(a) X is distributed normally.
(b) The median recovery time is 3 days.
(c) The z score of the patient who takes 4.2 days to recover is 0.75.
(d) The probability of spending more than 2.3 days in recovery is 66.64 %.
(e) The probability of spending between 3.7 and 4.2 days in recovery is 10.7 %.
(f) The 85th percentile for recovery times is 5.24 days.
(a) We are informed that a certain surgical procedure's recuperation time for patients is typically distributed. As a result, X is distributed normally.
(b) The median will be equal to the mean because the patient recovery time has a normally distributed distribution. The median is therefore 3 days.
(c) The formula for z score is given as:
z = X - μ / σ
Now, we have the mean μ = 3 days.
Standard deviation, σ = 1.6 days
The observed value, X = 4.2 days
Therefore,
z = ( 4.2 - 3) / 1.6
z = 1.2 / 1.6
z = 0.75
(d) When X = 2.3 days
Then the z score will be:
z = X - μ / σ
z = 2.3 - 3 / 1.6
z = - 0.7 / 1.6
z = - 0.4375
The corresponding area for z = 0.4375 is 0.3336.
In order to determine the likelihood for a period longer than 2.3 days, we must look at the region to the right, which we can locate by deducting 0.3336 from 1.
Therefore, the probability will be:
p = 1 - 0.3336
p = 0.6664
p = 66.64 %
(e) Now, for the probability between X = 3.7 days and 4.2 days.
z₁ = (3.7 - 3) / 1.6 = 0.7/1.6 = 0.4375
z₂ = (4.2 - 3) / 1.6 = 1.2 / 1.6 = 0.75
The area for a z score of 0.4375 is 0.1664 and the area to left for a z score 0.75 is 0.2734.
Then the probability between 3.7 days and 4.2 days will be:
p = 0.2734 - 0.1664
p = 0.107
p = 10.7 %
(f) For the 85th percentile:
For 0.85 the z score from the table is 1.4.
So, z = 1.4
z = X - μ / σ
1.4 = ( X - 3) / 1.6
(1.4)(1.6) = X - 3
2.24 = X -3
X = 2.24 + 3
X = 5.24 days
Learn more about standard deviation here:
https://brainly.com/question/475676
#SPJ9
The complete question is mentioned below:
The patient recovery time from a particular surgical procedure is normally distributed with a mean of 3 days and a standard deviation of 1.6 days. Let X be the recovery time for a randomly selected patient. Round all answers to 4 decimal places where possible.
a. What is the distribution of X?
b. What is the median recovery time? __________days
c. What is the Z-score for a patient that took 4.2 days to recover?
d. What is the probability of spending more than 2.3 days in recovery?
e. What is the probability of spending between 3.7 and 4.2 days in recovery?
f. The 85th percentile for recovery times is _________days.
I really need help!
In the diagram below of triangle HIJ, K is the midpoint of HJ and L is the
midpoint of IJ. If KL = -8x +96, and HI= -8x + 120, what is the measure
of KL?
H
L
Answer: 24
Step-by-step explanation: HI = 2 times KL
-8x + 120 = 2(-8x + 96)
-8x + 120 = -16x + 192
8x = 72
x = 9
KL = -8x + 96
KL = -8(9) + 96
KL = 24
Describing a Graph On a coordinate plane, points (1, 3), (5, 9), and (7, 12) are plotted. statements are true about this graph? Check all that apply. The three points do not form a straight line. The three points form a straight line. The graph passes through the origin. The graph does not pass through the origin. The graph shows a proportional relationship. The graph does not a show a proportional relationship.
The correct statements regarding the linear function in the graph are:
The three points form a straight line.The graph does not pass through the origin.The graph does not a show a proportional relationship.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.From the points, we have that:
When x changes by 4, y changes by 6.When x changes by 6, y changes by 9.When x changes by 2, y changes by 3.Hence these points form a straight line with a slope of 1.5, that is:
y = 1.5x + b.
When x = 1, y = 3, hence we use it to find b as follows:
3 = 1.5 + b
b = 1.5.
Hence the relation is:
y = 1.5x + 1.5.
Since the y-intercept is different of 0, we have that:
The graph does not pass through the origin.The graph does not a show a proportional relationship.More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
How many 5-pound bags of apples can be made from 400 apples, each weighing 1/4 pound?
Answer:
20 bags
Step-by-step explanation:
400/4 = 100, because it takes four apples to make a pound
100/5 because each bag holds 5 pounds,
20, bags filled with 5 pounds of apples
$850 at 7% compounded annually for 3 years how do you calculate earned interest?
Answer:
$191.29
Step-by-step explanation:
Use the formula
[tex]A = P(1 + \dfrac{r}{100})^n[/tex]
where P is amount deposited, A the accrued amount, n number of years and r the interest rate in % compounded annually
The division by 100 is necessary to convert r% to a decimal for calculations
We have P = 850, r = 7% and n = 3
Plugging these in we get
[tex]A = 850\cdot (1 + (\dfrac{7}{100})^3\\\\A= 850\cdot(1 + 0.07)^3\\A = 850\cdot1.07^3\\\A = \$1,041.29[/tex]
Interest = A - P = 1041.29 - 850 = $191.29
This is a new version of the question. Make sure you
start new workings.
Percy is trying to find angle t.
He finds angle r first and then he finds
angle t from angle r.
a) Which angle fact does he use to find
angle r?
b) Which angle fact does he then use to
find angle t?
t
127
Not drawn accurately
Answer:
a) The fact that corresponding angles are equal
b) The fact that alternate angles are equal
Step-by-step explanation:
I hope this helps
a) Measure of corresponding angles are equal.
b) Pair of alternate interior angles are of equal measure.
What is a transversal?We know when a transversal intersects two parallel lines at two distinct points,
Two pairs of interior and alternate angles are formed such that the measure of interior angles are same and the measure of alternate angles is also the same.
From the given figure the fact used to fund the measure of the angle r is
corresponding angles.
The fact that is used to find the angle t is in a parallelogram measure of opposite angles are equal.
Also, r and t are pairs of alternate interior angles so they measure the same.
learn more about transversals here :
https://brainly.com/question/17987539
#SPJ2
write polynomial in simplest form with given zeros 2, 3 √(5),-3 √(5)
For every 21 litres of petrol a car can run for 80 km.
How much petrol do you need (to 1 DP) to ensure the car has enough petrol of a trip that is 224 km?
For every 21 liters of petrol a car can run for 80 km- 58.2 liters of petrol would be required to ensure the car has enough petrol of a trip that is 224 km unitary method
It is provided that to run 80km car requires 21 liters of petrol
To know how much petrol is required for a trip of 224 km, we first would require to know how much petrol is required to run 1 km
This is called unitary method
Petrol required by car to run 1 km would be petrol required by car to cover 80kms of distance divided by 80 km of distance = 21 liters of petrol/ 80 km distance
= 21/80
=0.26 liters
So, petrol required by car for a trip of 224 km= 0.26 liters ×224km
= 0.26× 224
= 58.24 liters
to know more about unitary method - https://brainly.com/question/28276953
#SPJ9
Twenty less than four times an mover is twenty one what is the number
Answer:
10.25
Step-by-step explanation:
Define the variable
Let x be the unknown number.
Therefore:
[tex]\begin{aligned}& \textsf{Four times a number}: \quad & 4x\\& \textsf{Twenty less than four times a number}: \quad & 4x-20\\& \textsf{Twenty less than four times a number is twenty one}: \quad & 4x-20=21\end{aligned}[/tex]
To find the number, solve the found equation for x:
[tex]\begin{aligned}\implies 4x-20&=21\\4x-20+20&=21+20\\4x&=41\\\dfrac{4x}{4}&=\dfrac{41}{4}\\x&=10.25\end{aligned}[/tex]
Therefore, the unknown number is 10.25.
As an improper fraction, this is ⁴¹/₄.
As a mixed number, this is 10 ¹/₄.
Answer:
x = 10.25
Step-by-step explanation:
Given that,
→ Twenty less than four times a number is twenty one.
The equation we form,
→ 4x - 20 = 21
Now the value of x will be,
→ 4x - 20 = 21
→ 4x = 21 + 20
→ x = 41/4
→ [ x = 10.25 ]
Hence, the number is 10.25.
••••••••••••••help ••••••••••••••help
Answer:
c
Step-by-step explanation:
8 telephone calls per hour
Use Table 12-2 to solve.
Ron Sample is the grand prize winner in a college tuition essay contest awarded through a local organization's scholarship fund. The winner receives $8,000 at the beginning of each year for the next 5 years. How much (in $) should be invested at 6% interest compounded annually to award the prize? (Round your answer to the nearest cent.)
$
Based on the amount the winner receives, the interest rate to be compounded annually, and the number of years, the amount that should be invested to award the price is $35,720.80.
How much should be invested?The amount that should be invested is the present value of the $8,000 for the next 5 years. This amount would be the present value of an annuity due because constant payments that come at the beginning of a period are annuity dues.
Present value of annuity due = Annuity due x (Present value interest factor of annuity due, 6%, 5 years)
Solving for the amount to be invested to award the price gives:
= 8,000 x 4.4651
= $35,720.80
Find out more on annuity dues at https://brainly.com/question/19131462
#SPJ1
An angle measures 111.4° more than the measure of its supplementary angle. What is the measure of each angle?
The measure of the supplementary angles are 34.3 and 145.7 degrees.
What are supplementary angles?Supplementary angles are those angles that sum up to 180 degrees.
In other words, two angles are Supplementary when they add up to 180 degrees.
Therefore, the angles measures 111.4° more than the measure of it's supplementary angle.
Hence,
let
x = measure of the other angle
x + x + 111.4 = 180
2x + 111.4 = 180
subtract 111.4 from both sides
2x + 111.4 - 111.4 = 180 - 111.4
2x = 68.6
divide both sides by 2
x = 68.6 / 2
x = 34.3
Other angle = 34.3 + 111.4 = 145.7°
Therefore, the measure of the supplementary angles are 34.3 and 145.7 degrees.
learn more on supplementary angles here: https://brainly.com/question/15966137
#SPJ1
the x intercept of a function always occurs where y is equal to zero
Kadien had 60 magazines,if he sells x magazines per day for 5 days how many magazines will kadien have left. Write an expression
The expression to know many magazines kadien have left will be 60 - 5x.
How to illustrate the expression?From the information, Kadien had 60 magazines and he sells x magazines per day for 5 days.
The expression to calculate the number that will be left will be:
= 60 -(5 × x)
= 60 - 5x
The expression is 60 - 5x.
Learn more about expressions on:
brainly.com/question/723406
#SPJ1
Whats 16.3 x 7.6, i need help asap. show ur work
Answer:
123.88
Step-by-step explanation:
The age, a, decreased by 15 years
The expression that represents the statement is a - 15
How to represent the mathematical statement as an algebraic expression?The mathematical statement is given as:
The age, a, decreased by 15 years
The variable in the above mathematical statement is
Variable a
This means that the decrease the variable in the above mathematical statement by 15
When the variable in the above mathematical statement is decreased by 15 years, we have the following expression
a - 15
This means that the representation of the the variable in the above mathematical statement is a - 15
Hence, the expression that represents the statement is a - 15
Read more about expression at
https://brainly.com/question/723406
#SPJ1
4. Grade points are assigned as follows: A = 4, B = 3, C=2, D = 1, and F = O. Grades are weighted
according to credit hours. If a student receives an A in a four-unit class, a D in a two-unit class, a B in a
three-unit class and a C in a three-unit class, what is the student's grade point average?
Answer:
2.75
Step-by-step explanation:
A in a 4-unit class will be 4 x 4 = 16 points
B in a 3-unit class will be 3 x 3 = 9
C in a 3-unit class will be 2 x 3 = 6
D in a 2-unit class will be 1 x 2 = 2
Total points = 16 + 9 + 6 + 2 = 33
Total credit hours = 4 + 3 + 3 + 2 = 12
GPA = 33/12 = 2.75
Which 3 numbers have the same answer whether they're added or multiplied together?
Answer:
1, 2 and 3
Step-by-step explanation:
The numbers are 1, 2 and 3
When we add together : 1+ 2+ 3 = 6 and
When we multiply: 1 × 2 × 3 = 6
1. You are buying tile for your bathroom floor and
baseboards for your bathroom walls. In the figure,
the entire polygon represents the layout of the
floor. Each unit in the coordinate plane represents
1 foot.
a. Find the area of the floor.
b. Find the perimeter of the floor.
c. The cost of the baseboard is $2 per foot. The
cost of the tile is $2.50 per square foot. Find
the total cost to buy tile and baseboards for
your bathroom.
The solutions to the questions are
The area of the floor is 65 square feetThe perimeter of the floor is 50 feetThe total cost to buy tile and baseboards for your bathroom is $145a. Find the area of the floor.The figure represents the given parameter.
On the figure, we have the following shapes:
Rectangle 1: 7 units by 5 unitsRectangle 2: 3 units by 10 unitsThe area is calculated as
Area = Area of rectangle 1 + Area of rectangle 2
So, we have
Area = 7 * 5 + 3 * 10
Evaluate
Area = 65
Hence, the area of the floor is 65 square feet
b. Find the perimeter of the floor.On the figure, we have the following shapes:
Rectangle 1: 7 units by 5 unitsRectangle 2: 3 units by 10 unitsThe perimeter is calculated as
Perimeter = Perimeter of rectangle 1 + Perimeter of rectangle 2
So, we have
Perimeter = 2 *(7 + 5) + 2 * (3 + 10)
Evaluate
Perimeter = 50
Hence, the perimeter of the floor is 50 feet
c. Find the total cost to buy tile and baseboards for your bathroom.The total cost is calculated as
Total Cost = Cost of baseball * Area of baseball + Cost of tile * Area of tile
So, we have
Total Cost = 2 * 7 * 5 + 2.5 * 3 * 10
Evaluate
Total Cost = 145
Hence, the total cost to buy tile and baseboards for your bathroom is $145
Read more about areas at
https://brainly.com/question/24487155
#SPJ1
A designer paid $4/square foot for flooring to be used in a square room. If the designer spent $600 on flooring, about how long is one of the sides of the room? You can round to the nearest foot.
Side of the given square room flooring is 12 foot
What is a square and its area?
A Square is a closed, two dimensional shape which has four sides and all four sides are equal and at 90 degree angle to each other .
As all four sides are equal, Let each of the side of a square is a
Area of the square is given by = a*a
Given that a designer paid $4 per square feet for a square flooring
Total amount spent by the designer = $600
Total area of flooring = total amount spent /rate of per unit area
= $600/$4 square foot =150 sq foot
Let the side of the given square flooring be x
Then area of the floor = [tex]x^{2} =150\\[/tex]
Thus side of the room floor = [tex]x=\sqrt{150}[/tex] = 12.25 = 12 foot
Also, learn more about the squares from here
https://brainly.com/question/27776258
#SPJ1
Hi can someone please help me with these!
7. e = 2A - f
72. Area = 615.8 in.²
Circumference = 88.0 in.²
73. Area = 615.8 in.²
Circumference = 88.0 in.²
74. Missing length = √40 ≈ 6.3
75. Missing length = √45 ≈ 6.7
76. Scale factor = 18/6 = 3
77. Scale factor = 12/4 = 3
What is the Area and Circumference of a Circle?Area = πr²
Circumference = 2πr
7. A = (e + f)/2
2A = e + f
2A - f = e
e = 2A - f
72. r = 14 in.
Area = πr² = π(14²) = 615.8 in.²
Circumference = 2π(14) = 88.0 in.²
73. r = 30.2/2 = 15.1
Area = πr² = π(15.1²) = 615.8 in.²
Circumference = 2π(15.1) = 88.0 in.²
74. Missing length = √(6² + 2²) [Pythagorean Theorem]
Missing length = √40 ≈ 6.3
75. Missing length = √(6² + 3²) [Pythagorean Theorem]
Missing length = √45 ≈ 6.7
76. Scale factor = 18/6 = 3
77. Scale factor = 12/4 = 3
Learn more about area and circumference of circle on:
https://brainly.com/question/402655
#SPJ1
Solve 14x-7y= 21 for y
A. y = 2x - 21
B. y=-14x + 21
C. y = 14x +3
D. y=2x-3
Answer:D
Step-by-step explanation::
The perimeter of the classroom is 32 meters. what is the length of each side of the classroom? what is the area of the classroom?
Answer:
64
Step-by-step explanation:
because you use 8+8+8+8=32 so you multiply 8x8 to get 64
for perimeter you add all four side with the same number ad the four sides is 8
but for area you multiply the 2 side and the two sides is 8
LA Fitness charges $50 to be a member and $2 each
time you attend the gym. 24 Hour Fitness charges $4
each time you attend the gym and $30 to be a
member.
Using your answer from the lastquestion, you should
have got after 10 visits, the costs will be the same at
either gym.....
How much would each gym cost if you attended 10
times?
$80
$100
$90
$70
$60
Answer:
$70
Step-by-step explanation:
$50 to start do 2*10 to get 20 add those 50+20=70
Next, $30 to start do 4*10 to get 40 add those 30+40=70
They both come out o $70
On a number line, B is between a and c. AB = 1/3ac
We may infer from the number line that A and B are separated by 8 units (AB).
Let AB stand for the separation between points A and B, and let AC stand for the separation between points A and C. Let B stand for the separation between points B and C. Hence:
Point B being halfway between A and C, we can infer:
AB + BC Equals AC (Postulated segment addition)
As a result, since the distance between points A and B is equal to 1/3 of AC:
AC/3 = AB = 1/3(AC)
But as shown in the accompanying image:
AC equals 16 – (–8) to 24 units.
Therefore:
AB = 1/24 = 8 unit
A and B are separated by 8 units.
To learn more about distance from given link
https://brainly.com/question/17617637
#SPJ9
Complete question -On the number line, Point B is between points A and C. The distance between points A and B is 1/3 of AC. What is AB?
Which statement is true about the end behavior of the
graphed function?
0 As the x-values go to positive infinity, the function's
values 90 to negative infinity.
As the x-values go to zero, the function's values go
to positive infinity.
As the x-values go to negative infinity, the function's
values are equal to zero.
O As the x-values go to positive infinity, the function's
values go to positive infinity.
Answer: B) as the x-values go to negative infinity, the functions values go to positive infinity.
Step-by-step explanation:
what is 0.037854921 to the nearest hundreth
Answer:
0.04
Step-by-step explanation:
I hope this is the answer you are looking for and I hope this helps!
help pls i dont know how to do this
Answer:
(-7, 5)
Step-by-step explanation:
You want to know the image of the point (-4, -6) after reflection in the x-axis and translation 3 left and 1 down.
Composition of transformationsThe composition ...
[tex]T_{-3,-1}\circ r_{\text{x-axis}}[/tex]
is interpreted to mean reflection in the x-axis occurs first, then translation by (-3, -1).
That is, a composition of transformations is evaluated right to left.
ReflectionReflection in the x-axis moves a point from below the x-axis to the same distance above the x-axis. That is, the sign of the y-coordinate changes:
(-4, -6) ⇒ (-4, 6) . . . reflection in the x-axis
TranslationThe translation vector is added to the coordinates of the point:
(-4, 6) +(-3, -1) = (-4-3, 6-1) = (-7, 5)
The image of the point is located at (-7, 5).
Divide.
4857÷18
• 15
• 269 R 12
• 269
• 269 R 15
I’m confused as to what the R means.
Answer:
269 R 15
Step-by-step explanation:
R means remainder
So if u divide 4857 by 18 you will get 269 reminder 15.
The graph of g is a translation 2 units left and 3 units up, followed by a reflection
in the y-axis of the graph of f(x) = x² - 2x.
Graph of g is a translation where g(x) = (x+2)^2 - 2x – 1
f(x) = x^2 - 2x
g(x) = f(x+2) + 3
Translation is a movement of the graph either horizontally parallel to the x-axis or vertically parallel to the y-axis. A translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction. A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system. In a Euclidean space, any translation is an isometry.
Hence , g(x) = (x+2)^2 -2(x+2) + 3 = (x+2)^2 - 2x - 1. When we graph the equations, we can confirm that our answer is correct.
To know more about Graph, visit :
brainly.com/question/9058525
#SPJ1
Singer A and Singer B had the two top-grossing concert tours for a certain year, together generating $443 million in ticket sales. If Singer B took in $29 million less than Singer A, how much did each tour generate?
If Singer B took in $29 million less than Singer A, it means that Singer A generates $236 million and singer B generates $207 million in tickets sale.
How much does singer A takes in ticket sales?The fact that singer B generated $29 million less than singer A means that if singer A generates x million , singer would generate (x-29) million in tickets salessingers:
A's earnings=xsinger B's earnings=x-29total earnings=x+x-29total earnings=2x-29total earnings=443443=2x-29
443+29=2x
472=2x
x=472/2
x=236singer
B's earnings=236-29
singer B's earnings=207
Find out more about tickets sales on: brainly.com/question/2777438
#SPJ1
