Jacques is standing 1200 meters from a cliff he is planning to climb. The angle of elevation from the ground to the top of the cliff is 35º. To the nearest meter, how tall is the cliff?

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Complete Question

The weight of an organ in adult males has a bell shaped distribution with a mean of 320 grams and a standard deviation of 20 grams. Use the empirical rule to determine the following. A.) About 68% of organs will be between what weights? B.) what percentage of organs weighs between 280 grams and 360 grams? C.) what percentage of organs weighs less than 280 grams or more than 360 grams? D.) what percentage of organs weighs between 300 grams and 360 grams?

Answer:

A.) About 68% of organs will be between what weights?

Therefore, 68% of the organs will weigh between 300 and 340 grams.

B.) what percentage of organs weighs between 280 grams and 360 grams?

95%

C.) what percentage of organs weighs less than 280 grams or more than 360 grams?

5%

D.) what percentage of organs weighs between 300 grams and 360 grams?

81.5%

Step-by-step explanation:

Empirical formula states that:

68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

Where:

μ = Population mean

σ = Population standard deviation

From the above question, we have the following information

Mean weight = 320 grams

Standard deviation = 20 grams

a) About 68% of organs weight between:

To solve for this, we would use the empirical rule:

68% of the data values lie within 1 standard deviation of the mean

Hence, 68% of the data values lie in the range:

Mean - 1 standard deviation to Mean + 1 Standard Deviation.

Mean - 1 Standard Deviation

μ - σ

= 320grams - 20grams = 300 grams

Mean + 1 Standard Deviation

μ + σ

= 320grams + 20grams = 340 grams

Therefore, 68% of the organs will weigh between 300 and 340 grams.

B.) what percentage of organs weighs between 280 grams and 360 grams?

Mean weight = 320 grams

Standard deviation = 20 grams

Hence,

x - mean = 280 grams - 320 grams = -40 grams

x - mean = 360 grams - 320 grams = 40 grams

Note that both differences = 2 × standard deviation

Hence, from the empirical formula above,

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ applies

Therefore, 95% of the organs fall between 280 grams and 320 grams

C.) what percentage of organs weighs less than 280 grams or more than 360 grams?

Mean weight = 320 grams

Standard deviation = 20 grams

Hence,

x - mean = 280 grams - 320 grams = -40 grams

x - mean = 360 grams - 320 grams = 40 grams

So, from the empirical formula above,

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ applies

Therefore, 95% of the organs fall between 280 grams and 320 grams

It is important to note that finding the percentage of data that weighs less than or more than the given range of values, the formula is given as:

Percentage of Value outside( less than or more than) the range = 100% - Percentage of values within the range

100% - 95%

= 5%

Therefore, the percentage of organs weighs less than 280 grams or more than 360 grams is 5%

D.) what percentage of organs weighs between 300 grams and 360 grams?

Mean weight = 320 grams

Standard deviation = 20 grams

Hence,

x - mean = 300 grams - 320 grams = -20 grams

20 grams = 1 × standard deviation

For 300 grams, the empirical formula that states that:

68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ applies.

It is important to note that the percentage of values below the mean and above the mean must be the same.

But since this is a bell shaped distribution, the percentage of data between 300 and 320 grams = 68%/2

= 34%

x - mean = 360 grams - 320 grams = 40 grams

40 = 2 × standard deviation

For 360 grams , the empirical formula that states that,

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ applies

It is important to note that the percentage of values below the mean and above the mean must be the same.

Since this is a bell shaped distribution, the percentage between 320 and 360grams = 95%/2

= 47.5%

Therefore, the percentage of organs that weighs between 300 grams - 360 grams = 34% + 47.5%

= 81.5%

Answer:

Step-by-step explanation:

(7+4)/2 = 11/2 = 5.5

(1-1)/2 = 0/2 = 0

(5.5, 0)

answer is C

Answer:

C-(5.5,0)

Step-by-step explanation:

(x1+x2/2, y1-y2/2)

7+4/2, 1-1/2

11/2, 0/2

(5.5, 0)

Really hope this helps ;)

Answer:

If the two factors are equal (the same), like 4*4=16, then each of them is called a "square root." Note: a cube root is one of three equal factors of a number, for example, 2 is the cube root of 8 (that is, 2*2*2=8).

Step-by-step explanation:

Answer:

C/R = D

Step-by-step explanation:

When you divide rd by r, then r is eliminated and divided into the C

Hello There!

Write out your equation:

Substitute the values in:

Simplify:

Solve:

It is 6.25.

Therefore, your answer is 6 1/4.

Hope This Helps You!

Good Luck :)

the answer is:   [tex]x= -\frac{29}{3}[/tex]

Answer:

The answer is yes.

Step-by-step explanation:

All you have to do is substitute the y, which is 5, and the x, which is 2, into the equation. When you solve it the answer in the end will be 5=5, which means that point (2,5) does line on that line.

Answer: y=9x + 26

Step-by-step explanation:

Notice that for two lines to be parallel they must have the same slopes but different y intercept.

So the equation y =9x + 2 has a slope of 9 and y-intercept of 2  so using the points  we can determine  the y intercept of the line parallel to it to find the.

Using the slope intercept form formula which is y = mx + b  we can plot in the slope and the given coordinates to solve for b.

The coordinate is (-2,8)  which the y value is 8 and the x value is -2

so  8 = 9(-2) +b    solve for b

  8 = -18  + b

 +18   +18

b = 26  

The y intercept is 26  so the equation will be y=9x + 26

Answer:

A. x= 4

Step-by-step explanation:

[tex]2x + 2 = 10[/tex]

Collect like terms and simplify

[tex]2x =10-2\\2x =8[/tex]

Divide both sides of the equation by 2

[tex]\frac{2x}{2} = \frac{8}{2} \\\\x = 4[/tex]

Answer:

y=3/5x + 1

Step-by-step explanation:

It says to translate UP 5 units, meaning the constant of -4 is the one being affected. The translation of 5 units is +5 on the graph, so -4+5=1. Everything else should be the same if i'm correct so y=3/5x + 1 is the answer

Answer:

2x + 10 = y

Step-by-step explanation:

The term 10 more is plus 10, and 2 times the "number" which we know we can label as "x". 2x + 10 is the equation and we are told that y is the number of points so 2x + 10 = y is the answer.

Hope that helps, and have a great day!

Answer:

Answer= 23

Step-by-step explanation:

The problem would look like this: |(-4)(-6)| - |(2)(1/2)|

if solved it should look like this: |24| - |1|

which is: 24 - 1 = 23

Answer:

Width is 5 cm

Step-by-step explanation:

Since we know that the width is 25 meters, and the scale we are using is 5 meters = 1 cm, we can divide 25 by 5 to find the scaled measurement.

25/5 = 5cm

I hope this helps!

-TheBusinessMan

Answer:

17

Step-by-step explanation:

Hay dos cursos que se ofrecen en la escuela y se representan como fracciones.

Cursos corresponden a la enseñanza media = 8/25

Cursos de enseñanza básica =?

Sea el número total de cursos = 1

Cursos de enseñanza básica = 1 - 8/25

= 17/25

Dado que ambos cursos están en forma de fracciones, podemos convertirlos en razones

Relación de cursos corresponden a la enseñanza media a cursos de enseñanza básica

= 8:17

Donde el número total de cursos ofrecidos = 8 + 17 = 25

Por lo tanto, el número que representa los cursos de enseñanza básica = 17.

Answer:

8.3

Step-by-step explanation:

25÷3=8.3333333

I rounded it to this.

Answer: 7.5

25 * 0.3 is also 25 of 0.3, 0.3 of 25 so by multiplying you get 7.5

Hey there! I'm happy to help!

To find the distance between two points, you find the difference between the x values, square that, find the difference between the y values, square that, add the two numbers you got, and then find the square root.

We find the difference of the x values.

0-4=-4

Square it.

-4²=16

We find the difference between the y values.

2--1

2+1=3

And we square that.

3²=9

We add the two numbers we got.

16+9=25

And we find the square root.

√25=5

The distance between these points is 5. Now you can find the distance between any two points! Have a wonderful day! :D

Answer:

600 feet.

Step-by-step explanation:

1 hour and 15 minutes is equal to 75 minutes.

Therefore,

8 times 75 equals 600 feet.

Answer:

2.83 units

(results are in decimal form, rounded to the nearest 100th)

Answer:

$189 - $315 - $7x

Step-by-step explanation:

Given the following :

Amount in Mae's account = $189

Each month balance is below $750;

Amount charged = $7

She withdrew $315 from her account and makes no deposit or withdrawal for the next x months

Her balance :

Initial amount = $189

Withdrawal made = $315

Amount charged when balance falls below $750 = fee * number of months = 7 * x = 7x

Hence, her balance after x months will be :

$189 - $315 - $7x

The balance of Mae expressed algebraically will be 189 - 315 - 7x.

The following can be deduced from the question:

Therefore, the amount that is left in her account balance will be:

= 189 - 315 - (7 × x)

= 189 - 315 - 7x

Read related link on:

https://brainly.com/question/25783892

Answer: 7.5

Step-by-step explanation:

Answer:

x^2+8

Step-by-step explanation:

Answer:

(0.7, -1)

Step-by-step explanation:

To find the coordinates for the midpoint you add each coordinate together and divide by 2.

M = ([tex]\frac{1.8 - 0.4}{2}, \frac{-3.4 + 1.4}{2}[/tex])

M = [tex](\frac{1.4}{2}, \frac{-2}{2})[/tex]

M = (0.7, -1)

Step-by-step explanation:

They both have the same gradient of 1. (Their slope is 1)

Answer:

[tex] \boxed{ \bold{ \huge {\boxed{ \sf{ - 12 {x}^{2} - 5x - 8}}}}}[/tex]

Step by step explanation

[tex] \sf{ - 9 {x}^{2} + 3x - 8 - (3 {x}^{2} + 8x)}[/tex]

When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression

[tex] \dashrightarrow{ \sf{ - 9 {x}^{2} + 3x - 8 - 3 {x}^{2} - 8x}}[/tex]

Collect like terms

[tex] \dashrightarrow{ \sf{ - 9 {x}^{2} - 3 {x}^{2} + 3x - 8x - 8}}[/tex]

[tex] \dashrightarrow{ \sf{ - 12 {x}^{2} - 5x - 8}}[/tex]

Hope I helped!

Best regards!

======================================

Explanation:

Use your calculator to find that 89/6 = 14.8333 approximately

The whole part 14 means each of the six people get 14 chips

That means 6*14 = 84 chips have been eaten so far, leaving 89-84 = 5 chips left over for her sister.

----------

In other words,

89/6 = 14 remainder 5

which can be found through long division as shown below

Step-by-step explanation:

z = 3-2a

a = 3/2 - 0.5z

...........................

Answer: I dont know which to slove for so im going to put both :)

Step-by-step explanation:

SOLVING FOR Z:

Subtract  4 a from both sides of the equation.

2 z = 6 − 4 a

Divide each term by  2

and simplify.  z = 3 − 2 a

SOLVING FOR A:

Subtract a from both sides of the equation

2z=6-4a

Divide each term by 2 then simplify

z=3-2a

Answer:

y = 5

Step-by-step explanation:

Answer:

A. 1

Step-by-step explanation:

3(x+1)=-2(x-1)+6

3x+3=2x-2+6

x+3=4

x=1

Answer:

k=70

Step-by-step explanation:

to get k by itself you need to multiply k/7 by 7, and you multiply on both sides. 10 times 7 =70

Answer:

Step-by-step explanation:

k/7 = 10

or, k = 7*10

Therefore, k=70.