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vfiekz [6]
3 years ago
7

Emma is training for a 10-kilometer race. She wants to beat her last 10-kilometer time, which was 1 hour 10 minutes. Emma has al

ready run for 55 minutes. Which inequality can be used to find how much longer she can run and still beat her previous time? (1 hr = 60 min)
70 greater-than 7 minus 55
70 less-than t minus 55
70 less-than-or-equal-to t + 55
70 greater-than t + 55
x + 6 less-than negative 8

x + 4 greater-than-or-equal-to negative 6

x minus 3 greater-than negative 10

x + 5 less-than-or-equal-to negative 4

A
B
C
D
Mathematics
2 answers:
Mandarinka [93]3 years ago
7 0

Answer:

70 > 55 + t

Step-by-step explanation:

Given

Previous\ Time = 1\ hr\ 10\ mins

Current\ Time = 55\ mins

Required

Represent the additional time needed as an inequality

Convert the previous time to minutes

Previous\ Time = 1\ hr\ 10\ mins

Previous\ Time = 1 * 60\ mins + 10\ mins

Previous\ Time = 60\ mins + 10\ mins

Previous\ Time = 70\ mins

Let the additional time be t

<em>This means that she needs to run at least t minutes to beat her previous record</em>

<em />

To beat her previous record, the sum of current time and x must be less than her previous time. i.e.

55 + t < 70

This can be rewritten as:

70 > 55 + t

Mazyrski [523]3 years ago
4 0

Answer:the answer is D

Step-by-step explanation:

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irinina [24]

Answer:

g(x) = -2 • 5^x

Step-by-step explanation:

the reflection across the x-axis makes the equation negative. the 2 is the verticals stretch.

(also got the answer correct on a test)

7 0
3 years ago
At a certain gas station, 40% of the customers use regular gas (A1), 35% use plus gas (A2), and 25% use premium (A3). Of those c
grandymaker [24]

Answer:

a.)

P( A₂ ∩ B ) = P(B | A₂) × P(A₂)

P( A₂ ∩ B ) = 0.40 × 0.35

P( A₂ ∩ B ) = 0.14

b.)

P(B) = P( A₁ ∩ B )  + P( A₂ ∩ B ) + P( A₃ ∩ B )

P(B) = 0.08 + 0.14 + 0.125

P(B) = 0.345

c.)

For regular gas:

P(A₁ | B) = P( A₁ ∩ B ) / P(B)

P(A₁ | B) = 0.08 / 0.345

P(A₁ | B) = 0.232

For plus gas:

P(A₂ | B) = P( A₂ ∩ B ) / P(B)

P(A₂ | B) = 0.14 / 0.345

P(A₂ | B) = 0.406

For premium gas:

P(A₃ | B) = P( A₃ ∩ B ) / P(B)

P(A₃ | B) = 0.125 / 0.345

P(A₃ | B) = 0.362

Step-by-step explanation:

We are given the following information

40% of the customers use regular gas (A2)

P(A₁) = 0.40

35% use plus gas (A2)

P(A₂) = 0.35

25% use premium (A3)

P(A₃) = 0.25

Of those customers using regular gas, only 20% fill their tanks (event B).

P(B | A₁) = 0.20

Of those customers using plus, 40% fill their tanks

P(B | A₂) = 0.40

Whereas of those using premium, 50% fill their tanks.

P(B | A₃) = 0.5

a) What is the probability that the next customer will request plus gas and fill their tank?

We are asked to find P(A₂ ∩ B) = ?

Recall that Multiplicative law of probability is given by

P( A₂ ∩ B ) = P(B | A₂) × P(A₂)

P( A₂ ∩ B ) = 0.40 × 0.35

P( A₂ ∩ B ) = 0.14

b) What is the probability that the next customer fills the tank?

We are asked to find P(B) = ?

P(B) = P( A₁ ∩ B )  + P( A₂ ∩ B ) + P( A₃ ∩ B )

P( A₂ ∩ B ) is already calculated, we need to calculate

P( A₁ ∩ B ) and P( A₃ ∩ B )

So,

P( A₁ ∩ B ) = P(B | A₁) × P(A₁)

P( A₁ ∩ B ) = 0.20 × 0.40

P( A₁ ∩ B ) = 0.08

P( A₃ ∩ B ) = P(B | A₃) × P(A₃)

P( A₃ ∩ B ) = 0.50 × 0.25

P( A₃ ∩ B ) = 0.125

Finally,

P(B) = P( A₁ ∩ B )  + P( A₂ ∩ B ) + P( A₃ ∩ B )

P(B) = 0.08 + 0.14 + 0.125

P(B) = 0.345

c) If the next customer fills the tank, what is the probability that the regular gas is requested? Plus? Premium

For regular gas:

P(A₁ | B) = P( A₁ ∩ B ) / P(B)

P(A₁ | B) = 0.08 / 0.345

P(A₁ | B) = 0.232

For plus gas:

P(A₂ | B) = P( A₂ ∩ B ) / P(B)

P(A₂ | B) = 0.14 / 0.345

P(A₂ | B) = 0.406

For premium gas:

P(A₃ | B) = P( A₃ ∩ B ) / P(B)

P(A₃ | B) = 0.125 / 0.345

P(A₃ | B) = 0.362

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3 years ago
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Snezhnost [94]

Answer:

Step-by-step explanation:

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Answer:1760  

6 0
3 years ago
0.5
Diano4ka-milaya [45]
This is my work for the problem

5 0
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