The decay of 249 mg of an isotope is given by A=249e−0.015t , where t is time in years. Find the amount after 43 years.

Answer:

a=2.4

b=13.9

c= -8.1

Step-by-step explanation:

a= 3-0.6= 2.4

b= 12.5-(-1.4)= 13.9

c= -5.2-2.9= -8.1

Step-by-step explanation:

b^2=4ac

b= -26, a=1, c=?

-26^2=4*1*c

676=4c

c=676/4

c=169

Therefore, probability solution is estimating this likelihood without additional data or analysis is inappropriate correct response is option a.

The main goal of the mathematical branch known as statistical inference is to estimate the likelihood that a statement is accurate or that a particular event will take place. Any number among 0 and 1, where 1 typically denotes confidence and 0 typically denotes possibility, can be used to symbolise chance. A probability diagram illustrates the likelihood that a particular occurrence will take place.

Here,

Because of the skewed demographic distribution, the right response is (a).

We could use the normally distributed to compute probabilities because the length of adult American ladybirds is distributed normally with a known standard deviation. The normal distribution may not, however, correctly depict the distribution of ladybird lengths in the population due to the skewed population distribution.

Furthermore, even if the difference between the actual community mean and the assumed mean of 1 cm is tiny, the given size of the population of 440000 could result in a statistically significant outcome.

However, because the assumption of normality may not hold true, this does not imply that we can accurately determine the likelihood of a random ladybird in Raleigh being larger than 1.5 centimetres.

Therefore, estimating this likelihood without additional data or analysis is inappropriate.

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The number of bottles requires to pour the water into is gotten by dividing the total capacity of water by the capacity of the bottle

Answer = 10 bottles

Given Data

Let us find the number of bottle required

No of bottles = Total Capacity of the two bottle/Capacity of the small bottles

No of bottles =  51/5

No of bottles =10.2

10 approx.

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The correct answer is c. marginal; average total; minimum. When plotting marginal and average cost curves, the marginal cost curve intersects the average total cost curve at its minimum point.

This is because the average total cost curve is U-shaped, with a downward-sloping portion at low levels of output and an upward-sloping portion at high levels of output. The marginal cost curve intersects the average total cost curve at the point where the upward-sloping portion of the average total cost curve starts, which is also the point where the average total cost curve is at its minimum. At this point, the marginal cost is equal to the average total cost.

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We are given two rational expressions: one with (y² - 13y + 36) in the numerator and (y² + 2y – 3) in the denominator, and the other with (y² - y – 12) in the numerator and (y² - 2y + 1) in the denominator. We need to simplify these rational expressions.

Simplifying the first rational expression:
The numerator of the first expression, y² - 13y + 36, can be factored as (y – 4)(y – 9).
The denominator, y² + 2y – 3, can be factored as (y + 3)(y – 1).
Therefore, the first rational expression simplifies to (y – 4)(y – 9) / (y + 3)(y – 1).

Simplifying the second rational expression:
The numerator of the second expression, y² - y – 12, can be factored as (y – 4)(y + 3).
The denominator, y² - 2y + 1, can be factored as (y – 1)(y – 1) or (y – 1)².
Therefore, the second rational expression simplifies to (y – 4)(y + 3) / (y – 1)².

By factoring the numerator and denominator of each rational expression, we obtain the simplified forms:

First rational expression: (y – 4)(y – 9) / (y + 3)(y – 1)
Second rational expression: (y – 4)(y + 3) / (y – 1)²

These simplified expressions are in their simplest form, with no common factors in the numerator and denominator that can be further canceled.


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Given the triangle:

The Pythagorean Theorem states that:

From the figure, we identify:

Now, using the Pythagorean Theorem:

The rate at which the water level is rising when the water level is 6 cm is approximately 2.67 cm/s. if an inverted pyramid is filled with water at a constant rate of 55 cubic centimeters per second, the top of pyramid is in square shape with length of 8 cm and height of 14 cm.

Let's call this rate "r".

Volume of pyramid = (1/3) * base area * height

Since the pyramid has a square base, the base area is given by

Base area = (side length)^2

Substituting the given values

Base area = (8 cm)^2 = 64 cm^2

Height = 14 cm

V = (1/3) * 64 cm^2 * 14 cm = 298.67 cm^3

We know that the water is being added to the pyramid at a constant rate of 55 cm^3/s. Therefore, the rate at which the volume is increasing is

dV/dt = 55 cm^3/s

We also know that the volume of water in the pyramid at any given time is given by

V_water = (1/3) * base area * h_water

where h_water is the height of the water at that time.

To find the rate at which the water level is rising (r), we need to find dh_water/dt. We can do this by taking the derivative of both sides of the equation for V_water with respect to time

dV_water/dt = (1/3) * base area * dh_water/dt

Substituting the known values

dV_water/dt = (1/3) * (8 cm)^2 * dh_water/dt

dV_water/dt = (64/3) cm^2 * dh_water/dt

dh_water/dt = 3 * dV_water/dt / 64

dh_water/dt = 3 * 55 cm^3/s / 64 = 2.67 cm/s

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Answer:

300/1

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

2700÷9=300

so,he have to pay 300 per month.

The mean number of tomatoes for the Ultra Boy tomato plant is calculated by adding up all the quantities and dividing by the total number of plants, which is 10 in this case. So, the mean is (32+46+51+43+42+56+28+41+39+53)/10 = 43.1 tomatoes per plant.

To find the median number of tomatoes, we need to first arrange the quantities in numerical order: 28, 32, 39, 41, 42, 43, 46, 51, 53, 56. The median is the middle number in this list, which is 43.

Therefore, the median number of tomatoes for the Ultra Boy tomato plant is 43.

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You cannot solve it because you do not know what x and y are for the parallel line. which is the correct answer would be option (B).

We have to find out the y-intercept of the line that is parallel to y = 0.5x - 2,

As per the given options,

Since the parallel line goes through point (3, 0) substitute 3 for x and 0 for y and solves for b, the y-intercept.

This is not the correct answer.

You cannot solve it because you do not know what x and y are for the parallel line.

This is the correct answer.

Since the parallel line goes through the point (3, 0) substitute 0 for x and 3 for y and solve for b, the y-intercept.

This is not the correct answer.

Therefore, You can't solve it since you don't know what the parallel line's x and y coordinates are.

Hence, the correct answer would be option (B).

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Answer:

m = -5

Step-by-step explanation:

The equation is y= mx + b

m =  the slope

b = y-intercept

Our equation is y = -5x + 18

The slope is -5

So, our answer is m = -5

Answer: -5

Step-by-step explanation:

         This equation is given to us in slope-intercept form, meaning we can see the slope easily. Slope-intercept equations are written in y = mx + b form. The slope is the m value, which is -5 here.

The expanded form of 0.68 is written as 0 x 1 + 6 x 0.1 + 8 x 0.01.

To express decimal numbers in their expanded form simply means writing each number according to its place value. It can be done by multiplying each digit of the decimal by its place value and adding it all together.

Given the decimal 0.68 or sixty eight hundredths in words, first, multiply the digit 0 by its place value, which is 1.

0 x 1

Multiply the digit 6 by its place value, which is 0.1.

6 x 0.1

Multiply the digit 8 by its place value, which is 0.01.

8 x 0.01

Add it all together.

0 x 1 + 6 x 0.1 + 8 x 0.01

Hence, the expanded for of the decimal 0.68 is written as 0 x 1 + 6 x 0.1 + 8 x 0.01.

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(a) The interpret the p-value in context of 0.0016 indicates that the probability of obtaining a sample mean hemoglobin level of 11.3 g/dl or lower.

(b) The conclusion would make if a 0.05 is rejected because the p-value (0.0016) is less than the significance level.

If using a significance level of 0.01, the null hypothesis would still be rejected because the p-value is less than 0.01.

(a) The p-value of 0.0016 indicates that the probability of obtaining a sample mean hemoglobin level of 11.3 g/dl or lower, assuming that the true population mean is 12 g/dl (or higher), is only 0.0016. This suggests that the observed difference between the sample mean and the hypothesized population mean is statistically significant and unlikely to be due to chance alone.

(b) If using a significance level of 0.05, the null hypothesis (that the true population mean is 12 g/dl or higher) would be rejected because the p-value (0.0016) is less than the significance level. Therefore, it can be concluded that the sample provides evidence that the true population mean hemoglobin level is lower than 12 g/dl.

If using a significance level of 0.01, the null hypothesis would still be rejected because the p-value is less than 0.01. In this case, the evidence is even stronger, and the conclusion that the true population mean is lower than 12 g/dl would be even more robust.

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The number 32 can be written as a power with a base of 2 as 2^5

The index form of a number is defined as that number represented as an exponential expression, or even a single number raised to another number.

Example;

2^n

3^3

From the information given, we have to determine the index form of 32

It is expressed in the base of 2 as;

32 = 2 × 2 × 2 × 2 × 2

32 = 2^5

Thus, the number 32 can be written as a power with a base of 2 as 2^5

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Answer:

The answer will be A because you start at 4 and in between 4 and 5 you will go up to 7 and that will be your answer

Answer:

The answer is B

Step-by-step explanation:

The distance traveled by the particle during the time interval is 17.17 meters.

To find the displacement of the particle during the time interval, we need to integrate the velocity function:

∫v(t)dt = ∫(t^2 - t)dt = (1/3)t³ - (1/2)t² + C

We don't know the constant of integration, but it doesn't matter for finding the displacement, as we're only interested in the difference between the endpoints of the interval. Let's evaluate this expression at the endpoints of the interval:

(1/3)(5³) - (1/2)(5²) = 41.67

(1/3)(2²) - (1/2)(2²) = 1.17

The displacement of the particle during the time interval is the difference between these two values:

41.67 - 1.17 = 40.5 meters

To find the distance traveled by the particle during the time interval, we need to take the absolute value of the velocity function and integrate it:

∫|v(t)|dt = ∫|t² - t|dt

The velocity function changes sign at t=0 and t=1, so we need to split the integral into three parts:

∫|v(t)|dt = ∫(t²- t)dt, 0 ≤ t ≤ 1
            = ∫(t - t^²)dt, 1 ≤ t ≤ 2
            = ∫(t^² - t)dt, 2 ≤ t ≤ 5

Evaluating each of these integrals, we get:

(1/3) - (1/2) = -1/6
(3/2) - (7/6) = 1/3
(41/3) - (7/2) = 16.17

The distance traveled by the particle during the time interval is the sum of the absolute values of these values:

|(-1/6)| + (1/3) + (16.17)| = 17.17 meters.

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Answer:

y=1/2x-5

Step-by-step explanation:

From the picture you can see that (0, -5) is a point on the function and that (2, -4) is another point. Using these you can find the slope of the function with the equation

\((y_{2} -y_{1})/(x_{2}-x_{1} )\)

We can substitute in the points so it looks like

\((-4--5)/(2-0)\)  or  \(1/2\) which is the slope of the function

Now, since the y-intercept is (0, -5) on the graph, the b part in the slope-intercept form of the equation would be -5, leaving us with the equation y=1/2x-5

The assumption about normality is investigated by looking at a qq plot in a t-test. Therefore, the answer is e. normality assumption.

The qqplot helps to assess whether the sample data are normally distributed, which is an important assumption for the t-test to be valid. If the data deviate significantly from normality, then the t-test results may not be reliable.

Therefore, by examining a QQ plot, one can determine whether the data deviate from normality. If the data points in the QQ plot fall close to the diagonal line, it indicates that the data are normally distributed. If the points deviate from the diagonal line, it suggests that the data may not be normally distributed, and further investigation or alternative statistical tests may be necessary.

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There are a total of 15,504 different groups of five students that could be selected for the competition from the 20 students in the math club.

To arrive at this answer, we can use the combination formula, which is given by:

nCk = n! / (k! * (n-k)!)

where n is the total number of students in the math club (20), and k is the number of students selected for the competition (5).

Substituting these values into the formula, we get:

20C5 = 20! / (5! * (20-5)!) = 15,504

Therefore, there are 15,504 different groups of students that could be selected for the competition.

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71 citizens should be included in the sample to estimate the mean age of the citizens living in your community at a 98% level of confidence.

We need to find out the sample size of citizens that should be included in the sample to estimate the mean age of the citizens living in your community at a 98% level of confidence.

The formula for the Margin of error is

E: E = Zc/2 * (σ/√n)

Where E is the margin of error Zc/2 is the Z-value for the level of confidence cσ is the population standard deviation is the sample size.

So the formula for the sample size n is: n = (Zc/2 / E)² * σ²

We have Zc/2 = Z0.02/2 = Z0.01 = 2.33 (using z-table) σ = 22 years

E = 3 years

n = (2.33 / 3)² * 22²

n ≈ 70.36 ≈ 71 (rounded up)

Therefore, 71 citizens should be included in the sample to estimate the mean age of the citizens living in your community at a 98% level of confidence.

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Answer:

1cm³

Step-by-step explanation:

You do not need a calculator for this.

The formula for the volume of a rectangular prism is:

Length × Width × Height = Volume

If we substitute our numbers in:

5/4 × 4/3 × 3/5 = 1cm³

All you need to do is multiply across.

5 × 4 × 3 = 60

4 × 3 × 5 = 60

The numerator and denominator both equal 60. So the fraction would look like this if you were to keep it as a fraction.

60/60

Answer: A and E

Step-by-step explanation:

We have here four linear functions, and we have to compare the slopes of them as well as their y-intercept. For this, it is important to remember the general equation for the line in the slope-intercept form:

Where

• m is the slope of the line

• b is the y-intercept of the line (0, b)

The y-intercept is the point where the line passes through the y-axis, and at this point, we have that x = 0.

We have in this case that the function passes through the points:

• (0, 5), (1, 1)

We can find the equation of this line using the two-point form of the line equation:

Using the points above, we can label them as follows:

• (0, 5) ---> x1 = 0, y1 = 5

• (1, 1) ---> x2 = 1, y2 = 1

Then we have:

Therefore, the slope for this line is m = -4, and the y-intercept is (0, 5).

For Function 2 we need to do the same procedure as before. We have to select two points of the function to find its equation:

We can select the following points: (0, 1), (1, 6).

Then we can proceed as we did in the previous part:

• (0, 1) ---> x1 = 0, y1 = 1

• (1, 6) ---> x2 = 1, y2 = 6

Therefore, the slope in Function 2 is 5, m = 5, and the y-intercept is (0, 1).

We can see that Function 3 has already its line equation in slope-intercept form:

Then the slope for Function 3 is m = -1, and its y-intercept is (0, -2).

From the question, we have:

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\(b. {b}^{m} = {b}^{1 + m} \)

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