A number cube labeled 1 through 6 rolled three times. What is the probability that the first roll is a 1, the second roll is a 2, and the third roll is greater than 4?

Answer:

t = 23/32 + (i sqrt(623))/32 or t = 23/32 - (i sqrt(623))/32

Step-by-step explanation:

Solve for t:

16 t^2 - 23 t + 18 = 0

Divide both sides by 16:

t^2 - (23 t)/16 + 9/8 = 0

Subtract 9/8 from both sides:

t^2 - (23 t)/16 = -9/8

Add 529/1024 to both sides:

t^2 - (23 t)/16 + 529/1024 = -623/1024

Write the left hand side as a square:

(t - 23/32)^2 = -623/1024

Take the square root of both sides:

t - 23/32 = (i sqrt(623))/32 or t - 23/32 = -(i sqrt(623))/32

Add 23/32 to both sides:

t = 23/32 + (i sqrt(623))/32 or t - 23/32 = -(i sqrt(623))/32

Add 23/32 to both sides:

Answer: t = 23/32 + (i sqrt(623))/32 or t = 23/32 - (i sqrt(623))/32

Answer:

  1.  x^2 +2x -24 = 0

  2.  x^2 -7x +10 = 0

Step-by-step explanation:

If you look at the factored and expanded forms of a quadratic with solutions p and q, you see ...

  (x -p)(x -q) = x^2 -(p+q) +pq

The x-term coefficient is the opposite of the sum of solutions.

The constant is the product of solutions.

This knowledge lets you write down the standard form equation with no particular effort.

1.  x^2 +2x -24 = 0

2.  x^2 -7x +10 = 0

Answer:

x=20

Step-by-step explanation:

x/24 = 30/36 simplify

x/24 = 5/6 divide 24 by 6 and multiply it to 5

x = 20

The solution to the equation x/24 = 30/36 is x = 20.

Option A is the correct answer.

We have,

To solve the equation x/24 = 30/36, we can cross-multiply and solve for x.

Cross-multiplying gives us:

36x = 24 * 30

Simplifying further:

36x = 720

Now, we can divide both sides of the equation by 36 to isolate x:

x = 720/36

Simplifying the right side:

x = 20

Therefore,

The solution to the equation x/24 = 30/36 is x = 20.

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Answer:

160$

Step-by-step explanation:

160*.30=48

The compound inequality is: x<20 and x>10

Given,  a quantity of x is greater than 10 and less than 20.

A compound inequality (also known as a compounded inequality) is created when two or more inequalities are coupled with and. One part of an inequality must be true for a value to be a solution to an or inequality. It must make both parts true in order to be the solution to an inequality. X<3 or X>2, for instance.

Divide a compound inequality into two independent ones before attempting to solve it. Choose either a union of sets ("or") and an intersection of sets as the appropriate response ("and"). Then, resolve the graph and all inequalities.

Simply put, a compound inequality is more than one inequality that we want to address simultaneously. When referring to the resolution of both inequalities, we can either use the term "and" or "or."

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Answer:

383.7

Step-by-step explanation:

i doooooooont knoooooooooooooooow iiiittttttttttttttttttttttt

Answer:

7x

Step-by-step explanation:

Answer:

Step-by-step explanation:

V = 3.9V

I = 0.12A

Ohm's Law, V = IR

Rearranging Ohm's Law, R = V/I

R = 3.9/0.12 = 32.5Ω

Answer:

Your answer would be

- 2/25 x^3a^3

Or vice versa with the variables

- 2/25 a^3x^3

TO solve it’s pretty simple if you do it correctly.

So with all the variables in the two multiples, you can find a way to combine them

So ignoring everything else you’d get

a^2x * x^2a

You we can see the difference,

theres a^2 and a

Whilst there is also x^2 and x

Now we can combine them

a^3 x^3

Now we can do the normal multipacation with the fraction

2/5 * - 1/5 which is -2/25

Now combine

ANd you got it :D

Answer:

\( \frac{ {x}^{2} + 10x + 16 }{ {x } {}^{2} + 6x + 8} \div \frac{1}{x + 2} \)

\( \frac{ {x}^{2} + 8 x+ 2x + 16}{ {x}^{2} + 4x + 2x + 8} \times (x + 2)\)

\( \frac{x(x + 8) + 2 (x + 8)}{x(x + 4) + 2(x + 4)} \times (x + 2)\)

\( \frac{( x + 8)(x + 2)}{(x + 2)(x + 4)} \times ( x + 2)\)

\( \frac{( x + 8)(x + 2)}{(x + 4)} \)

The probability that a red card is drawn at least once by the third draw is 0.88.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Let, a card is drawn from a standard deck of 52 cards and then placed back into the deck.

In a standard 52 card deck the red cards are 26.

So,

P(red) =  n(red cards) / n(total cards)

          = 26 / 52

P(red) = 0.50

Now, X ≈ Bin (n = 3, P = 0.50)

P(X = x) = (n  x) p^x (1 - p)^n-x

(n  x) = \(\frac{n!}{x!(n-x)!}\)

P(X ≥ 1) = 1 - P(X < 1)

            = 1 - P(X = 0)

            = 1- (3  0)(0.5)^0(0.5)^3

            = 1 - 0.125

             = 0.875

P(X ≥ 1)  = 0.88

Hence, the probability that a red card is drawn at least once by the third draw is 0.88.

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To maximize the volume, of the rectangular prism, the carton should have dimensions of approximately 10.74 inches (length), 10.74 inches (width), and 5.37 inches (height).

Assuming the height of the rectangular prism is h inches.

According to the given information, the length and width of the prism will be twice the height, which means the length is 2h inches and the width is also 2h inches.

The total surface area of the rectangular prism is given by the formula:

Surface Area = 2lw + 2lh + 2wh

Substituting the values, we have:

576 = 2(2h)(2h) + 2(2h)(h) + 2(2h)(h)

576 = 8h² + 4h² + 4h²

576 = 16h² + 4h²

576 = 20²

h² = 576/20

h² = 28.8

h = √28.8

h = 5.37

The height of the prism is approximately 5.37 inches.

The length and width will be twice the height, so the length is approximately 2 * 5.37 = 10.74 inches, and the width is also approximately 2 * 5.37 = 10.74 inches.

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The bakery should use the range to determine whether or not the equipment changes have worked. The correct answer is C.

To determine whether the equipment changes made by the bakery have resulted in more uniform-sized muffins, they should use the measure of variability. The most suitable measure, in this case, would be the range.

The range is calculated by finding the difference between the maximum and minimum values in a data set. In this scenario, the bakery made 25 muffins and measured each one. By finding the range of the measurements, they can assess the spread of sizes among the muffins.

Here's how they can use the range to evaluate the effectiveness of the equipment changes:

Collect the measurements of all 25 muffins.

Determine the maximum and minimum measurements.

Calculate the range by subtracting the minimum measurement from the maximum measurement.

If the range of the muffin sizes is smaller compared to the range before the equipment changes, it suggests that the modifications have resulted in more uniform-sized muffins. Conversely, if the range remains similar or larger, it indicates that the changes might not have effectively improved the uniformity of muffin sizes.

Therefore, the bakery should use the range to determine whether or not the equipment changes have worked. The correct answer is C.

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Answer:

8. tenths

9. 90,000

Step-by-step:

tenths: ones are 10 times as small and move the decimal point one more time, tenths (note the ths)

90,000 the 9 in 295 is 90. 90*1000=90,000

Answer:

A = 2184 cm²

Step-by-step explanation:

the area (A) of the figure is calculated as

A = \(\frac{1}{2}\) h(b₁ + b₂)

where h is the perpendicular height between the bases b₁ and b₂

here h = 42 , b₁ = 52 , b₂ = 52 , then

A = \(\frac{1}{2}\) × 42 × (52 + 52) = 21 × 104 = 2184 cm²

Answer:

A = 2184 cm2

Step-by-step explanation:

Area of a parallelogram:

\(A = b*h\)

\(b=52,h=42\)

\(A=(42)(52)=2184cm^{2}\)

Hope this helps.

Answer:  x = ¹/₂ ± √⁸¹

                     ------------

                            2

Step-by-step explanation:

First write out the equation

x² - x - 20

Now we now write the equation by equating to 0

x² - x - 20 = 0

We now move 20 to the other side of the equation. So

x² - x    =  20,

We now add to both side of the equation square of the half the coefficient of the (x) and not (x²) which is (1) . So, the equation now becomes

x² - x + ( ¹/₂ )² = 20 + ( ¹/₂ )²

x² - ( ¹/₂ )²       = 20 + ¹/₄

( x - ¹/₂ )²       = 20  + ¹/₄, we now resolve the right hand side expression into fraction

( x - ¹/₂ )²          =  ⁸¹/₄ when the LCM is made 4

Taking the square root of both side to remove the square,we now have

x - ¹/₂               =  √⁸¹/₄

x - ¹/₂               =     √⁸¹/₂

Therefore,

                    x = ¹/₂ ± √⁸¹

                          -----------

                               2

Answer:

7sqrt2

Step-by-step explanation:

If angle K is 45 degrees then angle L will be 45 degrees

This means LM and KM will be the same length

Using pythagoras theorem you get KL =7sqrt2

Answer:

8.5

Step-by-step explanation:

The value when 6/24  is divided by 12/16 is equal to 1/3.

To divide the fraction 6/24 by 12/16, we can simplify the problem by multiplying the first fraction by the reciprocal of the second fraction.

Reciprocal of 12/16 is 16/12.

So, the division can be written as:

6/24 ÷ 12/16 = 6/24 × 16/12

6/24 = (6 ÷ 6) / (24 ÷ 6) = 1/4

16/12 = (16 ÷ 4) / (12 ÷ 4) = 4/3

Now, we have:

1/4 × 4/3

To multiply fractions, we multiply the numerators together and the denominators together:

(1 × 4) / (4 × 3)

= 4/12

The fraction 4/12 by dividing both the numerator and denominator by their greatest common divisor, which is 4:

(4 ÷ 4) / (12 ÷ 4)

= 1/3

Therefore, 6/24 divided by 12/16 is equal to 1/3.

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Step-by-step explanation:

The circumference of a circle is given by :

C=2πr, r is the radius of the circle

Also, 2r = D, diameter of the circle

⇒ C = πD

If the diameter of a circle is multiplied by 10, it means,

C = π(10)

⇒ C = 10π

Hence, if the diameter of a circle is multiplied by 10, then its circumference becomes 10π.

Question:

You play tennis against a player that you have a 20% chance of winning. What is the probability that you win no game out of 6 games?

Answer:

\(Probability = 0.262144\)

Step-by-step explanation:

Represent the probability of winning with P(Win)

\(P(Win) = 20\%\)

Required

Determine the probability of not winning 6 games

First, we calculate the probability of not winning a game.

Opposite probability add up to 1.

So, we have:

\(P(Win) + P(Lose) = 1\)

\(P(Lose) = 1 - P(Win)\)

\(P(Lose) = 1 - 20\%\)

\(P(Lose) = 100\% - 20\%\)

\(P(Lose) = 80\%\)

The sample space of losing 6 games is:

Lose Lose Lose Lose Lose Lose

Therefore, the probability is:

\(Probability = 80\% *80\% *80\% *80\% *80\% *80\%\)

\(Probability = 0.80*0.80*0.80*0.80*0.80*0.80\)

\(Probability = 0.262144\)

The solution of the given Question with help of BODMAS is\(-4\)

A mathematical expression is simplified by being replaced with a more straightforward equivalent.

I) Important Considerations for Handling Simplification Questions

II) Substitute "of" for "multiplication," and "/" for "division."

III) Always carry out operations in accordance with "BODMAS."

IV) Division and multiplication are equally important (start from the left)

V)  Both addition and subtraction are equally important.

\(16 - (6*2)/4(16-6) +5*2\)

Step 1: solve Brackets

\(16- (62)/4(16-6)+52\)

Step 2: solve Division

\(16- 3(10)+10\)

Step 3: solve Multiplication:

\(16-30+10\)

Step 4: solve Addition:

\(26-30\)

Solve :solve Subtraction

\(-4\)

Therefore the answer for the above simplification is\(-4\)

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The average rate of change of the school's enrollment during this time period is -49 students per year. This means that on average, the enrollment at the college has been decreasing by 49 students per year.

To determine the average rate of change of the school's enrollment during the given time period, we can use the formula:

Average rate of change = (Change in enrollment) / (Change in time)

The change in enrollment is calculated by subtracting the initial enrollment from the final enrollment, while the change in time is calculated by subtracting the initial year from the final year.

Given that in 2004 there were 975 students enrolled and in 2009 there were 730 students enrolled, we can calculate the change in enrollment:

Change in enrollment = 730 - 975 = -245 students

The change in time can be calculated as:

Change in time = 2009 - 2004 = 5 years

Now we can calculate the average rate of change:

Average rate of change = (-245 students) / (5 years) = -49 students per year

Therefore, the average rate of change of the school's enrollment during this time period is -49 students per year. This means that on average, the enrollment at the college has been decreasing by 49 students per year.

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Answer:

54

Step-by-step explanation: