Two fair dice are tossed and the number on each die is recorded, e.g. (3,2) indicates the first die had 3 and the second die had a 2. In total, there are 36 (equally likely) outcomes in the sample space. What is the probability the sum of the two dice is 7

4*3

12

12*6

72

hope it help

The surface area of the given box is 108 square inches.

The surface area of a box is the sum of the areas of its six faces. We can find the surface area of the given box by using the formula:

Surface Area = 2lw + 2lh + 2wh

where "l" is the length, "w" is the width, and "h" is the height of the box.

As per the question, we have

l = 3 inches, w = 3 inches, and h = 6 inches

Substituting the given values, we get:

Surface Area = 2(4 x 3) + 2(4 x 6) + 2(3 x 6)

Surface Area = 24 + 48 + 36

Surface Area = 108 square inches

Therefore, the surface area of the given box is 108 square inches.

Learn more about the cuboids here:

brainly.com/question/23118276

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Answer:

The correct option is b.

Step-by-step explanation:

Standard deviation is one of the measure of dispersion or spread of a dataset from the average value of the dataset. The standard deviation measures the absolute variability of the distribution of values.

The higher the spread or variability in the data set, the greater is the standard deviation value and thus greater will be the magnitude of the deviance of the value from their average.

It is provided that the  standard deviation of the distribution of house age is about 16 years.

The standard deviation of 16 years imply that the age for all the houses in the sample is 16 years from the mean.

Thus, the correct option is b.

i hop ....

i hope

ihope

solution

Step-by-step explanation:

5x+3x=12+4

8x=16

x=16÷8

x=2

Answer:

[tex] \boxed{ \bold{ \huge{\boxed{ \sf{x = 2}}}}}[/tex]

Step-by-step explanation:

[tex] \sf{5x - 4 = - 3x + 12}[/tex]

Move 3x to left hand side and change it's sign

⇒[tex] \sf{5x + 3x - 4 = 12}[/tex]

Move 4 to right hand side and change it's sign

⇒[tex] \sf{5x + 3x = 12 + 4}[/tex]

Collect like terms

⇒[tex] \sf{8x = 12 + 4}[/tex]

Add the numbers

⇒[tex] \sf{8x = 16}[/tex]

Divide both sides of the equation by 8

⇒[tex] \sf{ \frac{8x}{8} = \frac{16}{8} }[/tex]

Calculate

⇒[tex] \sf{x = 2}[/tex]

Hope I helped!

Best regards!!

(4×10)+(7×1\100) = 40+7/100 =4007/100

4007/100= 40,07

40,07 = 40,070

just add 0 to right side

(40,0700 also = 40,070)

Hope this helps ^-^

4mn. You are multiplying them all together.

Answer:

4mn

Step-by-step explanation:

you would multiply the 2s then the m and n cant multiply so they would stay beside eachother so it would be 4mn

Answer:

Step-by-step explanation:

Hello,

We will prove it by induction.

Step 1 - for n=2

2!=2*1=2

2^2=4

and 2 < 4 so this is true for n=2

Step2 - We assume that this is true for k and we have to prove it for k+1.

Induction hypothesis is [tex]k!<k^k[/tex]

[tex](k+1)!=(k+1)k![/tex]

We use the induction hypothesis and we we can write that

[tex](k+1)!=(k+1)k!<(k+1)k^k<=(k+1)(k+1)^k=(k+1)^{k+1}\\\\\text{As }k <= k+1[/tex]

so, we prove it for k+1

Step 3- conclusion

for n >= 2 we just proved that [tex]n!<n^n[/tex]

Answer:

C. 2.937

Step-by-step explanation:

Given the following :

H0 : p = 0.25

H1 : p > 0.25

Number of observations (n) = 647

p' = 30% = 0.3

SD = sqrt[(p(1 - p) / n)]

1 - p = 1 - 0.25 = 0.75

SD = sqrt[(0.25 * 0.75) / 647]

SD = sqrt[0.0002897]

SD = 0.0170234

Z = (p' - p) / SD

Z = (0.3 - 0.25) / 0.0170234

Z = 0.05 / 0.0170234

Z = 2.9371187 = 2.937

Answer:

please mark my answer brainliest

Step-by-step explanation:

A.....will be the answer....

Complete question:

Please find the attached file for task table

Answer:

The minimum cycle time is 50 s

The maximum  cycle time is 50.4 s

Step-by-step explanation:

Given;

production time, t = 7 hours

desired output = demand, D =  500 units

The minimum cycle Time is given by;

Minimum cycle time = maximum task time, from the table the maximum task time is 50 seconds.

Thus, Minimum cycle time = 50 s

The maximum cycle Time is given by;

[tex]CT = \frac{Production \ time}{D} \\\\CT = \frac{7*3600 s}{500 \ units} \\\\CT = 50.4 \ s[/tex]

Thus, Maximum cycle time = 50.4 s

Answer:

For every 72 eggs, 32 omelets can be made.

Step-by-step explanation:

The ratio for eggs to omelets is 9:4. Or 9/4 in fraction form. (Note that the ratio can be written interchangeable such as 4:9).

The ratio says for every 9 eggs, it makes 4 omelets.

72 can be multiplied by 9. (9*8=72).

If we multiply the "top" and the "bottom" of the ratio by 8/8 (8/8=1. We must multiply this way so the ratio will remain the same when reduced.)

We will get 72:32.

For every 72 eggs, 32 omelets can be made.

Answer:

We use the rule of three !

9 eggs ------------> 4 omoletes

72 eggs -----------> x

So x= (72 eggs × 4 omoletes ) / 9 eggs

We simplify by 《eggs 》 because it is in the numerator and the denominator.

So x=(72×4 omoletes) / 9

x =288 omoletes /9

x = 32 omoletes

So we can made 32 omeletes with 72 eggs !!

I hope this helps you

Answer:

20+2=22

Step-by-step explanation:

When you go down by 2, then use the Inverse Operation to add it up.

Answer:

42

Step-by-step explanation:

12880000/140900=94.41

Therefore there is 1 teacher in every 94.41 people so

3860/94.41=42.2

So we would find around 42 teachers in Marshall, IL

Answer:

  C: real number

Step-by-step explanation:

The set of real numbers includes rational and irrational numbers. It would be difficult (impossible) to draw a number line consisting of only rational numbers or only irrational numbers.* So, the number lines we draw represent all real numbers.

_____

* There are an infinite number of rational numbers between any pair of irrational numbers. Similarly, there are an infinite number of irrational numbers between any pair of rational numbers

Step-by-step explanation:

Remember: Coplanar definition: In the same plane.

Here, we can see that points G, N, and M make up the intersection of plane K and plane L, so that means our answers are: G, N, and M because we were looking forth e points that are on planes K and L. The other points are not the answer because they are either on only one of the planes or not on any of them at all.

I hope this helps! :)

Answer:

I THINK it is M,N,G they are coplanar and they intersect, hope i helped

Answer:

  see below

Step-by-step explanation:

The result of the expression is P∨Q, since the P∧¬R term is subsumed by the P term. That is, ..

  (P∨Q) ∨ (P∧¬R) = Q ∨ (P ∨ P∧¬R) = Q∨P

Answer:

Patient A receives 150 milligrams and Patient B receives 50 milligrams

Step-by-step explanation:

Patient A = 3x

Patient B = x

200 milligrams = 3x + x

200 milligrams = 4x

x = 50

Patient A = 3(50) = 150

Patient B = 50

I hope this helps!

-TheBusinessMan

Let the medicine received by patient B be x.

According to the question patient A receives 3 times as much,

The total amount of medicine administered to the two patients equals to 200 milligrams.

We can write the relation as ,

[tex]:\implies \sf \ \ \ x + 3x = 200 \\ \\ \\ [/tex]

[tex]:\implies \sf \ \ \ 4x = 200 \\ \\ \\ [/tex]

[tex]:\implies \sf \ \ \ x = \dfrac{200}{4} \\ \\ \\ [/tex]

[tex]:\implies \sf \ \ \ { \underline{ \boxed{ \bf{ \blue{x = 50}}}}} \ \bigstar \\ \\ [/tex]

Therefore,

Answer:1760

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

4|0.5x - 2.5| = 0

|0.5x - 2.5|  = 0 / 4

0.5x - 2.5 = 0

0.5x = 2.5

x = 2.5 / 0.5

x = 5

Answer:

Slope= 2.0003.000=1.500

x−intercept=−312​=−4

y−intercept= 12/2=6

Hoped I helped

Answer:

[tex]\huge\boxed{a = 10 \ , \ b = 0}[/tex]

Step-by-step explanation:

Conjugate of -1 + 3i = -1 - 3i

Their Product:

[tex]=(-1+3i)(-1-3i)\\Using \ Formula : (a+b)(a-b) = a^2-b^2\\=(-1)^2 - (3i)^2\\=1 - 9i^2\\We \ know \ that \ i^2 = -1\\=1 - 9(-1)\\=1 + 9\\=10[/tex]

Since the answer is 10, It seems like:

a + bi = 10

So, This means that:

a = 10

b = 0

Answer:

Step-by-step explanation:

Given: AC is angle bisector of <BAD.

=> So, <BAC = <CAD

30° = x-1 °

30 +1 = x

31 = x

Then, X = 31

Hope this helps.. Good luck :)

Answer:  A) sin 59° = cos 31°

Step-by-step explanation:

Based on the angle and the sides provided, we can establish that

tan 31° = 17/x

Since no hypotenuse is provided and we cannot solve for it, we can rule out options B, C, and D.

We know that the sum of the angles of a triangle is 180°. In a right triangle, we know that one of the angles is 90°, so the other two angles are complimentary  -->   sin Ф = cos (90 - Ф).

Therefore, option A is true.

Answer:

y+2x = 3

Step-by-step explanation:

The formula for finding the equation of a tangent line is expressed using the point slope equation y-y0 = m(x-x0) where:

m is the slope of the line and (x0, y0) is a point on the line.

m = dy/dx = dy/dt ÷ dx/dt

dy/dt = 2(t-1)

dx/dt = e^t

m = 2(t-1)/e^t

If x = e^t, and x = 1

1 = e^t

Taking ln of both sides

ln1 = lne^t

t = ln1

t = 0

Substituting t = 0 into the slope formula:

m = 2(t-1)/e^t

m = 2(0-1)/e^0

m = 2(-1)/1

m = -2/1

m = -2

Substituting the slope m= -2 and the given point (1,1) into the formula for calculating the equation of tangent line we will have;

y-1 = -2(x-1)

y-1 = -2x+2

y+2x = 2+1

y+2x = 3

Hence the equation of the tangent line in Cartesian coordinates for the given parameter t is y+2x = 3

Answer:

a. cosθ = ¹/₂[e^jθ + e^(-jθ)] b. sinθ = ¹/₂[e^jθ - e^(-jθ)]

Step-by-step explanation:

a.We know that

e^jθ = cosθ + jsinθ and

e^(-jθ) = cosθ - jsinθ

Adding both equations, we have

e^jθ = cosθ + jsinθ

+

e^(-jθ) = cosθ - jsinθ

e^jθ + e^(-jθ) = cosθ + cosθ + jsinθ - jsinθ

Simplifying, we have

e^jθ + e^(-jθ) = 2cosθ

dividing through by 2 we have

cosθ = ¹/₂[e^jθ + e^(-jθ)]

b. We know that

e^jθ = cosθ + jsinθ and

e^(-jθ) = cosθ - jsinθ

Subtracting both equations, we have

e^jθ = cosθ + jsinθ

-

e^(-jθ) = cosθ - jsinθ

e^jθ + e^(-jθ) = cosθ - cosθ + jsinθ - (-jsinθ)

Simplifying, we have

e^jθ - e^(-jθ) = 2jsinθ

dividing through by 2 we have

sinθ = ¹/₂[e^jθ - e^(-jθ)]