The domain of a relation is?
A)the output (y) values of the relation
B)the input (x) values of the relation
C)a set of points that pair input values with output values
D) x and y values written in the form (x, y)
​

Answer:

D.) Converges; 256

Step-by-step explanation:

x0= 192

x1 = 48 = 192/4

x2 = 12 = 192/(4 x 4)

Therefore, this series can be written as:

\(x_n = \frac{192}{4^n}\)

Applying limits at infinity:

\(\lim_{n \to \infty} x_n= \lim_{n \to \infty} (\frac{192}{4^n}) = \frac{192}{\infty}=0\)

Since the terms of the series tend to zero, we can affirm that the series converges.

The sum of an infinite converging series is:

\(S=\frac{x_0}{1-r} \\S=\frac{192}{1-\frac{1}{4} }\\S=256\)

Thus, the answer is D.) Converges; 256

The total volume of the tank is 300L.

The volume of a 3D figure is the space that it occupies.

Here, we are given that Yuki adds cleaning solution that is 7/900 of the tank's total volume.

Let the total volume of the tank be V

We know that the cleaning solution required to clean this tank is 2 1/3 L

Firstly, we need to convert this mixed fraction into an improper fraction, Thus, 2 1/3 = (2*3 + 1)/ 3

= 7/3 L

Thus, we can make the following equation,

(7/900)* V = 7/3

V = 7/3 (900/7)

V = 900/ 3

V = 300

Thus, the volume of the tank is 300L.

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Yuki works at an aquarium. To clean a tank, she calculates 7/ 900 of the tank's total volume, and she adds that much cleaning solution to the tank. For a certain tank, this works out to be  2 1/3 L of cleaning solution. What is the total volume of the tank?

Answer:

300L

Step-by-step explanation:

Just did it on Khan academy.

Answer:

Step-by-step explanation:

If f(x)=x²+4 then (fof⁻¹)(x)=(f⁻¹of)(x)=x is proved

A relation is a function if it has only One y-value for each x-value.

Composite functions are when the output of one function is used as the input of another.

If f(x)=x²+4

Then we have to prove f⁻¹of(x)=f⁻¹(f(x)

Let us consider fof⁻¹(x)

f(f⁻¹(x))

x

So (fof⁻¹(x))=x

Now f⁻¹of(x)=f⁻¹(f(x)

=x

Hence, If f(x)=x²+4 then (fof⁻¹)(x)=(f⁻¹of)(x)=x is proved

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Answer:

Step-by-step explanation:

What are the other colors?

if there are two colors ( red and another color ) then the probability of the pointer landing on red will be 1/2

similarly if there are 3 colors ( red and two other colors) then the probability of the pointer landing on red will be 1/3 ....

depends on how many colors are there

The way the flashback in these paragraphs advance the plot is C. It introduces Evan's motivation for working in the garden with Grandfather.

The technique of flashback in storytelling involves interrupting the chronological order of events to depict an earlier event or scene. It uses time travel to furnish the audience with necessary backstory, context, or a deeper understanding of the characters.

The technique of flashbacks is frequently employed as a means of divulging previous occurrences, recollections, or incidents that hold significance to the present narrative being conveyed.

Hence, it can be seen from the given text that the use of flashback helps show the motivation which Evans had for working in the garden with Grandfather

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Answer:

74

Step-by-step explanation:

its easy so you add 23 and 51 and you got the answer.

the value of the investment when she retires is $26434.92.

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

Formula:

A = P(1 + {r}/{n})^{n.t}

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

here, we have,

given that,

Leilamade a one-time investment of $12 000.00 in a

registered retirement savings plan (RRSP) at 2.65%, compounded

semi-annually.

She plans to withdraw the money when she retires in 30

years.

So, she get finally is,

using the formula we get,

$26434.92

hence,  the value of the investment when she retires is $26434.92.

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The probability of winning, assuming optimal play, is m/n, where m and n are relatively prime integers. Then 100m + n is 11.

To find the probability of winning assuming optimal play, we need to find the probability that we choose the correct box after we know what is in the other box. Let X be the event that the gemstone is in box B1. Then P(X) = 1/10.

After Auntie Hall opens a box, the probability of X changes. Let Y be the event that the opened box contains yoghurt. Then P(Y) = 2/3.

Given Y, the probability of X changes to P(X | Y) = P(X) / (P(X) + P(X complement given Y)). We can use Bayes' theorem:

P(X | Y) = P(Y | X) × P(X) / P(Y)

Since the box that Auntie Hall opens is selected randomly, P(Y | X) = 2/3 for each X complement. Thus,

P(X | Y) = 1/10 × 2/3 / (2/3) = 1/10

The probability of winning is the same regardless of whether we switch boxes or not, so the probability of winning is 1/10.

So, 100m + n = 100 × 1/10 + 1 = 11, and the answer is 100m + n = 100 × 1/10 + 1 = 11.

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Answer:

The mean of the sampling distribution of sample means is equal to the population mean, which is 5.3 years.

give thanks for more! your welcome!

Step-by-step explanation:

Answer:

A. 11

Explanation:

Given the expression:

When x=5 and y=38, we substitute to obtain:

The correct choice is A.

Option C. The statement that describes the graph of the equation y + 2 ≥ –4(x – 3)2 is a a parabola opening down, with shading above the vertex.

To do this you have to create a graph of the equation as seen in the attachment.

From the attachment we can see that the parabola is shaped downwards while we have the shading to be at the top of the vertex.

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Answer:

-5/6

Step-by-step explanation:

(9, 5) and (21, -5)

slope = m = (difference in y)/(difference in x)

m = (-5 - 5)/(21 - 9)

m = -10/12

m = -5/6

Answer: -5/6

The slope of the line that passes through points (9,5) and (21,-5) is -5/6.

We can use the two-point formula to find the slope for the given line. The formula is as follows:

(y2 - y1) = m*(x2 - x1)

Where (x1, y1, x2, and y2) represent the points on the line, and m is the slope of the line.

In the given case:

x1=9, x2=21

y1=5, y2=-5

Using these values in the two-point formula, we get:

(-5-5)=m*(21-9)

-10=m*12

m=-10/12

m=-5/6

Hence the slope of the line is -5/6.

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-0.13 is a rational​ number

\(-0.13 = -\dfrac{13}{100}\)

Answer:

Step-by-step explanation:

- 0.13 is a rational number .

It can be write as \(- \frac{13}{100}\) in p by q form.

Answer:

ribbon cost = $3.50 / yard

3 3/4 yards cost = 3.50 * 3.75 which equals

$13.125 or $13.13 rounded

Step-by-step explanation:

Answer:Thus in total the balls can be divided in 15 ways in the four indistinguishable boxes.May

Step-by-step explanation:

The number of ways that 4 balls which are distinguishable, can be placed in 4 boxes which are indistinguishable is 15 ways.

The situations that can happen are:

4 balls in one box - 1 way

3 balls in one box and 1 in another - 4 ways

2 balls in one box, 2 balls in another - 3 ways

2 balls in one box, 1 ball in another box, 1 ball in another box - 6 ways

1 ball in each box - 1 way

The total number of ways is:

= 1 + 4 + 3 + 6 + 1

= 15 ways

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Answer:

  15)  A) {3i√2, -3i√2}

  16)  C) {5i√2/3, -5i√2/3}

Step-by-step explanation:

15)

  \(6r^2=-108\\\\r^2=\dfrac{-108}{6}=-18\\\\r=\pm\sqrt{-18}\\\\\boxed{r=\pm3i\sqrt{2}}\)

__

16)

  \(9p^2-8=-58\\\\9p^2=-50\qquad\text{add 8}\\\\p^2=-\dfrac{50}{9}\qquad\text{divide by 9}\\\\p=\pm\sqrt{-\dfrac{50}{9}}\qquad\text{take the square root}\\\\\boxed{p=\pm\dfrac{5\sqrt{2}}{3}}\)

Answer:

3. 2x+12+3x-7=360

5x+5=360

5x=360-5

x=355/5

x=71

for exterior

2x+12=360

2x=360-12

x=348/2

x=174

Step-by-step explanation:

hope this will help you

The probability that the entire cargo will be approved is 0.078 = 7.8% using the Binomial probability distribution, while 92.2% will be refused. As a result, many will be rejected.

By Binomial probability distribution,

P(X = x) = \(C_{n,x}\) × \(p^{x}\) × \((1-p)^{n-x}\)

\(C_{n,x}\) , various combinations of x items from a collection of n elements given by,

\(C_{n,x}\) = n! ÷ x! (n - x)!

n=42, as 42 tablets are tested.

p=0.06 as 6% is defective.

If at most there is 1 defective piece then it will be accepted.

Therefore,

P(X ≤ 1) = P(X = 0) + P(X = 1)

P(X = x) = \(C_{n,x}\) × \(p^{x}\) × \((1-p)^{n-x}\)

P(X = 0) = \(C_{42,0}\) × \((0.06)^{0}\) × \((0.94)^{42}\) = 0.074

P(X = 1) = \(C_{42,1}\) × \((0.06)^{1}\) × \((0.94)^{41}\) = 0.0047

Thus,

P(X ≤ 1) = P(X = 0) + P(X = 1)

P(X ≤ 1) = 0.074 + 0.0047

P(X ≤ 1) = 0.0787

The probability that the entire shipment will be approved is 0.078 = 7.8%, while 92.2% will be refused.

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Answer:

integer

Step-by-step explanation:

can't be real rational or a whole.

The point where the two lines intersect is the solution to the system of linear equations, which is: A. (300, 108).

Given that:

y = total cost

x = miles

We are also given the system of linear equations that models the scenario given as:

y = 0.27x + 27 --> equation 1

y = 0.21x + 45 --> equation 2

To find the value of x, make both equations equal to each other and solve:

0.27x + 27 = 0.21x + 45

Combine like terms

0.27x - 0.21x = -27 + 45

0.06x = 18

Divide both sides by 0.06

0.06x/0.06 = 18/0.06

x = 300

To find the value of y, plug in the value of x into equation 1, and find y:

y = 0.27(300) + 27

y = 81 + 27

y = 108

Thus, the point where the two lines intersect is the solution to the system of linear equations, which is: A. (300, 108).

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Take the cross product of the given vectors to get one that is perpendicular to both of them.

\(\langle 3, 5, -2 \rangle \times \langle 2, 1, 0 \rangle = \langle 2, -4, -7 \rangle\)

The line parallel to this vector and passing through the origin is given by the vector function

\(\vec r(t) = \langle 2, -4, -7 \rangle t\)

where \(t\in\Bbb R\), and hence parametric equations

\(\begin{cases}x(t) = 2t \\ y(t) = -4t \\ z(t) = -7t \end{cases}\)

Translate this line by the vector \(\langle1,0,1\rangle\) to make it pass through the given point. So the line we want has vector function

\(\vec r(t) = \langle 2, -4, -7 \rangle t + \langle 1, 0, 1 \rangle\)

and parametric equations

\(\boxed{\begin{cases} x(t) = 2t + 1 \\ y(t) = -4t \\ z(t) = -7t + 1 \end{cases}}\)

If the two angles are complementary, then their sum is 90 degrees.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.

If the two angles are complementary, then their sum is 90 degrees.

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Answer: use  the app photomath. its free.  you take a picture and it will show you all the steps in depth

Step-by-step explanation:

Answer:

5) 10³: So you do 10* 10*10= 1,000

so 10³= 1,000

All you are doing is takeing the number and multiplying itself to the power.

6) (-7)⁴= so you are taking the -7 in parenthesis and making it positive, then you are taking the positive 7 and doing  7⁴. Once you do that you get positive 2401.

8) 3+6* (-5) to the second (i dont have the symbol) so you are going to do PEMDAS: Parenthesis, Expression, Multipulcation, Divison, Addition and Subtraction. so it would be 5+6*25to the second. So you do multipulcation first, so do 6*25=150. Then do addition and do 150+3=153

Step-by-step explanation:

5) 10³= 1,000

6)(-7)⁴= 7⁴= 2401

8)3+6* (-5) to the second= 3+6* (5) to the second= 3+6* 25= 6*25= 150+3= 153

Answer to 8 is= 153

I hoped this helped you :D

Answer:

since 7 times 3 is 21

Step-by-step explanation:

it would be 7+7+7 becuase you do seven times 3

hope that helped!

Use the double angle identity:

sin(2x) = 2 sin(x) cos(x)

Now rewrite

sin(2x) sin(x) + cos(x) = 0

as

2 sin²(x) cos(x) + cos(x) = 0

Factor out cos(x) :

cos(x) (2 sin²(x) + 1) = 0

Consider the two cases,

cos(x) = 0   OR   2 sin²(x) + 1 = 0

Solve for cos(x) and sin²(x) :

cos(x) = 0   OR   sin²(x) = -1/2

Squaring a real number always gives a non-negative number, so the second case doesn't offer any real solutions. We're left with

cos(x) = 0

Cosine is zero for odd multiples of π/2, so we have

x = (2n + 1) π/2

where n is any integer.

Answer:

5a. x = 15

5b. z = 125

Step-by-step explanation:

Please see attached photo.

y° = 4x – 5... (1) (Alternate angles are equal)

y° = 5x – 20. (2) (opposite angles are equal)

5a. Determination of the value of x.

We can obtain the value of x by equating equation 1 and 2 as shown below

y° = 4x – 5.... (1)

y° = 5x – 20... (2)

y° = y°

5x – 20 = 4x – 5

Collect like terms

5x – 4x = – 5 + 20

x = 15

5b. Determination of the value of z.

The value of z can be obtained as follow:

4x – 5 + z = 180 (angle on a straight line).

x = 15

4(15) – 5 + z = 180

60 – 5 + z = 180

55 + z = 180

Collect like terms

z = 180 – 55

z = 125

Is not possible to define a radius  nor a diameter in a trapezium.

Radius and diameter are two measures defined for circles.

Radius is the distance between the center and any point in the circumference, and the diameter is the distance between two opposite points in the circumference (so it does not need to be 3D to have radius/diameter).

At the same time, a trapezium is not a circle, is a quadrilateral, so it can't have any of these.

To get the area use the formula:

Area = (base1 + base2)*height / 2

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The value of y is 4√3

Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.

Also , the ratio of corresponding sides of similar triangles are equal.

There are two triangles that are similar

Therefore;

y /16 = 4/y

y² = 48

y = √48

y = √16 × √ 3

y = 4√3

Therefore, the value of y is 4√3

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Answer:

5000inches

Step-by-step explanation:

i think is that!