Kyra is making squares with toothpicks. She uses 4 toothpicks to make a square. Then she adds 3 more toothpicks to make two squares side by side. To build three squares in a line, she used a total of 10 toothpicks. If she continues this pattern, how many toothpicks will she use to make 90 squares in a straight line?

How many squares can Kyra make in this pattern if she has a box of 1,000 toothpicks?

The first term is 9, the second term is 17, and the third term is 25.

The 100th term of an arithmetic sequence is given by the formula:

Tn = a + (n-1)d

Where Tn is the nth term, a is the first term, n is the number of terms, and d is the common difference.

In this case, the 100th term is 783, the common difference is 8, and the first term is 9.

Plugging in the values into the formula, we get:

783 = 9 + (100-1)8

Solving for the first term, we get:

783 = 9 + 792

783 = 801

a = 9

The second term, Q2, can be found by adding the common difference to the first term:

Q2 = a + d

Q2 = 9 + 8

Q2 = 17

The third term, az, can be found by adding the common difference to the second term:

az = Q2 + d

az = 17 + 8

az = 25

the first term is 9, the second term is 17, and the third term is 25.

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The algae bloom that is covered a larger area when the chemicals were applied is the red arrow.

The algae population that is decreasing more rapidly is the blue dot.

A population in statistics is a group of comparable objects or occurrences that are relevant to a particular topic or experiment.

A statistical population can be a collection of real things or a hypothetical, possibly limitless collection of objects derived from experience.

It should be noted that the red arrow represents a larger area that is covered by algae.

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Answer:

x = 3.92699081 + 7.85398163n where n is an integer

The area of the triangle is approximately 6.696 square feet.

What is Area of Triangle?

The area of a triangle is the amount of space enclosed by the three sides of the triangle

To find the area of a triangle with two sides and the included angle, we can use the following formula:

Area = (1/2) x a x b x sin(C)

where "a" and "b" are the lengths of the two sides and "C" is the angle between them.

Substituting the given values, we get:

Area = (1/2) x 3.2 ft x 4.7 ft x sin(62 degrees)

Using a calculator, we can evaluate sin(62 degrees) to be approximately 0.88.

So, Area = (1/2) x 3.2 ft x 4.7 ft x 0.88

= 6.696 ft²

Therefore, the area of the triangle is approximately 6.696 square feet.

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Answer:

The answer is 6.64 ft^2

Step-by-step explanation:

Answer:

1 trillion times larger

Step-by-step explanation:

One kilogram (kg) is equal to 1,000,000,000,000 (1 trillion) nanograms (ng).

Therefore, one kilogram is 1 trillion times larger than one nanogram.

The number of bags of oranges that Ruth needs to sell on day 4 to have an average of 50 bags is 65.

Let the number of bags to be sold on day four be = x,

To have an average of 50 bags over 4 days,

The total number of bags Ruth sells in four days must be,

⇒ 4 days × 50 bags/day = 200 bags,

The total number of bags of oranges she sells in 3 days is,

⇒ 3 days × 45 bags/day = 135 bags,

So, to reach a total of 200 bags in 4 days, she needs to sell x bags on the fourth day, which is in equation form as :

⇒ x + 135 = 200

⇒ x = 200 - 135

⇒ 65

Therefore, Ruth needs to sell 65 bags on day four.

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If Bici expects to produce more than 500 bikes, then they should follow the second plan, and if they expect to produce fewer than 500 bikes, then they should follow the first plan.

Under the first plan, the total cost to design and build a prototype bicycle is $125,000, and the combined materials and labor costs for each bike made under this plan will be $225. This means that for each bike produced, the total cost will be $125,000 + $225 = $125,225.

Under the second plan, the total cost to design and build a prototype bicycle is $100,000, and the combined materials and labor costs for each bike made under this plan will be $275. This means that for each bike produced, the total cost will be $100,000 + $275 = $100,275.

To determine which plan is more cost-effective, we need to consider the breakeven point where the costs of both plans intersect:

125, 000 + 225x = 100, 000 + 275x

50x = 25, 000

x = 500 bicylces

If Bici Bicycle Company plans to produce more than 500 bikes, then the second plan would be more cost-effective. However, if Bici plans to produce fewer than 500 bikes, then the first plan would be more cost-effective.

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$$x = \frac{1}{21} \begin{bmatrix} 4b_1 + 2b_2 \\ 5b_1 - b_2 \end{bmatrix}.$$

To compute the least squared error solution to \( A x=b \), we will use the formula \(x = (A^T A)^{-1} A^T b\).

In this case, \(A = \begin{bmatrix} 4 & 1 \\ 5 & 1 \\ 6 & 1 \end{bmatrix}\), so \(A^T = \begin{bmatrix} 4 & 5 & 6 \\ 1 & 1 & 1 \end{bmatrix}\). Therefore, we have that

$$(A^T A)^{-1} A^T b = \left(\begin{bmatrix} 4 & 5 & 6 \\ 1 & 1 & 1 \end{bmatrix} \begin{bmatrix} 4 & 1 \\ 5 & 1 \\ 6 & 1 \end{bmatrix}\right)^{-1} \begin{bmatrix} 4 & 5 & 6 \\ 1 & 1 & 1 \end{bmatrix} b$$

From here, we can compute the inverse of the matrix \(A^T A\) to get

$$(A^T A)^{-1} = \frac{1}{21}\begin{bmatrix} -1 & 2 \\ 2 & -1 \end{bmatrix}$$

Substituting this into the equation above and multiplying through, we get

$$x = \frac{1}{21}\begin{bmatrix} -1 & 2 \\ 2 & -1 \end{bmatrix} \begin{bmatrix} 4 & 5 & 6 \\ 1 & 1 & 1 \end{bmatrix} b = \frac{1}{21} \begin{bmatrix} 4b_1 + 2b_2 \\ 5b_1 - b_2 \end{bmatrix}$$

Therefore, the least squared error solution to \( A x=b \) is $$x = \frac{1}{21} \begin{bmatrix} 4b_1 + 2b_2 \\ 5b_1 - b_2 \end{bmatrix}.$$

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Answer: Your welcome!

Step-by-step explanation:

Part A: 2x^2 + 3x^2 - 4 + 3xy + 6 + 6 = 7x^2 - 4xy + 6

Part B: 0 = 7x^2 - 4xy + 6 - (2x^2 + 3x^2 - 4 + 3xy + 6 + 6)

= 0 = 5x^2 - 4xy

A) The expression that represents the amount of canned food collected by the three friends is [tex]5x^2 + 3xy + 2[/tex].

B) The expression that represents the number of cans the friends still need to collect to meet their goal is [tex]2x^2 - 7xy + 4[/tex].

Given: Number of cans collected

Jessa: 2x²

Tyree: 3x² - 4

Ben: 3xy + 6

Goal : [tex](7x^2 - 4xy + 6)[/tex]

A) The total amount collected:

Total = Jessa + Tyree + Ben

         = [tex]2x^2 + (3x^2 - 4) + (3xy + 6)[/tex]

         = [tex]2x^2 + 3x^2 - 4 + 3xy + 6[/tex]

         = [tex](2x^2 + 3x^2 + 3xy) + (-4 + 6)[/tex]

         = [tex]5x^2 + 3xy + 2[/tex]

Therefore, the expression is [tex]5x^2 + 3xy + 2[/tex].

B) The number of cans the friends still need to collect to meet their goal is

Cans still needed = Goal - Total

                              [tex]= (7x^2 - 4xy + 6) - (5x^2 + 3xy + 2)[/tex]

                              [tex]= 7x^2 - 4xy + 6 - 5x^2 - 3xy - 2[/tex]

                              [tex]= (7x^2 - 5x^2) + (-4xy - 3xy) + (6 - 2)[/tex]

                              [tex]= 2x^2 - 7xy + 4[/tex]

Therefore, the expression is [tex]2x^2 - 7xy + 4[/tex].

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(fo)(fog)(x) = 7x^(2)-6x+1

(gof)(x) = 7x^(2)+8x

Domain is a real number.

The first step in finding (fo)(fog)(x) and (gof)(x) is to substitute the functions into each other. For (fo)(fog)(x), we will substitute g(x) into f(x) for x:

(fog)(x) = f(g(x))

= f(7x^(2)-6x-1)

= (7x^(2)-6x-1) + 1

= 7x^(2)-6x

Now we will substitute (fog)(x) into f(x) for x:

(fo)(fog)(x) = f((fog)(x))

= f(7x^(2)-6x)

= (7x^(2)-6x) + 1

= 7x^(2)-6x+1

For (gof)(x), we will substitute f(x) into g(x) for x:

(gof)(x) = g(f(x))

= g(x+1) = 7(x+1)^(2)-6(x+1)-1

= 7x^(2)+14x+7-6x-6-1

= 7x^(2)+8x

The domain of each function is the set of all real numbers, since there are no restrictions on the values of x. Therefore, the domain of (fo)(fog)(x) and (gof)(x) is all real numbers.

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The line passes through the point (2, 3), the equation of the line is y = 3.

3. To find the slope of a line, you can use the formula slope = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

4. a. The slope of the line that passes through the points (−2, 3) and (0, 0) is (0 - 3)/(0 - (-2)) = -3/2 = -1.5.
b. The slope of the line that passes through the points (2, 5) and (−2, 2) is (2 - 5)/(-2 - 2) = -3/-4 = 0.75.

5. The equation of a line parallel to the x-axis is y = b, where b is the y-coordinate of any point on the line. Since the line passes through the point (2, 3), the equation of the line is y = 3.

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The Vdp for the plug permeability is given as 0.46, which indicates that the variability of permeability in the plug is lower than that of the porosity and permeability in the core samples.

From the plots of porosity and permeability vs depth given in Question 2, we can say that both porosity and permeability have a certain degree of variability as they change with depth. However, the variability of permeability appears to be greater than that of porosity as the values of permeability change more drastically with depth compared to the values of porosity.

To calculate the coefficient of variation for both porosity and permeability, we can use the formula:

Coefficient of Variation (CV) = (Standard Deviation / Mean) * 100

For porosity:

Mean = (10 + 15 + 25 + 30 + 20) / 5 = 20

Standard Deviation = √[(10 - 20)² + (15 - 20)² + (25 - 20)² + (30 - 20)² + (20 - 20)²] / 5 = 7.07

CV = (7.07 / 20) * 100 = 35.35%

For permeability

Mean = (0 + 600 + 100 + 200 + 300 + 400 + 500) / 7 = 300

Standard Deviation = √[(0 - 300)² + (600 - 300)² + (100 - 300)² + (200 - 300)² + (300 - 300)² + (400 - 300)² + (500 - 300)²] / 7 = 200

CV = (200 / 300) * 100 = 66.67%
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The  general form of an explicit function for what the nth term of any arithmetic sequence would bean = a + (n-1)*d

An explicit function is a mathematical function containing only the independent variable or variables —opposed to an implicit function which is written in terms of both dependent and independent variables

The general arithmetic progression can be written as:

T₁ ,  T₂,   T₃,   T₄,   ......,  Tn.

Where n is any term

Now since a = 1 and d = common difference, The general arithmetic progression can be written as:

a, a+d,  a+2d,  a+3d, a+4d, a+(n-1)*d

Thus, the explicit function becomes a+(n-1)*d

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After 11 days, the concentration is 42.4 g/L.

The recursive formula for Cn can be written as Cn = Cn-1 + 0.14Cn-1. This formula shows that the concentration after n days is equal to the concentration after n-1 days plus 14% of the concentration after n-1 days.

To find the salt concentration after 11 days, we can use the recursive formula and plug in the values for C0 and n.

C0 = 10 g/L

C1 = C0 + 0.14C0 = 10 + 0.14(10) = 11.4 g/L

C2 = C1 + 0.14C1 = 11.4 + 0.14(11.4) = 13 g/L

C3 = C2 + 0.14C2 = 13 + 0.14(13) = 14.8 g/L

C4 = C3 + 0.14C3 = 14.8 + 0.14(14.8) = 16.9 g/L

C5 = C4 + 0.14C4 = 16.9 + 0.14(16.9) = 19.3 g/L

C6 = C5 + 0.14C5 = 19.3 + 0.14(19.3) = 22 g/L

C7 = C6 + 0.14C6 = 22 + 0.14(22) = 25.1 g/L

C8 = C7 + 0.14C7 = 25.1 + 0.14(25.1) = 28.6 g/L

C9 = C8 + 0.14C8 = 28.6 + 0.14(28.6) = 32.6 g/L

C10 = C9 + 0.14C9 = 32.6 + 0.14(32.6) = 37.2 g/L

C11 = C10 + 0.14C10 = 37.2 + 0.14(37.2) = 42.4 g/L

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Answer:

Step-by-step explanation:

The practical range is: $76.50 ≤ f(t) ≤ $153

The minimum number of hours is 5 hours, so the minimum money earned is:

minimum money = 15.30 * 5 = $76.50

The maximum number of hours is 10 hours, so the maximum money earned is:

maximum money = 15.30 * 10 = $153

2. Since the words “at least” and “not more than” are used, hence this is inclusive.

3. The practical range is: $76.50 ≤ f(t) ≤ $153

The domain is the number of hours he worked. It says that he works at least 16 hours, but not more than 24.

This means that the number of hours he worked can be any number between 16 and 24, including 16 and 24 as a possible number of hours.

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The percent increase in pipe footage sales is approximately 7%.

To find the percent increase in pipe footage sales, use the formula:

[(New Value - Old Value)/Old Value] × 100.

In this case, the new value is the amount of pipe sold in September (2,558 feet) and the old value is the amount of pipe sold in August (2,390 feet). Plugging these values into the formula, we get:

[(2,558 - 2,390)/2,390] × 100 = [168/2,390] × 100 = 0.0703 × 100 = 7.03%

Therefore, the correct answer is 7%, which is option A. The percent increase in pipe footage sales from August to September is 7%.

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Step-by-step explanation:

The price is $30.

please make me brainalist and keep smiling dude

Answer: They shared 40 grapes for Tommy and 48 grapes for Kim

Step-by-step explanation:

Let's assume that the initial number of grapes they shared is 5x for Tommy and 6x for Kim.

After Tommy eats half of his grapes, he will have 5x/2 grapes left.

Kim eats 4 more grapes than Tommy, so she will have 5x/2 + 4 grapes.

To find the total number of grapes they have after eating, we can add them together:

5x/2 + 4 + 5x/2 = 11x/2 + 4

Since they now have the same number of grapes, we can set this equal to the initial total number of grapes they shared:

5x + 6x = 11x

11x = 11x/2 + 4

Multiplying both sides by 2:

22x = 11x + 8

Subtracting 11x from both sides:

11x = 8

Dividing by 11:

x = 8/11

So the initial number of grapes they shared is:

5x + 6x = 11x = 11(8/11) = 8

Therefore, they shared 40 grapes (5x) for Tommy and 48 grapes (6x) for Kim at the beginning.

The solution to the inequality is x <= 50. This means that any value of x less than or equal to 50 will satisfy the inequality.

To solve the inequality 100 - 3x >= -50, we want to find the values of x that satisfy this inequality.

Makayla solved the equation 100 - 3x = -50 and got x = 50. This equation is not the same as the inequality we want to solve, but we can check whether Makayla's solution is a valid solution to the inequality.

Substituting x = 50 into the inequality, we get:

100 - 3x >= -50

100 - 3(50) >= -50

100 - 150 >= -50

-50 >= -50

This is a true statement, so x = 50 is a valid solution to the inequality.

However, we also need to check whether there are any other values of x that satisfy the inequality. We can do this by rearranging the inequality to isolate x:

100 - 3x >= -50

100 + 50 >= 3x

150 >= 3x

50 >= x

Therefore, the solution to the inequality is calculated to x <= 50.

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Angle, when two straight lines or rays intersect at a single endpoint,  then an angle is created.

The exterior angle of a triangle equals the sum of opposite interior angles. The angle between any side of a shape and a line that extends from the next side is known as the exterior angle.

∠XYZ  = ∠YWX + ∠WXY

10x - 5   = 3x + 17 + 3x + 2

10x - 5 = 6x + 19

10x - 6x  = 24

4x  = 24

x = 6

∠WXY =  3x + 2

= 3*6 + 2

= 20°

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Answer:

$948.34

Step-by-step explanation:

35% = .35

.35 x $2299

= $804.65

That is the total before the sales tax and after the sale.

6.25% = .0625

.0625 x $2299

= $143.69, and because that is 6.25% of the total, it must be added onto that as tax.

That means the total is $804.65 + $143.69

= $948.34

The Answers are:

            6. HCF is equal to 2

            7. HCF is equal to 2

            8. HCF is equal to 1

            9. HCF is equal to 2

            10. HCF is equal to 49

Highest Common Factor is the full form for this term. The highest factor that may divide two integers evenly is known as the HCF of two numbers. HCF can be assessed using two or more numbers. 

To find the HCF of the following:

HCF of (26, 32):

2      | 26, 32

| 13, 16

HCF is equal to 2.

HCF of (32, 58)

2 | 32, 58

| 16, 29

HCF is equal to 2.

HCF of (25, 37)

No common divisor except 1.

HCF is equal to 1.

HCF of (158, 200)

2 | 158, 200

| 79, 100

HCF is equal to 2.

HCF of (49, 98)

49 | 49, 98

| 1, 2

HCF is equal to 49.

Hence, 6. HCF is equal to 2

            7. HCF is equal to 2

            8. HCF is equal to 1

            9. HCF is equal to 2

            10. HCF is equal to 49

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The gradient of line A is 4 and the gradient of line B is -2.

Graph is a data structure that consists of nodes (or vertices) connected by edges. It is a way of representing data in a structured form and can be used to represent any type of real-world relationship. It can be used to represent geographical relationships between cities, social networks, and even computer networks. Graphs are often used in computer science, mathematics, and engineering to represent relationships between data points.

To calculate the gradient of a line, the formula is rise/run. Thus, the gradient of line A can be calculated as rise/run = 72/4 = 18. On the other hand, the gradient of line B can be calculated as rise/run = 6/-2 = -3

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f(x) is 5/2 times larger than g(x) for large positive or negative values of x, except at the two values x = 3 ± √7 where the expression is undefined.

A relation is a function if it has only One y-value for each x-value.

To find out how many times larger f(x) is than g(x), we need to divide the value of f(x) by the value of g(x).

Then we simplified the expression and found that it is always larger than g(x) except at two values of x where it is undefined.

To determine how much larger f(x) is than g(x), we looked at their leading coefficients and found that f(x) is always larger than g(x) for large positive or negative values of x.

Finally, we took the limit of f(x) / g(x) as x approaches infinity or negative infinity and found that it approaches -5/2.

Hence,  f(x) is 5/2 times larger than g(x) for large positive or negative values of x, except at the two values x = 3 ± √7 where the expression is undefined.

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Answer:See below

Step-by-step explanation:

answers from top left to top right, then bottom left to bottom right.

First one is alternate interior, because they are on the inside, and are on opposite sides.

the second one is supplementary, because they supplement each other, or add up to 180 degrees.

the third one is alternate exterior, because they are opposite to each other on the outside.

the last one is corresponding, because they are in the same position on each side, and are almost like a copy and paste.

I found a few images on the internet to help you understand.

Hope this helped!

Answer: $29.4

Step-by-step explanation: one taco cost 4.20 so multiply the price of the tacos times the amount of tacos gina buys and you should get your answer which is 29.4

Answer:

5 (3x+2)

Step-by-step explanation:

Hope this helps! :)

Step-by-step explanation:

Refer to pic............

Since the park is isosceles trapezoid-shaped, the two sides, AB and CD, that make up the parallel sides of the trapezoid are of equal length.

An isosceles triangle is a type of triangle with two sides of equal length. It has two equal angles opposite of the two equal sides, and the third angle is usually different. Isosceles triangles are named after the Greek term isoskelēs, which means “equal legs”. They are very common in geometry and are used in many applications, including architecture and engineering.

We can then use the midpoints of the adjacent sides of the trapezoid, E and F, to form a rhombus. Since the rhombus is formed from the midpoints of the two parallel sides, we know that the two sides AE and CF of the rhombus are of equal length. Similarly, the two sides BE and FD of the rhombus are also equal in length. This means that the trail, if constructed in the shape of the rhombus, will have all sides of equal length, satisfying the criteria set by the Parks Commission.

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