The following pieces of empirical evidence have been collected over the years: Historical trend data show an increase in temperature globally Levels of carbon dioxide gas are on the rise Levels of methane gas are on the rise Glacial ice is melting Antarctic and Artic sea ice is melting Which statement best explains the significance of this empirical evidence?



a
It provides a hypothesis for the climate of the past.
b
It provides data for science journals and textbooks.
c
It supports the scientific explanation for global warming.
d
It predicts future weather patterns.

Answer:

3

Step-by-step explanation:

If the value of b is 8. Then the value of the expression (9 - b) will be 1.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

The expression is given below.

⇒ 9 - b

If the value of b is 8. Then the value of the expression will be

⇒ 9 - b

⇒ 9 - 8

⇒ 1

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Answer:

a) The velocity of the ball after 2 seconds is -91 feet per second, b) The velocity of the ball after falling 364 feet is 155 feet per second, c) The equation of the parabola that passes through (0,1) and is tangent to the line y = 5x - 5 is \(y = 6\cdot x^{2}-7\cdot x +1\).

Step-by-step explanation:

a) The velocity function is obtained after deriving the position function in time:

\(v (t) = -32\cdot t -27\)

The velocity of the ball after 2 seconds is:

\(v(2\,s) = -32\cdot (2\,s) -27\)

\(v(2\,s) = -91\,\frac{ft}{s}\)

The velocity of the ball after 2 seconds is -91 feet per second.

b) The time of the ball after falling 364 feet is found after solving the position function as follows:

\(435\,ft - 364\,ft = -16\cdot t^{2}-27\cdot t + 435\,ft\)

\(-16\cdot t^{2} - 27\cdot t + 364 = 0\)

The solution of this second-grade polynomial is represented by two roots:

\(t_{1} = 4\,s\) and \(t_{2} = -5.688\,s\).

Only the first root is physically reasonable since time is a positive variable. Now, the velocity of the ball after falling 364 feet is:

\(v(4\,s) = -32\cdot (4\,s) - 27\)

\(v(4\,s) = -155\,\frac{ft}{s}\)

The velocity of the ball after falling 364 feet is 155 feet per second.

c) Let consider the equation for a second order polynomial that passes through (0, 1) and its first derivative that passes through (1, 0) and represents the give equation of the tangent line. That is to say:

Second-order polynomial evaluated at (0, 1)

\(c = 1\)

Slope of the tangent line evaluated at (1, 0)

\(5 = 2\cdot a \cdot (1) + b\)

\(2\cdot a + b = 5\)

\(b = 5 - 2\cdot a\)

Now, let evaluate the second order polynomial at (1, 0):

\(0 = a\cdot (1)^{2}+b\cdot (1) + c\)

\(a + b + c = 0\)

If \(c = 1\) and \(b = 5 - 2\cdot a\), then:

\(a + (5-2\cdot a) +1 = 0\)

\(-a +6 = 0\)

\(a = 6\)

And the value of b is: (\(a = 6\))

\(b = 5 - 2\cdot (6)\)

\(b = -7\)

The equation of the parabola that passes through (0,1) and is tangent to the line y = 5x - 5 is \(y = 6\cdot x^{2}-7\cdot x +1\).

Answer:

Step-by-step explanation:

Given an assistant bricklayer laying 50 bricks an hour has worked 2 hours longer than a master bricklayer laying 80 bricks an hour, you want an equation stating they have laid the same number of bricks. You also want to know how long each has worked.

The output of each bricklayer is the product of the rate at which they lay bricks and the time for which they do it. If t is the time spent by the master bricklayer, their output will be 80t. The time spent by the assistant will be (t+2) hours, and their output will be 50(t+2).

Here is the equation that says their output is the same:

  80t = 50(t+2)

Solving the equation for t, we have ...

  80t = 50t +100

  30t = 100 . . . . . . . . . subtract 50t

  t = 3 1/3 . . . . . . . divide by 30

The master bricklayer has worked 3 1/3 hours when they have laid the same number of bricks.

The assistant bricklayer has worked 5 1/3 hours at that time.

__

Additional comment

Each will have laid (80)(3 1/3) = 266 2/3 bricks.

Given that cos (0) = 0, we can use the Pythagorean identity sin^2(x) + cos^2(x) = 1 to find the value of sin (0).

sin^2(0) + cos^2(0) = 1

sin^2(0) = 1 - cos^2(0)

sin^2(0) = 1 - 0^2

sin^2(0) = 1

So, sin (0) = sqrt(sin^2(0)) = sqrt (1) = 1.

However, the given value is sin (0) = v3/6. This means that sin (0) = sqrt (3)/2, which is the value of sin (60). Therefore, the correct value of sin (0) is sqrt (3)/2, not 1.

trigonometry, the branch of mathematics deal with specific functions of angles and their application to calculations. There is total six functions of an angle commonly used in trigonometry.

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Rounding to the nearest whole number. The correct option is D) 216 m²; 244 m².

Since the prism has a rectangular base, we know that its lateral faces are all rectangles with heights equal to the height of the prism. Let's first find the lateral area of the prism using the formula:

Lateral Area = Perimeter of Base * Height

The perimeter of the base is the sum of the lengths of all four sides of the rectangle. Since there are two bases, we will add their perimeters together. The length and width of each base are 12 m and 7 m, respectively, so:

Perimeter of Base = 2 * (Length + Width) = 2 * (12 + 7) = 38 m

The height of the prism is given as 10 m, so:

Lateral Area = 38 * 10 = 380 m²

Next, we need to find the surface area of the prism. This consists of the lateral area we just found, plus the areas of the two bases. Each base has an area of 12 * 7 = 84 m², so:

Surface Area = 2 * Base Area + Lateral Area = 2 * 84 + 380 = 548 m²

Rounding to the nearest whole number, we get:

Lateral Area ≈ 380 m²

Surface Area ≈ 548 m²

Therefore, the answer is option D) 216 m²; 244 m².

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Answer: 2

Step-by-step explanation:

When x=-9, y=2. So, f(-9)=2.

Answer:

a. \(\frac{1}{36}\) chance you win.

b. The expected value of the game is -$2.08.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

You roll 2 die and if you toss 2 sixes

For each roll, 6 possible values, 1 of which is 6. So the probability of rolling two sixes is:

\(p = (\frac{1}{6})^2 = \frac{1}{36}\)

a. What is the chance you win?

\(\frac{1}{36}\) chance you win.

b. What is the expected value of the game?

1/36 probability of winning 100.

35/36 probability of losing 5. So

\(E = \frac{1}{36}*100 - \frac{35}{36}*5 = \frac{100 - 175}{36} = -\frac{75}{36} = -2.08\)

The expected value of the game is -$2.08.

Answer:

10 boys

Step-by-step explanation:

0.4x25= 10

Answer:

-4

Step-by-step explanation:

Take any 4 points,

(-7,21) & (-4,9) as  (x₁, y₁)/(x₂, y₂)

Slope(m) = (y₂-y₁)/(x₂-x₁)

(9-21)/(-4-(-7))

-12/(-4+7)

-12/3

-4

Answer:

\(\frac{20}{49\pi }\) when the pile is at 14ft

Step-by-step explanation:

To get your height in inches alone from the way it's usually presented (e.g. 5' 7"), multiply the total number of feet by 12 and then add the remainder. For example, a 5' 7" person is (5 × 12) + 7 = 67" tall. To convert inches to centimeters (in to cm), simply multiply by 2.54.

Answer:

Snell's Law states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the indices of refraction of the two media:

sin i / sin r = n2/n1

where i is the angle of incidence, r is the angle of refraction, n1 is the index of refraction of the initial medium (in this case air), and n2 is the index of refraction of the second medium (in this case the windshield).

We can rearrange Snell's Law to solve for n2:

n2 = n1 * sin i / sin r

Plugging in the given values, we have:

n2 = 1.0003 * sin 55° / sin 35.25°

Using a calculator, we get:

n2 ≈ 1.526

Therefore, the index of refraction of the windshield is approximately 1.526 to the nearest thousandth.

Answer:

C) 4/3

Step-by-step explanation:

distance / time = distance / time

1/3 ÷ 1/4 = d ÷ 1

\(\frac{1}{3}\) · \(\frac{4}{1}\) = \(\frac{d}{1}\)

\(\frac{4}{3}\) = \(\frac{d}{1}\)

3d = 4

d = 4/3

Answer:

see below and attachment

Step-by-step explanation:

a=30°

because, the marked angle of 30° is an alternate interior angle to angle a.  Alternate interior angles are congruent, and we know they are congruent because the 2 horizontal lines are parallel.

b=50°

because the marked angle of 50° is a vertical angle to angle b.  Vertical angles are congruent because 2 lines that intersect have opposite congruent angles, making them vertical angles to each other.

c=50°

because the marked angle of 50° is a corresponding angle (same side angle) to angle c.  These corresponding angles are congruent because the 2 horizontal lines are parallel.

d=100°

because the 3 interior angles of a triangle must add up to 180°.  We have 30°, 50°, so the last angle must be 100°.  We can also figure this out because the bottom horizontal line is a straight line, meaning the angle is also 180°.  We have angle a as 30°, angle c as 50°, so angle d must be 100°.

Hope this helps!  See attachment for visual.

9514 1404 393

Answer:

  x² +2/3x -1/9 = 0

Step-by-step explanation:

The quadratic with roots p and q can be written as ...

  (x -p)(x -q) = 0

  x² -(p+q)x +pq = 0

For p=(-1-√2)/3 and q=(-1+√2)/3, we have ...

  p +q = (-1-√2)/3 +(-1+√2)/3 = -2/3

  pq = ((-1-√2)/3)((-1+√2)/3) = (1 -2)/9 = -1/9

Then the quadratic is ...

  x² +2/3x -1/9 = 0

The value of 4 Superscript negative 4 is negative StartFraction 1 Over 4 Superscript negative 4 EndFraction.

In the given table, Tasha observed a pattern in the powers of 4. When the exponent decreases by 1, the previous value is divided by 4. Using this pattern, she determined the values for 4 squared, 4 Superscript 1, 4 Superscript 0, 4 Superscript negative 1, and 4 Superscript negative 2.

To find the value of 4 Superscript negative 3, she divided the previous value (StartFraction 1 Over 16 EndFraction) by 4, resulting in StartFraction 1 Over 64 EndFraction.

Similarly, for 4 Superscript negative 4, she divided the previous value (StartFraction 1 Over 64 EndFraction) by 4, yielding StartFraction 1 Over 256 EndFraction.

Finally, to rewrite the value for 4 Superscript negative 4, she expressed it as negative StartFraction 1 Over 4 Superscript negative 4 EndFraction.

Therefore, the value of 4 Superscript negative 4 is negative StartFraction 1 Over 4 Superscript negative 4 EndFraction, which simplifies to StartFraction 1 Over 256 EndFraction

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Answer: there are 7 in the water

Step-by-step explanation:

The correct answer is C. It is the graph of f(x) translated 11 units to the left.

The correct answer is:

C. It is the graph of f(x) translated 11 units to the left.

When we have a function of the form g(x) = f(x - a), it represents a horizontal translation of the graph of f(x) by 'a' units to the right if 'a' is positive and to the left if 'a' is negative.

In this case, g(x) = f(x - 11), which means that the graph of f(x) is being translated 11 units to the right. However, the answer options do not include this specific transformation. The closest option is option C, which states that the graph of g(x) is translated 11 units to the left.

The graph of f(x) = x is a straight line passing through the origin with a slope of 1. If we apply the transformation g(x) = f(x - 11), it means that we are shifting the graph of f(x) 11 units to the right. This results in a new function g(x) that has the same shape and slope as f(x), but is shifted to the right by 11 units.

Therefore, the correct answer is C. It is the graph of f(x) translated 11 units to the left.

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Answer:

a. 0.0498 = 4.98% probability of no off-the-job accidents during a one-year period

b. 0.8008 = 80.08% probability of at least two off-the-job accidents during a one-year period.

c. The expected number of off-the-job accidents during six months is 1.5.

d. 0.2231 = 22.31% probability of no off-the-job accidents during the next six months.

Step-by-step explanation:

We have the mean during a period, so we use the Poisson distribution.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\(\mu\) is the mean in the given interval.

Companies with 50 employees are expected to average three employee off-the-job accidents per year.

This means that \(\mu = 3n\), in which n is the number of years.

a. What is the probability of no off-the-job accidents during a one-year period (to 4 decimals)?

This is \(P(X = 0)\) when \(\mu = 3*1 = 3\). So

\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)

\(P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498\)

0.0498 = 4.98% probability of no off-the-job accidents during a one-year period.

b. What is the probability of at least two off-the-job accidents during a one-year period (to 4 decimals)?

Either there are less than two accidents, or there are at least two. The sum of the probabilities of these events is 1. So

\(P(X < 2) + P(X \geq 2) = 1\)

We want \(P(X \geq 2)\). Then

\(P(X \geq 2) = 1 - P(X < 2)\)

In which

\(P(X < 2) = P(X = 0) + P(X = 1)\)

\(P(X = 0) = \frac{e^{-3}*3^{0}}{(0)!} = 0.0498\)

\(P(X = 1) = \frac{e^{-3}*3^{1}}{(1)!} = 0.1494\)

\(P(X < 2) = P(X = 0) + P(X = 1) = 0.0498 + 0.1494 = 0.1992\)

\(P(X \geq 2) = 1 - P(X < 2) = 1 - 0.1992 = 0.8008\)

0.8008 = 80.08% probability of at least two off-the-job accidents during a one-year period.

c. What is the expected number of off-the-job accidents during six months (to 1 decimal)?

6 months is half a year, so \(n = 0.5\)

\(\mu = 3n = 3*0.5 = 1.5\)

The expected number of off-the-job accidents during six months is 1.5.

d. What is the probability of no off-the-job accidents during the next six months (to 4 decimals)?

This is P(X = 0) when \(\mu = 1.5\). So

\(P(X = 0) = \frac{e^{-1.5}*1.5^{0}}{(0)!} = 0.2231\)

0.2231 = 22.31% probability of no off-the-job accidents during the next six months.

Answer:

Clarissa needs a 95

Step-by-step explanation:

4 x 82.5 = 330

Keep trying numbers to see if they work

330 + 95 = 425

425 / 5 = 85

=>x+45+45=180°

=>x+90=180°

=>x=180°-90°

=>x=90°

Answer:

(13, -67.4°)

Step-by-step explanation:

In the general case, for a point (x, y), the same point written in polar coordinates is (r, θ), such that:

r = √(x^2 + y^2)

θ = Atg(y/x)

Then if we have the point with coordinates (-5, 12)

The polar coordinates will be:

r = √((-5)^2 + 12^2) = 13

θ = Atg(12/-5) = -67.4°

Then the polar coordinates are:

(13, -67.4°)

Answer:

4 months

Step-by-step explanation:

Answer:

4 months

Step-by-step explanation:

Using trigonometric ratio, the value of x is 63.6°

This is the ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

Trigonometric ratio are often coined as SOHCAHTOA

In the given triangle, we need to find the value of x using trigonomtric ratio.

Since we have the value of adjacent and hypothenuse, we definitely need to use cosine

cosθ = adjacent / hypothenuse

adjacent = 4

hypothenuse = 9

Substituting the values into the equation;

cos θ = 4 / 9

cos θ = 0.444

θ = cos⁻¹ 0.4444

θ = 63.6°

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Answer:5 and 3

Step-by-step explanation: They are tho samples bc they are the ones tht are duplicated (x2)

Answer:

f(n)=75+(n*3)

Step-by-step explanation:

1.) Probability of getting 1: 0.12 or 12%.

2.) Probability of getting 2: 0.16 or 16%.

3.) Probability of getting 3: 0.25 or 25%.

4.) Probability of getting 4: 0.18 or 18%.

5.) Probability of getting 5: 0.15 or 15%.

6.) Probability of getting 6: 0.14 or 14%.

To calculate the probability of getting a specific number on a fair die, we divide the number of times that number appears by the total number of rolls. In this case, the die was rolled 100 times, and the results are given as follows:

Number: 1 2 3 4 5 6

Times: 12 16 25 18 15 14

To find the probability of getting each number, we divide the corresponding number of times by the total number of rolls (100):

Probability of getting 1 = 12 / 100 = 0.12.

Probability of getting 2 = 16 / 100 = 0.16.

Probability of getting 3 = 25 / 100 = 0.25.

Probability of getting 4 = 18 / 100 = 0.18.

Probability of getting 5 = 15 / 100 = 0.15.

Probability of getting 6 = 14 / 100 = 0.14.

Therefore, the probabilities of getting each number on a fair die, based on the given results of 100 rolls, are approximately:

1: 0.12 or 12%,

2: 0.16 or 16%,

3: 0.25 or 25%,

4: 0.18 or 18%,

5: 0.15 or 15%,

6: 0.14 or 14%.

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Answer:

r=-12 (R equals negative 12)

Step-by-step explanation:

r/6=-2

r=-2*6

r=-12

Answer:

  $6.47 for each shirt

Step-by-step explanation:

If s is the cost of a shirt, then the cost of 5 shirts is ...

  5s = $32.35

  s = $32.35/5 = $6.47 . . . . . divide both sides of the equation by 5

The cost of each shirt was $6.47.

_____

Additional comment

The equation formalizes the math for you, perhaps helping you see that division by 5 is required.

To find cost per shirt, divide cost by shirts. "Per" can often be thought of as meaning "divided by."