The local nursery is waiting for its spring annuals to be delivered, and 20% of the plants ordered are petunias. If the first truck contains 120 plants packed at random, what is the probability that no more than 30 plants are petunias?

Step-by-step explanation:

Let the dimension of the box be x, y and z.

Volume of the box V = xyz

Since the box is a rectangular box, the base will be a square of equal length.

V = x²h where h is the height of the box

If the sum of the length, width, and height equals 180, then x+x+h = 180

2x+h = 180

h = 180-2x

Substitute h = 180-2x into the volume of the box

V = x²(180-2x)

V = 180x²-2x³

The box has its maximum volume when [tex]\frac{dV}{dx} = 0[/tex]

[tex]\frac{dV}{dx} = 360x-6x^{2}[/tex]

[tex]360x-6x^{2} = 0\\360x = 6x^2\\360 = 6x\\6x = 360\\x = \frac{360}{6}\\ x = 60[/tex]

Since 2x+h = 180

Substitute x = 60 into the equation ang get the height h

2(60)+h = 180

120+h = 180

h = 180-120

h = 60

Hence the dimension of the rectangular box is 60 by 60 by 60

The dimensions of the rectangular box of maximum volume are;

Length = 60

Length = 60Width = 60

Length = 60Width = 60Height = 60

Let the dimensions of the rectangular box be;

Length = x

Width = y

Height = h

Volume of a rectangular box is given by;

V = length × width × height

Thus;

Volume of this box in question is;

V = xyz

The box is called a rectangular box because it's sides are rectangular in shape but it's base will be square in shape.

Thus;

width = x and so;

V = x²h

We are given the sum of the length, width, and height of the rectangular box to be equal to 180.

Thus; x + x + h = 180

2x + h = 180

h = 180-2x

Put 180 - 2x for h in the equation for volume;

V = x²(180 - 2x)

V = 180x² - 2x³

The maximum volume will occur at the dimensions when dV/dx = 0. Thus;

dV/dx = 360x - 6x²

At dV/dx = 0, we have;

360x - 6x² = 0

6x² = 360x

x = 60

Recall that; h = 180 - 2x, thus;

h = 180 - 2(60)

h = 60

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Answer:

Irrational Number

Step-by-step explanation:

Given

[tex]Number = 1.56432..[/tex]

Required

Determine which set of number it is

The given number is not a natural number, whole number and it is not an integer because it contains decimal point

The given number is not rational because it can not be expressed as a fraction of two whole numbers.

Hence:

The set of the number is irrational

Answer:

<KLM = 48 degrees

Step-by-step explanation:

According to the instructions, we construct the triangle JKL and extend the side JL to point M. The information about the angles is shown in the attached image.

Recall that the addition of all internal angles of a triangle must give 180 degrees.

The angles we need to complete the addition is angle <JLK, which happens to be the supplementary angles to angle <KLM

Therefore <JLK = 180 - (8 x - 16) = 180 - 8 x + 16 = 196 - 8 x

The we can now solve for "x" in the equation of addition of internal angles of a triangle:

(2 x + 2) + (3 x + 6) + (196 - 8 x) = 180

Combining like terms on the left

- 3 x + 204 = 180

subtracting 204 from both sides:

- 3 x = 180 - 204

- 3 x = - 24

divide both sides by "-3" to isolate x

x = - 24 / (-3)

x = 8 degrees

Now that we know "x", we can find the measure of angle <KLM via its formula:

<KLM = 8 x - 16 = 8 (8) - 16 = 48 degrees

Answer:

64 different black jack hands

Step-by-step explanation:

there are 4 aces in a deck, and you can score a blackjack if any of these 4 aces is paired with any of the 16 different cards that are worth 10 points. Total number of different blackjack combinations = 4 aces x 16 different tens = 64.

Even though the number of possible blackjack hands might seem large, the possibilities of actually getting one are really low:

possibility of getting 1 ace = 4/52 = 1/13

possibility of getting 1 ten = 16/51

possibility of getting a blackjack = 16 / 663

if you start with the 10 first the odds are the same:

possibility of getting 1 ten = 16/52 = 4/13

possibility of getting 1 ace = 4/51

possibility of getting a blackjack = 16 / 663

Step-by-step explanation:

A.

Cost of 4 lots for $48,000= 48000*4

=$192,000

Sales made from all 7 lots = 33000*7

= $213,000

Profit =213,000-192,000

Profit =$39,000

Percent profit =(39000/192000) *100

=0.20*100

=20%

B.

Total interest formula=

Principal Loan Amount x Interest Rate x Time

Interest =30000x0.12x5

Interest = $18,000

Monthly payments for 5 years

= 18000/12*5

=18000/60

=$300

Answer:

It would be the first one (y-2=1/3(x-2))

Step-by-step explanation:

The first one is the same function as y=x(1/3)+(1+1/3) which is the same function as the photo.

Answer:

Yes

Step-by-step explanation:

Starting with 2, the step to the next number is 6.  Each step increases by 3.

When you are on 8, the next step is an increase of 9.  The next step is an increase of 12,  The next step not shown would increase by 15 for give you 44.

So the first step would be 3 below the number 6 which would be subtracted from 2 to give you - 1 as your first starting point.

The common difference is 3(n) where n is an integer starting with 0 and incrementing by 1 with each new Y2 and Y1 is  -1.

The equation Y2 = 3(n+1) + Y1    where n=0

Answer:

B. 3/4

Step-by-step explanation:

6/8=0.75

Answer: B

Step-by-step explanation:

6 = 8

3 = 4

1.5 = 2

0.75 = 1

Hope this helps!

Answer:

Using z score formula:

X = z ∂ + µ

 = 157.833

Step-by-step explanation:

Solution:

Mean = µ = 1262

Standard deviation = ∂ = 117

(a) 28th percentile for the number of chocolate chip.

P( z < z) = 28%

             = 0.28

P( z<- 0.58)  = 0.28

Z = -0.58

By using z score formula:

Z = x - µ /∂

-0.58= x – 117 / 1262

X = (- 0.58)(117) + (1262)

 =  1194.14

(b) Middle 97% of bag.

P(-z < z < z) = 97%

                    = 0.97

P( z < z) – p(z < -z) = 0.97

2p(z < z) -1 = 0.97

2p (z < z) = 1 + 0.97

P(z < z) = 1.97 / 2

            = 0.99

P(z < 2.33) = 0.99

Z ± 2.33

By using z score formula:

Z = x - µ / ∂

X = z ∂ + µ

  = - 2.33 x 117 + 1262

  =989.39

Z = 2.33

X = z ∂ + µ

  =  2.33 x 117 + 1262

 =1533.61

(c) What is the interquartile range of the number of chocolate chips in a bag of chocolate.

By using standard normal table,

The z dist’n formula:

P(z < z ) = 25%

            =0.25

P(z < -0.6745) = 0.25

Z = 0.6745

Using z score formula:

X = z∂ + µ

   = - 0.6745 x 117 + 1262

  = 1183.0835

First quartile = Q1 =1183.0835

The third quartile is:

P(z<z) = 75%

    = 0.75

P(z < 0.6745) = 0.75

Z = 0.6745

Using z score formula:

X = z ∂ + µ

  = 0.6745 x 117 + 1262

= 1340.9165

IQR = Q3 – Q1

     = 1340.9165 – 1183.0835

  = 157.833

Answer:

[tex]22[/tex]

Step-by-step explanation:

If FG= 8

and GH=14

G is a midpoint

To find FH you would add 8 and 14.

[tex]8 + 14 = 22[/tex]

Answer:

add it FH +GH

=8+14

=22 ans.....

Answer: 6 T-shirts

Step-by-step explanation:72/12=6

Answer:2.088

Step-by-step explanation:

2.088

Answer:

3.5 km between communities AC

Step-by-step explanation:

The idea is to find a common position for all the communities to locate the well

Kindly find attached a rough sketch of the problem for your reference.

Given that

AB=5km

AC=7km

From the diagram we can see that for all three communities to travel equal distance to the common well, the well has to be situated at 3.5km between communities AC.

Also, from the diagram the location of well is the intersection between the diagonals of the rectangular shape.

The required equation  that can be solved to find the number of days, d, it will take for the plant to be 65 cm tall is d=  [tex]\frac{5.5\times 65}{11}\\[/tex]

From the question given, we are told that when testing fertilizers on a plant that is 11 cm tall, it is growing at a rate of 2 cm/day. This can be expressed as:

We can get the number of days it will take the 11cm plant to grow:

11cm = x

2cm = 1 day

[tex]2x = 11 * 1\\2x = 11\\x = 11/2\\x = 5.5 days\\[/tex]

Since it will take 5.5days for 11 cm plant tall to grow, to calculate the number of days 'd' it will take a 65cm plant tall to grow, we can say:

11cm = 5.5days

65cm = "d"

Cross multiply

[tex]11d = 5.5 \times 65\\d = \frac{5.5\times 65}{11}\\[/tex]

Hence the required equation  that can be solved to find the number of days, d, it will take for the plant to be 65 cm tall is d=  [tex]\frac{5.5\times 65}{11}\\[/tex]

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5/4; it is an inproper fraction in a group of proper ones. it also doesnt have a 2 anywhere.

20/25; it is the only one that isnt simplified. it also has double didgits in both the numerator and denominator

Answer:

The total amount a member pays for an item with a regular price of x dollars is T (x) = 0.963x.

Step-by-step explanation:

Key points:

It is provided that the customers receive a 10% discount if they are members and all customers must pay 7% in sales tax.

Two functions are provided are:

f (x) = 0.90x ; the price of an item after the 10% member discount

g (x) = 1.07x ; the total amount customers pay for a purchase after sales tax is applied.

Compute the total amount a member pays for an item with a regular price of x dollars as follows:

T (x) = Discount × Sales Tax

       = 0.90 × 1.07 × x

       = 0.963x.

Thus, the total amount a member pays for an item with a regular price of x dollars is T (x) = 0.963x.

Answer:

1 4/5

Step-by-step explanation:

Download photogmath

Answer:

1 7/8

Step-by-step explanation:

9÷4 4/5

=9÷24

=9/1×5/24

=

9×5

-----------

1×24

=45/2

15/8=1 7/8

Answer:

dx/dt = 4 mph

Step-by-step explanation:

The two trains, with the station ( origin of the coordinates system) all, form a right triangle when we considered the distance between the two trains.

In that triangle:

distance between trains  D = 24 miles

leg (1 ) distance of train going west to origin  y = 15 miles

leg (2) distance of train going south x = ??

When d = 24 and y = 15

D² = y² + x²      ⇒   x² = D² - y²

x = √ (24)² - (15)²

x = √351

x = 18,73 miles

Now according to Pythagoras theorem

D² = x² + y²

Taking derivatives (respect to time) on both sides of the equation we get

2*D*dD/dt = 2*y*dy/dt  + 2*x*dx/dt

In this expression we are looking for dx/dt, all the rest of variables are known

2*24*25 = 2* 15*35  +  2*(18,73)* dx/dt

(1200 - 1050 )/37,46 = dx/dt

dx/dt = 4 mph

Answer: 4 1/6

Step-by-step explanation:

I don't understand what you are talking about, but I can list you the factor pairs of 16!

16=1,16; 2,8; 4,4

Thise are all the factor pairs

Answer:

1 x 16,

2 x 8

4 x 4

Factors of 16: 1, 2, 4, 8, 16

Answer:

Last option must be correct because you need to prove three things congruent to give a postulate.In which case you have two sides of each triangle that means it is incomplete.

thus last option is correct.

Answer:

Hello!!! erz here ^^

Step-by-step explanation:

I believe the answer is y = 8x - 3 (Option B)

Hope this helps!! :D

Answer:

a.No, Common Bank will save Sharon more money.

Step-by-step explanation:

There are two banks i.e. first state bank and the common bank that should be compared in the table depend upon the prices of both the banks

On seeing it we get to know that the first state bank would charged a fee on a monthly basis i.e. $4 while on the other hand the common bank has no fee on the monthly basis

Also the unsufficient bonds are more cheaper in the common bank if we compared with the first state bank

Moreover, the $7 is charged in the first state bank and $3 charged in the common bank.

Therefore the common bank would become cheaper

Hence, the correct option is a.

Answer:

Sharon wants to open a checking account from which to pay bills. She wants online services, and a debit card, which both banks provide for free. Based upon past experience, she expects to accidentally overdraft the account 1 time per year, due to unexpected charges and miscommunications. She expects no 2nd copies of statements, and to use network ATMs 4 times per month with either bank. She has $3300 in an emergency savings account at First State Bank, and thinks that the balance will be enough to cover overdrafts in the future if automatic transfers are made when needed.

A 4-column table with 5 rows. Column 1 is labeled First State Bank with entries monthly fee, non-sufficient funds fee, second copy of statement, network A T M usage, non-sufficient funds protection from a First State Bank savings account. Column 2 is labeled Description with entries 4 dollars, 36 dollars, 7 dollars, 3 dollars each transaction, 4 dollars on each day that a transfer occurs to cover an overdraft. Column 3 is labeled Common Bank with entries monthly fee, non-sufficient funds, second copy of statement, network A T M usage, non-sufficient funds protection from a Common Bank savings account. Column 4 is labeled Description with entries 0 dollars, 24 dollars, 4 dollars, 2 dollars each transaction, not offered with this account.

Based on the tables of fees, above, if Sharon chooses First State Bank, will it save her money over choosing Common Bank?

Step-by-step explanation:

Edge 2021

The required height of the parallelogram is 2/3. Option B is correct.

Given that,
The area of a parallelogram is 24 square units. One side of the parallelogramis 36 units long. The other side is 4 units long. Which could be the parallelogram's height is to be determined.

A parallelogram is a quadrilateral consisting of pairs of parallel side.

Here,
We have given the area of the parallelogram and the measure of its base. So,
Area of the parallelogram = base * height
                                       24 = 36 * height
                                       height = 2 / 3

Thus, the required height of the parallelogram is 2/3. Option B is correct.
 

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Answer:

The ball's speed will be 10 m/s at t=1.22 seconds

Step-by-step explanation:

The vertical motion of an object is controlled by the force of gravity. This means that there is a non-zero net force acting on the object that makes it accelerate downwards.

If the object is thrown upwards at speed vo, its speed at time t is:

[tex]v_f=v_o-g.t[/tex]

Where g is the acceleration of gravity [tex]g=9.8 m/s^2.[/tex]

Our ball is thrown upwards with v0=22 m/s. We need to calculate the time when its speed is vf=10 m/s.

Solving the above equation for t:

[tex]\displaystyle t=\frac{v_o-v_f}{g}[/tex]

Substituting:

[tex]\displaystyle t=\frac{22-10}{9.8}=\frac{12}{9.8}[/tex]

t=1.22 seconds

The ball's speed will be 10 m/s at t=1.22 seconds

Answer:

What I do not understand what you are asking, can you repeat it pls.

Step-by-step explanation:

Answer:

2.1087

Step-by-step explanation:

0.297

7.1 +

2.1087