The number of milligrams D (ht) of a certain drug that is in a patient's bloodstream h hours after the drug is injected is given by the following function.

D(h) = 25e -0. 4

When the number of milligrams reaches 6, the drug is to be injected again. How much time is needed between injections?

Round your answer to the nearest tenth, and do not round any intermediate computations.

Using the Pythagorean Theorem we can see that, the sides 9 in, 12 in and 15 in can form a right angle triangle.

In the given question, using the Pythagorean Theorem we have to determine if this is a right triangle.

The given sides are 12 in and 15 in.

A key concept in mathematics is the Pythagorean Theorem, which describes the relationship between the sides of a right-angled triangle.

To check the given sides form a right triangle or not. We have to check that the sum of the square of the sides given a proper square root.

We can also check using the triplet. As we know that 3, 4 and 5 is the triplet that can form a right angle triangle.

The multiple of these triplet also can from a right angle triangle.

So a right angle triangle can be formed by 9 in, 12 in and 15 in.

Using the Pythagorean theorem;

[tex]15^2 = 9^2+12^2[/tex]

225 = 81 + 144

225 = 225

Hence, Using the Pythagorean Theorem we can see that, the sides 9 in, 12 in and 15 in can form a right angle triangle.

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Answer:

a d e

Step-by-step explanation:

Step-by-step explanation:

the temperature of the water is always inversely proportional to the depth x. the larger the depth the lower the temperature.

just the rate of change changes at certain levels.

so, below 900 meters the relation is defined as

T = 4500/x

at 1200 m this means

T = 4500/1200 = 45/12 = 15/4 = 3.75°C

at 2500 m this means

T = 4500/2500 = 45/25 = 9/5 = 1.8°C

the difference in temperature at these 2 levels is

3.75 - 1.8 = 1.95°C

From the table that shows the cost of several bunches of bananas , the equation that is used to represent the cost "C" for "p" pounds is [tex]C=0.42\times p[/tex].

For 2.5 pounds of bunches of bananas the cost is = $1.05 ;

and the cost for 3.5 pounds of bananas , the cost is $1.47 ;

we can calculate the rate of 1 pound of bananas as : [tex]\frac{1.47-1.05}{3.5-2.5}[/tex] ;

On simplifying the above fraction ,

we get ;

⇒ 0.42 ;

the per pound cost for bananas is $0.42 ;

let the number of pounds of bananas be = p ; and

let the cost for p pounds of bananas be = C ;

Therefore, the equation for cost "C" can be represented as : [tex]C=0.42\times p[/tex].

The given question is incomplete , the complete question is

The table shows the cost of several bunches of bananas. What equation can be used to represent the cost C of a bunch that weights P pounds ?

Number of pounds     2.5       3.5       4        4.5

Cost($)                        1.05     1.47     1.68     1.89 .

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The number of solutions for the graphs are - for graph 1 and graph 4 there are infinite solutions, for graph 3 there is no solution and unique solution for graph 2.

What is the equation for a straight line?

A straight line can be written in the form of equation as, y = mx + c. Two straight lines intersect each other only at one point. When two straight lines are parallel to each other the angle between them is zero.

The graphs of a pair of lines for different cases are given.

Since, two equations have a unique solution for intersecting lines, infinite solutions for coinciding lines and no solution for parallel lines.

Given graphs can be considered as per the above rule as follows -

For graph 1 -

The pair of lines are coinciding. So, it has infinitely many solutions.

For graph 2 -

The pair of lines are intersecting each other. So it has a unique solution.

For graph 3 -

The pair of lines are parallel to each other. So, it has no solutions.

For graph 4 -

The pair of lines are coinciding. So, it has infinitely many solutions.

Therefore, the number of solutions for the given graphs are given as infinitely many solutions, unique solution, no solutions, and infinitely many solutions respectively.

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a) 7x

b) 2a + 6b

c) -3b + 7d + 3bd

d) 7ab - 2ac - c

e) 16a + 6

f) 26x - 2

g) 4b + 1

h) -5j - 10

i) 2g + 7

There are three ways to solve systems of linear equations in two variables graphing ,substitution method ,elimination method.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

What makes an equation linear?

When a linear equation is graphed, it always produces a straight line since each term in the equation has an exponent of 1. This is the basis for the term "linear equation" being used to describe it.

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The physical distance they need to travel to get to school, or the distance they need to measure in math class.

Distance for a student of Class 4 would likely refer to the physical distance they need to travel to get to school, or the distance they need to measure in math class. Without more context, it is difficult to provide a specific answer.

In mathematics, distance refers to the measurement of the difference between two points in a space or a geometric figure. It can be represented by a numerical value and is often used to determine the shortest path between two points. The most common distance formula used in Euclidean geometry is the distance between two points (x1, y1) and (x2, y2) is the square root of ((x2 - x1)^2 + (y2 - y1)^2). This is known as the Euclidean distance.

Therefore, The physical distance they need to travel to get to school, or the distance they need to measure in math class.

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The simplest form of the equation, y = 23x + 68, is the same equation of y = 23x + 68, as this is the simplest form.

y = 23x + 68 is a linear equation that it in the slope - intercept form which means that there is no need to simplify it further.

The slope - intercept form is:

y = mx + b

Where:

m = slope of the line

b = y - intercept of the line

The equation shows that the slope is 23 and that the y - intercept is 68. This means therefore , that the equation is as simple as it can be.

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The area of the Sophia's room door from one side with the given dimensions is equal to 1.854 square meters.

As given in the question,

Dimensions of the door of Sophia's room is given by :

Width of the door = 0.9m

Door Height = 2.06m

Doors are always in rectangular shape.

Area of the one side door = Length × Width

Substitute the values we get,

⇒ Area of the one side door =  2.06 × 0.9

⇒ Area of the one side door =  1.854 square meters

Therefore, the area of the one side door of the Sophia's room is equal to 1.854 square meters.

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Answer:

coefficient of xy^2 is : 864 and that of y^3 is 1728

Step-by-step explanation:

Using binomial theorem,

1st term is 1 (ax)^3 = 8x^3 from which a = 2

2nd term is 3(ax)^2(by) = -144x^2y from which b = -12

3rd term is 3(ax)(by)^2 = 3(2x)(-12y)^2 = 864

4th term is 1(by)^3 = 1(-12y)^3 = -1728y^3

Applying the triangle proportionality theorem, the length of AD that will make DE║AB is: AD = 60.

According to the triangle proportionality theorem, the equation or proportion we can create to find x is expressed as:

(2x - 4) / 5x = 3x / 8x

Cross multiply:

8x(2x - 4) = (3x)(5x)

16x² - 32x = 15x²

x² - 32x = 0

Solve to find x by factoring:

The equation x² - 32x = 0 can be solved by factoring:

x(x - 32) = 0

So either x = 0 or x - 32 = 0, meaning x = 32.

The solutions to the equation are x = 0 and x = 32.

Using x = 32:

AD = 2x - 4 = 2(32) - 4

AD = 60

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Team A won the competition by a narrow margin of 13 points.

Points in math are locations in the coordinate plane that can be described by an ordered pair of numbers. Points are often used to graph equations, draw diagrams, and find the solution to problems. Points can also be used to measure distances, angles, and other geometric objects. Points are an essential part of geometry, algebra, and other math topics.

Team A scored 13 goals and incurred 5 penalties, giving them a total of 8 points. On the other hand, team B scored 18 goals and incurred 12 penalties, giving them a total of 6 points. Therefore, team A won by a difference of 8-6=2 points.

It is important to note that any competition should be based upon fair play and sportsmanship. Foul play should not be allowed and all teams should be equally and fairly judged. Furthermore, proper rules and regulations should be implemented to ensure a fair and level playing field. The competition between teams A and B was a good example of how a competition should be conducted in a fair manner.

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The best describe Maria's solution to the equation is Maria incorrectly applied the associative property in going from the line(1) to line(2).

What is associative property?

Rearranging the parenthesis in an expression will not change the outcome since some binary operations in mathematics have the associative feature. Associativity is a legitimate rule of replacement for expressions in logical proofs in propositional logic.

Here, we have

Given:  The equation -2(3x - 5) = 40

-2(3x - 5) = 40

-6x + 10 = 40

-6x = 40 - 10

-6x = 30

x = -5

The solution to the equation is -5 instead of -25/3.

Hence, the best describe Maria's solution to the equation is Maria incorrectly applied the associative property in going from the line(1) to line(2).

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The vertex focus of the parabola is (3,15) and the directrix is x=3.

1. Rewrite the equation in the form y = a(x - h)^2 + k

y = x^2 - 6x + 15

y = 1(x - 3)^2 + 15

2. The vertex focus is (h, k) = (3, 15)

3. The directrix is x = h = 3

By rewriting the equation in the form of y = a(x - h)^2 + k, we can find the vertex focus and directrix of the parabola. The vertex focus of a parabola is the point at which the graph changes direction, and is equal to (h, k). The directrix is the line at which the vertex focus is located, and is equal to x = h. For this equation, h = 3 and k = 15, so the vertex focus is (3, 15) and the directrix is x = 3.

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The markup price of the skateboards is equal to $49.7.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Target sells skateboards for $35. To make a profit in the Spring and Summer months, Target increases the price with a 42% markup.

The markup price will be calculated as,

Markup price = $35 x 1.42

Markup price = $49.7

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Therefore , the solution of the given problem of function comes out to be x =15/2 and x = -4/3.

A science called mathematics studies numbers, their variants, mathematical and the local structures, shapes, and both their existing and projected places. The relationship between a group of inputs, which each have a corresponding output, is described by a function variable . A function is a collection of inputs that together produce a single, recognisable output by each input.

Here,

Given :

=> 2x = 15x²

=> 2 = 15x

=>  x =15/2

=> -6x =8x²

=> -6 = 8x

=>x = -4/3

thus , x =15/2 and x=-4/3

Therefore , the solution of the given problem of function comes out to be x =15/2 and x = -4/3.

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The null hypothesis is a common statistical theory that contends that there is no statistically significant association between any two sets of a single observed variable.

The hypothesis suggests no two given sets make any significance meaning until and unless they are proven wrong.

As given in the example,

The group of answer choices the (population) mean amount of time reading and sending e-mails daily is greater than 60 minutes and the (population) mean amount of time reading and sending e-mails daily is equal to 60 minutes.

You can see in one set the amount of reading and sending e-mails is more than 60 minutes and in other one the amount of time reading and sending e-mails is equal to 60 minutes which doesn't make any sense if you consider them both in a single set of information.

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Answer:

Step-by-step explanation:

angle ACD is corresponding to the angle BCE, hence the line DE is congruent to line AB

The solution for the inequality is x∈(-∞,4)U(1,+∞)

What is inequality?

Inequality is a statement that compares two values and states that one value is greater than, less than, or not equal to the other value.

To solve the inequality (x-4)(x-1)>0, we can first factor it:

(x-4)(x-1)>0

We can then use the Zero Product Property, which states that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero.

So we get:

x-4=0 or x-1=0

x = 4 or x = 1

Now we will test the sign of inequality for x-4 and x-1.

x<4 or x>1

Hence, the solution for the inequality is x∈(-∞,4)U(1,+∞)

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The Graph of quadratic functions gives parabolas that are U-shaped, and wide or narrow depending upon the coefficients of the function.

The graph of quadratic functions is a technique to study the nature of the quadratic functions graphically. The shape of the parabola is determined by the coefficient 'a' of the quadratic function f(x) = ax2 + bx + c, where a, b, c are real numbers and a ≠ 0.

the vertex of a quadratic function is. [tex]f(x)=a(x-h)^2+k, where (h,k)[/tex] is the vertex of parabola. When a>0 then function will be open upward if a<0 then function will be opens downward.

Steps to plot graph of quadratic function.

a[tex]x^2[/tex] is imply a vertical scaling of the parabola, if a<0 the parabola will also flip its mouth from the positive to negative side.

[tex]a(x+\frac{b}{2a} )^2[/tex] This is a horizontal shift of magnitude |[tex]\frac{b}{2a}[/tex]| units. The direction of the shift will be decided by the sign of b/2a. The new vertex of the parabola will be at (-b/2a,0).

This transformation is a vertical shift of magnitude |[tex]\frac{D}{4a}[/tex]| units. The direction of the shift will be decided by the sign of [tex]\frac{D}{4a}[/tex]. The final vertex of the parabola will be at ([tex]\frac{-b}{2a} ,\frac{-D}{4a}[/tex]).

So, The Graph of quadratic functions gives parabolas that are U-shaped, and wide or narrow depending upon the coefficients of the function.

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0 is the value of log 1 to base 7.

The inverse of an exponential function is named a logarithm. That means the logarithm of a number y to the base b is the exponent to which b must be raised, to produce y. For example, since 100 = 10², the logarithm base 10 of 100 is 2, or log₁₀ (100) = 2. The logarithm of x to base a is denoted as logₐ (x), or without parentheses, logₐ x, or even without the explicit base, log x.

As we know,

aˣ = N ⇔ [tex]log_{a}N[/tex] = x

Let log₇1 = x

⇒7ˣ = 1

⇒7⁰ = 1

Equating powers on both sides, we get

x = 0

⇒log₇1 = 0

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The areas in ascending order are: 0.004 m² (or 40 cm²), 3.7 cm², 41 cm², and 420 mm² (or 0.42 cm²).

What is an ascending order?

Ascending order is the arrangement of a set of numbers or data in a sequence from smallest to largest. It is a way of organizing data in increasing numerical or alphabetical order. For example, the numbers 1, 2, 3, 4, 5 in ascending order is a sequence where each number is greater than the previous one. Similarly, arranging words in alphabetical order from A to Z is also an example of ascending order.

The areas in ascending order are:

0.004 m² = 40 cm²

3.7 cm²

41 cm²

420 mm² = 0.42 cm²

So, the areas in ascending order are: 0.004 m² (or 40 cm²), 3.7 cm², 41 cm², and 420 mm² (or 0.42 cm²).

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A 15 degree angle can be created by using a compass or a straightedge.

1) Using a compass: Set the compass to the length of the angle's ray, and draw an arc that intersects the angle's vertex. Repeat the process with a second arc, and the point of intersection between the two arcs is the endpoint of the angle's ray.

2) Using a straightedge and 30-60-90 triangles: You can use a straightedge to bisect a 30-degree angle, then use the bisector to construct a 15-degree angle.

These are just a few ways to construct a 15-degree angle without a protractor, and there might be other methods as well.

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The polynomial 2x^3 - 3x^2 x 5 is known as a cubic polynomial.

A cubic polynomial is a polynomial of degree 3, or a polynomial with the highest power of x being 3. This means that the formula for a cubic polynomial can be written as ax^3 + bx^2 + cx + d, where a, b, c, and d are all constants.

In the example of 2x^3 - 3x^2 x 5, the coefficients are 2, -3, 0, and 5 respectively. To calculate the value of the cubic polynomial, one must substitute a value of x into the equation. For example, if x = 2, then the equation would be 2(2^3) - 3(2^2) x 5, which simplifies to 32 - 24 x 5, or 32 - 120, which equals -88.

Therefore, when x = 2, the polynomial 2x^3 - 3x^2 x 5 equals -88. This can be further verified by graphing the polynomial and observing the point (2, -88).

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Complete question: What type of polynomial is 2x3 − 3x2 x 5?

The percentage takes at least one science or math course is 73%.

62% of the students take math

so,

n(m)=62

49% take science

n(s)=49

38% take both science and math

n(M∩S)=38

now, we can use union formula

n(M∪S)=n(M)+n(S) -n(M∩S)

now, we can plug values

and we get

n(M∪S)=62+49 -38

n(M∪S)=73

so,

the percentage takes at least one science or math course is 73%.

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The weight of the flour pack used by the chef to make chicken nuggets is 0.04 pounds.

Quantity of flour used to make chicken nuggets by the chef = 0.28 pounds

If the chef used 1/7th of the pack of flour;

Quantity of flour used by the chef = 1/7 of 0.28 pounds

= 1/7 × 0.28

= 0.04 pounds

Therefore, the chef used 0.04 poundsof the flour pack

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Answer:

x = 110°, z = 32°

Step-by-step explanation:

x + 70 = 180 (Exterior angles)

x = 110

4z - 58 + 110 = 180 ( Linear pair)

4z = 128

z = 32

Pls mark as brainliest if possible and cheers!

Answer:yo mom

Step-by-step explanation:

If an equation describes the relation in the variables x and y, the equation of the inverse relation is obtained by replacing every x in the equation with y and every y in the equation with x. Their graphs are mirror images over the line of reflection y = x.

Now, According to the question:

What is graph of inverse relation?

The inverse of a relation is a relation obtained by interchanging or swapping the elements or coordinates of each ordered pair in the relation. Inverse relation in sets can be defined using the ordered pairs. The domain and range of an inverse relation can be written by swapping the domain and range of that relation.

If an equation describes the relation in the variables x and y, the equation of the inverse relation is obtained by replacing every x in the equation with y and every y in the equation with x. Their graphs are mirror images over the line of reflection y = x.

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D.0.125

What is probability?

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1.

Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means.

You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

Step by Step Exlaination:

A spinner is divided into 8 parts.

Numbered as 9 to 16.

S={9,10,11,12,13,14,15,16}

n(S)=8.

A:probability of getting reater than 15.

A={16}

m(A)=1

p(A)=m(A)/n(S).

      = 1/8.

      =0.125

p(A)=0.125

Probability of getting greater than 15 is 0.125

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