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nalin [4]
1 year ago
12

The credit remaining on a phone card (in dollors) is a linear function of the total calling trime made with the card ( in minute

s). The remaining credit after 22 minutes is $36.70, and the remaining credit after 52 mintues is $32.20. What is the remaining credit after 85 mintues of calls?
Mathematics
1 answer:
KATRIN_1 [288]1 year ago
7 0

After 85 minutes of calls, there are $27.25 left on the card.

<h3>What is the remaining credit after 85 minutes of calls?</h3>

A linear equation in slope-intercept form is:

y = a*x + b

Where a is the slope.

If the line passes through two points (x₁, y₁) and (x₂, y₂) the slope is:

a = \frac{y_2 - y_1}{x_2 - x_1}

In this case, we know that the line passes through the points (22, 36.7) and (52, 32,20)

(points of the form (time, dollars)).

So the slope is:

a = \frac{32.2 - 36.7}{52 -22} = -0.15

The linear equation is then:

y = -0.15*x + b

To find the value of b, we use the point (22. 36.7)

36.7 = -0.15*22 + b

36.7 + 0.15*22 = b = 40

Then the linear equation is:

y = -0.15*x +40

The amount remaining in the credit card after 85 minutes is given by evaluating the above equation in x = 85.

y = -0.15*85 + 40 = 27.25

This means that after 85 minutes of calls, there are $27.25 left on the card.

If you want to learn more about linear equations:

brainly.com/question/1884491

#SPJ1

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The following data are the distances between a sample of 20 retail stores and a large distribution center. The distances are in
sesenic [268]

Answer:

Variance = 1,227.27

Standard deviation = 35.03

Step-by-step explanation:

To calculate these, we use the following formulas:

Mean = (sum of the values) / n

Variance = ((Σ(x - mean)^2) / (n - 1)

Standard deviation = Variance^0.5

Where;

n = number of values = 20

x = each value

Therefore, we have:

Sum of the values = 29 + 32 + 36 + 40 + 58 + 67 + 68 + 69 + 76 + 86 + 87 + 95 + 96 + 96 + 99 + 106 + 112 + 127 + 145 + 150 = 1,674

Mean = 1,674 / 20 = 83.70

Variance = ((29-83.70)^2 + (32-83.70)^2 + (36-83.70)^2 + (40-83.70)^2 + (58-83.70)^2 + (67-83.70)^2 + (68-83.70)^2 + (69-83.70)^2 + (76-83.70)^2 + (86-83.70)^2 + (87-83.70)^2 + (95-83.70)^2 + (96-83.70)^2 + (96-83.70)^2 + (99-83.70)^2 + (106-83.70)^2 + (112-83.70)^2 + (127-83.70)^2 + (145-83.70)^2 + (150-83.70)^2) / (20 - 1) = 23,318.20 / 19 = 1,227.27

Standard deviation = 1,227.27^0.5 = 35.03

5 0
2 years ago
PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS PLS ASAP PLS PLS
zmey [24]

Answer:

i think it's <C and <R since they're 90 degree angles, though they are small

4 0
2 years ago
A repair bill for a car is $648.45. The parts cost $265.95. The labor cost is $85 per hour. Write and solve an equation to find
zysi [14]

Answer:

( t - p ) /  85x =  h

( t - 265.95 ) /  85x  = h

648.45 - 265.95 / 85x = 3.32h

h = 3.32

Therefore ( t - p ) /  85x =  3.32

Step-by-step explanation:

648.45 - 265.95

282.50 /85

= 3.32 hrs

Finding equation to find hours can be shown as

( t - p ) /  85x =  3.32

How we found equation to find total

Parts = 19 x 14 - 5/100 = 266- 0.05

648.45 - 265.95 = 282.5

282.5/85 = 3.323  near to 3,233529

Labour = 85x  = 17 (5 + x)

Equation = 17(5+ x) + 14(19) - 5/100 = 648.45 where x = 85

Equation = ( 85x x 3  1/3) + 265 - 19/20 = t

3 0
2 years ago
EXAMPLE 5 Find the maximum value of the function f(x, y, z) = x + 2y + 11z on the curve of intersection of the plane x − y + z =
Taya2010 [7]

Answer:

\displaystyle x= -\frac{10}{\sqrt{269}}\\\\\displaystyle y= \frac{13}{\sqrt{269}}\\\\\displaystyle z = \frac{23\sqrt{269}+269}{269}

<em>Maximum value of f=2.41</em>

Step-by-step explanation:

<u>Lagrange Multipliers</u>

It's a method to optimize (maximize or minimize) functions of more than one variable subject to equality restrictions.

Given a function of three variables f(x,y,z) and a restriction in the form of an equality g(x,y,z)=0, then we are interested in finding the values of x,y,z where both gradients are parallel, i.e.

\bigtriangledown  f=\lambda \bigtriangledown  g

for some scalar \lambda called the Lagrange multiplier.

For more than one restriction, say g(x,y,z)=0 and h(x,y,z)=0, the Lagrange condition is

\bigtriangledown  f=\lambda \bigtriangledown  g+\mu \bigtriangledown  h

The gradient of f is

\bigtriangledown  f=

Considering each variable as independent we have three equations right from the Lagrange condition, plus one for each restriction, to form a 5x5 system of equations in x,y,z,\lambda,\mu.

We have

f(x, y, z) = x + 2y + 11z\\g(x, y, z) = x - y + z -1=0\\h(x, y, z) = x^2 + y^2 -1= 0

Let's compute the partial derivatives

f_x=1\ ,f_y=2\ ,f_z=11\ \\g_x=1\ ,g_y=-1\ ,g_z=1\\h_x=2x\ ,h_y=2y\ ,h_z=0

The Lagrange condition leads to

1=\lambda (1)+\mu (2x)\\2=\lambda (-1)+\mu (2y)\\11=\lambda (1)+\mu (0)

Operating and simplifying

1=\lambda+2x\mu\\2=-\lambda +2y\mu \\\lambda=11

Replacing the value of \lambda in the two first equations, we get

1=11+2x\mu\\2=-11 +2y\mu

From the first equation

\displaystyle 2\mu=\frac{-10}{x}

Replacing into the second

\displaystyle 13=y\frac{-10}{x}

Or, equivalently

13x=-10y

Squaring

169x^2=100y^2

To solve, we use the restriction h

x^2 + y^2 = 1

Multiplying by 100

100x^2 + 100y^2 = 100

Replacing the above condition

100x^2 + 169x^2 = 100

Solving for x

\displaystyle x=\pm \frac{10}{\sqrt{269}}

We compute the values of y by solving

13x=-10y

\displaystyle y=-\frac{13x}{10}

For

\displaystyle x= \frac{10}{\sqrt{269}}

\displaystyle y= -\frac{13}{\sqrt{269}}

And for

\displaystyle x= -\frac{10}{\sqrt{269}}

\displaystyle y= \frac{13}{\sqrt{269}}

Finally, we get z using the other restriction

x - y + z = 1

Or:

z = 1-x+y

The first solution yields to

\displaystyle z = 1-\frac{10}{\sqrt{269}}-\frac{13}{\sqrt{269}}

\displaystyle z = \frac{-23\sqrt{269}+269}{269}

And the second solution gives us

\displaystyle z = 1+\frac{10}{\sqrt{269}}+\frac{13}{\sqrt{269}}

\displaystyle z = \frac{23\sqrt{269}+269}{269}

Complete first solution:

\displaystyle x= \frac{10}{\sqrt{269}}\\\\\displaystyle y= -\frac{13}{\sqrt{269}}\\\\\displaystyle z = \frac{-23\sqrt{269}+269}{269}

Replacing into f, we get

f(x,y,z)=-0.4

Complete second solution:

\displaystyle x= -\frac{10}{\sqrt{269}}\\\\\displaystyle y= \frac{13}{\sqrt{269}}\\\\\displaystyle z = \frac{23\sqrt{269}+269}{269}

Replacing into f, we get

f(x,y,z)=2.4

The second solution maximizes f to 2.4

5 0
3 years ago
Solve for x<br>-2x+2-7x= -70​
Lostsunrise [7]

Answer:

x=8

Step-by-step explanation:

-2x+2-7x=-70

Minus two from each side.

-2x-7x=-72

Combine like terms.

-9x=-72

Divide -9 from each side.

x=8

7 0
3 years ago
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