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3 years ago

What is the solution to this inequality? +8<5

Mathematics

1 answer:

tankabanditka [31]3 years ago

6 0

Answer:

-7 + 8 > 5

Step-by-step explanation:

The left side

is less than the right side

, which means that the given statement is always true.

True

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A group of young businesswomen wish to open a high fashion boutique in a vacant store, but only if the average income of househo

vova2212 [387]

Answer:

Based on the results the boutique could be located there.

Step-by-step explanation:

Note: The average income (the mean) is calculated by summing the total incomes then divided by the total sample–9.

The mean ù (average income) = $28,000 + $24,000 + $26,000 + $25,000 + $23,000 + $27,000 + $26,000 + $22,000 + $24,000= $225,000/9= $25,000 (which is ≥ $25,000.

Based on the results of the p-value, using the 5% significant level we fail to reject the null hypothesis (ú≥25,000).

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3 years ago

An ice sculpture is melting from the heat. it's height changes by -2/25 every hour, what will it be after 5 hours?

madreJ [45]

Answer:

Height will have changed by -2/5

Step-by-step explanation:

change in height = (change in height/hour) × hours

= (-2/25) × 5 = -2/5

7 0

3 years ago

In a circle with an 8-inch radius, a central angle has a measure of 60°. How long is the segment joining the endpoints of the ar

g100num [7]

Given the radius, circumference can be solved by the equation, C = 2πr. The circumference of the circle above is C = 2π(8 in) = 16π in. To solve for the length of the segment joining the arc is the circumference times the ratio of central angle and 360 degrees.

Length of the segment = (16π in)(60/360) = 8/3 π in

Thus, the length of the segment is approximately 8.36 in.

3 0

3 years ago

Read 2 more answers

Help me please I need it

7nadin3 [17]

Answer:

Step-by-step explanation:

The formula for a rectangular prism is length*width*height. Thus, the equation would be 6*4*16, which equals 384 cm^3.

6 0

2 years ago

The graphs of the polar curves r = 4 and r = 3 + 2cosθ are shown in the figure above. The curves intersect at θ = π/3 and θ = 5π

Gennadij [26K]

(a)

$\displaystyle \frac{1}{2} \cdot \int_{\frac{\pi}{3}}^{\frac{5\pi}{3}} \left(4^2 - (3 + 2\cos\theta)^2 \right) \, d\theta$

or, via symmetry

$\displaystyle\frac{1}{2} \cdot 2 \int_{\frac{\pi}{3}}^{\pi} \left(4^2 - (3 + 2\cos\theta)^2 \right) \, d\theta$

____________

(b)

By the chain rule:

$\displaystyle \frac{dy}{dx} = \frac{ dy/ d\theta}{ dx/ d\theta}$

For polar coordinates, x = rcosθ and y = rsinθ. Since
r = 3 + 2cosθ, it follows that

$x = (3 + 2\cos\theta) \cos \theta \\ 
y = (3 + 2\cos\theta) \sin \theta$

Differentiating with respect to theta

$\begin{aligned}
\displaystyle \frac{dy}{dx} &= \frac{ dy/ d\theta}{ dx/ d\theta} \\
&= \frac{(3 + 2\cos\theta)(\cos\theta) + (-2\sin\theta)(\sin\theta)}{(3 + 2\cos\theta)(-\sin\theta) + (-2\sin\theta)(\cos\theta)} \\ \\
\left.\frac{dy}{dx}\right_{\theta = \frac{\pi}{2}}
&= 2/3
\end{aligned}$

2/3 is the slope

____________

(c)

"distance between the particle and the origin increases at a constant rate of 3 units per second" implies dr/dt = 3

Angle θ and r are related via r = 3 + 2cosθ, so implicitly differentiating with respect to time

 $\displaystyle\frac{dr}{dt} = -2\sin\theta \frac{d\theta}{dt} \quad \stackrel{\theta = \pi/3}{\implies} \quad 3 = -2\left( \frac{\sqrt{3}}{2}}\right) \frac{d\theta}{dt} \implies \\ \\ \frac{d\theta}{dt} = -\sqrt{3} \text{ radians per second}$

5 0

3 years ago