light of 650 nm wavelength illuminates a single slit of width 0.20 mm . (figure 1) shows the intensity pattern seen on a screen behind the slit.

The ordered pair that respect the given conditions are: (6,-12) and (-12,6).

A system of equations is the given term of math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.

You can solve a system of equations by substitution or adding methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.

You should convert the text of the question into equations. See below.

From equation 1, you have x=-72/y. Thus, applying the substitution method, you can solve this question by following the steps below:

1) Replace  x=-72/y into equation 2. Then, you have:

[tex]\frac{-72}{y} +y=-6\\ \\[/tex]

-72+y²=-6y

y²+6y-72=0

2) Solving the quadratic equation y²+6y-72=0 for finding y:

Δ=b²-4ac

Δ=6²-4*1*(-72)

Δ=36+288

Δ=324

[tex]y=\frac{-b\pm \sqrt{\Delta} }{2a} =\frac{-6\pm \sqrt{324} }{2*1}=\frac{-6\pm18 }{2}[/tex]. Therefore,

y1=(-6-18)/2=-12

or

y2=(-6+18)/2=12/2=6

3) Finding x

If  x=-72/y and y=-12 or y=6. You have

For y=-12, x=-72/-12, thus x=6

For y=6, x=-72/6, thus x=-12

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If a whole number has a whole number square root, it means that there exists a number that you can multiply by itself to get that number.

Let us understand this statement by taking example, the whole number 9 has a whole number square root, which is 3. This means that 3 multiplied by itself gives 9: 3 x 3 = 9. Similarly, the whole number 16 has a whole number square root, which is 4. This means that 4 multiplied by itself gives 16: 4 x 4 = 16.

However, not all whole numbers have whole number square roots. For example, the whole number 2 does not have a whole number square root, which means that there is no whole number you can multiply by itself to get 2. In this case, we would say that 2 is an "irrational" number, because its square root is not a whole number or a fraction of whole numbers.

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Answer:8

Step-by-step explanation:8x1=8

In one of his experiments conducted with animals, Thorndike found that cats learned to escape from a puzzle box is increased gradually

To quantify the learning process, Thorndike used a mathematical formula known as the Law of Effect equation. The equation is:

B = f(log S1/S2)

where B represents the strength of the behavior, S1 represents the satisfaction of the positive consequence, and S2 represents the degree of frustration or negative consequence.

In the context of Thorndike's puzzle box experiment, the Law of Effect equation can be used to describe how the cat's behavior changed over time as it learned to escape the puzzle box more quickly and efficiently. Initially, the cat's behavior was weak because it did not know which actions would lead to a positive outcome.

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The required value is 1.5(IQR) equals 6.

A dataset is a collection of facts that relates to a particular subject. The test results of each pupil in a particular class are an illustration of a dataset. Datasets can be expressed as a table, a collection of integers in a random sequence, or by enclosing them in curly brackets.

The IQR (interquartile range) is the difference between the third quartile (Q3) and the first quartile (Q1). So, we first need to calculate IQR:

IQR = Q3 - Q1 = 16 - 12 = 4

Now we can calculate 1.5 times the IQR:

1.5(IQR) = 1.5(4) = 6

Therefore, 1.5(IQR) equals 6.

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Complete question:

The five-number summary of a data set is given below.

Minimum: 3 Q1: 12 Median: 15 Q3: 16 Maximum: 20

Which of the following equals 1.5(IQR)?

The probability that a randomly chosen card that is less than 7 is the 5 of diamonds is 5%.

There are four suits in a standard deck of 52 cards: diamonds, clubs, hearts, and spades. Each suit has 13 cards, with ranks ranging from 2 (low) to 10, jack, queen, king, and ace (high).

If a randomly chosen card from the deck is less than 7, there are only two possibilities: it is either a 2, 3, 4, 5, or 6 of any suit, or it is the 5 of diamonds.

There are 20 cards that are less than 7 in the deck (4 cards of each of the 5 ranks). Out of these 20 cards, only one is the 5 of diamonds.

Therefore, the probability that a randomly chosen card that is less than 7 is the 5 of diamonds is:

1/20 = 0.05 = 5%

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The median wait time for Speed Slide is 2 minutes longer than the median wait time for Wave Machine and the IQR for both rides is 6 minutes.

A box plot, also known as a box and whisker plot, is a graphical representation of a data set that shows the distribution of the data along a number line.

In the box plots show a random sample of wait times for two rides at a water park is shown in figure.

If we compare the wait times in the box plots,

then for, Speed Slide: Median = 11

IQR= Q1 - Q3           (Calculation formula of IQR)

      = 12 - 6

IQR = 6 minutes

for wave slide: median: 9

IQR= Q1 - Q3           (Calculation formula of IQR)

      = 11 - 9

IQR = 2 minutes

The median wait time for Speed Slide is 2 minutes longer than the median wait time for Wave Machine and the IQR for both rides is 6 minutes.

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Answer:

To subtract 1/9 - 1/14, we need to find a common denominator. The smallest number that both 9 and 14 divide into is 126.

So, we will convert both fractions to have a denominator of 126:

1/9 = 14/126

1/14 = 9/126

Now we can subtract them:

1/9 - 1/14 = 14/126 - 9/126

Simplifying the right-hand side by subtracting the numerators, we get:

5/126

Therefore, 1/9 - 1/14 = 5/126 as an improper fraction.

Answer:

1/9-1/14

=14-9/9*14

=5/126

= 25 1/5

The limit of f(x, y) as (x, y) approaches (0, 0) depends on the path taken, the limit does not exist, and we can conclude that the function f(x, y) do not have a limit as (x, y) → (0, 0).

To show that the function f(x, y) does not have a limit as (x, y) → (0, 0), we need to show that the limit does not exist, either because the limit is infinite or because the limit does not exist.

We are given that the limit of f(x, y) as (x, y) → (0, 0) when y → infinity is infinity. This means that as y approaches infinity, the function f(x, y) becomes arbitrarily large, regardless of the value of x. However, this does not imply that the limit of f(x, y) exists as (x, y) → (0, 0).

To see why, consider the sequence of points (x_n, y_n) = (1/n, n) as n approaches infinity. As y_n → infinity, we have

lim (x_n, y_n) → (0, 0) f(x_n, y_n) = infinity.

However, if we consider the sequence of points (x_n, y_n') = (1/n, n^2) instead, as n approaches infinity, we have

lim (x_n, y_n') → (0, 0) f(x_n, y_n') = 0.

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Answer: 27.3

Step-by-step explanation:

I took the outcomes of the Aces from the trial and found the average and the answer I got was 27.3%

Hope this helps.

The correct answer is:

The equation is [tex]7(c-0.75) = 2.80[/tex], and the regular price of a cookie is [tex]c =\$1.15[/tex].

Explanation:

c is the regular price of a cookie. We know that today they are $0.75 less than the normal price; this is given by the expression [tex]c-0.75[/tex].

We also know if we buy 7 of them, the total is $2.80. This means we multiply our expression, [tex]c-0.75[/tex], by 7 and set it equal to $2.80:

[tex]7(c-0.75) = 2.80[/tex]

To solve, first use the distributive property:

[tex]7 \times c-7\times0.75 = 2.80[/tex]

[tex]7c-5.25 = 2.80[/tex]

Add 5.25 to each side:

[tex]7c-5.25+5.25 = 2.80+5.25[/tex]

[tex]7c = 8.05[/tex]

Divide each side by 7:

[tex]7c\div7 = 8.05\div7[/tex]

[tex]c = \$1.15[/tex].

Answer:

The shaded region in all of the answers are equal.

Step-by-step explanation:

Since squares have equal sides, the area of each square is 12 squared or 144.

The area of the circle in A is pi*radius squared. The diameter is 12, because that is the side length of the square. This means the radius is 6 because the radius of a circle is always half the diameter. So, the area equals 36pi.

The area of the shaded region of A is 144-36pi.

In B, the diameter of each circle is half of what it was in the circles in answer A. So, the diameter is 6 and the radius is 3. The area of each circle is 9pi, and 9 pi * 4 circles is 36pi.

The area of the shaded region of B is 144-36pi.

In C, the diameter of each circle is a third of what it was in the circles in answer A. So, the diameter is 4, and the radius is 2. The area of each circle is 4pi, and 4pi * 9 circles is 36pi.

The area of the shaded region of C is 144-36pi.

Given: We have the expression [tex]\sqrt[3]{875x^5y^9}[/tex]

Step-1: [tex]\sqrt[3]{875x^5y^9}[/tex]

Step-2: [tex](875\times x^5 \times y)^{1/3}[/tex]                              [break the cube root as power [tex]1/3[/tex]]

Step-3: [tex](125.7)^{1/3}\times x^{5/3} \times y^{9/3}[/tex]                    [break [tex]875=125\times7[/tex]]

                                                                     [tex]125=5^3[/tex]

Step-4: [tex](5^3)^{1/3}\times7^{1/3}\times x^{(1+2/3)}\times y^{9/3}[/tex]       [ [tex]\frac{5}{3} =1+\frac{2}{3}[/tex] ]

Step-5: [tex]5^1\times7^{1/3}\times x^1\times x^{2/3}\times y^{3}[/tex]                [break the power of [tex]x[/tex]]

Step-6: [tex]5\times x\times y^{3} \ (7^{1/3}\times x^{2/3})[/tex]

Step-7: [tex]5xy^3 \ (7x^2)^{1/3}[/tex]

Step-8: [tex]5xy^3\sqrt[3]{7x^2}[/tex]

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Answer: Supergirl = 19 and Wonder Woman = 8

Step-by-step explanation:

Let g represent the quantity of Supergirl keychains and w represent the quantity of Wonder Woman keychains.

                            Qty       Cost

Supergirl                 g         $3g

Wonder Woman     w       $2w

Total                       27       $73

Qty:     g +  w  = 27  →   -2(g +  w  = 27)    →    -2g - 2w = -54

Cost: 3g + 2w = 73  →     1(3g + 2w = 73)  →     3g + 2w =  73

                                                                           g          =  19

Input g = 19 into one of the original equations to solve for w:

g  + w = 27

(19) + w = 27

        w = 8

Answer:

It is a tangent

Step-by-step explanation:

A tangent is a straight line that brushes the circumference of a circle.

Therefore, the possible number of pens in the box is p, where p is greater than 135.

Inequality refers to a situation in which there is a difference or disparity between two or more things, usually in terms of value, opportunity, or outcome. Inequality can take many forms, including social, economic, and political inequality.

Inequalities are mathematical expressions that compare two values using the symbols < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). To solve an inequality, you need to isolate the variable (the unknown quantity) on one side of the inequality symbol and determine the range of values for which the inequality holds true.

Here are some general steps to solve an inequality:

by the question.

Let's say there are 'p' pens in the box. Each pack has more than 15 pens, so we can write the inequality:

p/9 > 15

Multiplying both sides by 9, we get:

p > 135

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The equation that represents the value of the collection after 5 years is:

Value of collection after 5 years = 190 x (1 + 0.06)^5

Explanation:

To calculate the value of the collection after 5 years, we need to use the compound interest formula. This formula is represented as A = P x (1 + r)^n, where P is the principal amount (initial value of the collection), r is the rate of interest (in this case, 6%), and n is the number of years (in this case, 5).

Therefore, the equation for the value of the collection after 5 years is:

Value of collection after 5 years = 190 x (1 + 0.06)^5

This can also be written as:

Value of collection after 5 years = 190 x 1.31 (1.31 is the result of (1 + 0.06)^5)

Therefore, the value of the collection after 5 years is $246.90.

Answer: 254.26

Step-by-step explanation:

Answer:

x = 30

Step-by-step explanation:

We know

The three angles must add up to 180°. We know one is 20°, so the other two must add up to 160°.

2x + 3x + 10 = 160

5x + 10 = 160

5x = 150

x = 30

The matches of Histogram, Bin, Descriptive Statistics, Mean, Median and Standard Deviation are C, E, D, A, F, G and B respectively.

The Match the definition are given.

Histogram - C). is a graph of the frequency distribution of a set of data

Bin - E). a group in a histogram

Descriptive Statistics - D). values calculated from a data set and used to describe some basic characteristics of the data set

Mean - A). The scatter around a central point

Median - F). the middle value of a sorted set of data

Mode - G). is the most commonly occurring value in a data set

Standard Deviation - B). is a measure of a data’s variability

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The proof that the lines CD and XY are parallel is shown below in paragraghs

Given that

∠CAY ≅ ∠XBD

This means that the angles CAY and XBD are congruent angles

The above means that

By the corresponding angles, we have

∠BXY = ∠AYX

∠ACD = ∠BDC

By the congruent angles above, the following lines are parallel

Line AC and BX

Line AY and BD

Line CD and XY

Hence, the lines CD and XY are parallel

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Answer:

See step by step.

Step-by-step explanation:

lets define the events:
A: cuban festival        C: tropical Garden
B: street art show      D: african festival

a) theoretically the probability is

[tex]P(A)=P(B)=P(C)=P(D)= \frac{1}{4} = 0.25 \\[/tex]
This is 25% (for each one, equally)

b) The experimental probability is given by:

[tex]P(A)= \frac{32}{150} =0.2133[/tex]

[tex]P(B)= \frac{38}{150} =0.2533[/tex]

[tex]P(C)= \frac{35}{150} =0.2333[/tex]
[tex]P(D)= \frac{45}{150} =0.3000[/tex]

c) The theoretically probabilities are all equally, the experimental probabilities are close to 25% each one, but differ lightly each one, since is an experiment and the result is random.  

there is a 20% chance that the point chosen at random will lie on bg.

To find the probability that a point chosen at random will be on the line segment bg, we need to consider the length of bg in relation to the length of the entire line segment ak.

Let us assume that ak is a straight line segment, and bg is a smaller segment that lies entirely within it. To find the probability, we need to divide the length of bg by the length of ak.

Let the length of bg be x and the length of ak be y. Then the probability that a point chosen at random will be on bg is:

Probability = Length of bg / Length of ak

Probability = x / y

However, we need to be careful here. If we choose a point anywhere on ak, it may not necessarily lie on bg. There are an infinite number of points on ak, but only one segment bg. Therefore, the probability we are looking for is actually the ratio of the lengths of bg to ak.

So, if we know the lengths of bg and ak, we can find the probability by dividing them. For example, if bg is 2 units long and ak is 10 units long, the probability of choosing a point on bg is:

Probability = 2 / 10

Probability = 0.2 or 20%

In this case, there is a 20% chance that the point chosen at random will lie on bg.

In conclusion, the probability of a point chosen at random on ak being on bg is directly proportional to the length of bg in relation to the length of ak. Therefore, we need to find the ratio of the lengths of the two line segments to determine the probability.

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what is the probability  a point is chosen at random on ak and then the point will be on bg. dont forget to reduce the products?

Answer:

Let's assume the original price of the stock was x.

When the company announced it overestimated demand, the stock price fell by 40%.

So, the new price of the stock after the first decline was:

x - 0.4x = 0.6x

A few weeks later, when the seats were recalled, the stock price fell again by 60% from the new lower price of 0.6x.

So, the new price of the stock after the second decline was:

0.6x - 0.6(0.6x) = 0.24x

Given that the current stock price is $2.40, we can set up the equation:

0.24x = 2.40

Solving for x, we get:

x = 10

Therefore, the stock was originally selling for $10.

Therefore, the length of segment AB is approximately 7.4 units.

Area is a mathematical concept that describes the size of a two-dimensional surface. It is a measure of the amount of space inside a closed shape, such as a rectangle, circle, or triangle, and is typically expressed in square units, such as square feet or square meters. The area of a shape is calculated by multiplying the length of one side or dimension by the length of another side or dimension. For example, the area of a rectangle can be found by multiplying its length by its width.

Here,

To find the radius of the circle, we can use the formula for the area of a sector:

Area of sector = (θ/360) x π x r²

where θ is the central angle of the sector in degrees, r is the radius of the circle, and π is approximately 3.14.

We're given that the area of sector COD is 50.24 square units and the central angle of the sector is 90°. So we can plug in these values and solve for r:

50.24 = (90/360) x 3.14 x r²

50.24 = 0.25 x 3.14 x r²

r² = 50.24 / (0.25 x 3.14)

r² = 201.28

r = √201.28

r ≈ 14.2

Therefore, the radius of the circle is approximately 14.2 units.

Next, we need to find the length of segment AB. Since AB is a chord of the circle, we can use the formula:

AB = 2 x r x sin(θ/2)

where θ is the central angle of the sector in degrees, r is the radius of the circle, and sin() is the sine function.

We're given that the central angle of sector COD is 30°. So we can plug in this value and the radius we found earlier to solve for AB:

AB = 2 x 14.2 x sin(30/2)

AB = 2 x 14.2 x sin(15)

AB ≈ 7.4

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Answer:

Step-by-step explanation:

To find the adoption rate as a percentage, we need to divide the number of dogs adopted by the total number of dogs in the shelter, then multiply by 100.

adoption rate = (dogs adopted / total dogs) * 100%

adoption rate = (6 / 80) * 100%

adoption rate = 0.075 * 100%

adoption rate = 7.5%

Therefore, the adoption rate as a percent is 7.5%.

Answer:

9 CDs

Step-by-step explanation:

r u d0mb? 45 divided by 5 = 5 10 15 20 25 30 35 40 45

count the numbers

BOOM ANSWER

Answer:

I'd be happy to help!

a. From the picture of the window, we can identify the following quadrilaterals:

Rectangle: ABCD (all angles are right angles and opposite sides are parallel and congruent)

Parallelogram: EFGH (opposite sides are parallel and congruent)

Trapezoid: BCGH (at least one pair of opposite sides are parallel)

b. To identify the parallelograms in the picture, we would need to know the following properties of parallelograms:

Opposite sides are parallel and congruent

Opposite angles are congruent

Diagonals bisect each other

Using these properties, we can identify the following parallelograms in the picture:

Parallelogram EFGH: Opposite sides EF and GH are parallel and congruent, and opposite sides EG and FH are also parallel and congruent. Additionally, angles E and G are congruent, and angles F and H are congruent.

Rectangle ABCD: Opposite sides AB and CD are parallel and congruent, and opposite sides AD and BC are also parallel and congruent. Additionally, angles A and C are congruent, and angles B and D are congruent. The diagonals AC and BD bisect each other, meaning that they intersect at their midpoints.

Step-by-step explanation:

Answer:

x²  + 4x - 6

Step-by-step explanation:

x(x + (1 + x) + 2x) - 3(x² - x + 2) ← simplify parenthesis on left

= x(x + 1 + x + 2x)  - 3(x² - x + 2)

= x(4x + 1) - 3(x² - x + 2) ← distribute parenthesis

= 4x² + x - 3x² + 3x- 6 ← collect like terms

= x² + 4x - 6