20 points!! please help!!

The experimental probability that the next train to arrive at Danville Station will be on time is 3/4 or 0.75.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

The experimental probability of the next train to arrive at Danville Station being on time is given by the number of on-time trains divided by the total number of trains that arrived -

experimental probability = number of on-time trains / total number of trains

From the information given, we know that out of the last 20 trains to arrive, 15 were on time. Therefore -

number of on-time trains = 15

total number of trains = 20

Substituting these values into the equation, we get -

experimental probability = 15 / 20

Simplifying the fraction, we get -

experimental probability = 3/4

Therefore, the experimental probability value is obtained to be 3/4 or 0.75.

To learn more about probability from the given link

https://brainly.com/question/23286309

#SPJ1

Answer:

24x - 6y + 21

Step-by-step explanation:

3( 8x - 2y + 7 )

Multiply each term in the bracket by 3

= (3 x 8x) - ( 3 x 2y) + (3 x 7)

= 24x - 6y + 21

It switches between negative and positive every 40 seconds.  it switches between positive and negative every 80 seconds. So correct statements are B and E.

Mathematics' branch of algebra deals with symbols and the formulas used to manipulate them. It is an effective tool for dealing with issues involving mathematical expressions and equations. In algebra, variables—which are typically represented by letters—are used to represent unknowable or variable quantities.

Equations represent mathematical relationships between variables in algebra. An equation is made up of two expressions, one on either side of an equal sign, separated by an equation. Algebraic expressions can involve constants, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

As we can see from the first roller coaster's graph, Michael's height changes from positive to negative after 40 seconds, whereas it was positive for the first 40. It remains negative between 40 and 80 seconds. It continues to be positive from 80 to 120, and so forth.

As a result, every 40 seconds it alternates between negative and positive.

B is accurate.

We can see from the second roller coaster's table that it stays positive from 0 to 80. It continues to be negative from 80 to 160, and so forth.

As a result, every 80 seconds it alternates between positive and negative.

E is accurate.

The complete question is:

To know more about height visit:

https://brainly.com/question/17045372

#SPJ1

The length of each leg of an isosceles right triangle with a hypotenuse of 12 inches is approximately 8.49 inches.

In an isosceles right triangle, the two legs are congruent, so let's call the length of each leg "x". Then, using the Pythagorean theorem, we can write:

[tex]x^2 + x^2 = 12^2[/tex]

Simplifying the left side, we get:

[tex]2x^2 = 144[/tex]

Dividing both sides by 2, we get:

[tex]x^2 = 72[/tex]

Taking the square root of both sides, we get:

x = sqrt(72)

We can simplify this by factoring 72 as 36 * 2:

x = sqrt(36 * 2)

Taking the square root of 36, we get:

x = 6 * sqrt(2)

So each leg of the isosceles right triangle is approximately 8.49 inches long (rounded to two decimal places).

To learn more about isosceles please click on below link        

https://brainly.com/question/9872652

#SPJ1

The hypotenuse of an isosceles right triangle is 12 inches. What is the length of each leg?

The mode for the region A is 2.6.

What exactly is mode?

In statistics, the mode is the value that has highest frequency in a data set. It is one of the three measures of central tendency, along with the mean and median.

To find the mode of a data set, you simply identify the value that appears most often. If no value is repeated, the data set has no mode.

The mode is particularly useful when dealing with categorical data or data that can be easily grouped into categories, such as colors, types of fruit, or letter grades. In such cases, the mode can provide insight into which category is most common or prevalent.

Now,

As given Values for Region A are

2.3  2.5  2.6  2.6  2.6  2.7  2.7  2.8

Here 2.6 comes most times or frequency of 2.6 is highest of all.

Hence,

           The mode for the region A is 2.6.

To know more about Mode visit the link

https://brainly.com/question/30891252

#SPJ1

Answer:

$27

Step-by-step explanation:

$400 earns $6

$6÷$400= 0.015% interest

$1800 * 0.015% = $27

After answering the prοvided questiοn, we can cοnclude that Sο, we can  equatiοn chοοse values οf a and b such that Cοv(X¯, μ) < (1 − a)/2 σ/n and MSE(θˆ) > MSE(θ), like a = 0.9 and b = 0.5.

An equatiοn in mathematics is a prοcedure that affects the equaIity οf equatiοns. Twο sides οf an equatiοn are cοnnected by the algebraic οperatοr (=). Fοr instance, the claim "2x + 3 = 9" asserts that the cοmment "2x + 3" means the value "9" in tοtal. The gοal οf sοlving equatiοns is tο identify the factοr(s) that will cause the equatiοn tο be true.

Equatiοns may be straightfοrward οr cοmplex, cοnstant οr nοn-linear, and cοntain οne οr mοre variables. Examples include raising the variable x tο the pοwer οf 2 in the equatiοn "x² + 2x - 3 = 0," fοr example. In mathematics, particularly in algebra, equatiοns, and geοmetry, lines are frequently used.

MSE(θˆ) = E[(θˆ − θ)²]

= E[((X1 + · · · + Xn)/n − μ²)²]

= E[((X1 − μ) + · · · + (Xn − μ))/n]²

= V[(X1 − μ)/n + · · · + (Xn − μ)/n]

= V[(X1 − μ)/n] + · · · + V[(Xn − μ)/n] (since the Xi's are independent)

Thus, MSE(θˆ) = σ²/n

b. Fοr MSE(θˆ) < MSE(θ), we want:

We can see that this is satisfied fοr any value οf a such that 0 < a < 1.

c. Fοr MSE(θˆ) > MSE(θ), we want:

σ/n > V[(1 − a)X¯ + aμ] = (1 − a)²Var(X¯) + aVar(μ) + 2a(1 − a)Cοv(X¯, μ)

σ²/n > (1 − a)(σ²/n) + 2a(1 − a)Cοv(X¯, μ)

Cοv(X¯, μ) < (1 − a)/2 σ²/n

Sο, we can chοοse values οf a and b such that Cοv(X¯, μ) < (1 − a)/2 σ/n and MSE(θˆ) > MSE(θ), such as a = 0.9 and b = 0.5.

Learn more about equatiοn

https://brainly.com/question/29273511

#SPJ1

Approximately 60.68% of callers are on hold between 2.6 and 3.9 minutes.

What Is a Normal Distribution?

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

First, we standardize the value of 2.6 as follows:

z = (x - μ) / σ

where x is the value of 2.6, μ is the mean of 3.7 minutes, and σ is the standard deviation of 0.6 minutes:

z = (2.6 - 3.7) / 0.6 ≈ -1.83

z = (x - μ) / σ

where x is the value of 3.9, μ is the mean of 3.7 minutes, and σ is the standard deviation of 0.6 minutes:

z = (3.9 - 3.7) / 0.6 ≈ 0.33

We can use a standard normal distribution table or a calculator to find this area. Using a calculator, we can find the area as follows:

P(-1.83 < Z < 0.33) ≈ 0.6068

Therefore, approximately 60.68% of callers are on hold between 2.6 and 3.9 minutes.

To know more about Normal Distribution visit,

https://brainly.com/question/4079902

#SPJ1

Approximately 60.68% of callers are on hold between 2.6 and 3.9 minutes.

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

First, we standardize the value of 2.6 as follows:

z = (x - μ) / σ

where x is the value of 2.6, μ is the mean of 3.7 minutes, and σ is the standard deviation of 0.6 minutes:

z = (2.6 - 3.7) / 0.6 ≈ -1.83

z = (x - μ) / σ

where x is the value of 3.9, μ is the mean of 3.7 minutes, and σ is the standard deviation of 0.6 minutes:

z = (3.9 - 3.7) / 0.6 ≈ 0.33

We can use a standard normal distribution table or a calculator to find this area. Using a calculator, we can find the area as follows:

P(-1.83 < Z < 0.33) ≈ 0.6068

Therefore, approximately 60.68% of callers are on hold between 2.6 and 3.9 minutes.

To know more about Normal Distribution visit

brainly.com/question/4079902

#SPJ9

Answer:

a. Since the half-life of the isotope is 8 hours, we know that the decay rate is exponential and we can use the formula:

A(t) = A0 * (1/2)^(t/8)

where A0 is the initial amount of the substance, t is the time elapsed, and A(t) is the amount of substance remaining after t hours.

Substituting the given values, we get:

A(t) = 7 * (1/2)^(t/8)

b. To find the rate at which the substance is decaying, we need to take the derivative of A(t) with respect to t:

A'(t) = -7/8 * (1/2)^(t/8) * ln(1/2)

Simplifying, we get:

A'(t) = -ln(2) * (7/8) * (1/2)^(t/8)

c. To find the rate of decay at 14 hours, we can plug in t=14 into the equation we found in part b:

A'(14) = -ln(2) * (7/8) * (1/2)^(14/8) ≈ -0.4346 grams per hour (rounded to four decimal places)

In response to the stated question, we may state that As a result, the cylindrical container can carry around 196.35 cm3 of water. As a result, (a) 196.35 cm cubic is the right answer.

A cylinder seems to be a three-dimensional geometric shape made up of two parallel congruent circular bottoms and a curving surface linking the two bases. The bases of a cylinder are always perpendicular from its axis, which is an artificial straight line passing through the centre both of bases. The volume of a cylinder is equal to the product among its base area and height. A cylinder's volume is computed as V = r2h, within which "V" represents the volume, "r" represent the circle of the base, and "h" represents the height of the cylinder.

The volume of a cylinder is determined by the formula V = r2h, where r is the radius of the base, h is the cylinder's height, and is a mathematical constant close to 3.14.

In this situation, the radius is 2.5 cm since the base is 5 cm in diameter. The cylinder stands 10 cm tall. As a result, the volume of the cylinder is:

[tex]V = \pi(2.5 cm)^2(10 cm) (10 cm)\\V = 196.35 cm^3[/tex]

As a result, the cylindrical container can carry around 196.35 cm3 of water. As a result, (a) 196.35 cm cubic is the right answer.

To know more about cylinder visit:

https://brainly.com/question/16134180

#SPJ1

Answer:

we will do TanA = perpendicular / Base

A = 35°

Tan 35° = 217 / W

value of Tan 35° is approx = 0.7

0.7 = 217/ W

W = 217 / 0.7

W = 310

The probability that the cupcake picked at random contains walnuts is given as follows:

0.4 = 40%.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

There are 30 cupcakes in a tin, hence the total number of outcomes is given as follows:

30.

The number of cupcakes with walnuts is given as follows:

Hence the probability that the cupcake picked at random contains walnuts is obtained as follows:

p = (3 + 9)/30

p = 12/30

p = 0.4.

More can be learned about probability at https://brainly.com/question/24756209

#SPJ1

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

7xy+3x+3y−3

The width of the soccer field in the drawing is 116 inches if the ratio is 2 inches to 1 yard

If 2 inches on the drawing represents 1 yard in reality, then 1 inch on the drawing represents 1/2 yard in reality.

So, to find the width of the soccer field in the drawing, we can use the following proportion:

1 inch on drawing / (1/2) yard in reality = x inches on drawing / 58 yards in reality

Simplifying this proportion, we get:

x inches on drawing = (1 inch on drawing / (1/2) yard in reality) * 58 yards in reality

x inches on drawing = 2 * 58

x inches on drawing = 116

Therefore, the width of the soccer field in the drawing is 116 inches.

Read more about scale drawing at

https://brainly.com/question/29229124

#SPJ1

Answer:

C) Pi

Step-by-step explanation:

Pi is an irrational number, it cannot be written down as non-infinite decimal, basically meaning that in order for it to be a rational number you need an approximate value for Pi.

according the given question the exact value of given expression is [tex]$\cos\frac{x}{2} = -\sqrt{\frac{1}{2(1 - \left(-\frac{160}{81}\right)^2)}} = -\sqrt{\frac{81^2}{2(81^2 - 160^2)}} = \boxed{-\frac{81\sqrt{239}}{319}}$[/tex]

First, we need to find [tex]$\sin x$[/tex] using the identity[tex]$\cos^2x + \sin^2x = 1$:$\sin^2x = 1 - \cos^2x = 1 - \left(-\frac{4}{5}\right)^2 = \frac{9}{25}$[/tex]

Since  [tex]$\frac{\pi}{2} < x < \pi$[/tex], we know that  [tex]$\frac{\pi}{4} < \frac{x}{2} < \frac{\pi}{2}$[/tex]. Therefore, we can use the

identity [tex]$\tan\frac{x}{2} = \frac{\sin x}{1 + \cos x}$[/tex]:

[tex]$\tan\frac{x}{2} = \frac{\sqrt{\frac{9}{25}}}{1 - \frac{4}{5}} = \frac{\frac{3}{5}}{\frac{1}{5}} = \boxed{3}$[/tex]

[tex]If $\tan x = \frac{40}{9}$ and $\pi < x < \frac{3\pi}{2}$, find $\cos\frac{x}{2}$.[/tex]

First, we need to find [tex]$\sin x$[/tex] using the identity [tex]$\tan^2x + 1 = \sec^2x$[/tex]:

[tex]$\sin x = \frac{\tan x}{\sec x} = \frac{\frac{40}{9}}{-\frac{9}{40}} = -\frac{160}{81}$[/tex]

[tex]Since $\pi < x < \frac{3\pi}{2}$, we know that $\frac{\pi}{2} < \frac{x}{2} < \frac{3\pi}{4}$[/tex]. Therefore, we can use the identity [tex]$\cos\frac{x}{2} = \pm\sqrt{\frac{1 + \cos x}{2}}$[/tex]:

[tex]$\cos\frac{x}{2} = -\sqrt{\frac{1 + \cos x}{2}} = -\sqrt{\frac{1 + \frac{\cos^2x}{\sin^2x}}{2}} = -\sqrt{\frac{\sin^2x + \cos^2x}{2\sin^2x}} = -\sqrt{\frac{1}{2(1 - \sin^2x)}}$[/tex]

Plugging in [tex]$\sin x = -\frac{160}{81}$[/tex] , we get:

[tex]$\cos\frac{x}{2} = -\sqrt{\frac{1}{2(1 - \left(-\frac{160}{81}\right)^2)}} = -\sqrt{\frac{81^2}{2(81^2 - 160^2)}} = \boxed{-\frac{81\sqrt{239}}{319}}$[/tex]

To know more about problems related to expression , click here:

https://brainly.com/question/16804733

#SPJ1

Answer:

Step-by-step explanation:

To calculate the probability of a person driving while intoxicated or having a car accident, we need to use the formula for the union of events:

P(A or B) = P(A) + P(B) - P(A and B)

where A and B are the events of driving while intoxicated and having a car accident, respectively.

Using the probabilities given in the problem, we can calculate:

P(intoxicated) = 0.32

P(accident) = 0.09

P(accident | intoxicated) = 0.15

To find P(intoxicated or accident), we first need to find P(intoxicated and accident). We can use the formula for the conditional probability as follows:

P(intoxicated and accident) = P(accident | intoxicated) x P(intoxicated)

P(intoxicated and accident) = 0.15 x 0.32 = 0.048

Now we can use the formula for the union of events:

P(intoxicated or accident) = P(intoxicated) + P(accident) - P(intoxicated and accident)

P(intoxicated or accident) = 0.32 + 0.09 - 0.048

P(intoxicated or accident) = 0.362

Therefore, the probability of a person driving while intoxicated or having a car accident is 0.362, or approximately 36.2%.

Answer:

[tex]k = - 3[/tex]

Step-by-step explanation:

[tex]y = kx[/tex]

[tex]k \times ( - 1) = 3[/tex]

[tex] - k = 3[/tex]

[tex]k = - 3[/tex]

Answer:

[tex]k = -3[/tex]

Step-by-step explanation:

Step 1: Substitute

To solve this problem you are going to need to substitute the values of y and x into the problem y=kx.  Which would give you the problem of 3=-1k or 3 = -k to make things easier.

Step 2: Using properties of equality

In order to isolate the value of k you would need to divide both sides by -1 because division cancels out multiplication. You would get [tex]\frac{3}{-1} = \frac{-k}{-1}[/tex] or [tex]-3 = k[/tex]

Step 3: Check

In order to check this problem you would need to insert the values back into the original equation and solve. So that would be 3= -1*-3 which does equal 3. So the answer is correct

Answer:

(x - 2)(4x + 1)

According to the solving the area of the sidewalk is 138.16 square meters.

Size of a location on a surface is expressed in terms of area. As opposed to surface area, which refers to the area of an open surface or the border of a three-dimensional object, plane region or plane size refers to the area of a shape or planar lamina.

The width of the circular sidewalk is 2 m, which means that the radius of the entire area, including the flower bed and the sidewalk, is 10 m + 2 m = 12 m.

To find the area of the sidewalk, we need to subtract the area of the flower bed from the area of the larger circle.

Area of larger circle = πr²

= 3.14 x 12²

= 452.16 square meters (rounded to two decimal places)

Area of flower bed = πr²

= 3.14 x 10²

= 314 square meters

Area of the sidewalk = Area of larger circle - Area of flower bed

= 452.16 - 314

= 138.16 square meters (rounded to two decimal places)

Therefore, the area of the sidewalk is 138.16 square meters.

To know more about area visit:

https://brainly.com/question/27683633

#SPJ9

The probability of waiting between 2 and 3 minutes to use the ABC Ban ATM machine is 1/4 or 0.25, which means that approximately 25% of the time a customer has to wait between 2 and 3 minutes to use the ATM.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a numerical value between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to occur. For example, the probability of flipping a fair coin and getting heads is 1/2 or 0.5.

Since the waiting time for the ABC Ban ATM machine is uniformly distributed between 1 and 5 minutes, the probability density function is given by:

f(x) = 1/(5-1) = 1/4 for 1 ≤ x ≤ 5

To find the probability of waiting between 2 and 3 minutes, we need to find the area under the probability density function between 2 and 3. This is given by the definite integral of the probability density function over the interval [2, 3]:

P(2 ≤ x ≤ 3) = ∫2^3 f(x) dx

= ∫2^3 (1/4) dx

= (1/4) [x]2^3

= (1/4) (3-2)

= 1/4

Therefore, the probability of waiting between 2 and 3 minutes to use the ABC Ban ATM machine is 1/4 or 0.25, which means that approximately 25% of the time a customer has to wait between 2 and 3 minutes to use the ATM.

To know more about probability and given link below -

https://brainly.com/question/30034780

#SPJ1

Answer:

0.62 to 1

Step-by-step explanation:

62/100

Divide the numerator and denominator by 100.

62/100 = 0.62/1

The ratio is 0.62 to 1.

Answer:

Step-by-step explanation:

1 mile is equal to 1.60934 km

1km is equal to 0.621371 mile

Answer:

Step-by-step explanation:

Let x be the cost per pound of the cinnamon tea and y be the cost per pound of the spice tea.

From the first mixture, we have:

12x + 3y = 39

From the second mixture, we have:

16x + 6y = 58

We can solve this system of equations by elimination. Multiplying the first equation by 2 and subtracting it from the second equation gives:

16x + 6y = 58

(24x + 6y = 78)

-8x = -20

Dividing both sides by -8 gives:

x = 2.5

Substituting this value of x into the first equation, we get:

12(2.5) + 3y = 39

Simplifying, we get:

30 + 3y = 39

Subtracting 30 from both sides gives:

3y = 9

Dividing both sides by 3 gives:

y = 3

Therefore, the cost per pound of the cinnamon tea is $2.50 and the cost per pound of the spice tea is $3.

Answer: 46

Step-by-step explanation: i took quiz i swear the answer is

Answer:

9 seconds

Step-by-step explanation:

right side of the graph touches the x axis at 9

Comparing the numerator 9 < 15 thus, 9/10 is less than 3/2.

A multiple of the denominators of two or more fractions can be used as a common denominator to add, subtract, or compare the fractions. As fractions with dissimilar denominators cannot be added together or directly compared, they must be changed into comparable fractions with the same denominator. We must determine the least common multiple (LCM) of the fraction denominators in order to determine a common denominator. The lowest number that is a multiple of both denominators is known as the LCM. Once we have the common denominator, we may multiply the numerator and denominator by the same factor to change each fraction to an equal fraction with the same denominator.

The two values are 9/10 and 3/2.

Taking the LCM we have:

9/ 10 and 15/10

Now comparing the numerator 9 < 15 thus, 9/10 is less than 3/2.

Learn more about common denominator here:

https://brainly.com/question/29208201

#SPJ1

On number line we can compare 9/10 and 3/2 as 9/10 < 3/2.

What is number line?

A number line is a visual representation of numbers in order, usually shown horizontally. It is a line with a starting point and an endpoint that represent the smallest and largest numbers, respectively.

To compare 9/10 and 3/2 on a number line, we need to first convert them to the same denominator. The least common multiple of 10 and 2 is 10, so we can convert 3/2 to 15/10:

9/10 = 0.9

3/2 = 15/10 = 1.5

Now, we can plot these two numbers on a number line:

We can see that 9/10 is to the left of 3/2 on the number line.

Therefore we can compare 9/10 and 3/2 as 9/10 < 3/2.

To learn more about number line visit:

https://brainly.com/question/24644930

#SPJ1

The distance of the satellite from station A is approximately 47 miles

The satellite is approximately 911 miles above ground

Let the distance from station A to the satellite be a and the distance from the station B to the satellite be a + 48

Using trigonometry

tan 87 degrees = height of the satellite above the ground, h / a

tan 87 degrees = h / a

h = a * tan 87

while

tan 84 degrees = h / a + 48

h = (a + 48) tan 84

substituting for h

a * tan 87 = (a + 48) tan 84

a (tan 87 - tan 84) = 48 tan 84

a (9.567) = 48 tan 84

a = 48 tan 84 / 9.567

a = 47.436

The distance of the satellite from station A is approximately 47 miles

The height above ground

h = a * tan 87

h = 47.436 * tan 87

h = 910.857 miles

Learn more about angle of elevation at:

https://brainly.com/question/88158

#SPJ1

Answer:

It will be same as angle x because they are on the same line and are alternative angles

So, measurement of angle u will be u=152

Step-by-step explanation:

Hope this helps:)

Good luck

Answer:

150 cubic inches.

Step-by-step explanation:

the volume of a prism = cross-section area* length

                                    = 1/2*4*5*15

                                    = 150 cubic inches.

Answer:

The answer is 300 inches

Step-by-step explanation:

15*4*5