Answers
Answer:
x = 2, x = - 5
Step-by-step explanation:
To factor it, you can split the middle term to get:
x² - 2x + 5x - 10 = 0
Then, you can factor the first two and the last two to get:
x (x - 2) + 5(x - 2) = 0
And if you divide both sides by (x - 2) you get:
(x - 2) (x + 5) = 0
Finally, this can be solved by the Zero Product Property which states that if x*y=0, then x and/or y has to be equal to 0. If you apply it to the eqaution you get:
x - 2 = 0, x + 5 = 0
which results in:
x = 2, x = - 5
Related Questions
Intensive care units (ICUs) generally treat the sickest patients in a hospital. ICUs are often the most expensive department in a hospital because of the specialized equipment and extensive training required to be an ICU doctor or nurse. Therefore, it is important to use ICUs as efficiently as possible in a hospital. According to a 2017 large-scale study of elderly ICU patients, the average length of stay in the ICU is 3.4 days (Critical Care Medicine journal article). Assume that this length of stay in the ICU has an exponential distribution. Do not round intermediate calculations.
a. What is the probability that the length of stay in the ICU is one day or less (to 4 decimals)?
b. What is the probability that the length of stay in the ICU is between two and three days (to 4 decimals)?
c. What is the probability that the length of stay in the ICU is more than five days (to 4 decimals)?
Answers
Using the exponential distribution, it is found that there is a:
a) 0.2548 = 25.48% probability that the length of stay in the ICU is one day or less.
b) 0.1415 = 14.15% probability that the length of stay in the ICU is between two and three days.
c) 0.2298 = 22.98% probability that the length of stay in the ICU is more than five days.
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = e^{-\mu x}[/tex]
In this problem, the mean is of 3.4 days, hence, the decay parameter is:
[tex]\mu = \frac{1}{3.4}[/tex]
Item a:
[tex]P(X \leq 1) = 1 - e^{-\frac{1}{3.4}} = 0.2548[/tex]
0.2548 = 25.48% probability that the length of stay in the ICU is one day or less.
Item b:
[tex]P(X \leq 2) = 1 - e^{-\frac{2}{3.4}} = 0.4447[/tex]
[tex]P(X \leq 3) = 1 - e^{-\frac{3}{3.4}} = 0.5862[/tex]
[tex]P(2 \leq X \leq 3) = 0.5862 - 0.4447 = 0.1415[/tex]
0.1415 = 14.15% probability that the length of stay in the ICU is between two and three days.
Item c:
[tex]P(X > 5) = e^{-\frac{5}{3.4}} = 0.2298[/tex]
0.2298 = 22.98% probability that the length of stay in the ICU is more than five days.
A similar problem is given at https://brainly.com/question/17039711
Alexander Litvinenko was poisoned with 10 micrograms of the radioactive substance Polonium-210. Since radioactive decay follows a compounded continuously model, we can determine the amount of substance left in Alexander Litvinenko's body at any given time. If Polonium-210 has a decay rate of .502%, then determine the amount of Polonium-210 left in his body after 40 days. Provide 3 decimal places and units in your answer.
Answers
Compounded continuously model are evaluated using exponential functions
There are 8.177 bacteria left after 40 days
The given parameters are:
[tex]\mathbf{a = 10}[/tex] --- the initial number of bacteria
[tex]\mathbf{r = 0.502\%}[/tex] --- the decay rate
[tex]\mathbf{n = 40}[/tex] --- the number of days
The amount of bacteria left each day is calculated using:
[tex]\mathbf{T_n = a \times (1 - r)^n}[/tex]
So, we have:
[tex]\mathbf{T_{40} = 10 \times (1 - 0.502\%)^{40}}[/tex]
Express percentage as decimal
[tex]\mathbf{T_{40} = 10 \times (1 - 0.00502)^{40}}[/tex]
Simplify the expression in bracket
[tex]\mathbf{T_{40} = 10 \times 0.99498^{40}}[/tex]
Evaluate
[tex]\mathbf{T_{40} = 8.1766}[/tex]
Approximate
[tex]\mathbf{T_{40} = 8.177}[/tex]
Hence, there are 8.177 bacteria left after 40 days
Read more about compounded continuously model at:
https://brainly.com/question/73731
Can someone please help me figure out the answer to the question in the picture?
Answers
g=12-1/25(100)
g=12-4
g=8, d=100
d=200:
g =12-1/25(200)
g=12-8
g=4, d=200
d=300:
g =12-1/25(300)
g=12- 12
g=0, d=300
**PLEASE HELP OMG**
The square below is dilated by a scale factor of 3/2. Find the perimeter of the dilated square.
Answers
Answer:
W4 is our new scaled side
Step-by-step explanation:
Look at scale factor like this and it helps everytime so if it doesn’t help you there different methods.
3/2 has a larger number as a numerator so that means that the shape being scaled will get larger and if the number is smaller than denominator then the scaled figure will get smaller :3
In our case it gets bigger
do 16 divided by 2 which gives us 8 then times that by 3 to get 24
now thats how I solved this problem but if that not how you did it then you can do it your way :3
HOOE THIS HEEELPPED :DDD
Pls,
Find the area of the
parallelogram below.
8 cm
12 cm
Answers
Answer: Area = 96 cm squared
Explanation;
base x height = area
Base = 12
Height = 8
12 x 8 = 96
How many lines of symmetry does the figure have?
A. 1
B. 5
C. 2
D. 0
Answers
Answer:
B. 5
Step-by-step explanation:
Kind of hard to explain why
Answer: B. 5
Step-by-step explanation: The tiny lines on the sides of the pentagon are the lines of symmetry
Help??? Lma.o sorry I need the answer asap
Answers
Answer:
f(5)=38
Step-by-step explanation:
f(5) means x=5, or in this case, a=5. We plug in 5 as A. f(5)=7(5+1)-4. f(5)=7(6)-4.
f(5)=42-4
f(5)=38
14 blue cars out of 70 cars
Answers
Answer:
66 cars
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
Answer:
14-70=56
Step-by-step explanation:
its subtraction so you just need 70 and take away 14.
reasoning being that theyre all still cars no matter the color and you just need to take away 14 from 70, leaving you with 56.
using the rectangle below calculate the values of x and y
Answers
Answer:
x=4, y=9/7
Step-by-step explanation:
We will use the property that the opposite sides of a rectangle are equal
3(3y-1)=2(y+3)
9y-3=2y+6
7y=9
y=9/7
2x=4(x-2)
2x=4x-8
2x=8
x=4
I need help asap!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
1/2 yd 5/3 yds The first one
Step-by-step explanation:
Determine the intercepts of the line.
Do not round your answers.
y = 4r +7
Answers
Answer:
(-7/4, 0) (0, 7)
Step-by-step explanation:
I'm assuming r is x
0=4r+7
r=-7/4
y=0r+7
y=7
The number 1000 has been rounded to the nearest 100. Find its lower and upper bounds.
Answers
950 ≤ 1000 < 1050
Explanation
Mark Brainliest please
The lower bound is 950 and the upper bound is 1050 when the number 1000 has been rounded to the nearest 100.
What are the lower and upper bound?
The lower bound is the smallest value that would round up to the estimated value.
The upper bound is the smallest value that would round up to the next estimated value.
Here the number 1000 is rounded to the nearest 100 will be:
The Lower bound will be 950.
The Upper bound will be 1050
Hence the lower bound is 950 and the upper bound is 1050 when the number 1000 has been rounded to the nearest 100.
To know more about Lower and upper bound follow
https://brainly.com/question/15308347
math for college readiness question. please help
Answers
Answer: 3
Step-by-step explanation:
[tex](f \circ f)(2) = f(f(2)) = f(3) = \boxed 3[/tex]
The population of a city decreases by 1.1% per year. If this year's population is
79,000, what will next year's population be, to the nearest individual?
Answers
Answer:
Step-by-step explanation:
100% - 1.1% = 98.9% = 0.989
79000(0.989)¹ = 78,131
or
1.1% = 0.011
79000(0.011) = 869
79000 - 869 = 78,131
Translate to an equation and solve. Let x be the unknown number.
30% of 26 is what number?
Answers
Answer: x/30=26/100 would be the equation and then to get the answer you would cross multiply which would get you, x=7.8
Step-by-step explanation:
The water level in a lake was monitored and was noted to have changed -2 1/3 inches in one year. The next year it was noted to have changed -1 5/6 inches. What was the total change in the water level over the two years?
Answers
Answer:
The total change in water level over the past 2 years is [tex]\displaystyle -4 \frac{1}{6}[/tex].
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightFractions
Proper and ImproperNumbers
Least Common Multiple (LCM)Step-by-step explanation:
Step 1: Define
Identify
Year 1 water change: [tex]\displaystyle -2 \frac{1}{3}[/tex]
Year 2 water change: [tex]\displaystyle -1 \frac{5}{6}[/tex]
Step 2: Find Total Water Change
[Set up] Add yearly water changes: [tex]\displaystyle -2 \frac{1}{3} + -1 \frac{5}{6}[/tex][Fractions] Convert to improper: [tex]\displaystyle \frac{-7}{3} - \frac{11}{6}[/tex][Fraction] Rewrite [LCM]: [tex]\displaystyle \frac{-14}{6} - \frac{11}{6}[/tex][Order of Operations] Subtract: [tex]\displaystyle \frac{-25}{6}[/tex][Fraction] Convert to proper: [tex]\displaystyle -4 \frac{1}{6}[/tex]Can somebody answer this?
Answers
True
One from of the linear function is Y = mx + b where b is the y intercept.
The y intercept is where x is 0 so it would be at (0,6)
what is the measure of angle x?
Answers
Answer:
180
Step-by-step explanation:
Find the value of X in triangles by subtracting known angle measurements from 180 degrees. Since the value of all angles within a triangle must equal 180 degrees, if you know at least two angles, you can subtract them from 180 to find the missing third angle.
A line contains the points (1, 2) and (0,1). What is the equation of the line?
Answers
Answer:
y = x + 1
Step-by-step explanation:
Slope: (1-2)/(0-1) = -1/-1 = 1
y-intercept: 1 - (-2)(0) = 1
y = x + 1
Question 6 of 24
The function f(x) = x2 - 6x + 9 is shifted 5 units to the right to create g(x).
What is g(x)?
A. g(x) = (x - 5)2 - 6(x - 5) + 9
B. g(x) = (x + 5)2 - 6(x + 5) + 9
C. g(x) = (x2 - 6x + 9) + 5
D. g(x) = (x2 - 6x + 9) - 5
Micr
SUBMIT
Answers
Answer:
Step-by-step explanation: its b
BEST ANSWER GETS BRAINLIEST!!!!!!!
ruben the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On Monday there were 9 clients who did Plan A and 7 who did Plan B. On Tuesday there were 3 clients who did Plan A and 5 who did Plan B. Reuben trained his Monday clients for a total of 12 hours and his Tuesday clients for a total of 6 hours. How long does each of the workout plans last?
Answers
Let plan A be x
Plan B be y
Equations are
[tex]\\ \sf\longmapsto 9x+7y=12--(1)[/tex]
[tex]\\ \sf\longmapsto 3x+5y=6--(2)[/tex]
Multiplying (1) by 1 and (2) by 3
9x+7y=129x+15y=18Subtracting
[tex]\\ \sf\longmapsto -8y=-6[/tex]
[tex]\\ \sf\longmapsto y=3/4[/tex]
Putting in eq(2)
[tex]\\ \sf\longmapsto 3x+5(3/4)=5[/tex]
[tex]\\ \sf\longmapsto 3x+15/4=5[/tex]
[tex]\\ \sf\longmapsto 3x=5-4/15[/tex]
[tex]\\ \sf\longmapsto 3x=71/15[/tex]
[tex]\\ \sf\longmapsto x=71/45[/tex]
Please answer and show your work
Answers
Answer:
check online for more information
How do you know when to rewrite square trinomials and difference of squares binomials as separate factors?
Answers
Answer:
A trinomial is an expression that has three terms.
Square trinomial
A square trinomial is simply a perfect square trinomial.
Difference of square binomials
This is easily identified because, the terms of the square binomials are perfect squares.
When cubes are added or subtracted, they can be expressed using the following
5.
Identify the axis of symmetry of the parabola.
A. y = −1
B. x = −1
C. x = 1
D. y = 1
Answers
Answer:
B. x = −1
Step-by-step explanation:
In the graph, the vertex of the parabola hits point (-1,-2). Therefore, the axis of symmetry is x = -1. It is not y = -2, since the parabola opens vertically, not horizontally.
Function or not functional? Pls help tyyy
Answers
Answer:
not functional, 0 over laps with T and X. so that should make it not functional (I think )
If two resistors with resistances R, and Ry are wired in parallel, then their combined resistance R is given by the complex fraction R=
R, R₂
Evaluate this formula when R1 = 70 ohms and R2 = 125 ohms.
Answers
Answer:
The equivalent resistance of two resistances connected in parallel is given by 1/R = 1/R1 + 1/R2
R = (R1*R2)/(R1 + R2)
(dR)/(dt) = ((R1*(dR2)/dt + R2*(dR1)/dt)(R1 + R2) - (R1*R2*((dR1)/dt + (dR2)/dt)))/(R1 + R2)^2
R1 is increasing at a rate of 0.3 ohms/second and R2 is increasing and finish i am busy right now am sorry to finish this question here ur formula
URGENT, WILL GIVE BRAINLIEST!!
In △ABC, A=27∘, a=27 and c=24. Which of these statements best describes angle C?
C must be acute.
C must be obtuse.
C can be either acute or obtuse.
△ABC cannot be constructed.
Answers
Answer:
C must be acute, and ABC cannot be constructed
Step-by-step explanation:
24 degrees is under 90 degrees making angle c an acute angle.
ABC cannot be contructed because a triangle makes up of 180 degrees, and ABC does not make up 180 degrees.
Have a great day friend! :D
Answer:
C must be acute.
Step-by-step explanation:
The smaller the length of the side, the smaller is the angle opposite it, so C must be < 27.
Find all factors of 27.
Answers
Answer:
all the factors of 27 is 1, 3 ,9,and 27
An Olympic-size swimming pool is 50 meters long. How many yards long is
the pool, to the nearest tenth of a yard?
Answers
Answer:
10.9
Step-by-step explanation:
Answer:
54.7 yards
Step-by-step explanation:
1 meter = 1.094 yards
50 meters = 54.7 yards
If 2 students can clean the classroom in 20 min. How long will it take 8 students to clean the classroom?
(1) 160 min
(2) 80 min
(3) 5 min
(4) 10 min
Answers
Answer:
5 MIN
Step-by-step explanation: