Once ingested the presence of a certain vitamin supplement in the blood stream decreases exponentially over time. suppose a person takes 4 milligrams of the supplement. the amount of supplement remaining in the persons bloodstream x hours after taking it is given by the function g(x)=4(0.6)^x

L = lenght = 4w + 7

W = width

Perimeter = 2L + 2W

74 = 2 (4W + 7 ) + 2 W

74 = 8W + 14 + 2 W

74 = 10W + 14

74-14 = 10W

60 = 10W

60/10 = W

6 = W

L = 4W + 7

L= 4(6) +7

L= 24+7

L= 31

Answer:

Lenght = 31 inches

Width = 6 inches

Answer:

6

Step-by-step explanation:

4x + 8y = 16

4x = 16 - 8y

4x = 4 (4 - 2y)

x = 4( 4 - 2y)/4

X = 4 - 2y

X = -2y + 4

Answer:

m is -3/2

c is -5/2

Step-by-step explanation:

The standard linear equation is given by;

\({ \tt{y = mx + c}}\)

» m is the slope and c is the y-intercept

Then, our slope is;

\( { \tt{2y + 3x = - 5 }} \\ \\ { \tt{2y = - 3x- 5}} \\ \\ { \tt{y = - \frac{3}{2}x - \frac{5}{2} }}\)

Therefore, according to the squeeze theorem, the limit of x^2 cos(1/x^2) as x approaches 0 is also 0: lim(x→0) x^2 cos(1/x^2) = 0.

To prove that lim(x→0) x^2 cos(1/x^2) = 0, we can use the squeeze theorem.

First, we establish the following inequalities:

-1 ≤ cos(1/x^2) ≤ 1

Since -1 ≤ cos(1/x^2) ≤ 1 for all values of x, we can multiply each side of the inequality by x^2 to obtain:

-x^2 ≤ x^2 cos(1/x^2) ≤ x^2

Now, we need to evaluate the limits of the lower and upper bounds as x approaches 0:

lim(x→0) -x^2 = 0

lim(x→0) x^2 = 0

Since both lower and upper bounds approach 0 as x approaches 0, we can conclude that the function x^2 cos(1/x^2) is "squeezed" between these two functions.

Thus, the statement is proven.

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Answer:

here is your aneswer

the answer. will be 40

Answer:

see the attached  picture

Step-by-step explanation:

To solve for x, we just need to compute the inverse of A (if it exists) and multiply it by b. If A is invertible, then this method will give us the unique solution to the linear system Ax=b.

To solve a linear system of the form Ax=b using inverse matrices, we can first find the inverse of matrix A (if it exists) and then multiply both sides of the equation by \(A^-1\), giving us:

\(A^-1Ax = A^-1b\)

Since\(A^-1A\) is the identity matrix I, we can simplify the left-hand side to just x:

\(x = A^-1b\)

However, it's worth noting that computing the inverse of a matrix can be computationally expensive, particularly for large matrices.

So, while using inverse matrices can be a useful technique for solving small systems, it may not be the most efficient approach for larger systems. In those cases, other techniques such as Gaussian elimination or LU decomposition may be more appropriate.

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The total number of red marbles in the vase are 10.

A ratio is described as a comparison between two amounts with the same unit to determine the amount of 1 quantity is contained in the other. Ratios are divided into two sorts.

The first is a part-to-part ratio, and the second is a part-to-whole ratio. The part-to-part ratio expresses the relationship between 2 separate entities or groupings.

Now, according to the question;

Let 'x' be the red marbles in the vase.

Let 'y' be the orange marbles in the vase.

The total number of marbles in the vase are 60

x  + y = 60 (equation 1)

The ratio of red marbles to orange ones is 1:5.

Thus, x/y = 1/5

cross multiplying;

5x = y

or y = 5x

substitute the value of y in equation 1;

x  + y = 60 (equation 1)

x  + 5x = 60

6x = 60

x = 10  (red marbles)

Thus, the number of red marbles in the vase are 10.

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If area of "square-field" is 40000 ft square, and Mr. Blackburn is putting a fence diagonally in field, then the length of fence be is 282.84 ft.

The area of the square-field is = 40000 ft²,

We equate this with area formula,

We get,

⇒ (side)² = 40000,

⇒ side = 200,

substituting the side-length as 200 ft, in the diagonal formula,

we get,

⇒ Length of diagonal of field is = (side)√2,

⇒ Length of diagonal of field is = (200)√2,

⇒ Length of diagonal of field is ≈ 282.84 ft.

Therefore, the length of the fence of the field is 282.84 ft.

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Answer: 12 people

Step-by-step explanation:

insert 12 where the "x" is and type in the full equation into a calculator, and you will get 17.5

The regression equation for predicting Y from X based on the given data is Y = 3.5X + 13. The SSresidual is 56.125, and the standard error of estimate for the equation is approximately 4.73.

To find the regression equation for predicting Y from X, we can use the least squares method. By fitting a line to the data points, we determine the equation in the form of Y = aX + b, where 'a' is the slope and 'b' is the y-intercept. Using the given data points (X, Y), we can calculate the regression equation. The calculations result in the equation Y = 3.5X + 13, indicating that for every unit increase in X, Y is expected to increase by 3.5 units.

To calculate the Pearson correlation coefficient, we need to determine the strength and direction of the linear relationship between X and Y. The Pearson correlation coefficient ranges from -1 to +1, where +1 represents a perfect positive correlation, 0 indicates no correlation, and -1 indicates a perfect negative correlation. In this case, the Pearson correlation coefficient is calculated as 0.819, suggesting a strong positive correlation between X and Y.

Using the residuals (the differences between the actual Y values and the predicted Y values from the regression equation), we can calculate the sum of squares of the residuals (SSresidual). By using the rand SSy (the sum of squares of the Y deviations from their mean), we can calculate SSresidual as 56.125. The standard error of estimate for the equation is a measure of the average distance between the predicted Y values and the actual Y values. In this case, it is approximately 4.73. These values provide insights into the accuracy and precision of the regression equation in predicting Y based on X.

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(a) The eccentricity of the conic is 3/2.

(b) The equation of the conic is parabola.

(c) The equation of the directrix is, x = 5/3.

(d) The sketch of the graph of the given equation is given below.

Given that the polar conic equation is given by,

r = 5/( 2 + 3 sin θ )

The general form of eccentricity is,

r = ed/( 1 + e sin θ )

So simplifying the equation of polar conic equation we get,

r = 5/( 2 + 3 sin θ )

r = 5/[2 (1 + 3/2 sin θ)]

r = (5/2)/[1 + 3/2 sin θ]

r  = [(5/3) (3/2)]/[1 + 3/2 sin θ]

So, e = 3/2 and d = 5/3

So, e = 3/2 > 1. Hence equation of the conic is parabola.

The equation of the directrix is,

x = d

x = 5/3.

The graph of the curve is given by,

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The General Adaptation Syndrome model, people are most susceptible to diseases and infections when they are in the exhaustion stage.

During the exhaustion stage of the General Adaptation Syndrome, the body's stress response system becomes overwhelmed. Initially, when a person encounters a stressor, the body activates the alarm stage, followed by the resistance stage, where it attempts to adapt and cope with the stress. However, if the stressor persists or the person is unable to adequately recover, the body enters the exhaustion stage. In this stage, the body's resources, such as energy, hormones, and immune responses, become depleted. The prolonged activation of the stress response system weakens the immune system, making individuals more susceptible to diseases and infections. Additionally, the body's ability to repair and regenerate tissues is compromised, further increasing the risk of health issues.

In summary, the exhaustion stage of the General Adaptation Syndrome model is when individuals are most vulnerable to diseases and infections. Prolonged exposure to stress and inadequate recovery can deplete the body's resources and weaken the immune system, making it more difficult for the body to fight off illnesses effectively.

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Answer: -1

Step-by-step explanation:

\(\frac{-1}{2}\) is greater than -1 as it is closer to 0

\((2)-1=-2\)

-1 is greater than -2 as -1 is closer to 0

\(-1+(-1)^2\\-1+1\\0\)

The sum of -1 and its square is 0

We can conclude that the dilated triangle abc is similar to the original triangle ABC with a dilation factor of 3,

Dilation is a transformation that performs a proportional resize of a figure. It changes the size of the figure while maintaining its shape and orientation. To dilate triangle ABC to create triangle abc, we can multiply the coordinates of each vertex of ABC by a dilation factor of 3.

The coordinates of the vertices of the original triangle ABC are A(-3,-3), B(3,3), and C(0,3). Multiplying each coordinate by 3 gives the coordinates of the vertices of the dilated triangle abc : A(-9,-9), B(9,9), and C(0,9).

We can compare the two triangles to see how the dilation has affected them. The size of triangle abc is three times larger than that of triangle ABC. The shape and orientation of triangle abc are the same as that of triangle ABC. The vertices of the dilated triangle, abc, are located at three times the distance from the origin as the corresponding vertices of triangle ABC. That is why the coordinates of all vertices of triangle abc are three times the coordinates of the corresponding vertices of triangle ABC. since the triangle was resized proportionally and has the same shape and orientation.

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Answer:

Step-by-step explanation:

This is a probability question and we have to calculate the sample size.

given the sample size S= 30

3 rode a bike

7 drove a car

20 rode bus

The probability of selecting a person that will take a bus is

\(Pr(bus)= 20/30= 2/3\)

So to find any last digit of 3^2011 divide 2011 by 4 which comes to have 3 as remainder. Hence the number in units place is same as digit in units place of number 3^3. Hence answer is 7.

Answer:

3x² + 2x - 6+(x² - 4x + 10)

3x² + 2x - 6+x²-4x+10

3x²+x²+2x-4x-6+10

4x²-2x+4

Answer:

.53

Step-by-step explanation:

Answer:

0.5294 is a decimal and 52.94/100 or 52.94% is the percentage for 9/17.

It will take the town 21 years 4 months to reach 4600 in population

a rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

initial population = 3000

population increase every year = 2.5% of 3000

which is 2.5/100 x 3000 = 75

let the time taken to reach 4600 be d

increment for d number of years = 75d

Total population after d years is 75d + 3000

so 75d + 3000 = 4600

75d = 4600  - 3000

75d = 1600

d = 1600/75

d = 21.33 years which is 21 years 4 months

In conclusion 21 years 4 months is the time taken for the ton tto get tto 4600

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Answer:

k = \(\frac{2}{3}\)

Step-by-step explanation:

The equation of proportionality is

y = kx ← k is the constant of proportion

y = \(\frac{2}{3}\) x ← is in this form

with k = \(\frac{2}{3}\)

The length of the side BC is 12 units.

Two triangles are said to be similar if the ratio of their corresponding sides are in equal proportion and corresponding angles are also equal.

Given that, a right triangle ABC with altitude BD drawn to hypotenuse AC. and AC = 24 and DC = 6,

BD is the altitude, hence, it breaks Δ ABC into two similar triangles:

Therefore, Δ ABD ~ Δ BCD

Hence, The ratios of corresponding sides:

AD/BD = BD/DC ⇒ BD² = AD*DC ⇒ BD² = (24 - 6)*6 ⇒ BD² = 108

Also,

BC² = BD² + DC² ⇒ BC² = 108 + 6² = 144

BC = √144

BC = 12

Hence, the required length is 12 units.

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Answer:

y = 10x^2 + x +21

Step-by-step explanation:

The constant of proportionality of y and x in the graph is given as follows:

k = 3/4.

In a proportional relationship, the ratio between the output variable y and the input variable x is constant, and is called constant of proportionality, given as follows:

k = y/x.

A proportional relationship is a special case of a linear function, which has an intercept of zero, as is the case for the graph in this problem.

The marked point on the graph has the coordinates given as follows:

(4,3).

Meaning that the constant of proportionality of y and x in the graph is calculated as follows:

k = y/x = 3/4.

(division of the value of the y-coordinate by the value of the x-coordinate).

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Answer:

\(a_{n}\) = 2n - 3

Step-by-step explanation:

the nth term of an arithmetic sequence is

\(a_{n}\) = a₁ + d(n - 1)

where a₁ is the first term and d the common difference

given a₁ = - 1 and a₅ = 7 , then

a₁ + 4d = 7 , that is

- 1 + 4d = 7 ( add 1 to both sides )

4d = 8 ( divide both sides by 4 )

d = 2

then

\(a_{n}\) = - 1 + 2(n - 1) = - 1 + 2n - 2 = 2n - 3

\(a_{n}\) = 2n - 3

The probability that Anthony, Brian, and Chantal are in the same lab group today is approximately 0.8703, or about 87.03%.

There are 15 students in total, so there are 15 ways to choose the first student, 14 ways to choose the second student (since one has already been chosen), and 13 ways to choose the third student (since two have already been chosen). However, since the lab groups are identical, we need to divide by the number of ways to arrange the group of three students, which is 3! = 6. Therefore, the total number of ways to choose a group of three students is:

15 x 14 x 13

6

Simplifying this expression gives:

(15 x 14 x 13) / 6 = 455

There are 5 lab groups, and we want to find the probability that Anthony, Brian, and Chantal are all in the same group. There are 3 ways to choose which group they will be in, and then we need to choose 2 more students to join them, which can be done in:

12 x 11

2

ways, since there are 12 students remaining to choose from after we have chosen Anthony, Brian, and Chantal, and we need to choose 2 more students to join them. Therefore, the total number of ways that Anthony, Brian, and Chantal can be in the same group is:

3 x (12 x 11) = 396

Finally, we can calculate the probability by dividing the number of favorable outcomes (i.e., Anthony, Brian, and Chantal are in the same group) by the total number of possible outcomes:

P(Anthony, Brian, Chantal in same group) = 396 / 455

≈ 0.8703

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On average, a customer spends approximately 1.16 minutes waiting time on hold before they can start speaking to a representative.

To find the average waiting time for a customer on hold before they can start speaking to a representative, we need to consider both the arrival rate of calls and the average service time of the staff members.

Given:

9 staff members taking calls.

On average, one call arrives every 5 minutes (standard deviation of 5 minutes).

Each staff member spends on average 18 minutes with each customer (with a standard deviation of 27 minutes).

To calculate the average waiting time, we need to use queuing theory, specifically the M/M/c queuing model. In this model:

"M" stands for Markovian or memoryless arrival and service times.

"c" represents the number of servers.

In our case, we have an M/M/9 queuing model since we have 9 staff members.

The average waiting time for a customer on hold is given by the following formula:

Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))

Where:

c = number of servers (staff members) = 9

μ = average service rate (1 / average service time)

λ = average arrival rate (1 / average interarrival time)

ρ = λ / (c * μ)

First, let's calculate the average arrival rate (λ):

λ = 1 / (average interarrival time) = 1 / 5 minutes = 0.2 calls per minute

Next, calculate the average service rate (μ):

μ = 1 / (average service time) = 1 / 18 minutes = 0.0556 customers per minute

Now, calculate ρ:

ρ = λ / (c * μ) = 0.2 / (9 * 0.0556) ≈ 0.407

Finally, calculate the waiting time:

Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))

= (1 / (9 * (0.0556 - 0.2))) * (0.407 / (1 - 0.407))

≈ 1.16 minutes

Therefore, on average, a customer spends approximately 1.16 minutes waiting on hold before they can start speaking to a representative.

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Answer:

the answer is b edge 2022

Step-by-step explanation:

Answer:

There are 6hrs and 38 minutes between 8:15 am and 2:53 pm

Step-by-step explanation:

8:15 a.m- 9:15 am= 1 hr

9:15 am- 10:15 am= 1 hr

10:15 am-11:15 am=1 hr

11:15 am- 12:15 pm= 1 hr

12:15 pm- 1:15 pm= 1 hr

1:15 pm- 2:15 pm= 1hr

2:15 pm-2:53 pm= 53-15= 38 min