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iragen [17]
4 years ago
5

Betty claims that her dog can do simple addition problems. She showed her dog 8 different cards with simple addition problems, a

nd the dog was able to tap his paw to indicate whether the answer was correct or incorrect. The dog correctly identified all 8 cards. John didn't believe Betty's dog could do addition, so he set up a trial to test whether the dog was just guessing. He flipped 8 coins to see how many would land tails up. He did this 53 times, and the results are shown in the dot plot below:
3 dots on 1
6 dots on 2
9 dots on 3
12 dots on 4
9 dots on 5
8 dots on 6
5 dots on 7
1 dot on 8
Based on these results, can Betty’s dog add?
Mathematics
1 answer:
AVprozaik [17]4 years ago
5 0
Yes because if you add up the left side it equals 53 and he got it right 53/53 times or 100% of the time

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Aaron wants to mulch his garden. His garden is x^2+18x+81 ft^2 One bag of mulch covers x^2-81 ft^2 . Divide the expressions and
blsea [12.9K]

Answer:

Step-by-step explanation:

Given

Garden: x^2+18x+81

One Bag: x^2 - 81

Requires

Determine the number of bags to cover the whole garden

This is calculated as thus;

Bags = \frac{x^2+18x+81}{x^2 - 81}

Expand the numerator

Bags = \frac{x^2+9x+9x+81}{x^2 - 81}

Bags = \frac{x(x+9)+9(x+9)}{x^2 - 81}

Bags = \frac{(x+9)(x+9)}{x^2 - 81}

Express 81 as 9²

Bags = \frac{(x+9)(x+9)}{x^2 - 9\²}

Evaluate as difference of two squares

Bags = \frac{(x+9)(x+9)}{(x - 9)(x+9)}

Bags = \frac{(x+9)}{(x - 9)}

Hence, the number of bags is Bags = \frac{(x+9)}{(x - 9)}

3 0
3 years ago
Please help me with this​
denis23 [38]

Answer:

20) \displaystyle [4, 1]

19) \displaystyle [-5, 1]

18) \displaystyle [3, 2]

17) \displaystyle [-2, 1]

16) \displaystyle [7, 6]

15) \displaystyle [-3, 2]

14) \displaystyle [-3, -2]

13) \displaystyle NO\:SOLUTION

12) \displaystyle [-4, -1]

11) \displaystyle [7, -2]

Step-by-step explanation:

20) {−2x - y = −9

{5x - 2y = 18

⅖[5x - 2y = 18]

{−2x - y = −9

{2x - ⅘y = 7⅕ >> New Equation

__________

\displaystyle \frac{-1\frac{4}{5}y}{-1\frac{4}{5}} = \frac{-1\frac{4}{5}}{-1\frac{4}{5}}

\displaystyle y = 1[Plug this back into both equations above to get the x-coordinate of 4]; \displaystyle 4 = x

_______________________________________________

19) {−5x - 8y = 17

{2x - 7y = −17

−⅞[−5x - 8y = 17]

{4⅜x + 7y = −14⅞ >> New Equation

{2x - 7y = −17

_____________

\displaystyle \frac{6\frac{3}{8}x}{6\frac{3}{8}} = \frac{-31\frac{7}{8}}{6\frac{3}{8}}

\displaystyle x = -5[Plug this back into both equations above to get the y-coordinate of 1]; \displaystyle 1 = y

_______________________________________________

18) {−2x + 6y = 6

{−7x + 8y = −5

−¾[−7x + 8y = −5]

{−2x + 6y = 6

{5¼x - 6y = 3¾ >> New Equation

____________

\displaystyle \frac{3\frac{1}{4}x}{3\frac{1}{4}} = \frac{9\frac{3}{4}}{3\frac{1}{4}}

\displaystyle x = 3[Plug this back into both equations above to get the y-coordinate of 2]; \displaystyle 2 = y

_______________________________________________

17) {−3x - 4y = 2

{3x + 3y = −3

__________

\displaystyle \frac{-y}{-1} = \frac{-1}{-1}

\displaystyle y = 1[Plug this back into both equations above to get the x-coordinate of −2]; \displaystyle -2 = x

_______________________________________________

16) {2x + y = 20

{6x - 5y = 12

−⅓[6x - 5y = 12]

{2x + y = 20

{−2x + 1⅔y = −4 >> New Equation

____________

\displaystyle \frac{2\frac{2}{3}y}{2\frac{2}{3}} = \frac{16}{2\frac{2}{3}}

\displaystyle y = 6[Plug this back into both equations above to get the x-coordinate of 7]; \displaystyle 7 = x

_______________________________________________

15) {6x + 6y = −6

{5x + y = −13

−⅚[6x + 6y = −6]

{−5x - 5y = 5 >> New Equation

{5x + y = −13

_________

\displaystyle \frac{-4y}{-4} = \frac{-8}{-4}

\displaystyle y = 2[Plug this back into both equations above to get the x-coordinate of −3]; \displaystyle -3 = x

_______________________________________________

14) {−3x + 3y = 3

{−5x + y = 13

−⅓[−3x + 3y = 3]

{x - y = −1 >> New Equation

{−5x + y = 13

_________

\displaystyle \frac{-4x}{-4} = \frac{12}{-4}

\displaystyle x = -3[Plug this back into both equations above to get the y-coordinate of −2]; \displaystyle -2 = y

_______________________________________________

13) {−3x + 3y = 4

{−x + y = 3

−⅓[−3x + 3y = 4]

{x - y = −1⅓ >> New Equation

{−x + y = 3

________

\displaystyle 1\frac{2}{3} ≠ 0; NO\:SOLUTION

_______________________________________________

12) {−3x - 8y = 20

{−5x + y = 19

⅛[−3x - 8y = 20]

{−⅜x - y = 2½ >> New Equation

{−5x + y = 19

__________

\displaystyle \frac{-5\frac{3}{8}x}{-5\frac{3}{8}} = \frac{21\frac{1}{2}}{-5\frac{3}{8}}

\displaystyle x = -4[Plug this back into both equations above to get the y-coordinate of −1]; \displaystyle -1 = y

_______________________________________________

11) {x + 3y = 1

{−3x - 3y = −15

___________

\displaystyle \frac{-2x}{-2} = \frac{-14}{-2}

\displaystyle x = 7[Plug this back into both equations above to get the y-coordinate of −2]; \displaystyle -2 = y

I am delighted to assist you anytime my friend!

7 0
3 years ago
Evaluate <br>2/3 + 11/100​
Likurg_2 [28]
.7766 approximately
8 0
3 years ago
Read 2 more answers
Write the quadratic equation whose roots are 5 and 1, and whose leading coefficient is 5
zepelin [54]

Answer: the equation is

5x^2 -30x - 25

Step-by-step explanation:

A quadratic equation is one in which the highest power of the unknown is 2.

The general form of a quadratic equation is expressed as

ax^2 + bx + c

Where c is a constant and a is the leading coefficient

Assuming we want to write the quadratic equation in x, from the information given, the given roots are 5 and 1 and the leading coefficient is 5. We will just multiply the expression by the leading coefficient.

Therefore, the linear factors of the quadratic will be (x-5) and (x-1)

With the leading coefficient as 5, the equation becomes

5(x-5)(x-1)

= 5(x^2 - x - 5x + 5)

= 5(x^2 - 6x + 5)

= 5x^2 -30x - 25

3 0
3 years ago
Please help me. If you don't know the answer don't respond<br> I need a correct answer
kozerog [31]

Answer:

Step-by-step explanation:

Remark

You have to guess what the question is. I'm assuming that it is either the black triangle to the blue one or the blue one to the black one. Be careful when you post a question to see if you have included a question.

Answer

<em>Ratio of blue to black</em>

The distance of the left most point of the blue triangle to the y axis is 3. The same point on the black one is 1

blue/black = 3/1

<em>Ratio of black to blue</em>

ratio of the black triangle to the blue one is 1/3

The answer will depend on the question. Notice that the two answers are reciprocals.

6 0
3 years ago
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