If an island's only residents are penguins and bears, and if there are 24 heads and 64 feet on the island, how many penguins and how many bears are
on the island

Answer: x= 34

Step-by-step explanation:

Answer:

1-2i

Step-by-step explanation:

Divide: 5 + 2i by 3 + 4i.

Given data

5 + 2i by 3 + 4i.

We have the expression as

(5 + 2i)/(3 + 4i)

Rationalize the denominator

(5 + 2i)/(3 + 4i)* (3 -4i)/(3 -4i)

=(5*3-20i+6i-8i^2)/9-12i-12i+16i^2

=15-14i+8/9-16

=7-14i/-7

=1-2i

Answer:

y=15

Step-by-step explanation:

Answer:

Y=15

Step-by-step explanation:

4-1=3

18-3=15

15+3=18

So, 15+4-1=18

Answer:

0

Step-by-step explanation:

to evaluate the composite function work from the inside out

first evaluate h(2) , then substitute the value obtained into g(x) then substitute the value obtained here into f(x)

h(2) = \(\frac{1}{2}\) , then

g( \(\frac{1}{2}\) ) = \(\sqrt{2(\frac{1}{2}) }\) = \(\sqrt{1}\) = 1 , then

f(1) = 1² - 1 = 1 - 1 = 0

Answer:

41 kg of apples would cost $82.

Step-by-step explanation:

41 kg divided by 7 kg is 5.85714285714. 5.85714285714 multiplied by $14 is $82.

a) The exact solutions on [0, 2π) are t = π/3, π, and 5π/3. b) The exact solution on the interval [0, π) is t = 2π/3. c) The solutions are θ = π/3 and θ = 5π/3. d) The exact solutions on the interval [0, 2π) are: t = arcsin[(-1 +  \(\sqrt{41}\))/4] and t = 2π - arcsin[(-1 +  \(\sqrt{41}\))/4] using trigonometric identities.

a) We can rewrite the equation as:

2\(cos^{2}t\) + cos(t) - 1 = 0

Using the quadratic formula, we get:

cos(t) = [-1 ± \(\sqrt{1-4(2)(-1)}\) ] / (4)

cos(t) = [-1 ± \(\sqrt{9}\)]/4

cos(t) = [-1 ± 3]/4

Thus, we have two solutions:

cos(t) = 1/2, which gives us t = π/3 and t = 5π/3

cos(t) = -1, which gives us t = π

Therefore, the exact solutions on [0, 2π) are t = π/3, π, and 5π/3.

b) We can use the identity \(tan^{2}t\) + 1 = \(sec^{2}t\) to rewrite the equation as:

\(tan^{2}t\) = - \((3/2)^{2}\)

Taking the square root of both sides and remembering that tan(t) is negative in the third quadrant, we get:

tan(t) = -3/2

Using the identity tan(t) = sin(t)/cos(t), we can rewrite this as:

sin(t)/cos(t) = -3/2

Multiplying both sides by cos(t) and rearranging, we get:

sin(t) = -3cos(t)/2

Squaring both sides and using the identity \(sin^{2}t\) + \(cos^{2}t\) = 1, we get:

9\(cos^{2}t\)/4 + \(cos^{2}t\) = 1

Expanding and simplifying, we get:

13 \(cos^{2}t\) /4 = 1

\(cos^{2}t\)  = 4/13

Taking the square root of both sides and remembering that cos(t) is negative in the third quadrant, we get:

cos(t) = -2\(\sqrt{13}\) /13

Using the identity  \(sin^{2}t\) +  \(cos^{2}t\)  = 1, we can solve for sin(t) as:

sin(t) = -3/2 cos(t) = 3\(\sqrt{13}\) /13

Therefore, the exact solution on the interval [0, π) is t = 2π/3.

c) We can use the identity sin(2θ) = 2sin(θ)cos(θ) to rewrite the equation as:

sin(θ) = 2sin(θ)cos(θ)

Dividing both sides by sin(θ) (assuming sin(θ) is non-zero), we get:

1 = 2cos(θ)

cos(θ) = 1/2

Therefore, the solutions are θ = π/3 and θ = 5π/3.

d) We can use the identity cos(2t) = 1 - 2 \(sin^{2}t\)  and rearrange the equation as:

2 \(sin^{2}t\)  + sin(t) - 5 = 0

Solving this quadratic equation using the quadratic formula, we get:

sin(t) = [-1 ± \(\sqrt{41}\)]/4

Since the sine function has a range of [-1, 1], only the positive solution is possible, so we have:

sin(t) = (-1 + \(\sqrt{41}\))/4

Using the identity \(cos^{2}t\) = 1 -  \(sin^{2}t\) , we can solve for cos(t) as:

cos(t) =\(\sqrt{1-sin^{2}t}\) = \(\sqrt{17-\sqrt{41} }/4\)

Therefore, the exact solutions on the interval [0, 2π) are:

t = arcsin[(-1 +  \(\sqrt{41}\))/4] and t = 2π - arcsin[(-1 +  \(\sqrt{41}\))/4]

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800 ways meal be ordered.

There are 5 main courses to choose from, so there are 5 ways to choose a main course. There are 4 vegetables to choose from, so there are 4 ways to choose a vegetable. There are 5 beverages to choose from, so there are 5 ways to choose a beverage. And there are 4 desserts to choose from, so there are 4 ways to choose a dessert.

The total number of ways to order a meal is the product of the number of choices for each category.

So there are 5 * 4 * 5 * 4 = 800 ways to order a meal.

Hence, 800 ways meal be ordered.

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Try this option:

1) for the given function 'f': the the axis of its symmetry is x= -2;

2) for the function 'g':

g(x)=4x²-16x+12; ⇔ g(x)=4(x²-4x+3); ⇔ g(x)=4(x-1)(x-3).

It means the axis of its symmetry is x=2.

Answer: -2 and 2

Answer:

D          

Step-by-step explanation:

Answer:6.28 miles

Step-by-step explanation:

The circumference of a circle = 2*pi*radius

= 2*1 mile* 3.14

= 6.28 miles

The least square regression line implies a mathematical equation that models the relationship between the dependent and independent variables. Hence, it may be used to predict a value of y if the corresponding x value is given. The least square regression line also called the best fit line, gives a mathematical relationship between variables in slope-intercept form.The predicted value of y or x if the corresponding value of either variable is given.

what is regression?

A statistical method called regression links a dependent variable to one or more independent (explanatory) variables. A regression model can demonstrate whether changes in one or more of the explanatory variables are related to changes in the dependent variable.

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Required Probabilty = 161.1

n = 1111

Probability of getting correct P(c)= 1/2

Probability of getting wrong P(w)= 1/2

So it follows binomial distribution

P (x*r) = Ncr .(P)r . (q)n-r = P (33<X<55) = P(X-r) = 1111c4 .  (1/2) power of 44 . (1/2) power of 1111-44

Required Probabilty = 161.1

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In summary, the Fourier coefficients for the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5 are:

c₀ = -3 (DC component)

cₙ = 0 for n ≠ 0 (other coefficients)

To find the Fourier coefficients of the periodic function y(t) = -3 on the interval -5 ≤ t ≤ 5, we can use the formula for Fourier series coefficients:

cn = (1/T) ∫[t₀-T/2, t₀+T/2] y(t) \(e^{(-i2\pi nt/T)}\) dt

where T is the period of the function and n is an integer.

In this case, the function y(t) is constant, y(t) = -3, and the period is T = 10 (since the interval -5 ≤ t ≤ 5 spans 10 units).

To find the Fourier coefficient c₀ (corresponding to the DC component or the average value of the function), we use the formula:

c₀ = (1/T) ∫[-T/2, T/2] y(t) dt

Substituting the given values:

c₀ = (1/10) ∫[-5, 5] (-3) dt

  = (-3/10) \([t]_{-5}^{5}\)

  = (-3/10) [5 - (-5)]

  = (-3/10) [10]

  = -3

Therefore, the DC component (c₀) of the Fourier series of y(t) is -3.

For the other coefficients (cₙ where n ≠ 0), we can calculate them using the formula:

cₙ = (1/T) ∫[-T/2, T/2] y(t)\(e^{(-i2\pi nt/T) }\)dt

Since y(t) is constant, the integral becomes:

cₙ = (1/T) ∫[-T/2, T/2] (-3) \(e^{(-i2\pi nt/T)}\) dt

  = (-3/T) ∫[-T/2, T/2] \(e^{(-i2\pi nt/T)}\) dt

The integral of e^(-i2πnt/T) over the interval [-T/2, T/2] evaluates to 0 when n ≠ 0. This is because the exponential function oscillates and integrates to zero over a symmetric interval.

all the coefficients cₙ for n ≠ 0 are zero.

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Answer:

b. 1.97

Step-by-step explanation:

1cm≈0.032feet

60/0.032≈1.97feet

Answer:

12x-24y

Step-by-step explanation:

Youuuuuuuuuur Welcome

Answer:

15

Step-by-step explanation:

4x-8y=5

4x=8y+5

3(8y+5-8y)

3(5)

15

The probability that Jack will win is 0.00015. The result is obtained by dividing the number of tickets that Jack has by the total number of events.

Probability of an event is calculated by dividing the number of favorable outcomes by the total number of events in the sample space.

In a certain lottery are 100 balls numbered from 1 - 100 in a large basket. Three numbered balls are randomly drawn without replacement. To win the lottery, a player's ticket must have each of the numbers drawn in no particular order.

If jack buys 21 tickets, find the probability that he will win!

In any the order, the different triples of tickets that a player can have can be found by a combination.

The total number of events would be

\(= \: _{100}C_{3}\)

\(= \frac{100!}{3! \:97!} }\)

\(= \frac{98 \times 99 \times 100}{2 \times 3}\)

= 161700 different triples

Jack has 21 tickets. So, the probability that Jack will win is

P = 21/161700

P = 0.00013

Hence, Jack will win with the probability of 0.00013.

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Answer:

85 44/100

Step-by-step explanation:

I think this is the corect anser

Answer:

8 2/5

7 1/2 times 12 divided by 100 = 0.9

7 1/2 + 0.9 = 8.4

as a mixed number it would be 8 2/5

Step-by-step explanation:

The solution to the quadratic equations are

a) The number of seconds for the ball to reach the ground is t = 5 seconds

b) The number of seconds to reach the maximum height T = 2 seconds

c) The maximum height of the ball is h ( 2 ) = 144 feet

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as h ( t )

Now , the equation will be

h ( t ) = -16t² + 64t + 80   be equation (1)

a)

The number of seconds for the baseball to reach the ground be t

The height when the ball reaches the ground will be h = 0

Substituting the value of h ( t ) = 0 , we get

0 = -16t² + 64t + 80

On simplifying the equation , we get

16t² - 64t - 80 = 0

Divide by 16 on both sides of the equation , we get

t² - 4t - 5 = 0

On factorizing the equation , we get

t² + t -5t - 5 = 0

t ( t + 1 ) - 5 ( t + 1 ) = 0

( t - 5 ) ( t + 1 ) = 0

The value of t is time and it is not negative

So , when ( t - 5 ) = 0

Adding 5 on both sides of the equation , we get

t = 5 seconds

b)

The number of seconds the baseball to reach the maximum height be T

And graph of the function is a parabola open down because the leading coefficient is negative. Therefore, to get the maximum height we just have to find the vertex of this parabola

T = ( -b / 2a )

On simplifying the equation , we get

T = ( -64 / ( 2 ( 16 )

T = -64 / 32

T = 2 seconds

c)

The maximum height of the baseball is when T = 2

Substituting the value of t = 2 in the equation , we get

h ( t ) = -16t² + 64t + 80

h ( 2 ) = -16 ( 2 )² + 64 ( 2 ) + 80

On simplifying the equation , we get

h ( 2 ) = -64 + 128 + 80

h ( 2 ) = 64 + 80

h ( 2 ) = 144 feet

Hence , the equation is solved

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Given that the perimeter of the rhombus ABCD is 52 meters, each side has a length of 52/4 = 13 meters. Since AC is diagonal with a length of 24 meters, the area of rhombus ABCD is 120 square meters.

We know that a rhombus has all sides equal in length, so each side of $abcd$ must have a length of $13$ meters ($\frac{52}{4}=13$).

We also know that the diagonal $\overline{ac}$ splits the rhombus into two congruent triangles, each with base $13$ meters and height (or length of the other diagonal) $12$ meters (half of the length of $\overline{ac}$).

Since AC is a diagonal with a length of 24 meters, we can find the other diagonal BD by using the Pythagorean theorem in the right-angled triangles formed by the diagonals. Let BD = x meters.

In triangle ABD (right-angled at B): (13^2) = (x/2)^2 + (24/2)^2 169 = (x/2)^2 + 144 25 = (x/2)^2 x = 10 meters The area of a rhombus can be found using the formula: Area = (diagonal1 * diagonal2) / 2 Area = (24 * 10) / 2 Area = 120 square meters

To find the area of one of these triangles, we use the formula for the area of a triangle: $A = \frac{1}{2}bh = \frac{1}{2}(13)(12) = 78$ square meters

Since the rhombus is made up of two congruent triangles, the area of the entire rhombus is twice this amount: $A_{\text{rhombus}} = 2A_{\text{triangle}} = 2(78) = \boxed{156}$ square meters.

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The z-values for the given situations are approximate:

a. The area to the left of z is 0.1827. z = -0.90

b. The area between −z and z is 0.9830. z = 2.17

c. The area between −z and z is 0.2148. z = 0.85

d. The area to the left of z is 0.9997. z = 3.49

e. The area to the right of z is 0.6847. z= -0.48

a. For an area of 0.1827 to the left of z, the corresponding z-value can be found using a standard normal distribution table or a statistical calculator. The z-value is approximately -0.90.

b. To find the z-value for an area between -z and z equal to 0.9830, we need to find the value that corresponds to (1 - 0.9830)/2 = 0.0085 in the upper tail of the standard normal distribution. Using the table or calculator, the z-value is approximately 2.17.

c. Similarly, for an area between -z and z equal to 0.2148, we find the value that corresponds to (1 - 0.2148)/2 = 0.3926 in the upper tail. The z-value is approximately 0.85.

d. For an area of 0.9997 to the left of z, we find the value that corresponds to 0.9997 in the upper tail. The z-value is approximately 3.49.

e. To find the z-value for an area to the right of z equal to 0.6847, we find the value that corresponds to 1 - 0.6847 = 0.3153 in the upper tail. The z-value is approximately -0.48.

In summary, the z-values for the given situations are approximate:

a. -0.90

b. 2.17

c. 0.85

d. 3.49

e. -0.48

These values can be used to determine the corresponding percentiles or probabilities for the standard normal distribution. The values are typically found using standard normal distribution tables or statistical calculators that provide the cumulative probability distribution function (CDF) for the standard normal distribution.

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The money rate of interest that lenders pay for borrowed funds minus the real rate of interest equals the relationship between these different interest rates.

Subtracting the real rate of interest from the money rate of interest gives us the inflation component, which is then added to the real rate of interest to arrive at the nominal rate of interest.

The money rate of interest that lenders pay for borrowed funds minus the real rate of interest equals the nominal rate of interest. This is because the nominal rate of interest reflects both the money rate of interest and the inflation rate.

The real rate of interest, on the other hand, reflects the true return on investment after accounting for inflation.

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Answer:

50% increase.....

original=50.

new=100.

different between original and new(price increased) =50

then,

in percentage

\( \frac{50}{100} \times 100\%\)

=50%

Answer:

50% Increase..

Step-by-step explanation  :

The difference between the original and new, = 50. Then, in percentage 50/100 times 100% would equal 50%. Hope this helps! :D

Answer:

I don't get it

Step-by-step explanation:

but okay!!!!?!!?!?!?

The height of the dinosaur is approximately 55 feet.

Let's start by drawing a diagram of the situation described:

      |\

h      | \

       -----

distance = 40 ft

We can see that we have a right triangle formed by the dinosaur, the mirror, and Amir's eyes. The height h of the dinosaur is the length of the vertical leg of this triangle. The horizontal leg has length 40 feet (the distance from the base of the dinosaur to the mirror), and the hypotenuse has length 40 + 4 = 44 feet (the sum of the distance from the base of the dinosaur to Amir and the distance from Amir to the mirror).

We can use the properties of similar triangles to find the height h. The triangle formed by the dinosaur, mirror, and Amir's eyes is similar to the triangle formed by the mirror, the ground, and Amir's eyes. This means that the ratio of corresponding sides is the same in both triangles. In particular, the ratio of the height of the dinosaur to the distance from the dinosaur to the mirror is the same as the ratio of Amir's height above the ground to the distance from Amir to the mirror.

We know that Amir's eyes are approximately 5 feet 6 inches above the ground, which is equivalent to 5.5 feet. The distance from Amir to the mirror is 4 feet, so the ratio of Amir's height to the distance from Amir to the mirror is:

5.5 feet / 4 feet = 1.375

We can set up a proportion using this ratio and the known distance from the dinosaur to the mirror:

h / 40 feet = 1.375

Solving for h, we get:

h = 1.375 * 40 feet

h = 55 feet

So the height of the dinosaur is approximately 55 feet.

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Answer:

10100

Step-by-step explanation:

the sum of the first 100 even integers is equal to 10100.

Answer:

First hundred even numbers = 2, 4, 6, 8, 10, 12, 14, ....... , 200.

Sum of First hundred even numbers = 10100

Hope that helps...

The correct answer is option b. 15.77%. The annual discount rate, also known as the discount rate or the rate of return, can be calculated using the present value formula.

Given that a cash flow of £52 million in 5 years' time is currently valued at £25 million, we can use this information to solve for the discount rate.

The present value formula is given by PV = CF / (1 + r)^n, where PV is the present value, CF is the cash flow, r is the discount rate, and n is the number of years.

In this case, we have PV = £25 million, CF = £52 million, and n = 5. Substituting these values into the formula, we can solve for r:

£25 million = £52 million / (1 + r)^5.

Dividing both sides by £52 million and taking the fifth root, we have:

(1 + r)^5 = 25/52.

Taking the fifth root of both sides, we get:

1 + r = (25/52)^(1/5).

Subtracting 1 from both sides, we obtain:

r = (25/52)^(1/5) - 1.

Calculating this value, we find that r is approximately 0.1577, or 15.77%. Therefore, the annual discount rate is approximately 15.77%, corresponding to option b.

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The data set which consists of 900 values that follow a standard normal distribution with a mean of 90 and a standard deviation of 8 has 480 values that lie between 86 and 98.

We need to determine how many values in the data set lie between 86 and 98. The formula for calculating the Z-score is as follows: Z = (X - μ) / σwhereX = the value of interestμ = the meanσ = the standard deviation

Using this formula, we can find the Z-scores for the lower and upper bounds of the range as follows:Z lower = (86 - 90) / 8 = -0.5Z upper = (98 - 90) / 8 = 1.0We can then look up these Z-scores in the standard normal distribution table to find the corresponding probabilities.

Using the table, the probability of a Z-score being less than -0.5 is 0.3085, and the probability of a Z-score being less than 1.0 is 0.8413. Therefore, the probability of a Z-score being between -0.5 and 1.0 is:0.8413 - 0.3085 = 0.5328

Finally, we can convert this probability to the number of values in the data set that lie between 86 and 98 by multiplying it by the total number of values in the data set:900 x 0.5328 = 479.52 values

Therefore, there are approximately 480 values in the data set that lie between 86 and 98.

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Answer:

product

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

20+20% is equal to 24.