1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
yawa3891 [41]
3 years ago
13

Please help me on this

Mathematics
2 answers:
earnstyle [38]3 years ago
6 0
The answer is D because the square root of 3^15 is 2187 square root of 3. Now if you add 3^7 then that gives you 2187. So your answer would be D
Liula [17]3 years ago
4 0
<h2>Hello!</h2>

The answer is:

The correct option is D. \sqrt{3^{15} }=3^{7}* \sqrt{3}

<h2>Why?</h2>

To solve this problem, we must remember the following properties:

Product of powers with the same base:

a^{m}a^{n}=a^{m+n}

Power of a power:

(a^{m})^{n}=a^{m*n}

Also, we must remember that if we want to introduce a number into a root, in order to not change the expression, we need to introduce it with the same exponent:

a*\sqrt{b}=\sqrt{a^{2}*b }

So, solving the problem, we have:

\sqrt{3^{15} }=3^{7}*\sqrt{3}\\\\3^{7}*\sqrt{3}=\sqrt{(3^{7})^{2} *3}\\\\\sqrt{(3^{7})^{2} *3}=\sqrt{(3^{14} *3}\\\\\sqrt{3^{14} *3}=\sqrt{3^{14+1}

\sqrt{3^{14+1} } =\sqrt{3^{15}}

Hence,

\sqrt{3^{15} }=3^{7}* \sqrt{3}

So, the correct option is D. \sqrt{3^{15} }=3^{7}* \sqrt{3}

Have a nice day!

You might be interested in
If the filling equipment is functioning properly what is the probability that the volume of oil in a randomly selected barrel wi
Sophie [7]

Answer:

P(X>55.4)=P(\frac{X-\mu}{\sigma}>\frac{55.4-\mu}{\sigma})=P(Z>\frac{55.4-55}{0.5})=P(Z>0.8)

P(Z>0.8)=1-P(Z\leq 0.8)

P(Z>0.8)=1-0.788=0.212

Step-by-step explanation:

Assuming this previous info : "Trucks carry barrels of crude oil from a port in Texas to a distributer in New Mexico on long  trailers. Filling equipment is used to fill the barrels with the oil. When functioning properly,  the actual volume of oil loaded into each barrel by the filling equipment at the port is  approximately normally distributed with a mean of 55 gallons and a standard deviation of 0.5  gallons. If the mean is greater than 55.4 gallons, the filling mechanism is overfilling."

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the amount filling of a population, and for this case we know the distribution for X is given by:

X \sim N(55,0.5)  

Where \mu=55 and \sigma=0.5

We are interested on this probability

P(X>55.4)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X>55.4)=P(\frac{X-\mu}{\sigma}>\frac{55.4-\mu}{\sigma})=P(Z>\frac{55.4-55}{0.5})=P(Z>0.8)

And we can find this probability using the complement rule:

P(Z>0.8)=1-P(Z\leq 0.8)

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.  

P(Z>0.8)=1-0.788=0.212

8 0
3 years ago
9. What is the distance along the x axis from order pairs -8, 6 and 4,6
Blababa [14]

Answer:

12 units

Step-by-step explanation:

got it right on edg

5 0
3 years ago
Ms. Hagan invested twice as much money in an account that pays 7% interest as she did in an account that pays 6% in interest. He
Karo-lina-s [1.5K]

Answer: She invested $5000 in an account that pays 6% interest and $10000 in an account that pays 7% interest.

Step-by-step explanation:

Let P be the initial amount she invested in an account that pays 6% interest.

Then, amount invested in other account = 2P

Simple interest = Principal x rate x time

After one year, for the first account,

Interest = P(0.06)(1)  = 0.06P

For second account,

Interest = (2P)(0.07)(1)=0.14P

Total interest = 0.06P+0.14P=1000

\Rightarrow\ 0.20P=1000\\\\\Rightarrow\ P=\dfrac{1000}{0.20}\\\\\Rightarrow\ P=5000

2P = 2(5000)=10000

Hence, She invested $5000 in an account that pays 6% interest and $10000 in an account that pays 7% interest.

7 0
3 years ago
Find the coordinates of the point (x,y,z) on the planez=4x+3y+1 which is closest to the origin.
Nataliya [291]
Given plane &Pi; : f(x,y,z) = 4x+3y-z = -1
Need to find point P on &Pi;  that is closest to the origin O=(0,0,0).

Solution:
First step: check if O is on the plane &Pi; : f(0,0,0)=0 &ne; -1 => O is not on &Pi;
Next:
We know that the required point must lie on the normal vector <4,3,-1> passing through the origin, i.e. 
P=(0,0,0)+k<4,3,-1> = (4k,3k,-k)
For P to lie on plane &Pi; , it must satisfy
4(4k)+3(3k)-(-k)=-1
Solving for k
k=-1/26
=>
Point P is (4k,3k,-k) = (-4/26, -3/26, 1/26) = (-2/13, -3/26, 1/26)
because P is on the normal vector originating from the origin, and it satisfies the equation of plane &Pi;
Answer: P(-2/13, -3/26, 1/26) is the point on &Pi; closest to the origin.

8 0
2 years ago
What is the value of x in this figure?
slega [8]
Check the picture below.

\bf 10\cdot \stackrel{cos(30^o)}{\cfrac{\sqrt{3}}{2}}=x\implies 5\sqrt{3}=x

5 0
3 years ago
Other questions:
  • Given the straight libe MN = NP with M(12,-3) and N(-2,9), calculate the coordinates of P.​
    9·1 answer
  • The arrow on the spinner is to be spun once.
    15·1 answer
  • Explain why f(x) is continuous at x=3
    5·2 answers
  • Write two different ratios equal to 6:30
    7·2 answers
  • What is equivalent to 1/6
    13·1 answer
  • Please answer correctly!! You will be reported if you don't!!
    6·2 answers
  • PLZZZZZZZ NEED HELP!!!!!!
    11·1 answer
  • What is the answer to this​
    8·1 answer
  • The manager of a restaurant tracks the types of dinners that customers order from the menu correct amount of food is ordered fro
    14·1 answer
  • Which is more, 70 inches or 6 feet?
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!