Hello me with part B pleaseeee

We need to find the explicit equation for the sequence:

First, we can complete the given table. Notice that when we subtract 4 from the n-th term, we obtain the next term (n+1).

Then, to find a previous term, we can add 4. Thus. we obtain:

n t(n)

0 14+4 = 18

1 10+4 = 14

2 10

3 10-4 = 6

4 6-4 = 2

5 2-4 = -2

Now, observing the above relations, we need to write an expression for t(n) in terms of n:

n t(n)

0 18 = 18 - 0*4

1 14 = 18 - 1*4

2 10 = 18 - 2*4

3 6 = 18 - 3*4

4 2 = 18 - 4*4

5 -2 = 18 - 5*4

...

n 18 - n*4

Therefore, an explicit equation for the sequence is:

In mixed fraction the total distance of the fun run is 11 1/14

A school is organising a fun run. The fun run involves a 5 1/2

mile run around the field, then a 5 4/7 mile run back to the school.

The total distance is equal to summation of run around the field and run back to school.

total distance = 5 1/2 + 5 4/7

= 11/2 + 39/7

The L. C. M  of 2 and 7 is 14

= [tex]\frac{11.7}{2.7} + \frac{39.2}{7.2}[/tex]

(77 + 78)/14

155/14

Upon dividing 155 by 14, the quotient is 11 and the the remainder is 1

In mixed fraction it is 11 1/14

So in mixed fraction the total distance of the fun run is 11 1/14

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Given data:

The box is given.

The given expression can be written as,

Thus, the option (c) is correct.

ANSWER and EXPLANATION

We want to state the null and alternative hypotheses for the claim given.

A null hypothesis is a statement about a population parameter such that the likelihood can be tested to either accept or reject the alternative hypothesis.

An alternative hypothesis on the other hand is a statement that directly contradicts the null hypothesis.

Therefore, going by that, we see that the null hypothesis is:

and the alternative hypothesis is:

Answer:

4/1÷2 =4×1/2

Step-by-step explanation:

You have to invert and then multiply

so the answer will be 2

The width of the given rectangle is 2x²-3x+3.

Given that, area of rectangle = [tex]6x^4-8x^3+9x^2-3x-12[/tex] and the length of rectangle = 3x-4.

The area can be defined as the amount of space covered by a flat surface of a particular shape. It is measured in terms of the "number of" square units. The formula to find the area of a rectangle = Length × Width.

Now, (3x-4) × width = [tex]6x^4-8x^3+9x^2-3x-12[/tex]

⇒ Width = [tex]\frac{6x^4-8x^3+9x^2-3x-12}{3x-4}[/tex]

3x-4|[tex]6x^4-8x^3+9x^2-3x-12[/tex]|2x³-3x+3

       [tex]6x^4[/tex] - 8x³

      _________________

                 0+9x²-3x-12

                 (-) 9x²+12x
      _________________

                      0+9x-12

                     (-) 9x(+)12

        _________________

                              0

So, width = 2x²-3x+3

Therefore, the width of the given rectangle is 2x²-3x+3.

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The graph of the function (E) f(x) = (x + 10)(x - 3)²(x + 1) matches the given graph.

So, the function with which the given graph matches:

Therefore, the graph of the function (E) f(x) = (x + 10)(x - 3)²(x + 1) matches the given graph.

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To solve this problem we have to remember that diagonals of a parallelogram bisect each other. This means that they intersect in the midle point of each other. From this we can conclude that

Once we have our equations we can solve them. Let's find x

Now, let's find y

Then x=18 and y=9,

Answer:

I say w is equal to 4, because:

4 divided by 2 = 2

2 + 4 = 6

6 > 5

Step-by-step explanation:

Hope it helps! =D

Answer:

74.52

Step-by-step explanation:

[tex]P(10)=0.018(10)^3-0.294(10)^2+3.074(10)+55.180 \\ \\ =74.52[/tex]

The area when the length of a rectangle is six times its width is 216m².

Let the width = w

Let the length = 6 × w = 6w

Therefore the perimeter will be:

= 2(Length + Width) = 84

2(w + 6w) = 84

2 × 7w = 84

14w = 84

Divide

w = 84 / 14

w = 6

Width = 6m

Length = 6w = 6 × 6 = 36m

The area will be:

= Length × Width

= 36m × 6m

= 216m²

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Answer

12th term = 390,625

Explanation

On close observation, we can see that the given series is in geometric progression.

Geometric progression has a general formula of

aₙ = a (rⁿ⁻¹)

where

aₙ = nth term

a = First term

r = Common ratio

n = number or position of the term

For this question, we need to compute the common ratio

Common Ratio = (Next term) ÷ (Current term)

= (Second term) ÷ (First term)

= (Third term) ÷ (Second term)

For this question,

Common Ratio = 0.04 ÷ 0.008 = 5

OR

0.2 ÷ 0.04 = 5

And we can see that the first term is 0.008

So, the 12th term will have the formula

aₙ = a (rⁿ⁻¹)

a = 0.008

n = 12

r = 5

a₁₂ = 0.008 (5¹²⁻¹)

= 0.008 (5¹¹)

= 0.008 (48,828,125)

= 390,625

Hope this Helps!!!

Given the equation:

y = 828000 - 2700x

Where y is the value of the building and x is the number of months of use.

Let's find when the value of the building will be $666,000.

To find when the value will be $666,000, substitute 666000 for y in the equation and solve for x.

y = 828000 - 2700x

666000 = 828000 - 2700x

Subtract 828000 from both sides:

666000 - 828000 = 828000 - 828000 - 2700x

-162000 = -2700x

Divide both sided by -2700:

The value of the building will be $666,000 after 60 months.

Now, let's convert from months to years.

Where:

12 months = 1 year

Therefore, the value of the building will be $666,000 after 5 years.

ANSWER:

5 years.

The two inlet pipes can fill the tank in 4 hours and 10 hours.

The work done by the inlet pipes per hour is calculated to be:

The outlet pipe drains the tank in 2 hours. The work done will be:

Therefore, if both inlet pipes and the outlet pipes are opened at the same time, the work done by the pipes combined will be:

Since the work done to fill the tank is negative, it means that the tank will never get full as it empties faster than it fills up.

Measure of CAB is 84.4, by using supplementary angle theory.

In geometry, two angles are referred to as supplementary angles if their sum is 180 degrees. For instance, if A + B = 180°, then A and B are considered supplementary angles. Complementary angles always result in a straight angle when combined (180 degrees).

Angles that add up to a precise 90 degree angle are said to be complementary. For instance, 30 degrees and 60 degrees are complementary angles.

We have given, CAB= 4x+14 and DAB = 6x-18

Both are supplementary angle

Therefore, CAB + DAB = 180

4x+14+6x-18=180

10x-4=180

10x=176

x=17.6

hence, CAB = 4(17.6)+14 = 84.4

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Given:

m∠C = 70°

m∠CDE = 130°

Question 1:

To find ∠CDB, let's use the exterior angle theorem.

The exterior angle theorem states that the sum of 2 opposite interior angles is equal to the exterior angle.

Thus,

m∠C + m∠B = 130

70 + m∠B = 130

Subtract 70 from both sides:

70 - 70 + m∠B = 130 -70

m∠B = 60°

Now, use the triangle angle sum theorem to find ∠CDB.

The triangle angle sum theorem states that the sum of interior angles in a triangle is 180°

∠CDB = 180 - 70 - 60 = 50°

∠CDB = 50°

Question 2:

∠CBA = ∠C + ∠CDB

∠CBA = 70 + 50 = 120°

∠CBA = 120°

ANSWER:

∠CDB = 50°

∠CBA = 120°

Garry needs 18.4 oz of glue and 9.2 oz of glitter to make 4 bottles.

In direct proportion between two or more than two quantities if one quantity is multiplied or divided by some constant k other quantities will also be multiplied or divided by the same constant k.

Given, Making 1 bottle of glitter glue Garyy requires 4.6 oz of glue and 2.3 oz of glitter.

∴ 4 bottles of glitter glue require (4.6×4) = 18.4 oz of glue and (2.3×4) = 9.2 oz of glitter.

As the no. of bottles is multiplied by 4 thus material requirements will also be multiplied by a factor of 4.

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The mean salary of the employees is $17625.5.

The total number of employees in the company is 80.

The total salary for the first interval is [(5001+10000)/2]*17 = 127508.5.

The total salary for the second interval is [(10001+15000)/2]*15 = 187507.5.

The total salary for the third interval is [(15001+20000)/2]*16 = 280008.

The total salary for the fourth interval is [(20001+25000)/2]*13 = 292506.5.

The total salary for the fifth interval is [(25001+30000)/2]*19 = 522509.5.

In math, a mean is the average of a data collection, which is calculated by adding all of the numbers together and then dividing the total of the numbers by the number of numbers. The mean salary is the sum of all salaries divided by the total number of employees.

M = (127508.5 + 187507.5 + 280008 + 292506.5 + 522509.5)/80

M = 17625.5

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Answer

∛20 is between 2 and 3.

Explanation

The question asks us to find the cube root of 20.

∛20

The key to doing this without the calculator is to take the cube of numbers and the one that has 20 in between them is the answer.

1³ = 1

2³ = 8

3³ = 27

We can see that 20 is between 8 and 27.

So,the cube root of 20 has to be betwen 2 and 3.

The other way to do this with the calculator is to actually find the cube root of 20

∛20 = 2.71

Which is between 2 and 3.

Hope this Helps!!!

Answer:

The natural numbers, whole numbers, and integers are all subsets of rational numbers

Step-by-step explanation:

hope it helps

have a good day

Using the calculator for the line of best-fit, the measures are given as follows:

To find the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) given in the problem in the calculator. These points are given on a table or in a scatter plot in the problem.

From the given table, the points in this problem are as follows:

(22, 6.1), (13, 7.9), (29, 5.8), (11, 7.4), (28, 6.3), (6, 8.2).

Hence:

Hence, for a mother that smokes 40 cigarettes on a day, the predicted weight is of:

y = -0.1(40) + 8.77 = 4.77 grams.

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Answer:

2S-a1n/n

Step-by-step explanation:

S = n(a1 + an)/2

2S = n(a1 + an)

2S = na1 + nan

nan = 2S - na1

an = (2S - n a1)/n

Explanation:

First we have to solve the products, divisions and powers in each term. The terms are separated by + or - signs. In this expression there are two terms.

In the first term there's a product inside a parenthesis. This means that we have to solve that first:

Now we can solve the multiplication in the first term:

Solve the power in the second term:

And do the substraction:

Answer:

1/2(4x5) - 2³ = 2

We have the next two points:

- (1/2,5)

- (5/2,9)

And we must use the point-slope formula to write an equation of a line in slope-intercept

First, we need to calculate the slope of the line using the point-slope formula

Where (x1, y1) and (x2, y2) are the two points

Now, replacing the points

Now, we must replace the slope and one of the two points in the point-slope formula:

Replacing m = 2 and (1/2, 5)

Finally, we must simplify to obtain the slope-intercept form

ANSWER:

y = 2x + 4

Answer:

6  2/3 inches

Step-by-step explanation:

2 inches / 6 feet   * 20 feet = 6 2/3 inches

We can use a right triangle and the below trigonometric ratios.

In this case, we have:

As we can see, we need to know the value of the opposite leg. Since it is a right triangle, we can use the Pythagorean theorem formula.

Then, we have:

Finally, we have:

Then, we can find the value of tan(θ):