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2 years ago

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A developer of a new subdivision wants to build homes that are all different. there are three different interior plans that can

be combined with any of five different home exteriors. how many different homes can be built?

1 answer:

ad-work [718]2 years ago

4 0

Let $I_1, I_2, I_3$ to be interior plans and $E_1, E_2, E_3, E_4, E_5$ to be <span>interior plans.
</span>
For each interior plan a develepor has 5 choices of exterior plan that is together 15 possibilities.
(see the attached file for possibility tree)
Answer: 15 different houses.

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A rectangular prism must have a base with an area of no more than 27 square meters. The width of the base must be 9 meters less

den301095 [7]

Answer:

The maximum height of the prism is $12\ m$

Step-by-step explanation:

Let

x------> the height of the prism

we know that

the area of the rectangular base of the prism is equal to

$A=L*W$

$A\leq 27\ m^{2}$

so

$L*W\leq 27$ -------> inequality A

$W=x-9$ ------> equation B

$L=W+6$ -----> equation C

Substitute equation B in equation C

$L=(x-9)+6$

$L=x-3$ ------> equation D

Substitute equation B and equation D in the inequality A

$(x-3)*(x-9)\leq 27$ -------> using a graphing tool to solve the inequality

The solution for x is the interval----------> $[0,12]$

see the attached figure

but remember that

The width of the base must be $9$ meters less than the height of the prism

so

the solution for x is the interval ------> $(9,12]$

The maximum height of the prism is $12\ m$

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2 years ago

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What is the smallest positive prime factor of 2017^2019 +2019^2017

kogti [31]

Answer:

17

Step-by-step explanation:

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A sports company wants to package a ball with a 1.5-inch radius in sets of two. They have two options: a cylinder or a square pr

guajiro [1.7K]

Step 1

Find the Volume of the two balls

we know that

the Volume of a sphere is equal to

$V=\frac{4}{3} \pi r^{3}$

In this problem we have

$r=1.5\ in$

Substitute

$V=\frac{4}{3} \pi 1.5^{3}=4.5\pi\ in^{3}$

so

the volume of the two balls is equal

$V=2*4.5\pi=9 \pi\ in^{3}$

Step 2

Find the volume of a cylinder

we know that

The Volume of a cylinder is equal to

$V=\pi r^{2}h$

In this problem we have

$r=1.5\ in$

$h=4*r=4*1.5=6\ in$

Substitute

$V=\pi (1.5^{2})(6)=13.5 \pi\ in^{3}$

Step 3

Find the amount of wasted space in the cylinder

Subtract the volume of the two balls from the volume of the cylinder

$13.5\pi\ in^{3}-9\pi\ in^{3}=4.5\pi\ in^{3}=14.14\ in^{3}$

Step 4

Find the volume of the square prism

The volume of the prism is equal to

$V=Bh$

where

B is the area of the base of the prism

h is the height of the prism

In this problem we have

$B=(2*1.5)^{2}=9\ in^{2}$ -----> the base is equal to the diameter

$h=4*r=4*1.5=6\ in$

Substitute

$V=9*6=54\ in^{3}$

Step 5

Find the amount of wasted space in the prism

Subtract the volume of the two balls from the volume of the prism

$54\ in^{3}-9\pi\ in^{3}=25.73\ in^{3}$

Step 6

Compare the amount of wasted space

the amount of wasted space in the cylinder is $14.14\ in^{3}$

the amount of wasted space in the prism is $25.73\ in^{3}$

Find the difference

$25.73\ in^{3}-14.14\ in^{3}=11.59\ in^{3}=11.6\ in^{3}$

The package that has the least amount of wasted space is the cylinder

therefore

<u>the answer is the option</u>

the cylinder because it has approximately 11.6 in.3 less wasted space than the prism

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"If you switch to the late shift, you will receive a 10% wage increase." Great! I make $12.00 per hour now, and that extra 10% w

maxonik [38]

Answer:

$13.20/hr

Step-by-step explanation:

A 10% wage increase would amount to 0.10($12) = $1.20. Adding this increase to the starting rate $12/hr results in $13.20/ hr.

A faster way in which to do this is shown below:

Wages after a 10% increase = (1.10)($12/hr) = $13.20/hr

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2 years ago

arleen has a gift card for a local lawn and garden store. she uses the gift card to rent a roller for 4 days. it cost $17 per da

kaheart [24]

Answer:

We use negative values for the money Arleen spends.

a) We determine the change to the value on her gift card:

4(-35)+(-9)= -140+(-9)=-149

b) We determine the amount on money she has left on the gift card after renting the tiller and buying the rake:

200+(-149)=51

Since she has got $51 on her gift card and a wheelbarrow is $50 she is able to buy it:

51>50

RESULT

a) -$149 less b) yes

Step-by-step explanation:

7 0

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