find the missing number in the sequence

- 5, -1, 3​

The sequence is 3, 9, 15, 21, 27, and the recursive formula for this sequence is a_1 = 3, a_n = a_{n-1} + 6, and the next term is 33.

The sequence is an arithmetic sequence with a common difference of 6, starting at 3. A recursive formula for this sequence can be written as:

a_1 = 3

a_n = a_{n-1} + 6, for n > 1

This formula means that the first term in the sequence is 3, and every subsequent term is found by adding 6 to the previous term.

To find the next term in the sequence, we can use this formula to compute a_6:

a_6 = a_5 + 6

a_6 = 27 + 6

a_6 = 33

Therefore, the next term in the sequence is 33.

The given sequence is an arithmetic sequence, where each term is 6 more than the previous term, starting at 3.

A recursive formula is a mathematical formula that is used to define a sequence in terms of its previous terms. In this case, we can use the recursive formula a_1 = 3 and a_n = a_{n-1} + 6 to define the given sequence. The formula says that the first term in the sequence is 3, and each subsequent term can be found by adding 6 to the previous term.

Using this recursive formula, we can find the next term in the sequence, which is 33. We can continue to apply the formula to find any term in the sequence.

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Mode: The mode of this data is 8 hours. This is because 8 hours was the most frequently reported amount of time that the students watched TV during a school week.

Amount is a quantitative expression of magnitude, size, or degree of a particular quantity. It is typically used to describe an object, person, or an event. Amount is used to quantify something, to describe its size, duration, or extent. It can be used to measure a wide range of physical and abstract entities, such as money, time, energy, resources, and emotions. For example, you might say “there was a large amount of people at the event” or “I have a certain amount of money saved up.”

Range: The range of this data is 8 hours. This is because the difference between the highest amount of time reported (16 hours) and the lowest amount of time reported (8 hours) is 8 hours.

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At the 1% level of significance, both the number of security guards (g) and the unemployment rate (u) have a significant effect on the dollar loss from theft each week (t). This is indicated by the p-values for both variables, which are both less than 0.01 (0.0012 for g and 0.0096 for u).

This means that there is less than a 1% chance that the observed relationship between these variables and the dependent variable (t) is due to chance. Therefore, we can reject the null hypothesis that there is no relationship between these variables and the dependent variable, and conclude that they have a significant effect on the dollar loss from theft each week.

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You would need to deposit approximately $47.83 now to be able to withdraw $650 at the end of each year for 20 years, assuming an annual interest rate of 11% compounded annually.

It is typically expressed as an annual percentage rate (APR). Interest rates can be fixed, meaning they remain the same for the entire term of the loan, or variable, meaning they can change over time based on market conditions or other factors. The interest rate is an important factor to consider when borrowing money, as it affects the overall cost of the loan. It is also a key factor in investment decisions, as it determines the return on an investment.

To calculate the present value of an investment that will yield a future value of $650 for 20 years at 11% annual interest, we can use the formula for present value of an annuity:

PV = FV / (1 + r)ⁿ

where PV is the present value, FV is the future value, r is the interest rate per period, and n is the number of periods.

In this case, we want to find the present value of a 20-year annuity that pays $650 at the end of each year, with an annual interest rate of 11%. Plugging in the values, we get:

PV = $650 / (1 + 0.11)²⁰

PV = $650 / 13.584

PV = $47.83 (rounded to the nearest cent)

Therefore, you would need to deposit approximately $47.83 now to be able to withdraw $650 at the end of each year for 20 years, assuming an annual interest rate of 11% compounded annually.

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Check the picture below.

Make sure your calculator is in Degree mode.

[tex]\tan(43^o )=\cfrac{\stackrel{opposite}{4.1}}{\underset{adjacent}{x}}\implies x=\cfrac{4.1}{\tan(43^o )}\implies x\approx 4.4[/tex]

Using a trigonometric relation we can see that x = 4.4 units.

Here we can see a right triangle, where we can see that 4.1 is one of the legs, and x is the other leg.

We also can see that the angle adjacent to x is 43°.

Then we can use the trigonometric relation to find the value of x:

tan(43°) = 4.1/x

Solving for x:

x = 4.1/tan(43°)

x = 4.4

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Given:

Vince has 1/2 ton of gravel.

It is to be spread equally in 8 square yards.

To find:

How many tons of gravel will be spread in each square yard?

Solution:

Total gravel = 1/2 ton

To be spread equally in 8 square yards.

No. of tons of gravel will be spread in each square yard = (1/2) / 8 = 1/16 tons.

Therefore, 1/16 tons of gravel will be spread in each square yard.

Answer:

Given:

Vince has 1/2 ton of gravel.

It is to be spread equally in 8 square yards.

To find:

How many tons of gravel will be spread in each square yard?

Solution:

Total gravel = 1/2 ton

To be spread equally in 8 square yards.

No. of tons of gravel will be spread in each square yard = (1/2) / 8 = 1/16 tons.

Therefore, 1/16 tons of gravel will be spread in each square yard.

Step-by-step explanation:

Answer: 8

Step-by-step explanation:

Using SOHCAHTOA, we need TOA as we have the opposite (1) and the adjacent (7)

θ = [tex]tan^{-1}(\frac{1}{7} )[/tex] = 8.13 = 8

I disagree with Brian's assertion that there is less fluctuation in the number of mystery novels simply because the mean number of mystery books is fewer than the mean number of adventure books.

The mean is merely one measure of central tendency and provides no information about the data's dispersion or variability. We would need to look at a measure of dispersion such as the range, variance, or standard deviation to see whether there is less variety in the quantity of mystery novels. If the range or standard deviation of the number of mystery books is less than that of adventure novels, we may claim that the number of mystery books is less variable. If, however, the If the range or standard deviation of the number of mystery novels is greater than that of adventure books, Brian's statement is false. As a result, we cannot establish whether or not there is less fluctuation in the quantity of mystery novels without knowing the dispersion of the data.

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First vector v = [- 2 - 2 2] is in W and the second vector v = [6 - 1 - 3] is not in W.

W be the set of all vectors [x y x + y] with x and y real. To find: Whether each of the following vectors is in W. Let's check each vector whether it is in W or not: v = [- 2 - 2 2] To check the given vector is in W or not, we need to find the values of x and y such that the third component equals 2.So, x + y = 2 ⇒ y = 2 - x

The given vector can be written as v = [x y x + y]= [x, 2 - x, 2] Thus, given vector v is in W. v = [6 - 1 - 3]. To check the given vector is in W or not, we need to find the values of x and y such that the third component equals -3. So, x + y = -3 ⇒ y = -3 - x The given vector can be written as v = [x y x + y]= [x, -3 - x, -3]Thus, given vector v is not in W.

Moreover, Vectors, in Maths, are objects which have both, magnitude and direction. Magnitude defines the size of the vector. It is represented by a line with an arrow, where the length of the line is the magnitude of the vector and the arrow shows the direction.

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Answer:

First, let's simplify both sums by combining like terms:

3x + 5y - 2 + 2x - 3y + 1 = 5x + 2y - 1

4x - 8y + 3 - 5x + 6y + 7 = -x - 2y + 10

Now we can subtract the second sum from the first:

(5x + 2y - 1) - (-x - 2y + 10) = 5x + 2y - 1 + x + 2y - 10

Simplifying this expression, we get: 6x + 4y - 11

The length of the ramp is approximately 16 meters.

Trigonometric ratios are ratios of the sides of a right triangle that relate the angles of the triangle to its sides.

There are 3 basic trigonometric ratios are given by

sin θ = opposite side /hypotenuse.

cos θ = adjacent side /hypotenuse.

tan θ  = opposite side /adjacent.

Here we have

The angle of the incline of the ramp is 32 degrees.

The height of the ramp is 10m.

Represent the following data as a right-angled triangle  

where the height of the ramp will be opposite side to the angle of the incline and the length of the ramp will be adjacent side

Let's assume the length of the ramp is "x".  

From the trigonometric ratios,

tan(32°) = 10/x

Multiply both sides by x:

x × tan(32°) = 10

Divide both sides by tan(32°):

x = 10 / tan(32°)

x = 10/0.62

x = 16.0033 meters

x = 16 meters

Therefore,

The length of the ramp is approximately 16 meters.

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Answer:

34

Step-by-step explanation:

In all right triangles, the two shortest sides squared equals the longest side squared, given by the equation [tex]a^2+b^2=c^2[/tex].

We know the two shortest sides, so we can plug in

[tex]16^2+30^2=c^2\\256+900=c^2\\1156=c^2\\c=\sqrt{1156} \\c=34[/tex]

Answer:

The zeros of the polynomial function f(x) = x^4 - 2x^3 - 8x^2 + 10x + 15 are x = -1, x = 3 + √29/2, x = 3 - √29/2, and x = -0.4495 (approximately).

Step-by-step explanation:

To find all the zeros of the polynomial function f(x) = x^4 - 2x^3 - 8x^2 + 10x + 15, we can use the Rational Root Theorem and synthetic division.

Write the polynomial function in descending order of degree: f(x) = x^4 - 2x^3 - 8x^2 + 10x + 15.

Use the Rational Root Theorem to generate a list of possible rational zeros: ±1, ±3, ±5, ±15.

Use synthetic division to test each possible zero. We start with x = 1:

1 │ 1 -2 -8 10 15

│ 1 -1 -9 1

└───────────────

1 -1 -9 1 16

x = 1 is not a zero of the polynomial function.

We continue testing the remaining possible zeros:

-1 │ 1 -2 -8 10 15

│ -1 3 5 -15

└───────────────

1 -3 -3 15 0

Since the remainder is zero, we have found a zero of the polynomial function at x = -1.

We can use synthetic division to factor the polynomial function:

(x + 1)(x^3 - 3x^2 - 6x + 15)

Now we can solve for the remaining zeros of the polynomial function by factoring the cubic equation using the Rational Root Theorem and synthetic division:

3 │ 1 -3 -6 15

│ 3 0 -18

└─────────────

1 0 -6 -3

x = 3 is not a zero of the polynomial function.

-3 │ 1 -3 -6 15

│ -3 18 -36

└────────────

1 -6 12 -21

x = -3 is not a zero of the polynomial function.

The only remaining possible rational zeros are ±1/2 and ±5/2, but testing these values using synthetic division does not yield any more zeros.

However, we can see that the polynomial function can be factored as follows:

(x + 1)(x - 3)(x^2 - 3x - 5)

We can solve for the remaining zeros of the polynomial function by factoring the quadratic equation using the quadratic formula or factoring by grouping. Either way, we find that the remaining zeros are approximately x = (3 + √(29))/2 and x = (3 - √(29))/2.

Therefore, the zeros of the polynomial function f(x) = x^4 - 2x^3 - 8x^2 + 10x + 15 are x = -1, x = 3 + √29/2, x = 3 - √29/2, and x = -0.4495 (approximately).

Hopefully this helps, if not I'm sorry! If you need more help, you may ask me! :]

The volume of small pyramid with base length 2, base width 2, and height 2. Its volume was 8/3π. We then scaled it by a factor of 2 and verified the formula V' = V × k3 holds true.

To create the smallest pyramid possible, we will use a tool such as a ruler or protractor to measure and construct the pyramid. Let's assume that we are using a ruler and that the smallest pyramid we can construct has a base length of 2 units, a base width of 2 units, and a height of 2 units.

To calculate the volume of the pyramid, we use the formula:

V = (1/3) × base area × height

The base area of the pyramid is:

A = base length × base width = 2 × 2 = 4 square units

Therefore, the volume of the pyramid is:

V = (1/3) × 4 × 2 = 8/3 cubic units (in terms of π, this is 8/3π cubic units)

Now, let's scale the original pyramid by a factor of k = 2. To find the new dimensions of the scaled pyramid, we multiply each dimension of the original pyramid by the scale factor k:

Base length = 2 × 2 = 4 units

Base width = 2 × 2 = 4 units

Height = 2 × 2 = 4 units

The base area of the scaled pyramid is:

A' = base length × base width = 4 × 4 = 16 square units

The volume of the scaled pyramid is:

V' = (1/3) × A' × height = (1/3) × 16 × 4 = 64/3 cubic units (in terms of π, this is 64/3π cubic units)

Now, we can verify that the formula V' = V × k3 holds true for the scaled pyramid:

V' = 64/3 cubic units

V = 8/3 cubic units

k = 2

V' = V × k3

64/3 = (8/3) × 23

64/3 = 8/3 × 8

64/3 = 64/3

Therefore, the formula V' = V × k3 holds true for a pyramid, and we have successfully verified it using the scaled pyramid.

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P = 83.57% after rounding to the closest two decimal places.

As a result, roughly 83.57% of these procedures are successful and infection-free.

We must deduct the percentage of operations that fail, are infected, or both from 100% in order to get the proportion of operations that are successful and free of infection.

Let P represent the proportion of procedures that are both successful and infection-free.

We are aware that 14% of surgeries fail due to repair failure, and 3% of operations result in infection. Hence, 3% + 14% - 0.57% = 16.43% of surgeries have either an infection or a failure, or both.

Hence, 100% - 16.43% = 83.57% is the proportion of surgeries that are successful and free of infection.

P = 83.57% after rounding to the closest two decimal places.

As a result, roughly 83.57% of these procedures are successful and infection-free.

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The numbers 8 and 7, which have fixed values that never shift, are the constants.

A coefficient in mathematics is an integer or symbol that multiplies a variable or a variable product. In algebraic formulas, equations, and polynomials, coefficients are used. For instance, the coefficient of the variable x in the equation 3x + 5 is 3, and the coefficient of the constant term 5 is 1. The factors of x and y in the equation 2x + 3y = 7 are 2 and 3, respectively. Coefficients can be whole integers, fractions, or decimals and can have a positive, negative, or zero sign. They aid in the simplification of mathematical expressions and equations and serve to illustrate the relationship between variables.

given

3 coefficients

x is a variable.

8 and 7 are constants.

The coefficient in the equation 3x +  8 = 7 multiplies the variable x by the number 3.

We are looking for an unknown number, represented by the variable x. The numbers 8 and 7, which have fixed values that never shift, are the constants.

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Answer:

Step-by-step explanation:

Step-by-step explanation:

Let x be the number of suede coats and y be the number of cotton coats. Then, the system of inequalities representing the situation is:

150x + 69y ≥ 6200 (the total cost of the women's coats must be at least $6200)

x ≥ 0, y ≥ 0 (the number of coats cannot be negative)

Note that this system assumes that the store only sells suede and cotton coats for women, and that there are no other costs associated with these coats (such as shipping or storage costs).

The sum οf [tex](x - 5x^2 - 12)[/tex] and [tex](4 + 11x - 3x^2)[/tex] is [tex]12x - 8x^2 - 8.[/tex]

The term "sum" can alsο be used tο describe a specific sum οf mοney. Yοu cοuld spend a cοnsiderable amοunt οf mοney οn a new car. Hοwever, if yοu tοtal up οr add up all οf its advantages, yοu might be able tο justifiably justify spending sο much.

When yοu add up the cοsts οf everything yοu οrdered at the restaurant, yοu can determine the final tοtal. It's nοt necessary fοr sum tο οnly refer tο numerical values. A summary οr general statement abοut sοmething is what yοu are giving when yοu sum sοmething up.

Tο find the sum οf [tex](x - 5x^2 - 12)[/tex] and [tex](4 + 11x - 3x^2)[/tex], we need tο add the like terms. Like terms are thοse terms that have the same variable raised tο the same pοwer.

Sο, the sum οf  [tex](x - 5x^2 - 12)[/tex] and [tex](4 + 11x - 3x^2)[/tex] is:

[tex](x + 11x) + (-5x^2 - 3x^2) + (-12 + 4)[/tex]

Simplifying, we get:

[tex]12x - 8x^2 - 8[/tex]

Therefοre, the sum οf [tex](x - 5x^2 - 12)[/tex] and [tex](4 + 11x - 3x^2)[/tex]  is [tex]12x - 8x^2 - 8.[/tex]

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Using the conversion factor we know that Maya sled down a total of 60 ft of both hills.

A conversion factor is a number that is used to multiply or divide one set of units into another.

If a conversion is required, it must be done using the correct conversion factor to get an identical value.

For instance, 12 inches equals one foot when converting between inches and feet.

Conversion factors' function in the Medicare fee structure.

Every year, the CF is calculated using the CF from the year before, with the Medical Economic Index, the Update Adjustment Factor, Legislative Change, and Budget Neutrality factors are taken into account.

So, we know that:

1 inch = 0.0833333 ft

Then,

432 inches = 36 ft

Then, total ft Maya sled down:

= 24 ft + 36 ft

= 60 ft

Therefore, using the conversion factor we know that Maya sled down a total of 60 ft of both hills.

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Answer:

Step-by-step explanation:

708588 hope this helps

Answer: a. The equation for the total expenses E for n bikers is:

E = 30n + 125n + 700

b. The equation for the total income I for n bikers is:

I = 350n

c. The equation for the profit P for n bikers is:

P = I - E = 350n - (30n + 125n + 700) = 195n - 700

Answer:

6 + 5h
h = The number of hours he can work in the yard.

By answering the presented question, we may conclude that As a result, the probability of picking a clown performer from the circus is 1/3, or 0.33. (rounded to two decimal places).

Probabilistic theory is a branch of mathematics that calculates the chance that an event or statement will occur or be true. A risk is a number between 0 and 1, where 1 denotes certainty and 0 indicates how probable an event is to occur. Probability is a mathematical term for the likelihood of a certain event occurring. Probabilities can also be expressed as integers between 0 and 1 or as percentages ranging from 0% to 100%. In relation to all other outcomes, the ratio of occurrences among equally likely alternatives that result in a certain event.

The likelihood of picking a clown performer from the circus is proportional to the number of clowns to the total number of circus artists.

The probability of picking a clown performer is the number of clowns divided by the total number of performers.

So,

The likelihood of picking a clown performer is 5/15.

By dividing the fraction's numerator and denominator by 5, we get:

The likelihood of picking a clown performer is 1/3.

As a result, the likelihood of picking a clown performer from the circus is 1/3, or 0.33. (rounded to two decimal places).

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Answer:

5h

Step-by-step explanation:

300÷60=5

km÷km/h=h

=5h

There will be six possibilities in the sample space if a notebook is selected at random.

the shop sells two types of notebooks and each notebook is offered in red, blue or yellow.

each of the two notebook kinds is available in three different colors.

As a result, there are a total of the following possibilities in the sample space:2 types of notebooks x 3 colors each = 6

Hence, the sample space contains six distinct alternatives.

they are,

Red type 1 notepad

Blue Type 1 notepad

Yellow type 1 notepad

Red type 2 notepad

Blue Type 2 notepad

Yellow type 2 notepad

therefore, the sample space contains six distinct alternatives.

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Answer:

6)180-99=81

81+43=124

180-124=56

b=56

Answer:

3

Step-by-step explanation:

HCF(a, b) x LCM(a, b) = a x b

We are given that LCM(18, 21) = 126. Let's use this to find the HCF:

HCF(18, 21) x 126 = 18 x 21

HCF(18, 21) = (18 x 21) / 126

HCF(18, 21) = 3

Therefore, the HCF of 18 and 21 is 3.

The solution to the equation is (c) No, because there is only one real solution and the value is x = 4

The given equation is

(6 – 2x)(3 – 2x)x = 40

Next, we answer the question from the numbers given from the list of options

In option (c), we have

x = 4

By substitution, the equation becomes

(6 - 2 * 4)(3 - 2 * 4) * 4 = 40

Evaluate the product expression

40 = 40

The above equation is true

Hence, the solution is (c)

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