I just need to know how fast John and Amy run

Y = 5 cos(0.3185x) + 10 is the volume of oxygen as a function of time can be modeled by this cosine function.

What is  cosine function ?

The cosine function is a mathematical function that relates the ratio of the sides of a right triangle. In a right triangle, the cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. In trigonometry, the cosine function is defined as the ratio of the adjacent side to the hypotenuse in a right triangle. The cosine function is periodic, meaning it repeats itself at regular intervals, and has a range of values between -1 and 1. It is commonly used in mathematics, physics, and engineering to model periodic phenomena such as sound waves, electromagnetic waves, and oscillations.

According to the question:
To find the equation of the cosine function, we need to identify the amplitude, period, phase shift, and vertical shift of the function based on the given information.

Since point M is the minimum value of the function, the vertical shift is 10. This means that the equation of the function is of the form:

Y = A cos(Bx - C) + D

where D = 10.

To find the amplitude, we need to find the distance between the maximum and minimum values of the function. Since the graph of a cosine function oscillates between its maximum and minimum values, the amplitude is half the distance between these values.

From the graph, we can see that the maximum value of the function is 20, so the distance between the maximum and minimum values is:

20 - M = 20 - 10 = 10

Therefore, the amplitude is:

A = 10/2 = 5

To find the period, we need to find the distance between two consecutive peaks or troughs of the function. From the graph, we can see that the distance between two consecutive peaks is approximately 6.28 units. This means that the period is:

P = 6.28

To find the phase shift, we need to find the horizontal shift of the function from its standard form. Since the minimum value of the function occurs at x = 0, the phase shift is:

C =

Therefore, the equation of the cosine function is:

Y = 5 cos((2π/P)x - C) + D

Y = 5 cos((2π/6.28)x) + 10

Simplifying,

Y = 5 cos(0.3185x) + 10

So, the volume of oxygen as a function of time can be modeled by this cosine function.

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Answer:

lovely peachlings

Step-by-step explanation:

The simplified form of -20/2(7 2/3) is -230/3.

To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

First, let's convert the mixed number 7 2/3 to an improper fraction.

7 2/3 = (7 * 3 + 2) / 3 = 23/3

Now, let's substitute the value back into the expression:

-20/2 * (23/3)

Next, we simplify the multiplication:

-10 * (23/3)

To multiply a fraction by a whole number, we multiply the numerator by the whole number:

-10 * 23 / 3

Now, we perform the multiplication:

-230 / 3

Therefore, the simplified form of -20/2(7 2/3) is -230/3.

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Answer:

y = 98

Step-by-step explanation:

y=21x−7

Let x=5

y = 21*5 -7

y =105-7

y =98

Answer:

???

Step-by-step explanation:

Answer:

b = 5.7

A = 51.1°

B = 38.9°

Step-by-step explanation:

a = 7

c = 9

✔️Find b using Pythagorean theorem:

b = √(9² - 7²) ≈ 5.7

✔️Find A using trigonometric function:

Reference angle = A

Opposite = a = 7

Hypotenuse = c = 9

Apply SOH:

\( sin(A) = \frac{Opp}{Hyp} \)

\( sin(A) = \frac{7}{9} \)

\( A = sin^{-1}(\frac{7}{9}) \)

A = 51.0575587° = 51.1°

✔️B = 180 - (90 + 51.1) (sum of triangles)

B = 38.9°

Solution

We want to add

Solution

We will notice the like terms and then factorise

Therefore,

Answer:

I think this is probably late, but the answer is 4/11.

Step-by-step explanation:

0.36363636363 is the first repeating fraction and 36.36363636 is the second repeating fraction, because you multiply it by 100.

When 0.3636363636363 is multiplied by 100, the decimal moves from in front of the number 36 and moves behind it. So the answer is now 36.36363636

You're suppose to subtract those two minus each other, the denominator

the fraction is technically 36/99, but simplified version is 4/11. So the answer is indeed 4/11.

Thanks for your time!

Step-by-step explanation:

Answer:

:0.36 repeating can be expressed as 36/99

Step-by-step explanation:

0.36 is equal to 36100, but you can simplify it further by dividing 36 and 100 by 4 to get 925

Answer:

AC = 12

Step-by-step explanation:

If BC is parallel to DE then ∠D ≅ ∠B and ∠E ≅ ∠C. Therefore

ΔABC is similar to ΔADE.

The sides of smaller triangle are in proportion with sides of bigger triangle.

Therefore we have the equation:

AC/AE = AB/AD

Substitute the given numbers:

x/x+15 =8/18

18x= 8(x+15)

18x = 8x+120

10x = 120

x = 12

AC=12

Answer:

I would say it's C

Step-by-step explanation:

trust the process

We can Add 7 black beads to make ratio 3 : 1.

Since we can only change the number of black beads, decide how many black beads you will add based on how many white beads there are.

There are three white beads in the picture.

Total beads we will have (b meaning black)b : 3

Ratio black : white beads 3 : 1

Use the common ratio, which is a number that both sides of the original ratio multiply by to get to the new ratio.

Find common ratio by dividing total by ratio white beads: 3/1 = 3

Multiply ratio black beads by common ratio. 3 X 3 = 9

We need 9 black beads in total.

Check answer

9 : 3    

Both sides divisible by 3; reduce ratio

= 3 : 1        

Which is Correct ratio

Hence, There will be a total of 9 black beads, but we already have 2 black beads:

(9 total) - (2 original) = (7 to add)

Therefore , we need to add 7 black beads.

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Answer: the answer is (3,-2)

Step-by-step explanation: when you rotate a point about the origin 180 degrees clockwise, (x,y) turns into (-x,-y)

therefore

(-3,2) becomes (3,-2)

I'm pretty sure

Here are the correct matches to the expressions to their solutions.

The GCF of 28 and 60 is 4.

(-3/8)+(-5/8) = -4/4 = -1.

-1/6 DIVIDED BY 1/2 = -1/6 X 2 = -1/3.

The solution of 0.5 x = -1 is x = -2.

The solution of 1/2 m = 0 is m = 0.

-4 + 5/3 = -11/3.

-2 1/3 - 4 2/3 = -10/3.

4 is not a solution of -4 < x.

1. The GCF of 28 and 60 is 4.

The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 28 and 60, we can factor each number completely:

28 = 2 x 2 x 7

60 = 2 x 2 x 3 x 5

The factors that are common to both numbers are 2 and 2. The GCF of 28 and 60 is 2 x 2 = 4.

2. (-3/8)+(-5/8) = -1.

To add two fractions, we need to have a common denominator. The common denominator of 8/8 and 5/8 is 8. So, (-3/8)+(-5/8) = (-3 + (-5))/8 = -8/8 = -1.

3. -1/6 DIVIDED BY 1/2 = -1/3.

To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/2 is 2/1. So, -1/6 DIVIDED BY 1/2 = -1/6 x 2/1 = -2/6 = -1/3.

4. The solution of 0.5 x = -1 is x = -2.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate x by dividing both sides of the equation by 0.5. This gives us x = -1 / 0.5 = -2.

5. The solution of 1 m = 0 is m = 0.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate m by dividing both sides of the equation by 1. This gives us m = 0 / 1 = 0.

6. -4 + 5/3 = -11/3.

To add a fraction and a whole number, we can convert the whole number to a fraction with the same denominator as the fraction. In this case, we can convert -4 to -4/3. So, -4 + 5/3 = -4/3 + 5/3 = -11/3.

7. -2 1/3 - 4 2/3 = -10/3.

To subtract two fractions, we need to have a common denominator. The common denominator of 1/3 and 2/3 is 3. So, -2 1/3 - 4 2/3 = (-2 + (-4))/3 = -6/3 = -10/3.

8. 4 is not a solution of -4 < x.

The inequality -4 < x means that x must be greater than -4. The number 4 is not greater than -4, so it is not a solution of the inequality.

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A. The null hypothesis H₀ and the alternative hypothesis H₁ are:

H₀: μ = 35 minutes       H₁: μ > 35 minutes

B. If the consultant decides not to reject the null hypothesis, she might be making a Type II error.

C. A Type II error would be failing to reject the hypothesis that μ is = to 35 minutes when, in fact, μ is 43 minutes.

A Type II error occurs when the null hypothesis is false, but the test does not reject it.

In this case, the consultant would be concluding that the mean shopping time is 35 minutes, when in fact it is greater than 35 minutes.

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Answer:

8 1/5

Step-by-step explanation:

Answer:

8.2 or 41/5

Step-by-step explanation:Sorry if its wrong!!!!

9514 1404 393

Answer:

  A, E

Step-by-step explanation:

Solving for y, the coefficient of x tells us the slope of the given line.

  y = (-x +50)/5

  y = (-1/5)x +10 . . . . . the given line; has a slope of -1/5

The perpendicular line will have a slope that is the opposite reciprocal of this value:

  m = -1/(-1/5) = +5

That is, you want equations for lines that have a slope of +5.

__

As above, the slope is the x-coefficient when the equation is in y = ( ) form. This fact lets us identify A as one good choice, and reject B–D as incorrect choices.

When we divide the equation of E by 5 to put it into the desired form, we have ...

  y = 5x +2.6 . . . has a slope of 5

The equations of interest are ...

Answer:

\(Result = 27\)

Step-by-step explanation:

Given

\(2(8 - 4)^2 - 10 / 2\)

Required

Evaluate

\(Result = 2(8 - 4)^2 - 10 / 2\)

Solve the expression in the bracket

\(Result = 2(4)^2 - 10 / 2\)

Solve all exponents

\(Result = 2 * 16 - 10 / 2\)

Express 10 / 2 as 5

\(Result = 2 * 16 - 5\)

Express 2 * 16 as 32

\(Result = 32 - 5\)

\(Result = 27\)

There are 168 different area codes possible with this plan by using the multiplication principle of counting.

What is multiplication principle ?

The multiplication principle of counting, also known as the rule of product, is a counting principle in combinatorics that states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.

There are 7 possible choices for the first digit (0 through 6), 3 possible choices for the second digit (2, 3, or 4), and 8 possible choices for the third digit (any digit except 0 or 3). To find the total number of possible area codes, we can use the multiplication principle of counting:

Total number of area codes = Number of choices for first digit x Number of choices for second digit x Number of choices for third digit

Total number of area codes = 7 x 3 x 8

Total number of area codes = 168

Therefore, there are 168 different area codes possible with this plan.

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Answer:

B. 28 houses per hour

Step-by-step explanation:

\(\frac{84}{3}\) = 28

Answer:

28

Step-by-step explanation:

all you have to do is divide

84/3=28

Answer:

a) P = 6x + 13//

b) i) x = 5//

ii) 9//

Step-by-step explanation:

a) P = 2(x+2) + 2(2x-1) + 3 + 8 m

= 2x+4 + 4x-2 + 3 + 8

= 6x + 13//

b) i) P = 43 m

43 = 6x + 13

43-13 = 6x

30 = 6x

6 6

x = 5//

ii) longest side = (2x-1) m

2 × 5 - 1

10-1 = 9//

Answer: Q = 35, PR = 12.62, QR = 18.02

Step-by-step explanation:

Find Q
Sum of angles in a triangle is 180
So 180 = Q + R + P
180 - R - P = Q
we given P = 55 and R = 90
so 180 - 55 - 90 = 35
Q = 35

Find PR
we have hypotenuse QP = 22, and an angle P = 55
PR is adjacent to angle P, thus we can use cos ratio, cos x = H / A
so A = cos(x) * H
PR = cos(55) * 22
PR = 12.62

Find QR
QR is opposite to angle P, thus we can use sin ratio, sin x = H/O
So O = sin(x) * H
QR = sin(55) * 22
QR = 18.02

Answer:

$383,500.68  

Step-by-step explanation:

The amount needed is the present value of the $30,000 that Anna will withdraw for 25 years compounded at 6% annually

=pv(rate,nper,pmt,fv)

rate is the annual rate of 6%

nper is the number of years of withdrawal which is 95-70=25

pmt is the amount of annual withdrawal which is $30,000

fv is the amount of withdrawals which is unknown

=pv(6%,25,-30000,0)=$383,500.68  

The amount of she required at 70 is $$383,500.68   which gives her the benefit of withdrawing $30,000 per year at retirement

Answer:

\(\cos G=\dfrac{2}{3}\)

\(\csc E=\dfrac{3}{2}\)

\(\cot G=\dfrac{2}{\sqrt{5}}\)

Step-by-step explanation:

If the right angle of right triangle EFG is ∠F, then EG is the hypotenuse, and EF and FG are the legs of the triangle. (Refer to attached diagram).

Given ΔEFG is a right triangle, and EG = 6 and FG = 4, we can use Pythagoras Theorem to calculate the length of EF.

\(\begin{aligned}EF^2+FG^2&=EG^2\\EF^2+4^2&=6^2\\EF^2+16&=36\\EF^2&=20\\\sqrt{EF^2}&=\sqrt{20}\\EF&=2\sqrt{5}\end{aligned}\)

Therefore:

\(\hrulefill\)

To find cos G, use the cosine trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosine trigonometric ratio} \\\\$\sf \cos(\theta)=\dfrac{A}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the hypotenuse is EG.

Therefore:

\(\cos G=\dfrac{FG}{EG}=\dfrac{4}{6}=\dfrac{2}{3}\)

\(\hrulefill\)

To find csc E, use the cosecant trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cosecant trigonometric ratio} \\\\$\sf \csc(\theta)=\dfrac{H}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle E, the hypotenuse is EG and the opposite side is FG.

Therefore:

\(\csc E=\dfrac{EG}{FG}=\dfrac{6}{4}=\dfrac{3}{2}\)

\(\hrulefill\)

To find cot G, use the cotangent trigonometric ratio:

\(\boxed{\begin{minipage}{9 cm}\underline{Cotangent trigonometric ratio} \\\\$\sf \cot(\theta)=\dfrac{A}{O}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

For angle G, the adjacent side is FG and the opposite side is EF.

Therefore:

\(\cot G=\dfrac{FG}{EF}=\dfrac{4}{2\sqrt{5}}=\dfrac{2}{\sqrt{5}}\)

Answer:

y=-5/4x+3

Step-by-step explanation:

y=mx+c

m = (y1-y2)/(x1-x2) =(-2-3)/(4-0) =-5/4

sub the values y=3, x=0 to find c,

3 =-5/4(0) + c

c = 3

\(x^2 -8x-2=0\\\\x^2 -8x=2\\\\x^2 -8x+16=18\\\\(x-4)^2 =18\\\\x-4=\pm \sqrt{18}\\\\\boxed{x=4 \pm \sqrt{18}}\)

The limit of each function at the given point i n the question 10 to 14, is explained below.

A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit. Although the right- and left-hand limits are present in this scenario, the limit is not defined.

When a variable approaches its limit from the right, the function's right-hand limit is the value that approaches.a

10). The limit of f(z) = Arg z as z approaches Zo = 1 does not exist. This is because the argument function is not continuous at the point z = 1, where there is a branch cut.

11). The limit of f(z) = \((1 - lm z)^{-1}\) as z approaches z0 = -8 does not exist. This is because the function approaches infinity as z approaches -8 from the left, and negative infinity as z approaches -8 from the right.

However, if we consider the limit of f(z) as z approaches z0 = -8 + i from both the left and the right, the limit exists and is equal to 0. This is because in the complex plane, the value of Im z cannot exceed 1, so as z approaches -8 + i, the denominator (1 - Im z) approaches 0, and the function approaches infinity. However, the numerator approaches a finite value of 1, which cancels out the denominator, and the overall limit is equal to 0.

12). The limit of f(z) = (z - 2) log(z - 2) as z approaches z0 = 2 is 0. This is because the term (z - 2) approaches 0 as z approaches 2, and log(z - 2) approaches 0 as well because log(z - 2) is continuous at z = 2. Therefore, the limit is equal to 0.

13). The limit of f(z) = -1/z as z approaches z0 = 0 does not exist. This is because as z approaches 0, the magnitude of 1/z approaches infinity, but the direction of approach depends on which quadrant the limit is approached from. Since the limit does not approach a unique value from all directions, the limit does not exist.

14). The limit of f(z) = 2 + \(2^{1/z}\) as z approaches infinity does not exist. This is because as z approaches infinity, the term  \(2^{1/z}\) approaches 1, and the limit approaches 2 + 1 = 3. However, if we approach infinity along the real axis, the limit of \(2^{1/z}\) approaches 1, but if we approach infinity along the imaginary axis, the limit of \(2^{1/z}\) approaches infinity. Therefore, the limit of f(z) does not exist.

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