Write an equation in slope-intercept form to represent the total cost, y, of leasing a car for x months.

months costs
1 $1,859
3 $2,577
8 $4,372
12 $5,808

A trigonometric equation to express d in terms of t is d = A sin(Bt - C) + D, the weight is approximately 16 centimeters above the floor at 4 seconds.

The distance, d, of the weight above the floor at time t can be expressed as a sinusoidal function of the form:

d = A sin(Bt - C) + D

where A is the amplitude, B is the frequency, C is the phase shift, and D is the vertical shift.

We are given that the weight reaches its first high point (maximum) at 0.5 seconds, which means that the phase shift is 0.5 seconds. At this point, d = 42 centimeters, which means that the amplitude is 42/1 = 42 centimeters.

We are also given that the next low point (minimum) occurs at 1.2 seconds, which means that the function has completed one full period between 0.5 and 1.2 seconds. Therefore, the period of the function is:

T = 1.2 - 0.5 = 0.7 seconds

The frequency, B, is the reciprocal of the period:

B = 1/T = 1/0.7 ≈ 1.43

Finally, we need to find the vertical shift, D. At time t = 0, the weight is at its equilibrium position, which is the midpoint between the maximum and minimum heights:

D = (42 + 11)/2 = 26.5

Putting all of this together, we get:

d = 42 sin(1.43(t - 0.5)) + 26.5

To find the weight's distance from the floor at 4 seconds, we simply need to plug in t = 4 into the equation and round to the nearest centimeter:

d = 42 sin(1.43(4 - 0.5)) + 26.5 ≈ 16 centimeters

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Answer:

\(f'(x)= \frac{13}{(2x+3)^2}\\\)

Step-by-step explanation:

\(f(x)= \frac{3x-2}{2x+3} \\\)

\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)

\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)

A 10% increase in cigarette prices has been found to result in a 4% decrease of smokers.

An increase in cigarette price will result in a decrease in the demand for cigarettes.

Since more money needs to be spent to but the same product, less consumers can be able to afford it.

Therefore, a 10% increase in cigarette prices has been found to result in a 4% decrease of smokers.

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Answer:

40c

Step-by-step explanation:

it starts at 10c and goes up 30c you can just add 30 to 10 to get 40

The solution is, 40°C will be the new reading.

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

given that,

the reading on the thermometer reads 10°C

and the temperature rises 30°C

now, we have to add the temperature ,

so, the new reading will be,

30+10

=40°C

Hence, The solution is, 40°C will be the new reading.

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Answer:

45º

Step-by-step explanation:

Since we know the relatiionship of a 45-45-90 degree triangle, we can go two ways. Either we can use this to find CA and get the tangent of (6/6) or we can go straight to it. The hypotenuse in a 45-45-90 is always 6√2 and we know it is a right triangle so we can confirm this. So, measure of angle B is 45º.

Answer:

x^2+9x+20

Step-by-step explanation:

Answer: 0.029

Step-by-step explanation:

2.9/100

= 0.029

Answer:

Step-by-step explanation:

2.9% in a decimal is 0.029

The correct solution to the arithmetic expression (2 8)/2*9/3 using the order of operations as employed by Oracle 12c when solving equations is 4.

According to the Order of Operations, the first step is to evaluate expressions inside parentheses, then perform any multiplications or divisions, and finally perform any additions or subtractions. In this expression, the first step would be to evaluate the expression inside the parentheses: (28)/2. This evaluates to 14.

Next, the expression becomes 14 * 9/3. According to the Order of Operations, we need to perform the multiplication first, so 14 * 9 = 126. Finally, we perform the division: 126/3 = 42.

So, the correct solution to the expression (2 8)/2 * 9/3 is 42.

Order of operations is a set of rules used to determine the sequence in which arithmetic operations should be performed in a mathematical expression to obtain the correct result. The rules ensure that operations are performed in a consistent and predictable manner.

The order of operations is typically represented by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

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The volume of the given shape is required.

The required volume is 90π in³.

The given figure is made of a hemisphere and cylinder

Volume of a cylinder is given by \(\pi \text{r}^2\text{h}\)

Volume of a hemisphere is given by \(\dfrac{2}{3} \pi \text{r}^3\)

The total volume is

\(\text{V}= \pi \text{r}^2\text{h}+\sf \dfrac{2}{3} \pi \text{r}^3\)

\(\rightarrow\text{V}= \pi \text{r}^2 \ \huge \text (\sf h+\sf \dfrac{2}{3} {r}\huge \text)\)

\(\sf \rightarrow\text{V}= \pi \times3^2 \ \huge \text (\sf 8+\sf \dfrac{2}{3} \times3\huge \text)\)

\(\sf \rightarrow\text{V}= \bold{\underline{90\pi }}\)

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The correct trigonometric ratio to find the angle of the right triangle is tan x = 1 / 2.

A right angle triangle is a triangle with one of its angles as 90 degrees. The sides and angles of a triangles of a triangle can be found using trigonometric ratios as follows:

The sides of a right angle triangle can be named base on the angles position. They include adjacent side, hypotenuse sides and opposite side.

Therefore, let's find x using tangential ratio as follows;

tan x = opposite / adjacent

opposite side = 5

adjacent side = 10

Therefore,

tan x = 5 / 10

tan x = 1 / 2

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Answer:40%

Step-by-step explanation:20 divided by 50 is 0.4 then multiply that by 100 and get 40

Answer:

Well the equation for this would 50*.20 = ...

The first half of the answer would be 10.

BUT!

You need to subtract 10 from 50.

50-10 = 40!

There you go.

Step-by-step explanation:

(a) The function f(x) = 2x^3+3x-1 has at most one real root because its discriminant is positive, which means it has two complex roots and one real root at most.

(b) The function f(x) = 2x^3+3x-1 has a root in the interval [0,1] because f(0) is negative and f(1) is positive, and the intermediate value theorem guarantees the existence of a root between these values.

(c) Using two iterations of Newton's method starting with an initial guess of x_0 = 0.5, we can approximate the real root of f(x) to be x = 0.414217

(a) The function f(x) is a polynomial of degree three, which means it can have at most three roots. However, not all three roots need to be real. In this case, we can use the discriminant of the polynomial to determine the number of real roots. The discriminant is given by b^2 - 4ac, where a = 2, b = 3, and c = -1. Plugging these values into the formula, we get:

b^2 - 4ac = 3^2 - 4(2)(-1) = 17

Since the discriminant is positive, the polynomial has two complex roots and one real root at most.

(b) To show that the polynomial has a root in the interval [0,1], we can evaluate f(0) and f(1) and show that they have opposite signs. This is known as the intermediate value theorem. We have

f(0) = 2(0)^3 + 3(0) - 1 = -1

f(1) = 2(1)^3 + 3(1) - 1 = 4

Since f(0) is negative and f(1) is positive, there must be a root of f(x) in the interval [0,1].

(c) To use Newton's method to approximate the root of f(x), we need to start with an initial guess. Let's use x_0 = 0.5. The formula for Newton's method is

x_(n+1) = x_n - f(x_n)/f'(x_n)

We need to compute f(x_n) and f'(x_n). We have

f(x_n) = 2(x_n)^3 + 3(x_n) - 1

f'(x_n) = 6(x_n)^2 + 3

Plugging in x_0 = 0.5, we get

f(x_0) = 2(0.5)^3 + 3(0.5) - 1 = 0.375

f'(x_0) = 6(0.5)^2 + 3 = 4.5

Using these values in the Newton's method formula, we get

x_1 = x_0 - f(x_0)/f'(x_0) = 0.5 - 0.375/4.5 = 0.416666...

We can repeat the process with x_1 as the new guess

f(x_1) = 2(0.416666...)^3 + 3(0.416666...) - 1 = 0.007716...

f'(x_1) = 6(0.416666...)^2 + 3 = 4.238425...

Plugging these values into the formula, we get

x_2 = x_1 - f(x_1)/f'(x_1) = 0.416666... - 0.007716.../4.238425... = 0.414217...

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Answer:

25 , 1 , 34

Step-by-step explanation:

substitute x = - 12 into g(x)

g(- 12) = 1 - 2(- 12) = 1 + 24 = 25

substitute x = 0 into g(x)

g(0) = 1 - 2(0) = 1 - 0 = 1

substitute x = 4 into g(x)

- 5(1 - 2(4)) - 1 = - 5(1 - 8) - 1 = - 5(- 7) - 1 = 35 - 1 = 34

Answer:

50 cents ($0.50)

Step-by-step explanation:

We need to find the price for one orange. To get one orange, you have to divide 6 by 6. Anything you do to one side of the equation must be done to the other side. You have to divide 3 by 6. If you do this, you get .5, or 1/2. In money, that translates to 50 cents.

Hope this helps!

Step-by-step explanation:

the price of one orange is indeed 3/6 = 1/2 = $0.50.

the equation residential the price for any number of oranges contains then a variable, say x, to stand for the number of purchased oranges :

p(x) = 0.5x

meaning that the price of x oranges is 0.5×x.

Answer:

$54.01

Step-by-step explanation:

All you have to do is $300.00-$245.99 .

The length of WU is 7.615, which can be found by using the Pythagorean Theorem.

The length of WU can be found by using the Pythagorean Theorem. The Pythagorean Theorem states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides. In this case, the hypotenuse is WU and we know the length of the other two sides, which are 7 (side VU) and 3 (side UT). Substituting these values into the Pythagorean Theorem, we get \(WU^2 = 7^2 + 3^2\). Solving this equation, we get WU = √58 = 7.615. Therefore, the length of WU is 7.615.

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Answer:

D

Step-by-step explanation:

Answer:

function

Step-by-step explanation:

To be a function, each value of the x-coordinate can be used only once. In other words, all x-coordinates must be different.

Here, the x-coordinates are all different, so it is a function.

The probability that the mean daily temperature of a sample of 100 randomly selected days is greater than the mean daily temperature by at least 1.7°F is 0.002 .

Let the mean daily temperature be = x',

The mean daily temperature in Stuart is (μ) = 72.2,

The standard deviation is (σ) = 5.9,

The sample size is (n) = 100,

⇒ μₓ = μ = 72.2 ,

⇒ σₓ = σ/√n = 5.9/√100 = 0.59,

So, the required probability is written as :

⇒ P(x' - μ ≥ 1.7)

⇒ P( (x'-μ)/σₓ ≥ 1.7/0.59)

⇒ P( Z ≥ 2.8813) = 0.00198

≈ 0.002.

Therefore, the required probability is 0.002.

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The given question is incomplete, the complete question is

According to the National Weather Service, the mean daily temperature in Stuart is 72.2°F with a standard deviation of 5.9°F. Consider the mean daily temperature in Stuart for a sample of 100 randomly selected days.

Determine the probability that the mean daily temperature of a sample of 100 randomly selected days is greater than the mean daily temperature by at least 1.7°F.

Answer:

3 and 19/20

Step-by-step explanation:

3.95  =  395/100   =   79/20  =  3 19/20

Answer:

3 and 19/20

Step-by-step explanation:

3.95 = 3 + 0.95. 3 stays how it is. 0.95 = 95/100 as a fraction. Common factor of 5, divide on top and bottom. You get 19/20. Add back the 3. You get 3 and 19/20

Answer:

100.

Step-by-step explanation:

The 2 smaller triangles are similar, so:

48 / (x - 64) = 64 / 48

64(x - 64) = 48^2

x - 64 = 48^2/64

x = 48^2/64 + 64

= 100.

Answer:

B. s = 24t

Step-by-step explanation:

Since s varies directly with t, therefore, equation that will represent the relationship would take the form of s = my

m = rate of change

✔️Find the rate of change:

Rate of change using two given pairs, (0.5, 12) and (2.5, 60),

Rate of change (m) = ∆s/∆t = (60 - 12)/(2.5 - 0.5) = 48/2 = 24

✔️Substitute m = 24 into s = mt

s = 24t

Answer:

78.5

Step-by-step explanation:

Answer:

The number is 37

Step-by-step explanation:

The given parameters are;

The unit digit of a two-digit number = 4 + The tens digit

2 × The two-digit number  = 1  + The reversed number

Let x represent the unit digit and y represent the tens digit, we have;

x = 4 + y

2 × yx = xy + 1

Which gives;

2 × yy+4 = 2y2y+8

xy + 1 = 4 + yy + 1

y + 1 = 2y + 8 - 10 (we assume that the product of 2 and the unit digit is more than 10 so we subtract 10 from the product to equate the unit digits of the two numbers

10 + 1 - 8 = 2y - y

10 - 7 = y

y = 3

x = y + 4 = 3 + 4 = 7

x = 7

Therefore, the number = 37.

Answer:

37

Step-by-step explanation:

Answer:

(1.06)0 = 1  and positive powers of 1.06 are larger than 1, thus the minimum value N(t) attains, if t≥0, is 400.

From the point of view of the context, a CD account grows in value over time so with a deposit of $400 the value will never drop to $399.

Answer:

  32.4 inches

Step-by-step explanation:

Sam wants the increase to be 8% of 30 inches.

The amount of increase Sam wants in his waist size is ...

  8% × 30 in = 0.08×30 in = 2.4 in

Adding the wanted increase to his present size would make Sam's waist size be ...

  30 in + 2.4 in = 32.4 in

Sam wants his waist size to be 32.4 inches.

__

Additional comment

The larger size can also be computed from ...

  30 +8%×30 = (1 +8%)×30 = 1.08×30 = 32.4 . . . inches

Answer:

I think it is the first one as you add the 4 like from the other

Answer:

See below

Step-by-step explanation:

Because a constant never changes. It stays constant (it's in the word)! The function never changes since the slope is 0, therefore there's no vertical change.

Answer:

Step-by-step explanation:

The function value never changes and is always graphed as a horizontal line so theirs slopes become zero. This means there is no change that is vertical within and throughout the function.

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If Ariana removes the $4,800 rent from the set, the mean and median of the remaining rents will decrease because $4,800 is a very high value compared to the other rents.

Before removing the $4,800 rent, the mean can be calculated by adding up all the rents and dividing by the total number of rents (5):

Mean = (1,000 + 1,200 + 1,300 + 1,400 + 4,800) / 5 = 2,540

The median is the middle value in the set, which is 1,300.

After removing the $4,800 rent, the new mean can be calculated by adding up the remaining rents and dividing by the new total number of rents (4):

New Mean = (1,000 + 1,200 + 1,300 + 1,400) / 4 = 1,225

The new median is still 1,300 because it is the middle value in the remaining set.

Therefore, removing the $4,800 rent will decrease both the mean and median of the remaining rents.

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