Do the Math
Franklin has a total of 18 pennies and nickels worth 78 cents. How many pennies and
how many nickels does Franklin have?
Write a system of equations.
p+n=18
P+
n=78
Solve the system of equations.
Franklin has pennies and nickels.

The values of x and y in the parallel lines are 10 and -5 respectively.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, linear angles, alternate interior angles, alternate exterior angles, same side interior angles, vertically opposite angles etc.

Therefore, using same side interior angles,

6x + 2y + 130 = 180

2x - 4y + 140 = 180

Recall same side interior angles are supplementary

Hence,

6x + 2y = 50

2x - 4y  = 40

multiply equation(ii) by 3

6x + 2y = 50

6x - 12y = 120

subtract the equations

14y = - 70

y = -70 / 14

y = -5

Let's find x

6x + 2y = 50

6x = 50 - 2(-5)

6x = 50 + 10

6x = 60

x = 60 / 6

x = 10

Therefore,

x = 10 and y = -5

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The solution is Option A.

The value of the equation is g ( x - 3 ) = √ ( x - 12 )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as g ( x )

Now , the value of g ( x ) is

Substituting the values in the equation , we get

g ( x ) = √ ( x - 9 )    be equation (1)

On simplifying the equation , we get

when the value of x is x - 3 , we get

g ( x - 3 ) = √ ( x - 3 ) - 9

On further simplification , we get

g ( x - 3 ) = √ ( x - 3 - 9 )

g ( x - 3 ) = √ ( x - 12 )

Hence , the equation is g ( x - 3 ) = √ ( x - 12 )

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x=0 and x=-2 are the solutions of the equation 6x³+24x²+24x=0

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The given equation is 6x³+24x²+24x=0

Take 6x as common from the given equation.

6x(x²+4x+4)=0

6x=0 and x²+4x+4=0

x²+4x+4=0

x²+2x+2x+4=0

x(x+2)+2(x+2)=0

(x+2)(x+2)=0

(x+2)²=0

x=-2

Hence, x=0 and x=-2 are the solutions of the equation 6x³+24x²+24x=0

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The number of students that took all the three classes is 40

The number of students are in Group 2 is 51 students

(i) To find the number of students who have taken all three classes, we need to subtract the number of students who have taken only two classes from the number of students who have taken at least one class.

Let's call the number of students who have taken all three classes "x".

The number of students who have taken Calculus and Sociology is 15 + x.

The number of students who have taken Calculus and Spanish is 20 + x.

The number of students who have taken Sociology and Spanish is 13 + x.

Adding these three equations, we have:

15 + 78 + 72 = 15 + x + 78 + x + 72 + x

solving for x

165 = 45 + 3x

120 = 3x

isolating x

So, x = 40.

hence, 40 students have taken all three classes.

(ii) To find the number of students in Group 2, we need to add the number of students who have taken at least one class to the number of students who have taken none of the classes.

Let's call the number of students in Group 2 "y".

The number of students who have taken at least one class is

32 + 22 + 16 - 10 - 8 - 11 + 5 = 36.

Therefore, y = 36 + 15 = 51.

So, there are 51 students in Group 2.

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Answer:

[tex]\huge\boxed{\sf y = -4}[/tex]

Step-by-step explanation:

y = -3x + 2

Given that, x = 2

So,

y = -3(2) + 2

y = -6 + 2

y = -4

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

replace where x is with 2

[tex]y = ( - 3 \times 2) + 2[/tex]

[tex]y = - 6 + 2[/tex]

[tex]y = - 4[/tex]

Answer:

The y-intercept in this situation means that when the cab travels 0 miles, the total fee will be $14.00. This indicates that the cab service charges a flat fee of $14.00, regardless of the number of miles traveled.

Step-by-step explanation:

The y-intercept in this situation represents the base fee that the cab service charges regardless of distance traveled. In this case, when the cab travels 0 miles, the total fee is $14.00.

In this context, the y-intercept represents the base fee that the cab service charges, regardless of distance traveled. This is the amount you would pay for a cab ride of 0 miles. From the given table, we can't directly see the y-intercept, but we can infer it using the rate of change or slope, which represents the fee per mile. The amount increases by $1.50 for every additional mile (difference in y divided by difference in x), so to find the y-intercept, we back-calculate from one of the given points, like (2, 17). Subtracting 2 miles' worth of fees from $17 gives a y-intercept of $14. Therefore, when the cab travels 0 miles, the total fee is $14.00, which likely represents a starting charge or a minimum fare.

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Answer:

Step-by-step explanation:

oi gooot

The conditional probability that a tested person has cancer, given that their test result indicates so, is given as follows:

0.9268 = 92.68%.

Conditional probability is the probability of one event happening, considering the result of a previous event. The formula is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which:

The events for this problem are given as folows:

The probability of a positive test result are given as follows:

Hence:

P(A) = 0.95 x 0.4 + 0.05 x 0.6 = 0.41.

Hence the conditional probability is given as follows:

P(B|A) = 0.95 x 0.4/0.41 = 0.9268 = 92.68%.

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a) Distance between given points = 11 unit ; Midpoint is (0 , -1/2)

b) Distance between given points = 7 unit ; Midpoint is (-1/2 , 0)

c) Distance between given points = 4.47 unit ; Midpoint is (6 , 4)

d) Distance between given points = 8.06 unit ; Midpoint is (-1 , 1/2)

e) Distance between given points = 5 unit ; Midpoint is (4 , 5/2)

f) Distance between given points = 13 unit ; Midpoint is (1/2 , 2)

g) Distance between given points = 5√5 unit ; Midpoint is (5/2 , 5)

h) Distance between given points = √5 unit ; Midpoint is (3 , 1/2)

i) Distance between given points = 6 unit ; Midpoint is (6 , 1)

j) Distance between given points = 15 unit ; Midpoint is (1 , -5/2)

Distance between two points with coordinates (x₁ , y₁)  and (x₂ , y₂). is given by

D = √[(x₁ - x₂)² + (y₁ - y₂)²]

This formula is derived from the Pythagoras Theorem, as the points form a right triangle in plane, with the hypotenuse representing the distance between them.

Given,

a)  (0, 5) and (0 -6)

Distance = √[(0 - 0)² + (5 - -6)²] = √11² = 11 unit

Midpoint = [(x₁ + x₂)/2 + (y₁ + y₂)/2]

= [(0+0)/2 , (5 + -6)/2]

⇒ Midpoint = (0, -1/2)

b) (3, 0) and (-4, 0)

Distance = √[(3 - -4)² + (0 - 0)²] = √7² = 7 unit

Midpoint =  [(x₁ + x₂)/2 + (y₁ + y₂)/2]

= [(3+ -4)/2 , (0 + 0)/2]

⇒ Midpoint = (-1/2, 0)

Similarly,

c) (5, 2) and (7, 6)

Distance = 4.47 unit

Midpoint = (6 , 4)

d) (-3, 4) and (1, -3)

Distance = 8.06 unit

Midpoint = (-1 , 1/2)

e) (6, 4) and (2, 1)

Distance = 5 unit

Midpoint = (4 , 5/2)

f)(-2, -4) and (3, 8)

Distance = 13 unit

Midpoint = (1/2 , 2)

g) (0, 0) and (5, 10)

Distance = 5√5 unit

Midpoint = (5/2 , 5)

h) (2, 1) and (4, 0)

Distance = √5 unit

Midpoint = (3 , 1/2)

i) (6, 4) and (6, -2)

Distance = 6 unit

Midpoint = (6 , 1)

j) (-5, 2) and (7, -7)

Distance = 15 unit

Midpoint = (1 , -5/2)

Hence,

a) Distance between points is 11 unit ; Midpoint = (0 , -1/2)

b) Distance between points is 7 unit ; Midpoint = (-1/2 , 0)

c) Distance between points is 4.47 unit ; Midpoint = (6 , 4)

d) Distance between points is 8.06 unit ; Midpoint = (-1 , 1/2)

e) Distance between points is 5 unit ; Midpoint = (4 , 5/2)

f) Distance  between points is 13 unit ; Midpoint = (1/2 , 2)

g) Distance between points is 5√5 unit ; Midpoint = (5/2 , 5)

h) Distance between points is √5 unit ; Midpoint = (3 , 1/2)

i) Distance between points is 6 unit ; Midpoint = (6 , 1)

j) Distance between points is 15 unit ; Midpoint = (1 , -5/2)

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Answer: Its 4(x+1)

Step-by-step explanation:

You combine all the x's, creating 4x+4.

In the last answer, it has 4(x+1) which by distributing you should get 4x+4!

The correct answer is option A. The empirical rule provides precise statements regarding 1, 2, or 3 standard deviations.

The Empirical Rule, also known as the 68-95-99.7 rule, states that for a normal distribution (or approximately normal distribution), about 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. This rule assumes that the mean, median, and mode are equal and the data is symmetrical.

It is a quick and easy way to get a rough estimate of the spread of data in a normal distribution and the proportion of values that fall within certain intervals. However, it should be noted that this is an approximation and not always accurate, especially for distributions that are not close to being normal.

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Complete Question:

When applicable, the empirical rule provides the approximate percentage of observations that fall within how many standard deviations from the mean?

A. 1, 2, or 3 standard deviations

B. 4, 6, or 9 standard deviations

C. 2, 2, or 7 standard deviations

Answer:

A

Step-by-step explanation:

Answer:100

Step-by-step explanation:

40+40 =80 +20=100

The logic for the algorithm is Traverse both linked lists, comparing corresponding elements.

To determine if two circular linked lists, l and m, store the same sequence of elements, we can use the following algorithm:

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A) The maximum value to appear in the two rolls can take on any value from 2 to 6.

B) The minimum value to appear in the two rolls can take on any value from 1 to 5.

C) The sum of the two rolls can take on any value from 2 to 12.

D) The value of the first roll minus the value of the second roll can take on any value from -5 to 5.

If the die is assumed to be fair, the probabilities associated with the random variables in parts (a) through (d) can be calculated as follows:

A) The probability of the maximum value to appear in the two rolls is 1/6.

B) The probability of the minimum value to appear in the two rolls is 1/6.

C) The probability of the sum of the two rolls is 1/36 for each of the possible sums from 2 to 12.

D) The probability of the value of the first roll minus the value of the second roll is 1/11 for each of the possible values from -5 to 5.

Complete question:

Suppose that a die is rolled twice. What are the possible values that the following random variables can take on (a) the maximum value to appear in the two rolls: (b) the minimum value to appear in the two rolls (c) the sum of the two rolls; (d) the value of the first roll minus the value of the second roll? 4.8. If the die in Problem 4.7 is assumed fair, calculate the probabilities associated with the random variables in parts (a) through (d).

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This transfer function is a ratio between the gain of the controller (K) and the plant’s open-loop transfer function (G). The denominator is the sum of the gain and the plant’s transfer function, which results in the closed-loop feedback loop.

The closed-loop transfer function from the reference r(s) to the output y(s) for a unity feedback loop is given by:

y(s) = (K*G(s))/(1+K*G(s))

Where K is the gain of the controller, and G(s) is the plant’s open-loop transfer function. This can be derived by examining the block diagram of a unity feedback loop:

The input (r) is fed into a controller (K) whose output is then multiplied by the plant’s open-loop transfer function (G). The sum of the controller output and the plant output is then fed into the summing junction, and the output (y) is the result.

Therefore, the closed-loop transfer function representing the reference r(s) to the output y(s) can be derived as follows:

[tex]y(s) = r(s)*(K*G(s))/(1+K*G(s))\\= (K*G(s))/(1+K*G(s))[/tex]

This can be rearranged to give the final expression:

[tex]y(s) = (K*G(s))/(1+K*G(s))[/tex]

This transfer function is a ratio between the gain of the controller (K) and the plant’s open-loop transfer function (G). The denominator is the sum of the gain and the plant’s transfer function, which results in the closed-loop feedback loop.

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The HCF of the numbers 126, 119 and 196 is 7.

The Highest Common Factor (HCF) of two numbers is the highest possible number that divides both the numbers completely.

The Highest Common Factor (HCF) is also called the Greatest Common Divisor (GCD).

Given are the numbers -

126, 119, 196

We can write the Prime factorization of the numbers given as -

126 = 2 × 3 × 3 × 7

119 = 7 × 17

196 = 2 × 2 × 7 × 7

7 is common in the prime factorization of all the numbers.

Therefore, the HCF of the numbers 126, 119 and 196 is 7.

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{

Complete question in english -

Find the FCF of 126, 119, and 196 using the prime factorization method

}

The next three terms of the sequence are - 40.5, - 60.75 , -91.125

A geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

The nth term of a geometric sequence is given as a(n) = ar^n-1

where a is the first term and r is the common ratio

to find the common ratio:

r = a2/a1

r = -12/-8

r = 1.5

-27 is the fourth term = ar³

fifth term = ar³× r

= -27 × 1.5 = -40.5

sixth term = -40.5 × 1.5 =- 60.75

seventh term = -60.75 × 1.5 = -91.125

therefore the next three terms of the sequence are - 40.5, - 60.75 , -91.125

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The normal distribution is a probability distribution used to describe the probability of a given value of a continuous variable.

The normal distribution is characterized by two parameters, the mean and standard deviation. The mean, μ, represents the center of the distribution, and the standard deviation, σ, represents the spread of the distribution.

In a production process, the normal distribution can be used to predict the probability of defects and the number of defects expected for a given mean and standard deviation. The probability of a given defect can be calculated using the formula p = 1-N(x; μ, σ), where N(x; μ, σ) is the cumulative normal distribution function, x is the number of defects, μ is the mean, and σ is the standard deviation.

For example, if a production process produces items with a mean weight of 10 grams and a standard deviation of 1 gram, then the probability of a defect occurring is calculated using the formula: p = 1-N(x; 10, 1). If we assume a defect occurs at 8 grams, then the probability of a defect occurring is 1-N(8; 10, 1) = 0.1587. This means that there is a 15.87% chance of a defect occurring in the production process.

To calculate the expected number of defects, we can use the formula E(x) = μ + (σ * N’(p)), where N’(p) is the inverse normal distribution function and p is the probability of a defect occurring. Using the example above, we can calculate the expected number of defects as 10 + (1 * N’(0.1587)) = 10.24, meaning that we can expect 10.24 defects for every 100 items produced.

In this example, there is a 15.87% chance of a defect occurring in the production process, and we can expect 10.24 defects for every 100 items produced.

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The linear function that represents the table values is y = 3x + 5.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Using two points from the table, (0,5) and (2,11)

First, we determine the slope m.

Slope m = change in y / change in x

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Plug in the values

Slope m = ( 11 - 5 ) / ( 2 - 0 )

Slope m = 6 / 2

Slope m = 3

Plug the slope m =3 and point (0,5) into the point-slope formula and simplify.

y - y₁ = m( x - x₁ )

y - 5 = 3( x - 0 )

y - 5 = 3x - 0

y - 5 = 3x

Add 5 to both sides

y - 5 + 5 = 3x + 5

y = 3x + 5.

Therefore, the equation of the line is y = 3x + 5.

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Answer:

amounts of

Step-by-step explanation:

In a principal + interest loan, the principal (original amount borrowed) is divided into equal monthly amounts, and the interest (fee charged for borrowing) is calculated on the outstanding principal balance each month.

Hope this helps!

a) The region in the X-Y plane for which the joint density of X and Y is non-zero is a triangle with vertices at (0,0), (0,2), and (2,2).

b) The joint density function for X and Y is given by: f(x,y) = 1/2 for 0 < x < y < 2.

c) The marginal probability density for Y is given by: fY (y) = ∫ f(x,y) dx = (1/2) y for 0 < y < 2.

d) The conditional probability density of X, conditional on Y = y, is given by: fX|Y (x|y) = f(x,y)/fY (y) = 2 for 0 < x < y < 2.

This only exists for 0 < y < 2.

a) The region in the X-Y plane for which the joint density of X and Y is non-zero is a triangle with vertices at (0,0), (0,2), and (2,2). This is because the lengths of the two pieces of the ruler must be non-negative and must add up to 2.

b) The joint density function for X and Y is given by:

f(x,y) = 1/2 for 0 < x < y < 2.

c) The marginal probability density for Y is given by:

fY (y) = ∫ f(x,y) dx = (1/2) y for 0 < y < 2.

d) The conditional probability density of X, conditional on Y = y, is given by:

fX|Y (x|y) = f(x,y)/fY (y) = 2 for 0 < x < y < 2. This only exists for 0 < y < 2.

Note: The factor of 1/2 in the joint density function accounts for the uniform distribution of the two breaks on the ruler, while the factor of 2 in the conditional density function accounts for the change of variables from the joint density to the conditional density.

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The direction of t+ u+ v is 155°.

A vector is a quantity that possesses magnitude, direction, and adheres to the law of vector addition.

Given:

The magnitude and direction of vectors t, u, and v are shown in the table.

Vector   Magnitude  Direction

t                 5                 250°

u                6                  60°

v               12                 330°

The coordinates of the resultant vectors:

t + u + v,

= (5 cos250° + 6cos60° + 12cos330°, 5 Sin250° + 6Sin60° + 12Sin330°)

= (11.7, -5.5)

Now, the direction of t+ u+ v = arc tan(-5.5/11.7)

= 155°

Therefore, 155° is the direction.

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Answer:

335°

Step-by-step explanation:

I took the test and got it right :)

The expression of the given algebra word problem is; 10 - 2y

We are told that we should subtract y from 5, then double the result.

Subtracting y from 5 gives us;

5 - y

Now, doubling the result will mean we will multiply it by 2 and this will be expressed as;

2(5 - y)

Expanding the bracket using distributive property is;

2*5 - 2*y

= 10 - 2y

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Answer:

x > 81

In interval notation: (81, ∞)

Step-by-step explanation:

Inequality is
[tex]\dfrac{X}{9} > 9[/tex]

Multiply both sides by 9:

[tex]\dfrac{X}{9}\cdot 9 > 9 \cdot 9\\\\\implies X > 81\\[/tex]

The solution set expressed in interval notation is (81, ∞)

The accounting terms and their corresponding definitions and meanings are;

When a record is posted, it means that details of a transaction are copied from a journal to a ledger. Expenses are the costs incurred in operating a business.

The Debit side of transactions is the left side of an account and the Trial Balance shows the different accounts with their balances and transactions. Equity shows the assets that are not acquired by liabilities.

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The rest of the question is:

The correct answer is d. 260 tacos and 156 burritos and Dina gained 260 tacos and 156 burritos.

If each person specializes in the production of the good in which they have a comparative advantage and trade 260 tacos for 156 burritos, this means that both individuals benefit from trade as they can consume more of both goods than they would have without trade. Arturo specializes in producing tacos, which he trades for burritos produced by Dina. Similarly, Dina specializes in producing burritos, which she trades for tacos produced by Arturo. As a result, both individuals gain from trade, and the combined total of tacos and burritos remains the same after trade as before. In this case, both Arturo and Dina would end up with 260 tacos and 156 burritos each, which is the outcome of trade.

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When we have a population  data set it is like the scrambled phrase. statistic is the process of using visual, numerical, and tabular display to unscramble the data and discover the message behind it.

A collection of data is known as a data set (or dataset). In the case of tabular data, a data set relates to one or more database tables, where each row refers to a specific record in the corresponding data set and each column to a specific variable. The data set includes values for each of the variables, such as the object's height and weight, for each set member. Data sets can also be made up of a group of files or documents.

The analysis and manipulation of data is the essence of statistics. As we just covered in the introduction, statistics is the study of the calculation and analysis of numerical data. Let's examine other statistical definitions provided by various authors in this article.

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100% of the data lies within two standard deviations of the mean, 75% of the data lies within one standard deviation of the mean, and 50% of the data lies between 8 and 12.

Consider a sample with a mean of 10 and a standard deviation of 4. Use Chebyshev's theorem to determine the percentage of the data within each of the following ranges (to the nearest whole number):

- Between 2 and 18: 100%

- Between 6 and 14: 75%

- Between 8 and 12: 50%

Chebyshev's theorem states that at least 75% of the data will lie within two standard deviations of the mean, and at least 50% of the data will lie within one standard deviation of the mean. In this example, 100% of the data lies within two standard deviations of the mean, 75% of the data lies within one standard deviation of the mean, and 50% of the data lies between 8 and 12.

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30% of parts undergo electronic inspection. If inspected, the chance of no defects is 90%. If not inspected, chance of defects is 20%. Total chance of a defect is 27%. Chance of a defective part being inspected is 33%.

A. P(E) = 0.30, the probability that a part in the plant went through an electronic inspection.

B. P(D|E) = 0.90, the probability that a produced part which was inspected electronically has no defects.

C. P(D|E') = 0.20, the probability that a part produced in the plant is defective and was not inspected electronically.

D. P(E') = 0.70, the probability that a part in the plant did not go through an electronic inspection.

E. P(D|E) + P(D|E') = 0.90 + 0.20 = 1.10, which is not a valid probability value since it is greater than 1.

F. P(D) = P(D|E)P(E) + P(D|E')P(E') = 0.90 * 0.30 + 0.20 * 0.70 = 0.27, the probability that a part produced in the plant is defective.

G. P(E|D) = P(DE) / P(D) = 0.90 * 0.30 / 0.27 = 0.33, the probability that a defective part in the plant went through an electronic inspection.

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