29 + 43 using mental math

Answer:

The probability that Archie will receive a grade higher than a B in the course is 0.2164.

Step-by-step explanation:

We are given that Archie learns that 93% of past students who did not attend TA sessions received a grade of B or below in the course. Archie also learns that 11% of past students received a grade higher than B.

Let B = event that the student received a grade higher than B.

and T = event that the student discussion sessions with the TA.

So, P(B) = 0.11 and P(T) = [tex]\frac{4}{18}[/tex] = 0.22

Also, the probability that the students who did not attend TA sessions received a grade of B or below in the course = P(B'/T') = P(not B/not T) = 0.92

Now, we have to find the probability that Archie will receive a grade higher than a B in the course given he attended the discussion sessions with the TA = P(B/T)

As we know that the conditional probability formula is given by;

                           P(B/T) = [tex]\frac{\text{P}(\text{B} \bigcap \text{T})}{\text{P(T)}}[/tex]

Now, as it is given that P(not B/not T) = 0.92

So, [tex]\frac{\text{P}(\text{not B} \bigcap \text{not T})}{\text{P(not T)}} =0.92[/tex]

      [tex]\frac{\text{P}(\text{not B} \bigcap \text{not T})}{1 - \text{P(T)}} =0.92[/tex]

      [tex]\frac{\text{P}(\text{not B} \bigcap \text{not T})}{1 - 0.22}} =0.92[/tex]

[tex]{\text{P}(\text{not B} \bigcap \text{not T})} =0.92\times 0.78[/tex]

[tex]{\text{P}(\text{not B} \bigcap \text{not T})}[/tex] = 0.7176

Also, [tex]{\text{P}(\text{ B} \bigcup \text{ T})}= 1 - {\text{P}(\text{not B} \bigcap \text{not T})}[/tex]

[tex]{\text{P}(\text{ B} \bigcup \text{ T})}[/tex] = 1 - 0.7176 = 0.2824  

Now, the formula for [tex]{\text{P}(\text{ B} \bigcup \text{ T})}[/tex] is given by;

[tex]{\text{P}(\text{ B} \bigcup \text{ T})} = \text{P(B)} + \text{P(T)} - {\text{P}(\text{ B} \bigcap \text{ T})}[/tex]

0.2824 = 0.11 + 0.22 - [tex]\text{P(B} \bigcap \text{T})[/tex]

[tex]\text{P(B} \bigcap \text{T})[/tex] = 0.33 - 0.2824 = 0.0476

Now, the required probability P(B/T) = [tex]\frac{\text{P}(\text{B} \bigcap \text{T})}{\text{P(T)}}[/tex]

                                                         = [tex]\frac{0.0476}{0.22}[/tex] = 0.2164

Hence, the probability that Archie will receive a grade higher than a B in the course is 0.2164.

Answer:

834100

Step-by-step explanation:

1. Move the decimal FIVE times to the right

8.341 ----> 834100.

2. Solution

834100

Answer:

-1

Step-by-step explanation:

2x-y+7

Let x = -5 and y = -2

2(-5) -(-2) +7

-10 +2 +7

-10 +9

-1

Answer:

4.1

Step-by-step explanation:

Answer:

21

Step-by-step explanation

They jumped 3 meters above the water, jumped down 18, 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18, thats 15 away, the distance is 15, if I am worng (probably am) try 20, if not, Im retarted and dont trust me with this.

9514 1404 393

Answer:

  21 m

Step-by-step explanation:

The difference in height between +3 meters and -18 meters is ...

  3 -(-18) = 3 +18 = 21 . . . . meters

Answer:

35.56

Step-by-step explanation:

multiply the length value by 2.54

Answer:

35.56 cm.

Step-by-step explanation:

multiply the length value (the number) by 2.54

Answer:

y = -8/5

Step-by-step explanation:

Step 1: Write equation

5/8y = -1

Step 2: Solve for y

Step 3: Check

Plug in y to verify it's a solution.

Answer:

3?

Step-by-step explanation:

It would be 3 since he took 1 hour in one order it would take another 3 hours to complete 3 other orders. Sorry if I'm wrong. :)

Answer:

I think the answer is B

Step-by-step explanation:

he would need to factor 4x² in order to get his answer not just 4x

Answer:fgh

Step-by-step explanation:

Answer:

51.7 / 4 = 12.925

Step-by-step explanation:

Answer:

Step-by-step explanation:

Total population

Let handed population

Percentage of left handed population

Answer:

Step-by-step explanation:

estimated world population in 2011 = 7x10⁹

left handed = 682,000,000

find:

Approximately what percentage of the world population is left handed according to the 2011 estimation

percentage = left handed population

                            total population

                    =       682,000,000  

                           7,000,000,000

                    =     0.682

                            7.0

                    =  9.7 %

Answer:

150 adults and 270 children

Step-by-step explanation:

Let there are x adults and y children.

ATQ,

x+y=420

or

y=420-x ....(1)

Adult visitors pay $3 and children visitors pay $1. on one day, the zoo collected a total of $720.

ATQ,

3x+y=720...(2)

Put equation (1) in equation (2).

3x+420-x=720

2x=720-420

2x=300

⇒x=150

Put the value of x in equation (1)

y=420-150

⇒y=270

So, there are 150 adults and 270 children visited.

Answer:

yes

Step-by-step explanation:

Answer:  $5.40

Step-by-step explanation:

First we will find the tax amount for Dave by multiplying 8% by 15.

8% * 15 =  1.2  

Now add it to the original price of the baseball which is 15.

15 + 1.2= 16.20  This means Dave paid $16.20 in total.

Now find the tax amount for Mel.

20 * 8% = 1.6  

Add 1.6 to the original price which is $20.

1.6 + 20 = 21.60    

Mel also paid $21.60 in total.

To find the difference  we need to subtract the lowest amount from the highest amount.

21.60 - 16.20 = 5.40

Answer:

x = 12 degrees

Step-by-step explanation:

(9x-4)+(6x+4)=180                 Linear Pair Theorem

15x=180                                  Simplified

180/15 = x                               Division Property of Equality

x = 12 degrees                       Simplified

Hope this helped! ;)

Answer:

88% of people were infected by the cold virus

Step-by-step explanation:

153/135 multiplied by 100 will give the answer to be 88.235%. round to nearest percent is 88%

Answer:

yes you cam win money form playing this game but you can also lose money.

Step-by-step explanation:

Answer:

[tex]y+6=\frac{-8}{7} (x-7)[/tex]

Step-by-step explanation:

To find the slope of the equation use [tex]\frac{y_2-y_1}{x_2-x_1}[/tex].

So, [tex]\frac{-6-2}{7-0}[/tex] = [tex]\frac{-8}{7}[/tex]. Now we can use our slope and any of the two points to write in point-slope form, which is [tex]y-y_1=m(x-x_1)[/tex]. Using the point (7,-6), the formula will give [tex]y+6=\frac{-8}{7} (x-7)[/tex].

To check, you can plug in this equation and the points into a calculator to graph. The line passes through both points.

A. Changing the value of h will cause horizontal translation.

Transformations are of many types like translation, rotation, reflection and dilation.These transformations are of two types rigid transformation where the shape and size of image and pre image remains same and another one is non-rigid transformation in which size changes but shape of doesn't change.

We know that a quadratic function can be represented by a 2D co ordinate which has x axis and y axis.

Given a function f(X) = ( x - h) + k will cause horizontal transformation of h units to the left.

learn more about transformation here :

https://brainly.com/question/11709244

#SPJ2

Answer:

Step-by-step explanation:

The sum of opposite angle and sides of a parallelogram is 180 . If a parallelogram JKLM has angle measures J(2 x +9) and M(6 x -1), then <J + < M = 180

Substitute:

2 x +9+6x-1 = 180

collect like terms;

2x+6x+9-1 = 180

8x+8 = 180

8x = 180-8

8x = 172

x = 172/8

x = 21.8°

For the shape to be a quadrilateral, then the measure of angle k must 128 degrees

For quadrilateral PQRS to be an actual quadrilateral, then:

[tex]J + M = 180[/tex] implies that:

[tex]2x + 9 + 6x -1 = 180[/tex]

Collect like terms

[tex]2x + 6x = 180 -9 +1[/tex]

[tex]8x = 172[/tex]

Divide both sides by 8

[tex]x = 21.5[/tex]

We have:

[tex]K = M[/tex]

This becomes

[tex]K = 6x -1[/tex]

Substitute 21.5 for x

[tex]K = 6\times 21.5 -1[/tex]

[tex]K = 129 -1[/tex]

Subtract 1 from 129

[tex]K = 128[/tex]

Hence, the measure of angle K must be 128 degrees

Read more about quadrilaterals at:

https://brainly.com/question/25696839

Answer:

C

Step-by-step explanation:

Answer:

P = 20x - 12

Step-by-step explanation:

The Perimeter of a Rectangle is 2l + 2w, where l is the length and w is the width.

Now, let's substitute the given values.

2(8x - 9) + 2(2x + 3)

= 16x - 18 + 4x + 6

= 20x - 12                     <--- This is the answer

Hope this helps!

Answer:

were ate circles I'm suppose to use

Step-by-step explanation:

where is the circles

Answer:

5

Step-by-step explanation:

Answer:

well I actully you do 17,125 times 3 and then you get your answer

Step-by-step explanation:

17,125 times 3

Answer:

210,541

Step-by-step explanation:

17125 x 3 = 51375

51375 + 159166 = 210541