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Q1: A factory produces candy bars, with mean weight 5 grams. After the machines were updated with new tech, a worker worries the candy bars are now lighter on average. To test this theory, the worker collects a random sample of candy bars and measures their mean weight. Identify the null and alternative hypotheses in this situation.

Answer:

a) 7 in

b) 72 steps

Step-by-step explanation:

Angle of elevation formula:  [tex]tan(\theta)=\dfrac{y}{x}[/tex]

where [tex]\theta[/tex] is the angle of elevation, y is the vertical distance (rise) and x is the horizontal distance.

a)  Given:

[tex]\implies tan(32)=\dfrac{y}{12}[/tex]

[tex]\implies y=12tan(32)[/tex]

[tex]\implies y=7 \ \textsf{in (nearest inch)}[/tex]

b)  Given:

⇒ Total height = 21 + 21 = 42 feet

1 foot = 12 inches

⇒ 42 feet = 42 x 12 = 504 inches

Using vertical rise of 7 in per step found in part (a):

Number of steps = 504 ÷ 7 = 72

Increased accuracy

Using unrounded vertical rise of 12tan(32):

Number of steps = 504 ÷ 12tan(32) = 67 steps to the nearest step

Answer:

M' (- 6, 4 )

Step-by-step explanation:

Under a clockwise rotation about the origin of 90°

a point (x, y ) → (y, - x ) , then

M (- 4, - 6 ) → M' (- 6, 4 )

Answer:

There are two ways to do this problem algebraically or trigonometrically.

Algebraically/geometrically

The ratios of the sides of a 30/60/90 tri. are x, x√3, 2x (short leg, long leg, hyp). Therefore, if the long leg is 6 'units'. then 6 = x√3. x = 6√3.

The hyp is 2x then the hypotenuse is 2(6√3) = 12√3, rationalizing is 12√3/3 = 4√3

Using Trig.

We can use sinx = y/r = opp/hyp. The long leg of 6 is opposite 60 degrees (pi/3).

Therefore, sin(pi/3) = 6/r =

r = 6/sin(pi/3) = 6/(√3/2) = 12/√3, when you rationalize you get 12√3/3 = 4√3

The sine and cosine ratios for a 30°–60°–90° triangle with a hypotenuse of 6, when θ = 60° are  6√3 and 4√3.

This is defined as the longest side of a right-angled triangle and is opposite to the right angle.

The ratios of the sides of a 30/60/90 triangle are x, x√3, 2x (short leg, long leg, hyp). We can infer that the long leg is 6 'units' which is

6 = x√3

x = 6√3.

The hypotenuse is 2x then the hypotenuse is 2(6√3)

= 12√3 when rationalized

= 12√3/3 = 4√3.

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Chaos theory has a wide range of real-world applications and is used in fields such as weather prediction, finance, and biology.

Chaos theory is a branch of mathematics that studies the behavior of systems that are highly sensitive to initial conditions. The "butterfly effect" is a popular term used to describe the idea that small variations in initial conditions can lead to vastly different outcomes over time. This theory has many real-world applications in various fields.

One of the fields that makes use of chaos theory is weather prediction. Meteorologists use chaos theory to understand how small variations in atmospheric conditions can lead to large-scale weather patterns. They use computer simulations to model how different initial conditions can lead to different weather outcomes. This helps them make more accurate weather predictions and plan for extreme weather events.

Another field that uses chaos theory is finance. Financial analysts use chaos theory to understand how small fluctuations in financial markets can have a significant impact on the economy. They use mathematical models to analyze stock prices and interest rates and determine how small changes can lead to large market movements. This helps them make informed investment decisions and minimize risk.

Chaos theory is also used in biology to study the behavior of populations of animals, plants, and microorganisms. Biologists use chaos theory to understand how small changes in the environment can have a major impact on the growth and survival of populations. This helps them make informed decisions about the conservation and management of natural resources.

In conclusion, chaos theory has a wide range of real-world applications and is used in fields such as weather prediction, finance, and biology. The idea that small variations in initial conditions can lead to vastly different outcomes over time is a powerful tool for understanding complex systems and making informed decisions.

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Answer:

Story

Jane is 1.7 m tall.  She stands 250 m away from the base of the Eiffel tower and looks up at the top of the building.  The angle of elevation from her eyeline to the top of the building is 45°.

Question

Calculate an estimate of the height of the building. Give your answer to the nearest meter.

Calculation

Label the sides of the triangle O, A and H (where O is the side opposite to the angle, A is the side adjacent to the angle and H is the hypotenuse).

In the triangle, the angle and side A is known, and O must be calculated.

Therefore, use the trig ratio tan(x) = O/A:

⇒ tan(40) = O/250

⇒ 250tan(40) = O

⇒ O = 209.7749078...

Assume Jane's eye-level is approximately 1.5 m above the ground.

Therefore, the Eiffel tower is approximately:

209.7749078... + 1.5 = 211.2749078.. meters tall

Rounding to the nearest meter ⇒ 211 m

Step-by-step explanation:

8x+ 14y= 4

-6×-7y= -10

For elimination method we can decide to eliminate either the y or x variable I'm going to eliminate the x variable so either of the one am eliminating we multiply the first equation by the coefficient of the variable we are eliminating in other words

8x +14y=4.....*-6

-6×-7y= -10......*8

-48x-84y= -24

-48x-56y= 80

then we multiply the second equation all through by -1

-48x-84y= -24

48x+ 56y= -80

28y=-104

y= 26/7

x= 8/3

you took time typing help that you forgot your Question :D

Answer:
you saved $10.00

Step-by-step explanation:

Discount = Original Price x Discount %/100

Discount = 40 × 25/100

Discount = 40 x 0.25

Answer:

10

Step-by-step explanation:

What is 25% of 40?

Y is 25% of 40

Equation: Y = P% * X

Solving our equation for Y

Y = P% * X

Y = 25% * 40

Converting percent to decimal:

p = 25%/100 = 0.25

Y = 0.25 * 40

Y = 10

Answer: 1) 36 m and 60 m^2     2) 15π/2 + 10 m and 75π/4 m^2

Step-by-step explanation:

Using the pythagorean theorem in the first question, we get that the slope is 10 m so the perimeter = 10 + 14 + 6 + 6 = 36 m and the area is

(14 + 6)*6/2 = 60 m^2

So in the next question, the arc of the circle has a length of

2π*5*3/4 = 15π/2

So the perimeter is 15π/2 + 5 + 5 = 15π/2 + 10 m

And the area is 3/4*π*5*5=75π/4 m^2

Hope it helps

Answer:

4 miles

Step-by-step explanation:

4 miles because if if if 58 of mile which is just a half mile basically and she does 7 laps

7 x 0.58=4.06 which is 4 miles

Have a good day :}

[tex]\textit{internal division of a line segment using ratios} \\\\\\ P(-10,3)\qquad Q(a,b)\qquad \qquad \stackrel{\textit{ratio from P to Q}}{2:3} \\\\\\ \cfrac{P\underline{R}}{\underline{R} Q} = \cfrac{2}{3}\implies \cfrac{P}{Q} = \cfrac{2}{3}\implies 3P=2Q\implies 3(-10,3)=2(a,b)[/tex]

[tex](\stackrel{x}{-30}~~,~~ \stackrel{y}{9})=(\stackrel{x}{2a}~~,~~ \stackrel{y}{2b}) \\\\\\ R=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-30+2a}}{2+3}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{9+2b}}{2+3} \right)}~~ = ~~\stackrel{\textit{and we know that is}}{(4~~,~~7)} \\\\[-0.35em] ~\dotfill[/tex][tex]\cfrac{-30+2a}{5}~~ = ~~4\implies -30+2a=20\implies 2a=50\implies a=\cfrac{50}{2}\implies \boxed{a=25} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{9+2b}{5}~~ = ~~7\implies 9+2b=35\implies 2b=26\implies b=\cfrac{26}{2}\implies \boxed{b=13}[/tex]

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position. The coordinates of the point Q are (25,13).

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.

Let the coordinates of the point Q be represented by Q(a,b).

Given the Ratio from P to Q is 2:3.

The internal division of the line segment using the ratios will be,

PR/RQ = 2/3

3P = 2Q

3(-10, 3) = 2(a, b)

Now, the coordinates of R can be rewritten as,

[tex]R = (\dfrac{-30+2a}{2+3},\ \dfrac{9+2b}{2+3}) = (4,7)[/tex]

Comparing the coordinates,

(-30+2a)/(2+3) = 4

a = 25

(9+2b)/(2+3) = 7

b = 13

Hence, the coordinates of the point Q are (25,13).

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Answer:

10 miles

Step-by-step explanation:

Distance walked in 1 hour = 4 miles

So, distance walked in 2.5 hours

= 4 miles × 2.5

= 10 miles

Answer:

Step-by-step explanation:

sin 44° = [tex]\frac{63}{ST}[/tex]

ST = [tex]\frac{63}{sin44}[/tex]

ST ≈ 90.7

Answer:

the answer is x=12√2

hope it helps

Answer:

e= 2.15

Step-by-step explanation:

Subtract both sides by 6

2.15=e

Thus e is 2.15

Hope this helps!

Answer:

11/61

Step-by-step explanation:

cos b = adj side/hypotenuse

=11/61

Answer:

CosB = B/H

Base(B)= 11

Perpendicular (P)=60.

Hypotenuse (H)= 61

CosB = B/H

CosB= 11/61

It should cut into

2 ne t is accurate

Answer:

A)  net A

B) AB = 3 in    BC = 5 in    CD = 8.6 in

C) 106.6 in²

Step-by-step explanation:

Part A:  

Part B:

From inspection of the diagram:

Part C:

Area of a rectangle = width x length

Area of a triangle = 1/2 x base x height

Surface area = 2(4 x 8.6) + (3 x 8.6) + 2(1/2 x 4 x 3)

                     = 68.8 + 25.8 + 12

                     = 106.6 in²

Answer:

length = 6 cm, breadth = 3 cm, perimeter 18 cm

Step-by-step explanation:

Let the breadth be x,

Then the length will be 2x

area of rectangle = length * breadth

using the formula:

The breadth is 3 cm

Length:

perimeter of rectangle:

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Answer:

Step-by-step explanation:

Let the breadth = x cm

Length = 2x

2x *x = 18

     x² = 18/2

     x² =9

     x = √9

x = 3 cm

Breadth = 3 cm

Length = 2*3 = 6 cm

Perimeter = 2*(length + breadth)

 =2*(3+6)

= 2*9

Perimeter = 18 cm

Answer:

last one "kiki" is true...

Answer:

Option 2 and 4

Step-by-step explanation:

2) Number of science questions = (3/4) of total questions

                              = [tex]\dfrac{3}{4}*24[/tex]

4) Number of marbles in the jar = (3/4) of the total marbles

                  [tex]=\dfrac{3}{4}*24[/tex]

Answer:

-10 is the correct answer

Step-by-step explanation:

hope this helps

Answer:

-10

Because I worked it out on paper

Answer:

The answer is B!!HOPE THIS HELPS :)

Step-by-step explanation:

I just guessed it and its right :)

Answer:

b

Step-by-step explanation:

Answer:

21.43

Step-by-step explanation:

280+20=300=total spent

300÷14=21.4285714

21.4285714 to the nearest hundredths place= 21.43

Answer:

37

Step-by-step explanation:

（x+10)+x+(3x-5)=180

5x=185

x=37

The sum of angles in the triangle is 180 degrees. Therefore, the value of x in the triangle is 35

The sum of angles of a triangle is 180 degrees. This simply implies the sum of the three angles in a triangle is equals to 180 degrees.

Therefore,

x + 10 + 3x - 5 + x = 180

combine like terms

x + x + 3x + 10 - 5 = 180

5x + 5 = 180

subtract 5 from both sides of the equation

5x + 5 - 5 = 180 - 5

5x = 175

divide both sides by 5

5x / 5 = 175 / 5

x = 35

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The number of days for which the money is left to reach the 20,400$ mark is; 21.28 days

The final amount to be reached is; $20400

The principal amount is; $8,000 and at. rate of 4.75 % compounded.

Hence, it follows that;

Divide both sides of the equation by 8000; we have;

Take log of both sides;

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Answer:

= B

[tex]\frac{16}{40} +\frac{15}{40} = \frac{31}{40} \\\\\frac{2}{5} +\frac{3}{8} =\frac{31}{40}[/tex]

Answer:

The 4th term is geometric

Step-by-step explanation:

For geometry series we use Tn = a•r^n-1

r = -3

a = 3

Use the equation Tn = 3(-3)^n-1 and you'll see that it's geometric.