An appliance store decreases the price of a 19-in television set 25% to a sale price of $482.63. What is the original price?

The age of Nachelle would be 5 years and the age of Julian would be 7 years.

What is a quadratic equation?

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.

Let's suppose the age of Nachelle is 'x' years then Julian's age would be 'x+2'.

              x² + [2(x + 2)]² = 139

             x² + 4x² + 8x + 16 = 139

             5x² + 8x - 123 = 0

Simplifying this, we get

       x = 4.22 and x = -5.82

Age cannot be a negative number so

         x ≈ 5.

x + 2 = 7 years

Hence the age of Nachelle would be 5 years and the age of Julian would be 7 years.

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Answer:

7.654 ft

Step-by-step explanation:

The volume of a hemisphere is \(V=\frac{2}{3}\pi r^3\). Rearranging this equation gives \(r=\sqrt[3]{\frac{3V}{2\pi} }\). Plug in V=939 to find the value of r.

Answer:

its 5

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Protect economic freedom, so that a strong central government couldn't stop them from doing what they wanted to earn money.

***I hope this answer's correct. Plz lmk!!!

Answer:

C I think because it makes most sence sorry if wrong answer

Step-by-step explanation:

( I think this would be a diferent subject just saying)

hope this helps

Answer:

https://www.calculators.tech/standard-form-calculator

go on MATH.WAY. it'll give you the answer and explanation

Step-by-step explanation:

So

Actual length of square

Answer:

4212 ft²

Step-by-step explanation:

Given scale:

1 inch : 9 feet

⇒ (1 inch)² : (9 feet)²

⇒ 1 in² = 81 ft²

Therefore:

⇒ 52 in² = (81 × 52) ft²

⇒ 52 in² = 4212 ft²

The direction vector of the line l is given by (-3, -6, 9). A plane perpendicular to the line will have a normal vector in the direction of this direction vector. Therefore, a normal vector to the plane can be found by taking the direction vector of the line:

n = (-3, -6, 9)

To find the equation of the plane, we need to find the value of d in the equation of the plane, which is given by:

Ax + By + Cz + d = 0

where (A, B, C) is the normal vector to the plane.

Substituting the values of the normal vector and the point (2, 2, -1) into the equation of the plane, we get:

-3(x-2) - 6(y-2) + 9(z+1) + d = 0

Simplifying the equation, we get:

-3x - 6y + 9z + 33 + d = 0

Therefore, the equation of the plane is:

-3x - 6y + 9z + 33 = 0

or, dividing by -3 to simplify:

x + 2y - 3z - 11 = 0

So, the equation of the plane that is perpendicular to the line l(t) = (-3, -6, 9)t + (0, 7, 1) and passes through (2, 2, -1) is x + 2y - 3z - 11 = 0.

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Answer: There will be 30 tiles in each row.

Step-by-step explanation:

To find the number of tiles in each row, we need to determine the room's dimensions and the size of each tile. Given that the area of the square room is 225 square feet, we know that the room is a perfect square. Let's denote the length of one side of the square as "x" feet.

We can calculate the length of one side of the square by taking the square root of the area:

x = √225 = 15 feet

Since each tile is 6 inches by 6 inches, we need to convert the measurements to feet: 6 inches = 6/12 = 0.5 feet

To determine the number of tiles in each row, we divide the length of the side of the room by the length of each tile:

Number of tiles in each row = (Side length of the room) / (Length of each tile)

Number of tiles in each row = 15 feet / 0.5 feet = 30 tiles

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Non-random sampling bias could occur if each individual in the source population does not have an equal chance of being selected for the sample population.

What is a sample population?

The process of selecting the sample from the population is known as the sample population. Sample refers to the group of people in a population. It is a specific group that you will collect the data from. The sample size is always less than the total size of the population.  It is very easier and it has an effective cost to process the smaller subset of the population rather than the entire group. The sample mean and sample population can be obtained from the sample. It is a statistical method used to calculate the sample mean from the sample population. Let us have a simple example,

people living in America are the sample of the population. It is used in testing when the population size is too large for all the members or observations to be included in the test.

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Answer:

\(y = - \frac{ {x}^{2} }{16} \)

Step-by-step explanation:

First, notice the diretcrtirx is a negative horinzontal lie so this means we have a parabola facing downwards

Equation of a Parabola with center (h,k) >

\((x - h) {}^{2} = - 4p(y - k)\)

Where p is the distance of the vertex to focus/ or distance to vertex to directrix

This emans that the vertex is halfway of (-4,0) and x=4.

Since this is a upwards parabola, the y value that lies on focal axis doesn't change so know this means that

The vertex is halfway between (-4,0) and (4,0).

So the vertex is (0,0).

Plugging that in we get,

\( {x}^{2} = - 4py\)

The distance to the vertex or either the focus or directrix is 4 so p=4

\( {x}^{2} = - 4(4)y\)

\( {x}^{2} = - 16y\)

\(y = - \frac{ {x}^{2} }{16} \)

Answer:

Part A)

Approximately 318.1318 meters.

Part B)

Approximately 137.7551 meters.

Step-by-step explanation:

The path of a projectile is given by the equation:

\(\displaystyle y = \sqrt{3} x -\frac{49x^2}{9000}\)

Part A)

The range of the projectile will be given by the difference between its starting point and landing point. In other words, its two zeros.

Let y = 0 and solve for x:

\(\displaystyle 0 = \sqrt{3}x - \frac{49x^2}{9000}\)

Factor:

\(\displaystyle 0 = x\left(\sqrt{3} - \frac{49x}{9000}\right)\)

Zero Product Property:

\(\displaystyle x = 0 \text{ or } \sqrt{3} - \frac{49x}{9000} = 0\)

Solve for each case:

\(\displaystyle x = 0 \text{ or } x = \frac{9000\sqrt{3}}{49}\approx 318.1318\)

Hence, the range of the projectile is approximately (318.1318 - 0) or 318.1318 meters.

Part B)

Since the equation is a quadratic, the maximum height is given by its vertex. Recall that the vertex of a quadratic is given by:

\(\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)\)

In this case, a = -49/9000 and b = √3.

Find the x-coordinate of the vertex:

\(\displaystyle x = - \frac{(\sqrt{3})}{2\left(\dfrac{-49}{9000}\right)} = \frac{4500\sqrt{3}}{49}\)

Then the maximum height will be:

\(\displaystyle \displaystyle \begin{aligned} y\left(\frac{4500\sqrt{3}}{49}\right) &=\sqrt{3} \left(\frac{4500\sqrt{3}}{49}\right) -\frac{49\left(\dfrac{4500\sqrt{3}}{49}\right)^2}{9000} \\ \\ &= \frac{13500}{49} -\frac{6750}{49}\\ \\ &=\frac{6750}{49}\\ \\ &\approx 137.7551\text{ meters}\end{aligned}\)

The maximum height reached by the projectile will be 137.7551 meters.

The measures of position that divide a set of data into four equal parts are called quartiles.

Quartiles are statistical measures that divide a dataset into four equal parts, each containing approximately 25% of the data. These quartiles are denoted as Q1, Q2, and Q3.

Q1, also known as the first quartile or the 25th percentile, represents the value below which 25% of the data falls. It splits the lowest 25% of the dataset from the rest.

Q2, also known as the second quartile or the 50th percentile, is the median of the dataset. It represents the value below which 50% of the data falls, dividing the dataset into two equal parts.

Q3, also known as the third quartile or the 75th percentile, represents the value below which 75% of the data falls. It separates the highest 25% of the dataset from the rest.

These quartiles are useful in analyzing the distribution and dispersion of data, providing insights into the spread and central tendency.

They are commonly used in box plots, where the box represents the interquartile range (IQR), which is the range between Q1 and Q3, while the line inside the box represents the median (Q2).

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The probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1.

A. The sampling distribution of X, the sample mean for a sample of 15,000 individuals from this population, can be approximated by a normal distribution with a mean of 100 and a standard deviation of 4/15,000 = 0.0026667.

B. The probability that a simple random sample of 15,000 individuals from this population will provide a sample mean that is within one hour of the population mean can be found by finding the area of the normal curve that is between 99 and 101: 0.9772.

C. This result would indicate that there is a 97.72% chance that the mean annual number of hours of vacation time earned for a sample of 15,000 blue-collar and service employees who work for small private establishments and have at least 10 years of service is within one hour of the population mean.

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The race horse's speed is approximately 256 furlongs per fortnight.

To determine the race horse's speed in furlongs per fortnight, we need to convert both the distance and time units to their respective values.

1 furlong is equal to 180 yards, so the horse's speed in yards per second (7 yards/second) can be converted to furlongs per second:

Speed in furlongs per second = (7 yards/second) / (180 yards/furlong) = 7/180 furlongs/second

Next, we need to convert the time from seconds to fortnights. Since a fortnight is a time period of two weeks, and there are 7 days in a week, a fortnight consists of 14 days:

Time in seconds per fortnight = (14 days/fortnight) * (24 hours/day) * (60 minutes/hour) * (60 seconds/minute) = 1,209,600 seconds/fortnight

Finally, we can calculate the horse's speed in furlongs per fortnight by multiplying the speed in furlongs per second by the time in seconds per fortnight:

Speed in furlongs per fortnight = (7/180 furlongs/second) * (1,209,600 seconds/fortnight) = 46,080/180 furlongs/fortnight ≈ 256 furlongs/fortnight

The race horse's speed is approximately 256 furlongs per fortnight.

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The derivative of \(f(x) = (3 + \tan x)\cdot (4 + 3\cdot \cos x)\) is \(f'(x) = \frac{4+3\cdot \cos x-9\cdot \sin x \cdot \cos^{2}x+3\cdot \sin^{2}x\cdot \cos x}{\cos^{2}x}\).

In this question we shall use the following derivative rules:

Derivative of a sum of functions

\(\frac{d}{dt}(f(t) + g(t)) = \frac{df(t)}{dt} + \frac{dg(t)}{dt}\) (1)

Derivative of a product of functions

\(\frac{d}{dt}(f(t)\cdot g(t)) = \frac{df(t)}{dt}\cdot g(t) + f(t)\cdot \frac{dg(t)}{dt}\) (2)

Derivative of a constant

\(\frac{d}{dt}(k) = 0\), \(\forall k \in \mathbb{R}\) (3)

Derivative of a function multiplied by a constant

\(\frac{d}{dt}(c\cdot f(t)) = c\cdot \frac{df(t)}{dt}\), \(\forall\, c\in \mathbb{R}\) (4)

Derivative of the cosine function

\(\frac{d}{dt} \cos t = -\sin t\) (5)

Derivative of the tangent function

\(\frac{d}{dt}\tan t = \sec^{2} t\) (6)

Chain rule

\(\frac{d}{dt}f[u(t)] = \frac{df(u)}{du}\cdot \frac{du(t)}{dt}\) (7)

Let be \(f(x) = (3 + \tan x)\cdot (4 + 3\cdot \cos x)\), then the derivative of \(f(x)\) is:

\(f'(x) = \sec^{2}x\cdot (4 + 3\cdot \cos x) + (3+\tan x)\cdot (-3\cdot \sin x)\)

\(f'(x) = 4\cdot \sec^{2}x+3\cdot \sec x -9\cdot \sin x -3\cdot \sin x\cdot \tan x\)

\(f'(x) = \frac{4+3\cdot \cos x}{\cos^{2}x} -\frac{9\cdot \sin x \cdot \cos x+3\cdot \sin^{2}x}{\cos x}\)

\(f'(x) = \frac{4+3\cdot \cos x-9\cdot \sin x \cdot \cos^{2}x+3\cdot \sin^{2}x\cdot \cos x}{\cos^{2}x}\)

The derivative of \(f(x) = (3 + \tan x)\cdot (4 + 3\cdot \cos x)\) is \(f'(x) = \frac{4+3\cdot \cos x-9\cdot \sin x \cdot \cos^{2}x+3\cdot \sin^{2}x\cdot \cos x}{\cos^{2}x}\).

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Step-by-step explanation:

length is x

p=(33+×)2

(33+×)2>776

66+2×>776

×>710

×>355

the length of the rectangle is greater/equals 355

The carrying capacity of the population is 1250 individuals.

The logistic equation that describes the growth of a population is

given by:

\(dP/dt = rP(1 - P/K)\)

where P is the population, t is the time, r is the growth rate, and K is the carrying capacity.

The logistic equation is a differential equation that describes the change in population over time.

Comparing the given equation:

\(dP/dt = 0.2P - 0.0008P^2\)

to the logistic equation, we see that:

r = 0.2

1/K = 0.0008

To find the carrying capacity, we need to solve for K.

We can rearrange the equation 1/K = 0.0008 to get:

K = 1/0.0008

K = 1250

Therefore, the carrying capacity of the population is 1250 individuals.

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The angle of depression from the top of the cliff to the edge of the water

is 54.46°.

Trigonometric functions, often known as circular functions, are, in a nutshell, the functions of the angle of a triangle. This indicates that the relationship between a triangle's angles and sides is provided by these trig functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant, and cosecant.

Given the height of the cliff = 70 feet,

the lake water reaches 50 ft away from the cliff.

distance from the base of the cliff to lake water = 50 feet

the angle of depression is found by tanФ

where Ф = angle of depression

tanФ = perpendicular/base

perpendicular = height = 70 feet

base= 50 feet

tanФ = 70/50

Ф = tan⁻¹(1.4)

Ф = 54.46°

Hence angle of depression is 54.46°.

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the answer is b, 7/25

Answer:

$18.00

Step-by-step explanation:

Answer: 18$

Step-by-step explanation:

17.59 is the current amount if you round to the nearest dollar the .5 will make the 7 go up in value meaning it will turn into a 8

In the iteratiοn nοtatiοn,The answers are,

1. first dοse= 150 mg, secοnd dοse= 210 mg,  third dοse= 186 mg, fοurth dοse= 178.4 mg.

2. M(n) = 0.4M(n-1) + 150

3. M(n) = \(0.4^{(n-1)\) * 150 + 150

4. fοrmula frοm questiοn 3.

5. 150.8 mg οf medicatiοn

6.  an expοnential decay curve 7. 517.15 minutes

Iteratiοn nοtatiοn is a mathematical nοtatiοn used tο represent the repetitiοn οf a mathematical οperatiοn οr functiοn. It is alsο knοwn as sigma nοtatiοn οr summatiοn nοtatiοn, and is typically used tο represent the sum οf a series οf terms.

1. After the first dose, Aldi has 150 mg of medication in his bloodstream. After the second dose, he has \(0.4(150) + 150 = 210\) mg of medication in his bloοdstream. After the third dοse, he has \(0.4(210) + 150 = 186\) mg of medication in his bloοdstream. After the fourth dοse, he has

=>  \(0.4(186) + 150 = 178.4\) mg of medication in his blοodstream.

2. The recursive definitiοn for the amount of medication in Aldi's bloodstream after each dose is:

\(M(n) = 0.4M(n-1) + 150\),

where M(n) is the amοunt of medication in Aldi's bloοdstream after the nth dose.

This definition is geometric since each subsequent dοse contains 40% of the previous dose.

3. To cοnvert the recursive definition into iteration notation, we can use the initial cοndition M(1) = 150 and write:

=>\(M(n) = 0.4^(n-1) * 150 + 150\)

The first three iterates are:

\(M(1) = 150M(2) = 0.4(150) + 150 = 210M(3) = 0.4(210) + 150 = 186\)

4. Tο determine the iterates, we used the iterative formula from question 3, plugging in the values of n for each iterate.

5. To find the amount of medicatiοn in Aldi's bloodstream right before Haidar gives him his last dose of medicatiοn, we need to find M(10) using the iterative formula:

\(M(10) = 0.4^9 * 150 + 150 = 150.796\)

So, Aldi has apprοximately 150.8 mg of medication in his bloodstream before the last dose.

6.\(lim(n- > \infty) M(n) = lim(n- > \infty) 0.4^{n-1} * 150 + 150 = 150\)

Sο, the amοunt οf medicatiοn in Aldi's system seems tο be apprοaching 150 mg.

We can use Desmοs tο plοt the first 9 iterates:

The shape οf the pοints appears tο be an expοnential decay curve.

7. The half-life οf amοxicillin is apprοximately 62 minutes, which means that after 62 minutes, half οf the amοunt οf medicatiοn in Aldi's blοοdstream will decay. We can use this infοrmatiοn tο determine when the amοunt οf medicatiοn in Aldi's blοοdstream is effectively 0.

After the last dοse, Aldi has 150.796 mg οf medicatiοn in his blοοdstream. After 62 minutes, half οf this amοunt will decay, leaving him with apprοximately 75.398 mg. After anοther 62 minutes, half οf this amοunt will decay, leaving him with apprοximately 37.699 mg. This prοcess will cοntinue until the amοunt οf medicatiοn in Aldi's blοοdstream is effectively 0.

=>\(0.4^{(t/62)} * 150 = 1\)

where t is the time in minutes. Sοlving for t, we get:

t ≈ 517.15 minutes

So, it will take apprοximately 517 minutes

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Answer:

67.5 miles

Step-by-step explanation:

22.5 miles = 20 minutes

67.5 miles = 60 minutes

The transformation between the points is (x, y) = (x, -y + 10)

From the question, we have the following parameters that can be used in our computation:

G(9, 12), H(−2, −15), J(3, 8) and

G'(9, -2), H'(-2, 25), J'(3, 2)

We can see that the x coordinates of the image and the preimage are equal

However, the relationship between the y-coordinates is

y' = -y + 10

This means that

(x, y) = (x, -y + 10)

The above rule is a translation transformation

Translation transformation is a transformation that moves each point in a figure or object by a fixed distance in a specified direction.

Hence, the transformation is (x, y) = (x, -y + 10)

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Complete question

26. G(9, 12), H(−2, −15), J(3, 8) and G'(9, -2), H'(-2, 25), J'(3, 2)

Write out the transformation rule from GHJ to G'H'J'

Answer:

An equation would be 24 - 14 = n. Another one you could write would be 14 + n = 24. The answer is 10 for the amount of old trees.

Answer:

5 days

Step-by-step explanation:

12/4 = 3 So this means that she sends 3 postcards a day.  

15/3 = 5 So she has to be on vacation 5 days in order to send 15 postcards.

Answer:

for sending 12 postcards she had to be on vacation for 4 days

for sending 1 postcard she would to be on vacation for 4/12=1/3 days

for sending 15 postcards she would to stay

1/3*15

5 days

Answer:

BC = 7

Step-by-step explanation:

AB + BC = AC

Substitute values for the line segments:

6 + BC = 13

Isolate line segment BC by subtracting both sides by 6:

6 - 6 + BC = 13 - 6

0 + BC = 13 - 6

BC = 7

Check your work:

6 + 7 = 13

13 = 13

Correct!