solve for x in the diagram below

Answer:

14π or 43.96

Step-by-step explanation:

C = 2πr and we know that r = 7 so C = 14π or 43.96.

Step-by-step explanation:

a).

It is given that rate at which the population increases is directly proportional to size of the population. Thus we have,

[tex]\frac{dP}{dt}\propto P[/tex]

It is given in the question that the population increases by 2% in one day. Now we know that the time in days is a continuous variable, so we have

2% of P = [tex]$\frac{2}{100}\times P$[/tex]

[tex]$\therefore \frac{dP}{dt}=0.02 P $[/tex]

b).

It is given that the population is harvested by 4 % in one day

[tex]$\therefore \frac{dP}{dt} =0.02P-0.04P$[/tex]

(Since 4% of the P is harvested.)

[tex]$\therefore \frac{dP}{dt}=-0.02P$[/tex]

c).

It is given that 1000 fish are being harvested or removed in one day.

[tex]$\therefore \frac{dP}{dt}= 0.02 P-1000$[/tex]

d).

The threshold is given by

[tex]$0.02 P_{eq}-1000=0$[/tex]

[tex]$\therefore P_{eq}=\frac{1000}{0.02}$[/tex]

or  [tex]$P_{eq}=5\times 10^4$[/tex]

sine(X) = opposite side / hypotenuse

sine(X) = (2√11) / (4√11)

sine(X) = (2/4)

sine(X) = 0.5

X = arcsine(0.5)

X = 30°  

Answer: m∠x = 30°

Step-by-step explanation:

In a right triangle, if the short side of the right angle is Half the length of the hypotenuse, the triangle has angles of 30°, 60° and 90°

∠x is the smallest one, so  m∠x = 30°

It is possible to figure the sine and get the angle from that, but in this case it might not be necessary.  ;-)

Answer:

1,880.82

Step-by-step explanation:

Answer:

The value of the cosine function at 37º is 0.80. A. 0.80

Step-by-step explanation:

The correct statement is: "If the secant of 37º is 1.25, the cosine value to the hundredths degree is:"

Secant and cosine functions are related by the following trigonometric identity:

[tex]\sec 37^{\circ} = \frac{1}{\cos 37^{\circ}}[/tex]

[tex]\cos 37^{\circ} = \frac{1}{\sec 37^{\circ}}[/tex]

[tex]\cos 37^{\circ} =\frac{1}{1.25}[/tex]

[tex]\cos 37^{\circ} = 0.80[/tex]

The value of the cosine function at 37º is 0.80. The right answer is A.

Answer:

Step-by-step explanation:

Using elimination method:

2x - y = 7

3x + y = 3

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

5x = 10

Divide both sides of the equation by 5

[tex] \frac{5x}{5} = \frac{10}{5} [/tex]

Calculate

[tex]x = 2[/tex]

Now, substitute the given value of X in the equation

3x + y = 3

[tex]3 \times 2 + y = 3[/tex]

Multiply the numbers

[tex]6 + y = 3[/tex]

Move constant to R.H.S and change it's sign

[tex]y = 3 - 6[/tex]

Calculate

[tex]y = - 3[/tex]

The possible solution of this system is the ordered pair ( x , y )

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

Check if the given ordered pair is the solution of the system of equation

[tex]2 \times 2 - ( - 3) = 7[/tex]

[tex]3 \times 2 - 3 = 3[/tex]

Simplify the equalities

[tex]7 = 7[/tex]

[tex]3 = 3[/tex]

Since all of the equalities are true, the ordered pair is the solution of the system

Hope this helps..

Best regards!!

Answer:

Option D is correct.

Angle C = 70°

Step-by-step explanation:

The sum of angles in a triangle = 180°

So,

(Angle A) + (Angle B) + (Angle C) = 180°

(Angle A) = 67°

(Angle B) = 43°

(Angle C) = ?

67° + 43° + (Angle C) = 180°

Angle C = 180 - 67 - 43 = 70°

Angle C = 70°

Hope this Helps!!!

Answer:

56 number of ways

Step-by-step explanation:

This question is a combination question since it involves selection.

Generally, if r objects are to be selected from n pool of objects, this can be done in nCr number of ways.

nCr = n!/(n-r)!r!

If a manager receives 8 applications for a specific position and wants to narrow it down to 5, the number of ways he can do this is 8C5

8C5 = 8!/(8-5)!5!

= 8!/3!5!

= 8*7*6*5!/3*2*5!

= 8*7*6/3*2

= 8*7

= 56 number of ways.

This means that the manager can rank 5 applications in 56 number of ways

The number of ways that can she rank 5 applications should be 6720.

Since A manager receives 8 applications for a specific position. She wants to narrow it down to 5.

So here we do apply the permutation here:

[tex]= 8!\div 5!3! \times 5!\div 0!\\\\= 8\times 7\times 6\times 5\times 4[/tex]

= 6720

Hence, The number of ways that can she rank 5 applications should be 6720.

Learn more about ways here: https://brainly.com/question/18988173

Answer:

The final price to be paid after the 2% discount has been made will be $ 16,645.30.

Step-by-step explanation:

Since there is a 2% discount on the price of the Honda Shadow in the event that the dealer pays Honda within 15 days, and that after a rebate the price of the vehicle is $ 16,985, to obtain the value of the discount and the final amount to be paid must be calculated as follows:

16,985 x 2/100 = X

33,970 / 100 = X

339.70 = X

Thus, the discount to be made will be $ 339.70, with which the final price to be paid after the 2% discount has been made will be $ 16,645.30.

Complete Question

The standard deviation of samples from supplier A is 0.4582, while the standard deviation of samples from supplier B is 0.3358. Which supplier would you be likely to choose based on these data and why?

1 Supplier A, as their standard deviation is higher and, thus easier to fit into our production line

2 Supplier B, as their standard deviation is higher and, thus, easier to fit into our production line

3 supplier B, as their standard deviation is lower and, thus, easier to fit into our production line

4 Supplier A, as their standard deviation is lower and, thus, easier to fit into our production line

Answer:

Option 3 is  correct

Step-by-step explanation:

From the question we are told that

     The  standard deviation of A is  [tex]\sigma_a = 0.4582[/tex]

      The  standard deviation of B is  [tex]\sigma _b = 0.3358[/tex]

Generally standard deviation defines the deviation element of a data set with respect to the mean of the set

So sample  it mean that samples from A deviates more from it mean(the standard value) than the samples from B so the best supplier to chose is B

Answer:

-38

Step-by-step explanation:

it's subtracting 7 everytime, and -31-7=-38

Answer:

Step-by-step explanation:

2.8 kilometers farther. Subtract 12.1km for Winchester and 9.3 for Stamford to get 2.8 kilometers.

Answer:

r = 90/30

r = 3

T12 = 10 × 3¹¹

T12 = 1771470

Answer:

Step-by-step explanation:

121212121211212 its B

Answer:

answer is B

Step-by-step explanation:

Answer:

third option

Step-by-step explanation:

We just have to calculate 2x² - 4x - (x² + 6x). 2x² - x² = x² and -4x - 6x = -10x so the answer is x² - 10x.

Answer:

x^2-10x

Step-by-step explanation:

f(x)-g(x)

(2x^2-4x)-(x^2+6x)

carry through the negative

2x^2-4x-x^2-6x

x^2-10x

Answer:

[tex]\frac{109}{122}[/tex]

Step-by-step explanation:

Well first we need to find the total amount of Winter Olympic medals won.

550 + 540 + 130

= 1220

Now we need to find the amount won from the Western and Northern Europe.

550 + 540

= 1090

Now we can make the following fraction,

1090/1220

Simplify

= 109/122

Thus,

the answer is [tex]\frac{109}{122}[/tex].

Hope this helps :)

Hi there!! (✿◕‿◕)

⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐

Northern Europe: 550 medals

Western Europe: 540 medals

550 + 540 = 1,090

Northern Europe and Western Europe: 1,090

Other: 130

1,090 + 130 = 1,220

European Regions: 1,220 medals

1,090/1,220 = 109/122

Hope this helped!!  ٩(◕‿◕｡)۶

Answer:

c. $50.37

Step-by-step explanation:

Close price was $56.11 and net change was $5.74. so subtract the net change from the close to get yesterday's price.

Answer:

c.50.37

Step-by-step explanation:

Answer:

75

Step-by-step explanation:

x = 75°

yes x = 75°(OPPOSITE ANGLES ARE EQUAL)

..

Answer:

176 mm

Step-by-step explanation:

The circumference of a circle is the perimeter of a circle (length of a circle). The circumference of a circle is given as:

Circumference (C) = 2πr = πd, where d is the diameter

The circumference of a circle with diameter 7 mm is:

C = πd = 22/7(7) = 22 mm

The length of the paper to round the cylindrical pencil is the same as the perimeter of the pencil which is 22 mm.

To round the pencil 8 times, the length of the paper needed = 8 × 22 mm = 176 mm

Answer:

False.

Step-by-step explanation:

This is NOT an example of a binomial random variable, because a binomial random variable can only have TWO possible outcomes: success or failure. In the case of rolling a die, there are SIX possible outcomes: 1, 2, 3, 4, 5, or 6.

So, rolling a 6-sided die and counting the number of each outcome that occurs is NOT a binomial random variable.

Hope this helps!

The given statement "Rolling a 6-sided die and counting the number of each outcome that occurs" is false.

A common discrete distribution is used in statistics, as opposed to a continuous distribution is called a Binomial distribution. It is given by the formula,

P(x) = ⁿCₓ (pˣ) (q⁽ⁿ⁻ˣ⁾)

Where,

x is the number of successes needed,

n is the number of trials or sample size,

p is the probability of a single success, and

q is the probability of a single failure.

The given statement "Rolling a 6-sided die and counting the number of each outcome that occurs" is not an example of the binomial random variable. This is because the binomial random variable can only have two possible outcomes, which is not true in the case of a die that had six faces and six outcomes for each through.

Although if the probability is needed to be calculated for the same digit occurring or not it can be calculated using the binomial random variable.

Hence, The given statement "Rolling a 6-sided die and counting the number of each outcome that occurs" is false.

Learn more about Binomial Distribution:

https://brainly.com/question/14565246

#SPJ5

Answer:

[tex]\large \boxed{\text{5.29 s}}[/tex]

Step-by-step explanation:

The appropriate free fall equation is  

y = v₀t + ½gt²

Data:

v₀ = 0

g = 32.17 ft·s⁻²

Calculation:

[tex]\begin{array}{rcl}450 &=& v_{0}t + \dfrac{1}{2}gt^{2}\\\\& = & 0 \times t + \dfrac{1}{2}\times 32.17t^{2}\\\\& = & 16.08t^2\\t^{2}& = & \dfrac{450}{16.08}\\\\& = & 27.97\\t & = & \textbf{5.29 s}\\\end{array}\\\text{It took $\large \boxed{\textbf{5.29 s}}$ for the phone to reach the ground.}[/tex]

Answer:

P = 0,3749       or    P = 37,49 %

Step-by-step explanation:

17 girls play football  10 boys do   ⇒ 27 students

24 girls running  3 boys do   ⇒ 27 students

then  6 girls play tennis  and  12 boys do ⇒ 18 students

Probability of student running P is equal to P1 (probability of student (boy) running ) plus P2 (probability of student (girl) running )

P = P1  +  P2

P1 (probability of girl running ) is equal to choose a girl out of 72 students, times the probability of the girl running

Probability of girl   47/72      =   0,6528

Probability of running is equal to 24/47  = 0,5106

Then the probability of girl running is equal to

P2 = 0,6528*0,5106  =  0,3333    or   33,33 %

P2 = 0,3333    or     P2 = 33,33 %

Now we have 72 students 25 boys, then the probability of choosing a boy is  = 25/72    =  0,3472

And the probability of running is 3/25 = 0,12

Then

P1 = 0,3472*0,12

P1 = 0,04166   and

P = P1 + P2

P = 0,04166 + 0,3333

P = 0,3749       or    P = 37,49 %

Answer:

95% confidensce interval of the mean (two-tail) =  [132.2, 139.2]

Step-by-step explanation:

Given:

N = size of sample = 61

m = sample mean = 135.7

s = sample standard deviation 13.7

Need 95% confidence interval

Solution.

alpha (95% confidence interval) = 0.05

(1-alpha/2) = 0.975   [two sided]

Equation for confidence interval of the mean

= m +/- t(1-alpha/2,N-1) * s / sqrt(N)

= 135.7 +/- 2.0003 * 13.7 / sqrt(60)

= [132.16, 139.24]

Amplitude:4

Equation of Midline: 2

Period of function:3

Function shifted left:0.5

Function shifted up: 2

From the graphed cosine function we are given, we have;

1) Amplitude = 4

2) Equation of midline; m = 2

3) Period of the function = 3π

4) The function shifted 0.5 units left.

5) The function shifted 2 units up.

Read more; https://brainly.com/question/16280305

Answer:

d) d(x)

Step-by-step explanation:

Derivative Rules

Answer:

Step-by-step explanation:

The height of the house, the ground and the ladder forms a right angle triangle, with the following parameters stated below.

1. the hypotenuse is the length of the ladder which is 30 feet

2.the opposite is the height of the house, which is 25 feet

3. the adjacent is the distance of the ladder away from the building, this is the parameter we are solving for.

Since we have two sides of the triangle given, we can employ Pythagoras theorem to solve for the third side of the triangle

let the the opposite be x

we know that

[tex]hyp^2= opp^2+adj^2\\\\ 30^2= x^2+25^2\\\\ 900= 625+x^2\\[/tex]

Solving for x we have

[tex]x^2= 900-625\\\\X^2= 275\\\\x=\sqrt{275} \\\\x= 16.58[/tex]

Hence the maximum distance away from house that he can place

the ladder is 16.6 ft to the nearest foot

Answer:

A. a straight line passing

Step-by-step explanation:

Answer:

a straight line passing

Step-by-step explanation:

Answer:

[tex]\huge\boxed{x=\dfrac{5}{4}}[/tex]

Step-by-step explanation:

[tex]\left(\dfrac{1}{2}\right)^{x-1}=2^{3x-4}\qquad\text{use}\ a^{-1}=\dfrac{1}{a}\\\\\left(2^{-1}\right)^{x-1}=2^{3x-4}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\2^{(-1)(x-1)}=2^{3x-4}\qquad\text{use the distributive property}:\ a(b+c)=ab+ac\\\\2^{(-1)(x)+(-1)(-1)}=2^{3x-4}\\\\2^{-x+1}=2^{3x-4}\iff-x+1=3x-4\qquad\text{subtract 1 from both sides}\\\\-x+1-1=3x-4-1\\\\-x=3x-5\qquad\text{subtract}\ 3x\ \text{from both sides}\\\\-x-3x=3x-3x-5\\\\-4x=-5\qquad\text{divide both sides by (-4)}[/tex]

[tex]\dfrac{-4x}{-4}=\dfrac{-5}{-4}\\\\x=\dfrac{5}{4}[/tex]

Answer:

Sample size 'n' = 1067

Step-by-step explanation:

Explanation:-

Given margin of error of the true proportion

M.E  = 0.03

The margin of error is determined by

                   [tex]M.E =Z_{\alpha } \frac{\sqrt{p(1-p)} }{\sqrt{n} }[/tex]

Level of significance = 0.95

The critical value Z₀.₀₅ = 1.96

 The margin of error is

                   [tex]0.03 =1.96 \frac{\sqrt{p(1-p)} }{\sqrt{n} }[/tex]

we know that

             [tex]\sqrt{p(1-p} \leq \frac{1}{2}[/tex]

                [tex]0.03 =\frac{1.96 X\frac{1}{2} }{\sqrt{n} }[/tex]

    on cross multiplication , we get

                √n  = 32.66

Squaring on both sides, we get

               n = 1066.6≅1067

Answer:

95% of confidence interval of the proportion of all people who pick their noses at red lights

(0.3342 , 0.5258)

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 100

Given data  43 out of a random sample of 100 people said they pick their noses at red lights.

sample proportion

                           [tex]p^{-} = \frac{x}{n} = \frac{43}{100} = 0.43[/tex]

Level of significance = 0.05

Z₀.₀₅ = 1.96

Step(ii):-

95% of confidence interval of the proportion of all people who pick their noses at red lights

[tex](p^{-} -Z_{\alpha } \sqrt{\frac{p(1-p)}{n} } ,p^{-} +Z_{\alpha } \sqrt{\frac{p(1-p)}{n} })[/tex]

[tex](0.43 -1.96 \sqrt{\frac{0.43(1-0.43)}{100} } ,0.43 +1.96 \sqrt{\frac{0.43(1-0.43)}{100} })[/tex]

( 0.43 -  0.0958 , 0.43 + 0.0958)

(0.3342 , 0.5258)

Conclusion:-

95% of confidence interval of the proportion of all people who pick their noses at red lights

(0.3342 , 0.5258)