Find the minimum value of
C = 4x + 3y
Subject to the following constraints:
x 20
y20
2x + 3y > 6
3x – 2y = 9
x + 5y = 20

Answer:

A system of equations that allows you to solve for how many bags of each candy Oscar bought is [tex]16x+8(x+5)=400[/tex] and The number of bags of lemon drops and number of bags of beans are 15 and 20 respectively

Step-by-step explanation:

Let x be the number of bags of lemon drops

We are given that The number of bags of beans was 5 more than the number of bags of lemon drops

So, The number of bags of beans =x+5

Jelly bean bags weigh 8 ounces, and drop bags weigh 16 ounces each.

So, Weight of x bags of lemon drops = 16x

So, Weight of (x+5) bags of lemon drops = 8(x+5)

The total weight of all the bags of candy was 400 ounces.

So, [tex]16x+8(x+5)=400[/tex]

[tex]16x+8x+40=400[/tex]

[tex]24x+40=400[/tex]

[tex]24x=360[/tex]

[tex]x=\frac{360}{24}[/tex]

x= 15

The number of bags of lemon drops are 15

The number of bags of beans =x+5 =15+5=20

Hence a system of equations that allows you to solve for how many bags of each candy Oscar bought is [tex]16x+8(x+5)=400[/tex] and The number of bags of lemon drops and number of bags of beans are 15 and 20 respectively

Answer: 37

Step-by-step explanation:

Let X represents the score for the eighth test

Hence ( 29+36+32+38+35+34+39+X ) ÷8 =35

243+X /8 =35

243+X =35×8

243+X=280

X = 280-243

X= 37

Answer:

The measure of the arc is 160 degrees

Step-by-step explanation:

The picture of the question in the attached figure

we know that

The measure of the external angle is the semi-difference of the arches it covers.

so

[tex]20^o=\frac{1}{2}[(360-x)^o-x^o][/tex]

solve for x

[tex]40^o=360^o-2x[/tex]

[tex]2x=360^o-40^o\\2x=320^o\\x=160^o[/tex]

The arc measure that the satellite can see is 20°.

An arc measure is the central angle that corresponds to a given arc on a circle. In this case, the satellite views the earth at an angle of 20°. The arc measure that the satellite can see is also 20°.

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Answer:

9

Step-by-step explanation:

because 3+6=9 so he is 9 miles from his starting point

Answer: 30 min.

Step-by-step explanation: for this, you have to find the gcf of 5 and 6, which is 30.

Final answer:

Mike and Sam will both cross the starting line together after 30 minutes of running, as 30 minutes is the least common multiple of their individual lap times of 5 and 6 minutes.

Explanation:

To find out how long it will take for Mike and Sam to cross the starting line together again, we need to determine the least common multiple (LCM) of their lap times. Mike runs a lap in 5 minutes and Sam runs a lap in 6 minutes. The LCM of 5 and 6 will give us the first time they both cross the starting line at the same time after they start running.

To calculate the LCM of 5 and 6, we list the multiples of each number until we find a common one:

5, 10, 15, 20, 25, 30, ...

6, 12, 18, 24, 30, ...

The smallest common multiple of 5 and 6 is 30. Therefore, Mike and Sam will both cross the starting line together after 30 minutes of running.

The cost of one hot dog is $1.75

The cost of one hamburger is $1.5

Step-by-step explanation:

Let,

The equations can be formed as :

7x + 4y = 18.25  --------(1)

4x + 7y = 17.50  --------(2)

Multiply eq (1) by 4 and eq (2) by 7,

   28x + 16y = 73

- (28x + 49y = 122.5)

         - 33y = - 49.5

y = 49.5/33

y = 1.5

The cost of one hamburger is $1.5

Substitute y=1.5 in eq (1),

7x + 4(1.5) = 18.25

7x = 18.25 - 6

x = 12.25/7

x = 1.75

The cost of one hot dog is $1.75

Answer:

  the number of cookies ordered

Step-by-step explanation:

When an equation is written in the form ...

  (left variable) = (some expression involving one or more right variables)

we usually describe the "left variable" as the "dependent variable" and the "one or more right variables" as the "independent variable(s)".

Here, the equation is given as ...

  C = 3s + 30

__

This tells you C is the dependent variable, and s is the independent variable. The description also says "C is the number of cookies." Since you know that the dependent variable is the number of cookies, you can answer the question ...

  the dependent quantity is the number of cookies ordered.  (matches the first choice)

Answer:

x = -4/3

Step-by-step explanation:

Step 1:  Distribute

3(5x + 8) = 4(6x + 9)

15x + 24 = 24x + 36

Step 2:  Subtract 15x from both sides

15x + 24 - 15x = 24x + 36 - 15x

24 = 9x + 36

Step 3:  Subtract 36 from both sides

24 - 36 = 9x + 36 - 36

-12 = 9x

Step 4:  Divide both sides by 9

-12 / 9 = 9x / 9

-4/3 = x

Answer:  x = -4/3

Answer:

Here the degree of the polynomial is 11.

Step-by-step explanation:

To find the degree of the multivariate polynomials, we need to add up the powers of all the variables.   So the total degree is given by the sum of all the powers of the highest powers terms.

Now in the given polynomial [tex]-3w+x^6y^5-2+5y^4w^3x^2[/tex]

the term with the highest total powers is [tex]x^6y^5[/tex] and thus the total power is 6+5=11.

And hence the degree of this polynomial is 11.

Answer:

24

Step-by-step explanation:

5x/6=20

Multiple 20 by 6 then you get 120.

Then divide 120 by 5 which is 24.

Answer:

x = 24

Step-by-step explanation:

Simplify both sides of the equation, then isolate the variable.

Answer: charlene:52, aaron:44

Step-by-step explanation:

Add 8 to aarons age and you find your answer

Answer:

Aaron is 18 years old

Charlene is 26 years old

Step-by-step explanation:

Aaron = A

Charlene = 8 + A

Aaron + Charlene = 44

Substitute

A + 8 + A = 44

Simplify

2A + 8 = 44

Subtract 8 from both sides of the equation

2A = 36

Divide by 2

A = 18

C = 26

Hope this was useful to you!

Answer:

In 18 years time, the population of the city is approximately 705,084

Step-by-step explanation:

From the given information, the initial population is

[tex]P_0=200000[/tex]

The growth rate is 7% or r=0.07.

For a population with a continuous growth rate, the equation is that models it is:

[tex]P(t)=P_0 {(e)}^{rt} [/tex]

[tex]P(t)=200000 {(e)}^{0.07t} [/tex]

To find the find the population after 18 years, we substitute t=18 into:

[tex]P(18) = 200000{(e)}^{18\times 0.07} [/tex]

[tex]P(18)=705084.3[/tex]

Answer:

x=3

Step-by-step explanation:

[tex]5^{x} = 125\\5^{x} = 5^{3} \\x=3[/tex]

Answer: 5 raised to power of 3

Step-by-step explanation:

5×5×5=125

Answer:

9

Step-by-step explanation:

32

-5

----

27

÷3

----

9

Hope it helped

There are 9 invitations mail that has already been mailed.

A fraction is a quantity that is not a whole number. In maths, a fraction usually has a numerator and a denominator.

Lee is sending out 32 birthday invites she gives 5 to family and a third of the rest,

The number of invitations Leah has already mailed is given by;

Number of invitations mailed = 1/3 x (total invitation - invitation mom delivered)

Number of invitations mailed =1/3 x (32 - 5)

Number of invitations mailed =1/3 x (27)

Number of invitations mailed = 9

Hence, there are 9 invitations mail that has already been mailed.

Learn more about fractions here;

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Answer:

See attachment

Step-by-step explanation:

To graph

[tex]y \: < \: \frac{1}{4} x[/tex]

You first graph the boundary line

[tex]y = \frac{1}{4} x[/tex]

This is a dashed line going through the origin with slope 1/4.

We test the point (0,1) to get: 1<0 which is false. So we shade the lower half-plane.

To graph

[tex]y \: < \: - 6x + 6[/tex]

We first graph line

[tex]y = - 6x + 6[/tex]

By plotting (0,6), and (1,0)

We draw a dashed boundary line.

We test the origin:

0<6 which is true so we shade the left half-plane .

The intersection of both shaded regions represent the solution set.

The graph us shown in attachment.

Its C if you are estimating. But there is no other exact answer.

Answer:

Question 5.

89.10

Question 6.

Yes, Lucy will have enough money.

Step-by-step explanation:

Question 5.

3*4*9=108

108/2=54

54*1.65=89.10

Question 6.

26*5=130

They will make $130 from fundraising. $89.10 are needed to purchase the soil. 130>89.1

Answer:

D

Step-by-step explanation:

that what I think but not sure

Answer:

D

Step-by-step explanation:

It is D because A would be 8:13, B would also be 8:13, and C would be 13:21. Also, we know that D is correct because for every 13 passes, Harrison catches 8 which is 13 to 8 or 13:8.

Answer:

755*17 cents=12835 cents= 128.35$

Step-by-step explanation:

Margit's piecework pay is calculated by multiplying the number of units she produced (755 units) by the pay she receives per unit (17 cents). Therefore, her piecework pay was $128.35 for last week.

To find out Margit's piecework pay, we need to multiply the number of units she produced by the pay she receives per unit. In this case, Margit produced 755 units and she earns 17 cents per unit. So, her piecework pay is calculated as follows: 755 units * $0.17/unit.

Therefore, Margit's piecework pay for last week was $128.35.

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Answer:

[tex]8^2[/tex]

Step-by-step explanation:

Step 1:  Convert words into an expression

What’s the algebraic expression for 8 squared

8 squared -> [tex]8^2[/tex]

Answer:  [tex]8^2[/tex]

If needed, solve:

[tex]8^2[/tex]

8 * 8

64

Answer:

Step-by-step explanation:

Order is impotant since you could easily make a positve number negative and vice versa. You switch the order of 5 subtracted by y to y-5.

Answer:

a) 2/3

b)[tex]y = \frac{2}{3} x + 5[/tex]

Step-by-step explanation:

b) From my previous answer...

Since parallel lines have the same gradient,

the gradient of the line is 2/3 too.

Thus, m= 2/3.

y= 2/3x +c

Now substitute a coordinate into the equation to find c, the y-intercept.

When x=6, y=9,

9= (2/3)(6) +c

9= 4 +c

c= 9 -4

c= 5

Thus the equation of the line is y= 2/3x +5.

Time that will be taken at speed of 45 miles/hr is 1.8 hrs

Step-by-step explanation:

Distance = Speed × Time

               = 54 × 1.5 = 81 miles

TIme = Distance/Speed

        = 81/45 = 1.8 hrs

Answer:

The generalization will be biased because people living in cities that are not as big as New York, Los Angeles and rural areas of the country were excluded from the possibility of being included in the sample.

Step-by-step explanation:

The sample is therefore not a true representation of the population.

Final answer:

The generalization would be biased because it only includes opinions from large cities, which aren't representative of the entire population, leading to sampling bias. This results in a biased sample as it overlooks the diversity in lifestyles and circumstances found in different geographic areas.

Explanation:

If a company conducts a survey among people who only live in large cities like New York and Los Angeles, and then makes a generalization from this survey, the generalization will be biased. This is because the perspectives of people living in large cities are not necessarily representative of the entire population, which includes people from smaller towns, rural areas, and different socioeconomic backgrounds. Such a sampling method leads to a sampling bias, since it does not adequately reflect the diversity of the whole population.

For instance, urban populations may have different lifestyles, access to services, and daily challenges compared to those living in suburban or rural areas. Therefore, if a survey's findings from a city population are applied to the general population, it may result in an inaccurate picture of the opinions, behaviors, or characteristics of the entire population. This exemplifies a biased sample, as the sampling method does not capture the full range of variables affecting the population as a whole.

Answer:

26.25

Step-by-step explanation:

Answer:

Part 1) Vertical line : [tex]x=1[/tex]

Part 2) Horizontal line :  [tex]y=-4[/tex]

Step-by-step explanation:

Part 1) Write the equation for the vertical line passing through the point (1,-4)

we know that

The equation of a vertical line (parallel to the y-axis) is equal to the x-coordinate of the point that passes through it

so

The x-coordinate is 1

therefore

The equation of the line is

[tex]x=1[/tex]

Part 2) Write the equation for the horizontal line passing through the point (1,-4)

we know that

The equation of a horizontal line (parallel to the x-axis) is equal to the y-coordinate of the point that passes through it

so

The y-coordinate is -4

therefore

The equation of the line is

[tex]y=-4[/tex]

the surface area of the equilateral triangular pyramid is approximately 21.03 square inches.

Let's calculate the surface area of the pyramid.

The lateral area of the pyramid, which is the sum of the areas of the three triangular faces, can be calculated using the formula:

[tex]\[ LA = \frac{1}{2} \times \text{perimeter of the base} \times \text{slant height} \][/tex]

We've already determined the perimeter of the base is 4.8 inches and the slant height is 8.3  inches. Substituting these values:

[tex]\[ LA = \frac{1}{2} \times 4.8 \times 8.3 = 19.92 \text{ square inches} \][/tex]

However, this only gives us the lateral area. To find the total surface area, we need to add the area of the base. Since it's an equilateral triangle, we can use the area formula for equilateral triangles:

[tex]\[ A_{\text{base}} = \frac{\sqrt{3}}{4} \times (\text{side length})^2 \][/tex]

The side length is [tex]\( \frac{4.8}{3} = 1.6 \)[/tex] inches, so:

[tex]\[ A_{\text{base}} = \frac{\sqrt{3}}{4} \times (1.6)^2 = \frac{\sqrt{3}}{4} \times 2.56 \approx 1.1084 \text{ square inches} \][/tex]

The total surface area is then the sum of the lateral area and the area of the base:

[tex]\[ SA = LA + A_{\text{base}} = 19.92 + 1.1084 = 21.0284 \text{ square inches} \][/tex]

Thus, the surface area of the equilateral triangular pyramid is approximately 21.03 square inches.

The question probable maybe:

An equilateral triangular pyramid has a slant height of 8.3 inches. The triangular base has a perimeter of 4.8 inches and an area of 1.1084 square inches. Find the surface area of the pyramid.

Answer:

Step-by-step explanation:

Maria:

No. of cans in a pack = 6

No.of cans in 17 pack = 6 * 17 = 102 cans

No. of cans bought by Heather = 9 cans

Total cans = 102 + 9 = 111 cans