Which expressions are equivalent to -8/13

The requried quantity of drug that remains in the body, in the long run, is 220 mg.

Let's denote the amount of drug in the body just before taking the nth tablet by [tex]D_n[/tex]. We know that [tex]D_0 = 0[/tex](since the patient hasn't taken any tablets yet) and that 5% of the drug is present in the body just before taking a tablet remains in the body. Therefore, we can write:

[tex]D_1 = 110\\D_2 = 0.95 * D_1 + 110 = 203.5\\D_3 = 0.95 * D_2 + 110 = 292.225\\D_4 = 0.95 * D_3 + 110 = 376.81375[/tex]

We can see that the formula for [tex]D_n[/tex] is:

[tex]D_n = 110 * (1 - 0.05)^n + 110 * (1 - (1 - 0.05)^n) / 0.05[/tex]

Simplifying this formula, we get:

[tex]D_n = 220 * (1 - 0.95^n)[/tex]

Now, we want to find the amount of drug that remains in the body in the long run. This means we want to find the limit of [tex]D_n[/tex]  as n goes to infinity. Using the formula above, we can see that:

[tex]lim_ {n- > oo} D_n = lim_ {n- > oo} 220 * (1 - 0.95^n) = 220[/tex]

Therefore, the quantity of drug that remains in the body, in the long run, is 220 mg.

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In a a case whereby factory that has 6 X 10³ workers makes 2.4 X 105 products each day, the average amount of products made per worker is 4 *10^1 products per worker

The term "average" in mathematics typically refers to a measure of central tendency, which is a way to describe the typical or common value in a set of numbers. There are several types of averages.

We can calculate the required value as

( 2.4 X 10^5 )/ (6 X 10³)

=4 *10^1 products per worker

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Answer:

1/8

Step-by-step explanation:

If "over" refers to (4 * 6) as a whole,

[tex]\frac{3}{4*6}\\\\=\frac{3}{24}\\\\=\frac{1}{8}[/tex]

If "over" refers to division,

[tex]3 \div 4 \times 6\\= 0.75 \times 6\\= 4.5[/tex]

I would suppose it's the first one, so, ignore the second one if you haven't learnt BODMAS yet.

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Note that the median of the distribution or the density curve is -6. (Option C)

If the curve is a straight line and the area under the curve appears to be a rectangle, then we can assume that the density curve is a uniform distribution. In this case, the median of the distribution is simply the midpoint of the interval, which would be

(-10 + (-2))/2

= -6.

A density curve is a mathematical model used to describe the overall pattern of a dataset. It is a smooth curve that approximates the distribution of the data and shows the relative frequencies of observations at different values.

The area under the curve represents the total proportion of observations in the dataset, and the curve is normalized such that the total area under the curve equals one. Density curves are used in statistics to analyze and interpret data, and can be used to make predictions about future observations.

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Answer:

Tyshawn would have to sell 6 computers on a given day to get paid $225

Step-by-step explanation:

We can use the information in the table to find the equation of the linear relationship between a (the number of computer sales) and p (Tyshawn's total pay):p = 75 + 25aThis equation tells us that Tyshawn's total pay is $75 plus $25 for each computer he sells.To find out how many computers Tyshawn would have to sell in order to get paid $225 on a given day, we can substitute p = 225 into the equation and solve for a:225 = 75 + 25a150 = 25aa = 6

One such tool that enables us to visualise the given math issue using various-sized rectangles or bars is the bar model.

A bar model in mathematics is a visual representation of a subject or problem where the known and unknown quantities are represented by bars or boxes. To answer issues involving the four operations of addition, subtraction, multiplication, and division, bar models are most frequently utilised.

To help kids "see" mathematical structure, the bar model is utilised in teaching for mastery. It is not a method for solving issues, but rather a strategy to uncover the mathematical underpinnings of a problem and obtain knowledge and clarity to aid in its resolution.

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Image attached below,

a) the exponential equation equivalent to log8 1/64 = 2 is 1/64 = [tex]8^{(-2)}[/tex]

b)  the logarithmic equation equivalent to 3^0 = 1 is log3 1 = 0.

What is exponential equation?

An exponential equation is one in which the exponent contains a variable.

(a) We can rewrite the logarithmic equation as an exponential equation by using the definition of logarithms. The logarithmic equation

log8 1/64 = 2

means that 8 raised to the power of 2 is equal to 1/64:

[tex]8^2 = 1/64[/tex]

Thus, we can write the exponential equation as:

[tex]1/64 = 8^{(-2)}[/tex]

Therefore, the exponential equation equivalent to log8 1/64 = 2 is 1/64 = [tex]8^{(-2)}.[/tex]

(b) We can rewrite the exponential equation as a logarithmic equation by using the definition of logarithms. The exponential equation

[tex]3^0 = 1[/tex]

means that the logarithm of 1 to the base 3 is equal to 0:

log3 1 = 0

Therefore, the logarithmic equation equivalent to 3^0 = 1 is log3 1 = 0.

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Answer: The formula for compound interest is:

A = P(1 + R/100)^t

where A is the amount after t years, P is the principal amount, R is the rate of interest per annum, and t is the time period in years.

Here, P = Rs. 3,500, R = 8%, and t = 2 years.

So, the amount after 2 years will be:

A = 3,500(1 + 8/100)^2

= 3,500(1.08)^2

= 3,892.32

Therefore, the compound interest for 2 years will be:

CI = A - P

= 3,892.32 - 3,500

= 392.32

Hence, the compound interest on Rs. 3,500 for 2 years at the rate of 8% per annum is Rs. 392.32.

Step-by-step explanation:

The owner can advertise 400 different sound systems. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

All real numbers can be explained using the four fundamental operations, generally known as "arithmetic operations." In mathematics, operations like quotient, product, sum, and difference occur after operations like division, multiplication, addition, and subtraction.

We are given that the owner of a stereo store carries 5 different CD players, 8 different receivers, and 10 different speakers and each sound system consists of one of each item.

So, the different sound systems that the owner can advertise is obtained by using the multiplication operation, which gives:

⇒ Different sound systems = 5 * 8 * 10

⇒ Different sound systems = 400

Hence, the owner can advertise 400 different sound systems.

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The truth table for the given expression can be given using p= T q = T, p^q = T, ~p = F, ~q = F, ~q v ~p = T, and  (p ^ q) =~p v ~q = T, thus proving the required.

The field of symbolic logic known as propositional logic, also referred to as sentential logic or statement logic, is concerned with propositions or statements, which are declarative phrases that can be true or untrue. To represent propositions and their relationships, propositional logic employs symbols and operators.

Many disciplines, including mathematics, computer science, philosophy, and others, employ propositional logic as a tool for debating the truth or falsity of propositions and analysing arguments.

The truth table for the given expression can be given as:

p  |  q  |  p ^ q  |  ~p  |  ~q  |  ~q v ~p  |  (p ^ q) =~p v ~q

-------------------------------------------------------------

T  |  T  |    T    |   F  |  F   |    T     |         T

T  |  F  |    F    |   F  |  T   |    T     |         T

F  |  T  |    F    |   T  |  F   |    T     |         T

F  |  F  |    F    |   T  |  T   |    T     |         T

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Using the total area of the rectangular pool we know that the required width of the pathway is 3.6 ft respectively.

In the Euclidean plane, a rectangle is a quadrilateral with four right angles.

A parallelogram with a right angle or an equiangular quadrilateral, where equiangular means that all of its angles are equal, are other ways to define it.

A rectangle with four equal-length sides is a square.

Squares are not always rectangles, but rectangles are always squares.

So, the pool and walkway together have a 360 square foot total space.

Assume that the walkway is w feet in width.

Since the pool has an additional w feet of width on both sides, the total area's measurements can be expressed as (8 + 2w) by (10 + 2w).

Thus, we can construct the following equation:

(8 + 2w) x (10 + 2w) = 360

By enlarging and condensing the left side, we obtain:

4w² + 36w - 80 = 0

Using the quadratic formula, we can find w:

w = (-b ± √(b² - 4ac)) / 2a

Here, an equals 4, b equals 36, and c equals -80. When these values are added to the formula, we obtain:

w = (-36 ± √(36² - 4(4)(-80))) / 8

w = (-36 ± √(1872)) / 8

w ≈ -5.6 or w ≈ 3.6

We can ignore the first option because the width cannot be negative. Consequently, the pathway should be around 3.6 feet wide.

Therefore, using the total area of the rectangular pool we know that the required width of the pathway is 3.6 ft respectively.

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The total expenses of the tournament are $1,023.60 and the total income is $2,048. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

With the help of the four fundamental operations, often known as "arithmetic operations," any real number may be explained. Operations like quotient, product, sum, and difference come last in mathematics, while operations like division, multiplication, addition, and subtraction come first.

From the information given in the question, we have

⇒ Expenses include:

Permit for the event costing $75.60

Rent of the Gym for 8 hours = $62.50 x 8 = $500

Cost of caretaker for 8 hours on a Saturday =  $56 x 8 = $448

Now, using the addition operation, we get

Total expenses = $75.60 + $500 + $448

Total expenses = $1,023.60

Similarly, using multiplication operation, we have

⇒ Income including

Entry fee per player =  $32 x 8 = $256 per team

Income from 8 teams =  $256 x 8 = $2,048

So,

Total income = $2,048

Hence, the total expenses of the tournament are $1,023.60 and the total income is $2,048.

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The probability that y is between 5.1 and 5.7 is approximately 0.4292.

Probability is a way to gauge how likely or unlikely something is to happen. It is a number between 0 and 1, where 0 denotes an improbable event and 1 denotes an inevitable one.

Since the sample size is large (n = 70), we can use the Central Limit Theorem to approximate the sampling distribution of the sample mean as normal with mean μ = 5 and standard deviation σ/sqrt(n) = 2/sqrt(70) ≈ 0.24.

Now we want to find the probability that y, the sample mean, is between 5.1 and 5.7. We can use the standard normal distribution to do this by standardizing y:

z = (y - μ) / (σ / sqrt(n)) = (y - 5) / 0.24

The probability that y is between 5.1 and 5.7 is equivalent to the probability that z is between:

z1 = (5.1 - 5) / 0.24 ≈ 0.42

and

z2 = (5.7 - 5) / 0.24 ≈ 2.92

Using a standard normal distribution table or calculator, we can find that the probability of z being between z1 and z2 is approximately 0.4292.

Therefore, the probability that y is between 5.1 and 5.7 is approximately 0.4292.

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Answer:

hope this will help you...

The correct option -D. 5;  Thus, the value of x for the given external secant segment and the tangent on the circle is found as:x = 5.

A line that precisely intersects a circle at two points is said to be a secant.

The size of the angle created when two tangents, two secants, or two tangents cross outside of a circle is equal to one-half a positive difference between the sizes of the intercepted arcs.

Using the Theorem:

The square of a length of tangent is equal the the product of such external secant segment and the overall length of the secant if one secant and one tangent both drawn to a circle from a single exterior point:

4(4 + x) = 6²

16 + 4x = 36

4x = 36 - 16

4x = 20

x = 20/4

x = 5

Thus, the value of x for the given external secant segment and the tangent on the circle is found as:x = 5.

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The statements that provide support for Chloe's claim are A<0 because A is to the left of zero, B>0 because B is to the right of zero. So correct option is A and F.

Comparison algebra is a branch of algebra that deals with inequalities and comparisons between different quantities or expressions. In comparison algebra, the goal is to determine the relationships between different expressions or quantities, such as whether one expression is greater than, less than, or equal to another expression.

Comparison algebra involves the use of comparison symbols, such as "<" (less than), ">" (greater than), and "=" (equal to), to express these relationships. For example, if we have two expressions, A and B, we can use the "<" symbol to express the relationship that A is less than B, as in A < B.

In comparison algebra, we can also manipulate inequalities and equations in similar ways as we do with regular algebraic expressions. For instance, we can add, subtract, multiply, or divide both sides of an inequality or equation by the same number or expression, while maintaining the inequality's direction.

The statements that provide support for Chloe's claim are:

A. A<0 because A is to the left of zero.

F. B>0 because B is to the right of zero.

Statement A supports Chloe's claim because Point A is to the left of zero on the number line, which means its value is negative. Statement F also supports Chloe's claim because Point B is to the right of zero on the number line, which means its value is positive.

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Step-by-step explanation:

to find the interest she needs to pay back every month, we need to use this formula:

I = PRT/12

in this case the principle is $300,000, the rate is 7% p.a. and the amount of time is 1 year, if we substitute in our values we:

I = (300,000)(7)(1)/12 = $17,500 in interest every month

to find her yearly income from rent, we have to multiply the monthly rent by 12

1500 × 12 = $18,000

to calculate her loss percentage in a year, we have to subtract 18,000 from 3000 which is 15,000

she said that she hopes the property's value will increase to cover the loss she made.

to cover the loss of $15000 per year, the property needs to increase in value by at least $15000. the percentage increases value can be written as

Percentage increase = (difference in increase/Original price) × 100

so

percentage increase = (15000/300000) × 100 = 5%

so the property needs to increase in value by at least 5% per year to cover the loss.

The woman needs to pay $1750 monthly as interest. Her yearly income from the rent is $18,000. After considering all other costs, she is at a loss of $6000 per year, so the property needs to increase in value by 2% per year to cover this loss.

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Answer:

(-1, -8) is:(x + 7)^2 + (y + 4)^2 = 52

Step-by-step explanation:

i literally just learned this today so here we go:

The equation of a circle with center (h, k) and radius r is given by:

(x - h)^2 + (y - k)^2 = r^2

We are given the center of the circle as (-7, -4), so we can substitute these values for h and k:

(x - (-7))^2 + (y - (-4))^2 = r^2

(x + 7)^2 + (y + 4)^2 = r^2

We also know that the circle contains the point (-1, -8).

We can substitute these values for x and y, and solve for r:

(-1 + 7)^2 + (-8 + 4)^2 = r^2

36 + 16 = r^2

r^2 = 52

Substituting this value of r^2 into the equation for the circle, we get:

(x + 7)^2 + (y + 4)^2 = 52

Therefore, the equation of the circle with center (-7, -4) containing the point (-1, -8) is:(x + 7)^2 + (y + 4)^2 = 52

Answer: To calculate the annual depreciation expense of the equipment using the straight-line method, we need to first determine the depreciable cost of the asset, which is the cost of the asset minus its estimated residual value.

Depreciable Cost = Cost of asset - Estimated Residual Value

Depreciable Cost = $212,000 - $14,000

Depreciable Cost = $198,000

Next, we can use the following formula to calculate the annual depreciation expense:

Annual Depreciation Expense = Depreciable Cost / Useful Life

Annual Depreciation Expense = $198,000 / 15 years

Annual Depreciation Expense = $13,200 per year

Therefore, the annual depreciation expense of the equipment using the straight-line method is $13,200 per year.

Step-by-step explanation:

Answer:

5.4

Step-by-step explanation:

square of 29 = 5.385164807

5.385164807 estimated is 5.4

It would take approximately 1,980 minutes (33 hours) for the tester to eat all possible cheeseburgers.

The histogram should be modified as follows:

A histogram is a type of graphical representation that displays the distribution of a dataset. It is a bar graph-like chart where the data is divided into intervals, called "bins", which are represented by adjacent rectangular bars of varying heights.

Then the height of the histogram gives the number of observations into each data interval.

Hence the histogram should be modified as follows:

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A person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.

How to determine the amount of carpet needed for a rectangular room?

To determine the amount of carpet needed for a rectangular room, you need to convert the measurements to the same unit of measurement. Since the carpet is sold in square yards, we need to convert the dimensions of the room to yards.

The length of the room is given in yards, so we don't need to make any conversions for that dimension. However, the width of the room is given in feet, so we need to convert it to yards by dividing by 3 (since there are 3 feet in a yard),

18 feet ÷ 3 feet/yard = 6 yards

So the dimensions of the room in yards are 10 yards by 6 yards.

To find the total area of the room, we need to multiply the length and width,

10 yards × 6 yards = 60 square yards

Therefore, a person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.

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a) The angular velocity = 0.4π rad/s b) The linear velocity of the hamster = 4π cm/s.

Linear velocity is the rate of change of an object's position with respect to time. It measures how fast an object is moving in a straight line, and is often expressed in units of distance per time, such as meters per second or kilometers per hour.

a) The angular velocity of the wheel can be calculated as follows:

Angular velocity = (2π * number of revolutions) / time

Here, the wheel completes one revolution in 5 seconds, so the number of revolutions is 1 and the time is 5 seconds. Therefore,

Angular velocity = (2π * 1) / 5

Angular velocity = 0.4π rad/s (or approximately 1.26 rad/s)

b) The linear velocity of the hamster can be calculated as follows:

Linear velocity = radius * angular velocity

Here, the radius of the wheel is 10 cm, and the angular velocity we found in part (a) is 0.4π rad/s. Therefore,

Linear velocity = 10 cm * 0.4π rad/s

Linear velocity = 4π cm/s (or approximately 12.57 cm/s)

So the hamster is running at a linear velocity of approximately 12.57 cm/s.

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Answer:

$3.25

Step-by-step explanation:

An ice cream cone that has x scoops of ice cream costs 1 + 0.75x.

So an ice cream cone that has 3 scoops of ice cream costs
1 + 0.75×3 = 3.25 (dollars)

Answer:

D

Step-by-step explanation:

A rotation and translation preserves the length measures of the sides, so FD is equal to 7 inches

Answer: D

Step-by-step explanation:

Answer:

33 thats with the 1 dollar subtracted for the entry fee

Step-by-step explanation:

first you add all the number of marbles you have then you get 41 then divide it by 12 because you have 2 gold and 10 silver and you get 3.4 and multiply that by 10 because its 6 and 4 and you get 34 subtract the entry fee

Answer:

0.222

Step-by-step explanation:

2 divided by 9 is:

0.222 (rounded to the nearest thousandth)

The value of GH in the right angle triangle, given FH and Angle FHG is 22.46 inches.

Since we have the adjacent side (FH) and want to find the hypotenuse (GH), we can use the cosine function.

cos(35°) = adjacent side (FH) / hypotenuse (GH)

We know that FH = 18.4 in. So, we can write the equation as:

cos(35°) = 18.4 / GH

GH = 18.4 / cos(35°)

GH = 18.4 / 0.81915

=  22.46 inches

So, the length of GH, the hypotenuse, is approximately 22.46 inches.

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The flow chart is complete and the answers are given below.

Those figures that have same shape and size are called Congruent Figures.

The flow diagram will be completed as follows

∠2 ≅ ∠4 (  vertical angle theorem )

∠1   ≅  ∠2  ( Given )

∠1  ≅ ∠ 3  ( Vertical Angle Theorem)

∠3   ≅  ∠4  ( Transitive Property of congruence)

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