The Greens are moving. Their real estate agent located 79 houses listed for sale in their price range. Of those bouses listed for sale: 49 had a finished basement. 56 had a three car garage. 37 had a finished basement. How many had a finished bsement but not a three car garage?

Answer:

Step-by-step explanation:

A housing contractor has subdivided a farm into 100 building lots. She has designed two types of homes for these lots: colonial and ranch style. A colonial requires $30,000 of capital and produces a profit of $2000 when sold. A ranch-style house requires $40,000 of capital and provides an $8000 profit. If the contractor has $3.2 million of capital on hand, how many houses of each type should she build for maximum profit?

? colonials

? ranches

For maximum profit, the contractor should build 80 colonial houses and 20 ranch-style houses. The maximum profit achievable is $740,000.

Let x be the number of colonial houses built.

Let y be the number of ranch-style houses built.

Now, we can set up the objective function, which represents the total profit:

Total Profit (P) = 3000x + 7000y

The total cost of the houses built cannot exceed the available capital, which is $3.8 million (or $3,800,000):

30,000x + 40,000y ≤ 3,800,000

The number of building lots used cannot exceed the total number of lots available, which is 100:

x + y ≤ 100

Also, we need to consider that the number of houses (x and y) must be non-negative:

x ≥ 0

y ≥ 0

Now, we have the linear programming model with the objective function and constraints.

We need to find the values of x and y that maximize the total profit (P).

Graph the feasible region determined by the constraints (x + y ≤ 100, x ≥ 0, y ≥ 0, 30,000x + 40,000y ≤ 3,800,000), and then evaluate the objective function (P = 3000x + 7000y) at each corner point of the feasible region to find the maximum profit.

The feasible region is a polygon with vertices at the following points:

(0, 0)

(0, 95) (Intersection of x = 0 and y = 95)

(80, 20) (Intersection of x = 80 and y = 20)

(100, 0) (Intersection of x = 100 and y = 0)

Now, evaluate the objective function (P) at each corner point:

(0, 0): P = 0

(0, 95): P = 665,000

(80, 20): P =  740,000

(100, 0): P = 300,000

The maximum profit of $740,000 occurs when the contractor builds 80 colonial houses and 20 ranch-style houses

Hence, for maximum profit, the contractor should build 80 colonial houses and 20 ranch-style houses.

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Answer:

[tex]\huge\boxed{\overrightarrow{u}-\overrightarrow{v}=\left<-10;\ -3\right>}[/tex]

Step-by-step explanation:

[tex]\overrightarrow{u}=\left<-8;\ 4\right>;\ \overrightarrow{v}=\left<2;\ 7\right>\\\\\overrightarrow{u}-\overrightarrow{v}=\left<-8;\ 4\right>-\left<2;\ 7\right>=\left<-8-2;\ 4-7\right>=\left<-10;\ -3\right>[/tex]

Answer:

Step-by-step explanation:

-u-v = 6,-11

u-v = -10,-3

v-u = 10,3

Answer:

83  

I know because I did this problem a few years ago

Answer:

48 pieces

Step-by-step explanation:

20÷5/12=20*12/5=240/5=48

Answer:

$1,094.93

Step-by-step explanation:

The income is how much money you make. You lose the money you spend. To find how much money you have left, just subtract the income with everything you spent.

This means the final answer is: 2725.98 - (1250.00 + 325.78 + 55.27) = $1,094.93

Based on the information the number of people that will there after 20 years is: d.)  2.97 million.

Using this formula

P(t) = Population ×(1+ rate)^t

Where:

Population=2 million

rate=2%

time=20 years

Let plug in the formula

P(t) = 2×(1+.02)^20

P(t) = 2×(1.02)^20

P(t) = 2×1.485947

P(t) = 2.97 million

Inconclusion the number of people that will there after 20 years is: d.)  2.97 million.

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The vertical shift of the function [tex]f(x) = 9|x + 1| + 2[/tex] is 2 units up

The absolute function is given as:

[tex]f(x) = 9|x + 1| + 2[/tex]

An absolute function is represented as:

[tex]f(x) = a|x - h| + k[/tex]

Where k represents the vertical shift.

By comparison, the value of k is:

[tex]k = 2[/tex]

This means that the vertical shift is 2 units

Hence, the vertical shift of the function [tex]f(x) = 9|x + 1| + 2[/tex] is 2 units up

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Answer:

37/8

Step-by-step explanation:

5/8+32/8

5+32/8

37/8

Answer:

first one is f(x)=-5

second one is f(x)=7

third one is x=-3

4th one is x=0

5th one is f(x)=1

6th one is x=-4

Step-by-step explanation:

first one. plug in x as -2:

f(x)=2*-2-1=-4-1=-5

second one is the same way:

f(x)=4*2-1=8-1=7

third one is a different one:

2x-1=-7

2x=-6

x=-3

4th one is the same way:

2x-1=-1

2x=0

x=0

5th way is the same thing as previous:

f(x)=2*1-1=2-1=1

Finally, the 6th one is the same thing as the 4th one:

2x-1=-9

2x=-8

x=-4

Done!

this makes no sense so maybe  try something better

Answer:37.5 hrs

Step-by-step explanation:

15/4 = 3.75

3.75*10=37.5

The answer is 37.5 hours

Answer:

|-5| is greater than |-2|

Step-by-step explanation:

the absolute value of -5, is 5, which is greater than the absolute value of -2, which is 2. Have a wonderful rest of your day! I hope this helps!

Step-by-step explanation:

equate the two equations

Answer:

18; 36

Step-by-step explanation:

If there's 9 rows of "onion, onion, garlic, flower", then you repeat this cycle 9 times.

onion, onion, garlic, flower(1)

onion, onion, garlic, flower(2)

onion, onion, garlic, flower(3)

onion, onion, garlic, flower(4)

onion, onion, garlic, flower(5)

onion, onion, garlic, flower(6)

onion, onion, garlic, flower(7)

onion, onion, garlic, flower(8)

onion, onion, garlic, flower(9)

Add up the garlic and flower bulbs, which equals 18. Then add up all of the bulbs, which is 36.

-hope it helps

Step-by-step explanation:

there is no mathematical problem to solve.

just follow the instructions as given.

this is an exercise for you to get a feeling about what is what. it is imperative that you do it.

there is really nothing to solve.

remember, that a positive slope means the line goes up (from left to right), and a negative slope means the line goes down (again from left to right).

and I am sure you know what vertical and horizontal means.

Step-by-step explanation:

3/4 ÷ 3

recall that the inverse of division is multiplication

=3/4 x 1/3

=1/4

Answer:

Melanie and 2 times ½ a mile

Hopes This helps

Answer:

I think its A ratio reduced, since a scale factor is the ratio of the length of a side of one figure to the length of the corresponding side of the other figure.

Answer:

It isn't either of the first two. My best guess would be the units of a ratio, (sorry if it's actually a ratio reduced). It's worded very weirdly

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

Explanation:

Recall that y = mx+b is the slope intercept form of any linear equation

The given equation has m = 4/5 as the slope. Flip the fraction to get 5/4 and then flip the sign to get -5/4

The original slope is 4/5 and the perpendicular slope is -5/4. Note how the slopes multiply to -1.

The slope for the answer is -5/4 and the y intercept for the answer is -8

Therefore, the perpendicular line is y = (-5/4)x - 8

Answer:

112 in.³

Step-by-step explanation:

This box is a combination of two rectangular prisms:

bottom - 9 in. by 2 in. by 4 in.

top - 5 in. by 2 in. by 4 in.

total volume = 9 in. × 2 in. × 4 in. + 5 in. × 2 in. × 4 in.

total volume = 112 in.³

Answer:

its 112

Step-by-step explanation:

first see how it looks like 2 boxes on top of each other, break it into major parts then multiply depth by wighth by highth

Answer:

[tex]y=x+7[/tex]

Step-by-step explanation:

Let's simply rearrange bringing y to the RHS, -7 to the LHS and reading right to left:

[tex]x+7=y \rightarrow y=x+7[/tex]

Answer:17/23

Step-by-step explanation:

Answer:  17/40 of the students are girls.

Step-by-step explanation:

First, to find the number of girls in the class, we can subtract the number of boys (23) from the total number of students (40) to get:

40 - 23 = 17

There are 17 girls in the class.

Finally, to get the fraction of the girl students of the class, we can divide the number of girls (17) by the total number of students (40) to get:

17 ÷ 40 = [tex]\frac{17}{40}[/tex]

Since the fraction [tex]\frac{17}{40}[/tex] is already simplified, the final answer comes out to be [tex]\frac{17}{40}[/tex].

The balloon’s vertical distance above the ground is 556 feet

The set up will form a right triangle.

Given the following parameters

To get the height above the ground, we will use the SOH CAH TOA identity as shown;

Opposite = h

Adjacent = 1004 feet

Tan theta = h/1004

Tan 29 = h/1004

h = 1004 tan 29

h = 1004(0.5543)

h = 556.52 feet

Hence the balloon’s vertical distance above the ground is 556 feet

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Answer:

It's not possible to answer precisely. About 1/5 of 109,500,000 is equal to about 109,500,000*.2 which is about 21,900,000.

Step-by-step explanation:

The first thing to note is that the amount of yellow M&Ms isn't precisely 1/5th. It's about 1/5th.

So, applying the math, 109,500,000 times 1 and divided by 5 = 21,900,000, but that's not the answer, because of the uncertainty.

The answer has to be "about 21,900,000."

Answer: negative 2 arrow to the left

Step-by-step explanation:

Answer:

Every positive integer can be written as the sum of three palindromes, numbers that remain the same when their digits are reverse. For example, 389 = 11 + 55 + 323. This holds not just for base 10 but for any base b ≥ 5.