Answer:
$114.3
Step-by-step explanation:
Number of hours worked last week = 12hrs
Amount earned for her work hours = $98
The rate at which she earned = ?
Rate =
Rate =
= $8.17/hr
Now;
Since the total hours she worked during the weekend = 14hrs
Amount earned = $8.17/hr x 14hrs = $114.3
<h3>To find the product of 42.12 and 10^3, move the decimal point in 42.12 3 places to the right because 10^3 has 3 zeros</h3>
<em><u>Solution:</u></em>
Given that,
![\text{ product of } 42.12 \text{ and } 10^3](https://tex.z-dn.net/?f=%5Ctext%7B%20product%20of%20%7D%2042.12%20%5Ctext%7B%20and%20%7D%2010%5E3)
Which means,
![42.12 \times 10^3](https://tex.z-dn.net/?f=42.12%20%5Ctimes%2010%5E3)
Here, the exponent of 10 is positive ( which is 3)
When the exponent is positive, we have to move the decimal point to right
When you multiply a number by a power of 10, ( 10!, 10^2, and so on ) move the decimal point of the number to the right the same number of places as the number of zeros in the power of 10
Here, exponent is 3 , therefore move the decimal point right 3 places in 42.12
Therefore,
![42.12 \times 10^3 = 42120](https://tex.z-dn.net/?f=42.12%20%5Ctimes%2010%5E3%20%3D%2042120)
Answer:
mode which is c
Step-by-step explanation:
Answer:
Using trigonometric ratio:
![\sec \theta = \frac{1}{\cos \theta}](https://tex.z-dn.net/?f=%5Csec%20%5Ctheta%20%3D%20%5Cfrac%7B1%7D%7B%5Ccos%20%5Ctheta%7D)
![\tan \theta = \frac{\sin \theta}{\cos \theta}](https://tex.z-dn.net/?f=%5Ctan%20%5Ctheta%20%3D%20%5Cfrac%7B%5Csin%20%5Ctheta%7D%7B%5Ccos%20%5Ctheta%7D)
From the given statement:
and sin < 0
⇒
lies in the 3rd quadrant.
then;
![\sec \theta = \frac{1}{-\frac{4}{5}} = -\frac{5}{4}](https://tex.z-dn.net/?f=%5Csec%20%5Ctheta%20%3D%20%5Cfrac%7B1%7D%7B-%5Cfrac%7B4%7D%7B5%7D%7D%20%3D%20-%5Cfrac%7B5%7D%7B4%7D)
Using trigonometry identities:
Substitute the given values we have;
![\sin \theta = \pm\sqrt{1-(\frac{-4}{5})^2 } =\pm\sqrt{1-\frac{16}{25}} =\pm\sqrt{\frac{25-16}{25}} =\pm \sqrt{\frac{9}{25} } = \pm\frac{3}{5}](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%20%3D%20%5Cpm%5Csqrt%7B1-%28%5Cfrac%7B-4%7D%7B5%7D%29%5E2%20%7D%20%3D%5Cpm%5Csqrt%7B1-%5Cfrac%7B16%7D%7B25%7D%7D%20%3D%5Cpm%5Csqrt%7B%5Cfrac%7B25-16%7D%7B25%7D%7D%20%3D%5Cpm%20%5Csqrt%7B%5Cfrac%7B9%7D%7B25%7D%20%7D%20%3D%20%5Cpm%5Cfrac%7B3%7D%7B5%7D)
Since, sin < 0
⇒![\sin \theta = -\frac{3}{5}](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%20%3D%20-%5Cfrac%7B3%7D%7B5%7D)
now, find
:
![\tan \theta = \frac{\sin \theta}{\cos \theta}](https://tex.z-dn.net/?f=%5Ctan%20%5Ctheta%20%3D%20%5Cfrac%7B%5Csin%20%5Ctheta%7D%7B%5Ccos%20%5Ctheta%7D)
Substitute the given values we have;
![\tan \theta = \frac{-\frac{3}{5} }{-\frac{4}{5} } = \frac{3}{5}\times \frac{5}{4} = \frac{3}{4}](https://tex.z-dn.net/?f=%5Ctan%20%5Ctheta%20%3D%20%5Cfrac%7B-%5Cfrac%7B3%7D%7B5%7D%20%7D%7B-%5Cfrac%7B4%7D%7B5%7D%20%7D%20%3D%20%5Cfrac%7B3%7D%7B5%7D%5Ctimes%20%5Cfrac%7B5%7D%7B4%7D%20%3D%20%5Cfrac%7B3%7D%7B4%7D)
Therefore, the exact value of:
(a)
![\sec \theta =-\frac{5}{4}](https://tex.z-dn.net/?f=%5Csec%20%5Ctheta%20%3D-%5Cfrac%7B5%7D%7B4%7D)
(b)
![\tan \theta= \frac{3}{4}](https://tex.z-dn.net/?f=%5Ctan%20%5Ctheta%3D%20%5Cfrac%7B3%7D%7B4%7D)
Answer - 8
explanation -
6/3 = 2, meaning each “fourth” is 2. the whole team, (4/4) would be 4x2, which is 8