Solve each of the following equations for the indicated variable f = (1+i)"-1 for i​

Set of sophomores taking discrete math = A ∩ B. Set of sophomores not taking discrete math = A - B or A ∩ B^c. Set of students who are sophomores or in discrete math = A ∪ B. Set of students who are not sophomores or not in discrete math = (A ∩ B)^c or A ∪ B^c.

The set of sophomores taking discrete math at your school is the intersection of the set of sophomores A and the set of students in discrete math B. So, it can be expressed as A ∩ B.

The set of sophomores at your school who are not taking discrete math is the difference between the set of sophomores A and the set of students in discrete math B. So, it can be expressed as A - B or A ∩ B^c, where B^c is the complement of B (i.e., the set of students who are not in discrete math).

The set of students at your school who either are sophomores or are taking discrete math is the union of the set of sophomores A and the set of students in discrete math B. So, it can be expressed as A ∪ B.

The set of students at your school who either are not sophomores or are not taking discrete math is the complement of the intersection of the set of sophomores A and the set of students in discrete math B.

This can be expressed as (A ∩ B)^c or as A ∪ B^c, where B^c is the complement of B (i.e., the set of students who are not in discrete math). Note that this set includes all students who are either juniors, seniors, or not enrolled in discrete math.

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Answer:

Step-by-step explanation:

use the formula of gradient:

                                        slope=change in y/ change in x

                                             =    [tex]\frac{Y2-Y1}{X2-X1}[/tex]

                                             = [tex]\frac{-6-2}{-9--9}[/tex]

                                             =[tex]\frac{-8}{0}[/tex]

      the answer is definite because we cannot divide by 0.

a. X= number of unbroken eggs in a standard carton. b. Y= number of absent students on first day of a course. c. U= number of swings before hitting a golf ball. d. X= length of a rattlesnake.

e. Z= royalties earned from selling a first edition of 10,000 textbooks. f. Y= pH of a soil sample. g. X= tension (psi) of a tennis racket. h. X= total coin tosses required for three individuals to get a match.

a. X can take on values 0, 1, 2, 3, 4, 5, 6, as there can be zero to six unbroken eggs in a standard egg carton. X is a discrete random variable.

b. Y can take on values 0, 1, 2, 3, ..., n, where n is the total number of students on the class list. Y is a discrete random variable.

c. U can take on values 1, 2, 3, .... U is a discrete random variable.

d. X can take on any positive real value, as the length of a rattlesnake can vary continuously. X is a continuous random variable.

e. Z can take on any non-negative real value, as the amount of royalties earned can be any non-negative amount. Z is a continuous random variable.

f. Y can take on any value between 0 and 14, as the pH of a soil sample can range from 0 to 14. Y is a continuous random variable.

g. X can take on any positive real value, as the tension at which a tennis racket has been strung can vary continuously. X is a continuous random variable.

h. X can take on values 3, 4, 5, 6, ... as there must be at least three coin tosses and the tosses must continue until a match is obtained. X is a discrete random variable.

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1. The functiοn [tex]f(x) = 3x2^x+4-1[/tex]undergοes the fοllοwing transfοrmatiοns

A vertical translatiοn dοwnward by 1 unit (the [tex]"-1[/tex]" at the end)

An upward vertical stretch by a factοr οf 3 (the "3" cοefficient in frοnt)

An expοnential grοwth with base 2 (the expοnent "x" in the term [tex]"2^x"[/tex])

A hοrizοntal shift tο the left by 4 units (the "-4" in the expοnent οf [tex]"2^x"[/tex])

2. The functiοn [tex]f(x) = -1/2x5^x-2+6[/tex] undergοes the fοllοwing transfοrmatiοns:

3. The functiοn [tex]g(x) = 1/5log(x+5)+3[/tex] undergοes the fοllοwing transfοrmatiοns:

4. The functiοn [tex]g(x) = -4log(x)-2[/tex] undergοes the fοllοwing transfοrmatiοns:

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We can see here the values of the interior angles will be: A) m∠X = 131º, m∠Y = 16º, m∠Z = 33º.

An interior angle is an angle created between two adjacent sides of a polygon. To put it another way, it is the angle created by two polygonal sides that have a shared vertex.

Sum of interior angles of a triangle = 180°

[tex]2p + \frac{1}{4} p + \frac{1}{2} p = 180[/tex]

11p/4 = 180°

p = 720°/11

m∠X = 2p = 2 ×  720°/11 = 130.9 ≈ 131°

m∠Y = [tex]\frac{1}{4} p[/tex] = 1/4 × 720°/11 = 16.3 ≈ 16°

m∠Z = [tex]\frac{1}{2} p[/tex] = 1/2 × 720°/11 = 32.7 ≈ 33°

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In linear equation, 24 is the original number of the man​ .

What in mathematics is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.  

                                    Equations with power 1 variables are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

Original job = x men * 40 days = 40x man days  to complete

 now add 8 men     =    x+8  men

                                          man days now is   (x+8) (30)  to complete job

so     40x = (x+8)(30)

       40x = 30x + 240

         10 x = 240

             x = 24 men originally.

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The gravitational force that the moon produces on the Earth is approximately [tex]1.98 \times 10^{20}\ \mathrm{N}$.[/tex]

What is gravitational force?

Gravitational force is the force of attraction that exists between any two objects in the universe with mass. This force is directly proportional to the masses of the objects and inversely proportional to the square of the distance between their centers.

The gravitational force that the moon produces on the Earth can be calculated using the formula:

[tex]F = G \cdot \frac{m_1 \cdot m_2}{r^2}[/tex]

where:

[tex]G$ = gravitational constant = $6.67430 \times 10^{-11}\ \mathrm{N(m/kg)^2}$[/tex]

[tex]m_1$ = mass of the moon = $7.34 \times 10^{22}\ \mathrm{kg}$[/tex]

[tex]m_2$ = mass of the Earth = $5.97 \times 10^{24}\ \mathrm{kg}$ (approximate)[/tex]

[tex]r$ = distance between the centers of the Earth and the moon = $3.88 \times 10^8\ \mathrm{m}$[/tex]

Substituting these values into the formula, we get:

[tex]F &= 6.67430 \times 10^{-11} \cdot \frac{7.34 \times 10^{22} \cdot 5.97 \times 10^{24}}{(3.88 \times 10^8)^2} \&= 1.98 \times 10^{20}\ \mathrm{N}[/tex]

Therefore, the gravitational force that the moon produces on the Earth is approximately [tex]1.98 \times 10^{20}\ \mathrm{N}$.[/tex]

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Case 1: The constant c of the piecewise function is equal to 1 / 7.

Case 2: The value of the constant b of the piecewise function with the greater absolute value is equal to 20.

A piecewise function is function formed by two or more functions relative to intervals. A piecewise function is continuous if they do not have any jump on graph. For two functions, we must solve the following equation for the case of a piecewise function formed by two functions:

g(a) = h(a)

Case 1 - g(y) = c · y + 3, h(y) = c · y² - 3, a = 7

c · a + 3 = c · a² - 3

c · (a² - a) = 6

c = 6 / (a² - a)

c = 6 / (7² - 7)

c = 6 / 42

c = 1 / 7

The value of the constant c is equal to 1 / 7.

Case 2 - g(x) = b - 2 · x, h(x) = - 150 / (x - b), a = 5

b - 2 · a = - 150 / (a - b)

(b - 2 · a) · (a - b) = - 150

a · b - b² - 2 · a² + 2 · a · b = - 150

- b² + 3 · a · b - 2 · a² = - 150

b² - 3 · a · b + 2 · a² - 150 = 0

b² - 15 · b - 100 = 0

(b - 20) · (b + 5) = 0

b₁ = 20 or b₂ = - 5

The solution with the greater absolute value is b = 20.

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The value of sinθ = -[tex]\frac{7}{8}[/tex] using trigonometry.

One of the most significant areas of mathematics, trigonometry has a wide range of applications. Trigonometry is a field of mathematics that primarily focuses on the analysis of how a right-angle triangle's sides and angles relate to one another.  Therefore, using trigonometric formulas, functions, or trigonometric identities can be helpful in determining the absent or unknown angles or sides of a right triangle. Angles in geometry can be expressed as either degrees or radians. 0°, 30°, 45°, 60°, and 90° are some of the trigonometric angles that are most frequently used in computations.

In this question,

sin²θ + cos²θ= 1

sin²θ + (-1/4)² = 1

sin²θ = 1- (1/8)

sinθ = ± √(7/8)

since, it is in the third quadrant,

sinθ= -[tex]\frac{7}{8}[/tex]

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Answer:

$31122.00

Step-by-step explanation:

We know

She works 35 hours a week, earning $17.10 an hour.

17.10 x 35 = $598.50 a week

How much does she earn in one year?

We Take

598.50 x 52 = $31122.00

So, she earns $31122.00 one year.

There are 81 potential outcomes in Andy's sample space.

Potential Outcomes is a list of every scenario that could happen as a result of an occurrence. For instance, while rolling a dice, the possible results are 1, 2, 3, 4, 5, and 6. 6. Favorable Result - the intended outcome. For instance, if you roll a 4 on a dice, the only possible result is 4.

The total number of cards (i.e., 4 + 3 + 2 = 9) determines the number of outcomes that can occur in each draw.

We must multiply the total number of results for each draw in order to determine the total number of possible outcomes for the two draws.

For two draws with replacement, there are exactly as many outcomes available as the product of the amount of outcomes that could occur in each draw.

9 × 9 = 81.

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Step-by-step explanation:

240g divided in ratios.

divide 240g in the ratio 5:4:3

To divide 240g in the ratio 5:4:3, we need to determine the amount of each part of the ratio.

First, we need to find the total number of parts in the ratio, which is 5 + 4 + 3 = 12.

Next, we divide the total amount (240g) by the total number of parts (12) to find the value of one part:

240g ÷ 12 = 20g

Therefore, one part of the ratio is equal to 20g.

To find the amount of each part of the ratio, we can multiply the value of one part by the corresponding number in the ratio.

The amounts are:

5 parts: 5 × 20g = 100g

4 parts: 4 × 20g = 80g

3 parts: 3 × 20g = 60g

Therefore, to divide 240g in the ratio 5:4:3, we need 100g, 80g, and 60g for each part of the ratio, respectively.

Answer

100g , 80g , 60g

Step-by-step explanation:

      Ratio = 5 : 4 : 3

Let the unit share be 'x'.

So, three shares are 5x, 4x and 3x.

Total weight = 240 g

Total shares = 5x + 4x + 3x =  12x

Sum of all the shares equal to the total weight.

          12x = 240g

             x = 240 ÷ 12 = 20

The value of unit share is 20 g. From this we can find the weight of each share.

5x = 5 * 20 = 100g

4x = 4 * 20 = 80 g

3x = 3 * 20 = 60 g

Answer:

the answer will be 117

Step-by-step explanation:

you need to multiply

When there are few rolls, it is expected that the experimental probability will be significantly higher than the theoretical chance.

The study of random occurrences or phenomena falls under the category of probability, which is a branch of mathematics. It is used to determine how likely or unlikely an occurrence is to occur. An event's likelihood is expressed as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty of occurrence. The symbol P stands for the probability of an occurrence A. (A). It is determined by dividing the number of positive results of event A by all the potential outcomes.

given

(a) The result of rolling 3 or 6 times is 6 + 9 = 15.

Experimental chance = (Total number of rolls) / (Number of times 3 or 6 were rolled) = 15/40 = 0.375

(b) The theoretical likelihood of rolling either a 3 or a 6 on a fair number cube is equal to the total of those odds, which is 1/6 + 1/6 = 1/3 = 0.333. (rounded to three decimal places).

(c) When there are few rolls, it is expected that the experimental probability will be significantly higher than the theoretical chance.

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Answers of angle degrees of p and q

q = 79

p = 101

Explanation

Each angle given has an adjacent angle creating a straight angle of 180 degrees.

First I found the missing adjacent angle degree - see attachment.

We know four of the five interior angle degrees are 85, 136, 138, 102.

Since we know the sum of angles in a pentagon = 540°, we can subtract the known angles from 540 to find “q”

540 - 85 - 136 - 138 - 102 = 79 angle q

To find “p” we know p and q create a straight angle of 180 degrees. We can subtract to find p.

180 - 79 = 101 angle p.

I attached a picture to help

Using SSS theorem of congruency in triangles, we can prove that in all the cases, each triangle is congruent to the other.

Whether two or more triangles are congruent depends on the size of the sides and angles. A triangle's size and shape are consequently determined by its three sides and three angles. If the pairings of the respective sides and accompanying angles are equal, two triangles are said to be congruent. Both of these are the exact same size and shape. Triangles may satisfy a number of distinct congruence requirements.

The SSS criterion is also known as the Side-Side-Side criterion. This standard states that two triangles are congruent if the sum of the three sides of each triangle is the same.

Here in the question,

It is given that the two sides of each triangle are equal to the corresponding sides of the other triangle.

Now as two sides of a triangle is equal to the two sides of another triangle, it is obvious that he third side will be equal to the corresponding sides of the other triangle.

Now as per the SSS criteria, as all the sides are equal to the corresponding sides of the other triangle, the triangle are congruent.

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Answer:

smallest no-- 9829, 9289.

greatest no. 9982,9929.

The volume of the globe is 905 cubic inches, for the given surface area.

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. The region that includes the base(s) and the curved portion is referred to as the total surface area. It is the overall area that the object's surface occupies. The total area of a form with a curved base and surface is equal to the sum of the two areas.

The volume of the globe is given as:

V = 4/3πr³

The surface area if given as:

SA = 4πr²

Substituting the values of the given SA we have:

452.39 = 4 * 3.14(r²)

r = 6.01

Now, substitute the value of r in the equation of volume we have:

V = 4/3(3.14)(6.01)³

V = 904.78.

Hence, the volume of the globe is 905 cubic inches, for the given surface area.

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Answer:

x = 6

Step-by-step explanation:

If 3 or more parallel lines are intersected by two or more transversals , the parallel lines divide the transversals proportionally.

here 3 parallel lines are intersected by two transversals , then

[tex]\frac{1+4x}{20}[/tex] = [tex]\frac{15}{27-15}[/tex]

[tex]\frac{1+4x}{20}[/tex] = [tex]\frac{15}{12}[/tex] ( cross- multiply )

12(1 + 4x) = 20 × 15 = 300 ( divide both sides by 12 )

1 + 4x = 25 ( subtract 1 from both sides )

4x = 24 ( divide both sides by 4 )

x = 6

We can say with 90% confidence that the true proportion of voters who cast their ballot for the candidate lies between 0.564 and 0.636. We can calculate it in the following manner.

To calculate the 90% confidence interval for the proportion of voters who cast their ballot for the candidate, we need to use the following formula:

CI = p ± z√(p(1-p)/n)

where:

CI is the confidence interval

p is the sample proportion

z is the z-score corresponding to the desired confidence level (90% in this case)

n is the sample size

Assuming we have a sample of size n and a sample proportion of p who voted for the candidate, we need to find the value of z for the 90% confidence level. The z-score can be found using a z-table or a calculator, and for a 90% confidence level, the z-score is 1.645.

Substituting the values into the formula, we get:

CI = p ± 1.645√(p(1-p)/n)

For example, if the sample size is 1000 and the sample proportion is 0.6 (60% of voters voted for the candidate), then the 90% confidence interval would be:

CI = 0.6 ± 1.645√(0.6(1-0.6)/1000) = (0.564, 0.636)

Therefore, we can say with 90% confidence that the true proportion of voters who cast their ballot for the candidate lies between 0.564 and 0.636.

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Full question here:

Calculate the 90% confidence interval for the proportion of voters who cast their ballot for the candidate. Number of votes: 125

Voter Response Dummy Variable

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Correct option is A - Ellipse with center at (-5,4) ; B - Ellipse with center at (4,-5) ; C - Hyperbola with center at (4,-5) ; D - Hyperbola with center at (-5,4).

What is conic section ?

Conic sections are curves that are formed by the intersection of a plane and a double cone. The conic sections include circles, ellipses, parabolas, and hyperbolas. Each of these curves has a unique set of characteristics that can be described by mathematical equations.

Explanation of the correct matching :

A - The equation represents an ellipse with center at (-5,4). The values 100 and 225 in the equation represent the squared lengths of the major and minor axes, respectively. The center of the ellipse is (h,k), which is (-5,4) in this case.

B - The equation represents an ellipse with center at (4,-5). The values 16 and 9 in the equation represent the squared lengths of the major and minor axes, respectively. The center of the ellipse is (h,k), which is (4,-5) in this case.

C - The equation represents a hyperbola with center at (4,-5). The values 64 and 81 in the equation represent the squared distances between the center and the vertices on the y-axis and x-axis, respectively. The center of the hyperbola is (h,k), which is (4,-5) in this case.

D - The equation represents a hyperbola with center at (-5,4). The values 16 and 9 in the equation represent the squared distances between the center and the vertices on the x-axis and y-axis, respectively. The center of the hyperbola is (h,k), which is (-5,4) in this case.

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Answer:

C A D B

Step-by-step explanation:

on edge

Answer

Connie can cut the ribbon into 12 foot pieces.

Step-by-step explanation:

For these problems we should find the GCF, which is 12.

The mean of x is 1.25 and the variance of x is approximately 0.1458.

The continuous uniform distribution has a constant probability density function (PDF) between its minimum and maximum values. In this case, the minimum value is 1/2 and the maximum value is 2.

The mean of a continuous uniform distribution is the average of the minimum and maximum values:

mean = (minimum + maximum) / 2

    = (1/2 + 2) / 2

    = 1.25

The variance of a continuous uniform distribution is defined as:

[tex]variance = (maximum - minimum)^2 / 12[/tex]

        [tex]= (2 - 1/2)^2 / 12[/tex]

        = 7/48

        ≈ 0.1458

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A quadratic function in standard form that passes through the points [tex](-8,0), (-5,-3), and (-2,0)[/tex] is equals to the [tex]f(x) = (1/3)( x^{2} + 10x + 16)[/tex].

f(x) = ax2 + bx + c, in which a, b, and c are integers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph.

In other terms, you have a quadratic equation if a times the squares of the expression after b plus b twice that same equation not square plus c equals 0.

[tex]f(x) = ax^{2} + bx + c ----(1)[/tex]

is determined by three points and must be [tex]a[/tex] not equal [tex]0[/tex]. That is for determining the f(x) we have to determine value of three values a, b, and c. Now, we have three ordered pairs [tex](-8,0), (-5,-3)[/tex], and [tex](-2,0)[/tex] and we have to determine quadratic function passing through these points. So, firstly, plug the coordinates of point[tex]( -8,0), x = -8, y = f(x) = 0[/tex] in equation [tex](1)[/tex],

[tex]= > 0 = a(-8)^{2} + b(-8) + c[/tex]

[tex]= > 64a - 8b + c = 0 -------(2)[/tex]

Similarly, for second point [tex]( -5,-3) , f(x) = -3, x = -5[/tex]

[tex]= > - 3 = a(-5)^{2} + (-5)b + c[/tex]

[tex]= > 25a - 5b + c = -3 --(3)[/tex]

Continue for third point [tex](-2,0)[/tex]

[tex]= > 0 = a(-2)^{2} + b(-2) + c[/tex]

[tex]= > 4a -2b + c = 0 --(4)[/tex]

So, we have three equations and three values to determine.

Subtract equation [tex](4)[/tex] from [tex](2)[/tex]

[tex]= > 64 a - 8b + c - 4a + 2b -c = 0[/tex]

[tex]= > 60a - 6b = 0[/tex]

[tex]= > 10a - b = 0 --(5)[/tex]

subtract equation [tex](4)[/tex] from [tex](3)[/tex]

[tex]= > 21a - 3b = -3 --(6)[/tex]

from equation (4) and (5),

[tex]= > 3( 10a - b) - 21a + 3b = -(- 3)[/tex]

[tex]= > 30a - 3b - 21a + 3b = 3[/tex]

[tex]= > 9a = 3[/tex]

[tex]= > a = 1/3[/tex]

from [tex](5)[/tex] , [tex]b = 10a = 10/3[/tex]

from [tex](4)[/tex], [tex]c = 2b - 4a = 20/3 - 4/3 = 16/3[/tex]

So,[tex]f(x)= (1/3)( x^{2} + 10x + 16)[/tex]

Hence, required values are [tex]1/3, 10/3,[/tex] and [tex]16/3[/tex].

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Answer:

-------------------------------------

Given 3 points of a quadratic function and two of them lie on the x-axis:

These two points are representing the roots of the function. With known roots we can show the function in the factor form:

Substitute the roots into the equation and use the third point with coordinates x = - 5, f(x) = - 3, find the value of a:

This gives us the function in the factor form:

Convert this into standard form of f(x) = ax² + bx + c:

Hello, I think the answer is D. Since the scores arent that huge of a gap, dot plot because small number scores are reported individually

The solution for question a), b) and c) are as follows. The number of ways to choose 24 candies is 20475. And the number of  of ways to choose 24 candies with at least a piece of each flavor is 7700. Similarly, the total number of ways to choose 24 candies with at least 2 cherry and at least 2 lemon is 272.

(a) To choose 24 candies from 5 types of hard candies, we can use the stars and bars method. We need to distribute 24 candies among 5 types, where each type can have 0 or more candies.

We can represent this by 24 stars (*) and 4 bars (|) to separate the candies of different types. The number of ways to arrange these stars and bars is the same as the number of ways to choose 4 positions out of 28 to place the bars. Therefore, the number of ways to choose 24 candies is:

(28 choose 4) = 20475

(b) To choose 24 candies with at least a piece of each flavor, we can first choose 5 candies, one of each flavor, and then choose 19 candies from the remaining candies. The number of ways to choose 19 candies from 20 candies (excluding one candy of each flavor) is:

(19 + 4 - 1) choose (4 - 1) = 22 choose 3 = 1540

Therefore, the total number of ways to choose 24 candies with at least a piece of each flavor is:

5 * 1540 = 7700

(c) To choose 24 candies with at least 2 cherry and at least 2 lemon, we can use the inclusion-exclusion principle. Let A be the event that we choose at least 2 cherry, and let B be the event that we choose at least 2 lemon. Then the number of ways to choose 24 candies with at least 2 cherry and at least 2 lemon is:

P(A union B) = P(A) + P(B) - P(A intersect B)

To calculate P(A), we can choose 2 cherry and then choose 20 candies from the remaining 3 types, which is:

(2 choose 2) * (20 + 3 - 1) choose (3 - 1) = 22 choose 2 = 231

Similarly, P(B) is also 231.

To calculate P(A intersect B), we can choose 2 cherry, 2 lemon, and then choose 18 candies from the remaining 3 types, which is:

(2 choose 2) * (2 choose 2) * (18 + 3 - 1) choose (3 - 1) = 20 choose 2 = 190

Therefore, the total number of ways to choose 24 candies with at least 2 cherry and at least 2 lemon is:

2 * 231 - 190 = 272

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The equation of the line passing through (2,5) with a slope of 3 is y = 3x - 1.

This question is incomplete, the complete question is:

What is the equation of line passing through: (2,5), and with a slope = 3​?

The equation of a line in slope-intercept form is expressed as:

y = mx + b

Where m is the slope and b is the y-intercept.

Given that, the point (2, 5) and the slope of the line is 3.

We can use the point-slope form of the equation of a line to find the equation in slope-intercept form:

y - y1 = m(x - x1)

Where x1 and y1 are the coordinates of the given point ( 2,5 ) and m is slope 3.

Substituting the given values, we get:

y - y1 = m(x - x1)

y - 5 = 3(x - 2)

Expanding and rearranging, we get:

y - 5 = 3x - 6

y = 3x - 1

Therefore, the equation of the line is y = 3x - 1.

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the intensity pattern visible on a screen at 1.168 metres behind the slit.

That is the answer to the question "650 nm light shines on two slits that are separated by 0.20 mm. The image depicts the intensity pattern visible on a screen hidden behind the slits (Figure 1).

How far away from you is the screen?"

It is possible to specify that the distance to the screen is d=1.168m.

The answer to the question is that 650 nm light illuminates two slits that are 0.20 mm apart. The image depicts the intensity pattern visible on a screen hidden behind the slits (Figure 1).

How far is the screen from you?

The equation for the distance is typically presented mathematically as

d=1.168m

As a result,

d=1.168m is the distance to the screen.

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Answer:

its 5

Step-by-step explanation:

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