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4 years ago

Need help in algebra fast

Mathematics

1 answer:

Gennadij [26K]4 years ago

5 0

Answer:

Step-by-step explanation:

This is a strict inequality so the line must be dotted, meaning it can only be A or D.

The inequality says that y is less than -2x+4 so we want the region under the line, making A the correct answer.

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In 1998, Cathy's age is equal to the sum of the four digits in the year of her birthday, then how old was Cathy in 1998?

ycow [4]

Answer:

Cathy was born in 1980 and she was 18 years old in 1998

Step-by-step explanation:

Equations

This is a special type of equations where all the unknowns must be integers and limited to a range [0,9] because they are the digits of a number.

Let's say Cathy was born in the year x formed by the ordered digits abcd. A number expressed by its digits can be calculated as

$x=1000a+100b+10c+d$

In 1998, Cathy's age was

$1998-(1000a+100b+10c+d)$

And it must be equal to the sum of the four digits

$1998-(1000a+100b+10c+d)=a+b+c+d$

Rearranging

$1998=1001a+101b+11c+2d$

We are sure a=1, b=9 because Cathy's age is limited to having been born in the same century and millennium. Thus

$1998=1001+909+11c+2d$

Operating

$88=11c+2d$

If now we try some values for c we notice there is only one possible valid combination, since c and d must be integers in the range [0,9]

c=8, d=0

Thus, Cathy was born in 1980 and she was 18 years old in 1998. Note that 1+9+8+0=18

5 0

4 years ago

18 questions answered correctly on a test. that is 75% of the total number of questions. How many questions were on the test?

adelina 88 [10]

Answer:

24 = questions on test

Step-by-step explanation:

Questions answered correctly = questions on test * percent answered correctly

We know that she answered 18 correctly and that 75% were answered correctly

Substitute this information into the equation

18 = questions on test *.75

Divide by .75 on each side

18/.75 = questions on test *.75/.75

24 = questions on test

7 0

3 years ago

Jasmine bought a new IPhone for $1000. The value of the phone depreciates 9% each year. What will the phone be worth after 4 yea

shtirl [24]

The phone will be worth 685.74$

4 0

3 years ago

What is the solution to the inequality? −6x+5>−1

Bogdan [553]

Answer:

$\boxed{x$

Step-by-step explanation:

$-6x+5>-1\qquad\text{subtract 5 from both sides}\\\\-6x>-6\qquad\text{change the signs}\\\\6x$

3 0

3 years ago

An automatic car wash takes exactly 5 minutes to wash a car. On average, 10 cars per hour arrive at the car wash. Suppose that,

77julia77 [94]

Answer:

0.9595724

Step-by-step explanation:

Time taken to wash a car (μ) = 5 minutes

Hence, Number of cars washed per hour = 60/5 = 12 cars

If 5 cars arrive, 30 minutes to closing ; it takes 25 minutes to finish up ;

If 1 more car arrives, then it takes exactly 30 minutes

Hence, there will be no one in line at closing ;

IF 0 or 1 car arrives, if more than 1 car arrives, then there will be people in line at closing.

Hence, probability of waiting in line at closing :

1 - [p(0) + p(1)]

Using poisson :

P(x) = [(e^-μ) * (μ^x)] / x!

If x = 0

P(0) = [(e^-5) * (5^0)] / 0!

P(0) = (0.0067379 * 1) / 1

P(0) = 0.0067379

X = 1

P(1) = [(e^-5) * (5^1)] / 1!

P(0) = (0.0067379 * 5) / 1

P(0) = 0.0336897

Hence,

1 - (0.0067379 + 0.0336897)

1 - 0.0404276

= 0.9595724

Hence, the probability that anyone would be in the car washing line after closing is 0.9595724

4 0

2 years ago