All categories

2 years ago

Answer the question

Mathematics

1 answer:

nasty-shy [4]2 years ago

5 0

We can do anything to an equation as long as we do it to both sides

given: $\sqrt{3+\frac{(4+\sqrt{x+3})^2}{6}}=3$
square both sides
$3+\frac{(4+\sqrt{x+3})^2}{6}=9$
minus 3 from both sides
$\frac{(4+\sqrt{x+3})^2}{6}=6$
multiply both sides by 6
$(4+\sqrt{x+3})^2=36 square root both sides, remember to take the positive and negative roots [tex]4+\sqrt{x+3}=+/-6$
minus 4
$\sqrt{x+3}=-4+/-6$
square both sides
do for -4+6 and -4-6 (2 and -10)
$x+3=4$ and $x+3=100$
minus 3
$x=1$ and $x=97$
test for extraneous roots
x=97 doesn't work

the answer is x=1

You might be interested in

What is the midline of the function?<br> A. Y=0<br> B. Y=2<br> C. Y=1<br> D. Y=4pi

navik [9.2K]

Answer:

Step-by-step explanation:

The trig equation

$a \sin(bx) + d$

where d represent the midline.

D is represented by positive 1 so y=1 is the midline.

4 0

2 years ago

The amount of time that people spend at Grover Hot Springs Spa is normally distributed with a mean of 63 minutes and a standard

PtichkaEL [24]

Answer:

a) $X \sim N(63,18)$

Where $\mu=63$ and $\sigma=18$

b) $P(X>90)=P(\frac{X-\mu}{\sigma}>\frac{90-\mu}{\sigma})=P(Z>\frac{90-63}{18})=P(Z>1.5)$

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

$P(Z>1.5)=1-P(Z$

c) $P(X$

$P(Z$

d) $P(60$

$P(-0.167$

e) IQR = 75.13-50.87=24.26

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".

Part a

Let X the random variable that represent the amount of time that people spend at Grover Hot Springs of a population, and for this case we know the distribution for X is given by:

$X \sim N(63,18)$

Where $\mu=63$ and $\sigma=18$

Part b

We are interested on this probability

$P(X>90)$

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:

$P(X>90)=P(\frac{X-\mu}{\sigma}>\frac{90-\mu}{\sigma})=P(Z>\frac{90-63}{18})=P(Z>1.5)$

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

$P(Z>1.5)=1-P(Z$

Part c

We are interested on this probability

$P(X$

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:

$P(X$

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

$P(Z$

Part d

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

$P(60$

And we can find this probability with this difference:

$P(-0.167$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(-0.167$

Part e

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.75$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.25 of the area on the left and 0.75 of the area on the right it's z=-0.674. On this case P(Z<-0.674)=0.25 and P(z>-0.674)=0.75

If we use condition (b) from previous we have this:

$P(X$

$P(z$

But we know which value of z satisfy the previous equation so then we can do this:

$z=-0.674$

And if we solve for a we got

$a=63 -0.674*18=50.87$

So the value of height that separates the bottom 25% of data from the top 75% is 50.87.

Since the distribution is symmetrical we repaeat the procedure for Q1 but now with z= 0.674

$z=0.674$

And if we solve for a we got

$a=63 +0.674*18=75.13$

And then the IQR = 75.13-50.87=24.26

3 0

2 years ago

A book result sells for $28 if the book is on sale for 20% off how much the sale

zaharov [31]

So it's 28% so you do 20\28= 15 dollars

6 0

2 years ago

If numerous large random samples or repetitions of the same size are taken from a population, the frequency curve made from prop

Evgen [1.6K]

Using the Central Limit Theorem, the shape of the frequency curve will be approximately normal.

<h3>What does the Central Limit Theorem state?</h3>

It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1 - p)}{n}}$ , as long as $np \geq 10$ and $n(1 - p) \geq 10$ .