(6Q) Find the domain and range.

Answer:

4 cups

Step-by-step explanation:

Answer:

The conic is parabola, its equation is (y + 5)² = -(x + 1)

Step-by-step explanation:

- The general equation for any conic section is  

Ax² + Bxy + Cy² + Dx + Ey + F = 0  

where A , B , C , D , E and F are constants. A, B, and C are not all zero

- When we change the values of some of the constants, the shape  

of the corresponding conic will also change.  

- It is important to know the differences in the equations to  

identify the type of conic that is represented by a given equation.  

# If B² − 4AC is less than zero, if a conic exists, it will be either a  

circle or an ellipse  

# If B² − 4AC equals zero, if a conic exists, it will be a parabola  

# If B² − 4AC is greater than zero, if a conic exists, it will be a  

hyperbola  

* How to identify the type of the conic

- Rewrite the equation in the general form,  

Ax² + Bxy + Cy² + Dx + Ey + F = 0  

- Identify the values of A and C from the general form.  

- If A and C are nonzero, have the same sign, and are not equal

to each other, then the graph is an ellipse.

- If A and C are equal and nonzero and have the same sign, then

the graph is a circle  

- If A and C are nonzero and have opposite signs, and are not equal

then the graph is a hyperbola.

- If either A or C is zero, then the graph is a parabola

* Now lets solve the problem

- The equation is y² + x + 10y + 26 = 0

 A = 0 , B = 0 , C = 1 , D = 1 , E = 10 and F = 26

∵ A = 0

∴ The equation is a parabola its standard form is:

  (y - k)² = 4 p (x - h), where (h , k) is the vertex point of the parabola,

   with a horizontal axis y = k

- Lets change the standard form to the general form

∵ (y - k)² = 4 p (x - h) ⇒ open the brackets

∴ y² - 2ky + k² = 4px - 4ph

- Put all of them in one side

∴ y² - 4px - 2ky + k² + 4ph = 0

- Compare it with the equation

  y² - 4px - 2ky + k² + 4ph = 0 ⇒ y² + x + 10y + 26 = 0

∵ -4px = 1x ⇒ cancel x

∴ -4p = 1 ⇒ divide both sides by -4

∴ p = -1/4

∵ -2ky = 10y ⇒ cancel y

∴ -2k = 10 ⇒ divide both sides by -2

∴ k = -5

∵ k² + 4ph = 26 ⇒ (-5)² + 4(-1/4)h = 26 ⇒ simplify

∴ 25 - h = 26 ⇒ subtract 25 from both sides

∴ h = -1

- Now we can write the standard form of the equation

∴ (y - -5)² = 4(-1/4)(x - -1)

∴ (y + 5)² = -(x + 1)

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:

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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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:

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.

Answer:

14 or about 43.98 feet

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:

The minimum number of paintings Monica needs to sell is 4 to reach her goal.

Step-by-step explanation:

Let

p-----> the number of paintings that Monica needs to sell

we know that

[tex]140+15p\geq 200[/tex]

Solve for p

Subtract 140 both sides

[tex]15p\geq 200-140[/tex]

[tex]15p\geq 60[/tex]

Divide by 15 both sides

[tex]p\geq 60/15[/tex]

[tex]p\geq 4\ painting[/tex]

The minimum number of paintings Monica needs to sell is 4 to reach her goal.

Answer:

1 : 4

Step-by-step explanation:

Given 2 similar figures, then

linear ratio = a : b and

area ratio = a² : b²

here the area ratio = 24 : 384 = 1 : 16, hence

linear ratio = [tex]\sqrt{1}[/tex] : [tex]\sqrt{16}[/tex] = 1 : 4

Answer:

a)  60°

b)  60°

Step-by-step explanation:

A regular hexagon can be broken down into 6 equilateral triangles.

*** Note: Attached picture shown.

a)

The angle between two consecutive radii would be taken as EO and OD.

Since all of these 6 angles (of 6 triangles) create a circle, the sum is 360. So each angle (between two radii) would be 360/6 = 60°

b)

To find angle between side and radius of a polygon, let's take the radii as EO and side as ED.

Since we already found the angle between 2 radii to be 60, we have two angle left of a triangle (same size, let's call it x). We know sum of 3 angles in a triangle is 180, thus we can write:

60 + x + x = 180

60 + 2x = 180

2x = 180 - 60

2x = 120

x = 120/2

x = 60°

Answer with Step-by-step explanation:

We are given a data set:

0.24  0.42  0.37  0.38  0.24

We arrange them in ascending order:

0.24 0.24 0.37 0.38 0.42

Mean=sum of all data elements/number of elements

Mean =(0.24+0.24+0.37+0.38+0.42)/5

Mean=0.33

Mode is the element with the highest frequency i.e. element which comes most.

Hence, Mode=0.24

Median is the middle element of the data set.

Median=0.37

Hence, correct option is:

c.

mean: 0.33, median: 0.37, mode: 0.24

Hence, best answer from the choices provided is:

C

Answer:

c

Step-by-step explanation:

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.

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:

$79.94=4x+$5.98 or you could write it the other way 4x+$5.98=$79.94 either way you get same answer

Step-by-step explanation:

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.

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:

If this helps, the equation to solve for the volume of a prism is V=Bh.

Step-by-step explanation:

B is the base and h is the height. You have to multiply them to find the volume. Hope this helps.

Volume of the prism = area of the triangle x the thickens the triangles make;

V= {[(9/4)x (10/3)]/2} x (22/3)= (90/12) x(1/2) x(22/3)= 90x22/12x2x3=

30x11/12=330/12= 27 1/2

Answer:The answer is B.

Start with 11.5. Multiply 1.5 by 2. Add this product to 11.5. Then add 3.25 and 6 to the answer.

hope this hepls!!!

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:

$817.08

Step-by-step explanation:

Answer:

x=9

Step-by-step explanation:

9+5+5=19

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:

10 + 2.50x

Step-by-step explanation:

What helps is solving word problems without any numbers.

If we wanted the cost of the total we would have:

Admission Cost + Ride Ticket Cost = Total Cost

We use "x" to represent how many ride tickets there is.

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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Check the picture below.

make sure your calculator is in Degree mode.

A figure which is formed by two rays or lines that shares a common endpoint is called an angle.

The measurement of the angle is 22.02 degrees.

A bike ramp is 8 feet long and has an end height of 3 feet.

A figure which is formed by two rays or lines that shares a common endpoint is called an angle.

The measure of the angle is determined by the following formula;

[tex]\rm Sin\theta = \dfrac{opposite \ side}{Hypotenuse}[/tex]

Where the opposite side is 3 and the hypotenuse is 8.

Substitute all the values in the formula;

[tex]\rm Sin\theta = \dfrac{opposite \ side}{Hypotenuse}\\\\\rm Sin\theta = \dfrac{3}{8}\\\\\theta = sin{-1} \left ( \dfrac{3}{8} \right )\\\\\theta = 22.02 \ degrees[/tex]

Hence, the measurement of the angle is 22.02 degrees.

To know more about Angle click the link given below.

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The correct answer is D) a+2b.

Hope it helps!

Answer:

a + 2b

Step-by-step explanation:

To find the equivalent of the given expression, we must open up the parenthesis by multiplying each element in the parenthesis by 2, we would then collect like terms and simplify the algebraic expression.

2(a + 2b) - a - 2b

= 2a + 4b - a - 2b

= 2a - a + 4b  - 2b

= a + 2b

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

Answer:

723.36

Step-by-step explanation:

I calculated it to be roughly 723.36 hope this helps

Answer:

Step-by-step explanation:

Let's say we wanted to find the LCM of 6 and 8.

First, write the prime factorization of both:

6 = 2×3

8 = 2³

Let's include all the exponents:

6 = 2¹×3¹

8 = 2³×3⁰

The LCM needs to have the prime factors with the highest exponents.  

So we need prime factors of 2 and 3.  The exponent of the 2 will be three, and the exponent of the 3 will be one.

LCM = 2³×3¹

LCM = 24