The solution set for the inequality |x-2|>3 is x < -1 or x > 5, represented by the union of the open intervals (-∞, -1) and (5, ∞) on the number line.
To graph the inequality |x-2| > 3 on a number line, we can start by finding the values of x that satisfy the inequality:
|x-2| > 3
x-2 > 3 or x-2 < -3
x > 5 or x < -1
This means that any value of x that is greater than 5 or less than -1 will satisfy the inequality.
On a number line, we can mark -1 and 5 with open circles to indicate that they are not included in the solution set, and shade the regions to the left of -1 and to the right of 5 to show that any value in those regions satisfies the inequality.
The graph should look like this:
<=========(================>)=========
-1 2 5
The open circles at -1 and 5 indicate that those values are not included in the solution set, while the shaded regions to the left of -1 and to the right of 5 indicate that any value in those regions satisfies the inequality.
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Urgent!!!!!
Help guys I need to answer the questions
I would appreciate it.
The function for the concentration of the drug in the bloodstream indicates;
a. The concentration will be 0.5 mg/L when t = 20 - 6·√(11) and t = 20 - 6·√(11) hours
b. Please find the completed table of values in the following section
c. The domain is all positive values of t, including t = 0, which is [0, ∞)
d. The patient should receive the drug after about 19.78 hours
e. The shape of the concentration graph are similar, but the concentration of the oral drug is higher than the concentration of the drug administered intravenously
What is a function?A function is a rule that maps input variables to output values.
a. The function modelling the concentration of the drug in the bloodstream after t hours indicates;
c(t) = 20·t/(t² + 4)
When the concentration is 0.5 mg/L, we get;
c(t) = 20·t/(t² + 4) = 0.5
(t² + 4) × 0.5 = 20·t
t² + 4 = 20·t ÷ 0.5 = 40·t
t² - 40·t + 4 = 0
t = (40 ± √((-40)² - 4 × 1 × 4))/(2 × 1) = (40 ± 12·√(11))/(2) = 20 ± 6·√(11)
The concentration will be 0.5 mg/L when t = 20 + 6·√(11) and t = 20 - 6·√(11)
b. The completed table of values, obtained using MS Excel can be presented as follows;
t [tex]{}[/tex] 0 2 4 6 8 10 12 14 16 18 20
c(t) [tex]{}[/tex]0 5 4 3 2.35 1.92 1.62 1.4 1.23 1.09 0.99
c. The denominator, t² + 4, indicates that the denominator is positive for all values of x, whereby the time is a natural, a possible domain for the function is the set [0, ∞)
d. The values in the table indicates that to maintain a concentration above 1 mg/L and below 8 mg/L, the patient must receive the next intravenous dose between the values obtained as follows;
The maximum value of the function is 5 mg/L when t = 2 hours, therefore, when c(t) = 1 mg/L, we get;
c(t) = 20·t/(t² + 4) = 1, which indicates that t = 10 ± 4·√6, which indicates that the time at which the concentration reduces to 1 mg/L again in the bloodstream is 10 + 4·√6 ≈ 19.78 hours
The patient should receive the next dose, after about 19.78 hours
e. The concentration of the oral drug, obtained from a similar question on the website, indicates that the maximum concentration is 64 mg/L, which is higher than the maximum concentration of the drug administered intravenously, which has a maximum concentration of 5 mg/L
However, the maximum bloodstream is reached at about the same period for both drugs administration methods
The concentration of the drug administered by oral administration in the first part is about four times the drug administered intravenously after 20 hours.
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Encuentra el siguen termino de la sucesión 23,18,13
Answer: 8
Step-by-step explanation:
We see that each term is 5 less than the previous one. We will subtract 5 from 13 to find the next term in the sequence.
13 - 5 = 8
find the perimeter of ABC
The perimeter of the triangle ABC is 146.
Given that a triangle we need to find it perimeter,
We know that the tangents from a common point to the circle are equal,
Therefore,
DB = BE
EC = FC
FA = AD
So,
FA = AC - FC
FA = 52-13 = 39
Therefore,
FA = AD
AD = 39
Now,
9x-56 = 17x - 120
8x = 64
x = 8
DB = BE = 16
AB = 16 + 39 = 55
BC = 16+13 = 29
AC = 52
Perimeter = AC + BC + AB = 55 + 29 + 52 = 146
Hence the perimeter of the triangle ABC is 146.
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The figure on the right shows the cross-section of a pipe. The internal radius is 5cm and the thickness of the metal is 6mm. What is the external circumference of the pipe? (Take π = 22)
The external circumference of the metal pipe is approximately 31.4 centimeters.
We know that the circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.
The circumference of the circle = 2πr
We are given that internal radius is 5cm and the thickness of the metal is 6mm.
The circumference of the external circle = 2πr
= 2 x 3.14 x 5
= 31.4
The circumference of the metal pipe is approximately 31.4 centimeters.
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What is the average of the points A, B and C with weights 1, 4 and 1
respectively?
The weighted average of the points A, B, and C with weights 1, 4, and 1 respectively is (A + 4B + C) / 6.
To find the weighted average of the points A, B, and C with weights 1, 4, and 1 respectively, we first need to multiply each point by its corresponding weight and then add them together.
Finally, we divide the sum by the total weight.
The weighted sum of the points is:
(1 × A) + (4 × B) + (1 × C) = A + 4B + C
The total weight is:
1 + 4 + 1 = 6
Therefore, the weighted average of the points A, B, and C with weights 1, 4, and 1 respectively is:
(A + 4B + C) / 6
Note that the weight of B is four times that of A and C.
Therefore, the weighted average will be closer to B than A or C, reflecting the fact that B has a larger weight.
For example, if A = 3, B = 5, and C = 4, then the weighted average is:
(A + 4B + C) / 6 = (3 + 4 × 5 + 4) / 6 = 26 / 6 = 4.33.
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If log10^2=m and log10^3=n, find log10^24 in term of m and n
let's recall that whenever omitted, the base is assumed to be 10.
[tex]\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\log_{10}(2)=m\implies \log(2)=m\hspace{5em}\log_{10}(3)=n\implies \log(3)=n \\\\[-0.35em] ~\dotfill\\\\ \log_{10}(24)\implies \log(24)\implies \log(8\cdot 3)\implies \log(2^3\cdot 3) \\\\\\ \log(2^3)+\log(3)\implies 3\log(2)+\log(3)\implies 3m+n[/tex]
Three brothers share some money. The oldest 5/11 of the money. The next boy gets gets 7/12 of the remainder. What fraction of the money does the youngest boy get?
The fraction of the money the youngest boy does get is 5x/22.
Given that, three brothers share some money. The oldest 5/11 of the money.
Let the total money be x.
Share of oldest boy = 5/11 ×x
= 5x/11
Remainder = x-5x/11
Remainder = 6x/11
The next boy gets 7/12 of the remainder.
Share of next boy = 7/12 × 6x/11
= 7x/22
Share of youngest boy = 6x/11 - 7x/22
= (12x-7x)/22
= 5x/22
Therefore, the fraction of the money the youngest boy does get is 5x/22.
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Makayla’s local movie theater has a moviegoer club. The charts in the annual registration fee of $25. However movie tickets are discounted remembers at six dollars per ticket instead of the regular nine dollars per ticket. Let him represent the number of movie tickets Makayla’s purchase a need to write a function tomorrow the amount of money Makayla spent going to the movies doing the club
Answer:
m = 25 + 6n
Step-by-step explanation:
To write a function for the amount of money Makayla spent going to the movies during the club, you need to consider two things: the annual registration fee and the discounted ticket price. The annual registration fee is a fixed amount that does not depend on the number of movie tickets Makayla purchases. The discounted ticket price is a variable amount that depends on the number of movie tickets Makayla purchases. You can use a letter, such as n, to represent the number of movie tickets Makayla purchases. Then, you can write an expression for the amount of money Makayla spent on movie tickets, which is 6 times n, or 6n. To find the total amount of money Makayla spent going to the movies during the club, you need to add the annual registration fee and the amount of money spent on movie tickets. This gives you the expression 25 + 6n. You can use another letter, such as m, to represent the total amount of money Makayla spent going to the movies during the club. Then, you can write an equation that relates m and n, which is m = 25 + 6n. This equation is a function that models the amount of money Makayla spent going to the movies during the club as a function of the number of movie tickets she purchased.
Find the value of x.
Answer: x = 11
Step-by-step explanation:
We know that vertical angles are congruent to each other. We will create an equation to help us solve. Then, will isolate the x-variable with inverse operations.
128° = 8x + 40°
8x + 40° = 128°
8x = 88°
x = 11
pls help guys calculus 30pts
A certain disease has an incidence rate of 0.4%. If the false negative rate is 6% and the false positive rate is 4%, compute the probability that a person who tests positive actually has the disease.
Give your answer accurate to at least 3 decimal places
Based on the values in the table below, find the slope and y-intercept to write the equation of the line in the form y=mx+b.
The y-intercept of the line is 2. the equation of the line in the form y=mx+b is y = 2x + 2.
To find the equation of the line in the form y=mx+b, we need to first find the slope (m) and the y-intercept (b).
Looking at the table:
x | y
--|--
1 | 4
2 | 6
3 | 8
We can use the formula for slope:
m = (y2 - y1) / (x2 - x1)
Let's use the first two points (1, 4) and (2, 6):
m = (6 - 4) / (2 - 1)
m = 2 / 1
m = 2
So the slope of the line is 2.
To find the y-intercept, we can use the formula:
b = y - mx
Let's use the first point (1, 4) and the slope we just found:
b = 4 - (2)(1)
b = 4 - 2
b = 2
So the y-intercept of the line is 2.
Putting it all together, the equation of the line in the form y=mx+b is:
y = 2x + 2.
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what is the inverse of the function? pls help thank you sm
Step-by-step explanation:
y= rad(x+3)
y²=x+3
x= y²-3
change the variables
y= x²-3
{1, √2, √√3, 2, √5, ...}
need help knowing the sequence and the 3 next terms
Answer:
3, 2√2, √7
Step-by-step explanation:
compute the square roots of the next three prime numbers:
√7
√11
√13
Therefore, the next three terms of the sequence are:
{1, √2, √3, 2, √5, √7, √11, √13}
chatgpt
chat
Joe has to take two quizzes tomorrow. He has only enough time to study for one of them.
• The science quiz has 7 true-or-false questions.
• The English quiz has 5 multiple-choice questions.
Joe calculates the probability that he will get each question correct by guessing.
Science
English
To get 100% correct:
Answer 7 of 7 correctiv
Answer 5 of 5 correctiv
P(guess is correct)
0.5
0.25
Joe will study for the quiz on which he is likely to do worse by guessing. Which quiz should he study for?
• A. Science, because the probability of getting all questions correct is
(0.008), which is lower than for English (0.125).
• B. English, because the probability of getting all questions correct is 0.001, which is lower than for science (0.008).
• c. English, because the probability of getting all questions correct is
(0.125), which is lower than for science (0.5).
• D. Science, because he must get more questions correct.
Answer: B
Step-by-step explanation:
English: 0.25^5=0.001
Science:0.5^7=0.008
English is harder to get 100% on, since the probability 0.001 is lower than 0.008.
Enter the number that belongs in the green box 11 12 20
The number that belongs in the green box, using the law of cosines, is given as follows:
15.97º.
What is the law of cosines?The Law of Cosines states that for any triangle with sides a, b, and c and angle C opposite to side c, the following equation is true to obtain the missing length:
c² = a² + b² - 2abcos(C)
For this problem, the parameters are given as follows:
c = 11, a = 12, b = 20.
Hence the missing angle measure is given as follows:
11² = 12² + 20² - 2 x 11 x 20cos(C)
440cos(C) = 423
cos(C) = 423/440
C = arccos(423/440)
C = 15.97º.
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What is the measure of an interior angle of a regular 12-gon?
Answer:
150°
Step-by-step explanation:
Measure of and interior angle of 12-gon:
[tex]\sf \boxed{\text{\bf Sum of all angles of n-polygon = (n -2) * 180}}[/tex]
n is the number of sides.
Sum of all angles of 12-gon = (12 - 2) * 180
= 10 *180
= 1800°
In a regular 12-gon, all the interior angles will be equal.
[tex]\text{\bf Measure of each interior angle = $\bf \dfrac{Sum \ of \ all \ the \ angles}{number \ of \ sides}$}[/tex]
[tex]\sf = \dfrac{1800}{12}\\\\=150^\circ[/tex]
Si la secuencia es 7,12,17,22 y la regla es agregar 5 cuales son los siguentes dos terminos ?
the next two terms in the sequence would be 12 and 17.
746x75755 tell me the answer please because its my only answer
Answer: number is the number so we can be a number
Step-by-step explanation:
Answer:
56,513,230
Step-by-step explanation:
Hope this helps! pls mark as brainiest!
Convert the following binary to decimal numbers 1112
[tex]1\cdot2^2+1\cdot2^1+1\cdot2^0=4+2+1=7\\\\111_2=7_{10}[/tex]
If the variance for a set of data equals 8.1, find the standard deviation.
The standard deviation for this set of data is approximately 2.85.
To find the standard deviation, we first need to take the square root of the variance. Therefore, the standard deviation for the given data set is the square root of 8.1, which is approximately 2.846.
To find the standard deviation of a set of data when the variance is given, you simply need to take the square root of the variance. In this case, the variance equals 8.1.
Step 1: Identify the variance, which is 8.1.
Step 2: Take the square root of the variance.
Standard Deviation = √(Variance) = √(8.1)
Step 3: Calculate the square root of 8.1.
Standard Deviation ≈ 2.85
So, the standard deviation for this set of data is approximately 2.85.
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4. Graph the exponential function y = 2* and its inverse y = log₂ x. Table of values: (3 marks) Graph: y (2 marks)
The graph of the exponential function y = 2ˣ and its inverse y = log₂ x are shown in figure.
Since, A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Here, Functions are,
⇒ y = 2ˣ
And, Its inverse function is,
⇒ y = log₂ x
Thus, The graph of the exponential function y = 2ˣ and its inverse y = log₂ x are shown in figure.
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In a data distribution that is skewed left.
The median will be greater than the mean in a left-skewed distribution
We have,
In statistics, skewness is a measure of the asymmetry of a probability distribution around its mean.
A distribution is said to be skewed left if it has a long tail on the left side and the bulk of the data is on the right side.
When the data is skewed left, it means that the distribution is being pulled towards the left side.
This is because there are a few extreme values on the left side that are pulling the mean in that direction.
In contrast, the median is the middle value of the dataset, and it is not influenced by outliers.
For a left-skewed distribution,
The median will be greater than the mean because the mean is being pulled towards the left by the few extreme values.
In a data distribution that is skewed left, the mean will be less than the median.
This is because the mean is sensitive to outliers and is pulled towards the direction of the skewness, while the median is not affected by extreme values and is a more robust measure of central tendency.
Therefore,
The median will be greater than the mean in a left-skewed distribution
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What is the side length of AB
Answer:
AB ≈ 8.1
Step-by-step explanation:
using the cosine ratio in the right triangle
cos40° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{6.2}{AB}[/tex] ( multiply both sides by AB )
AB × cos40° = 6.2 ( divide both sides by cos40° )
AB = [tex]\frac{6.2}{cos49}[/tex] ≈ 8.1 ( to the nearest tenth )
Find the value of the missing coefficient in the factored form of 27f^3+125g^3=(3f+5g)(9f^2-?fg+25g^20
The value of the missing coefficient is 12
Lets explain how to factorize the difference of two cubes
- The factorization of the difference of two cubes like a³ - b³, is a
product of a binomial and trinomial
- The binomial is the cube root of the first term and the second term
∵ The ∛a³ = a and ∛b³ = b
∴ The binomial is (a - b)
- We will find the trinomial from the binomial by square the 1st term
of the binomial and multiply the 1st term and the 2nd term of the
binomial with opposite sign of the binomial and square the 2nd
term of the binomial
∴ The trinomial is (a² + ab + b²
∴ The factorization of (a³ - b³) is (a - b)(a² + ab + b²)
* Lets solve the problem
∵ 8f³ - 216g³ is the difference of two cubes
∵ ∛(8f³) = 2f
∵ ∛(216g³) = 6g
∴ The binomial is (2f - 6g)
- Lets make the trinomial
∵ (2f)² = 4f²
∵ (2f)(6g) = 12fg
∵ (6g)² = 36g²
∴ The trinomial = (4f² + 12fg + 36g²)
∴ The factorization of 8f³ - 216g³ = (2f - 6g)(4f² + 12fg + 36g²)
∴ The value of the missing coefficient is 12.
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complete question:
Find the value of the missing coefficient in the factored form of 8f^3-216g^3
8f^3-216g^3=(2f-6g) (4f^2+?fg+36g^2)
The value of ? =
Find the mean of 7,9,4,3,9,4 graphically
Answer:
6
Step-by-step explanation:
To find the mean you've got to add 7, 9,4,3,9 and 4 (which gives you 36) and divide that by the number of figures/numbers (which is 6 numbers in total) and it gives you 6
What is the exact value of cos 30°?
Enter your answer, as a simplified fraction, in the box.
cos 30° can be evaluated using the trigonometric identity: cos 30° = cos(π/6) = (√3)/2.
Therefore, the exact value of cos 30° is (√3)/2.
Answer:
cos30 = √3 / 2
or cos30 ≈ 0.8660254037
A laptop has a listed price of $710.98 before tax. If the sales tax rate is 7.25%, find the total cost of the laptop with sales tax included.
Answer:
$762.53
Step-by-step explanation:
think of 710.98 as the whole.
then 7.25% = an increase of 0.0725.
710.98 X (1 + 0.0725)
= $762.53 (to nearest cent)
Given f(x) = x − 2 and g(x) = 5x + 3, evaluate the function for f(g(4))?
select ALL the correct answers.
Which data set could be used to create the box plot below?
Im sorry but I dont see a Box Plot.
Answer:
provide more data
Step-by-step explanation:
no solution
