#3 only Fractions help

The difference in volume between a large scoop and a small scoop of ice cream is approximately 410.5 cubic centimeters.

To find the difference in volume between a large scoop and a small scoop of ice cream, we need to calculate the volume of each scoop and then subtract the volume of the small scoop from the volume of the large scoop.

The volume of a sphere can be calculated using the formula V = (4/3)πr³, where r is the radius. Since the diameter of the small scoop is 6 cm, the radius is 3 cm. Plugging this into the formula, we get V = (4/3)π(3 cm)³. Evaluating this expression, we find that the volume of the small scoop is approximately 113.1 cm³.

Similarly, the diameter of the large scoop is 10 cm, so the radius is 5 cm. Using the same formula, we find that the volume of the large scoop is approximately 523.6 cm³.

To find the difference in volume, we subtract the volume of the small scoop from the volume of the large scoop: 523.6 cm³ - 113.1 cm³ = 410.5 cm³. Therefore, the difference in volume between a large scoop and a small scoop of ice cream is approximately 410.5 cubic centimeters.

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The final answer is 410.5 cubic centimeters.

1. Calculate the volume of a small scoop:

- Given the diameter of the small scoop, [tex]\( d_{\text{small}} = 6 \) cm[/tex].

- Radius of small scoop, [tex]\( r_{\text{small}} = \frac{d_{\text{small}}}{2} = \frac{6}{2} = 3 \)[/tex] cm.

- Volume of a sphere [tex]\( V = \frac{4}{3} \pi r^3 \).[/tex]

- Substitute the radius into the volume formula: [tex]\( V_{\text{small}} = \frac{4}{3} \pi (3)^3 = \frac{4}{3} \pi (27) \)[/tex].

- Calculate:

[tex]\( V_{\text{small}} = 36 \pi \)[/tex] cubic centimeters.

2. Calculate the volume of a large scoop:

- Given the diameter of the large scoop,[tex]\( d_{\text{large}} = 10 \) cm[/tex].

- Radius of large scoop, [tex]\( r_{\text{large}} = \frac{d_{\text{large}}}{2} = \frac{10}{2} = 5 \) cm[/tex].

- Volume of a sphere [tex]\( V = \frac{4}{3} \pi r^3 \)[/tex].

- Substitute the radius into the volume formula:

[tex]\( V_{\text{large}} = \frac{4}{3} \pi (5)^3 = \frac{4}{3} \pi (125) \)[/tex].

- Calculate:

[tex]\( V_{\text{large}} = 166.7 \pi \)[/tex] cubic centimeters.

3. Find the difference:

- Difference in volume: [tex]\( V_{\text{large}} - V_{\text{small}} = 166.7 \pi - 36 \pi \)[/tex].

- Calculate: [tex]\( V_{\text{large}} - V_{\text{small}} = 130.7 \pi \)[/tex].

- Approximate [tex]\( \pi \)[/tex] to 3.14.

- [tex]\( 130.7 \times 3.14 = 410.498 \)[/tex].

- Rounded to the nearest tenth, the difference is approximately 410.5 cubic centimeters.

Answer:

56

Step-by-step explanation:

8C3 = 56

Answer:

Step-by-step explanation:

For a point to be a relative extreme, there must be points on both sides that are not as extreme. That is, the ends of the interval may be extreme values, but do not qualify as relative extrema, since there are not points on both sides.

In the interval [-3, 3], the relative extrema are the turning points.

The relative minimum is at y = -9 on the y-axis.

The relative maxima are at y = -6, between 1 and 2 on either side of the y-axis.

Answer:

minimum: -9

maximum: -6

Step-by-step explanation:

Answer:

  4. 16

  5. $88

  6. $687.50

Step-by-step explanation:

4. Let n represent the number.

An expression representing the number multiplied by 0.9 and 6.3 subtracted from the product is ...

  0.9n -6.3

We want that result to be 4.5, so we have the equation ...

  0.9n -6.3 = 4.5

Since all of the coefficients are divisible by 0.9, we can divide by 0.9 to get ...

  n -7 = 9

Adding 7 gives ...

  n = 16

The number is 16.

_____

5. For a problem like this, I like to work it backward. If Craig got an extra $18, then everyone's share was $32 -18 = $14. That was the share from a 5-way split, so the amount the friends split evenly was 5×$14 = $70. The total they started with must have been $70 +18 = $88.

The amount they split unevenly was $88. The amount they split evenly, after setting aside $18 for Craig's parents, was $70.

__

It is a bit tricky to write one equation for the amount the friends started with before they did any splits. Call that amount A. Then after setting aside $18, they split (A-18) five ways. Each of those splits was then (A-18)/5. When the $18 was added to one of those, the result was the $32 that Craig got. So, we have ...

  (A -18)/5 +18 = 32

and the solution process is similar to the "working backward" description above: subtract 18, multiply by 5, add back 18.

  (A -18)/5 = 14

  A -18 = 70

  A = 88 . . . . . . . . the amount the friends split unevenly

_____

6. Let P represent the original price of the laptop. We're told the price after all of the discounts was 500, so we have ...

  P -50 -(0.20P) = 500

  0.80P = 550 . . . . . add 50, collect terms

  P = 687.50 . . . . . . . divide by the coefficient of P

The original price was $687.50.

Answer:

HL theorem.

Step-by-step explanation:

This states that if the hypotenuse (H) and  one leg (L) of one  right triangle are congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent.

Answer:

ASA Postulate

Step-by-step explanation:

[tex] In \:\triangle QTS \:\&\:\triangle SRQ\\\\

QT || SR\\\\

\angle QTS \cong \angle SRQ... (each\: 90°)\\\\

TS \cong QR.... (given) \\\\

\angle QST \cong \angle SQR.. (alternate\:\angle s) \\\\

\therefore \triangle QTS \cong \triangle SRQ\\.. (By \: ASA \: Postulate) [/tex]

RHS Postulate can also be applied to prove both the triangles as congruent.

Answer: The system of inequalities that models this situation are

p + b ≤ 30

12.5p + 9.5b ≥ 300

Step-by-step explanation:

Let p represent the number of hours he works at the pizzeria.

Let b represent the number of hours he works at the bookstore.

He cannot work more than 30 hours per week in order to attend classes. This means that

p + b ≤ 30

Marcus is working at a local pizzeria where he makes $12.50 per hour and is also working at the university bookstore where he makes $9.50 per hour. He must make at least $300 per week to cover his expenses. This means that

12.5p + 9.5b ≥ 300

Answer:

The new break even point in units = 34400 units

Step-by-step explanation:

Fixed cost ( F ) = $ 645000

Selling price ( s )= $ 50

Variable Cost ( v ) = [tex]\frac{60}{100}[/tex] × 50 = 30

Break Even Quantity ( [tex]x_{BEP}[/tex] ) = [tex]\frac{F}{s - v}[/tex]

⇒ [tex]x_{BEP}[/tex] = [tex]\frac{645000}{50 - 30}[/tex]

⇒ [tex]x_{BEP}[/tex] = [tex]\frac{645000}{20}[/tex]

⇒ [tex]x_{BEP}[/tex] = 32250 units

Now the new fixed cost ( [tex]F_{1}[/tex] ) = $ 645000 + $ 215000 = $ 860000

Selling price ( s )= $ 50

Variable Cost ( v ) = [tex]\frac{50}{100}[/tex] × 50 = $ 25

Break Even Quantity ( [tex]x_{BEP}[/tex] ) = [tex]\frac{F_{1} }{s - v}[/tex]

⇒ [tex]x_{BEP}[/tex] = [tex]\frac{860000}{50 - 25}[/tex]

⇒ [tex]x_{BEP}[/tex] = 34400 units

Therefore, The new break even point in units = 34400 units

Answer: the speed of the plane is 130 mph

Step-by-step explanation:

Let x represent the speed of the plane. If the car travels 80 mph slower than the plane, then the speed of the car would be (x - 80) mph.

Time = Distance/speed

plane can fly 520 miles in the same time as it takes a car to go 200 miles. This means that the time it takes the plane to fly 520 miles is

520/x

Also, the time it takes the car to drive 200 miles is

200/(x - 80)

Since the time is the same, it means that

520/x = 200/(x - 80)

Cross multiplying, it becomes

520(x - 80) = 200 × x

520x - 41600 = 200x

520x - 200x = 41600

320x = 41600

x = 41600/320

x = 130 mph

Answer:

0.3 liters

Step-by-step explanation:

Molly made 3600mL of tea for a party.

The tea was served equally in 12 cups.

We are to determine how many liters of tea Molly put in each cup.

Total Volume of Tea = 3600mL

Number of Cups=12

Volume Per Each Cup = 3600/12 = 300mL

Next, we convert our Volume Per Each Cup from mL to Liters

1000 Milliliter = 1 Liter  

300 Milliliter =[tex]\frac{300}{1000}[/tex] liters =0.3 liters

Molly put 0.3 liters of tea in each cup.

Answer:

General Revenue Sales Tax

Step-by-step explanation:

The ¼ percent would be recorded as general revenue sales tax in government activities journal.

This is because the revenue from the tax are categorised as the revenues generated from payrolls (which are imposed on employers), income and profits taxes, social security contributions, taxes levied on goods and services.

Options:

Program Revenue-Culture and Recreation-Sales Tax.

Program Revenue-Culture and Recreation-Operating Grants and Contributions.

General Revenue-Sales Tax.

General Revenue-Culture and Recreation-Sales Tax.

Answer:

General Revenue - Sales Tax

Step-by-step explanation:

General revenue is the income that is generated by the state which may be used to serve any administrative purpose by the state, and tax revenue is the income that is generated by the state through taxation.

Since the sales tax is a way of generating income by the state, it should be recorded as sales tax under general revenue.

Answer:

15 feet

Step-by-step explanation:

525 = ½(30+40)h

525 = 35h

h = 525/35

h = 15 feet

Answer:

(D) 0.006

Step-by-step explanation:

Total number of cards :52

Please note that, all cards have a the possibility of appearing 4 times.

Hence total possible number of a '2' is 4 cards and so it is also for a '10'

Having this Understanding, let's solve the question properly.

The probability that the FIRST CARD is 2 = 4/52

Probability that the second card without replacement is a 10 = 4 / 51

P( 1st two and 2nd four)

4/52 * 4/51 = 4/663

= 0.0060332

Rounding to 3 decimal places = 0.006

Answer:

2nd option (B)

Step-by-step explanation:

(0,-6) works

(3,-7) works

(-3,-5) works

This means the answer is B

Answer:

TRUE

Step-by-step explanation:

Answer:

(i)Ratio of the Number of Girls in the School to the Total Population

=5:27

(ii)Ratio of the Number of Boys in the School to the Total Population=22:27

Step-by-step explanation:

Below is the steps on how the given ratio are derived

If the school has 880 boys and 200 girls

Total Population of the School=880+200=1080

Ratio of Girls to all Student is 5:27

Now, this is derived from this:

Ratio of the Number of Girls in the School to the Total Population

=200:1080[tex]=\frac{200}{1080} =\frac{5}{27}[/tex]

Which in reduced form is 5:27

You can do likewise for boys

Ratio of the Number of Boys in the School to the Total Population=880:1080[tex]=\frac{880}{1080} =\frac{22}{27}[/tex]

Which in reduced form is 22:27

Answer:

  you're not doing anything wrong

Step-by-step explanation:

In order for cos⁻¹ to be a function, its range must be restricted to [0, π]. The cosine value that is its argument is cos(-4π/3) = -1/2. You have properly identified cos⁻¹(-1/2) to be 2π/3.

__

Cos and cos⁻¹ are conceptually inverse functions. Hence, conceptually, cos⁻¹(cos(x)) = x, regardless of the value of x. The expected answer here may be -4π/3.

As we discussed above, that would be incorrect. Cos⁻¹ cannot produce output values in the range [-π, -2π] unless it is specifically defined to do so. That would be an unusual definition of cos⁻¹. Nothing in the problem statement suggests anything other than the usual definition of cos⁻¹ applies.

__

This is a good one to discuss with your teacher.

For this case we must factor the following expression:

[tex]100k ^ 3-75k ^ 2 + 120k-90[/tex]

We take common factor 5:

[tex]5 (20k ^ 3-15k ^ 2 + 24k-18) =[/tex]

We have two groups within the parentheses:

Group 1: [tex]20k ^ 3-15k ^ 2[/tex]

Group 2: [tex]24k-18[/tex]

We factor each group:

Group 1: [tex]6 (4k-3)[/tex]

Group 2: [tex]5k ^ 2 (4k-3)[/tex]

Rewriting we have:

[tex]5 (5k ^ 2 (4k-3) +6 (4k-3)) =\\5 ((5k ^ 2 + 6) (4k-3))[/tex]

Answer:

[tex]5 (5k ^ 2 + 6) (4k-3)[/tex]

Final answer:

The question asks to demonstrate that for a nonnegative integer-valued random variable X, the expected value E(X) equals the summation over all k of the probability P(X ≥ k). This is shown by expressing P(X ≥ k) as an infinite sum, switching the order of summation, and counting each probability P(X = i) exactly i times.

Explanation:

The student's question pertains to the calculation of the expected value (E(X)) of a nonnegative integer-valued random variable. Specifically, the question asks to show that for such a random variable X, the expected value can be expressed as E(X) = ∑₋∞ k=1 P(X ≥ k). To demonstrate this, we begin with the definition of expected value:

E(X) = μ = ∑ xP(x).

Next, we unpack P(X ≥ k) by writing it as an infinite sum of probabilities for all integers i starting from k:

P(X ≥ k) = ∑₋∞ i=k P(X = i).

To find the expected value, we consider the sum of all such probabilities over all k:

∑₋∞ k=1 P(X ≥ k) = ∑₋∞ k=1 ∑₋∞ i=k P(X = i).

We then switch the order of summation, so that we first sum over all possible values of i and then for each i, we sum over the corresponding k that contributes to P(X = i):

E(X) = ∑₋∞ i=1 P(X = i) ∑₉ i k=1.

By doing this, we count each P(X = i) exactly i times, which leads us to the initial definition of expected value, thus proving the given formula.

To solve this problem, we can use the concept of exponential decay, where the value of the computer decreases by half every two years. Let's denote the initial value of the computer as [tex]\( V_0 \)[/tex]. After the first two years, its value will be [tex]\( \frac{1}{2}V_0 \)[/tex], after another two years (total of 4 years), its value will be [tex]\( \frac{1}{4}V_0 \)[/tex], and after three years, its value will be [tex]\( \frac{1}{8}V_0 \).[/tex]

Given that after three years its value is $425, we can set up the equation:

[tex]\[ \frac{1}{8}V_0 = 425 \][/tex]

Now, let's solve for [tex]\( V_0 \):\[ V_0 = 425 \times 8 \]\[ V_0 = 3400 \][/tex]

So, the initial value of the computer was $3400.

[tex]7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{54}[/tex] simplified as [tex]11\sqrt{3}- 7\sqrt{6}[/tex] or [tex]1.909[/tex] .

Step-by-step explanation:

We need to Simplify seven square root of three end root minus four square root of six end root plus square root of forty eight end root minus square root of fifty four. Which is equivalent to [tex]7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{54}[/tex] :

[tex]7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{54}[/tex]

⇒ [tex]7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{44}[/tex]

⇒ [tex]7\sqrt{3}- 4\sqrt{6} + \sqrt{16(3)} - \sqrt{9(6)}[/tex]

⇒ [tex]7\sqrt{3}- 4\sqrt{6} + 4\sqrt{(3)} - 3\sqrt{(6)}[/tex]

⇒ [tex]11\sqrt{3}- 4\sqrt{6}- 3\sqrt{(6)}[/tex]

⇒ [tex]11\sqrt{3}- 7\sqrt{6}[/tex]

[tex]\sqrt{3} = 1.732 , \sqrt{6} = 2.449[/tex]

⇒ [tex]11(1.723)- 7(2.449)[/tex]

⇒ [tex]1.909[/tex]

Therefore, [tex]7\sqrt{3}- 4\sqrt{6} + \sqrt{48} - \sqrt{54}[/tex] simplified as [tex]11\sqrt{3}- 7\sqrt{6}[/tex] or [tex]1.909[/tex] .

Answer:

11√3 - 7√6

Step-by-step explanation:

I took the test and got it right.

Answer:

[tex]\frac{17}{6}[/tex] or [tex]2\frac{5}{6}[/tex]

Step-by-step explanation:

1.Find the Least Common Denominator (LCD)

 LCD = 6

2.Make the denominators the same as the LCD.

   [tex]2+\frac{1*3}{2*3} + \frac{1*2}{3*2}[/tex]

3.Simplify. Denominators are now the same

   [tex]2+\frac{3}{6} + \frac{2}{6}[/tex]

4. Join the denominators

   [tex]2+\frac{3+2}{6}[/tex]

5.Simplify

   [tex]2\frac{5}{6}[/tex] = [tex]\frac{17}{6}[/tex]

Answer:

1 1/3

Step-by-step explanation:

Given function:

Rewrite:

Find the solution:

Therefore, 2y+x=1 1/3..

Answer:

there are n flute players so that means that you have a n amount of flute players.

Step-by-step explanation:

You would need n flute players to play ou would have n trumpet players

Answer: height = 10 feet

Base = 24 feet

Step-by-step explanation:

Let h represent the height of the triangular flower bed.

Let b represent the base of the triangular flower bed

The formula for determining the area of a triangle is expressed as

Area = 1/2 × base × height

The area of a triangular flower bed in the park has an area of 120 square feet. This means that

1/2 × bh = 120

bh = 120 × 2

bh = 240- - - - - - - - - - - - - - - 1

The base is 4 feet longer than twice the height. This means that

b = 2h + 4

Substituting b = 2h + 4 into equation 1, it becomes

h(2h + 4) = 240

2h² + 4h = 240

2h² + 4h - 240 = 0

Dividing through by 2, it becomes

h² + 2h - 120 = 0

h² + 12h - 10h - 120 = 0

h(h + 12) - 10(h + 12) = 0

h - 10 = 0 or h + 12 = 0

h = 10 or h = - 12

Since the height cannot be negative, then h = 10

Substituting h = 10 into equation 1, it becomes

10b = 240

b = 240/10

y = 24

The answers are : (a) The height [tex]\( h \)[/tex] of the triangular flower bed is [tex]10\ feet[/tex]. (b) The base [tex]\( b \)[/tex] of the triangular flower bed is [tex]24 \ feet[/tex]

Let's denote the height of the triangular flower bed as [tex]\( h \)[/tex] feet.

According to the problem, the base of the triangle is [tex]4\ feet[/tex] longer than twice the height. Therefore, the base [tex]\( b \)[/tex] can be expressed as:

[tex]\[ b = 2h + 4 \][/tex]

The formula for the area [tex]\( A \)[/tex] of a triangle is given by

[tex]\[ A = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]

Given that the area [tex]\( A \)[/tex] of the triangular flower bed is [tex]120\ square\ feet[/tex], we can write the equation:

[tex]\[ \frac{1}{2} \times b \times h = 120 \][/tex]

Substituting [tex]\( b = 2h + 4 \)[/tex] into the area equation:

[tex]\[ \frac{1}{2} \times (2h + 4) \times h = 120 \][/tex]

Now, solve for [tex]\( h \)[/tex]

[tex]\[ (2h + 4) \times h = 240 \][/tex]

[tex]\[ 2h^2 + 4h = 240 \][/tex]

[tex]\[ 2h^2 + 4h - 240 = 0 \][/tex]

Divide the entire equation by [tex]2[/tex] to simplify:

[tex]\[ h^2 + 2h - 120 = 0 \][/tex]

Now, solve this quadratic equation using the quadratic formula, [tex]h = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1 \), \( b = 2 \), and \( c = -120 \)[/tex]

[tex]\[ h = \frac{-2 \pm \sqrt{(2)^2 - 4 \times 1 \times (-120)}}{2 \times 1} \][/tex]

[tex]\[ h = \frac{-2 \pm \sqrt{4 + 480}}{2} \][/tex]

[tex]\[ h = \frac{-2 \pm \sqrt{484}}{2} \][/tex]

[tex]\[ h = \frac{-2 \pm 22}{2} \][/tex]

The solutions for [tex]\( h \)[/tex] are:

[tex]\[ h = \frac{20}{2} = 10 \][/tex]

[tex]\[ h = \frac{-24}{2} = -12 \][/tex]

So, the height [tex]\( h \)[/tex] of the triangular flower bed is [tex]10\ feet.[/tex]

Now, calculate the base [tex]\( b \)[/tex]

[tex]\[ b = 2h + 4 \][/tex]

[tex]\[ b = 2 \times 10 + 4 \][/tex]

[tex]\[ b = 20 + 4 \][/tex]

[tex]\[ b = 24 \][/tex]

The complete Question is

The area of a triangular flower bed in the park has an area of 120 square feet. The base is 4 feet longer than twice the height.

a. What is the base of the triangle ?

b. What is the height of the triangle ?

Answer:

[tex]vXw =-36i+33j+26k[/tex]

Step-by-step explanation:

v = 3i + 8j – 6k

w = –4i – 2j – 3k

The cross product

[tex]v X w=\left|\begin{array}{ccc}i&j&k\\3&8&-6\\-4&-2&-3\end{array}\right|[/tex]

[tex]=i\left|\begin{array}{cc}8&-6\\-2&-3\end{array}\right|-j\left|\begin{array}{cc}3&-6\\-4&-3\end{array}\right|+k\left|\begin{array}{cc}3&8\\-4&-2\end{array}\right|\\[/tex]

[tex]=i(-24-12)-j(-9-24)+k(-6+32)\\vXw =-36i+33j+26k[/tex]

Answer:

A chord

Step-by-step explanation:

By the definition of a chord, it is a line segment whose endpoints lie on the circle, (and in this case circle is meant by the set of points equidistant from a center point, or as an algebraic term: circumference)

Answer:

6.93

Step-by-step explanation:

f(x) = 15 / (1 + 4e^(-0.2x))

f(x) = 15 (1 + 4e^(-0.2x))^-1

Taking first derivative:

f'(x) = -15 (1 + 4e^(-0.2x))^-2 (-0.8e^(-0.2x))

f'(x) = 12 (1 + 4e^(-0.2x))^-2 e^(-0.2x)

f'(x) = 12 (1 + 4e^(-0.2x))^-2 (e^(0.1x))^-2

f'(x) = 12 (e^(0.1x) + 4e^(-0.1x))^-2

Taking second derivative:

f"(x) = -24 (e^(0.1x) + 4e^(-0.1x))^-3 (0.1e^(0.1x) − 0.4e^(-0.1x))

Set to 0 and solve:

0 = -24 (e^(0.1x) + 4e^(-0.1x))^-3 (0.1e^(0.1x) − 0.4e^(-0.1x))

0 = 0.1e^(0.1x) − 0.4e^(-0.1x)

0.1e^(0.1x) = 0.4e^(-0.1x)

e^(0.1x) = 4e^(-0.1x)

e^(0.2x) = 4

0.2x = ln 4

x = 5 ln 4

x ≈ 6.93

Graph: desmos.com/calculator/zwf4afzmav

The point of maximum growth rate for the logistic function f(x) is at (7.5, 7.926).

Given is the function f(x) as follows -

f(x) = 15/(1+4[tex]$e^{-0.2x}[/tex] )

The given logistic function is -

f(x) = 15/(1+4[tex]$e^{-0.2x}[/tex] )

So, we can say that at {x} = N = 15/2 = 7.5, the point of maximum growth exists. At {x} = 7.5, the value of {y} = 7.926. Refer to the graph of the function attached.

Therefore, the point of maximum growth rate for the logistic function f(x) is at (7.5, 7.926).

To solve more questions on exponential equations, visit the link below -

brainly.com/question/29506679

#SPJ3

Answer: 28 fl oz

Step-by-step explanation:

84 fl oz. = 10.5 cups of water

10.5/3=3.5*8=28

why 3.5 times 8 is to get the exact amount of fluid ounces

Answer: he would need 14 fluid ounces of concentrated soap.

Step-by-step explanation:

The directions call for 4 fluid ounces of concentrated soap for every 3 cups of water.

1 cup = 8 fluid ounces

Converting 3 cups of water to fluid ounces, it becomes

3 cups = 3 × 8 = 24 fluid ounces

Kevin uses 84 fluid ounces of water to make an all-purpose cleaner. This means that the amount of concentrated soap that he would use is

(84 × 4)/24 = 336/24 = 14 fluid ounces of concentrated soap

Answer:

21 years old.

Step-by-step explanation:

Given:

Waneta is 8 years old

Waneta is 4/7 as old as Elizabeth.

Chun is 1/2 as old as Elizabeth.

George is 3 time as old as Chun.

Question asked:

How many years old is George ?

Solution:

Let age of Elizabeth = [tex]x[/tex] years

Waneta is 4/7 as old as Elizabeth. ( given )

Age of Waneta = [tex]\frac{4}{7} \ of \ Elizabeth[/tex]

[tex]8=\frac{4}{7} \times x\\\\8=\frac{4}{7}x[/tex]

By cross multiplication:

[tex]4x=56[/tex]

By dividing both sides by 4

[tex]x=14\\[/tex]

Age of Elizabeth = [tex]x[/tex] = 14 years

Chun is 1/2 as old as Elizabeth. ( given )

Age of Chun = [tex]\frac{1}{2} \ of \ Elizabeth\\[/tex]

                     = [tex]\frac{1}{2} \times14= 7\ years[/tex]

George is 3 time as old as Chun.  ( given )

Age of George = [tex]3\ times \ of \ Chun\\[/tex]

                         [tex]=3\times7=21\ years[/tex]

Therefore, George is 21 years old.

Answer:

it's Quadrant 1 because both of he cordnates

Step-by-step explanation:

Answer:

w(2,-3)

Step-by-step explanation:

the initial coordinates of point w are  w(-2,3), to differentiate the different coordinates of w we will place sub-indexes (according to the graph)

the point w is reflected over the x axis to create point w₁(-2,-3) point w is then reflected over the y axis to create point w₂(2,-3)