The planet Mercury orbits around the sun at 29.74 miles per second. How many miles will mercury travel in 1 minute?

In this exercise we have to use the knowledge of probability to calculate if the treated events are independent:

The  events A,B, C are not independent.

Using the information given in the text, we can identify that:

Using the probability formula we find that:

P (A ∩ B ∩ C) = P (A) P(B) P(C)  

1/365≠ 1/365 * 1/365 * 1/365

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Answer:

The answer is the triangle that has points (0, 400) and (16,0)

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Final answer:

Jessie received a 25% discount on the t-shirt, which is calculated by subtracting the sale price from the original price and then finding the discount percentage.

Explanation:

To find the discount Jessie received on the t-shirt, we need to subtract the sale price from the original price. The original price of the t-shirt was $8, and Jessie bought it for $6. The discount can be calculated as follows:

Determine the difference between the original price and the sale price: $8 - $6 = $2.

Calculate the discount percentage: ($2 $8) 100 = 25%.

Therefore, Jessie received a 25% discount on the t-shirt.

Answer: slope = -1,5

Step-by-step explanation:

We can use slope formula to find the slope of a line that passes through two points (x₁ , y₁) and (x₂ , y₂)

m = ∆y/∆x = (y₂ - y₁)/(x₂ - x₁)

Given points are: p(x₁ , y₁) = (5 , −9) and q(x₂ , y₂) = (−5 , 6)

Substituting these two known points in the slope formula, we have:

m = (6-(-9))/(-5-5) = 15/-10 = -1,5

Therefore, the slope of this line = -1,5  

Answer: slope = -1,5

The number of outcomes in the sample space is 32. There are 16 outcomes for drawing an even number, 12 outcomes for drawing a number more than 2 and a red card, and 30 outcomes for drawing a number less than 3 or not drawing a club.

To determine the number of outcomes in the sample space for the described experiment, one can use the fundamental counting principle. In this case, there are 8 possible marbles that can be drawn and 4 possible suits from a card in a standard deck. So, the total number of outcomes in the sample space is the product of these possibilities, which is 8 marbles × 4 suits = 32 outcomes.

The event "an even number is drawn" corresponds to drawing one of the even-numbered marbles (2, 4, 6, or 8) and any of the 4 suits from the deck. There are 4 even-numbered marbles and 4 suits, resulting in 4 marbles × 4 suits = 16 possible outcomes.

For the event "a number more than 2 is drawn and a red card is drawn," we consider only marbles numbered 3 to 8 (6 possibilities) and the 2 red suits (hearts and diamonds) from the deck, resulting in 6 marbles × 2 red suits = 12 outcomes.

Finally, the event "a number less than 3 is drawn or a club is not drawn" includes two scenarios. The first is drawing marble number 1 or 2 (2 possibilities) and any of the 4 suits (8 outcomes). The second scenario includes drawing any of the 8 marbles and any of the 3 non-club suits (24 outcomes). Since the two scenarios are mutually exclusive, you add the outcomes: 8 + 24 = 32 outcomes. However, you must subtract the overlapping outcomes of drawing 1 or 2 with non-club suits (2 outcomes), resulting in 32 - 2 = 30 distinct possible outcomes for this event.

The stock market changed by a net -70.25 points from the high to the end of the day, calculated by subtracting the decrease of 100 3/4 points from the initial increase of [tex]30\frac{1}{2}[/tex] points.

To calculate the net change in the stock market from the high to the end of the day, you subtract the amount the market went down from the amount it went up initially. First, convert the mixed numbers to improper fractions. 30 1/2 points is equal to (30 * 2) + 1 = 61/2 points, and 100 3/4 points is equal to (100 * 4) + 3 = 403/4 points.

Next, to find the change, you subtract the decrease from the initial increase:

61/2 - 403/4 = (61 * 4) / (2 * 4) - (403 * 2) / (4 * 2)

= 244/8 - 806/8

= (244 - 806) / 8

= -562/8

Finally, simplify the fraction:

= -70.25

So, the stock market changed by a net -70.25 points from the high to the end of the day. This means the market ended lower by 70.25 points from its highest point that day.

Answer:  The correct option is (c) [tex]\dfrac{4}{3}.[/tex]

Step-by-step explanation:  We are to select the correct value that is equivalent to the following expression :

[tex]E=\log_8{16}.[/tex]

We will be using the following logarithmic properties :

[tex](i)~\log a^b=b\log a,\\\\(ii)~\log_ab=\dfrac{\log b}{\log a}.[/tex]

So, the given expression becomes

[tex]E\\\\=\log_8{16}\\\\\\=\dfrac{\log16}{\log8}\\\\\\=\dfrac{\log2^4}{\log2^3}\\\\\\=\dfrac{4\log2}{3\log2}\\\\\\=\dfrac{4}{3}.[/tex]

Thus, the required value is [tex]\dfrac{4}{3}.[/tex]

Option (c) is CORRECT.

The linearized equation is y = a * ln(x) + b, where a and b are the parameters determined through linear regression. After performing the regression analysis, the values obtained for a and b are a = 2.5 and b = 1.8. Thus, at x = 1.6, the predicted value of y is approximately y = 4.09.

To linearize the equation, we transform it by taking the natural logarithm of both sides: ln(y) = a * ln(x) + b. This transformation allows us to apply linear regression, converting the non-linear equation into a linear form y = mx + c, where y = ln(y), x = ln(x), m = a, and c = b.

By conducting linear regression on the transformed data points (ln(x), ln(y)), we determine the parameters a and b. Using the regression analysis, we find a = 2.5 and b = 1.8. These values represent the slope and intercept of the linearized equation, y = 2.5 * ln(x) + 1.8.

Now, to predict y at x = 1.6, we substitute this value into the linearized equation: y = 2.5 * ln(1.6) + 1.8. After calculations, the predicted value of y at x = 1.6 is approximately y = 4.09.

The linearization process helps in fitting a linear model to non-linear data, making it feasible to apply linear regression techniques. By transforming the equation using logarithms, we simplified it to a linear form. The determined parameters a and b through regression analysis enabled us to predict y at the specified x value, facilitating the estimation of y in a non-linear scenario.

Answer:

-22.7

Step-by-step explanation:

Since the temperature fell, that would means that it's was cooler outside.

Hotter = Temperature goes up

Colder = Temperature goes down

15.7 - 38.4 = -22.7

Answer:

-22.7

Step-by-step explanation:

did the test

The formula for the volume of a cone is ...

... V = (1/3)πr²h = (1/3)π(d/2)²h = (π/12)d²h

for height h and diameter d.

Then the volume of the cone is ...

... V = (π/12)·(2 in)²·(4 in) = 4π/3 in³ ≈ 4.189 in³

___

The formula for the volume of a cylinder is ...

... V = πr²h = π(d/2)²h = (π/4)d²h

Then the volume of the cylinder is ...

... V = (π/4)·(2 in)²·(6 in) = 6π in³ ≈ 18.850 in³

_____

The difference in volume is ...

... 18.850 in³ - 4.189 in³ = 14.661 in³ ≈ 14.7 in³

By calculating the distance an athlete covers per minute (1/6 km), we can multiply by 60 to determine they can run 10 kilometers in an hour.

If a long-distance athlete can run 1/2 kilometer in 3 minutes, we first want to find out how many kilometers they can run in one minute, and then use that to calculate how many kilometers they can run in an hour (60 minutes).

Firstly, calculate the distance covered per minute:

Therefore, the athlete can run 10 kilometers in one hour.

The probability that at least 10% of the boards are defective can be approximated using a normal distribution, while the exact probability of having 10 defectives in the batch can be calculated using the binomial formula. For large samples, normal approximation can be used for convenience.

To find the probability that at least 10% of the boards are defective, we can use the binomial distribution since each board's condition is independent of the other boards. The formula for binomial probability is P(X = k) = (n choose k) * pk * (1-p)(n-k), where n is the number of trials, p is the probability of success on each trial, and k is the number of successes. However, for large sample sizes and when the sample proportion is close to the population proportion, we can approximate the binomial distribution with a normal distribution.

To use the normal approximation, we calculate the mean and standard deviation with the formulas μ = n * p and σ = √(n * p * (1-p)). For the batch of 250 boards with 5% defective rate, μ = 250 * 0.05 = 12.5 and σ = √(250 * 0.05 * 0.95) ≈ 3.4641. We then convert the problem into a z-score and use standard normal distribution tables or software to find the probability that Z > (25 - 12.5)/3.4641.

To find the exact probability of having exactly 10 defectives in the batch, we use the binomial formula since the normal approximation is less accurate for exact probabilities. The calculation would be P(X = 10) = (250 choose 10) * 0.0510 * 0.95240.

Final answer:

To find the base and height of the triangle with an area of 75 square inches and the base exceeding the height by 5 inches, we set up a quadratic equation from the area formula A = (bh)/2. The height is found to be 10 inches and the base 15 inches after solving the quadratic equation.

Explanation:

To solve for the base and height of a triangle given the area, we can use the formula for the area of a triangle which is A = (bh)/2, where A is the area, b is the base and h is the height. Here, the question states that the base exceeds the height by 5 inches and the area is 75 square inches. Let's define h as the height and then the base will be h + 5. Substituting the given values into the area formula, we get:

75 = (h + 5)h/2

By multiplying both sides by 2 to eliminate the fraction, we get:

150 = h(h + 5)

This expands to a quadratic equation:

h² + 5h - 150 = 0

Solving for h using the quadratic formula, the positive solution is the height of the triangle:

h = (-5 + √(5² + 4·150))/2

h = (-5 + √625)/2

h = (-5 + 25)/2

h = 20/2

h = 10 inches. Therefore, the base is:

b = 10 + 5

b = 15 inches.

The height of the triangle is 10 inches, and the base is 15 inches.

It will take approximately 286.8 years for half of the initial amount (900 grams) to decay.

To find the time it takes for half of the initial amount to decay, we need to find the value of t when D(t) is half of the initial amount (900 grams).

Half of the initial amount = 900 grams / 2 = 450 grams

Now, set D(t) equal to 450 and solve for t:

[tex]450 = 900 * e^{-0.002415 * t}[/tex]

Divide both sides by 900:

[tex]e^{-0.002415 * t} = 0.5[/tex]

To find t, take the natural logarithm (ln) of both sides:

[tex]ln(e^{-0.002415 * t}) = ln(0.5)[/tex]

Now, use the property that [tex]ln(e^x) = x:[/tex]

-0.002415 * t = ln(0.5)

Now, solve for t:

t = ln(0.5) / -0.002415

Using a calculator, we get:

t ≈ 286.8 years

So, it will take approximately 286.8 years for half of the initial amount (900 grams) to decay.

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