Tim drives his car. His data is in the table below.

Mathematics

1 answer:

Alex Ar [27]3 years ago

3 0

Answer:

i like cats

Step-by-step explanation:

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Find the value of k for which the given function is a probability density function. f(x = kekx on [0, 2]

liraira [26]

Reading this as

$f_X(x)=\begin{cases}ke^{kx}&\text{for }x\in[0,2]\\0&\text{otherwise}\end{cases}$

For $f_X(x)$ to be a valid PDF, the integral over its support must equal 1:

$\displaystyle\int_{-\infty}^\infty f_X(x)\,\mathrm dx=\int_{x=0}^{x=2} ke^{kx}\,\mathrm dx=1$

Let $y=kx$ , so that $\dfrac{\mathrm dy}k=\mathrm dx$ and the integral becomes

$\displaystyle\int_{y=0}^{y=2k}ke^y\,\dfrac{\mathrm dy}k=\int_0^{2k}e^y\,\mathrm dy=e^y\bigg|_{y=0}^{y=2k}=1$
$e^{2k}-e^0=1$
$e^{2k}-1=1$
$e^{2k}=2$
$\ln e^{2k}=\ln2$
$2k=\ln 2$
$k=\dfrac{\ln 2}2=\ln\sqrt2$

8 0

4 years ago

Write the inverse variation function given that y varies inversely with x, and y = 0.25 when x = 8.

storchak [24]

Answer:

Step-by-step explanation:

If a given variable varies inversely with another variable, an increase in the value of the given variable would cause a corresponding decrease in the value of the other variable. Also, a decrease in the value of the given variable would cause a corresponding increase in the value of the other variable.

If y varies inversely with x, we would introduce a cost of variation, k so that the expression becomes

y = k/x

When y = 0.25, x = 8

Substituting into the expression above, it becomes

0.25 = k/8

k = 0.25 × 8

k = 2

The inverse variation function is

y = 2/x

5 0

3 years ago

How much will you pay in all for the $78 lunch bill with a 15% tip ?

Sergeeva-Olga [200]

→ You will pay $ 89.7.

The tip value is based on the bill value. Hence, to find the total payment you have to <u>multiply 78 by 1.15</u> (this includes the tip, 1.15).

$\Large \text {$Total = 78 \times 1.15 = 89.7 $}$