Divide write your answer in scientific notation. look at the picture!

Solve. Use the strategy "work backward."

cestrela7 [59]

Let that be x

ATQ

$\\ \rm\Rrightarrow 3x-6/5=9$

Arrange accordingly to work backwards(Every thing is reversed)

$\\ \rm\Rrightarrow 9(5)+6/3=x$

$\\ \rm\Rrightarrow 45+6/3=x$

$\\ \rm\Rrightarrow 51/3=x$

$\\ \rm\Rrightarrow x=17$

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8 0

2 years ago

Accuracy in taking orders at a drive-through window is important for fast-food chains. Periodically, QSR Magazine publishes "The

pav-90 [236]

Answer:

a) 0.7412 = 74.12% probability that all the three orders will be filled correctly.

b) 0.0009 = 0.09% probability that none of the three will be filled correctly

c) 0.0245 = 2.45% probability that at least one of the three will be filled correctly.

d) 0.9991 = 99.91% probability that at least one of the three will be filled correctly

e) 0.0082 = 0.82% probability that only your order will be filled correctly

Step-by-step explanation:

For each order, there are only two possible outcomes. Either it is filled correctly, or it is not. Orders are independent. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The percentage of orders filled correctly at Burger King was approximately 90.5%.

This means that $p = 0.905$

You and 2 friends:

So 3 people in total, which means that $n = 3$

a. What is the probability that all the three orders will be filled correctly?

This is P(X = 3).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 3) = C_{3,3}.(0.905)^{3}.(0.095)^{0} = 0.7412$

0.7412 = 74.12% probability that all the three orders will be filled correctly.

b. What is the probability that none of the three will be filled correctly?

This is P(X = 0).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{3,0}.(0.905)^{0}.(0.095)^{3} = 0.0009$

0.0009 = 0.09% probability that none of the three will be filled correctly.

c. What is the probability that one of the three will be filled correctly?

This is P(X = 1).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 1) = C_{3,1}.(0.905)^{1}.(0.095)^{2} = 0.0245$

0.0245 = 2.45% probability that at least one of the three will be filled correctly.

d. What is the probability that at least one of the three will be filled correctly?

This is

$P(X \geq 1) = 1 - P(X = 0)$

With what we found in b:

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0009 = 0.9991$

0.9991 = 99.91% probability that at least one of the three will be filled correctly.

e. What is the probability that only your order will be filled correctly?

Yours correctly with 90.5% probability, the other 2 wrong, each with 9.5% probability. So

$p = 0.905*0.095*0.095 = 0.0082$

0.0082 = 0.82% probability that only your order will be filled correctly

7 0

3 years ago

Identify the four step used to solve this equation 4(x-7)=2x-6

irinina [24]

1. Solve the bracket 4×x and 4 × -7
4x-28=2x-6
2. Get the x on one side and the numbers on the other so: first +28
4x=2x+22 now -2x
so 2x=22 and now you only need to divide into 2
x=11

3 0

3 years ago

(a) Derive an equation of the line passing through the points A(0, 545) and B(4, 726). (Let t be the independent variable and y

a_sh-v [17]

Answer:

The equation of the line is $y=45.25t+545$

Step-by-step explanation:

The general for of a line is:

$y=mt+n$ (1)

where:

$m$ is the slope of the line and $m$ is the intercept with the axis of the dependent variable, $y$ in this case.

In order to obtain the value of the slope ( $m$ ) we can use the corresponding slope formula:

$m=\frac{y_{2}-y_1 }{t_2-t_1}$ (2)

where $t_1, t_2, y_1$ and $y_2$ are the corresponding coordinates of the given points. In this case:

$t_1=0\\t_2=4\\y_1=545\\y_2=726\\$

Substituting these values in equation (2) we obtain:

$m=\frac{726-545}{4-0}=\frac{181}{4}=45.25\\m=45.25$

Hence, the line equation is now:

$y=45.25t+n$ (3)

Now to obtain the value of $n$ you can follow two options:

You can substitute one of your points, $A$ or $B$ , in equation (3). In this way, you will obtain an equation where the variable is $n$

Note that for this question, it is easier to select point A because of having the independent variable equals to zero $t=0$ . Hence, substituting point A in equation (3):

$45.25*0+n=545\\n=545$

Therefore, the line equation is: $y=45.25t+545$

The second option to find $n$ is to think of the meaning of the <em>intercept</em>. The <em>intercept </em>of a line is defined as the point in which the line crosses the axis of the dependent variable, which also means that the value of the independent variable for this point is zero. From this, we could have automatically said that $n$ is equal to $545$ .

See the attachment for a plot of the line.

7 0

3 years ago

A family spent $186 per week for food. This was 20% of its weekly income. What was the weekly income?

geniusboy [140]

It was $930.

To over check, multiply it by 20% , you will get $186.

Hope this helps !

5 0

3 years ago

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