Use the table from problem 1 to complete this problem.
Write an exponential decay function to represent the amount of medicine, M, left in the body after t, hours.
A.M(t)=(0.85)t

B.M(t)=400(0.85)t

C.M(t)=15(400)t

D.M(t)=400(0.15)t

Patrick received a total of approximately $6,785.97 over the course of 52 weeks.

To calculate the total amount of money Patrick received over the 52 weeks, we can use the concept of a geometric sequence. The first term of the sequence is $10, and each subsequent term is 10% more than the previous term.

To find the sum of a geometric sequence, we can use the formula:

Sn = a * (r^n - 1) / (r - 1),

where Sn is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = $10, r = 1 + 10% = 1.1 (common ratio), and n = 52 (number of weeks).

Plugging these values into the formula, we can calculate the sum of the sequence:

S52 = 10 * (1.1^52 - 1) / (1.1 - 1)

After evaluating this expression, we find that Patrick received approximately $6,785.97 over the 52 weeks.

As a result, Patrick collected about $6,785.97 in total over the course of 52 weeks.

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Answer:

x < 45

Step-by-step explanation:

Answer:

1 1/15

Step-by-step explanation:

1. Change the division sign to a multiplication sign. (4/5) x (3/4)

2. Flip 3/4. (4/5) x (4/3)

3. Multiply the numerators together and multiply the denominators together. 16/15

4. Simplify. 1 1/15

4/5 ÷ 3/4 is 1 1/15

4/5 ÷ 3/4

To perform division :

Numerator = 4/5

Numerator = 4/5 Denominator = 3/4

Take the reciprocal of the denominator and use the multiplication operator :

Reciprocal of 3/4 = 4/3

4/5 × 4/3 = (4 × 4) / (5 × 3) = 16/15 = 1 1/15

Hence, 4/5 ÷ 3/4 = 1 1/15

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Answer:

(x,y) => (x, -y)

Step-by-step explanation:

\(y = 7x + 3\)

\( - y = 7x + 3\)

\(y = - 7x - 3\)

so

\(g(x) = - 7x - 3\)

Hence, \(g(x) = - 7x - 3\).

What is the function?

Functions are often defined by a formula that describes a combination of arithmetic operations and previously defined functions; such a formula allows computing the value of the function from the value of any element of the domain.

Here given that,

Let \(g(x)\) be the reflection across the x-axis of the function \(f(x) = 7x + 3\). Identify the rule for \(g(x)\).

So,

\(y = 7x + 3\\-y= 7x + 3\\y = - 7x - 3\\g(x)=- 7x - 3\)

Hence, \(g(x) = - 7x - 3\).

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The smallest positive solution to 5 cos (2x) = 4 accurate to at least two decimal places is x ≈ 0.52.

We can start solving for x by isolating the cosine term and then taking the inverse cosine of both sides

5 cos(2x) = 4

cos(2x) = 4/5

Taking the inverse cosine of both sides, we get

2x = cos^(-1)(4/5) + 2πn or 2x = -cos^(-1)(4/5) + 2πn

where n is any integer.

Solving for x, we divide both sides by 2 and simplify

x = (cos^(-1)(4/5) + 2πn)/2 or x = (-cos^(-1)(4/5) + 2πn)/2

To find the smallest positive solution, we need to set n = 0 and choose the solution with the smallest value of x. Using a calculator, we get

x ≈ 0.5236 or x ≈ -0.5236

Since we want the smallest positive solution, we choose

x ≈ 0.5236

x ≈0.52

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Answer:

50+100x=300x+75x

Step 1: Simplify both sides of the equation.

50+100x=300x+75x

100x+50=(300x+75x)(Combine Like Terms)

100x+50=375x

100x+50=375x

Step 2: Subtract 375x from both sides.

100x+50−375x=375x−375x

−275x+50=0

Step 3: Subtract 50 from both sides.

−275x+50−50=0−50

−275x=−50

Step 4: Divide both sides by -275.

\(\frac{-275x}{-275}\) =  \(\frac{-50}{-275}\)

x= \(\frac{2}{11}\)

A fraction is a way to describe a part of a whole. The quotient of the fraction is 1/(t+4)².

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

The quotient of  \(\dfrac{\dfrac{t+3}{t+4}}{t^2+7t+12}\) can be found by factorizing the denominator of the fraction. Therefore, the factors of the denominator are,

t² + 7t + 12

= t² + 4t + 3t + 12

= t(t+4) +3(t+4)

= (t+4)(t+3)

Now, quotient will be,

\(\dfrac{\dfrac{t+3}{t+4}}{t^2+7t+12}\\\\\\=\dfrac{\dfrac{t+3}{t+4}}{(t+4)(t+3)}\\\\\\=\dfrac{(t+3)}{(t+4)(t+3)(t+4)}\\\\\\= \dfrac1{(t+4)^2}\)

Hence, the quotient of the fraction is 1/(t+4)².

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Answer:

Step-by-step explanation:

3x+4y=38

The polynomial that represents the volume of the rectangular box is 3x² - x - 24 = 0

The dimension of the rectangular box are 9 inches, 8 inches and 3 inches.

The volume of the rectangular box can be expressed as follows:

volume of the rectangular box = l w h

where

Therefore,

w = x inches

l = 3x

h = 3x - 1

volume of the rectangular box = 72x

Therefore, the polynomial that represents the volume of the rectangular box is as follows:

72x = 3x × x × (3x - 1)

72x = 3x²(3x - 1)

72x = 9x³ - 3x²

9x³ - 3x² - 72x = 0

3x(3x²- x - 24) = 0

3x² - x - 24 = 0

Therefore,

x = 3 or - 8 / 3

we can only use positive values.

Hence, the dimension of the rectangular box is as follows:

w = 3 inches

l = 3(3) = 9 inches

h = 3(3) - 1 = 8 inches

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Answer:

EM = 42

Step-by-step explanation:

If M is the midpoint, then we can say that EM = MG.

So now, I can set up an equation:

7x = 8x - 6

And solve for x.

7x = 8x - 6

 -8x     -8x

-x = -6

x = 6

Since we are trying to find EM, and EM is 7x, we can multiply x by 7 to find our answer:

7x

7(6)

42

EM = 42

Answer:

0.02 inches per minute

Step-by-step explanation:

1 Week = 10080 minutes

Formaul: multiply the time value by 10080  to find the minutes in a week or do it the long way 60x24x7 = 10080

230/10080 = 0.02281746031 or 0.02 rounded to nearest hundert.

The correct inequality is:

A. 0.095x < 65.00.

To determine the inequality that represents the numbers of kilowatt-hours a customer could use in a month for the cost to be less than $65.00, we need to look for the rate at which the cost of electricity changes with the amount of electricity used.

From the table, we can see that the cost of electricity increases as the amount of electricity used increases.

We can also see that the cost per kilowatt-hour (the rate) is not constant. For example, the cost per kilowatt-hour for the first month is:

27.55 / 290 ≈ 0.095

But for the fourth month, it is:

47.50 / 500 ≈ 0.095

This means that the rate is not constant, and we cannot simply use a proportion to determine the numbers of kilowatt-hours that will result in a cost of less than $65.00.

However, we can use the data to create an inequality that represents the numbers of kilowatt-hours that will result in a cost less than $65.00. We can start by finding the highest cost per kilowatt-hour:

43.70 / 460 ≈ 0.095

This means that the cost per kilowatt-hour is always less than or equal to 0.095.

Next, we can set up the inequality:

0.095x < 65.00

This inequality represents the numbers of kilowatt-hours that will result in a cost less than $65.00, because if the cost per kilowatt-hour is always less than or equal to 0.095, then the total cost will be less than $65.00 if and only if the number of kilowatt-hours used is less than 684.21 (which is the result of dividing $65.00 by 0.095).

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The frequency of revision times is given by the product of the frequency

density value and the class width.

Correct response:

The estimate of the number of students who revised for less than 45

minutes is given by the area, A, under the histogram to the left of the 45

minute mark as follows;

Frequency, f = Frequency density × Class width

Number of students = ∑f

Therefore;

A = 5 × 2 + 10 × 2.2 + 20 × 1.6 + 10 × 0.8 = 72

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The amount of plastic wrap that is required to cover the entire wedge is 316cm²². This would be the same as the total surface area. The nearest option is (Option 3)

The quickest way to determine the amount of wrapper that will cover the above shape is to find the surface area of each of the parts:

Base = 12 * 9 = 108cm². Since this occurs in two places, the total surface area of the base and the top = 108*2 = 216cm²

The area Right Triangle sides = (1/2 b * h) *2

= 1/2 * 5 * 12 *2

= 60 cm²

The area of the rectangluar side = Lxw

= 9 * 5

= 40cm²

Thus the total surface area =

216 + 60 + 40
= 316cm²

Hence the total amount or wrapper needed to cover the entire shape is 316cm² and the nearest option is option 3 - 330cm².

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Answer:

The first one.

Step-by-step explanation:

The fraction 4/7 represents the feet.

Answer:

A I’m pretty sure.

Step-by-step explanation:

If Mrs brown uses 1/4 package of graph paper for each class, needs 1 1/2 packages to serve all of her classes, she teaches 6 classes.

If Mrs. Brown uses 1/4 package of graph paper for each class, then the total number of classes she teaches can be found by dividing the total number of packages she needs by the amount used per class.

Let x be the number of classes Mrs. Brown teaches. Then, we can set up the following equation:

1/4 * x = 1 1/2

To solve for x, we need to isolate x on one side of the equation. We can start by converting the mixed number 1 1/2 to an improper fraction:

1 1/2 = 3/2

Substituting this value into the equation, we get:

1/4 * x = 3/2

Multiplying both sides by the reciprocal of 1/4, which is 4/1, we get:

x = 3/2 * 4/1 = 6

Therefore, Mrs. Brown teaches 6 classes. We can check this answer by verifying that 1/4 of a package of graph paper is indeed used per class, and that 1 1/2 packages are needed for all 6 classes:

1/4 * 6 = 1 1/2

So the answer is 6 classes.

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7 test scores are 85 or greater according to the given scenario.

The third quartile (Q3) is a measure of central tendency that represents the value separating the lower 75% of a dataset from the upper 25%. In this case, the third quartile has a value of 85, meaning that 75% of the test scores are 85 or lower.

Since there are 30 exams in total, 30 x 0.75 = 22.5 exams have scores of 85 or lower. To find the number of exams with scores of 85 or greater, we subtract the number of exams with scores of 85 or lower from the total number of exams, which is 30 - 22.5 = 7. This means that 7 exams have scores of 85 or greater.

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The law of sine or the sine law states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.

The law of sine is used to find unknown angles or sides of oblique triangles. An oblique triangle is defined as any triangle that is not a right triangle. The law of sine must work simultaneously for at least two angles and measurements on each side.

In general, the law of sine is defined as the ratio of the side length to the sine of the opposite angle. Applies to all three sides of his triangle, or to its sides and corners.

a/SinA=b/sinB=c/SinC

In a triangle, dividing side "a" by the sine of angle A and dividing side "b" by the sine of angle B equals side "c" divided by the sine of angle C.  

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Carl Friedrich Gauss, the "Prince of Mathematicians," made groundbreaking contributions to number theory, geometry, physics, and statistics, leaving a lasting impact on the field of mathematics.

We have,

Carl Friedrich Gauss, known as the "Prince of Mathematicians," made significant contributions to number theory, geometry, physics, and statistics.

He formulated the fundamental theorem of arithmetic, developed concepts in differential geometry such as intrinsic curvature and Gaussian curvature, and formulated Gauss's law for electric fields.

Gauss's work laid the foundation for modern mathematics and his emphasis on rigor and precision influenced subsequent generations of mathematicians.

His legacy as one of the greatest mathematicians of all time is based on his profound theorems, laws, and concepts that continue to shape the field.

Thus,

Carl Friedrich Gauss, the "Prince of Mathematicians," made groundbreaking contributions to number theory, geometry, physics, and statistics, leaving a lasting impact on the field of mathematics.

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Answer:

(5x5)squared is basically 25squared

Step-by-step explanation:

Answer:

1/10

Step-by-step explanation:

The fraction 5/10 is equal to 1/2 and 1/5 of the girls wears glasses so if you multiply 1/2 and 1/5 you get 1/10.

\(\frac{1}{5}\)·\(\frac{1}{2}\)= \(\frac{1}{10}\)

When multiplying fractions you multiply across so the numerators are multiplied together and the denominators are multiplied together.

Answer:

B

Step-by-step explanation:

(f – g)(x) = f (x) – g(x)=

\(3 {x}^{2} - 4x + 3 \\ - 2 {x}^{2} + 6x + 4 \\ = 5 {x}^{2} - 10x - 1\)

Answer:

a =3/4

Step-by-step explanation:

2/3 times 3/4 = 1/2

1/2 (or 3/6) - 1/6 = 2/6

2/6 simplifies to 1/3

If there are 6 students and one is selected for best student and another is selected for runner up, then 15 different ways that we can arrange the students

Total number of students in the class = 6 students

Number of students for best student = 1 student

Number of students for runner up = 1 students

Total number of students needed = 2

Here we have to use the combination

6\(C_2\) = 6! / 2!(6 - 2)!

= 6! / 2! × 4!

Split the terms and cancel it

= 6 × 5 / 2 × 1

Multiply the terms

= 30 / 2

Divide the numbers

= 15 combinations

Therefore, there are 15 combinations

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The mass of iron III sulfate is  300 g.

If 1 mole of iron III sulfate is produced when 3 moles of hydrogen is produced

x moles of iron III sulfate is produced when 2.25 moles of hydrogen is produced

x = 1 * 2.25/3

= 0.75 moles

Mass of the iron III sulfate = 0.75 moles * 400 g/mol

= 300 g

Number of moles of iron = 85 g/56 g/mol

= 1.5 moles

If 2 moles of iron produces 1 mole of   iron III sulfate

1.5 moles of iron produces 1.5 * 1/2

= 0.75 moles

Mass of the  iron III sulfate = 0.75 moles * 400 g/mol

= 300 g

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A) The rearranged formula is:

r = d/t

B) Using the above formula we can see that the rate is 25,000 m/h.

C) Here we have the linear equation:

d = (25,000 m/h)*t

Here we need to use the formula:

distance = rate*time.

To solve this formula for the rate, we need to divide both sides by the time, so we will get:

rate = distance/time.

Writing this with the given variables:

r = d/t.

b) Now we know that the distance is 800,000 meters and the time is 4 hours, then the rate will be:

r = 100,000m/4h = 25,000 m/h

The rate is 25,000 meters per hour.

c) Now we wil get the linear equation:

d = r*t

d = (25,000 m/h)*t

This linear equation gives the distance traveled in a time t.

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Part A:

Rearrange the distance formula, d = rt, to solve for rate. The distance formula is given by d = rt, where d is the distance traveled, r is the rate at which the distance is being traveled, and t is the time taken to travel the distance.
To solve for rate, we can rearrange the formula as follows: d = rt d/t = r [dividing both sides by t] r = d/t

Therefore, the formula for rate is r = d/t.

Part B: Find the falcon's rate in meters per hour. Given that the falcon flies 800,000 meters in 4 hours, we can use the formula for rate to find its speed. r = d/t r = 800,000/4 r = 200,000 meters per hour.

Therefore, the falcon's rate is 200,000 meters per hour.

Part C: Rearrange the distance formula, d = rt, to solve for time. To solve for time, we can rearrange the formula as follows: d = rt t = d/r [dividing both sides by r]

Therefore, the formula for time is t = d/r.

Rotation is the rigid type of transformation which is equivalent to the two reflections across intersecting lines.

Therefore, the rigid type transformation which is equivalent to two reflection across the intersecting lines is called rotation.

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