i have exactly ten coins whose total value is $. if three of the coins are quarters, what are the remaining coins?

Answer: To convert a Senary (base 6) number to decimal, we can use the following formula:

Decimal = (5 * 6^4) + (4 * 6^3) + (7 * 6^2) + (2 * 6^1) + (5 * 6^0)

= (5 * 1296) + (4 * 216) + (7 * 36) + (2 * 6) + (5 * 1)

= 6480 + 864 + 252 + 12 + 5

= 7603

So the Senary (base 6) number 54724 is equivalent to the decimal number 7603.

Step-by-step explanation:

Sum of the given geometric sequence is -100.

A geometric sequence is the special type of sequence in which the ratio of every two successive terms is constant.

Sum of each infinite geometric sequence

-50, -25, -12.5, ...

The infinite sum of geometric sequence is given by,

[tex]s_{\infty} =\frac{a}{1-r}[/tex]

Where a is the first term in the sequence and r is the common ratio.

[tex]s_{\infty} =\frac{-50}{1-(-0.5)}[/tex]

      = -100.

Hence, sum of the given geometric sequence is -100.

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The value of variables x and y are,

⇒ x = 80°

⇒ y = 130°

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

Since, A parallelogram is forming here,

Then, Opposite angels are going to be equal.

Thus, We get;

⇒ y = (x + 50)°

Now, As you know that sum of all angles of a quadrilateral equals 360°

Hence, We get;

2 {(x + 50) + (x - 30)} = 360°

(x + 50) + (x - 30) = 180°

2x + 20 = 180

2x = 160

x = 80°

So, We get;

⇒ y = (x+50)

      = 80 +50

      = 130°

And,

⇒ x = 80°

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Answer: eat grass whor

Step-by-step explanation:

The percent will the fraction decrease should be 80%.

Important information:

In the case when its numerator is decreased by 85% and its denominator is decreased by 25%

Calculation of percentage:

= (100-85) ÷ (100 - 25)

=  15%÷ 75%

= 20%

Now the decrease in percentage should be

= 100% - 20%

= 80%

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The correct answer is 80%

52 students passed only one subject

Let's use the following variables to represent the number of students who passed each subject:

P(Ga): the number of students who passed Ga

P(Fante): the number of students who passed Fante

From the problem statement, we know that:

P(Ga) = P(Fante) + 6, since the number of students who passed Ga is 6 more than the number who passed Fante

P(Ga ∩ Fante) = 8, since 8 students passed both subjects

P(Ga ∪ Fante) = 60, since every student passed at least one subject

We want to find the number of students who passed only one subject, which is equal to the total number of students who passed Ga minus the number of students who passed both subjects, plus the number of students who passed Fante but not Ga. In symbols:

P(Ga) - P(Ga ∩ Fante) + (P(Fante) - P(Ga ∩ Fante))

Substituting the values we know:

(P(Fante) + 6) - 8 + (P(Fante) - 8)

Simplifying:

2P(Fante) - 10

We also know that P(Ga) + P(Fante) - P(Ga ∩ Fante) = P(Ga ∪ Fante) = 60.

Substituting the values we know:

P(Ga) + P(Fante) - 8 = 60

P(Ga) + P(Fante) = 68

Substituting P(Ga) = P(Fante) + 6:

2P(Fante) + 6 = 68

2P(Fante) = 62

P(Fante) = 31

Therefore, the number of students who passed only one subject is:

2P(Fante) - 10 = 2(31) - 10 = 52

Therefore, 52 students passed only one subject.

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3

Step-by-step explanation:

35 times 3.sub

The speed of the plane is 135 km/h and wind speed is 23 km/h. The solution has been obtained by forming linear equations.

What is a linear equation?

This is the linear equation with the largest degree of one. This demonstrates that there are no variables in linear equations with exponents greater than 1. A straight line appears on the graph as a result of such an equation.

Let the plane speed be 'P' and the wind speed be 'W'.

We are given that while flying to Kampala with a tailwind a plane averaged 158 km/h.

So, we get an equation as

P + W = 158       ...(1)

Also, on the return trip plane only averaged 112 km/h while flying back into the same wind.

So, we get another equation as

P - W = 112       ...(2)

Now, on adding the equations we get,

⇒P + W + P - W = 158 + 112

⇒2P = 270

⇒P = 135

Now substituting the value into either equation, we get

⇒P + W = 158

⇒135 + W = 158

⇒W = 23

Hence, the speed of the plane is 135 km/h and wind speed is 23 km/h.

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The hourly rate that the batches of cookies were made is given as follows:

4.85 batches per hour.

The hourly rate is obtained applying the proportions in the context of the problem.

A proportion is applied as the rate is obtained dividing the total production by the time in hours.

The parameters for this problem are given as follows:

Hence the rate is given as follows:

40/8.25 = 4.85 batches per hour.

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Using arithmetic operation Jude's typing rate is 182 characters per minute, which is option C.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

To find the typing rate in characters per minute, we need use arithmetic operation of division.

Divide the number of characters by the number of minutes -

Typing rate = Number of characters / Number of minutes

In this case, Jude types 1,274 characters in 7 minutes, so her typing rate is -

Typing rate = 1274 / 7 = 182

Therefore, the typing rate is 182 characters/minute.

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We can solve this equation by setting B2 = [c d], so that AB2 = [c+d 1] = [0 1]. This gives us the system of equations c + d = 0 and c = 1. Solving this system, we have c = 1, where I is the 2x2 identity matrix

Let A be the given 2x2 matrix A = [1 2 ; 1 1]. To find a 3x2 matrix B such that AB = I, where I is the 2x2 identity matrix, we can use the hint provided: If B1 and B2 are the columns of B, then ABj = Ij. This means that for each column j of B, we need to solve the equation ABj = Ij. For j = 1, we have AB1 = I1 = [1 0]. We can solve this equation by setting B1 = [a b], so that AB1 = [a+b 1] = [1 0]. This gives us the system of equations a + b = 1 and a = 0. Solving this system, we have a = 0 and b = 1, so B1 = [0 1].For j = 2, we have AB2 = I2 = [0 1]. We can solve this equation by setting B2 = [c d], so that AB2 = [c+d 1] = [0 1]. This gives us the system of equations c + d = 0 and c = 1. Solving this system, we have c = 1.

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Answer: 2.25 per gallon

Step-by-step explanation:

4.50 divided by 2 = 2.25

The pair of figures is similar by SSS

The complete question is added as an attachment

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

Triangles BDC and FGC

When the side lengths of the triangle are compared, we have:

Side lengths of FGC are 5/3 multiplied by the side lengths of BDC

This means that the triangles are similar

And the similarity statement is SSS

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Answer:

7 cents

Step-by-step explanation:

0.072222 rounded to the nearest cent is 0.07

There are two solutions to the system of linear equations depicted in the graph: one at (0,4) and one at (-3,0). There is only one distinct solution to the system of equations where the two lines intersect at the points (-3,0) and (0,4).

If the slopes are the same but the y-intercepts vary, the system has no solution. If the slopes are different, the system only has one solution. The system has an endless number of solutions if the slopes and y-intercepts match.

There are therefore countless possible answers. A different kind of linear equation system is a system with two parallel lines represented by the equations is referred to be an inconsistent system. The lines have distinct y-intercepts but the same slope.

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Answer:

98 km

Step-by-step explanation:

To find the area of the figure;

Total Area = Area A + Area B + Area C

Area A = 14 * 2 = 28 km2

Area B = 11 * 2 = 22 km2

Area C = 12 * 4 = 48 km2

Total Area = 98 km2

Answer:

AAS

Step-by-step explanation:

[tex]\overline{PR} \cong \overline{PR}[/tex] by the reflexive property.

The two major properties of similar shapes include the following:

In Mathematics, two (2) geometric shapes are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):

This ultimately implies that, two (2) similar geometric shapes can have different sizes depending on the scale factor that is applied because it would either enlarge (increase) or reduce (decrease) them.

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Answer: D

Step-by-step explanation:

The size of the key space is 256^8, or 2^64. The average key search time would be 2^64/processing power of PC, which would be a very large number.

The question is asking about the size of the key space if 8 randomly chosen 8-bit ASCII characters are used, and how long it would take to find a key on a single PC.

The size of the key space if all 8 characters are randomly chosen 8-bit ASCII characters is 256^8 = 2^64 = 18,446,744,073,709,551,616.

The average key search time with a single PC would be 18,446,744,073,709,551,616 / 2,000,000,000,000 (2 trillion) operations per second = 9,223,372,036,854,775.8 seconds, which is approximately 292,030 years.

The size of the key space for an 8-bit ASCII character is 2^64 combinations. On average, it will take a single PC 2^64 / (processing speed of PC in Hz) seconds to search through the entire key space.

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If we are only interested in the total number of games the Yankees win, the possible events for the two games are: 0 wins: LL , 1 win: LW, WL and 2 wins: WW

What is event in probability ?

In probability, an event is a subset of the sample space of a random experiment. In other words, an event is a collection of possible outcomes of the experiment.

For example, consider flipping a fair coin. The sample space of this experiment is {heads, tails}. An event could be defined as "getting heads", which is a subset of the sample space that includes only one outcome.

There are four possible outcomes for the double-header, which can be represented using W for a win and L for a loss:

WW (Yankees win both games)

WL (Yankees win the first game, but lose the second game)

LW (Yankees lose the first game, but win the second game)

LL (Yankees lose both games)

Therefore , If we are only interested in the total number of games the Yankees win, the possible events for the two games are: 0 wins: LL , 1 win: LW, WL and 2 wins: WW

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Answer:

m<20

Step-by-step explanation:

The slope of the line that passes through the points (0, - 4) and (30, -9) is -1/6.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Based on the information provided, we can logically deduce the following data points on the line:

Substituting the given data points into the slope formula, we have the following;

Slope, m = (-9 + 4)/(30 - 0)

Slope, m = -5/30

Slope, m = -1/6.

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The probability that the actor will get his lines straight for the first time on the fourth attempt is 0.0864, rounded to three decimal places.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
The probability that the actor will get his lines straight on any one take is 0.40. This means that the probability of him not getting his lines straight on any one take is 1 - 0.40 = 0.60.

P(getting lines straight on 4th attempt)
= P(not getting lines straight on 1st, 2nd, or 3rd attempt) x P(getting lines straight on 4th attempt)

P(not getting lines straight on any one attempt) = 0.60

P(not getting lines straight on 1st, 2nd, or 3rd attempt) = 0.60 x 0.60 x 0.60 = 0.216

P(getting lines straight on 4th attempt) = 0.40

P(getting lines straight for the first time on the fourth attempt) = P(not getting lines straight on 1st, 2nd, or 3rd attempt) x P(getting lines straight on 4th attempt)
= 0.216 x 0.40 = 0.0864

Therefore, the probability that the actor will get his lines straight for the first time on the fourth attempt is 0.0864, rounded to three decimal places.

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Answer:

6 is not the solution.  7 is the solution.

Step-by-step explanation:

5(x -3) = x + 13  Substitute 6 for x

5(6 -3) = 6 + 13

5(3) = 19

15 ≠ 19

6 is not a solution because it results in a false statement.  The two sides do not equal each other.

5(x - 3) = x + 13   Distribute the 5

5x -15 = x + 13  Subtract x from both sides

5x - x - 15 = x - x + 13

4x - 15 = 13  Add 15 to both sides

4x - 15 + 15 = 15 + 13

4x = 28  Divide both sides by 4

x = 7

7 is the solution to the equaion.

The relation:

{x = y : x, y ε A}.

And this relation is a function.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.

Given:

A={2,4,6} and B={135}

R={(2,2), (4,4), (6,6)} is a relation on A.

That means, each value of set A connects to the same point.

The relation:

{x = y : x, y ε A}

Hence, {x = y : x, y ε A}.

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Answer:

360-137+x+y

Step-by-step explanation:

The minimum number of tables the store must sell is 5.

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

Using t and c as variables, we get

100c + 400t ≥ 3000

c+t≤16

The online furniture store must sell at least $3000 worth of chairs and tables each day, and can ship at most 16 pieces of furniture.

If the store sells 9 chairs for a total of $900, it needs to sell at least 5 tables to reach a total revenue of $3000.

Since the total number of pieces of furniture sold is 14 (9 chairs + 5 tables), which is less than the maximum of 16, the store meets the daily shipping requirement.

Therefore, the minimum number of tables the store must sell is 5.

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