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.
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
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
-11b+7=4 someone help I’ve been stuck on this problem forever
Answer: Hi!
First, we will use inverse operations to remove the 7. Subtract 7 on both sides:
7 - 7 = 0
4 - 7 = -3
Our equation now looks like this:
-11b = -3
Now we will use inverse operations to isolate the b. Divide -11 on both sides:
-11b ÷ -11 = b
-3 ÷ -11 = 3/11
Our equation now looks like this:
3/11 = b
3/11 is equal to b. This is your answer!
Hope this helps!
at the rate of 50 mph a car can travel 14.6 miles for each gallon of gas used. On a trip Mr. Hanson used 12.5 gallons of gas traveling at a speed of 50 mph. the number of miles covered during the trip was:
Answer:
182.5 miles in the rate of 50 mph.
Step-by-step explanation:
1 gallon = 14.6 miles in the rate of 50 mph
12.5 gallons = ?
12.5 × 14.6 = 182.5 miles in the rate of 50 mph.
The number of miles covered during the trip was 182.5 miles.
Given that, at the rate of 50 mph, a car can travel 14.6 miles for each gallon of gas used. On a trip, Mr Hanson used 12.5 gallons of gas travelling at a speed of 50 mph.
What is a unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Now, 1 gallon = 14.6 miles at the rate of 50 mph
12.5 × 14.6 = 182.5 miles in the rate of 50 mph.
Therefore, the number of miles covered during the trip was 182.5 miles.
To learn more about the unitary method visit:
https://brainly.com/question/22056199.
#SPJ2
The domain of this function is {-12, -6, 3, 15}. y=-2/3x+7 Complete the table based on the given domain.
Answer:
Step-by-step explanation:
Domain of a function represents the set of x-values (input values) and y-values (output values) of the function represent the Range of the function.
Given function is,
[tex]y=-\frac{2}{3}x+7[/tex]
If Domain (input values) of this function is,
{-12, -6, 3, 15}
Table for the input-output values of this function,
x -6 3 15 -12
y 11 5 -3 15
Answer:
Step-by-step explanation:
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.
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
To get from home to work, Felix can either take a bike path through the rectangular park or ride his bike along two sides of the park. How much farther would Felix travel by riding along two sides of the park than he would by taking the path through the park?
Answer:
c=5.9/6(G)
Step-by-step explanation:
first find the 2 distances.
a^2+b^2=c^2 c=2.4+.7
7^2+2.4^2=c^2 c=3.1
.49+5.85=c^2
c^2=6.34
c=√6.34
c=2.51.
next subtract the two distances to find the difference.
c=2.51-3.1
c=.59
so the distance would be .59 which can be rounded up to .60/G
explanation on how I knew the answer.
Im reviewing for the math 8th grade staar.
The formula for centripetal acceleration, a, is given below, where v is the velocity of the object and r is the object's distance from the center of the circular path.
This is the same as writing v = sqrt(ar)
===========================================
Work Shown:
[tex]a = \frac{v^2}{r}\\\\ar = v^2\\\\v^2 = ar\\\\v = \sqrt{ar}\\\\[/tex]
I multiplied both sides by r to isolate the v^2 term, then I applied the square root to fully isolate v.
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
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
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.
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
1. Given thatA={1,2,3,4,5} and B={3,5,10,11,12} and such that U= AUB. I) list down the elements of U,A' and A'UB'. ii) how many subsets do set A have?
Answer:
U = {1, 2, 3, 4, 5, 10, 11, 12}A' = {10, 11, 12}A'∪B' = {1, 2, 4, 10, 11, 12}A has 32 subsetsStep-by-step explanation:
i) The union of the two sets is the list of elements that are in either. Duplicates are listed only once.
U = {1, 2, 3, 4, 5, 10, 11, 12}
A' = U - A = {10, 11, 12}
A'∪B' = {10, 11, 12}∪{1, 2, 4} = {1, 2, 4, 10, 11, 12}
__
ii) A has 5 elements, so has 2^5 = 32 subsets, including the empty set and the whole set.
Which of the functions below is not exponential or logarithmic?
Answer:
f(x) = 5x² + 3
Step-by-step explanation:
Exponential Function: [tex]a(b)^x+c[/tex]
Logarithmic Function: [tex]alog_bx+c[/tex]
5x² + 3 is a quadratic function. Therefore, it is not an exponential or logarithmic function and is incorrect.
log₅x is a logarithmic function. Therefore, it is correct.
5log₃x + 3 is a logarithmic function. Therefore, it is correct.
5ˣ + 3 is an exponential function. Therefore it is correct.
The circle shown below is a unit circle, where ∠a=π/3 and the radius of the circle is 1.
Answer:
Step-by-step explanation:
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.
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
ASAP!!! PLEASE help me solve this question! No nonsense answers, and solve with full solutions.
Answer:
when two inscribed angles in one circle both equal 75°, the two angles must intercept the same arc that measures 75°.
Step-by-step Explanation:
The relationship between an intercepted arc and an inscribed angle is given as:
the measure of the intercepted arc = twice the inscribed angle that intercepts it.
Also, by virtue of this, when two inscribed angles intercepts the same arc, both inscribed angles are said to be congruent. And the measure of both angles equal the measure of the arc they both intercept.
Therefore, if the measure of an arc, that is intercepted by 2 inscribed angles, is given as 75°, both inscribed angles equal 75° as well. Thus, each of the inscribed angles is half the measure of the intercepted arc.
Therefore, the statement that is true about inscribed angles is: "when two inscribed angles in one circle both equal 75°, the two angles must intercept the same arc that measures 75°."
Can integers be written as fractions?
Answer:
Step-by-step explanation:
Yes you can just write them with denominator 1,
So 3 = 3/1 and -6 = -6/1.
Answer:
Yes.
Step-by-step explanation:
ALL real numbers can be written as fractions, and since integers fall under the category of real numbers, it is official that they can be written as fractions.
I am joyous to assist you at any time.
In the diagram of the right triangle shown find the value of c.
Answer:
Hey there!
20^2+25^2=c^2
400+625=c^2
1025=c^2
Square root 1025 is the correct answer, so option C.
Let me know if this helps :)
Answer: B
Step-by-step explanation:
1/2x+1/3y=2
1/3x+1/2y=13/6 (x is not equal to 0, y is not equal to 0)
by substitution method,
step by step
Answer:
x=2
y=3
Step-by-step explanation:
x/2+y/3=2 so
3x/6+2y/6=12/6
then multiply by 6
3x+2y=12
equation number 2
x/3+y/2=13/6
2x/6+3y/6=13/6
multiply by 6
2x+3y=13
so the system is now
3x+2y=12
2x+3y=13
from the first equation 2y=12-3x, y=6 - 3x/2
then put y in the second equation
2x+3*(6-3x/2)=13
2x+18-9x/2=13
2x-9x/2=13-18
4x/2-9x/2=-5
-5x/2=-5
*(-1/5) *(-1/5)
x/2=1
*2 *2
x=2
so y=6-3*2/2=6-3
y=3
Step-by-step explanation:
Given that:
(1/2x)+(1/3y) = 2 --------(1)
(1/3x)+(1/2y) = 13/6-----(2)
Put 1/x = a and 1/y = b then
(1) becomes
(a/2 )+( b/3) = 2
⇛ (3a+2b)/6 = 2
⇛ 3a+2b = 2×6
⇛ 3a+2b = 12 --------(3)
(2) becomes
(a/3)+(b/2)=13/6
⇛ (2a+3b)/6 = 13/6
⇛ 2a+3b=13----------(4)
On adding (3)&(4) then
3a+2b=12
2a+3b=13
(+)
_________
5a+5b = 25
_________
⇛ 5a+5b = 25
⇛ 5(a+b)=25
⇛ a+b=25/5
⇛ a+b=5 -------------(5)
On subtracting (3) from (4)
2a+3b=13
3a+2b=12
(-)
_________
-a+b = 1
_________
⇛ -a+b = 1
⇛ b = 1+a --------(6)
On Substituting the value of b in (5) then
a+1+a = 5
⇛2a+1 = 5
⇛ 2a = 5-1
⇛ 2a = 4
⇛ a = 4/2
⇛ a = 2
On Substituting the value of a in (6) then
b = 1+2
b = 3
Now,
a = 2
⇛ 1/x=2
⇛ “x” = 1/2
and
b= 3
⇛ 1/y = 3
⇛“y” = 1/3
Answer:- Hence, the value of x and y with be 1/2 and 1/3 respectively.
The solution for the given problem is (1/2,1/3)
Check:-
If x = 1/2 and y = 1/3 then
LHS = (1/2x)+(1/3y)
= 1/2(1/2)+1/3(1/3)
= 1/(2/2)+1/(3/3)
= (1/1)+(1/1)
= 1+1
=2
= RHS
LHS=RHS is true
and
LHS=(1/3x)+(1/2y)
⇛ 1/3(1/2)+ 1/2(1/3)
⇛ 1/(3/2)+1/(2/3)
⇛ (2/3)+(3/2)
⇛ (4+9)/6
⇛ 13/6
⇛ RHS
LHS = RHS is true
also read similar questions: Simultaneous equations: 1. 2x+2y=10 X+2y=6 2. 3x+y=18 2x+y=13 3. X+y=1 X-y=5 4. 3x+4y=29 X-4y=-17 5. 4c+3y=11 2x+y=7
https://brainly.com/question/12286263?referrer
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
Drag the labels to the correct locations on the table. Each label can be used more than once.
Match each function to all of the function types it belongs to.
Linear
Quadratic
Exponential
Polynomial
f(x) = 2x + 3
f(x) = x2 + 2x - 3
f(x) = 3* - 2
Answer:
Linear f(x) = 2·x + 3
Quadratic f(x) = x² + 2·x - 3
Exponential f(x) = 3ˣ - 2
Step-by-step explanation:
1) Linear function
The general form of the linear equation is of the form, f(x) = y = m·x + c
Where;
m = The slope
c = y-intercept (Constant)
The linear function is therefore, f(x) = 2·x + 3
2) Quadratic function
The general form of the quadratic function is f(x) = a·x² + b·x + c
Where;
a, and b are the coefficients of x² and x respectively and c is the constant term
Therefore, f(x) = x² + 2·x - 3, is a quadratic function, with a = 1, b = 2, and c = -3
3) Exponential function
The general form of the exponential function is f(x) = a·bˣ + k
Where;
a = The initial
b = The multiplier (growth or decay value)
k = vertical shift
Therefore, the function f(x) = 3ˣ - 2 is an exponential function with the initial = 1, b= 3, and k = -2
evaluate 15.2% of a 726 + 12.8% of 673
Answer:
196.496
Step-by-step explanation:
0.152x726+0.128x673
110.352+86.144
=196.496
I NEED HELP ANSWERING THESE QUESTIONS FIRST ANSWER GET BRAINLIEST!
Answer:
3 - b=12
4- b=14.1
Step-by-step explanation:
Area of the bookshelf=864 square inches
the book shelf is a rectangular prism
if we have height=4b, width=3b, length=b
then the area=length * width
A=(l*w)*2 ( we have 2 shelves)
864=(b*3b)*2
864=6b²
b²=864/6=144
b=√144= 12 inches
4- to cover the sides :
(height * length)*2 ( we have 2 sides)
(4b*b)×2=1600
8b²=1600
b²=1600/8=200
b=√200=14.1
Answer:
Question #3: b = 12 in
Question #4: b = 14.1 in
Step-by-step explanation:
Please see in the image attached the actual proportions that the furniture manufacturer uses to build the furniture in question:
Height = 4 b
Width = 3 b
Depth = b
So for question #3, given that the customer wants a total surface of the shaded shelves to be 864 [tex]in^2[/tex]
we can write that one wants twice the area of each rectangle of width 3 b and depth b to total 864:
[tex]2\,(3b\,*\,b)=864\\6 b^2=864\\b^2=864/6\\b^2=144\\b=12\,\,in[/tex]
Question # 4:
The total lateral surface to be covered by the silk is 1600 [tex]in^2[/tex], therefore if we consider the surface of each lateral plank as:
Area of each lateral plank :
[tex](4b)\,(b) = 4\,b^2[/tex]
Then twice these is: [tex]8\, b^2[/tex]
So we can solve for be requesting that these total surface equal the amount of silk:
[tex]8\,b^2=1600\\b^2=1600/8\\b^2=200\\b=\sqrt{200} \\b\approx 14.1421\,\,in[/tex]
which rounded to the nearest tenth of an inch gives:
[tex]b\approx 14.1\,\,in[/tex]
What is equivalent to 9 3/4?
The answer is supposedly is 3 square root 3, but how is that the answer? can someone tell me the steps?
Step-by-step explanation:
We need to say that [tex]9^{3/4}[/tex] is equivalent to what.
We know that, (3)² = 9
So,
[tex]9^{3/4}=((3)^2)^{3/4}\\\\=3^{3/2}[/tex]
We can write [tex]3^{3/2} =3\times 3^{1/2}[/tex]
And [tex]3^{1/2}=\sqrt{3}[/tex]
So,
[tex]3\times 3^{1/2}=3\sqrt{3}[/tex]
So, [tex]9^{3/4}[/tex] is equivalent to [tex]3\sqrt{3}[/tex].
Hence, this is the required solution.
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.
