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Answer:

Addition and Subtraction of Fractions · 1. Add: (i) 7/ 10 + 2/15 (ii) 2²/₃ + 3¹/₂ · 2. Simplify: (i) 15/16 – 11/12 (ii) 11/15 – 7/20 · 3. Simplify: 4⁵/₆ – 2³/₈ + .

Answer:

7/10 + 2/15= 5/6

2 3/3 + 3 1/2= 6 1/2

15/16 - 11/12= 1/48

11/15 - 7/20= 23/60

Step-by-step explanation:

When adding or subtracting fraction with different denominators, we must find there LCM to be their new denominators. Then divide the new denominator by the old denominator, do for both fractions, then multiply the answer with the numerator, do for both fractions to get their new numerators. Then add or subtract the fractions. Then simplify the answer if needed.

Ex 1:

The LCM of 10 and 15 is 30

7/10 + 2/15

(30 ÷ 10=3, 3 × 7= 21)(30 ÷ 15= 2, 2 × 2=4)

=21/30 + 4/30= 25/30 or 5/6

With whole numbers, add the two whole numbers together. Then n add the fractions. Lastly add both of the answers together.

Ex:

The LCM of 3 and 2 is 6

2 3/3 + 3 1/2

=2 + 3= 5

= 3/3 + 1/2= 9/6 or 1 3/6 or 1 1/2

= 5 + 1 1/2

= 6 1/2

Always remember to simplify if possible or necessary.

I hope this helps! I'm sorry if it's wrong or too complicated.

Answer:

[tex]\huge \boxed{y=\sqrt{30} }[/tex]

Step-by-step explanation:

We can use ratios to solve for the problem.

y/5 = 6/y

Cross multiply.

y × y = 5 × 6

y² = 30

Take the square root of both sides.

y = [tex]\sqrt{30}[/tex]

Answer:

Step-by-step explanation:

finding the first term by putting n=1

t(1)=4.[tex](1)^{2}[/tex] +2 = 4.1 +2 = 4+2 = 6

finding the second term by putting n=2

t(2)=4.[tex](2)^{2}[/tex] +2 = 4.4 +2 = 16+2 = 18

finding the third term by putting n=3

t(3)=4.[tex](3)^{2}[/tex] +2 = 4.9 +2 = 36+2 = 38

hence first three terms are:

               6,18,38,......,4[tex]n^{2}[/tex] +2

Answer:

You must drink  52 7/12 ounces or 52.58 ounces to reach the goal.

Step-by-step explanation:

Total amount of the water already drank is found by adding the fractions

So

3 1/10 ounces + 2 1/15 ounces + 6 5/20

Converting into improper fractions

31/10 + 31/15+ 125/20

Now finding the lcm of 10,15,20

so  Factors of 10 = 2 x 5

Factors of 15 = 5 x 3

Factors of 20 = 2 x2 x5

LCM= 5x2x2x3= 60

31*6/60 + 31*4/60 + 125*3/60

= 186+124+375/60

= 685/60 = 11.42 ounces

The amount of water already drank is 11.42 ounces

The amount remaining is found by subtracting the amount drank from the total amount

so

64 ounces - 11.42= 52.58

It can be solved in fractions as

64- 11 5/12

Again taking making improper fraction and taking lcm

64- 137/12

= 768-137/12 = 631/12= 52 7/12 ounces

Answer:

40 km/h

Step-by-step explanation:

s = ut where s - Distance

u - Speed

t - Time

when t = 10 min

= 10/60 hours

S1 = 30 * 10/60

= 5km

when t= 20 min

= 20/60 hours

S2 = 45 *20/60

= 15 km

Then total distance = S1 + S2

= 5 + 15

= 20 km

Total time period = (10 + 20 ) / 60 hours

= 1/2 hours

Then average speed = U

S = UT

U = S/ T

= 20/ 0.5 km/ h

= 40 km/ h

Answer: c).

Both options are true. You can see that the whiskers of data set 2 (The lines extending on either side of the box plots) represent a much larger range of data than data set 1, and that the median in data set 2 (the line down the middle of the boxes) is greater than data set 1.

Hope this helps!

Answer:

P(spades) = 7/10

Step-by-step explanation:

there are 10 different cards that can be picked, out of which what we want to pick is spades which are 7. and so there are 7 chances that we will get to pick spades out of all the 10 possibilities. hope it is easy to understand

hope you understand..................................................................

Answer:

a) The perimeter of a rectangle is written as:

P = 2*L + 2*W

where L is the length amd W is the width (broad in this case).

here we have:

L = 8cm and W = b

then the perimeter is:

P = 2*8cm + 2*b

And we know that:

18cm ≤ P ≤ 50cm

where ≤ is used because there is written "not more" and "not less", so the equalities are allowed

now we can replace P by the above equation:

18cm ≤ 16cm + 2*b ≤ 50cm

now we can subtract 16cm in each side and get:

18cm - 16cm ≤ 2*b ≤ 50cm - 16cm

2cm ≤ 2*b ≤ 34cm

Now we can divide each side by 2.

1cm ≤ b ≤ 34cm/2 = 17cm

1cm ≤ b ≤ 17cm.

b) Here we have missing information, so this can not be answered.

(only knowing that one side length is x, and another side length is x + 3cm, we can know that x > 0cm, so the minimum value of x is really close to 0cm)

Find the number in the tenth place  1  and look one place to the right for the rounding digit  9 . Round up if this number is greater than or equal to  5  and round down if it is less than  5 .

5.2

Step-by-step explanation:

In the plane geometry Abeka, second edition, it is given :

Principle 2 states that between any two points, only one straight line can be drawn.

And according to principle 3 two straight lines interacts at one point only.

Thus this can be well illustrated by two straight lines which are represented by the streets of a city and these two streets intersects at a point.

Answer:

f(2) = 16

or

y = 16

Step-by-step explanation:

Step 1: Write out function

y = 6x + 4

Step 2: Define variable for problem

x = 2

Step 3: Plug into function f(x)

f(2) = 6(2) + 4

f(2) = 12 + 4

f(2) = 16

Step 4: Change f(2) to y

y = 16

Answer:

There are 20 cups of coffee in two pots of coffee and 36 donuts in 3 boxes of donuts

Step-by-step explanation:

The rule of three or is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them. That is, what is intended with it is to find the fourth term of a proportion knowing the other three.

If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other), the direct rule of three must be applied as follow:

a ⇒ b

c ⇒ x

So [tex]x=\frac{c*b}{a}[/tex]

In this case, the rule of three can be applied as follows:

[tex]amount of cups of coffe=\frac{2coffe pots*10 cups of coffee}{1 coffe pot}[/tex]

amount of cups of coffe= 20

[tex]amount of donuts=\frac{3 boxes*12 donuts}{1 box}[/tex]

amount of donuts= 36

There are 20 cups of coffee in two pots of coffee and 36 donuts in 3 boxes of donuts

Answer:

Think of the double angle formula for

sin

2

x

Explanation:

sin

2

x

=

sin

x

2

sin

x

cos

x

=

sin

x

2

sin

x

cos

x

−

sin

x

=

0

sin

x

(

2

cos

x

−

1

)

=

0

Solution A:

sin

x

=

0

⇒

x

=

k

π

,

k

∈

Z

Solution B:

2

cos

x

=

1

⇒

cos

x

=

1

2

,

x

=

±

π

3

+

2

k

π

=

π

3

(

6

k

±

1

)

,

k

∈

Z

∴

x

=

k

π

or

x

=

π

3

(

6

k

±

1

)

,

k

∈

Z

Step-by-step explanation:

Answer:

       [tex]\bold{x=\frac\pi3+2k\pi\quad \vee\quad x=\frac{5\pi}3+2k\pi\quad \vee\quad x=k\pi\ ,\quad k\in\mathbb Z}[/tex]

Step-by-step explanation:

[tex]\sin 2x=\sin x\\\\\sin2x - \sin x=0\\\\2\sin x\cos x-\sin x=0\\\\(2\cos x-1)\sin x=0\\\\2\cos x-1=0\qquad\qquad\qquad\qquad or\qquad \sin x=0\\\\2\cos x=1\quad\qquad\qquad\qquad\qquad\ or\qquad \sin x=0\\\\\cos x=\frac12\qquad\qquad\qquad\qquad\qquad or\qquad \sin x=0\\\\x=\frac\pi3+2k\pi\quad \vee\ \ x=\frac{5\pi}3+2k\pi\quad\ \ \vee\ \ x=0+k\pi\ ,\quad k\in\mathbb Z[/tex]

Answer:

1.8 hours.

Step-by-step explanation:

It is important to note that:

Speed = Distance ÷ Time

We have two trains.

Step 1

We have to find the distance that each train travelled.

Since Speed = Distance ÷ Time

Distance = Speed × Time

First train

It travels at 105 miles per hour

Distance travelled by first train =

105 × x hours

= 105x miles

Second Train

It travels at 85 miles per hour

Distance travelled by the second train = 85 miles × x hours

= 85x miles

We are told that: the two trains leave stations 342 miles apart at the same time and travel toward each other

Hence, the time it would take each train to meet each other is calculated as:

105x + 85x = 342 miles

190x = 342 miles

x = 342/190

x = 1.8 hours.

2 hours 45 minutes

12h30m - 9h45m =

= (12×60m + 30m) - (9×60m + 45m)

= 750m - 585m

= 165 minutes

= 120m + 45m

= 2 hours 45 minutes

Answer:

x^1/4

Step-by-step explanation:

[tex]\frac{x^{\frac{1}{2}}}{x^{\frac{1}{4}}}\\\\\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}\\\\\frac{x^{\frac{1}{2}}}{x^{\frac{1}{4}}}=x^{\frac{1}{2}-\frac{1}{4}}\\\\\mathrm{Simplify}\:x^{\frac{1}{2}-\frac{1}{4}}:\\\\\quad x^{\frac{1}{4}}[/tex]

Answer:

A square root of a number is a value that, when multiplied by itself, gives the number.

Example: 4 × 4 = 16, so a square root of 16 is 4.

The symbol for a square root is √ which always means the positive square root.

Example: √36 = 6 (because 6 x 6 = 36)

Answer:

As the number of files increases, the storage space used increases.

Answer:D

Step-by-step explanation:

Answer:

49

Step-by-step explanation:

(-7)² = (-7)(-7) = 49

Answer:

6x³y

Step-by-step explanation:

(2xy) * 3x²

We know that 2 * 3 = 6 and x * x² = x¹ * x² = x⁽¹⁺²) = x³ so the final answer is 6x³y.

Answer:

A

Step-by-step explanation:

true true true true true true

Answer:

False

Step-by-step explanation:

In order to tell if an inverse is a function, you have to do the horizontal line test. Create an imaginary line going horizontally on the map and if the graphed function goes through more than one line, then the inverse won't be a function. There can only be one point going through the imaginary line. Does that make sense?

Answer:

Monday, at 12:15 AM

Step-by-step explanation:

Do this question in parts. First, add 2 days to Friday to get Sunday at 5:45 PM. Then, add 6 hours to 5:45 to get 11:45 PM. Finally, add 30 minutes to 11:45 PM. That takes you to 12:15, and since you passed midnight, Sunday is now Monday. That means the bus arrives Monday, at 12:15 AM.

Answer:

z = -1

Step-by-step explanation:

0 = 8z + 8

-8 = 8z

-8/8 = z

z = -1

check:

0 = 8*-1  +  8

0 = -8 + 8

Answer:

K(3, 5)

Step-by-step explanation:

let K(x, y)

then x + 7 = 5*2 and y + 7 = 6*2 by the midpoint theorem.

solving, x = 3, y = 5

Answer:

0.8208 ; 0.8448

Step-by-step explanation:

Given the following :

Number of tosses = 4

Probability of head on any toss :

P(head) = 0.4

Therefore ;

(1 - p(head)) = (1 - 0.4) = 0.6

Binomial probability :

P(X) = nCx * P^x * (1 - P) ^(n-x)

Where:

n = number of trials ; x = number of success ; P = probability of success.

P(X≤2) = P(0) + P(1) + p(2)

using binomial probability calculator to ensure faster computation:

P(X≤2) = 0.1296 + 0.3456 + 0. 3456

= 0.8208

B)

P(1 ≤ X ≤ 3) = P(1) + P(2) + P(3)

P(1 ≤ X ≤ 3) = 0.3456 + 0.3456 + 0.1536

= 0.8448

Answer:

Reflection, Translation, and possibly Rotation

Answer:

5,5,15

Step-by-step explanation: