(a) What is a sequence? A sequence is an unordered list of numbers. A sequence is the sum of an ordered list of numbers. A sequence is an ordered list of numbers. A sequence is the sum of an unordered list of numbers. A sequence is the product of an ordered list of numbers. (b) What does it mean to say that lim n → ∞ an = 8? The terms an approach 8 as n becomes large. The terms an approach 8 as n becomes small. The terms an approach infinity as n become large. The terms an approach -infinity as 8 approaches n. The terms an approach infinity as 8 approaches n. (c) What does it mean to say that lim n → ∞ an = ∞? The terms an become large as n becomes large. The terms an become large as n becomes small. The terms an approach zero as n becomes large. The terms an become small as n becomes small. The terms an become small as n becomes large.

Answer:

90

Step-by-step explanation:

10x - x = 81

9x = 81

x = 9

larger number = 10 x 9 = 90

For this case we have that "x" is the variable that represents the smallest number to find. Let and the variable that represents the largest number, then:[tex]y = 10x\\y-x = 81[/tex]

Substituting the first equation in the second:

[tex]10x-x = 81\\9x = 81\\x = \frac {81} {9}\\x = 9[/tex]

So, the biggest number is:

[tex]y = 10 * 9 \\y = 90[/tex]

Answer:

10x

90

Answer:

-7x+3y+3

Step-by-step explanation:

(4-5+4)=3

(-2x-5x)=-7x

(-4y+7y)=3y

For this case we must simplify the following expression:

[tex]4-5-2x-4y + 4-5x + 7y[/tex]

We must combine similar terms, taking into account that equal signs are added and the same sign is placed, while different signs are subtracted and the sign of the greater is placed:

[tex]4-5 + 4-2x-5x-4y + 7y =\\3-7x + 3y[/tex]

Answer:

[tex]3-7x + 3y[/tex]

Answer:

Step-by-step explanation: Half life period means half of the initial amount will be remaining after decay which is the same as half of the initial amount is decayed.  

Nt= N0 *1/2 ^ (t/th)  

After one hour Nt = N0 *√ 0.5 ^ (1/2) =0.7 N0 remaining or 0.3 has decayed  

Hence it is TRUE that  

After 1, less than 50 %of the original atoms in the container will have decayed  

But the statement  

After 1 hours, more than 50% of the original atoms in the container will have decayed is false.  

======================================...  

After 2 hours  

Nt= *0.5 ^ (2/2) N0= 0.5 N0 is remaining and 0.5 of N0 has decayed.  

Hence it is TRUE that  

After 2 hours, 50% of the original atoms in the container will have decayed.  

======================================...  

After 4 hours  

Nt= 0.5 ^ (4/2) N0= 0.5^2 N0 = 0.25 N0 is remaining or 0.75N0 has decayed.  

Hence it is false that  

After 4 hours, 25 %of the original atoms will have decayed and  

After 4 hours, 25 %of the original atoms will have decayed  

======================================...

Answer:

YES

Step-by-step explanation:

Answer:

Step-by-step explanation:

Unit prefix:

mili = 0.001

kilo = 1,000

A. 11 grams = 11 · 1,000 miligrams = 11,000 miligrams ≠ 1,000 miligrams

B. 7 liters = 7 · 1,000 mililiters = 7,000 mililiters > 700 mililiters  CORRECT :)

C. 5 mililiters < 5 liters = 5,000 mililiters

D. 4 kilograms = 4 · 1,000 grams = 4,000 grams > 3,000 grams

Answer: OPTION B

Step-by-step explanation:

Let's make the conversions:

A. 11 grams to milligrams (Remember that 1 gram= 1,000 milligrams):

[tex](11\ grams)(\frac{1,000\ milligrams}{1\ gram})=11,000\ milligrams[/tex]

The [tex]11\ grams=11,000\ milligrams[/tex]

B. 7 liters to milliliters (Remember that 1 liter= 1,000 milliliters):

[tex](7\ liters)(\frac{1,000\ milliliters}{1\ liter})=7,000\ milliters[/tex]

Then:

[tex]7,000\ milliters>700 milliliters[/tex] or [tex]7\ liters>700 milliliters[/tex]

C. 5 milliliters to liters:

[tex](5\ milliliters)(\frac{1\ liter}{1,000\ milliliters})=0.005\ liters[/tex]

Then:

[tex]0.005\ liters<5 liters[/tex] or [tex]5\ milliliters<5 liters[/tex]

D. 4 kilograms to grams (Remember that 1 kilogram= 1,000 grams):

[tex](4\ kilograms)(\frac{1,000\ grams}{1\ kilogram})=4,000\ grams[/tex]

Then:

[tex]4,000\ grams>3,000\ grams[/tex] or  [tex]4\ kilograms>3,000\ grams[/tex]

Therefore, the option that shows the correct comparisson is the option B.

[tex]\bf \textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=&radius\\ \theta =&angle~in\\ &radians\\ \cline{1-2} r=&10\\ \theta =&\frac{2\pi }{3} \end{cases}\implies s=10\left( \cfrac{2\pi }{3} \right)\implies s=\cfrac{20\pi }{3}\implies s\approx 20.94[/tex]

Answer:

C

Step-by-step explanation:

Answer:

y = 650·0.922^t

Step-by-step explanation:

At the end of each year, 92.2% of the amount at the beginning of the year remains. That is, the beginning amount is multiplied by 0.922. The exponent t in 0.922^t tells how many times (years) that multiplication has taken place. At the end of t years, the amount remaining in milligrams (y) is ...

y = 650·0.922^t

Answer:

  24/35, about 69%

Step-by-step explanation:

The data given can be put into a 2-way table (attached). It shows that 0.48 of all calls were answered and resulted in a mortgage application. Altogether, 0.70 of all calls resulted in a mortgage application. Thus the conditional probability of interest is ...

  p(spoke to attendant | applied for a mortgage) = p(spoke & applied)/p(applied)

  = 0.48/0.70 = 24/35 ≈ 69%

The probability can be calculated by dividing the probability of speaking to an attendant and applying for a mortgage by the probability of applying for a mortgage.

To calculate the probability that a person initially spoke to an attendant, given that he or she applied for a mortgage, we need to use conditional probability. Let's break it down step by step:

Let's do the calculations:

Probability of speaking to an attendant = 60% = 0.6

Probability of attending and applying for a mortgage = 80% of 60% = 0.8 * 0.6 = 0.48

Probability of applying for a mortgage = (Probability of attending and applying for a mortgage) + (Probability of receiving a same-day return call and applying for a mortgage) + (Probability of receiving a next-day return call and applying for a mortgage)

= 0.48 + (0.75 * 0.4 * 0.6) + (0.25 * 0.4 * 0.4) = 0.48 + 0.18 + 0.04 = 0.7

Conditional probability = (Probability of attending and applying for a mortgage) / (Probability of applying for a mortgage) = 0.48 / 0.7 = 0.6857

https://brainly.com/question/10567654

#SPJ3

Answer:

No:   number of tables in Honeycomb Cafe

Yes:   number of patrons in Honeycomb Cafe at noon

Yes:   number of minutes it takes to be served at Honeycomb Cafe

Step-by-step explanation:

Answer:

A normal distributed data is a probability distributed data. It has a shape of a bell curve. This shows that the normal distribution is always symmetrical about the mean.

Number of tables in Honeycomb Cafe  - No

Number of patrons in Honeycomb Cafe at noon -Yes

Number of minutes it takes to be served at Honeycomb Cafe - No

Step-by-step explanation:

20% of the coins are dimes, and 10 coins are selected, so the expected number of dimes is 0.20 * 10 = 2.

So the number generator is fair. It shows that 20% of the coins selected are dimes most of the time.

The correct description is given by the number generator is fair. It shows that 20% of the coins selected are dimes most of the time.

The correct option is (c).

The distribution is a mathematical function that describes the relationship of observations of different heights. A distribution is simply a collection of data, or scores, on a variable

As 20% of the coins are dimes, and 10 coins are selected,

So, the expected number of dimes is,

=[tex]20[/tex] % of 10

= [tex]\frac{20}{100} * 10[/tex]

= 0.20 * 10

= 2.

Thus, the number expected number of dimes is 2

So, the number generator is fair. It shows that 20% of the coins selected are dimes most of the time.

Learn more about distribution here:

https://brainly.com/question/15077367

#SPJ2

Answer:

42.4

Step-by-step explanation:

1) use this formula of Area of the triangle:

[tex]A=\frac{1}{2} a*b*sin(a,b)[/tex]

2) using the formula described above:

A=0.5*14*11*0.55≈42.4 (mm²)

Answer:

a) see your problem statement for the explanation

b) 2.54539334183

Step-by-step explanation:

(b) Many graphing calculators have a derivative function that lets you define the Newton's Method iterator as a function. That iterator is ...

  x' = x - f(x)/f'(x)

where x' is the next "guess" and f'(x) is the derivative of f(x). In the attached, we use g(x) instead of x' for the iterated value.

Here, our f(x) is ...

  f(x) = 3x^4 -8x^3 +6

An expression for f'(x) is

  f'(x) = 12x^3 -24x^2

but we don't need to know that when we use the calculator's derivative function.

When we start with x=2.545 from the point displayed on the graph, the iteration function g(x) in the attached immediately shows the next decimal digits to be 393. Thus, after 1 iteration starting with 4 significant digits, we have a result good to the desired 6 significant digits: 2.545393. (The interactive nature of this calculator means we can copy additional digits from the iterated value to g(x) until the iterated value changes no more. We have shown that the iterator output is equal to the iterator input, but we get the same output for only 7 significant digits of input.)

___

Alternate iterator function

If we were calculating the iterated value by hand, we might want to write the iterator as a rational function in Horner form.

  g(x) = x - (3x^4 -8x^3 +6)/(12x^3 -24x^2) = (9x^4 -16x^3 -6)/(12x^3 -24x^2)

  g(x) = ((9x -16)x^3 -6)/((12x -24)x^2) . . . . iterator suitable for hand calculation

The equation must have a root in the interval [2, 3] based on the Intermediate Value Theorem. Newton's method can be used to approximate the root to six decimal places.

To show that the given equation must have a root in the interval [2, 3], we use the Intermediate Value Theorem. The function f(x) = 3x4 − 8x3 + 6 is continuous on [2, 3], and f(2) < 0 while f(3) > 0. Therefore, by the Intermediate Value Theorem, there must be a number c in the interval (2, 3) such that f(c) = 0. This implies that the equation 3x4 − 8x3 + 6 = 0 has a root in the interval [2, 3].

To approximate the root of the equation using Newton's method, we start with an initial guess, let's say x0 = 2.5. We iterate using the formula xi+1 = xi - f(xi)/f'(xi) until we obtain the desired level of accuracy. By repeating this process, we can approximate the root of the equation correct to six decimal places.

https://brainly.com/question/33823181

#SPJ3

Answer:

78

Step-by-step explanation:

The tricky part of this is figuring out how to assign the unknowns.  We are told that we are working with two consecutive even integers.  Consecutive means "next to" or "in order" and sum means to add.  If we use 2 and 4 as examples of our 2 consecutive even integers and assign x to 2, then in order to get from 2 to 4 we have to add 2.  So the lesser of the 2 integers is x, and the next one in order will be x + 2.  (2 and 4 are just used as examples; they mean nothing to the solving of this particular problem.  You could pick any 2 even consecutive integers and find the same rule applies.  All we are doing here with the example numbers is finding a rule for our integers.)  Now we have the 2 expressions for the integers, we will add them together and set the sum equal to 158:

x + (x + 2) = 158

The parenthesis are unnecessary since we are adding, so when we combine like terms we get

2x + 2 = 158 and

2x = 156 and

x = 78

That means that the lesser of the 2 integers in 78, and the next one in order would be 80, and 78 + 80 = 158

Answer:

2A + (2A +2)  = 158

4A = 156

A= 39

2A = 78 and (2A + 2) = 80

Answer is A

Step-by-step explanation:

Answer:

The function that this scenario represents is:

[tex]P(x) = 5(4) ^ x[/tex]

Step-by-step explanation:

The initial number of foxes was 5. The following year they had

year 1: [tex]5 * (4) = 20[/tex] foxes

year 2: [tex]5 * 4 * (4) = 80[/tex] foxes

year 3: [tex]5 * 4 * 4 * (4) = 320[/tex] foxes

year x: [tex]5 * 4 ^ x[/tex] foxes

Then the equation that models the situation is an equation of exponential growth. Where P(x) is the population of foxes in year x.

So:

[tex]P(x) = 5(4) ^ x[/tex]

Answer:

D

Step-by-step explanation:

Only perfect squares can be rational numbers. the square root of 80 is the only one that is not a perfect square.

D. Square Root of 80

Answer:

  see the attachment

Step-by-step explanation:

When the function is reflected across the line y=x (x and y are interchanged in the function definition), the result is the inverse function. The function and its inverse are shown in graph (A).

Answer: Option B

[tex]x = 800\ gr[/tex]

Step-by-step explanation:

We know that the mass of the empty container is 600 gr

And when they put 8 cans of equal mass then the final weight of the container is 7 kilograms or 7000 grams

If we call x the weight of the cans then this situation can be represented by the following linear equation.

[tex]8x + 600 = 7000[/tex]

Now we solve the equation for the variable x.

[tex]8x = 7000 -600\\\\8x = 6400\\\\x = \frac{6400}{8}\\\\[/tex]

[tex]x = 800\ gr[/tex]

For this case we must find the solutions of the following quadratic equation:

[tex]2x ^ 2-2x-9 = 0[/tex]

The roots will come from:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]

Where:

[tex]a = 2\\b = -2\\c = -9[/tex]

Substituting:

[tex]x = \frac {- (- 2) \pm \sqrt {(- 2) ^ 2-4 (2) (- 9)}} {2 (2)}\\x = \frac {2 \pm \sqrt {4 + 72}} {2 (2)}\\x = \frac {2 \pm \sqrt {76}} {4}\\x = \frac {2 \pm \sqrt {2 ^ 2 * 19}} {4}\\x = \frac {2 \pm2 \sqrt {19}} {4}[/tex]

The roots are:

[tex]x_ {1} = \frac {2 + 2 \sqrt {19}} {4} = \frac {1+ \sqrt {19}} {2}\\x_ {2} = \frac {2-2 \sqrt {19}} {4} = \frac {1- \sqrt {19}} {2}[/tex]

Answer:

Option C

Answer: Option C

The solutions of the quadratic equation are:

[tex]x = \frac{1\±\sqrt{19}}{2}[/tex]

Step-by-step explanation:

Use the quadratic formula to solve this equation.

For a quadratic function of the form [tex]ax^2 +bx +c=0[/tex] the quadratic formula is:

[tex]x = \frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]

In this case:

[tex]a=2\\b=-2\\c=-9[/tex]

So

[tex]x = \frac{-(-2)\±\sqrt{(-2)^2-4(2)(-9)}}{2(2)}[/tex]

[tex]x = \frac{1\±\sqrt{19}}{2}[/tex]

Answer:

You have your x and y mixed up

Step-by-step explanation:

Look at your table.  You labeled y1 and y2 where the x's are.  y2 = 8, y1 = 4, x2 = 12 and x1 = 6.  The slope then is (8-4)/(12-6) which is 4/6 or 2/3.  You did run over rise instead of rise over run.  Be careful.  I see that a lot when I teach the concept to beginners.  

Call these numbers [tex]x,y[/tex]. Then [tex]x+y=7[/tex] or [tex]y=7-x[/tex].

We want to maximize their product,

[tex]f(x,y)=xy\implies f(x,7-x)=F(x)=7x-x^2[/tex]

We could consider the derivative, but I think that's overkill. Instead, let's complete the square:

[tex]7x-x^2=-\left(x^2-7x+\dfrac{49}4\right)+\dfrac{49}4=\dfrac{49}4-\left(x-\dfrac72\right)^2[/tex]

whose graph is a parabola opening downward with vertex at [tex]\left(\dfrac72,\dfrac{49}4\right)[/tex], so that the maximum product is [tex]\dfrac{49}4[/tex].

Now if [tex]x=\dfrac72[/tex], it follows that [tex]y=7-\dfrac72=\dfrac72[/tex].

The two numbers that have the maximum possible product and a sum of 7are 3.5 and 3.5

Let the two number be x and y

If the sum of the numbers is 7, then;

x + y = 7 ........................ 1

If their product is at maximum, then;

xy = P ............................. 2

From equation 1, y = 7 - x

Substitute into equation 2 to have:

x(7-x) = P
P = 7x - x²

If the function is at maximum, then;

dP/dx = 7 - 2x
0 = 7 - 2x
x = 7/2
x = 3.5

Recall that x + y = 7
x = 7 - y
x = 3.5

Hence the two numbers are 3.5 and 3.5

learn more on system of equation here: https://brainly.com/question/14323743

Answer:

  tan(∠B) = 2

Step-by-step explanation:

In a right triangle, the relationships of the tangents of the acute angles is ...

  tan(∠B) = cot(∠A) = 1/tan(∠A)

For tan(∠A) = 0.5, this means ...

  tan(∠B) = 1/0.5 = 2

Answer: 227.5*10^6 km or 227.5 million km

Step-by-step explanation:

x^3/2*.02=686.3

686.3/.2=x^3/2*.2/.2

x^3/2=3431.5

x=227.50415642

Answer:

The average distance of Planet Upper D from the center​ star is 227.5 millions of kilometers (227.5 × 10^6 kilometers)

Step-by-step explanation:

* Lets explain information to solve the problem

- x is the average distance of the planet from the center​ star, in millions

 of kilometers

- The formula of Earth days in the year of Planet is 0.2 x^(3/2)

- The Earth days in the year of Plant D is approximately 686.3

* Lets solve the problem

∵ The number of Earth days in a planet's year = 0.2 x^(3/2)

∵ The Earth days in the year of Plant D is approximately 686.3

- Lets substitute this value in the formula

∴ 686.3 = 0.2 x^(3/2) ⇒ divide both sides by 0.2

∴ 686.3/0.2 = 0.2/0.2 x^(3/2)

∴ 3431.5 = x^(3/2)

- We can use this rule to solve the equation

# If x^n = a, where a is a constant, then x = a^(1/n)

  that means we reciprocal the power and take it to the other side

∴ x = (3431.5)^(2/3)

- Now use your calculator to find the answer

∴ x ≅ 227.5

* The average distance of Planet Upper D from the center​ star is

  227.5 millions of kilometers (227.5 × 10^6 kilometers)

Answer:

Step-by-step explanation:

Pick any pair of angles and write the equation that expresses their relationship. Solve for x, then use that value in any of the angle expressions to find the corresponding angle value.

For example, ...

  ∠AOD + ∠AOB = 180°

  (5x -1) +(9x +41) = 180

  14x = 140 . . . . . collect terms, subtract 40

  x = 10 . . . . . . . . divide by 14

Now the angles are ...

  ∠AOD = (5·10 -1)° = 49°

  ∠AOB = (9·10 +41)° = 131° . . . . . supplementary to 49°

The remaining linear or vertical angles are equal to one or the other of these.

Answer:

4!=4 x 3 x 2 x 1=24

So the answer is 24.

Answer:

24 ways.

Step-by-step explanation:

If i have n different trophies to arrange on top shelf of a book case then the number of ways in which we can arrange the trophies will be

     = n!

When n = 4

Then number of ways in which we can arrange the books

= 4!

= 4 × 3 × 2 × 1

= 24

Therefore, answer is 24 ways.

Answer:

  [4, ∞)

Step-by-step explanation:

The vertex of the upward-opening quadratic is (0, 4), so the function will take on values of 4 or more. The range is 4 to infinity, inclusive of 4.

Answer:

The value of x is 100

Step-by-step explanation:

* Lets revise how to find the missing number of the given Mean

- Add up the numbers you know.

- Set up your equation by adding the sum of the numbers plus “x”

- Divide the sum by the number of numbers given.

- Equate them by the value of the mean

- Solving for "x"

- Check the Answer

* Now lets solve the problem

- The numbers are 99 , 123 , 105 , 114 , 107

- The sum of the numbers = 99 + 123 + 105 + 114 + 107 = 548

- The equation is ⇒ (548 + x)/6 = 108 ⇒ × 6 both sides

∴ 548 + x = 648 ⇒ subtract 548 from both sides

∴ x = 100

* Now lets check the answer

- The mean = (99 + 123 + 105 + 114 + 107 + 100)/6 = 648/6 = 108

∴ The answer x = 100 is correct

* The value of x is 100

Answer:

The value of X = 100

Step-by-step explanation:

Points to remember

Mean of a data set is given by,

Mean = (sum of data)/number of data

To find the value of X

It is given a data set,99, 123, 105, 114, 107, X

Sum of data set = 99 + 123 + 105 + 114 + 107 + X =  548 + X

Mean = 108

Mean =  (sum of data)/number of data

108 = (548 + X)/6

548 + X = 108 * 6 = 648

X = 648 - 548 = 100

Therefore the value of X = 100

Answer:

distance

Step-by-step explanation:

Usually the absolute value of a complex number is called its magnitude. The squared magnitude is the algebraic quantity that's preferable to work with.

Let

[tex]z = a+bi[/tex]

[tex]|z|^2 = z^* z = zz^* = |a+bi|^2= (a+bi)(a-bi) = a^2 - i^2 b^2 = a^2+b^2[/tex]

[tex]|a+bi| = \sqrt{a^2+b^2}[/tex]

That's the distance from the origin to (a,b)

The absolute value of any complex number a + bi is the distance from (a, b) to (0, 0) in the complex plane.

This is a number which is in the form of a + bi in which a and b are expressed as real numbers.

|a + bi| = √a²+b² depicts the magnitude which therefore expresses the distance from the origin.

Read more about Complex number here https://brainly.com/question/1245664

#SPJ9

ANSWER

[tex]12y \sqrt{3} [/tex]

EXPLANATION

The given expression is

[tex]\sqrt{3y^2} + 4\sqrt{12y^2} - y\sqrt{75}[/tex]

We identity and remove the perfect squares to obtain

[tex]y\sqrt{3} + 16y\sqrt{3} - 5y\sqrt{3}[/tex]

We now observe that, the three terms are all similar.

We combine the similar terms to get:

[tex]y\sqrt{3} + 16y\sqrt{3} - 5y\sqrt{3} = 12y \sqrt{3} [/tex]

Answer:

4y square root of 3

Step-by-step explanation:

Answer:

The rectangle has the greater area

Is area is [tex]2\ cm^{2}[/tex] greater

Step-by-step explanation:

we know that

The area of rectangle is equal to

[tex]A=(6)*(4\frac{1}{2})=(6)*(\frac{9}{2})=27\ cm^{2}[/tex]

The area of the square is equal to

[tex]A=5^{2}=25\ cm^{2}[/tex]

therefore

The rectangle has the greater area

Find the difference

[tex]27\ cm^{2}-25\ cm^{2}=2\ cm^{2}[/tex]

Is area is [tex]2\ cm^{2}[/tex] greater

Answer:

  see the graph below

Step-by-step explanation:

The function ...

  g(x) = f(x+1) -2

tells you that the graph of f(x) is shifted 1 unit to the left and 2 units down. That means the vertex will be (-1, -2) and another point will be (0, -1).

Point (1, 1) is on the graph of the f(x) parabola. You can pick any other point you like and shift it left 1 and down 2 to find a point on g(x).

The graph of the function g(x) = (1 + x)² - 2 is added as an attachment

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

f(x) = x²

Also, we have

g(x) = (1 + x)² - 2

The above function is a quadratic function that has been transformed from f(x) = x² as follows

Next, we plot the graph using a graphing tool by taking note of the above transformations

The graph of the function is added as an attachment

Read more about functions at

brainly.com/question/2456547

#SPJ3