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3 years ago

A factory inspector found 3 defective microchips out of a total of 750

Mathematics

1 answer:

Y_Kistochka [10]3 years ago

5 0

Answer:

Option B

Step-by-step explanation:

Proportion of number of defective pieces to the number of microchips in a batch can be represented by the ratio = $\frac{\text{Number of microchips not in good condition}}{\text{Total numbers of microchips}}$

If 3 microchips are defective in a batch of 750 microchips,

Proportion = $\frac{3}{750}$

If 'x' chips are defective in a batch of 10000 microchips,

Proportion = $\frac{x}{10000}$

If both the proportions are equal,

$\frac{3}{750}=\frac{x}{10000}$

Therefore, Option B will be the answer.

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F(x)=(-3x+2) and g(x)=(2x^2-5x-1)

pashok25 [27]

Answer: -6x² + 15x + 5

Step-by-step explanation:

To solve this problem, you only need to substitute g(x)'s equation as the value of the x in f(x), then simplify.

Step 1: f(x) = -3(2x² - 5x - 1) + 2

Step 2: Apply the distributive property

-3(2x²) + -3(-5x) + -3(-1)

-6x² + 15x + 3

Step 3: Simplify

f(x) = -6x² + 15x + 3 + 2

f(x) = -6x² + 15x + 5

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3 years ago

A woman a walked 12km at 3km/hr and cycled 18km at 9km/hr. what is her average speed for the whole journey.

Deffense [45]

Answer:

5 km/h

Step-by-step explanation:

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3 years ago

Find the equation of the tangent line to the curve (a lemniscate)

olya-2409 [2.1K]

Answer:

$m=\frac{9}{13}$ and $b=\frac{40}{13}$

Step-by-step explanation:

The equation of curve is

$2(x^2+y^2)^2=25(x^2-y^2)$

We need to find the equation of the tangent line to the curve at the point (-3, 1).

Differentiate with respect to x.

$2[2(x^2+y^2)\frac{d}{dx}(x^2+y^2)]=25(2x-2y\frac{dy}{dx})$

$4(x^2+y^2)(2x+2y\frac{dy}{dx})=25(2x-2y\frac{dy}{dx})$

The point of tangency is (-3,1). It means the slope of tangent is $\frac{dy}{dx}_{(-3,1)}$ .

Substitute x=-3 and y=1 in the above equation.

$4((-3)^2+(1)^2)(2(-3)+2(1)\frac{dy}{dx})=25(2(-3)-2(1)\frac{dy}{dx})$

$40(-6+2\frac{dy}{dx})=25(-6-2\frac{dy}{dx})$

$-240+80\frac{dy}{dx})=-150-50\frac{dy}{dx}$

$80\frac{dy}{dx}+50\frac{dy}{dx}=-150+240$

$130\frac{dy}{dx}=90$

Divide both sides by 130.

$\frac{dy}{dx}=\frac{9}{13}$

If a line passes through a points $(x_1,y_1)$ with slope m, then the point slope form of the line is

$y-y_1=m(x-x_1)$

The slope of tangent line is $\frac{9}{13}$ and it passes through the point (-3,1). So, the equation of tangent is

$y-1=\frac{9}{13}(x-(-3))$

$y-1=\frac{9}{13}(x)+\frac{27}{13}$

Add 1 on both sides.

$y=\frac{9}{13}(x)+\frac{27}{13}+1$

$y=\frac{9}{13}(x)+\frac{40}{13}$

Therefore, $m=\frac{9}{13}$ and $b=\frac{40}{13}$ .

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3 years ago

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devlian [24]

Milk carton
Perfume bottle

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At the city museum, child admission is 6.10 and adult admission is 9.40. On wednesday, 125 tickets were sold for a total sales o

murzikaleks [220]

55 adult tickets. Set up 2 equations: c+a=125 and 6.1c+9.4a=944. Isolate either variable from first equation and plug into second to find that 55 adult tickets were sold and 70 children’s tickets

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3 years ago