<span>First, we need to know that the current recommended daily allowance of Vitamin E is 15 milligrams. If Leena ate four tablespoons of peanut butter, thus receiving only 6 milligrams, then we can determine the percentage by first dividing 100 into 15 parts (which gives us 6.66), and then multiply that answer by 6 (6 x 6.66), which gives us precisely 40. Thus, the answer is 40 percent.</span>
Answer:
Step-by-step explanation:
Hello,
<em>"Ray says the third-degree polynomial has four intercepts. Kelsey argues the function can have as many as three zeros only."</em>
We know that Kelsey is right, a polynomial of degree 3 has maximum 3 zeroes, so it means that the graph of this polynomial has maximum 3 x-intercepts.
<u>So how Ray can be right too?</u>
we need to think of y-intercept, if we add the y-intercept then Ray can be right too,
as you can see in one example below
there are 3 x-intercepts and 1 y-intercept.
This being said, Ray is not always right. For instance 
has only 1 zero (multiplicity 3) its graph has only 1 intercept in the point (0,0)
hope this helps
Find <span>tan<span>(<span><span>5π</span>12</span>)</span></span> and sin ((5pi)/12)
Answer: <span>±<span>(2±<span>√3</span>)</span>and±<span><span>√<span>2+<span>√3</span></span></span>2</span></span>
Explanation:
Call tan ((5pi/12) = t.
Use trig identity: <span><span>tan2</span>a=<span><span>2<span>tana</span></span><span>1−<span><span>tan2</span>a</span></span></span></span>
<span><span>tan<span>(<span><span>10π</span>12</span>)</span></span>=<span>tan<span>(<span><span>5π</span>6</span>)</span></span>=−<span>1<span>√3</span></span>=<span><span>2t</span><span>1−<span>t2</span></span></span></span>
<span><span>t2</span>−2<span>√3</span>t−1=0</span>
<span>D=<span>d2</span>=<span>b2</span>−4ac=12+4=16</span>--> <span>d=±4</span>
<span>t=<span>tan<span>(<span><span>5π</span>12</span>)</span></span>=<span><span>2<span>√3</span></span>2</span>±<span>42</span>=2±<span>√3</span></span>
Call <span><span>sin<span>(<span><span>5π</span>12</span>)</span></span>=<span>siny</span></span>
Use trig identity: <span><span>cos2</span>a=1−2<span><span>sin2</span>a</span></span>
<span><span>cos<span>(<span><span>10π</span>12</span>)</span></span>=<span>cos<span>(<span><span>5π</span>6</span>)</span></span>=<span><span>−<span>√3</span></span>2</span>=1−2<span><span>sin2</span>y</span></span>
<span><span><span>sin2</span>y</span>=<span><span>2+<span>√3</span></span>4</span></span>
<span><span>siny</span>=<span>sin<span>(<span><span>5π</span>12</span>)</span></span>=±<span><span><span>√<span>2+<span>√3</span></span></span>2</span></span></span>
Answer:
By the Central Limit Theorem, the average value for all of the sample means is 14.
Step-by-step explanation:
We use the central limit theorem to solve this question.
The Central Limit Theorem estabilishes that, for a random variable X, with mean 
and standard deviation 
, the sample means of size n can be approximated to a normal distribution with mean and standard deviation, which is also called standard error 
If the population mean is μ = 14, then what is the average value for all of the sample means?
By the Central Limit Theorem, the average value for all of the sample means is 14.
12 inches go into one foot, so we can calculate the volume of the tank in inches to make the calculations that follow easier. Therefore, to calculate the volume of the tank, we use length x breadth x height = 4 x 2 x 2 = 16 square feet x 12 for square inches = 192 square inches.
Every 12 square inches Joseph can fit a one inch fish. The fish that he has are 3 inches long, therefore he can only fit one fish every 36 square inches.
That means that if we take the total volume of the tank and divide it by the space that a 3 inch fish will take up, we are left with 192/36 = 5.3 fish.
You cannot have a third of a fish, so we round off to the nearest whole number, and we determine that Joseph can put 5 fish in his new aquarium.
