Ask question

Ask question

All categories

2 years ago

10

Rahm used a payment plan to purchase wood for a home project. The wood he bought cost $500. The clerk at the store offered him t

his payment plan instead.

1 answer:

faust18 [17]2 years ago

5 0

Answer: 210

Step-by-step explanation:

55×12=660-500=160+50(down payment)=210

You might be interested in

An automated egg carton loader has a 1% probability of cracking an egg, and a customer will complain if more than one egg per do

vaieri [72.5K]

Answer:

a) Binomial distribution B(n=12,p=0.01)

b) P=0.007

c) P=0.999924

d) P=0.366

Step-by-step explanation:

a) The distribution of cracked eggs per dozen should be a binomial distribution B(12,0.01), as it can model 12 independent events.

b) To calculate the probability of having a carton of dozen eggs with more than one cracked egg, we will first calculate the probabilities of having zero or one cracked egg.

$P(k=0)=\binom{12}{0}p^0(1-p)^{12}=1*1*0.99^{12}=1*0.886=0.886\\\\P(k=1)=\binom{12}{1}p^1(1-p)^{11}=12*0.01*0.99^{11}=12*0.01*0.895=0.107$

Then,

$P(k>1)=1-(P(k=0)+P(k=1))=1-(0.886+0.107)=1-0.993=0.007$

c) In this case, the distribution is B(1200,0.01)

$P(k=0)=\binom{1200}{0}p^0(1-p)^{12}=1*1*0.99^{1200}=1* 0.000006 = 0.000006 \\\\ P(k=1)=\binom{1200}{1}p^1(1-p)^{1199}=1200*0.01*0.99^{1199}=1200*0.01* 0.000006 \\\\P(k=1)= 0.00007\\\\\\P(k\leq1)=0.000006+0.000070=0.000076\\\\\\P(k>1)=1-P(k\leq 1)=1-0.000076=0.999924$

d) In this case, the distribution is B(100,0.01)

We can calculate this probability as the probability of having 0 cracked eggs in a batch of 100 eggs.

$P(k=0)=\binom{100}{0}p^0(1-p)^{100}=0.99^{100}=0.366$

5 0

2 years ago

For the binomial expansion of (x + y)^10, the value of k in the term 210x 6y k is a) 6 b) 4 c) 5 d) 7

Sloan [31]

Answer:

a) 6

Step-by-step explanation:

Expanding the polynomial using the formula:

$(x+y)^n=\sum_{k=0}^n \binom{n}{k} x^{n-k} y^k$

Also

$\binom{n}{k}=\frac{n!}{(n-k)!k!}$

I think you mean $210x^6y^4$

We can deduce that this term will be located somewhere in the middle. So I will calculate $k= 5; k=6 \text{ and } k =7$ .

For $k=5$

$\binom{10}{5} (y)^{10-5} (x)^{5}=\frac{10!}{(10-5)! 5!}(y)^{5} (x)^{5}= \frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5! }{5! \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 } \\ =\frac{30240}{120} =252 x^{5} y^{5}$

Note that we actually don't need to do all this process. There's no necessity to calculate the binomial, just $x^{n-k} y^k$

For $k=6$

$\binom{10}{6} \left(y\right)^{10-6} \left(x\right)^{6}=\frac{10!}{(10-6)! 6!}\left(y\right)^{4} \left(x\right)^{6}=210 x^{6} y^{4}$

5 0

2 years ago

Jessica is 5 years older than her sister Jenna. Jenna tells her sister that in 5 years, she will be as old as Jessica was 5 year

emmasim [6.3K]

      Jenna's age    Jessica's age

today    x    x + 5

in 5 years x+5

5 years ago    x + 5 - 5

Equality x + 5 = x + 5 - 5

=> x + 5 = x

The equation is x + 5 = x

That equation has not any solution, because it reduces to 5 = 0, which is an absurd.

So, the conclusion is that information given by Jenna is wrong.

It is logical: if the difference of the ages is 5, in five years Jenna will have 10 years more than what her sister had 5 years ago, no 5 as she told Jessica.

5 0

2 years ago

Read 2 more answers

20% of the tickets sold at a water park were adult tickets. If the park sold 55 tickets in all,how many did it sell?

djyliett [7]

Answer:

11 adult tickets

Step-by-step explanation:

I guess you want the number of adult tickets sold.

That is 20% of 55

= 0.20*55

= 11 (answer)

8 0

2 years ago

Read 2 more answers

Simplify the function f (x) = one-third (81) Superscript StartFraction 3 x Over 4 EndFraction. Then determine the key aspects of

Nikitich [7]

Answer:

The answer is given below

Step-by-step explanation:

Given that:

$f(x)=\frac{1}{3}(81)^ \frac{3x}{4} \\Using\ exponent\ rule:a^{xy}=a^xa^y\\f(x)=\frac{1}{3}(81^{1/4})^ {3x}\\f(x)=\frac{1}{3}(3})^ {3x}\\f(x)=\frac{(3)^ {3x}}{3^1} \\Using\ exponent\ rule:a^x/a^y=a^{x-y}\\f(x)=3^ {3x-1}$

The function is an exponential function.

The domain is the set of all independent variables i.e the input values (x values). For an exponential function, the domain is the set of all real numbers. That is:

Domain: x = (-∞, ∞)

The range is the set of all dependent variables i.e the values of y. For an exponential function, the range is the set of all real numbers greater than zero. That is:

Range: y = (0, ∞)

8 0

2 years ago

Read 2 more answers