a parking row has 8 spaces. four cars are pulled in randomly to park in the parking row. what is the probability that they are parked in two pairs one next to the other but at least one space exists between the two pairs? assume all four cars are different.

Answer:

(3x - 9)/(x² - 5x + 12)

Step-by-step explanation:

Answer attached, please refer it.

Hope it helps :)

Scientists found an animal skull during an excavation and tested the amount of carbon -14 left in it. They found that 55 percent of the carbon-14 in the skull remained.

55% of the Carbon is left in the skull.

If A₀ was the original amount of Carbon, the amount of Carbon that is remaining will be 55% of A₀  which equals 0.55A₀

Using the given equation:

\(A = A_{o}e^{-0.000124t}\\\\ 0.55A_{o} = A_{o}e^{-0.000124t}\\ \\0.55 = e^{-0.000124t}\\\\In(0.55) = In(e^{-0.000124t})\\\\In(0.55) = -0.000124t*In(e)\\\\In(0.55) = -0.000124t\\\\\)

\(t = \frac{In(0.55)}{-0.000124} \\\\t = 4821\)

Rounding of to nearest year, we can conclude that the animal was buried 4821 years ago.

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Answer: A) 23

Step-by-step explanation:

3^2 + ( 6 - 2 ) ⋅ 4 -6/3

3^2 + 4 ⋅ 4 -6/3

9 + 4 ⋅ 4 -6/3

9 + 16 -6/3

25 - 6/3

75/3 -6/3 = 69/3

69/3 = 23

Answer:

23

Step-by-step explanation:

3^2 + (6 - 2) x 4 - 6/3

3^2 + 4 x 4 - 6/3

9 + 16 - 6/3

25 - 6/3

6/3 = 2

25 - 2 = 23

Answer:

-1

Step-by-step explanation:

-2/3 - 1/3

Since the denominators are the same, we can combine the numerators

-3/3

Simplify

-1

Answer:

125

Step-by-step explanation:

Assuming the lines are parallel :

n = 180-125

= 55

x = n

x = 55

z = 180-55

= 125

The surface area of the box is 1048 square inches

The formula for calculating the surface area of the prism is expressed as:

Surface area = 2(lw + wh +lh)

Given the following

l = 20in

w = 8in

h = 13in

Substitute the given parameters'

Surface area = 2(lw + wh +lh)

Surface area = 2(20(8) + 8(13) +20(13))

Surface area = 2(160+104+260)

Surface area = 1048 square inches

Hence surface area of the box is 1048 square inches

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The vertex of the parabola is (-2, -3/2).

First, let's expand the given expression:

\(1/2(x-3)(x+5) = 1/2(x^2 + 2x - 15)\)

Now, we can see that the coefficient of\(x^2\) is positive, which means the parabola opens upwards.

To find the vertex, we can use the formula:

Vertex = (-b/2a, f(-b/2a))

where a = 1/2, b = 2, and f(x) =\(1/2(x^2 + 2x - 15).\)

Substituting the values, we get:

Vertex = (-2/(21/2), f(-2/(21/2))) = (-2, f(-2))

To find f(-2), we can substitute x = -2 in the expression for f(x):

f(x) = \(1/2(x^2 + 2x - 15)\)

f(-2) = \(1/2((-2)^2 + 2(-2) - 15)\)

      = 1/2(-3)

      = -3/2

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Answer:

The answer is the top right corner. (pi* 3* 12^2)

I did this in TTM

Answer:

π⋅3⋅12^2

Step-by-step explanation:

Answer:

B 4 is the correct answer

Step-by-step explanation:

b - 12 = - 8

b = 12 - 8

b = 4

Answer:

C.

Step-by-step explanation:

You would take your servings (3) and multiply it by .20.

The, you would just add the 70 into the equation.

3 x .20 = .60, 70 + .60 is 70.60 :)

Hope this helps!

See attachment for math work and answer.

Answer: 19 should have been subtracted from both sides.

The probability that x is between 40 and 50 will be 0.5.

From the information, the continuous random variable x is uniformly distributed on the interval [35, 45].

The probability that x is between 40 and 50 will be:

(45 - 40)/(45 - 35)

= 5/10

= 0.5

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Outliers have a significant impact on a sample's parameters, errors, variance, and standard deviation. Instead of being regarded as outliers, Z-scores between -1.96 and +1.96 represent values that fall within the expected range.

Outliers can have a significant impact on the parameters, errors, variance, and standard deviation of a sample. Parameters, such as the mean and standard deviation, are influenced by outliers because they are sensitive to extreme values. Outliers can pull the mean towards their value, resulting in a biased estimate.

Similarly, outliers can inflate the variance and standard deviation, making them less representative of the majority of the data. Z-scores are a measure of how many standard deviations a data point is away from the mean. Z-scores falling between -1.96 and +1.96 (corresponding to approximately the 95% confidence interval) are not considered outliers.

These z-scores represent data points within a range that is expected and common for normally distributed data. Outliers are typically defined as data points that fall beyond a certain threshold, often defined as three standard deviations from the mean. When calculating z-scores for skewness and kurtosis, we use standard error instead of standard deviation.

This is because standard error takes into account the sample size and provides an estimate of the variability of the statistic being calculated. Since skewness and kurtosis are sample statistics, the standard error is used to assess the precision of these statistics in representing the corresponding population parameters.

In conclusion, outliers can greatly affect the parameters, errors, variance, and standard deviation of a sample. Z-scores falling between -1.96 and +1.96 are not considered outliers but rather represent values within the expected range.

Standard error is used when calculating z-scores for skewness and kurtosis to account for the sample size and provide a measure of precision for these statistics.

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Step-by-step explanation:

1 : complementary

2: supplementary

3: neither

________________

1: x = 6

2: x = 14

3: x = 34

The value of b that satisfies the equation is 7/2. To solve the given equation without using LaTeX, let's rewrite it in a different form.

We have the equation:

b/7 + b^2/7^2 + b^3/7^3 + ... = 7.

Notice that the left-hand side is an infinite geometric series with the first term (a) equal to b/7 and the common ratio (r) equal to b/7.

The sum (S) of an infinite geometric series is given by the formula:

S = a / (1 - r),

where |r| < 1.

Applying this formula to our equation, we get:

7 = (b/7) / (1 - b/7).

To simplify, let's multiply both sides of the equation by (1 - b/7) to get rid of the denominator:

7(1 - b/7) = b.

Expanding the left side, we have:

7 - b = b.

Moving the b term to the left side:

7 = 2b.

Finally, divide both sides by 2:

b = 7/2.

Therefore, the value of b that satisfies the equation is 7/2.

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The correct values for a, b, c, d, and e are a = 16, b = 29, c = 24, d = 22, and e = 30 for group of 75 students on asking whether they like Algebra or Geometry.

For the values of a, b, c, d, and e, we can use the information provided in the table. Let's break it down step-by-step:

We are given that a total of 75 math students were surveyed. Therefore, the total number of students should be equal to the sum of the students who like algebra, the students who like geometry, and the students who do not like either subject.

75 = 45 (Likes Algebra) + 53 (Likes Geometry) + 6 (Does Not Like Either)

Simplifying this equation, we have:

75 = 98 + 6

75 = 104

This equation is incorrect, so we can eliminate options c and d.

Now, let's look at the information given for the students who do not like geometry. We know that a + b = 6, where a represents the number of students who like algebra and do not like geometry, and b represents the number of students who do not like algebra and do not like geometry.

Using the correct values for a and b, we have:

16 + b = 6

b = 6 - 16

b = -10

Since we can't have a negative value for the number of students, option a is also incorrect.

The remaining option is option e, where a = 29, b = 16, c = 24, d = 22, and e = 30. Let's verify if these values satisfy all the given conditions.

Likes Algebra: a + c = 29 + 24 = 53 (Matches the given value)

Does Not Like Algebra: b + d = 16 + 22 = 38 (Matches the given value)

Likes Geometry: c + d = 24 + 22 = 46 (Matches the given value)

Does Not Like Geometry: b + e = 16 + 30 = 46 (Matches the given value)

All the values satisfy the given conditions, confirming that option e (a = 29, b = 16, c = 24, d = 22, and e = 30) is the correct answer.

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Answer:

Step-by-step explanation:

Range is y thing, where as domain is an x thing. The way you state a range (or a domain, for that matter) is to start from the low point on the graph and go up to the high point. Our graph doesn't have a starting point; therefore, the "low" end of the graph comes up from -∞. The high point on the graph maxes out at 3. Therefore, the proper way to state the range (depending upon whether you use set-builder or not) is

R = (-∞, 3] or another way to state this is

R = {y | y ≤ 3} which reads "y such that y is less than or equal to 3".

Answer: 32

Step-by-step explanation:

This is a simple question:

If you want to know if its divisible by 3 then just add up the digits in 96.

In this scenario 3 is divisible because 9+6=15 and 15 divided by 3 = 5

Now use long division to solve:

96 divided by 3 = 32

Hope this helps! :)

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The length of the radius AB is 6 units.

The angle ∠BAC is 90 degrees. The length of arc BC is 3π. The length of  

radius AB can be found as follows:

Hence,

length of arc = ∅ / 360 × 2πr

where

Therefore,

length of arc = 90 / 360 × 2πr

3π = 1 / 4 × 2πr

cross multiply

12π = 2πr

divide both sides by 2π

r = 6 units

Therefore,

radius AB = 6 units

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The amount of hamburguer meat that the cook should order is given as follows:

30 pounds.

The amount of hamburguer meat that the cook should order is obtained applying the proportions in the context of the problem.

To make hamburguers for x students, the amount needed is given as follows:

y = x/5.

Hence, for 150 students, we must divide the number of students of 150 by 5, as follows:

150/5 = 30 pounds.

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The interval estimate for the true population proportion is 45.25% to 64.75% and we can conclude that the majority of the community supports water rationing

The given parameters are:

The error margin is calculated using:

\(E = z * \sqrt{\frac{p* (1 - p)}{n}}\)

Where z is the critical value.

At 95% confidence level, the critical value is:

z = 1.96

So, we have:

\(E = 1.96 * \sqrt{\frac{0.55 * (1 - 0.55)}{100}}\)

Evaluate

\(E = 1.96 * \sqrt{0.002475}\)

Evaluate

E = 0.0975

Hence, the error margin is 0.0975

This is calculated using:

I = p ± E

So, we have:

I = 0.55 ± 0.0975

Expand

I = (0.55 - 0.0975, 0.55 + 0.0975)

Evaluate

I = (0.4525, 0.6475)

Express as percentage

I = (45.25%, 64.75%)

Hence, the interval estimate for the true population proportion is 45.25% to 64.75%

From the simulation,

The values are approximately the interval estimates.

i.e.

45.25% ≈ 45% and 64.75% ≈ 65%

Hence, we can conclude that the majority of the community supports water rationing

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To factor this expression, you take out the greatest factor of 48 and 8 and also the greatest power of x that is in both terms. The greatest common factor of 48 and 8 is 8, and the greatest power of x is x to the 4th power. You rewrite the expression like this: 8x^4(6x - 1)

Answer:

62.2 m

Step-by-step explanation:

From 148m away at ground level, the angel of elevation to the tower base is 18 degrees. Imagining this as a right angled triangle, if considering the angle of 18 degrees, 148m is the adjacent and the opposite is the height of the hill:

tanA=opposite/adjacent

tan18=opposite/148

opposite = 57.8357059295m

From 148m away at ground level, the angel of elevation to the tower top is 34 degrees. Imagining this as a right angled triangle, if considering the angle of 34 degrees, 148m is the adjacent and the opposite is the height of the hill+the tower:

tanA=opposite/adjacent

tan34=opposite/148

opposite = 120.062515998m

Knowing the height of the hill and tower is 120.062515998m and the height of the hill is 57.8357059295m, we can say the height of the tower is the difference:

120.062515998 - 57.8357059295 = 62.2268100685 m

Let's use the furthest left point on the triangle to figure out the translation.

Blue triangle = (-5,1)

Black triangle = (-3,-1)

To get from -5 to -3 we moved the triangle 2 units to the right, which means that we added 2.

To get from 1 to -1, we moved the triangle 2 units down, which means we subtracted 2.

Rule: {2, -2}

Hope this helps!

Answer:

9 ounces

Step-by-step explanation:

He uses 3 ounces 3 different days. That is 3x3 which equals 9. Hope you get a 100! :)

A sphere thrown upward at a 45-degree angle to the horizontal in a classroom elastically bounces off the ceiling while still rising

At time t = 0, a sphere is launched with an initial velocity at a 45-degree angle to the horizontal in a classroom. The sphere follows a parabolic trajectory as it rises due to the upward component of its initial velocity and experiences the downward pull of gravity. While the sphere is still ascending, it reaches the ceiling and collides with it.

During the elastic collision, the sphere's motion is reversed. It rebounds off the ceiling, changing its direction but maintaining its kinetic energy. As a result, the sphere starts descending with the same speed it had before the collision but in the opposite direction. The angle of descent will also be 45 degrees to the horizontal, mirroring the angle of the initial launch.

Throughout the entire process, neglecting air resistance, the total mechanical energy of the sphere is conserved since the collision with the ceiling is elastic.

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