WILL MARK THE BRAINLIEST!! What are the amplitude, period, phase shift, and midline of f(x) = 2 sin(x + π) − 4?

Answer: OPTION A

Step-by-step explanation:

The formula that is used to calculate the surface area of a cone is:

[tex]SA=\pi rl+\pi r^2[/tex]

Where "r" is the radius and "l" is the slant height.

You can identify in the figure that:

[tex]l=12units\\r=3units[/tex]

Then, you need to substitute these values into the formula [tex]SA=\pi rl+\pi r^2[/tex].

Therefore, the surface area of this right cone is:

[tex]SA=\pi (3units)(12units)+\pi (3units)^2[/tex]

[tex]SA=45\pi\ units^2[/tex]

Answer:

Step-by-step explanation:

a) The proportion remaining (p) after d days can be described by ...

  p = (1 -0.73)^(d/180) = 0.27^(d/180)

Then p=1/2 when ...

  0.50 = 0.27^(d/180)

  log(0.50) = (d/180)log(0.27)

  180(log(0.50)/log(0.27) = d ≈ 95.3

The half-life is about 95.3 days.

__

b) For the proportion remaining to be 60/100, we can use the same solution process. In the end, 0.50 will be replaced by 0.60, and we have ...

  d = 180(log(0.60)/log(0.27) ≈ 70.2 . . . days

60 mg will remain of a 100 mg sample after 70.2 days.

The half-life of the unknown radioactive element, which decays and reduces radioactivity by 73% in 180 days, is approximately 64.44 days. For a sample of 100 mg of this element, it would take about the same duration of one half-life (64.44 days) to decay to a mass just below 60 mg.

The subject of this question relates to radioactive decay and half-life, part of physics in nuclear chemistry. In this scenario, we have an unknown element that decays and diminishes in radioactivity by 73% over the course of 180 days.

We can find the half-life using the formula: t(half-life) = t(total time)/log2(1/% remaining). Substituting the given values into this formula, we get: t(half-life) = 180/log2(1/0.27) = 64.44 days. So, the half-life of the unknown radioactive element is approximately 64.44 days.

For the second part of the question, we first need to ascertain how many half-lives it would take for a 100mg sample to decay to 60mg. Each half-life reduces the substance's amount by half. So, we need to find out the number of half-lives where halving still results in a mass greater than 60mg. This occurs after one half-life (100mg to 50mg), so approximately one half-life (64.44 days) is needed for the sample to decay from 100mg to just below 60mg.

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It will take approximately 14.2 years for the money to triple in the savings account.

Step 1: Set up the formula and define variables

We know the initial amount (P) is $600, and we want the final amount (A) to be triple the initial amount, which is 3 * $600 = $1800. The interest rate (r) is 4.8% (converted to decimal: 0.048) and we want to find the time (t) in years.

We'll use the compound interest formula continuously compounded: A = Pe^rt.

Step 2: Solve for time (t)

We can rewrite the formula to solve for t: t = ln(A/P) / r

Plug in the known values:

t = ln($1800 / $600) / 0.048

Step 3: Solve and round

Calculate the result using a calculator and round to the nearest tenth of a year.

t ≈ 14.2 years

Answer:

723.36

Step-by-step explanation:

I calculated it to be roughly 723.36 hope this helps

ANSWER

a=53°

b=106°

c=74°

d=37°

EXPLANATION

A semicircle creates a right angle on the circumference.

d+53°=90°

d=90°-53°

d=37°

Angle subtended at the center by an arc is twice the angle subtended at the circumference by the same arc.

c=2d

c=2(37)

c=74°

Adjacent angles on a straight line add up to 180°

c+b=180°

b=180°-c

b=180°-74°

b=106°

The sum of interior angles in an isosceles triangle is 180°

a+a+c=180°

2a+74=180

2a=180-74

2a=106

a=53°

Answer:

[tex]\frac{6x-14}{x^{4} +4x}[/tex]

Step-by-step explanation:

I have to [tex]\frac{\frac{3x-7}{x^{2} } }{\frac{x^{2} }{2}+\frac{2}{x}}[/tex]

Let's start by joining the macro denominator with a common denominator. So, by applying a minimum common multiple [tex]\frac{x^{2} }{2} +\frac{2}{x}=\frac{x^{3}+ 4 }{2x}[/tex]

Now I can write the expression as

[tex]\frac{\frac{3x-7}{x^{2}}}{\frac{x^{3}+ 4 }{2x}}[/tex]

Now to convert both fractions into one, I multiply the numerator of the one above by the denominator of the one below, and the denominator of the one above with the numerator below, remaining that way.

[tex]\frac{\frac{3x-7}{x^{2}}}{\frac{x^{3}+4}{2x}}=\frac{(3x-7)(2x)}{(x^{2})(x^{3}+ 4)}[/tex]

Having the fraction in this way, I could simplify the x of the "2x" of the numerator with an x^2 (x^2=x*x) of the denominator

[tex]\frac{(3x-7)(2x)}{(x^{2})(x^{3}+4)}=\frac{2(3x-7)}{x(x^{3}+ 4)}[/tex]

finally, applying distributive property, I have to

[tex]\frac{(6x-14)}{(x^{4}+ 4x)}[/tex]

Done

Combine fractions with common denominator [tex]\(2x^2\),[/tex] then simplify numerator and denominator separately: [tex]\(\frac{12x^2 - 28x^3}{x^4 + 8x^3}\).[/tex]

let's simplify the complex fraction step by step:

1. Start by finding a common denominator for all the fractions involved. In this case, the least common denominator is [tex]\(2x^2\).[/tex]

2. Rewrite each fraction with the common denominator:

  - [tex]\(\frac{3x - 7}{x^2}\)[/tex]  becomes [tex]\(\frac{3x - 7}{x^2} \cdot \frac{2}{2}\)[/tex] to match the denominator [tex]\(2x^2\).[/tex] So, it becomes[tex]\(\frac{6 - 14x}{2x^2}\).[/tex]

  -[tex]\(\frac{x^2}{2}\)[/tex] remains the same.

  - [tex]\(\frac{2}{x}\)[/tex]  becomes [tex]\(\frac{2}{x} \cdot \frac{2x}{2x}\)[/tex] to match the denominator [tex]\(2x^2\).[/tex] So, it becomes [tex]\(\frac{4x}{2x^2}\).[/tex]

3. Now, combine all the fractions:

[tex]\[ \frac{\frac{6 - 14x}{2x^2}}{\frac{x^2}{2} + \frac{4x}{2x^2}} \][/tex]

4. Combine the terms in the numerator and denominator:

  - The numerator remains the same: [tex]\(6 - 14x\).[/tex]

  - The denominator becomes[tex]\(\frac{x^4 + 8x^3}{2x^2}\).[/tex]

5. Divide the numerator by the denominator:

[tex]\[ \frac{6 - 14x}{\frac{x^4 + 8x^3}{2x^2}} \][/tex]

6. Multiplying the numerator by the reciprocal of the denominator:

[tex]\[ (6 - 14x) \cdot \frac{2x^2}{x^4 + 8x^3} \][/tex]

7. Distribute the numerator:

 [tex]\[ \frac{12x^2 - 28x^3}{x^4 + 8x^3} \][/tex]

So, the simplified form of the complex fraction is [tex]\(\frac{12x^2 - 28x^3}{x^4 + 8x^3}\).[/tex]

Answer:

x=9

Step-by-step explanation:

9+5+5=19

Answer:

14 or about 43.98 feet

Step-by-step explanation:

Answer:

option d.

Step-by-step explanation:

We have the following set of data:

x     0   1    2   3  4

f (x)   18 14  10 6  2

Let's assume the function is linear, then, the equation of the line would ne:

(y - y0) = m(x-x0)

where m= (y1-y0) / (x1-x0)

And (x1, y1) = (1, 14)

(x0, y0) = (0, 18)

You can choose any of the points given in the set of data.

Then,

m = (14-18)/(1-0) = -4.

Then the equation of the line is:

(y - 18) = -4x

y = -4x + 18.

If the function is linear, then all the points given in the set of data will satisfy the function. Let's try:

(2, 10):

10 = -4(2) + 18.

10 = 10

SATISFIES THE EQUATION

(3, 6):

6 = -4(3) + 18.

6 = 6

SATISFIES THE EQUATION

(4, 2)

2 = -4(4) + 18.

6 = 6

SATISFIES THE EQUATION

So, the function is linear. And the correct option is option d.

Answer:

D. Line.ar; -4x + 18

Step-by-step explanation:

Answer:

4 cups

Step-by-step explanation:

Answer:

The ratio of chocolate covered caramels to solid chocolates is 1 to 2. Or 1 : 2

Step-by-step explanation:

Answer: 1/2

Step-by-step explanation: We can write a ratio using the word "to," using a colon, or using a fraction bar. I would personally write the ratio using a fraction bar since it's easier to write in lowest terms.

So we need to compare the number of chocolate covered caramels to the number of solid chocolates.

We know that we have 4 chocolate covered caramels so we write 4 in the numerator of our ratio. We know that we have 8 solid chocolates so we put an 8 in the denominator of our ratio.

Now we have the fraction 4/8.

Notice however that 4/8 is not in lowest terms so we need to divide the numerator  and denominator by the greatest common factor of 4 and 8 which is 4 to get 1/2. So the ratio of the number of chocolate covered caramels to the number of solid chocolates is 1/2.

Answer:

C) The expected value is -$2000, so the detective should not take the job.

Step-by-step explanation:

The expected value is the sum of products of income and probability:

E = -10,000·1.00 + 80,000·0.10 = -10,000 +8,000 = -2,000

The detective can be expected to lose money on the job, so should not take it.

Answer:

B. 6 inches

Step-by-step explanation:

We know that the lenght of AB is 12 inches. Given that any two point that passes through the center P equals to the diameter, we know that AP is going to be half of diameter.

So, if AB = 12, then P = AB/2 = 6 inches.

The triangles are not the same size so a dilation made the original one smaller and a translation moved it to map ABC to A'B'C'.

Answer:

Domain is set of all real numbers

Range is set of all real numbers

Step-by-step explanation:

Domain is the set of x values for which the function is defined

to find domain we look at the graph and check if there is any restriction for x

WE have line graph for all x values

So there is no restriction for x. Hence, Domain is set of all real numbers

Range is the set of y values for which the function is defined

to find range we check the continuity on graph

The graph is contininious and there is no break . The graph is continious for all y values

So range is set of all real numbers

Answer:

its d.

i just took it

Step-by-step explanation:

Answer:

y = 5 cos ((2π/3)x - 2) + 2

Step-by-step explanation:

Cosine function takes a general form of  y = A cos (Bx + C) + D

Where

A is the amplitude

2π/B is the period

C is the phase shift ( if -C, then phase shift right, if +C phase shift left)

D is the vertical displacement (+D is above and -D is below)

Given the conditions of the function to build and the general form, we can write:

** Note: period needs to be 3, so 2π/B = 3, hence B = 2π/3

Now we can write:

y = 5 cos ((2π/3)x - 2) + 2

first answer choice is right.

Final answer:

The equation for a cosine function with an amplitude of 5, a period of 3, a phase shift of 2, and a vertical displacement of 2 is y = 5 cos(2π/3 (x - 2)) + 2.

Explanation:

To write an equation for a cosine function with the given parameters, we need to understand several key features of the function: amplitude, period, phase shift, and vertical displacement.

The general form of a cosine function is y = A cos(B(x - C)) + D, where A is the amplitude, T = 2π/B (where T is the period), C is the phase shift, and D is the vertical displacement.

Given an amplitude (A) of 5, a period (T) of 3, a phase shift (C) of 2, and a vertical displacement (D) of 2, we can substitute these values into the general form:

Putting it all together, the equation of the cosine function is: y = 5 cos(2π/3 (x - 2)) + 2

Answer:

$817.08

Step-by-step explanation:

Answer:

6.05 units

Step-by-step explanation:

We are given that radius,r=3 units

Volume of cone=57 cubic units

We have to find the height of cone.

We know that

Volume of cube=[tex]\frac{1}{3}\pi r^2 h[/tex]

Where [tex]\pi=3.14[/tex]

Using the formula

[tex]57=\frac{1}{3}\times 3.14\times (3)^2\times h[/tex]

[tex]h=\frac{3\times 57}{3.14(3)^2}[/tex]

h=6.05 units

Hence, the height of cone=6.05 units

Answer:

FALSE

Step-by-step explanation:

What we have here is experimental probability:   12 heads out of 20 tosses.

The fraction 12/20 reduces to  6/10, or 0.60, which corresponds to 60%.

The answer to this question is FALSE, because this is not theoretical probability.

Answer:

false

Step-by-step explanation:

Here is your answer

d) 7y(-4x + 5)

EXPLANATION:

Given,

[tex]-28xy + 35y[/tex]

It can be written as-

[tex]7×(-4)xy + 7×5y[/tex]

The two terms [tex]7×4xy[/tex] and [tex]7×5y[/tex] have 7y common in them.

So, it can be further written as-

[tex]7y(-4x + 5)[/tex]

HOPE IT IS USEFUL

Answer:

Option D

Step-by-step explanation:

The equation to predict the amount saved is

[tex]y = 6x ^ 2 + 75x + 200.[/tex]

Assuming that the variable x represents the saving months, then substitute [tex]x = 25[/tex] in the quadratic equation and solve for y.

[tex]y = 6 (25) ^ 2 +75 (25) +200\\\\y = \$\ 5,825[/tex]

The answer is the option D  $5,825

Use the chain rule:

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm dt}\cdot\dfrac{\mathrm dt}{\mathrm dx}[/tex]

So we have

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm dt}}{\frac{\mathrm dx}{\mathrm dt}}[/tex]

[tex]x=t^2+4\implies\dfrac{\mathrm dx}{\mathrm dt}=2t[/tex]

[tex]y=t^3+3t\implies\dfrac{\mathrm dy}{\mathrm dt}=3t^2+3[/tex]

[tex]\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{3t^2+3}{2t}[/tex]

Now write [tex]f(t)=\dfrac{\mathrm dy}{\mathrm dx}[/tex]. Then by the chain rule,

[tex]\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac{\mathrm dy}{\mathrm dx}\right]=\dfrac{\mathrm df}{\mathrm dx}=\dfrac{\mathrm df}{\mathrm dt}\cdot\dfrac{\mathrm dt}{\mathrm dx}=\dfrac{\frac{\mathrm df}{\mathrm dt}}{\frac{\mathrm dx}{\mathrm dt}}[/tex]

so that

[tex]\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\frac{\mathrm d}{\mathrm dt}\left[\frac{3t^2+3}{2t}\right]}{2t}=\dfrac{3(t^2-1)}{4t^3}[/tex]

The curve is concave upward when the second derivative is positive:

[tex]\dfrac{3(t^2-1)}{4t^3}>0\implies t^2>1\implies\sqrt{t^2}>\sqrt1\implies|t|>1[/tex]

or equivalently, when [tex]t<-1[/tex] or [tex]t>1[/tex].

The dy/dx is equal to 1 + 3/2t, and the d2y/dx2 is 3/2t. The curve is concave upward for t values in the (0, Infinity) interval.

To answer your question, we first need to take the derivatives of x and y with respect to t. The derivatives of x = t^2 + 4 and y = t^2 + 3t by t yield dx/dt = 2t and dy/dt = 2t + 3. Now, dy/dx = (dy/dt) / (dx/dt) = (2t + 3) / 2t = 1 + 3/2t.

Next the second derivative d2y/dx2 (concavity), is obtained as the derivative of dy/dx = 1 + 3/2t with respect to t, which is 3/2t. Now, the curve will be concave upward whenever d2y/dx2 > 0. Solving 3/2t > 0 gives the interval for t as (0, Infinity), which indicates the values of t for which the curve is concave upward.

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Answer:

So 2 and 4

Step-by-step explanation:

The difference between a pyramid and prism is that a prism has two bases. A pyramid only has one base. The sides of the pyramid will always be triangular in shape.

The prism has two parallel bases and the pyramid has only one base. Then the correct option is B.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

A prism is a closed solid that has two parallel bases connected by a rectangle surface.

The difference between the prism and pyramid will be

The prism has two parallel bases and the pyramid has only one base.

More about the geometry link is given below.

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Answer:

Option A

Domain = Range = (-∞,∞)

Step-by-step explanation:

We can easily solve this question by using a graphing calculator or any plotting tool.

The function is

f(x) = -2x + | 3 sin(x) |

Which can be seen in the picture below

We can notice that f(x) is a line with periodical ups and downs thanks to the sinusoidal term, but there are no restrictions over the domaoin or range of the function.

It can take any real value as an input, and can produce any real value as an output

Answer:

y = tan(1/2 x + π/2) ⇒ answer c

Step-by-step explanation:

* Lets revise some fact of y = tanx

- The domain of tanx is all x(≠ π/2) + nπ, where n is the number of cycle

- The range is all real numbers

- The period of tanx is π ÷ coefficient of x

* Lets revise some transformation

- A horizontal stretching is the stretching of the graph away from

 the y-axis

• if 0 < k < 1 (a fraction), the graph is f (x) horizontally stretched by

 dividing each of its x-coordinates by k (x × 1/k)

- A horizontal compression is the squeezing of the graph toward

 the y-axis.

• if k > 1, the graph f (x) horizontally compressed by dividing each

 of its x-coordinates by k. (x × 1/k)

* Look to the graph of y = tanx ⇒ red graph

- the graph of tanx intersect x-axis at the origin

- The period of tanx is π

* Look to the blue graph (the problem graph)

∵ The graph intersect x-axis at points (-π , 0)

- That means the graph of tanx moved to the left by π units

∴ y = tan(x + π)

- The period of the graph is 2π

∵ The period = π/coefficient of x

∴ 2π = π/coefficient of x ⇒ using cross multiplication

∴ Coefficient of x = π/2π = 1/2

- That means the graph stretched horizontally

∴ y = tan1/2(x + π)

* y = tan(1/2 x + π/2)

Answer:

The answer is: yes; k = -3 and y = -3x ⇒ the 3rd answer

Step-by-step explanation:

* Lets revise how to know the relation is direct proportion

- If all the ratios of x/y are proportion (equal ratios), then they

 are varies directly

* Now lets check the relation between x and y

∵ x = 1 and y = -3

∴ y/x = -3/1 = -3

∵ x = 3 and y = -9

∴ y/x = -9/3 = -3

∵ x = 5 and y = -15

∴ y/x = -15/5 = -3

∵ All ratios are equal -3 (they are proportion)

∴ y varies directly with x

* y ∝ x

∴ y = k x

∴ The constant of variation k is -3

∴ y = -3x

* The answer is: yes; k = -3 and y = -3x

Answer:

$80

Step-by-step explanation:

If $100 is 25% more than Dwayne's original amount (a), you have ...

a + 0.25a = 100

1.25a = 100

a = 100/1.25 = 80

Dwayne originally had $80.

Answer:

The range is defined as the difference between the term with the highest value and the term with the lowest value. This statistic is used to measure the variability of a series of data because it provides information on how far apart the values of a tail of the distribution are from the values at the other end of the tail.

Imagine that you manufacture a type of spare part for cars that must have a measurement of 10 cm with a margin of error of 1 cm.

This is:

10 ± 1 cm

Then you expect your manufacturing process to produce pieces with identical dimensions, that is, with little variability.

If you randomly select a sample of n pieces and measure them, the variability is expected to be low, so that your process is of quality, then expect a low range preferably less than 1 cm.

{10, 10.1, 10.5, 9.8, 9,6, 10.2} Range= 10.5 - 9.6 = 0.9 cm low variability

But if you find that the range is up to 8 cm, this would mean that not all pieces measure around 10 cm, it means that the variability of the measurements is high.

{14, 12, 11, 8, 7, 11, 12, 15} Range = 15 - 7 = 8 cm   high variability

The range can help describe a data set by evaluating the whole of a data set, showing spread within a data set, and comparing the spread between similar data sets. Simply put, it is the amount of variation from the lowest number to the highest and indicates the size of the statistical dispersion.

100% on Edge, used Google to come up with the answer.

Answer:

The volume is equal to [tex]320\pi\ cm^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the cone is equal to

[tex]V=\frac{1}{3}\pi r^{2} h[/tex]

we have

[tex]r=8\ cm[/tex]

[tex]h=15\ cm[/tex]

substitute the values

[tex]V=\frac{1}{3}\pi (8)^{2}(15)[/tex]

[tex]V=320\pi\ cm^{3}[/tex]

Final answer:

volume of 320π cm³.

Explanation:

To calculate the volume of the oblique cone with the given dimensions, use the formula for the volume of a cone,

The volume of the oblique cone can be calculated using the formula V = 1/3 * π * r^2 * h.

Answer:

27 in^2

Step-by-step explanation:

   To solve this, we must first find the height. We can split the trapezoid into a triangle and rectangle! Since 11-7=4, one of the legs of the triangle is 4, and the height of the trapezoid is 3 because 3,4,5 is a pythagorean triple. Since the area of a trapezoid is the average of the bases times the height, we multiply 9, the average, by 3 and we get 27 in^2.