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3 years ago

Christian’s Gym charges a one-time fee of $50 plus $30 per session for a personal trainer.

Mathematics

1 answer:

nydimaria [60]3 years ago

3 0

Answer: For 10 sessions, the cost of the two plans the same.

Step-by-step explanation:

Let x= Number of sessions.

Given: Christian’s Gym charges a one-time fee of $50 plus $30 per session for a personal trainer.

Total charge for x sessions = 50+30x

Nicole's fitness center charges a yearly fee of $250 plus $10 for each session with a trainer.

Total charge for x sessions = 250+10x

When both plan charges the same, then

$50+30x=250+10x\\\\\Rightarrow\ 30x-10x=250-50\\\\\Rightarrow\ 20x=200\\\\\Rightarrow\ x=10$

i.e. For 10 sessions, the cost of the two plans the same.

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If the diagonal path is 750 feet long and the width of the park is 450 feet, what is the length, in the feet, of the park?

disa [49]

Answer:

The length is 600 ft

Step-by-step explanation:

We can use the Pythagorean theorem since we know the diagonal which is the hypotenuse and the width

a^2 + b^2 = c^2

450 ^2 + b^2 = 750^2

b^2 = 750^2 - 450^2

b^2 =562500-202500

b^2 =360000

Taking the square root of each side

sqrt(b^2) = sqrt(360000)

b =600

4 0

3 years ago

dentify the type of data (qualitative/quantitative) and the level of measurement for the native language of survey respondents.

ohaa [14]

Answer:

The correct option is D i.e. Quantitative because numerical values found by either measuring or counting are used to describe the data.

Step-by-step explanation:

As the number of respondents is a numerical value and is identified by counting thus it is a quantitative variable. Also all the other options are incorrect.

A is incorrect because the reason described is not the property of quantitative data.

B is incorrect because the data is not described in descriptive terms.

C is incorrect because the reason described in not a property of qualitative data.

7 0

3 years ago

Finding an Equation of a tangent Line in Exercise, find an equation of the tangent line to the graph of the function at the give

frutty [35]

Answer:

$y=\dfrac{3x}{e}+\dfrac{4}{e}$

this is the equation of the tangent at point (-1,1/e)

Step-by-step explanation:

to find the tangent line we need to find the derivative of the function g(x).

$g(x) =e^{x^3}$

we know that $\frac{d}{dx}(e^{f(x)})=e^{f(x)}f'(x)$

$g'(x) =e^{x^{3}}(3 x^{2})$

$g'(x) =3 x^{2} e^{x^{3}}$

this the equation of the slope of the curve at any point x and it also the slope of the tangent at any point x. hence, g'(x) can be denoted as 'm'

to find the slope at (-1,1/e) we'll use the x-coordinate of the point i.e. x = -1

$m =3 (-1)^{2} e^{(-1)^{3}}\\m =3e^{-1}\\m=\dfrac{3}{e}$