There are 21 students in your class. The teacher wants to send 4 students to the
library each day. The teacher will choose the students to go to the library at random
each day for the first four days from the list of students who have not already gone.
What is the probability you will be chosen to go on the first day? State the answer as
a fraction.

[tex]{ \sf{ \: factorise \: \: \: { \underline{ \green{2 {x}^{5} - 7 {x}^{3} - 4x}}}}} \\ \\ { \dashrightarrow{ \blue{ \sf{taking \: x \: common}}}}[/tex]

[tex]{ \leadsto{ \sf{ \green{ \:x(2 {x}^{4} - 7 {x}^{2} - 4)}}}} \\ \\ { \dashrightarrow{ \sf{ \blue{let \: {x}^{2} be \: equal \: to \: a}}}} \\ \\ { \leadsto{ \sf{ \green{ \: x( 2{a}^{2} - 7a - 4)}}}}[/tex]

[tex]{ \leadsto{ \sf{ \green{x(2 {a}^{2} - (8a \: - a) - 4}}}} \\ \\ { \leadsto{ \sf{ \green{x(2 {a}^{2} - 8a + a - 4)}}}} \\ \\ { \leadsto{ \sf{ \green{x(2a(a - 4) + 1(a - 4))}}}}[/tex]

[tex]{ \leadsto{ \sf{ \green{x(2a + 1)(a - 4)}}}} \\ \\ { \sf{ \: now \: putting \: the \: value \: of \: a}}[/tex]

[tex]{ \leadsto{ \green{ \sf{x(2 {x}^{2} + 1)( {x}^{2} - 4)}}}} \\ \\ { \leadsto{ \green{ \sf{ x( {x}^{2} + 1)( {x}^{2} - {2}^{2} )}}}} \\ \\ { \leadsto{ \green{ \sf{x( {x}^{2} + 1)(x + 2)(x - 2)}}}}[/tex]

Answer:

Step-by-step explanation:

30(total num of sections)-5(amount of sections with concert ticket)=25

25x70(seats per section)=1750

1750 will get coupons

(you  dont  need the bits in brackets tehy are there to just explain so you know whay and why im  doind a calculation)      

Hence, the bags will get coupons are [tex]1750[/tex].

What is the simplification?

Simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

Here given that,

Jamie's company prepares a gift bag for each seat at an awards ceremony. The theater has [tex]30[/tex] sections, each with [tex]70[/tex] seats. Gift bags for [tex]5[/tex] sections will have concert tickets. The rest of the gift bags will have coupons.

Total number of sections are [tex]30[/tex]

Amount of sections with concert tickets are [tex]5[/tex]

So,the gift bags will have coupons is

[tex]30-5=25[/tex]

As each sections has [tex]70[/tex] seats so,

[tex]25[/tex] x [tex]70[/tex] [tex]=1750[/tex]

Hence, the bags will get coupons are [tex]1750[/tex].

To know more about the simplification

https://brainly.com/question/12795317

#SPJ5

Answer:

4n+ 12 = -268, or 4n = -280, or n = -70. This would imply that the four consecutive ODD integers are -70, -68, -66, -64.

Step-by-step explanation:

Hope this helps         :)

Answer:

12

Step-by-step explanation:

12 - 4 = 8

The square of 8 is 64

Answer:

6

Step-by-step explanation:

(n + 4)^2 = n^2 + 64

n^2 + 8n + 16 = n^2 + 64

8n = 48

n = 6

Answer:

35

Step-by-step explanation:

6 x 5 = 30

We can assume each seed packet has 5 seeds

6 x 7 = 35

Answer:

[tex]x = -2, y = 6[/tex]

Step-by-step explanation:

[tex]-x + 4 = -4x-2[/tex]

[tex]x = -2[/tex]

Plug back into either one of the equations to get y  = 6

Answer:

i cant see it...

Step-by-step explanation:

...

Answer:

y=2/3x-6

Step-by-step explanation:

i hope this helps :)

Answer:

angle 6=54*

Step-by-step explanation:

Transversal lines/alternate angles theorem

Answer:

x = 9

Step-by-step explanation:

This is a 45-45-90 right triangle so the sides are in the ratio x: x: [tex]x\sqrt{2}[/tex]

Complete question :

It takes Carol 30 minutes to drive to work using two roads. She drives 24 mph on a small road 1/2 for hour. Then she drives 56 mph on a highway for 1/4 hour. How far does Carol travel to work?

Answer:

26 miles

Step-by-step explanation:

The distance traveled is given by :

Distance = speed * time

Distance covered on small road :

24 mph * 1/2 hours = 12 miles

Distance covered in highway :

56 mph * 1/4 hours = 14 miles

Total miles traveled = 12 + 14 = 26 miles

Answer:

The answer is x + 33

Step-by-step explanation:

1) Remove parentheses.

[tex]45 + x - 12[/tex]

2) Collect like terms.

[tex]x + (45 - 12)[/tex]

3) Simplify.

[tex]x + 33[/tex]

Therefor, the answer is x + 33.

Answer:

x+33 is your answer

Step-by-step explanation:

45 + (x - 12)

45+x-12

x+45-12

x+33

Answer:

80%

Step-by-step explanation:

150/100*20=$30

150-30=120

120/150=0.8=80%

Answer:

Congruent figures have the same measurements in angles (degrees) and sides (units).

Similar figures are figures that have the same general shape and don't necessarily have to have the same size or measurements.

Something they have in common are corresponding angles and corresponding sides.

Answer:

LOOK AT YOUR ANSWER IN PICTURE

Answer:

area = 250 in²

Step-by-step explanation:

5 x 2.5 = 12.5 in

8 x 2.5 = 20 in

area = 20 x 12.5 = 250 in²

Answer:

[tex]\frac{1}{12}[/tex]

Step-by-step explanation:

[tex]\frac{2}{3}[/tex] = [tex]\frac{8}{12}[/tex]

[tex]\frac{12}{12}[/tex] - [tex]\frac{8}{12}[/tex] = [tex]\frac{4}{12}[/tex]

[tex]\frac{4}{12}[/tex] * [tex]\frac{1}{4}[/tex] = [tex]\frac{4}{48}[/tex] = [tex]\frac{1}{12}[/tex]

Answer:

32+32÷32=32+1=33 is your answer

Answer:

[tex]\boxed{x=73.74}[/tex]

[tex]\boxed{y=16.26}[/tex]

[tex]\boxed{z=25}[/tex]

Step-by-step explanation:

Hello there!

Algebra 1

The first thing we should find is the missing angle

Because this is a right triangle we can solve it using the Pythagorean Theorem

The Pythagorean theorem states that the sum of the two legs squared equal the hypotenuse squared

the formula... [tex]a^2+b^2=c^2[/tex] where a and b = legs and c = hypotenuse

we are given two legs so we plug in a and b and solve for c

[tex]7^2+24^2=c^2\\7^2=49\\24^2=576\\576+49=625\\625=c^2\\\sqrt{c^2} =c\\\sqrt{625} =25\\c=25[/tex]

so we can conclude that the missing side length ( or z) equals 25

now to solve for the angles

Trigonometry

We can solve for y using sin

sin = opposite side divided by the hypotenuse

the opposite of y is 7 and the hypotenuse is 25

so we set up an equation [tex]sin(y)=\frac{7}{25}[/tex]

now we solve for y

[tex]\frac{7}{28} =.28\\arcsin(y)=y\\arcsin(.28)=16.26020471[/tex]

then we round to the nearest hundredth

so we can conclude that angle labeled y = 16.26

basic geometry

Remember all of the angles in a triangle add up to equal 180 so we can find x by subtract the known angles from 180

180 - 90 - 16.26 = 73.74 so we can conclude that x = 73.74

Answer:

3/14

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

To find how many 1/12 are in 2 divide 2 by 1/12

2/(1/12) = 2 x 12 = 24

Answer:

35/40

I think that’s what you mean? Hope this helped

Step-by-step explanation:

Answer:

y = -3/4x + 5/4

Step-by-step explanation:

Points: (7, -4) and ( -1, 2)

Slope:

m=(y2-y1)/(x2-x1)

m=(2+4)/(-1-7)

m=6/(-8)

m= -3/4

Slope-intercept:

y - y1 = m(x - x1)

y + 4 = -3/4(x - 7)

y + 4 = -3/4x + 21/4

y = -3/4x + 5/4

Answer:

y = -3/4x + 5/4

Step-by-step explanation:

Hope this helps

Step-by-step explanation:

the formula can be;

X+9x=10

10x=10X=10/10=1

X=1+9(1)=1+9=10 Answer

Answer:

3,468

Step-by-step explanation:

i multiplied 2,844 by 3 and got 8,532 i then subtracted that from 12,000 and got 3,468

Answer:

B

Step-by-step explanation:

sin60°=x/12

⇒x= 6√3

Answer:

the cat can eat 1 1/4 bag of cat food n 1 month

Step-by-step explanation: