a student in a statistics class decided to analyze the number of candies per package for a project. a dot plot of the counts of candies in one package is shown below. what was the most common number of candies in a package?

The value of p(-9) is -10.2.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given is an equation,

p(x) =  -37 + (2/5) (x² - 14)

To find the value of p(-9), substitute -9 in the place of x.

p(-9) = -37 + (2/5) ((-9)² - 14)

        = -37 + (2/5) (81 - 14)

        = -37 + (2/5) × 67

        = -37 + 26.8

        = -10.2

Hence the value of the function when x = -9 is -10.2.

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To divide powers that have the same base and different​ exponents, keep the​ base and​ subtract the exponents.

When dividing two powers that have the same base but different exponents, you keep the base and subtract the exponents.

For example, if you want to divide a^m by a^n,

you can write it as a^m / a^n

= a^(m-n).

The new exponent is the result of subtracting the exponents of the two powers.

hence the division will result to a^(m-n).

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The solution to the system of equations is x = 0, y = 3, and z = 4.

What is algebraic equation ?

An algebraic equation or polynomial equation is an equation of the form P=0 where P is a polynomial with coefficients in some field, often the field of the rational numbers.

First, multiply the first equation by 2 and add it to the second equation to eliminate x:

-3x - 5y + z = -8

2 * (-3x - 5y + z) = 2 * -8

-6x - 10y + 2z = -16

2x + 8y - z = -4

-6x - 10y + 2z + 2x + 8y - z = -16 - 4

-4x - 2y + 3z = -20

Next,  divide the third equation by 3 to obtain y:

x + 2y - z = 2

y = (2 - x + z) / 2

x + 2y - z = 2

x + 2 * (2 - x + z) / 2 - z = 2

x + 2 - x + z - z = 2

z = 4 - x,

y = (2 - x + 4 - x) / 2

y = (2 - 2x + 4) / 2

y = (6 - 2x) / 2

z = 4 - x

4 = 4 - x

x = 0

Plugging in the values of x and z into the equation for y:

y = (6 - 2x) / 2

y = (6 - 2 * 0) / 2

y = 6 / 2

y = 3

So, the solution to the system of equations is x = 0, y = 3, and z = 4.

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The solution to the system of equations for all three variables is x = -3, y = -5, and z = -15.

We can solve this system of equations using the elimination method or substitution method. Here, I will use the elimination method:

Starting with the first equation:

-3x - 5y + z = -8

Adding the second equation:

-3x - 5y + z + 2x + 8y - z = -8 + (-4)

-x + 3y = -12

Adding the third equation:

-x + 3y + x + 2y - z = -12 + 2

2y = -10

Solving for y:

y = -5

Substituting y back into the first equation:

-3x - 5(-5) + z = -8

-3x + 25 + z = -8

-3x + z = -33

Substituting y back into the second equation:

2x + 8(-5) - z = -4

2x - 40 - z = -4

2x - z = 36

Adding the two equations to eliminate x:

-3x + z + 2x - z = -33 + 36

-x = 3

Solving for x:

x = -3

Substituting x and y back into the third equation:

-3 + 2(-5) - z = 2

-3 - 10 - z = 2

-13 - z = 2

Solving for z:

z = -15

Therefore, the solution is x = -3, y = -5, and z = -15.

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The empirical formula of a compound is the simplest and lowest whole number ratio of the atoms of each element that makes up a compound.

To find the empirical formula from percentages, you need to first calculate the mass of each element present in the compound, based on the percentage of each element. Once you have the mass of each element, divide each mass by the atomic mass of that element to get the number of moles of each element. Then divide each mole by the smallest number of moles to get the mole ratio. This ratio is the empirical formula for the compound.

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The running time of the algorithms of addition, multiplication and division of two numbers are O(N), O(N^2), and O(N^2) respectively.

For the typical algorithms used to perform calculations by hand:

A. Adding two N-digit integers typically takes O(N) time. This is because each digit of the larger number needs to be added to the corresponding digit of the other number and the carry over needs to be taken into account.

B. Multiplying two N-digit integers typically takes O(N^2) time. This is because each digit of one number needs to be multiplied by each digit of the other number, and the intermediate results need to be summed.

C. Dividing two N-digit integers typically takes O(N^2) time. This is because the process of long division involves repeatedly dividing, multiplying, and subtracting the digits of the dividend and the divisor until the result is obtained.

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Answer:

19

Step-by-step explanation:

step by step

Answer:

1 : 2

Step-by-step explanation:

9 : 18

Both numbers are divisible by 9, thus:

9/9 : 18/2

[1 : 2]

So, the values of the trigonometric functions of t are sin(t) = 1/7, cos(t) = -√(1 - (1/7)^2) and tan(t) = -(1/7)/(-√(1 - (1/7)^2)).

Given that csc(t) = 7 and cos(t) < 0, we can find the values of the other trigonometric functions of t using the relationships between the trigonometric functions.

csc(t) = 1/sin(t), so sin(t) = 1/7

Since cos(t) < 0, t is in the second or third quadrant, where sin(t) is positive. Hence, t is in the third quadrant.

Therefore, the values of the trigonometric functions of t are:

sin(t) = 1/7

cos(t) = -√(1 - sin^2(t)) = -√(1 - (1/7)^2)

tan(t) = sin(t)/cos(t) = -(1/7)/(-√(1 - (1/7)^2))

Note that the values of the other trigonometric functions, such as cot(t), sec(t), and csc(t), can be found using the definitions of these functions and the values of sin(t) and cos(t) that we have found.

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So, the values of the trigonometric functions of t are  [tex]Sin(t)=\frac{1}{7}[/tex], [tex]Cos(t)=-\sqrt{[1-(\frac{1}{7})^2] }[/tex]  and  [tex]tan(t)=\frac{\frac{1}{7} }{-\sqrt{1-(\frac{1}{7})^2 } }[/tex].

Given that csc(t) = 7 and cos(t) < 0, we can find the values of the other trigonometric functions of t using the relationships between the trigonometric functions.

[tex]Cosec(t)=7[/tex]

We known

⇒ [tex]Sin(t)=\frac{1}{Cosec(t)} =\frac{1}{7}[/tex]

Since cos(t) < 0, t is in the second or third quadrant, where sin(t) is positive. Hence, t is in the second quadrant.

Therefore, the values of the trigonometric functions of t are:

⇒ [tex]Sin(t)=\frac{1}{7}[/tex]

⇒ [tex]Cos(t)=-\sqrt{[1-(Sin^2t)]}[/tex]

⇒ [tex]Cos(t)=-\sqrt{[1-(\frac{1}{7})^2] }[/tex]

⇒ [tex]tan(t)=\frac{Sin(t)}{Cos(t)}[/tex]

⇒ [tex]tan(t)=\frac{\frac{1}{7} }{-\sqrt{1-(\frac{1}{7})^2 } }[/tex]

∴ Note that The definitions of the other trigonometric functions, along with the values of Sin(t) and Cos(t), can be used to determine the values of cot(t), Sec(t), and Cosec(t).

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Answer:

1/6 and 1/6^1 so the second and 4th one.

Step-by-step explanation:

Look it up bud

Use the information in provided in each part of the question to analyze the probability is 42.

Use the information in provided in each part of the question to analyze the probability.

A dealer deals a hand consisting of 3 spades, 4 diamonds. 6 clubs and 5 hearts. If two cards are picked at random from that hand without replacement,

The two types of compound events are calculated using several formulas: If two occurrences, A and B, are mutually exclusive, then P(A or B) = P (A) + P (B). P (A or B) = P(A) + P(B) - P for mutually inclusive occurrences (A and B).

Once the first event has occurred, multiply the likelihood of the subsequent event by the previous event's probability to arrive at the compound probability of dependent events.

P (A) + P (B)

3(4) + 6(5) = 12 + 30 = 42.

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Answer:

38

Step-by-step explanation:

Since the figure shown of ABCD has two pairs of parallel lines, it can be classified as a parallelogram.

Opposite sides are congruent in a parallelogram, so:

AB = CD = 9

BC = AD = 10

To find the perimeter you sum together all the sides. Therefore the perimeter of ABCD would be AB + BC + CD + AD. This is equal to:

9 + 10 + 9 + 10 = 38

Answer: The irreflexive closure of a relation R R R cannot contain any elements of the form ( a , a ) ∉ R (a,a)\notin R (a,a)∈/R (by the definition of reflexive).

Step-by-step explanation:

We can write {x} as follows -

{x} = (4/3) - (c/3)

An function in mathematics defines a relationship between one variable (the independent variable, x)  and another variable (the dependent variable, y). Example -

y = f{x} = ax + b

Given is a equation as -

3x + c = 4

The given equation is -

3x + c = 4

3x = 4 - c

x = (4 - c)/3

x = (4/3) - (c/3)

Therefore, we can write {x} as follows -

{x} = (4/3) - (c/3).

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The sum can be used when sum gives the situations in which the probability of a union of events can be calculated by summing probabilities together. and product rule  If there are n(A) ways to do A and n(B) ways to do B, then the number of ways to do A and B is n(A) × n(B)

What is Probability?

Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

Reason:

The probability rule of sum describes scenarios in which the probability of a union of events can be computed by adding probabilities. It is frequently used on mutually exclusive occurrences, which are events that cannot occur at the same moment.

If there are n(A) ways to perform A and n(B) ways to do B, then the total number of ways to accomplish A and B is n(A) n. (B). This is true if the number of possible ways to do A and B are independent; the number of options for doing B is the same regardless of the option you chose for A.

The probability product rule states that P(AnB) = P(A) * P (B)

This implies that the events must be distinct.

In contrast, for the probability sum rule.

P(A + B) = P(A) + P(B) (B)

This suggests that P(AnB) = 0, indicating that they are disjoint or mutually exclusive.

Box 2 states that the sum rule is used when events are independent, however this is not correct; it is employed when events are mutually exclusive.

Two events are said to be mutually exclusive in probability theory if they cannot occur at the same time or concurrently. In other words, discontinuous events are those that are mutually exclusive. If two occurrences are regarded discontinuous, the likelihood of both occurring at the same time is zero.

If A and B are the two events, then the probability of their disjoint is stated as:

P (A and B) = 0 for the probability of a disjoint (or mutually exclusive) event.

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The sum can be used when sum gives the situations in which the probability of a union of events can be calculated by summing probabilities together. and product rule  If there are n(A) ways to do A and n(B) ways to do B, then the number of ways to do A and B is n(A) × n(B)

What is Probability?

Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

Reason:

The probability rule of sum describes scenarios in which the probability of a union of events can be computed by adding probabilities. It is frequently used on mutually exclusive occurrences, which are events that cannot occur at the same moment.

If there are n(A) ways to perform A and n(B) ways to do B, then the total number of ways to accomplish A and B is n(A) n. (B). This is true if the number of possible ways to do A and B are independent; the number of options for doing B is the same regardless of the option you chose for A.

The probability product rule states that P(AnB) = P(A) * P (B)

This implies that the events must be distinct.

In contrast, for the probability sum rule.

P(A + B) = P(A) + P(B) (B)

This suggests that P(AnB) = 0, indicating that they are disjoint or mutually exclusive.

Box 2 states that the sum rule is used when events are independent, however this is not correct; it is employed when events are mutually exclusive.

Two events are said to be mutually exclusive in probability theory if they cannot occur at the same time or concurrently. In other words, discontinuous events are those that are mutually exclusive. If two occurrences are regarded as discontinuous, the likelihood of both occurring at the same time is zero.

If A and B are the two events, then the probability of their disjoint is stated as:

P (A and B) = 0 for the probability of a disjoint (or mutually exclusive) event.

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After determining the mean the variance is 1.5689 and standard deviation is 1.253.

The values are 7.2, 7.6, 8.5, 8.7, 9.0, 9.3, 9.4, 10.2, 10.9, 11.3.

Firstly we find the mean of the numbers.

Mean = Sum of the Numbers/Total numbers

Mean = (7.2 + 7.6 + 8.5 + 8.7 + 9.0 + 9.3 + 9.4 + 10.2 + 10.9 + 11.3)/10

Mean = 92.1/10

Mean = 9.21

Now we determine the variance.

The formula of variance is:

x                             x - Mean                                     (x - Mean)^2

7.2                         (7.2-9.21) = -2.01                                4.0401

7.6                         (7.6-9.21) = -1.61                                 2.5921

8.5                         (8.5-9.21) = -0.71                                0.5041

8.7                          (8.7-9.21) = -0.51                                0.2601

9.0                          (9.0-9.21) = -0.21                               0.0441

9.3                          (9.3-9.21) = 0.09                                0.0081

9.4                          (9.4-9.21) = 0.19                                 0.0361

10.2                         (10.2-9.21) = 0.99                              0.9801

10.9                         (10.9-9.21) = 1.69                                2.8561

11.3                          (11.3-9.21) = 2.09                                 4.3681

Total =                                                                                 15.689

Variance = ∑(x - Mean)^2/10

Variance = 15.689/10

Variance = 1.5689

Standard Deviation = √Variance

Standard Deviation = √1.5689

Standard Deviation = 1.253

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The probability that either A happens or B happens is equal to the sum of the probabilities of A and B. Option C is the answer.

Probability is a measure of the likelihood of a particular event occurring, expressed as a number between 0 and 1. A probability of 0 means an event is impossible, while a probability of 1 means an event is certain. A probability of 0.5 means an event has a 50-50 chance of happening.

In the question given, the probability that either A happens or B happens is equal to the sum of the probabilities of A and B.

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They allowed their opponents to score 134 more runs than they scored.

What is the differential equation?

A differential equation is an equation that contains at least one derivative of an unknown function, either a normal differential equation.

A differential equation is an equation that contains at least one derivative of an unknown function, either a normal differential equation or a partial differential equation.

A run differential of +134 for the Atlanta Braves in the 2021 season means that the team scored 134 more runs than their opponents over the course of the season.

A positive run differential indicates that a team has outscored their opponents, while a negative run differential means that a team has been outscored by their opponents.

Hence, They allowed their opponents to score 134 more runs than they scored.

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Two ratios have proportional relationship.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

A ratio is a mathematical expression written in the form of a:b, where a and b are any integers.

Given question,

What is the relationship between the ratios?

Ratio defines the relationship between the quantities of two or more objects. It is used to compare the quantities of the same kind. If two or more ratios are equal, then it is said to be in proportion.

Hence, two ratio have the proportional relationship.

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The correct equation to represent "Ehren worked 36 hours last week and earned a total of $500" is,

⇒ 36x = 500

Where, x represent the amount earn in per hour.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

"Ehren worked 36 hours last week and earned a total of $500"

Let the amount earn in per hour = x

Hence, For Ehren worked 36 hours last week and earned a total of $500, the correct equation is,

⇒ 36x = 500

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Answer:

The balance after 6 years, assuming the deposit of 5000 earns 4% interest compounded yearly, would be 7400. This is calculated by using the formula A=P(1+r/n)^nt, where A is the balance, P is the principal (5000), r is the interest rate (0.04), n is the number of times the interest is compounded per year (1), and t is the number of years (6).

Answer:

AB≈50.27in²

Step-by-step explanation:

AB=πr2=π·42≈50.26548in²

Answer: 16π squared inches

Step-by-step explanation:

The base area of a cone is the area of a circle.

Formula for area of a circle = π[tex]r^{2}[/tex]

Since your r= 4 inches, you plug in 4 inches into the formula.

Area = π * [tex]4^{2}[/tex] = 16π

Assuming the side lengths in the new phone are proportional to the old phone, the width of the new phone would be equal to 3.23 inches.

In Mathematics, a proportion simply refers to an equation which is typically used to represent the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

By applying direct proportion to the given information, we have the following mathematical expression:

1.2 inches = 3.4 inches

1.14 inches = w inches

Cross-multiplying, we have the following:

1.2w = 3.4 × 1.14

1.2w = 3.876

w = 3.876/1.2

w = 3.23 inches.

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-7  must you multiply the second equation by so that the sum of the x-coefficients is zero.

Two or more expressions with an Equal sign is called as Equation.

The system of equations are

7x−y=55..(1)

x+3y=33..(2)

We have to multiply with -7 second equation by so that the sum of the x-coefficients is zero

-7x-21y=-231..(3)

Add equation 1 and equation 2

7x−y-7x-21y=33-231

-22y=-198

Hence, -7  must you multiply the second equation by so that the sum of the x-coefficients is zero.

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Answer:We got 0.56 as the answer when you convert 5/9 to a decimal.

For the system of equation " 2x₁ – x₂ = h ; -6x₁ + 3x₂ = k " , it will be consistent for all the values of h and k , which satisfy "k = -3h" .

The System Of Linear Equations is considered as consistent if it has at least one solution.

The system of equation is :

⇒ 2x₁ – x₂ = h .....equation(1) ;

⇒ -6x₁ + 3x₂ = k    ....equation(2) ;

Now replacing the equation(2) by its sum with 3 times the first equation, the the system of equations become :

⇒ 2x₁ – x₂ = h .....equation(1) ;

⇒ 0 = k + 3h ;

Simplifying further ,

we have ;

⇒ k = -3h .

Therefore , the system will be consistent for values of "h" and "k" satisfying  k = -3h .

The given question is incomplete , the complete question is

For what values of h and k the system Of Equations is consistent ?

2x₁ – x₂ = h ; -6x₁ + 3x₂ = k

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The solution to the equation is (0, 7/2)

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

x-2y=-7 3x+2y=7

Add the two equations to elimiate y

4x = 0

So, we have

x = 0

This means that

0 - 2y = -7

So, we have

y = 7/2

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The augmented matrix for the given  systems of linear equations are obtained. a. x – 3y=5  b. x+2y=0 x+y=1  c. x - y + z=2 x - z=1  d. y + 2x=0 y+z=0

Two matrices are combined to form enhanced matrices.

Thus, augmented matrix for the given  systems of linear equations are obtained as:

a. x – 3y = 5 : [1  - 3 : 5]

b. x+2y=0 x+y=1 : [1  2 : 0]

                            [1   1 :  1]

c. x - y + z=2 and x - z=1  :  [1  -1  1 : 2]

                                           [1  0  -1 :  1]

d. y + 2x=0 y+z=0  : [2  1  0 : 0]

                                [0  1   1 :  0]

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There are 149.91 pounds in 68 kilogram, or 68 kilogram weighs 149.91 pounds.

The Price Per Kilogram (Pk) shall replace the Price Per Pound (Pp) (Kg)

Just divide the kg price by 2.2046 to get the lb price to convert cost per kilogramme to cost per pound.

In principle, two pounds are equal to one kilogramme (there is a longer decimal position, but I abbreviate it to 2.2046).

The weight of a kilogramme is roughly 2.2046226218 pounds. The technique can be used to convert kilogrammes to pounds and is relatively simple. The value of a kilogramme merely needs to be multiplied by 2.2046226218.

68 kg weights 149.91 pounds, or 68 kg is 149.91 pounds. Conversion of wages 149.91434 pounds (lb), 68 kilogrammes (kg)

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500 m is equal to 0.310686 mi. This is due to the fact that one mile is equal to the errant total of 1,609.344 meters.

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