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3 years ago

Bob earned $2100. He spent 1/5 of his money on rent and 1/3 of it on food. How much money did he have left?

Mathematics

2 answers:

Nimfa-mama [501]3 years ago

8 0

He should have $980 left

Mandarinka [93]3 years ago

3 0

Answer:

$980

Step-by-step explanation:

Step 1: Find $\frac{1}{5}$ of 2100 = 420

$\frac{1}{5}\times \:2100$

Convert 2100 to a fraction: $\:2100=\frac{2100}{1}$

$=\frac{1}{5}\times \frac{2100}{1}$

Cross Divide

$2100 \div 5 = 420$

Step 2: Find $\frac{1}{3}$ of 2100 = 700

$\frac{1}{3}\times \:2100$

Convert 2100 to a fraction: $\:2100=\frac{2100}{1}$

$=\frac{1}{3}\times \frac{2100}{1}$

Cross Divide

$2100 \div 3 = 700$

Step 3: Add both results together

$420 + 700 = 1120$

Step 4: Subtract the result from how much Bob earns ($2,100)

$2100 - 1120 = 980$

Bob has $960 left

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Write an explicit formula for An, the nth term of the sequence 7, -42, 252, ....

erik [133]

Answer:

$A_n = 7(-6)^{n-1}$

Step-by-step explanation:

Key skills needed: Explicit formula, Geometric sequence

1) This is a geometric sequence, meaning a constant (like 6 or 3.5) is being multiplied to every term. First we need to find the constant.

This can be done by doing -42 ÷ 7 or 252 ÷ -42

-42 ÷ 7 equals -6.

252 ÷ -42 also equals -6.

2) This means that constant is -6.

3) The general form for an explicit formula of a geometric sequence is:

$a_n = a_1(r)^{n-1}$

--> r means the constant (or common ratio) that is being multiplied.

--> $a_1$ means the first term

--> $a_n$ means the "nth" numbered term (so $a_3$ is the 3rd term, $a_{10}$ is the 10th term and so on).

--> $n-1$ is just the "n" in $a_n$ minus 1.

4) We can use this formula to create an explicit formula for the geometric sequence in the problem.

--> $r = -6$ (Since we got -6 as the constant/common ratio).

--> $a_1 = 7$ (Since 7 is the 1st term)

This means that our formula would be --> $A_n = 7(-6)^{n-1}$

Hope you understood and have a nice day!! :D

8 0

3 years ago

3 1/3 /20 what is the quotient

AleksAgata [21]

Answer:

1/6

Step-by-step explanation:

(3 1/3)/20=(10/3)×(1/20)=10/60=1/6

3 0

3 years ago

The number of people arriving for treatment at an emergency room can be modeled by a Poisson process with a rate parameter of si

OverLord2011 [107]

Answer:

a) P(x=3)=0.089

b) P(x≥3)=0.938

c) 1.5 arrivals

Step-by-step explanation:

Let t be the time (in hours), then random variable X is the number of people arriving for treatment at an emergency room.

The variable X is modeled by a Poisson process with a rate parameter of λ=6.

The probability of exactly k arrivals in a particular hour can be written as:

$P(x=k)=\lambda^{k} \cdot e^{-\lambda}/k!\\\\P(x=k)=6^k\cdot e^{-6}/k!$

a) The probability that exactly 3 arrivals occur during a particular hour is:

$P(x=3)=6^{3} \cdot e^{-6}/3!=216*0.0025/6=0.089\\\\$

b) The probability that at least 3 people arrive during a particular hour is:

$P(x\geq3)=1-[P(x=0)+P(x=1)+P(x=2)]\\\\\\P(0)=6^{0} \cdot e^{-6}/0!=1*0.0025/1=0.002\\\\P(1)=6^{1} \cdot e^{-6}/1!=6*0.0025/1=0.015\\\\P(2)=6^{2} \cdot e^{-6}/2!=36*0.0025/2=0.045\\\\\\P(x\geq3)=1-[0.002+0.015+0.045]=1-0.062=0.938$

c) In this case, t=0.25, so we recalculate the parameter as:

$\lambda =r\cdot t=6\;h^{-1}\cdot 0.25 h=1.5$

The expected value for a Poisson distribution is equal to its parameter λ, so in this case we expect 1.5 arrivals in a period of 15 minutes.

$E(x)=\lambda=1.5$

3 0

3 years ago

What is the area of the shape above ?

Oliga [24]

Answer:

D 341

Step-by-step explanation:

19 × 12 = 228

$\pi {6}^{2} = 113 \\ 228 + 113 = 341$

7 0

3 years ago

Read 2 more answers

Tom [10]

I’m sorry I’m just now I’m sorry I didn’t answer my

3 0

3 years ago