The amount of syrup that people put on their pancakes is normally distributed with mean 60 mL and standard deviation 11 mL. Suppose that 12 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible.

What is the distribution of
X
?
X
~ N(
,
)
What is the distribution of
¯
x
?
¯
x
~ N(
,
)
If a single randomly selected individual is observed, find the probability that this person consumes is between 59.3 mL and 61.2 mL.
For the group of 12 pancake eaters, find the probability that the average amount of syrup is between 59.3 mL and 61.2 mL.
For part d), is the assumption that the distribution is normal necessary? YesNo

Answer:

You need to attach the pictures and ask again.

Step-by-step explanation:

I cannot see any attachments.

Answer:

[tex]x =\sqrt{5} ,-\sqrt{5} ,-i,i[/tex]

Step-by-step solution:

[tex]0=x^4-4x^2-5[/tex]   [tex]u = x^2[/tex]
[tex]0 = u^2-4u-5[/tex]
[tex]0 = (u -5)(u+1)[/tex]
[tex]u = 5[/tex]  [tex]u=-1[/tex]
[tex]x^2 =5[/tex]    [tex]x^2 = -1[/tex]
[tex]x= +-\sqrt{5}[/tex]   [tex]x = +-i[/tex]

Answer:

one sixth plus 4 sixths

Step-by-step explanation:

from one sixth you have to add 4/6 to get to 5 sixths(5/6)

Answer:

the length of the shorter leg : 7 cm

the length of the longer leg : 24 cm

the length of the Hypotenuse : 25 cm

Step-by-step explanation:

a = 3b + 3

c = 3b + 4

and we know the general Pythagoras :

c² = a² + b²

(3b + 4)² = (3b + 3)² + b²

9b² + 24b + 16 = 9b² + 18b + 9 + b²

24b + 16 = 18b + 9 + b²

6b + 7 = b²

b² - 6b - 7 = 0

the general solution to such a quadratic equating is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x is called b.

a = 1

b = -6

c = -7

b = (6 ± sqrt((-6)² - 4×1×-7))/(2×1) = (6 ± sqrt(36 + 28))/2 =

= (6 ± sqrt(64))/2 = (6 ± 8)/2

b1 = (6+8)/2 = 14/2 = 7 cm

b2 = (6-8)/2 = -2/2 = -1 cm

a negative number did not make sense for a side length, so,

b = 7 cm

is our solution for one leg.

a = 3b + 3 = 3×7 + 3 = 24 cm

c = 3b + 4 = 25 cm

Answer:

Volume: x(x+6)(x+2) Area: [tex]x^{2}[/tex] + 8x +12

Step-by-step explanation:

Volume Explanation:

To find the volume of a 3d figure, we must multiply the length, width, and the height. Therefore we multiply (x)(x+6)(x+2)= [tex]x^{3}[/tex] + 8[tex]x^{2}[/tex] + 12x. Simplify this equation and we will get x(x+6)(x+2) for the formula to find the volume of the 3D figure.

Area:

To find the area of a 2D figure, we must multiply length x height. Therefore, we multiply the equations (x+6)(x+2)= [tex]x^{2} + 2x + 6x +12[/tex] to get a final answer of [tex]x^{2} +8x +12[/tex].  This will be the formula when you find the area of the 2D figure in question.

The function that represents the growth of this culture of bacteria as a function of time is; P = 1500e^(1.0986t)

The formula for exponential growth is;

P = P₀e^(rt)

where;

P = current population at time t

P₀ = starting population

r = rate of exponential growth/decay

t = time after start

Thus, from our question we have;

4500 = 1500 * e^(r * 1)

4500/1500 = e^r

e^r = 3

In 3 = r

r = 1.0986

Thus, the function that represents the growth of this culture of bacteria as a function of time is;

P = 1500e^(1.0986t)

For the culture to double, then;

P/P₀ = 2. Thus;

e^(1.0986t) = 2

In 2 = 1.0986t

t = 0.6931/1.0986

t = 0.631 hours

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[tex]m = \frac{ - u}{v} = \frac{ - 9}{3} = - 3 [/tex]

[tex]km = - 1 \\ k = - \frac{1}{m} = \frac{ - 1}{-3}=1/3 [/tex]

The slope of the perpendicular line will be 1/3.

Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The equation of the line is given below.

9x + 3y = 36

3y = 36 - 9x

y = 12 - 3x

The slope of the given equation is - 3.

Let m be the slope of the perpendicular line. Then the slope of the perpendicular line will be 1/3.

m (-3) = -1

Simplify the equation, then we have

m (-3) = -1

3m = 1

m = 1/3

The slope of the perpendicular line will be 1/3.

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Answer:

The set notation for the diagram is P-Q

[tex]\frak{Hi!}[/tex]

[tex]\orange\hspace{300pt}\above3[/tex]

                      If two lines are perpendicular to each other, their slopes

                     are negative inverses of each other.

                     Thus,

                    [tex]\boldsymbol{\sf{Slope\:of\:this\:line=4}}}[/tex]

                    [tex]\boldsymbol{\sf{Negative \ Inverse=-\displaystyle\frac{1}{4}}}[/tex]. See how this works?

                    We took 4, then took its opposite, and flopped that over

[tex]\orange\hspace{300pt}\above3[/tex]

Definition-:

Perpendicular lines are lines that intercept each other at a 90 deg. angle, which is usually called the right angle.

The value of card(B) is card(B) = 4954

The set is given as:

B={1,3,5,7,9,….9907}

The above set is the set of odd numbers from 1 to 9907.

The number of elements is the cardinality

And it can be calculated using

L = a + (n - 1)d

Where

L = 9907

a = 1

d = 2

So, we have:

9907 = 1 + (n - 1)2

Subtract 1 from both sides

9906 = (n - 1)2

Divide by 2

n - 1 = 4953

Add 1 to both sides

n = 4954

This means that

card(B) = 4954

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Answer:

2 y + x = 5 , 5 x − y = 3

Step-by-step explanation:

suppose x represents the smaller number and y represent the larger number.

Then

• The statement: “Twice a number added to a smaller number is 5”

means  2 y + x = 5

On the other hand,

•• The statement: “The difference of 5 times the smaller number and the larger number is 3”

means  5 x − y = 3

We currently have two fractions: y / 1 and (y - 3) / 3.

In both cases, we are only concerned with the denominator. Yes, the numerator will change when we change the denominator, but that will not affect the answer to this question.

As such, we need to find the least common multiple of 1 and 3. That is 3. Therefore, the common denominator is 3.

Hope this helps!

Answer:

Step-by-step explanation:

hello :

f(x) = a(x+h)²+k

(h;k) the vertex    so : h=3   and k= 5

now calculate  a   given f(0) = 12

means : a(0+3)²+5 = 12

9a=7   so : a=7/9

the equation is : y= (7/9)(x+3)²+5

Answer:I can’t see

Step-by-step explanation:show fullscreen

Answer:

8.2

Step-by-step explanation:

We can find the unit rate of this problem by dividing 18.68 by 24 to get .82. .82*10 is equal to 8.2.

Step-by-step explanation:

1A

the travel paths of the plane build a right-angled triangle.

one travels north, which creates the vertical leg.

the other travels west, which creates the horizontal leg.

their distance is the Hypotenuse (the baseline opposite of the 90° angle), which we can get via Pythagoras

c² = a² + b²

c being the Hypotenuse, a and b being the legs.

how long are the legs ?

the plane going north travels at 240 km/h for 90 minutes.

the plane going west travels at 180 lm/h for 90 minutes.

90 minutes = 1.5 hours (1 hour 30 minutes).

so,

plane 1 went 240×1.5 = 360 km.

plane 2 went 180×1.5 = 270 km.

distance² = 360² + 270² = 129600 + 72900 = 202500

distance = sqrt(202500) = 450 km

2A

again Pythagoras :

130² = 80² + (2nd leg)²

16900 = 6400 + (2nd leg)²

10500 = (2nd leg)²

2nd leg = 102.4695077... m

so, the full perimeter is

130 + 80 + 102.4695077... = 312.4695077... m

312.4695077... = 100%

1% = 100%/100 = 3.124695077... m

how many % are 220 m ? well as many as how often 1% fits into 220 m :

220 / 3.124695077... = 70.40686998... %

3A

again Pythagoras :

the legs of that inner right-angled triangle are (as you correctly wrote) 40 m and 45 m.

the fence is the Hypotenuse, and we get

fence² = 40² + 45² = 1600 + 2025 = 3625

fence = 60.20797289... m ≈ 60 m

please burn that into your brain forever for any right-angled triangle situations :

a² + b² = c²

Pythagoras

The value of the expression [tex]\frac{x^2 + 3y^2}{xy}[/tex] is [tex]\frac{6y^2 + 2xy}{xy}[/tex]

The equation is given as:

[tex]x^2 - 2xy - 3y^2 = 0[/tex]

Add 3y^2 to both sides

[tex]x^2 - 2xy = 3y^2[/tex]

Add 3y^2 to both sides

[tex]x^2 + 3y^2 - 2xy = 6y^2[/tex]

Add 2xy to both sides

[tex]x^2 + 3y^2 = 6y^2 + 2xy[/tex]

Divide through by xy

[tex]\frac{x^2 + 3y^2}{xy} = \frac{6y^2 + 2xy}{xy}[/tex]

Hence, the value of [tex]\frac{x^2 + 3y^2}{xy}[/tex] is [tex]\frac{6y^2 + 2xy}{xy}[/tex]

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Answer:

80 mm

Step-by-step explanation:

the same amount (and that means the same volume) of pepper is in each shaker.

the volume of a cylinder is

base area × height = pi×r² × height

with r being the radius (which is always half of the diameter).

the volume of the filled in pepper in the first shaker is then

pi×(32/2)²×45 = pi×16²×45 = pi×256×45 = 11,520pi mm³ =

= 36,191.14737... mm³

now let's see what height in the second shaker we will reach by filling the same 11,520pi mm³ of pepper into it.

so, we have

pi×(24/2)²×height = 11,520pi

12²×height = 11,520

144×height = 11,520

height = 11,520/144 = 80 mm

so, the shaker on the right is filled up to 80 mm with pepper.

Answer:

80 mm

Step-by-step explanation:

I got it right on edmentum

The length of the rectangle that makes the area to be 273 square feet is 21 feet.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the length of the rectangle, hence:

Length * width = area

13 * x = 273

x = 21 feet

The length of the rectangle that makes the area to be 273 square feet is 21 feet.

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The relationship between segment AC and segment A double prime C double prime is AC = A''C'' /2.

The ratio by which the new image is bigger or smaller than the original image is the scale factor.

It is given that

Triangle A″B″C″ is formed using the translation (x + 0, y + 2)

and the dilation by a scale factor of 2 from the origin.

coordinate plane with triangle ABC at A (- 3,  3), B (1, - 3), and C (- 3, -3).

segment AC is equal to A''C'' over 2

Scale factor = 2

The coordinates are

A (- 3,  3), B (1, - 3), and c (- 3, -3) is translated using  (x + 2, y + 0),

new coordinates

A'(- 1,  3), B'(3, - 3), and C'(- 1, -3).

The dilation by a scale factor of from the origin

A″ (-2, 6), B″ (6, -6) and C″(-2, -6)

By the distance formula

AB = [tex]\rm \sqrt {52}[/tex]

A''B'' = [tex]\rm \sqrt{ 8^2 + 12^2}\\[/tex] = 2 [tex]\rm \sqrt {52}[/tex]

Therefore

AB = A''B'' /2

Similarly AC = A''C'' /2

The relationship between segment AC and segment A double prime C double prime is AC = A''C'' /2.

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Recall the Pythagorean identity,

[tex]\sin^2(\theta) + \cos^2(\theta) = 1[/tex]

Since [tex]\theta[/tex] belongs to Q3, we know both [tex]\sin(\theta)[/tex] and [tex]\cos(\theta)[/tex] are negative. Then

[tex]\cos(\theta) = -\sqrt{1 - \sin^2(\theta)} = -\dfrac7{25}[/tex]

Recall the half-angle identities for sine and cosine,

[tex]\sin^2\left(\dfrac\theta2\right) = \dfrac{1 - \cos(\theta)}2[/tex]

[tex]\cos^2\left(\dfrac\theta2\right) = \dfrac{1 + \cos(\theta)}2[/tex]

Then by definition of tangent,

[tex]\tan^2\left(\dfrac\theta2\right) = \dfrac{\sin^2\left(\frac\theta2\right)}{\cos^2\left(\frac\theta2\right)} = \dfrac{1 - \cos(\theta)}{1 + \cos(\theta)}[/tex]

[tex]\theta[/tex] belonging to Q3 means [tex]180^\circ < \theta < 270^\circ[/tex], or [tex]90^\circ < \theta < 135^\circ[/tex], so that the half-angle belongs to Q2. Then [tex]\sin\left(\frac\theta2\right)[/tex] is positive and [tex]\cos\left(\frac\theta2\right)[/tex] is negative, so [tex]\tan\left(\frac\theta2\right)[/tex] is negative.

It follows that

[tex]\tan\left(\dfrac\theta2\right) = -\sqrt{\dfrac{1 - \cos(\theta)}{1 + \cos(\theta)}} = \boxed{-\dfrac43}[/tex]

Answer:

[tex]dy \ = \ 0.1[/tex]

Step-by-step explanation:

Considering the Leibniz notation to represent the derivative of [tex]y[/tex] with respect to [tex]x[/tex], suppose [tex]y \ = \ f\left(x\right)[/tex] is a differentiable function, let [tex]dx[/tex] be the independent variable such that it can be designated with any nonzero real number, and define the dependent variable [tex]dy[/tex] as

                                                  [tex]dy \ = \ f'\left(x\right) \ dx[/tex],

where [tex]dy[/tex] is the function of both [tex]x[/tex] and [tex]dx[/tex]. Hence, the terms [tex]dy[/tex] and [tex]dx[/tex] are known as differentials

Dividing both sides of the equation by [tex]dy[/tex], yield the familiar expression

                                                         [tex]\displaystyle\frac{dy}{dx} \ = \ f'\left(x\right)[/tex].

Given that [tex]f\left(x\right) \ = \ x[/tex] and [tex]dx \ = \ 64.1 \ - \ 64 \ = \ 0.1[/tex], hence

                                                 [tex]f'\left(x\right) \ = \ 1[/tex].

Subsequently,

                                               [tex]dy \ = \ f'\left(64\right) \ \times \ 0.1 \\ \\ dy \ = \ 1 \ \times \ 0.1 \\ \\ dy \ = \ 0.1[/tex].

Substituting into vertex form, we can write the equation of the parabola as

[tex]y=a(x-0)^{2}+9\\\\y=ax^{2}+9[/tex]

To find the value of a, we can substitute in the coordinates of another point the graph passes through, such as (3,0).

[tex]0=a(3)^{2}+9\\\\0=9a+9\\\\-9=9a\\\\a=\boxed{-1}[/tex]

Answer:

(m+n) [x-y]

Step-by-step explanation:

(m+n) (2x-y)-x(m+n)

We can factor out (m+n)

(m+n) [(2x-y)-x]

Combine like terms

(m+n) [2x-x-y]

(m+n) [x-y]

Answer:

The diagonal length of the desk is 7.42462120246 inches.

Step-by-step explanation:

Since it is a square then all sides are equal which means we can easily formulate the pythagorean theorem on the diagonal length of the desk.

a^2 + b^2 = c^2

A and B are the same (width and length) since it is a square.

5.25^2 + 5.25^2 = c^2

27.5625 + 27.5625 = c^2

55.125 = c^2

Put c^2 under a square root (apply to both sides)

square root of 55.125 = 7.42462120246 = c

Answer:

x = 47°

y = 27°

Explanation:

The angles lie on parallel lines which sum ups to 180 degrees.

2x + 1 + 85 = 180

2x = 180 - 86

2x = 94

x = 47

2y + 126 = 180

2y = 180 - 126

2y = 54

y = 27

Answer:

Step-by-step explanation:

its  A y+6=-2