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White raven [17]
3 years ago
10

What is the answer its for a grade

Mathematics
1 answer:
kolezko [41]3 years ago
8 0
The answers is x=14.
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Tiana is on a 25-foot ladder that is leaning against her house. Its base is 7 feet from the base of the house. The ladder slips
Lostsunrise [7]

Answer:

4 ft downwards

Step-by-step explanation:

old height off the ground :

7^2+b^2=25^2

49+b^2=625

b^2=576

b=24

new height off the ground :

7+8=15

15^2+ b^2 =25^2

225+b^2 = 625

b^2 = 400

b=20

difference between heights :

24 - 20 =  4

4 0
3 years ago
What is the area of a rectangle that is 4 inches long and 1 3/4 inches wide ​
BigorU [14]

Answer: 7 inches

Step-by-step explanation:

4 times 1 3/4 is 7

6 0
3 years ago
Here is a graph of the relationship between the number of quarters and the number of dimes when there are a total of 17 coins.
kirill115 [55]
Point a has more what she said
8 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

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  

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.  

Q3

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
Are two lines parallel, perpendicular or neither 3x+7y=15 and 7x-3y=6
maw [93]

Answer:

The lines are perpendicular

Step-by-step explanation:

we know that

If two lines are parallel, then their slopes are equal

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

we have

3x+7y=15 ----> equation A

isolate the variable y

7y=-3x+15

Divide by 7 both sides

y=-\frac{3}{7}x+\frac{15}{7}

The slope of the line A is m_A=-\frac{3}{7}

7x-3y=6 ----> equation B

isolate the variable y

3y=7x-6

Divide by 3 both sides

y=\frac{7}{3}x-2

The slope of the line B is m_B=\frac{7}{3}

Compare the slope of both lines

m_A=-\frac{3}{7}

m_B=\frac{7}{3}

so

m_A \neq m_B ----> the lines are not parallel

Find the product of the slopes

-\frac{3}{7}(\frac{7}{3})=-1 ----> the lines are perpendicular

4 0
3 years ago
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