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2 years ago

What number must we multiply by $-\frac23$ to get a product of $\frac34$?

Mathematics

1 answer:

stich3 [128]2 years ago

7 0

Let x be unknown number. If number x is multiplied by $-\dfrac{2}{3}$ and the product is equal to $\dfrac{3}{4},$ then

$x\cdot \left(-\dfrac{2}{3}\right)=\dfrac{3}{4}.$

To find x you should divide $\dfrac{3}{4}$ by $-\dfrac{2}{3}:$

$x=\dfrac{\dfrac{3}{4}}{-\dfrac{2}{3}}=\dfrac{3}{4}\cdot \left(-\dfrac{3}{2}\right)=-\dfrac{3\cdot 3}{4\cdot 2}=-\dfrac{9}{8}.$

Answer: $x=-\dfrac{9}{8}$

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The equation y = 14x represents the number of pages Printer A can print over time, where y is the number of pages and x is time

Crank

Printer A
y = 14x

Printer B
Time(min) | 3 | 5 | 8 | 12 |
Pages printed | 48 | 80 | 128 | 192 |

Printer A prints 14(1) = 14 pages per minute.
Printer B prints 48/3 = 16 pages per minute.

The printer that prints at a faster rate is printer B.

8 0

1 year ago

Read 2 more answers

Which of the following is a zero of the function f(x) = x3 - x2 - 21x + 45.

marin [14]

The zeros are 3 and -5. Hope this helps!

5 0

1 year ago

Yi Min is a pitcher on her softball team. This season,

almond37 [142]

Answer:

Step-by-step explanation:

0.8 times 60= 48

4 0

2 years ago

Use Stokes' Theorem to evaluate S curl F · dS. F(x, y, z) = x2 sin(z)i + y2j + xyk, S is the part of the paraboloid z = 9 − x2 −

Korolek [52]

The vector field

$\vec F(x,y,z)=x^2\sin z\,\vec\imath+y^2\,\vec\jmath+xy\,\vec k$

has curl

$\nabla\times\vec F(x,y,z)=x\,\vec\imath+(x^2\cos z-y)\,\vec\jmath$

Parameterize $S$ by

$\vec s(u,v)=x(u,v)\,\vec\imath+y(u,v)\,\vec\jmath+z(u,v)\,\vec k$

where

$\begin{cases}x(u,v)=u\cos v\\y(u,v)=u\sin v\\z(u,v)=(9-u^2)\end{cases}$

with $0\le u\le3$ and $0\le v\le2\pi$ .

Take the normal vector to $S$ to be

$\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial v}=2u^2\cos v\,\vec\imath+2u^2\sin v\,\vec\jmath+u\,\vec k$

Then by Stokes' theorem we have

$\displaystyle\int_{\partial S}\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

$=\displaystyle\int_0^{2\pi}\int_0^3(\nabla\times\vec F)(\vec s(u,v))\cdot\left(\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial v}\right)\,\mathrm du\,\mathrm dv$

$=\displaystyle\int_0^{2\pi}\int_0^3u^3(2u\cos^3v\sin(u^2-9)+\cos^3v\sin v+2u\sin^3v+\cos v\sin^3v)\,\mathrm du\,\mathrm dv$

which has a value of 0, since each component integral is 0:

$\displaystyle\int_0^{2\pi}\cos^3v\,\mathrm dv=0$

$\displaystyle\int_0^{2\pi}\sin v\cos^3v\,\mathrm dv=0$

$\displaystyle\int_0^{2\pi}\sin^3v\,\mathrm dv=0$

$\displaystyle\int_0^{2\pi}\cos v\sin^3v\,\mathrm dv=0$

4 0

1 year ago

If the test scores of a class of 35 students have a mean of 74.3 and the test scores of another class of 28 students have a mean

STALIN [3.7K]

Let the total sum of the scores of the first class of 35 students be a. The mean is 74.3 .

So
$\frac{a}{35}=74.3\\\\a=35\cdot74.3= 2600.5$

Also, let the total sum of the scores of the second class of 28 students be b. The mean is 67.6 .

so
$\frac{b}{28}=67.6\\\\ b=28\cdot67.6= 1892.8$

The combined group has 35+28=63 students. The sum of their scores is

a+b=2600.5+1892.8=4493.3

Thus, the mean of the combined group is $\frac{4493.3}{63}= 71.32$

6 0

1 year ago