SECTION B
Answer ALL questions. Write your answers in the spaces provided.
1 Data set A has a median value of 3.1
Here is data set B.
14
-9
28
-38
-13
-2
(a) Write a statement to compare the median values of the two sets of data.
(2)

Answer:

x=5

y=3/2

Step-by-step explanation:

Take it or leave it, that's what the computer said.

Answer:

20

Step-by-step explanation:

a)x^2+16^2=a^2

b)x^2+25^2=b^2

c)a^2+b^2=(16+25)^2

a+b)2x^2+25^2+16^2=41^2=a^2+b^2

2x^2=800

x=20

Answer:

[tex] g(x)=-8|x |+1. = 9552815 \geqslant 6[/tex]

9514 1404 393

Answer:

Step-by-step explanation:

a) Angle CAE can be found using the tangent relation.

  tan(∠CAE) = CE/AE

  tan(∠CAE) = 6/20

  ∠CAE = arctan(6/20) ≈ 16.7°

__

b. The length of DF can be found using the law of cosines.

  DF² = FA² +DA² -2·FA·DA·cos(A)

  DF² = 14² +10² -2·14·10·cos(16.7°) ≈ 27.8086

  DF ≈ √27.8086

  DF = 5.3

Answer:

0.3758 = 37.58% probability that at most one of her first 10 arrows hits the target

Step-by-step explanation:

For each shot, there are only two possible outcomes. Either they hit the target, or they do not. The probability of a shot hitting the target is independent of any other shot, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Each arrow with a probability 0.2

This means that [tex]p = 0.2[/tex]

First 10 arrows

This means that [tex]n = 10[/tex]

What is the probability that at most one of her first 10 arrows hits the target?

This is:

[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]

So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074[/tex]

[tex]P(X = 1) = C_{10,1}.(0.2)^{1}.(0.8)^{9} = 0.2684[/tex]

Then

[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.1074 + 0.2684 = 0.3758[/tex]

0.3758 = 37.58% probability that at most one of her first 10 arrows hits the target

Answer:

12

Step-by-step explanation:

10 - 1/2 x = 12-4/3x

60 - 3x = 72-2x

-12 = - x

Answer:

36.87

Step-by-step explanation:

sin(b)/12 = .05

arcsin(.6) = 36.87

Answer:

3

Step-by-step explanation:

x 1，2，3，4

y-3，-5，-7，-9

[tex]y = - 3 - (x - 1) \times 2[/tex]

The linear function is given by y = 7x - 4

A linear function is in the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the y intercept

From the table, using the points (1, 3) and (4, 24):

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-3=\frac{24-3}{4-1}(x-1)\\\\ y=7x-4[/tex]

The linear function is given by y = 7x - 4.

Find out more on linear function at: https://brainly.com/question/4025726

Answer:

Here's your answer.

Step-by-step explanation:

Just multiply in

Answer:

1/4 = x

Step-by-step explanation:

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

Step 1 :- Distribute 2

x - 2 × 3x - 2 × 1 = 3x

x - 6x + 2 = 3x

Step 2:- Combine like terms

-5x + 2 = 3x

Step 3 :- Add 5x to both sides

-5x + 5x + 2 = 3x + 5x

2 = 8x

Step 4 :- Divide both side by 8

2/8 = 8x / 8

1/4 = x

Answer:

let x represent the bigger number

x+x-47=125

2x-47=125

2x=125+47

2x=172

2x/2=172/2

x=86

the smaller number=x-47

86-47

39

therefore the answer is a) 39 and 86

Answer:

A

Step-by-step explanation:

To find the sum of 125, you have to add the numbers.

39+86 = 125

To find the difference of 47, you have to subtract the numbers.

86-39 = 47

Answer:

D

Step-by-step explanation:

Slope of the first line = (1-3)/1 = -2

can you show a picture of the symbols

Answer:

z = 3.6

Step-by-step explanation:

Given that,

z varies directly with x and inversely with the square of y. We can write it as :

[tex]z\propto \dfrac{x}{y}\\\\z=\dfrac{kx}{y}[/tex]

Where

k is constant

Put z = 16 when x = 4 and y = 1

[tex]16=\dfrac{k\times 4}{1}\\\\k=4[/tex]

Now put k = 4, x = 8 and y = 9

[tex]z=\dfrac{4\times 8}{9}\\\\z=3.6[/tex]

So, the value of z is equal to 3.6.

Answer:

2

Step-by-step explanation:

Answer:

Common Ratio=-3

Step-by-step explanation:

To find any common ratio in a sequence, always take the second number in the sequence and divide it by the first number. However, you must be careful because the common ratio should only be negative if the values in the sequence are alternating between negative and positive. Therefore, if the sequence of numbers is simply decreasing in value, this does not mean that the common ratio is negative. The common ratio would still be positive. If the sequence is decreasing in value, this means that the common ratio would be a fraction or a decimal less than one.

Step-by-step explanation:

here is the answer. Feel free to ask for more.

Answer:

452.2 cm

Step-by-step explanation:

A = 4πr²

A = 4 (3.14) (6)²

A = 4 (3.14) (36)

A = 452.16

A = 452.2 cm (nearest tenth)

Answer:

200 test tubes will fill the container

Step-by-step explanation:

Hi there!

We need to find out how many 5 milliliter tubes will fill a 1 liter container

First, let's convert everything to the same unit, as the tubes and the container are in different units.

Let's do milliliters, as those are smaller than liters and we will avoid having decimals.

there are 1,000 milliliters in a liter (the unit prefix "milli-" means "thousand")

Let's say the number of test tubes needed to fill the container is x

As each tube has 5 milliliters of water, 5x milliliters will equal 1,000 milliliters (1 liter)

as an equation, that's

5x=1,000

divide both sides by 5

x=200

So that means 200 test tubes will fill the container

Hope this helps! :)

Answer:

Here is how to start

Step-by-step explanation:    7  2  13  42

1 milliliter is one one thousands of a liter      1 milliliter  = 0.001 liter

1000 milliliter is equal to 1 liter

How many 5 milliliter test tubes are in 1 liter?

1000 milliliter / 5 milliliter per test tube   =  ________  test tubes

Answer:

[tex]{ \tt{2x + 4y = 8 - - - (a)}} \\ { \tt{x = 3y - 6 - - - (b)}} [/tex]

Substitute for x in equation (a) :

[tex]{ \tt{2(3y - 6) + 4y = 8}} \\ { \tt{6y - 12 + 4y = 8}} \\ { \tt{10y = 20}} \\ y = 2[/tex]

Substitute for y in equation (b) :

[tex]{ \tt{x = (3 \times 2) - 6}} \\ x = 0[/tex]

2x+4y =8

x=3y-6 ——> x–3y=–6

x–3y = – 6 ] ×(–2) ——> –2x +6y=12

2x+4y=8

–2x+6y =12

__o_o____

0+10y=20 —> 10y= 20 —> y= 20/10 —> y= 2

2x+4y=8 —> 2x + 4(2) = 8 —> 2x + 8=8 —> 2x = 0 —> x=0

(x,y) —> (0,2)

Answer:

18x2 is 36 but you have to minus it so the answer is 28.

This question is incomplete, the complete question is;

A given population proportion is .25. What is the probability of getting each of the following sample proportions

a) n = 110 and = p^ ≤ 0.21, prob = ?

b) n = 33 and p^ > 0.24, prob = ?

Round all z values to 2 decimal places. Round all intermediate calculation and answers to 4 decimal places.)

Answer:

a) the probability of getting the sample proportion is 0.1660

b) the probability of getting the sample proportion is 0.5517

Step-by-step explanation:

Given the data in the questions

a)

population proportion = 0.25

q = 1 - p = 1 - 0.25 = 0.75

sample size n = 110

mean = μ = 0.25

S.D = √( p( 1 - p) / n ) = √(0.25( 1 - 0.25) / 110 ) √( 0.1875 / 110 ) = 0.0413

Now, P( p^ ≤ 0.21 )

= P[ (( p^ - μ ) /S.D) < (( 0.21 - μ ) / S.D)

= P[ Z < ( 0.21 - 0.25 ) / 0.0413)

= P[ Z < -0.04 / 0.0413]

= P[ Z < -0.97 ]

from z-score table

P( X ≤ 0.21 ) = 0.1660

Therefore, the probability of getting the sample proportion is 0.1660

b)

population proportion = 0.25

q = 1 - p = 1 - 0.25 = 0.75

sample size n = 33

mean = μ = 0.25

S.D = √( p( 1 - p) / n ) = √(0.25( 1 - 0.25) / 33 ) = √( 0.1875 / 33 ) = 0.0754

Now, P( p^ > 0.24 )  

= P[ (( p^ - μ ) /S.D) > (( 0.24 - μ ) / S.D)

= P[ Z > ( 0.24 - 0.25 ) / 0.0754 )

= P[ Z > -0.01 / 0.0754  ]

= P[ Z > -0.13 ]

= 1 - P[ Z < -0.13 ]

from z-score table

{P[ Z < -0.13 ] = 0.4483}

1 - 0.4483

P( p^ > 0.24 )  = 0.5517

Therefore, the probability of getting the sample proportion is 0.5517

y=3× + 7 , y=×- 9 , 3×- 9 , 3×- y= 1 , 7× + 2y = 37.

Answer:

[tex]\cos(\theta)= \frac{\sqrt{377}}{29}[/tex]

Step-by-step explanation:

Given

[tex]\sin(\theta) = -\frac{4}{\sqrt{29}}[/tex] -- the correct expression

Required

[tex]\cos(\theta)[/tex]

We know that:

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

Make [tex]\cos^2(\theta)[/tex] the subject

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

Substitute: [tex]\sin(\theta) = -\frac{4}{\sqrt{29}}[/tex]

[tex]\cos^2(\theta)= 1 - (-\frac{4}{\sqrt{29}})^2[/tex]

Evaluate all squares

[tex]\cos^2(\theta)= 1 - (\frac{16}{29})[/tex]

Take LCM

[tex]\cos^2(\theta)= \frac{29 - 16}{29}[/tex]

[tex]\cos^2(\theta)= \frac{13}{29}[/tex]

Take square roots of both sides

[tex]\cos(\theta)= \±\sqrt{\frac{13}{29}}[/tex]

cosine is positive in the 4th quadrant;

So:

[tex]\cos(\theta)= \sqrt{\frac{13}{29}}[/tex]

Split

[tex]\cos(\theta)= \frac{\sqrt{13}}{\sqrt{29}}[/tex]

Rationalize

[tex]\cos(\theta)= \frac{\sqrt{13}}{\sqrt{29}} * \frac{\sqrt{29}}{\sqrt{29}}[/tex]

[tex]\cos(\theta)= \frac{\sqrt{13*29}}{29}[/tex]

[tex]\cos(\theta)= \frac{\sqrt{377}}{29}[/tex]

Answer:

n = 4 is 10

hope it helps and have a good day

Answer:

it is 61-28 but I not sure u can scan for any application to make sure u get it ur answer thx for

Hello!

3a = 7b =>

=> 3 × a = 7 × b =>

=> a/b = 7/3

Good luck! :)

Answer:

59

Step-by-step explanation:

Just get the supplement of 121.

So angle 1 is 180-121 = 59 degrees

Answer:

50% i believe

Step-by-step explanation:

because in every scenario theres 2 teams and if they are well matched it be half and half on every game assuming they're the same level of comp