The diagram below shows rectangle ABC is a midtsin of
BC, such that D,E and F are on the same line API AD
i = 53, 13" BE-sm
and DE 2 EF
84
2176
F
with reasons
3.1 Prove
AB - BF
3.2. Calculate AD
3.3 Complece. In are rigter angled A BEF, son 53, 13" - BE

Answer:

a) 0.4658 = 46.58% probability that the chosen ball is blue

b) 0.322 = 32.2% probability that it came from the first urn

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

a. What is the probability that the chosen ball is blue?

6/20 = 0.3 of 0.5(first urn)

12/19 = 0.6316 out of 0.5(second urn).

So

[tex]P(A) = 0.3*0.5 + 0.6316*0.5 = 0.4658[/tex]

0.4658 = 46.58% probability that the chosen ball is blue.

b. If the chosen ball is blue, what is the probability that it came from the first urn?

Event A: Blue Ball

Event B: From first urn

From item a., [tex]P(A) = 0.4658[/tex]

Probability of blue ball from first urn:

0.3 of 0.5. So

[tex]P(A \cap B) = 0.3*0.5 = 0.15[/tex]

Probability:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.15}{0.4658} = 0.322[/tex]

0.322 = 32.2% probability that it came from the first urn

Answer:

it was very nice step so they wine so anther bed boys decided to take his legs and round and round to good boys

Answer:

[tex]P = 8 + 2\sqrt{26}[/tex]

Step-by-step explanation:

Given

[tex]W = (-2, 4)[/tex]

[tex]X = (2, 4)[/tex]

[tex]Y = (1, -1)[/tex]

[tex]Z = (-3,-1)[/tex]

Required

The perimeter

First, calculate the distance between each point using:

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 -y_2)^2[/tex]

So, we have:

[tex]WX = \sqrt{(-2- 2)^2 + (4-4)^2 } =4[/tex]

[tex]XY = \sqrt{(2- 1)^2 + (4--1)^2 } =\sqrt{26}[/tex]

[tex]YZ = \sqrt{(1- -3)^2 + (-1--1)^2 } =4[/tex]

[tex]ZW = \sqrt{(-3--2)^2 + (-1-4)^2 } =\sqrt{26}[/tex]

So, the perimeter (P) is:

[tex]P = 4 + \sqrt{26} + 4 + \sqrt{26}[/tex]

[tex]P = 8 + 2\sqrt{26}[/tex]

Answer:

its D.

Step-by-step explanation:

took test

Both the question and options given doesn't seem to be properly formatted. A well formatted form of the question is written in the comment section below.

Answer:

10a^4

Step-by-step explanation:

Given the expression :

7a^4+3a^4

The sum of the expression given above could be taken directly Since the power of each individual value is the same.

7a^4+3a^4

Adding the coefficients

(7+3)a^4

10a^4

Answer:165.47

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

1 and 1

2 and 2

3 and 3

4 and 4

5 and 5

6 and 6

6/36 = 1/6

Answer:

1/6.

Step-by-step explanation:

The favourable outcomes are 1,1  2,2  3,3  4,4   5,5 and 6,6  = 6 outcomes.

All the possible outcomes for 2 regular dice = 36.

Therefore the required probability = 6/36

= 1/6.

Answer:

distinctly over here I think so

Answer:

the scores on her last test is x (x > 0)

because on her last tests she scored 4 points lower than she did on her fifth test

=> the scores in the 5th test is x + 4

because Angela’s average for six math tests is 87, we have:

[tex] \frac{93 + 87 + 82 + 86 + x + x + 4}{6} = 87 \\ \\ < = > \frac{352 + 2x}{6} = 87 \\ \\ < = > 352 + 2x = 522 \\ \\ < = > 2x = 170 \\ \\ < = > x = 85[/tex]

=> on her last test, she had 85

=> on her 5th test, she had 85 + 4 = 89

Answer:

B. 9

Step-by-step explanation:

We are given that y varies inversely with x. Recall that inverse variation has the form:

[tex]\displaystyle y=\frac{k}{x}[/tex]

Where k is the constant of variation.

We are given that y = 18 when x = 12. Hence:

[tex]\displaystyle (18)=\frac{k}{(12)}[/tex]

Solve for k. Multiply both sides by 12:

[tex]k=12(18)=216[/tex]

Thus, our equation is:

[tex]\displaystyle y=\frac{216}{x}[/tex]

We want to find x when y = 24. Substitute:

[tex]\displaystyle \frac{24}{1}=\frac{216}{x}[/tex]

Cross-multiply:

[tex]24x=216[/tex]

Divide both sides by 24. Hence:

[tex]x=9[/tex]

Our answer is B.

Answer:

B

Step-by-step explanation:

Given that y varies inversely with x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

To find k use the condition y = 18 when x = 12 , then

18 = [tex]\frac{k}{12}[/tex] ( multiply both sides by 12 )

216 = k

y = [tex]\frac{216}{x}[/tex] ← equation of variation

When y = 24 , then

24 = [tex]\frac{216}{x}[/tex] ( multiply both sides by x )

24x = 216 ( divide both sides by 24 )

x = 9

Answer:

Y' = - 1

Step-by-step explanation:

Y' = - 2x +3

So y' (2,2) =-2*2 +3= - 1

Answer:

https://www.omnicalculator.com/finance/compound-interest

Step-by-step explanation:

this is a link to a compound interest calculator and it helped me with similar problems hope it helps you

Answer:

[tex]\frac{1}{g^{5nd+10v+20dv} }[/tex]

Step-by-step explanation:

Answer:

shall I have to answer for x pls tell

Answer:

D, B, C, A

Step-by-step explanation:

Answer:

10 times

Step-by-step explanation:

Multiply 40 by 28

1120

Multiply 16 by 7

112

Divide the two numbers

You get 10

Hope this helps!

Answer:

98.93

Step-by-step explanation:

we're looking for

4 ft 9 <x<6 ft 4

Let's convert this into inches

4 ft 9 = 57 in

6 ft 4= 76

so we're looking for

57<x<76

which is equal to

p(76)-p(57)

let's start by p(76)

(76-62.3)/2.3= 5.946521 which on a ztable is equal to 1

p(57)=

(57-62.3)/2.3= -2.3

which is equal to 1-.9893= .0107

Finally,

1-.0107= .9893 = 98.93%

Answer:

I think it is 160 x2 so you would probably divide 160 by x2 which would 144

Step-by-step explanation:

Answer:

[tex]\text{Perimeter: }48\:\mathrm{m},\\\text{Area: }84\:\mathrm{m^2}[/tex]

Step-by-step explanation:

The area of a triangle with side lengths [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] is given by:

[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex], where [tex]s=\frac{a+b+c}{2}[/tex]

Substituting [tex]a=21, b=17, c=10[/tex], we have:

[tex]A=\sqrt{24(24-21)(24-17)(24-10)},\\A=\sqrt{24(3)(7)(14)},\\A=\sqrt{7,084},\\A=\boxed{84\:\mathrm{m^2}}[/tex]

The perimeter of a polygon is given by the sum of its sides. Since the triangle has sides 10, 17, and 21, its perimeter is [tex]10+17+21=\boxed{48\:\mathrm{m}}[/tex].

Answer:

338

Step-by-step explanation:

1×2=2 2+6+10+14+18+22+26+30

3×2=6 +34+36+38+42+46+50=338

5×2=10

7×2=14

9×2=18

11×2=22

13×2=26

15×2=30

17×2=34

19×2=38

21×2=42

23×2=46

25×2=50

Answer:

12x2 – 75 = 3 (2x+5)(2x – 5)

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

since it's negative so it will get smaller

Answer:

[tex]x^{3}cos(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+3}}{(2n)!}[/tex]

[tex]x^{3}sin(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+5}}{(2n+1)!}[/tex]

Step-by-step explanation:

A

Let's start with the first function:

[tex]x^{3}cos(x^{2})=x^{3}-\frac{x^{7}}{2!}+\frac{x^{11}}{4!}-\frac{x^{15}}{6!}+...[/tex]

In order to find the expression for the general term, we will need to analyze each part of the sum. First, notice that the sign of the terms of the sum will change with every new term, this tells us that the expression must contain a

[tex](-1)^{n}[/tex].

This will guarantee us that the terms will always change their signs so that will be the first part of our expression.

next, the power of the x. Notice the given sequence: 3, 7, 11, 15...

we can see this is an arithmetic sequence since the distance between each term is the same. There is a distance of 4 between each consecutive power, so this sequence can be found by adding a 4n to the original number, the 3. So the power is given by 4n+3.

so let's put the two things together:

[tex](-1)^{n}x^{4n+3}[/tex]

Finally the denominator, there is also a sequence there: 0!, 2!, 4!, 6!

This is also an arithmetic sequence, where we are multiplying each consecutive value of n by a 2, so in this case the sequence can be written as: (2n)!

So let's put it all together so we get:

[tex]\frac{(-1)^{n}x^{4n+3}}{(2n)!}[/tex]

So now we can build the whole series:

[tex]x^{3}cos(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+3}}{(2n)!}[/tex]

B

Now, let's continue with the next function:

[tex]x^{3}sin(x^{2})=x^{5}-\frac{x^{9}}{3!}+\frac{x^{13}}{5!}-\frac{x^{17}}{7!}+...[/tex]

In order to find the expression for the general term, we will need to analyze each part of the sum. First, notice that the sign of the terms of the sum will change with every new term, this tells us that the expression must contain a

[tex](-1)^{n}[/tex].

This will guarantee us that the terms will always change their signs so that will be the first part of our expression.

next, the power of the x. Notice the given sequence: 5, 9, 13, 17...

we can see this is an arithmetic sequence since the distance between each term is the same. There is a distance of 4 between each consecutive power, so this sequence can be found by adding a 4n to the original number, the 5. So the power is given by 4n+5.

so let's put the two things together:

[tex](-1)^{n}x^{4n+5}[/tex]

Finally the denominator, there is also a sequence there: 1!, 3!, 5!, 7!

This is also an arithmetic sequence, where we are multiplying each consecutive value of n by a 2 starting from a 1, so in this case the sequence can be written as: (2n+1)!

So let's put it all together so we get:

[tex]\frac{(-1)^{n}x^{4n+5}}{(2n+1)!}[/tex]

So now we can build the whole series:

[tex]x^{3}sin(x^{2})=\sum _{n=0} ^{\infty} \frac{(-1)^{n}x^{4n+5}}{(2n+1)!}[/tex]

[tex]option(c) \: cylinder[/tex]

Step-by-step explanation:

You can see that in the figure, this is rectangle. Here, ABCD is rotated around the vertical line through A and D. So, you will get Cylinder shape as you rotate it.

Answer:

Quadrants

Step-by-step explanation:

When two lines intersect such that they are perpendicular to each other, then  quadrants are said to be formed. So that a given space would be divided into four quadrants when two perpendicular lines are drawn on it.

Each section which is called quadrant is at right angle to one another. So that the addition of their angles at the meeting point is the sum of four right angles i.e [tex]360^{o}[/tex]. Thus each of the four sections created by the intersecting lines is called a quadrant.

The options are;

1) AB is bisected by CD

2) CD is bisected by AB

3) AE = 1/2 AB

4) EF = 1/2 ED

5) FD= EB

6) CE + EF = FD

Answer:

Options 1, 3 & 6 are correct

Step-by-step explanation:

We are told that Point E is the midpoint of AB. Thus, any line that passes through point E will bisect AB into two equal parts.

The only line passing through point E is line CD.

Thus, we can say that line AB is bisected by pine CD. - - - (1)

Also, since E is midpoint of Line AB, it means that;

AE = EB

Thus, AE = EB = ½AB - - - (2)

Also, we are told that F is the mid-point of CD.

Thus;

CF = FD

Point E lies between C and F.

Thus;

CE + EF = CF

Since CF =FD

Thus;

CE + EF = FD - - - (3)

Answer:

[tex]9 + 7i[/tex]

Step-by-step explanation:

[tex]7i^5+9i^8[/tex]

[tex]i^5 = i\\ i^8 = 1[/tex]

9514 1404 393

Answer:

  6,364.8 lb

Step-by-step explanation:

The centroid of the plate is its center, so is 1.5 ft above the bottom of the pool, or 8.5 ft below the surface. The area of the plate is (3 ft)(4 ft) = 12 ft². Then the fluid force is ...

  (62.4 lb/ft³)(8.5 ft)(12 ft²) = 6,364.8 lb

Answer:

ok so if the lion is 3 times bigger we have to multiply the length of the cat by

3

3*76=228

so the lion is 228 cm long

now we divide by 100 for meters

228 divided by 100=2.28 meters

Hope This Helps!!!

Answer:

2.28 Meters

Step-by-step explanation:

If the lion is 3 times as long as the cat and the cat is 76cm long you just multiply 76*3=228 convert that to meters and it gives you 2.28 meters in length for the lion