Brooke bought all seven members of her family a chocolate bar at the chocolate factory in Hershey, Pennsylvania. Each chocolate bar was .8 ounces. How many ounces of chocolate did Brooke buy?

Answer:

a).[tex]P_{t}=\frac{5}{3}P_{t-1}[/tex]

b).[tex]A_{t}=300e^{0.1277\times t}[/tex]

c). 6429 bacteria

Step-by-step explanation:

Population of the bacteria grows exponentially.

Therefore, growth of the bacteria will be represented by the formula

[tex]P_{t}=P_{0}e^{kt}[/tex]

Where [tex]P_{t}[/tex] = Population of the bacteria after time t

[tex]P_{0}[/tex] = Initial population of the bacteria

k = growth constant

t = time taken for growth

Now we plug in the values in the formula

[tex]P_{t}[/tex] = 500

[tex]P_{0}[/tex] = 300

Time t = 4 hours

[tex]500=300e^{4k}[/tex]

[tex]e^{4k}=\frac{500}{300}[/tex]

Now we take the natural log (ln) on both the sides

[tex]ln(e^{4k})=ln(\frac{500}{300})[/tex]

4k(lne) = ln(500) - ln(300)

4k = 6.2146 - 5.7038

4k = 0.5108

k = [tex]k=\frac{0.5108}{4}=0.1277[/tex]

a). Recursive formula for the sequence formed by the bacterial growth

Since [tex]P_{t}=(1+r)P_{t-1}[/tex]

500 = (1 + r)300

[tex](1+r)=\frac{5}{3}[/tex]

r = [tex]\frac{5}{3}-1=\frac{2}{3}[/tex]

Therefore, the recursive formula will be

[tex]P_{t}=\frac{5}{3}P_{t-1}[/tex]

b). Explicit formula for the number of the bacteria will be

[tex]A_{t}=300e^{0.1277\times t}[/tex]

c). We have to calculate the number of bacteria after 24 hours

[tex]A_{t}=300e^{0.1277\times 24}[/tex]

[tex]A_{t}=300e^{3.0648}[/tex]

[tex]A_{t}=300\times 21.43[/tex]

[tex]A_{t}=6429[/tex] bacteria

In the painting 'Three Flags' by Jasper Johns, the size of the largest flag would depend on the canvas or surface used.

In the painting Three Flags by Jasper Johns, he used his encaustic process to create the artwork. Each flag reduced about twenty-five percent in scale as he stacked canvas flags, with the largest one receding into the background. The congealed wax drippings gave the painting a dimensional sculptural appearance.

The stripes and stars on the flags also grow smaller, adding to the illusion of three separate elements. Therefore, in terms of the largest flag Jake can draw, it would depend on the size of the canvas or surface that he is working with.

Answer: -2

Step-by-step explanation:

To solve this problem, we have to make use of the standard probability distribution tables for z test.

Since we are asked to find for the 72 percent level confidence, then this means we are to look for the value of z which gives (100-72)/2 = 14% on both sides of the tail.

So at 14% tail on one side, the z value is approximately:

1.08

Answer:

± 1.08

Answer:

[tex]C(x)=16.99x[/tex]

Step-by-step explanation:

Let x be the number of staplers and C(x) be total cost in dollars of x stapler.

Cost of each stapler = $16.99

So, the formula for total cost is

Total cost = Cost of each units × Number of units

Substitute 16.99 for Cost of each units and x for number of units in the above formula.

Total cost = [tex]16.99\times x[/tex]

Total cost = [tex]16.99x[/tex]

C(x) be total cost in dollars of x stapler. So, the cost function is

[tex]C(x)=16.99x[/tex]

Therefore, the function C(x)=16.99x represents the given situation.

a. The highest 5 percent time is approximately 15.29 minutes. b. The lowest 50 percent time is 12 minutes. c. The middle 95 percent interval is approximately 8.08 minutes to 15.92 minutes. d. The lowest 80 percent time is approximately 10.32 minutes.

a. To find the highest 5 percent, we need to find the value that separates the highest 5 percent from the rest. This value is called the upper 5th percentile. Using the z-score formula, z = (x - mean) / standard deviation, we can find the z-score associated with the upper 5th percentile. By looking up this z-score in the z-table, we can find the corresponding value. In this case, the z-score is approximately 1.645. Using the formula, x = z * standard deviation + mean, we can calculate the time needed for the highest 5 percent: x = 1.645 * 2 + 12 = 15.29 minutes.

b. To find the lowest 50 percent, we need to find the value that separates the lowest 50 percent from the rest. This value is called the median. The median of a normally distributed data set is equal to the mean. Hence, the lowest 50 percent time is the mean of 12 minutes.

c. To find the time for the middle 95 percent interval, we need to find the values that separate the middle 95 percent from the rest. These values are called the lower 2.5th percentile and the upper 2.5th percentile. Using the z-score formula, we can find the z-scores associated with the lower and upper 2.5th percentiles. By looking up these z-scores in the z-table, we can find the corresponding values. In this case, the z-scores are approximately -1.960 and 1.960. Using the formula, x = z * standard deviation + mean, we can calculate the times: lower 2.5th percentile = -1.960 * 2 + 12 = 8.08 minutes, and upper 2.5th percentile = 1.960 * 2 + 12 = 15.92 minutes.

d. To find the lowest 80 percent, we need to find the value that separates the lowest 80 percent from the rest. This value is called the lower 20th percentile. Using the z-score formula, we can find the z-score associated with the lower 20th percentile. By looking up this z-score in the z-table, we can find the corresponding value. In this case, the z-score is approximately -0.841. Using the formula, x = z * standard deviation + mean, we can calculate the time needed for the lowest 80 percent: x = -0.841 * 2 + 12 = 10.32 minutes.

Answer:

Ricardo paid $2.29 too much

Step-by-step explanation:

Great question, it is always good to ask away and get rid of any doubts that you may be having.

To begin answering this question we need to calculate the total before applying anything. We calculate this by adding up all the amounts of each item purchased. Like so,

[tex](2*3.49)+(2*2.89)+(3*5.39)+(4*3.49) = Total[/tex]

[tex]6.98+5.78+16.17+13.96 = Total[/tex]

[tex] 42.89= Total[/tex]

Now that we have the total we can apply the 5% discount to this total.

[tex]42.89 * (1-0.05) = 40.75[/tex] ... rounded up

Finally we can apply the 7% sales tax to this purchase to calculate the final price that Ricardo should have paid.

[tex]40.75*(1+0.07) = 43.58[/tex] ... rounded up

As we can see Ricardo paid $2.29 too much

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Answer:  The correct option is (A) 0.

Step-by-step explanation:  We are given to find the difference between the mean and median of the following data set:

{22, 8, 10 ,18 ,12, 20}.

MEAN:  It is the sum of all the values together divided by the number of values in the set.

So, the MEAN of the given data set is

[tex]m=\dfrac{22+8+10+18+12+20}{6}\\\\\\\Rightarrow m=\dfrac{90}{6}\\\\\Rightarrow m=15.[/tex]

MEDIAN: The median of a data set is given by the middle-most value in the data.

If there is an even number of items in the data set, then the median is found by taking the mean of the two middlemost numbers.

Arranging the given data in ascending order, we have

8, 10, 12, 18, 20, 22.

Since there are 6 values, that is even number of values. so the MEDIAN is given by

[tex]M=\dfrac{12+18}{2}\\\\\Rightarrow M=\dfrac{30}{2}\\\\\Rightarrow M=15.[/tex]

Therefore, m = M.

That is, mean and median of the given data are equal.

Hence, the difference is

m - M = 15 - 15 = 0.

Thus, option (A) is CORRECT.

Answer:

Option A - 0

Step-by-step explanation:

Given : Data set {22, 8, 10 ,18 ,12, 20}

To find : What is the difference between the mean and the median of the data set?

Solution :

Data set in increasing order {8, 10 ,12,18, 20,22}

Mean is defined as the division of sum of set values by total number of values.

[tex]M=\frac{\sum x}{n}[/tex]

Substitute the values we get,

[tex]M=\frac{8+10+12+18+20+22}{6}[/tex]

[tex]M=\frac{90}{6}[/tex]

[tex]M=15[/tex]

So, The mean of the set is 15.

Median of even numbers is the average of two middle terms.

[tex]m=\frac{3rd+4th}{2}[/tex]

[tex]m=\frac{12+18}{2}[/tex]

[tex]m=\frac{30}{2}[/tex]

[tex]m=15[/tex]

So, The median of the set is 15.

Now, The difference of the mean and the median of the set is

[tex]d=M-m[/tex]

[tex]d=15-15[/tex]

[tex]d=0[/tex]

Therefore,Option A is correct.

The difference of the mean and the median of the set is 0.

Final answer:

The sequence 5, 10, 15 represents multiples of 5, where each number is 5 units apart from the last.

This pattern can also be observed in a multiplication table in the row or column of the number 5.

Explanation:

The question asks us to describe a pattern in the sequence 5, 10, 15.

This sequence represents the multiples of 5. A clear pattern that can be observed is that each number increases by 5 to get to the next multiple.

For instance, starting with 5, adding 5 gives us 10, and adding another 5 to 10 gives us 15.

This pattern continues indefinitely with the series 20, 25, 30, and so on.

Answer:

Larry received 1/3 pound of candy from his grandmother and 2/5 pound of candy from his best friend. Larry's sister ate 1/2 pound of candy. How many pounds of candy does Larry have?

the answer is 7/30

Step-by-step explanation:

The smaller number of the two numbers that have a difference of 30 and a ratio of 7:2 is 12.

The difference between the two numbers is 30.

The ratio of the bigger number to the smaller number is 7:2.

The smaller number can be calculated as follows;

let

x = bigger number

y = smaller number

Hence, the difference in the numbers is as follows:

x - y = 30

Also, the ratio of the bigger number to the smaller number is 7:2.

The bigger number can be found using the ratio. Recall x + y is the total sum of the numbers.  

x = 7 / 9(x + y)

x = 7 / 9x + 7 / 9y

x - 7 / 9x = 7 / 9 y

2 / 9 x  = 7 / 9 y

multiply both sides by 9

2x  = 7y

The bigger number is 7 / 2 of the smaller number.

x = 7 / 2 y

Therefore, let's substitute the value of x in equation(i).

Recall x - y = 30

7 / 2 y - y = 30

5 / 2 y = 30

cross multiply

5y = 60

y = 60 / 5

y = 12

Hence,

x = 30 + 12

x = 42

Therefore,

smaller number = 12

learn more on differences and number: https://brainly.com/question/28476518

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To calculate 1206 × 5 using expanded form, break 1206 into its place values, multiply each by 5, and then add the results. This gives 6030.

Finding 1206 × 5 Using Expanded Form

To find the product of 1206 and 5 using expanded form, we break down 1206 into its place values:

Now, we multiply each component by 5:

Finally, we add all these products together:

5000 + 1000 + 0 + 30 = 6030

Therefore, 1206 × 5 equals 6030.