You have been tasked with filling 4 ounce and 3 ounce bags from a 41 ounce container of candy.
A. How many different combinations of full bags could you have?
B. If you would like to keep the total number of bags used to a minimum, which solution uses the fewest number of bags?
C. If 3 ounce bags cost 5 cents and 4 ounce bags cost 7 cents, which solution offers the cheapest way to fill the bags ?
D. If 3 ounce bags cost 5 cents and 4 ounce bags cost 6 cents, which solution offers the cheapest way to fill the bags ?
E. If the 4 ounce bags of candy sell for $2 each and the 3 ounce bags of candy sell for $1.50 each, which solution offers the greatest revenue?

Answer:

36 fruit tarts

Step-by-step explanation:

90 x .40 = 36

Answer:

Average rate of change = 2

Step-by-step explanation:

We need to find the average rate of change of f(x) over the interval [-4,-1], so first we need to find the end points at x=-4 and x=-1.

From graph we see that y=-3 when x=-4, So the point is (-4,-3)

From graph we see that y=3 when x=-1, So the point is (-1,3)

Now we can plug these points into average rate of change formula:

[tex]Average\ rate=\frac{f\left(b\right)-f\left(a\right)}{b-a}[/tex]

where (a,f(a)) and (b,f(b)) are the given points.

[tex]Average\ rate=\frac{-3-3}{-4-\left(-1\right)}[/tex]

[tex]Average\ rate=\frac{-3-3}{-4+1}[/tex]

[tex]Average\ rate=\frac{-6}{-3}[/tex]

[tex]Average\ rate=2[/tex]

Hence final answer is 2.

m = 3 is the slope of the given line; also its the slope of anything parallel to the given line

(x1,y1) = (1,3) is the given point the parallel line goes through

y - y1 = m(x-x1) .... point slope form

y - 3 = 3(x - 1) .... plug in the given values; solve for y

y - 3 = 3x - 3

y - 3+3 = 3x - 3 + 3

y = 3x + 0

y = 3x

Final Answer: y = 3x

side note: if you plugged in x = 1 it leads to y = 3 which confirms that (x,y) = (1,3) is on this parallel line.

Answer:

[tex]a \geq \frac{1}{\sqrt{2} -1}[/tex]

Step-by-step explanation:

This equation is more intimidating than the problem you have to solve.

You know that the sine of everything is always between -1 and +1. So for the entire expression to be >= 0, the a*tan(pi/8) bit has to be 1 at least. Given this, we can forget about the sin(...) term of the equation for the remainder of solving it.

You already figured out that tan(pi/8) is sqrt(2)-1.

So what we're saying is a * (sqrt(2) - 1) has to be 1 at least.

If we solve a(sqrt(2)-1) >= 1 for a we get:

a = 1/(sqrt(2)-1)

[tex]c)\\\tan\left(\dfrac{\pi}{8}\right)=\tan\left(\pi-\dfrac{7\pi}{8}\right)=\tan\left(-\dfrac{7\pi}{8}\right)=-\tan\left(\dfrac{7\pi}{8}\right)\\\\=-(1-\sqrt2)=\sqrt2-1\\\\y=\sin(2x-1)+a\tan\dfrac{\pi}{8}\\\\\text{We know}\ -1\leq\sin(2x-1)\leq1.\\\\y\geq0\ \text{therefore}\ a\tan\dfrac{\pi}{8}\geq1\\\\\text{We have to move the graph at least one unit up}\\\\a(\sqrt2-1)\geq1\qquad\text{divide both sides by}\ (\sqrt2-1)>0\\\\a\geq\dfrac{1}{\sqrt2-1}\cdot\dfrac{\sqrt2+1}{\sqrt2+1}\\\\a\geq\dfrac{\sqrt2+1}{(\sqrt2)^2-1^2}[/tex]

[tex]a\geq\dfrac{\sqrt2+1}{2-1}\\\\a\geq\dfrac{\sqrt2+1}{1}\\\\a\geq\sqrt2+1\\\\Answer:\ \boxed{a=\sqrt2+1}[/tex]

Answer:

V = [tex]\frac{4}{3} \pi r^3[/tex]

Step-by-step explanation:

Final answer:

To find the volume of a sphere, use the formula: Volume = 4/3 (pi) (radius)^3

Explanation:

The volume of a sphere can be calculated using the formula:

Volume = 4/3 (pi) (radius)^3

To find the volume, you need to know the radius of the sphere. Plug in the value for the radius and then evaluate the expression using the order of operations. Finally, multiply the result by 4/3 and pi to find the volume of the sphere.

y = x + 4     (*)

x - y = -4    (**)

Substitute (*) to (**):

x - (x + 4) = - 4

x - x - 4 = - 4

- 4 = - 4     TRUE

x ∈ R

y = x + 4

Answer:

x= -8      y= -4

Step-by-step explanation:

SOLVING FOR X

y=x+4

x-y=-4

----------------------

x-x+4= -4

   -4     -4

---------------------

x-x= -8

x= -8

SOLVING FOR Y

plug in the x in any equation

y=(-8)+4

y= -8+4

y= -4

Answer:

We have 45 dogs when we have 30 cats

Step-by-step explanation:

If the ratio of dogs to cats is 3:2

We want to get to 30 cats so we need to multiply by 15  (2*15 =30)

What we do on one side we do on the other

3*15 : 2 * 15

45 :30

We have 45 dogs when we have 30 cats

First, we solved the system of equations by substitution and found x = -3, y = -6. Then, by employing the elimination method, we determined the solution to the second system as x = 7, y = 6.

To solve the system of equations by substitution and elimination, let's start with the substitution method.

Solve the system by substitution:

Given equations: 6 = −4x + y and −5x − y = 21.

Step 1: From the first equation, isolate y: y = 4x + 6.

Step 2: Substitute y in the second equation: -5x - (4x + 6) = 21.

Step 3: Solve for x: -9x = 27, so x = -3.

Step 4: Substitute x back into the equation for y: y = 4(-3) + 6 = -6.

Solution: x = -3, y = -6.

Solve the system by the elimination method:

Given equations: 2x + y = 20 and 6x − 5y = 12.

Step 1: Multiply the first equation by 5, and the second by 1, to align coefficients of y.

Step 2: Add the modified equations to eliminate y: 10x + 5y + 6x - 5y = 100 + 12.

Step 3: Combine like terms and solve for x: 16x = 112, so x = 7.

Step 4: Substitute x back into one of the original equations to solve for y: 2(7) + y = 20, so y = 6.

Solution: x = 7, y = 6.

Answer:

unlikely

Step-by-step explanation:

there is less that a 50 % chance

Answer:

unlikely is the answer

Answer:

answer is 525.

Hopefully I could Help :)

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (7, 6) and (-7, -6). Substitute:

[tex]m=\dfrac{-6-6}{-7-7}=\dfrac{-12}{-14}=\dfrac{12}{14}=\dfrac{6}{7}[/tex]

Final answer:

The slope of the line passing through the points (7, 6) and (-7, -6) is 6/7, which is not reflected in the provided options, hinting at an error in the question or the answer choices.

Explanation:

To find the slope of the line passing through the points (7, 6) and (-7, -6), we use the slope formula, which is:

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

Substituting the given points into the formula gives us:

m = (-6 - 6) / (-7 - 7)

Which simplifies to:

m = (-12) / (-14)

And further simplifies to:

m = 6/7

However, this result is not among the provided options, which suggests there may have been an error in the question or in the options given. The correct slope calculated from the provided points is 6/7, not any of the options presented (A, B, C, D).

Answer:

(d)              

Step-by-step explanation:

Bond's par value = $500

market value of the bond = 88.754% * 500

                                           = 443.77

Commission rate charged by broker A = 3.1%

Commission of broker A = [tex]\frac{3.1}{100}[/tex]*443.77

                                        = $13.75687

Commission of broker B = $24

Difference between the commission of broker A and broker B = 24-13.756

                                                                                                      = $10.24

Hence, (d) Broker A's commission will be $10.24 less then Broker B's.

Answer:He should take the option one of sales commission of 3.1% on

each bond. If he takes the 2nd option, he is required to pay 24$ per

bond. But if he takes the ist option, he is required to pay 15.5$ per bond.

88.754 is the market rate. Total investment is of 500$. Multiply the commission

rate with the amount and you get 15.5 $. There is a difference of 8.5 dollars

between the two options.

The answer is D

Answer:

144 is the answer

Answer:

144

Step-by-step explanation:

Steps:

a times b = 3 times 4. That equals 12.

Then you put 12^2. 12 times 12 equals 144.

Answer: c[p(g)] = 0.896g

Step-by-step explanation:

Answer:

The correct answer is The graph of f(x) is horizontally stretched.

Step-by-step explanation:

We can tell it is horizontally stretched by the fact that there is a coefficient of less than 1 in the front.

We know that (-4, 6) isn't a vertex, because it is in vertex form. The vertex is the opposite of the number being added to x and the y value is the constant. Since the constant is -6, it is not a vertex.

The negative coefficient in the front makes it open down, so it doesn't open up.

The domain should be all real numbers as there is no number that cannot be put into the equation.

Answer:

B. c <_ 250

Step-by-step explanation:

NO MORE THAN 250 =  AT MOST 250 = less or greater than.

Answer:

A) 25.872

Step-by-step explanation:

A tip when multiplying numbers that are decimals, make the numbers whole numbers without decimals:

862.4 * 10 = 8624

0.03 * 100 = 3

8624 * 3 = 25,872

Then divide by the amount you multiplied the numbers by:

25,872 ÷(100 * 10) = 25.872

So your answer is A) 25.872

Answer:

25.872

Step-by-step explanation:

you just line up the desimals and do your regular multipication.

5±x[tex]\frac{-3}{√8}[/tex] is an irrational number because there's a radical in the denominator. It wouldn't result in a whole number. It would have to be rationalized or smth

Answer:

[tex] \dfrac{5^7}{2} = \dfrac{78125}{2} [/tex]

Step-by-step explanation:

[tex] \left( \dfrac{4}{5} \right)^2 \times 5^4 \times \left( \dfrac{2}{5} \right)^{-2} \div \left( \dfrac{5}{2} \right)^{-3} = [/tex]

[tex] = \dfrac{4^2}{5^2} \times 5^4 \times \dfrac{5^2}{2^2} \times \dfrac{5^3}{2^3} [/tex]

[tex] = \dfrac{(2^2)^2}{5^2} \times 5^4 \times \dfrac{5^2}{2^2} \times \dfrac{5^3}{2^3} [/tex]

[tex] = \dfrac{2^4}{5^2} \times 5^4 \times \dfrac{5^2}{2^2} \times \dfrac{5^3}{2^3} [/tex]

[tex] = 2^{4 - 2 - 3} \times 5^{- 2 + 4 + 2 + 3} [/tex]

[tex] = 2^{-1} \times 5^{7} [/tex]

[tex] = \dfrac{5^7}{2} [/tex]

[tex] = \dfrac{78125}{2} [/tex]

Answer: Choice A)

y + 3 = (2/3)(x - 5)

====================================================

Explanation:

Point slope form is

y - y1 = m(x - x1)

m = 2/3 is the given slope

(x1,y1) = (5,-3) is the point the line goes through

So we have

y - y1 = m(x - x1)

y - (-3) = (2/3)(x - 5)

y + 3 = (2/3)(x - 5)

Answer:

true

Step-by-step explanation:

The angle bisector and perpendicular bisector of a triangle are distinct concepts.

False: The angle bisector and perpendicular bisector of a triangle are distinct concepts.

The angle bisector of a triangle divides the opposite angle into two equal angles, while the perpendicular bisector of a segment is a line perpendicular to a segment at its midpoint.

It is possible for the angle bisector of a triangle and the perpendicular bisector of different segments within the triangle to coincide, but in general, they are not the same.

[tex]\text{Use}\ a^3-b^3=(a-b)(a^2+ab+b^2)\\\\27x^3-125=3^3x^3-5^3=(3x)^3-5^3=(3x-5)[(3x)^2+(3x)(5)+5^2]\\\\=\boxed{(3x-5)(9x^2+15x+25)}[/tex]

Answer:

The rate of change per year equals: (125.000-180000)/ 5= -11000

That means that the business loses 11000 $ each year

Step-by-step explanation:

Answer:

7 years

Step-by-step explanation:

Let x  be number of years the populations be equal

City A's population of 1115000 is decreasing at a rate of 15000 per year.

The population is decreasing at a constant rate so we use equation

y= mx + b

where m is the slope(rate), b is the initial population

m= -15000 (decreasing) , b= 1115000

y= -15000 x + 1115000

City B's population of 698000 is increasing at a rate of 45000 per year.

m= 45000 (increasing) , b= 698000

y= 45000 x + 698000

Now we set the equations equal and solve for x

45000 x + 698000 = -15000 x + 1115000

Add 15000 on both sides

60000 x + 698000 = 1115000

Subtract 689000 on both sides

60000 x = 417000

Divide by 60000 on both sides

x= 6.95

So after 7 years the population will be equal.

Final answer:

To find the number of years until the populations are equal, set up an equation based on the population change per year for both cities. Solve for the variable representing years, and round to the nearest whole number. The populations of City A and City B will be equal in approximately 7 years.

Explanation:

To solve for the number of years until the populations of City A and City B are equal, let's set up an equation. Begin with the populations at the starting point: City A has 1,115,000 residents and is losing 15,000 per year, while City B has 698,000 residents and is gaining 45,000 per year. Let x represent the number of years after which the populations will be equal.

For City A, the population after x years will be 1,115,000 - 15,000x. For City B, the population after x years will be 698,000 + 45,000x. Therefore, we can set up the following equation to find when they are equal:

1,115,000 - 15,000x = 698,000 + 45,000x

To solve for x, combine like terms and get all the x terms on one side:

1,115,000 - 698,000 = 45,000x + 15,000x

417,000 = 60,000x

Divide both sides by 60,000 to solve for x:

x = 417,000 / 60,000

x ≈ 6.95

Since we round to the nearest whole number, the populations will be equal in approximately 7 years.

Answer:

It will take Chris 13 weeks of allowance to save enough to buy the computer.

Step-by-step explanation:

Chris needs $858 to buy a computer.

She has already saved $575.

She gets $15 an hour for babysitting and will babysit 12 hours in the next month, then she will get for babysitting:

($15/hour)(12 hours)=$180

Then, Chris will need:

A=$858-$575-$180→A=$103

She can save &8 a week form her allowance, then she will need:

Number of weeks: n = $103 / ($8/week) → n=12.875 weeks

Rounding:

n=13 weeks

Chris will need 13 weeks of saving her allowance to have enough money to buy the computer.

Chris needs to save a total of $858 for a computer and has already saved $575.

To determine how many weeks she will need to save her allowance to purchase the computer, we must first calculate the additional amount she will earn from babysitting.

Chris earns $15 an hour for babysitting and will babysit for 12 hours in the next month, earning her an additional 15 x 12 = $180.

Adding this to her current savings of $575 gives us a total of $575 + $180 = $755.

The remaining amount needed to buy the computer is $858 - $755 = $103.

Since Chris saves $8 per week from her allowance, we divide the remaining amount by her weekly savings to find the number of weeks required: $103 / $8 = 12.875 weeks.

Since partial weeks of savings are not possible, we round up to the nearest whole number, which means Chris will need 13 weeks to save enough from her allowance to buy the computer.

Answer:

Mean: 57; Range: 19

Step-by-step explanation:

Answer:

The y coordinate is -3

Step-by-step explanation:

To find the midpoint, we use

midpoint = (x1+x2)/2, (y1+y2)/2

You only ask for the y coordinate.

y midpoint = (y1+y2)/2

y midpoint = (8+-14)/2

                 = -6/2

                   = -3

Answer:

-3

Step-by-step explanation:

usatestprep answer

Answer:

x=22

Step-by-step explanation:

1408/64

Answer:

22

Step-by-step explanation:

1,408/64

Answer:

She must sell $1,300 to make her goal.

Step-by-step explanation:

In order to find this you can create an equation in which x is the total number of sales she makes. Firstly, you know she gets 10% (or .1) of that number.

y = .1x

We also know that she works 10 hours at $7 per hour. That means we can add $70 to the end.

y = .1x + 70

Now we are looking to make $200, which means we can put 200 in for y and solve for the total amount of sales.

200 = .1x + 70

130 = .1x

1,300 = x

Final answer:

Michelle must generate at least $1300 in sales each week to achieve her weekly earnings goal of $200, given that she works 10 hours per week at an hourly wage of $7 and earns a 10% commission on sales.

Explanation:

To calculate the total sales Michelle must achieve to reach her goal of $200 per week when she earns $7 per hour and a 10% commission on the sale price of each item, we'll set up an inequality. Michelle wants to work only 10 hours each week.

Her earnings from the hourly wage are $7hour times 10 hours, which gives us $70. Now, let's say the total sales she needs to make are represented by x. Therefore, 10% of x represents her earnings from commission. Michelle's weekly earnings goal is $200, so we can write the inequality as:

Hourly earnings: $7*10 hours = $70

Commission earnings: 10% of x (0.10x)

Total earnings (hourly + commission): $70 + 0.10x [tex]\geq[/tex] $200

To find the total sales required, we solve the inequality for x:

$70 + 0.10x [tex]\geq[/tex]$200

0.10x [tex]\geq[/tex]$130

x  [tex]\geq[/tex] $1300

So Michelle must generate at least $1300 in sales to meet her weekly earnings goal of $200.