If you can buy 6 bulbs of elephant garlic for $18 then how many can you buy with $54?

Answer:

1. 120\(m^{2}\)

2. 192\(ft^{2}\)

3. 48\(cm^{2}\)

Step-by-step explanation:

First triangle:

1. Find out the height

   \(h^{2} +8^{2} =17^{2}\)

   \(h^2+64=289\)

         -64     -64

   \(h^2=225\)

  h=15

2. Find the area

A=1/2 x 16 x 15

A=120\(m^{2}\)

Second triangle:

1. Find out the height

   \(h^2+16^{2} =20^{2}\)

   \(h^2+256=400\)

         -256   -256

   \(h^{2} =144\)

   h=12

2. Find the area

A=1/2 x 32 x 12

A=192\(ft^{2}\)

Third triangle:

1. Find out the height

\(h^2+6^2=10^{2}\)

\(h^2+36=100\\\)

     -36    -36

\(h^2=64\)

h=8

2. Find the area

A=1/2 x 12 x 8

A=48\(cm^{2}\)

Answer:

30

Step-by-step explanation:

The equation will be:

x - (10% of x) = 27

x - 0.1x = 30

0.9x = 30

Divide by 0.9

x = 30

The number is 30

Second question:

Length = 2x - 3

Width = x

Perimeter = 72

Perimeter = 2(l + w)

= 2(2x - 3 + x) = 72

4x - 6 + 2x = 72

6x = 72 + 6

6x = 78

w = 78/6 = 13

The width is 13 meters

According to the given data we have the following:

The price of 4 citrons and 3 fragrant wood apples=50 units

The price of 3 citrons and 4 fragrant wood apples=48 units

In order to find the price of a citron and the price of a wood apple we would formulate a system of equations:

So, let x=citrons

let y=wood apple

Hence:

1) 4x+3y=50

2) 3x+4y=48

Multiply equation 1 with 3, multiply equation 2 with -4

So:

12x +9y=150

-12x -16y=-192

-7y=-42

y=-42/-7

y=6

Substitute the value of y=6 in the original equation of 4x+3y=50

So, 4x +3(6)=50

4x+18=50

4x=32

x=32/4

x=8

Therefore, the price of a citron is 8 and the price of a wood apple is 6

Answer:

$15.48

Explanation:

100 ÷ 6.46 = 15.479876

Given two lines, line A and line B, we are asked to estimate line A as a percentage of line B.

If we measure line A and B with a ruler by placing it on the screen, we would get line A to be approximately 3.5cm and line B to be 4.0cm

We can then find the estimated percentage using the formula below;

Therefore, the answer would give;

Answer:

$23,465

$4,693

Step-by-step explanation:

To find a percent of a number, multiply the percent by the number.

6.5% of $361,000 = 0.065 × $361,000 = $23,465

20% of $23,465 = 0.2 × $23,425 = $4,693

Answer:

The slope is -3

Step-by-step explanation:

Use the slope formula to find the slope.

The formula is .... ⏬

Answer:

47.5

Step-by-step explanation:

Answer:

- 36

Step-by-step explanation:

1. y= - \(\frac{1}{9}\) x --> substitute y with 4 (given value)

2. 4 = - \(\frac{1}{9}\) x --> by multiplying 9 both side get rid of the 1/9

         (4= - \(\frac{1}{9}\) x)9 --> 36= - x

3. multiply " - " to both side to make "- x" to "x" --> (36= - x) - --> - 36 = x

          - 36 = x => x = -36

Answer:

Speed of the jet is 563.02 miles/hr

Speed of the jet stream is 122.83 miles/hr

Step-by-step explanation:

The average time for going from Seattle to New York is 4.3 hours

The distance between these places is 2421 miles

The average time for going back (impaired by jet stream) is 5.5 hours

If we designate the speed of the jet = v

and the speed of the jet stream = u

then on the return trip, the relative speed of the jet = v - u

Also, recall that distance = speed x time

For the going trip, the distance covered by the jet = 4.3 x v = 2421 miles

For the return trip, the distance covered by the jet = 5.5 x (v - u)  = 2421 miles

= 5.5(v - u)

these translate into the following equation written below

4.3v = 2421              ....equation 1

5.5(v - u) = 2421      ....equation 2

solving, equation 1, we'll have

4.3v = 2421

v = 2421/4.3 = 563.02 miles/hr  this is the speed of the jet

substituting the value of v into equation 2, we'll have

5.5(v - u) = 2421

5.5(563.02 - u) = 2421

3096.61 - 5.5u = 2421

3096.61 - 2421 = 5.5u

675.61 = 5.5u

u = 675.61/5.5

u = 122.83 miles/hr   this is the speed of the jet stream

Answer:

Hint: everything in that big [] is to the power of zero. anything to the power of zero is one. so

1+(6-8)=?

Answer:

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

Formula for area of a rectangle with dimensions l and w is:

Substitute 10 for l and 4 for w:

Answer:   middle.

Step-by-step explanation:   closest to each side.

Solving the system of equations,

To find the number of seats each section holds, we solve a system of equations.

A system of equations is a set of equations that contain two or three unknowns.

Let

Given that A stadium has 53,600 seats. Seats sell for $40 in section A, $30 in section B, and for $15 in section C.

We have that

x + y + z = 53600  (1)

Also, seats sell for $40 in section A, $30 in section B, and for $15 in section C and for each sold-out event, the stadium takes in $1,682,500, we have that

40x +30y + 15z = 1,682,500  (2)

Finally, the number of seats in section A equals the sum of the number of seats in sections B and C. so,

x = y + z  (3)

So, the system of equations are

x + y + z = 53600  (1)

40x +30y + 15z = 1,682,500  (2)

x = y + z  (3)

Substituting (3)into (1) and (2), we have

x + y + z = 53600  (1)

y + z + y + z = 53600  (1)

2y + 2z = 53600

y + z = 26800  (4)

Also,

40x +30y + 15z = 1,682,500  (2)

40(y + z) +30y + 15z = 1,682,500  (2)

40y + 40z +30y + 15z = 1,682,500  (2)

70y + 55z = 1,682,500

14y + 11z = 336500   (5)

From equation (4),

y = 26800 - z   (6)

Substituting equation (6) into (5), we have

14y + 11z = 336500   (5)

14(26800 - z) + 11z = 336500   (5)

373800 - 14z + 11z = 336500

375200 - 3z = 336500

-3z = 336500 - 375200

-3z = -38700

z = -38700/-3

z = 12900

Since y = 26800 - z   (6)

Substituting z = 12900, we have

y = 26800 - 12900

= 13900

Also, x = y + z (3)

Substituting y = 13900 and z = 12900 into the equation, we have

x = 13900 + 12900

= 26800

So,

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Answer:

The correct function is

\(f(b) = {b}^{2} - 4\)

Answer:

y= -3x+1

Step-by-step explanation:

x1= -2 x2=2 y1=7 y2=-5

using the formula

(y-y1)/(x-x1)=(y2-y1)/(x2-x1)

(y-7)/(x-(-2))=(-5-7)/(2-(-2))

(y-7)/(x+2)=(-5-7)/(2+2)

(y-7)/(x+2)=(-12)/4

(y-7)/(x+2)=-3

cross multiply

y-7=-3(x+2)

y-7=-3x-6

y=-3x-6+7

y=-3x+1

Answer: $9.66

Step-by-step explanation: perimeter = 345mm + 345mm + 345mm + 345mm = 1380

We need 1380 millimeters which is equivalent to 1.38 meters.

We can multiply the number of meters by the cost of meters to find the total

Answer:

$4.95

Step-by-step explanation:

If jelly beans cost $2.75 per pound then multiplying the cost per pound by the amount of jelly beans purchased will give the answer of $4.95 per 1.8 pounds of jelly beans.

Answer:

I am pretty sure it is when you have a sequence of numbers that you are subtracting or adding from by the same constant over and over

Step-by-step explanation:

an=a1+(n-1)d

d=common difference

an= the nth term in the sequence

a1 first term in the sequence. (Usually you can plug in 1, as the n, and work from there)

Answer:

(3xy - 1)/3x = b

Step-by-step explanation:

make b the subject of formula

then simply it

did you get it

Answer:

b=Y-x/3

Step-by-step explanation:

Solve for b by simplifying both sides of the equation, then isolating the variable.

have a great day and thx for your inquiry :)

Answer:

5km

Step-by-step explanation:

A - her office

E - her home

AB = 1km; BC = CE = 4km

AE - the shortest disctance between her office and home.

ADE - right triangle, where AD = 4km, ED = 3 (EC - CD) =>

According to the Pythagorean theorem , we make up the equation:

AE = √ED^2 + AD^2 = √25 = 5km

Let f(x) = lnx and g(x) = log₂x. for all 0 < x < 1, f(x) < g(x): True.

In this scenario and exercise, we would determine the corresponding output value for the functions f(x) and g(x) under the given mathematical operation and independent variables.

When x = 1, the output value for f(x) based on the table of values is given by;

f(x) = lnx

f(1) = ln(1).

f(1) = 0.

When x = 2, the output value for f(x) based on the table of values is given by;

f(x) = lnx

f(2) = ln(2).

f(2) = 0.69314718

When x = 1, the output value for g(x) based on the table of values is given by;

g(x) = log₂x

g(1) = log₂(1)

g(1) = 0.

When x = 2, the output value for g(x) based on the table of values is given by;

g(x) = log₂x

g(2) = log₂(2)

g(2) = 1.

In this context, we can logically deduce that the function f(x) is less than function g(x) for all 0 < x < 1.

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Answer:

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

Let the numbers be s and l.

We are given that:

Set up equations:

Eliminate l:

Solve for s:

Find l:

To solve this problem one must be aware of the concepts of standard deviation and variance of raw data.

There is a direct formulae to calculate the variance of the data,

Variance = \(σ^{2} =\frac{Sigma(xi-m)^{2}}{n}\)

Now here we need to verify ∑x and ∑\(x^{2}\).

∑x = 21+19+15+32+27

     = 114

and ∑\(x^{2}\) = \(21^{2} +19^{2} +15^{2} +32^{2} +27^{2}\)

             = 441+361+225+1024+729

             = 2780

So, the given relation is true.

Now the variance of the given data by putting the values in the formulae is  equal to 45.2.

And Standard deviation=\(\sqrt{Variance}\)

                                     = \(\sqrt{45.2}\)

                                      = 6.72

And for population α²=36.16 and deviation=6.01.

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Answer:

Most people know Pi up to 2 decimal places (3.14) because you can always refer to the internet for those extra decimal places anytime you want.

Step-by-step explanation:

It's easy to create rational approximations for π. Every time you write down π to a few decimal places, that's a rational approximation.

Depending on the purpose of a calculation, π can be approximated by using fractions for ease of calculation. The most notable such approximations are 22⁄7 (relative error of about 4·10−4) and 355⁄113 (relative error of about 8·10−8).

ANSWER :

Mean = 1.54

Mode = 1.3

Median = 1.5

Range = 0.9

EXPLANATION :

From the problem, we have the following weights.

1.1, 1.9, 1.5, 1.3, 2.0, 1.3, 1.7

Arrange the data from least to greatest.

1.1, 1.3, 1.3, 1.5, 1.7, 1.9, 2.0

The mean is the average of the data

That will be :

The mode is the data with the most number of appearance.

In this case, 1.3 appears twice.

So the mode is 1.3

The median is the middle data, since there are 7 data, the middle term is the 4th term

That will be 1.5

The range is the difference between the greatest and least data.

That will be 2.0 - 1.1 = 0.9

Answer:

.

Step-by-step explanation:

Answer:

You'll have $2.19.

Step-by-step explanation:

Quarters:

0.25 + 0.25 + 0.25 + 0.25 = 1.00

1.00 + 0.25 = 1.25 + 0.25 = 1.50

Dimes:

1.50 + 0.10 + 0.10 = 1.70 + 0.10 = 1.80 + 0.10 + 0.10 = 2.00

Nickles:

2.00 + 0.05 = 2.05 + 0.05 = 2.10 + 0.05 = 2.15

Pennies:

2.15 + 0.04 = 2.19

Answer:

Highest Elevation: 14240

Lowest Elevation: -285

Step-by-step explanation:

Given

\(Highest\ Elevation = 14,240\ ft\) above sea level

\(Lowest\ Elevation = 285\ ft\) below sea level

Required

Represent both altitudes as an integer

For the Mountain:

Take the sea level as 0 feet

\(Altitude = Highest\ Elevation - Sea\ Level\)

\(Altitude = 14240 - 0\)

\(Altitude = 14240\)

Hence, the integer is 14240

For the Valley:

Take the sea level as 0 feet

\(Altitude = Sea\ Level - Lowest\ Elevation\)

\(Altitude = 0 - 285\)

\(Altitude = -285\)

Hence, the integer is -285

Answer:

Part A:

1. Computation of Basic EPS

Basic EPS = (Net Income - Preferred Dividends) / Weighted Average Shares Outstanding²

Net Income = $120,000

Preferred Dividends = 4% x $50,000 = $2,000

Weighted Average Shares Outstanding = 100,000 (assuming no change in common stock during the year)

Basic EPS = ($120,000 - $2,000) / 100,000

Basic EPS = $1.18

2. Individual dilution/anti-dilution with decision making

We need to check if any of the convertible securities or stock options are dilutive or anti-dilutive by comparing their impact on EPS with the basic EPS.

Convertible Preferred: Each preferred share can be converted into 1.9 common shares (1,900 / 1,000). The conversion would increase the common shares outstanding by 1,900 and decrease the preferred dividends by $2,000.

EPS after conversion = ($120,000 - $0) / (100,000 + 1,900)

EPS after conversion = $1.16

Since this is lower than the basic EPS of $1.18, the convertible preferred is dilutive and should be included in the diluted EPS calculation.

Stock Options - A: Each option can be exercised at $12 to buy one common share when the average market price is $11. This means that the options are out of the money and would not be exercised by the holders. Therefore, they have no impact on EPS and are anti-dilutive.

Stock Options - B: Each option can be exercised at $7 to buy one common share when the average market price is $8. This means that the options are in the money and would be exercised by the holders. The exercise would increase the common shares outstanding by 4,000 and generate cash proceeds of $28,000 ($7 x 4,000). The cash proceeds can be used to buy back some common shares at the market price of $8. The number of shares bought back is 3,500 ($28,000 / $8). The net increase in common shares outstanding is 500 (4,000 - 3,500).

EPS after exercise = ($120,000 - $2,000) / (100,000 + 500)

EPS after exercise = $1.17

Since this is lower than the basic EPS of $1.18, the stock options - B are dilutive and should be included in the diluted EPS calculation.

Convertible Bonds: Each bond can be converted into 40 common shares (40,000 / 1,000). The conversion would increase the common shares outstanding by 40,000 and decrease the interest expense by $50,000 ($1,000,000 x 5%). The interest expense is net of tax, so we need to multiply it by (1 - tax rate) to get the after-tax amount. The tax rate is 30%.

EPS after conversion = ($120,000 - $2,000 + $50,000 x (1 - 0.3)) / (100,000 + 40,000)

EPS after conversion = $1.19

Since this is higher than the basic EPS of $1.18, the convertible bonds are anti-dilutive and should be excluded from the diluted EPS calculation.

3. Ranking of potential dilutors

We need to rank the potential dilutors from the most dilutive to the least dilutive based on their impact on EPS.

The most dilutive security is the convertible preferred with an EPS of $1.16.

The second most dilutive security is the stock options - B with an EPS of $1.17.

The least dilutive security is the convertible bonds with an EPS of $1.19.

4. Step-by-step inclusion of individual dilutors to arrive at reportable EPS with decision making.

We need to include the potential dilutors in order of their dilution until we reach a point where the next security would be anti-dilutive.

The first security to include is the convertible preferred.

EPS with convertible preferred = ($120,000 - $0) / (100,000 + 1,900)

EPS with convertible preferred = $1.16

The next security to include is the stock options - B.

EPS with stock options - B = ($120,000 - $0) / (100,000 + 1,900 + 500)

EPS with stock options