Scott and Greg were asked to add two whole numbers. Scott subtracted two numbers and got 10. Greg multiplied them and got 651. What is the correct sum?

Answer:

[tex]\dfrac{1}{6}[/tex]

Step-by-step explanation:

Given that two fair dice are tossed.

Total outcomes as we toss two dice are given as:

{

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

}

Where (a, b) represents a is the outcome of the die rolled for the 1st time and b is the outcome of 2nd toss of the die.

Total number of outcomes = 36

The outcomes with sum = 7 are :

{(1, 6), (2, 5), (3, 4) , (4, 3), (5, 2), (1, 6)}

Number of outcomes = 6

Probability of an event E is given as:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

[tex]P(sum=7) = \dfrac{6}{36}\\\Rightarrow \bold{P(sum=7) = \dfrac{1}{6}}[/tex]

Answer:

42 or 4^2

hope this helps

Answer:

4^12

Step-by-step explanation:

Answer:

She's 12 years old! i hope this helps you!

Step-by-step explanation:

Answer:

z=-75/17

Step-by-step explanation:

Expand this equation:

-4z+8+4=-21z-63

-4z+21z=-63-8-4

17z=-75

z=-75/17

Answer:

It will take 5.4 hour to paint 720 square feet

Step-by-step explanation:

The question should be like this"Andy painted 400 square  feet in 3 hours. How long  would it take him to paint  720 square feet?"

In 3 hours = 400 square  feet is painted

1 square feet is painted in [tex]\dfrac{3}{400}\ h[/tex]

To find time to paint 720 square feet multiply the above term by 720 as follows :

[tex]720\ ft^2=\dfrac{3}{400}\times 720\ h\\\\=5.4\ h[/tex]

So, it will take 5.4 hour to paint 720 square feet.

Answer:

The side of the square is 15m

The side of the triangle is 20m

Step-by-step explanation:

P square = 4s  where s is the side length

P triangle = 3 x where x is the side length

x = s+5

The perimeters are equal

4s = 3x

Replace x with s+5

4s = 3(s+5)

Distribute

4s = 3s+15

Subtract 3s from each side

4s-3s = 15

s = 15

The side of the square is 15

x =s+5

  =15+5

   = 20

The side of the triangle is 20

Answer:

[tex]\Large \boxed{\mathrm{square: 15 \ meters}} \\\\ \Large \boxed{\mathrm{triangle: 20 \ meters}}[/tex]

Step-by-step explanation:

The perimeter of a square is [tex]\sf P=4s[/tex], where s is the side length.

The perimeter of an equilateral triangle is [tex]\sf P=3a[/tex], where a is the side length.

The side length of the equilateral triangle is 5 more than the side length of the square.

[tex]\sf a = s+5[/tex]

The perimeter of the square and equilateral triangle are equal.

[tex]\sf 4s=3(s+5)[/tex]

Expanding brackets.

[tex]\sf 4s=3s+15[/tex]

Subtracting 3s from both sides.

[tex]\sf s=15[/tex]

The side length of the square is 15 meters.

[tex]\sf a=15+5 \\\\\\ a=20[/tex]

The side length of the triangle is 20 meters.

Because if you substitute x = 4 and y = 1 in the equation of y = 3x + 1, you'll see that both sides are different.

So if we substitute x = 4 and y = 1 in the equation, we get:

1 = 3(4)+1

1 = 12+1

1 = 13

The equation isn't true though. Also we can explain why (4,1) isn't the solution to the equation by graph (you can go draw the graph of y = 3x + 1 and notice that the line doesn't pass through (4,1) )

Also how about another example? But this time, we use (0,1) which is the solution of y = 3x + 1.

Substitute x = 0 and y = 1 in the equation as we get:

1 = 3(0)+1

1 = 0 + 1

1 = 1

Since the equation is true, that means the (0,1) is one of the solution of y = 3x + 1.

Maybe, you want another example again? How about (1,4) which is also one of the solution of y = 3x + 1.

Again, substitute x = 1 and y = 4.

4 = 3(1)+1

4 = 3+1

4 = 4

Since the equation is true. Therefore (1,4) is also one of the solution of y = 3x + 1.

Also here's why (4,1) is not the solution of y = 3x + 1

Basically, from (x,y), 4 is the x and 1 is the y. If we substitute "x" in any equations, we get the "y". Meaning that the x value can be meant as "input" and we get the output "y" like Function which is it.

If we substitute x = 4 in the equation...

y = 3(4)+1

y = 12+1

y = 13

Meaning that the actual y value is 13, not 1. This explains why (4,1) isn't the right solution.

Maybe, what if we substitute y instead? Well that works. Now let's try substitute both y = 1 and y = 13 to see which is the right value.

(1) For y = 1,

1 = 3x+1

1-1=3x

0=3x

x=0 (Therefore, x = 0 and y = 1)

So the actual order is (0,1).

(2) For y = 13

13 = 3x+1

13-1 = 3x

3x = 12

x = 4 (Therefore, x = 4 and y = 13)

so the actual order for (2) is (4,13).

Basically, (4,1) is false for y = 3x + 1.

Answer:

See below

Step-by-step explanation:

Given the point (4,1) means

(x,y) = (4,1)

So, x = 4 , y = 1

Given the equation y = 3x+1

Put x = 4 and y = 1

=> 1 = 3(4)+1

=> 1 = 12 + 1

=> 1 ≠ 13

Since Left hand side doesn't equal right hand side, (4,1) is not the solution to y = 3x+1

Answer:

12.5

Step-by-step explanation:

that is to say 20 -15 because it went late =5

then 2.5×5

Answer: $51

Step-by-step explanation:

If 15% discount is applied then 85% of the price will be the left to pay.

so 85% * 60   will give you the price of the shirt after the discount.

85% * 60 = 51

Answer:

Step-by-step explanation:51.00$

Answer:

yes it is

Step-by-step explanation:

Hope this helps✨

Answer:

Option B. √x + 3

Step-by-step explanation:

f(x) = (x - 3)²

We can obtain the inverse f¯¹(x) of the above expression as follow:

f(x) = (x - 3)²

Replace f(x) with

f(x) = (x - 3)²

y = (x - 3)²

Next, interchange x and y

y = (x - 3)²

x = (y - 3)²

Make y the subject

x = (y - 3)²

Take the square root of both side

√x = y - 3

Add 3 to both side

√x + 3 = y - 3 +3

√x + 3 = y

y = √x + 3

Finally, replace y with f¯¹(x)

y = √x + 3

f¯¹(x) = √x + 3

Its conjugate is

7 - i√2

Answer:

-13/30

Step-by-step explanation:

take 1/6 to other side,

x=-3/5 -1/6

taking LCM of denominators,

-8-5/30

=-13/30

Answer:

X=23/30

Step-by-step explanation:

X + 1/6 = -3/5

X + 5/30 = -18/30

-5/30 -5/30

X = -23/30

I feel like i did something wrong... but im pretty sure its right. Let me know if it's right! Hope it helps.

Answer:

28 times

Step-by-step explanation:

Create an equation where x represents the number of times the bus is used:

1.75x = 0.5x + 35

Solve for x:

1.75x = 0.5x + 35

1.25x = 35

x = 28

So, the bus has to be used 28 times for the prices to be the same.

Answer:

Step-by-step explanation:

y= 0

x + 2(0) = 10

x = 10

(10, 0)

x = 0

0 + 2y = 10

2y = 10

y = 5

(0,5)

Answer:

The answer is

Step-by-step explanation:

[tex] \frac{9x + 3}{12x + 4} [/tex]

To solve the rational expression factorize both the numerator and the denominator.

For the numerator

9x + 3

Factorize 3 out

We have

3( 3x + 1)

For the denominator

12x + 4

Factorize 4 out

That's

4( 3x + 1)

So we now have

Reduce the expression with (3x + 1)

We have the final answer as

Hope this helps you

Answer:12

Step-by-step explanation:

Answer:

12+x goes to 19

3x+y goes to 25

4y-10 goes to 6

1/2xy goes to 14

x=7 and y=4 all you have to do is substitute for example 12+x substituted it's 12+7 then just do the math. That's it.

Answer:

700 Minutes

Step-by-step explanation:

For this problem, we need to write an expression that represents the cost per the amount of time used for each phone plan, and set the two expressions equal to each other to find how many minutes would be needed for the costs to be equal.

For the first phone plan, we have a base $28 and additional $0.09 per minute of call.  This can be expressed as:

28 + 0.09x                  Where x is the number of minutes used

For the second phone plan, we have a flat $0.13 per minute of call.  This can be expressed as:

0.13x                           Where x is the number of minutes used

To find how many minutes would be used to make the cost equal, we simply set these expressions as equivalent, and solve for x.

28 + 0.09x = 0.13x

28 + 0.09x + -0.09x = 0.13x + -0.09x

28 = 0.04x

28 = (1/25)x

28 * 25 = (1/25)x * 25

28 * 25 = x

700 = x

Thus, for the cost of these phone plans to be equal, you would have to use 700 minutes per month.

Cheers.

Answer:

7.5 seconds

Step-by-step explanation:

[tex]h = - 16 {t}^{2} + 120t \\ \because \: we \: have \: to \: find \: the \: time \: required \: \\ for \: the \: object \: to \: return to \: its \: \\ point \: of departure. \\ \therefore \: plug \: h = 0 \: in \: the \: given \: euation. \\ \therefore \: 0 = - 16 {t}^{2} + 120t \\ \therefore \:16 {t}^{2} - 120t = 0 \\ \therefore \:8t(2t - 15) = 0 \\ \therefore \:8t = 0 \: \: or \: \: (2t - 15) = 0 \\ \therefore \:t = \frac{0}{8} \: or \: t = \frac{15}{2} \\ \therefore \:t = 0 \: or \: t = 7.5 \\ \because \: t = 0 \: is \: not \: possible \\ \huge \purple{ \boxed{ \therefore \: t = 7.5 \: seconds}}[/tex]

Thus, the time required for the object to return to its point of departure is 7.5 seconds.

Answer:

Step-by-step explanation:

The standard form of a point slope equation of a line is expressed as shown;

y-y₀ = m(x-x₀) where;

m is the slope of the line

(x₀, y₀) is the coordinate of the point that lies in the line.

Comparing the standard equation given with the equation in question

y - 3 = 4(x + 7) to get the point on the line we will have;

y₀  = 3 and -x₀ = 7

for -x₀ = 7;

multiply both sides with a minus sign

-(-x₀) = -7

x₀ = -7

Hence the coordinate of the point required (x₀, y₀) is (-7, 3).

Step-by-step explanation:

Let's look at our expression:

[tex]1.7+8.23-3.4+4.7j[/tex]

The numbers without a variable at the end are like terms here. Let's add them up.

[tex]1.7+8.23=9.93\\9.93-3.4=6.53[/tex]

Then, let's add our answer, 6.53, to the term with a variable, 4.7j.

Our final answer: 6.53 + 4.7j

I hope this helps you!

Answer:

Step-by-step explanation:

Hello,

What other numbers are of this form have exactly four factors?

[tex]8=2^3\text{ has 4 factors } 1, 2, 2^2, 2^3\\\\\text{For any prime p, }p^3\text{ has 4 factors } 1, p, p^2, p^3\\\\[/tex]

Do all the perfect cubes have exactly four factors?

[tex]\text{If p is not prime, then it is not true anymore} \\ \\\text{For instance, }8^3\text{ has more than 4 factors } 1, 2^2, 2^3, 2^4, etc..[/tex]

Is it true that all numbers that have exactly four factors are perfect cubes?

6 has 4 factors : 1, 2, 3, 6 but this is not a perfect cube.

Thank you.

We know that any number can be decomposed as a product of prime numbers.

For example:

[tex]8 = 1\cdot 2\cdot 2\cdot 2[/tex]

8 has four factors if we count the 1.

Now we need to answer some questions regarding this:

What other numbers are of this form have exactly four factors?

8 is a cube number.

Remember that all cube numbers X can be written as:

[tex]X = n\cdot n\cdot n \cdot 1[/tex]

Now, if n is prime, then we can say that X is of the form of 8 and also has 4 factors.

But let's see the case:

[tex]8\cdot 8\cdot8= 512[/tex]

512 is a perfect cube, and if we decompose it we get:

[tex]512 = 8\cdot 8\cdot 8 = (2\cdot 2\cdot 2)\cdot (2\cdot 2\cdot 2)\cdot (2\cdot 2\cdot 2)\cdot 1[/tex]

So we found a perfect cube that has 10 factors.

This means that not all perfect cubes have exactly 4 factors.

Now, all numbers that have exactly four factors are perfect cubes?

This is also false, just let's create a counterexample.

[tex]1\cdot 2\cdot 3\cdot 5 = 30[/tex]

the number 30 is not a perfect cube, and we can see that it has exactly 4 factors.

If you want to learn more, you can read:

https://brainly.com/question/832797

Answer:

36

Step-by-step explanation:

Starting with 4, 9.

9 - 4 = 5 then + 2

So forward.

Answer:

1, 4, 9, 16, 25, 36

Step-by-step explanation:

This is because as you see 1 + 3 = 4, then 4 + 5 = 9, then 9 + 7 = 16. So we see that it goes like 3 + 5 + 7 + 9 + 11 + 13  . . .  That is the pattern. Hope this helps!

Answer:

x = -7

Step-by-step explanation:

4x — 3 = —31

Add 3 to each side

4x — 3+3 = —31+3

4x = -28

Divide by 4

4x/4 = -28/4

x = -7

Your answer would be x=-7 or -7!

In U.S. dollars, the equivalent money will be $100.74

Given is your dinner in London cost 82 British pounds

Then in U.S. dollars, the equivalent money will be equivalent to -

x = 82 pounds = 82 x 1.2286 = $100.74

x = $100.74

Therefore, in U.S. dollars, the equivalent money will be $100.74

To solve more questions on Equations, Equation Modelling and Expressions visit the link below -

brainly.com/question/14441381

#SPJ2

Answer:

rational numbers

Step-by-step explanation:

They cannot be negative numbers because the product of two negative numbers is positive.

They cannot be prime numbers because the product of two prime numbers is not a prime number.

The product of two complex numbers can be a complex number, but it may also be a real number.

The product of two rational numbers is always rational.

Answer: rational numbers