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3 years ago

12

If 4 cartons are needed to pack 30 paperback books, how

2 answers:

Arada [10]3 years ago

3 0

Answer:

45

Step-by-step ex

abruzzese [7]3 years ago

3 0

Answer:

10 cartons

Step-by-step explanation:

30/4= 7.5 paperback books for 1 carton then, 75/7.5= 10.

75 paperbacks= 10 cartons

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Can someone help me with this angle

Zarrin [17]

Answer:

60 degrees

Step-by-step explanation:

6 0

3 years ago

Kevin rode 24 km in 2 hours. At that rate, how long would it take him to ride 120 km?

liberstina [14]

24/2=12 so you would do 120/12 and get 10. Your answer is 10 hours.

6 0

3 years ago

Let c be a positive number. A differential equation of the form dy/dt=ky^1+c where k is a positive constant, is called a doomsda

stich3 [128]

Answer:

The doomsday is 146 days

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Step-by-step explanation:

Given

$\frac{dy}{dt} = ky^{1 +c}$

First, we calculate the solution that satisfies the initial solution

Multiply both sides by

$\frac{dt}{y^{1+c}}$

$\frac{dt}{y^{1+c}} * \frac{dy}{dt} = ky^{1 +c} * \frac{dt}{y^{1+c}}$

$\frac{dy}{y^{1+c}} = k\ dt$

Take integral of both sides

$\int \frac{dy}{y^{1+c}} = \int k\ dt$

$\int y^{-1-c}\ dy = \int k\ dt$

$\int y^{-1-c}\ dy = k\int\ dt$

Integrate

$\frac{y^{-1-c+1}}{-1-c+1} = kt+C$

$-\frac{y^{-c}}{c} = kt+C$

To find c; let t= 0

$-\frac{y_0^{-c}}{c} = k*0+C$

$-\frac{y_0^{-c}}{c} = C$

$C =-\frac{y_0^{-c}}{c}$

Substitute $C =-\frac{y_0^{-c}}{c}$ in $-\frac{y^{-c}}{c} = kt+C$

$-\frac{y^{-c}}{c} = kt-\frac{y_0^{-c}}{c}$

Multiply through by -c

$y^{-c} = -ckt+y_0^{-c}$

Take exponents of $-c^{-1$

$y^{-c*-c^{-1}} = [-ckt+y_0^{-c}]^{-c^{-1}$

$y = [-ckt+y_0^{-c}]^{-c^{-1}$

$y = [-ckt+y_0^{-c}]^{-\frac{1}{c}}$

i.e.

$y(t) = [-ckt+y_0^{-c}]^{-\frac{1}{c}}$

Next:

$t= 3$ i.e. 3 months

$y_0 = 2$ --- initial number of breeds

So, we have:

$y(3) = [-ck * 3+2^{-c}]^{-\frac{1}{c}}$

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

We have the growth term to be: $ky^{1.01}$

This implies that:

$ky^{1.01} = ky^{1+c}$

By comparison:

$1.01 = 1 + c$

$c = 1.01 - 1 = 0.01$

$y(3) = 16$ --- 16 rabbits after 3 months:

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

$y(3) = [-ck * 3+2^{-c}]^{-\frac{1}{c}}$

$16 = [-0.01 * 3 * k + 2^{-0.01}]^{\frac{-1}{0.01}}$

$16 = [-0.03 * k + 2^{-0.01}]^{-100}$

$16 = [-0.03 k + 0.9931]^{-100}$

Take -1/100th root of both sides

$16^{-1/100} = -0.03k + 0.9931$

$0.9727 = -0.03k + 0.9931$

$0.03k= - 0.9727 + 0.9931$

$0.03k= 0.0204$

$k= \frac{0.0204}{0.03}$

$k= 0.68$

Recall that:

$-\frac{y^{-c}}{c} = kt+C$

This implies that:

$\frac{y_0^{-c}}{c} = kT$

Make T the subject

$T = \frac{y_0^{-c}}{kc}$

Substitute: $k= 0.68$ , $c = 0.01$ and $y_0 = 2$

$T = \frac{2^{-0.01}}{0.68 * 0.01}$

$T = \frac{2^{-0.01}}{0.0068}$

$T = \frac{0.9931}{0.0068}$

$T = 146.04$

<em>The doomsday is 146 days</em>

4 0

3 years ago

Cora is building towers of two different sizes using prism- and pyramid-shaped blocks. The diagram shows the ratio of prisms and

Musya8 [376]

There are 20 blocks needed for tower A, and 43.75 blocks needed for tower B

From the tape diagrams, we have the following ratio

Prism : Pyramid = 4 : 1

From the table, we have:

Tower A = 16 prisms

So, the ratio becomes

16 : Pyramid = 4 : 1

Multiply the ratio on the right-side by 4

16 : Pyramid = 16 : 4

By comparison, we have:

Pyramid = 4

This means that, 4 pyramid blocks are needed for tower A

So, the total number of blocks needed is:

Total = Pyramid + Prism

This gives

Total = 4 + 16

Evaluate the sum

Total = 20

Hence, there are 20 blocks needed for tower A

For table B, we have:

Tower A = 35 prisms

So, the ratio becomes

35 : Pyramid = 4 : 1

Express as fractions

$\frac{Pyramid}{35} = \frac 14$

Multiply through by 35

Pyramid = 8.75

This means that, 8.75 pyramid blocks are needed for tower B

So, the total number of blocks needed is:

Total = 8.75 + 35

Evaluate the sum

Total = 43.75

Hence, there are 43.75 blocks needed for tower B

Read more about ratios at:

brainly.com/question/16981404

8 0

3 years ago

Read 2 more answers

At a factory three workers produced 87, 93 and 102 units respectively in one day what is the average production in units of thes

slega [8]

Answer:

94

Step-by-step explanation:

Add units together. 87+93+102=282.

Divide total number by number of days. 282/3=94

6 0

3 years ago