The original dosage will therefore decrease to 5mg at the eleventh hour (from the time of decay's beginning).
how to solve an equation ?A logical statement that two forms are equal is known as an equation. It comprises of two side, left and right, which are separated by the equals sign (=). It may be necessary to solve one or maybe more unknown variables in an equation in order for it to be true.
As an illustration, the expression 3x + 5 = 14 has one unknown quantity, x. In order to solve for x, we must rewrite the equation using operations that preserve equality, such as deducting 5 both from sides of the equation:
given
We may change A = 5 into the equation above and solve for t to get the time at which there are 5mg left: 5 = 20(1/2)(t/5)
20 divided by both sides:
Using base 2, take the logarithm of both sides:
log2(1/4) = t/5 -2 = t/5
t = -10 after multiplying both sides by 5.
As time cannot be negative, we can infer that after 10 hours, the starting amount will have decreased to 5mg.
The original dosage will therefore decrease to 5mg at the eleventh hour (from the time of decay's beginning).
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A line segment is shown on the coordinate grid.
Select all of the numbers that are included within the range of the line segment.
Without the specific details or an image of the line segment on the coordinate grid, I'm unable to provide you with the specific numbers included in the range.
To help you generally, a line segment is a part of a line with two endpoints, and it is located on a coordinate grid, which is a two-dimensional plane formed by the intersection of horizontal and vertical lines (x and y axes).
To determine the range of the line segment, you need to identify the y-coordinates of the two endpoints.
The range includes all the y-coordinates between those two points, inclusive of the endpoints. To find the range, observe the line segment and note the y-coordinates of both endpoints. Then, list all the numbers (whole or fractional) between those values, including the endpoints themselves.
Once you have the necessary details or an image of the line segment, feel free to ask again, and I'll be happy to help you identify the numbers within the range.
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21. In the diagram at the right, the orange figure is a translation image
of the red figure. Write a rule that describes the translation.
Move the figure 2 units to the right and Move the figure 3 units downwards are the rules to translate any point on the red figure to the corresponding point on the orange figure, and vice versa
To describe the translation rule for the red figure to the orange figure, we need to determine how the red figure was moved to obtain the orange figure.
First, we can see that the orange figure is shifted to the right of the red figure. This means that the x-coordinate of every point on the orange figure is greater than the corresponding point on the red figure.
Second, we can see that the orange figure is shifted downwards from the red figure. This means that the y-coordinate of every point on the orange figure is less than the corresponding point on the red figure.
Therefore, the translation rule for the red figure to the orange figure is:
• Move the figure 2 units to the right (add 2 to the x-coordinate of every point), and
• Move the figure 3 units downwards (subtract 3 from the y-coordinate of every point).
We can use this rule to translate any point on the red figure to the corresponding point on the orange figure, and vice versa. This translation rule can be used in various applications such as computer graphics, engineering, and architecture, where precise translations of objects are necessary.
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At a real estate agency, an agent sold a house for 343000$. The commission rate is 7.5% for the real estate agency and the commission rate for the agent is 30% of the amount the real estate agency gets. How much did the agency make on the house? How much did the agent earn in commission?
Answer: The commission rate for the real estate agency is 7.5% of the sale price, which is:
0.075 x 343000 = $25,725
The agent's commission is 30% of the amount the agency gets, which is:
0.3 x 25725 = $7,717.50
Therefore, the real estate agency made $25,725 on the house and the agent earned a commission of $7,717.50.
Step-by-step explanation:
Spenser is now working with the landscape architect to design the common backyard area. She knows she wants each swimming pool to cover an area of 630 square feet.
Which of these dimensions would work for the swimming pool? Select all that apply. PLEASE ANSWER ASAP
These dimensions would work for the swimming pool are
9 feet by 70 feet
10 feet by 63 feet
14 feet by 45 feet
15 feet by 42 feet
18 feet by 35 feet
21 feet by 30 feet
How to find dimensions of the swimming pool?
to find the dimensions of the swimming pool that covers an area of 630 square feet, we can use the formula:
Area = Length x Width = 394
Let x and y be the length and width of the
swimming pool, respectively. Then we have:
x * y = 630
We need to find the values of x and y that satisfy this equation. We can do this by finding the factors of 630 and checking which pairs multiply to 630.
1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630
From this list, we can see that the following dimensions would work for the swimming pool:
9 feet by 70 feet
14 feet by 45 feet
10 feet by 63 feet
21 feet by 30 feet
15 feet by 42 feet
18 feet by 35 feet
So, the dimensions that would work for the swimming pool.
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A rain drop hitting a lake makes a circular ripple. If the radius, in inches, grows as a function of time in minutes according to r(t)=15t+2−−−−√
, find the area of the ripple as a function of time. Find the area of the ripple at t=2
.
The area of the ripple at t=2 is 32π square inches.
What is area ?
Area is the measure of the size of a two-dimensional surface enclosed by a closed boundary, such as a polygon or a circle. It is typically measured in square units such as square meters, square feet, or square inches.
The equation for the radius of the circular ripple is given by r(t) = √(15t+2). The equation for the area of a circle with radius r is A(r) = πr².
Therefore, the area of the ripple as a function of time is given by:
A(t) = π[r(t)]²
Substituting the expression for r(t), we get:
A(t) = π[(√(15t+2))²]
A(t) = π(15t+2)
A(t) = 15πt + 2π
To find the area of the ripple at t=2, we substitute t=2 into the expression for A(t):
A(2) = 15π(2) + 2π
A(2) = 30π + 2π
A(2) = 32π
Therefore, the area of the ripple at t=2 is 32π square inches.
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I need help what is the square for CDEF
Using the area formula for square, we can find that the area of square CDEF is = 289-unit².
Define a square?In geometry, a square is a two-dimensional plane object with four equal sides and four equal, 90° angles. Although a rectangle only has its opposite sides equal, a rectangle and a square have some properties in common. As a result, a rectangle can only be described as a square if its four sides are equal in length.
As per the question,
In right-angled ΔABC, as per Pythagoras theorem:
AC = √ (AB² + BC²)
= √ (12² + 9²)
= √ 225
= 15.
Similarly, in ΔACD as per Pythagoras theorem:
CD = √ (AC² + AD²)
= √ (15² + 8²)
= √289
= 17
Now, in square CDEF:
Side of square CDEF, CD = 17.
Area = side²
= 17²
= 289-unit².
Therefore, area of square CDEF is = 289-unit².
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Need help
40 points!! I’m
Answer:
1 shorter than 2 longer than 3 short
NEED IMMEDIATELY: The circumference of a circular garden is 65.94 feet what is the diameter of the garden is 3.14 for pie and do not round your answer 
pi x 2r = circ
2r = circ/pi
r = circ /(2 x pi) = 65.94/(2 x 3.14) = 10.5 feet
x>12 on a number graph
On a number line graph, the inequality X > 12 would be represented as follows:
What is number line?A number line is a mathematical tool used to represent and visualize numbers, particularly real numbers, in a linear manner.
On a number line graph, the inequality X > 12 would be represented as follows(check attachment)
The line represents all real numbers, with the arrow pointing towards the right indicating that any number greater than 12 is a solution to the inequality. The circle at the end of the line is an open circle, indicating that 12 is not included in the solution set because the inequality is strict, i.e., X is strictly greater than 12.
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Without evaluating explain why (-8.4)^5 is less than 2^2
Answer:
When you have a negative base and an odd exponent, you always get a negative answer. For example, (-9)^3 written out is -9 * -9 *-9. Although the answer becomes positive for the first two 9s (81) it becomes negative again for the third 9 (-729). A base with a positive exponent will always yield a positive number. Positive numbers are greater than 0 and are always greater than negative numbers.
For f(x)=3x2 +x2,find: {x: f(x)=0}
By answering the presented question, we may conclude that Therefore, the solution set to the equation f(x) = 0 is {0}.
what is function?In mathematics, a function seems to be a link between two sets of numbers in which each member of the first set (known as the domain) corresponds to a specific member of the second set (called the range). In other words, a function takes input from one collection and creates output from another. The variable x has frequently been used to represent inputs, whereas the variable y has been used to represent outputs. A formula or a graph can be used to represent a function. For example, the formula y = 2x + 1 depicts a functional form in which each value of x generates a unique value of y.
the equation:
[tex]3x^2 + x^2 = 0\\4x^2 = 0\\x^2 = 0\\x = 0[/tex]
Therefore, the solution set to the equation f(x) = 0 is {0}.
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I just want to know the answer of that question
Answer:
I think a
good luck
have a good day
On Monday, Tuesday, and Wednesday, Cheryl ran 1 miles each day. On Thursday, she ran 2 miles. On Friday,
she ran 3 miles.
How many miles, in total, did Cheryl run for those five days?
Write your answer as a decimal.
Cheryl ran a total of 8 miles in five days.
1 + 1 + 1 + 2 + 3 = 8
Written as a decimal, this is 8.0 miles.
which functions are symmetric with respect to the origin? y=arcsinx and y=arccosx
Function[tex]y = arcsin(x)[/tex]is symmetric with respect to the origin, while function [tex]y = arccos(x)[/tex] is not. This is as inverse sine function is an odd function, while inverse cosine function is an even function.
If [tex]f(-x) = -f(x)[/tex] for all values of x in the function's domain, then the function is symmetric with regard to the origin. In other words, a function is said to be symmetric with regard to the origin if it passes through the origin and has the same shape on each side of the y-axis.
We must substitute -x for x in each function and simplify to find out if the functions [tex]y = arcsin(x)[/tex] and [tex]y = arccos(x)[/tex] are symmetric with respect to the origin.
According to the equation [tex]y = arcsin(x)[/tex], we get:
[tex]-arcsin = arcsin(-x) (x)[/tex]
Because it is odd, the function[tex]y = arcsin(x)[/tex] is symmetric with respect to the origin.
According to the equation [tex]y = arccos(x)[/tex]:
[tex]x(-arccos) = -arccos (x)[/tex]
Because it is not odd, the function[tex]y = arccos(x)[/tex] is not symmetric with respect to the origin.
In conclusion, [tex]y = arccos(x)[/tex]is not symmetric with regard to the origin, but [tex]y = arcsin(x[/tex] is. Due to the fact that the inverse cosine function is an even function, whereas the inverse sine function is an odd function, this is the case.
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The line of its elements from the upper left corner to the lower right of the second order determinant is called?
Help please!!! Due in a little. Thanks sm
Answer:108 degrees
Step-by-step explanation:easy
Simplify |x/3| if x>0
Answer: -31x
Step-by-step explanation:
|x|31 becomes -x31 which is -31x
Find all integer solutions of
x+y=3
3xy-z*z=9
In conclusion, the integer solutions of the given system of equations are [tex]$(x, y, z) = (1, 2, 0)$ and $(x, y, z) = (-1, 4, 0)$.[/tex]
What is the integer?An integer is a positive, negative, or zero-valued whole number. It is a number without a fractional or decimal component.
To find all integer solutions of the given system of equations:
[tex]x + y &= 3 \[/tex]
[tex]3xy - z^2 &= 9[/tex]
We can start by solving the first equation for one of the variables. Let's solve for y in terms of x:
[tex]x + y &= 3 \[/tex]
[tex]y &= 3 - x[/tex]
Now we substitute this expression for y into the second equation:
[tex]3xy - z^2 &= 9 \[/tex]
[tex]3x(3-x) - z^2 &= 9 \quad \text{Substituting } y = 3-x \[/tex]
[tex]9x - 3x^2 - z^2 &= 9 \[/tex]
[tex]3x^2 + z^2 &= 9x - 9 \[/tex]
[tex]3x^2 - 9x + z^2 &= -9 \quad \text{(1)}[/tex]
Now we will examine equation (1) for integer solutions.
Case 1: [tex]z= 0[/tex]
If then equation (1) becomes:
[tex]3x^2 - 9x &= -9 \quad \text{(1a)} \[/tex]
[tex]3x(x-3) &= -9[/tex]
Since we are looking for integer solutions, 3x and x-3 must have opposite signs. The possible pairs of factors of -9 with opposite signs are (3,-3) and (-3,3). So we have two possible sets of equations to solve:
The discriminant is negative, there are no integer solutions. Therefore, there are no integer solutions for the original system of equations when [tex]z \neq 0.[/tex]
In conclusion, the integer solutions of the given system of equations are [tex]$(x, y, z) = (1, 2, 0)$ and $(x, y, z) = (-1, 4, 0)$.[/tex]
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Find the Area of the figure below, composed of a parallelogram and one semicircle.
Rounded to the nearest tenths place
12
9
22
The area of the figure is approximately 163.8 square units, rounded to the nearest tenths place.
To find the area of this figure, we need to find the area of the parallelogram and the area of the semicircle, and then add them together.
The area of the parallelogram is given by the formula:
A = base x height
In this case, the base is 12 and the height is 9, so:
A_parallelogram = 12 x 9 = 108
The area of a semicircle is given by the formula:
[tex]A = (πr^2)/2[/tex]
where r is the radius of the semicircle.
The diameter of the semicircle is equal to the base of the parallelogram, which is 12. So, the radius of the semicircle is half of the diameter, or 6.
Substituting the values, we get:
A_semicircle = [tex](π x 6^2)/2 = 18π[/tex]
Adding the areas of the parallelogram and the semicircle, we get:
A = A_parallelogram + A_semicircle = 108 + 18π
Using a calculator to approximate π to the nearest tenths place, we get:
A ≈ 108 + 18 x 3.1 = 163.8
Therefore, the area of the figure is approximately 163.8 square units, rounded to the nearest tenths place.
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Geometry kites homework
The value of X when <1 = 3x+15 = 25. Then the value of the missing part of the sides of the kite (KITE) is given as follows;
X = 25
a.) ET = 60
b.) KE = 20
How to calculate the missing parts of the KITE?One of the properties of a kite is that it has two pairs of adjacent equal sides and the longer diagonal bisects the shorter one with the formation of angle 90°.
Therefore to calculate for X when <1 = 3x+15 is as follows;
<1 = 90°
90= 3x+15
3x = 90-15
3x = 75
X = 75/3
X = 25
But IT = ET
Given IT = 2x +20
X = 25
IT = ET = 2(20)+20
= 40+20 = 60
But KI = KE
Given that KI = 2x-30
X = 25
KI= KE = 2(25)-30
= 50-30 = 20
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Use the spinner below:
P(8 or 4) =
The probability of getting an 8 or 4 on the spinner is 1÷4 or 25%.
What is Probability ?
Probability is a branch of mathematics that deals with the study of random events or outcomes. It is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
the probability of getting an 8 or 4 by assuming that the spinner has equally likely outcomes for each number from 1 to 8.
There are two possible outcomes that satisfy the condition of getting an 8 or 4: either the spinner lands on 8 or it lands on 4.
Since there are 8 equally likely outcomes on the spinner, the probability of getting an 8 or 4 is:
P(8 or 4) = number of favorable outcomes ÷ total number of outcomes
= 2 ÷ 8
= 1÷4
Therefore, the probability of getting an 8 or 4 on the spinner is 1÷4 or 25%.
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Candice makes bracelets that contain 2 oval-shaped beads and 8 circular-shaped beads.
She has 32 oval-shaped beads and 38 circular-shaped beads.
How many bracelets can she make?
A relay race is 1 /4 space m i l e s.
There are three relay runners on the team.
Each person runs the same distance.
How far does each person run?
The total distance run by each runner is 1/12 mile.
What is a relay race:
A relay race is a track and field event where athletes compete as part of a team, taking turns running a certain distance and passing a baton to the next runner until all team members have completed their portion of the race.
Here we have
A relay race is 1 /4 space mile
The number of relay runners on the team is 3
Let each runner, runs for x miles
The total distance run by 3 relays = 3x
From the data,
The relay race is 1/4 miles
=> 3x = 1/4 miles
=> 12x = 1 miles
=> x = 1/12 miles
Hence,
The total distance run by each runner is 1/12 mile.
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Lulu observes that when she dilates a quadrilateral from a center of dilation outside the
quadrilateral, the corresponding sides of the original figure and its dilated image are
parallel. Which statement best explains why this occurs?
As a result, the original figure's corresponding sides and those of its enlarged image are parallel.
what is quadrilateral ?A quadrilateral is a closed, two-dimensional form in geometry that has four straight sides. Four sides, four edges, and four angles make up the polygonal shape. The total of a quadrilateral's internal angles is 360 degrees. Kites, squares, rectangles, parallelograms, and trapezoids are examples of quadrilaterals.
given
Each side of the original figure is expanded to meet the dilation scale factor when a quadrilateral is dilated from an outer centre of dilation, and the sides of the dilated image are parallel.
Parallel lines continue to be parallel after scaling because dilatation scales each side of the quadrilateral by a constant factor.
As a result, the original figure's corresponding sides and those of its enlarged image are parallel.
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Help with math problems
The value of the equation are 1. (-2√3 + 2)(√3 - 5) = -16 + 8√3 2. (5 - 4√5)(-2 + √5) = -30 + 21√. 3. (-2 - 3√5)(5 - √5) = -5 - 17√5. 4. (√5 - √3)(√5 + √3) = 2.
What are expressions and equations?An expression is a mathematical sentence without the equal sign that can include variables, operators, and integers. Although it can be appraised or simplified, there isn't a single perfect answer. An expression is, for instance, 3x + 2y.
A mathematical statement that has an equal sign and expresses the equivalence of two expressions is called an equation, on the other hand. To determine the values of variables that meet an equality, equations can be solved. One equation is 3x + 2y = 7, for instance.
1. Multiplying (-2√3 + 2)(√3 - 5), we get:
= -2√3 × √3 + (-2√3 × -5) + (2 × √3) + (2 × -5)
= -2√(3 × 3) + 10√3 - 2√3 - 10
= -2(3) + 8√3 - 10
= -16 + 8√3
Therefore, (-2√3 + 2)(√3 - 5) = -16 + 8√3.
2. Multiplying (5 - 4√5)(-2 + √5), we get:
= 5(-2) + 5√5 + (-4√5)(-2) + (-4√5)(√5)
= -10 + 13√5 + 8√5 - 4(5)
= -30 + 21√5
Therefore, (5 - 4√5)(-2 + √5) = -30 + 21√5.
3. Multiplying (-2 - 3√5)(5 - √5), we get:
= (-2 × 5) + (-2 × √5) + (-3√5 × 5) + (-3√5 × -√5)
= -10 - 2√5 - 15√5 + 3(5)
= -5 - 17√5
Therefore, (-2 - 3√5)(5 - √5) = -5 - 17√5.
4. Multiplying (√5 - √3)(√5 + √3), we get:
= (√5 × √5) - (√3 × √3)
= 5 - 3
= 2
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Jennifer pours 1/3 quart of milk equally into 4 glasses. How much milk, in quarts, does Jennifer pour into each glass?
Answer:
1 ⅓
Step-by-step explanation:
there 4 glasses and you put ⅓ in each one therefore 4 x ⅓ = 1 ⅓
Define and provide real world example for each of the following terms: a. The scarcity principle. b. Rational person c. Economic surplus d. Marginal benefit
Scarcity principle: Resources are limited and choices must be made, b. Rational person: Makes decisions based on logical thinking and self-interest, c. Economic surplus: Net gain to society from producing and consuming a good, d. Marginal benefit: Additional benefit from consuming one more unit of a good or service.
What is statement ?A statement is a declarative sentence that expresses a fact, opinion, or idea. It is a sentence that makes a claim or assertion that can be true or false, and it can be either affirmative (positive) or negative. A statement can be a simple sentence, or it can be a complex sentence that includes multiple clauses
According to the given information:a. The scarcity principle is the economic principle that states that resources are limited and cannot satisfy all human wants and needs. This principle recognizes that we live in a world of limited resources, and therefore, we must make choices about how to allocate those resources to satisfy our wants and needs. For example, a farmer may have limited land and water resources to cultivate crops, and he must choose which crops to grow based on their profitability, water requirements, and market demand.
b. A rational person is an individual who uses logical thinking and makes decisions based on self-interest to achieve the best possible outcome. A rational person weighs the pros and cons of each option and selects the alternative that maximizes their satisfaction or utility. For example, a consumer may compare prices and quality of different brands before purchasing a product to get the best value for their money.
c. Economic surplus is the difference between the total value that consumers place on a good or service and the total cost of producing it. It represents the net gain to society from producing and consuming the good or service. For example, if a firm produces 100 units of a product at a total cost of $500 and sells them for a total of $700, then the economic surplus is $200.
d. Marginal benefit is the additional benefit that a person receives from consuming one more unit of a good or service. It is the change in total benefit divided by the change in the quantity consumed. For example, if a consumer derives 10 units of satisfaction from consuming the first slice of pizza and 8 units of satisfaction from consuming the second slice, then the marginal benefit of the second slice is 8-10=-2 units of satisfaction.
Therefore, a. Scarcity principle: Resources are limited and choices must be made, b. Rational person: Makes decisions based on logical thinking and self-interest, c. Economic surplus: Net gain to society from producing and consuming a good, d. Marginal benefit: Additional benefit from consuming one more unit of a good or service.
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The value of an industrial embroidery machine is decreasing according to the function defined by:
V(t) = 11,700(3)^-0.15
Where t is the number of years since the machine was purchased. What does the y-intercept represent?
A. The value of the machine after 3 years
B. The amount of time it takes for the value of the machine to reach zero
C. The rate at which the value of the machine depreciates
D. The original value of the machine
I think it is A. The value of the machine after 3 years
What do you think?
The product of eight and two, minus the product of three and four
Answer:
4
Step-by-step explanation:
The product of eight and two is 8 x 2 = 16.
The product of three and four is 3 x 4 = 12.
So, the expression "the product of eight and two, minus the product of three and four" can be written as:
16 - 12 = 4
Therefore, the answer is 4.
Luther Williams’ charge account statement shows an unpaid balance of $3,987.11. The monthly finance charge is 1.75 percent of the unpaid balance. What is the new account balance? Show your work.
By adding the monthly finance charge to the unpaid balance, the new account balance is $4,056.91.
What is addition?
Addition is a mathematical operation that involves combining two or more numbers to produce a sum or total. It is commonly denoted by the plus sign (+) and is one of the four basic arithmetic operations.
To find the new account balance, we need to add the monthly finance charge to the unpaid balance.
First, we need to calculate the monthly finance charge:
Monthly finance charge = 1.75% of unpaid balance
= 0.0175 * $3,987.11
= $69.80
Next, we add the monthly finance charge to the unpaid balance:
New account balance = Unpaid balance + Monthly finance charge
= $3,987.11 + $69.80
= $4,056.91
Therefore, the new account balance is $4,056.91.
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