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3 years ago

Write the ratio as a fraction in simplest form with whole numbers in the 3.5 to 4.2

Mathematics

1 answer:

svp [43]3 years ago

5 0

$\frac{3.5}{4.2} \times \frac{10}{10} = \frac{35}{42} = \frac{7\times 5}{7\times 6} \\\\ = \boxed{\bf{\frac{5}{6}}}$

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The perimeter of a rectangle is 28.8 centimeters. The length of the rectangle is twice as long as it’s with. Find the length and

Mazyrski [523]

Answer:

$Length=9.6 cm\\\\Width=4.8 cm$

Step-by-step explanation:

Length=2*Width

L=2*W

Perimeter=28.8 cm

Perimeter of a rectangle= 2(Length+Width)

$28.8=2(2W+W)\\\\28.8=2(3W)\\\\3W=28.8/2\\\\3W=14.4\\\\W=14.4/3\\\\W=4.8 cm\\\\$

$Length=2*Width\\\\=2*4.8\\\\=9.6 cm\\\\$

$Length=9.6 cm\\\\Width=4.8 cm$

6 0

2 years ago

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Do these equations have infinite solutions 2x + 5y= 31 and 6x -y = 13

katovenus [111]

$2x = 31 - 5y \\ x = \frac{31}{2} - \frac{5}{2}y$

$6x = 13 + y \\ x = \frac{13}{6} + \frac{1}{6} y$

8 0

3 years ago

We want to determine if the probability that a student enrolled in an accelerated math pathway is independent of whether the stu

Molodets [167]

Answer:

The correct option is (c).

Step-by-step explanation:

The complete question is:

The data for the student enrollment at a college in Southern California is:

Traditional Accelerated Total

Math-pathway Math-pathway

Female 1244 116 1360

Male 1054 54 1108

Total 2298 170 2468

We want to determine if the probability that a student enrolled in an accelerated math pathway is independent of whether the student is female. Which of the following pairs of probabilities is not a useful comparison?

a. 1360/2468 and 116/170

b. 170/2468 and 116/1360

c. 1360/2468 and 170/2468

Solution:

If two events <em>A</em> and <em>B</em> are independent then:

$P(A|B)=P(A)\\\\\&\\\\P(B|A)=P(B)$

In this case we need to determine whether a student enrolled in an accelerated math pathway is independent of the student being a female.

Consider the following probabilities:

$P (F|A) = \farc{116}{170}\\\\P(A|F)=\frac{116}{1360}\\\\P(A)=\frac{170}{2468}\\\\P(F)=\frac{1360}{2468}$

If the two events are independent then:

P (F|A) = P(F)

P (A|F) = P (A)

But what would not be a valid comparison is:

P (A) = P(F)

Thus, the correct option is (c).

4 0

3 years ago

Solve the inequality p/5 < -3

Tema [17]

Answer:

p < - 15

Step-by-step explanation:

Given

$\frac{p}{5}$ < - 3 ( multiply both sides by 5 to clear the fraction )

p < - 15

8 0

2 years ago

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In this problem we consider an equation in differential form Mdx+Ndy=0. (4x+2y)dx+(2x+8y)dy=0 Find My= 2 Nx= 2 If the problem is

zheka24 [161]

Answer:

$f(x,y)=2x^2+4y^2+2xy=C_1\\\\Where\\\\y(x)=\frac{1}{4} (-x\pm \sqrt{-7x^2+C_1} )$

Step-by-step explanation:

Let:

$M(x,y)=4x+2y\\\\and\\\\N(x,y)=2x+8y$

This is and exact equation, because:

$\frac{\partial M(x,y)}{\partial y} =2=\frac{\partial N}{\partial x}$

So, define f(x,y) such that:

$\frac{\partial f(x,y)}{\partial x} =M(x,y)\\\\and\\\\\frac{\partial f(x,y)}{\partial y} =N(x,y)$

The solution will be given by:

$f(x,y)=C_1$

Where C1 is an arbitrary constant

Integrate $\frac{\partial f(x,y)}{\partial x}$ with respect to x in order to find f(x,y):

$f(x,y)=\int\ {4x+2y} \, dx =2x^2+2xy+g(y)$

Where g(y) is an arbitrary function of y.

Differentiate f(x,y) with respect to y in order to find g(y):

$\frac{\partial f(x,y)}{\partial y} =2x+\frac{d g(y)}{dy}$

Substitute into $\frac{\partial f(x,y)}{\partial y} =N(x,y)$

$2x+\frac{dg(y)}{dy} =2x+8y\\\\Solve\hspace{3}for\hspace{3}\frac{dg(y)}{dy}\\\\\frac{dg(y)}{dy}=8y$

Integrate $\frac{dg(y)}{dy}$ with respect to y:

$g(y)=\int\ {8y} \, dy =4y^2$

Substitute g(y) into f(x,y):

$f(x,y)=2x^2+4y^2+2xy$

The solution is f(x,y)=C1

$f(x,y)=2x^2+4y^2+2xy=C_1$

Solving y using quadratic formula:

$y(x)=\frac{1}{4} (-x\pm \sqrt{-7x^2+C_1} )$

4 0

3 years ago