4b) Work out the mean and standard deviation of the following: picture included

Note: I ended up with the simultaneous equations, which are correct according to the markscheme BUT the answers I got upon solving them were incorrect.
μ = 170 + 1.6449σ
μ = 180 - 0.8416σ

What I got after solving these were:
μ = 169.5306859
σ = 12.44864932

But according to the markscheme, I should have gotten:
μ = 176.615...
σ = 4.021...

Can someone explain to me where I've gone wrong?

Circle theorem states that the angle that an arc subtends at the center of a

circle is twice the angle subtended at the circumference.

The values are as follows;

Reasons:

[tex]\displaystyle 1. \ \mathbf{m\angle EDA} = \frac{1}{2} \cdot m\angle EPC[/tex] Angle subtended at center is twice angle at circumference.

m∠EPC = 180°

∴  m∠EDA = 0.5 × 180° = 90°

2. [tex]m\widehat{BC}[/tex] = 42°, therefore, m∠BPC = 42°

[tex]\displaystyle \ m\angle BDC= \frac{1}{2} \cdot m\angle BPC[/tex]

m∠BDC = 0.5 × 42° = 21°

3. m∠BEC = m∠BDC = 21°

4. [tex]m\widehat{AB}[/tex] = 180° - (58° + 42°) = 80°

5. [tex]\mathbf{m\widehat{AB}}[/tex] = m∠APB by definition

m∠AEB = 0.5 × m∠APB

m∠AEB = 0.5 × 80° = 40°

6. m∠ECA = 0.5 × m∠AE

Therefore;

m∠ECA = 0.5 × [tex]m\widehat{EA}[/tex]

m∠ECA = 0.5 × 58° = 29°

m∠ECA =  29°

7. m∠BAC = 0.5 × [tex]\mathbf{m\widehat{BC}}[/tex]

m∠BAC = 0.5 × 42° = 21°

m∠BAC = 21°

8. [tex]m\widehat{ED}[/tex]  = 180° - [tex]\mathbf{m\widehat{CD}}[/tex]

[tex]m\widehat{ED}[/tex]  = 180° - 90° = 90°

[tex]\mathbf{m\widehat{ED}}[/tex]  =  90°

9. m∠ECD = 0.5 × [tex]\mathbf{m\widehat{ED}}[/tex]

m∠ECD = 0.5 × 90° = 45°

10. m∠ACB = 0.5 × [tex]m\widehat{AB}[/tex]

m∠ACB = 0.5 × 80° = 40°

11. m∠EBD = 0.5 × [tex]\mathbf{m\widehat{ED}}[/tex]

m∠EBD = 0.5 × 90° = 45°

12. m∠ADB = 0.5 × [tex]\mathbf{m\widehat{AB}}[/tex]

m∠ADB = 0.5 × 80° = 40°

13. m∠CAD = 0.5 × [tex]\mathbf{m\widehat{CD}}[/tex]

m∠CAD = 0.5 × 90° = 45°

14. m∠EAB = 0.5 ×[tex]\mathbf{m\widehat{EABC}}[/tex]

m∠EAB = 0.5 × 180° = 90°

15. m∠EBC = 0.5 ×[tex]\mathbf{m\widehat{EABC}}[/tex]

m∠EBC = 0.5 × 180° = 90°

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Answer: I think its 106 calories

Step-by-step explanation:

sorry if im wrong

Answer:2.78301

12.21699

Step-by-step explanation:

Multiply:

2.78301 x 12.21699 = 34

Add

2.78301 + 12.21699 = 15

Answer:

Yes, this equation is a system of equations because the two equations do intersect at the point, (0.323529411763, -1.23529411765), making them have a solution. *Work Below*

Step-by-step explanation:

Lets use the elimination method which is ...

4x-3y=5

2x+7y=-8

Multiply the bottom part by -2

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

which equals...

-4x-14y=16

Rewrite the equations

4x-3y=5

-4x-14y=16

Add and the x's cancel making..

-17y=21

Divide by -17 to isolate y

y=-1.23529411765

Replace y with -1.23529411765 on one of the equations

4x-3(-1.23529411765) =5

x=0.323529411763

solution : (0.323529411763, -1.23529411765)

Answer:

y-intercept is -2 slope is up 2 right 1(2/1)

Step-by-step explanation:

Step-by-step explanation:

PT=2QS = 2×8 = 16m

therefore perimeter of ∆PRT = 6+16+14 = 36m

hope this helps you.

Arlen already established that ΔRST and ΔUTS has two pairs of congruent angles and a pair of congruent included sides, which meet the ASA Congruence Criterion. Therefore:

The ASA Congruence Criterion states that for two triangles to be considered congruent to each other, both triangles must have a pair of congruent included sides and two pairs of congruent angles.

Thus, the two-column proof that shows that RS ≅ TU that Arlen is trying to write, has already established that ΔRST and ΔUTS has the following:

Two pairs of congruent angles - ∠RST ≅ ∠UTS and ∠RTS ≅ ∠UST.

A pair of congruent included sides - ST ≅ S.

These satisfy the ASA Congruence Criterion. Therefore:

Learn more about the ASA Congruence Criterion on:

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Answer:

No solution

Step-by-step explanation:

Answer:

The answer is C. (a + -a = 0 )

Step-by-step explanation:

"The additive inverse of a number a is the number that, when added to a, yields zero"

Answer:

Equilateral triangles have 3 congruent angles, measuring 60 degrees each. Isosceles triangles have 2 congruent angles, and scalene triangles have no congruent angles.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Slope is defined as the "Rise" over the "Run" of a straight line.  The Rise is the change in y, and the Run is the change in x.  For the given points:

(5,6) and (5,9) the Rise and Run are (going from left to right).

Rise (9-6) = 3

Run = (5-5) = 0

The slope is 3/0, which is undefined (can't divide by zero).

Answer:

I don't know I wanna say the 3rd one

Step-by-step explanation:

Answer:

no property

Step-by-step explanation:

Name the property used: no property

Answer:

174.6

Step-by-step explanation:

88 kg = 194.007 - 10%

194 * 10% = 194 - 19.4 = 174.6

Answer:

126

Step-by-step explanation:

The percentage of data that lies within 2 standard deviations of the mean in a normal distribution is 95%.

A normal distribution is a probability distribution that is symmetric around the mean of the distribution. This means that the there are more data around the mean than data far from the mean. A normal distribution is also known as the Gaussian distribution. When depicted on a graph, a normal distribution is bell-shaped.

For a normal distribution:

Please find attached an image of a normal distribution. A similar question was answered here: https://brainly.com/question/17101164

Answer:

I believe it is 95%

Step-by-step explanation:

Answer:

[tex] \boxed{\bf \dfrac{64}{729} }[/tex]

Hence,

[tex]\boxed{\bf \: \bigg( \dfrac{2}{3} \bigg) {}^ {6} = \dfrac{64}{729}} [/tex]

Step-by-step explanation:

Given arithmetic expression is :-

[tex]\sf \longmapsto(2/3) {}^{6} [/tex]

This expression may be rewritten as :-

[tex]\sf \longmapsto \bigg(\dfrac{2}{3} \bigg) {}^{6} [/tex]

6 is the index and 2/3 is the base.

In words, this may be represented as 2/3 raised to the Power 6.

Let's calculate.

It means that 2 is raised to the power of 6 and 3 is also raised to the power 6.

That is,

[tex]\sf \longmapsto \dfrac{ {2}^{6} }{ { 3}^{6} } [/tex]

It will be represented as,

[tex]\sf \longmapsto \: \dfrac{2 \times 2 \times 2 \times 2 \times 2 \times 2}{3 \times 3 \times 3 \times 3 \times 3 \times 3} [/tex]

On Simplification:-

[tex]\sf \longmapsto \dfrac{64}{729} [/tex]

In Decimal:-

[tex]\sf \longmapsto0.08(approx .)[/tex]

______________________________________

I hope this helps!

Please let me know if you have any questions.

~MisterBrian

Answer:

7

Step-by-step explanation:

48/6=8

56/8=7

Answer:

7

Step-by-step explanation:

the second triangle is 1/8 of the first so 56 divided by 8 is 7

Answer:

1/2

Step-by-step explanation:

You need to add all the fractions up to get 1/2 is what food the costumers brought home

Answer:

1/2

Step-by-step explanation:

i got it correct!!

Answer:

This is not possible with 2 equal symbols

Answer:

x=6

Step-by-step explanation

So, the formula for this is the Pythagorean Theorum which is a^2 +b^2=c^2.

If the longest side is the square root of 72, then it is the hypotenuse, or c. Now the equation looks like this. a^2 + b^2 = square root of 72.

Since we know that a and b are the same, and that they equal the square root of 72, just divide 72 by two for the square root of 36. Just find the square root of 36 now, which is 6. :) Hope this helps!

Answer:

Step-by-step explanation:

1 meter = 39.3701, by definition.

3 meters = 3*(39.3701)

3 meters of wire = 118 inches

Answer:

3 meters ≈ 118 inches

Step-by-step explanation:

1 meter = 3.28084 feet

1 foot = 12 inches

3 · 3.28084 =  9.84252

9.84252 · 12 = 118.11024

Answer:

0.5 pounds of butter.

Explanation

X pounds for 0.25 gallons.

0.5 gallon of cream - 1 pound of butter

0.25 gallons of cream - X pounds of butter

Applying cross multiplication:

0.5X = 0.25

X = 0.25 over 0.5 or 0.25/0.5

X = 0.5

Therefor, you could make 0.5 pounds of butter with 0.25 gallons of cream.

By the 0.25 gallons of cream, we can make 0.5 pounds of butter.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Given that,

It takes 0.5 gallons of cream to make 1 pound of butter.

So,

0.5 gallons of cream ⇒  1 pound of butter

Divide both sides by 2

0.5/2 gallons of cream ⇒  1/2 pound of butter

0.25 gallons of cream ⇒ 0.5 pounds of butter

Hence "By the 0.25 gallons of cream, we can make 0.5 pounds of butter".

For more information about ratio and proportion,

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Answer:

300

Step-by-step explanation:

Let the value that we are trying to find be x.

If 60 is 20% of x, then we have the following equation:

1/5x = 60.

Then, we can multiply by 5 to get:

x = 300

Answer:

20 percent of 60 minutes is 1/3

Step-by-step explanation:

I'm not sure if that is what you're asking, but if it is I hope it helps!

Answer:

A - infinite

Step-by-step explanation:

The 2 lines are on top of each other making any point on either line a solution.

Hope that helps

Answer:

-27

Step-by-step explanation:

18 + x = -9

subtract by 18 on both sides

x = -27

You can check this by...

18 - 27 = -9

I hope this helps!!

this is your answer hope it's helpful for you