What is the probability of rolling a number greater than or equal to 8 with the
sum of two dice, given that at least one of the dice must show a 6?

Answer:

Option B. A = (5/6)^-⅛

Step-by-step explanation:

From the question given above, we obtained:

(5/6)ˣ = A¯⁸ˣ

We can obtain the value of A as follow:

(5/6)ˣ = A¯⁸ˣ

Cancel x from both side

5/6 = A¯⁸

Recall:

M¯ⁿ = 1/Mⁿ

A¯⁸ = 1/A⁸

Thus,

5/6 = 1/A⁸

Cross multiply

5 × A⁸ = 6

Divide both side by 5

A⁸ = 6/5

Take the 8th root of both sides

A = ⁸√(6/5)

Recall

ⁿ√M = M^1/n

Thus,

⁸√(6/5) = (6/5)^⅛

Therefore,

A = (6/5)^⅛

Recall:

(A/B)ⁿ = (B/A)¯ⁿ

(6/5)^⅛ = (5/6)^-⅛

Therefore,

A = (5/6)^-⅛

Answer:

Step-by-step explanation:

[tex]5u\leq 8u-21[/tex]

Subtract 8u from both sides

[tex]-3u\leq -21[/tex]

Divide by -3 on both sides

[tex]u\geq 7[/tex]

Interval notation: [greater/less than or equal to], (greater or equal to)

[7,∞)

The solution to the inequality is u ≥ 7, which means that u is greater than or equal to 7. In interval notation [ 7, ∞).

In mathematics, an inequality is a remark that two values or expressions are not equal. An inequality uses one of the comparison symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), "≥" (greater than or equal to), or "≠" (not equal to).

Here,

To solve the inequality 5u ≤ 8u - 21, we can start by isolating u on one side of the inequality. We can do this by subtracting 5u from both sides:

5u ≤ 8u - 21

-3u ≤ -21

Divide both sides by -3. Note that dividing by a negative number will reverse the direction of the inequality:

u ≥ 7

Therefore, the solution to the inequality is u ≥ 7, which means that u is greater than or equal to 7. In interval notation [ 7, ∞).

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The answer is B

the method use to solved this is called foil

Answer:

B and C

Step-by-step explanation:

Using the Pythagorean theorem a²+b²=c², those are the correct answers

Answer:

2 hours

Step-by-step explanation:

10/50 * 10 = 2

Answer:

neither, since the gradients are not the same, as well as the c value

Step-by-step explanation:

First line : y = -4x + 7

Second line : y = -4x + 3

We know that the standard form of equation of a line is y = mx + c

where :

m is the slope

c is the y intercept

Comparing both line equations with the standard form, we can notice that :

⊕  Slope of the first line = -4

⊕  Slope of the second line = -4

We know that Slopes of parallel lines are same

So, We can conclude that the given two lines are parallel to each other

Answer : Parallel because the slopes are the same

9514 1404 393

Answer:

  90° CCW

Step-by-step explanation:

The transformation from B to B' is ...

  B(-4, 1) ⇒ B'(-1, -4)

  (x, y) ⇒ (-y, x) . . . . . matches the transformation for 90° CCW

Answer:

90 degrees

Step-by-step explanation:

Answer:

(-1.5, 0.5)

Step-by-step explanation:

x = -1.5

y = 0.5

(-1.5, 0.5)

Answer:

Z = 51º

Step-by-step explanation:

sinZ/12.5 = sin76/15.5

multiply both sides by 12.5

sinZ = sin76/15.5 * 12.5

Use calculator

sinZ = 0.782496553448384

Z = arcsin 0.782496553448384

Use calculator again

Z = 51.48972926377471º

Rounded

Z = 51º

Answer:

1. Volume of cone =  

where h is the height of the cone and r is the radius.

2. The bottom section is a cone with radius 6/2 = 3 (cm) and height= 8 cm

so the volume =  ()

3. The volume of the top section is the volume of the cone - volume of bottom cone, which we already found.

V(cone)=

V(top section)=192-24=168

Step-by-step explanation:

Answer:

- 0.125

Step-by-step explanation:

Given the equation :

(0.020(5/4) + 3 ((1/5) – (1/4)))

0.020(5/4) = 0.025

3((1/5) - (1/4)) = 3(1/5 - 1/4) = 3(-0.05) = - 0.15

0.025 + - 0.15 = 0.025 - 0.15 = - 0.125

9514 1404 393

Answer:

  B) if the x-coordinate is negative, the cosine will equal a negative value

Step-by-step explanation:

The cosine of the angle is the x-coordinate of the point where the terminal ray intersects the unit circle. Its sign will match the sign of the coordinates of point A on the terminal ray.

  if the x-coordinate is negative, the cosine will be negative

9514 1404 393

Answer:

  B.

Step-by-step explanation:

Use t=0 and t=2 and locate the graph with those two points on it. (We choose these because the horizontal grid is 2 years for each grid line.)

For t=0, C(0) = 50000(0.9^0) -2000 = 480000

For t=2, C(2) = 50000(0.9^2) -2000 = 40500 -2000 = 38500

The only graph that has y-intercept of 48000 and crosses (2, 38500) is the one shown in choice B.

Given:

The number [tex]\sqrt{63}[/tex] lies between two whole numbers.

To find:

The two consecutive whole numbers.

Solution:

The perfect squares of natural numbers are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, ... .

The number 63 lies between 49 and 64.

[tex]49<63<64[/tex]

Taking square root on each side, we get

[tex]\sqrt{49}<\sqrt{63}<\sqrt{64}[/tex]

[tex]7<\sqrt{63}<8[/tex]

Therefore, the number [tex]\sqrt{63}[/tex] lies between two whole numbers 7 and 8.

Answer: [tex]72.95 =6.00+5.15x[/tex]  , Required equation

The number of  people Mark invited to the party = 13

Step-by-step explanation:

According to the question,

Total amount spent = (Price of bunch of ballons)+(cost per gift) x (Number of persons)

Given: Total amount spent =$72.95 , Price of bunch of ballons =$6.00 ,

cost per gift =$5.15

thus,

[tex]72.95 =6.00+5.15x[/tex]  , Required equation

To solve , first

subtract 6 from both sides, we get

[tex]66.95=5.15x\\\\\Rightarrow\ x=\dfrac{66.95}{5.15}\\\\\Rightarrow\ x=13[/tex]

The number of  people Mark invited to the party = 13

Answer:

the answer is 3.5

Step-by-step explanation:

Answer:$6.25

Step-by-step explanation:we have that

x------------------> represent the number of hours Steven babysits

y----------------- > represent the amount he charges

for x=6 hours

y=$37.50 ----------------> y/x=37.5/6=6.25

for x=8 hours

y=$50---------------------> y/x=50/8=6.25

therefore

y=6.25x

Answer:

16 ounces.

Step-by-step explanation:

An 8% solution is 2 times stronger than a 4% solution.

So in the 8% solution we will have 1/2 of the volume as a 4% , so 1/2 * 32

= 16 ounces of water must be evaporated.

The number 16 ounces of water must be evaporated from 32 ounces of a 4% salt solution to make an 8% salt solution.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

To find the amount of water that must be evaporated from 32 ounces of a 4% salt solution to make an 8% salt solution:

0.96(32) - x = 0.92(32 - x)

30.72 - x = 29.44 - 0.92x

x - 0.92x = 30.72 - 29.44

0.08x = 1.28

x = 16

Therefore, 16 ounces must be evaporated.

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Answer:

angle M = 60

angle Q = 70

Step-by-step explanation:

M 180/3 = 60

Q 180-40 = 140/2 = 70

it is true

tbh am not sure

Answer:

1

Step-by-step explanation:

The y intercept is when x =0

We need to use the second equation

-x+1  since -2 < 0 <3

0+1

The y intercept is 1

Answer:

76 sq. meters

Step-by-step explanation:

10 · 4 = 40m

2 · 6 = 12m

8 · 6 = 48/2 = 24m

40 + 12 + 24 = 76 sq. meters

Answer:

There are many outcomes or data that needs to be collected... like does the iPhone and android share the same speaker? or are your speaker grills blocked out by something? or is your iPhone old, because they do change the speaker each gen.

Answer:

Auto Credit Express, Carvana, Capital one auto loan

Answer:

I think this is right hope you understand

Answer:

(8x + 1)° + ( 4x+11)° = 180° (linear pair )

8x +1 + 4x +11 = 180

8x + 4x + 1 + 11 = 180

12x + 12 = 180

12x = 180 - 12

12x = 168

x= 168/12

x = 14

t-3.2 ≤ 7.5

"at most" means less than or equal to

Answer:

0.7888 = 78.88% probability that the first machine produces an acceptable cork.

0.9772 = 97.72% probability that the second machine produces an acceptable cork.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

First machine:

Mean 3 cm and standard deviation 0.08 cm, which means that [tex]\mu = 3, \sigma = 0.08[/tex]

What is the probability that the first machine produces an acceptable cork?

This is the p-value of Z when X = 3.1 subtracted by the p-value of Z when X = 2.9. So

X = 3.1

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{3.1 - 3}{0.08}[/tex]

[tex]Z = 1.25[/tex]

[tex]Z = 1.25[/tex] has a p-value of 0.8944

X = 2.9

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2.9 - 3}{0.08}[/tex]

[tex]Z = -1.25[/tex]

[tex]Z = -1.25[/tex] has a p-value of 0.1056

0.8944 - 0.1056 = 0.7888

0.7888 = 78.88% probability that the first machine produces an acceptable cork.

What is the probability that the second machine produces an acceptable cork?

For the second machine, [tex]\mu = 3.04, \sigma = 0.03[/tex]. Now to find the probability, same procedure.

X = 3.1

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{3.1 - 3.04}{0.03}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a p-value of 0.9772

X = 2.9

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2.9 - 3.04}{0.03}[/tex]

[tex]Z = -4.67[/tex]

[tex]Z = -4.67[/tex] has a p-value of 0

0.9772 - 0 = 0.9772

0.9772 = 97.72% probability that the second machine produces an acceptable cork.