A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 160-cm and a standard deviation of 1.2-cm. For shipment, 15 steel rods are bundled together. Find the probability that the average length of a randomly selected bundle of steel rods is less than 159.4-cm. P(M < 159.4-cm) = 0.3085 Enter your answer as a number accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer:

I think it's D

Step-by-step explanation:

Answer:  I think its D

Step-by-step explanation:

Rigid transformation moves a shape without changing the size of the shape.

See attachment for the diagram that shows the position of D'

[tex]\\ \sf\longmapsto f(2+h)[/tex]

[tex]\\ \sf\longmapsto 4(2+h)-3[/tex]

[tex]\\ \sf\longmapsto 4h+8-3[/tex]

[tex]\\ \sf\longmapsto 4h+5[/tex]

Answer:

no it's not a defined state it's undefined

Answer:

x=24

Step-by-step explanation:

Hi there!

We are given the following proportion:

[tex]\frac{2}{10}=\frac{3}{x-9}[/tex]

And we want to solve for x.

First, let's reduce [tex]\frac{2}{10}[/tex], as reducing fractions typically makes the process easier

[tex]\frac{2}{10}[/tex] is the same as [tex]\frac{1}{5}[/tex]

So:

[tex]\frac{1}{5}=\frac{3}{x-9}[/tex]

We can't do anything to [tex]\frac{3}{x-9}[/tex], but that's okay.

Now we can cross multiply, as this is a proportion

Multiply x-9 by 1 and 3 by 5

1(x-9)=3(5)

Multiply

x-9=15

Now this is an equation

Our goal is to isolate x on one side

So let's add 9 to both sides to remove it from the left side

x-9=15

 +9 +9

_________

x=24

Hope this helps!

Answer:

24

Step-by-step explanation:

Cross multiply:

2(x - 9) = 2x - 18

3(10) = 30

2x-18 = 30

   +18   +18

-----------------

  2x = 48

 -----   -----

   2       2

     x = 24

Hope this helped.

Answer:

$532

Step-by-step explanation:

We do 51,072 / 96 which is 532.

Each employee received $532.

Answer:

x=2.24

Step-by-step explanation:

To do this problem, you must find the scale factor. Using two corresponding sides you can find it.

Using 2.4 and 3:

2.4 / 3 = 0.8

Scale factor: 0.8

Now find x:

2.8 × 0.8 = 2.24

x = 2.24

Hope this helped.

Answer:

a = 56.3°

Step-by-step explanation:

tan(a) = 9/6 = 1.5

atan(1.5) = 56.31°

Answer:

[tex]\boxed {\boxed {\sf 56.3 \textdegree}}[/tex]

Step-by-step explanation:

We are asked to find the measure of angle a.

This triangle is a right triangle because of the small triangle in the corner representing a 90 degree or right angle. Therefore, we can use trigonometric functions. The three main functions are:

The side measuring 6 is adjacent or next to angle a. The side measuring 9 is opposite angle a. Therefore, we will use the tangent function.

[tex]tan \theta= \frac{ opposite}{adjacent}[/tex]

[tex]tan \ a = \frac{ 9}{6}[/tex]

Since we are solving for an angle measure, we use the inverse trigonometric function.

[tex]tan ^{-1} * tan \ a = tan ^{-1} * \frac{9}6}[/tex]

[tex]a= tan ^{-1} * \frac{9}6}[/tex]

[tex]a= 56.30993247[/tex]

Round to the nearest tenth. The 0 in the hundredth place tells us to leave the 3 in the tenth place.

[tex]a \approx 56.3[/tex]

The measure of angle a is approximately 56.3 degrees.

Answer:

Step-by-step explanation:

The standard form for a circle is

[tex](x-h)^2+(y-k)^2=r^2[/tex] and what's important here is that the x- and the y- remain that way in the equation. Filling in our values,

[tex](x-(6))^2+(y-(-3))^2=25[/tex] which tells us that our center is

        6      and     -3 -------------------> (6, -3)

The radius is the square root of 25 which is 5.

Answer:

600

Step-by-step explanation:

Volume=l*b*h=5*12*10=600

Answer:

Step-by-step explanation:

B OR TRUE

Answer:

Step-by-step explanation:

0.9*2b = 1.8b

0.9*-1 = -0.9

So far we have 1.8b-0.9. It can't be simplified further.

Then, we add the 2nd part, -0.5b+1.

We have:

1.8b-0.9-0.5b+1. Next we combine like terms.

1.8b-0.5b = 1.3b.

-0.9+1 = 0.1

Then we put it together.

1.3b+0.1 is our answer.

Hope this helped! Have a nice day :D

Hi there!  

»»————-　★　————-««

I believe your answer is:

1.3b + 0.1

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Simplifying...}}\\\\0.9(2b-1)-0.5b+1\\--------------\\\rightarrow 1.8b - 0.9 - 0.5b + 1\\\\\rightarrow 1.8b - 0.5b - 0.9 + 1\\\\\rightarrow \boxed{1.3b +0.1}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

A 6.09

Step-by-step explanation:

Answer:

Step-by-step explanation:

Remark

The cos(60) = 1/2

The radii marked 6 is the adjacent side. You have to solve for the hypotenuse.

Why?

Because the hypotenuse is the distance from the center of the circle to the point of intersection of the angle. Once you have the hypotenuse, you can find the length of the tangent, which will lead to the area of the kite. Then take away 1/3 the area of the circle.

Hypotenuse

Cos(60) = 1/2

cos(60) = adjacent / hypotenuse        Multiply both sides by the hypotenuse

hypotenuse * cos(60) = adjacent       Divide by Cos(60)

hypotenuse = adjacent / cos(60)  

adjacent = 6

hypotenuse = 6/0.5

hypotenuse = 12

Tangent

tangent^2 = 12^2 - 6^2

tangent^2 = 144 - 36

tangent^2 = 108

tangent = sqrt(108)

tangent = 6sqrt(3)

Triangles

The area of the triangle = 1/2 6sqrt(3) * 6

The area of the triangle = 18 sqrt(3)

There are two triangles so the area = 36 sqrt(3) That's the area of the kite.

Circle sector.

Area of the circle sector = 1/3 * pi * r^2

r = 6

Leave pi as it is.

Area of the circle sector = 1/3 * pi * 6^2

area of the circle sector = 12 pi

Answer

Area of the red part = area of the triangles - the area of circle sector

Area of the red part = 36*sqrt(3) - 12* pi            

Answer:

3(5+x)

Step-by-step explanation:

15+3x

5*3 + 3*x

Factor out 3

3(5+x)

Answer:

C.47,5cm²

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]f(x)=\frac{x+9}{7-4x} \\put ~f(x)=y\\flip~x~and~y\\f(y)=x\\y=f^{-1}(x)\\y=\frac{x+9}{7-4x} \\flip~x~and~y\\x=\frac{y+9}{7-4y} \\x(7-4y)=y+9\\7x-4xy=y+9\\-4xy-y=9-7x\\or\\4xy+y=7x-9\\y(4x+1)=7x-9\\y=\frac{7x-9}{4x+1} \\or~f^{-1}(x)=\frac{7x-9}{4x+1}[/tex]

Answer:

$1272.36 ( average weekly sales for first 3 weeks )

Step-by-step explanation:

weekly online sales = S(t)

Determine average weekly sales for first 3 weeks

S(t) = 2e^t

total sales = ∫ S(t) dt        

∴ Average weekly sales for first 3 weeks  ( note : S(t) = 2e^t  )

=  [tex]\int\limits^3_0 {2e^t \, dt / ( 3 - 0 )[/tex]            

= 2 [ e^t ] ³₀ / 3 = 2 ( e^3 - e^0 ) / 3 =  2 ( 6.3618 ) = 12.7236 hundreds

= $1272.36 ( average weekly sales for first 3 weeks )

Answer:

Step-by-step explanation:

the answer is b

Answer:

C

Step-by-step explanation:

C is the set with whole numbers as it contains 0 and natural numbers

Answer:

0.48

Step-by-step explanation:

hope it can work for you mark me as a brain liest

Answer:

k = 5/6

Step-by-step explanation:

First, we can make this have the form of a quadratic function, or ax²+bx+c=0. To do this, we can first subtract 10x from both sides to get

(2k+1)x²-8x=-6

Next, we can add 6 to both sides, resulting in

(2k+1)x²-8x+6 = 0

For a quadratic function of form ax²+bx+c=0, we can see that a=2k+1, b=-8, and c=6. We can then apply the quadratic equation, or

x= (-b ± √(b²-4ac))/(2a) to get our roots to be

x= (8 ± √(64-4(6)(2k+1)))/(2*(2k+1))

=  (8 ± √(64-(48k+24)))/(4k+2)

=  (8 ± √(40-48k))/(4k+2)

For the roots to be equal, we must have the two roots equal to each other. We can write this as

(8 + √(40-48k))/(4k+2) = (8 - √(40-48k))/(4k+2)

multiply both sides by (4k+2) to remove the denominator

8+√(40-48k) = 8 - √(40-48k)

subtract 8 from both sides to isolate the square roots

√(40-48k) = - √(40-48k)

The only number that is equal to its negative self (and is real) is 0. Therefore, √(40-48k) = - √(40-48k) = 0, so we have

√(40-48k) = 0

square both sides to remove the square root

40-48k = 0

add 48k to both sides to isolate the k and its coefficient

40 = 48k

divide both sides by 48 to isolate k

k = 40/48 = 5/6

Answer:

Which one have same variable gather or decrease up

Step-by-step explanation:

2x^2-4.6x^2=1.4x^2

-7x+7x=0

1.4x^2+2<0

x<0

Answer:

48.5 ft

Step-by-step explanation:

Answer:

18. 28 cm*2

19. 24 m

Step-by-step explanation:

18. length × l = 16

l*2= 16

l = 4

RQ = 4 cm

PR =7cm

Area of parallelogram = b×h

= 7×4

=28cm*2

19. 8 +8 + (6-2) +( 6- 2)

=24 m

Answer:

(b) It is symmetrical about [tex]x = 1[/tex]

Step-by-step explanation:

Given

[tex]y = 2(x - 1)^2 - 5[/tex]

See attachment for options

Required

True statement about the graph

First, we check the line of symmetric

[tex]y = 2(x - 1)^2 - 5[/tex]

Expand

[tex]y = 2(x^2 - 2x + 1) - 5[/tex]

Open bracket

[tex]y = 2x^2 - 4x + 2 - 5[/tex]

[tex]y = 2x^2 - 4x -3[/tex]

A quadratic equation [tex]y = ax^2 + bx + c[/tex] has the following line of symmetry

[tex]x = -\frac{b}{2a}[/tex]

By comparison, the equation becomes:

[tex]x = -\frac{-4}{2*2}[/tex]

[tex]x = \frac{4}{4}[/tex]

[tex]x = 1[/tex]

Hence, the line of symmetry is at: [tex]x = 1[/tex]

(b) is true.

Answer: It is symmetrical about x=1

Step-by-step explanation:

Answer:

Step-by-step explanation:

Sum of those 4 integers is:

If the smallest ones are 1, 2 and 3, then the greatest possible integer is:

Answer:

750 meters

Step-by-step explanation:

Answer:

750m

Step-by-step explanation:

Distance= Speed x Time

Speed = 25m/s

Time = 30s

Distance = 25 x 30

              = 750 m

Answer:

3 loaves 2 bananas left.

Step-by-step explanation:

The answer is asking how many loaves of three bananas Seth can make. 11 can be divided by 3 a total of 3 times, leaving a remainder of 2 bananas that would not be enough to make another loaf.

Answer: -46

Step-by-step explanation:

[tex]u_1=50=50-(1-1)*4\\u_2=46=50-(2-1)*4\\u_3=42=50-(3-1)*4\\...\\\\u_n=50-(n-1)*4\\\\\\u_{25}=50-(25-1)*4=-46\\\\\\Answer\ -46\\[/tex]