Today Mary's aunt and grandmother came to visit. Her aunt visits every six days and her grandmother visits every eight days. The next time they will both visit Mary on the same day will be how many days?

Answer: The quotient is 3y² + 2y - 1.

Step-by-step explanation:

You can use long division to solve this expression by setting the dividend under the roof and the divisor outside as you would normally do when dividing numbers.

1) Look at the first term of the dividend, 15y³, and the first term of the divisor, 5y. Determine what value multiplied by 5y would give you 15y³. The answer is 3y², and given the number, you multiply it by the WHOLE divisor.

3y²(5y + 6) = 15y³ + 18y² <-- subtract this from the dividend.

2) Continue this process and make sure to drag down the next term for each new value you form after subtracting. Keep in mind of any negative values! When you reach up to -5y, determine what value multiplied by 5y would give you the value of -5y, which would be -1.

3) You should be left with a remainder of 0, leaving you with a quotient of 3y² + 2y - 1.

According to the information, we can infer that the correct expression is (10 * 7) + (2 * 7) (option D).

To find the correct expression we must look at the graph and interpret the information it has. In this case, some tiles are white and others are gray, so they would represent different elements. In this case, the white area is 10 * 7 tiles, so this would be the first part of the expression.

On the other hand, the second part of the expression would be 7 * 2, which represents the length, length and width of the gray area. According to the above, the correct expression would be (10 * 7) + (2 * 7), the first part in parentheses represents the white area and the second part in parentheses represents the gray area.

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Answer:

The jumping dolphin is approx. 6 meters under sea level

The flying seagull is approx. 8 meters under sea level

The mobula ray is approx. 2 meters under sea level

The clownfish is approx.t 4 meters under sea level

The octopus is approx.  8 meters under sea level

The jumping dolphin: The mobula ray is 9 meters lower than the jumping dolphin.

The flying seagull: The mobula ray is 11 meters lower than the flying seagull.

The octopus: The mobula ray is 11 meters higher than the octopus.

The jumping dolphin: The albatross is 1 meter lower than the jumping dolphin.

The flying seagull: The albatross is 3 meters lower than the flying seagull.

The octopus: The albatross is 13 meters higher than the octopus.

The jumping dolphin: The clownfish is 8 meters lower than the jumping dolphin.

The flying seagull: The clownfish is 10 meters lower than the flying seagull.

The octopus: The clownfish is 6 meters higher than the octopus.

If the new dolphin is above the dolphin in the picture, then its distance from the surface of the ocean is 6 - 3 = 3 meters.

If the new dolphin is below the dolphin in the picture, then its distance from the surface of the ocean is 6 + 3 = 9 meters.

✧☆*: .｡. Hope this helps, happy learning! (✧×✧) .｡.:*☆✧

Case 1: a = 0; b = 0 --> Real Number

Case 2: a = 0; b ≠ 0 --> Non-Real Complex Number

Case 3: a ≠ 0; b = 0 --> Real Number

Case 4: a ≠ 0; b ≠ 0 --> Non-Real Complex Number

For each case, we can determine whether the expression a + bi represents a real number or a non-real complex number based on the values of a and b.

Case 1: a = 0; b = 0

In this case, both a and b are zero. The expression a + bi simplifies to 0 + 0i, which is equal to 0. Therefore, the expression represents a real number.

Case 2: a = 0; b ≠ 0

Here, a is zero, but b is nonzero. The expression a + bi becomes 0 + bi, where b is a nonzero real number multiplied by the imaginary unit i. Since the expression contains a nonzero imaginary part, it represents a non-real complex number.

Case 3: a ≠ 0; b = 0

In this case, a is nonzero, but b is zero. The expression a + bi simplifies to a + 0i, which is equal to a. As there is no imaginary part in the expression, it represents a real number.

Case 4: a ≠ 0; b ≠ 0

Here, both a and b are nonzero. The expression a + bi contains both a real part (a) and an imaginary part (bi). Thus, it represents a non-real complex number.

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Answer:

7

Step-by-step explanation:

It adds 2 each time to the function. Y-Intercept is 1, so you add 2 three times.

2*3=6

6 plus the starting dog (1)= 7

(6,8) is the answer also this could be the answer too (6,2)

hope this helps

Answer:

If both sides are equal

Step-by-step explanation:

If both sides are equal and are the same in both sides of the equation, than it is a solution.

For instance, the solution for 2x = 4, is x = 2 because 2(2) = 4 is 4 = 4.

here x+3y=13

x=13-3y.....1st equation

-3x+2y=27......2nd euation

now putting the value of x from equation 1st in 2nd we will get

-3(13-3y)+2y=27

-49+9y+2y=27

11y=27+49

y=76÷11

y=6.9

now again putting the value of y in equation 1st we get

x=13-3×6.9

x=13-20.7

x=7.7

Answer:

✔ 10/y – 4 + 8

.

Second,

✔ substitute

2 in for the variable, y.

Third,

✔ simplify

by using

✔ order of operations

.

The answer is

✔ 9

Step-by-step explanation:

i hope this helps-

The surface area of the rectangular prism in this problem is given as follows:

A. 426 m².

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas. -> net method.

The dimensions for this problem are given as follows:

5 m, 12 m and 9 m.

Hence the surface area of the prism is given as follows:

S = 2(5 x 12 + 5 x 9 + 12 x 9)

S = 426 m².

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Answer:

2hrs 30 mins

Step-by-step explanation:

if the buoy Is 12 up and 16 right than you can use Pythagorean theorem

a²+b²=c²

144+256=c²

400=c²

√400=√c²

20=c

20/8=2.5

2 hrs 30 mins

Answer:

24 square inches

Step-by-step explanation:

Based on the diagram or figure given, The  area of the figure is known to be 24 square inches.

The area of a figure is known to be the rate or the number of unit squares that is said to have cover the surface of a closed figure.

Note that the area is often measured in square units such as (cm²) and in the case above, the Based on the diagram or figure given, The  area of the figure is known to be 24 square inches.

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Answer:

The first box : -4  the second one : 6

Step-by-step explanation:

subtract 7 from 3 for the first box, then add 10 to -4 for the second one.

The true statement based on the relationship depicted in the Venn diagram is that no rhombuses are trapezoids (option D).

To identify the true statement using the relationship represented in the Venn diagram, we need to analyze the overlapping regions and the properties of the shapes involved.

A trapezoid is a quadrilateral with at least one pair of parallel sides, while a rhombus is a quadrilateral with all sides of equal length. Let's evaluate the options:

A. All trapezoids are rhombuses: This statement is not true based on the diagram. The overlapping region between the trapezoids and rhombuses shows that there are trapezoids that are not rhombuses. Therefore, option A is incorrect.

B. All rhombuses are trapezoids: This statement is true based on the diagram. The entire region representing rhombuses is also included within the region representing trapezoids. Every rhombus can be considered a trapezoid because it has at least one pair of parallel sides. Thus, option B is correct.

C. No trapezoids are rhombuses: This statement is not true based on the diagram. The overlapping region indicates that there are trapezoids that are indeed rhombuses. Therefore, option C is incorrect.

D. No rhombuses are trapezoids: This statement is true based on the diagram. There is no overlap between the regions representing rhombuses and trapezoids, implying that no rhombus can be considered a trapezoid. Hence, option D is correct.

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Answer:

true

Step-by-step explanation:

Answer:

true.

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

7,750÷155=50

The answer to the expression is  (x+3)/(x-1)

You should recall that a quadratic expression is an algebraic expression of the form ax2 + bx + c = 0, where a ≠ 0

The given expressions are

(x² - 3x - 18) / (x²- 7x +6

(x²-6x +3x +19) / (x²-x -6x +6)

This implies that {(x²-6x)+(3x-18)} / {(x²-x) -(6x+6)}

⇒[x(x-6)+3(x-6)] / [x(x-1) - 6(x-1)]

This means that [(x+3)(x-6)] / [(x-6)(x-1)]

Dividing by (x-6) to have

Therefore the value of the expression is (x+3)/(x-1)

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To do a dot plot you have to put dots in a vertical line corresponding to the achieved goal.

So for the table given, you will have this plot:

See that each vertical tick corresponds to each column.

Maraging (18% Ni) steel has a better tolerance to defects and fracture toughness compared to Medium strength steel.

The tolerance to defects and fracture toughness of a material can be evaluated using its fracture toughness parameter, Kic. The higher the Kic value, the better the material's tolerance to defects and fracture toughness.

To compare the two materials, we can use the concept of critical stress intensity factor (Kic) and factor of safety (FoS). The critical stress intensity factor is the maximum value of stress intensity factor (K) that a material can withstand without fracturing. The factor of safety is the ratio of the maximum allowable stress to the design stress, and it is used to ensure a safety margin in the design.

Assuming that the two materials have the same defect to tolerance ratio, we can calculate the maximum allowable stress for each material using the following formula:

σmax = FoS * Kic / (π * a)

where σmax is the maximum allowable stress, FoS is the factor of safety (assumed to be 2), Kic is the fracture toughness parameter, and a is the size of the defect.

Let's assume a defect size of 1 mm for both materials. Using the values given in the question, we get:

For Maraging (18% Ni) steel:

σmax = 2 * 82 * 10^6 / (π * 1 * 10^-3) = 52.1 GPa

For Medium strength steel:

σmax = 2 * 50 * 10^6 / (π * 1 * 10^-3) = 31.8 GPa

Therefore, Maraging steel has a higher maximum allowable stress, which indicates that it has a better tolerance to defects compared to medium strength steel.

To compare the fracture toughness of the two materials, we can use their respective Kic values. The higher Kic value indicates a better tolerance to defects and fracture toughness.

Comparing the given values, we can see that Maraging (18% Ni) steel has a higher fracture toughness parameter (Kic= 82 MNm-3/2) compared to Medium strength steel (Kic= 50 MNm-3/2).

Therefore, Maraging (18% Ni) steel has a better tolerance to defects and fracture toughness compared to Medium strength steel.

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He can make 6 different flags with 3 parts to them and use either stripes or spots for each of the flags.

The flag has 3 different parts and he uses either stripes or spots to design the three parts.

The number of different design of flag he can make can be calculated below:

So, he can make 6 different flags.

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Given the following information:

We can find a and b as follows:

Now we know the values of a and b, we can find a+b:

Answer:

(a) 0

As group size increases, the complexity of the group increases (option A).

What is group size?

Even within the same species, group size can vary greatly, so we frequently need statistical tests to evaluate these measurements between two or more samples as well as statistical measures to quantify group size. Since group sizes typically follow an aggregated (right-skewed) distribution, where most groups are small, few are large, and a very small number are very large, group size measures are infamously challenging to handle statistically.

As group size increases, the complexity of managing and coordinating the group also increases.

The larger the group, the more difficult it is to communicate effectively, to make decisions, and to ensure that everyone is working towards a common goal.

This is why larger organizations often have more complex hierarchies and more formalized communication and decision-making processes.

Therefore, the correct option is A.

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Answer:

The statement in the question is wrong. The series actually diverges.

Step-by-step explanation:

We compute

\(\lim_{n\to\infty}\frac{n^2}{(n+1)^2}=\lim_{n\to\infty}\left(\frac{n^2}{n^2+2n+1}\cdot\frac{1/n^2}{1/n^2}\right)=\lim_{n\to\infty}\frac1{1+2/n+1/n^2}=\frac1{1+0+0}=1\ne0\)

Therefore, by the series divergence test, the series \(\sum_{n=1}^\infty\frac{n^2}{(n+1)^2}\) diverges.

EDIT: To VectorFundament120, if \((x_n)_{n\in\mathbb N}\) is a sequence, both \(\lim x_n\) and \(\lim_{n\to\infty}x_n\) are common notation for its limit. The former is not wrong but I have switched to the latter if that helps.

Answer:

\(\displaystyle \sum^{\infty}_{n = 1} \frac{n^2}{(n + 1)^2} = \text{div}\)

General Formulas and Concepts:

Calculus

Limits

Series Convergence Tests

Step-by-step explanation:

*Note:

Always apply the nth Term Test as the first test to use for convergence.

Rules:

Step 1: Define

Identify

\(\displaystyle \sum^{\infty}_{n = 1} \frac{n^2}{(n + 1)^2}\)

Step 2: Find Convergence

∴ by the nth Term Test, the series diverges.

Topic: AP Calculus BC (Calculus I + II)

Unit: Convergence Tests

Answer:

{-3, 2}U{2, 5}

Step-by-step explanation:

For an equation to be negative, it would need to be in a negative range (below the x-axis or the coordinates are negative y-values). Therefore, we can examine this question and see that the graph is negative when the function crosses the x-axis at -3 and it remains negative until you reach 2 on the x-axis.

Therefore, the first set of negative values is (-3, 2).

Secondly, applying the same logic as before, the function decreases at 2 and then touches the x-axis again at 5. Therefore, the second negative value would be (2, 5).

The negative values are {-3, 2}U{2, 5}.

Answer:

{-3, 2}U{2, 5}

Step-by-step explanation:

Answer:

the minimum sample size n = 11.03

Step-by-step explanation:

Given that:

approximate value of the population standard deviation \(\sigma\) = 49

level of significance ∝ = 0.01

population mean = 38

the minimum sample size n = ?

The minimum sample size required can be determined by calculating the margin of error which can be re[resented by the equation ;

Margin of error = \(Z_{ \alpha /2}} \times \dfrac{\sigma}{\sqrt{n}}\)

\(38 = \dfrac{2.576 \times 49}{\sqrt{n}}\)

\(\sqrt{n} = \dfrac{2.576 \times 49}{38}\)

\(\sqrt{n} = \dfrac{126.224}{38}\)

\(\sqrt{n} = 3.321684211\)

\(n= (3.321684211)^2\)

n ≅ 11.03

Thus; the minimum sample size n = 11.03

Navern's manufacturing cycle efficiency (MCE) for its elevators is: 41.4%

The formula for obtaining the manufacturing cycle efficiency is value-added time divided by the production cycle time * 100. In the data given, the process and inspection times qualify as a value-added time

Process time = 23 days

Inspection time = 13 days

Value added time = 23 + 13 = 36days

The production cycle time = Move time + process time + queue time + inspection time + wait time

= 22 + 12 + 23 + 13 + 17 days

= 87 days

So, the manufacturing efficiency time = 36/87 * 100

= 41.4%

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