After one hour 0.75 mg of medicine remains in the bloodstream. Find an equation that defines f.

The solution set in interval notation, 19(7 − x) ≥ 88 − 14x, is (-∞, 9]

To solve the inequality 19(7 - x) ≥ 88 - 14x, we will first distribute the 19 on the left side of the inequality and then combine like terms to isolate the variable x.

19(7 - x) ≥ 88 - 14x
133 - 19x ≥ 88 - 14x
-5x ≥ -45
x ≤ 9

Now, we can write the solution set in interval notation. Interval notation uses brackets or parentheses to indicate the endpoints of an interval. Brackets indicate that the endpoint is included in the interval, while parentheses indicate that the endpoint is not included.

Since x is less than or equal to 9, the solution set in interval notation is (-∞, 9]. This means that any value of x less than or equal to 9 will satisfy the inequality.

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Answer: 137.8 cm

Step-by-step explanation:

Using Pythagorean's Theorem, a² + b² = c², we can find the length of one of the braces.

Plug in your values:

115² + 76² = c²

13225 + 5776 = c²

19001 = c²

√19001 = c

c ≈ 137.8 cm

The braces are 137.8 cm long.

Hope this helps!

Answer:

kindly update the question

Austin would have approximately $2,108 more than Josiah.

Approximately means "nearly" or "close to" an exact amount or number. It is often used to describe a quantity that is not exact, but can be estimated or rounded off. For example, "There were approximately 25 people in the room" means that the number was close to 25, but not necessarily exactly 25.

Using the formula A = P(1 + r/n)^nt, where P is the principal amount, r is the interest rate, n is the number of times compounded, and t is the number of years, we can calculate the amount of money Austin and Josiah would have in 17 years.
For Austin: A = $92,000(1 + 5.875/365)^365*17 = $120,308.05
For Josiah: A = $92,000(1 + 0.0575)^17 = $118,200.43
Therefore, Austin would have approximately $2,108 more than Josiah.

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Answer:

For two linear equations : a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0;

To determine if two such straight lines are parallel, then you should check for the following conditions :

a₁/a₂ = b₁/b₂ ≠ c₁/c₂ , where a,b are coefficients of x and y for each line.

if this condition is true for the coefficients of x,y, and the intercept of lines (c₁ and c₂) then they are parallel.

for instance,

let's say we have two lines :

x + 2y - 4 = 0,

2x + 4y - 12 = 0;

Now to check if they are parallel you simply check if the condition for parallel lines is met or not.

for these two lines :

a₁ = 1 , b₁ = 2, and c₁ = -4;

a₂ = 2, b₂ = 4, and c₂ = -12;

evaluating the values in the condition we have :

[tex]\frac{1}{2}[/tex] = [tex]\frac{2}{4}[/tex] ≠[tex]\frac{-4}{-12}[/tex] ;

since the condition for parallel is true for these two lines, we can conclude they are parallel.

To test with hundreds, thousands, or millions of numbers, MAX_NUM and MAX_COUNT should be adjusted in the code as needed.

The Bubble Sort algorithm is a simple sorting algorithm that repeatedly steps through a given array, comparing elements and swapping them if they are in the wrong order. The sequential Bubble Sort algorithm can be implemented using a for loop that iterates through the array and swaps the elements if they are in the wrong order. The even-odd pass variant of the Sequential Bubble Sort adds two for loops, one for even elements and one for odd elements, which makes it more amenable to a parallel implementation.

Using multiple processes and threads to implement a parallel version of the Bubble Sort algorithm involves using system calls such as fork(), pipe(), pthread_create() and pthread_join(), and shmget(), shmat(), shmdt(), and shmctl() system calls. When implementing this parallel version of the Bubble Sort algorithm, care must be taken to avoid race conditions by properly synchronizing processes and threads.

To test the sequential and even-odd pass variants of the Bubble Sort algorithm, one should use the gettimeofday() function to measure and print the sorting time for different values of N. To test with hundreds, thousands, or millions of numbers, MAX_NUM and MAX_COUNT should be adjusted in the code as needed, and very large output can be redirected to a file using the operator.

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The area of the parallelogram is ∇19.

To determine the area of the parallelogram, we will use the formula: Area = ||u x v||, where u and v are vectors representing two sides of the parallelogram.

First, we need to find the vectors u and v. We can do this by subtracting the coordinates of two adjacent vertices:
u = (−4,9,5) - (−7,7,6) = (3,2,-1)
v = (−10,6,6) - (−7,7,6) = (-3,-1,0)

Next, we need to find the cross product of u and v:
u x v = [(2)(0) - (-1)(-1), (-1)(-3) - (3)(0), (3)(-1) - (2)(-3)] = [-1, 3, -3]

Finally, we need to find the magnitude of the cross product, which will give us the area of the parallelogram:
Area = ||u x v|| = ∇((-1)^2 + (3)^2 + (-3)^2) = ∇(1 + 9 + 9) = ∇19

Therefore, the area of the parallelogram is ∇19.

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Answer:

B. Left 2 units, down 9 units

Step-by-step explanation:

You would determine the x value by making the equation for x equal to 0. In this case we have x + 2 = 0. Subtract 2 from both sides to get x = -2. Determine the y value by the last digit which is -9. You now have the coordinate -2, -9, which is left 2 units and down 9 units.

Answer:

Step-by-step explanation:

I can't see anything.

The measure of angle D is \( 125^{\circ} 88^{\prime} 5^{\prime \prime} \).

The interior angles of a quadrilateral are measured as A \( 51^{\circ} 22^{\prime} 30^{\prime \prime} \), B \( 105^{\circ} 38^{\prime} 48^{\prime \prime} \), C \( 78^{\circ} 10^{\prime} 37^{\prime \prime} \), and D \( 124^{\prime} 46^{\prime \prime} \).

To find the measure of angle D, we can use the fact that the sum of the interior angles of a quadrilateral is 360 degrees.

Add the measures of angles A, B, and C:
\( 51^{\circ} 22^{\prime} 30^{\prime \prime} \) + \( 105^{\circ} 38^{\prime} 48^{\prime \prime} \) + \( 78^{\circ} 10^{\prime} 37^{\prime \prime} \) = \( 234^{\circ} 71^{\prime} 55^{\prime \prime} \)

Subtract the sum of angles A, B, and C from 360 degrees to find the measure of angle D:
360^{\circ} - \( 234^{\circ} 71^{\prime} 55^{\prime \prime} \) = \( 125^{\circ} 88^{\prime} 5^{\prime \prime} \)

Therefore, the measure of angle D is \( 125^{\circ} 88^{\prime} 5^{\prime \prime} \).

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The best possible equation of the line of best fit would be →

y = 8.6x + 10.5.

A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data

Given is a scatter plot as shown in the image.

For the given graph the correlation is positive. So, we can write the slope of the line of the best fit as positive. So, we can write the equation of the line of best fit as → y = 8.6x + 10.5.

Therefore, the best possible equation of the line of best fit would be →

y = 8.6x + 10.5.

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The equation of the red graph is g(x) = x² + 3.

Option C.

The equation of the red graph can be determined by considering upscaling or transformation on the x - axis.

Since the equation focuses on the function g(x) and not on upscaling in the y-axis, any changes should not affect the x-axis. Therefore, we can eliminate (x - 3)² and (x + 3)² from the options given, since they involve modifying the x-axis.

In conclusion, as the transformation involves increasing the y-values along the y-axis, the correct choice is x² + 3 rather than x² - 3.

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The area of the figure composed of a rectnagle and a triangle is 128in².

The figure in the the image is composed of rectangle and a triangle.

The area of a rectangle = length × width

Area of a triangle = 1/2 × base × height

Hence;

Area of the composite figure will be;

A = area of a rectangle + area of a triangle

From the image;

Now, we solve for thr area of the composite figure.

A = area of a rectangle + area of a triangle

A = ( 12in × 9in ) + ( 1/2 × 5in × 8in )

A = ( 108in² ) + ( 20in² )

A = 128in²

Therefore, the total area of the figure id 128 squared inch.

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The mean of the values will be 9.4, the median will be 3 points and the mode will be 4

It should be noted that mean in mathematics simply means the total added values of all the data in a set of divided by the number of days in a set.

The mean of the values will be:

= (10 + 8 + 11 + 12 + 6) / 5

= 47 / 5

= 9.4

The median of the set of numbers is the number on the middle when arranged ascending or in a descending manner. This is 3 points. The mode is 4.

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The answer is d

because you're waiting too long.

Answer:

0.81,74%,5/8,31/50

Step-by-step explanation:

74% means 74/100 which equals to 0.74, and 5/8 is 0.625, and lastly 32/50 is 0.62 so it leaves us with 0.81 as the greatest so we can start ordering them

0.81,74%(0.74),5/8(0.625), 31/50(0.62)

The correct answer is c. Failed to reject the null hypothesis.

Failed to reject the null hypothesis.

Explanation:

In this problem, we are given the price of drugs for human doses and animal doses from different pharmacies. We are asked to form a statistical decision using the p-value method. The null hypothesis is that the prices for the animal doses are equal to the prices for the human doses, while the alternative hypothesis is that the prices for the animal doses are significantly less than the prices for the human doses.


To form a statistical decision, we need to compare the p-value with the level of significance (α). If the p-value is less than or equal to α, we reject the null hypothesis. If the p-value is greater than α, we fail to reject the null hypothesis.


In this case, the level of significance is 1% (α=0.01). Since the p-value is not given in the problem, we cannot make a decision. Therefore, the correct answer is c. Failed to reject the null hypothesis.

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The scientific notation or representation of expression (2.5 X 1/10²)(4.2 X 10⁶) is equal to 10.5×10⁴.

Scientific notation is a way of writing very large or very small numbers. Numbers are written in scientific notation as a number from 1 to 10 multiplied by a power of 10.For example, 650,000,000 can be written in scientific notation as 6.5 ✕ 10⁸. 

Scientific notation is utilized by scientists, mathematicians, and engineers whilst they may be operating with very huge or very small numbers

Solution for scientific notation according to the information given:

(2.5 X 10^-2)(4.2 X 10⁶) = 2.5 ×(1/10²) × 4.2 × 10⁶

                                        = 2.5 × 4.2 × 10⁴

                                        = 10.5 × 10⁴

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There are three possible triangles that can be formed using the given measurements.

Measurement is the process of quantifying or comparing the amount, size, or extent of something. It is an important concept for scientists, engineers, and other professionals in order to compare and understand the world around them. Measurement involves the use of physical tools, such as rulers, scales, and protractors, and mathematical equations, such as formulas and equations.

We can use the Law of Cosines to solve for the missing side:

[tex]b^2 = a^2 + c^2 - 2ac\cos(B)\\$b^2 = 43^2 + 15^2 - 2(43)(15)\cos(123^\circ)$\\$b^2 \approx 799.5$\\$b \approx 28.3$[/tex]

Now we can use the Law of Sines to solve for the remaining angles:

[tex]\frac{\sin(A)}{a} = \frac{\sin(B)}{b}\\$\sin(A) = \frac{a\sin(B)}{b}$\\$\sin(A) \approx 0.977$\\$A \approx 79.4^\circ$\\$B \approx 23.6^\circ$[/tex]

So the triangle is [tex]$\triangle ABC$[/tex] where [tex]$A=79.4^\circ$[/tex], [tex]$B=23.6^\circ$[/tex], [tex]$C=77^\circ$[/tex], [tex]$a=43$[/tex], [tex]$b\approx 28.3$[/tex] , and [tex]$c=15$[/tex].

We can use the Law of Cosines to solve for the missing side:

[tex]b^2 = a^2 + c^2 - 2ac\cos(B)\\$b^2 = 36^2 + 47^2 - 2(36)(47)\cos(47^\circ)$\\$b^2 \approx 1666.5$\\$b \approx 40.8$[/tex]

Now we can use the Law of Sines to solve for the remaining angles:

[tex]\frac{\sin(A)}{a} = \frac{\sin(B)}{b}\\$\sin(A) = \frac{a\sin(B)}{b}$\\$\sin(A) \approx 0.647$\\$A \approx 40.9^\circ$\\$C \approx 92.1^\circ$[/tex]

So the triangle is [tex]$\triangle ABC$[/tex] where [tex]$A=40.9^\circ$[/tex], [tex]$B=47^\circ$[/tex], [tex]C\approx 92.1^\circ, a\ =36$[/tex], [tex]$b\approx 40.8$[/tex],

We can use the Law of Cosines to solve for the missing side:

[tex]h^2 = k^2 + p^2 - 2kp\cos(K)\\$h^2 = 47^2 + 10^2 - 2(47)(10)\cos(139^\circ)$\\$h^2 \approx 2363.7$\\$h \approx 48.6$[/tex]

Now we can use the Law of Sines to solve for the remaining angles:

So the triangle is [tex]$\triangle KHP$[/tex] were [tex]$K=139^\circ$[/tex], [tex]$H\approx 56.5^\circ$[/tex], [tex]$P\approx 124.5^\circ$[/tex], [tex]$k=47$[/tex], [tex]$h\approx 48.6$[/tex], and [tex]$p=10$[/tex].

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Answer:

Step-by-step explanation:

1 ticket costs 1 × $4.50 = $4.50

2 tickets cost 2 × $4.50 = $9.00

3 tickets cost 3 × $4.50 = $13.50

4 tickets cost 4 × $4.50 = $18.00

The first table is the only one that matches these values.

The formula for the nth term of the arithmetic sequence is 3(3n-1) or -3+9n(option B)

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that arithmetic progression.

The nth term of a n arithmetic sequence is given as:

a(n) = a+(n-1)d

where a is the first term and d is the common difference

a = 6

d = 15-6 = 9

a(n) = 6+( n-1) 9

= 6+9n -9

a(n) = 9n-3

a(n) = 3(3n-1)

therefore the formula for the nth term of the sequence is 3(3n-1)

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it definitely should be (-2,3)

Answer: there 28/29 days

Step-by-step explanation:

Answer: 28/29

Step-by-step explanation:

28 Days

29 Days for a leap year

[[-2, 0, 10, 2, 0], [1, -1, 9, 2, -1]]

The product of the two matrices is [[-2, 0, 10, 2, 0], [1, -1, 9, 2, -1]].

To calculate the product of two matrices, multiply each row of the first matrix with each column of the second matrix. Begin by multiplying the first row of the first matrix [-2, 0] with each column of the second matrix [-1, 0, 5, 1, 0]. This produces the values -2, 0, 10, 2, 0 which will be the first row of the product matrix.

Next, multiply the second row of the first matrix [1, -1] with each column of the second matrix [-1, 0, 5, 1, 0]. This produces the values 1, -1, 9, 2, -1 which will be the second row of the product matrix.

Therefore, the product of the two matrices is [[-2, 0, 10, 2, 0], [1, -1, 9, 2, -1]].
The given matrices are:
[[-2, 0],
[1, -1]]
[[-1, 0, 5, 1, 0],
[1, -1, 3, 1, -1]]

To find the product of two matrices, we need to follow a few steps:

Multiply the first row of the first matrix by the first column of the second matrix, and then add the results.
Multiply the first row of the first matrix by the second column of the second matrix, and then add the results.
Multiply the second row of the first matrix by the first column of the second matrix, and then add the results.
Multiply the second row of the first matrix by the second column of the second matrix, and then add the results.

By following these steps, we can obtain the product of the matrices. So, we can proceed as follows:

-2×(-1) + 0×1 = 2
-2×0 + 0×(-1) = 0
1×(-1) + (-1)×1 = -2
1×0 + (-1)×(-1) = 1

Hence, the product of the given two matrices is:
[[2,0,10,2,0],
[-2,2,-8,-2,2]]

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Answer:

19. Angelique=0.3, Jamila=0.1  20.15.2

Step-by-step explanation:

19 Angelique=0.3

          Jamila=0.1

20.

[tex]x^{2} =8.7^{2}+12.5^{2} \\x^{2} =231.94\\x=15.229...\\x=15.2[/tex]

Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

The two functions are not equivalent.

The given functions f(x,y) = x^2 + 3y^2 and f′(x,y) = x^2 + 4xy + 7y^2 are not equivalent.

To determine if two functions are equivalent, we can compare their equations and see if they are the same. In this case, the equations of the two functions are different. The first function, f(x,y), has a term of 3y^2, while the second function, f′(x,y), has a term of 4xy and a term of 7y^2.

Therefore, the two functions are not equivalent.

It is important to note that two functions can have different equations but still be equivalent if they produce the same output for any given input. However, in this case, the two functions will produce different outputs for the same input, so they are not equivalent.

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Step-by-step explanation:

steps are in the image above

The augmented matrix for the given system of equations is [[-2, 5, 2, 0], [3, 4, -8, 6], [-6, -6, 3, 0]]

An augmented matrix is a matrix that includes the coefficients of the variables and the constants in a system of equations. Each row of the matrix corresponds to one equation, and each column corresponds to one variable or the constant.

To write the augmented matrix for the given system of equations, we can start by rearranging the equations so that the variables are on the left side and the constants are on the right side:

5x + 2z = 2
3x + 4y - 8z = -6
-6x + 6y - 3z = 0

Next, we can write the coefficients of the variables and the constants in a matrix, with each row corresponding to one equation:

[5, 0, 2, 2]
[3, 4, -8, -6]
[-6, 6, -3, 0]

Finally, we can combine these rows into a single matrix to get the augmented matrix:

[[-2, 5, 2, 0], [3, 4, -8, 6], [-6, -6, 3, 0]]

This is the augmented matrix for the given system of equations.

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The trinomial [tex]x^(2)+7x-18[/tex] factors into (x+9)(x-2), and the trinomial [tex]x^(2)-7x-18[/tex] factors into (x-9)(x+2). The signs in each binomial are opposite.

In the first trinomial, the signs are positive and negative, while in the second trinomial, the signs are negative and positive. This is because the signs in the binomials are determined by the signs of the constant term and the coefficient of the linear term in the trinomial.

For the first trinomial, the constant term is -18 and the coefficient of the linear term is 7. To factor this trinomial, we need to find two numbers that multiply to -18 and add to 7. The numbers 9 and -2 satisfy this condition, so the trinomial factors into (x+9)(x-2).

For the second trinomial, the constant term is -18 and the coefficient of the linear term is -7. To factor this trinomial, we need to find two numbers that multiply to -18 and add to -7. The numbers -9 and 2 satisfy this condition, so the trinomial factors into (x-9)(x+2).

In both cases, the signs in the binomials are opposite because one of the numbers is positive and the other is negative.

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Answer:

Traduction:

Ann and Barbara are comparing their ages. They find that Barbara is the age that Ann was when Barbara was the age that Ann was when Barbara was half the age that Ann is today. If the sum of their current ages is 44 years, what is Ann's age today?

Soit x l'âge d'Ann aujourd'hui.

On sait que l'âge de Barbara est x - (x/2) = x/2 (car Barbara avait la moitié de l'âge d'Ann lorsque l'écart d'âge entre elles était de x/2).

On sait également que l'âge d'Ann lorsque Barbara avait x/2 ans est (x/2 - x) = -x/2 ans de moins que son âge actuel.

Donc, l'âge d'Ann lorsque Barbara avait l'âge qu'avait Ann à ce moment-là est x - (x/2) - (-x/2) = 2x/2 = x ans.

Ainsi, l'âge de Barbara aujourd'hui est également x ans.

La somme de leurs âges actuels est 44 ans, donc :

x + x = 44

2x = 44

x = 22

Donc, l'âge d'Ann aujourd'hui est 22 ans.