Owen settled on a price of $7,870 for a new car. The dealer had to add 4.5% sales tax to this price, but allowed a $1,200 trade-in for Owen's old car. Although not a universal practice, please add the sales tax to the price of the new car first and then deduct the trade- in value. If the dealer required a 15% down payment, calculate the amount of the purchase price that Owen financed.

To find the probability that a person actually has the disease given a positive test result, we can use Bayes' theorem. Given the probabilities of a positive test result given the person has the disease and does not have the disease, as well as the probability of having the disease, we can calculate the conditional probability.

To find the probability that a person actually has the disease given a positive test result, we can use Bayes' theorem. Let's define the events: A = person has the disease, B = person tests positive. We are given that P(B|A) = 0.9 (probability of a positive test given the person has the disease), P(B|A') = 0.06 (probability of a positive test given the person does not have the disease), and P(A) = 0.16 (probability that a person has the disease).

Bayes' theorem states: P(A|B) = (P(B|A) * P(A)) / P(B).

Substituting the given values, we have: P(A|B) = (0.9 * 0.16) / P(B).

We don't have the value of P(B), but we can calculate it as follows: P(B) = (P(B|A) * P(A)) + (P(B|A') * P(A')). Plugging in the values, we have: P(B) = (0.9 * 0.16) + (0.06 * 0.84).

Now we can substitute the value of P(B) into the formula for P(A|B) to calculate the probability.

Therefore, the probability that the person actually has the disease given a positive test result is approximately 0.231.

Answer:

The number of large size candles sells are 12 and the number of small size candles are 5 .

Step-by-step explanation:

As given

Sia sells large candles for $3 each and small candles for $2 each.

She sold 17 candles for $46.00.

Let us assume that the large size candle sells are x .

Let us assume that the small size candle sells are y.

Equation becomes

x + y = 17

3x + 2y = 46

Multiply x + y = 17 by 3 and subtracted from 3x + 2y = 46 .

3x - 3x + 2y - 3y = 46 - 51

-y = - 5

y = 5

Put in the equation x + y = 17 .

x + 5 = 17

x = 17 - 5

x = 12

Therefore the number of large size candles sells are 12 and the number of small size candles are 5 .

Sia sells 12 large candles and 5 small candles in order to earn $46 and this can be determined by forming the linear equation in two variables.

Given :

Let the total number of large candles be 'x' and the total number of small candles be 'y'. So the linear equation that represents the total number of candles is:

x + y = 17

x = 17 - y       ---- (1)

Now, the linear equation that represents the total earning of Sia is:

3x + 2y = 46     ---- (2)

Substitute the value of 'x' in equation (2).

3(17 - y) + 2y = 46

Simplify the above equation in order to determine the value of 'y'.

51 - 3y + 2y = 46

51 - 46 = y

y = 5

Now, substitute the value of 'y' in equation (1).

x = 17 - 5

x = 12

So, Sia sells 12 large candles and 5 small candles in order to earn $46.

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Answer:

He will bake 300 loaves of bread.

Step-by-step explanation:

Paul bakes loaves of bread and bread rolls in the ratio of 2 : 5

Suppose, the number of loaves of bread he will bake [tex]=x[/tex]

Given that, he bakes 750 bread rolls.

So, according to the given ratio, we will get......

[tex]\frac{loaves\ of\ bread}{bread\ rolls}=\frac{2}{5}\\ \\ \frac{x}{750}=\frac{2}{5}\\ \\ 5x=1500\ [by\ cross\ multiplication]\\ \\ x=\frac{1500}{5}\\ \\ x=300[/tex]

So, he will bake 300 loaves of bread.

Answer:  The required product is [tex]\dfrac{5}{4k^2}.[/tex]

Step-by-step explanation:  We are to calculate the following product:

[tex]P=5\dfrac{k}{6}\times \dfrac{3}{2k^3}.[/tex]

We will be using the following property of exponents:

[tex]\dfrac{a^x}{a^y}=a^{x-y}.[/tex]

We have

[tex]P\\\\\\=5\dfrac{k}{6}\times\dfrac{3}{2k^3}\\\\\\=\dfrac{5}{6}\times\dfrac{3}{2}k^{1-3}\\\\\\=\dfrac{5}{4}k^{-2}=\dfrac{5}{4k^2}.[/tex]

Thus, the required product is [tex]\dfrac{5}{4k^2}.[/tex]

Answer:  The correct option is (C) [tex]\dfrac{1}{2}.[/tex]

Step-by-step explanation:  Given that Jane altered by using [tex]\dfrac{3}{4}[/tex] of the amount of butter called for the recipe and she used 6 tablespoons of butter.

We are to find the number of cups of butter that the recipe call for.

Let x represents the total number of teaspoons of butter that the recipe call for.

Then, according to the given information, we have

[tex]\dfrac{3}{4}x=6\\\\\Rightarrow 3x=24\\\\\Rightarrow x=8.[/tex]

So, the total number of tablespoons of butter that the recipe call for is 8.

Now, 16 tablespoons = 1 cup.

Therefore, we get

[tex]8~\textup{tablespoons}=\dfrac{1}{16}\times 8=\dfrac{1}{2}~\textup{cups}.[/tex]

Thus, the recipe call for [tex]\dfrac{1}{2}[/tex] cup of butter.

Option (C) is CORRECT.

Answer:

6/31

Step-by-step explanation:

4 1/3 divided by 5 1/6

Change the mixed numbers to improper fractions

4 1/3 = (3*4+1)/3 =13/3

5 1/6 = (6*5+1)/6 =31/6

13/3 ÷ 31/6

Copy dot flip

13/3 * 6/31

13*2/31

26/31

The question is asking what fraction should we end up multiplying by(the flip fraction)

That is 6/31

Answer:

The Answer is A) 6/31

Step-by-step explanation:

Answer:

272

Step-by-step explanation:

Mutilpy the base then divide by 1/2

[tex]4\\[/tex] more workers are needed to do this job in 12 hours.

Given,

Three workers can do a job in 28 hours.

Let [tex]x[/tex] no. of worker needed.

workers          3       [tex]x[/tex]

time (hours)   28      12

The fewer workers there are the more the hours that are required,  

and the more workers there are the fewer hours that are required.  

Therefore workers and hours are inversely proportional.

So,  

[tex]3 \times28=x \times12[/tex]

[tex]x=\frac{3 \times28}{12} \\\\x=7[/tex]

So, 7 workers can do that job in 12 hours.

Hence ([tex]7-3=4[/tex]) [tex]4[/tex] more workers needed to do this job in 12 hours.

For more details on Inverse proportion follow the link:

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Final answer:

To complete a job in 12 hours rather than 28, 4 additional workers are needed, considering the work rate is directly proportional to the number of workers.

Explanation:

The question relates to the optimization of workers to complete a job in a certain amount of time, a common problem in work-rate mathematics.

To solve it, we first determine the rate at which three workers complete the job: since they can complete one job in 28 hours, their combined rate is 1 job per 28 hours, or 1/28 job per hour. Now, we need to find out how many workers are required to complete the job in 12 hours. This means we want the workers to work at a rate that completes 1 job in 12 hours, or 1/12 job per hour.

To find the number of workers needed, we set up the proportion: (3 workers)/(1/28 job per hour) = (x workers)/(1/12 job per hour). Solving for x gives us x = (3 workers) × (1/12 job per hour) / (1/28 job per hour), which simplifies to x = 7 workers. Since we already have 3 workers, we need an additional 4 workers to complete the job in 12 hours.

This is a clear example of positive reinforcement. Positive reinforcement involves the addition of a positive stimulus that act as a reinforcement to a desired behavior in order to make the behavior more likely happen again in the future. When Jemma praises and hugs his baby, she is using positive reinforcement, so her baby associates the behavior of saying “thank you” with a reward making him more inclined to say thank you again in the future.

We can conclude that Jemma's reinforcement schedule is positive reinforcement.

Without the specific results from the survey, we cannot determine which juice is most popular. Based on the description, it seems the juice bar used a systematic sampling method to survey customers.

Without more specific information presented from the juice bar's survey, such as the breakdown of customer preferences for each juice drink, we cannot determine which juice drink is most popular. The provided options - Power Pear, Tangy Apple, Lemon Lift, or Wild Berry - don't have accompanying survey data. So, any inference about the most popular juice would be a guess and not based on survey results.

However, what we can infer from the provided information is about the sampling method used by the juice bar. The juice bar appeared to use a systematic sampling technique, selecting every 10th customer over a week and surveyed a total of 75 customers.

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Answer:

Both P & Q

Step-by-step explanation

Just a bit late..

Answer: D) 4.5 Standard Deviations Above the Mean

Step-by-step explanation:

The length of the sides of a square with a perimeter between 14 and 72 feet inclusive ranges from 3.5 to 18 feet. By dividing the perimeter limits by 4, we find the possible side lengths, leading to the answer: 3.5 ≤ x ≤ 18 (option a)).

The student is asking about the possible lengths of the sides of a square given that the perimeter must be between 14 and 72 feet inclusive. To solve this, we recall that the perimeter (P) of a square with side length (a) is given by P = 4a. Therefore, if P is between 14 and 72 feet, we divide these values by 4 to find the possible values for a.

The lower limit for the side length is 14 ÷ 4 = 3.5 feet, and the upper limit is 72 ÷ 4 = 18 feet. So the possible values for the side length of the square can be represented as 3.5 ≤ x ≤ 18. Hence, the correct answer to the student's question is option a).