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svetlana [45]
3 years ago
6

What is -3y(y-8)(2y+1)=0

Mathematics
1 answer:
Marta_Voda [28]3 years ago
7 0

Step-by-step explanation:

(-3y^2+24y)(-6y^2-3y)

open the bracket and collect the like terms

-3y^2-6y^2+24y-3y

-9y^2+21y

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Hensley earns $8.50 per hour at an amusement park. She received a 12% raise when she becomes a manager at the gift store. How mu
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First, find 12% of $8.50.

12% of $8.50 = 12% * $8.50 = 0.12 * $8.50 = $1.02

The raise is $1.02 per hour.

$8.50 + $1.02 = $9.52

Hear new hourly earnings are $9.52/hour.
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What is the least common multiple of 4 and 6?<br><br><br><br> Enter your answer in the box.
Schach [20]
12 is the least common multiple
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The radius of a circle is 19 in. Find its circumference in terms of \piπ
Ulleksa [173]

Answer:

38π

Step-by-step explanation:

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10 + 3x &lt; 4 or 2x + 5 &gt; 11 in interval notation​
Stella [2.4K]

Answer:

( − ∞ , ∞ ) hope i help

Step-by-step explanation:

First, solve each inequality. I'll solve the first one first.

7 ≥ 2 x − 5

12 ≥ 2 x

6 ≥ x

Therefore, x could be any number less than or equal to 6. In interval notation, this looks like:

( − ∞ , 6 ]

The parenthesis means that the lower end is not a solution, but every number above it is. (In this case, the lower end is infinity, so a parenthesis must be used, since infinity is not a real number and so it cannot be a solution.) The bracket means that the upper end is a solution. In this case, it indicates that not only could  

x

be any number less than 6, but it could also be 6.

Let's try the second example:

3 x − 2 4 > 4

3 x − 2 > 16    3 x > 18 x > 6

Therefore, x could be any number greater than 6, but x couldn't be 6, since that would make the two sides of the inequality equal. In interval notation, this looks like:

( 6 , ∞ )  

The parentheses mean that neither end of this range is included in the solution set. In this case, it indicates that neither 6 nor infinity are solutions, but every number in between 6 and infinity is a solution (that is, every real number greater than 6 is a solution).

Now, the problem used the word "OR", meaning that either of these equations could be true. That means that either  x  is on the interval  ( − ∞ , 6 ] or the interval  ( 6 , ∞ )

. In other words,  x

is either less than or equal to 6, or it is greater than 6. When you combine these two statements, it becomes clear that  

x

could be any real number, since no matter what number  

x

is, it will fall in one of these intervals. The interval "all real numbers" is written like this:

( − ∞ , ∞ )

6 0
3 years ago
Allen�s hummingbird (Selasphorus sasin ) has been studied by zoologist Bill Alther A small group of 15 Allen� s hummingbirds has
Bogdan [553]

Answer:

1) 80% CI: [3.04; 3.26]gr

d= 0.11

2) n= 28 hummingbirds

Step-by-step explanation:

Hello!

The study variable of this experiment is:

X: the weight of a hummingbird. (gr)

And it has a normal distribution, symbolically: X~N(μ;σ²)

And (I hope I got it correctly) its population standard deviation is σ= 0.33

There was a sample of n= 15 hummingbirds taken, its sample mean X[bar]= 3.15 gr

1) You need to construct an 80% Confidence Interval for the population mean of the hummingbird's weight.

Since the study variable has a normal distribution, you can use either the standard normal distribution or the Student's t distribution. Both are useful to estimate the population mean. Since the population standard variance is known, the best choice is the Standard normal.

Z= <u> X[bar] - μ </u>~ N(0;1)

       σ/√n

The formula for the interval is:

X[bar] ± Z_{1- \alpha /2} * (σ/√n)

Z_{1- \alpha /2}= Z_{0.90} = 1.28

3.15 ± 1.28 * (0.33/√15)

[3.04; 3.26]gr

The margin of error (d) of a confidence interval is hal its amplitude (a)

a= Upper bond - Lower bond

d= (Upper bond - Lower bond)/2

d= \frac{(3.26-3.04)}{2} = 0.11

2) You need to calculate a sample size for a 80% Confidence interval for the average weight of the hummingbirds with a margin of error of d= 0.08

As I said before, the margin of error is half the amplitude of the interval, the formula you use to estimate the population mean has the following structure:

"point estamator" ± "margin of error"

Then the margin of error is:

d= Z_{1- \alpha /2} * (σ/√n)

Now what you have to do is rewrite the formula based on the sample size

d= Z_{1- \alpha /2} * (σ/√n)

\frac{d}{Z_{1- \alpha /2}}= σ/√n

√n * \frac{d}{Z_{1- \alpha /2}}= σ

√n = σ * \frac{Z_1- \alpha /2}{d}

n = (σ * \frac{Z_1- \alpha /2}{d})²

n=  (0.33 * \frac{1.28}{0.08})²

n= 27.8784 ≅ 28 hummingbirds.

I hope it helps!

4 0
3 years ago
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