A gallbladder can involve an injection of 0. 6 mL (about one-tenth of a teapoon) of a radioactive material called Technetium-99m. Technetium-99m ha a half-life of 6 hour. How much of the radioactive material will be left in the patient' bloodtream after 21 hour?

Answer:

5 hours.

Step-by-step explanation:

280 divided by 56 is 5.

The expected value for the number on which the pointer lands is 21/8.

Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes.

Given the pointer shown to the right can land on every number, and

the respective probability that the pointer can land is

shown in the table below,

table for probability,

outcome        probability

1                           1/4

2                          1/4

3                           1/8    

4                           3/8

expected value is given by,

E(x) = ∑ [tex]x_i.p(x_i)[/tex]

  = 1(1/4) + 2(1/4)  + 3(1/8)  + 4(3/8)

 = 1/4 + 1/2 + 3/8 + 3/2

   =  (2 + 4 + 3 + 12)/8

 =  21/8 = 2.625

Hence expected value is 21/8 or 2.625.

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By applying the linear equation concept, it can be concluded that:

A. The slope of the line is 15

B. The standard form of the equation is 15x - y + 325 = 0

C. The function notation of the equation is g(x) = 15x + 325

D. The balance in the bank account after 12 days is $505

Linear equation is an equation that contains one or more variables, where each variable has the power of one.

The standard form of a linear equation is y - y₁ = m(x - x₁) or ax + by + c = 0, where m is the slope of the function.

Slope of the function represents the change in y (Δy) over the change in x (Δx). m = Δy / Δx

We have the following table:

x         0       5       10

g(x)   325   400   475

A. To find the slope of the line, we calculate the value of Δy  dan Δx:

Δy = y₂ - y₁

    = 400 - 325

    = 75

Δx = x₂ - x₁

     = 5 - 0

     = 5

m = Δy / Δx

   = 75 / 5

   = 15

B. To find its standard form, we can input the value of one point into y - y₁ = m(x - x₁):

            y - y₁ = m(x - x₁)

        y - 325 = 15 (x - 0)

        y - 325 = 15x - 0

15x - y + 325 = 0

C. function notation changes the y to g(x), so we get:

   15x - y + 325 = 0

15x - g(x) + 325 = 0

                  g(x) = 15x + 325

D. The balance in the bank account after 12 days can be calculated by substituting the value of x = 12 into the function:

g(x) = 15x + 325

      = 15 · 12 + 325

      = 180 + 325

      = $505

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Answer:

Let x be the amount Pam has, then Dan has x - $3.00 and Sam has x + x - $3.00 + $1.00 = 2x + $1.00

The total amount of money they have is x + x - $3.00 + 2x + $1.00 = 31.00

So, 4x + $1.00 = 31.00

Subtracting $1.00 from both sides gives 4x = 30.00

Finally, dividing both sides by 4 gives x = $7.50

So Pam has $7.50, Dan has $7.50 - $3.00 = $4.50, and Sam has $7.50 + $4.50 + $1.00 = $13.00.

Answer:

B

Step-by-step explanation:

Matthew's monthly take-home pay is approximately $2,960.69 (47,530 / 12). To calculate the exact amount, we need to subtract the state income tax from his monthly salary:

$47,530 / 12 = $3,961.67

$3,961.67 * 0.0307 = $122.57

$3,961.67 - $122.57 = $3,839.10

Therefore, the correct answer is B) $3,839.24

In the number 652.12, the 2 in the hundredths place has a place value of 0.02 and the 2 in the ones place has a place value of 2. This means that the 2 in the ones place is 100 times greater in value than the 2 in the hundredths place.

In the number 652.12, the value of the 2 in the hundredths place is much smaller than the value of the 2 in the ones place. In this number, the 2 in the hundredths place represents 0.02, which is two hundredths of a unit. On the other hand, the 2 in the ones place represents 2 units.

To understand the difference in value, consider that the decimal point separates the number into its integer part (to the left of the decimal point) and its fractional part (to the right of the decimal point). The place value of each digit depends on its position relative to the decimal point. The rightmost digit is the ones place, the digit to its left is the tens place, and so on. The place value of the digits to the right of the decimal point is determined by powers of 10 that are negative, starting from -1 for the hundredths place, -2 for the thousandths place, and so on.

Therefore, in the number 652.12, the 2 in the hundredths place has a place value of 0.02 and the 2 in the ones place has a place value of 2. This means that the 2 in the ones place is 100 times greater in value than the 2 in the hundredths place.

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In the number 652.12, the 2 in the hundredth place has a place value of 0.02 and the 2 in the ones place has a place value of 2. This means that the 2 in the ones place is 100 times greater in value than the 2 in the hundredths place.

In the number 652.12, the value of the 2 in the hundredths place is much smaller than the value of the 2 in the ones place. In this number, the 2 in the hundredths place represents 0.02, which is two hundredths of a unit. On the other hand, the 2 in the ones place represents 2 units.

To understand the difference in value, consider that the decimal point separates the number into its integer part (to the left of the decimal point) and its fractional part (to the right of the decimal point). The place value of each digit depends on its position relative to the decimal point. The rightmost digit is the ones place, the digit to its left is the tens place, and so on. The place value of the digits to the right of the decimal point is determined by powers of 10 that are negative, starting from -1 for the hundredths place, -2 for the thousandths place, and so on.

Therefore, in the number 652.12, the 2 in the hundredths place has a place value of 0.02 and the 2 in the ones place has a place value of 2. This means that the 2 in the ones place is 100 times greater in value than the 2 in the hundredths place.

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The number of hot dogs will Team A need to sell to reach its goal is 690.

What is the linear equation in one variable?

A linear equation in one variable is an equation that can be written in the form: y = mx + b,where "x" is the independent variable, "y" is the dependent variable, "m" is the slope of the line, and "b" is the y-intercept.

Let the number of dogs be x.

1.48x - 20 = 1000
1.48x = 1020
x = 1020/1.48
x = 690

Hence, the number of hot dogs will Team A need to sell to reach its goal is 690.

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The simplification of the given equation would be = k = 1/2(X+y+z)

Division can be defined as one of the major arithmetic operation which is used to share or distribute a whole value between two or more values.

The equation that is given;

k = x3+y3+z3/6

k =3(X+y+y)/6

Divide through by 3;

k = =X+y+y/2 or

k = 1/2(X+y+z)

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The function of parking in the garage is C(t) = 6 + 2.4t

From the question, we have the following parameters that can be used in our computation:

Rate each hour = 2.40

Initial rate = 6.00

The function is then represented as

C(t) = Initial rate + Rate each hour * number of hours

So, we have:

C(t) = 6 + 2.4t

Hence, the function is C(t) = 6 + 2.4t

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Answer:

The square root of 200 in its simplest radical form is 10√2.

Step-by-step explanation:

If we know the prime factorization of a number, we can write the radical form of the square root of that number.

Answer: 10√2.

Step-by-step explanation: the prime factorization of 200 is 2 × 2 × 2 × 5 × 5. As a result, the square root of 200 in the simplest radical form should be 10√2.

Answer: x = -2

Step-by-step explanation:

A) The total no. of students taking only maths is 220 students.

let's say the total no. of students taking only maths = M

M = 360 - (100 + 40) = 220 students.

B) The total no. of students in the survey is 960 students.

let's say the total no. of students in the survey = S

S = 360 + 280 + 300 - (100 + 120 + 110) + 40 = 960 students.

C) The total no. of students who are taking exactly two of the courses is 330 students.

let's say the total no. of students who are taking exactly two of the courses = T

T = 100 + 120 + 110 = 330 students.

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Answer:

400

Step-by-step explanation:

percent means per one hundred so

p/100=5/8

p=500/8

p=62.5%

so, 62.5% have paid their yearly fees .

400(5/8) =200

250 member paid their fees .

Answer:

250

Step-by-step explanation:

If a group contains 400 members

Then the 5/8 of 400 who didn't pay the fees are as follows:-

=5/8*400

=5*50

=250 out of 400

So, the fees is only paid by 250 members out of 400.

40 minutes in decimal is 0.666.

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The amount of chicken meat required by the lion to meet his protein diet is 6.66 ounces.

A 120-pound lion need 50 gram of protein a day.

The protein provided by the 4-ounce chicken is 30 grams.

By using unitary method,

We can write,

4 ounce chicken = 30 grams protein

4/30 ounce chicken = 1 grams protein

Now, the required amount of protein is 50 grams.

So, the chicken meat needed is,

50 grams = 4/30 x 50 ounces

50 grams protein = 6.66 ounces.

So, a total of 6.66 ounces of chicken meat is required.

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The equation with the given values for pipe length and elapsed time to calculate the initial head needed to achieve the desired velocity.

The velocity of water, v (m/s), discharged from a cylindrical tank through a long pipe can be computed using the equation:

v= √2gH tanh (√2gH/2L. T)

where g = 9. 81 m/s2, H = initial head (m), L = pipe length (m), and t = elapsed time (s).

To plot the velocity function f(H) versus H for H = 0 to 4 m, we can use MATLAB to create a script that uses the equation to calculate the velocity for each value of H. We can then plot the points on a graph, with H on the x-axis and v on the y-axis.

To determine the initial head needed to achieve υ = 5 m/s in 2. 5 s for a 4-m long pipe, we can use the LastNameBisect method with initial guesses of xl = 0 and xu = 4 m. This will use the equation with the given values for pipe length and elapsed time to calculate the initial head needed to achieve the desired velocity.

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When multiplying decimal numbers, you move the decimal point to the left of the amount of integers in the equation that are to the right of the decimals.25.5 x 0.81 = 20.655

When multiplying decimal numbers, you move the decimal point to the left of the amount of integers in the equation that are to the right of the decimals.

After multiplication, you would move the decimal three places to the left because there is one number after the decimal point in 25.5 and two numbers after the decimal point in 0.81.

25.5 x 0.81 = 20.655

( notice there are 3 numbers to the right of the decimal point) ( note there are 3 numbers to the right of the decimal point)

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The equivalent fractions are
1.) 5/6 > 4/6

5.) 7/8 > 4/8
9.) 8/10 < 15/10
13.) 6/8 < 7/8

what is a fraction?

A fraction is a mathematical expression that represents a part of a whole or a division of one quantity into equal parts. It consists of two parts, a numerator and a denominator. The numerator represents the number of equal parts of the whole and the denominator represents the total number of parts the whole is divided into.

1.) 5/6 ___ 2/3

To compare these fractions, it's best to find equivalent fractions with a common denominator. A common denominator for 6 and 3 is 6. So, to make the denominator of 2/3 equal to 6, multiply both the numerator and denominator by 2:

2/3 * 2/2 = 4/6

Now, both 5/6 and 4/6 have a common denominator of 6. So, we can easily compare:

5/6 __ 4/6

5/6 is greater than 4/6, so the answer is 5/6 > 4/6

5.) 7/8 ___ 1/2

To compare these fractions, it's best to find equivalent fractions with a common denominator. A common denominator for 8 and 2 is 8. So, to make the denominator of 1/2 equal to 8, multiply both the numerator and denominator by 4:

1/2 * 4/4 = 4/8

Now, both 7/8 and 4/8 have a common denominator of 8. So, we can easily compare:

7/8 __ 4/8

7/8 is greater than 4/8, so the answer is 7/8 > 4/8

9.) 8/10 ___ 3/4

To compare these fractions, it's best to find equivalent fractions with a common denominator. A common denominator for 10 and 4 is 10. So, to make the denominator of 3/4 equal to 10, multiply both the numerator and denominator by 5/5:

3/4 * 5/5 = 15/10

Now, both 8/10 and 15/10 have a common denominator of 10. So, we can easily compare:

8/10 __ 15/10

8/10 is less than 15/10, so the answer is 8/10 < 15/10

13.) 3/4 ___ 7/8

To compare these fractions, it's best to find equivalent fractions with a common denominator. A common denominator for 4 and 8 is 8. So, to make the denominator of 3/4 equal to 8, multiply both the numerator and denominator by 2:

3/4 * 2/2 = 6/8

Now, both 6/8 and 7/8 have a common denominator of 8. So, we can easily compare:

6/8 __ 7/8

6/8 is less than 7/8, so the answer is 6/8 < 7/8

Hence, the equivalent fractions are
1.) 5/6 > 4/6

5.) 7/8 > 4/8
9.) 8/10 < 15/10
13.) 6/8 < 7/8

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When 14 cm is converted into inches it will be 5.51181 inches.

Here given the value is 14cm.

To convert to inches it is equal to,

14 x 0.393701

= 5.51181 inches.

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Answer: (-1, 0)

not sure

Step-by-step explanation:

The function that describes the scenario is y = 7.25 + 0.65x

From the question, we have the following parameters that can be used in our computation:

Initial = 7.25

Rate = 0.65

Represent the number of miles with x

So, we have the following representation

y = 7.25 + 0.65x

Where the total cost is y

Hence, the function is represented above

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The value of P(D OR E) = 0.1 + 0.4 - 0.02 = 0.48, P(D AND E) = 0.1 * 0.2 = 0.02,P(E | D) = 0.02 / 0.1 = 0.2

a. P(D AND E) = P(D) * P(E | D)

P(D) = 0.1 (10% of students have taken a distance learning class)

P(E | D) = 0.2 (20% of part-time students have taken a distance learning class)

Therefore, P(D AND E) = 0.1 * 0.2 = 0.02

b. P(E | D) = P(D AND E) / P(D)

P(E | D) = 0.02 / 0.1 = 0.2

c. P(D OR E) = P(D) + P(E) - P(D AND E)

P(D) = 0.1 (10% of students have taken a distance learning class)

P(E) = 0.4 (40% of students are part-time students)

P(D AND E) = 0.02 (10% of students have taken a distance learning class and that 40% of students are part-time students)

Therefore, P(D OR E) = 0.1 + 0.4 - 0.02 = 0.48

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Answer: y = -4x + 29

Step-by-step explanation:

To find the equation of the line passing through the points (-3, 17) and (2, -3), we can use the slope-point form of a line, which is given by:

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line, m is the slope of the line, and (x, y) are the coordinates of any other point on the line. To find the slope of the line, we can use the formula:

m = (y2 - y1) / (x2 - x1)

Plugging in the coordinates of the two points, we have:

m = (-3 - 17) / (2 - (-3)) = -20 / 5 = -4

Next, we plug in the coordinates of one of the points and the slope into the slope-point form of a line:

y - 17 = -4(x - (-3))

Expanding the right side:

y - 17 = -4x + 12

Adding 17 to both sides:

y = -4x + 29

So the equation of the line passing through the points (-3, 17) and (2, -3) is: y = -4x + 29

Hyperbola is formed when two cones that touch at their vertices and a plane cutting through the left cone parallel to its base to form a curve

A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane.

We have to find the conic section which is formed by two cones that touch at their vertices and a plane cutting through the left cone parallel to its base to form a curve circle parabola ellipse hyperbola.

A hyperbola is formed when the interesting plane is parallel to the axis of the cone, and intersect with both the nappes of the double cone.

Hence, Hyperbola is formed when two cones that touch at their vertices and a plane cutting through the left cone parallel to its base to form a curve

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Answer:

ellipse.

Step by-step explanation:

Answer:

16.

Step-by-step explanation:

Let x be the number.

32% of x = (32/100)x = 0.32x.

Ten more than 32% of x = 0.32x + 10.

0.32x + 10 = 26.

0.32x = 16.

x = 50.

So the number is 50, and 32% of it is 0.32 * 50 = 16.

Answer:

surface of 3cm cube=l³

=3³

=27

The area bounded by the graphs of y and y0 over the given interval is A = ∫y0 dy|2-∫y0 dy|0.

The area bounded by the graphs of the indicated equations y and y0 over the given interval can be calculated using the formula A=∫y0 dy. To calculate the area, we need to first find the antiderivative of y0, which is F(y0) = ∫y0 dy. Then, we need to evaluate the integral from the lower limit of the given interval to the upper limit of the given interval. For example, if the given interval is from x=0 to x=2, then the area bounded by the two graphs would be A=F(y0)|2-0 = ∫y0 dy|2-0. Once we have evaluated the integral, we can calculate the area of the graph by subtracting the lower limit result from the antiderivative In this example, A=F(y0)|2-0 = ∫y0 dy|2-0 = F(y0)|2-F(y0)|0 = ∫y0 dy|2-∫y0 dy|0. Thus, the area bounded by the graphs of y and y0 over the given interval is A = ∫y0 dy|2-∫y0 dy|0.

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The solutions of Ax=0 in parametric vector​ form:

[tex]x_2\left[\begin{array}{c}-3&1&0&0\\\\\end{array}\right] +x_3\left[\begin{array}{c}0&0&1&0\\\\\end{array}\right] +x_4\left[\begin{array}{c}4&0&0&1\\\\\end{array}\right][/tex]

we have a matrix where A is the row equivalent to that matrix:

[tex]\left[\begin{array}{cccc}1&3&0&-4\\2&6&0&-8\\\end{array}\right][/tex]

The given matrix can be written in an Augmented form as:

[tex]\left[\begin{array}{ccccc}1&3&0&-4&0\\2&6&0&-8&0\\\end{array}\right][/tex]

Row Reduced Echelon Form can be obtained using the following steps.

Interchanging the rows R₁ and R₂

.[tex]\left[\begin{array}{ccccc}2&6&0&-8&0\\1&3&0&-4&0\\\end{array}\right][/tex]

Applying the operation R₂-->2R₂-R₁, to make the second.

[tex]\left[\begin{array}{ccccc}2&6&0&-8&0\\1&3&0&-4&0\\\end{array}\right][/tex]  R₂-->2R₂-R₁,

[tex]\left[\begin{array}{ccccc}2&6&0&-8&0\\0&0&0&0&0\\\end{array}\right][/tex]

Dividing the first row by 2 to generate 1 at the

[tex]\left[\begin{array}{ccccc}2&6&0&-8&0\\0&0&0&0&0\\\end{array}\right][/tex]  R₁--->1/2R₁

[tex]\left[\begin{array}{ccccc}1&3&0&-4&0\\0&0&0&0&0\\\end{array}\right][/tex]

From here the following equation can be deducted:

x₁+3x₂-4x₄=0

Making the subject of the equation:

x₁=-3x₂+4x₄

Hence, the Ax=0 parametric vector form’s solutions can be written as:

[tex]X=\left[\begin{array}{c}-3x_2+4x_4&x_2&x_3&x_4\\\\\end{array}\right] \\\\\\=\left[\begin{array}{c}-3x_1&x_2&0&0\\\\\end{array}\right] +\left[\begin{array}{c}0&0&x_3&0\\\\\end{array}\right] +\left[\begin{array}{c}4x_4&0&0&x_4\\\\\end{array}\right] \\\\\\ =x_2\left[\begin{array}{c}-3&1&0&0\\\\\end{array}\right] +x_3\left[\begin{array}{c}0&0&1&0\\\\\end{array}\right] +x_4\left[\begin{array}{c}4&0&0&1\\\\\end{array}\right][/tex]

Numerical Result:

[tex]x_2\left[\begin{array}{c}-3&1&0&0\\\\\end{array}\right] +x_3\left[\begin{array}{c}0&0&1&0\\\\\end{array}\right] +x_4\left[\begin{array}{c}4&0&0&1\\\\\end{array}\right][/tex]

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The student must earn a 74 on the final exam to pass the course with an average of 70.

The student's current average score is (64 + 69 + 73) / 3 = 66.

To find the score the student needs to earn on the final exam to maintain an average of 70, we can set up an equation:

(64 + 69 + 73 + x) / 4 = 70

Where x is the score the student needs to earn on the final exam.

Solving for x:

(64 + 69 + 73 + x) = 280

x = 280 - 64 - 69 - 73 = 74

So, the student must earn a 74 on the final exam to pass the course with an average of 70.

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The percentage gain of the company is calculated to be 10%.

The percentage gain is calculated by multiplying the fraction of the gain and the initial amount by 100.

we shall calculate for the percentage gain of the company as follows:

gain = $33 - $30 = $3

initial amount = $30

percentage gain = ($3/$30) × 100

percentage gain = (1/10) × 100

percentage gain = 10%

Therefore, the percentage gain of the company is calculated to be 10%.

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