A culture of bacteria is growing at the rate of 20e^.8t cells per day, where t is the number of days since the culture was started. Suppose that the culture began with 50 cells.
Find a formula for the total number of cells in the culture after t days

Answer:

1 : 4

Step-by-step explanation:

Given:

Favorite Music :

Pop _____ 7

Country __ 5

Dance ___ 4

Total number of students surveyed :

(pop + country + dance). = (7 + 5 + 4) = 16

Number who chose dance = 4

Ratio of dance to total number surveyed

4 : 16 = 1 : 4

1 :4 (lowest term)

The weight οf the kayak is 49 pοunds and 8 οunces. Sο the weight οf the kayak is 49 pοunds and 8 οunces.

A unit cοnversiοn expresses the same prοperty as a different unit οf measurement. Fοr instance, time can be expressed in minutes instead οf hοurs, while distance can be cοnverted frοm miles tο kilοmeters, οr feet, οr any οther measure οf length.

Tο cοnvert 792 οunces tο pοunds and οunces, we need tο divide the tοtal number οf οunces by the number οf οunces in a pοund (which is 16).

The quοtient will be the number οf pοunds, and the remainder will be the number οf remaining οunces.

Here are the calculatiοns:

792 οunces ÷ 16 οunces/pοund = 49.5 pοunds

The number befοre the decimal pοint (49) represents the pοunds, and the number after the decimal pοint (0.5) represents the remaining οunces.

Tο cοnvert the remaining οunces tο pοunds, we can multiply the decimal by 16 (the number οf οunces in a pοund).

0.5 * 16 = 8 οunces

Therefοre, the weight οf the kayak is 49 pοunds and 8 οunces.

Sο the weight οf the kayak is 49 pοunds and 8 οunces.

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The statement that 99% of all confidence intervals with a 99% confidence level should contain the population parameter of interest is false.

A confidence interval (CI) is essentially a range of estimates for an unknown parameter in frequentist statistics. The most frequent confidence level is 95%, but other levels, such 90% or 99%, are infrequently used for generating confidence intervals.

The confidence level is a measurement of the proportion of long-term associated CIs that include the parameter's true value. This is closely related to the moment-based estimate approach.

In a straightforward illustration, when the population mean is the quantity that needs to be estimated, the sample mean is a straightforward estimate. The population variance can also be calculated using the sample variance. Using the sample mean and the true mean's probability.

Hence we can generally infer that the given statement is false.

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True. Both distributions are bell-shaped and symmetric, which means they exhibit the characteristic shape of a normal distribution. The peak of a normal distribution represents the highest point of the curve and corresponds to the mean of the distribution. In other words, the mean determines where the peak falls on the number line.

For Distribution 1, with a mean of 100, the peak will be centered around 100 on the number line. This indicates that the majority of the data points in the distribution cluster around the mean value of 100.

Similarly, for Distribution 2, with a mean of 500, the peak will be centered around 500. This means that the data points in this distribution are concentrated on the mean value of 500.

The symmetry of the distributions implies that the data is equally likely to fall on either side of the mean, resulting in a balanced and symmetric bell-shaped curve. This characteristic is a fundamental property of normal distributions.

Therefore, the peak of a normal distribution is determined by the mean, and both Distribution 1 and Distribution 2 are bell-shaped and symmetric, with the peak aligned with their respective means.

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The formula C = 5(F - 32), is misspelled.

The formula °C = 5/9 (°F - 32), is the formula to convert degrees Fahrenheit to degrees Celsius. Therefore it is True.

Answer:

the Larger poster is 9ft long by 6ft wide

Step-by-step explanation:

In order to find the length and width values of the large poster we first need to find the width of the smaller poster since we are already given the length. Since we are also provided with the perimeter we can add the length twice and subtract it from the perimeter which would give us the value of both width sides of the rectangle, then we simply divide by 2 to get the value of the individual width.

10ft = 3ft + 3ft + w + w

10ft = 6ft + 2w

4ft = 2w

2ft = w

Since the larger poster is 3 times as big for the length and the width we simply multiply the smaller poster's length and width by 3...

L = 3 * 3 = 9ft

W = 2 * 3 = 6ft

Finally, we can see that the Larger poster is 9ft long by 6ft wide

The interval of convergence of the series ∑a_n x^n is given by |x|∞} |a_{n+1} nx^n| / |a_n x^(n-1)|.We can write L as L = lim_{n->∞} |a_{n+1}| / |a_n| x, where x is the same in the numerator and denominator. Since the series ∑a_n x^n converges for |x|<2, we have lim_{n->∞} |a_{n+1}| / |a_n| = L' < 2. Thus, L = L' x.

For the series to converge, we need L < 1, which gives |x| < 1 / L'. Thus, the radius of convergence of the series ∑a_n nx^(n-1) is 1 / L'.Since the radius of convergence is the same as that of the series ∑a_n x^n, we get L' = 2. Thus, the radius of convergence of the series ∑a_n nx^(n-1) is 1 / L' = 1/2. Thus, the interval of convergence of the series ∑a_n nx^(n-1) is |x| < 1/2. However, since the interval of convergence of the series ∑a_n x^n is |x| < 2, we have |nx^(n-1)| = n|x^(n-1)| <= 2n for |x|<=1. Thus, we have |a_n nx^(n-1)| <= |a_n| 2n for |x|<=1, which shows that the series converges for x=-1, and thus for -1<=x<=1. Also, we have |a_n nx^(n-1)| <= |a_n| 2^n for |x|<=2, which shows that the series converges for x=2, and thus for -2<=x<=2. Thus, the possible interval of convergence of the series ∑a_n nx^(n-1) is [-2, 2].

The possible interval of convergence of the series ∑a_n nx^(n-1) is [-2, 2].

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Answer:

Our friends score after level 2 is 23

Step-by-step explanation:

Here, we want to find our friends score after level 2 of the game

From the question;

Your score is 24 points less than your friends;

Let the friends score be x

Thus;

x-24 = -1

x = -1 + 24

x = 23

Answer: X = 16

Step-by-step explanation:

so 6^(X-4) = 6^12

X = ?

we can rewrite it as X - 4 = 12 since the bases are the same

now solve for X

X = 12 + 4

X = 16

The expression for the no. of sweets Sue has is (13 - x) and for Tony it is

(18 + x)/2.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, Sue has 18 sweets and Tony also has 18 sweets.

Sue gives Tony x sweets, so she now has 18 - x sweets, So Tony has 18 + x sweets.

Sue then eats 5 of her sweets which is 18 - x - 5 = 13 - x sweets.

Tony then eats half of his sweets which is (18 + x)/2 sweets.

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Answer:

a it is

Step-by-step explanation:

Answer:

Step-by-step explanation: the answer is .75. your welcome

the answer is 3/4 or 0.75

Using a linear function, it takes 4.4 minutes for the sub to reach the certified depth.

A linear function is modeled according to the following rule:

y = mx + b

In which:

For this problem, the velocity is constant, which is why a linear function is used.

The slope and intercept are given as follows:

Hence the depth after t minutes is given by:

D(t) = -872.42 + 50.6t.

The certified depth is reached when D(t) = -650, hence:

D(t) = -872.42 + 50.6t.

-650 = -872.42 + 50.6t.

t = (872.42 - 650)/50.6

t = 4.4 minutes.

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In the given Markov chain, State 1 is absorbing, State 4 is periodic, State 1 is recurrent, and States 3, 4, and 5 are recurrent.

A Markov chain is a stochastic model that represents a sequence of states where the probability of transitioning from one state to another depends only on the current state. Let's analyze the given Markov chain to determine the properties of each state.

State 1: This state has a probability of 1 in the first row, indicating that it is an absorbing state. An absorbing state is one from which there is no possibility of leaving once it is reached. Therefore, statement a) is correct, and State 1 is absorbing.

State 2: There are no transitions from State 2 to any other state, which means it is an absorbing state as well. However, since it is not explicitly mentioned in the question, we cannot determine its status based on the given information.

State 3: This state has non-zero probabilities to transition to other states, indicating that it is not absorbing. Furthermore, it has a loop back to itself with a probability of 1/6, making it recurrent. Hence, statements c) and e) are incorrect, while statement f) is correct. State 3 is recurrent.

State 4: State 4 has a transition probability of 1/3 to State 3, which means there is a possibility of leaving this state. However, there are no outgoing transitions from State 4, making it an absorbing state. Moreover, since there is a loop back to itself with a probability of 2/3, it is also recurrent. Therefore, statement b) is correct, and State 4 is periodic and recurrent.

State 5: Similar to State 4, State 5 has a transition probability of 2/3 to State 3 and no outgoing transitions. Hence, State 5 is also an absorbing and recurrent state. Consequently, statement e) is correct.

To summarize, State 1 is absorbing and recurrent, State 4 is periodic and recurrent, and States 3 and 5 are recurrent.

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Answer:

\(18\sqrt{3}\)

Step-by-step explanation:

Please see the attached image

I'm assuming you've already learned the special properties of a 30-60-90 triangle.

By drawing a 30-60-90 triangle by constructing line BC, and using the special proportions that come from it, we can find that

AB=AC/2=36/2=18

and

BC=AB*\(\sqrt{3}\)=\(18\sqrt{3}\)

Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.

The amount Janelle will earn with the compound interest option can be calculated using the formula for compound interest:

\(A = P(1 + r/n)^{(nt)}\)

Where:
A is the total amount after interest has been compounded
P is the principal amount (the initial deposit)
r is the annual interest rate (expressed as a decimal)
n is the number of times interest is compounded per year
t is the number of years

In this case, Janelle deposits 3,000 at an interest rate of 3% for 7 years. We'll compare the simple interest and compound interest options.

For the simple interest option, the interest is calculated using the formula:

I = P * r * t

Where:

I is the total interest earned

Using the given values, we can calculate the interest earned with simple interest:

I = 3000 * 0.03 * 7
I = 630

Now, let's calculate the total amount earned with the compound interest option.

Since the interest is compounded monthly, the interest rate needs to be divided by 12 and the number of years needs to be multiplied by 12:

r = 0.03/12

t = 7 * 12

Using these values, we can calculate the total amount with compound interest:

\(A = 3000 * (1 + 0.03/12)^{(7*12)}\)

A ≈ 3,729.19

To find out how much more Janelle will earn with the compound interest option, we subtract the initial deposit from the total amount with compound interest:

Difference = A - P
Difference = 3,729.19 - 3,000
Difference ≈ 729.19

Therefore, Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.

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For the first part, the number of license plates is: 65,780,800 and for the second part, the number of license plates with 3 consecutive digits is: 16,524,288.

If there are no restrictions on where the digits and letters are placed, the number of 8-place license plates consisting of 5 letters and 3 digits with no repetitions allowed can be found using the permutation formula:

nPr = n! / (n-r)!

where n is the number of available characters (26 letters and 10 digits) and r is the number of characters needed for the license plate (8).

Therefore, the number of license plates is:

(26 P 5) x (10 P 3) = (26!/21!) x (10!/7!) = 65,780,800

If the 3 digits must be consecutive, there are 8 possible positions for the block of digits (either the first 3, second 3, or last 3). Once the position of the block is chosen, the number of license plates can be found by counting the number of ways to arrange the letters and the block of digits. The number of ways to arrange the letters is 26 P 5, and the number of ways to arrange the block of digits is 10 (since there are only 10 possible sets of consecutive digits).

Therefore, the number of license plates with 3 consecutive digits is:

8 x (26 P 5) x 10 = 16,524,288

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The complete question goes thus:

If there are no restrictions on where the digits and letters are placed, how many 8

-place license plates consisting of 5

letters and 3

digits are possible if no repetitions of letters or digits are allowed? What if the 3

digits must be consecutive?

The original recipe had 0.9 cups of bananas.

Using only fresh ingredients, strawberry banana smoothie is a simple, nutritious dish. It is creamy, sweet, nutritious, and dairy- or dairy-free can be used to make it. The ideal summertime smoothie. Putting the strawberries, frozen banana, milk, and yoghurt in a blender and mixing until smooth and creamy is all that is required to make it.

Cups of strawberries = 1.75

No. of cups added of banana = 1/2

                                            = 0.5

No. of cups of banana smoothie have = 14.

The original recipe had = 1.4 - 0.5

                                   = 0.9

Hence, the original recipe had 0.9 cups of bananas.

Correct Question :

to make a strawberry banana smoothie, a recipe calls for 1.75 cups of strawberries and some bananas. to make the recipe taste more like banana, 1/2 cup more banana was added to the blender. the smoothie now has 1.4 cups of bananas. how many cups of bananas were in the original recipe?

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Answer:

41 square units

Step-by-step explanation:

this polygon can be split into several sub-shapes, for which we can calculate their areas much easier. and then we simply add all the sub-results for the total result.

for me this split would be

1. square CDEF, with F being an additional point at (6,5) : 4 units to the right of C.

2. a right-angled triangle ABF (the same F as for 1.).

the area of a square is the square of a side length.

the side length in 1. is 4.

so, its area is 4×4 = 16 square units.

the area of a right-angled triangle is

a×b/2

with a and b being the sides enclosing the 90 degree angle.

in our case here a = BF = 10, b = FA = 5

so the area of the triangle is 10×5/2 = 25 square units.

so, the total area is 16 + 25 = 41 square units.

The statement If a simple random sample is chosen with replacement, each individual has the same chance of selection on every draw is True.

If a simple random sample is chosen with replacement, it means that after each selection, the chosen individual is placed back into the population before the next selection is made. In this case, each individual in the population has the same chance of being selected for every draw.

The process of replacing the selected individual ensures that the selection probabilities remain constant throughout the sampling process. As a result, each individual has an equal probability of being chosen on each draw, making the statement true.

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The equation for the linear relationship in slope-intercept form is

y = 250x + 250

We have,

From the graph,

The coordinates are: (1, 250) and (2, 500)

Now,

The equation can be written as:

y = mx + c

Now,

m = (500 - 250) / (2 - 1)

m = 250

Now,

(0, 250) = (x, y)

250 = 250 x 0 + c

c = 250

Now,

y = mx + c

y = 250x + 250

Thus,

The equation for the linear relationship in slope-intercept form is

y = 250x + 250

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The speed of the raft if the speed of the patrol-boat was 12 km/hour, and it caught the raft in 5 hours 20 min later is 2.857 km/hours.

What is the speed of a body?

The speed of a body is the rate at which it covers the total distance is in the time taken. The speed of the body is given as,

\(S=\frac{D}{T}\)

Here, (d) is the distance travelled by the body, and (t) is time taken by the body to cover that distance.

A raft was sent away from point A downstream. A patrol-boat left A 5 hour and 20 min later and caught up with the raft 20 km away from point A.

Total time the patrol boat took in hours is,

\(T = 5 + \frac{20}{60}\)

T=5+0.3333

T=5.3333 hours

The speed of the patrol boat is 12 km/hour, and it caught up with the raft 20 km away from point A. Thus, the time taken with this speed to cover 20 km distance is,

\(T=\frac{20}{12}\)

T=1.6667 Hours

Thus, the total time is,

T=5.3333+1.6667

T=7 Hours

Now as the raft travel 20 km in 7 hours. Therefore, find the speed of raft by putting the values in above formula as,

\(S=\frac{20}{7}\)

S=2.857 kmph

We don't know if she will reject the null hypothesis without knowing the level of significance. But if the p-value is smaller than the level of significance, she would reject the null hypothesis

The correct explanation for the P-value is option B: "If the​ P-value for a particular test statistic is ​, she expects results at least as extreme as the test statistic in about of 100 samples if the null hypothesis is true."

This means that if the null hypothesis is true, there is a certain probability (represented by the P-value) that we would observe a test statistic as extreme or more extreme than the one we observed in our sample.

As for the conclusion, we cannot determine whether or not the researcher would reject the null hypothesis based solely on the P-value. The decision to reject or not reject the null hypothesis depends on the level of significance (alpha) chosen by the researcher. If the P-value is smaller than the chosen alpha, then the researcher would reject the null hypothesis.

Otherwise, she would fail to reject it. Without knowing the level of significance chosen, we cannot determine the conclusion.

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Answer:

11/20

Step-by-step explanation:

To be able to find the fraction of the cake that Jake ate if you know that he ate 55% of it, you have to turn the 55% into a fraction. To do this, first you have to divide the percent by 100:

55/100

Then, you have to simplify the fraction. In this case, you can do it by dividing by 5:

11/20

According to this, the fraction of the cake that Jake ate is 11/20.

22 ml of rboh is titrated with 35 ml of 0.9 m hf. The concentration of the base is 1.43M.

Titration is a method of chemical analysis in which the amount of a sample's ingredient is determined by adding an exact known amount of a different substance to the measured sample in which the desired constituent interacts in a specific, known proportion. Titrating reagent, or titrant, is often added to a standard solution (i.e., a solution of known concentration) using a burette, which is essentially a long, graduated measurement tube with a stopcock and a delivery tube at its bottom end. When the equivalence point is achieved, the addition is terminated.

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Answer:

7(2a+6) = 4

and the answer is:

19/7

Step-by-step explanation:

7(2a+6) = 4

7*2a + 7*6 = 4

14a + 42 = 4

14a = 4 - 42

14a = -38

a = -38/14

a = -19/7