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Pachacha [2.7K]

3 years ago

10

The number of red shirts sold must be between 4 and 50, inclusive. Write an inequality.

1 answer:

Rina8888 [55]3 years ago

6 0

Answer:

4 > x > 50, given x is red shirts

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Klio2033 [76]

Answer:

Step-by-step explanation:

Dont know

4 0

3 years ago

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The angles of depression of two ships from the top of the light house are 45° and 30° towards east. If the ships are 200 m apart

azamat

Answer:

273 meters

Step-by-step explanation:

See image attached for the diagram I used to represent this scenario.

The distance between the ships, at angles 30 and 45, is 200 meters. The distance between the left ship and the lighthouse is x meters.

We can use trigonometric ratios to solve this problem. We can use the tangent ratio $\big{(} \frac{\text{opposite}}{\text{adjacent}} \big{)}$ to create an equation with the two angles.

$\displaystyle \text{tan(45)} = \frac{h}{x}$
$\displaystyle \text{tan(30)} = \frac{h}{x+200} }$

Let's take these two equations and solve for x in both of them.

<h2> $\textbf{Equation I}$ </h2>

$\displaystyle \text{tan(45)} = \frac{h}{x}$

tan(45) = 1, so we can rewrite this equation.

$\displaystyle 1=\frac{h}{x}$

Multiply x to both sides of the equation.

$\displaystyle x = h$

<h2> $\textbf{Equation II}$ </h2>

$\displaystyle \text{tan(30)} = \frac{h}{x+200} }$

Multiply x + 200 to both sides and divide h by tan(30).

$\displaystyle \text{x + 200} = \frac{h}{\text{tan (30)}}$

Subtract 200 from both sides of the equation.

$\displaystyle \text{x} = \frac{h}{\text{tan (30)}} - 200$

Simplify h/tan(30).

$x=\sqrt{3}h - 200$

<h2> $\textbf{Equation I = Equation II}$ </h2>

Take Equation I and Equation II and set them equal to each other.

$h=\sqrt{3}h-200$

Subtract √3 h from both sides of the equation.

$h-\sqrt{3}h=-200$

Factor h from the left side of the equation.

$h(1-\sqrt{3}) =-200$

Divide both sides of the equation by 1 - √3.

$\displaystyle h=\frac{-200}{1-\sqrt{3} }$

Rationalize the denominator by multiplying the numerator and denominator by the conjugate.

$\displaystyle h=\frac{-200}{1-\sqrt{3} } \big{(} \frac{1+\sqrt{3} }{1+\sqrt{3}} \big{)}$
$\displaystyle h=\frac{-200+200\sqrt{3} }{1-3}$
$\displaystyle h =\frac{-200+200\sqrt{3} }{-2}$

Simplify this equation.

$\displaystyle h=100+100\sqrt{3}$
$h=273.20508075$

The height of the lighthouse is about 273 meters.

5 0

3 years ago

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A manufacturer of small appliances purchases plastic handles for coffeepots from an outside vendor. If a handle is cracked, it i

sp2606 [1]

Answer: 119

Step-by-step explanation:

Since the prior estimate of population proportion of defective handles (p) is unknown , so we take p= 0.5

Given : Margin of error : E=0.09

Critical value for 95% confidence interval : $z_{\alpha/2}=1.96$

Required sample size :-

$n=0.5(1-0.5)(\dfrac{z_{\alpha/2}}{E})^2\\\\=0.25(\dfrac{1.96}{0.09})^2\\\\=118.567901235\approx119$

Hence, the minimum sample size required = 119

i.e. 119 handles from the shipment should be inspected.

3 0

4 years ago

Pls help! I have no idea what to do can someone please help me!

Andreyy89

3x3x3x3x3x3 which will give you your answer of 279

4 0

3 years ago

Hello...........................................

Kruka [31]

Answer:

hii i youre doing well so far :))

<em>have a great day !</em>

7 0

3 years ago

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