Write the ratio as a fraction in simplest form.
0.65 to 0.15

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.

Answer:

3

= 15/5

= [tex]\sqrt[3]{27}[/tex]

= 1.5*2

= 3/1

= 3*1

= 3¹

= 1/3⁻¹

= 3⁴ / 3³

= 3⁵ * 3⁻⁴

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.

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.

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

Answer:

1. 98.7 km

2. 303.5 degree

Step-by-step explanation:

Using the alternate angle, the angle at B will be 50 + 10 = 60 degree.

To calculate the length AC of the returning journey, use cosine formula to calculate it.

To find the bearing of the returning journey, use sine rule to calculate it.

Please find the attached file for the solution

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:

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:

Answer:

15 lawns

Step-by-step explanation:

The Xbox costs $400 and his parents gave him $100. He needs to earn $300 more. $20 each lawn so $100 for 5 lawns. 5 lawns times three.

Xbox cost =400

Daniel's money =100

Xbox cost - Daniel money=300

yard cost =20

therefore 400 -100 /20

Daniel's need 15 yards to get the xbox

Answer:

Step-by-step explanation:

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]

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.

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.

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:

Step-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

Hope this helps you

Answer:

5x-4y = -32

Step-by-step explanation:

First write the equation in point slope form

y-y1 = m(x-x1)

y - -2 = 5/4 ( x- -8)

y+2 = 5/4 (x+8)

Multiply each side by 4 to clear the fraction

4( y+2 )= 4*5/4 (x+8)

4y +8 = 5(x+8)

4y+8 = 5x+40

Subtract 4y from each side

8 = 5x-4y +40

Subtract 40 from each side

-32 = 5x-4y

5x-4y = -32

Answer:

The answer is

Step-by-step explanation:

To write an equation of a line given a point and slope use the formula

y - y1 = m( x - x1)

where

m is the slope

( x1 , y1) is the point

From the question

slope = 5/4

point (-8 , -2)

So the equation of the line is

Multiply through by 4

4y + 8 = 5( x + 8)

4y + 8 = 5x + 40

5x - 4y = 8 - 40

We have the final answer as

Hope this helps you

A) Here, We'll use "Pythagoras Theorem" which tells:

a² + b² = c²

So, PR² = PQ² + QR²

PR² = 14² + 9²

PR² = 196 + 81

PR = √277

In short, Your Answer would be 16.64 Feet

B) Again, Use the Pythagoras Theorem,  

c² - a² = b²

18² - 14² = b²

b² = 324 - 196

b = √128

b = 11.31

In short, Your Answer would be 11.31 Feet

Part A: Using the Pythagorean Theorem. a^2 + b^2 = c^2

PQ^2 + QR^2 = PR^2  (The rods make a right triangle, where PR would be the hypotenuse, and QR and PQ would be legs a and b.)

14^2 + 9^2 = PR^2

196 + 81 = PR^2

Square root of 277 = PR 

16.64 = PR

So, the hypotenuse would be equal to 16.64 ft.

Part B: Using the Pythagorean Theorem. a^2 + b^2 = c^2

PR^2 - PQ^2 = QR^2 (Trying to find the height of QR this time, not the hypotenuse, since we know what it is already. Subtracting the value of leg a from the hypotenuse will give us the value of leg b, QR.)

18^2 - 14^2 = QR^2

324 - 196 = QR^2

Square root of 128 = QR

So, the new height of QR would be 11.31 ft.

Answer:

196.496

Step-by-step explanation:

0.152x726+0.128x673

110.352+86.144

=196.496

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.

Answer:

47

Step-by-step explanation:

Using the follwing property

[tex]x^{2} -y^2=(x+y)(x-y)[/tex]

in which x=24 and y=23

so

[tex]24^2-23^2=(24-23)(24+23)\\=1(47)\\=47[/tex]

Answer:

47

Step-by-step explanation:

Lets say 24 is x and 23 is y.

the equation would be x^2 - y^2

this is = to (x-y)(x+y)

substitute the numbers in

(24-23)(24+23)

which simplifies to

(1)(47)

which equals 47

Answer:

Step-by-step explanation:

If he were to find the mean then he would need to add all the numbers up and divide by the number of numbers. The answer of this would 69.1

If you find the median you would need to put the numbers in order,

2, 38, 75, 80, 88, 90, 92, 92, 95, then find the middle which would be 88.

So the better option would be finding the median. I think that this would be the best way to get the the most favorable measure of center.

I hope this helps.

Answer:

653.12 ft²

Step-by-step explanation:

2πrh + 2πr²

2(3.14)(8)(5) + 2(3.14)(8)²

251.2 + ²401.92 = 653.12

Step-by-step explanation:

Here,

radius of a cylinder (r)= 8 ft.

height (h)= 5 ft.

now,

area of a cylinder (a)= 2.pi.r(r+h)

now, putting the values we get,

a = 2×3.14×8(8+5)

after simplification we get,

Area of cylinder is 653.12 sq.ft.

Hope it helps....

Answer:

[tex]\huge\boxed{Exterior\ angle = 70\°}[/tex]

Step-by-step explanation:

The measure of exterior angle is equal to the sum of opposite interior angles.

So,

Exterior angle = 43+27

Exterior angle = 70°

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

Answer:

0.25%

Step-by-step explanation:

Rate of commission

= (commission*100)/cost of land

=( 20000*100)/8000000

= 2000000/8000000

=2/8

= 0.25%

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

Answer:

3.5 hours

Step-by-step explanation:

Paul:

Mary:

Since the distance is same, we have:

Answer: Paul's travel took 3.5 hours

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.

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

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:

Answer:$60,000

Step-by-step explanation:

If he bought it for $50,000 and then spent $5,000 on repairs then he spent a total of $55,000. For a profit of $5,000 he would need to sell it for $60,000 Because

60,000 - 55,000 = 5,000