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2 years ago

11

Pete's checking account showed a balance at the beginning of the month of $180. After 3 days the checking account showed a balan

ce of $160. Write a linear equations to represent the total in the checking account f(x) according to the day x.

1 answer:

Cerrena [4.2K]2 years ago

5 0

Answer:

180 - 172 =$8 8/3=2.56

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Two shipments of components were received by a factory and stored in two separate bins. Shipment I has 2% of its contents defe

leva [86]

<h2>Answer:</h2>

The probability that a defective component came from shipment II is:

$0.7143\ or\ 71.43\%$

<h2>Step-by-step explanation:</h2>

Let A denote the event that the defective component was from shipment I

Also, P(A)=2%=0.02

and B denote the event that the defective component was from shipment II.

i.e. P(B)=5%=0.05

Also, P(shipment I is chosen)=1/2=0.5

and P(shipment II is chosen)=1/2=0.5

The probability that a defective component came from shipment II is calculated by Baye's rule as follows:

$=\dfrac{\dfrac{1}{2}\times 0.05}{\dfrac{1}{2}\times 0.02+\dfrac{1}{2}\times 0.05}}\\\\\\=\dfrac{0.05}{0.07}\\\\=\dfrac{5}{7}\\\\=0.7143\ or\ 71.43\%$

Hence, the answer is:

$0.7143\ or\ 71.43\%$

6 0

2 years ago

Suppose that the prevalence of a certain type of tree allergy is 0.26 in the general population. If 100 people randomly chosen f

laiz [17]

Answer:

0.0906

Step-by-step explanation:

Given that the prevalence of a certain type of tree allergy is 0.26 in the general population

X- the no of persons having tree allergy is binomial since each persons is independent of the other and there are two outcomes.

Here n = 100

Required probability = the probability that exactly 26 of them will have this allergy

= $P(x=26)=100C26(0.26)^{26} (1-0,26)^{100-26}\\ =0.09063\\=0.0906$

4 0

2 years ago

Read 2 more answers

6. Charlie can spend up to $8 on lunch. He wants to buy a tuna sandwich, a bottle of

PilotLPTM [1.2K]

Answer:

The maximum number of pounds of potato salad that Charlie can buy is 0.375

Step-by-step explanation:

see the attached figure to better understand the problem

Let

a ----> the cost of one tuna sandwich

b ----> the cost of a bottle of apple juice

c ----> the cost per pound of potato salad

x ----> pounds of potato salad

we have

$a=\$4.25$

$b=\$2.25$

$c=\$4.00/lb$

we know that

He wants to buy a tuna sandwich, a bottle of apple juice, and x pounds of potato salad and can spend up to $8

The inequality that represent this situation is

$a+b+cx \leq 8$

substitute the given values

$4.25+2.25+4.00x \leq 8$

Solve for x

Combine like terms

$6.50+4.00x \leq 8$

Subtract 6.50 both sides

$4.00x \leq 8-6.50$

$4.00x \leq 1.50$

Divide by 4 both sides

$x \leq 1.50/4.00$

$x \leq 0.375\ lbs$

therefore

The maximum number of pounds of potato salad that Charlie can buy is 0.375

3 0

2 years ago

The ratio of money in Brian's wallet to Colin's wallet one day was 5:1. Brian spent £27 that day. Brian now had £3 less than Col

myrzilka [38]

Answer:

Brian had $30 initially.Brian had $30 initially.

Step-by-step explanation:

WE are given the following in the question:

Let Brian have x dollars and Colin have y dollars.

Ration of Brian's money to Colin's money is 5:1. This, we can write the equation:

$\dfrac{x}{y} = \dfrac{5}{1}\\\\x = 5y$

"Brian spent £27 that day. Brian now had £3 less than Colin."

Thus, we can write the equation:

$x-27 = y-3\\x-y = 24$

Solving the two equation by substitution, we get,

$x - y - 24\\5y - y = 24\\4y = 24\\y=6\\x = 5y =30$

Thus, Brian had $30 initially.

7 0

2 years ago

Your utility company charges 13 cents per kilowatt-hour of electricity. What is the daily cost of keeping lit a 75 watt light bu

Tresset [83]

we know that

$1 Kw=1000 w$

The company charges $13$ cents per kilowatt-hour of electricity

$13 cents=0.13 dollars\\\\ 75w=\frac{75}{1000} kw\\\\ 15w=\frac{15}{1000} kw$

Step $1$

Find the cost for the light bulb

a) in one day

$\frac{75}{1000} *12=0.9\ kw\ hour$

$Cost=0.13*0.9$

Cost=$ $0.117$

b) In a year

$\frac{75}{1000} *12=0.9\ kw\ hour$

$0.9*365=328.5\ kw\ hour$

$Cost=0.13*328.5$

Cost=$ $42.71$

Step $2$

Find the cost for the led bulb

a) in one day

$\frac{15}{1000} *12=0.18\ kw\ hour$

$Cost=0.13*0.18$

Cost=$ $0.0234$

b) In a year

$\frac{15}{1000} *12=0.18\ kw\ hour$

$0.18*365=65.7\ kw\ hour$

$Cost=0.13*65.7$

Cost=$ $8.54$

Step $3$

Find the difference in cost

$Save=42.71-8.54\\ Save=34.17 dollars$

therefore

the answer is

$34.17 dollars$

3 0

2 years ago

Read 2 more answers