**Yoxelt buys 4 1/ 2 gallons of soda. One-fourth of the soda he bought was Pepsi and the rest was Sprite. How many gallons of Pepsi did Yoxelt buy? Show all work below.

Answer:

10

Step-by-step explanation:

(-1 - 3i)(-1 + 3i) = 1 - 3i + 3i -9i²

1 - 9i²; i² = -1, therefore 1 - 9(-1) = 1 + 9 = 10

Answer:

5/3

Step-by-step explanation:

5×(10×1/3)

=10×5/3

=since 5×(10×1/3) gives 50/3 so thus 10×5/3.

The fraction is therefore 5/3

Answer:

Nina can run:

13 1/2 km in 1 hour

Step-by-step explanation:

4 1/2 = 4 + 1/2 = 8/2 + 1/2 = 9/2

proportions:

9/2 hours ⇔  1/3 hour

N hours ⇔ 1 hour

N = (9/2)*1 / (1/3)

N = (9/2) / (1/3)

N = (9*3) / (2*1)

N = 27/2

27/2 = 26/2 + 1/2 = 13 + 1/2 = 13 1/2

Nina can run:

13 1/2 km/h

13 1/2 km in 1 hour

Nina can run [tex]13\frac{1}{2}[/tex] km in an hour

The distance Nina can run in an hour can be determined by dividing the distance she can run in 1/3 of an hour by 1/3

Distance Nina can run in an hour = distance run ÷ [tex]\frac{1}{3}[/tex]

[tex]4\frac{1}{2}[/tex] ÷ [tex]\frac{1}{3}[/tex]

Convert the mixed fraction to an improper fraction [tex]\frac{9}{2}[/tex] × 3 = [tex]\frac{27}{2}[/tex]

Convert the improper fraction back to an mixed fraction = [tex]13\frac{1}{2}[/tex] km

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Answer:

Hope it helps U can still ask me if u have confusions

Answer:

  60+16√30 cm² ≈ 147.64 cm²

Step-by-step explanation:

You can figure the height of the object from ...

  V = Bh

  120 cm^3 = (30 cm^2)h

  4 cm = h . . . . . divide by 30 cm^2

However, this is insufficient to tell you the surface area.

__

If you assume that the base is square, then its side length is

  A = s^2

  s = √A = √(30 cm^2) = (√30) cm

The lateral surface area can then be found from the perimeter of the base and the height

  LA = Ph = (4√30 cm)(4 cm) = 16√30 cm^2

The total surface area will be the sum of this lateral area and the area of the two bases:

 total area = 16√30 cm^2 +2·30 cm^2

 total area = (60 +16√30) cm^2 ≈ 147.64 cm^2

__

For any other shape, the total area will be larger. It can be arbitrarily large, unless limits are put on the dimensions of the object.

Hello!

Answer:

[tex]\huge\boxed{x = 27}[/tex]

Given:

3x - 4y = 65 where y = 4;

Substitute in 4 for "y":

3x - 4(4) = 65

Simplify:

3x - 16 = 65

Add 16 to both sides:

3x - 16 + 16 = 65 + 16

3x = 81

Divide both sides by 3:

3x/3 = 81/3

x = 27.

Hope this helped you! :)

Answer:

x=27

Step-by-step explanation:

3x-4y=65

Let y=4

3x - 4(4) = 54

3x -16 = 65

Add 16 to each side

3x -16+16 = 65+16

3x = 81

Divide each side by 3

3x/3 =81/3

x =27

Answer:

The answer is $40.

Step-by-step explanation:

According to the equation given in the question, we can assume that 550 is constant and was there when Mai started saving into a checking account.

Then as x gets increased by 1 each week, the amount of change in the account per week is $40.

I hope this answer helps.

Answer:

approximately 12.04 units

Step-by-step explanation:

We'll use the Pythagorean Theorem to solve this problem.

There are two points here.  The horizontal distance between them is 8 units and the vertical distance is 9.

According to the Pythagorean Theorem (or the Distance Formula), the distance between the two points is

d = √(8^2 + 9^2) = √(64 + 81) = √145 units, or approximately 12.04 units.

Answer:

The perimeter of the Rhombus is 100 cm

Step-by-step explanation:

First of all, we will need to find the length of the other diagonal.

let’s call the diagonals p and q

Mathematically, the area of the Rhombus is;

pq/2 = Area of Rhombus.

Let’s call the missing diagonal p

So;

(p * 14)/2 = 336

14p = 672

p = 672/14

p = 48 cm

Now, we can find the perimeter of the Rhombus using these diagonals.

Mathematically;

P = 2 √(p^2 + q^2)

Substituting these values, we have;

P = 2 √(14)^2 + (48^2)

P = 2 √(2500)

P = 2 * 50

P = 100 cm

The perimeter of the rhombus is the sum of its side lengths

The perimeter of the Rhombus is 100 cm

The length of one of its diagonal is given as:

[tex]p= 14[/tex]

And the area is given as:

[tex]A = 336[/tex]

Assume the other diagonal is q.

The area of the rhombus is represented as:

[tex]A = \frac{pq}2[/tex]

So, we have:

[tex]336 = \frac{14q}2[/tex]

This gives

[tex]336 = 7q[/tex]

Divide both sides by 7

[tex]48 = q[/tex]

Rewrite as:

[tex]q = 48[/tex]

The perimeter (P) of the rhombus is calculated as:

[tex]P =2\sqrt{p^2 + q^2[/tex]

So, we have:

[tex]P =2\sqrt{48^2 + 14^2[/tex]

Evaluate the squares

[tex]P =2\sqrt{2500[/tex]

Take positive root of 2500

[tex]P =2 \times 50[/tex]

[tex]P =100[/tex]

Hence, the perimeter of the Rhombus is 100 cm

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Answer:

$6488.19

Step-by-step explanation:

To solve this problem we use the compounded interest formula:

[tex]amount = principal(1 + (r \n))^({n}{t})[/tex]

a = $2600(1+(0.0675/1))¹*¹⁴

a = $6488.19

Answer:

6450g

Step-by-step explanation:

1kg = 1000g

6.45kg = 6450

The watermelon weighs 6450 grams.

Given that a watermelon weighs 6.45 kilograms.

We need to convert its unit into grams.

To convert kilograms to grams, you need to multiply the weight in kilograms by 1000, as there are 1000 grams in 1 kilogram.

The watermelon weighs 6.45 kilograms, you can use the following formula to convert it to grams:

Weight in grams = Weight in kilograms × 1000

Let's do the math:

Weight in grams = 6.45 kilograms × 1000 = 6450 grams

So, the watermelon weighs 6450 grams.

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Answer:

[tex]1035[/tex]

Step-by-step explanation:

(63756×60)/(70×5280)

=1035

Answer:

convert into a whole number 6

Answer:

1. tan A = 1/(tan B)

Step-by-step explanation:

By definition,

tangent A = opposite / adjacent = a / b

and

tangent B = opposite / adjacent = b / a

Therefore tangent A = a/b = 1/tan(B)

Answer: Tan a=tan b

I belive

Step-by-step explanation:

Answer:

x = 33

Step 1:

First, let's add the values together from both parentheses.

2x + x = 3x

1 + (-10) = -9

Now we are left with:

3x - 9 = 90.

Step 2:

Add 9 on the left side to cancel out the 9. Add it to the right side.

3x = 99

Finally, divide both sides by 3 to get our answer.

3x / 3 = x

99 / 3 = 33

x = 33

Answer:

y = 6x -27

Step-by-step explanation:

y-3=6(x-5)

Distribute

y-3 = 6x-30

Add 3 to each side

y-3+3 = 6x-30+3

y = 6x -27

This is in slope intercept form  y=mx+b where m is the slope and b is the y intercept

Hey there! I'm happy to help!

Slope intercept form is y=mx+b. So, the first thing we want to do is isolate y on side of the equation.

y-3=6(x-5)

We use distributive property to undo parentheses.

y=3=6x-30

We add 3 to both sides.

y=6x-27

Now, this in slope intercept form.

Have a wonderful day! :D

Answer:

It does not matter which color you add first because either way you will end up with the same color, purple. We can relate this to the commutative property of addition because blue + red = red + blue.

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━━━━━━━☆☆━━━━━━━

▹ Answer

x = 3

▹ Step-by-Step Explanation

[tex]\frac{9}{150} \\\\150/3 = 50\\9/3 = 3\\\\x = 3[/tex]

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

The shaded area is 18 ft^2

Step-by-step explanation:

First find the area of the total trapezoid

A = bh

A = 1/2 ( b1+b2) *h

   = 1/2 ( 6+12) *6

   = 1/2 ( 18)*6

   =54

Now find the area of the triangle

A = 1/2 bh

   = 1/2 ( 12) * 6

   = 36

Subtract the triangle from the trapezoid

54-36

18

The shaded area is 18 ft^2

Answer:

D. 18 sq.ft

Step-by-step explanation:

Lets make it simple and short.

Area of a triangle is 1/2 b h

b = 6

h = 6

Area = 1/2 * 6 * 6

Area = 18 sq.ft

Answer:

0.0276

Step-by-step explanation:

The computation of the probability that the next driver is texting while driving is shown below:

= Fourth pull failure × fifth pull success

where,

Fourth pull failure is (1 - 0.52)^4

And, the fifth pull success is 0.52

Now placing these values to the above formula

So,

= (1 - 0.52)^4 × 0.52

= 0.0276

Hence, the probability is 0.0276

Answer:

Graph D

Step-by-step explanation:

(h)t = -16t^2 + 80

At time t = 0 the screwdriver is at 0+80 =80 ft

As time increases the height will decrease so we can eliminate graph B

We know this is a downward parabola by the - in front of the t^2 so we can eliminate graph A

We need to find where it meets the x axis

0 = -16t^2 + 80

-80 = -16t^2

5 = t^2

t = sqrt(5)

t =2.23

This is Graph D

Answer:

Q = 6

Step-by-step explanation:

Step 1: Write equation

4 - Q = -2

Step 2: Subtract 4 on both sides (Subtraction Equality)

-Q = -6

Step 3: Divide -1 on both sides (Division Equality)

Q = 6

And we have our answer!

Answer:

Step-by-step explanation:

[tex] \mathrm{4 - Q = - 2}[/tex]

Move constant to R.H.S and change its sign

[tex] \mathrm{ - Q = - 2 - 4}[/tex]

Calculate

[tex] \mathrm{ - Q = - 6}[/tex]

Change the signs on both sides of the equation

[tex] \mathrm{Q = 6}[/tex]

Hope I helped!

Best regards!

Answer:

$26532.98

Step-by-step explanation:

Given:

Sum is:

Answer: D

Step-by-step explanation:

The common difference is  -2/3  so using the last term which is -8/27 multiply it by -2/3 to find the next terms.

[tex]-\frac{8}{27} * -\frac{2}{3}[/tex] = [tex]\frac{16}{81}[/tex]    

[tex]\frac{16}{81} * -\frac{2}{3} = -\frac{31}{243}[/tex]  

[tex]-\frac{32}{243} * -\frac{2}{3} = \frac{64}{729}[/tex]  

Answer:

y=3/4x-2

Step-by-step explanation:

two points from graph (0-2) and (8,4)

find slope m: y2-y1/x2-x1

m=4+2/8-0

m=6/8=3/4

x=0 then y=b=-2

y=3/4x-2

Answer:

Step-by-step explanation:

The expression 4 raised to 4 can be written in mathematical term as [tex]4^4[/tex] and this means the value of 4 in four places as shown;

[tex]4^4\\\\= 4 * 4* 4* 4\\\\= (4 * 4)* (4* 4)\\\\= 16*16\\\\= 256\\\\[/tex]

Hence the expression 4 raised to 4 is equivalent to 256

Answer:

4%

Step-by-step explanation:

There are ₁₃C₃ ways to choose 3 diamonds from 13.

There are ₃₉C₁ ways to choose 1 non-diamond from 39.

There are ₅₂C₄ ways to choose 4 cards from 52.

Therefore, the probability is:

₁₃C₃ ₃₉C₁ / ₅₂C₄

= 286 × 39 / 270,725

≈ 0.04

The approximate probability that exactly three of the cards are diamonds is 4%.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

We are given that standard deck of 52 playing cards contains 13 cards in each of four suits: hearts, diamonds, clubs, and spades.

Since we can see that there are ₁₃C₃ ways to choose 3 diamonds from 13.

₃₉C₁ ways to choose 1 non-diamond from 39.

₅₂C₄ ways to choose 4 cards from 52.

Therefore, the probability is:

₁₃C₃ ₃₉C₁ / ₅₂C₄

= 286 × 39 / 270,725

≈ 0.04

Therefore, the answer could be 4 percent.

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Answer:

2 in

Step-by-step explanation:

18/3=6 , 6 is the scale factor

12/6=2

Answer:

width= 2

Step-by-step explanation:

18 inches is the original height and we are now reducing that to 3 inches.

In order to do that, we have to divide 18 by 3 which equals 6.

Next, take the width of the rectangle, which is twelve and divide it by the scale factor of 6 which  equals 2.

Your final answers should be: width= 2

Answer:

40°

Step-by-step explanation:

The circumference of a circle is equal to 360°

The arc AB is 180°, the arc AC is given as 100° so the arc CB is 80° and since <A is an inscribed angle it is equal to the half of the arc it sees

80 ÷ 2 = 40

Answer:

1/7 is left

Step-by-step explanation:

What is left to read after the first week

1 - 3/7

7/7 - 3/7

4/7

He read 3/4 of this the second week

4/7 * 3/4

3/7 was read

4/7 - 3/7 is what is left

1/7 is left

Answer:

The correct answer is

Step-by-step explanation:

1/7 of the book is left to read.

Hope this helps....

Have a nice day!!!!

Answer:

13. [tex]\frac{\sqrt[5]{x^4} }{x}[/tex].

14. [tex]v = \pm3\sqrt{5}[/tex]

15. 2.

Step-by-step explanation:

13. [tex]x^{1/5} * x^{-2/5}[/tex]

= [tex]x^{1/5 + (-2/5)}[/tex]

= [tex]x^{1/5 - 2/5}[/tex]

= [tex]x^{-1/5}[/tex]

= [tex]\frac{1}{x^{1/5}}[/tex]

= [tex]\frac{x^{4/5}}{x^{1/5 + 4/5}}[/tex]

= [tex]\frac{x^{4/5}}{x}[/tex]

= [tex]\frac{\sqrt[5]{x^4} }{x}[/tex].

14. [tex]v^2 - 45 = 0[/tex]

[tex]v^2 = 45[/tex]

[tex]\sqrt{v^2} = \pm\sqrt{45}[/tex]

[tex]\sqrt{v^2} = \pm\sqrt{3^2 * 5}[/tex]

[tex]v = \pm3\sqrt{5}[/tex].

15. [tex]\sqrt[3]{2} * \sqrt[3]{4}[/tex]

= [tex]\sqrt[3]{2 * 4}[/tex]

= [tex]\sqrt[3]{2 * 2 * 2}[/tex]

= [tex]\sqrt[3]{2 ^3}[/tex]

= 2.

Hope this helps!