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4 years ago

15

Suppose y varies directly as x and y=21 when x 3 find x when y=42

1 answer:

irga5000 [103]4 years ago

7 0

<span> 35
y=kx, where k is a constant
substitute in y=21 and x=3, you will get k=7
y=7(5)
y= 35 </span>

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An employee at a department store is stocking cell phone cases. He has a box of 80 cases. Among the 80 cases, 40 are black, 10 a

Salsk061 [2.6K]

Answer:

$\sf \dfrac{203}{4108}$

As a decimal = 0.05 (nearest hundredth)

Step-by-step explanation:

$\sf Probability \ of \ an \ event \ occurring = \dfrac{Number \ of \ ways \ it \ can \ occur}{Total \ number \ of \ possible \ outcomes}$

First pick:

$\sf \implies P(pink)=\dfrac{30}{80}$

As the case is NOT replaced, second pick:

$\sf \implies P(pink)=\dfrac{30-1}{80-1}=\dfrac{29}{79}$

As the case is NOT replaced, third pick:

$\sf \implies P(pink)=\dfrac{29-1}{79-1}=\dfrac{28}{78}$

Therefore,

$\sf \implies P(pink \ and \ pink \ and \ pink)=\dfrac{30}{80} \times \dfrac{29}{79} \times \dfrac{28}{78}=\dfrac{203}{4108}$

Answer as a decimal = 0.05 (nearest hundredth)

6 0

3 years ago

I need answers please just a few is fine

alina1380 [7]

The second one is correct so its 2

4 0

4 years ago

You are looking at the New York ball drop on New Year’s Eve at a distance of 100 m away from the base of the structure. If the b

Fofino [41]

The question is an illustration of related rates.

The rate of change between you and the ball is 0.01 rad per second

I added an attachment to illustrate the given parameters.

The representations on the attachment are:

$\mathbf{x = 100\ m}$

$\mathbf{\frac{dy}{dt} = 2\ ms^{-1}}$ ---- the rate

$\mathbf{\theta = \frac{\pi}{4}}$

First, we calculate the vertical distance (y) using tangent ratio

$\mathbf{\tan(\theta) = \frac{y}{x}}$

Substitute 100 for x

$\mathbf{y = 100\tan(\theta) }$

$\mathbf{\tan(\theta) = \frac{y}{100}}$

Differentiate both sides with respect to time (t)

$\mathbf{ \sec^2(\theta) \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot \frac{dy}{dt}}$

Substitute values for the rates and $\mathbf{\theta }$

$\mathbf{ \sec^2(\pi/4) \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot 2}$

This gives

$\mathbf{ (\sqrt 2)^2 \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot 2}$

$\mathbf{ 2 \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot 2}$

Divide both sides by 2

$\mathbf{ \frac{d\theta}{dt} = \frac{1}{100} }$

$\mathbf{ \frac{d\theta}{dt} = 0.01 }$

Hence, the rate of change between you and the ball is 0.01 rad per second

Read more about related rates at:

brainly.com/question/16981791

8 0

3 years ago

Plz help I will give brainliest

natali 33 [55]

Answer:

Should be the second and third ones. If you multiply the values together, 3/4s will equal 3/16 and 3/32 with the other value.

5 0

3 years ago

Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth. −6y2 − 9y = −1

Tomtit [17]

$-6y^2 - 9y = -1$

$y= \dfrac{-9+ \sqrt{9^2-4*-6} }{2*6}, \dfrac{-9-\sqrt{9^2-4*-6}}{2*6}$

$y= \dfrac{-9+ \sqrt{105} }{12}, \dfrac{-9- \sqrt{105} }{12}$

8 0

4 years ago