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marissa [1.9K]
2 years ago
3

The Johnson family is going to build a new home. They need to have working drawings of their house plans created by a design fir

m. They will choose between Rock the House Digital Designs and Elegant Home Architects. Rock the House Digital Designs charges $500.00 for the initial consultation with the Johnson family, plus $50.00 for every additional hour of work for the house plans. Elegant Home Architects charge $75.00 per hour for the house plans. Let ℎ represent the number of hours for which the Johnson family hires the design firm. Which of the following statements are true? Select all that apply.The Johnson family is going to build a new home. They need to have working drawings of their house plans created by a design firm. They will choose between Rock the House Digital Designs and Elegant Home Architects. Rock the House Digital Designs charges $500.00 for the initial consultation with the Johnson family, plus $50.00 for every additional hour of work for the house plans. Elegant Home Architects charge $75.00 per hour for the house plans. Let ℎ represent the number of hours for which the Johnson family hires the design firm. Which of the following statements are true? Select all that apply. -The expression 50ℎ represents the total charge for Rock the House Digital Designs. -The expression 75ℎ represents the total charge for Elegance Home Architects. -The cost for using Rock the House Digital Designs for an initial consultation only is $550. -If the Johnson family hires the design firm for 15 hours, then Elegance Home Architects will be cheaper. -If the Johnson family hires the design firm for 40 hours, then Rock the House Digital Designs will be cheaper.
Mathematics
1 answer:
Ray Of Light [21]2 years ago
3 0

Answer:

The expression 75ℎ represents the total charge for Elegance Home Architects.

If the Johnson family hires the design firm for 15 hours, then Elegance Home Architects will be cheaper.

If the Johnson family hires the design firm for 40 hours, then Rock the House Digital Designs will be cheaper.

Step-by-step explanation:

Given the following :

Rock the house digital designs :

Initial consultation charge = $500

Additional hour of work for house plan = $50 /hr

Elegant Home Architect:

Charge = $75 / hr

h = number of hours fro which Johnson's family hires the design firm

Total amount charged by Elegant home Architect = 75 × h = 75h

Total amount charged by Rock the house digital design = (500 + 50h)

If h = 15 hours :

Total amount charged by Elegant home Architect = 75 × 15 = $1,125

Total amount charged by Rock the house digital design = (500 + 50(15)) = 500 + 750 = $1,250

Hence, Elegant home Architect is cheaper.

If h = 40 hours :

Total amount charged by Elegant home Architect = 75 × 40 = $3,000

Total amount charged by Rock the house digital design = (500 + 50(40)) = 500 + 2000 = $2,500

Hence, Rock the house digital design is cheaper.

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Addition and substitution properties of equality*

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* The addition property says if A=B, then A+C=B+C. The substitution property further says if C=D, then A+C=B+D (D can be substituted for C). IMO, both properties are needed together to get from A=B and C=D to A+B=C+D.

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2 years ago
Nancy was laid off and applied for unemployment benefits in July. In her state, the weekly unemployment benefit is 55% of the ​2
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$277.91

Step-by-step explanation:

"The ​26-week average of the two highest salaried quarters of the year leading to her application" would be the average of $13,500 and $12,775, or

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2 years ago
Triangle XYZ has vertices X(–1, –1), Y(–2, 1), and Z(1, 2). What is the approximate measure of angle Z?
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Read 2 more answers
Find the value of sin100.sin120.sin140.sin160​
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The value of sin100.sin120.sin140.sin160 is 0.1875

Step-by-step explanation:

To find the value of sin100.sin120.sin140.sin160, let us find the value of each angle.

The value of sin100=0.9848

The value of sin120=\frac{\sqrt{3} }{2}

The value of sin140=0.6428

The value of sin160=0.3420

Substituting the values of sin, we get,

sin100.sin120.sin140.sin160=0.9848*\frac{\sqrt{3} }{2} *0.6428*0.3420

Multiplying the values of sin, we get,

sin100.sin120.sin140.sin160=0.1875

Thus, the value of sin100.sin120.sin140.sin160 is 0.1875

8 0
2 years ago
A high percentage of people who fracture or dislocate a bone see a doctor for that condition. Suppose the percentage is 99%. Con
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Answer:

(i) 0.15708

(ii) 0.432488

(iii) 3

Step-by-step explanation:

Given that, 99% of people who fracture or dislocate a bone see a doctor for that condition.

There is only two chance either the person having fracture or dislocation of bone will either see the doctor or not.

As per previous data, if one person got a fracture or dislocation of bone, the chance of seeing the doctor is 0.99. Assuming this chance is the same for every individual, so the total number of people having fractured or dislocated a bone can be considered as Bernoulli's population.

Let p be the probability of success represented by the chances of not seeing a doctor by any one individual having fractured or dislocated a bone.

So, p=1-0.99=0.01

According to Bernoulli's theorem, the probability of exactly r success among the total of n randomly selected from Bernoulli's population is

P(r)=\binom{n}{r}p^r(1-p)^{n-r}\cdots(i)

(i) The total number of persons randomly selected, n=400.

The probability that exactly 5 of them did not see a doctor

So, r=5 , p=0.01

Using equation (i),

P(r=5)=\binom{400}{5}(0.01)^5(1-0.01)^{400-5}

=\frac{400!}{(400-5)!\times 5!}(0.01)^5(0.99)^{395}

=0.15708

(ii) The probability that fewer than four of them did not see a doctor

=P(r

=P(r=0)+P(r=1)+P(r=2)+P(r=3)

=\binom{400}{0}(0.01)^0(0.99)^{400}+\binom{400}{1}(0.01)^1(0.99)^{399}+\binom{400}{2}(0.01)^2(0.99)^{398}+\binom{400}{3}(0.01)^3(0.99)^{397}

=0.017951+0.072527+0.146154+0.195856

=0.432488

(iii) The expected number of people who would not see a doctor

=np

=300\times 0.01

=3

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2 years ago
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