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natita [175]
3 years ago
14

On a survey ⅞ students said that they preferred music over Art of those students who chose music 5/7 of them want to learn a ins

trument what fraction represents the students who chose music and want to learn an instrument
Mathematics
1 answer:
SashulF [63]3 years ago
5 0

Let x be the total number of students.

We know that 7/8x chose music over art.

5/7 of those students want to learn an instrument, so we have to multiply the number of students who chose music by 5/7:

\dfrac{7x}{8}\cdot \dfrac{5}{7}=\dfrac{5x}{8}

So, 5/8 of the students want to learn an instrument.

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qaws [65]
X + 2 - 2 = 3 - 2

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What customary unit would you use to estimate? A car is about 15 _____ long. inches meters yards feet
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3 years ago
Diego is solving the equation x^2-12x = 21
uysha [10]

Answer:

The solutions to the quadratic equations will be:

x=\sqrt{57}+6,\:x=-\sqrt{57}+6

Step-by-step explanation:

Given the expression

x^2-12x\:=\:21

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x^2-12x\:=\:21

Add (-6)² to both sides

x^2-12x+\left(-6\right)^2=21+\left(-6\right)^2

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x^2-12x+\left(-6\right)^2=57

Apply perfect square formula: (a-b)² = a²-2ab+b²

i.e.

x^2-12x+\left(-6\right)^2=\left(x-6\right)^2

so the expression becomes

\left(x-6\right)^2=57

\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}

solve

x-6=\sqrt{57}

add 6 to both sides

x-6+6=\sqrt{57}+6

Simplify

x=\sqrt{57}+6

also solving

x-6=-\sqrt{57}

add 6 to both sides

x-6+6=-\sqrt{57}+6

Simplify

x=-\sqrt{57}+6

Therefore, the solutions to the quadratic equation will be:

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5 0
3 years ago
What is 3 1/2 x r = 28​
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3 years ago
Read 2 more answers
Two streams flow into a reservoir. Let X and Y be two continuous random variables representing the flow of each stream with join
zlopas [31]

Answer:

c = 0.165

Step-by-step explanation:

Given:

f(x, y) = cx y(1 + y) for 0 ≤ x ≤ 3 and 0 ≤ y ≤ 3,

f(x, y) = 0 otherwise.

Required:

The value of c

To find the value of c, we make use of the property of a joint probability distribution function which states that

\int\limits^a_b \int\limits^a_b {f(x,y)} \, dy \, dx  = 1

where a and b represent -infinity to +infinity (in other words, the bound of the distribution)

By substituting cx y(1 + y) for f(x, y)  and replacing a and b with their respective values, we have

\int\limits^3_0 \int\limits^3_0 {cxy(1+y)} \, dy \, dx  = 1

Since c is a constant, we can bring it out of the integral sign; to give us

c\int\limits^3_0 \int\limits^3_0 {xy(1+y)} \, dy \, dx  = 1

Open the bracket

c\int\limits^3_0 \int\limits^3_0 {xy+xy^{2} } \, dy \, dx  = 1

Integrate with respect to y

c\int\limits^3_0 {\frac{xy^{2}}{2}  +\frac{xy^{3}}{3} } \, dx (0,3}) = 1

Substitute 0 and 3 for y

c\int\limits^3_0 {(\frac{x* 3^{2}}{2}  +\frac{x * 3^{3}}{3} ) - (\frac{x* 0^{2}}{2}  +\frac{x * 0^{3}}{3})} \, dx = 1

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c\int\limits^3_0 {(\frac{9x}{2}  +\frac{27x}{3} )  \, dx = 1

Add fraction

c\int\limits^3_0 {(\frac{27x + 54x}{6})  \, dx = 1

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Rewrite;

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The \frac{1}{6} is a constant, so it can be removed from the integral sign to give

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Integrate with respect to x

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\frac{c}{6} *  \frac{729}{2}    = 1

\frac{729c}{12}    = 1

Multiply both sides by \frac{12}{729}

c    =  \frac{12}{729}

c    =  0.0165 (Approximately)

8 0
3 years ago
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