Find the quotient: a 3 ft 4 in b 3 ft 9 in c 4 ft d 3 ft 8 in

Aimi is making Valentine’s Day cards for everyone in her class. She plans to use a whole sheet of paper for each of her 6 closes

DaniilM [7]

34 - 6 = 28
28 x 8 = 224

After making the 6 whole sheet of paper cards for her closest friends Aimi will have 28 pieces of paper left.

Since she wants to use 1/8 of a sheet per valentine (think of it as one piece of paper can make 8 valentines) you can do 28 pieces of paper multiplied by 8 which gives you 224 valentines.

8 0

3 years ago

O 4. LABC is a 40° angle.

ohaa [14]

LABC is a 30°angle point B is at (3,2)

5 0

3 years ago

Given r=3 and a center of (3,5)? Find the equation of the circle in standard and general form.

alukav5142 [94]

9514 1404 393

Answer:

(x -3)^2 +(y -5)^2 = 9
x^2 +y^2 -6x -10y +25 = 0

Step-by-step explanation:

The standard form equation for a circle of radius r and center (h, k) is ...

(x -h)^2 +(y -k)^2 = r^2

For radius 3 and center (3, 5), this is ...

(x -3)^2 +(y -5)^2 = 9 . . . . standard form equation

Expanding this and subtracting the constant on the right gives ...

x^2 -6x +9 +y^2 -10y +25 -9 = 0

x^2 +y^2 -6x -10y +25 = 0 . . . . general form equation

8 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

Q1

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:

$P(X$