Andre is running in an 80-meter hurdle race. There are 8 equally-space hurdles on the race track. The first hurdle is 12 meters from start line and the last hurdle is 15.5 meters from the finish line Estimate how far the hurdles are from one another. Explain your reasoning ​

Answer:

x=0

Step-by-step explanation:

(1): "^-2" was replaced by "^(-2)".

rearrange the equation: x/81^(-2)/729^1-x-(9^2*x)=0

STEP

1

:

1.1 9 = 32

(9)2 = (32)2 = 34

Equation at the end of step

1

:

x

(—————— ÷ (7291)-x)-(34•x) = 0

(81-2)

STEP

2

:

2.1 729 = 36

(729)1 = (36)1 = 36

Equation at the end of step

2

:

x

(—————— ÷ 36 - x) - 34x = 0

(81-2)

STEP

3

:

3.1 81 = 34

(81)-2 = (34)(-2) = (3)(-8)

Equation at the end of step

3

:

x

(——————— ÷ 36 - x) - 34x = 0

(3)(-8)

STEP

4

:

1

Divide x by ——

38

Equation at the end of step

4

:

38x

(——— - x) - 34x = 0

36

STEP

5

:

38x

Simplify ———

36

Dividing exponents:

5.1 38 divided by 36 = 3(8 - 6) = 32

Equation at the end of step

5

:

(9x - x) - 34x = 0

STEP

6

:

Equation at the end of step 6

-73x = 0

STEP

7

:

Solving a Single Variable Equation:

7.1 Solve : -73x = 0

Multiply both sides of the equation by (-1) : 73x = 0

Divide both sides of the equation by 73:

x = 0

One solution was found :

x=0

Answer: B. XIX

Step-by-step explanation: If Sarah is 3 years older than Ben, she is 3 years older than 16. That means she is 19 years old. In Roman numerals, we need to think of it as she is 10+9 years old.

X represents 10.

IX represents 9 Because...

... in order to represent a number less than ten, we need to think about how much less than ten it is. Since 9 is one less than 10, you write it as IX since a smaller numeral in front of X represents subtraction.

So you combine the 10 and 9 to get XIX.

Complete Question

A recipe needs 1/2 cup of sugar. Mary plans to make 7 batches of the recipe. How many cups of sugar will Mary needs A: 7 1/2 B: 3 1/2 C:2 1/3 D: 5 1/2 PLZ ANSWER PLS!

Answer:

B: 3 1/2

Step-by-step explanation:

From the Question,

Recipe = 1 batch

1 batch of recipe = 1/2 cup of sugar

7 batches of recipe = x

Cross Multiply

x = 1/2 cup of sugar × 7 batches of recipe/1 batch of recipe

x = 7/2

x = 3 1/2 cups of sugar.

Option B is the correct answer.

Answer:

D {36,47,60}

Step-by-step explanation:

it would have to be {37,48,60} for it to be a right triangle

hope this helps you out

Answer:

7

Step-by-step explanation:

The gradient of a line is a measure of how steep the line is. It is calculated as the change in the y-value (the "rise") divided by the change in the x-value (the "run").

In the equation y = 7x + 8, the coefficient of x (7) is the gradient of the line. This means that for every 1 unit change in the x-value, the y-value changes by 7 units.

So the gradient of the line y = 7x + 8 is 7.

The value of n is calculated as -14 which was found using the slope formula and given data.

When coordinates are provided, the following formulae can be used to determine a line's slope:

Step 1: Determine the line's coordinates.

Step 2: Enter their values into the equation slope(m) = (y₂-y₁)/(x₂-x₁).

Given: There is a line that contains the points (-9, n) (-10, 5).

We need to find the value of n.

We know that,

slope(m) = (y₂-y₁)/(x₂-x₁)

           -9   = (5-n)/(-10+9)

           -9(-10+9) = 5-n

           90-81 = 5-n

           9+5 = -n

              n = -14

Therefore, the value of n is -14 which was found using the slope formula and given data.

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the maximum height of a quadratic equation can be find Use the formula: x = -b / (2a) then Substitute the value of x back into the quadratic equation to find the corresponding maximum height.

To find the maximum height of a quadratic equation, you need to determine the vertex of the parabolic curve. The vertex represents the highest or lowest point of the quadratic function, depending on whether it opens upward or downward.

A quadratic equation is generally written in the form of y = ax² + bx + c, where "a," "b," and "c" are coefficients.

The x-coordinate of the vertex can be found using the formula: x = -b / (2a). This formula gives you the line of symmetry of the parabola.

Once you have the x-coordinate of the vertex, substitute it back into the original equation to find the corresponding y-coordinate.

The resulting y-coordinate represents the maximum height (if the parabola opens downward) or the minimum height (if the parabola opens upward) of the quadratic equation.

Here's an example:

Consider the quadratic equation y = 2x² - 4x + 3.

1. Identify the coefficients:

a = 2

b = -4

c = 3

2. Find the x-coordinate of the vertex:

x = -(-4) / (2 * 2) = 4 / 4 = 1

3. Substitute x = 1 back into the equation to find the y-coordinate:

y = 2(1)² - 4(1) + 3 = 2 - 4 + 3 = 1

Therefore, the maximum height of the quadratic equation y = 2x² - 4x + 3 is 1.

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The maximum height of a quadratic equation can be found by determining the vertex of the parabolic shape represented by the equation. The x-coordinate of the vertex can be found using the formula x = -b / (2a), and the corresponding y-coordinate represents the maximum height.

To find the maximum height of a quadratic equation, we need to determine the vertex of the parabolic shape represented by the equation. The vertex is the point where the parabola reaches its highest or lowest point.

The general form of a quadratic equation is ax^2 + bx + c, where a, b, and c are constants. To find the x-coordinate of the vertex, we can use the formula x = -b / (2a).

Once we have the x-coordinate, we can substitute it back into the equation to find the corresponding y-coordinate, which represents the maximum or minimum height of the quadratic equation.

Let's take an example to illustrate this process:

Suppose we have the quadratic equation y = 2x^2 + 3x + 1. To find the maximum height, we first need to find the x-coordinate of the vertex.

Using the formula x = -b / (2a), we can substitute the values from our equation: x = -(3) / (2 * 2) = -3/4.

Now, we substitute this x-coordinate back into the equation to find the y-coordinate: y = 2(-3/4)^2 + 3(-3/4) + 1 = 2(9/16) - 9/4 + 1 = 9/8 - 9/4 + 1 = 9/8 - 18/8 + 8/8 = -1/8.

Therefore, the maximum height of the quadratic equation y = 2x^2 + 3x + 1 is -1/8.

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To determine the angle from the vernal equinox to the station at the time of measurement, we need to use the following formula:

Angle = (Sidereal Time at Greenwich + Longitude of the Station - Hour Angle of the Object) * 15 degrees/hour

First, we need to determine the Hour Angle of the Object, which is the amount of time since the object (in this case, the radar measurement) passed over the Greenwich meridian. We know that the radar measurement occurred 2.8 hours after noon on January 1, so the Hour Angle of the Object is:

Hour Angle = 2.8 hours * 15 degrees/hour = 42 degrees

Next, we can plug in the values we know into the formula:

Angle = (100 degrees + (-4 degrees) - 42 degrees) * 15 degrees/hour
Angle = 54 degrees * 15 degrees/hour
Angle = 810 degrees/hour

Therefore, the angle from the vernal equinox to the station at the time of the radar measurement is 810 degrees/hour.

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Step 1. The party will be thrown by Steve, Jo, Lucy, Max, and Alex --> 5 people.

On Monday, each invites 3 friends. So for, the number of people invited is:

Step 2. On Tuesday, the friends that were invited (15) invited 3 more people each. The number of people invited now is:

Step 3. On Wednesday, the 45 people invited on Tuesday, each invite 3 more people. The number of people invited again multiplies by 3:

Step 4. The trend continues so for Thursday, the number of people invited on the previous day multiplies by 3:

Step 5. On Friday the number of people invited is:

Step 6. Finally, on Saturday, the day of the party, the number of people invited is multiplied one last time by 3:

Answer:

3,645

Answer:

all of CO2 if go UC FL LG ex Vi if FC no of go on NJ TX FM NC ch UFC Vk jaa

Step-by-step explanation:

DJ ND fixUC guy if fu TX Vk kg go UC Chi UC ch UFC

There are 9 possible schedules to play basketball such that dave can play on monday or wednesday or both which is union of two set .

so this question seems like we have to take union of ways of palying on monday or wednesday

let n(m) be number of ways of playing on monday

n(w) be number of ways of playing on wednesday

we have to find n(m∪w)

n(mUw) = n(m) +n (w) - n(m∩ w)

so n(m) = \(4_C__2\) as one day is now fixed which is monday so we have 4 available days and 2 days to play.

n(m) = \(4_C__2\)  = 6

similary n(m) = n(w) = 6

now  n(m∩w) = \(3_C__1\) as now we have  2 fixed day and we have 3 day remaining and only one day to play.

n(m∩w) = \(3_C__1\) =3

now n(mUw) = n(m) +n (w) - n(m∩ w)

=> 6 + 6 -3

=> 12 - 3

so n(mUw) = 9

so we have 9 schedules to paly keeping condition given in the question.

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Answer:

Step-by-step explanation:

A. What is the ratio of songs by the group from Michigan to the number of songs played?  3/15

B. In lowest terms, 3/15 is 1/5.

C. Suppose the station continues to play the ratio of songs. How many songs from the Michigan group will Blake hear in the next three hours?  To answer this, multiply the 1-hour unit rate by 3:  3*3 = 9 Michigan group songs over the next 3 hours.

Answer:

360 units squared

Step-by-step explanation:

10*10 = 100

10*13*2 = 260

260 + 100 = 360

Answer:

No, it is not reasonable. The scaled drawing would be 12 inches wide by 30 inches tall.

Step-by-step explanation:

First, scale down the sides. 48in divided by 4 is 12in , and 120 in divided by 4 is 30 in. So no, it would not fit on her paper.

Answer:

I think 51% is the rate of mexicans who consider them white out of every 10,000 people. I am not sure tho.

Step-by-step explanation:

let

6,830,536/13,393,208=x/10,000

x would be 5100 approximately

now

5100/10,000×100%

51%

Answer:

B

Step-by-step explanation:

Using an Excel calculator or a similar tool, we can find that P(X > 6) is approximately 0.0688. The binomial distribution is appropriate here because we are interested in the number of successes out of a fixed number of trials with a constant probability of success (15%).

The formula for the binomial distribution is:

\(P(X = k) = (n C k) * p^k * (1 - p)^(n - k)\)

where P(X = k) is the probability of getting exactly k successes, (n C k) is the binomial coefficient (n choose k), p is the probability of success, and (1 - p) is the probability of failure.

a) Probability that fewer than 6 of the 20 sampled invoices receive the discount:

P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

Using the binomial distribution formula with p = 0.15, n = 20, and k = 0, 1, 2, 3, 4, 5, we can calculate the individual probabilities and sum them up.

P(X < 6) = BINOMDIST(0, 20, 0.15, TRUE) + BINOMDIST(1, 20, 0.15, TRUE) + BINOMDIST(2, 20, 0.15, TRUE) + BINOMDIST(3, 20, 0.15, TRUE) + BINOMDIST(4, 20, 0.15, TRUE) + BINOMDIST(5, 20, 0.15, TRUE)

Using an Excel calculator or a similar tool, we can find that P(X < 6) is approximately 0.9132.

b) Probability that more than 6 of the 20 sampled invoices receive the discount:

P(X > 6) = 1 - P(X ≤ 6) = 1 - [P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)]

Using the same binomial distribution formula as above, we can calculate the individual probabilities and subtract them from 1.

P(X > 6) = 1 - (BINOMDIST(0, 20, 0.15, TRUE) + BINOMDIST(1, 20, 0.15, TRUE) + BINOMDIST(2, 20, 0.15, TRUE) + BINOMDIST(3, 20, 0.15, TRUE) + BINOMDIST(4, 20, 0.15, TRUE) + BINOMDIST(5, 20, 0.15, TRUE) + BINOMDIST(6, 20, 0.15, TRUE))

Using an Excel calculator or a similar tool, we can find that P(X > 6) is approximately 0.0688.

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Answer:

5h

Step-by-step explanation:

Can u help me out with my newest one???

Answer:

5h

Step-by-step explanation:

Answer:

La altura del globo con respecto al suelo es 449,6 metros.

Step-by-step explanation:

La afirmación está incompleta. El enunciado completo es: "Un globo vuela entre dos ciudades A y B, que distan entre sí 1.500 m. Los tripulantes del globo ven la ciudad A con un ángulo de depresión de 27°, mientras que para ver la ciudad B es de 36°. ¿Cuál es la altura aproximada del globo con respecto al suelo?

El diagrama geométrico de la situación se encuentra descrita en el archivo adjunto. La altura aproximada del globo puede obtenerse con ayuda de las funciones trigonométricas, en este caso, se recomienda utilizar la función tangente de los ángulos de depresión:

Ciudad A

\(\tan 27^{\circ} = \frac{h}{1500\,m-x}\)

\(0,510 = \frac{h}{1500\,m-x}\)

Ciudad B

\(\tan 36^{\circ} = \frac{h}{x}\)

\(0,727 = \frac{h}{x}\)

Donde \(h\) y \(x\) son la altura con respecto al suelo y la distancia horizontal con respecto a la ciudad A.

A continuación, se elimina la altura de ambas ecuaciones por igualación y se determina la distancia horizontal del globo con respecto a la ciudad A:

\(0,727\cdot x = 0,510\cdot (1500\,m-x)\)

\(1,237\cdot x = 765\,m\)

\(x = 618,432\,m\)

Finalmente, la altura del globo con respecto al suelo es:

\(h = 0,727\cdot x\)

\(h = 0,727\cdot (618,432\,m)\)

\(h = 449,600\,m\)

La altura del globo con respecto al suelo es 449,6 metros.

If two methods agree perfectly in a method comparison study, the slope equals 1.0 and the y-intercept equals 0.0. Therefore, option (b) is the correct answer.

In a method comparison study, the goal is to compare the agreement between two different measurement methods or instruments. The relationship between the measurements obtained from the two methods can be described by a linear equation of the form y = mx + b, where y represents the measurements from one method, x represents the measurements from the other method, m represents the slope, and b represents the y-intercept.

When the two methods agree perfectly, it means that there is a one-to-one relationship between the measurements obtained from each method. In other words, for every x value, the corresponding y value is the same. This indicates that the slope of the line connecting the measurements is 1.0, reflecting a direct proportional relationship.

Additionally, when the two methods agree perfectly, there is no systematic difference or offset between the measurements. This means that the line connecting the measurements intersects the y-axis at 0.0, indicating that the y-intercept is 0.0.

Therefore, in a perfect agreement scenario, the slope equals 1.0 and the y-intercept equals 0.0, which corresponds to option (b).

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The equation that shows the relationship between the angles in the triangle is m∠1 + m∠2 + m∠3 = 180.

The equation that shows the relationship between the angles in the triangle is determined as follows;

The sum of angles in a triangle is equal to 180 degrees.

So based on this information, the equation that shows the relationship between the angles in the triangle is formulated as;

angle 1 + angle 2 + angle 3 = 180

We can re-write the equation as follows;

m∠1 + m∠2 + m∠3 = 180

Thus, the equation that shows the relationship between the angles in the triangle is the sum of angle 1 plus angle 2 plus angle 3.

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Answer:

I am not super positive this is the answer but I think it is 900

Step-by-step explanation:

Volume = LxWxH

Value of x = 42.5 ° and measure of angle 4 = 37.5 ° .

measure of angle 3 = measure of angle 8

( 3 x + 15 ) ° = ( x + 100 ) °

2 x = 85

x = 42.5 °

measure of angle 3 + measure of angle 4 = 180 °

measure of angle 3 = ( 3 x + 15 ) °

                                 = ( 3 * 42.5 ) + 15  

                                  = 142.5 °

Hence , measure of angle 4 = 180 - 142.5 ° = 37.5 ° .

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Answer:

22(c)

Step-by-step explanation:

Our current proportion is

15 miles

-------------

1 hour

We need feet per second.

Lets convert!

15 miles= 79200 feet(used googl to find this)

1 hour=3600 seconds(also used googl to find this)

( i know its not spelled that way brainly wont let me write the whole word out)

Now, our proportion is:

79200 feet

-----------------

3600 seconds

HOWEVER, this can be simplified!!!!

79200/3600=22

Final answer: 22, or C.

The point-slope equation of the line is y - 8 = 3(x - 6)

The points are given as:

(x1, y1) = (6, 8)

The slope is given as:

m= 3

The equation is then calculated as:

y - y1 = m(x - x1)

This gives

y - 8 = 3(x - 6)

Hence, the point-slope equation of the line is y - 8 = 3(x - 6)

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Answer:

y-4=1/5(x-7)

Step-by-step explanation:

First, you need to find the slope of the line. From the point (2,3) to the point (7,4), the line rises 1 unit while moving sideways 5. Therefore, the slope of the line is 1/5. Hence, the equation of the line is y-4=1/5(x-7). Hope this helps!

The probability of running out of water decreases.

The given problem can be solved by using the concept of the normal distribution. Normal distribution, also called Gaussian distribution, is a probability distribution that occurs naturally in many situations. In this distribution, data values cluster around a central point, and the further away a value is from the center, the less likely it is to occur. The normal distribution has two parameters: the mean (μ) and the standard deviation (σ). The mean is the center of the distribution, and the standard deviation is a measure of how spread out the distribution is. The normal distribution is symmetric about the mean. It is a continuous distribution, meaning that it can take any value between negative infinity and positive infinity. The area under the normal curve represents the probability of a random variable taking a certain value or falling within a certain range of values. The total area under the normal curve is equal to 1.
Given:
The average person drinks 3 Liters of water when hiking the Mission Peak (with a standard deviation of 1 Liter).
You are planning a hiking trip to the Mission Peak for 10 people and will bring 35 Liters of water.
What is the probability that you will run out?
We need to find the probability that the amount of water consumed by 10 people will be greater than 35 Liters. Let X be the random variable representing the amount of water consumed by each person. X is normally distributed with mean μ = 3 Liters and standard deviation σ = 1 Liter.
Then, the total amount of water consumed by 10 people is given by the sum of 10 independent identically distributed (i.i.d.) random variables:
Y = X1 + X2 + ... + X10
where X1, X2, ..., X10 are i.i.d. random variables with the same distribution as X.
The total amount of water you bring is 35 Liters. Therefore, you will run out of water if:
Y > 35
or equivalently:
(Y - μ10) / σ10 > (35 - μ10) / σ10
where μ10 = 10μ = 30 Liters and σ10 = √(10)σ = √(10) Liters.
Thus, the probability that you will run out of water is:
P(Y > 35) = P[(Y - μ10) / σ10 > (35 - μ10) / σ10]
= P(Z > (35 - μ10) / σ10)
where Z is the standard normal variable.
Using the standard normal table, we find that:
P(Z > (35 - μ10) / σ10) = P(Z > (35 - 30) / √10)
= P(Z > 1.5811)
= 0.0564 (rounded to four decimal places)
Therefore, the probability that you will run out of water when hiking the Mission Peak with 10 people is 0.0564.
What if the hiking trip will have 20 people and the amount of water you bring also doubles to 70 Liters. What is the probability you will run out?
In this case, the number of people has doubled, so the total amount of water consumed will also double. Thus, the total amount of water consumed by 20 people is given by:
Y = X1 + X2 + ... + X20
where X1, X2, ..., X20 are i.i.d. random variables with the same distribution as X.
The total amount of water you bring is 70 Liters. Therefore, you will run out of water if:
Y > 70
or equivalently:
(Y - μ20) / σ20 > (70 - μ20) / σ20
where μ20 = 20μ = 60 Liters and σ20 = √(20)σ = 2.2361 Liters.
Thus, the probability that you will run out of water is:
P(Y > 70) = P[(Y - μ20) / σ20 > (70 - μ20) / σ20]
= P(Z > (70 - μ20) / σ20)
where Z is the standard normal variable.
Using the standard normal table, we find that:
P(Z > (70 - μ20) / σ20) = P(Z > (70 - 60) / 2.2361)
= P(Z > 4.4721)
= 0 (rounded to four decimal places)
Therefore, the probability that you will run out of water when hiking the Mission Peak with 20 people is zero.

Will the probability of running out of water increase or decrease? Why?

The probability of running out of water decreases when the number of people increases and the amount of water brought doubles. This is because the total amount of water consumed increases proportionally to the number of people, but the standard deviation of the distribution of the amount of water consumed decreases proportionally to the square root of the number of people. This means that the distribution of the total amount of water consumed becomes narrower and more concentrated around the mean as the number of people increases.

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Answer:

to find parallel;

first of all, parallel equations should have the same slope and a different y-intercept!

when were given a point (x,y), we write our equation in the y = mx + b form, then substitute the given point for (x,y) and solve for B!

However, to find the slope of the perpendicular equation, you need to get the negative reciprocal of the slope!

For example, if the slope is 3 in the original equation, it would be - 1/3 in perpendicular equation.

We then substitute the given point for (x,y)!

hope this helps :)

Leave a comment if you need further explanation

Step-by-step explanation: