1. x/-3=-15
x=45
2. -7+3(-12)÷-3
-7+12
5
3. f(-4)=(-4)²-(-4)
f(-4)=16-(-4)
f(-4)=20
4. x-9=17
5. 2x+3=35
6. -8-12-(-20)
-20-(-20)
0
7. -2(-3)²(-1)
-2(9)(-1)
-18(-1)
18
8. x-(-2)
9. subtract 7 then divide by -2
10. 6+(-18)+(-13)+9
-12-4
-16
11. 5x=11
12. division property
13. -3³ = -27
14. x/2-3=7
x/2=10
x=20
15. 2x-5=15
16. x/-4-(-8)=12
x/-4=4
x=-16
17. 168
18. 16-20-(-8)-9
-4-(-8)-9
4-9
-5
Given that mean=3750 hours and standard deviation is 300:
Then:
<span>a. The probability that a lamp will last for more than 4,000 hours?
P(x>4000)=1-P(x<4000)
but
P(x<4000)=P(z<Z)
where:
z=(x-</span>μ)/σ
z=(4000-3750)/300
z=0.833333
thus
P(x<4000)=P(z<0.8333)=0.7967
thus
P(x>4000)=1-0.7967=0.2033
<span>b.What is the probability that a lamp will last less than 3,000 hours?
P(x<3000)=P(z<Z)
Z=(3000-3750)/300
z=-2.5
thus
P(x<3000)=P(z<-2.5)=0.0062
c. </span><span>.What lifetime should the manufacturer advertise for these lamps in order that only 4% of the lamps will burn out before the advertised lifetime?
the life time will be found as follows:
let the value be x
the value of z corresponding to 0.04 is z=-2.65
thus
using the formula for z-score:
-2.65=(x-3750)/300
solving for x we get:
-750=x-3750
x=-750+3750
x=3000</span>
Answer:
10.35 am
Step-by-step explanation:
Find the LCM
LCM = 275 minutes ÷ 60 minutes to change into hours
= 4hrs 35 min
6.00am + 4hrs 35min
= 10.35 am
Hey there!!
In order to solve this equation, we will have to use the distributive property.
What is distributive property?
We will need to distribute one term to the other terms preset.
Example : 4 ( 3x - 1 )
sing distributive property, we will have to distribute the term outside the parenthesis to the terms inside. In this case, we will have to distribute 4 to 3x and -1
( 4 × 3x ) + ( 4 × -1 )
12x + ( -4 )
= 12x - 4
This is after implementing the distributive property.
Now moving back onto the question
4 ( x + 5 ) = 3 ( x - 2 ) - 2 ( x + 2 )
Let us first solve 4 ( x + 5 )
Distribute 4 to x and 5
( 4 × x ) + ( 4 × 5 )
4x + 20
Now let's solve 3 ( x - 2 )
Distribute 3 to x and -2
( 3 × x ) + ( 3 × - 2 )
3x - 6
Solve for -2 ( x + 2 )
Distribute -2 to x and 2
( -2 × x ) + ( -2 × 2 )
-2x - 4
Now, let's get everything back together
4x + 20 = 3x - 6 - 2x - 4
Combine all the like terms
4x + 20 = x - 10
Adding 10 on both sides
4x + 20 + 10 = x - 10 + 10
4x + 30 = x
Subtracting 4x on both sides
4x - 4x + 30 = x - 4x
30 = -3x
Dividing by -3 on both sides
30 / -3 = -3x / -3
- 10 = x
<h2>x = - 10 </h2><h3>Hope my answer helps!</h3>
Answer:
Step-by-step explanation:
The total surface area of this triangular prism consists of three rectangles and two triangles. Adding the areas of each of these shapes allows us to find the total surface area of this 3D figure:
Area of both triangles:
Area of all three rectangles:
Therefore, the total surface area of this figure is:
