All categories

3 years ago

By what percent will a fraction change if its numerator is decreased by 10% and its denominator is decreased by 50%?

Mathematics

1 answer:

Alexeev081 [22]3 years ago

4 0

Answer:

80% increase

Step-by-step explanation:

let the given fraction $f=\frac{x}{y}$

numerator= $x$

denominator= $y$

Given

numerator decreased by 10%
denominator decreased by 50%

let new numerator $=x_{new}=x-\frac{10}{100} x=\frac{9}{10} x$

let new denominator $=y_{new}=y-\frac{50}{100} y=\frac{1}{2} y$

Therefore new fraction, $f_{new}=\frac{x_{new} }{y_{new} }=\frac{\frac{9}{10}x}{\frac{1}{2}y }=\frac{9\times2}{10} \frac{x}{y}=\frac{9}{5} \frac{x}{y}$

Percentage increase $=\frac{f_{new} -f}{f} \times 100=\frac{\frac{9}{5} \frac{x}{y} -\frac{x}{y} }{\frac{x}{y} }\times 100=\frac{4}{5} \times100= 80$

⇒ Percentage increase of function $f$ = 80%

You might be interested in

In a certain Algebra 2 class of 29 students, 7 of them play basketball and 24 of them play baseball. There are 3 students who pl

antiseptic1488 [7]

Answer:

$\frac{5}{29}$

Step-by-step explanation:

Let $n(A)$ represent students playing basketball, $n(B)$ represent students playing baseball.

Then, $n(A)=7$ , $n(B)=24$

Let $n(S)$ be the total number of students. So, $n(S)=29$ .

Now,

$P(A)=\frac{n(A)}{n(S)}=\frac{7}{29}$

$P(B)=\frac{n(B)}{n(S)}=\frac{24}{29}$

3 students play neither of the sport. So, students playing either of the two sports is given as:

$n(A\cup B)=n(S)-3\\n(A\cup B)=29-3=26$

∴ $P(A\cup B)=\frac{n(A\cup B)}{n(S)}=\frac{26}{29}$

From the probability addition theorem,

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$

Where, $P(A\cap B)$ is the probability that a student chosen randomly from the class plays both basketball and baseball.

Plug in all the values and solve for $P(A\cap B)$ . This gives,

$\frac{26}{29}=\frac{7}{29}+\frac{24}{29}+P(A\cap B)\\\\\frac{26}{29}=\frac{7+24}{29}+P(A\cap B)\\\\\frac{26}{29}=\frac{31}{29}+P(A\cap B)\\\\P(A\cap B=\frac{31}{29}-\frac{26}{29}\\\\P(A\cap B=\frac{31-26}{29}=\frac{5}{29}$

Therefore, the probability that a student chosen randomly from the class plays both basketball and baseball is $\frac{5}{29}$

6 0

3 years ago

Factorize 7√2 k^2 - 10k - 4√2<br> <br>

d1i1m1o1n [39]

Answer:

7k√2 - 10k - 4√2

Step-by-step explanation:

Factor the polynomial.

Factor : One of two or more expressions that are multiplied together to get a product.

Polynomial : An algebraic expression consisting of one or more summed terms, each term consisting of a constant multiplier and one or more variables raised to integral powers.

5 0

3 years ago

Use the Quadratic Formula to solve the equation 4x^2−7=4x.

tino4ka555 [31]

Answer:

$\large\boxed{x=\dfrac{1}{2}-\sqrt2\ or\ x=\dfrac{1}{2}+\sqrt2}$

Step-by-step explanation:

$\text{The quadratic formula of}\ ax^2+bx+c=0:\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

$\text{We have:}\\\\4x^2-7=4x\qquad\text{subtract}\ 4x\ \text{from both sides}\\\\4x^2-4x-7=0\\\\a=4,\ b=-4,\ c=-7\\\\b^2-4ac=(-4)^2-4(4)(-7)=16+112=128\\\\\sqrt{b^2-4ac}=\sqrt{128}=\sqrt{64\cdot2}=\sqrt{64}\cdot\sqrt2=8\sqrt2\\\\x=\dfrac{-(-4)\pm8\sqrt2}{(2)(4)}=\dfrac{4\pm8\sqrt2}{8}\qquad\text{simplify by 4}\\\\x=\dfrac{1\pm2\sqrt2}{2}\to x=\dfrac{1}{2}\pm\sqrt2$