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Arlecino [84]
3 years ago
7

Cos²45+Sin²60 + sin^2 30​

Mathematics
1 answer:
denpristay [2]3 years ago
4 0

Step-by-step explanation:

{ \cos}^{2} 45 \degree +  { \sin}^{2} 60 +  { \sin}^{2} 30 \degree \\  =  \bigg( \frac{1}{ \sqrt{2} }  \bigg)^{2}  +  \bigg( \frac{ \sqrt{3} }{ 2}  \bigg)^{2}  +  \bigg( \frac{1}{2}  \bigg)^{2}   \\  \\  =  \frac{1}{2}  +  \frac{3}{4}  +  \frac{1}{4}  \\  \\  =  \frac{2}{4}  + \frac{3}{4}  +  \frac{1}{4}  \\   \\  =  \frac{2 + 3 + 1}{4}  \\  \\  =  \frac{6}{4}  \\  \\  =  \frac{3}{2}  \\  \\  = 1 \frac{1}{2}  \\

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prohojiy [21]
It will take 2 years.

Year 1 :
4% 2.5k = 2.5k/100 × 4 = $100 in interest

$2.5k + $0.1k = $2.6k

Year 2 :
4% 2.6k = 2.6k/100 × 4 = $104 in interest

$100 + $104 = $204 > $200

There may be a simpler way to solve this using a formula for example, but I just solved this step by step. Please feel free to ask if you have any questions
7 0
3 years ago
Who was targeted by the crusaders wh ile heading to constantinople​
Likurg_2 [28]

Answer:

I believe Jerusalem was captured

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3 years ago
A dog and a cat are 200 meters apart when they see each other. The dog can run at a speed of 30 meter per second, while the cat
LenKa [72]

Answer:

They'll meet after 200 meters , if they simultaneously start running towards each other.

Step-by-step explanation:

Let x =distance travelled by dog and 200-x be the distance travelled by cat. Inorder to meet, the sum of their travelled distances shall be equal to 200 meters as they are far apart by 200 meters.

Dog: Distance =Speed x time: x=30t

Cat: Distance = 200-x

=24t

The sum of their distance travelled shall be 200 meters: 30t+ 24t= 200;54t=200;t=200/54=3.7secs

So they will meet after 3.7 seconds

To check:

Distance travelled by dog :x=30(3.7)

=111.11 meters

Distance travelled by cat: 24t=24(3.7)

=88.89 meters

Therefore since they are travelling towards each other and their distance apart is 200 meters, after 3.7 seconds they will meet because dog travelled 111.11 meters and cat travelled 88.89 meters and they covered already 200 meters as the sum of 111.11+ 88.89

=200 meters

6 0
2 years ago
Can you help me in write the perimeter of the triangle in a simplest form
Angelina_Jolie [31]

I got 6x+3



The three equations are:

(2x-6) + (3x+1) + (x+8) =perimeter

2x+3x+x/1x=6x

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8 0
3 years ago
A doctor wants to estimate the mean HDL cholesterol of all​ 20- to​ 29-year-old females. The number of subjects needed to estima
Ludmilka [50]

Answer:

n=(\frac{1.64(14.7)}{3})^2 =64.57 \approx 65

So the answer for this case would be n=65 rounded up to the nearest integer

And the sample size would decrease by 160-65=95 subjects

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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".

\bar X represent the sample mean for the sample  

\mu population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

ME represent the margin of error

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

2) Solution to the problem

Since the new Confidence is 0.90 or 90%, the value of \alpha=0.1 and \alpha/2 =0.05, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that z_{\alpha/2}=1.64

Assuming that the deviation is known we can express the margin of error is given by this formula:

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}    (a)

And on this case we have that ME =\pm 3 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

n=(\frac{z_{\alpha/2} \sigma}{ME})^2   (b)

Replacing into formula (b) we got:

n=(\frac{1.64(14.7)}{3})^2 =64.57 \approx 65

So the answer for this case would be n=65 rounded up to the nearest integer

And the sample size would decrease by 160-65=95 subjects

8 0
3 years ago
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