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Novay_Z [31]
3 years ago
6

Prove that for all integers a and b, if a mod 7 = 5 and b mod 7 = 6 then ab mod 7 = 2.

Mathematics
1 answer:
sergiy2304 [10]3 years ago
6 0
Hello :
if : a <span>≡ 5 ( mod 7) ....(1)
     b </span><span>≡ 6 ( mod 7) ...(2)
(1)×(2) : ab </span><span>≡ 30 ( mod 7)
</span>but : 30 = 7×4  + 2  ..... so : 30  ≡ 2 ( mod 7)
then : ab ≡ 2 ( mod 7)
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PLEASE HELP!!!!!! TIMED QUESTION!!!! FIRST CORRECT ANSWER WILL GET BRAINLIEST....PLEASE ANSWER NOW!!!!
Margarita [4]

Answer:

Option (3)

Step-by-step explanation:

From the picture attached,

Bar graph sketched shows the grades earned by the students in an exam.

Number of students who achieved the grade A = 17

Number of students who achieved grade B = 14

Number of students with grade C = 5

Number of students with grade D = 9

Total students who took the exam = 17 + 14 + 5 + 9 = 45

Option (1)

"\frac{1}{5} of the students earned a C"

Fraction of students who earned C = \frac{\text{Students who earned C}}{\text{Total students}}

                                                          = \frac{5}{45}

                                                          = \frac{1}{9}

Therefore, this option is incorrect.

Option (2)

"3% more students earned an A then B"

Percentage of students who earned A = \frac{\text{Students got A}}{\text{Total students who took the exam}}\times 100

                                                                = \frac{17}{45}\times 100

                                                                = 37.78%

Percentage of students who earned B = \frac{\text{Students got B}}{\text{Total students who took the exam}}\times 100

                                                                = \frac{14}{45}\times 100

                                                                = 31.11%

Difference in percentage = 37.78 - 31.11

                                          = 6.67%

Therefore, this option is not correct.

Option (3)

"20% of the students earned a D"

Percentage of students who earned D = \frac{\text{Students got D}}{\text{Total students who took the exam}}\times 100

                                                                 = \frac{9}{45}\times 100

                                                                 = 20%

Option (3) is the correct option.

Option (4)

" \frac{1}{4} of the class earned a B"

Fraction of class who earned B = \frac{\text{Students got B}}{\text{Total students who took the exam}}

                                                    = \frac{14}{45}

Therefore, Option (4) is not correct.                                        

6 0
3 years ago
During a sale all pillows are 1/4 of th regular price write an expression that represents the amount of money saved on a pillow
grin007 [14]
D(1-1/4)
=3/4d
3/4d represents the money saved on a pillow
3 0
3 years ago
Please help asap 32 pts
Over [174]
-8-5(-4)
-8+20
f(-4)=12
6 0
2 years ago
Read 2 more answers
Please answer ASAP!
7nadin3 [17]

Answer:

h = 4.5 inches

Step-by-step explanation:

The area of a trapezoid is given by

A = 1/2 (b1+b2) h

We know A b1 and b2

20.25 = 1/2 (5+4)*h

20.25 = 9/2 h

Multiply each side by 2/9 to isolate h

2/9 * 20.25 = 2/9 *9/2 h

4.5 =h

6 0
3 years ago
(-5xy2 z) (7x 6 y 2 z-3x5 y - 4xz)
kumpel [21]

Step-by-step explanation:

la respuesta es no es porque es falsa

4 0
2 years ago
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