A sequence can be generated by using an= 3an-1, where a1 = 10 and n is a whole number greater than 1.
What are the first 3 terms in the sequence?
A. 3, 13, 23
B. 10, 30, 90
C. 10, 13, 16
D. 3, 30, 300

The graph of the given function is attached.

Given is a function for the rainfall in 5 months in inches.

We need to display the data,

So, as we can see that the data is not showing any proportion or pattern,

So, it can be displayed as a line chart.

Hence the chart is attached for the function.

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Answer:

d² - 24d + c = (d - 12)² - 144 + c

5 holes have been punched into a 12 cm by 12 cm square piece of paper. The area of remaining paper will be 27.714 cm².

Firstly, we will calculate the area of the square of paper in which the holes are punched.

Side of square = 12 cm

Area of square = side²

= (12) ²

= 144 cm²

Now, we will calculate the area of the bigger punch holes

Radius of big punch hole = 3 cm

Area of 1 big punch = π (radius) ²

= 22/7 × (3)²

22 / 7 × 9

= 198 / 7 cm²

Area of 4 punches = 4 × 198/7

= 792/7 cm²

Now, we will calculate the area of smaller punch whose radius is 1cm

Area = 22/7 × 1²

= 22/7 cm²

Now, we will calculate the total area covered by circles

Total area covered by circles = area of small punch + area of 4 big punch

= 22/7 + 792/7

= 814 /7 cm²

Remaining area = area of square - area of circles

= 144 - 814/7

= (1008 - 814) / 7

= 194 / 7

= 27.714 cm²

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The perimeter of the rectangular polygon is given by P = 20.2 units

Given data ,

Let the perimeter of the polygon be represented as P

Now , the value of P is

Perimeter P of rectangle = 2 ( Length + Width )

Now , width is 3.8 and the length is 6.3

On simplifying , we get

P = 2 ( 3.8 + 6.3 )

P = 20.2 units

Hence , the perimeter is P = 20.2 units

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Answer:

12

Step-by-step explanation:

The figure is a right triangle with hypotenuse = QS

The  base from the graph = 4 units
(or you can just subtract the x-coordinates 2 - (-2) = 4)

The height from the graph is 3 units
(Or you can subtract the y-coordinates: 1 - (-2) = 3)

Since this is a right triangle the square of the hypotenuse = sum of squares of the other two sides

QS² = 3² + 4² = 9 + 16 = 25

QS, the hypotenuse = √25 = 5

The perimeter = sum of the sides = 3 + 4 + 5 = 12 units

Answer: x= 10

Step-by-step explanation:

2x+4=24

2x=24-4

2x=20

x=10

Answer:

Step-by-step explanation:

2x+4=4

subtract 4 from both sides

2x=0

divide by 2 on both sides

x=0

Answer:

26 inches

Step-by-step explanation:

The snail starts 20 inches above the ground: +20

The snail slips (goes down) 6 inches: 20 - 6 = 14

The snail goes up 12 inches: 14 + 12 = 28

The snail is 28 inches above the ground.

Hope this helps!

572 square inches nylon will Lyndon need.

To determine how much nylon Lyndon will need to make a case for his snare drum, we need to calculate the surface area of the drum.

The surface area of a cylinder can be calculated using the formula:

Surface Area = 2π[tex]r^2[/tex] + 2πrh

where r is the radius of the base of the cylinder and h is the height of the cylinder.

Since the diameter of the drum is 14 inches, the radius is 7 inches.

The height of the drum is 6 inches.

So, the surface area of the drum is:

Surface Area = 2π[tex](7)^2[/tex] + 2π(7)(6)

Surface Area = 2π(49) + 2π(42)

Surface Area = 98π + 84π

Surface Area = 182π

Surface Area = 182 pi

Surface Area = 182 x 22/7

Surface Area = 572 squae inches

Therefore, Lyndon will need 182π square inches of nylon to make a case for his snare drum.

This is approximately 572 square inches when rounded to the nearest hundredth.

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Answer: I believe the answer is Yolanda.

Step-by-step explanation: Because Maurice ran 110 meters in 20.9 seconds, which is slower than Yolanda. Completing the race in 20 seconds is better than 20.9 seconds.

Answer:

Eat that cookie and you will not regret about it

Answer:

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Step-by-step explanation:

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Answer:

I apologize, I am not able to provide visual drawings or diagrams. However, I can still provide a step-by-step guide to solve the problem.

To find the area of each shape, we need to use rectangles to determine the areas of right triangles that are inside the rectangles. Here are the steps:

1. Draw the given shape on geoboard paper.

2. Surround each triangle with a rectangle so that the vertices of the triangle are on the exterior of the rectangle.

3. Identify the right triangles that are inside the rectangles.

4. Use the formula for the area of a triangle, which is A = (base x height) / 2, to find the area of each right triangle.

5. Use the formula for the area of a rectangle, which is A = length x width, to find the area of each rectangle.

6. Add up the areas of the triangles and rectangles to find the total area of the shape.

Remember to label your answers with the correct units (square units).

On performing , the "row-operation" 2R₁ + R₂ → R₂ on the matrix "M", the resulting new-matrix is [tex]\left[\begin{array}{ccc}5&1&-5\\10&0&-8\end{array}\right][/tex] .

The matrix "M" is given as : [tex]\left[\begin{array}{ccc}5&1&-5\\0&-2&2\end{array}\right][/tex],

We have to apply the Row-Operation : 2R₁ + R₂ → R₂, on the matrix "M",

Performing the row-operation "2R₁ + R₂ → R₂" on a matrix "M" means multiplying the first-row of "M" by 2, and then adding the resulting values to the second-row of "M" to produce a new value for each element in the second row.

This operation does not affect the first row of "M" and changes the values in the second row of "M".

⇒ [tex]\left[\begin{array}{ccc}5&1&-5\\2\times5+0&2\times 1-2&2\times(-5)+2\end{array}\right][/tex],

⇒ [tex]\left[\begin{array}{ccc}5&1&-5\\10+0&2-2&-10+2\end{array}\right][/tex],

⇒ [tex]\left[\begin{array}{ccc}5&1&-5\\10&0&-8\end{array}\right][/tex].

Therefore, the new-matrix is [tex]\left[\begin{array}{ccc}5&1&-5\\10&0&-8\end{array}\right][/tex].

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The statements that complete the function transformations are left, up, stretch and stretch

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

f(x) = (x + 94)²

Also, we have

f(x) = x²

This implies that f(x) = (x + 94)² is obtained by shifting f(x) = x² left by 94 units

Next, we have

f(x) = x² + 94

This implies that f(x) = x² + 94² is obtained by shifting f(x) = x² up by 94 units

Next, we have

f(x) = 94√x from f(x) = √x

This implies that f(x) = 94√x can be obtained from vertically stretching f(x) = √x by a factor of 94

Also, the graph of f(x) = √94x can be obtained from horizontally stretching f(x) = √x by a factor of 1/94

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Answer:

7

Step-by-step explanation:

Finding the common difference of an arithmetic sequence is easy peasy lemon squeezy. All you have to do is take any term and subtract it from the next one. For instance, if you take 1 and subtract it from 8, you get 7. If you take 8 and subtract it from 15, you get 7 again. You can do this for any pair of terms and you will always get 7. That's the common difference of the sequence 1, 8, 15, 22, 29, 36, 43. It means that you just add 7 to each term to get the next one. Isn't that neat?

The number line that shows the solution to the inequality is given as follows:

First number line.

The inequality in the context of this problem is defined as follows:

-6x + 5 >= 17

-6x >= 12.

Due to the negative sign of the leading coefficient, we should change the sign of all terms, including the sign, as follows:

6x <= -12.

Then the solution is given as follows:

x <= -2.

Which is composed by the numbers to the left of the closed interval at x = -2, hence the first number line gives the solution to the inequality.

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The number line that shows the solution to the inequality is: C. graph C.

In Mathematics and Geometry, an inequality refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

Based on the information provided above, we have the following equation (inequality);

-6x + 5 ≥ 17

By subtracting 5 from both sides of the equation (inequality), we have;

-6x + 5 - 5 ≥ 17 - 5

-6x ≥ 12

x ≤ 12/6

x ≤ 2 (it would be shaded to the left with a closed circle at 2).

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The graph of the logarithmic function is attached below with a vertical asymptote at x = -8 and two integer coordinates at (2, -7) and (1, -10).

The basic logarithmic function is of the form f(x) = logax (r) y = logax, where a > 0. It is the inverse of the exponential function ay = x. Log functions include natural logarithm (ln) or common logarithm (log).

To plot the graph of the given function, we simply need to use a graphing calculator.

The given function is;

f(x) = -3log₃(x + 8) - 4

To find the asymptotes of the graph;

x + 8 > 0

x > -8

The vertical asymptotes is at x = -8

The two points with integer coordinates are (2, -7) and (1, -10)

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The rays in Tiffany’s design are EA, FB, GC, GH, ED

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

Tiffany’s design

By definition, the rays in Tiffany’s design are lines that have one fixed endpoint and the other endpoint extends indefinitely

Using the above as a guide, we have the following:

The rays in Tiffany’s design are EA, FB, GC, GH, ED

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Based on the contribution margin and the sales volume, Menu Item D is the most profitable and popular.

The contribution margin is the profitability that is shown in the difference between the selling price and the variable cost per unit of an item.

The contribution margin can be computed per unit or in total.  Using the sales volume to multiply the contribution margin per item gives the total contribution margin in dollars.

 Breakfast     Selling Price    Food Cost       Sales     Contribution Margin

Menu Item               ($)                  ($)           Volume         Unit         Total

А                         $10.00             $3.00           250          $7.00      $1,750

B                         $16.00             $6.00             50        $10.00        $500

C                         $18.45             $8.00             60        $10.45        $627

D                         $14.75             $4.25           300        $10.50      $3,150

E                          $8.75             $2.50             80          $6.25        $500

F                        $12.50              $5.75            180         $6.75       $1,215

G                        $9.00              $2.60           280         $6.40      $1,792

TOTAL                                                          1,200

Thus, we can conclude that Menu Item D enjoys the highest profitability and popularity.

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Alondra will be able to withdraw approximately $1,427 per month to take withdrawals for 22 years from her retirement account.

To calculate the monthly withdrawal amount, we need to use the present value formula, which is:

PMT = (PV * r) / (1 - (1 + r)⁻ⁿ)

where:

PV = present value = $350,000

r = monthly interest rate = 2.9% / 12 = 0.002417

n = number of months = 22 years * 12 months/year = 264 months

Substituting the values into the formula, we get:

PMT = (350000 * 0.002417) / (1 - (1 + 0.002417)⁻²⁶⁴)

PMT ≈ $1,427.07

This calculation assumes that the interest rate remains constant throughout the 22-year period, which may not be the case in reality.

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I cannot solve that problem at the moment.

Step-by-step explanation:

But I will help you in the future

The probability of a student being female given that they got a 'B' is 87/315.

We can use Bayes' theorem to find the probability of a student being female given that they got a 'B'. Let's first find the total number of students who got a 'B':

Total number of students who got a 'B'

= 7 + 9 + 6 + 13 + 16 + 12

= 63

Out of these 63 students, the number of females who got a 'B' is:

Number of females who got a 'B' = 13 + 16 = 29

So, the probability of a student being female given that they got a 'B' is:

P(Female | B) = P(B | Female) x P(Female) / P(B)

From the given data, we can calculate these probabilities as follows:

P(B | Female) = 29/25

P(Female) = 25/63

P(B) = 63/175

Plugging in these values, we get:

P(Female | B)

= (29/25) x (25/63) / (63/175)

= 87/315

Therefore, the probability of a student being female given that they got a 'B' is 87/315.

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Answer:

1 1/6 metre

Step-by-step explanation:

1/3 pink + 5/6 purple

To add, we need to get a common denominator

1/3 *2/2 = 2/6

2/6 + 5/6

7/6

Change from an improper fraction to a mixed number

1 1/6 metre

The distance that the plane traveled from point A to point B is given as follows:

10,750 ft.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

The altitude of 5375 feet is the opposite angle, hence the position A is obtained as follows:

tan(15º) = 5375/A

A = 5375/tangent of 15 degrees

A = 20060 ft.

The position B is obtained as follows:

B = 5375/tangent of 30 degrees

B = 9310 ft.

Hence the distance is of:

20060 - 9310 = 10,750 ft.

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The estimated population of the town in 2023 is 57,344.

(a) Let P be the population in t years after 2014.

Since the population doubles every year, we can use the formula :

P = P₀(2)ⁿ, where P₀ is the initial population in 2014.

We have P₀= 112, so the equation is P = 112(2)ⁿ.

(b) To find the population in 2023, we need to find t when t + 2014 = 2023.

So t = 2023 - 2014 = 9.

Substituting t = 9 into the equation from part (a), we get:

P = 112(2)⁹

P ≈ 57,344

Therefore, the estimated population of the town in 2023 is 57,344.

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The area of the figure as shown in the diagram is 24 in².

Area is the region bounded by a plane shape.

To calculate the area of the figure, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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Answer:

108 sq ft

Step-by-step explanation:

The formulas are given in the bottom right.

For the triangles*, the base = 8 ft. The height = 6 feet.

Area = (bh)/2.

Area = (8*6)/2 = (48)/2 = 24 sq ft.

There are two of those identical triangles. 24+24 = 48.

(*Another way to look at this is to say that the base = 8+8 = 16. Area = (bh)/2 = (16*6)/2 = 96/2 = 48. It doesn't matter, mathematically. I can't tell if they have tried to show this as 2 triangles or one.)

For the bottom rectangle, area = length x width = 6*10 = 60 sq ft.

Add them up! 24 + 24 + 60 = 108 sq ft.

The actual distance between the two cities is 432 miles.

The figure shows a map of two cities, with a distance between them measured at 4.5 inches.

The scale of the map is given as 1/8 inch to 12 miles.

This means that 1/8 inch on the map represents a distance of 12 miles in real life.

To determine the actual distance between the two cities, we can use the scale provided.

1/8 inch on the map represents 12 miles in real life.

A proportion to find the actual distance between the cities:

1/8 inch on map = 12 miles in real life

4.5 inches on map = x miles in real life

To solve for x, we can cross-multiply and simplify:

1/8 × x = 12 × 4.5

x = 12 × 4.5 × 8

x = 432 miles

Maps with scales can be useful for determining distances, sizes, and proportions of objects in real life.

It allows us to visually represent complex spatial relationships and make measurements without physically being present at the location.

Remember to use the correct scale and make sure to convert units properly in order to accurately determine real-life measurements.

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