Every morning, siblings Jack and Jill roll a regular six-sided die to determine who will get to ride in the front seat on the way to school. If the number is even, Jack gets to ride in the front. If the number is odd, Jill gets to ride in the front.

Answer:

5 m/s

Step-by-step explanation:

cos 60 = 300/x

x = 300/cos 60 = 600

600m / 120sec

5 m/s

==========================================

Work Shown:

Given info

P(A) = 7/20

P(A∩B)=49/400

P(B) = unknown

--------------------

P(A∩B) = P(A)*P(B), assuming A and B are independent events

49/400 = (7/20)*P(B)

(7/20)*P(B) = 49/400

P(B) = (20/7)(49/400)

P(B) = (20*49)/(7*400)

P(B) = (20*7*7)/(7*20*20)

P(B) = 7/20

---------------------

Note how

P(A∩B) = P(A)*P(B)

P(A∩B) = (7/20)*(7/20)

P(A∩B) = (7*7)/(20*20)

P(A∩B) = 49/400

which helps to confirm the answer.

Answer:

[tex]\bold{ 9x = (x+35)\times 5 }[/tex]

Step-by-step explanation:

Jim completed half of the floor in 9 hours.

Let the rate of Jim = [tex]x[/tex] tiles/hr

So, number of tiles that Jim lays in 9 hours = Rate of Jim multiplied by number of hours i.e. [tex]9 \times x[/tex] ..... (1)

Let [tex]y[/tex] tiles/hr be the rate at which Pete lays the tiles.

As per the given question, Pete can lay 35 more tiles per hour than Jim.

i.e. [tex]\bold{ y =x+35}[/tex]

It is given that half of the floor is done by Jim and other half by Pete.

So, we can say that number of tiles for both of them are equal.

Number of tiles by Pete = Rate of Pete [tex]\times[/tex] Number of hours = [tex](x+35) \times 5[/tex]...(2)

Now, we can equate the equations (1) and (2) because the number of tiles are same.

i.e.

The equation that we can use is:

[tex]\bold{ 9x = (x+35)\times 5 }[/tex]

Answer:

(-1, 3, 1)

x=-1, y=3, z=1.

Step-by-step explanation:

So we have the three equations:

[tex]3x+2y-z=2\\2y+z=7\\-2x-4z=-2[/tex]

And we want to find the value of each variable.

To do so, look at the equations and try to think about what we can do to isolate one of the variables by itself.

We can see that both the second and equation has a variable and then the variable z.

In other words, we can solve for y in the second equation and x in the third equation and then substitute them in the first equation to isolate the variable z and then solve for z. With that, we can then easily arrive at our solution.

Therefore, solve for y in the second equation:

[tex]2y+z=7[/tex]

Subtract z from both sides. The zs on the left side cancels:

[tex](2y+z)-z=(7)-z\\2y=7-z[/tex]

Now, divide both sides by 2. The 2s on the left cancel and we've isolated the y variable:

[tex]\frac{(2y)}{2} = \frac{(7-z)}{2}\\y=\frac{(7-z)}{2}[/tex]

Now, do the same for the third equation. Isolate the x variable:

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

First, divide everything by -2 to make things simpler:

[tex]\frac{(-2x-4z)}{-2}=\frac{(-2)}{-2}\\ x+2z=1[/tex]

Now, subtract 2z from both sides to isolate the x variable:

[tex](x+2z)-2z=1-2z\\x=1-2z[/tex]

We have isolated the x and y variables. They are:

[tex]y=\frac{(7-z)}{2}\\x=1-2z[/tex]

Now, we can substitute them back into the first equation. Therefore:

[tex]3x+2y-z=2\\3(1-2z)+2(\frac{7-z}{2})-z=2[/tex]

Distribute the first and second terms. The second term cancels out:

[tex]3(1)-3(2z)+(7-z)-z=2\\3-6z+7-z-z=2[/tex]

Combine like terms:

[tex]-6z-z-z+3+7=2\\-8z+10=2\\[/tex]

Subtract 10 from both sides:

[tex](-8z+10)-10=2-10\\-8z=-8[/tex]

Divide both sides by -8:

[tex]z=1[/tex]

Now that we've determined that z=1, plug it back into the isolated second and third equations:

Second equation:

[tex]y=\frac{(7-z)}{2}\\y=(7-1)/2\\y=(6)/2=3[/tex]

Third equation:

[tex]x=1-2z\\x=1-2(1)\\x=1-2=-1[/tex]

Therefore, our answer is (-1, 3, 1)

Answer:

  (x, y, z) = (-1, 3, 1)

Step-by-step explanation:

Any of a number of web sites will solve systems of equations for you. Your graphing calculator will, too.

The solution is the right-most column in reduced row echelon form. Top to bottom, the variables are in order x, y, z.

  (x, y, z) = (-1, 3, 1)

_____

If you like, you can use substitution to do this by hand.

  z = 3x +2y -2 . . . . from the first equation

  2y +(3x +2y -2) = 7 . . . . substituting into the second equation

  3x +4y = 9 . . . . . in standard form

  -2x -4(3x +2y -2) = -2 . . . . substituting for z into the third equation

  14x +8y = 10 . . . . . in standard form

Subtract half the second equation from the first:

  (3x +4y) -(7x +4y) = (9) -(5)

  -4x = 4 . . . simplify

  x = -1 . . . . . divide by 4

  y = (9 -3x)/4 = (9 -3(-1))/4 = 12/4 = 3

  z = 3(-1) +2(3) -2 = 1

The solution is (x, y, z) = (-1, 3, 1).

Answer:

[tex]\huge \boxed{25>23} \\ \\ \huge \boxed{25 \geq 23}[/tex]

Step-by-step explanation:

25 is greater than 23.

greater than ⇒ [tex]>[/tex]

25 is greater than or equal to 23.

greater than or equal to ⇒ [tex]\geq[/tex]

Answer:

1) [tex]25 > 23[/tex]

2) [tex]25 \geq 23[/tex]

Step-by-step explanation:

25 is greater than 23

=> [tex]25 > 23[/tex]

25 is also almost equal to 23

=> [tex]25 \geq 23[/tex]

Answer:

The simplest form of the given expression is 7x³ + 5x² + x + 2

Step-by-step explanation:

(4x³ + 6x - 7) + (3x³ - 5x² - 5x + 9)

Group like terms together.

(4x³ + 3x³) + 5x² + (6x - 5x) + (-7 + 9)

Combine like terms.

7x³ + 5x² + x + 2

So, this will be your simplest form of the given equation.

Answer:

7x³ + 5x² + x + 2

Step-by-step explanation:

Answer: Hi!

To solve this equation, we first distribute to the terms inside of the parentheses.

10*4 = 40

10*-3i = -30i

Our equation now looks like this:

40 - 30i

There is nothing left to simplify, so you're done!

Hope this helps!

Answer:

9b+1

Step-by-step explanation:

combine like terms

7b-1b+3b=9b

Answer:

9b+1

Step-by-step explanation:

7b-b+1+3b

(7b-b+3b) +1

(7-1+3)b +1

9b+1

The two angles are corresponding angles. Corresponding angles are congruent when we have parallel lines like this. The double arrow markers on the two lines show the lines are parallel.

Corresponding angles are angles that are on the same side of the parallel line, and also on the same side of the transversal line. Both 50 and x are in the upper right corner of each X four corner region.

Answer: 80 items

Step-by-step explanation:

The equation x=0.7x + 24   can be rewritten as 1x = 0.7x + 24 because the is a number on in front  of any variable.  

1x = 0.7x + 24   subtract 0.7 from both sides

-0.7  -0.7

0.3x = 24

x = 80

Answer:

See explanation below

Step-by-step explanation:

In all cases you need to isolate x on one side of the inequality symbol using inverse operations.

1.-

[tex]15+x\leq -45\\15-15+x\leq -45-15\\x\leq -60[/tex]

where we subtracted from both side 15 in order to leave x by itself on the left.

2.-

[tex]x-14>12\\x-14+14>12+14\\x>26[/tex]

where we added 14 in order to isolate x on the left

3.-

In this case we need to divide both sides by -5 in order to isolate the x which is being multiplied by the factor -5, but he have to recall that multiplying or dividing by a negative number changes the direction of the inequality symbol (in our case from <  into > )

[tex]-5x<35\\\frac{-5\,x}{-5} >\frac{35}{-5} \\x>-7[/tex]

4.-

[tex]2x>-42\\\frac{2\,x}{2} >\frac{-42}{2} \\x>-21[/tex]

In this case we simply divide both sides by two, and there is no change in the direction of the inequality because the number we are using to divide is a positive number (2)

Answer:

2x (x - 4)

Step-by-step explanation:

Answer:

Distributive property (Reversed)

Step-by-step explanation:

With the distributive property, it is possible to simplify expressions that consist of an expression term such as (a + b) being multiplied by one singular term such as c given as follows

c ×(a + b) = c·a + c·b

Factoring, which is the reverse  use of the distributive property enables the difference or the sum of two products, each having a common factor to be the presented as the difference  or the sum of two numbers multiplied by the common factor as follows;

2·x - 2·y = 2·(x - y).

Answer:

Step-by-step explanation:

The square of an even number is an  even .

The square of an odd number is an odd.

2826-even

7779-odd

30018-even

8204-even

Hi there! Hopefully this helps!

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|[tex](a^{3} - 2a^{2}) - (3a^{2} - 4a^{3} )[/tex]

|

| To find the opposite of [tex]3a^{2} -4a^{3}[/tex], find the opposite of each term.

\/

[tex]a^{3} - 2a^{2} - 3a^{2} + 4a^{3}[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

|

|Combine [tex]-2a^{2}[/tex] and [tex]-3a^{2}[/tex] to get [tex]-5a^{2}[/tex].

\/

[tex]a^{3} - 5a^{2} + 4a^{3}[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

|

|Combine [tex]a^{3}[/tex] and [tex]4a^{3}[/tex] to get [tex]5a^{3}[/tex].

\/

Answer:

5

Step-by-step explanation:

the degree is 5

As degree means the largest exponent of a term

Answer:

3√6

Step-by-step explanation:

[tex] {a}^{2} = {b}^{2} + {c}^{2} [/tex]

[tex] = {1}^{2} + {( \sqrt{53} )}^{2} [/tex]

[tex] = 1 + 53[/tex]

[tex] {a}^{2} = 54[/tex]

[tex]a = \sqrt{54} = 3 \sqrt{6} [/tex]

Answer:

z = 27

Step-by-step explanation:

Given that z² is proportional to x³ then the equation relating them is

z² = kx³ ← k is the constant of proportion

To find k use the condition z = 8 when x = 4, thus

8² = k × 4³

64 = 64k ( divide both sides by 64 )

k = 1

z² = x³ ← equation of proportion

When x = 9, then

z² = 9³ = 729 ( take the square root of both sides )

z = [tex]\sqrt{729}[/tex] = 27

Resposta: a) R $ 114,40

Explicação passo a passo:

Dado o seguinte:

Preço à vista da mercadoria = R $ 130

Pagamento inicial = 20% na compra

O saldo pode ser parcelado, o que adicionará 10% ao saldo devedor.

Portanto ; Pagamento inicial :

20% * 130

0,2 * 130 = R $ 26

Saldo devedor = R $ (130 - 26) = R $ 104

Parcela total devida:

Saldo de débito + 10% do saldo de débito

10% do saldo devedor:

0,1 * 104 = R $ 10,40

Parcela total:

R $ (104,00 + 10,40) = R $ 114,40

Answer:

The value of x = 7

Step-by-step explanation:

To solve this, we will have to fist of all know that the sum of all the angles in a right-angled triangle is 180 degrees.

In addition to that, since the triangle is a right-angled triangle, automatically, one of the angles is = 90 degrees

The next thing to do is to add all the angles together and equate them to 180 degrees.

Angle WXZ + Angle ZXY + 90 = 180 degrees

7x+8 + 5x-2 + 90 = 180

12x + 96 = 180

12x = 84

x = 7

Answer:

125

×

250

_____

000

6250

25000

answer 31250

125

⋅

250

is

31250

Answer:$31250

Step-by-step explanation: 125x250=000+6250+25000=$31250

Answer:

x = - 7

Step-by-step explanation:

8x - 2 = -9 + 7x   (add 2 to both sides)

8x - 2 + 2 = -9 + 7x + 2

8x = 7x - 7           (subtract 7x from  both sides)

8x - 7x = 7x - 7 - 7x

x = - 7

Answer:x=-7

Step-by-step explanation:

Regroup terms.

8x-2=7x-98x−2=7x−9

2 Subtract 7x7x from both sides.

8x-2-7x=-98x−2−7x=−9

3 Simplify  8x-2-7x8x−2−7x  to  x-2x−2.

x-2=-9x−2=−9

4 Add 22 to both sides.

x=-9+2x=−9+2

5 Simplify  -9+2−9+2  to  -7−7.

x=-7x=−7

Answer:

7) 9.135x10^10

8) 3.428x10^-2

9) 2.5x10^-7

10) 4x10^10

Step-by-step explanation:

You’re only supposed to have one number to the left of the decimal point in scientific notation.

7) 9.135x10^10

8) 3.428x10^-2

9) 2.5x10^-7

10) 4x10^10

Answer:

The vertex is ( -4,1)

Step-by-step explanation:

The equation for a parabola can be written as

y = a( x-h)^2 +k  where ( h,k) is the vertex

y = 2 (x + 4)² + 1

Rewriting

y = 2 (x -  -4)² + 1

The vertex is ( -4,1)

Answer:

the vertex is located at (-4, 1)

Step-by-step explanation:

The vertex equation of a vertical parabola is

y = a(x - h)^2 + k

where (h, k) is the vertex.  

Comparing this to the given

y = 2(x + 4)² + 1, we see that the vertex is located at (-4, 1) and that the graph is stretched vertically by a factor of 2.

Answer:

Step-by-step explanation:

Amount of Jeff tuition per year = $9,000

If Jeff has a scholarship that pays 70% of his tuition, the amount the scholarship will pat Jeff = 70% of his yearly tuition fee.

Scholarship amount = 70/100 * $9,000

Scholarship amount  = 70*90

Scholarship amount  = $6,300

Hence the scholarship will pay Jeff $6,300

If the amount saved by Jeff is $3,000

Total amount that Jeff has = Scholarship amount + Amount saved

Total amount that Jeff has = $6,300 + $3000 = $9300

Since the total amount that Jeff has is more than the yearly tuition fee, this shows that he has enough to pay for the first year's tuition

Answer:

Perimeter = 2 x length + 2 x width

Width = x

Length = x + 71

234 = 2*(x + 71) + 2*(x)

234 = 2x + 142 + 2x

234 = 4x + 142

4x = 234 - 142

4x = 92

x = 23

Width = 23 inches

Length = 94 inches

Step-by-step explanation:

The dimensions of the rectangular carpet are 100 and 17 inches.

Given the following data:

Translating the word problem into an algebraic equation, we have;

[tex]L = W + 83[/tex]

To find the dimensions of the rectangular carpet;

Mathematically, the perimeter of a rectangle is given by the formula;

[tex]Perimeter = 2(L+W)[/tex]

Substituting the values into the formula, we have;

[tex]234 = 2(W + 83 + W)[/tex]

[tex]234 = 2(2W + 83)\\\\234 = 4W + 166\\\\4W = 234 - 166\\\\4W = 68\\\\W = \frac{68}{4}[/tex]

Width, W = 17 inches

Next, we would find the value of L;

[tex]L = W + 83[/tex]

Substituting the value of W, we have;

[tex]L = 17 + 83[/tex]

L = 100 inches.

Therefore, the dimensions of the rectangular carpet are 100 and 17 inches.

Find more information: brainly.com/question/897975

Answer:

The y-intercept is –2.

The slope is Negative three-fifths

Step-by-step explanation:

A linear function is a function whose graph is a straight line. A linear function can be represented as:

f(x) = y = a + bx

where y is the dependent variable and x is the independent variable. The equation of a linear function in slope intercept form is given as:

y = mx + c

Where m is the slope and c is the y intercept.

Given that:

[tex]y=-\frac{3}{5}x-2[/tex], and comparing with y = mx + c:

The slope (m) = [tex]-\frac{3}{5}[/tex]

The y intercept (c) = -2

Answer:

The y-intercept is –2.

The slope is Negative three-fifths

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

You have the values for the hypotenuse (50) and one of the sides (48).  You now have to find the second side using the Pythagorean Theorem.

a² + b² = c²

(48)² + b² = (50)²

2304 + b² = 2500

b² = 196

b = √196

b = 14