What is the area of the circle shown below? Please
answer quickly! 20 points

Answer:

[tex]sinx=-\dfrac{12}{13}[/tex]

[tex]cosx=-\dfrac{5}{13}[/tex]

[tex]cotx=\dfrac{5}{12}[/tex]

Step-by-step explanation:

Given that:

[tex]\dfrac{12}{5} = tan(x)[/tex]

[tex]\pi <x < 3\pi/2[/tex]

i.e. x is in 3rd quadrant. So tan is positive.

To find:

sin(x), cos(x), and cot(x).

Solution:

Given that:

[tex]\dfrac{12}{5} = tan(x)[/tex]

We know by trigonometric identities that:

[tex]tan\theta =\dfrac{Perpendicular}{Base}[/tex]

Comparing with the given values:

[tex]\theta=x[/tex]

Perpendicular = 12 units

Base = 5 units

Using pythagorean theorem, we can find out hypotenuse:

According to pythagorean theorem:

[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}[/tex]

[tex]\Rightarrow Hypotenuse=\sqrt{12^2+5^2}\\\Rightarrow Hypotenuse=\sqrt{169} = 13 units[/tex]

We can easily find out the values of:

[tex]sinx, cos x\ and\ cot x[/tex]

[tex]sin\theta =\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]sinx =\dfrac{12}{13}[/tex]

Given that x is in 3rd quadrant, sinx will be negative.

[tex]\therefore sinx =-\dfrac{12}{13}[/tex]

[tex]sin\theta =\dfrac{Base}{Hypotenuse}[/tex]

[tex]cosx =\dfrac{5}{13}[/tex]

Given that x is in 3rd quadrant, cosx will be negative.

[tex]\therefore cosx =-\dfrac{5}{13}[/tex]

[tex]cot\theta = \dfrac{1}{tan\theta}[/tex]

Given that x is in 3rd quadrant, cotx will be positive.

[tex]cotx = \dfrac{1}{\dfrac{12}{5}} = \dfrac{5}{12}[/tex]

Answer:

8 lies in the domain of f(g)

Answer:

30 feet

Step-by-step explanation:

We can use ratios to answer this question:

8 foot shadow: 20 feet high

Therefore if we multiply both sides by 1.5

12 foot shadow: 30 feet high

Answer:

  A. $3246.74

Step-by-step explanation:

The monthly payment can be found from the amortization formula.

  A = P(r/n)/(1 -(1 +r/n)^(-nt))

where P is the principal amount, r is the annual rate compounded n times per year for t years.

Filling in the values, we compute the monthly payment to be ...

  A = $170,000(.072/12)/(1 -(1 +.072/12)^(-12·30)) = $1153.94

__

The remaining balance after t years will be ...

  B = P(1 +r/n)^(nt) -A((1 +r/n)^(nt) -1)/(r/n)

For the given initial principal and the computed payment, after 18 years, the balance will be ...

  B = $170000(1 +.072/12)^(12·18) -$1153.94((1 +.072/12)^(12·18) -1)/(.072/12)

  B = $111,054.71

The prepayment penalty appears to be ...

  (r/2)(0.80B) = (.072/2)(0.80)($111,054.71) = $3,198.38

The closest listed answer choice is ...

  A.  $3246.74

_____

Please ask your teacher how to get the answer, since none of the offered choices appear to be correct.

The Answer is 171 kg m/s

Answer:

Hello please your question is in-complete attached is the complete question

degree of freedom = -62.90 ( e )

Step-by-step explanation:

The formula for calculating the F-statistic/test statistic is

test - statistic  = Coef ( LBW) / SE Coef ( LBW )

                       = -0.72399 / 0.01151

                       = - 62.90

the degree of freedom the F-statistic has = -62.90

F-statistic test is any statistical test in which the test statistic has an F-distribution under the null hypothesis. the value of the test can be gotten from running an ANOVA test or regression analysis on the statistical models

Using the definition of degrees of freedom, it is found that the F-statistic has 63 df.

When a hypothesis is tested, the number of degrees of freedom is one less than the sample size.

In this problem, the sample size is of n = 64.

Hence:

df = n - 1 = 64 - 1 = 63

The F-statistic has 63 df.

A similar problem is given at https://brainly.com/question/16194574

Answer:

me too

Step-by-step explanation:

Answer:

The sampling distribution of the sample proportion of adults who have credit card debts of more than $2000 is approximately normally distributed with mean [tex]\mu = 0.39[/tex] and standard deviation [tex]s = 0.0488[/tex]

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question:

[tex]p = 0.39, n = 100[/tex]

Then

[tex]s = \sqrt{\frac{0.39*0.61}{100}} = 0.0488[/tex]

By the Central Limit Theorem:

The sampling distribution of the sample proportion of adults who have credit card debts of more than $2000 is approximately normally distributed with mean [tex]\mu = 0.39[/tex] and standard deviation [tex]s = 0.0488[/tex]

Answer:

Convergent. The sum is 2.

Step-by-step explanation:

First let's find the rate of the series. We can find it by dividing one term by the term before:

[tex]0.5 / 1 = 0.5[/tex]

[tex]0.25 / 0.5 = 0.5[/tex]

[tex]0.125 / 0.25 = 0.5[/tex]

So the rate of the series is 0.5. The series is convergent if the rate is between 0 and 1, so this series is convergent.

We can find its sum with the following equation:

[tex]S = a_1 / (1 - r)[/tex]

Where a_1 is the first term and r is the rate.

So we have that:

[tex]S = 1/ (1 - 0.5)[/tex]

[tex]S = 2[/tex]

The sum of the series is 2.

Answer:

see below

Step-by-step explanation:

9 dollars / 33 lbs = .272727 dollars per lb

.39 / 1 lbs = .39 per lb

The large bag is less expensive

Answer: x = 120

Step-by-step explanation:

Here we have 3 triangles, one big and two smaller ones, one at the left and other at the right.

Now, the right sides is shared by the right smaller triangle and the big triangle, if this length is Z, we have that (using the angle in top of it, A, such that 64 is adjacent to A.)

Cos(A) = 64/Z

Cos(A) = Z/(64 +225)

We can take the quotient of those two equations and get:

[tex]1 = \frac{64*(64 + 225)}{Z^2} = \frac{18496}{Z^2}[/tex]

Then:

Z = √(18,496) = 136.

now, we have that for the smaller triangle one cathetus is equal to 64 and the hypotenuse is equal to 136.

Then, using the Pythagorean theorem:

64^2 + x^2 = 136^2

x = √(136^2 - 64^2) = 120

Answer:

Hey there!

Slope of the line: [tex]\frac{y2-y1}{x2-x1}[/tex]

Slope of the line: [tex]\frac{12}{4}[/tex], which is equal to 3.

Point slope form: y2-y1=m(x2-x1)

Point slope form: y-7=3(x-5)

Y intercept form: y-7=3x-15

Y intercept form: y=3x-8

Let me know if this helps :)

Answer:

Null hypothesis:[tex]p \leq 0.5[/tex]  

Alternative hypothesis:[tex]p > 0.5[/tex]  

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing we got:

[tex]z=\frac{0.512-0.5}{\sqrt{\frac{0.5(1-0.5)}{344}}}=0.445[/tex]  

Step-by-step explanation:

Information given

n=344 represent the random sample taken

X=176 represent the anumber of boys babies

[tex]\hat p=\frac{176}{344}=0.512[/tex] estimated proportion of boys babies

[tex]p_o=0.5[/tex] is the value that we want to check

z would represent the statistic

[tex]p_v[/tex] represent the p value

Hypotheis to verify

We want to check if the true proportion of boys is less than 50% then the system of hypothesis are .:  

Null hypothesis:[tex]p\leq 0.5[/tex]  

Alternative hypothesis:[tex]p > 0.5[/tex]  

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing we got:

[tex]z=\frac{0.512-0.5}{\sqrt{\frac{0.5(1-0.5)}{344}}}=0.445[/tex]  

Answer:

p= 0.5

p>0.5

Step-by-step explanation:

Answer:

The probability of "heads" is ½ and the probability of "tails" is ½.

This means that if we flip this coin several times, we expect it to land on "heads" for half of the time.

If we flip the coin 4000 times, we would expect it to land on "heads" 2000 times, because ½ × 4000 = 2000

Answer:

The correct option is (c)

Justin is working with continuous quantitative type of data.

Step-by-step explanation:

We are given that Justin is collecting data on reaction time.

The reaction time is obtained through measurements and it can take any value within a range therefore, it falls in the category of continuous data.

Moreover, since reaction time can be measured thus have numerical value therefore, it is a quantitative type of data.

Therefore, we can conclude that Justin is working with continuous quantitative type of data.

Other examples of continuous quantitative type of data are

measuring height

measuring temperature

Answer:

The percentage  is  %z [tex]= 41.9[/tex]%    

Step-by-step explanation:

From the question we are told that

     The mean is  [tex]\mu = 63.5 \ g[/tex]

     The  standard deviation is  [tex]\sigma = 12.2 \ g[/tex]

      The  random number is  x  = 66 g

Given the the population is normally distributed

   The  probability is mathematically represented as

        [tex]P(X > 66 ) = P(\frac{X - \mu }{\sigma} > \frac{x - \mu }{\sigma } )[/tex]  

Generally the z-score for this population is mathematically represented as

         [tex]Z = \frac{ X - \mu}{ \sigma}[/tex]

  So

      [tex]P(X > 66 ) = P(Z > \frac{66 - 63.5 }{12.2 } )[/tex]  

      [tex]P(X > 66 ) = P(Z > 0.2049 )[/tex]  

Now the z-value for 0.2049 from the standardized normal distribution table is  

     [tex]z = 0.41883[/tex]

=>    [tex]P(X > 66 ) = 0.41883[/tex]  

The  percentage  is

     % z     [tex]= 0.41883 * 100[/tex]  

     %z   [tex]= 41.9[/tex]%    

Answer:

21cm; 28cm; 14cm

Step-by-step explanation:

There is no info in the problem/s  text which one of the triangle's  side is 21 cm. That is why we have to try all possible variants.

Let the triangle is ABC . Let the AK is the angle A bisector and BM is median.

Let O is AK and BM cross point.

Have a look to triangle ABM.  AO is the bisector and AOB=AOM=90 degrees (means that AO is as bisector as altitude)

=> triangle ABM is isosceles => AB=AM  (1)

1. Let AC=21   So AM=21/2=10.5 cm

So AB=10.5 cm as well.  So BC= P-AB-AC=63-21-10.5=31.5 cm

Such triangle doesn' t exist ( is impossible), because the triangle's inequality doesn't fulfill.  AB+AC>BC ( We have 21+10.5=31.5 => AB+AC=BC)

2. Let AB=21 So AM=21 and AC=42 .So  BC= P-AB-AC=63-21-42=0 cm- such triangle doesn't exist.

3. Finally let BC=21 cm. So AB+AC= 63-21=42 cm

We know (1) that AB=AM so AC=2*AB.  So AB+AC=AB+2*AB=3*AB

=>3*AB=42=> AB=14 cm => AC=2*14=28 cm.

Let check if this triangle exists ( if the triangle's inequality fulfills).

BC+AB>AC    21+14>28 - correct=> the triangle with the sides' length 21cm,14 cm, 28cm exists.

This variant is the only possible solution of the given problem.

Answer:

Step-by-step explanation:

When two variables vary inversely, it means that an increase in one would lead to a decrease in the other and vice versa. Since the volume of a gas, V in a container varies inversely with the pressure on the gas, P, if we introduce a constant of proportionality, k, the expression would be

V = k/P

If V = 370 in³ and P = 15psi, then

370 = k/15

k = 370 × 15 = 5550

The equation that relates the volume, V, to the pressure, P would be

V = 5550/P

if the pressure was increased to 25psi, the volume would be

V = 5550/25 = 222 in³

Answer:

v=5550/p

222

Step-by-step explanation:

The element X will take 22.10 minutes to decay to 26 grams.

The radioactive radiations are the radiations that an atom nucleus releases.

It is a sequence of numbers which have common difference.

The decaying acts like an arithmetic progression in which a=670,d=-30.45 (per minute decaying) and n we have to find with the an value of 26 gram.

So, the formula of nth term of an arithmetic progression is

nth term=a+(n-1)d

26=670+(n-1)*(-30.45)

-644=-30.45n+30.45

-674.45=-30.45n

n=22.10 (after rounding off)

Hence the element X would take 22.10 minutes to decay to 26 grams.

Learn more about arithmetic progression at https://brainly.com/question/6561461

#SPJ2

Answer:

y=a(.5)^{\frac{t}{h}}

y=a(.5)

h

t

​

y=30 \hspace{15px} a=670 \hspace{15px} h=11 \hspace{15px} t=?

y=30a=670h=11t=?

30=670(.5)^{\frac{t}{11}}

30=670(.5)

11

t

​

\frac{30}{670}=\frac{670(.5)^{\frac{t}{11}}}{670}

670

30

​

=

670

670(.5)

11

t

​

​

0.0447761=(.5)^{\frac{t}{11}}

0.0447761=(.5)

11

t

​

\log(0.0447761)=\log((.5)^{\frac{t}{11}})

log(0.0447761)=log((.5)

11

t

​

)

\log(0.0447761)=\frac{t}{11}\log(.5)

log(0.0447761)=

11

t

​

log(.5)

Power Rule.

11\log(0.0447761)=t\log(.5)

11log(0.0447761)=tlog(.5)

Multiply by 11.

\frac{11\log(0.0447761)}{\log(.5)}=\frac{t\log(.5)}{\log(.5)}

log(.5)

11log(0.0447761)

​

=

log(.5)

tlog(.5)

​

Divide by log(.5).

t=\frac{-14.838489}{-0.30103}

t=

−0.30103

−14.838489

​

t=49.29239\approx 49.3 \text{ minutes}

t=49.29239≈49.3 minutes

Step-by-step explanation:

Answer: The 1 because it’s value is The Thousands place.

Each Value Broken down and then Added together:

1000 + 500 + 60 + 7 = 1567

As you can visually see here the 1 is the greatest value number.

Answer:1

Step-by-step explanation: 1 takes place in the thousands place which is greater than 5 (hundreds) , 6 (tenths) , and 7 (ones)

Answer:

25%

Step-by-step explanation:

Total cards = 4

The number 4 = 1

p(4) = 1/4

In %age:

=> 25%

Answer:

25%

Step-by-step explanation:

There is only 1 four card from the 4 cards.

1 card out of 4 cards.

1/4 = 0.25

P(4) = 25%

Answer:

A lies along the positive x-axis and B lies along negative x - axis .

Step-by-step explanation:

They tell us that we have two vectors, A and B. And they give us a series of conditions for this, now, what would be the correct possibility.

A lies along the positive x-axis and B lies along negative x - axis .

This is because when both vectors will be in x axis but opposite to each other, then the angle between them will be 180 ° and cos180 ° is -1.

Answer:

75000lb

Step-by-step explanation:

There are 25000 residents. Times it by the 3lb of waste per person and that's how much waste is made from 25000 residents.

Answer:

Step-by-step explanation:

Answer:

Option D is correct.

This statement shows the use of relative difference.

Step-by-step explanation:

Taking each of the answer choices one at a time

- Absolute Change

This expresses the exact value of alterations or modifications that happen to a particular quantity. It gives exactly how much the value of the same quantity has changed at different times or conditions. The statement in this question compares two different quantities (price of new CD burner at two different stores), hence it doesn't give the absolute change.

- Absolute Difference

This expresses the exact value of the difference between two quantities. The statement in the question on its own cannot give us the absolute value of the difference between the cost of new CD burner at the two stores being compared. Hence, this isn't the correct answer.

- Relative Change

Thìs expresses how much a particular quantity has changed with respect to its value at some other period of time or under some other condition(s). The question in this statement compares two different quantities and isn't the right answer.

- Relative Difference

This expresses the difference between two quantities wit respect to or relative to one of the two quantities being compared. This is exactly what the statement in the question expresses by saying that the new CD burner costs 12% less at the new electronics store.

It compares the telative difference of the new CD burner at the new and old electronics store.

Hope this Helps!!!

Answer: 3 1/3 hours

Step-by-step explanation:

Tina rate: 1/5 job/hr

Together rate: 1/2 job/hr

Tyra rate: 1/x job/hr

---------

Equation:

rate + rate = together rate

1/5 + 1/x = 1/2

2x + 10 = 5x

3x = 10

x = 3 1/3 hrs (time for Tyra to do the job alone)

Answer:

3 1/3 hours

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Given

[tex]\sqrt{x-6}[/tex] + 5 = 12 ( subtract 5 from both sides )

[tex]\sqrt{x-6}[/tex] = 7 ( square both sides )

x - 6 = 49 ( add 6 to both sides )

x = 55

Answer:

B. Subtract 5 from both sides and then square both sides.

Step-by-step explanation:

First, subtract 5 from both sides in order to get [tex]\sqrt{x-6}=7^{2}[/tex]

Second, square both sides in order to get [tex]x-6=49[/tex] (p.s. squaring both sides gets rid of the square root)

Third, add 6 to both sides in order to get x=55

Last, see that the answer is B, as you had to subtract 5 from both sides and then square both sides to get your answer

There you go, and good luck on the other questions!

Answer:

12.2%

Step-by-step explanation:

82 · [tex]\frac{100-x}{100}[/tex] = 72         When multiplied by a certain percent we get 72  

82(100-x) = 7200  

                            100(A whole as you may say) - *a percent* = the markdown

8200-82x=7200

82x = 1000

x ≈ 12.2

Tell me if you need further explanation

Answer:

12.20%

Step-by-step explanation:

$82 went down to $72.

$82 - $72 = $10

The price went down $10.

Now we find the percent that $10 is of $82.

percent = part/whole * 100%

percent = 10/82 + 100% = 12.195%

Answer: 12.20%

Answer: V(W) = (1/3)*(*W^2*800ft - 8W^3) and the domain is 0 < W < 100ft.

Step-by-step explanation:

The dimensions of the box are:

L = length

W = width

H = heigth.

We know that:

L = 4*W

And the girth of a box is equal to: G = 2*W + 2*H

then we have:

2*W + 2*H + H = 200ft

2W + 3*H = 200ft

Then we have two equations:

L = 4*W

2W + 3*H = 200ft

We want to find the volume of the box, which is V = W*L*H

and we want in on terms of W.

Then, first we can replace L by 4*W (for the first equation)

and:

2*W + 3*H = 200ft

3*H = 200ft - 2*W

H = (200ft - 2*W)/3.

then the volume is:

V(W) = W*(4*W)*(200ft - 2*W)/3

V(W) = (1/3)*(*W^2*800ft - 8W^3)

The domain of this is the set of W such that the volume is positive, then we must have that:

W^2*800ft > 8W^3

To find the maximum W we can see the equality (the minimum extreme is 0 < W, because the width can only be a positive number)

W^2*800ft = 8W^3

800ft = 8*W

100ft = W.

This means that if W is equal or larger than 100ft, the equation gives a negative volume.

Then the domain is 0 < W < 100ft.

Answer:

150, 15x

Step-by-step explanation:

After ten minutes he will be 15 * 10 = 150 feet below sea level.

We can call the number of minutes the diver has been underwater for as x so the integer is 15 * x = 15x.