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Okay, here we have this:

We need to meke the composition (f•g)(x), so in the function f we will replace x with the function g:

Now let's find the domain of (f•g)(x):

2X+8≥0

2X≥-8

X≥-4

Finally we obtain the following domain: [-4,∞)

To be able to determine how many dogs can Jimmy Jump per hour, let's divide how many dogs can Jimmy Jump by the number of hours he took to complete that certain number of jumps. Thus, we generate this equation,

Given:

Jimmy jumped = 40 dogs

No. of hours Jimmy took to jump 40 dogs = 5 hours

We get,

Therefore, Jimmy can jump 8 dogs per hour.

Answer:

Step-by-step explanation:

9+4=

13

13*2=

26

Answer:

Step-by-step explanation:

(9 multiplied by 4) multiplied by 2

= 72

We are given two complementary angles (QRS and SRT).

Two angles are called complementry if they sum up to 90 degrees.

Therefore, by defination

mQRS + mSRT = 90

(8x+10) + (8x) = 90

8x + 8x + 10 = 90

16x = 90-10

16x = 80

x = 80/16

x = 5

Now, put the values in both the euqations and we will get the values of both the angles.

mQRS = 8x + 10 = 8(5) + 10 = 40 + 10 = 50 degrees

mSRT = 8x = 8(5) = 40 degrees

Answer

7 remainder 3

Explanation

38 : 5 can be written as 38/5

And we know that that will give

(38/5) = 7 remainder 3

Hope this Helps!!!

Solution

We want to get why

Reason 1: Commutation Law Does Not Hold For Division (or quotient)

Generally,

Reason 2: Actual Computation

First

Secondly

It is now obvious that

Starting with the equation:

Use the distributive property to expand the parenthesis in the left hand side of the equation:

Use the commutative property to rewrite the right hand side of the equation, swapping the terms:

Since both sides of the equation are the same, any value of b is a solution to the equation.

Therefore, all numbers are a solution for the equation 4(b-1)=-4+4b.

Deciding if each statement about a and b is true or false.

a)False

b)True

c)True

d)False

Given:

The quotient of a and b is negative.

a.

If quotient is negative means the dividend or divisor any one is negative so when the quotient b+a is always negative so given statement is false.

b.

The product ab is always negative because if the quotient is negative means either a or b is negative so ab is negative.

So given statement is true.

c.

Either a or b must be negative is true because if no element a or b is not negative we cannot produce a negative quotient hence either a or b must be negative.

d.

The quotient -a+b is negative is false because if the quotient is negative the values of a and b is one positive and one negative the positive number that is b greater than -a in that case the statement is false.

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Step 1

The domain includes all the x-values that fall within the function

Hence, the domain of this function is [ All real values of x]

Step 2

Find the range

The range includes all values of y that fall within the function

Hence the range of the function is [-∞, 9]

the initial expression is:

We can see that they have in common a factor of 4 so we can rewrite it like:

When looking at the graph, we can discard two of the options, rotation (as they don't have any intersection, there are no possibilities of having a rotation axis) and reflection. It occured a translation. To know which of the options is correct, we can see the y intercepts of both lines. The y intercept of f(x) is 0 and the y intercept of g(x) is -4, which means that the line was translated down 4 units.

It means the right answer is D. Vertical Translation down 4 units.

x - 9 = 35x

Subtract x from both sides:

x - 9 -x = 35x - x

-9 = 34x

Divide both sides by 34:

-9/34 = 34x/34

x = -9/34

Ok, so:

Let x and y be coordinate of the point C that partitions the segment.

And Let A = ( 2, -1 ) and B = ( 9 , 6 ).

So, given that C partitions the segment into a ratio of 5 to 2, we have:

Total parts of the segment: 5+2 = 7.

So, the point C is 5/7 of way from A to B.

Let me draw the situation:

Now, we know that the right distance is 7 and the upper distance is 7.

Now we multiply 5/7 per both distances.

5/7 * 7 = 5

5/7 * 7= 5

Now, we take the initial point A ( 2, -1 ), and sum 5 to each coordinate.

Then, the point C = ( 7 , 4 )

Step 1: Problem

There is a class with 6 women and 12 men. a) If I randomly pick 5 students, with replacement. What is the probability that at least 4 of them will be man? b) If I randomly pick 6 students, what is the probability that at least one of them will be a man?​

Step 2: Concept

Let the minimum score be x

(85 + 77 + 63 + 90 + x)/5 = 80

315 + x = 400

x = 400 - 315

= 85

Julia must get a minimum score of 85 to get a B average

The functions [tex]F(x)=-\frac{1}{2}x^{4}-x^{3}+x+2[/tex] could have created this graph of downward parabola.

Option D is correct because the leading coefficient of given function is negative. That's why it is making the downward parabola.

As we can see from the graph that the the parabola is downward.

And we know that if the leading coefficient is less than zero, thus the graph will be downward parabola.

Lets check all the option:

For option A:

[tex]F(x)=x^{3}+x^{2}+x+1[/tex], this is a cubic polynomial and the graph will be a cubic curve.

For option B:

[tex]F(x)=x^{2}+5[/tex], this is a quadratic polynomial and leading coefficient is positive, so the graph will be upward parabola.

For option C:

[tex]F(x)=x^{4}-2x[/tex], for x = 0, F(x) =0, so it will not intersect the y-axis. Also the graph will be upward parabola.

Hence, the option D, [tex]F(x)=-\frac{1}{2}x^{4}-x^{3}+x+2[/tex], could have created this graph of downward parabola.

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Solution

solution given;

let length be x

its

volume be x ³

we have when length is increased by 1cm volume increased by 19 cm³ so

(x+1)³=x³+19cm³

x³+1³+3x²+3x=x³+19

3x²+3x-18=0

3(x²+x-6)=0

x²+3x-2x-6=0

x(x+3)-2(x+3)=0

(x+3)(x-2)=0

either

x=-3 rejected

or

x=2cm

Hence the correct answer for the length of each cube = 2cm

Recall the following identities:

Since sin(t)=12/13 and cos(t)=5/13, then:

Given

Number of patients = 6,663

- For Sunday

Patients = 1,187

Percent is:

- For Monday

Patients = 755

Percent:

Monday is correct.

- For Tuesday

Patients = 1,085

Percent:

Tuesday is correct.

- For Wednesday

Patients = 1,031

Percent:

Wednesday is correct.

- For Thursday

Patients = 1,024

Percent:

- For Friday

Patients = 808

Percent:

Friday is correct.

- For Saturday

Patients = 773

Percent:

Saturday is correct.

Answer:

Errors

Sunday ---> 17.8%

Thursday ---> 15.4%

We define the following variables for our problem:

P = population of mooses

t = number of years since 1990

m = growth ratio

In terms of the variables that we defined above and the fact that the population of moose in terms of the year is linear, we have the following equation:

Now, we use the data of the problem:

1) In 1994 the moose population was 4930, so we have:

2) In 1999 the moose population was 6180, so we have:

Now, using the data above and the equation for P(t) we construct the following system of equations:

We solve the system of equations.

First, we solve the equations for P0:

Now, because the right-hand-side of both equations is equal to P0, we equal them and then we solve for the variable m:

Finally, we replace the value of m in one of the equations of P0 and solve for it:

A) The formula for the moose population, P, in terms of t, the years since 1990 is:

B) We want to know the value of the moose population in 2006.

First, we compute the value of t:

Now, we replace the value of t in the equation of P(t) above:

Answer: 7930

If Vegetable Oil costs $3.47 for 48 ounces, the cost of 1 tablespoon of vegetable oil is 4 cents.

1 tablespoon has alomst 0.5 ounce

If Vegetable Oil costs $3.47 for 48 ounces

Cost of 48 ounces of vegetable oil = $3.47

cost of 1 ounce of vegetable oil = $ 3.47 / 48 = $0.0722

cost of 0.5 ounce of vegetable oil = $0.0722/2 = $0.0361

cost of 0.5 ounce of vegetable oil is $0.0361

1 dollar = 100 cents

0.0361 dollar = 0.0361 x 100 cents

0.0361 dollar = 3.6 cents = 4 cents (approx)

Therefore, if Vegetable Oil costs $3.47 for 48 ounces, the cost of 1 tablespoon of vegetable oil is 4 cents.

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The Solution:

Given:

We are required to find the percentage that is between 34 grams and 42 grams.

By z-score statistic,

The lower limit is:

The upper limit is:

The probability is:

Therefore, the correct answer is 84%

For this problem, we are given the distance a construction crew built a road and the time in days it took to build it. We need to determine the unit rate for this problem, which is achieved by dividing the distance and time. We have:

The unit rate is 3 miles per day.

ANSWER:

For item 14: 1/36 (there is only one possible way of having both dice as 3)

For item 15: 1/18 (because there are 2 ways that one is 5 and one is 6 so it is 2/36 or 1/18)

For Item 16: 5/9 (because there 20 ways we can have a 5 or 6. 20/36)

For item 17: 11/36 (because there are 11 ways of having at least one six)

For item 18: 25/36 (because there are 25 ways having numbers other than 6)

For item 19: 5/18 (because there are 10 ways having exactly one six 10/36)

B) (-5,3)

1) We need to locate the vertex location since the point here is to find the coordinates of C'. So, let's do it before applying the required transformation.

C(5,3)

2) Since we want to know the coordinates of C', and there was a reflection across the y-axis, we can write the following:

C(5,3) Rule (x,y) --> (-x,y) C'(-5,3)

3) Thus, the answer is (-5,3)

You need to add 10 ounces of 20% alcohol solution.

x = ounces of 20% alcohol solution to add to the 15 oz of 25% solution

15 oz of a 25% solution = 3.75 oz of pure alcohol

The total amount can be described 15+x ounces.

We solve the problem in terms of the amount of pure alcohol

2x + 3.75 = .23(15+x)

2x + 3.75 = 3.45 + .23x

Subtracting .2x from both sides

3.75 = .03x + 3.45

Subtracting 3.45 from both sides

3 = .03x

Multiply by 100

30 = 3x

Divide by 3

10 = x

x = 10

So, you have to add 10 oz of 20% alcohol solution to 15 oz of 25% alcohol.

At the end we would have 25 oz that we believe would be 23% alcohol. If that is true, then we would have:

23 * 25 = 5.75 oz of pure alcohol in the solution.

We have shown (above) that we have 3.75 oz of pure alcohol in the 15 oz of 25% solution.

How many oz of pure alcohol is there in 10 oz of 20% alcohol?

2*10 = 2 oz

3.75 + 2 = 5.75 oz, which is exactly what we needed

You need to add 10 ounces of 20% alcohol solution.

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The function is (-x+3)/ (3x-2) and we get f(1)=1 and differentiation is f'(x)=-7/ (9x²- 12x+4).

Given that,

The function is (-x+3)/ (3x-2)

We have to find f(1) and f'(x).

Take the function expression

f(x)= (-x+3)/ (3x-2)

Taking x as 1 value

f(1)= (-1+3)/(3(1)-2)

f(1)=2/1

f(1)=1

Now, to get f'(x)

With regard to x, we must differentiate.

f(x) is in u/v

We know

u/v=(vu'-uv')/ v²        (formula)

f'(x)= ((3x-2)(-1)- (-x+3)(3))/ (3x-2)²

f'(x)= ((-3x+2)-(-3x+9))/ 9x²- 12x+4

f'(x)=(-3x+2+3x-9)/ 9x²- 12x+4

f'(x)=2-9/ (9x²- 12x+4)

f'(x)=-7/ (9x²- 12x+4)

Therefore, The function is (-x+3)/ (3x-2) and we get f(1)=1 and differentiation is f'(x)=-7/ (9x²- 12x+4).

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The solution of the system of equations is where both lines cross each other.

solution = (0,1)

The required (a) cost per ream becomes 59.99 and (b) the markdown per ream is  30.

Given that,
Printer Paper Store normally sells laser paper for 89,99 per ream, It has a special, 1 ream free with the purchase of 2. If you buy 2 reams and get 1 free.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
Cost of the 1 ream = 89,99
Cost of the 2 reams = 179.98
According to the question,
Cost of the 3 reams = 179.98
Cost of the one ream among the 3 reams = 179.88/3 = 59.99
markdown per ream = 89.99 - 59.99 = 30

Thus, the required (a) cost per ream becomes 59.99 and (b) the markdown per ream is  30.

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An orange has about 1/4 cup of juice. To find how many oranges are needed to make 2 1/2 cups of juice, we can use the next proportion

Solving for x: