Answer:
False
Step-by-step explanation:
Required
State if the product of rational numbers and integer is an integer
The statement is false and the proof is as follows
Literally, rational numbers are decimal numbers that can be represented as a fraction of two integers;
Take for instance: 0.2, 0.5, 2.25, etc.
When any of these numbers is multiplied by an integer, the resulting number can take any of two forms;
1. It can result to an integer:
For instance;
[tex]0.2 * 5 = 1[/tex]
[tex]0.5 * 4 = 2[/tex]
[tex]2.25 * 8 = 18[/tex]
2. It can result in a decimal number
For instance;
[tex]0.2 * 3 = 0.6[/tex]
[tex]0.5 * 5 = 2.5[/tex]
[tex]2.25 * 7 = 15.75[/tex]
From (1) above, we understand that the product can result in an integer.
Hence, the statement is false
Pregunta N° 1: ¿Cuántas fracciones propias e irreductibles con denominador 24 existen? 1 punto A) 2 B) 4 C) 6 D) 8 E) 10 Pregunta N° 2: ¿Cuántas fracciones impropias e irreductibles con numerador 25 existen? 1 punto A) 19 B) 21 C) 25 D) 29 E) 33 Pregunta N° 3: La edad de Miguel es 4/5 de la edad de su novia. Si las edades de los dos suman 63 años, calcule la edad de la novia de Miguel. 1 punto A) 20 años B) 26 años C) 32 años D) 35 años E) 40 años Pregunta N° 4: Si son las 8 a. m., ¿qué fracción del día ha transcurrido? 1 punto A) 1 B) 2 C) 1/2 D) 1/3 E) 1/5
ayuden porfavor
Answer:
Pregunta 1: Opcion D. 8
Pregunta 2: Opción A. 19 (aunque lo correcto es decir que son 20)
Pregunta 3: 28 años (no está como opción)
Pregunta 4: Opción D. 1/3
Step-by-step explanation:
Las fracciones irreductibles son aquellas que después de dividirlas por un común divisor, una vez que no se pueden dividir más se dice que son irreducibles, por lo tanto no existe ningún número que sea divisor común del numerador y del denominador más que 1.
Fracciones irreductibles con común denominador 24.
Como máximo divisor tenemos el 24 y como mínimo el 1
entre 1/24 y 1 estarán nuestras fracciones o sea:
1/24 < x/24 < 1. Ahora convertimos el 1 en fracción de 24, lo que sería 24/24 para igualar el numerador en ambos lados de la ecuación, para poder determinar x
1/24 < x/24 < 24/24
Como vemos que x tiene que estar entre 1 y 24, las respuestas serán:
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22 y 23
Eliminamos los números divisores de 24, aquellos pares, y nos focalizamos en los que no podriamos dividir por nada con 24, o sea los números primos
5, 7, 11, 13, 17, 19, 23. Como nos falta el 1, obtenemos un total de 8 fracciones: 1/24, 5/24, 7/24, 11/24, 13/24, 17/24, 19/24, 23/24
Mismo procedimiento para el 25:
1/25 es una de las fracciones irreductibles. Pensamos en los valores de x
1/25 < x/25 < 25/25
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25
Los números divisibles por 25, son los multiplos de 5, asi que esas respuestas no irían. Las fracciones irreductibles son:
1/25, 2/25, 3/25, 4/25, 6/25, 7/25, 8/25, 9/25, 11/25, 12/25, 13/25, 14/25, 16/25, 17/25, 18/25, 19/25, 21/25, 22/25, 23/25 y 24/25 haciendo un total de
20. Por alguna razón está mal formulada la pregunta, son 20 pero no está como opción y como te piden fraccion impropia (numerador > denominador), contamos a partir de 26. FIjate que hasta el proximo entero que sería 50/25, también son 20 fracciones (irreductibles e impropias)
26/25, 27/25, 28/25, 29/25, 31/25, 32/25, 33/25, 34/25, 36/25, 37/25, 38/25, 39/25, 41/25, 42/25, 43/25, 44/25, 46/25, 47/25, 48/25, 49/25
Próxima pregunta:
Miguel tiene 4/5 de la edad de la novia, y ambas edades suman 63.
Plantiemos la siguiente ecuacion donde x es la edad de la novia
4/5x + x = 63
9/5x = 63
x = 63 . 5/9 (como 9/5 pasa al otro lado de la igualdad dividiendo, damos vuelta la fraccion multiplicandola)
x = 35
Si la novia tiene 35 años y la edad de Miguel es 4/5 de esa edad
4/5 .35 = (35 .4) /5 = 28
Es raro porque no está la respuesta como tal.
Próxima pregunta:
Al ser las 8 am, quiere decir que han pasado 8 horas de que empezó el día
y el día tiene 24 horas.
8 horas transcurridas / 24 horas totales = 1/3
20 points! I would really like some help! :) (Question attached below)
Answer:
See below.
Step-by-step explanation:
(a)
To multiply two polynomials, multiply every term of the first polynomial by every term of the second polynomial. Then combine like terms.
[tex] (\dfrac{1}{2}x - \dfrac{1}{4})(5x^2 - 2x + 6) = [/tex]
[tex] = \dfrac{1}{2}x \times 5x^2 - \dfrac{1}{2}x \times 2x + \dfrac{1}{2}x \times 6 - \dfrac{1}{4} \times 5x^2 + \dfrac{1}{4} \times 2x - \dfrac{1}{4} \times 6 [/tex]
[tex]= \dfrac{5}{2}x^3 - x^2 + 3x - \dfrac{5}{4}x^2 + \dfrac{1}{2}x - \dfrac{3}{2}[/tex]
[tex] = \dfrac{5}{2}x^3 - \dfrac{9}{4}x^2 + \dfrac{7}{2}x - \dfrac{3}{2} [/tex]
(b)
No. Since the binomials are different, the product of two different binomials and the same trinomial will give different results.
Let n be the number of five-digit positive integers which are divisible by 36 and have their tens digit and unit digit equal. Find n/100
Answer:
1.) 10044
2.) 100.44
Step-by-step explanation:
Since n is a number of five-digit positive integers which are divisible by 36, start multiplying 36 by number. Starting from 278.
Five digits numbers start from multiplying 36 by 278. Any multiplication below 278 by 36 will give four digits numbers.
36 × 278 = 10,008
36 × 279 = 10,044
10,044 tens digit and unit digit equal. Therefore n = 10044
To find n/100, divide 10044 by 100
10044 / 100 = 100.44
F/4-5=-9 how do you do this problem
Answer:
F = -16
Step-by-step explanation:
F/4-5=-9
Add 5 to each side
F/4-5+5=-9+5
F/4=-4
Multiply each side by 4
F/4 *4=-4*4
F = -16
Duke wants to hire someone to re-tile his bathroom. The research he found for three local tilers is presented in the table below. He was able to find the average area of their tiling jobs and the time it took the tilers to complete the job.
Tiler Area Tiled
(square feet) Time
(hours:minutes)
Toni's Tiles 803 2:12
Bob's Bathrooms 1,460 4:00
Rhonda's Restroom Redos 753 1:30
Calculate the unit rate for each tiler above to determine if proportional relationships exist.
The rates at which Toni's Tiles and Bob's Bathrooms tile are ?
to one another.
The rates at which Toni's Tiles and Rhonda's Restroom Redos tile are ?
to one another.
The rates at which Bob's Bathrooms and Rhonda's Restroom Redos tile are ?
to one another.
Two items are in a proportional relationship if they ?
the same unit rate.
Answer:
Toni's Tiles and Bob's Bathrooms are in a proportional relationship as they have the same unit rate
Step-by-step explanation:
The given parameters are;
, Area Tiled (ft²) Time (Hr:min)
,
Toni's Tiles, 803 2:12
Bob's Bathrooms, 1,460 4:00
Rhonda's Restroom Redos 753 1:30
The unit rate for each tiler
Toni's Tiles = 803/2:12 = 803/(2×60 + 12) = 6.083 ft²/min
Bob's Bathrooms = 1460/(4×60) = 6.083 ft²/min
Rhonda's Restroom Redos = 753/(60 + 30) = 8.37 ft²/min
Therefore we have;
The rates at which Toni's Tiles and Bob's Bathrooms tile are to one another = 6.083 to 6.083 = 1:1
The rates at which Toni's Tiles and Rhonda's Restroom Redos tile are to one another = 73/12×30/251 = 365:502
The rate at which Bob's Bathrooms and Rhonda's Restroom Redos tile are to one another = 73/12×30/251 = 365:502
Therefore, Toni's Tiles and Bob's Bathrooms are in a proportional relationship as they have the same unit rate.
This is the question
For answers, please refer to the picture attached
Answer:
I can't give a full answer because I can't see the image whilst giving an answer but I'll try so....
Step-by-step explanation:
Angles in a straight line add to 180° so when you have one of two of them angles are them together and take away from 180°
Angles around a full point add to 360° so add angles together and take away from 360°
On A I think it is you have a 360° angle and have to work out 3 and you have one already done and the opposite angle is the same as that so you basically have two angles then you add them together then take from 360 then divide the answer by two and then that would be the angles for a and x
And for the last one you have been given two angles with a right angle and a right angle equals 90 so add them together and take from 180 to get the missing angle
Hope this helps :)
A baker has three banana muffin recipes. Recipe AAA uses 333 bananas to make 121212 muffins. Recipe BBB uses 555 bananas to make 242424 muffins. Recipe CCC uses 111111 bananas to make 484848 muffins. Order the recipes by number of bananas per muffin from least to greatest.
Answer:
The order from least to greatest is B, A, C
Step-by-step explanation:
Given
Recipe A = 3 bananas to 12 Muffins
Recipe B = 5 bananas to 24 Muffins
Recipe C = 11 bananas to 48 Muffins
Required
Order the recipe from least to greatest
To solve this, we have to divide the number of bananas by number of muffins; this will give the unit banana per muffin
Recipe A: 3 bananas to 12 Muffins
[tex]A = \frac{3}{12}[/tex]
[tex]A = 0.25[/tex]
Recipe B: 5 bananas to 24 Muffins
[tex]B = \frac{5}{24}[/tex]
[tex]B = 0.2083[/tex]
Recipe C: 11 bananas to 48 Muffins
[tex]C = \frac{11}{48}[/tex]
[tex]C = 0.229167[/tex]
By comparison;
Recipe B (0.2083) is the smallest; followed by Recipe C (0.229167) then Recipe A (0.25)
Hence; the order from least to greatest is B, A, C
Answer:
its BCA
Step-by-step explanation:
The triangle shown below has an area of 4 units
Find the missing side.
Answer:
[tex]\boxed{4 units}[/tex]
Step-by-step explanation:
Hey there!
Well if the base is 4 and we use the formula,
b*h / 2
4*4 = 16
16/2 = 8
So x is 4.
Hope this helps :)
Answer:
x = 2 unitsStep-by-step explanation:
Area of a triangle is given by
base × height
[tex] A = \frac{1}{2} base × height[/tex]
From the question
Area = 4 units²
height = 4 units
let x represent the base
We have
[tex]4 = \frac{1}{2} \times x \times 4[/tex]
4 = 2x
Divide both sides by 2
x = 2 unitsHope this helps you
A point P has coordinates (-8, -2). What are its new coordinates after reflecting point P across the x-axis?
Answer:
(-8,2)
Step-by-step explanation:
This is because when you reflect a point across the x-axis, the x-coordinate fo the point remains the same and the y-coordinate's sign gets switched.
(x,y) --> (x,-y)
(-8,-2) --> (-8,2)
Sarah has $20 saved. She gets $10 per week for her allowance, and she saves her allowance for the next 3 weeks. At the end of the week, she gets $150 in birthday money. How much money will she have after the 3 weeks? Which of the following sets of equations represents this problem?
Answer:
$200
Step-by-step explanation:
We know that she already has $20. And we know that every week, for three weeks she gets $10.
20+3(10)+150=m
We add all of this up, and we find that at the end of 3 weeks Sarah has $200 saved.
Points C and D are on a number line (not shown).
The coordinate of point C is -16 and the coordi-
nate of point D is 14. Point E is a point on line
segment CD. If the distance from point E to point C
is 1
4
the distance from point E to point D, what is
the coordinate of point E?
Answer:
17
Step-by-step explanation:
You and your friend are playing a game. The two of you will continue to toss a coin until the sequence HH or TH shows up. If HH shows up first, you win. If TH shows up first, your friend wins. What is the probability of you winning?
Answer:
The probability of friend A winning with HH = 1/4.
Step-by-step explanation:
The probability of an event, A is P(A) given by the relationship;
P(A) = (The number of required outcome)/(The number of possible outcomes)
The parameters given are;
The condition of friend A winning = Coin toss sequence HH shows up
The condition of friend B winning = Coin toss sequence TH shows up
The number of possible outcomes = TT, TH, HH, HT = 4
(TH and HT are taken as different for the game to be fair)
The number of required outcome = HH = 1
Therefore;
The probability of friend A winning with HH = 1/4.
Does The TI-Nspire works just like the TI-84 ?
Answer:
TI-Nspire models automatically detect most points of interest such as x and y-intercepts, maximum values, and minimum values when you are in trace mode. TI-84 Plus models require you to use a series of left and right bounds and guesses to find those same values.
Hey, please help solve the question.
Answer:
75%=x-125
90%=x+250
subtract the second from the first
15%=375
100%=?
100%×375/15
100%=2500marked price is 2500
2500+250=2750
90%=2750
100%=?
cost price=3055.56
Find the value of the variable(s). If your answer is not an integer, leave it in simplest radical form.
x = 22, y = 11[tex]\sqrt{3}[/tex]
x = 11, y = 22[tex]\sqrt{3}[/tex]
x = 22[tex]\sqrt{3}[/tex], y = 11
x = 11[tex]\sqrt{3}[/tex], y = 22
Answer:
D
Step-by-step explanation:
Since this is a right triangle, and we are given that one of the other angles is 30°, we have a 30°, 60°, 90° triangle.
In a 30°, 60°, 90° triangle, the side lengths are all related as shown below.
We should determine a first. a is the measure of the side opposite to the 30° angle. Thus:
[tex]a=11[/tex]
The side opposite to the 60° angle is given by a√3. Since a = 11, the side opposite to the 60° angle or x is:
[tex]x=(11)\sqrt{3}=11\sqrt3[/tex]
Finally, the hypotenuse will be 2a. Since a = 11, the hypotenuse or y will be:
[tex]y=2(11)=22[/tex]
Hence, x = 11√3 and y = 22.
Our answer is D.
someone please expain how to do this, i’m really confused.
Answer:
13
Step-by-step explanation:
Basically, we have to plug in 4 for r into g(r). Doing so gives us g(4) = 25 - 3 * 4 = 25 - 12 = 13.
Some more examples:
g(6) = 25 - 3 * 6 = 25 - 18 = 7
g(1) = 25 - 3 * 1 = 25 - 3 = 22
Answer:g(4)=13
Step-by-step explanation:
g(4)=25-3r
25-3(4)
25-12
g(4)=13
9 ÷ (-4 1/2) = L.
What is L.
Answer:
[tex]\huge\boxed{L = -2}[/tex]
Step-by-step explanation:
L = 9 ÷ [tex](-4 \frac{1}{2} )[/tex]
L = 9 ÷ [tex](-\frac{9}{2} )[/tex]
L = 9 × [tex](-\frac{2}{9} )[/tex]
L = 1× (-2)
L = -2
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
[tex]\boxed {l = \frac{-18}{41} }[/tex]
[tex]\frac{\frac{9}{-41} }{2} = l[/tex]
Simplifies to:
[tex]\frac{-18}{41} = l[/tex]
Let's solve your equation step-by-step.
[tex]\frac{-18}{41} = l[/tex]
Step 1: Flip the equation.
[tex]l = \frac{-18}{41}[/tex]
So your answer would be : [tex]\boxed {l = \frac{-18}{41} }[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Have a great day/night!
❀*May*❀
If the cost of fencing a rectangular garden per meter is rupees 5 . Find the amount needed to do the fencing of the garden with length 400 m and breadth 150 m .
Answer:
6500 rupees
Step-by-step explanation:
We are given a rectangular garden is the dimensions of:
Length = 400 m
Breadth = 150 m
Perimeter of a rectangle = 2(L + B)
= 2(400 + 150)
= 2(650)
= 1300m
We are told that the cost of fencing a rectangular garden per meter is rupees 5
1 m = 5 rupees
1300m =
Hence, the cost to fence the entire garden = 1300 × 5 rupees
= 6500rupees
solve the following: - 3 raised to 1 by 5 the whole raised to 4 (3^1/5)^4
Answer:
8.30256
Step-by-step explanation:
Step 1: Write out expression
[tex]((-3)^{\frac{1}{5} })^{4(3^{\frac{1}{5} })^4[/tex]
Step 2: Use BPEMDAS to evaluate
[tex](-1.24573)^{4(3^{\frac{1}{5} })^4[/tex]
[tex](-1.24573)^{4(1.24573)^4[/tex]
[tex](-1.24573)^{4(2.40822)[/tex]
[tex](-1.24573)^{9.6329}[/tex]
= 8.30256
And we have our answer!
Pls help me , idk how to do
Answer:
PQRS is a parallelogram with right-angle corners
Step-by-step explanation:
We know that the midsegment of a triangle is parallel to the base.
QR is the midsegment of triangle BCD, so is parallel to BD.
SP is the midsegment of triangle DAB, so is parallel to BD.
QR and SP are both parallel to BD, so are parallel to each other.
RS is the midsegment of triangle CAD, so is parallel to AC.
PQ is the midsegment of triangle ABC, so is parallel to AC.
RS and PQ are both parallel to AC, so are parallel to each other.
__
We have shown that opposite sides of PQRS are parallel to each other, so the figure is at least a parallelogram.
__
By virtue of the congruence of corresponding angles where a transversal crosses parallel lines, each of the so-far named lines can be shown to be perpendicular to any of the lines it meets.* Hence the figure PQRS must be a parallelogram with right angles, a rectangle.
_____
* Transversal BD crosses PQ, AC, and RS at right angles. Hence, transversals RS and PQ cross QR, BD, and SP at right angles. That is, the angles at corners P, Q, R, and S of the parallelogram are right angles.
I NEED HELP PLEASE !!!!
Answer:
No, all of her work is correct.
Step-by-step explanation:
Answer:
No, all of her work is correct.
Step-by-step explanation:
All of her work is correct.
The first step is showing factorization of √50
The second step is simplifying the factorization
The third step is simplifying the entire radical.
When you take a square root of a square, they cancel out, so:
√5² = 5
We multiply it with our leftover √2 and we get:
5√2
Find the median of the following frequency distribution
Answer:
3
Step-by-step explanation:
First right out all the data in numerical order from left to right.
2, 2, 2, 3, 4, 5, 7
The median is the middle number in the set. If there is an even amount of data points, find the average of the two middle numbers. If there is an odd number of data points, like in this data set, just take the middle number as you median.
There are 7 data points in this set so the fourth number in the set written in numerical order would be your median.
When writing this set out in numerical order, repeated numbers must be repeated, we find that the fourth, or middle, number is 3. Therefore, 3 is the median of this data set.
What is the product 1/2 * 1/8
Answer:
1/16
Step-by-step explanation:
........ .. .............
Answer:
1/16.
Step-by-step explanation:
If the question says to find the product, it means to multiply these numbers.
1/2✖️1/8.
Because you cannot cancel out any numbers, you can just multiiply the numerator and the denominator, which gives 1/16.
Hope this helped!
Have a nice day:)
If Eric can paint $3$ cars in $4$ hours and $2$ trucks in $5$ hours, then how long, in hours, would it take him to paint $4$ cars and a truck? Express your answer as a common fraction.
Answer:
47/6
Step-by-step explanation:
Given that :
Time taken to paint 3 cars = 4 hours
Time taken to paint 2 trucks = 5 hours
How long will it take him to paint 4 cars and a truck
If 3 cars = 4 hours ;
Then ;
1 car = (4/3)hours
If 2 trucks = 5 hours
Then;
1 truck = (5/2) hours = 2 1/2 hours
Time required To paint 4 cars :
4 × (4/3) = 16/3 hours
Time required to paint 1 truck :5/2 hours
Total time required :
(16/3 + 5/2) = (32 + 15) / 6 = 47/6
Divide 50 by 25 and find the remainder to complete the equation:
50 = 25 x ? + ?
Answer:
0
Step-by-step explanation:
Hello, do you agree that 25 * 2 = 50 ?
So, we can write that [tex]50 = 25 * \boxed{2} + \boxed{0}[/tex]
the remainder is 0.
Thank you
Coordinate plane with two lines graphed. The equations of the lines are y equals negative two-thirds x plus four and the other line is y equals two-thirds x. Determine the number of solutions the system of linear equations has and the solution(s) to the equations represented by these two lines? The system of equations has 0 solutions, because the graph has no point of intersection. The system of equations has infinite number of solutions and all real numbers satisfy both equations. The system of equations has 1 solution and it is (3, 2). The system of equations has 1 solution and it is (3, 0).
Answer:
Step-by-step explanation:
y = -2/3x + 4
y = 2/3x
2/3x = -2/3x + 4
4/3x = 4
4x = 12
x = 3
y = 2/3(3)
y = 2
(3,2) one solution
option 3
Consider the perfect square trinomial identity:
a2 + 2ab + b2 = (a + b)2.
For the polynomial x2 + 10x + 25,
and b =
a =
Answer:
a = x
b = 5
Step-by-step explanation:
for the polynomial x² + 10x + 25, b = 5 and a = x.
In the polynomial x² + 10x + 25, we can observe that the first term, x², is the square of x, and the last term, 25, is the square of 5. This suggests that the polynomial follows the perfect square trinomial identity.
The middle term, 10x, can be rewritten as 2ab, where a represents x and b represents a term that when squared equals the last term, 25.
In this case, b = 5, because 5² = 25.
To find a, we can take the square root of the first term, x². The square root of x² is x, so a = x.
Therefore, for the polynomial x² + 10x + 25, b = 5 and a = x.
Learn more about trinomial identity here
https://brainly.com/question/17033454
#SPJ2
nine hundred fifty-three thousand nine hundred two
Answer:
953 902
Step-by-step explanation:
Answer:
953,902
Step-by-step explanation:
nine hundred =900
fifty-three=53
thousand=1000
nine hundred=900
two=2
ANSWER QUICKLY PLZZZZZZ ASAP
Answer:
number 4 on edge
Step-by-step explanation:
Answer:
a. 92 minutes b. 7:56am
Step-by-step explanation:
He should leave at 7:56 so he gets to the bus at 8:05,
he gets to Coventry at 9:37 with enough time to walk 12 minutes to get to work before 10am.
The pregnancy length in days for a population of new mothers can be approximated by a normal distribution with a mean of days and a standard deviation of days. (a) What is the minimum pregnancy length that can be in the top % of pregnancy lengths? (b) What is the maximum pregnancy length that can be in the bottom % of pregnancy lengths? (a) The minimum pregnancy length is 280 days.
Answer:
(a) 283 days
(b) 248 days
Step-by-step explanation:
The complete question is:
The pregnancy length in days for a population of new mothers can be approximated by a normal distribution with a mean of 268 days and a standard deviation of 12 days. (a) What is the minimum pregnancy length that can be in the top 11% of pregnancy lengths? (b) What is the maximum pregnancy length that can be in the bottom 5% of pregnancy lengths?
Solution:
The random variable X can be defined as the pregnancy length in days.
Then, from the provided information [tex]X\sim N(\mu=268, \sigma^{2}=12^{2})[/tex].
(a)
The minimum pregnancy length that can be in the top 11% of pregnancy lengths implies that:
P (X > x) = 0.11
⇒ P (Z > z) = 0.11
⇒ z = 1.23
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\1.23=\frac{x-268}{12}\\\\x=268+(12\times 1.23)\\\\x=282.76\\\\x\approx 283[/tex]
Thus, the minimum pregnancy length that can be in the top 11% of pregnancy lengths is 283 days.
(b)
The maximum pregnancy length that can be in the bottom 5% of pregnancy lengths implies that:
P (X < x) = 0.05
⇒ P (Z < z) = 0.05
⇒ z = -1.645
Compute the value of x as follows:
[tex]z=\frac{x-\mu}{\sigma}\\\\-1.645=\frac{x-268}{12}\\\\x=268-(12\times 1.645)\\\\x=248.26\\\\x\approx 248[/tex]
Thus, the maximum pregnancy length that can be in the bottom 5% of pregnancy lengths is 248 days.
