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3 years ago

There there are eight pencils in each pack how many packs will be needed of 28 children of each children get four pencils

1 answer:

4 0

14 packs of pencils will be needed. Every 2 children use a pack and 28/2=14. Of course there are other ways to solve it too.

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Write a linear function f with f(0)=7 and f(3)=1.

choli [55]

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a = ( 0 , 7 ) & b = ( 3 , 1 )

First need to find the slope using the following equation :

$slope = \frac{y(b) - y(a)}{x(b) - x(a)} \\$

$slope = \frac{1 - 7}{3 - 0} \\$

$slope = \frac{ - 6}{3} \\$

$slope = - 2$

_________________________________

We have following equation to find the point-slope form of the linear functions using the slope and one of the through points .

$y - y(0) = m \times ( \: x - x(0) \: )$

$x(0) = x - coordinate \: \: of \: \: through \: \: point \\$

$y(0) = y - coordinate \: \: of \: \: through \: \: point \\$

$m = slope$

I choose point (( a )) to put in the equation.

$y - 7 = - 2 \times (x - 0)$

$y - 7 = - 2x + 0$

$y - 7 = - 2x$

Add sides 7

$y - 7 + 7 = - 2x + 7$

$y = - 2x + 7$

This the slope-intercept form .

Done...

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7 0

2 years ago

I needddd heelpppp please

Nostrana [21]

Okay I am not 100% sure because that is an extremely confusing question. But here is what I got.

(A) 2c² = 2bc + ac/2 Given

(B) 4c² = 2bc + ac Multiplication and Distribution

(C) 4c = 4b + a Division and Distribution

(D) 4c - a + 4b Subtraction

(E) 4b = 4c - a Symmetric

6 0

3 years ago

Write down the explicit solution for each of the following: a) x’=t–sin(t); x(0)=1

Kay [80]

Answer:

a) x=(t^2)/2+cos(t), b) x=2+3e^(-2t), c) x=(1/2)sin(2t)

Step-by-step explanation:

Let's solve by separating variables:

$x'=\frac{dx}{dt}$

a) x’=t–sin(t), x(0)=1

$dx=(t-sint)dt$

Apply integral both sides:

$\int {} \, dx=\int {(t-sint)} \, dt\\\\x=\frac{t^2}{2}+cost +k$

where k is a constant due to integration. With x(0)=1, substitute:

$1=0+cos0+k\\\\1=1+k\\k=0$

Finally:

$x=\frac{t^2}{2} +cos(t)$

b) x’+2x=4; x(0)=5

$dx=(4-2x)dt\\\\\frac{dx}{4-2x}=dt \\\\\int {\frac{dx}{4-2x}}= \int {dt}\\$

Completing the integral:

$-\frac{1}{2} \int{\frac{(-2)dx}{4-2x}}= \int {dt}$

Solving the operator:

$-\frac{1}{2}ln(4-2x)=t+k$

Using algebra, it becomes explicit:

$x=2+ke^{-2t}$

With x(0)=5, substitute:

$5=2+ke^{-2(0)}=2+k(1)\\\\k=3$

Finally:

$x=2+3e^{-2t}$

c) x’’+4x=0; x(0)=0; x’(0)=1

Let $x=e^{mt}$ be the solution for the equation, then:

$x'=me^{mt}\\x''=m^{2}e^{mt}$

Substituting these equations in c)

$m^{2}e^{mt}+4(e^{mt})=0\\\\m^{2}+4=0\\\\m^{2}=-4\\\\m=2i$

This becomes the solution m=α±βi where α=0 and β=2

$x=e^{\alpha t}[Asin\beta t+Bcos\beta t]\\\\x=e^{0}[Asin((2)t)+Bcos((2)t)]\\\\x=Asin((2)t)+Bcos((2)t)$

Where A and B are constants. With x(0)=0; x’(0)=1:

$x=Asin(2t)+Bcos(2t)\\\\x'=2Acos(2t)-2Bsin(2t)\\\\0=Asin(2(0))+Bcos(2(0))\\\\0=0+B(1)\\\\B=0\\\\1=2Acos(2(0))\\\\1=2A\\\\A=\frac{1}{2}$

Finally:

$x=\frac{1}{2} sin(2t)$

7 0

3 years ago

Put the fractions in order smallest first 7/10 3/5 9/20 23/30 4/5

Studentka2010 [4]

9/20, 3/5, 7/10, 23/30, 4/5

4 0

3 years ago

A researcher is conducting a study and you are hired to help them analyse their data. They have already looked at scatterplots a

zhenek [66]

Answer:

There is a strong positive relationship between sales of firewood and cough drops.

Step-by-step explanation:

Correlation Coefficient

Correlation is a technique that help us to find or define a relationship between two variables.
It is a measure of linear relationship between two quantities.
Values between 0 and 0.3 tells about a weak positive linear relationship, values between 0.3 and 0.7 shows a moderate positive correlation and a correlation of 0.7 and 1.0 states a strong positive linear relationship.

Thus, a coefficient correlation of 0.85 between weekly sales of firewood and cough drops over a 1-year period suggest that there is a strong positive relationship between sales of firewood and cough drops.

Thus, as the sale of firewood increase there is an increase in the sale of cough drops.

3 0

3 years ago