The equation m (t) = 2t^3 - 21t^2 +40t represent the money in Mr. Sully's bank account over time t, measured in days.

A.) find m(2).

B.) when will Mr. Sully have no money?

Answer:

Amplitude = -4; period = π; phase shift: x = π/2

Step-by-step explanation:

* Lets revise the trigonometry translation  

- If the equation is y = A sin (B(x + C)) + D  

* A is the amplitude  

- The amplitude is the height from highest to lowest points and  

  divide the answer by 2  

* The period is 2π/B  

- The period is the distance from one peak to the next peak

* C is the horizontal shift  (phase shift)

- The horizontal shift is how far the function is shifted to left  

  (C is positive) or to right (C is negative) from the original position.  

* D is the vertical shift  

- The vertical shift is how far the function is shifted vertically up

  (D is positive) or down (D is negative) from the original position.  

* Now lets solve the problem

∵ f(x) = A sin (B(x + C)) + D  

∵ f(x) = -4 sin (2x + π) - 5 ⇒ take 2 from the bract (2x + π) common factor

∴ f(x) = -4 sin 2(x + π/2) - 5

∴ A = 4 , B = 2 , C = π/2 , D = -5

∵ A is the amplitude

∴ The amplitude is -4

∵ The period is 2π/B  

∴ The period = 2π/2 = π

∵ C is the horizontal shift  (phase shift)

∴ The phase shift π/2 (to the left)

* Amplitude = -4; period = π; phase shift: x = π/2

The amplitude of the function f(x) = −4 sin(2x + π) − 5 is 4, its period is π, and it has a phase shift of x = -π/2.

The amplitude of a trigonometric function like f(x) = −4 sin(2x + π) − 5 is the coefficient in front of the sine function which determines the maximum and minimum value of the function's graph. In this case, the amplitude is the absolute value of -4, which is 4.

The period of the function is found by taking 2π divided by the coefficient of x inside the sine function, which is 2 in this case, yielding a period of π.

The phase shift of the function is determined by solving the equation 2x + π = 0 for x, which gives us a phase shift of x = -π/2. Therefore, the correct description is amplitude of 4, a period of π, and a phase shift of x = -π/2.

Answer:

The volume of the pyramid is [tex]130\frac{2}{3}\ units^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the pyramid is equal to

[tex]V=\frac{1}{3}BH[/tex]

where

B is the area of the base

H is the height of the pyramid

Find the area of the base B

In this problem we have a square base

[tex]B=7^{2} =49\ units^{2}[/tex]

we have

[tex]H=8\ units[/tex]

substitute

[tex]V=\frac{1}{3}(49)(8)=\frac{392}{3}\ units^{3}[/tex]

Convert to mixed number

[tex]\frac{392}{3}=\frac{390}{3}+\frac{2}{3}=130\frac{2}{3}\ units^{3}[/tex]

you do length x width x be aight divided by 3 to get 392/3

Answer:

The dog should receive 400 mL of the i.v. bag.

Step-by-step explanation:

40% x 1000 = 400

Answer:

Step-by-step explanation:

Givens

To know how many mL the dog received, we just need to find the 40% of 100 mL.

We know that 40% equals 0.40, then we multiply it

[tex]0.40(1000mL)=400mL[/tex]

Therefore, the dog received 400mL

Answer:

1.A. X6Y5

Step-by-step explanation:

#2 I have no clue on that one.

So sorry but I simply forgot to answer your questions.

The answer to question 1 is A.

The answer to question 2 is D.

Answer:

A

Step-by-step explanation:

Define each of the terms.

f(x) is the total level of radioactivity.

x is the total number of weeks.

[tex]\frac{1}{2}[/tex] is the weekly decay factor.

30 is the initial level of radioactivity.

Answer:

Principal Amount= $500

Formula for compound interest:

[tex]A = p (1 + \frac{r}{n} )^{nt}[/tex]

Formula for simple interest:

A = p(1 + r(t) )

Answer:

The trip lasted for a total of 8 hours.

Step-by-step explanation:

Distance planned = S = 640 miles

Constant speed = V

Thus the time to be taken would be = T = V/S

We have an equation 640 = VT ----- eq (a)

Time For First Quarter = T/4

speed = V

Distance = 640/4 = 160

After first quarter, there is a rest of 1.2 hours and to complete his trip on time, he increased the velocity by 20 mph.

So, the remaining distance = 640 - 160 = 480 miles.

Speed = V + 20 mph

Time remaining = [(T-T/4) - 1.2] = 3T/4 - 1.2 hours

We have an equation for remaining distance s = vt

=> 480 = (V+20)(3T/4 - 1.2) ----- eq (b)

using eq (a), we have V = 640/T. Putting it in eq (b), we have:

[tex]480 = (\frac{640}{T} + 20)(3\frac{T}{4} - 1.2)\\480 = 480 - \frac{768}{T}  + 15T - 24\\=> 15T - \frac{768}{T} -24 = 0\\=> 15T^{2} - 24T - 768 = 0\\[/tex]

Solving the equation, we get T = 8 or T = -32/5(which is not possible.

So, the right answer is T = 8 hours

As for a specific equation, I could not say. However, I can tell you how to find x!

The first thing to remember is that a straight line has a 180 degree angle.

You see on the bottom side that we have a 146 degree angle. Now look at the top side. Look closely, and you will see that the two sides are actually identical!

Don't see it? Look at the line on top between x and 56, and imagine it is not there. You see that we actually have the same 146 degree angle, just flipped right side up!

However, this angle does not say 146, but makes an extra line between them with x and 56. This means that x + 56 equals 146!

So we can find x by subtracting 56, from 146, which is... 90!

Answer:

B

Step-by-step explanation:

The expression can be written as

[tex]\sqrt{-20}[/tex]

The - can be taken out from under the radicand and a 2 can be factored out of the expression to leave you with the expression

[tex]2i\sqrt{5}[/tex]

Answer:

Correct option is:

B

Step-by-step explanation:

We have to find a expression which is similar to:

[tex]\sqrt{-20}[/tex]

Now we start solving

[tex]\sqrt{-20}[/tex] could also be written as:

[tex]\sqrt{-2\times 2\times 5}[/tex]

When we take - sign out of the square root it becomes i

i.e. [tex]\sqrt{-1}=i[/tex]

And there are two 2's inside the square root when we take square root it becomes 2

Hence, [tex]\sqrt{-20}=2i\sqrt{5}[/tex]

Hence, Correct option is:

B

Answer:

Step-by-step explanation:

You don't say whether this is compound interest or simple interest.

I will assume it's compounding that interests you.

The appropriate formula is

A = P(1 + r)^t, where r is the interest rate as a decimal fraction, t is the time in years, and P is the original amount.  Thus:

A = $1000·(1 + 0.05)^t, or  A = $1000·(1.05)^t

Please note:  There were apparently possible answer choices.  Next time, please be sure to list such choices.  Thank you.

Final answer:

The equation modeling the value of an investment, V, after t years, for an initial investment of $1,000 at a 5% annual interest rate is V = 1000(1 + 0.05)^t, incorporating the principles of compounding interest.

Explanation:

The question asks about the equation modeling the value of an investment, V, after t years, given an initial investment of $1,000 at a 5% annual interest rate. Using the formula for the future value of a single sum, V = P(1 + r)^t, where P is the principal amount ($1,000), r is the annual interest rate (5% or 0.05), and t is the number of years, we can determine that the equation modeling the value of the investment is V = 1000(1 + 0.05)^t. This formula is applied to calculate the future value of the investment, taking into account the compounding interest over a period t years.

The value of 0.6239 as a fraction or proportion is

A fraction is a mathematical expression that represents a part or a division of a whole. It is used to represent numbers that are not whole numbers or integers. A fraction consists of two components:

1. Numerator: The numerator is the number on the top of the fraction. It represents the quantity or part of the whole being considered.

2. Denominator: The denominator is the number at the bottom of the fraction. It represents the total number of equal parts into which the whole is divided.

Multiply and divide 0.6239 by 10000,

0.6239 = [tex]\frac{0.6239}{10000} \times[/tex] 10000

            = [tex]\frac{6239}{10000}[/tex].

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Answer: 1.8

Step-by-step explanation:

Answer:

1.8

Step-by-step explanation:

(67 degrees - 58 degrees) / 5 minutes

1.8 degrees per minute

Step 1: Subtract 25 to both sides. This will cancel 25 on the left side and bring it over to the right

(25 - 25) - 3x = 40 - 25

(0) - 3x = 15

-3x = 15

Step 2: Isolate x by dividing -3 to both sides (the opposite of multiplication is division).

-3x ÷ (-3) = 15 ÷ (-3)

x = -5

Check:

25 - 3(-5) = 40

25 + 15 = 40

40 = 40 ....................................Correct!

Hope this helped!

The value of x in this equation is -5.

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation in algebra.

Equation given in the question:

25 - 3x = 40

25 - 40 = 3x

-15 = 3x

x = -5

The value of x in this equation is -5.

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The answer would be 0.6 if you divide 21/35.

Answer:

[tex]\frac{3}{5}[/tex]

Step-by-step explanation:

To simplify divide the numerator/denominator by the highest common factor of 21 and 35, that is 7

[tex]\frac{21}{35}[/tex] = [tex]\frac{3}{5}[/tex] ← in simplest form

t must equal √2h/g but I don't see that in the choices above

Answer:

t=2hg√g

Step-by-step explanation:

took the test!

First, set up a proportional fraction.

[tex]\frac{5 sec}{30 gallons}[/tex] = [tex]\frac{x sec}{1gallon}[/tex]

Cross multiply

5 * 1 = 5

30 * x = 30x

So,

30x = 5

Divide 5 by 30

x = 5 / 30

x = 1 / 6 or 0.17

Do the same thing to find for 17 gallons.

30x = 85

x = 85 / 30

x = 17 / 6 or 2.8

Answer:

I would say 50%

Step-by-step explanation:

The answer is 50%. Hope that helps!

Answer:

x=-7

Step-by-step explanation:

Since you are solving for x, you need to work backwards. Add 2 to both sides: -2 and 2 cancel out, and 19 plus 2 is 21. Isolate the x by dividing both sides by -3. -3 cancels out, and 21 divided by -3 is -7.

Answer:

-7

Step-by-step explanation

−2−3x=19

−2+−3x=19

−3x−2=19

Step 2: Add 2 to both sides.

−3x−2+2=19+2

−3x=21

Step 3: Divide both sides by -3.

−3x

−3

=

21

−3

x=−7

Answer:  D) at least 6mm

Step-by-step explanation:

95% confidence is 2 standard deviations.

5mm + 2(0.5) = 5 + 1 = 6

The oysters must be at least 6 mm

Answer:

θ = π/3, 5π/3

Step-by-step explanation:

2 cos θ - 1 = 0

2 cos θ = 1

cos θ = 1/2

θ = π/3, 5π/3

ANSWER

EXPLANATION

The given trigonometric equation is:

[tex]2 \cos( \theta) - 1 = 0[/tex]

[tex] \implies \: 2 \cos( \theta) = 1[/tex]

[tex]\implies \: \cos( \theta) = \frac{1}{2} [/tex]

The cosine ratio is positive in the first and fourth quadrants.

In the first quadrant,

[tex]\theta = \cos ^{ - 1} ( \frac{1}{2}) [/tex]

[tex]\theta = \frac{\pi}{3} [/tex]

In the fourth quadrant,

[tex]\theta =2 \pi - \cos ^{ - 1} ( \frac{1}{2}) [/tex]

[tex]\theta =2 \pi - \frac{\pi}{3} [/tex]

[tex]\theta = \frac{5\pi}{3} [/tex]

Therefore on the interval, [0,2π] the solution to the given trigonometric equation is:

[tex]\theta = \frac{\pi}{3} \: and \: \frac{5\pi}{3} [/tex]

the correct answer is OB. 7.

Final answer:

To calculate the number of complete revolutions a bicycle wheel makes after traveling 440 meters, we find the wheel's circumference using its diameter and then divide the travel distance by the circumference. With a diameter of 0.7 meters and using 22/7 as an approximation for π, the wheel's circumference is 2.2 meters. The wheel makes 200 complete revolutions to cover 440 meters.

Explanation:

Finding the Number of Complete Revolutions

To find the number of complete revolutions made by a bicycle wheel when the bicycle travels a certain distance, we firstly need to calculate the circumference of the wheel. The circumference 'C' of a circle can be found using the formula C = πd, where π (Pi) is a constant (approximately 22/7 or 3.14) and 'd' is the diameter of the circle. In this case, we are given that the diameter of the bicycle wheel is 0.7 meters.

Using the approximation for π of 22/7 and the given diameter, the circumference is: C = π × d = (22/7) × 0.7 meters = 2.2 meters.

To find the number of complete revolutions 'N', we divide the total distance the bicycle travels by the circumference of the wheel: N = total distance / circumference = 440 meters / 2.2 meters. So, the number of complete revolutions the wheel makes is 200.

Answer:

106°

Step-by-step explanation:

A quadrilateral inside a circle is a cyclic quadrilateral.

It means that the angles opposite are supplementary (add up to 180).

If we draw the quadrilateral ABCD, the angles A and C are supplementary and the angles B and D are supplementary.

Since we know A and C, we can write:

A + C = 180

x^2 + 3x = 180

x^2 +3x - 180 = 0

(x+15)(x-12) = 0

x= -15, or x = 12

Now, if we put x = -15, some angles become negative, so we disregard it and take x = 12.

Now finding B:

B = 7x - 10

B = 7(12) - 10

B = 74

We also know that B + D = 180, so:

B + D = 180

74 + D = 180

D = 180 - 74 = 106

Answer:

B=-27

Step-by-step explanation:

Answer:

-27

-1/3b=9

Divide both sides by -1/3 to get b by itself

-1/3b=9

/-1/3 /-1/3

b=-27

Answer:

Probability of getting three jacks = [tex] \frac { 3 } { 5 2 } [/tex]

Step-by-step explanation:

It is given that you deal three cards from a regular deck which contains 52 cards.

We are to find the probability of getting all three Jack cards.

We know that there are a total of 4 jacks in a regular deck of 52 cards.

Therefore, the probability of getting three jacks = [tex] \frac { 3 } { 5 2 } [/tex]

3 chances of jacks out of 52 cards

Answer:

z = 19

Step-by-step explanation:

Given

2(4z - 9 - 7) = 166 - 46 ← simplify both sides

2(4z - 16) = 120 ← distribute parenthesis on left side

8z - 32 = 120 ( add 32 to both sides )

8z = 152 ( divide both sides by 8 )

z = 19

Answer:

z = 19.

Step-by-step explanation:

2(4z − 9 − 7) = 166 − 46

 2(4z − 9 − 7) = 120

Divide both sides by 2:

4z − 9 − 7 = 60

4z = 76

z = 19.

Answer:

Step-by-step explanation: a is adjacent, b is opposite, c is the hypotenuse

Answer:

D

Step-by-step explanation:

Answer:

[tex]\boxed{\$8378}[/tex]

Step-by-step explanation:

The formula for compound interest is:

A = P(1 + r)ⁿ

Data:

    P = 3300

APR = 8.5 %

     t = 11 yr

Calculations:

n = 11 × 12 = 132

r = 0.085/12 = 0.007 083

A = 3300(1 + 0.007 083)¹³²

  = 3300 × 1.007 083¹³²

  = 3300 × 2.5539

  = 8378

[tex]\text{The investment will be worth }\boxed{\mathbf{\$8378}}[/tex]

Answer:

The equation that best describes the situation is:

[tex]g +400 -1800 = 1,500[/tex]

Step-by-step explanation:

The initial amount of gravel is g.

[tex]g[/tex]

Then we know that 400 pounds are added

[tex]g +400[/tex]

Two orders of 900 pounds are sold and the gravel is removed from the mound. This is:

[tex]g +400 -2 * 900[/tex]

[tex]g +400 -1800[/tex]

At the end of the day, the mound has 1,500 pounds of serious. This is:

[tex]g +400 -1800 = 1,500[/tex]

The equation that best describes the situation is:

[tex]g +400 -1800 = 1,500[/tex]

And

[tex]g= 1500 +1800 - 400\\\\g=2900[/tex]

The equation that best describes the given situation is[tex]\rm g + 400 - (2\times 900) = 1500[/tex]  and this can be determined by forming the linear equation with the help of given data.

Given :

Let the initial amount of gravel be 'g'. Then after the addition of 400 pounds of gravel, the total gravel becomes:

= g + 400

Given that two orders of 900 pounds are sold and the gravel is removed from the mound so, the total gravel now becomes:

[tex]\rm = g + 400 - (2\times 900)[/tex]

= g + 400 - 1800

= g - 1400

At the end of the day, the mound has 1,500 pounds of gravel, that is:

g - 1400 = 1500

g = 1500 + 1400

g = 2900

Therefore, the equation that best describe the given situation is:

g + 400 - 1800 = 1500

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Answer:

[tex]30+42=6(5+7)[/tex]

Step-by-step explanation:

Let [tex]a,b,c\in \mathbb R[/tex], according to the distributive property:

[tex]a(b+c)=ab+ac[/tex]

The prime factorization of 30 is

[tex]30=2\cdot 3\cdot 5[/tex]

The prime factorization of 42 is

[tex]42=2\cdot 3\cdot 7[/tex]

The Greatest common factor is [tex]2\times 3=6[/tex]

[tex]\implies 30+42=6\times5+6\times7[/tex]

[tex]\implies 30+42=6(5+7)[/tex]

Answer:

Step-by-step explanation:

6(5+7