What is the solution of √1-3x = x+3 ?


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Step-by-step explanation:

s1 = 5

s2 = s1 × -2 = 5×-2 = -10

s3 = s2 × -2 = -10 × -2 = 20

...

now, we could do all that manually.

but there is also a formula for geometric sequence.

in fact, there are 2 - one for finite and one for infinite sequences.

and I was not completely honest, each of these 2 had some sub-forms depending on the size of the multiplier or ratio.

since we need the sum of the first 5 terms, which of the 2 do you think we need ?

of course, finite, because 5 is a normal number we can "touch". it is not infinity.

so, the formulas for finite sums of geometric sequences are :

if |r| < 1, Sn = a(1 - r^n)/(1 - r)

if |r| > 1, Sn = a(r^n - 1)/(r - 1)

if r = 1, Sn = na

if r = -1, then Sn = a or 0 depending on if n is odd or even.

the sequence is in general

s1 = a

sn = sn-1 × r

in our case a = 5, r = -2.

so, what form of the formula do we need ?

|-2| = 2, and 2 > 1, so ...

S5 = 5(-2^5 ‐ 1)/(-2 - 1) = 5(-32 - 1)/-3 = 5×-33/-3 =

= 5 × 11 = 55

quick check, as the 5 terms are

5

-10

20

-40

80

and their sum is : 55

correct !

Answer:

D

The numbers are already in order so you don't need to do anything

Answer:

its b for me but d for yall

Step-by-step explanation:

all you do is count up hope this helps can u mark me brainlest

The scale factor is: 1.8

because of :

\(\frac{36}{20}=1.8\\ \\\\\frac{25.2}{14}=1.8\)

Answer: 5.8%

Step-by-step explanation: .

The surface area of a cylinder with circular bases of radius r and height h is equal to the sum of the areas of the two circular faces and the area of the rectangular lateral surface:

A = 2πr² + 2πrh

If you know the height h, then you can solve the quadratic equation for r.

Answer:

90%

Step-by-step explanation:

100%=120 pupils

           108pupils

 108 x 100= 10800/120=90 %

Answer:

Hello! After reading your question I have deduced that the correct answer is 288² cm.

Step-by-step explanation:

The way I came to this conclusion was as follows:

Firstly:

If said rectangle is two squares put side by side (adjacent), then a valid assumption is that both squares are the same size.

This is because all four sides of a square have to be equal.

Thus if the two squares are joined together on one side, then all the other sides of both the squares will be the same length.

Thus both of the squares are going to be the same size, so they will have the same area.

Secondly:

If the area of one square is 144² cm then the area of the other square should also be 144² cm.

Thus if you combine the areas of both the squares, that make up the rectangle, you are left with the area of the rectangle being 288² cm.

I hope this helped!

The probability that the technician arrives exactly at 4:00 pm is 1/5.

Probability is the chance of occurring a certain event out of the total no. of events that can occur in a given context. The probability of an event is always greater than equal to zero and less than equal to one.

If we distribute arrival time uniformly in terms of hours the no. of sample space N(s) = 5.     (3:00pm, 4:00pm, 5:00pm, 6:00pm, 7:00pm).

∴ The probability that he arrives exactly at 4:00 pm is,

= 1/5.

The probability of arriving at 4:00 pm is 1/5.

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Answer:

105

Step-by-step explanation:

Answer:

105.5 or 105 1/2

Step-by-step explanation:

3165/3000 = 1.055

1055* 100 = 105.5 or 105 1/2

Answer:

A line that is parallel to y = 3x - 9 will have the same slope as the given line. The slope of y = 3x - 9 is 3. Therefore, the equation of the line that passes through (1, 2) and is parallel to y = 3x - 9 is:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the point (1, 2)

Substituting the values we get:

y - 2 = 3(x - 1)

Simplifying the equation we get:

y - 2 = 3x - 3

y = 3x - 1

Therefore, the equation of the line that passes through (1, 2) and is parallel to y = 3x - 9 is y = 3x - 1 .

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Answer:

648

Step-by-step explanation:

8x3x3x3x3=8x81=648

The theoretical probability of exactly 4 students from your school being selected as contestants out of 10 possible contestant spots is approximately 0.009.

Assuming that each member of the audience has an equal chance of being selected as a contestant, the total number of possible ways to select 10 contestants from the audience is:

\(150 $ choose 10 = 150! / (10! \times (150 - 10)!) = 2,535,316,699,000\)

To calculate the probability of exactly 4 students from your school being selected as contestants, we need to count the number of ways this can happen and divide it by the total number of possible outcomes.

There are 30 students from your school and 120 students from other schools in the audience.

We need to choose 4 students from your school and 6 students from other schools for the contestant spots.

The number of ways to do this is:

\(30 $ choose 4 \times 120 $ choose 6 = (30! / (4! \times 26!)) \times (120! / (6! \times 114!)) = 23,400,140,040,000\)

Therefore, the probability of exactly 4 students from your school being selected as contestants is:

P(4 students selected) = (number of ways to select 4 students from your school and 6 students from other schools) / (total number of ways to select 10 contestants from the audience)

P(4 students selected) = 23,400,140,040,000 / 2,535,316,699,000.

P(4 students selected) ≈ 0.00923 (rounded to 3 decimal places).

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True for x is equal to 1 and 0 (Sometimes True)

\(( {x}^{a} )( {x}^{b} ) = {x}^{ab} \)

True for x greater than or equal to 0 (Sometimes True)

\( { \sqrt{x} }^{2} = x\)

Always True

\( { \sqrt{x} }^{ 3 } = \sqrt{ {x}^{3} } \)

True for x does not equal 0 (Sometimes True)

\( \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ \)

Never True

\( {x}^{0} = 0\)

True for x is equal to 0 (Sometimes True)

\( {x}^{2} + {x}^{2} = {x}^{4} \)

Answer:

-3268.72

Step-by-step explanation:

Answer:

I got -3268.72

The taxi ride was 7 miles

Mia took a taxi from her house to the airport

The taxi charged a pick up fee of $1.30

They also charged $4.25 per mile

The total fare was $31.05

The number of miles can be calculated as follows

31.05 - 1.30 = 4.25x

29.75= 4.25x

Divide both sides by the coefficient of x which is 4.25

29.75/4.25= 4.25x/4.25

x= 7

Hence the taxi ride was 7 miles

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Answer:

Step-by-step explanation:

Let the length be 9x, then the width is 4x

perimeter = 2(9x + 4x) = 2(13x) = 26x = 78, so x = 78/26 = 3

So

the length = 9x = 9(3) = 27 mm

the width = 4x = 4*3 = 12 mm.

Answer:

f^-1(0) = 4

Step-by-step explanation:

slope = -1/2 => y = -1/2x + 2

=> 1/2x = 2 - y

=> x = -2y + 4

=> f^-1(x) = -2x + 4

f^-1(0) = 4

The temperature at the bottom of the mountain is 50.9 °C.

Let's work through the given information step by step to find the temperature at the bottom of the mountain.

The temperature in the hotel is 21 °C.

The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.

Let's denote the temperature at the top of the mountain as T_top.

So, the temperature in the hotel can be expressed as T_top + 26.7 °C.

The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.

Let's denote the temperature at the bottom of the mountain as T_bottom.

So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.

Now, let's combine the information we have:

T_top + 26.7 °C = T_bottom - 3.2 °C

To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:

T_bottom = T_top + 26.7 °C + 3.2 °C

T_bottom = T_top + 29.9 °C

Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:

T_bottom = 21 °C + 29.9 °C

T_bottom = 50.9 °C

Therefore, the temperature at the bottom of the mountain is 50.9 °C.

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Answer:

median: 3

mode: 2 (appeared 4 times)

range: 13

Step-by-step explanation:

Answer:

tjrjrkrkrkrkurjrjrjrjrnr s jkalsmrnrnd

Answer:

The rate of change for A is 4. For B, it is 2

Step-by-step explanation:

the slope of A is 4 and for B it is 2. Slope is the same as rate of change.

Each of the five friends needs to pay £14.40 to cover the cost of the birthday person's meal.

To calculate how much each of the five friends needs to pay, we can use the concept of averages or mean.

The total cost of the meal for 6 people is £12 per person. This means that the total cost of the meal is 6 * £12 = £72.

Since the other five friends have decided to pay for the birthday person's meal, they will evenly divide the total cost of £72 among themselves.

To find the average amount each friend needs to pay, we divide the total cost by the number of friends paying, which is 5:

£72 / 5 = £14.40

Using the concept of averaging or finding the mean allows us to distribute the cost equally among the friends, ensuring fairness in sharing the expenses.

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Answer:

8 years is around 2,920 days

Step-by-step explanation:

Answer: 2920 days

Step-by-step explanation:

1 year = 365 days

8 years = ?

8 years x 365 days = 2920 days

Answer:

Step-by-step explanation:

25 + 14 / (5-3)

25 + 14 / 2

25 + 7

32

The scale factor and the value of x for each figure is given as follows:

A) Scale factor of 1/3, x = 7 m.

B) Scale factor 0.4747, x = 4.5 in.

For Figure A, we have that the ratio between the areas is given as follows:

510/4590 = 1/9.

As the area is measured in square units, while the side lengths are measured in units, the scale factor is the square root of 1/9, hence it is given as follows:

1/3.

Then the value of x is obtained as follows:

x = 21 x 1/3

x = 7 m.

For Figure B, we have that the ratio between the areas is given as follows:

16/71 = 0.22535.

The scale factor is then the square root of 0.22535, which is given as follows:

0.4747.

Then the value of x is given as follows:

x = 9.5 x 0.4747

x = 4.5 in.

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762/3=254... therefore, 762-254=508

So your fourth integer is 508

The probability that:

First, check if it is appropriate to use the normal approximation to the binomial distribution. The rule of thumb is that this approximation is reasonable if both np and n(1-p) are greater than 5. In this case, p = 0.83 (probability of failure), n = 70 (number of trials).

So,

np = 700.83 = 58.1,

n(1-p) = 700.17 = 11.9.

Both quantities are larger than 5, so use the normal approximation.

Convert this to a problem involving a normal distribution. The mean of this distribution is np = 58.1 and the standard deviation is √(np(1-p)) = √(700.830.17) = 6.35.

(a) within 2 years 47 or more fall:

This corresponds to a Z-score of (47.5 - 58.1) / 6.35 = -1.67. The probability that a standard normal variable is greater than -1.67 is 0.9525.

So the probability that 47 or more products fail is approximately 0.9525.

(b) within 2 years 58 or fewer fail:

This corresponds to a Z-score of (58.5 - 58.1) / 6.35 = 0.063. The probability that a standard normal variable is less than 0.063 is 0.5250.

So the probability that 58 or fewer products fail is approximately 0.5250.

(c) within 2 years 15 or more succeed:

Since the probability of success is 1-p, this is equivalent to fewer than (70 - 15 = 55) failing. This corresponds to a Z-score of (54.5 - 58.1) / 6.35 = -0.567.

The probability that a standard normal variable is greater than -0.567 is 0.7151.

So the probability that 15 or more products succeed is approximately 0.7151.

(d) within 2 years fewer than 10 succeed:

This is equivalent to more than (70 - 10 = 60) failing. This corresponds to a Z-score of (60.5 - 58.1) / 6.35 = 0.377.

The probability that a standard normal variable is less than 0.377 is 0.6478.

However, since we want more than 60 failing, the probability that the variable is greater than 0.377, which is 1 - 0.6478 = 0.3522.

So the probability that fewer than 10 products succeed is approximately 0.3522.

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Answer:

it is 500

Step-by-step explanation:

Answer:

153

Step-by-step explanation:

Step-by-step explanation:

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Answer:

New: $44,840 Original: 47,200

Step-by-step explanation:

You have to multiply 47,200 by 95% or 0.95