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3 years ago

EXPALIN PLEEASSE!!::))))))))

Mathematics

1 answer:

sladkih [1.3K]3 years ago

8 0

The measure of angle 1 is 106°, because since it is a straight line they measure would have to add up to 180°.

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Express the given quantity as a single logarithm:

Naya [18.7K]

Hello,

1) Conditions:

x+2>=0==>x>-2
x>=0
So x>=0

1/5 ln(x+2)^5 +1/2 [ln x -ln(x^2+3x+2)^2]
=ln(x+2)+ ln√x - ln(x+1)(x+2)
$=ln (x+2)+ln(\dfrac{ \sqrt{x} }{(x+1)(x+2)}) \\\\

= ln(\dfrac{ \sqrt{x} }{x+1} )$

7 0

3 years ago

Read 2 more answers

What is y=-2(x+3)^2+2

cupoosta [38]

Answer:

y = -2(x + 3)² + 2

y = 2{ -(x + 3)²+ 1}

y = 2{ -(x² + 6x + 9) + 1}

y = 2{ -x² - 6x - 9 + 1}

y = 2{ -x² - 6x - 8 }

<u>y = -2 { x² + 6x + 8}</u>

<u>y = -2{(x + 4)(x + 2)}</u>

5 0

3 years ago

Suppose two adjacent endpoint of a rotated square are located at (-4, -6) and (5, -1) on the coordinates axes. What is the lengt

kompoz [17]

To find the length of side of square, we have to use distance formula.
Points are (-4,-6) and (5,-1)
Formula for distance between two points.
$d= \sqrt{( x_{2}-x_1 )^2+(y _2-y_1)^2 } \\ 
Put \ values \\
d= \sqrt{( 5+4)^2)+(-1+6)^2 } \\ 
d= \sqrt{( 9)^2)+(5)^2 } \\ 
d=\sqrt{106} \\ 
d=10.3 \ units
$
So length of side of square is 10.3 units.

Answer: 10.3 units

4 0

3 years ago

Thirty-seven percent of all Americans drink bottled water more than once a week (Natural resources Defense Council, December 4,

lesantik [10]

Answer:

a) The sampling distribution for n=540 has a mean sample proportion of p=0.37 and a standard deviation of σs=0.0208.

b) probability = 0.99998

d) probability = 0.99874

e) You gain 0.12% in probability for an increase of 80% in sample size.

The increase in sample size is not justified by the increase in probability, for this margin of error (Δp=0.09).

Step-by-step explanation:

a) We have a known population proportion π=0.37 and we have to describe the sampling distribution when the sample size is n=540.

The mean sample proportion is expected to be the same as the population proportion:

$\bar p = \pi = 0.37$

The standard deviation of the sampling will be the population standard deviation divided by the square root of the sample size:

$\sigma_s=\dfrac{\sigma}{\sqrt{n}}=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.37*0.63}{540}}=\sqrt{0.000431667}=0.0208$

Then, we can say that the sampling distribution will have a p=0.37 and a standard deviation σs=0.0208.

b) We have to calculate the probability that the sample proportion will be within 0.09 of the population proportion.

We can calculate the z-value as:

$z_1=\dfrac{p_1-\bar p}{\sigma_s}=\dfrac{0.09}{0.0208}=4.3269\\\\\\z_2=\dfrac{p_2-\bar p}{\sigma_s}=\dfrac{-0.09}{0.0208}=-4.3269$

As the distribution is symmetrical, we can calculate the probabilty that he sample proportion will be within 0.09 of the population proportion as:

$P(|p-\bar p|$

probability = 0.99998

d. Now the sample is smaller (n=300), so the standard deviation of the samping distribution:

$\sigma_s=\dfrac{\sigma}{\sqrt{n}}=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.37*0.63}{300}}=\sqrt{0.000777}=0.0279$

We have to recalculate the z-scores:

$z_1=\dfrac{p_1-\bar p}{\sigma_s}=\dfrac{0.09}{0.0279}=3.2258\\\\\\z_2=\dfrac{p_2-\bar p}{\sigma_s}=\dfrac{-0.09}{0.0279}=-3.2258$

And the probability is:

$P(|p-\bar p|$

probability = 0.99874

e. The increase in sample size is 80%

$\Delta n\%=\dfrac{n_1}{n_2}-1=\dfrac{540}{300}-1=1.8-1=0.8=80\%$

and the increase in probability is 0.12%

$\Delta P\%=\dfrac{P_1}{P_2}-1=\dfrac{0.99998}{0.99874}-1=1.0012-1=0.0012=0.12\%$

You gain 0.12% in probability for an increase of 80% in sample size.

The increase in sample size is not justified by the increase in probability, for this margin of error (Δp=0.09).

7 0

3 years ago

which three digit numbers round to 500 when rounded to the nearest hundred, and also round to 460 when rounded to the nearest te

egoroff_w [7]

455, 456, 457, 458, 459, 460, 461, 462, 463,464

5 0

3 years ago