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2 years ago

40 POINTS

Mathematics

1 answer:

mixer [17]2 years ago

6 0

Answer:

Step-by-step explanation:

Linear equation form: y = mx + b

(where m is the slope and b is the y-intercept)

The rate of change for a line is the slope.

Function 1: y = 6

⇒ the slope is zero so the rate of change is zero

Function 2: y = 2x + 7

⇒ the slope is 2 so the rate of change is 2

Therefore, 2 - 0 = 2

So the rate of change of function 2 is 2 more than the rate of change of function 1

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A restaurant will select 1 card from a bowl to win a free lunch, jimmy puts 10 cards in the bowl. The bowl has a total of 150 ca

Phantasy [73]

The odds of jimmy winning a free lunch is 0.066.

<h3>What is Probability ?</h3>

Probability is the likeliness of an event to happen.

It is given that

A restaurant will select 1 card from a bowl to win a free lunch,

jimmy puts 10 cards in the bowl.

The bowl has a total of 150 cards in it

The odds of jimmy winning a free lunch is given by

= No. of chances / Total Outcomes

= 10/150

= 1/15

= 0.066

Therefore the odds of jimmy winning a free lunch is 0.066.

To know more about Probability

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3 0

2 years ago

A bag contains 22 red marbles, 8 white marbles, and 3 gray marble. You randomly pick out a marble, record its color, and put it

frez [133]

Total marbles : 33

W + G marbles : 11

Probability of picking either a W or G : 11/33

Number of W or G marbles = 11/33 × 45 = 15

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3 years ago

How many solutions does -46+23=46x+23

Slav-nsk [51]

Answer:

x = -1

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

−46+23=46x+23

(−46+23)=46x+23(Combine Like Terms)

−23=46x+23

Step 2: Flip the equation.

46x+23=−23

Step 3: Subtract 23 from both sides.

46x+23−23=−23−23

46x=−46

Step 4: Divide both sides by 46.

46x/46 = -46/46

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3 years ago

Match each vector operation with its resultant vector expressed as a linear combination of the unit vectors i and j.

Cloud [144]

Answer:

3u - 2v + w = 69i + 19j.

8u - 6v = 184i + 60j.

7v - 4w = -128i + 62j.

u - 5w = -9i + 37j.

Step-by-step explanation:

Note that there are multiple ways to denote a vector. For example, vector u can be written either in bold typeface "u" or with an arrow above it $\vec{u}$ . This explanation uses both representations.

$\displaystyle \vec{u} = \langle 11, 12\rangle =\left(\begin{array}{c}11 \\12\end{array}\right)$ .

$\displaystyle \vec{v} = \langle -16, 6\rangle= \left(\begin{array}{c}-16 \\6\end{array}\right)$ .

$\displaystyle \vec{w} = \langle 4, -5\rangle=\left(\begin{array}{c}4 \\-5\end{array}\right)$ .

There are two components in each of the three vectors. For example, in vector u, the first component is 11 and the second is 12. When multiplying a vector with a constant, multiply each component by the constant. For example,

$3\;\vec{v} = 3\;\left(\begin{array}{c}11 \\12\end{array}\right) = \left(\begin{array}{c}3\times 11 \\3 \times 12\end{array}\right) = \left(\begin{array}{c}33 \\36\end{array}\right)$ .

So is the case when the constant is negative:

$-2\;\vec{v} = (-2)\; \left(\begin{array}{c}-16 \\6\end{array}\right) =\left(\begin{array}{c}(-2) \times (-16) \\(-2)\times(-6)\end{array}\right) = \left(\begin{array}{c}32 \\12\end{array}\right)$ .

When adding two vectors, add the corresponding components (this phrase comes from Wolfram Mathworld) of each vector. In other words, add the number on the same row to each other. For example, when adding 3u to (-2)v,

$3\;\vec{u} + (-2)\;\vec{v} = \left(\begin{array}{c}33 \\36\end{array}\right) + \left(\begin{array}{c}32 \\12\end{array}\right) = \left(\begin{array}{c}33 + 32 \\36+12\end{array}\right) = \left(\begin{array}{c}65\\48\end{array}\right)$ .

Apply the two rules for the four vector operations.

$\displaystyle \begin{aligned}3\;\vec{u} - 2\;\vec{v} + \vec{w} &= 3\;\left(\begin{array}{c}11 \\12\end{array}\right) + (-2)\;\left(\begin{array}{c}-16 \\6\end{array}\right) + \left(\begin{array}{c}4 \\-5\end{array}\right)\\&= \left(\begin{array}{c}3\times 11 + (-2)\times (-16) + 4\\ 3\times 12 + (-2)\times 6 + (-5) \end{array}\right)\\&=\left(\begin{array}{c}69\\19\end{array}\right) = \langle 69, 19\rangle\end{aligned}$

Rewrite this vector as a linear combination of two unit vectors. The first component 69 will be the coefficient in front of the first unit vector, i. The second component 19 will be the coefficient in front of the second unit vector, j.

$\displaystyle \left(\begin{array}{c}69\\19\end{array}\right) = \langle 69, 19\rangle = 69\;\vec{i} + 19\;\vec{j}$ .

$\displaystyle \begin{aligned}8\;\vec{u} - 6\;\vec{v} &= 8\;\left(\begin{array}{c}11\\12\end{array}\right) + (-6) \;\left(\begin{array}{c}-16\\6\end{array}\right)\\&=\left(\begin{array}{c}88+96\\96 - 36\end{array}\right)\\&= \left(\begin{array}{c}184\\60\end{array}\right)= \langle 184, 60\rangle\\&=184\;\vec{i} + 60\;\vec{j} \end{aligned}$ .

$\displaystyle \begin{aligned}7\;\vec{v} - 4\;\vec{w} &= 7\;\left(\begin{array}{c}-16\\6\end{array}\right) + (-4) \;\left(\begin{array}{c}4\\-5\end{array}\right)\\&=\left(\begin{array}{c}-112 - 16\\42+20\end{array}\right)\\&= \left(\begin{array}{c}-128\\62\end{array}\right)= \langle -128, 62\rangle\\&=-128\;\vec{i} + 62\;\vec{j} \end{aligned}$ .

$\displaystyle \begin{aligned}\;\vec{u} - 5\;\vec{w} &= \left(\begin{array}{c}11\\12\end{array}\right) + (-5) \;\left(\begin{array}{c}4\\-5\end{array}\right)\\&=\left(\begin{array}{c}11-20\\12+25\end{array}\right)\\&= \left(\begin{array}{c}-9\\37\end{array}\right)= \langle -9, 37\rangle\\&=-9\;\vec{i} + 37\;\vec{j} \end{aligned}$ .

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3 years ago

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GaryK [48]

Where is the above table?

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3 years ago

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