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3 years ago

If sin(2x)=cos (x+30°), what is the value of x?

Mathematics

1 answer:

denis23 [38]3 years ago

5 0

Step-by-step explanation:

$\sin(2x)= \cos (x+30°) \\ \\ \therefore \: \cos(90 \degree - 2x)= \cos (x+30°)\\ \{\because \sin \theta = \cos(90°-\theta)\} \\ \\ \therefore \: 90\degree - 2x = x+30° \\ \\ \therefore \: 90\degree - 30\degree = x + 2x \\ \\ \therefore \: 60\degree =3 x\\ \\ \therefore \: x = \frac{60\degree}{3} \\ \\ \huge \red{ \boxed{ \therefore \: x = 20 \degree }}$

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Please help, I am super stuck and I cant lose points<br><br> this homework is 16 points total

bekas [8.4K]

Hello,

7) A∪C={1,2,3,4,5,7,9}

8) A∩B={2,4}

C'= complement of C ={2,4,6}

9) A∪B∩C'={1,2,3,4,6,8}∩{2,4,6}={2,4,6}

10) A∪(B∩C')={1,2,3,4}∩{2,4,6}={1,2,3,4,6}

Are you blind?

4 0

3 years ago

What is the equation of the line that passes through the point (4. -2) and has a<br> slope of 5/4?

KIM [24]

Answer:

y = 5/4 x - 7

Step-by-step explanation:

y - y1 = m(x - x1)

y + 2 = 5/4 (x - 4)

y + 2 = 5/4 x - 5

y = 5/4 x - 7

7 0

1 year ago

In the production of a plant, a treatment is being evaluated to germinate seed. From a total of 60 seed it was observed that 37

djyliett [7]

Answer:

More than 50% would germinate

Step-by-step explanation:

Given that in the production of a plant, a treatment is being evaluated to germinate seed. From a total of 60 seed it was observed that 37 of them germinated

Let us check whether more than 50% will germinate using hypothesis test

$H_0: p = 0.50\\H_a: p>0.50\\$

(right tailed test)

Sample proportion p = $\frac{37}{60} =0.617\\q = 0.383\\Std error = \sqrt{\frac{pq}{n} } =0.0628$

p difference = 0.117

Test statistic Z = p difference/std error = 1.864

p value =0.0312

Since p value <0.05 our significance level of 5% we reject null hypothesis

It is possible to claim that most of the seed will germinate (i.e. more than 50%)

7 0

3 years ago

A blueprint uses a scale factor of 3 inches = 2 feet. What is the area on the blueprint of a 3,500 square foot house in inches?

lyudmila [28]

Answer:

7875 square inches

Step-by-step explanation:

4ft^2 = 2ft * 2ft

4ft^2 = 3in * 3in

4ft^2 = 9in^2

For 3,500 square foot

3,500 square foot = x

Divide bith expressions

4/3500 = 9/x

4x = 9 * 3500

4x = 31500

x = 31500/4

x = 7875 square inches

Hence the area of the house in inches is 7875 square inches

6 0

3 years ago

A company with a large fleet of cars wants to study the gasoline usage. They check the gasoline usage for 50 company trips chose

Nookie1986 [14]

Answer:

The 95% confidence interval is given by (25.71536 ;28.32464)

And if we need to round we can use the following excel code:

round(lower,2)

[1] 25.72

round(upper,2)

[1] 28.32

And the interval would be (25.72; 28.32)

Step-by-step explanation:

Notation and definitions

n=50 represent the sample size

$\bar X= 27.2$ represent the sample mean

$s=5.83$ represent the sample standard deviation

m represent the margin of error

Confidence =88% or 0.88

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".

Calculate the critical value tc

In order to find the critical value is important to mention that we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 88% of confidence, our significance level would be given by $\alpha=1-0.88=0.12$ and $\alpha/2 =0.06$ . The degrees of freedom are given by: