A Tourist Information Center is between a Bus Station and a Train Station. When mapped on a grid, the Tourist Information Center is
located at (15,2) and the Bus Station is located at (5,-10).
The Train Station is located at point?

9514 1404 393

Answer:

  -2/a^3

Step-by-step explanation:

Anything (except 0) to the 0 power is 1, so b^0 = 1. This immediately simplifies the expression to -2a^-3. If you also want it with positive exponents, this will be ...

  -2/a^3

I believe the given limit is

[tex]\displaystyle \lim_{x\to\infty} \bigg(\sqrt[3]{3x^3+3x^2+x-1} - \sqrt[3]{3x^3-x^2+1}\bigg)[/tex]

Let

[tex]a = 3x^3+3x^2+x-1 \text{ and }b = 3x^3-x^2+1[/tex]

Now rewrite the expression as a difference of cubes:

[tex]a^{1/3}-b^{1/3} = \dfrac{\left(a^{1/3}-b^{1/3}\right)\left(a^{2/3}+a^{1/3}b^{1/3}+b^{2/3}\right)}{\left(a^{2/3}+a^{1/3}b^{1/3}+b^{2/3}\right)} \\\\ = \dfrac{a-b}{a^{2/3}+a^{1/3}b^{1/3}+b^{2/3}}[/tex]

Then

[tex]a-b = (3x^3+3x^2+x-1) - (3x^3-x^2+1) \\\\ = 4x^2+x-2[/tex]

The limit is then equivalent to

[tex]\displaystyle \lim_{x\to\infty} \frac{4x^2+x-2}{a^{2/3}+(ab)^{1/3}+b^{2/3}}[/tex]

From each remaining cube root expression, remove the cubic terms:

[tex]a^{2/3} = \left(3x^3+3x^2+x-1\right)^{2/3} \\\\ = \left(x^3\right)^{2/3} \left(3+\dfrac3x+\dfrac1{x^2}-\dfrac1{x^3}\right)^{2/3} \\\\ = x^2 \left(3+\dfrac3x+\dfrac1{x^2}-\dfrac1{x^3}\right)^{2/3}[/tex]

[tex](ab)^{1/3} = \left((3x^3+3x^2+x-1)(3x^3-x^2+1)\right)^{1/3} \\\\ = \left(\left(x^3\right)^{1/3}\right)^2 \left(\left(3+\dfrac3x+\dfrac1{x^2}-\dfrac1x\right)\left(3-\dfrac1x+\dfrac1{x^3}\right)\right)^{1/3} \\\\ = x^2 \left(9+\dfrac6x-\dfrac1{x^3}+\dfrac4{x^4}+\dfrac1{x^5}-\dfrac1{x^6}\right)^{1/3}[/tex]

[tex]b^{2/3} = \left(3x^3-x^2+1\right)^{2/3} \\\\ = \left(x^3\right)^{2/3} \left(3-\dfrac1x+\dfrac1{x^3}\right)^{2/3} \\\\ = x^2 \left(3-\dfrac1x+\dfrac1{x^3}\right)^{2/3}[/tex]

Now that we see each term in the denominator has a factor of x ², we can eliminate it :

[tex]\displaystyle \lim_{x\to\infty} \frac{4x^2+x-2}{a^{2/3}+(ab)^{1/3}+b^{2/3}} \\\\ = \lim_{x\to\infty} \frac{4x^2+x-2}{x^2 \left(\left(3+\dfrac3x+\dfrac1{x^2}-\dfrac1{x^3}\right)^{2/3} + \left(9+\dfrac6x-\dfrac1{x^3}+\dfrac4{x^4}+\dfrac1{x^5}-\dfrac1{x^6}\right)^{1/3} + \left(3-\dfrac1x+\dfrac1{x^3}\right)^{2/3}\right)}[/tex]

[tex]=\displaystyle \lim_{x\to\infty} \frac{4+\dfrac1x-\dfrac2{x^2}}{\left(3+\dfrac3x+\dfrac1{x^2}-\dfrac1{x^3}\right)^{2/3} + \left(9+\dfrac6x-\dfrac1{x^3}+\dfrac4{x^4}+\dfrac1{x^5}-\dfrac1{x^6}\right)^{1/3} + \left(3-\dfrac1x+\dfrac1{x^3}\right)^{2/3}}[/tex]

As x goes to infinity, each of the 1/x ⁿ terms converge to 0, leaving us with the overall limit,

[tex]\displaystyle \frac{4+0-0}{(3+0+0-0)^{2/3} + (9+0-0+0+0-0)^{1/3} + (3-0+0)^{2/3}} \\\\ = \frac{4}{3^{2/3}+(3^2)^{1/3}+3^{2/3}} \\\\ = \frac{4}{3\cdot 3^{2/3}} = \boxed{\frac{4}{3^{5/3}}}[/tex]

y = -1/4x + 2

yeah

that's it

Answer:

1. 2x + 4= slope: 2 | y intercept: (0,4)

2. 2x + 4= slope: 2 | y intercept: (0,4)

3. -1/4x + 2= slope: -1/4 | y intercept: (0,2)

4. -1/4x + 2= slope: -1/4 | y intercept: (0,2)

Answer:

Q1. 3.14 × 0.8 = 2.512

Q2. 6.28 × 6.8 = 42.704

Q3. 25.5 × 9.3 = 237.15

Q4. 1.3 × 5.7 = 7.41

Q5. 7.41 × 3.7 = 27.417

Answer:

1. f(x)+g(x)=3x−7+x2+5x

2. 5x+x2-7+3x

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Ok, first the formula for this is a^2+b^2=c^2

or leg^2+ leg^2= hypotenuse^2

so (12)^2+(9)^2=hy^2

144+81, 225=hy^2

hy=square root of 225: 15

Answer:

b

Step-by-step explanation:

The sum of angles 7 and 8 is 180, so to find angle 8 you would subtract angle 7 from 180. So:

180 - 92 = 88  

The answer is B, 88 degrees.

Answer:

88° is your answer......

Answer:

- ASA stands for "angle, side, angle" and means that we have two triangles where we know two angles and the included side are equal.

- If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

Step-by-step explanation:

Step-by-step explanation:

1.)  y = - |x - 4| - 5 is an absolute value graph, where its vertex occurs at point (4, -5). The general form of the absolute value function is y = a |x – h| + k, where where:

The given absolute value function, y = - |x - 4| - 5 is a downward-facing graph, where it is translated 4 units to the right (as given by the value of h = 4), and 5 units downward (as given by the value of k = 5).  

2.) The Vertical Line Test allows us to know whether or not a graph is actually a function.  If a vertical line intersects the graph in all places at exactly one point, then the relation is a function. To use the vertical-line test, imagine dragging a ruler held vertically across the  graph from left to right. If the graph is that of a function, the edge of the ruler would hit the graph only once for every x -value.  If you do this for the given graph, every vertical line intersects the graph in at most one point.

Attached is the graph of the given function, where I performed the Vertical Line Test.  As evidenced in the graph, every green vertical line intersects the graph at exactly one point (red dots on the graph). Thus, the graph passed the Vertical Line Test, thereby qualifying as a function.  

Please mark my answers as the Brainliest if you find this explanation helpful :)    

Answer:

No solution, this is not an arithmetic sequence

Step-by-step explanation:

An arithmetic sequence is the same number being added over and over. This is not the case.

Answer:

Step-by-step explanation:

???what

Answer:

The domain is the set of x-values:

The range is the set of y-values:

This can be a function as each x- value has exactly one corresponding y- value.

Points are

All x values has a unique image in y so it's a function

[tex]\\ \sf\longmapsto D_f=\{-4,-2,1,4,2\}[/tex]

[tex]\\ \sf\longmapsto R_f=\{-1,1,-2,-4,4\}[/tex]

Answer:

The decimal point should be moved 4 places to the right

Step-by-step explanation:

38.75x10000= 387500

The sum of 15 and twice Carlos' age.

The sum would be addition. So;

[tex]15\: +[/tex]

Twice means 2 times Carlos' age. And [tex]c[/tex] is the variable, so;

[tex]15+2c[/tex]

Note that 2 and c together like that is multiplication.

Answer:

x + 93 = 124

Step-by-step explanation:

4x = x + 93  {Vertically opposite angles are equal}

Subtract 'x' from both sides

4x - x = 93

3x = 93

Divide both sides by 3

x = 93/3

x = 31

x + 93 = 31+ 93 = 124

Answer:

0.4⎯⎯

Step-by-step explanation:

BRAINLIEST?

Answer:

X=6 Because if you multiply 16×3= 48

and If you do it with 2 it is 2×3= 6

Step-by-step explanation:

16×3= 48

2×3=6

Answer:

x=30o+n90on∈Z

Step-by-step explanation:

cos2x=sin(90o−2x)=sin(2x−30o)

Which mean 90o−2x=2x−30o+n360o

or 90o−2x+2x−30o=(2n+1)180o

The later cannot be true.

so x=30o+n90on∈Z

[tex]▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ { \huge \mathfrak{Answer}}▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ [/tex]

The value of tan x is :

solution is in attachment !

Answer:

I would estimate 923

Step-by-step explanation:

6- (-2) - 3(-5)

= 6- (-2) +15

= 6+ 2 +15

= 8+ 15

=23.

Thus, your answer is 23

Answer:

look at the photo..............

Answer:

₹ 19 1/8.

Step-by-step explanation:

That is 8 1/2 * 2 1/4

= 17/2 * 9/4

= 153/8

= 19 1/8.

Answer:

₹ 19.125 or ₹ 19 1/8

Step-by-step explanation:

1 kg = ₹ 8 1/2

2 1/4 kg = x

8 1/2 can be written as 8.25

2 1/4 can be written as 2.25

To find x:

1. Multiply both sides by 2.25:

1kg × 2.25 = 2.25kg

₹ 8.5 × 2.25 = ₹ 19.125

Answer = ₹ 19.125 or ₹ 19 1/8

Answer:

$7

Step-by-step explanation:

Wyatt will have $7 more in his account than Sophie.

Compound interest is the interest you earn on interest.

Given that, Sophie invested $170 in an account paying an interest rate of [tex]2\tfrac{3}{4}[/tex]% compounded continuously.

Wyatt invested $170 in an account paying an interest rate of [tex]3\tfrac{1}{8}[/tex]% compounded monthly.

We need to find how much more money would Wyatt have in his account than Sophie after 9 years,

For compounded continuously = [tex]Amount = Principal \times e^{rt[/tex]

Sophie =

[tex]Amount = 170 \times e^{0.0275 \times 9[/tex]

A = $217.74

Therefore, Sophie will have $217.74 in her account after 9 years.

For Wyatt,

So, using the formula of CI,

[tex]Amount = Principal(1+r/n)^{nt[/tex]

So,

[tex]= 170(1.0026)^{108[/tex]

A = $225

Therefore, Wyatt will have $225 in his account after 9 years.

The amount Wyatt have more than Sophie = 225-217.74 = $7.26 ≈ $7.

Hence Wyatt will have $7 more in his account than Sophie.

Learn more about compound interest click;

https://brainly.com/question/14295570

#SPJ2

Using the binomial distribution, it is found that:

a) The possible values of X are between 0 and 20.

b) 0.0596 = 5.96% probability that exactly 3 experience insomnia as a side effect.

c) 0.9842 = 98.42% probability 3 or fewer experience insomnia.

d) 0.639 = 63.9% probability that between 1 and 4 experience insomnia.

e) Since [tex]4 > E(X) + 2.5\sqrt{V(X)}[/tex], it would be unusual to find 4 or more patients experience insomnia as a side effect.

For each patient, there are only two possible outcomes, either they experience insomnia, or they did not. The probability of a patient having experienced insomnia is independent of any other patient, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n trials, with p probability.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]  

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]  

The expected value is:

[tex]E(X) = np[/tex]

The standard deviation is:

[tex]\sqrt{V(X)} = \sqrt{np(1 - p)}[/tex]

If a measure is more than 2.5 standard deviations above the mean, it is considered unusual.

In this problem:

Item a:

The possible values of X are always between 0 and n, thus in this case, it is between 0 and 20.

Item b:

This probability is P(X = 3), thus:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{20,3}.(0.05)^{3}.(0.95)^{17} = 0.0596[/tex]

0.0596 = 5.96% probability that exactly 3 experience insomnia as a side effect.

Item c:

This probability is [tex]P(X \leq 3)[/tex], given by:

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]

Then:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{20,0}.(0.05)^{0}.(0.95)^{20} = 0.3585[/tex]

[tex]P(X = 1) = C_{20,1}.(0.05)^{1}.(0.95)^{19} = 0.3774[/tex]

[tex]P(X = 2) = C_{20,2}.(0.05)^{2}.(0.95)^{18} = 0.1887[/tex]

[tex]P(X = 3) = C_{20,3}.(0.05)^{3}.(0.95)^{17} = 0.0596[/tex]

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.3585 + 0.3774 + 0.1887 + 0.0596 = 0.9842[/tex]

0.9842 = 98.42% probability 3 or fewer experience insomnia.

Item d:

This probability is:

[tex]P(1 \leq X \leq 4) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]

Then

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{20,1}.(0.05)^{1}.(0.95)^{19} = 0.3774[/tex]

[tex]P(X = 2) = C_{20,2}.(0.05)^{2}.(0.95)^{18} = 0.1887[/tex]

[tex]P(X = 3) = C_{20,3}.(0.05)^{3}.(0.95)^{17} = 0.0596[/tex]

[tex]P(X = 4) = C_{20,4}.(0.05)^{4}.(0.95)^{16} = 0.0133[/tex]

[tex]P(1 \leq X \leq 4) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.3774 + 0.1887 + 0.0596 + 0.0133 = 0.639[/tex]

0.639 = 63.9% probability that between 1 and 4 experience insomnia.

Item e:

[tex]E(X) = np = 20(0.05) = 1[/tex]

[tex]\sqrt{V(X)} = \sqrt{np(1 - p)} = \sqrt{20(0.5)(0.95)} = 0.975[/tex]

[tex]E(X) + 2.5\sqrt{V(X)} = 1 + 2.5(0.975) = 3.44[/tex]

Since [tex]4 > E(X) + 2.5\sqrt{V(X)}[/tex], it would be unusual to find 4 or more patients experience insomnia as a side effect.

A similar problem is given at https://brainly.com/question/24863377

Answer:22% or A!

Step-by-step explanation: 400 x 9 = 3600 he has ran 792 so far so its about 22.%  

Step-by-step explanation:

y = 5x - 2…Equation 1

3x - 5y = 4…Equation 2

Subtitute value of y to Equation 2 :

3x - 5(5x - 2) = 4

3x - 25x + 10 = 4

-22x + 10 = 4

10 - 4 = 22x

6 = 22x

6/22 = x

3/11 = x

Subtitute value of x to one of Equation :

for example Equation 2…

3x - 5y = 4

3(3/11) - 5y = 4

9/11 - 5y = 4

9/11 - 4 = 5y

(9 - 44)/11 = 5y

(-35)/11 = 5y

(-35)/11 × 1/5 = y

-7/11 = y

Answer:

9-22=c

-13=c

The football team lost 13 yards in overall change in field position. Meaning, the team didn't gain any yards, they lost 13.

Let's say c is the cost of the cantaloupe, and that p is how many pounds the cantaloupe weights.

In that case, $1.19 is the amount of money it will cost per pound of cantaloupe.

If the cantaloupe you buy is 3.5 pounds, it will cost you $4.165, but since money is only two decimal places, and since you can only round up when it's a 5 at the end, it becomes $4.17.

In other words, each pound of cantaluope you buy will cost you $1.19, and a cantaloupe that weighs 3.5 pounds will cost you $4.17.