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2 years ago

11

Eliminate the parameter in the equations x =t Superscript one-half and y = t – 4. How can the rectangular equation be described?

cubic linear quartic quadratic
ANSWER: A

2 answers:

garri49 [273]2 years ago

8 0

Answer:

Cubic

Step-by-step explanation:

miskamm [114]2 years ago

5 0

Answer:

A. CUBIC

Step-by-step explanation:

I got it right on edg21

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Find the mean of each distribution.

Vanyuwa [196]

Answer:

a) 23 °C

b) 5.81 m² (2 dp)

Step-by-step explanation:

<h3><u>Part (a)</u></h3>

This set of data is presented as a <u>Dot Plot</u>.

The frequency (how often a data value occurs) is represented by the number of dots above each data value.

For example, in this dot plot, there are 3 dots above the data value 21 °C and so this means that there are three of this particular data value in the set of data.

To find the mean, we need to multiply each data value by its frequency, add them up, then divide by the total frequency.

$\begin{aligned}\textsf{mean}&=\dfrac{3 \times 21+1 \times 22+2\times 23+5\times 24+1\times 25}{3+1+2+5+1}\\\\ & = \dfrac{63+22+46+120+25}{12}\\\\& = \dfrac{276}{12}\\\\&=23^{\circ} \sf C\end{aligned}$

<h3><u>Part (b)</u></h3>

This set of data is presented as a <u>stem and leaf diagram</u>, where the units and tenths are split. The units column is the 'stem' and the tenths become the 'leaf'.

Therefore, the first row of this stem and leaf diagram represents 2 data values: 4.3 and 4.8

To find the mean, sum the data values, then divide by the total frequency.

To find the total frequency, simply count the number of values in the leaf part of the diagram.

Data values = 4.3, 4.8, 5.1, 5.1, 5.2, 5.5, 5.7, 6.6, 6.9, 7.3, 7.4

Total frequency = 11

$\begin{aligned}\textsf{mean} &=\dfrac{4.3 + 4.8 + 5.1+5.1+5.2+5.5+5.7+6.6+6.9+7.3+7.4}{11}\\ & = \dfrac{63.9}{11}\\\\& = 5.81\:\textsf{(2 dp)}\end{aligned}$

4 0

1 year ago

Read 2 more answers

Your swimming pool containing 60,000 gal of water has been contaminated by 6 kg of a nontoxic dye that leaves a swimmer's skin a

Paul [167]

[a] Dye is removed from the pool at a rate of

(250 gal/min) * (<em>q</em>/60,000 g/gal) = -<em>q</em>/240 g/gal

where <em>q</em> denotes the amount of dye in the pool at time <em>t</em>. Clean water is pumped back into the pool, so no dye is being re-added.

So the net rate of change of the amount of dye in the pool is given by the differential equation,

$\dfrac{\mathrm dq}{\mathrm dt}=-\dfrac{q(t)}{240}$

with the intial value, <em>q</em>(0) = 6000 g (or 6 kg).

[b] The ODE above is separable as

$\dfrac{\mathrm dq}q=-\dfrac{\mathrm dt}{240}$

Integrate both sides to get

$\ln|q|=-\dfrac t{240}+C$

$e^{\ln|q|}=e^{-t/240+C}$

$\implies q(t)=e^{-t/240+C}=e^{-t/240}e^C=Ce^{-t/240}$

Now plug in the initial condition:

$6000=Ce^0\implies C=6000$

so the particular solution to the IVP is

$q(t)=6000e^{-t/240}$

[c] The acceptable concentration of the dy is 0.03 g/gal, which in a pool containing 60,000 gal of water corresponds to

(0.03 g/gal) * (60,000 gal) = 1800 g = 1.8 kg

of dye. Find the time <em>t</em> when this occurs:

$1800=6000e^{-t/240}\implies0.3=e^{-t/240}$

$\implies\ln0.3=-\dfrac t{240}$

$\implies t=-240\ln0.3\approx288.953$

so the amount of dye in the pool is within the acceptable tolerance after about 289 min have passes, or about 4.82 hrs. So no, the filtration system is not up to the task.

8 0

3 years ago

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What is 8.545 rounded to nearest tenth

valina [46]

8.545 rounded to the nearest tenth is 8.5. I hope this helps.

4 0

3 years ago

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What is the solution to the equation below? square root of 4-3x divided by square root of 3x equals 2

PSYCHO15rus [73]

Answer:

B. $x=\frac{4}{15}$

Step-by-step explanation:

$\frac{\sqrt{4-3x}}{\sqrt{3x} } =2$ can be simplify by doing some algebra.
Particulary, in this case, $\frac{\sqrt{4-3x}}{\sqrt{3x} } =\sqrt{\frac{4-3x}{3x} }$ , because of the distributive property with respect to division and multiplication.
Then, by dividing numerator and denominator by 3x inside the power we get $\sqrt{\frac{\frac{4}{3x}-1}{1}}=\sqrt{\frac{4}{3x}-1} =2$ .
To dispose of the squared root, we raise to power 2 both sides of the equation, to obtain the following expression: $\frac{4}{3x}-1=4$ .
Finally, we just have to clear out the value of x from this expression, by addding 1 both sides of the equation: $\frac{4}{3x}=5$ , and then by multiplying both sides by 3x, and then dividing the result by 15. This yields $x=\frac{4}{15}$

3 0

3 years ago

Which ordered pairs are solutions to the inequality y−2x≤−3?

topjm [15]

I hope this helps you

4 0

3 years ago

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