}=4](https://tex.z-dn.net/?f=%5Cbar%7Bx%7D%3D4)
Sample standard deviation = s = 2
We are supposed to to test Ha :u= 5 versus H : u < 5 using a sample of 25 teachers
![H_a:\mu=5\\H_0:\mu < 5](https://tex.z-dn.net/?f=H_a%3A%5Cmu%3D5%5C%5CH_0%3A%5Cmu%20%3C%205)
n = 25
Since n<30 and population standard deviation is unknown
So, we will use t test
Formula : ![t=\frac{x-\mu}{\frac{s}{\sqrt{n}}}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Cfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D%7D)
![t=\frac{4-5}{\frac{2}{\sqrt{25}}}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B4-5%7D%7B%5Cfrac%7B2%7D%7B%5Csqrt%7B25%7D%7D%7D)
t=-2.5
![\alpha = 0.05](https://tex.z-dn.net/?f=%5Calpha%20%3D%200.05)
Degree of freedom = n-1 = 25-1 = 24
Refer the t table
![t_{df,\frac{\alpha}{2}}=t_{24,\frac{0.05}{2}}=2.064](https://tex.z-dn.net/?f=t_%7Bdf%2C%5Cfrac%7B%5Calpha%7D%7B2%7D%7D%3Dt_%7B24%2C%5Cfrac%7B0.05%7D%7B2%7D%7D%3D2.064)
t critical > t calculated
So, We are failed to reject null hypothesis
So, teachers in his school district have less than 5 yearſ of experience on average is true.
Using relations in a right triangle, it is found that:
sin(x) = cos(y) = 0.6.
Since angles x and y are complementary, we have that sin(x) = cos(y), that is, the ratio is of 1.
<h3>What are the relations in a right triangle?</h3>
The relations in a right triangle are given as follows:
- The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.
- The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.
- The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.
Applying the Pythagorean Theorem, the hypotenuse is given by:
h² = 3² + 4²
h² = 25
h = 25.
Hence, applying the definitions:
Since angles x and y are complementary, we have that sin(x) = cos(y), that is, the ratio is of 1.
More can be learned about relations in a right triangle at brainly.com/question/26396675
#SPJ1
Answer:
The length of the long piece is 33 meter.
Step-by-step explanation:
Given : For their homecoming parade, the students of U-Math have created a colorful banner, 43 meters in length, that is made of two pieces of parachute material. The short price is 23 meters shorter than the long piece.
To find : The length of each piece ?
Solution :
Let the length of the longer piece be 'x'
and the length of the shorter piece be 'y'
Total length is 43 meters.
So,
...(1)
The short price is 23 meters shorter than the long piece.
i.e.
...(2)
Solving (1) and (2) by adding (1) and (2),
![x+y+x-y=43+23](https://tex.z-dn.net/?f=x%2By%2Bx-y%3D43%2B23)
![2x=66](https://tex.z-dn.net/?f=2x%3D66)
![x=33](https://tex.z-dn.net/?f=x%3D33)
Substitute in (1),
![33+y=43](https://tex.z-dn.net/?f=33%2By%3D43)
![y=10](https://tex.z-dn.net/?f=y%3D10)
The length of the short piece is 10 meter.
The length of the long piece is 33 meter.