Let f(x) = -2x + 7 and g(x) = -6x + 3. Find fg and state its domain.

Answer:

[tex]x + y = \frac{1000}{9}[/tex]

Step-by-step explanation:

Step 1: Identify the approach:

With this problem, the general solution is to try manipulate given data and transform data into a new form, in which, the desired value [tex](x + y)[/tex] is on the left side and all of other components which do not contain [tex]x[/tex] or [tex]y[/tex] are on the right side.

Step 2: Analyze:

[tex]9x + 2y^{2} - 3z^{2} = 132\\9y - 2y^{2} + 3z^{2} = 867[/tex]

Realize that in both equations, the [tex]2y^{2}[/tex] and [tex]3z^{2}[/tex] are in form of different signs. Then adding up corresponding sides of both equation can help eliminate these undesired components.

Step 3: Perform manipulation:

[tex]9x + 2y^{2} - 3z^{2} + 9y - 2y^{2} - 3z^{2} = 132 + 867[/tex]

Rearrange:

[tex](9x + 9y) + (2y^{2} - 2y^{2}) +(3z^{2} - 3z^{2}) = 132 + 867[/tex]

Simplify:

[tex]9(x + y) + 0 + 0 = 1000[/tex]

Simplify:

[tex]x + y = \frac{1000}{9}[/tex]

Hope this helps!

:)

Answer:

1/24

Step-by-step explanation:

1/4*1/2*1/3 = 1/24

Answer:

0.0178

Step-by-step explanation:

For computation of probability that all fourteen bets lose first we need to find out the Probability of losing in 1 bet is shown below:-

Probability of losing in 1 bet = 1 - P(winning)

= 1 - 0.25

= 0.75

With the help of probability of losing in 1 bet we can find out the Probability of losing in 8 bets which is here below:-

= Probability of losing in 1 bet ^ Number of loosing bets

= 0.75 ^ 14

= 0.017817948

or

= 0.0178

Therefore for computing the probability that all fourteen bets lose we simply applied the above formula.

Answer:

17.85 feet.

Step-by-step explanation:

Area = 1/4 * 3.14 * r^2  where r is the radius

So r^2 = 19.625 / (1/4 * 3.14)

r^2 = 25

r = 5 feet.

The perimeter = 2r + 1/4 * 2* 3.14*r

= 2*5 + 7.85

= 17.85 feet.

Answer:

It will take 800seconds to you to run 5000m

Step-by-step explanation:

Let time taken to run 5000m is x

Using ratio and proportion

200:32=5000:x

200/32=5000/x

200*x=5000*32

200x=160000

x=800seconds

Answer:

Step-by-step explanation:

a. The sample size for the poll would be at most 10% of the total readers of the tennessean.

b. Categorical data...data collected in groups or categories.

c. Yes it would make more sense to use percentages as this gives a better estimate for proportion.

d. The number of individual that provided this response is 67% of the sample size (which is at most 10% of the total population of readers of the online newspaper).

Answer:

100 muffins

Step-by-step explanation:

We can use a ratio to solve

6 cups          15 cups

-------------   = -----------

40 muffins     x muffins

Using cross products

6x = 40*15

Divide each side by 6

6x/6 = 40*15/6

x =100

100 muffins

Answer:

100 muffins

Step-by-step explanation:

If she could bake 40 muffins with 6 cups, then she could bake 80 muffins with 12 cups. Then, we have 3 cups left over, which is half of 6, meaning she can only bake half of her regular amount with 3 cups, which would be 20. 80+20=100

40+40+20=100

Answer:

We use the binomial distribution to describe this situation.

The mean number of phone sales is 749.7 with a standard deviation of 15.

Step-by-step explanation:

For each shopper, there are only two possible outcomes. Either they plan to purchase the newly released smart phone, or they do not. Each customer is independent of other customers. So we use the binomial distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Fifty random shoppers at an electronics store have been interviewed and 35 of them intend to purchase a newly released smart phone.

This means that [tex]p = \frac{35}{50} = 0.7[/tex]

What are its mean and standard deviation of phone sales if we are concerned about 1071 shoppers that day

1071 shoppers, so [tex]n = 1071[/tex]

Mean

[tex]E(X) = 1071*0.7 = 749.7[/tex]

Standard deviation

[tex]\sqrt{V(X)} = \sqrt{1071*0.7*0.3} = 15[/tex]

The mean number of phone sales is 749.7 with a standard deviation of 15.

Answer:50%

Step-by-step explanation:670/1340 = 1/2 = 50%

Answer:

-3/4

Step-by-step explanation:

Find two points on the line

(0,1) and (-4,4)

We can use the slope formula

m = (y2-y1)/(x2-x1)

   = (4 -1)/(-4 -0)

    = 3/-4

    = -3/4

Answer:

A, B, and E

Step-by-step explanation:

Answer:

abe

Step-by-step explanation:

Answer:

  4u²

Step-by-step explanation:

  [tex]\dfrac{12u^3 + 48u^2v}{3u+12v}=\dfrac{12u^2(u+4v)}{3(u+4v)}=\boxed{4u^2}[/tex]

Common factors cancel from numerator and denominator. The one factor that might make the expression undefined is given as non-zero, so no additional restrictions apply.

Answer:

  see below

Step-by-step explanation:

The way the problem is worded, we expect "n" to represent the year number we're at the beginning of. That is the initial balance is that when n=1, and the balance at the beginning of year 5 (after interest accrues for 4 years) is the value of obtained when n=5.

After compounding interest for 4 years, the balance will be ...

  500·1.04^4 = 584.93

The matching answer choice is shown below.

Answer:

b

Step-by-step explanation:

Answer:

  You can work no more than 10 hours teaching, and must work at least 5 hours cashiering. The remaining hours can be worked at the other job until the goal is reached.

Step-by-step explanation:

The restrictions give rise to two inequalities. If we  ...

  let x represent teaching hours

  let y represent cashiering hours

then the restrictions are ...

  x + y ≤ 15 . . . . total hours cannot exceed 15

  6x +8y ≥ 100 . . . . you want to earn at least $100

The solution set for these inequalities is a triangular area on a graph with vertices at ...

  (x, y) = (10, 5), (0, 12.5), (0, 15)

You must work at least 5 hours cashiering, and the remainder of necessary time at teaching.

Answer:

y = (-3/4)x + 7/4

Step-by-step explanation:

Step 1: Define general form of equation of line

An equation of a straight line on two-dimensional plane could be represented in form of: y = Mx + b, with M is slope and b is y-intercept

Step 2: Set up the system to solve for parameters of equation of line

(solve for M and b)

That equation passes 2 points, which are represented in form of (x, y), (5, -2) and (-3, 4).

Substitute these values of x and y into the original equation in step 1:

-2 = 5M + b

4 = -3M + b

Step 3: Solve the system of equations in step 2 for M and b

Subtract 1st equation from 2nd equation:

     6 = -8M

=> M = -6/8 = -3/4

Substitute M back into 1st equation:

=> -2 = 5*(-3/4) + b

=>  b = -2 + 15/4

=>  b = 7/4

=>  The equation of the line that passes through (5, -2) and (-3, 4):

      y = (-3/4)x + 7/4

Hope this helps!

:)

Answer:

Y= -4/3(x-7/2)

Step-by-step explanation:

So first calculate the difference between them,

changes by 8 x units, and -6 y units.

Then substitute them into y/x to find gradient

-6/8 = -4/3

so now we have a part of the equation:

Y= -4/3(x-a)

substitute Y= -2 and x=5 (from (5,-2))

-2= -4/3(5-a)

-2= -20/3+4a/3

Multiply by 3 on both sides

-6= -20+4a

add 20 on both sides

14=4a

a=7/2

use this as the value of a

Y= -4/3(x-7/2)

Answer:

[tex] P= 2*Lenght + 2*Width[/tex]

Since the perimeter is 56 inches we can solve for the lenght with this equation:

[tex] 56 in = 2*12in + 2*Length[/tex]

And solving for the length we got:

[tex] Length = \frac{56in -24 in}{2} 16 in[/tex]

So then the lenght = 16 inhes and the width of 12 inches

Step-by-step explanation:

For a rectangle of width 12 inches and lenght y inches we know that the perimeter is given by:

[tex] P= 2*Lenght + 2*Width[/tex]

Since the perimeter is 56 inches we can solve for the lenght with this equation:

[tex] 56 in = 2*12in + 2*Length[/tex]

And solving for the length we got:

[tex] Length = \frac{56in -24 in}{2} 16 in[/tex]

So then the lenght = 16 inhes and the width of 12 inches

Answer:

6/4

Explanation:

If Alex can file the papers in the cabinets for 6 hours and 4 hours with Millie, then the fraction to represent the papers filed with Millie would be 6/4.

Hope this helps!

You are given the equation [tex]f(x)=x+6[/tex] and [tex]g(x)=x^4[/tex]. When you combine G(F(x))  your equation would come out as [tex]g(f(x))=x^4(x+6)[/tex]. Once you distribute the equation you will get [tex]g(f(x))=(x+6)^4[/tex]

Therefore you answer choice would be B. [tex](x+6)^4[/tex]

Answer:

I think it’s -4

Step-by-step explanation:

-2 plus -2 is -4

since 2 plus 2 is 4

Hope this helps ;)

Answer:

Step-by-step explanation:

It is because 2 plus 2 is 4

so -2 plus -2 is -4

hth!

Answer:

0-4: Make it 2 units tall

5-9: Make it 5 units tall

10-14: Make it 1 unit tall

15-19: Make it 4 units tall

20-24: Make it 4 units tall

Step-by-step explanation:

0-4: 2, 2 (2 numbers)

5-9: 6, 7, 7, 8, 9 (5 numbers)

10-14: 14 (1 number)

15-19: 15, 16, 16, 18 (4 numbers)

20-24: 21, 23, 23, 24 (4 numbers)

The right answer is (1/2 , 5)

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

Answer:

E:

Step-by-step explanation:

The equation of circles is

(x-a)²+(y-b)²=r²

Where

Center = (a,b) = (-6,-3) and r = 12

Now

The equation becomes

(x+6)²+(x+3)²=144

Answer:

x =44

Step-by-step explanation:

0.2x + (-0.9) + 1.7 = 9.6

Combine like terms

.2x +.8 = 9.6

Subtract .8 from each side

.2x +.8 -.8 = 9.6 -.8

.2x = 8.8

Divide each side by .2

.2x/.2 = 8.8/.2

x =44

Answer:

1/2

Step-by-step explanation:

Find two points on the line

(2,0) and (4,1)

The slope is given by

m= (y2-y1)/(x2-x1)

   =(1-0)/(4-2)

   = 1/2

Answer:

The coefficients for the quadratic regression curve are

a = (-2/3) = -0.6667

b = (11/3) = 3.6667

c = 1 = 1.0000

y(x) = -0.6667x² + 3.6667x + 1.0000

Step-by-step explanation:

Quadratic regression curve gives a general expression of

y = ax² + bx + c

And the points on the curve include

(1, 4), (3, 6), (4, 5), (5, 2)

Taking the points one at a time and substituting them into general quadratic curve expression

(1, 4), x = 1, y = 4

y = ax² + bx + c

4 = a + b + c (eqn 1)

(3, 6), x = 3, y = 6

6 = a(3²) + b(3) + c

6 = 9a + 3b + c (eqn 2)

(4, 5), x = 4, y = 5

5 = a(4²) + b(4) + c

5 = 16a + 4b + c (eqn 3)

Combining the 3 equations and solving simultaneously

4 = a + b + c

6 = 9a + 3b + c

5 = 16a + 4b + c

From eqn 1, c = 4 - a - b

Substituting this into eqn 2 and 3, we have

6 = 9a + 3b + 4 - a - b

2 = 8a + 2b (*)

5 = 16a + 4b + 4 - a - b

1 = 15a + 3b (**)

8a + 2b = 2

15a + 3b = 1

a = (-2/3), b = (11/3)

c = 4 - a - b

c = 4 - (-2/3) - (11/3)

c = 1

Hence, the coefficients for the quadratic regression curve are

a = (-2/3) = -0.6667

b = (11/3) = 3.6667

c = 1 = 1.0000

y(x) = -0.6667x² + 3.6667x + 1.0000

Hope this Helps!!!

The complete question is;

A marine biologist is preparing a deep-sea submersible for a dive. The sub stores breathing air under high pressure in a spherical air tank that measures 78.0 cm wide. The biologist estimates she will need 2600 L of air for the dive. Calculate the pressure to which this volume of air must be compressed in order to fit in to the air tank. Write you answer in atmospheres

Answer:

10.5 atm

Step-by-step explanation:

Formula for Volume of a sphere is;

V = (4/3)πr³

r = 78/2 = 39 cm

V = (4/3)π(39)³

V = (4/3)*π*59319

V = 248475 cm³

Now, from conversions, 1000 cm³ = 1L

So,

V = 248475/1000

V = 248.5 L

This is the volume of the storage tank

If we assume that the 2600 L of air is measured at 1 atmosphere pressure, then we will obtain the following relationship:

From Boyles law,

P1 × V1 = P2 × V2

Thus;

(1 atm) × (2600 L) = (P2) × (248.5 L)

P2 = 2600/248.5

P2 = 10.463 atmospheres

Approximating to 3 significant figures is; P2 = 10.5 atm

Answer:

Step-by-step explanation:

For a rectangular prism, a plane intersecting this prism produces a two dimensional figure as its cross section and in this case the cross section is a rectangle.

For a triangular prism, a plane intersecting this prism produces a two dimensional figure as its cross section and in this case the cross section is a triangle.

Since our first equation reads y = 2x + 3, we can substitute a 2x + 3

in for y in our second equation and then solve from there.

So we have 2x + 3 = x + 2.

Now subtract x from both sides to get x + 3 = 2.

Now subtract 3 from both sides to get x = -1.

To find y, plug -1 back into either equation.

I have chosen to plug it into the second.

So we have y = (-1) + 2 which simplifies to 1.

So our solution to this system is (-1, 1).

Answer:

Step-by-step explanation:

Consider the calculations in the table below with the respective columns being: Name | Laps | Time | Time(in hours) |Total Distance | Unit Rate

[tex]\left|\begin{array}{c|c|c|c|c|c}---&---&---&----&----&---\\Amber&3&40&\frac{40}{60}&3*\frac{3}{4}=2.25&2.25 \div \frac{40}{60}= 3\frac{3}{8} \\\\Bruno&4&54&\frac{54}{60}&4*\frac{3}{4}=3&3 \div \frac{54}{60}= 3\frac{1}{3}\\\\Cady&5&75&\frac{75}{60}&5*\frac{3}{4}=3.75&3.75 \div \frac{75}{60}= 3 \\\\Drake&6&72&\frac{72}{60}&6*\frac{3}{4}=4.5&4.5 \div \frac{72}{60}= 3\frac{3}{4} \end{array}\right|[/tex]

We can then match each walker to their respective unit rates in miles per hour.