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Andreyy89
3 years ago
8

Dennis got 85 percent of the questions on the math test correct, which was out of 40. what was his actual mark?​

Mathematics
1 answer:
makkiz [27]3 years ago
4 0

Answer:

34/40

Step-by-step explanation:

85/100 cross multiply x/40

100x/100=3400/100

x=3400/100

3400/100=34

x=34

Picture included

(Sorry about my handwriting)

Hope this helps!! :)

Stay safe and have a wonderful day/night!!!!!

Brainliest?!?!

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5 1/2 divided by 3 1/3
Sophie [7]

Answer:

1 13/20

Step-by-step explanation:

5 1/2 ÷ 3 1/3

11/2 ÷ 10/3
11/2 x 3/10 = 33/20

33/20 = 1 13/20

Hope this helps :)

5 0
2 years ago
Read 2 more answers
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.

<h3>1.</h3>

\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}.

<h3>2.</h3>

\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}.

<h3>3.</h3>

\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}.

<h3>4.</h3>

\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}.

7 0
3 years ago
Suppose you own two stocks, A and B. In year 1, stock A earns a 2% return and stock B earns a 9% return. In year 2, stock A earn
Verizon [17]

Answer:

Both the stock have the same expected return.

Step-by-step explanation:

In year 1 the return earned by stocks A and B are:

Stock A = 2% return

Stock B = 9% return

In year 2 the return earned by stocks A and B are:

Stock A = 18% return

Stock B = 11% return

Compute the expected return for stock A as follows:

Expected\ return\ for\ A=\frac{2+18}{2}=10\%

Compute the expected return for stock B as follows:

Expected\ return\ for\ B=\frac{9+11}{2}=10\%

Thus, both the stock have the same expected return.

7 0
3 years ago
Can someone please help me with this. (please show work)​
marysya [2.9K]
This for the first one

6 0
3 years ago
HEY THERE! PLEASE ANSWER THE MATH QUESTION IN THE PHOTO! THE CORRECT ANSWER SHALL BE MARKED AS BRAINLIEST AND I WILL FOLLOW YOU(
ella [17]

Answer:

a) x =  7.5

b) x = 1

Step-by-step explanation:

a)

  • (4x - 1)/2 = x + 7
  • 4x - 1 = 2(x + 7)
  • 4x - 1 = 2x + 14
  • 2x = 15
  • x = 15/2 or 7.5

b)

  • 3x + 2 = (2x +13)/3
  • 3(3x + 2) = 2x + 13
  • 9x + 6 = 2x +13
  • 7x = 7
  • x = 1

7 0
3 years ago
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