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4 years ago

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Find the indicated limit, if it exists. limit of f of x as x approaches negative 5 where f of x equals x plus 4 when x is less t

han negative 5 and f of x equals 4 minus x when x is greater than or equal to negative 5

1 answer:

Debora [2.8K]4 years ago

4 0

$\displaystyle f(x)=\begin{cases} x+4, & x$

$\displaystyle \lim_{x\to -5^-}\not =\lim_{x\to -5^+}$ so limit doesn't exist.

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Solve x (give answer as fractions or integers). 2^x =1/2

Rudik [331]

Answer:

x = -1

Step-by-step explanation:

When an exponent is negative, you have to move it to the denominator (or to the numerator if it's already on the denominator). Since the answer is $\frac{1}{2}$ , you know that the 2 has been raised to the power of 1 (any number to the power of 1 is the same number), so you just make it negative. Hope that helps!

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3 years ago

What function is graphed below?<br><br><br><br> y = 2x<br> y = x + 3<br> y = 2x + 3<br> y = 2x + 2

vagabundo [1.1K]

Answer:

y=2x+3

Step-by-step explanation:

The coefficient has to be 2, since the graph has a slope of 2, and the constant has to be 3 because the y- intercept is 3.

y=2x+3

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3 years ago

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3 years ago

If outliers are discarded, then the retirement savings by residents of Econistan is normally distributed with a mean of $100,000

zavuch27 [327]

Answer:

$P(X>117000)=P(\frac{X-\mu}{\sigma}>\frac{117000-\mu}{\sigma})=P(Z>\frac{117000-100000}{20000})=P(z>0.85)$

And we can find this probability using the complement rule and the normal standard table or excel:

$P(z>0.85)=1-P(z$

The firgure attached illustrate the problem

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the retirement savings of a population, and for this case we know the distribution for X is given by:

$X \sim N(100000,20000)$

Where $\mu=100000$ and $\sigma=20000$

We are interested on this probability

$P(X>117000)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X>117000)=P(\frac{X-\mu}{\sigma}>\frac{117000-\mu}{\sigma})=P(Z>\frac{117000-100000}{20000})=P(z>0.85)$

And we can find this probability using the complement rule and the normal standard table or excel:

$P(z>0.85)=1-P(z$

The firgure attached illustrate the problem

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3 years ago

Find an equation equivalent to r = 10sin ø in rectangular coordinates.

kherson [118]

Answer: x^2 + y^2 -10y = 0

Step-by-step explanation:

Cartesian coordinates, also called the Rectangular coordinates, isdefined in terms of x and y. So, for the problem θ has to be eliminated or converted using basic foundations that are described by the unit circle and the right triangle trigonometry.

r= 10sin(θ)

Remember that:

x= r × cos(θ)

y= r × sin(θ)

r^2= x^2 + y^2

Multiply both sides of the equation by r. This will give:

r × r = 10r × sin(θ)

r^2 = 10r × sin(θ)

x^2 + y^2= 10r × sin(θ)

Because y= r × sin(θ), we can make a substitution. This will be:

x^2 + y^2= 10y

x^2 + y^2 -10y = 0

The above equation is the Rectangular coordinate equivalent to the given equation.

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4 years ago