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Dovator [93]
3 years ago
10

Matt has 11 white buttons. He has 9 fewer brown buttons than white buttons. Matt has 17 more grey buttons than brown buttons. Ho

w many buttons does Matt have in all?
Mathematics
1 answer:
In-s [12.5K]3 years ago
7 0

Answer: 32 buttons

Step-by-step explanation:

Matt has 11 white buttons.

Matt has 9 fewer brown buttons than white buttons. This means he has (11 -9) = 2 brown buttons

Matt has 17 more grey buttons than brown buttons. This means that he has (2 + 17) = 19 grey buttons.

The total number of buttons that Matt has will be;

= 11 white + 2 brown + 19 grey

= 32 buttons

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Suppose that a and b are integers, a ≡ 4 ( mod 13 ) and b ≡ 9 ( mod 13 ) . Find the integer c with 0 ≤ c ≤ 12 such that: c ≡ 9 a
g100num [7]

Answer:

A) For c ≡ 9 a ( mod 13 ) ; C is 10

B) For c ≡ 11 b ( mod 13 ) ; C is 8

C) For c ≡ a + b ( mod 13 ); C is 0

D) For c ≡ a² + b² ( mod 13 ); C is 6

E) For c ≡ a² − b² ( mod 13 ) ; C is 0

Step-by-step explanation:

This is a modular arithmetic problem where a ≡ 4 ( mod 13 ) and b ≡ 9 ( mod 13 ).

And 0 ≤ c ≤ 12.

A) c ≡ 9 a ( mod 13 )

Substituting the value of a to obtain;

c ≡ 9 x4 ( mod 13 ) = 36 mod 13

To find 36 mod 13 using the Modulo Method, we first divide the Dividend (36) by the Divisor (13).

Second, we multiply the whole part of the Quotient in the previous step by the Divisor (13).

Then finally, we subtract the answer in the second step from the Dividend (36) to get the answer. Here is the math to illustrate how to get 36 mod 13 using Modulo Method:

36 / 13 = 2.769231

2 x 13 = 26

36 - 26 = 10

Thus, the answer to "What is 36 mod 13?" is 10

So C = 10

B) c ≡ 11 b ( mod 13 ) = 11 x 9 ( mod 13 ) = 99 ( mod 13 )

Using the same method as above,

99 ( mod 13 );

99 / 13 = 7.6155

7 x 13 = 91

99 - 91 = 8

So, C = 8

C)c ≡ a + b ( mod 13 ) = 4 + 9 (mod 13) = 13 (mod 13)

Thus;

13 / 13 = 1

1 x 13 = 13

13 - 13 = 0

So, C = 0

D)c ≡ a² + b² ( mod 13 ) = 4² + 9²( mod 13 ) = 16 + 81 ( mod 13 ) = 97 ( mod 13 )

Thus;

97 / 13 = 7.46154

7 x 13 = 91

97 - 91 = 6

So, C = 6

E)c ≡ a² − b² ( mod 13 )= 4² - 9²( mod 13 ) = 16 - 81 ( mod 13 ) = - 65 ( mod 13 )

Thus;

-65 / 13 = - 5

-5 x 13 = - 65

-65 - (-65) = 0

So, C = 0

3 0
3 years ago
Find all the square roots of x2 ≡ 53 (mod 77)
Nikolay [14]

Answer:

x=\pm\sqrt{77n+53}

Step-by-step explanation:

We have been given an equivalence equation x^2\equiv 53\text{ (mod } 77). We are asked to find all the square root of the given equivalence equation.

Upon converting our given equivalence equation into an equation, we will get:

x^2-53=77n

Add 53 on both sides:

x^2-53+53=77n+53

x^2=77n+53

Take square root of both sides:

x=\pm\sqrt{77n+53}

Therefore, the square root for our given equation would be x=\pm\sqrt{77n+53}.

3 0
3 years ago
Kayla says that the point labeled C in the diagram below is the center. Raymond says that point C is the radius.
frutty [35]

Answer:

Kayla is correct The center is a fixed  point in the middle of the sphere

Step-by-step explanation:

In mathematics we have certain habit of rules for notation of points, coordinates, segments, angles and so on.

Usually we denote points,  by letters even more we denote with the first letter of the object we are denoting

Occasionally, we also denote  segments as radius in a circle and in a sphere, with letters,  that is r stands for  radius, h stands for height, in most cases we denote point for capital letters ( in a segment)  

When we denote radius, with small letter it should be placed at the center or over the segment we are traying to denote.

For points we only need to place the letter close to the to the point we want to denote.

Therefore Kayla is correct when says that c stand for " the center of the sphere"

8 0
3 years ago
Read 2 more answers
Let P = 0.5 0.1 0.5 0.9 be the transition matrix for a Markov chain with two states. Let x0 = 0.5 0.5 be the initial state vecto
max2010maxim [7]

Answer:

Complete solution is given in the images attached below for better demonstration

7 0
3 years ago
26) Hailey is 3 times as old as Maverick.
Dahasolnce [82]

Let H = Hailey's age and M = Maverick

Hailey is 3 times as old as Maverick: H = 3M

The sum of their ages is 48 years: H + M = 48

Since H = 3M, substitute 3M in place of H in the second equation:

H + M = 48

3M + M = 48

4M = 48

M = 12

Maverick is 12 years old. Hailey = 3M = 3(12) = 36 years old.

5 0
3 years ago
Read 2 more answers
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