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a survey was taken of 400 shoppers. the shoppers were asked about purchases they had made within the past 30 days. they were asked whether they had made their purchases at a big-box store, a locally-owned store, and/or an online store.

how many shoppers made a purchase at an online store, a locally-owned store, and a big-box store?

a. 377
b. 18
c. 127
d. 109

Shoppers that made a purchase at an online store, a locally-owned store, and a big-box store is 18 shoppers.

Given Information:

n(A ∩ B)=Shoppers who purchased at an online store and at a locally-owned store.

n(B ∩ C)=Shoppers who purchased at a locally-owned store and at a big-box store.

n(C ∩ A)=Shoppers who purchased at an online store and at a locally-owned store and at an online store.

From Studying the Venn diagram,

n(A) = 109

n(B) = 34

n(C) =  107

n(B∩ C) = 38

n(A ∩ C) = 17

n(C ∩ A) = 57

On Comparing the Venn Diagrams, we could find that  shoppers made a purchase at an online store, a locally-owned store, and a big-box store [n( A ∩ B∩ C)] = 18

Learn more about Venn Diagram:

link

Option B) 18 is the correct answer.

Step-by-step explanation:

Let n(A) be the shoppers who purchased at an online store

Let n(B)  be the shoppers who purchased at a locally-owned store

Let n(C)  be the shoppers who purchased at  a big-box store

n(A ∩ B) is the shoppers who purchased at an online store and at a locally-owned store

n(B ∩ C) be the shoppers who purchased at a locally-owned store and at  a big-box store

n(C ∩ A)  is the shoppers who purchased at an online store and at a locally-owned store and at an online store

From the Venn diagram,

n(A) = 109

n(B) = 34

n(C) =  107

n() = 38

n(B ∩ C) = 17

n(C ∩ A) = 57

On Comparing the Venn Diagrams, we could find that  shoppers made a purchase at an online store, a locally-owned store, and a big-box store [n( A ∩ B∩ C)] = 18

step-by-step explanation:

1) the property is   ixi = a ⇔x = a   o x = -a

4(x-5)+3= 15⇒4x-20+3 = 15⇒4x-17= 15⇒4x = 15+17⇒4x = 32⇒x =32/4= 8

4(x-5) +3= -15⇒4x-20 +3 = -15⇒4x-17= -15⇒4x =-15+17⇒4x = 2⇒x =2/4= 1/2

the values are x =8 and x = 0,5