An iPhone costs 7 times as much as an AirPods. Together they cost $1,200. Find the price of the laptop and iPod.

Answer:

\((f+g)(x)=f(x)+g(x)=4^{x} +12x+5x-1=4^{x}+17x-1\)

Answer:

4^x +17x -1

Step-by-step explanation:

F(x)=4^x+12x

g(x) = 5x-1

(f+g)(x)= 4^x +12x + 5x-1

Combine like terms

     = 4^x +17x -1

Answer:

10+the actual quantity of x=7 would be one of the 4 awnser choices you have made

Answer: x = 3

Step-by-step explanation: Move all terms not containing

x

x

to the right side of the equation.

Given

Equation

x tea chart __, 0, 2, __

y tea chart 0,__, __, 3

Procedure

y = 0

12x = 16

x = 16/12

x = 4/3

x = 0

-8y = 16

y = 16/-8

y = -2

x = 2

12(2) - 8y = 16

24 - 8y = 16

-8y = 16-24

-8y = -8

y = 1

y = 3

12x - 8(3) = 16

12x - 24 = 16

12x = 16+24

12x = 40

x = 40/12

x = 20/6

x tea chart 4/3, 0, 2, 20/6

y tea chart 0, -2, 1, 3

Answer: 1/10

Step-by-step explanation:

2/5 x 1/4= 1/10

keep, change, flip

Answer:

aₙ = 6aₙ - 18

Step-by-step explanation:

a₃ = 0, a₄ = 6, a₅ = 12, a₆ = 18, a₇ = 24...

aₙ = 6aₙ - 18

a₃ = (6 × 3) - 18 = 0

a₄ = (6 × 4) - 18 = 6

a₅ = (6 × 5) - 18 = 12

a₆ = (6 × 6) - 18 = 18

a₇ = (6 × 7) - 18 = 24

I hope this helps!

Pythagoras was an ancient Greek mathematician who founded the Pythagorean school of thought. The Pythagorean theorem is a fundamental concept in mathematics that is attributed to Pythagoras and his followers.

It states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. While this theorem is considered a cornerstone of mathematics today, it is important to understand that Pythagoras did not have access to the advanced mathematical tools and methods that we have today.

He had to rely on geometric constructions and reasoning to prove his theorem. Furthermore, Pythagoras believed that all numbers could be expressed as ratios of whole numbers, which is not always true in reality. Despite these limitations, the Pythagorean theorem has stood the test of time and continues to be a crucial tool in mathematics and other fields.

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Answer:

x = 8.12

Step-by-step explanation:

36+x^2 = y^2

121 + x^2 = z^2

z^2 + y^2 = 289

(121+x^2)+(36+x^2) = 289

157 + 2x^2 = 289

2x^2 = 132

x^2 = 66

x = 8.12

HOPE THIS HELPS!!!

Answer:

I know that the equation has infinity many solution

12x+8=12x+8

That would be the final answer

Answer:

Step-by-step explanation:

complex numbers , real numbers , rational numbers , natural numbers , whole numbers

Jamie rides a ferris wheel for five minutes. the diameter of the wheel is 10 meters, and its center is 6 meters above the ground. each revolution of the wheel takes 30 seconds. being more than 9 meters above the ground causes jamie to suffer an anxiety attack.Jamie feels uncomfortable for 150 seconds.

To solve this question, we can calculate how long it takes for Jamie to reach the height of 9 meters.

The diameter of the wheel is 10 meters, so the circumference is 2π x 10 = 62.83 meters.

As each revolution of the wheel takes 30 seconds, Jamie would reach the height of 9 meters after

62.83 / 30 = 2.094 revolutions.

Therefore, it would take Jamie 2.094 x 30 = 62.83 seconds to reach the height of 9 meters and feel uncomfortable. Since Jamie rides the ferris wheel for five minutes, that would mean Jamie feels uncomfortable for

5 x 60 = 300 seconds minus

the time it took to reach the height of 9 meters, which is 300 - 62.83 = 150 seconds.

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Answer:

Option B,14.6 cm and D,20.3 cm

Step-by-step explanation:

Let a and b represent the lengths of the two known sides such that a≥b. Let c represent the length of the unknown side, the length of c must fall within  

a−b<c<a+b

11.9-9.1<c<11.9+9.1

2.8<21

By elimination,

Option B and D remain, i.e 14.6 cm & 20.3 cm

Answer: There is no proof that the population increased by 10% every year. it is possible the first year increased by 8 the first year then 12 the next, giving a 20% increase.

Extra: the answer the the first and second year is x you must figure the x out if you want the answer to those

a) There are 34,459 possible committees. b) There are 1,001 committees consisting of all juniors. c) There are 4,845 committees consisting of no juniors. d) There are 29,614 committees consisting of at least one junior by using combinations.

a) The number of committees possible can be calculated using the combination formula:

Number of committees = C(n, r) = n! / (r! * (n - r)!)

In this case, there are 34 students in total (14 juniors + 20 seniors) and we need to select 4 members for the committee.

Number of committees = C(34, 4) = 34! / (4! * (34 - 4)!)

= 34! / (4! * 30!)

= (34 * 33 * 32 * 31) / (4 * 3 * 2 * 1)

= 34,459

Therefore, there are 34,459 possible committees.

b) To find the number of committees consisting of all juniors, we need to select 4 juniors from the 14 juniors available:

Number of committees consisting of all juniors = C(14, 4) = 14! / (4! * (14 - 4)!)

= 14! / (4! * 10!)

= (14 * 13 * 12 * 11) / (4 * 3 * 2 * 1)

= 1,001

There are 1,001 committees consisting of all juniors.

c) To find the number of committees consisting of no juniors, we need to select 4 seniors from the 20 seniors available:

Number of committees consisting of no juniors = C(20, 4) = 20! / (4! * (20 - 4)!)

= 20! / (4! * 16!)

= (20 * 19 * 18 * 17) / (4 * 3 * 2 * 1)

= 4,845

There are 4,845 committees consisting of no juniors.

d) To find the number of committees consisting of at least one junior, we subtract the number of committees consisting of no juniors from the total number of committees:

Number of committees consisting of at least one junior = Total number of committees - Number of committees consisting of no juniors

= 34,459 - 4,845

= 29,614

There are 29,614 committees consisting of at least one junior.

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Answer:

m∠1 = 130°

m∠2 = 158°

Step-by-step explanation:

For the given figure, we have;

The measure of angle m∠1 is given by the exterior angle theorem as the sum of the two opposite interior angles as follows;

m∠1 = 99° + 31° = 130°

m∠1 = 130°

Similarly, the measure of angle m∠2 is given by the exterior angle theorem as the sum of the two opposite interior angles as follows;

m∠2 = 28° + m∠1 = 28° + 130° = 158°

m∠2 = 158°.

Answer:

30

Step-by-step explanation:

Answer:

7x^2 - 7x + 6

Step-by-step explanation:

Rearrange equation so its easier

-2x^2 + 9x^2 - 8x + x +3 + 3

Then simplify

7x^2 - 7x + 6

Answer: PQ = 18

Step-by-step explanation:

You would divide 21/14 to see what the size difference in the triangles is to get 1.5. 1.5x12=18

Answer:

18

Step-by-step explanation:

length of PQ is 18

Answer:

x^2-x-3 is the answer

Step-by-step explanation:

Answer:

the answer is yes

Answer:

Yes, it is greater because the higher a negative number is the less the value. If that makes sense.

Step-by-step explanation:

The required probability is 0.4408.

The operating characteristics of the loading gate problem are:

L = λ/ (μ - λ)

W = 1/ (μ - λ)

Lq = λ^2 / μ (μ - λ)

Wq = λ / μ (μ - λ)

ρ = λ / μ

P0 = 1 - λ / μ

Where, L represents the average number of cars either being loaded or waiting.

W represents the average time a car spends either being loaded or waiting.

Lq represents the average number of cars waiting.

Wq represents the average waiting time of a car.

ρ represents the utilization factor.

ρ = λ / μ represents the ratio of time the worker spends loading cars to the total time the system is busy.

P0 represents the probability that the system is empty.

The probability that there will be more than six cars either being loaded or waiting is to be determined. That is,

P (n > 6) = 1 - P (n ≤ 6)

Now, the probability of having less than or equal to six cars in the system at a given time,

P (n ≤ 6) = Σn = 0^6 [λ^n / n! * (μ - λ)^n]

Putting the values of λ and μ, we get,

P (n ≤ 6) = Σn = 0^6 [(6/ 48)^n / n! * (8/ 48)^n]

P (n ≤ 6) = [(6/ 48)^0 / 0! * (8/ 48)^0] + [(6/ 48)^1 / 1! * (8/ 48)^1] + [(6/ 48)^2 / 2! * (8/ 48)^2] + [(6/ 48)^3 / 3! * (8/ 48)^3] + [(6/ 48)^4 / 4! * (8/ 48)^4] + [(6/ 48)^5 / 5! * (8/ 48)^5] + [(6/ 48)^6 / 6! * (8/ 48)^6]P (n ≤ 6) = 0.5592

Now, P (n > 6) = 1 - P (n ≤ 6) = 1 - 0.5592 = 0.4408

Therefore, the required probability is 0.4408.

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The calculated sum of the geometric series are

(a) \(\sum\limits^{\infty}_{0} {(0.8)^n\) = 5

(b) \(\sum\limits^{\infty}_{0} {(1 - p)^n\) = 1/p

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

(a) \(\sum\limits^{\infty}_{0} {(0.8)^n\)

In the above series, we have

First term, a = 1

Common ratio, r = 0.8

The sum to infinity of a geometric series is

Sum = a/(1 - r)

So, we have

Sum = 1/(1 - 0.8)

Evaluate

Sum = 5

Next, we have

(b) \(\sum\limits^{\infty}_{0} {(1 - p)^n\)

In the above series, we have

First term, a = 1

Common ratio, r = 1 - p

The sum to infinity of a geometric series is

Sum = a/(1 - r)

So, we have

Sum = 1/(1 - 1 + p)

Evaluate

Sum = 1/p

Hence, the sum of the geometric series are 5 and 1/p

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Question

5. Find the sum of the following geometric series:

(a) \(\sum\limits^{\infty}_{0} {(0.8)^n\)

(b) \(\sum\limits^{\infty}_{0} {(1 - p)^n\) where 0 < p < 1. (Your answer will be in terms of p)

Answer:

1286 meters long

Step-by-step explanation:

421,808 divided by the width of the plot gives you 1,286 meters for the width.

The given 9th order, linear, homogeneous, constant coefficient differential equation has a characteristic equation that factors into two parts: (r^2 + 2r + 5)^2 and r^3(r - 3)^4. To find the fundamental solutions to the differential equation, we consider each factor separately. Thus, the nine fundamental solutions are e^((-1+2i)t), t * e^((-1+2i)t), (t^2) * e^((-1+2i)t), e^(3t), t * e^(3t), (t^2) * e^(3t), (t^3) * e^(3t), (t^4) * e^(3t), and (t^5) * e^(3t).

  The given characteristic equation is (r^2 + 2r + 5)^2 * r^3 * (r - 3)^4 = 0. We can break it down into two separate parts: (r^2 + 2r + 5)^2 and r^3 * (r - 3)^4.

For the first part, (r^2 + 2r + 5)^2, we have a repeated root at r = -1 + 2i. This gives us a complex conjugate pair of solutions in the form of e^((-1+2i)t) and e^((-1-2i)t). However, since we are looking for real-valued solutions, we can use Euler's formula to rewrite the complex exponentials as cos((2t) - 1) and sin((2t) - 1). Since the equation has a squared factor, we have two sets of solutions for this part.

For the second part, r^3 * (r - 3)^4, we have a simple root at r = 0 and a repeated root at r = 3. This gives us solutions of e^(3t), t * e^(3t), (t^2) * e^(3t), (t^3) * e^(3t), (t^4) * e^(3t), and (t^5) * e^(3t).

Combining both parts, we have the nine fundamental solutions to the differential equation: e^((-1+2i)t), e^((-1-2i)t), t * e^((-1+2i)t), t * e^((-1-2i)t), (t^2) * e^((-1+2i)t), (t^2) * e^((-1-2i)t), e^(3t), t * e^(3t), (t^2) * e^(3t), (t^3) * e^(3t), (t^4) * e^(3t), and (t^5) * e^(3t).

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the parametric equation for the line is:

x = 1 + 5t

y = -3 + 3t

z = 5 - t

We can write the parametric equation of the line as:

x = 1 + 5t

y = -3 + 3t

z = 5 - t

where t is a parameter.

Note that the direction vector of the line is (5, 3, -1), which is parallel to the given vector 5i + 3j - k. We can see that the x-coordinate changes by 5t, the y-coordinate changes by 3t, and the z-coordinate changes by -t.

Since the line passes through the point (1, -3, 5), we substitute t=0 into the above equations to get:

x = 1

y = -3

z = 5

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Answer:

SP = (100-d%)/100 × MP

ans.12.36

3600 in. is equal to 25 square feet, calculated using two unit multipliers.

To convert 3600 in. to square feet, there are two unit multipliers we can use: 1 ft/12 in and (1 ft/12 in)^2. Here's how to perform the conversion:

Multiply 3600 in. by 1 ft/12 in (the first multiplier) to convert inches to feet:

3600 in. × (1 ft/12 in) = 300 ft

Multiply 300 ft by (1 ft/12 in)^2 (the second multiplier) to convert square feet back to square inches:

300 ft × (1 ft/12 in)^2 = 3600 sq in.

Since you initially had 3600 sq in, which is equivalent to 25 sq ft (because 1 sq ft = 144 sq in), your final answer is:

3600 in. = 25 sq ft

Therefore, 3600 in. is equal to 25 square feet.

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The probability that the household has a dog given that the household has a cat is 37.5%

The probability that the household has a dog given that the household has a cat can be found using Bayes' Theorem.

Applying that, we have P(dog | cat) = P(cat and dog) / P(cat) = (P(cat) * P(dog | cat)) / P(cat) = (0.20 * P(dog | cat)) / 0.20 = P(dog | cat)

P(cat or dog) = P(cat) + P(dog) - P(cat and dog) = 0.45

P(cat and dog) = P(cat) * P(dog | cat) = 0.20 * P(dog | cat)

P(dog) = P(dog or cat) - P(cat) = 0.30

P(cat and dog) = P(dog or cat) - (P(dog) - P(cat and dog)) = 0.45 - (0.30 - P(cat and dog))

P(cat and dog) = 0.45 - 0.30 + P(cat and dog)

P(cat and dog) = 0.15 + P(cat and dog)

2 * P(cat and dog) = 0.15 + 2 * P(cat and dog)

P(cat and dog) = 0.15 / 2

P(dog | cat) = P(cat and dog) / P(cat) = 0.15 / (2 * 0.20) = 0.375

In conclusion, the probability that the household has a dog given that the household has a cat is 37.5%.

The given proposition is "pv ((p +r)^(p +-2)^(p+ -))" and we have to answer the questions.

The truth table of the proposition "pv ((p +r)^(p +-2)^(p+ -))" will have 8 rows as it has 3 atomic statements.

(b) Using logical equivalence rules (NOT a truth table), prove that the proposition is a tautology.

Here is the solution:

pv ((p +r)^(p +-2)^(p+ -))                   //Given Proposition- p v (p + r)   // using A ^ A = A(p + r) ^ p +- 2 ^ p + -   // using A ^ A

= Ap v r               // using distributive property on the first two terms(p + -2) v (p + -)            // using distributive property on the last two terms(p + -2) v T                   // using A + -A = T(p + -2) = T                   // using A V T

= Tp

= T                                   // using A V T = T.

The above equation has a tautology "T" on both sides.

Therefore, the given proposition is a tautology. Here, we have used the following logical equivalence rules:

Distributive law: A ^ (B v C) = (A ^ B) v (A ^ C)A v (B ^ C) = (A v B) ^ (A v C)

Commutative law: A ^ B = B ^ AA v B = B v A

Associative law: A ^ (B ^ C) = (A ^ B) ^ CA v (B v C) = (A v B) v C

Cancellation law: A ^ -A = TA + -A = T

Identity law: A ^ T = AT ^ F = A De

Morgan's law: - (A ^ B) = - A v - B- (A v B) = - A ^ - B

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