Simplify the expression.

x^3-(x^2-3x)(x+3)

5. The bacteria population declined from 280,000 to 700 in 42 hours. To determine the population at 30 hours, we can use the rate of decay and calculate the approximate number of bacteria.

The decline in bacteria population is given as 280,000 - 700 = 279,300 bacteria over 42 hours. To find the rate of decay per hour, we divide the total decline by the number of hours: 279,300 / 42 = 6,650 bacteria per hour.  Now, to estimate the population at 30 hours, we multiply the rate of decay by the number of hours: 6,650 * 30 = 199,500 bacteria. Therefore, at approximately 30 hours, there would be around 199,500 bacteria.

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6. The researcher starts with 600 bacteria that grow at a rate of 8% per hour. To determine the number of bacteria after 3 hours, we can use the growth rate and calculate the approximate number of bacteria.

The bacteria population grows at a rate of 8% per hour. To find the growth per hour, we multiply the initial population by the growth rate: 600 * 0.08 = 48 bacteria per hour. Now, to estimate the population after 3 hours, we multiply the growth per hour by the number of hours: 48 * 3 = 144 bacteria. Therefore, after approximately 3 hours, the researcher will find around 144 bacteria.

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To solve the separable differential equation dy/dx = 8y, we must first separate the variables, resulting in two separate integrals. We will have dy/y = 8 dx. Now, we need to find the integrals:

1) Integral of dy/y:
∫(1/y) dy

2) Integral of 8 dx:
∫8 dx

Next, we solve the integrals:

1) ∫(1/y) dy = ln|y| + C₁
2) ∫8 dx = 8x + C₂

Now, we combine these results to find the general solution:
ln|y| = 8x + C, where C = C₂ - C₁.

To solve for y, we take the exponent of both sides:
y = e^(8x + C) = e^(8x)e^C. We can write e^C as a new constant k, so y = ke^(8x).

Now, we need to find the particular solution satisfying the initial condition y(0) = -2. To do this, plug in the values into the equation:

-2 = k * e^(8 * 0)
-2 = k * e^0
-2 = k * 1
k = -2

So the particular solution satisfying the initial condition is y(x) = -2e^(8x).

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Answer:

Step-by-step explanation:

Perimeter 165 cm

1st.   65 cm < 2s

3rd.  10 cm < s

The 2nd side is twice than the first side but 10cm longer than the

3rd side, so it'll be

2nd.   2s + 10

a triangle has a perimeter of 165 cm. the first side is 65cm less than twice the second side. the third side is 10cm less than the second side. write and solve an equation to find the length of each side of the triangle

FIRST, we need variables. Once we define variables, it's much easier to turn this word problem into a math problem.

Let a = first side

Let b = second side

Let c = third side

NOW, we can turn the words into equations:

"a triangle has a perimeter of 165 cm."

a + b + c = 165

"the first side is 65cm less than twice the second side."

a = 2b - 65

"the third side is 10cm less than the second side."

c = b - 10

Before we finish, I have to ask: Who writes problems like this??? Pointless problems like these are why kids don't like math! Ugh. Drives me crazy. It's a shame, because solving math problems really does have a certain satisfaction, once you learn how. [Okay. I'm done. Back to the problem.]

If we could get this to have only one variable, we could solve it. Substitution to the rescue!

a + b + c = 165 (rewrote equation from above)

(2b - 65) + b + (b - 10) = 165 (substituted "a" and "c" from equations above)

See how that works? Let's solve it.

2b - 65 + b + b - 10 = 165 (dropped the parentheses, because there was nothing to distribute, not even a minus sign)

4b - 75 = 165 (combined like terms)

4b = 240 (added 75 to both sides)

b = 60 (divided both sides by 4)

We found the second side! We can find the first and third sides using those equations from above:

a = 2b - 65

a = 2*60 - 65

a = 120 - 65

a = 55

c = b - 10

c = 60 - 10

c = 50

All done.

Answer: The are of square 3 is 9cm

the area of square = a^2

= 3 ^2 = 9

Step-by-step explanation:

Answer:

In this problem, I can not tell what is V, so I will answer it in a general way.

A polynomial is something of the form:

a*x^5 + b*x^4 + c*x^3 + d*x^2 + e*x + f

a, b, c, d, e, and f are real numbers and constant.

Where the degree of the polynomial is equal to the greatest power (in this case 5).

You write:

4x^2 + 3Vx + 5

Now, if V is a real number, then we have that this is a polynomial of degree 2.

Because we can write this as:

4*x^2 + (3V)*x + 5

So the answer is true.

Now, if V is a variable or an operation, the answer will be false.

Answer:

\(-9x-10y\)

Step-by-step explanation:

\(10yi^2-9x \\ \\ =10y(-1)-9x \\ \\ =-9x-10y\)

Answer:

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line -3x-4y-9 = 0 and calculate its properties. Graph of a Straight Line : Calculate the Y-Intercept : Notice that when x = 0 the value of y is 9/-4 so this line "cuts" the y axis at y=-2.25000. y-intercept = 9/-4 = -2.25000.

Step-by-step explanation:

Find the X and Y Intercepts 3x-4y=9. 3x − 4y = 9 3 x - 4 y = 9. Find the x-intercepts. Tap for more steps... To find the x-intercept (s), substitute in 0 0 for y y and solve for x x. 3 x − 4 ⋅ 0 = 9 3 x - 4 ⋅ 0 = 9. Solve the equation. Tap for more steps... Simplify 3 x − 4 ⋅ 0 3 x - 4 ⋅ 0.

Answer:

1

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

if i am not wrong i think it is 1 bc u can only cut a verticle line in the middle, then i dont see any other ways.

The athlete that has the shortest training ride is athlete A.

The athlete that has the shorter range is Athlete B.

The athlete that has the greater median is Athlete B.

The athlete that has the greater IQR is  athlete A.

A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. the two lines are known as whiskers. The first whisker represents the minimum number and the second whisker represents the maximum number. The difference between the whiskers is known as range.

Range of Athlete A = 36 - 13 = 13

Range of Athlete B = 30 - 19 = 11

Training ride of  Athlete A = 16

Training ride of  Athlete B = 21

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.

Median of  Athlete A = 20

Median of  Athlete B = 25

IQR of  Athlete A = 30 - 16 = 14

IQR of  Athlete B = 28 - 21 = 7

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Answer:

B

Step-by-step explanation:

Answer:

In the longer rectangle

length=5+4+5=14cm

breadth=4

Area=l×b

or, A=14×4

or, A=56cm^

Also,

In the shorter rectangle

length=4cm

breadth=3

Area=l×b

or, A=4×3

or, A=12cm^2

At last,

Total Area=12+56

or, Total Area=68cm^2

Answer:

\(17.3\:\mathrm{m}\)

Step-by-step explanation:

The circumference of a circle is given by \(C=2r\pi\), where \(r\) is the radius of the circle.

By definition, the radius is equal to half the diameter. Therefore, a circle with a diameter of 5.5 meters has a radius of \(5.5\cdot \frac{1}{2}=2.75\) meters.

Thus, the circumference of the silo must be:

\(C=2\cdot 2.75\cdot \pi=17.2787595947\approx \boxed{17.3\:\mathrm{m}}\)(rounded to one decimal place as requested by question).

*Units for circumference should be in the same units as the radius/diameter is given in, since the circumference just refers to the perimeter of a circle.

**Your work for question 2 should include an equals sign, not an addition sign, between the part where you're adding the sevens and multiplying them: \(\implies 7+7+7+7+7+7\boxed{=}7\cdot 6\)

Based on the properties of similar triangles, the two true statements are:

In Mathematics, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Based on the properties of similar triangles, we have the following points:

In this scenario, we can can logically deduce that the two true statements are:

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Answer: B, D

Step-by-step explanation: AXC-CXB, ACB-AXC

Weighing using a tared container is not appropriate due to the potential for errors and inaccuracies. This method can impact the results by introducing uncertainties in the measurements.

Using a tared container involves placing the substance to be weighed on a container that has already been weighed and then subtracting the weight of the container to obtain the weight of the substance alone. While this method is commonly used for qualitative analysis or when the accuracy requirements are not strict, it is not suitable for quantitative preparation where precise measurements are essential.

The use of a tared container introduces several potential sources of error. First, the accuracy of the tare weight might not be exact, leading to uncertainties in subsequent measurements. Additionally, the tare weight may change over time due to factors like evaporation or contamination, further affecting the accuracy of subsequent measurements. Moreover, the process of transferring the substance to the tared container introduces the risk of loss or gain of material, leading to errors in the final measurements.

Overall, relying on weighing with a tared container for quantitative preparation can result in inaccurate quantities of the substance being weighed, compromising the reliability and reproducibility of experimental results. Therefore, more precise weighing techniques, such as using calibrated weighing balances or analytical techniques, should be employed for quantitative preparations.

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When Kati and Mateo remove all 24 face cards from the 2 decks of cards each with 52 cards, they use the remaining 80 cards to play the game.

Therefore the answer is 80.

Number of decks of cards is 2 and each deck has 52 cards. Therefore total number of cards they initially have is

= 2 × 52

= 104

So they take 104 cards in the starting to play the game.

They remove all 24 face cards. So the number of cards remaining is given by

= 104 - 24

= 80

So they use 80 cards for playing the game.

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It takes 40 seconds (400 / 10) for the entire caravan to line up before the second toll booth.

It takes 100 seconds (20 * 5) for the entire caravan to receive service at the first toll booth.

Assuming that the cars line up at the second toll booth right after receiving service at the first toll booth, the time it takes for the entire caravan to line up before the second toll booth depends on the speed of the cars.

Since the speed of the cars is 10 kilometers per second, in the 100 seconds it takes for the entire caravan to receive service at the first toll booth, the entire caravan travels a distance of 1000 kilometers (100 * 10).

Since the distance between the first and second toll booths is 400 km, it takes 40 seconds (400 / 10) for the entire caravan to line up before the second toll booth.

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It takes 40 seconds (400 / 10) for the entire caravan to line up before the second toll booth.

It takes 100 seconds (20 * 5) for the entire caravan to receive service at the first toll booth.

Assuming that the cars line up at the second toll booth right after receiving service at the first toll booth, the time it takes for the entire caravan to line up before the second toll booth depends on the speed of the cars.

Since the speed of the cars is 10 kilometers per second, in the 100 seconds it takes for the entire caravan to receive service at the first toll booth, the entire caravan travels a distance of 1000 kilometers (100 * 10).

Since the distance between the first and second toll booths is 400 km, it takes 40 seconds (400 / 10) for the entire caravan to line up before the second toll booth.

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A - 0 would be 0mins B - 1 would be 2.5mins C - 2 would be 5mins D - 3 would be 7.5mins E - 4 would be 10mins

Step-by-step explanation:

every 2 questions equals 5 minutes. so 0 questions would obv be 0 mins 1 question would be half of 5 mins which would be 2.5 and so on

The estimated area under the graph of f(x) = 4cos(x) from x = 0 to x = π/2 is approximately equal to π.

What is the area of the rectangle?

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

To estimate the area under the graph of f(x) = 4cos(x) from x = 0 to x = π/2, we can use numerical methods such as the midpoint rule or the trapezoidal rule.

Let's use the trapezoidal rule to estimate the area. The formula for the trapezoidal rule is given by:

∫(a to b) f(x) dx ≈ (b - a) * [(f(a) + f(b)) / 2],

where a and b are the limits of integration.

In this case, a = 0 and b = π/2. Substituting the values into the formula, we get:

∫(0 to π/2) 4cos(x) dx ≈ (π/2 - 0) * [(4cos(0) + 4cos(π/2)) / 2]

                            = (π/2) * [(4(1) + 4(0)) / 2]

                            = (π/2) * (4/2)

                            = (π/2) * 2

                            = π.

Therefore, the estimated area under the graph of f(x) = 4cos(x) from x = 0 to x = π/2 is approximately equal to π.

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The probability that a sample of 33 randomly selected adults in the US has a mean weight greater than 151.52 lbs is:

38.21%.

To find the probability that a sample of 33 randomly selected adults in the US has a mean weight greater than 151.52 lbs, we need to use the Central Limit Theorem. Assuming that the population standard deviation is known or the sample size is large enough (greater than or equal to 30), the distribution of the sample means will be approximately normal.

First, we need to calculate the standard error of the mean (SEM) using the formula:

SEM = standard deviation / square root of sample size

Let's assume that the population standard deviation is 30 lbs (this is just an estimate) and the sample size is 33. Then,

SEM = 30 / sqrt(33) = 5.22 lbs

Next, we need to calculate the z-score using the formula:

z = (sample mean - population mean) / SEM

Let's assume that the population mean is 150 lbs (again, just an estimate). Then,

z = (151.52 - 150) / 5.22 = 0.30

Finally, we can use a standard normal distribution table or calculator to find the probability that the z-score is greater than 0.30. This is equivalent to finding the area under the standard normal curve to the right of 0.30. Using a standard normal distribution table or calculator, we find that the probability is approximately 0.3821 or 38.21%.

Therefore, the probability that a sample of 33 randomly selected adults in the US has a mean weight greater than 151.52 lbs is approximately 38.21%.

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The lower limit of a 95% confidence interval for the population means would be Option B. approximately 176.

To calculate the confidence interval, we need to use the formula:

Confidence interval = sample mean ± (critical value) x (standard error)

The critical value can be found using a t-distribution table with degrees of freedom (df) equal to n-1, where n is the sample size. For a 95% confidence level with 99 degrees of freedom, the critical value is approximately 1.984.

The standard error is calculated as the sample standard deviation divided by the square root of the sample size. In this case, the standard error would be:

standard error = 20 / sqrt(100) = 2

Therefore, the confidence interval would be:

confidence interval = 180 ± (1.984) x (2) = [176.07, 183.93]

Since we are looking for the lower limit, we take the lower value of the interval, which is approximately 176.

In other words, we can say that we are 95% confident that the true population means falls within the interval of [176.07, 183.93].

Therefore, Option B. Approximately 176 is the correct answer.

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Answer:

D. y=3x+15

Step-by-step explanation:

find the slope

\(\frac{1-(-5)}{-3-(-1)} =3\)

y=mx+b

plug in known values

3=3(-4) + b

b=15

y=3x+15

The value that will always be within the upper and lower limits of a confidence interval for the question is the sample mean.

To explain this step-by-step:

First, you collect a sample from the population you want to study.

Next, you calculate the sample mean, which is the average of all the data points in your sample.

Then, you determine the standard deviation of the sample, which measures the dispersion of the data points around the sample mean.

After that, you choose a desired level of confidence (e.g., 95%) to estimate the range within which the true population mean is likely to fall.

Finally, you calculate the confidence interval using the sample mean, the standard deviation of the sample, and the sample size. The confidence interval provides a range of values within which the population mean is likely to be found with a certain level of confidence.

Since the confidence interval is constructed around the sample mean, the sample mean will always be within the upper and lower limits of the confidence interval. In contrast, the sample size, standard deviation of the sample, and population mean are not guaranteed to be within the confidence interval.

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The three values (60, 62, and 84) are identified as outliers for the age group 40 years to 50 years is D. Only 60 and 84 are identified as outliers

we need to use the same method as for the age group 20 years to 30 years.

The interquartile range (IQR) for the age group 40 years to 50 years is calculated as follows:

Q3 - Q1 = 76 - 70 = 6

To identify outliers, we consider values that are either 1.5 times the IQR greater than the upper quartile (Q3 + 1.5 * IQR) or 1.5 times the IQR less than the lower quartile (Q1 - 1.5 * IQR).

For the age group 40 years to 50 years:

Upper limit = Q3 + 1.5 * IQR = 76 + 1.5 * 6 = 85

Lower limit = Q1 - 1.5 * IQR = 70 - 1.5 * 6 = 61

Now let's compare these limits with the three values:

60 is less than the lower limit (61), so it is considered an outlier.

62 is between the lower and upper limits, so it is not considered an outlier.

84 is greater than the upper limit (85), so it is considered an outlier.

Therefore, the values identified as outliers for the age group 40 years to 50 years are 60 and 84. The value 62 is not considered an outlier.

The correct answer is (D) Only 60 and 84 are identified as outliers.

By applying the same method of identifying outliers based on the 1.5 times IQR rule, we can determine which values fall outside the acceptable range for each age group. Therefore, Option D is correct

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The coordinates of the vertices after a reflection over the line x = 2.

D = (8, 5)

E = (6, 5)

F = (4, 8)

G = (7, 8)

There are two ways of translation.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

The coordinates:

D = (-4, 5)

E = (-2, 5)

F = (0, 8)

G = (3, 8)

The line x = 2.

We count the units from the line x = 2.

After the reflection, the number of units of each coordinate from the line

x = 2 must be equal to the number of units from the line x = 2 before the reflection.

Thus,

The reflected coordinates of the vertices are:

D = (8, 5)

E = (6, 5)

F = (4, 8)

G = (7, 8)

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1 liter would water 6/7 of the garden plus 1/6 of a liter to water all off the garden. 1 1/6 liters.

Tthe temperature first reaches 42 degrees 7.67 hours after midnight, or approximately at 7:40 AM.

The temperature variation over a day can be represented as a sinusoidal function in the form of y = A sin(Bx - C) + D, where A is the amplitude, B is the frequency, C is the phase shift, and D is the vertical shift.

In this case, the midline of the temperature function is (33 + 57)/2 = 45 degrees. Therefore, D = 45.

The amplitude of the function is (57 - 33)/2 = 12 degrees. Therefore, A = 12.

Since the average temperature first occurs at 10 AM, which is 10 hours after midnight, the phase shift can be determined as C = (10/24) * 2π.

To find the frequency B of the function, we need to use the fact that the temperature function repeats every 24 hours. Therefore, B = 2π/24 = π/12.

Putting all the values in the equation y = 12 sin(π/12(x - 5/3)) + 45, we need to solve for x when y = 42.

42 = 12 sin(π/12(x - 5/3)) + 45

-3 = 12 sin(π/12(x - 5/3))

-1/4 = sin(π/12(x - 5/3))

π/2 = π/12(x - 5/3)

x - 5/3 = 6

x = 23/3

Therefore, the temperature first reaches 42 degrees 7.67 hours after midnight, or approximately at 7:40 AM.

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Answer:

see explanation

Step-by-step explanation:

Since BD bisects ∠ ABC , then

∠ ABD = ∠ DBC , substitute values

3x + 4 = 55 ( subtract 4 from both sides )

3x = 51 ( divide both sides by 3 )

x = 17

Step-by-step explanation:

Statement                                          Reason

BD bisects ∠ABC                              Given

m∠ABD = (3x + 4)°, m∠DBC = 55°    Given

∠ABD ≅ ∠DBC                                  Definition of angle bisector

3x + 4 = 55                                         Definition of congruence

3x = 51                                                Subtraction property

x = 51/3                                               Division property

x = 17                                                   Proved