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Cerrena [4.2K]
2 years ago
9

On a number line, point F is at 4, and point G is at -2. Point H lies between point F and point G. If the ratio of FH to HG is 3

:9, where does point H lie on the number line?
Mathematics
1 answer:
Mademuasel [1]2 years ago
7 0

Here, we are required to determine the point where point H lie on the number line.

The point H is at point 2.5 on the number line.

The distance between point F and G on the number line is:

4 - (-2) = 6 numbers on the number line.

And since the ratio of FH to HG is 3:9

  • Then, let point H be at no. X on the number line.

Therefore; FH/HG = (4 - x)/(x - (-2))

i.e 3/9 = (4 - x)/ (x +2).

By cross multiplication, 3x + 6 = 36 - 9x.

Therefore, 12x = 30

and, x = 2.5

Therefore, the point H is at point 2.5 on the number line.

Read more:

brainly.com/question/18329661

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4.Rebecca biked 4.5 miles today and 3.2 miles
Fudgin [204]

Answer:

10-(4.5+3.2)

= 10-7.7

=2.3 miles

6 0
3 years ago
An electronics hobbyist has three electronic parts cabinets with two drawers each.
Andrews [41]

Answer:

a) 0.5 = 50% probability that an NPN transistor will be selected.

b) 0.3333 = 33.33% probability that it came from the cabinet that contains both types

c) 66.67% probability that it comes from the cabinet that contains only NPN transistors

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

P(B|A) = \frac{P(A \cap B)}{P(A)}

In which

P(B|A) is the probability of event B happening, given that A happened.

P(A \cap B) is the probability of both A and B happening.

P(A) is the probability of A happening.

a) What is the probability that an NPN transistor will be selected?

1/3 probability that the first cabinet is chosen. This cabinet has two transistors, both of which are NPN, so 100% probability of selecting a NPN transistor.

1/3 probability that the second cabinet is chosen. This cabinet has two transistors, both of which are PNP, so 0% probability of selecting a NPN transistor.

1/3 probability that the second cabinet is chosen. This cabinet has two transistors, one of which is NPN, so 50% probability of selecting a NPN transistor.

So

p = \frac{1}{3}*1 + \frac{1}{3}*0 + \frac{1}{3}*0.5 = \frac{1}{3} + \frac{1}{6} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6} = 0.5

0.5 = 50% probability that an NPN transistor will be selected.

b) Given that the hobbyist selects an NPN transistor, what is the probability that it came from the cabinet that contains both types?

Here we use the conditional probability formula.

Event A: NPN transistor

Event B: From the third cabinet.

50% probability that an NPN transistor will be selected, so P(A) = 0.5.

1/6 probability that it is from the third cabinet and NPN, so P(A \cap B) = \frac{1}{6}

The desired probability is:

P(B|A) = \frac{\frac{1}{6}}{0.5} = 0.3333

0.3333 = 33.33% probability that it came from the cabinet that contains both types.

c) Given that an NPN transistor is selected what is the probability that it comes from the cabinet that contains only NPN transistors?

Either it comes from the cabinet with only NPN transistors, or it comes from the cabinet with both types of transistors. The sum of the probabilities of these outcomes is 100%. So

x + 33.33 = 100

x = 66.67

66.67% probability that it comes from the cabinet that contains only NPN transistors

6 0
3 years ago
According to a certain central bank from 2000 to 2016 the average price of a new home in a certain region increased by 62 % to $
Alla [95]

Answer:  $ 290 thousand

Step-by-step explanation:

Given : According to a certain central bank from 2000 to 2016 the average price of a new home in a certain region increased by 62 % to $470 thousand.

Let X be the the average price of a new home in 2000 .

Then , the 62 % increase in price is given by :-

x+0.62(x)=x(1+0.62)=1.62x

Since , the the average price of the home in 2016 = $470 thosand

1.62x=470\\\\\Rightarrow\ x=\dfrac{470}{1.62}=290.12345679\approx290

Hence, the average price of a new home in 2000 =  $ 290 thousand .

3 0
3 years ago
An easy question all wrong or unhelpful or no-work answers will be reported.
miss Akunina [59]
Elimination:

7x - 3y = 20
5x + 3y = 16
(add)
12x = 36
÷ 12
x = 3

(5 × 3) + 3y = 16
15 + 3y = 16
- 15
3y = 1
÷ 3
y = 1/3

Substitution:

5x + 3y = 16
- 3y
5x = 16 - 3y
÷ 5
x = 3.2 - 0.6y

5(3.2 - 0.6y) + 3y = 16
16 - 3y + 3y = 16
16  = 16
- 16
6y = 0
÷ 6
y = 0

Sorry the substitution messed up for some reason, I'll fix it after I've answered the other question

6 0
3 years ago
Can someone please please help with these questions?
wolverine [178]
The answer to number seven is EDF!
5 0
3 years ago
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