Is the relationship shown by the data linear? If so, model the data with an equation.

Answer:

See below

Step-by-step explanation:

a)

[tex]2\sin(x) +\sqrt{3} =0 \implies 2\sin(x)=-\sqrt{3} \implies \boxed{\sin(x)=-\dfrac{\sqrt{3}}{2} }[/tex]

[tex]\therefore x=\dfrac{4\pi }{3}[/tex]

But note, as sine does represent the [tex]y[/tex] value, [tex]\dfrac{5\pi }{3}[/tex] is also solution

Therefore,

[tex]x=\dfrac{4\pi }{3} \text{ and } x=\dfrac{5\pi }{3}[/tex]

This is the solution for [tex]x\in[0, 2\pi ][/tex], recall the unit circle.

Note: [tex]\sin(x)=-\dfrac{\sqrt{3}}{2} \implies \sin(x)=\sin \left(\pi +\dfrac{\pi }{3} \right)[/tex]

b)

[tex]\sqrt{3} \tan(x) + 1 =0 \implies \tan(x) = -\dfrac{1}{\sqrt{3} } \implies \boxed{ \tan(x) = -\dfrac{\sqrt{3} }{3} }[/tex]

Once

[tex]\tan(x) = -\dfrac{\sqrt{3} }{3} \implies \sin(x) = -\dfrac{1}{2} \text{ and } \cos(x) = \dfrac{\sqrt{3} }{2}[/tex]

As [tex]\tan(x) = \dfrac{\sin(x)}{\cos(x)}[/tex]

[tex]\therefore x=-\dfrac{\pi }{6}[/tex]

c)

[tex]4\sin^2(x) - 1 = 0 \implies \sin^2(x) = \dfrac{1}{4} \implies \boxed{\sin(x) = \pm \dfrac{\sqrt{1} }{\sqrt{4} } = \pm \dfrac{1}{2}}[/tex]

Therefore,

[tex]\sin(x)=\dfrac{1}{2} \implies x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6}[/tex]

[tex]\sin(x)=-\dfrac{1}{2} \implies x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]

The solutions are

[tex]x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6} \text{ and }x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]

Answer:

its the same above

Step-by-step explanation:

Answer:

Step-by-step explanation:

CE and are the sides making up the sine of an angle.

CE is the side opposite the angle

DE is the side hypotenuse.

<D = 61 degrees

Sin(D) = opposite / hypotenuse

hypotenuse = 8

Sin(61) = 0.8746

CE = ?

sin(61) = CE / 8                multiply both sides  by 8

8 sin(61) = CE

CE = 8 * 0.8746

CE = 6.9969

CE = 7.0

That 0 should be included in the answer, but I think it is safe to say that if you enter 7, you will get it right.

Answer:

7.0

Step-by-step explanation:

Answer:

±√6

Step-by-step explanation:

[tex]15n=10(n+\frac{3}{n} )[/tex] is your expression first muiltiply out the 10 to get 15n= 10n+10 3/n next subtract  10 n from both sides to get 5n=10+3/n multiply both sides by n to get 5n^2=13 combine both sides and use the quadratic equation to solve to get your solution of ±√6

The identity as been verified/proved as:

[tex]1 - \tan\ a\ tan\ b = 1 - \tan\ a\ tan\ b[/tex]

Given that:

[tex]\frac{\cos(a + b)}{\cos\ a\cos b} = 1 - \tan\ a\ tan\ b[/tex]

Apply cosine identity to the numerator

[tex]\frac{\cos\ a\ cos\ b - \sin a\ sin\ b}{\cos\ a\cos b} = 1 - \tan\ a\ tan\ b[/tex]

Split the fraction:

[tex]\frac{\cos\ a\ cos\ b}{\cos\ a\cos b} - \frac{\sin a\ sin\ b}{\cos\ a\cos b} = 1 - \tan\ a\ tan\ b[/tex]

Cancel out common terms

[tex]1 - \frac{\sin a\ sin\ b}{\cos\ a\cos b} = 1 - \tan\ a\ tan\ b[/tex]

In trigonometry, we have:

[tex]\frac{\sin \theta}{\cos \theta} = \tan \theta[/tex]

So, the equation becomes:

[tex]1 - \tan\ a\ tan\ b = 1 - \tan\ a\ tan\ b[/tex]

Hence, the identity has been verified

Read more about trigonometry identities at:

https://brainly.com/question/21055284

Answer:

n= (z)22E2

n=10× 99%÷ 0.07

Answer:

one solution

Step-by-step explanation:

3 -2x=5-x+3+4x

Combine like terms

3-2x = 8+3x

Add 2x to each side

3-2x+2x = 8+3x+2x

3 = 8+5x

Subtract 8 from each side

3-8 =8+5x-8

-5 =5x

Divide by 5

-5/5 = 5x/5

-1 =x

There is one solution

Answer:

10/16=5/8

6+6+4=16

The probability is 5/8

Answer:

Years = natural log (Total / Principal) / Rate

Years = natural log (1,000,000 / 2,500) / .02

Years = natural log (400) / .02

Years =  5.9914645471 / .02

It would take  299.573227355 Years

Source: http://www.1728.org/rate2.htm

Step-by-step explanation:

Answer:

14w -14

Step-by-step explanation:

6w + 2(4w - 7)

Distribute

6w+ 8w -14

Combine like terms

14w -14

Answer:

6w+(2×4w)-(2×7)

(6w+8w)-14=14w-14

Answer:

The right response is Option c ($185,870,742).

Step-by-step explanation:

Given:

n = 30

r = 5.4%

or,

 = 0.054

Periodic payment will be:

[tex]R = \frac{360000000}{30}[/tex]

   [tex]=12000000[/tex] ($)

Now,

The present value will be:

= [tex]R+R(\frac{1-(1+r)^{-n+1}}{r} )[/tex]

By substituting the values, we get

= [tex]12000000+12000000(\frac{1-(1+0.054)^{-30 + 1}}{0.054} )[/tex]

= [tex]12000000+12000000\times 14.4892[/tex]

= [tex]185,870,742[/tex] ($)

Answer:

CI 90% = ( 0.227 ; 0.273)

Step-by-step explanation:

Information from the survey:

sample size   n = 938

number of people with yes answer  x = 235

proportion of people  p = 235/938

p = 0.25    then  q = 1 - 0.25    q = 0.75

Confidence Interval 90 % .

CI 90% = ( p ± SE )

CI 90% = ( p ± z(c)*√(p*q)/n)

CI 90 %   then significance level is  α = 10 %   α/2 = 5%

α/2 = 0.05  we find in z-table z (c) = 1.64

√(p*q)/n  = √0.25*0.75/938

√(p*q)/n  = √0.000199

√(p*q)/n  = 0.014

CI 90% = ( p ± z(c)*√(p*q)/n)

CI 90% = ( 0.25 ± 1.64*0.014)

CI 90% = ( 0.25 ± 0.023 )

CI 90% = ( 0.227 ; 0.273)

Answer:

d. The average amount of weight loss is greater than 2.5 pounds.

Step-by-step explanation:

After running a mile a day over a period of two weeks, the average amount of weight loss is 2.5 pounds.

At the null hypothesis, we test if this mean is of 2.5, that is:

[tex]H_0: \mu = 2.5[/tex]

A dietitian, who publishes health articles in a newspaper, states their new diet program helps with additional weight loss.

With the additional weight loss, the dietitian claims that the mean is more than the value presented at the null hypothesis, that is, more than 2.5, and thus, the correct answer is:

[tex]H_1: \mu > 2.5[/tex]

And thus, the correct option is given by option d.

Answer:

is 7 pieces are remian

Step-by-step explanation:

9: total

2: eaten

so, 9-2 = 7 pieces?

Answer:

team a and team c scored 74 points which is 48 points more than team b, scoring 26 points.

Step-by-step explanation:

Answer:

Answer 2/B

Step-by-step explanation:

The one with Parentheses

-(log6 x-4)

9514 1404 393

Answer:

Step-by-step explanation:

(a) As you might imagine, the disposition of apples in inventory will be one of "sold" or "discarded". (They could also be "stolen", but we'll call that "discarded", since they're not sold.) Then the inventory turnover T is the sum of numbers sold and discarded:

  T = s + d

__

(b) The value of d for Friday will be ...

  d = T -s = 34848 -29837 = 5,011 . . . value of d for Friday

Answer:          

35/5 (if you mean 10.6)    

1000000 (if you mean 10 to the sixth power)      

0.000001 (if you mean 10/6)

Answer:

There are 126 inches in 10'6

Step-by-step explanation:

take our feet and multiply the value by 12

Answer:

18

Step-by-step explanation:

The diameter is equal to twice the length of the radius

So if the radius is 9 then the diameter is 9 * 2 = 18

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{= (3^{-1}+4^{-1})^{-2}}\\\\\\\mathsf{3^{-1} = \bf {\dfrac{1}{3}}}\\\\\\\mathsf{4^{-1} = \bf \dfrac{1}{4}}\\\\\\\mathsf{= (\dfrac{1}{3}+\dfrac{1}{4})^{-2}}\\\\\\\mathsf{\dfrac{1}{3} + \dfrac{1}{4} = \bf \dfrac{7}{12}}\\\\\\\mathsf{= (\dfrac{7}{12})^{-2}}\\\\\large\text{Simplify above and you have your overall answer...}\\\\\\\boxed{\boxed{\large\textsf{Answer: }\mathsf{\bf \dfrac{144}{49}}}}\huge\checkmark[/tex]

[tex]\huge\textsf{Good luck on your assignment \& enjoy your day!}\\\\\\\\\frak{Amphitrite1040:)}[/tex]

Answer:

Inverses

Step-by-step explanation:

One things I could tell about the earth from this graph is that the northern and southern hemispheres are inverses because when the temp of one goes up over the months, the other goes down.

Answer:

x-4y=2 can be written as y=(x-2)/4

(2,0) when x=2, y=0 and (6,1) when x=6, y=1

9514 1404 393

Answer:

  asymptotes: x = ±6

  zero: x = 0

Step-by-step explanation:

The vertical asymptotes of the function will be at the values of x where the denominator is zero. The denominator is x^2 -36, so has zeros for values of x that satisfy ...

  x^2 -36 = 0

  x^2 = 36

  x = ±√36 = ±6

The vertical asymptotes of the function are x = -6 and x = +6.

__

The zero of the function is at the value of x that makes the numerator zero. This will be the value of x that satisfies ...

  6x = 0

  x = 0 . . . . . divide by 6

The zero of the function is x=0.

__

As a check on this work, we have had a graphing calculator graph the function and identify the zero.

Answer:

f = 10

g = 2 sqrt(3)

h = 20

Step-by-step explanation:

The short leg is opposite the smaller angle so it is f

The longer leg is opposite the larger angle so it is g

The hypotenuse is opposite the right angle so it is 20

We know f = x

g = x sqrt(3)

h = 2x = 20

2x = 20  so x = 10

f = 10

g = 2 sqrt(3)

h = 20

Answer:

Step-by-step explanation:

Not a clear list of options and/or reference frame

Probably     0.5      if angle t is measured from the positive x axis.

We're told that "the claim that the population of student course evaluations has a mean equal to 3.50". So this means μ=3.50 makes up the null H0

The alternative would be H1: μ ≠ 3.50 since it's the opposite of the claim made in the null.

We go with answer choice D to form the null and alternative hypotheses.

The sign ≠ in the alternative hypothesis tell us that we have a two tail test.

---------------------------------------

Let's compute the test statistic

z = (xbar - mu)/(s/sqrt(n))

z = (3.44 - 3.50)/(0.67/sqrt(89))

z = -0.84483413122896

z = -0.84

The test statistic is roughly -0.84

---------------------------------------

Despite not knowing what sigma is (aka the population standard deviation), we can see that n > 30 is the case. So we can use the Z distribution. This is the standard normal distribution. When n > 30, the T distribution is fairly approximately the same as the Z distribution.

Use a calculator or a Z table to determine that

P(Z < -0.84) = 0.2005

which is approximate

Because we're doing a two-tail test, this means we double that result to get 2*0.2005 = 0.401

The p-value is roughly 0.401

-----------------------------------------

Since the p-value is larger than alpha = 0.05, we don't have enough evidence to reject the null. So you can say that we fail to reject the null, or we accept the null.

The conclusion based on that means that μ=3.50  must be true (unless other evidence comes along to disprove this). In other words, the mean evaluation score from students appears to be 3.50

Answer:

Step-by-step explanation:

3x - 5 = 0

3x = 5

x = 5/3

2x - 10 = 0

2x = 10

x = 10/2 = 5

Answer:

A. yes

Step-by-step explanation: