Given directed line segment PR, find the coordinates of Q on PR such that the ratio of PQ to QR is 2:1.

What is the result when the number 64 is decreased by 8% ? Round your answer to the nearest te th

VladimirAG [237]

Answer:

58.9

Step-by-step explanation:

64-(8% of 64)=64-(8/100)×64=64(1-8/100)=

64×92/100=58.88

Rounded to tenth: 58.9

5 0

3 years ago

On the unit circle, if s is the length of the arc subtended by a central angle θ, measured in radians, then s = θ.

Gennadij [26K]

<span>a. True The question is pretty much the entire definition of a radian. For an unit circle, its entire circumference is 2Ď€ and the entire circle has 2Ď€ radians. A quarter circle, or 90Â°, or Ď€/2 radians, have 1/4th of the circumference. And 2Ď€/4 is Ď€/2. This natural relationship is WHY higher mathematics uses radians for the measurement of angles rather than arbitrary units such as degrees.</span>

6 0

3 years ago

A machine at a bottling company fills water bottles. the number of bottles filled is proportional to the amount of time the mach

Whitepunk [10]

In the table shown below:

Let N be the number of bottles filled,

Let T be the time in hours.

Given that the number of bottles filled is proportional to the amount of time the machine runs, we have

$\begin{gathered} N\propto T \\ \text{Introducing a proportionality constant, we have } \\ N\text{ = kT} \\ \Rightarrow k\text{ = }\frac{N}{T} \\ \end{gathered}$

Let's evaluate the value of k for each day.

Thus, on monday,

$\begin{gathered} N\text{ = 9900} \\ T\text{ = 5.5} \\ \text{thus,} \\ k\text{ = }\frac{9900}{5.5} \\ \Rightarrow k\text{ = 1800} \end{gathered}$

Tuesday:

$\begin{gathered} N\text{ = }11160 \\ T\text{ = }6.2 \\ \text{thus,} \\ k\text{ = }\frac{11160}{6.2} \\ \Rightarrow k\text{ = 1800} \end{gathered}$

Wednesday:

$\begin{gathered} N\text{ = }12330 \\ T\text{ = }6.25 \\ \text{thus,} \\ k\text{ = }\frac{12330}{6.25} \\ \Rightarrow k\text{ = 1972.8} \end{gathered}$

Thursday:

$\begin{gathered} N\text{ = }10440 \\ T\text{ = }5.80 \\ \text{thus,} \\ k\text{ = }\frac{10440}{5.8} \\ \Rightarrow k=1800 \end{gathered}$

It is observed that all exept wednesday have the same value of k.

Thus, the amount of time required for the number of bottles filled on wednesday is evaluated as

$\begin{gathered} N\text{ = }12330 \\ k\text{ = 1800} \\ T\text{ = ?} \\ \text{but} \\ k\text{ = }\frac{N}{T} \\ 1800\text{ = }\frac{12330}{T} \\ \Rightarrow T\text{ = }\frac{\text{12330}}{1800} \\ T\text{ = 6.85} \end{gathered}$

Hence, the incorrect day is Wednesday. The amount of time for that many bottles should be 6.85 hours.

3 0

1 year ago

Solve <img src="https://tex.z-dn.net/?f=%20%5Csqrt%7B3%7D%20%20%3D%20%20%5Cfrac%7Bh%7D%7Bh%20-%203000%7D%20" id="TexFormula1" ti

dezoksy [38]

<span> $\sqrt{3}(h-3000)=h$
</span> $(\sqrt{3}h-\sqrt{3}(3000)=h$
$(\sqrt{3}-1)h=\sqrt{3}(3000)$
$h=\frac{\sqrt{3}(3000)}{(\sqrt{3}-1)}$
$=\frac{\sqrt{3}(3000)}{(\sqrt{3}-1)}$
$=7098.076$ (approximately)

8 0

3 years ago

A set of equations is given below:

TEA [102]

The 3rd selection is appropriate.

.. 5b +1 = a = 3b +5
by the transitive property of equality,
.. 5b +1 = 3b +5

6 0

3 years ago