Bruce wants to make 50 ml of an alcohol solution with a 12% concentration. He has a 10% alcohol solution and a 15% alcohol solution. The equation 0.10x + 0.15(50 – x) = 0.12(50) can be used to find the amount of 10% alcohol solution Bruce should use.

Using composite functions, we have that:

a) f(x) = x² + 3.

b) \(g(x) = \sqrt{x}\)

c) f(g(x)) = x + 3.

d) \((g \circ f)(6) = \sqrt{39}\)

The composite function of f(x) and g(x) is given by:

(f ∘ g)(x) = f(g(x)).

For item a, we want a non-linear function, which has a highest exponent different of 1, that does not go through the origin, hence the function can be:

f(x) = x² + 3.

For item b, we also want a non-linear function with a radical, hence the function can be:

\(g(x) = \sqrt{x}\).

For item c, the composite function is:

\(f(g(x)) = f(\sqrt{x}) = (\sqrt{x})^2 + 3 = x + 3\)

For item d, the composite function is:

\(g(f(x)) = g(x^2 + 3) = \sqrt{x^2 + 3}\)

At x = 6, we have that:

\((g \circ f)(6) = \sqrt{6^2 + 3} = \sqrt{39}\)

More can be learned about composite functions at https://brainly.com/question/13502804

#SPJ1

Answer: $329.05

Step-by-step explanation:

Since she pays $245.82 monthly and she is paying for 6 months, the amount paid will be:

= $245.82 × 6

= $1474.92

Since she buys the full golf club set for $1,145.87, then her finance charge will be:

= $1474.92 - $1,145.87

= $329.05

The finance charge is $329.05

The distance traveled by the car before it comes to a stop can be found by using the formula for distance traveled under constant acceleration:

\(d = v_0t + (1/2)at^2\)

where d is the distance traveled, v0 is the initial velocity, a is the acceleration, and t is the time.

We are given that \(v_0 = 20 m/s\) and \(a = -30/t + 20 m/s^2\). We need to find the time t when the car comes to a stop, which is when the final velocity is 0.

Using the formula for final velocity under constant acceleration:

\(v_f = v_0 + at\)

We can set vf = 0 and solve for t:

\(0 = 20 + (-30/t + 20)t \\0 = 20t - 30 + 20t \\30 = 40t \\t = 30/40 = 0.75 s\)

Now we can plug this value of t back into the formula for distance traveled to find the distance traveled before the car comes to a stop:

\(d = (20)(0.75) + (1/2)(-30/0.75 + 20)(0.75)^2\\ d = 15 + (1/2)(-40 + 20)(0.5625)\\ d = 15 + (1/2)(-20)(0.5625) \\d = 15 - 5.625\\ d = 9.375 m\)

Therefore, the distance traveled before the car comes to a stop is 9.375 m.

For more about Distance traveled:

https://brainly.com/question/29055485

#SPJ11

Answer:

$225:  the expression may look like $300-25%.    

Step-by-step explanation:

First decide what is 1/4 of $300.  ($300 / 4 = $75)

then subtract that amount from the original price. ($75-$300)

Answer:

first create an equation for Jeb flower then for Lori

then solve them by simultaneous linear equations

Answer:

One rose = $2.75

One carnations = $1.25

Step-by-step explanation:

Lets make the rose = x

and carnations = y

Jeb >> 6x + 3y = 20.25

Lori >> 8x + 3y = 25.75

Solve simultaneously using elimination method.

8x + 3y = 25.75

- 6x + 3y = 20.25

_______________

2x =5.5

2x/2 = 5.5/2

x = 2.75

plug 2.75(x) into any of the two equations to find y.

6(2.75) + 3y = 20.25

16.5 + 3y = 20.25

3y = 20.25 - 16.5

3y = 3.75

3y/3 = 3.75/3

y = 1.25

Answer:

3/9

1 x 3

1 x 9

Step-by-step explanation:

Answer: A rectangle is ALWAYS a parallelogram and not all parallelograms are rectangles. (ex. Rhombus, square are both parallelograms) So Ainsley is wrong.

Step-by-step explanation: Parallelograms is a quadrilateral shape with 2 pairs of parallel sides. So, a rectangle has to always be one.

The solution to the system of equations is:

X = -171, Y = -531, and Z = 363.

To solve the system of equations:

2X + 4Y + 2Z = 144 (Equation 1)

0.5X + 0.25Y = 60 (Equation 2)

1.5X + 0.5Y + Z = 36 (Equation 3)

We can use row operations to simplify and solve the system.

Let's start with Equation 2. Multiply both sides of Equation 2 by 4 to eliminate decimals:

2X + Y = 240 (Equation 4)

Now, let's solve Equations 1 and 4 using row operations. Multiply Equation 4 by -2 and add it to Equation 1:

-4X - 2Y = -480 (Equation 5)

2X + 4Y + 2Z = 144 (Equation 1)

   2Y + 2Z = -336  (Equation 6)

Next, let's solve Equations 3 and 6 using row operations. Multiply Equation 6 by -3 and add it to Equation 3:

-3Y - 3Z = 1008 (Equation 7)

1.5X + 0.5Y + Z = 36 (Equation 3)

1.5X - 2.5Z = -972 (Equation 8)

We now have a simplified system of equations:

2Y + 2Z = -336 (Equation 6)

1.5X - 2.5Z = -972 (Equation 8)

-3Y - 3Z = 1008 (Equation 7)

Now, we can solve this system by using additional row operations.

Multiply Equation 6 by 1.5 and add it to Equation 8:

-4Z = -1452

Solving for Z, we get Z = 363.

Substituting the value of Z back into Equation 6, we can solve for Y:

2Y + 2(363) = -336

2Y = -1062

Y = -531.

Finally, substituting the values of Y and Z into Equation 7, we can solve for X:

-3(-531) - 3(363) = 1008

X = -171.

Therefore, the solution to the system of equations is:

X = -171, Y = -531, and Z = 363.

for such more question on system of equations

https://brainly.com/question/4262258

#SPJ8

Answer:

B)

Step-by-step explanation:

Answer: the answer is B hope this helps

Step-by-step explanation:

Using probability,

a) 61/100

b) 61/210

c) 305/536

The probability formula can be used to calculate the likelihood of an event by simply dividing the favourable number of possibilities by the total number of options.

The likelihood of an event occurring can range from 0 to 1, as there can never be more favourable outcomes than there are potential outcomes. Because of this, the percentage of effective outcomes cannot be 0.

Here in the question,

It has asked to find probability that a randomly selected person did not have a child under 18 years old, given that they said no is:

P = 305/500

= 61/100

It is asked to find probability that a randomly selected person said No, given that the person did not have a child under 18 years old is:

P = 305/1050

= 61/210

It is asked to find probability that a randomly selected person from the group did not have a child under 18 years old and said no is:

P = 305/536

To know more about probability, visit:

https://brainly.com/question/30034780

#SPJ1

Answer:

-6x+2=4

3(-3x+1)=6

-2(3x-1)=4

-3x=1

x=-1/3

Step-by-step explanation:

Using a system of equations, the quantity of Type A coffee that Trey's Coffee Shop blended with Type B coffee was 78 pounds.

A system of equations or simultaneous equations is two or more equations solved concurrently, simultaneously, or at the same time.

Unit Cost Per Pound:

Type A coffee = $5.80

Type B coffee = $4.25

The total quantity of pounds of the blend = 142 pounds

The total cost of 142 pounds = $724.40

Let the number of Type A coffee = x

Let the number of Type B coffee = y

x + y = 142 ... Equation 1

5.8x + 4.25y = 724.40 ... Equation 2

Multiply Equation 1 by 4.25:

4.25x + 4.25y = 603.5 ... Equation 3

Subtract Equation 3 from Equation 2:

5.8x + 4.25y = 724.40

-

4.25x + 4.25y = 603.5

1.55x = 120.9

x = 78

Substitute x = 78 in either equation:

x + y = 142

78 + y = 142

y = 64

Thus, 78 pounds of Type A coffee was used for the mixture.

Learn more about a system of equations at https://brainly.com/question/13729904.

#SPJ1

a) Slope intercept form

We see in the graph that the y-intercept is y=4, so b=4.

Then, using another known point like (3,0) we can calculate the slope:

Then, the equation becomes:

b) Point slope form

We will use the known slope m=-4/3 and one of the points (3,0):

c) Perpendicular line that pases through the point (5,-4):

In order to be perpendicular, the line slopes has to be opposite reciprocals:

Then, the perpendicular line has a slope of 3/4.

To make it go through the point (5,-4), we replace this values in the equation and calculate the y-intercept b:

The equation of the perpendicular line that goes through (5,-4) is:

d) Parallel line that goes through (0,3).

Parallel lines have the same slope.

In this case, the slope is -4/3.

If we replace the values of x and y with the point (0,3) we get thte y-intercept b:

We could have already now that the intercept was 3 because this is the value when x=0.

The equation of the line is:

Answer:

c/sin(60°) = 14/sin(25°)

c = 14sin(60°)/sin(25°) = 28.7

The experimental and theoretical probability of the name Fred being chosen is 0.11 and 0.167  respectively.

The question is asking for the experimental and theoretical probabilities of choosing the name Fred when six different names are put into a hat and a name is chosen 100 times.

To find the experimental probability of choosing the name Fred, divide the number of times Fred is chosen by the total number of trials (100 times). In this case, Fred is chosen 11 times.

Experimental probability of choosing Fred = (number of times Fred is chosen) / (total number of trials)
= 11 / 100
= 0.11 or 11%

For the theoretical probability, since there are six different names in the hat and each name has an equal chance of being chosen, the probability of choosing Fred is:

Theoretical probability of choosing Fred = 1 / 6
≈ 0.167 or 16.67%

If the number of names in the hat were different, the theoretical probability would change because the denominator (total number of names) would be different. For example, if there were 5 names instead of 6, the theoretical probability of choosing Fred would be 1/5 or 20%.

The experimental probability would also likely change since the outcomes of the trials would be different with a different number of names.

To know more about probability refer here:

https://brainly.com/question/30034780?#

#SPJ11

Answer:

The missing fraction is 6/12

(you can further simplify this but the question requires that you don't do that)

Step-by-step explanation:

To add fractions easily, their denominators should have the same value, so the denominator should be 12,

Then, to get 16 in the numerator, we need to find a number that on adding to 10, gives 16, or,

10 + x = 16

x = 16 - 10

x = 6

So, the numerator should be 6

so we get the fraction, 6/12

We can also solve it in an alternate way,

\(10/12 + x = 16/12\\x = 16/12 - 10/12\\x = (16-10)/12\\x = 6/12\)

Answer:

(x - 4) (2x - 1)(3x + 2)

Step-by-step explanation:

Dividing:

x - 4)6x^3 - 23x^2 - 6x + 8 (6x^2 + x- 2 <----Quotient

        6x^3 -24x^2

                       x^2 - 6x

                       x^2 - 4x

                              -2x + 8

                              -2x + 8

6x^2 + x - 2

= 6x^2 - 3x + 4x - 2

= 3x(2x - 1) + 2(2x - 1)

= (3x + 2)(2x - 1)

Answer:

1,176 | 588

Step-by-step explanation:

118 + 168 + 151 + 151 = 588

588 x 2 = 1,176

That's possible when function tends to zero

\(\\ \rm\hookrightarrow 0.25x^2-x+9.5=0\)

\(\\ \rm\hookrightarrow 1/4x^2-x+19/2=0\)

\(\\ \rm\hookrightarrow x^2-x+38=0\)

\(\\ \rm\hookrightarrow x=\dfrac{1\pm\sqrt{1-152}}{2}\)

\(\\ \rm\hookrightarrow x=\dfrac{1\pm\sqrt{151}i}{2}\)

Answer:

8.5 ft

Step-by-step explanation:

\(f(x) = 0.25x^2 - x + 9.5\)

To find the minimum point of the function, differentiate:

\(f'(x) = 0.5x - 1\)

set to zero and solve for x:

\(f'(x) =0\\ \implies0.5x - 1=0\\\implies x=2\)

Substitute found value of x into function to find y (height):

\(f(2) = 0.25(2)^2 - 2 + 9.5=8.5\)

Therefore, the lowest point on the bottom edge of the banner is 8.5 ft above the floor.

As per the given function, the time take bey the object to reach the ground is 4.31 seconds.

The term function in math is defined as the relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Here we have given that model for the height on a launched object on the top of a hill, h, as a function of time t, defined by h(t)=-16t²-32t+160.

Here we also know that the height is measured in feet and the time is measured in seconds.

In order to find the solution, lets substitute the value of h(t) as zero, then we get the function like the following,

=> -16t²-32t+160 = 0

But we are trying find solution using the method of perfect square.

=> (-32)±√(-32)² -(4 x -16 x 160) / 2 x -16

When we simplify this one then we get the value of t as

=> t = 4.31

To know more about function here.

https://brainly.com/question/28193995

#SPJ4

The correct answer is (d) No, it is not continuous because lim x→3 f(x) ≠ lim x→3 f(x).

To determine if the function f(x) = (x+3)/(x²-9) is continuous at x=3, we need to check if the limit of the function exists as x approaches 3 from both the left and the right, and whether this limit is equal to the value of the function at x=3.

First, we can check the limit as x approaches 3 from the left:

lim x→3- f(x) = lim x→3- (x+3)/(x²-9) = (-3)/(0-) = ∞

Next, we can check the limit as x approaches 3 from the right:

lim x→3+ f(x) = lim x→3+ (x+3)/(x²-9) = (6)/(0+) = ∞

Since both one-sided limits are infinite, the limit as x approaches 3 does not exist.

Therefore, the function f(x) = (x+3)/(x²-9) is not continuous at x=3.

The correct answer is (d) No, it is not continuous because lim x→3 f(x) ≠ lim x→3 f(x).

To know more about continuity visit:

brainly.com/question/21447009

#SPJ1

Answer:

Step-by-step explanation:

Angles (7x + 3)° and (8x + 1)° are corresponding angles

Therefore:

m║n      ⇒      (7x + 3)° = (8x + 1)°

(7x)° + 3° = (8x)° + 1°     {subtract (7x)° from both sides}

3° = x° + 1°                   {subtract 1° from both sides}

2° = x°                          

x = 2

Answer:

2x-2

Step-by-step explanation:

Being specifically asked to rationalise the denominator we focus on it as required.

To rationalise a term it has to be multiplied by its inverse.

The inverse of

\( \sqrt{x} - \sqrt{2 - x} \)

is

\( \sqrt{x} + \sqrt{2 - x} \)

Multiplying this two vives us a difference of two squares

\( {( \sqrt{x} })^{2} - {( \sqrt{2 - x} )}^{2} \)

which gives us

x-(2-x)

=2x-2

The correct answer for the next step when bisecting line segment AB using a string is C. Set the string length at point A and at the top of the arc. Optio C

When bisecting a line segment using a string, the method involves creating congruent arcs on either side of the line segment. This is done by fixing the length of the string and using it as a compass to draw arcs. The goal is to find the point that lies on the perpendicular bisector of the line segment AB.

To achieve this, the steps would be as follows:

Place the string's endpoint at point A, and use the other endpoint to draw an arc that intersects line segment AB on both sides.

Without changing the length of the string, move the endpoint to the top of the arc (the point where it intersects the circumference). This ensures that the length of the string remains constant.

With the endpoint at the top of the arc, draw another arc intersecting the previous arc on both sides.

By following this procedure, the two arcs will intersect at two points. The perpendicular bisector of line segment AB passes through these points, effectively bisecting the line segment.

Therefore, option C, is correct.

For more such questions on line segment visit:

https://brainly.com/question/280216

#SPJ8

Answer:

the asnwer is (2,3)

Step-by-step explanation:

Answer:

The measure of angle WVX is 140°.

Step-by-step explanation:

Let x be the measure of angle WVX.

\( \frac{14}{9} \pi = 2x\)

\( x = \frac{7}{9} \pi( \frac{180}{\pi}) = 140 \: degrees\)

Answer:

angle = arc length/radius
in this case, the arc length is 14/9*\(\pi\) and the radius is 2. Upon multiplying these, you get 140.

so, the answer is 140 degrees.

The length of arc XW is 9,60 metres

The length of arc YVU is 44.93 metres

A. M<XZW = 180 degrees - M<VZW

= 180 - 108

= 72 degrees.

XV = 180/360 x 2\pi r =

r = 7.639

XW= 72/360 x 2\pi r

= 9.60 metres.

B. M<UZY = M<XZW = 72 degrees

MYVU= 85 + 180 + 72 = 337 degrees

YVU = 337/360 x 2 pi r

=44.93 metres

Read more about geometry here:

https://brainly.com/question/19241268

#SPJ1

Answer:

(0,2)

Step-by-step explanation:

Answer:

Carla's Cafe charges more than Dino's dinner for 4 sandwiches because

$32 > $16

Step-by-step explanation: