All categories

3 years ago

I need help with #2 and 4 please help me T^T

Mathematics

1 answer:

pav-90 [236]3 years ago

4 0

Answer:

2. w = -90

4. b = 8

Step-by-step explanation:

Multiply both sides by the reciprocal of the number multiplying the variable.

$-\dfrac{2}{3}w = 60$

$-\dfrac{3}{2} \times (-\dfrac{2}{3}w) = -\dfrac{3}{2} \times 60$

$w = -\dfrac{180}{2}$

$w = -90$

$9.6 = 1.2b$

$\dfrac{1}{1.2} \times 9.6 = \dfrac{1}{1.2} \times 1.2b$

$8 = b$

$b = 8$

You might be interested in

Solve the inequality 2x + 7 - 3x < 13 +2X. You must show your work and describe the graph of the solution on the number line.

kozerog [31]

Cancel equal terms on both sides of inequality

7-3x < 13

move constant to the right side and change its sign

-3x<13-7

subtract the numbers

-3x<6

divide both sides of inequality by -3 and flip the inequality sign

answer is: x>-2

4 0

3 years ago

I need to finish this question ASAP Someone please help!

Helga [31]

Answer:

Step-by-step explanation:

g(r) = 0 ⇒ $r^{2} -2r-17=0$ ⇒r= $1+3\sqrt{2}$ và r= $1-3\sqrt{2}$

4 0

3 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:

$P(X$