A culture of bacteria has an initial population of 8300 bacteria and
doubles every 10 hours. Using the formula Pt = P0 2^t/d, where Pt is
the population after t hours, P0 is the initial population, t is the time in
hours and d is the doubling time, what is the population of bacteria in the culture after 3 hours, to the nearest whole number?

On solving the provided question, we can say that Amount of commission = Total sales value x Rate of commission = 3,200

aggregate attempting to calculate the time required, total number or quantity. The quantity at hand or under consideration is incredibly energetic. the overall result, importance, or import. Principal, interest, and a third accounting. amounts, amounting, and amounted are word forms. flexible noun The quantity of something is how much there is, how much you have, how much you require, or how much you obtain. He requires that sum of money to get by.

[tex]Amount of commission = 3,200\\Total sales value = 80,000//[/tex]

Rate of commission = 4% on sales

Amount of commission = Total sales value x Rate of commission

Amount of commission = 80,000 x 4%

Amount of commission = 3,200

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Uncle Harry rented 4 games, and using  that he also rented 8 movies.Therefore, the Lupine family has 8 horror movies and 4 gory games for their vacation.

What is word problem?

A word problem is a type of mathematical problem that is presented using words instead of or in addition to mathematical symbols and equations. Word problems often describe a real-world scenario or situation, and they require the solver to use math skills and critical thinking to identify the relevant information, determine the mathematical operation or operations required, and arrive at a solution to the problem.

Let's assume that the number of movies Uncle Harry rented is "m" and the number of games is "g". We want to find the values of "m" and "g".

From the problem statement, we know that:

The total number of movies and games rented is 12: m + g = 12

The cost of each movie is $3.99: 3.99m

The cost of each game is $4.50: 4.5g

The total cost before tax is $49.92: 3.99m + 4.5g = 49.92

We can use the first equation to express "m" in terms of "g":

m = 12 - g

Substituting this expression for "m" in the second equation, we get:

3.99(12 - g) + 4.5g = 49.92

Expanding the brackets and simplifying, we get:

47.88 - 3.99g + 4.5g = 49.92

0.51g = 2.04

g = 4

So Uncle Harry rented 4 games, and using the first equation, we find that he also rented 8 movies.

Therefore, the Lupine family has 8 horror movies and 4 gory games for their vacation.

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Mei concluded that

We are 90% confident that the true proportion of times the die would land on the number 4 is between 0.398 and 0.562. Since this includes 0.5, the die appears to be fair.

It is based on a statistical analysis of the data collected by Mei.

The proportion of times the die landed on the number 4 is calculated as 48/100 = 0.48.

Using a statistical method called a confidence interval, we can estimate the range of values that the true proportion of times the die would land on the number 4 is likely to fall within, with 90% confidence.

The confidence interval calculated for this data is 0.398 to 0.562.

Since this interval includes the value of 0.5  (which would be the proportion of times a fair die would land on the number 4), By using statistical method we cannot reject the hypothesis that the die is fair.

Hence,

By using statistical method, we can conclude that the die would land on the number 4 is between 0.398 and 0.562 as 0.5 the die appears to be fair.

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Cindy spent a total of $128.09 on ingredients for pies. She will be able to make 18 slices of pie with this amount of ingredients.

1. Cindy spent $65.25 on ingredients for blueberry pies and $62.84 on ingredients for cherry pies.

2. Add the two amounts together: $65.25 + $62.84 = $128.09

3. Each slice of pie sells for $3.50.

4. Divide the total spent on ingredients by the cost of a slice of pie: $128.09 / $3.50 = 18 slices of pie.

the complete question is :

Cindy spent $65. 25 on ingredients for blueberry pies and $62. 84 on

ingredients for cherry pies. Each slice of pie sells for $3. 50.How much did Cindy spend on ingredients for blueberry and cherry pies, and how many pies can she make from that?

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Answer:

there is no solution

Step-by-step explanation:

The probability of a player spinning the color green and then rolling an even number is 1/12.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Spinner:

= {red, purple, blue, green, white, orange}

Cube:

= {1, 2, 3, 4, 5, 6}

Now,

The sample space of spinning and rolling a cube.

= {red, purple, blue, green, white, orange} x {1, 2, 3, 4, 5, 6}

The number of outcomes.

= 6 x 6

= 36

Now,

The outcome of spinning a green and an even number.

= (green, 2), (green, 4), (green, 6)

Number of outcomes = 3

Now,

The probability of a player spinning the color green and then rolling an even number.

= 3/36

= 1/12

Thus,

The probability of a player spinning the color green and then rolling an even number is 1/12.

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Answer:44

Step-by-step explanation:44444444

The values for the angle B and the side lengths of the right-angled triangle ABC are B = 41°, a = 9.6 , and b = 8.3 using the trigonometric ratios of sine and cosine of angle 49°.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths. The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the right-angled triangle ABC, we shall calculate for the angle B and side lengths a and b as follows:

A + B + C = 180° {sum of interior angles of a triangle}

49° + B + 90° = 180°

B = 180° - 139°

B = 41°

sin49 = a/12.7 {opposite/hypotenuse}

a = 12.7 × sin49 {cross multiplication}

a = 9.5848

cos49 = b/12.7 {adjacent/hypotenuse}

b = 12.7 × cos49 {cross multiplication}

b = 8.3319

Therefore, the values for the angle B and the side lengths of the right-angled triangle ABC are B = 41°, a = 9.6 , and b = 8.3 using the trigonometric ratios of sine and cosine of angle 49°..

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The percentage of students doing cycles is 37.98% ((204/535)*100).

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent symbol, "%," is frequently used to indicate it.

A % is a number without dimensions and without a measurement system.

The other answers are:

After the dealer discount, the car will cost €10,540 (€12,400 * 0.85).

The current price of the television is €638.50 (€510.80 * 1.25).

The Netflix connection will cost €13.80 after the discount (€17.25 * 0.8).

The family will pay €252 in cash (30% of €840), and the amount of each monthly installment will be €126.

You have been discounted by 20% ((60-48)/60*100).

The car will cost €9,000 with the bonus (€12,000 - €3,000), and the family will save 25% of the original price (€3,000/€12,000*100).

The capital will produce €683.10 of interest (€3000 * 0.045 * 5).

The capital that the bank will return is €3,855 (€3700 + (€3700 * 0.075 * 6/12)).

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Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.Find the value of day/dx when X = 1 and when Y = 1.

Answer:

The volume of a rectangular prism with length 25 cm and width 40 cm can be calculated as follows:

Volume = Length * Width * Height

Since the height is not given, we cannot calculate the exact volume.

Step-by-step explanation:

The pair of figures is similar by SSS

The complete question is added as an attachment

From the question, we have the following parameters that can be used in our computation:

Triangles BDC and FGC

When the side lengths of the triangle are compared, we have:

Side lengths of FGC are 5/3 multiplied by the side lengths of BDC

This means that the triangles are similar

And the similarity statement is SSS

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The expression that shows an equivalent expression include the following:

1/4(14x - 8 + 6x) = 5x - 2.

In Mathematics, an expression is sometimes referred to as an equation and it can be defined as a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).

Based on the information provided above, we have the following mathematical expression:

1/4(14x - 8 + 6x)

By opening and expanding the bracket, we have the following mathematical expression:

1/4(14x - 8 + 6x) = 1/4(20x - 8)

1/4(20x - 8) = 5x - 2

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The average rate of change over the interval [3,4] is given as follows:

3.

The average rate of change of a function is given by the change in the output divided by the change in the input.

The numeric values for the ends of the interval are given as follows:

Then the change in the output is of:

32 - 29 = 3.

The change in the input is of:

4 - 3 = 1.

Hence the rate is of:

r = 3/1

r = 3.

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Answer:

(175, 175) -> $3,150

(200, 150) -> $3,300

(225, 125) -> $3,450

Explain: I hope this helps

At least 174 participants for the clinical trial, with half of them assigned to the current drug group and half assigned to the new drug group.

To answer this question, we need to consider some statistical concepts. The event rate, or the percentage of patients who progress to cancer, is a key factor in this scenario. The current drug has an event rate of 28%, while the new drug is expected to reduce this further to 23%. We want to detect a difference between these two rates, which is 5 percentage points.

The power of a statistical test is the probability of detecting a true difference between two groups, given that such a difference exists. In this case, we want the power to be at least 80%, which means that we want to have an 80% chance of detecting a true difference of 5 percentage points between the current and new drugs.

To calculate the sample size needed for the clinical trial, we need to consider the expected event rates, the desired power, and the level of statistical significance. The level of significance is typically set at 5%, which means that we are willing to accept a 5% chance of making a type I error (i.e., rejecting the null hypothesis when it is actually true).

Assuming a two-sided test (i.e., testing for a difference in both directions), we can use a formula or an online calculator to determine the sample size. The formula is:

n = (Zα/2 + Zβ)² [p₁(1-p₁) + p₂(1-p₂)] / (p₁ - p₂)²

where n is the sample size, Zα/2 is the critical value of the standard normal distribution at the 2.5% level (for a two-sided test), Zβ is the critical value of the standard normal distribution at the desired power (in this case, 80%), p₁ is the event rate for the current drug (28%), p₂ is the event rate for the new drug (23%), and (p₁ - p₂) is the expected difference in event rates.

Plugging in the values, we get:

n = (1.96 + 0.84)² [(0.28)(0.72) + (0.23)(0.77)] / (0.28 - 0.23)²

n = 173.2

Rounding up to the nearest whole number, we get a sample size of 174 participants.

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The number of possible combinations are 12.

Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements. The number of combinations of n different things taken r at a time, denoted by nCr and it is given by, nCr=n!/r!(n−r)!,where 0 ≤ r ≤ n.

Given that, Esther can choose a 2 or 4 door car with leather or cloth interiors in black, silver, or white.

Now, C(3, 1)×C(2, 1)×C(2, 1)

= 3×2×2

= 12

Therefore, the number of possible combinations are 12.

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"Your question is incomplete, probably the complete question/missing part is:"

When buying a car, Esther can choose a 2 or 4 door car with leather or cloth interiors in black, silver, or white. How many possible combinations of her car selection?

The graph of the inequality is added as an attachment

From the question, we have the following parameters that can be used in our computation:

yz|x+2

Express properly

So, we have the following representation

y < x + 2

The above expression is an inequality that implies that

The value of y does not exceed 2 added to x

Next, we plot the graph

See attachment for the graph of the inequality

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The number of persons that can use the room at the same time is 36.

The volume of the cuboid = length x width x height

The room is a cuboid.

Volume of the room = length x width x height

L = 10m, W = 6m, Height = 3m.

Volume = 10 x 6 x 3 = 180 cubic meter.

If each person takes 5 cubic meter of air space,

Then the total person who can occupy the room at the same time is 180/5 = 36.

A cuboid is a three-dimensional geometric shape that is bounded by six rectangular faces, where each face is a parallelogram. It is also known as a rectangular prism. The faces of a cuboid are called its base and lateral faces. The base of a cuboid is the top and bottom rectangular faces, while the lateral faces are the four rectangular faces that connect the base.

Cuboids have eight vertices or corners, where three edges meet, and 12 edges, which are the straight lines that connect the vertices. The length, width, and height of a cuboid are the dimensions of the three pairs of parallel sides of its rectangular faces, and these measurements are usually denoted by l, w, and h, respectively.

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The number of hours taken to have the same number of pages completed is 5 hours.

The solution to the system of equations is (5, 50).

In order to write a system of linear equations that could be used to model the situation and determine the number of hours it would take to complete the workbook, we would assign variables to the number of hours and the number of pages respectively as follows:

Next, we would translate the word problem into system of linear equations as follows:

Isaiah: y = x + 45

Brenna: y = 9x + 5

When the same number of pages are completed, the number of hours taken can be calculated as follows;

x + 45 = 9x + 5

9x - x = 45 - 5

8x = 40

x = 5 hours.

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Sampling type which will yield a representative sample is stratified random sampling.

A representative sample is a subset of a population that seeks to accurately reflect the characteristics of the larger group. For example, a classroom of 30 students with 15 males and 15 females could generate a representative sample that might include six students: three males and three females.

This method uses stratified random sampling to help identify its components. Other methods can include random sampling and systematic sampling. A representative sample seeks to choose components that match with key characteristics in the entire population being examined.

Stratified random sampling is a method of sampling that involves the division of a population into smaller subgroups known as strata. In stratified random sampling, or stratification, the strata are formed based on members' shared attributes or characteristics, such as income or educational attainment.

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Mr. Titus travels a total of 7476 miles annually between Charlotte, North Carolina, and New York City.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

Given that twelve times a year, Mr. Titus makes the trip from Charlotte to New York City and back. Each round trip covers a total distance of 623 miles.

The total distance will be calculated as:-

Distance = 12 x 623

Distance = 7476 miles

Therefore, Mr. Titus' annual mileage between Charlotte, North Carolina, and New York City is 7476 miles.

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the probability of getting (a, b), i.e. the first card is a and the second card is b is 2/3 by conditional probability.

The potential of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability. It is computed by dividing the likelihood of the earlier occurrence by the likelihood of the subsequent, or conditional, event.

This is where the independent event and dependent event notion is used. Consider a student who misses class twice each week, omitting Sunday. What are the possibilities that he will take a leave of absence on Saturday of the same week if it is known that he will be absent from school on Tuesday? It has been noted that situations where the outcome of one event influences the outcome of a subsequent event are termed as conditional probability

We can work this out directly from the definition of conditional probability,

[tex]P(G_1|G_2)=P(G_1nG_2)/(P(G_1)[/tex]

Exactly one of the three cards has sides, so

P(G1∩G2)=1/3

and P(G1)=1/2

THEN

the probability of getting (a, b), i.e. the first card is a and the second card is b IS = 1/3÷1/2 = 2/3

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[tex]\left[\begin{array}{ccc}-1&5\\7&-2\end{array}\right]\left[\begin{array}{ccc}x\\y&\end{array}\right] =\left[\begin{array}{ccc}7\\3&\end{array}\right][/tex] is the representation of system of equation x+5y=7, 7x-2y=3

A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns.

The system of linear equations

-x + 5y = 7

7x - 2y = 3

can be represented in matrix form as:

[tex]\left[\begin{array}{ccc}-1&5\\7&-2\end{array}\right]\left[\begin{array}{ccc}x\\y&\end{array}\right] =\left[\begin{array}{ccc}7\\3&\end{array}\right][/tex]

The matrix on the left represents the coefficients of the variables x and y, and the matrix on the right represents the constants on the right-hand side of each equation.

The vector on the left contains the variables x and y, and the vector on the right contains the constants.

Hence, [tex]\left[\begin{array}{ccc}-1&5\\7&-2\end{array}\right]\left[\begin{array}{ccc}x\\y&\end{array}\right] =\left[\begin{array}{ccc}7\\3&\end{array}\right][/tex] is the representation of system of equation x+5y=7, 7x-2y=3

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Answer:a is 3:9 B is 6:9

Step-by-step explanation:

Answer:

504

Step-by-step explanation:

2 to the power of 9 is 512 2 to the power of 3 is 8 so 512-8 is 504 (hope w this helps!)

Answer:

504

Step-by-step explanation:

2^9 = 512

2^3= 8

512-8=504

The radius of the circle is 2.8feet (nearest tenth)

Arc length is the distance between two points along a section of a curve.

The length of an arc is expressed as ;

L = (tetha) / 360 × 2πr

L is the length of the arc

tetha is the angle made by the two radii and the arc.

In radian 360° = 2π

therefore ;

8 = 2.9/ 2π × 2πr

8 = 2.9 r

r = 8/2.9

r = 2.76 ft

therefore the radius of the circle is 2.8 feet( nearest tenth) .

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Step-by-step explanation: