Troy puts $200.00 into an account to use for school expenses. The account earns 7% interest, compounded annually. How much will be in the account after 5 years? Use the formula A=P1+ r n nt, where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years. Round your answer to the nearest cent.

The concentration of pyrenbutyrate in the patch when first applied to the patient's skin should be 150 mg/cm^3.

the concentration of pyrenbutyrate in the patch when first applied to the patient's skin, we can use Fick's first law of diffusion. Fick's first law states that the rate of diffusion is proportional to the concentration gradient and the diffusion coefficient.

Step 1: Calculate the concentration gradient
The concentration gradient is the difference in concentration between the patch and the skin. In this case, the concentration in the patch is unknown, but we can assume it to be zero initially since the drug is just applied. The concentration in the skin is also unknown, but it is given that the required rate of drug delivery is 3.4 x 10^3 mg/s. We can use this information to calculate the concentration gradient.

Step 2: Calculate the diffusion coefficient
The diffusion coefficient is a measure of how easily the drug can move through the skin. It is given that the diffusivity of the drug in the epidermis (outer layer of skin) is 1 x 10 cm/s, and in the dermis (inner layer of skin) is 1 x 10^5 cm/s. Since the drug needs to penetrate both layers, we can assume an average diffusivity of (1 x 10 + 1 x 10^5)/2 = 5 x 10^4 cm/s.

Step 3: Calculate the concentration of pyrenbutyrate in the patch
Now we can use Fick's first law to calculate the concentration of pyrenbutyrate in the patch.

Rate of diffusion = -D * (change in concentration/change in distance)

The rate of diffusion is given as 3.4 x 10^3 mg/s, the diffusion coefficient (D) is 5 x 10^4 cm/s, and the distance is the thickness of the epidermis (0.002 mm) + the thickness of the dermis (0.041 mm).

Substituting the values into the equation:

3.4 x 10^3 mg/s = -5 x 10^4 cm/s * (change in concentration)/(0.002 mm + 0.041 mm)

Step 4: Solve for the change in concentration
Rearranging the equation and solving for the change in concentration:

(change in concentration) = (3.4 x 10^3 mg/s * 0.002 mm + 0.041 mm) / (5 x 10^4 cm/s)

(change in concentration) = 150 mg/cm^3

Step 5: Calculate the concentration in the patch
Since the concentration in the patch is initially zero, the concentration in the patch when first applied to the patient's skin is 150 mg/cm^3.

Therefore, the concentration of pyrenbutyrate in the patch when first applied to the patient's skin should be 150 mg/cm^3.

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Answer:

114

Step-by-step explanation:

let 'n' = original value

(17.1 - n) / n = -85/100

cross-multiply:

1710 - 100n = -85n

1710 = 15n

n = 1710/15

n = 114

Answer:

8. 1.5

9 (a) $90

   (b) $510

Step-by-step explanation:

8.

\(\frac{1}{4} - \frac{2x-7}{8} = \frac {x}{2}\)

Multiply all by 8

\(2 - (2x-7) = 4x\\2 - 2x + 7 = 4x\\9 = 4x + 2x\\9 = 6x\\\frac{9}{6} = x\\1.5 = x\)

9. (a)

x = cost of one DVD

Since, a blue-ray disc is equal to 2 DVD minus by 10 dollar, then a blue-ray disc = (2x-$10)

$ 610 = 3x + 2(2x - $10)

$ 610 = 3x + 4x - $ 20

$ 610 + $ 20 = 7x

$ 630 = 7x

Divide both side by 7

x = $ 90

Thus, one DVD cost $ 90.

(b)

Blue-ray disc cost = (2x - $10)

3 Blue-ray disc cost = 3(2x - $10)

= 6x - $30

Replace x with $90, since x = $90

= 6 ($90) - $30

= $ 540 - $30

= $510

Answer:   D

d. because they are not subtracted(C), the two fractions do not add up to 13(B), and the number is not equal to 2(A).

The probability that the three pieces can be assembled into a triangle is 25%

Let the length of the stick be 1, so each break can occur at a position in the interval [0,1]. Let x and y be the two breaks in the stick. Then the area of the region in the square bounded x=0, x=1, y=0, y=1, which represents combinations of x and y, for which we can form a triangle. Since the area of the whole square is 1, the area of the region inside is the probability of the triangle.

If y>x, then the lengths of the pieces are x, y-x, and 1-y.

The triangle inequality must hold for each combination of edges.

for  y>x ...

x+y−x≥1−y

x+1−y≥y−x

y−x+1−y≥x

these simplify to...

for  y>x ...

y≥1/2

x+1/2≥y

x≤1/2

If we cut our 1x1 square into two triangles along the line x=y,

then the region in the upper triangle which satisfies the inequalities above forms a smaller triangle which connects the midpoints of the upper triangle.

The lower triangle (x>y), is just a reflection about x=y of the upper triangle, so together, the entire region looks like a bow-tie at a 45 degree angle.

This region takes up 25% of the square,

Thus, the probability that the three pieces can be assembled into a triangle is 25%

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Linear factors are the factors of a polynomial

What went wrong is that: Tyler's linear factors are incorrect

The polynomial function is given as:

Rewrite as:

Further rewrite as:

Factorize the above polynomial

Factor out x - 1 from the polynomial

This means that:

The linear factors are x - 1 and x^2 - 8x + 15

From the given diagram, Tyler's linear factors are x - 1 and x^2 - 8x - 15

Hence, Tyler's linear factors are incorrect

Answer:

4.5

Step-by-step explanation:

Answer:

above sea level

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

The height of the cone is 8 feet by using the Pythagorean theorem.

The height of a cone can be found using the Pythagorean theorem and the slant height and radius (or diameter) of the base.

Given that the slant height of the cone is 17 feet and the diameter of the base is 30 feet, we can use the following formula to find the height:

height = √(slant height² - (diameter/2)²)

So in this case, the height of the cone would be:

height = √(17² - (30/2)²) = √(289 - 225) = √(64) = 8

Thus, the height of the cone is 8 feet.

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The value of the numerical expression 1 x 10,000 + 7 x 1,000 + 4 x 100 + 0 x 10 + 2 x 1 will be 17,402.

The outcome of the expression corresponds to the outcome of the computation it represents when the pertinent elements and fundamental operations of a mathematical model are assigned values.

Making something a little less complicated while also making it simpler to accomplish or understand is the concept of easiness.

The numerical expression is written below.

⇒ 1 x 10,000 + 7 x 1,000 + 4 x 100 + 0 x 10 + 2 x 1

Simplify the expression, then we have

⇒ 1 x 10,000 + 7 x 1,000 + 4 x 100 + 0 x 10 + 2 x 1

⇒ 10,000 + 7,000 + 400 + 0 + 2

⇒ 17,402

The value of the numerical expression 1 x 10,000 + 7 x 1,000 + 4 x 100 + 0 x 10 + 2 x 1 will be 17,402.

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The complete question is given below.

Find the value of the expression.

1 x 10 000 + 7 x 1 000 + 4 x 100 + 0 x 10 + 2 x 1.

The zeros of the polynomial function appear as the x-intercepts on the graph.

For a polynomial function:

y = p(x)

The zeros x₁, x₂, ...

Are inputs such that:

P(x₁) = P(x₂) = ... = 0

On the graph, these are the values of x such that the graph of the polynomial intercepts the x-axis.

So the complete statement can be "the zeros of a polynomial function appear as the x-intercepts of the polynomial function"

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The zeros of a polynomial function appear as x-intercepts or roots on the graph of the polynomial function.

The zeros of a polynomial function are the values of x for which the function evaluates to zero. Geometrically, these zeros correspond to the points where the graph of the polynomial function intersects or crosses the x-axis. When a polynomial function is graphed, the x-intercepts or roots represent the locations on the x-axis where the function value is zero.

For example, if a polynomial function has zeros at x = -2, x = 0, and x = 3, then the graph of the polynomial will intersect the x-axis at these three points. The x-intercept at x = -2 means that the function value is zero when x = -2, and similarly for the other zeros.

These zeros play a significant role in understanding the behavior and properties of polynomial functions. They provide information about the solutions to equations involving the polynomial and can help determine the factors of the polynomial. Therefore, by identifying the zeros on the graph of a polynomial function, we can gain insights into the behavior and characteristics of the function.

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We have the following:

We must calculate the slope through the points:

(x1, y1) = (-9, 7)

(x2, y2) = (-6, -3)

replacing:

for b,

x = -9

y = 7

m = -10/3

replacing:

Therefore, the equation is:

Answer:

I don't know this answer

Answer:

Step-by-step explanation:

Can't do the solution but you can do it.

Just learn how to solve the multiplication with partitioning strategy, grid method, and expanded method. You can search it and learn it by watching and understanding how to solve all of them. But I want to say sorry, because I can't answer the number 4 cause I don't know to do it. Really sorry.

Hope it helps

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Rounding to the nearest hundredth, we find that Xenia earned approximately 282.60 in the first two weeks of June.

What is linear equation?

A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. It is an equation of the form:

y = mx + b

Let's start by finding Xenia's hourly wage, which we can use to calculate her earnings. We know that in the first week, when she worked 15 hours, she earned a certain amount, and in the second week, when she worked 22 hours, she earned 47.60 more than in the first week.

Let's use the variable x to represent Xenia's hourly wage. Then, in the first week, she earned:

15x dollars

In the second week, she earned:

22x + 47.60 dollars

We can now calculate her total earnings for the two weeks by adding up her earnings from the first and second weeks:

15x + (22x + 47.60) = 37x + 47.60 dollars

We don't know Xenia's hourly wage, but we do know that it must be the same in both weeks. This means that the x term is the same in both expressions above.

We can now use the information given in the problem to set up an equation:

22x + 47.60 = 15x + 47.60 + 47.60

The left-hand side represents Xenia's earnings in the second week, and the right-hand side represents her earnings in the first and second weeks combined. We added an extra 47.60 to the right-hand side to account for the fact that she earned that much more in the second week than in the first.

Simplifying the equation, we get:

7x = 47.60

Dividing both sides by 7, we find:

x = 6.80

So Xenia's hourly wage is 6.80.

To find her total earnings for the first two weeks of June, we can substitute x = 6.80 into our expression for her combined earnings:

37x + 47.60 = 37(6.80) + 47.60 \approx 282.60

Rounding to the nearest hundredth, we find that Xenia earned approximately 282.60 in the first two weeks of June.

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Answer:

432,106

Step-by-step explanation:

Hope this works, let me know if you didn't understand it

Answer:

the y is y=mx+b

Step-by-step explanation:

if this helps say also have a brillint day

Answer: $7.65 for a dozen/12

Step-by-step explanation: 2.55 x 3

 1) -  Hence, OPTION (A ):  BC  = √58

2) -  The measure of the Angle to the Nearest Tenth is:  73.6 degrees

1) - ΔABC  is a Right Triangle.  If  AB  =  3  and  AC  =  7,  Find BC. Leave in Simplest Radical Form.

AB^2  +  AC^2   =  BC^2

       AC  = 7, AB  =  3  Into  AB^2  +  AC^2  = BC^2

        3^2  +  7^2  =  BC^2

Hence,  Option (A):   BC  =  √58

2) - The tangent of an angle is 3.4. What is the measure of the angle to the nearest tenth?

Let Angle  Be:  ∝

tan ∝  =  3.4

      ∝  =  tan^-1 (3.4)

      ∝   =  73.6104597 degrees

      ∝   =   73.6 degrees

Therefore, the measure of the Angle is:  73.6 degrees

I hope this helps you!

Answer:

C

Step-by-step explanation:

Both the given equations are of Perpendicular lines.

Perpendicular lines are defined as two lines that meet or intersect each other at right angles (90°).

Given are two equations of lines

y-2= x+20

y = x+20+2

y = x+22.....(i)

y-2= -(x+20)

y = -x-20+2

y = -x-18,,,,,,,(ii)

The slopes of the equation are 1 and -1, We know that perpendicular lines have slopes that are negative reciprocals of one another.

Hence, The lines given are perpendicular lines

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The approximate area of the trapezoid is determined as  13.95 unit².

The approximate area of the trapezoid is calculated as follows;

Area = ¹/₂(b₁ + b₂)h

Where;

The y-coordinates of the points on the curve at x=3/2 and x=4 is calculated as follows;

y(3/2) = - (3/2)²/2 + 3/2 + 5

y(3/2) = -9/8 + 3/2 + 5

y(3/2) = 5.375

y(4) = -4²/2 + 4 + 5

y(4) = -8 + 9

y(4) = 1

h = 5.375 - 1 = 4.375

The approximate area of the trapezoid is calculated as;

Area = ¹/₂(5.375 + 1) x 4.375

Area = 13.95 unit²

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A. The domain for a quadratic equation is ALL REAL NUMBERS OR (-~,~) negative infinity to positive infinity.

B).The possible values or Minimum value the graph can attain.

x=-b/2a(Note...This also corresponds to the vertex).

a=1

b=5

c=6

x= -b/2a = -5/2(1) = -5/2

To get the corresponding value for y... substitute x=-5/2 into the eqn

y=(-5/2)²+5(-5/2)+6

y=25/4 - 25/2 + 6

y=-1/4

Range (-5/2,-1/4)

C)To get x-intercept.

Values of x that satisfies the equation or the points where the graph crosses to the other side.

Set y=0

x²+5x+6=0

x²+3x+2x+6=0

By Grouping

(x²+3x)+(2x+6)=0

x(x+3)+2(x+3)=0

x+2=0 or x+3 =0

x=-2 or -3.

These are x-intercepts

D). To get y-intercept... Set x =0

Doing that

y=0²+5(0)+6

y=6.

This is the y-intercept.

E). The Vertex corresponds to the range

So the vertex is where the graph divides symmetrically or equally

(-5/2,-1/4).

F. Axis of symmetry = -b/2a = -5/2.

Answer: 1/3

Step-by-step explanation:

The probability of selecting a chocolate cream pie can be found by dividing the number of chocolate cream pies by the total number of pies:

Probability of selecting a chocolate cream pie = Number of chocolate cream pies / Total number of pies

Probability of selecting a chocolate cream pie = 4 / 12

Simplifying this fraction by dividing the numerator and denominator by 4 gives:

Probability of selecting a chocolate cream pie = 1/3

Therefore, the probability of selecting a chocolate cream pie from Annie's Pie Shop is 1/3.

Answer:

4x +3y

Step-by-step explanation:

Answer:

No Solutions

Step-by-step explanation:

3(4x - 8) = -24 + 12x

12x - 24 = -24 + 12x

12x - 12x - 24 = -24

12x -12x = -24 +24

0 = 0

No Solutions

Answer:

W = 35/4 aka 8 3/4 or 8.75

Step-by-step explanation:

Answer: w = 35/4

Step-by-step explanation: w−

2

1

​

=8

4

1

​

Multiply both sides of the equation by 4, the least common multiple of 2,4.

4w−2=8×4+1

Multiply 8 and 4 to get 32.

4w−2=32+1

Add 32 and 1 to get 33.

4w−2=33

Add 2 to both sides.

4w=33+2

Add 33 and 2 to get 35.

4w=35

Divide both sides by 4.

w= 35/4

​

A normal distribution is a type of continuous probability distribution for a real-valued random variable in statistics.

Yes, the large-sample confidence interval will be valid.

A normal distribution is a type of continuous probability distribution for a real-valued random variable in statistics.

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data far from the mean.

The confidence interval will be valid regardless of the shape of the population distribution as long as the sample is large enough to satisfy the central limit theorem.

A sample is considered large when n ≥ 30.

By 'valid', it means that the confidence interval procedure has a 95% chance of producing an interval that contains the population parameter.

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Step-by-step explanation:

Q.1

6×sqrt(27) + 11×sqrt(75) =

= 6×sqrt(3×9) + 11×sqrt(3×25) =

= 3×6×sqrt(3) + 5×11×sqrt(3) =

= 18×sqrt(3) + 55×sqrt(3) = 73×sqrt(3)

Q.2

53×sqrt(5) × (-103×sqrt(50)) =

= 53×-103 × sqrt(5)×sqrt(50) =

= -5459 × sqrt(5×50) = -5459 × sqrt(250) =

= -5459 × sqrt(10×25) = -5459 × 5×sqrt(10) =

= -27,295 × sqrt(10)

Q.3

1/4 + 1/2 rational (as both terms are rational)

sqrt3 + 4 irrational (as sqrt(3) is not rational)

sqrt4 + 7 rational (sqrt(4) = 2, 2+7 = 9)

2 x sqrt9 rational (sqrt(9) = 3, 2×3 = 6)

7 x sqrt6 irrational (sqrt(6) is not rational)

4x2sqrt3 irrational (sqrt(3) is not rational)

3. 7 x (1/3) rational (all terms are rational)

7 x sqrt81 rational (sqrt(81) = 9, 7×9 = 63)