After an alcoholic beverage is consumed, the concentration of alcohol in the bloodstream (blood alcohol concentration, or BAC) surges as the alcohol is absorbed, followed by a gradual decline as the alcohol is metabolized. The function C(t)=0.135 t e^{-2.802 t}C(t)=0.135te −2.802t models the average BAC, measured in g/dL, of a group of eight male subjects t hours after rapid consumption of 15 mL of ethanol (corresponding to one alcoholic drink) What is the maximum average BAC during the first 3 hours? When does it occur?

Answer:

25 and 30

Step-by-step explanation:

30-25=5

Answer:

-1.5

Step-by-step explanation:

The common difference of the given arithmetic sequence is -1.5.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression

Arithmetic progression or arithmetic sequence is a number sequence in which the difference between consecutive terms is constant.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The common difference is calculated by subtracting the next term from the previous term.

Common diference = 5 - 6.5

Common difference = -1.5

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Answer:

The first one

Step-by-step explanation:

Do you really want an explanation  :v

Answer:

Can’t really see the end of the question but if it is 3/w it is most likely

c

Step-by-step explanation:

Statement (c) is correct for a simple graph. Every trail is a path, and every path is a trail.

In graph theory, a simple graph is an undirected graph with no loops or multiple edges between the same pair of vertices. A path in a graph is a sequence of vertices where each consecutive pair is connected by an edge. A trail in a graph is a path that allows for repeated vertices and edges.

Statement (a) is not correct because not every path is a trail. A path does not allow for repeated vertices or edges, whereas a trail does.

Statement (b) is not correct because not every trail is necessarily a path. A trail may contain repeated vertices or edges, but a path does not.

Statement (d) is not correct because paths and trails do have a relation. A trail is a more general concept that encompasses paths by allowing for repetition of vertices and edges.

Therefore, statement (c) is the correct statement. In a simple graph, every trail is a path, and every path is a trail.

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Answer:

\(2\frac{8}{15}\)

Step-by-step explanation:

The calculation of average speed in kilometres per hour is shown below:-

As we know that

\(Speed = \frac{Distance}{Time}\)

So, the average speed is

\(= 3\frac{1}{6} \div 1\frac{1}{4}\)

Now we will convert into a mixed number i.e

\(3\frac{1}{6} = \frac{19}{6} \\\\ 1\frac{1}{4} = \frac{5}{4}\\\\ = \frac{19}{6} \div\frac{5}{4}\\\\ = \frac{19}{6} \times \frac{4}{5}\)

Now the cross cancel common factor is 2

So,

\(= \frac{19}{2}\times \frac{2}{5} \\\\ = \frac{38}{15} \\\\ = 2\frac{8}{15}\)

hence, the average speed is \(2\frac{8}{15}\) in kilometers per hour

Therefore we simply applied the above formulas to determine the average speed that comes in kilometers per hour

The larger integer is 19 and the smaller integer is 12.

Given that, the larger integer is x, and the smaller integer is y.

The sum of two positive integers is 31.

x+y=31 ------(i)

The difference between the two integers is 7.

x-y=7 ------(ii)

Add equation (i) and (ii), we get

x+y+x-y=31+7

2x=38

x=38/2

x=19

Substitute x=19 in equation (i), we get

19+y=31

y=31-19

y=12

Therefore, the larger integer is 19 and the smaller integer is 12.

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Answer:

\(\huge\boxed{\sf \frac{y-5}{y-3} }\)

Step-by-step explanation:

Solving it by mid-term break method:

\(\displaystyle =\frac{y^2-3y-40}{y^2-11y+24} \\\\= \frac{y^2 -8y+5y-40}{y^2-3y-8y+24} \\\\= \frac{y(y-8)+5(y-8)}{y(y-3)-8(y-3)} \\\\Take \ (y-8) \ and \ (y-3)\ common\\\\= \frac{(y-8)(y-5)}{(y-8)(y-3)} \\\\= \frac{y-5}{y-3} \\\\\rule[225]{225}{2}\)

Hope this helped!

Answer:

\(\frac{y+5}{y-3} \textrm{ where } y \ne 8\)

Step-by-step explanation:

We'll first factorize the quadratic equations by finding their zero-points:

\(y^2 - 3y - 40 = 0\\\Delta = (-3)^2 - 4\cdot 1 \cdot -40 = 9 + 160 = 169\\\sqrt{\Delta} = 13\\y = \frac{3 \pm 13}{2}\\y_1 = 8\\y_2 = -5\\y^2 - 3y - 40 = (y - 8)(y + 5)\\~\\y^2 - 11y + 24 = 0\\\Delta = (-11)^2 - 4\cdot 1\cdot 24 = 121 - 96 = 25\\\sqrt{\Delta}} = 5\\y = \frac{11 \pm 5}{2}\\y_1 = 8\\y_2 = 3\\y^2 - 11y + 24 = (y - 8)(y - 3)\)

Now we can use this to simplify the whole division:

\(\frac{y^2-3y-40}{y^2-11y+24} = \frac{(y-8)(y+5)}{(y-8)(y-3)} = \frac{y+5}{y-3} \textrm{ where } y \ne 8\)

Answer: I think u have to multiply all da numbers.

Step-by-step explanation:

Answer:

ooofffffffff

Step-by-step explanation:

Given :

h(x) = 5 - 9x - equation (1)

h(x) = -67 - equation (2)

since, both of them are equal, let's equate :

⇒h(x) = 5 - 9x

⇒h(x) = -67

⇒h(x) = 5 - 9x ........ (Ⅰ)

⇒h(x) = -67 ......... (ⅠⅠ)

⇒5 - 9x = -67

⇒-9x = -67 - 5 (Combining like terms)

⇒-9x = -72 (Since, (-) is common in L.H.S & R.H.S we'll cancel it out & we will get the values positive)

⇒x = 72/9 (Transposing 9 to R.H.S)

⇒x = 8 (Required Answer)

D. The energy used is the same for both segments, the power while running is greater.

Walking and running both require energy, but the distance covered and the time taken are different. In this case, the person covers the same distance of 1 km in both segments.

Therefore, the energy used is the same for both. However, since running involves covering the same distance in less time, the power while running is greater. Power is the rate at which energy is used, and since running takes less time, the power output is higher.

D. The energy used is the same for both segments, the power while running is greater.

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Answer:

2 real number solutions.

Step-by-step explanation:

You check the value of the discriminant b^2 - 4ac.

Here it = (-10)^2 - 4*2* 6)

= 100 - 48

= 52. (Positive)

This means that it has 2 real number solutions.

If the discriminant = 0 it has one real number solution and if negative it has no real number solutions.

Answer:

i think its 2 real number

Step-by-step explanation:

Answer:

90

Step-by-step explanation:

Answer:2.51

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

since they have the same distance they are congruent

Answer:

yes

Step-by-step explanation:

because they have the same distance, they're congruent.

The additional information we would need to prove that ΔABC≅ΔDEF by SSS is that : Side AC is congruent to side DF

We are given that

Side AB=5 cm

BC=6 cm

Side DE=5 cm

Side EF= 6cm

We have to find an additional information would  need to prove that  by SSS.

When two triangles are congruent by SSS it means three sides of one triangle are congruent to corresponding sides of other triangle.

We have in triangle ABC and triangle DEF

AB ≅ DE = 5 cm

BC ≅ EF = 6 cm

AC ≅ DF

then, ΔABC ≅ Δ DEF

Reason : SSS postulates

Hence side AC is congruent to side DF.

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Number of miles to travel for result in both taxi services costing the same amount for that trip will be 60 miles.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Taxi service A costs $5 plus $0.25 for every mile traveled.

And, Taxi service B costs $8 plus $0.20 for every mile traveled.

Now,

Let the number of miles for both taxi reach at same time = x

So, We can formulate;

For Taxi A;

The total cost for x mile = $5 + $0.25x

For Taxi B;

The total cost for x mile = $8 + $0.20x

So, For same number of miles,

⇒ $5 + $0.25x = $8 + $0.20x

⇒ 0.25x - 0.20x = 8 - 5

⇒ 0.05x = 3

⇒ x =3/0.05

⇒ x = 300/5

⇒ x = 60 miles

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Answer:

To find the percentage of employees who are students, we can use the following formula:

Percentage = (part/whole) x 100%

In this case, the "part" is the number of students (14) and the "whole" is the total number of employees (25). So, we can plug these values into the formula:

percentage = (14/25) x 100%

percentage = 0.56 x 100%

percentage = 56%

Therefore, 56% of the employees in the pizza shop are students.

Answer:

56%

Step-by-step explanation:

You want to take 14/25 and that is .56 take that and times it by 100

The results of the vector operations are u · v = 6, v · v = 25, u^2 = (9, 4), (u · v)v = (24, -18), u · (5v) = 30

Let's calculate the given vector operations using the provided vectors u = (3, 2) and v = (4, -3):

u · v (dot product of u and v):

The dot product of two vectors is calculated by multiplying the corresponding components and summing them.

u · v = (3 * 4) + (2 * -3) = 12 - 6 = 6.

v · v (dot product of v with itself):

The dot product of a vector with itself gives the square of its magnitude.

v · v = (4 * 4) + (-3 * -3) = 16 + 9 = 25.

u^2 (square of u):

To square a vector, we square each component.

u^2 = (3^2, 2^2) = (9, 4).

(u · v)v (scalar projection of u onto v):

To find the scalar projection of u onto v, we first calculate the dot product of u and v, and then multiply the result by v.

(u · v)v = 6 * (4, -3) = (24, -18).

u · (5v) (vector projection of 5v onto u):

To find the vector projection of 5v onto u, we multiply 5v by the scalar projection of 5v onto u.

u · (5v) = (3, 2) · (5 * 4, 5 * -3) = (3, 2) · (20, -15) = (3 * 20) + (2 * -15) = 60 - 30 = 30.

Therefore, the results of the vector operations are as follows:

u · v = 6

v · v = 25

u^2 = (9, 4)

(u · v)v = (24, -18)

u · (5v) = 30

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a. The MRS is constant (not diminishing) at 1/3.

U(x,y) = 3x + y

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = 1 / 3

The MRS is constant (not diminishing) at 1/3.

b. The MRS is diminishing because as y increases, the MRS decreases.

U(x,y) = x * y

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = 1 / y

The MRS is diminishing because as y increases, the MRS decreases.

c. The MRS is diminishing because as y increases, the MRS decreases.

U(x,y) = x * y

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = 1 / y

Similar to the previous case, the MRS is diminishing because as y increases, the MRS decreases.

d. The MRS depends on the ratio of y to x and can vary.

U(x,y) = x^2 - y^2

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = -2y / 2x = -y / x

The MRS depends on the ratio of y to x and can vary. It is not necessarily diminishing.

e. The MRS depends on the values of x and y and can vary.

U(x,y) = x + y / (x * y)

The MRS for this utility function can be found by taking the partial derivative of x concerning y:

MRS = ∂U/∂y / ∂U/∂x = -1 / (y^2) + 1 / (x^2 * y)

The MRS depends on the values of x and y and can vary. It is not necessarily diminishing.

Now let's move on to the second part of the question:

For parts a, b, and c, we need more specific information about the utility functions, such as the values of α and β, to calculate the demand curves for x and y, the indirect utility function, and the expenditure function.

To show that the demand curve is homogeneous in degree zero in terms of income and prices, we need the specific functional form of the utility functions and information about the prices of x and y. Please provide the necessary details for parts A, b, and c to continue the analysis.

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For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}, the process is still "in order," while for the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}, the process might be "out of order."

To determine whether the process is still "in order" or "out of order," we can compare the current sample of output to the known mean and standard deviation of the process.

For the first sample {2.038 2.054 2.053 2.055 2.059 2.059 2.009 2.042 2.053 2.047}:

Calculate the sample mean by summing up all the values in the sample and dividing by the number of values (n = 10):

Sample mean = (2.038 + 2.054 + 2.053 + 2.055 + 2.059 + 2.059 + 2.009 + 2.042 + 2.053 + 2.047) / 10 = 2.048.

Compare the sample mean to the known process mean (2.050):

The sample mean (2.048) is very close to the process mean (2.050), indicating that the process is still "in order."

Calculate the sample standard deviation using the formula:

Sample standard deviation = sqrt(sum((x - mean)^2) / (n - 1))

Using the formula with the sample values, we find the sample standard deviation to be approximately 0.019 liters.

Compare the sample standard deviation to the known process standard deviation (0.020):

The sample standard deviation (0.019) is very close to the process standard deviation (0.020), further supporting that the process is still "in order."

For the second sample {2.022 1.997 2.044 2.044 2.032 2.045 2.045 2.047 2.030 2.044}:

Calculate the sample mean:

Sample mean = (2.022 + 1.997 + 2.044 + 2.044 + 2.032 + 2.045 + 2.045 + 2.047 + 2.030 + 2.044) / 10 ≈ 2.034

Compare the sample mean to the process mean (2.050):

The sample mean (2.034) is noticeably different from the process mean (2.050), indicating that the process might be "out of order."

Calculate the sample standard deviation:

The sample standard deviation is approximately 0.019 liters.

Compare the sample standard deviation to the process standard deviation (0.020):

The sample standard deviation (0.019) is similar to the process standard deviation (0.020), suggesting that the process is still "in order" in terms of variation.

In summary, for the first sample, the process is still "in order" as both the sample mean and sample standard deviation are close to the known process values.

However, for the second sample, the difference in the sample mean suggests that the process might be "out of order," even though the sample standard deviation remains within an acceptable range.

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To find the zeros of y = tan(2x), we need to solve the equation sin(2x) = 0 to determine the x-values where sin(2x) is zero. These x-values will correspond to the zeros of the function tan(2x).

To find the zeros of the function y = tan(2x), we can utilize the fact that tan(x) is equal to sin(x)/cos(x).

Given y = tan(2x), we can rewrite it as:

y = sin(2x) / cos(2x)

Now, let's consider the numerator of this expression, which is sin(2x). If we set sin(2x) equal to zero, we can determine the values of x that make the numerator zero:

sin(2x) = 0

By solving this equation, we can find the zeros of sin(2x). The solutions will be the values of x for which sin(2x) equals zero.

Similarly, we can look at the denominator of the expression y = sin(2x) / cos(2x), which is cos(2x). If cos(2x) equals zero, the denominator will be zero, which leads to undefined values for y. These points will be vertical asymptotes of the function tan(2x).

To find the zeros of y = tan(2x), we need to solve the equation sin(2x) = 0 to determine the x-values where sin(2x) is zero. These x-values will correspond to the zeros of the function tan(2x).

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Answer:

(B)\(\dfrac{1}{m^8}\)

StartFraction 1 Over m Superscript 8 EndFraction

Step-by-step explanation:

We want to find the simplified form of: \(m^{-8}p^0\)

\(m^{-8}p^0=m^{-8}$ X p^0\\p^0=1\\m^{-8}=\frac{1}{m^8} \\$Therefore:\\m^{-8}$ X p^0=\dfrac{1}{m^8} X 1\\=\dfrac{1}{m^8}\)

The correct option is B.

Answer:

I am 80% sure its 1 if not then its 1/p

Step-by-step explanation:

ATQ

Substracting both

\(\\ \sf\longmapsto 2y=54\)

\(\\ \sf\longmapsto y=27\)

each paid

\(\\ \sf\longmapsto \dfrac{27}{3}=9\)

Now

Total students went on trip

\(\\ \sf\longmapsto \dfrac{360}{9}\)

\(\\ \sf\longmapsto 40\)

Answer:

101  

Step-by-step explanation:

100- (-1) NEGATIVE MINUS NEGATIVE CANCEL OUT ON EACH OTHER AND GIVE POSITIVE: 100 + 1 = SO THE ANSWER IS  101^F

The difference between these two extreme temperatures is of

101° F.

We have the highest temperature recorded in the town of Westgate which is equal to 100°F. Last winter, the lowest temperature recorded was -1°F.

We have to find the difference between these two extremes.

Degree of hotness or coldness measured on a definite scale is called Temperature. When the temperature of the body is high it is called hot body and when it is low it is called cold body.

According to question, we have -

Highest temperature recorded = 100°F

Lowest temperature recorded = -1°F

Let the the difference between these two extreme temperatures be x. Then -

x = Highest temperature recorded - Lowest temperature recorded

x = 100 - (- 1) = 101° F

Hence, the difference between these two extreme temperatures is of

101° F.

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Answer:

$591.10

Step-by-step explanation:

First, add up $475.88 and $609.00 together. Then, subtract it from $1675.88. They need $591.10 more for their vacation.

Answer: 16/20

Step-by-step explanation:

If ur asking for the sine of angle C

Answer:

'y', "addition", '9'.

Step-by-step explanation:

The variable is an unknown value in an algebraic equation or expression. It is represented by a letter.

'y' would be the variable in the given equation.

The operation in the expression is addition. The '+' sign represents addition, which means 9 and 'y' would be added together to get the sum.

Constants are terms in a expression or equation that contains no variables. This means that constants are only numbers.

'9' would be the given constant in the expression.

Hope this helps.

Answer:

y

+

9

Step-by-step explanation:

The maximum number of interior angles of a convex n-gon that can have measure 131° is equals to the seven.

A polygon is said to be convex n-gon when no line segments between the points, goes inside and all the vertices are pointed outside away from the center. The interior angles of a convex polygon are less than 180°. Sum of interior angles of n sided polygon

= 180(n- 2) degrees

We have, Alex assume that one of interior angle of convex n-gon is 131° . Let total maximum number of interior angles of a convex n-gon or polygon that can have measure 131° be "x".

Total measures of all remaining interior angles, (n - x) of this polygon

= 180(n- 2) - 131x

But for a convex n-gon, interior angles of a convex polygon are less than 180°. So,

180(n- 2) - 131x < (n - x) 180

Now, solve this Inequality,

=> 180n - 360 - 131x < 180n - 180x

=> -360 + 180x - 131x < - 180x + 180x

=> - 360 + 49x < 0

=> 49x < 360

=> x < 360/49

=> x < 7.34 ~ 7

So, the required value of x is 7 .

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Answer:

HA = 16.2 m

DE = 17 m

Step-by-step explanation:

From the base of the cuboid, HDA will form a right angle triangle, where;

DA = 15 m

HA = 6 m

HA is the hypotenuse

Using pythagoras theorem;

HA = √(15² + 6²)

HA = √(225 + 36)

HA = √261

HA = 16.155 m

Approximating to 1 decimal place gives;

HA = 16.2 m

Similarly, HDE will also form a right angle triangle.

Thus;

DE = √((HD)² + (HE)²)

HD = 16.2 m

HE = 5 m

Thus;

DE = √(16.2² + 5²)

DE = 16.95 m

Approximating to 1 decimal place gives

DE = 17 m