After eating La Huerta your subtotal was 25.72$ you want to leave a 15% tip. 15% as a decimal is

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Answer 1

Answer: 15% as a decimal is 0.15

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WORTH 100 POINTS WORTH 100 POINTS WORTH 100 POINTS WORTH 100 POINTS HELPPPPPWrite an equation parallel to x-4y=20 that passes through the point 2,-5

Answers

Answer:

x - 4y = 22

Step-by-step explanation:

Given line:

x - 4y = 20

Convert the equation into slope-intercept form:

x - 4y = 20
4y = x - 20
y = 1/4x - 5

It has a slope of 1/4.

Parallel lines have equal slopes.

Find the parallel line lines that passes through the point (2, - 5):

y = 1/4x + b

Substitute x and y values to work out the value of b:

- 5 = 1/4*2 + b
- 5 = 1/2 + b
b = - 5 - 1/2
b = - 11/2

The line is:

y = 1/4x - 11/2

Covert this into standard form:

y = 1/4x - 11/2
4y = x - 22
x - 4y = 22

x-4y=20

Isolate y

$\n \sf\longmapsto x-20=4y$

$\n \sf\longmapsto y=(1)/(4)x-5$

m=1/4
Parallel lines have equal slope

Equation of line in point slope form

$\n \sf\longmapsto y-y_1=m(x-x_1)$

$\n \sf\longmapsto y+5=1/4(x-2)$

$\n \sf\longmapsto 4y+20=x-2$

$\n \sf\longmapsto x-4y+22=0$

2(x + 25) =100 hellppppppp meee

Answers

Answer:

x=25

Step-by-step explanation:

2(x+25)=100

2x+50=100

2x=50

x=25

If x3 = 8 and y3 = 125, what
is the value of y - x?

Answers

Answer:

X to power 3is=2 while y to power 3is=5so5-2=3

Step-by-step explanation:

x cubed is =8 so cube root of 8is 2

y cubed is =125so cube root of 125is 5

therefore 5-2=3

6.2.Find the triangle bounded by the y-axis the line f(x)=9- 6/7x and the line perpendicular to it that passes through the origin

Answers

First.

We need to find the triangle bounded by the y-axis the line $f(x)=9-(6)/(7)x$ and the line perpendicular to it that passes through the origin.

This triangle is illustrated in the First Figure bellow. The triangle has been dotted with black dots. So, let's identify each part of this graph:

The y-axis has been identified by the green line.
The line $f(x)=9-(6)/(7)x$ has been identified by the red line.
To plot the line perpendicular to the previous one that passes through the origin, we need to know that the product of the slopes of two perpendicular lines is $m_(1)m_(2)=-1 \therefore Since \ m_(1)=-(6)/(7) \ then \ m_(2)=(7)/(6)$

Therefore, this line is the blue one and is written as:

$f(x)=(7)/(6)x$

Second.

a.

To find $y(t)$ we need to find the slope and y-intercept. So, taking two points:

$P_(1)(15,150) \ and \ P_(2)(25,450) \n \nm=(450-150)/(25-15)=30$

So:

$Using \ P_(1)(15,150) \n\ny=30t+b\n\n150=30(15)+b \therefore b=-300 \n\n\boxed{y(t)=30t-300}$

Third.

b.

The y-intercept is $b=-300$ and has been calculated above. This value represents the profit in thousands of dollars in 1980, that is, there is no any profit or there is a lost of $300.000.

Fourth.

c.

The x-intercept can be found when y=0 (year 1980), that is:

$y(t)=30t-300 \n\n0=30t-300 \therefore t=10$

This value shows that there is no any profit for the company at the year that represents t=10 (year 1990), because at this point the company starts earning money.

Fifth.

d.

The slope of this function is $m=30$

This value tells you that the profit increases $30.000 each year.

Hello,

Please, see the attached files.

Thanks.

Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.y = e^x^2 ln 4x^3

Answers

$(d(lnx))/(dx)=(1)/(x)$

Answer:

$(dy)/(dx)=e^(x^2)((2x^2ln(4x^3)+3)/(x))$

Step-by-step explanation:

We are given that a function

$y=e^(x^2)ln(4x^3)$

We have to differentiate w.r.t x

$(dy)/(dx)=e^(x^2)* 2xln(4x^3)+e^(x^2)* (1)/(4x^3)* 12x^2$

By using formula

$(d(lnx))/(dx)=(1)/(x)$

$(d(e^x))/(dx)=e^x$

$(dy)/(dx)=e^(x^2)(2xln(4x^3)+(3)/(x))$

$(dy)/(dx)=e^(x^2)((2x^2ln(4x^3)+3)/(x))$

Hence, the derivative of function

$(dy)/(dx)=e^(x^2)((2x^2ln(4x^3)+3)/(x))$

The probability is 1 in 4,011,000 that a single auto trip in the United States will result in a fatality. Over a lifetime, an average U.S. driver takes 46,000 trips.(a) What is the probability of a

Answers

Answer:

0.0114

Step-by-step explanation:

(a) What is the probability of a fatal accident over a lifetime?

Suppose A be the event of a fatal accident occurring in a single trip.

Given that:

P(1 single auto trip in the United States result in a fatality) = P(A)

Then;

P(A) = 1/4011000

P(A) = 2.493 × 10⁻⁷

Now;

P(1 single auto trip in the United States NOT resulting in a fatality) is:

P( $\mathbf{\overline A}$ ) = 1 - P(A)

P( $\mathbf{\overline A}$ ) = 1 - 2.493 × 10⁻⁷

P( $\mathbf{\overline A}$ ) = 0.9999997507

However, P(fatal accident over a lifetime) = P(at least 1 fatal accident in lifetime i.e. 46000 trips)

= 1 - P(NO fatal accidents in 46000 trips)

Similarly,

P(No fatal accidents over a lifetime) = P(No fatal accident in the 46000 trips) = P(No fatality on the 1st trip and No fatality on the 2nd trip ... and no fatality on the 45999 trip and no fatality on the 46000 trip)

= $[P(\overline A)] ^(46000) \ \ \ (since \ trips \ are \ independent \ events)$

= $[0.9999997507]^(46000)$

= 0.9885977032

Finally;

P(fatal accident over a lifetime) = 1 - 0.9885977032

P(fatal accident over a lifetime) = 0.0114022968

P(fatal accident over a lifetime) ≅ 0.0114

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