Identify the first term and common difference, then write
a recursive rule for each of the sequences below:
a) 1, -4,-9, -14, ....
b) 11, 23, 35, 47, ....

The  product of 3∛6 and 2∛6 is equals to 18.

What is underroot ?

In mathematics, the symbol "√" is called the radical symbol, and the expression written under it is called a radicand.

To simplify 3∛6, we can use the fact that the cube root of a number can be written as a power of that number with an exponent of 1/3. Therefore, 3∛6 can be rewritten as 6^(1/3) raised to the power of 3.

D) To add 3∛6 and 2∛6, we can first factor out the common term of ∛6:

3∛6 + 2∛6 = (3 + 2)∛6 = 5∛6

So the sum of 3∛6 and 2∛6 is 5∛6.

E) To subtract 2∛6 from 4∛6, we can again factor out the common term of ∛6:

4∛6 - 2∛6 = (4 - 2)∛6 = 2∛6

So the difference between 4∛6 and 2∛6 is 2∛6.

F) To multiply 3∛6 by 2∛6, we can use the fact that the product of two roots with the same index can be found by multiplying the radicands together:

3∛6 x 2∛6 = (3 x 2)∛(6 x 6) = 6∛36

Since the cube root of 36 is 3 (3 x 3 x 3 = 27 and 4 x 4 x 4 = 64), we can simplify this further:

6∛36 = 6 x 3 = 18

Therefore, the product of 3∛6 and 2∛6 is equals to 18.

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The conclusion which can be drawn from the data is that for the 10 weeks, City A received more rainfall, on average, than City B. The Option A is correct.

From the data, we can calculate the average (mean) rainfall for each city over the 10 weeks.

The average rainfall for City A is:

= (0.2+0+1.5+1.3+2.5+3+0.4+0.3+0.2+1) / 10

= 1.04 inches per week.

The average rainfall for City B is:

= (0+0+0.4+0.2+0.3+1+1+1+0.1+0.1) / 10

= 0.41 inches per week.

We can see that for the 10 weeks, City A received more rainfall, on average, than City B..

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Answer:

GCF 2(12) + 3(12)

Distributive property 24 + 32 = 2(12) + 3(12) = (2 + 3)(12) = 5(12)

Step-by-step explanation:

By making and solving the respective equation x + 4x + 3 = 63, we can conclude that the age of Adam is 12 years.

According to a mathematical equation, two amounts or values are equivalent to a meaningful term, for example, 6 x 4 = 12 x 2.

When two or more factors must be taken into account together in order to comprehend or describe the entire situation, an equation is used.

So, we know that:

Jeff is 3 years older than four times of Adam.

Now, let Adam be x and Jeff be 4x + 3.

Then, the equation will be:

x + 4x + 3 = 63

5x + 3 = 63

5x = 63 - 3

5x = 60

x = 60/5

x = 12

Adam: = x = 12 years

Therefore, by making and solving the respective equation x + 4x + 3 = 63, we can conclude that the age of Adam is 12 years.

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Answer:

60 minutes

Step-by-step explanation:

we can see that the number of minutes increases by 8 each day

(12 + 8 = 20, 20 + 8 = 28, 28 + 8 = 36...)

So, because we have the value for the previous day (day 6) we know that we can simply add 8

52 + 8 = 60

So, the predicted number of minutes for day 7 is 60

hope this helps!!

Answer:

Given:

To Find:

Solution:

★ Firstly, we have to find the amount:

According, to the question by using the formula, we get:

\( \longmapsto \: { \bold{ \boxed{\pink{ \rm{A \: = P \left( 1 + \frac{ \frac{r}{2} }{100} \right)^{2n} }}}}}\)

Here,

So by putting their values, we get:

\( { \large{\longrightarrow{ \rm{A = 5000 \left( 1 + \frac{ \frac{10}{2} }{100} \right)^{2 \times 2} }}}}\)

\( { \large{ \longrightarrow{ \rm{A = 5000 \left( 1 + \frac{10}{2} \times \frac{1}{100} \right)^{4} }}}}\)

\( {\large{ \longrightarrow{ \rm{A = 5000 \left( 1 + \frac{10 \times 1}{2 \times 100} \right)^{4} }}}}\)

\({ \large{ \longrightarrow{ \rm{A = 5000 \left(1 + \frac{10}{200} \right)^{4} }}}}\)

\({ \large \longrightarrow {\rm{A =5000 \left( \frac{200 \times 1 + 10}{200} \right)^{4} }}}\)

\({ \large \longrightarrow{ \rm{A = 5000 \left( \frac{200 + 10}{200} \right)^{4} }}}\)

\({ \large{ \longrightarrow{ \rm{A = 5000 \left( \frac{210}{200} \right)^{4} }}}}\)

\({ \large{ \longrightarrow{ \rm{A = 5000 \left( \frac{210}{200} \times \frac{210}{200} \times \frac{210}{200} \times \frac{210}{200} \right)}}}}\)

\({ \large{ \longrightarrow{ \rm{A = 5000 \left( \frac{210 \times 210 \times 210 \times 210}{200 \times 200 \times 200 \times 200} \right)}}}}\)

\({ \large{ \longrightarrow{ \rm{A = 5000 \left( \frac{1944810000}{1600000000} \right)}}}}\)

\({ \large{ \longrightarrow{ \rm{A = 5000 \times \frac{1944810000}{1600000000} }}}}\)

\({ \large{ \longrightarrow{ \rm{A = 5000 \times \frac{194481}{160000} }}}}\)

\({ \large{ \longrightarrow{ \rm{A = 5 \times \frac{194481}{160} }}}}\)

\({ \large{ \longrightarrow{ \rm{A = \frac{972405}{160} }}}}\)

\({ \large{ \longrightarrow{ \rm{A = 6077.53 \: (approx.)}}}}\)

Hence, the amount is Rs 6078.

★ Now, we have to find the compound Interest:

According, to the question by using the formula, we get:

\({ \large{ \dashrightarrow{ \boxed{\green{ \rm{Compound \: Interest = A \: - \: P}}}}}}\)

Here,

So, by putting their values we get:-

\( { \large{ \dashrightarrow{ \rm{Compound \: Interest = Rs \: 6078 \: - \: Rs \: 5000}}}}\)

\({ \large{ \dashrightarrow{ \rm{Compound \: Interest = Rs \: 1078}}}}\)

Hence, Compound Interest is Rs 1078.

X=pi/2 only in the interval 0 to 4 . We have the maximum value of f(x) = sinx = 1

What is  function interval ?

If the value of the function f (x) grows with an increase in the value of x, the function interval is said to be positive.

                         The function interval, on the other hand, is said to be negative if the value of the function f (x) decreases as the value of x increases.

First of all to apply the extreme value theorem function must be countions at the interval 0 to 4.

F(x)=(x^2-16)/(x^2+x-20) is countinious int the given interval .

Now we find

F'(x)= d(F(x))/dx=1/(x+5)^2 so here we don't have in critical point therefore this choice is incorrect

Similarly if we take

F(x)= sinx

F'(x) = cosx

For critical point ,

Cosx =0

X=pi/2 only in the interval 0 to 4

And this point we have the maximum value of f(x) = sinx = 1

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Answer:

a)

sin30=high of steps/175

sin30=1/2

so

high of steps= 175/2

high of steps=87.5cm

b)

cos30=wide/175

cos30=3^1/2÷2

wide=175*3^1/2÷2

3^1/2=1.73

so

wide=175*1.73/2

wide=151.37

Answer:

1.6667 meters per minute

Step-by-step explanation:

To convert meters per second into meters per minute, let's first think about the difference between seconds and minutes.

There are 60 seconds in one minute, so to find our meters per minute speed, we will divide the distance by 60.

100 / 60 = 1.6667 meters per minute

Hope this helped!

Answer:

it is d my guy :)

Step-by-step explanation:

The concept of statistical significance is mathematically defined and widely accepted by those who use it to assess the usefulness of scientific claims.

However, there is no single definition for practical significance. It is subjective in nature, experiential, and each person decides what it is based on their own experiences.

Thus, it is clear that while Practical significance lacks a common definition, statistical significance has a mathematical definition and is widely accepted by those who use it to assess the usefulness of scientific claims. It is a subjective concept that each person decides for themselves based on their personal experiences.

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We assume that the population standard deviation are known, the samples from each population are independent, the population is normally distributed if we use t test of two samples.

Given T test of significance has been used.

T test is a statistical test that is like z test. Z test is used when n>30 and t test is used when n<30. It is used in hypothesis testing.

We know that there are many test which can be used to test a hypothesis.

The requirements to perform a two sample t procedure are as follows:

1)The two samples have equal variance. Hence the variance should be known.

2) The samples for which the two sample t procedure is performed must be independent.

3) The data are in alignment with the normal distribution probability.

4) The sample are random samples taken from different respective population.

Hence when two sample t procedure is performed we have to assume population standard deviation is known and population is normally distributed.

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Step-by-step explanation:

78+x=180 and x=102

50+52+x=180

102+x=180

x=180-102

x=78

The distance of the boat from its starting point is 156.226 .

According to the question

A boat sails on a bearing of 63 degree for 124 miles

i.e

By making 63 degree covers 124 miles

therefore ,

In figure below

AC = 124 miles

Then turns and sails 201 miles on a bearing of 192 degree

therefore ,

In figure below

CD = 201 miles  

Now,

According to the sum of triangle

∠ACB + ∠ABC + ∠BAC = 180°

∠ACB + 90° + 63° = 180°

∠ACB = 27°

CE = 180°  (Straight line )

therefore,

∠DCE = 192°  -  180°

          = 12°

As ∠C = 90°

therefore

∠ACD = ∠C - ∠DCE - ∠ACB

          = 90° - 12°- 27 °

          = 51°

Now,

The distance of the boat from its starting point = AD

By using Law of Cosines

As

The Law of Cosines can be used to find the unknown parts of an oblique triangle(non-right triangle), such that either the lengths of two sides and the measure of the included angle is known (SAS) or the lengths of the three sides (SSS) are given.

The Law of Cosines (also called the Cosine Rule) says:

c² = a² + b² − 2ab cos(C)

As we have 2 sides and one angle available we can use   Law of Cosines

Therefore,

by substituting the value

(AD)² = (AC)² + (CD)² − 2(AC)(CD) cos(∠ACD)

(AD)² = (124)² + (201)² − 2*124*201 cos(51)

AD = 156.226

Hence, the distance of the boat from its starting point is 156.226 .

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Answer:

Step-by-step explanation:

Step: 1

-Graph the 6x: It will start at (0,0) and will have a rise of 6 and a run of 1

Step: 2

-Graph the 90: From what I understand it should be a horizontal line with its point on 90y

Sorry if this doesn't help very late where I am.

Answer:

Point A' should be 2 units left and 8 units above of Point C.

Point B' should be 10 units right and above Point C.

Point C stays the same.

In the initial list, there were 4 integers.

We have the following system if the mean is m, x is the list's initial sum, and n is the number of integers in the list:

m = x/n , m + 2 = (x + 15) / (n + 1) and m + 1 = (x + 16) / (n + 2).

The initial equation is x = mn.

Therefore, changing x in the other two equations:

m + 2 = (mn + 15) / (n + 1) ..............(1)

m + 1 = (mn + 16) / (n + 2)...............(2)

Based on equation (1):

(m + 2)(n + 1) =  mn + 15

mn + m + 2n + 2 = mn + 15

m + 2n + 2  = 15

m + 2n = 13

m = 13 - 2n.

Now change m in equation (2) to:

13 - 2n + 1 = ( n(13 - 2n) + 16) / (n + 2)

14 - 2n = (13n - 2n^2 + 16) / (n + 2)   Through-multiplication by n + 2:

(14 - 2n)(n + 2) =  13n - 2n^2 + 16

14n + 28 - 2n^2 - 4n =  13n - 2n^2 + 16

10n + 28 = 13n + 16

12 = 3n

n = 4.

Hence, there were 4 integers in the original list.

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Answer: The product of 7(-3) = -21

Step-by-step explanation:

The first step is to know what 7 × 3 is. We know that 7 × 3 = 21. When we multiply a negative number by a positive number, the product is a negative number. Therefore 7(-3) = -21

I hope I helped and have a great day! ^-^

If one item is chosen from m items, a second item is chosen from n items, and a third item is chosen from p items, the total number of three-item choices is MNP.

Probability  can be regarded as a  measure of the likelihood of an event  that can take place.

It should be noted that  Many events cannot be predicted with total certainty, hence , If one item is chosen from m items, a second item is chosen from n items, and a third item is chosen from p items, the total number of three-item choices is MNP.

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Answer:

1/7

Step-by-step explanation:

It's the only option that doesn't give a whole number

We then substitute -1 for x in the equation x + y = 4 to get -1 + y = 4, which we can then subtract -1 from both sides to get y = 5. The solution is x = -1 and y = 5.

3x + y = 7

-x + y = 1

Add the equations together:

2x + 2y = 8

Divide both sides by 2:

x + y = 4

Subtract the second equation from the first:

-x + y = 1

x - y = -3

Add the equations together:

2x = -2

Divide both sides by 2:

x = -1

Substitute -1 for x in the equation x + y = 4:

-1 + y = 4

Subtract -1 from both sides:

y = 5

The solution is x = -1 and y = 5.

We begin by solving the system of linear equations by elimination. We need to get the variables to one side of the equation and the constants to the other side. We start by adding the two equations together: 3x + y = 7 and -x + y = 1. This gives us 2x + 2y = 8, which we can then divide both sides by 2 to get x + y = 4. We then subtract the second equation from the first to get -x + y = 1 and x - y = -3. We then add these two equations together to get 2x = -2 and divide both sides by 2 to get x = -1. We then substitute -1 for x in the equation x + y = 4 to get -1 + y = 4, which we can then subtract -1 from both sides to get y = 5. The solution is x = -1 and y = 5.

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The coordinates of B are (r, 0).

In a rectangle, opposite sides are parallel and equal in length. Since A and D are on the bottom line, and B and C are on the top line with B over A, the height of the rectangle remains constant. Therefore, the y-coordinate of B is the same as the y-coordinate of A, which is 0.

The x-coordinate of B is the same as the x-coordinate of C, which is r. Therefore, the coordinates of B are (r, 0).

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Answer:

got u

Step-by-step explanation:

Numbers can be ordered in ascending or descending order.

The length of fishes from greatest to least is

Given

\(Emma = 12.7\)

\(Anne = 12 \frac 35\)

\(Emily = 12 \frac 34\)

Convert all fractions to decimals

\(Emma = 12.7\)

\(Anne = 12.6\)

\(Emily = 12.75\)

Arrange from greatest to least

\(Emily = 12.75\)

\(Emma = 12.7\)

\(Anne = 12.6\)

Hence, the length of fishes from greatest to least is

\(Emily = 12 \frac 34\)     \(Emma = 12.7\)       \(Anne = 12 \frac 35\)

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Answer

A $15

Step-by-step explanation: Babyton my name

The statement that, If the value of the sum of squares due to regression (SSR) can never be larger than the value of the sum of squares total (SST)  is True.

To explain this, let's define both terms:

1. Sum of squares due to regression (SSR): This represents the variation in the dependent variable that is explained by the independent variable(s) in the regression model.

2. Sum of squares total (SST): This represents the total variation in the dependent variable, without considering any explanatory variables.

Now, let's consider their relationship.

The total variation in the dependent variable (SST) can be decomposed into two components: the variation explained by the regression model (SSR) and the unexplained variation, which is the sum of squares due to error (SSE).

In other words:

SST = SSR + SSE

Since SSE represents the unexplained variation and is always non-negative, SSR can never be larger than SST. This confirms that the statement is True.

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The plane is 354.7 miles from its original position. Rounded to the nearest tenth, the answer is D. 354.7.

Given that;

An aeroplane travels 160 miles on a heading of N 33°W.

To determine the distance of the plane from its original position, use the concept of vector addition.

Let's break down the motion of the plane into its north and west components.

For the first leg of the journey, travelling 160 miles on a heading of N 33°W, we can find the north and west components using trigonometry.

The north component is given by,

160 sin(33°) ≈ 86.3 miles

And the west component is given by 160 cos(33°) ≈ 134.7 miles.

For the second leg of the journey, travelling 205 miles on a heading of N 49°W, we can find the north and west components in a similar manner.

The north component is given by,

205 sin(49°) ≈ 154.9 miles

The west component is given by,

205 cos(49°) ≈ 134.9 miles.

Now, to find the total north and west components, we add the north and west components from both legs.

The total north component is,

86.3 + 154.9 ≈ 241.2 miles

And the total west component is,

134.7 + 134.9 ≈ 269.6 miles.

Using the Pythagorean theorem the magnitude of the resultant vector (distance from the original position) by taking the square root of the sum of the squares of the north and west components.

The magnitude is,

√((241.2)² + (269.6)²) ≈ 354.7 miles.

Therefore, the plane is 354.7 miles from its original position. Rounded to the nearest tenth, the answer is D. 354.7.

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This problem is solved by vector addition and trigonometry. Using the cosine rule, with the legs of the flight as vectors and the difference between the flight headings as the angle, the distance from the original position is calculated to be approximately 361.5 miles.

This is a problem of vector addition and trigonometry. We can use the cosine rule to solve this. The Cosine Rule, also known as the Law of Cosines, describes the relationship between the lengths of the sides of a triangle and the cosine of one of its angles. In the case of the airplane, the two vectors are the two legs of the flight, and the angle between them is determined by the difference between the flight headings.

Here is how you can apply that:

So the correct answer would be B. 361.5 miles.

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The value of ∠s is equal to 93.4°.

Using the Law of Cosines, we can find the length of the side opposite angle r:

rs² = sq² + qr² - 2(sq)(qr)cos(r)

rs² = (5.1)² + (2.9)² - 2(5.1)(2.9)cos(135°)

rs ≈ 5.3 cm

Next, we can use the Law of Sines to find angle s:

sin(s)/5.3 = sin(135°)/2.9

sin(s) ≈ 0.308

s ≈ 18.1° or s ≈ 161.9°

Since s is an angle in a triangle, it must be acute, so the answer is ∠s = 93.4° (to the nearest 10th of a degree).

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Answer:

C) 2

Step-by-step explanation:

14 = 4x + 6

14 - 6 = 4x

8 = 4x

8/4 = x

2 = x