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3 years ago

Heather opens a bank account with $125. Each week, starting the following week, she deposits $25 into her account.

Mathematics

2 answers:

Rufina [12.5K]3 years ago

7 0

Total money in account=125+25n

ICE Princess25 [194]3 years ago

4 0

Answer:

125+25n

Step-by-step explanation:

We are given that

Heather opens a bank account with=$125

Each week she deposited money into her account=$25

We have to find the explicit rule for amount of money which has Heather after n weeks.

Heather has money after 1 week=125+25=$150

Heather has money after 2 week=125+2(25)=$175

Heather has money after 3 weeks=125+3(25)=$200

Heather has money after n weeks=125+25(n)

Hence, the explicit rule for amount of money which has Heather after n weeks is given by

125+25n

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A train leaves Philadelphia at 2:00 PM. A second train leaves the same city in the same direction at 4:00 PM. The second train t

polet [3.4K]

Answer: First train speed shall be 42 mi/hr

Second train speed shall be 84 mi/hr

Yes it is the valid answer, it gets annoying when almost everyone enters the wrong answer for a good laugh. Either way, hope this helps! Have a spectacular day.

Step-by-step explanation:

What is the 1st train's head start in miles?

Let +s+ = the speed of the 1st train in mi/hr

From 2PM to 4PM is 2 hrs

+d%5B1%5D+=+s%2A2+

---------------------

Let +d+ = distance the 2nd train travels until

it overtakes the 1st train

From 4PM to 6PM is 2 hrs

Start time when the 2nd train leaves

---------------------

Equation for 1st train:

(1) +d+-+2s+=+s%2A2+

Equation for 2nd train:

(2) +d+=+%28+s%2B42+%29%2A2+

--------------------

Substitute (2) into (1)

(1) +%28+s%2B42+%29%2A2+-+2s+=+s%2A2+

(1) +2s+%2B+84+-+2s+=+2s+

(1) +2s+=+84+

(1) +s+=+42+

and

+s%2B+42+=+42+%2B+42+

+s+%2B+42+=+84+

------------------

The 1st train's speed is 42 mi/hr

The 2nd train's speed is 84 mi/hr

---------------------------

check:

(2) +d+=+%28+s%2B42+%29%2A2+

(2) +d+=84%2A2+

(2) +d+=+168+

and

(1) +d+-+2s+=+s%2A2+

(1) +d+-+2%2A42+=+42%2A2+

(1) +d+=+84+%2B+84+

(1) +d+=+168+

8 0

2 years ago

Simplify the expression. -216) + 3(5 – 4 x 2)

masya89 [10]

Answer:

Step-by-step explanation:

If it's (-216):

(-216) + 3(5 - 4 x 2)

(-216) + 3( -3)

(-216) -9

-225

If it's -2(16):

-2(16) + 3(5 - 4 x 2)

-2(16) + 3(-3)

-32 - 9

-41

4 0

3 years ago

What is the inverse function of f(x) = 25x-3?

Harrizon [31]

Answer:

The answer is

Step-by-step explanation:

$f(x) = 25x - 3$

To find the inverse of f(x) , equate f(x) to y

That's

y = f(x)

We have

$y = 25x - 3$

Next interchange the terms that's x becomes y and y becomes x

$x = 25y - 3$

Next solve for y

Move 3 to the other side of the equation

That's

$25y = x + 3$

Divide both sides by 25

$\frac{25y}{25} = \frac{x + 3}{25}$

We have the final answer as

${f}^{ - 1} (x) = \frac{x +3 }{25}$

Hope this helps you

5 0

2 years ago

What does the equation "m=7.50" mean in this situation?

Naddik [55]

Answer:

1. It means that m equals 7.5

2. It means 4.5 plus s equals m

3. It means n times s equals 6

4. It means m plus n times s equals t

Step-by-step explanation:

Source: Just trust me bro

3 0

2 years ago

Suppose a certain capsule is manufactured so that the dosage of the active ingredient follows the distribution Y ~ N(μ = 10 mg,

lianna [129]

Answer:

(a) Probability that Y falls into the dangerous region is 0.0013.

(b) Probability that the mean Y-bar falls into the dangerous region is 0.00001.

Step-by-step explanation:

We are given that a certain capsule is manufactured so that the dosage of the active ingredient follows the distribution Y ~ N(μ = 10 mg, σ = 1 mg).

A dosage of 13 mg is considered dangerous.

Let Y = dosage of the active ingredient

The z-score probability distribution for normal distribution is given by;

Z = $\frac{ Y-\mu}{\sigma} } }$ ~ N(0,1)

where, $\mu$ = population mean = 10 mg

$\sigma$ = standard deviation = 1 mg

(a) Probability that Y falls into the dangerous region is given by = P(Y $\geq$ 13 mg)

P(Y $\geq$ 13 mg) = P( $\frac{ Y-\mu}{\sigma} } }$ $\geq$ $\frac{ 13-10}{1} } }$ ) = P(Z $\geq$ 3) = 1 - P(Z < 3)

= 1 - 0.9987 = 0.0013

The above probability is calculated by looking at the value of x = 3 in the z table which has an area of 0.9987.

(b) We are given that a dosage of 13 mg is considered dangerous. And we sample 49 capsules at random.

Let $\bar Y$ = sample mean dosage

The z-score probability distribution for sample mean is given by;

Z = $\frac{\bar Y-\mu}{\frac{\sigma}{\sqrt{n} } } } }$ ~ N(0,1)

where, $\mu$ = population mean = 10 mg

$\sigma$ = standard deviation = 1 mg

n = sample of capsules = 49

So, Probability that the mean Y-bar falls into the dangerous region is given by = P( $\bar Y$ $\geq$ 13 mg)

P(Y $\geq$ 13 mg) = P( $\frac{\bar Y-\mu}{\frac{\sigma}{\sqrt{n} } } } }$ $\geq$ $\frac{13-10}{\frac{1}{\sqrt{49} } } } }$ ) = P(Z $\geq$ 21) = 1 - P(Z < 21)

= 0.00001

6 0

2 years ago