The life of light bulbs is distributed normally. The standard deviation of the lifetime is 15 hours and the mean lifetime of a bulb is 520 hours. Find the probability of a bulb lasting for at most 528 hours. Round your answer to four decimal places.

Answer:

17

Step-by-step explanation:

So, this is a percentage problem.

Start off by finding how many students 0.28% is:

If 100% = 5780

0.01% = 0.578                          

Now:

0.01% = 0.578

0.28% = 16.184

The exercise tells you to round for a whole person, so 16.184 turns 17

And that's the answer!

Answer:

The grocery bill before the coupons were used was 10 times as much as the bill after the coupons were used.

Step-by-step explanation:

The price after coupons were used is 20, and the price before was 200. 20x10 =200

Answer:

[tex]791.7\:\mathrm{ft^3}[/tex]

Step-by-step explanation:

The volume of a cylinder with radius [tex]r[/tex] and height [tex]h[/tex] is given by [tex]A_{cyl}=r^2h\pi[/tex].

By definition, all radii of a circle are exactly half of all diameters of the circle. Therefore, if the diameter of the circular base of the cylinder is 6 feet, the radius of it must be [tex]6\div 2=3\text{ feet}[/tex].

Now we can substitute [tex]r=3[/tex] and [tex]h=28[/tex] into our formula [tex]A_{cyl}=r^2h\pi[/tex]:

[tex]A=3^2\cdot 28\cdot \pi,\\A=9\cdot28\cdot \pi,\\A=791.681348705\approx \boxed{791.7\:\mathrm{ft^3}}[/tex]

Answer:

your can only divide then up in that specific sequence one time

Answer:

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

( − ∞ , ∞ )

Set-Builder Notation:

{ x | x ∈ R }

Step-by-step explanation:

hope that helps bigger terms

Answer:

12 x sin(85)

12x 0.99619

155.40

Solution:

12 x sin (85) = 11.95 (Since sin85 is 0.996194)

So, the answer is 11.95.

Answer: (-1, 2)

Step-by-step explanation:

It's a counter-clockwise rotation, that means (x, y) changes to (y, -x).

(-2, -1) ⇒ (-1, -(-2)) ⇒ (-1, 2)

If it's a clockwise rotation, then (x, y) will change to (-y, x)

(-2, -1) ⇒ (-(-1), -2) ⇒ (1, -2)

Answer:

The unlimited mileage plan would save money for Lia from 410 miles onwards.

Step-by-step explanation:

Since Lia can rent a van for either $ 90 per day with unlimited mileage or $ 50 per day with 250 free miles and an extra 25 ¢ for each mile over 250, to determine for what number of miles traveled in one day would the unlimited mileage plan save Lia money, the following calculation must be performed:

90.25 - 50 = 40.25

40.25 / 0.25 = 161

161 + 250 = 411

Therefore, the unlimited mileage plan would save money for Lia from 410 miles onwards.

Answer:

Orange

Step-by-step explanation:

As the chance of choosing orange is 18% which is the least.

Answer:

9 + i

Step-by-step explanation:

You just simplify by combining the real and imaginary parts of each expression.

Hope this helps you!!

Answer:

There are 824 deer in the preserve.

Step-by-step explanation:

Since to determine the number of deer in a game preserve, a conservationist catches 412 deer, tags them and lets them loose, and later, 316 deer are caught, 158 of them are tagged, to determine how many deer are in the preserve you must perform the following calculation:

316 = 100

158 = X

158 x 100/316 = X

50 = X

50 = 412

100 = X

824 = X

Therefore, there are 824 deer in the preserve.

Answer:

m=5

n=-3

Step-by-step explanation:

3m+2m=9

3m-3n=24

3(5)+2(-3)=9

15-6=9 correct

Answer:

4,-1 that is the answer so

For now, I'll focus on the figure in the bottom left.

Mark the point E at the base of the dashed line. So point E is on segment AB.

If you apply the pythagorean theorem for triangle ABC, you'll find that the hypotenuse is

a^2+b^2 = c^2

c = sqrt(a^2+b^2)

c = sqrt((8.4)^2+(8.4)^2)

c = 11.879393923934

which is approximate. Squaring both sides gets us to

c^2 = 141.12

So we know that AB = 11.879393923934 approximately which leads to (AB)^2 = 141.12

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

Now focus on triangle CEB. This is a right triangle with legs CE and EB, and hypotenuse CB.

EB is half that of AB, so EB is roughly AB/2 = (11.879393923934)/2 = 5.939696961967 units long. This squares to 35.28

In short, (EB)^2 = 35.28 exactly. Also, (CB)^2 = (8.4)^2 = 70.56

Applying another round of pythagorean theorem gets us

a^2+b^2 = c^2

b = sqrt(c^2 - a^2)

CE = sqrt( (CB)^2 - (EB)^2 )

CE = sqrt( 70.56 - 35.28 )

CE = 5.939696961967

It turns out that CE and EB are the same length, ie triangle CEB is isosceles. This is because triangle ABC isosceles as well.

Notice how CB = CE*sqrt(2) and how CB = EB*sqrt(2)

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

Now let's focus on triangle CED

We just found that CE = 5.939696961967 is one of the legs. We know that CD = 8.4 based on what the diagram says.

We'll use the pythagorean theorem once more

c = sqrt(a^2 + b^2)

ED = sqrt( (CE)^2 + (CD)^2 )

ED = sqrt( 35.28 + 70.56 )

ED = 10.2878569196893

This rounds to 10.3 when rounding to one decimal place (aka nearest tenth).

==============================================================

Now I'm moving onto the figure in the bottom right corner.

Draw a segment connecting B to D. Focus on triangle BCD.

We have the two legs BC = 3.7 and CD = 3.7, and we need to find the length of the hypotenuse BD.

Like before, we'll turn to the pythagorean theorem.

a^2 + b^2 = c^2

c = sqrt( a^2 + b^2 )

BD = sqrt( (BC)^2 + (CD)^2 )

BD = sqrt( (3.7)^2 + (3.7)^2 )

BD = 5.23259018078046

Which is approximate. If we squared both sides, then we would get (BD)^2 = 27.38 which will be useful in the next round of pythagorean theorem as discussed below. This time however, we'll focus on triangle BDE

a^2 + b^2 = c^2

b = sqrt( c^2 - a^2 )

ED = sqrt( (EB)^2 - (BD)^2 )

x = sqrt( (5.9)^2 - (5.23259018078046)^2 )

x = sqrt( 34.81 - 27.38 )

x = sqrt( 7.43 )

x = 2.7258026340878

x = 2.7

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

As an alternative, we could use the 3D version of the pythagorean theorem (similar to what you did in the first problem in the upper left corner)

The 3D version of the pythagorean theorem is

a^2 + b^2 + c^2 = d^2

where a,b,c are the sides of the 3D block and d is the length of the diagonal. In this case, a = 3.7, b = 3.7, c = x, d = 5.9

So we get the following

a^2 + b^2 + c^2 = d^2

c = sqrt( d^2 - a^2 - b^2 )

x = sqrt( (5.9)^2 - (3.7)^2 - (3.7)^2 )

x = 2.7258026340878

x = 2.7

Either way, we get the same result as before. While this method is shorter, I think it's not as convincing to see why it works compared to breaking it down as done in the previous section.

Answer:

Qu 2    =  10.3 cm

Qu 3.   = 2.7cm

Step-by-step explanation:

Qu 2. Shape corner of a cube

We naturally look at sides for slant, but with corner f cubes we also need the base of x and same answer is found as it is the same multiple of 8.4^2+8/4^2 for hypotenuse.

8.4 ^2 + 8.4^2 = sq rt 141.42 = 11.8920141 = 11.9cm

BD = AB =  11.9 cm  Base of cube.

To find height x we split into right angles

formula slant (base/2 )^2 x slope^2  = 11.8920141^2 - 5.94600705^2 =  sq rt 106.065

= 10.2987863

height therefore is x = 10.3 cm

EB = 5.9cm

BC = 3.7cm

CE^2  = 5.9^2 - 3.7^2  = sqrt 21.12 = 4.59565012 = 4.6cm

2nd triangle ED = EC- CD

= 4.59565012^2- 3.7^2 = sq rt 7.43000003 =2.72580264

ED = 2.7cm

x = 2.7cm

Answer:

D

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

i think it's correct if not I'm sorry

Answer:

yes

Step-by-step explanation:

the answer is c well thats what my teacher said

Answer:

B

Step-by-step explanation:

using sine rule

[tex] \frac{y}{sin \: 45} = \frac{5}{sin \: 45} \\ y = 5[/tex]

using sin rule

[tex] \frac{x}{sin \: 90} = \frac{5}{sin \: 45} \\ \\ 5sin90 = xsin45 \\ \\ x = \frac{5 \: sin \: 90}{sin \: 45} \\ x = \frac{5}{0.7071} \\ x = 7.071[/tex]

x=5√2

here you go it's too easy

Step-by-step explanation:

Explanation is in the attachment .

Hope it is helpful to you ❣️☪️❇️

Answer:

Step-by-step explanation:

I don't think so. This equation has but one definite answer and the left and right sides don't produce the same result.

subtract 5m from both sides

6 = 4m - 5m

6 = - m                 Multiply both sides by - 1

-6 = m

An identity is something like 4x + 5x = 9x

It doesn't matter what x is. Any value of x will make the right side = to the left side. This becomes more important when you will study trigonometry.

Answer:

B

substract the variables

Answer:

1.5%

Step-by-step explanation:

house value x property tax rate = property taxes

70,000 x property tax rate = 1050

property tax rate = 1050/70000

property tax rate = .015 0r 1.5%

Answer:

The remainder is 3x - 4

Step-by-step explanation:

[Remember] [tex]\frac{Dividend}{Divisor} = Quotient + \frac{Remainder}{Divisor}[/tex]

So, [tex]Dividend = (Quotient)(Divisor) + Remainder[/tex]

In this case our dividend is always P(x).

Part 1

When the divisor is [tex](x - 1)[/tex], the remainder is [tex]4[/tex], so we can say [tex]P(x) = (Quotient)(x - 1) + 4[/tex]

In order to get rid of "Quotient" from our equation, we must multiply it by 0, so [tex](x - 1) = 0[/tex]

When solving for [tex]x[/tex], we get

[tex]x - 1 = 0\\x - 1 + 1 = 0 + 1\\x = 1[/tex]

When [tex]x = 1[/tex],

[tex]P(x) = (Quotient)(x - 1) + 4\\P(1) = (Quotient)(1 - 1) + 4\\P(1) = (Quotient)(0) + 4\\P(1) = 0 + 4\\P(1) = 4[/tex]

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

Part 2

When the divisor is [tex](x + 3)[/tex], the remainder is [tex]104[/tex], so we can say [tex]P(x) = (Quotient)(x + 3) + 104[/tex]

In order to get rid of "Quotient" from our equation, we must multiply it by 0, so [tex](x + 3) = 0[/tex]

When solving for [tex]x[/tex], we get

[tex]x + 3 = 0\\x + 3 - 3 = 0 - 3\\x = -3[/tex]

When [tex]x = -3[/tex],

[tex]P(x) = (Quotient)(x + 3) + 104\\P(-3) = (Quotient)(-3 + 3) + 104\\P(-3) = (Quotient)(0) + 104\\P(-3) = 0 + 104\\P(-3) = 104[/tex]

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

Part 3

When the divisor is [tex](x^2 - x + 1)[/tex], the quotient is [tex](x^2 + x + 3)[/tex], and the remainder is [tex](ax + b)[/tex], so we can say [tex]P(x) = (x^2 + x + 3)(x^2 - x + 1) + (ax + b)[/tex]

From Part 1, we know that [tex]P(1) = 4[/tex] , so we can substitute [tex]x = 1[/tex] and [tex]P(x) = 4[/tex] into [tex]P(x) = (x^2 + x + 3)(x^2 - x + 1) + (ax + b)[/tex]

When we do, we get:

[tex]4 = (1^2 + 1 + 3)(1^2 - 1 + 1) + a(1) + b\\4 = (1 + 1 + 3)(1 - 1 + 1) + a + b\\4 = (5)(1) + a + b\\4 = 5 + a + b\\4 - 5 = 5 - 5 + a + b\\-1 = a + b\\a + b = -1[/tex]

We will call [tex]a + b = -1[/tex] equation 1

From Part 2, we know that [tex]P(-3) = 104[/tex], so we can substitute [tex]x = -3[/tex] and [tex]P(x) = 104[/tex] into [tex]P(x) = (x^2 + x + 3)(x^2 - x + 1) + (ax + b)[/tex]

When we do, we get:

[tex]104 = ((-3)^2 + (-3) + 3)((-3)^2 - (-3) + 1) + a(-3) + b\\104 = (9 - 3 + 3)(9 + 3 + 1) - 3a + b\\104 = (9)(13) - 3a + b\\104 = 117 - 3a + b\\104 - 117 = 117 - 117 - 3a + b\\-13 = -3a + b\\(-13)(-1) = (-3a + b)(-1)\\13 = 3a - b\\3a - b = 13[/tex]

We will call [tex]3a - b = 13[/tex] equation 2

Now we can create a system of equations using equation 1 and equation 2

[tex]\left \{ {{a + b = -1} \atop {3a - b = 13}} \right.[/tex]

By adding both equations' right-hand sides together and both equations' left-hand sides together, we can eliminate [tex]b[/tex] and solve for [tex]a[/tex]

So equation 1 + equation 2:

[tex](a + b) + (3a - b) = -1 + 13\\a + b + 3a - b = -1 + 13\\a + 3a + b - b = -1 + 13\\4a = 12\\a = 3[/tex]

Now we can substitute [tex]a = 3[/tex] into either one of the equations, however, since equation 1 has less operations to deal with, we will use equation 1.

So substituting [tex]a = 3[/tex] into equation 1:

[tex]3 + b = -1\\3 - 3 + b = -1 - 3\\b = -4[/tex]

Now that we have both of the values for [tex]a[/tex] and [tex]b[/tex], we can substitute them into the expression for the remainder.

So substituting [tex]a = 3[/tex] and [tex]b = -4[/tex] into [tex]ax + b[/tex]:

[tex]ax + b\\= (3)x + (-4)\\= 3x - 4[/tex]

Therefore, the remainder is [tex]3x - 4[/tex].

2x^2 + 8x - 12 = 0..divide by 2

x^2 + 4x - 6 = 0

x^2 + 4x = 6...add 4 to both sides of the equation

x^2 + 4x + 4 = 6 + 4

(x + 2)^2 = 10....<== ur constant is 10

x + 2 = (+-)sqrt 10

x = -2 (+ - ) sqrt 10

x = -2 + sqrt 10

x = -2 - sqrt 10

Answer:

(2k, k)

Step-by-step explanation:

x + y = 3k

x - y = k

Add the equations.

2x = 4k

x = 2k

2k + y = 3k

y = k

Answer: (2k, k)

Answer:

86°

Step-by-step explanation:

180° is the sum of all angles in a triangle

The two angles given are 68° and 26°

The equation is : 180° - 68° - 26° = x°

180° - 68° - 26° = 86°

x° = 86°

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

3/1 : 1/3

Step-by-step explanation:

Just simplify it.

Answer:

The correct answer is 3x-2

Step-by-step explanation:

It gives you the expression for JM and LM, and it asks for JL. Therefore, if you take away LM from JM, you are left with JL. You must subtract 2x-6 from 5x-8.

∴5x-8-(2x-6)

Do not forget to distribute the negative since you are subtracting, so instead of subtracting 6 from 8, you will be adding 6 to 8 because two negatives make a positive.

So a Quadratic function,A quadratic function is one of the form f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero