The initial size of a culture of bacteria is 1000. After one hour the bacteria count is 8000.(a) Find a function n(t) = n0ert that models the population after t hours.(b) Find the population after 1.5 hours.(c) After how many hours will the number of bacteria reach 15,000?(d) Sketch the graph of the population function.

If a rancher has 720 feet of fencing with which to enclose two adjacent rectangular corrals, the dimensions are 90 feet and 120 feet

From the figure

4x + 3y = 720

3y = 720 - 4x

y = 240 - (4/3)x

The area = l × w

Where l is the length

w is the width

Substitute the values in the equation

A = 2x × y

= 2x (240 - (4/3)x)

Apply the distributive property

= 480x - (8/3)x^2

Differentiate the values

0 = (-16/3)x + 480

(16/3) x = 480

x = 480 / (16/3)

x = 90 feet

Then,

y = 240 - (4/3)(90)

= 120 feet

Hence, the dimensions are 90 feet and 120 feet

I have answered the question is general, as the given question is incomplete.

The complete question is

A rancher has 720 feet of fencing with which to enclose two adjacent rectangular corrals (see figure). what dimensions should be used so that the enclosed area will be a maximum?

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Answer:

Step-by-step explanation:

∠R= 110°, ∠U= 70°, ∠T= 110° are the missing angle measures in parallelogram RSTU.

A parallelogram is a simple quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposite or facing sides are of equal length, and its opposite angles are of equal measure.

Because RSTU is a parallelogram, we may use parallelogram characteristics to calculate S=U=70° ( Opposite angles of parallelogram are equal).

Using the property, sum of adjacent angles is equal to 180°, therefore,

⇒∠S+∠R= 180°

⇒70°+∠R= 180°

⇒∠R= 180°- 70°

⇒∠R=110°

Also, ∠R= ∠T= 110° (Opposite angles of parallelogram are equal).

Thus, ∠R=110°, ∠T= 110° and ∠U=70°

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Answer:

Step-by-step explanation:

You want the volume and surface area of a rectangular crate that is 15 in long, 4 in wide, and 10 in high.

The volume is given by the formula ...

  V = LWH

For the given crate, the volume is ...

  V = (15 in)(4 in)(10 in) = 600 in³

The area is given by the formula ...

  A = 2(LW +H(L +W))

For the given dimensions, the crate has an area of ...

  A = 2((15 in)(4 in) +(10 in)(15 in +4 in)) = 2(60 in² +(10 in)(19 in))

  = 2(60 in² +190 in²) = 500 in²

The crate's volume is 600 cubic inches; its area is 500 square inches.

The best interpretation of the mean of X is in the long run, a player will lose an average of $0.15 per carnival game played.

The average of the specified collection of numbers is what is referred to as mean. It indicates a data set's values are distributed equally.

Given:

Amount =      $1        $1       $10

Probability = 0.80    0.15    0.05

In mathematics and statistics, the arithmetic mean is the sum of a set of integers divided by the total number of the numbers in the set. When the context is clear, it is also referred to as the mean or average. A set of experiments or survey findings are typically included in the collection.

Hence, the correct option is (A) In the long run, a player will lose an average of $0.15 per carnival game played.

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The radius of the circle will be 4.6m.

What is area of a circle?

The measurement of the circle's boundaries is called as the circumference or perimeter of the circle. whereas the circumference of a circle determines the space it occupies. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units like cm or unit m are typically used to measure it. The circle's radius is considered while calculating the circumference of the circle using the formula. As a result, in order to calculate the circle's perimeter, we must know the radius or diameter value. The area of the circle will be A = [tex]\pi r^{2}[/tex].

The area of the circle given is = 15 m²

Sector of a circle with a central angle of 5π/11 rad

The area will be (1/2) * r² * Ф

15 = (1/2) * r² * (5π/11)

⇒r² = 30 * (11/5π)

⇒r² = 21.00

⇒r=4.6m

Hence, the radius of the circle will be 4.6m.

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The array that has been sorted using insertion sorting 1 2 3 4 5 6 7 8 9.

A straightforward sorting algorithm called insertion sort functions like how you might arrange playing cards in your hands.

Initial Pass: 2 9 8 7 6 5 1 4 3

The array's first two members are initially compared using an insertion sort.

Since 9 is bigger than 2, they are not arranged in ascending order, and 2 is not in the proper place. So, switch 9 and 2.

Therefore, 2 is currently kept in a sorted sub-array.

Second Pass: Continue with the next two elements and compare them.

2 8 9 7 6 5 1 4 3

Here, 9 is bigger than 8, therefore both items appear to be in ascending order; as a result, there won't be any switching. Along with 8, 9 is also kept in a sorted sub-array.

Third pass: Currently, the sorted sub-array has two entries, which are 2 and 8.

Moving on to the following two components, which are 9 & 7,

2 7 8 9 6 5 1 4 3

Continue sorting similarly; the results would be 1 2 3 4 5 6 7 8 9.

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The two-column proof shown above should be completed with the following theorems:

Statements                              Reasons

ΔADB ≅ ΔCDB                             HL.

AD ≅ CD                                    CPCTC.

In Geometry, there are five (5) major types of triangle based on the length of their sides and angles, and these include the following;

In Mathematics, CPCTC is an acronym for corresponding parts of congruent triangles are congruent and it can be defined as a theorem which states that the corresponding angles and side lengths of two (2) or more triangles are congruent if they are both congruent.

By applying the corresponding parts of congruent triangles are congruent (CPCTC) theorem to triangle ABC (ΔABC), we have the following;

Statement                              Reason

AD ≅ CD                                    CPCTC.

In Mathematics, HL is an acronym for hypotenuse leg and it can be defined as a theorem which states that if the hypotenuse and one (1) leg in a right-angled triangle are congruent to the hypotenuse and leg of another right-angled triangle, then the two (2) triangles would be congruent i.e ΔADB ≅ ΔCDB.

By applying the hypotenuse leg (HL) theorem to triangle ABC (ΔABC), we have the following;

Statement                              Reason

ΔADB ≅ ΔCDB                             HL.

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Answer:

685

Step-by-step explanation:

they would normally pay 720

but they got 35 credit

720-35 is 685

The probability of getting heads at least twice is 0.5

Since we are given two-sided coin, where the probability of getting heads is equal to the probability of getting tails.NO of outcomes in this case is 2,The probability of getting a head = 1/2, similarly probability of getting a  tail is =1/2 .So when a coin is flipped three times, the sample space for the event will be (HHH, HHT, HTH, HTT, THH, THT, TTH, TTT),  H stands for head and T stands for tails, here for tossing the coin the number of outcomes is 8  .So the probability of getting at least two heads is:  4/8= 1/2 =0.5

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True , the null hypothesis of zero difference between the two population means cannot be rejected at a 0.10 level of significance.

Given :

f a 90% confidence interval for the difference in the two population means contains zero, then the null hypothesis of zero difference between the two population means cannot be rejected at a 0.10 level of significance.

at 10 % significance:

z score = 1.282

at 90 % confidence interval :

z score = 1.645

[tex]H_0 :[/tex] differences between population mean = 1.282

so true the null hypothesis of zero difference between the two population means cannot be rejected at a 0.10 level of significance.

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A 5% chance exists of concluding there is a difference when there isn't at a significance level of 0.05. Lower levels of significance suggest that you need more proof before you can rule out the null hypothesis.

In statistics, the analysis of variance (ANOVA) method is used to compare the means of two groups.

In an experiment with a completely randomized design, samples are at random assigned to either a treatment group or a placebo group.

For instance, if 40 persons are chosen to evaluate the effects of an analgesic,

four groups—Groups A, B, C, and D—could be created. Different dosages of the medication can be administered to Groups A, B, and C, while Group D receives a placebo. Due to the random grouping of the participants

, this is an illustration of a randomized design.

We assume that the sample populations are normally distributed and have the same variances in order for an ANOVA test to display completely randomized design.

Hence, A 5% chance exists of concluding there is a difference when there isn't at a significance level of 0.05. Lower levels of significance suggest that you need more proof before you can rule out the null hypothesis.

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The correct is b i.e; the critical value times the standard error of the sampling distribution

Given options are :

a. The biggest sampling error that can be made while maintaining a certain level of confidence.

b. the critical value multiplied by the sampling distribution's standard error

c. the discrepancy between the parameter and the point estimate.

Margin of error

= C * SE

Where C is critical value of on

of is the Standard error

The multiple of Critical Value and Standard error is the margin of error

Correct Option is b i. e the critical value times the Standard error of Sampling distribution

Therefore, The margin of error is the product of Critical Value and Standard Error.

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Answer:

you have to divide

Step-by-step explanation:

621/9=69 so there are 69 blouses on each of the 9 racks

Answer:

g(x) = x+3

Step-by-step explanation:

f(x) = x+1

g(x) = f(x+2)

so g(x) = (x+2)+1

g(x)=x+3

The distance of 40 lb will be 5ft, according to the question.

What do you mean by distance?

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

According to the given question,

We have the given information:

The fulcrum be located from the 40 lb.

The weight of bar is 9ft long.

Now, we will calculate the distance,

40x = 50(x-1)

40x = 50x - 50

40x - 50x = -50

-10x = -50

x = 5

Therefore, the required answer is 5ft.

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The total number of nickels and quarters with Veronica are 5 and 9, respectively.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the number of nickels be represented by x, while the number of quarters be represented by y.

It is known that a nickel is worth 5 cents, while a quarter is worth 25 cents. Therefore, the given statements can be written in the form of equations as,

Veronica has 4 more nickels than quarters,

x = y + 4

Coins have a combined value of 170 cents,

5x + 25y = 170

Substitute the value of x from the first equation in the second,

5x + 25y = 170

5(y + 4) + 25y = 170

5y + 20 + 25y = 170

30y = 170 - 20

30y = 150

y = 150/30

y = 5

Therefore, the number of quarters are 5.

Since, Veronica has 4 more nickels than quarters,

x = y + 4

x = 5 + 4

x = 9

Hence, the total number of nickels and quarters are 5 and 9, respectively.

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The value of the expression 7x² - 2x + 2 when x = 3 is 59.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

Based on the information given, the expression is:

7x² - 2x + 2

Put x = 3

= 7x² - 2x + 2

= 7(3)² - (2 × 3) + 2

= 63 - 6 + 2

= 59

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The Answer is A: 50

just remember that the line in the middle is half of the one on the outside of the triangle

The total area bounded by curve f(x)=x³+1 between (0,2) will be 6 units.

The summing of discrete data is indicated by the integration. To determine the given functions that will characterize the area, displacement, and volume that result from a combination of small data that cannot be measured separately and integrals are calculated. The concept of limit is employed broadly in calculus whenever algebra and geometry are applied.

Given Graph = x³+1

Area between interval x€[0,2]

To get the desired area we have to integrate between x€[0,2]

[tex]\int\limits^2_0 {(x^3 + 1)} \, dx[/tex]

∫x³dx + ∫1dx

[tex]\frac{x^4}{4}[/tex] + x + c

We can find the area by lower limit - upper limit

Putting x = 0

we get result as c

Putting x = 2

We get result as 6+c

So desired area will be ( 6+c ) - c = 6

Hence the total area bounded by curve between (0,2) will be 6 units.

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a function that determines a string's hask key. The average position of each letter in the alphabet divided by the size of the table yields the hash key.

def char_position(char):

   alphabet = list("abcdefghijklmnopqrstuvwxyz")

   return alphabet.index(char)

def hash_key(string):

   total = 0

   for char in string.lower():

       total += char_position(char)

   return total / len(string)

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4 bracelets and 3 Necklaces are made by the Jeweler.

Two or more expressions with an Equal sign is called as Equation.

Let us represent Bracelet as B and Necklace as N

B+N=7..(1)

7B+18N=82..(2)

From equation 1,

B=7-N

Now plug in B value in equation 2

7(7-N)+18N=82

49-7N+18N=82

49+11N=82

Subtract 49 on both sides

11N=33

N=3

Now we have to find B

B+N=7

B+3=7

Subtract 3 on both sides

B=4

Hence, 4 bracelets and 3 Necklaces are made by the Jeweler.

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The distance between you and your friend is changing at a rate of 20 miles per hour.

What is the Pythagorean theorem?

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Here, we

Let the east direction is denoted by x and

the north direction is denoted by y.

dx / dt = 16 miles per hour

dy / dt = 12 miles per hour

x = 4 miles

Let the distance between both the friends be s.

Time is taken by you to travel 4 miles,

time = distance / speed = 4 / 12 = 1/4 hour

Distance traveled by your friend in time t,

y = speed x time = 12 x 1/4 = 3 miles

By Using the Pythagorean theorem,

x² + y²  = s²     ..... (1)

Substitute, x = 4 mile, y = 3 mile

s²  = 16 + 9 = 25

s = 5 miles

Now, Differentiate equation (1) with respect to t, we get

2x dx/dt + 2y dy/dt = 2s ds/dt

4 (16) + 3 (12) = 5 ds/dt

ds/dt = 20 miles per hour

Hence, the distance between you and your friend is changing at a rate of 20 miles per hour.

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Answer:

11 or 12  ....?

Step-by-step explanation:

This seems simple... so simple i feel like im overthinking it (x_x)

Answer:

Step-by-step explanation:

01:06

Answer:

1:06

Step-by-step explanation:

11:06 + 2:00 = 13:06

13:06-12:00= 1:6

Answer: (A) There is 1 unit between 0 and 1.

(B) There are 1 units between 0 and 1

(C) There are 0 and -3 so the sum of these two values is 3 units.

Step-by-step explanation:

How to find a distance between two integers? Easy!

First find the absolute value! Its gonna help a lot!

500 Different number of committees are possible.

Initially we have 7 men and 6 women.

We have to select 4 men and 3 women to form a committee

Number of men are possible 7C4 = 35

Number of women are possible 6C3 = 20

2 of the men are refusing to server together

so we have to subtract the possibilities when these 2 men are sitting together.

we are considering 2 men are already sitting together.

now, we have only need of 2 men  from remaining 5 men.

number of ways to select 2 men from 5 men is 5C2 = 10

We have to subtract 10 from number of men possible.

Number of men possible when 2 of the men refuse to serve together =

35 - 10 = 25.

Number of possible committees are 25*20 = 500.

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The predicted number of calories in a sandwich containing 32 grams of fat is 559.

In algebra, the slope-intercept form of a linear equation is a typical approach to express a line on a graph. A linear equation is written as y = mx + b in standard form.

The y-intercept, or place where the line crosses the y-axis, is represented by the letters b and m, respectively. The point where the lines contacts the y-axis is known as the y-intercept, and the slope is a measurement of how steep the line is. Because it explicitly displays the slope and y-intercept, this equation's form is known as the slope-intercept form.

y = mx + b

Where m is the slope, x is the value of the independent variable, and b is the y-intercept. In this case, the slope is 13 and the y-intercept is 143. So, the equation of the line of best fit is:

y = 13x + 143

To predict the number of calories in a sandwich containing 32 grams of fat, you can plug in 32 for x in the equation:

y = 13 * 32 + 143

y = 416 + 143

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In the given question, the absolute percentage increase is 1050 and the relative percentage increase is 32.3076%.

When you want to analyze how a value has evolved over time, a percentage increase is helpful.

Although percentage increase and absolute increase are fairly comparable, the former is more helpful when contrasting different data sets.

For instance, a change from 1 to 51 and a change from 50 to 100 both have an absolute change of 50, but the first change grew significantly more due to the higher percentage growth of 5000% compared to the second change of 100%.

The most popular method of assessing growth is percentage increase because of this.

So, the absolute and relative percentage increase is:

The town's population grew from 3,250 in 2008 to 4,300 in 2010.

2008: P1 = 3250

2010: P2 = 4330

Absolute variation:

Absolute difference = P2 - P1

Absolute difference = 4330 - 3250

Absolute difference = 1050

Relative increase:

Relative percentage = P2 - P1/P1 * 100

Relative percentage = 1050/3250 * 100

Relative percentage = 32.3076

Therefore, in the given question, the absolute percentage increase is 1050 and the relative percentage increase is 32.3076%.

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Correct question:
The population of the town increased from 3,250 in 2008 to 4,300 in 2010. Find the absolute and relative(percent) increase.

(-1 , 0) is the point that represents the point on the unit circle and corresponds to -π.

Option (D) is the correct one.

Given, a unit circle

and we have to mention the point on the unit circle that corresponds to -π.

As, the equation of a unit circle is

x² + y² = 1

now -π is represented by the left side of the x-axis

therefore to represent the given point we have to take a point on x-axis that will be at the left side of the origin and at the unit distance from the origin.

So, (-1 , 0) is the point that represents the point on the unit circle and corresponds to -π.

Hence, (-1 , 0) is the point that represents the point on the unit circle and corresponds to -π.

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Your question is incomplete kindly find the complete question below.

Which point on a unit circle corresponds to -π ?

(a) (1 , 0)

(a) (0 , -1)

(c) (0 , 1)

(d) (-1 , 0)

Answer:

(-1,0)

Step-by-step explanation:

I just took the quiz :)