How do I solve this using Sin or Cosine law?

The weight of this pack of gum is heavier than the mean weight by 3.11 standard deviations.

The supplied z-score of 3.11 can be best translated as "This pack of gum weighs 3.11 standard deviations more than the mean weight." A z-score indicates how many standard deviations an observation is from the population mean. When an observation has a positive z-score, it is above the mean; when it has a negative z-score, it is below the mean. The selected pack of gum weighs more than the population's mean weight because the specified z-score is positive. Furthermore, a z-score of 3.11 means that the pack of gum weighs 3.11 standard deviations more than the population's mean weight.

Learn more about standard deviations here:

brainly.com/question/23907081

#SPJ1

Answer:

  £216

Step-by-step explanation:

The total prize will be the sum of the divisions of the prize. The difference of those divisions is given.

__

Let P represent the value of the prize. The 1:11 ratio of the parts tells us there are 1 +11 = 12 total parts, and their ratio is P/12 : 11P/12. The sum of these divisions is the whole prize:

  P/12 +11P/12 = 12P/12 = P

The difference of the two divisions of the prize is ...

  11P/12 -P/12 = £180

  10P = £2160 . . . . . . . . multiply by 12 and simplify

  P = £216 . . . . . . . . divide by 10

The total prize is £216.

_____

Additional comment

The divisions of the prize are

  £216/12 = £18  and  11×£18 = £198

The sum of those divisions is the total prize: £18 +198 = £216.

The total price (prize)the difference between the shares is £180 is £216.

Let's represent the total price as "P." According to the information given, the price is divided into a ratio of 1:11.

The total number of parts in the ratio is 1 + 11 = 12 (1 part for the first share and 11 parts for the second share).

Let the first share be "x" and the second share be "11x" (since the ratio is 1:11).

Now, the difference between the shares is £180:

11x - x = £180

Simplifying:

10x = £180

Now, divide both sides by 10 to find the value of "x":

x = £180 / 10

x = £18

Now, we can find the total price "P" by adding the shares together:

P = x + 11x

P = £18 + £198

P = £216

So, the total price (prize) is £216.

Learn more about shares at https://brainly.com/question/32126629

#SPJ3

Answer:

-5

Step-by-step explanation:

x² - 4x - 45 = 0

(x - 9)(x + 5) = 0

x = 9 or -5

x² - 25 = 0

(x + 5)(x - 5) = 0

x = 5 or -5

-5 is a common factor between both of them

Answer:

36 Minutes

Step-by-step explanation:

You have to find the lowest common multiple which you can do by listing the times tables for each number.

9,18,27,36,45,54

12,24,36,48,60,72

and finding the lowest multiple that matches.

Both the train will meet after 36 minutes.

Thus, both the train will meet after 36 minutes.

Learn more about LCM here:

https://brainly.com/question/21504246

#SPJ2

Answer:

Emily has about 73 beads and Martha has about 62

Step-by-step explanation:

E = M · 1.2

M + ( .25 · E ) = m

m = 80

Now work backwards to find the answer.

Note that to find the answer you must get rid of the variable E, so you must use the expression M · 1.2 to represent E.

M + ( .25 · M · 1.2 ) = 80

M + .3M = 80

1.3M = 80

Divide both sides by 1.3

M = 61.5

Round to the nearest one

M = 62

Now use this to find E

E = 62 · 1.2

E = 74.4

Round to nearest one

E = 73

This might be confusing but I hope it was helpful!

Also, can I get brainliest because this took a lot of work to figure out.

The distance to the earth’s horizon from point P is 281.6 miles

The tangent line from P meets the radius of the earth at a right angle.

This means that the triangle is a right triangle.

The length of x is then calculated as:

(3959 + 10)^2= 3959^2 + x^2

Rewrite as:

x^2 = (3959 + 10)^2- 3959^2

Evaluate

x^2 = 79280

Take the square root of both sides

x = 281.6

Hence, the distance to the earth’s horizon from point P is 281.6 miles

Read more about distance at:

https://brainly.com/question/3503424

#SPJ1

Answer:

Answer above is wrong. See answer below.

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\frac{8+x}{12+x} =\frac{80}{100} =\frac{4}{5} \\40+5x=48+4x\\5x-4x=48-40\\x=8[/tex]

so she wins next 8 consecutive games to reach winning percentage of 80%.

let she loses next y games to reach winning percentage of 50 %.

[tex]\frac{16}{12+8+y} =\frac{50}{100} =\frac{1}{2} \\\frac{16}{20+y} =\frac{1}{2} \\32=20+y\\y=32-20=12y=12[/tex]

Hence she loses next 12 games to reach winning percentage of 50 %.

Answer:

[tex]540cm^{3}[/tex]

Step-by-step explanation:

A group of students from your school is part of the audience for a TV game show, the theoretical probability of students is mathematically given as  

P=2.7%

Generally, the equation for Probability  is mathematically given as

[tex]P=\frac{Desired outcomes}{Total outcomes}[/tex]

Where Desired outcomes

D=40C5 *110C3

D=1420112865560

And Total outcomes

T=150C8 *

T=5.2572*10^10{12}

Hence, Probability  

[tex]P=1420112865560/ 5.2572*10^10{12}[/tex]

P=0.0270

P=2.7%

In conclusion, the theoretical probability

P=2.7%

Read more about probability

https://brainly.com/question/11234923

#SPJ1

Answer:

white chocolates = 3

milk chocolates = 8

ratio= 3:8

[tex] \frac{3}{8} [/tex]

0.375

A line is a distance between two points. The possible equation of the line will be g(x) = 4x - 7

A line is a distance between two points. The equation of a line in slope-intercept form is expressed as y = mx + b

where:

Given the equation of the line graphed by Chin expressed as f(x) = 4x + 3, the equation similar the line must have the same slope. The possibe equation of the line will be g(x) = 4x - 7

Learn more on equation of a line here: https://brainly.com/question/13763238

#SPJ1

Answer:

C. y – 7 = 4(x – 1)

Step-by-step explanation:

I did the test and got it correct.

Answer:

5x-4y=10

solution

first find x intercept is the graph cross x-axis.to find the x intercept,we set y¹=0 and the Solve x.

5x-4y=10

5x-4(0)=0

x¹ =2 y¹=0

y intercept

5x-4y=10

5(0)-4y=10

y²=2.5 x²=0

Answer:

LN = 64 units

Step-by-step explanation:

Given M lies on LN, so LN = LM + MN --------------(1)

LN = 12x + 16

LM = 10x + 8

MN = 5x - 4

Substituting the values in equation 1, we get:

12x + 16 = (10x + 8) + (5x - 4)

12x + 16 = 15x + 4

15x - 12x = 16 -4

3x=12

Therefore x=4

LN= 12(4) + 16 = 64 units

Answer:

Each person get 4 slice of pizza and 2 is remaining

As AB and ED are parallel, they have the same slope. This means that since lines that are colllinear with parallel segments are parallel, lines l and m are parallel.

By counting the total number of outcomes, we conclude that the spinner has 4 sections.

Let's say that the spinner has N sections.

If we spin it twice, for the first outcome we have N possible outcomes and for the second spin there are N possible outcomes.

Then for the experiment of spinning the spinner twice, the number of outcomes is:

O = N*N

And we know that the number of possible outcomes for spinning the spinner twice is 16, then we have:

16 = N*N = N^2

Solving for N, we have:

N = √16 = 4

Then we conclude that the spinner has 4 sections.

If you want to learn more about outcomes:

https://brainly.com/question/10837034

#SPJ1

Answer:

x = 144

Step-by-step explanation:

Angle sum of heptagon = 900

5x + 90 + 90 = 900
5x + 180 = 900
5x + 180 - 180= 900 - 180
5x = 720
Divide both sides by 5
x = 144

Answer:

The graph is wider and is reflected across the x axis.

Step-by-step explanation:

See attached image.

The data points that fall within the mean absolute deviation are 2.9 and 3.1.

The mean absolute deviation is the mean average distance between every data point and the mean of the data set.

From the information given:

The mean absolute deviation is:

= (|5.3 - 2|)/1

= 3.3

Thus, the data points that fall within the mean absolute deviation are 2.9 and 3.1.

Learn more about mean absolute deviation here:

https://brainly.com/question/447169

#SPJ4

The statements that are true about the given points on the line are; Options B, C and D

A plane is defined by a line and a point outside of it. Meanwhile, a line is defined by two points. Thus, whenever we have 3 non-collinear points, we can define a plane.

Let us check each of the given options;

A) There are exactly two planes that contain points A, B, and F;

If these points are collinear, they can't make a plane and If they are not collinear, they define a plane.

Since we can't make two planes with them, then the statement is false.

B) There is exactly one plane that contains points E, F, and B;

Due to the same reasoning in part A, the statement is true assuming the points are not collinear.

C) The line that can be drawn through points C and G would lie in plane X;

The statement is true because both points C and G lie on plane X, and as such the line that connects them also should lie on the same plane.

D) The line that can be drawn through points E and F would lie in plane Y; Similar to above, this statement is true.

E) The only points that can lie on plane Y are points E and F.

This statement is false because infinite points can lie on a plane.

Read more about plane points at; https://brainly.com/question/11958640

#SPJ1

Answer:

3 sides

Step-by-step explanation:

If the interior angle measures 60 degrees, this means the exterior angle measures 120 degrees.

The exterior angle of a regular polygon is given by 360/n, where n is the number of sides, so setting this equal to 120, we get that n=3 sides

A. Four ways to solve a quadratic equation

---Factoring

---Completing the square

---Quadratic equation

---Graphing

B. Solve the equation by completing the square

x^2 - 4x - 11 = 0

x^2 - 4x = 11

x^2 - 4x + 4 = 11 + 4

(x - 2)^2 = 15

x - 2 = +/- 15

x - 2 = 15 || x = 17

x - 2 = -15 || x = -13

C. Solve the equation using the quadratic formula

Quadratic formula = [tex]\frac{-b +/-\sqrt{b^2 - 4ac} }{2a}[/tex]

Equation = 2x^2 + 16x + 24 = 0

a = 2

b = 16

c = 24

[tex]\frac{-16 +/- \sqrt{16^2 - 4(2)(24)} }{2(2)}[/tex]

[tex]\frac{-16 +/- \sqrt{256 - 192} }{4}[/tex]

[tex]\frac{-16 +/- \sqrt{64} }{4}[/tex]

[tex]\frac{-16 +/- 8 }{4}[/tex]

[-16 + 8] / 4 = -2

[-16 - 8] / 4 = -6

x = -6, -2

Hope this helps!

Answer:

the median will be 200.

the mode will be 402 n 398.

the mean will be 400.

The answer 19/24 is not reasonable because 5/6 is closer to 1 than to 1/2, and 3 is close to 1/2, making the difference close to 1/2.

Step-by-step explanation:

the third answer.

5/6 is almost 1, 3/8 is almost 1/2, so their difference is close to 1 - 1/2 = 1/2.

and 19/24 is much bigger than 1/2 (which would be 12/24).

in real numbers

5/6 - 3/8 = 5×4/24 - 3×3/24 = 20/24 - 9/24 = 11/24.

which is indeed very close to 1/2 (or 12/24).

The series is a convergence series and the sum of the series is -8/3

The series is given as:

[tex]\sum\limits^{\infty}_{n = 1} -4(-\frac 12)^{n-1}[/tex]

The above series has the following properties:

Start by calculating the absolute value of the common ratio

Absolute value = |-1/2|

This gives

Absolute value = 1/2

The above value is less than 1.

It means that the series converges.

This is calculated using:

[tex]S_{\infty} = \frac{a}{1 -r}[/tex]

So, we have:

[tex]S_{\infty} = \frac{-4}{1 + \frac 12}[/tex]

Evaluate the sum

[tex]S_{\infty} = \frac{-4}{\frac 32}[/tex]

Evaluate the quotient

[tex]S_{\infty} = \frac{-8}{3}[/tex]

Hence, the sum of the series is -8/3

Read more about geometric series at:

https://brainly.com/question/24643676

#SPJ1

Answer:

what are you asking for? the area of the inner circle? the area of the outer circle? the area shaded only yellow?

Answer:

124

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