A family has to travel 380 miles to reach their vacation spot. They plan to stop for lunch after driving 2/5 of the distance. How far will they have traveled when they stop for lunch?

Answer:

0.36ml

Step-by-step explanation:

Note: micrograms = [tex]10^{-6} g[/tex]

Given the concentration,

[tex]500*10^{-6} g = 1ml\\1*10^{-6}g =\frac{1}{500} ml\\180*10^{-6} g=(\frac{1}{500} *180)ml\\180micrograms = 0.36ml[/tex]

By using the table, we see that the correct options are:

a) f(2) = 7

b) f(x) = 3 when x = 8.

c) f⁻¹(7) = 2

d) f⁻¹(x) = 8 when x = 3.

Here we have a table of x and f(x).

First, we want to find f(2). To get that, we need to go to the row where we have x = 2.

In that same row we can see that f(x) = 7.

Then f(2) = 7.

Then it says:

"if f(x) = 3, then x = ?"

This time we do the opposite. We find the row where f(x) = 3, and then we see the value of x in that row.

In the second row (counting from the bottom) we can see that when x = 8, f(x) = 3.

Then:

"if f(x) = 3, x = 8"

Then we want to get the inverse of f(x) evaluated in 7.

Here we use the rule:

[tex]f(x) = y\\f^{-1}(y) = x[/tex]

Then

[tex]f(2) = 7\\f^{-1}(7) = 2[/tex]

The answer here is 2.

Finally:

"if the inverse evaluated in x si 8, then what is the value of x"

Similar to before, we know that when we evaluate f(x) in 8, the outcome is 3.

Then when we evaluate the inverse in 3, the outcome is 8.

So here we must have x = 3.

If you want to learn more about inverse functions:

https://brainly.com/question/14391067

#SPJ1

The equation solved for w is w = 6g - 40

The complete question is in the attached image

The equation is given as:

g = 1/6(w + 40)

Multiply both sides by 6

6g = w + 40

Subtract 40 from both sides

w = 6g - 40

Hence, the equation solved for w is w = 6g - 40

Read more about equations at:

https://brainly.com/question/12895249

#SPJ1

Answer:

8

Step-by-step explanation:

12+4=16

16 divided by 2= 8

1) Between the years 2003 and 2009, 768 students joined the school.

2) It took 6 years for the population to grow from 1219 students to 1987 students.

3) The average population growth per year is 128 students per year.

P = 128 students per year

4) The population of students in the year 2000 was a total of 835 students.

5) 1219 + (p3) = 1987

6) 1987 + (p3) = 2371

P3 = 384

The calculation of 129 ÷ 3.332 rounded to the appropriate number of significant digits is 39.

Given that;

129 ÷ 3.332

First we convert 3.332 to fraction

3.332 = 3.332/1

3.332 = 3.332/1 × 1000/1000 = 3332/1000

3.332 = 833/250

Hence we have;

129 ÷ 833/250

This can be written as

= 129 × 250/833

= 32250/833

= 38.71549 ≈ 39

Therefore, the calculation of 129 ÷ 3.332 rounded to the appropriate number of significant digits is 39.

Learn more about divisions here: https://brainly.com/question/21416852

#SPJ1

Answer:

N=15

Step-by-step explanation:

The complete inequality is y < x and y< -x

The expressions are given as:

y[ ]x and y[ ]-x

From the graph, we can see that:

Only the lower regions are shaded

This represents the less than inequality sign

Hence, the complete inequality is y < x and y< -x

Read more about inequality at:

https://brainly.com/question/20383699

#SPJ1

Answer:

Step-by-step explanation:

The attached graph shows the graph opens downward, so the vertex at (-2, 6) is a maximum. The y-intercept is the constant, +2.

The range is the vertical extent of the function. Its upper limit is the maximum value of the function (6), and its lower limit is negative infinity.

  The range is {y l y ≤ 6}.

The graph opens downward, so it is increasing to the left of its maximum value, and decreasing to the right of its maximum. The x-coordinate of the maximum (-2) defines the upper limit of the increasing interval.

  The function is increasing over the interval (-∞, -2).

The y-intercept of the graph is where it crosses the y-axis. The value of x is zero there, so the value of the function is the value of its constant, +2.

  The function has a positive y-intercept.

Answer:

-1

Step-by-step explanation:

Simply plug in (-1) to both equations and add.

Equation 1:

2(-1)^2 = 2

3(-1) = -3

2 + -3 - 1 = -2

Equation 2:

-( - 1) = 1

Add both together:

-2 + 1 = -1

Answer:

The equation is 2x² + 3x - 1 and here f(x) is -1

Putting f(x) = -1.

[tex]f(x) = 2 {( - 1)}^{2} + 3( - 1) - 1[/tex]

[tex]f(x) = 2 (1) - 3 - 1[/tex]

[tex]f(x) = 2 - 3 - 1[/tex]

[tex]f(x) = - 1 - 1[/tex]

[tex]f(x) = - 2[/tex]

For g(x) put as -1

[tex]g(x) = - ( - 1)[/tex]

[tex]g(x) = 1[/tex]

Last step,

-2 + 1 = -1

So, option ( a) is correct

Answer:

  B.  360 meters

Step-by-step explanation:

The triangles shown are similar, so their corresponding parts are proportional.

There are a couple of useful proportions here. We can equate the ratio of horizontal segments to the ratio of diagonal segments:

  (600 m)/(250 m) = ??/(150 m)

Or, we can equate the ratios of the diagonal segment to the corresponding horizontal segment:

  ??/(600 m) = (150 m)/(250 m)

Either way, when we multiply the equation by the denominator of ??, we get the result ...

  ?? = (600)(150/250) m = 360 m

The distance from F to G is 360 meters.

Answer:

Step-by-step explanation:

Answer:

.

Step-by-step explanation:

Answer:

Proof:

By the inscribed angle theorem, we know that angle BAC is equal to angle DEC. By the second corollary to the inscribed angle theorem, we know that line segment AE is perpendicular to line segment AC. Therefore, line segment AE is tangent to circle C.

Step-by-step explanation:

Analyze and ensure the answer is correct.

Answer:

Step-by-step:

By the inscribed angle theorem, we know that angle BAC is equal to angle DEC. By the second corollary to the inscribed angle theorem, we know that line segment AE is perpendicular to line segment AC. Therefore, line segment AE is tangent to circle C.

The mean of the data about students size of Mr. Sirac classes is 24.

Given students size of each of Mr. Sirac'sclasses 21,20,22,23,24,25,26,28,27 and we have to find the mean of the data.

We know that mean is the basically sum of numbers divided by the number. It is also known as average.

Mean =∑X/n where n is number of values and ∑X is sum of all the values.

∑X=21+20+22+23+24+25+26+28+27

=216

n=9

Mean is calculated by dividing sum by n.

Mean =216/9

=24

Hence the mean of the data about students size of each of Mr. Sirac classes is 24.

Learn more about mean at https://brainly.com/question/1136789

#SPJ4

The product is equal to:

[tex]\frac{18}{25}(cos(165) + i*sin(165))[/tex]

Remember that we can write a complex number in polar form as:

[tex]R*e^{i*a} = R*(cos(a) + i*sin(a))[/tex]

Then the given product:

[tex]\frac{6}{5}*(cos(120) + i*sin(120))*\frac{3}{5}*(cos(45) + i*sin(45))[/tex]

can be rewritten to:

[tex](\frac{6}{5}*e^{i*120})*(\frac{3}{5}*e^{i*45})[/tex]

Now is easier to solve the product:

[tex](\frac{6}{5}*e^{i*120})*(\frac{3}{5}*e^{i*45})\\\\= \frac{6}{5} *\frac{3}{5} *e^{i*(120 + 45)}\\\\= \frac{18}{25}*e^{i*165}\\\\= \frac{18}{25}(cos(165) + i*sin(165))[/tex]

If you want to learn more about complex numbers:

https://brainly.com/question/10662770

#SPJ1

Answer:

Step-by-step explanation:

x=40

Answer:

here is

Step-by-step explanation:

5x-20=180

5x=180+20

=200

X=200/5

40

A) A parallelogram has 4 sides.

B) The opposite angles of parallelogram are congruent.

C) [tex]\angle A \cong \angle C, \angle B \cong \angle D\\\\\implies m\angle C=115^{\circ}, m\angle D=65^{\circ}[/tex]

Answer:

f-(g/h) is an algebraic expression of the difference of f and the quotient of g and h.

Step-by-step explanation:

[tex]f - ( \frac{g}{h} )[/tex]

I hope it was helpful for you..m

The requried algebraic expression of English phrase is given as f - g/h.

The algebraic expression consists of constants and variables. eg x, y, z, etc.

the equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

here,
The difference between f and the quotient of g and h.
The difference represents the subtraction of values, and the quotient can be obtained by division of g by h.
So,
Required algebraic expression,
= f - g/h

Thus, the required expression is given as f - g/h.

Learn more about algebraic expression here:

https://brainly.com/question/953809

#SPJ2

Answer:

[tex]g(x)= -3x^{2} +4x +5[/tex]

Step-by-step explanation:

Five more = Addition of 5

Opposite = (-)

3 times = Multiplication by 3

Square = To the power (exponent) of two

4 times the number = Multiplication by 4

The number = unknown number = x

The slope m = 3/2 and the y-intercept = ( 0, -6 ).

The graph is a solid line and shaded area below the boundary line since y is less than (3/2)x - 6.

Given that:

3x -2y ≥ 12

First we write the inequality in slope intercept form y = mx + b.

Solve for y

3x -2y ≥ 12

-2y ≥ 12 - 3x

Now, divide each term by -2

y ≤ -6 + 3x/2

We re-arrange

y ≤ (3/2)x - 6

Using the slope intercept form y = mx + b. we can see that;

m = 3/2

b = -6

Hence, the slope m = 3/2 and the y-intercept = ( 0, -6 ).

The graph is a solid line and shaded area below the boundary line since y is less than (3/2)x - 6.

Learn more about inequality here: https://brainly.com/question/13790048

#SPJ1

Answer:

Step-by-step explanation:

This problem is similar to many others in which the sum of two quantities and their difference are given. The solution can be found easily when the equations for the relations are written in standard form.

Let s and h represent numbers of sodas and hot dogs sold, respectively. The given relations are ...

Adding the two equations eliminates one variable.

  (s +h) +(s -h) = (235) +(59)

  2s = 294 . . . . simplify

  s = 147 . . . . . .divide by 2

  h = 147 -59 = 88 . . . . h is 59 less

147 sodas and 88 hot dogs were sold.

__

Additional comment

The solution to a "sum and difference" problem is always the same. One of the numbers is half the sum of those given, and the other is half their difference. ((235-59)/2 = 88)

The range of the given relation is:   range = { 3, 9, 10}

Range is the out come of the event is know as y.

Here, the given relation:

               R = {(0,3), (8,9), (16,10)

Now, range = { 3, 9, 10}

Thus, the range of the given relation is: range = { 3, 9, 10}

Learn more about Range from:

https://brainly.com/question/15697193

#SPJ1

Answer:

x^2=ab

Step-by-step explanation:

Please mark as brainlist

Answer:

  22

Step-by-step explanation:

The segment addition theorem tells us the whole is the sum of the parts. We can use this to write an equation relating the expressions for segment length.

  OQ = OP +PQ . . . . . segment addition theorem

  4x +2 = (3x -3) +(4x -10) . . . . substitute given expressions

  15 = 3x . . . . . . add 13 -4x to both sides

  5 = x . . . . . . . divide by 3

  OQ = 4x +2 = 4(5) +2 = 22

The length of OQ is 22 units.

Answer:The answer is 27.04

Step-by-step explanation:

The solution is in the attached

Answer:

2.75 is the median

Answer:

1.25 is the median

Step-by-step explanation:

it is the middle of the number sequence.

to find the median, place the numbers in value order and find the middle

since there is an even amount of numbers, add 2.5 and 0 (the two middle numbers) and divide them by two