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3 years ago

Please help on test

Mathematics

1 answer:

dolphi86 [110]3 years ago

3 0

150 * 5/100=7.5

150+7.5=157.5$

145*7/100= 10.15

145+10.15= 155.15$

140*8/100= 11.2

140+11.2= 151.2$

135*9/100= 12.15

135+12.25= 147.15$

Purchase D is least Expensive. 147.15$

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Let R be the relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) ∈ R if and only if ad = bc. Ar

Veseljchak [2.6K]

Answer:

The given relation R is equivalence relation.

Step-by-step explanation:

Given that:

$((a, b), (c, d))\in R$

Where $R$ is the relation on the set of ordered pairs of positive integers.

To prove, a relation R to be equivalence relation we need to prove that the relation is reflexive, symmetric and transitive.

1. First of all, let us check reflexive property:

Reflexive property means:

$\forall a \in A \Rightarrow (a,a) \in R$

Here we need to prove:

$\forall (a, b) \in A \Rightarrow ((a,b), (a,b)) \in R$

As per the given relation:

$((a,b), (a,b) ) \Rightarrow ab =ab$ which is true.

$\therefore$ R is reflexive.

2. Now, let us check symmetric property:

Symmetric property means:

$\forall \{a,b\} \in A\ if\ (a,b) \in R \Rightarrow (b,a) \in R$

Here we need to prove:

$\forall {(a, b),(c,d)} \in A \ if\ ((a,b),(c,d)) \in R \Rightarrow ((c,d),(a,b)) \in R$

As per the given relation:

$((a,b),(c,d)) \in R$ means $ad = bc$

$((c,d),(a,b)) \in R$ means $cb = da\ or\ ad =bc$

Hence true.

$\therefore$ R is symmetric.

3. R to be transitive, we need to prove:

$if ((a,b),(c,d)),((c,d),(e,f)) \in R \Rightarrow ((a,b),(e,f)) \in R$

$((a,b),(c,d)) \in R$ means $ad = cb$ .... (1)

$((c,d), (e,f)) \in R$ means $fc = ed$ ...... (2)

To prove:

To be $((a,b), (e,f)) \in R$ we need to prove: $fa = be$

Multiply (1) with (2):

$adcf = bcde\\\Rightarrow fa = be$

So, R is transitive as well.

Hence proved that R is an equivalence relation.

8 0

3 years ago

Divers in a competition are scored by an international panel of judges. The highest and the lowest scores are dropped. The total

Luden [163]

Let

x--------> the degree of difficulty of the dive

we know that

1) The highest and the lowest scores are dropped

highest scores= $8.5$

lowest scores= $6.5$

the remaining scores= $[7.5, 8.0, 7.0, 7.5, 7.0]$

2) Find the total of the remaining scores

$=[7.5+8+7+7.5+7]\\ =37$

3) The total of the remaining scores is multiplied by the degree of difficulty of the dive

$37*x$

4) This product is multiplied by .6 to determine the final score

$[37*x]*0.6=77.7\\ 22.2*x=77.7\\ x=3.5$

therefore

the answer is

the degree of difficulty of the dive is $3.5$

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4 years ago

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3 years ago

HELP there due to tomorrow :/

Cerrena [4.2K]

Answer:

First Answer:

$15,060.

Second Answer:

9.96 miles.

Third Answer:

$3.27.

Step-by-step explanation:

First Question:

Cost of the rented car = 50 + 0.20 = $50.20

How much did Matt's family spend for the car:

1 mile = $50.20

300 miles = ?

300 × 50.20

= $15,060.

Second Question:

If Hayden spent $500 for her rented car, how many miles did she drive:

$50.20 = 1 mile

$500 = ?

500 ÷ 50.20 = 9.96 miles.

Third Question:

What is the cost per gallon of gas:

24 gallons = $78.48

1 gallon = ?

78.48 ÷ 24 = $3.27.

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3 years ago

A 3.5 ft by 5.5 ft mirror is placed in a wooden frame. What is the area of the frame

Alborosie

Answer:

19.25ft

Step-by-step explanation:

area = length x width so 3.5 x 5.5 = 19.25

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