What is the answer to: if T(n)=4n-1

A department store surveyed 428 shoppers, and the following information was obtained: 216 shoppers made a purchase, and 294 were

Maurinko [17]

Answer:

(a) 169

(b) 341

(c) 125

(d) 87

Step-by-step explanation:

Consider the Venn diagram below.

The total number of shoppers surveyed is, N = 428.

Number of shoppers who made a purchase, n (P) = 216

Number of shoppers who were satisfied with the service they received,

n (S) = 294

Number of shoppers who made a purchase but were not satisfied with the service, $n(S^{c}\cap P)$ = 47

(a)

The number of shoppers who made a purchase and were satisfied with the service = n (S ∩ P)

$n(S\cap P)=n(P)-n(S^{c}\cap P)\\=216-47\\=169$

(b)

The numbers of shoppers who made a purchase or were satisfied with the service = n (P ∪ S)

$n(P\cup S)=n(P)+n(S)-n(P\cap S)\\=n(P)+n(S)-n(S\cap P)\\=216+294-169\\=341$

(c)

The numbers of shoppers who were satisfied with the service but did not make a purchase = $n(S\cap P^{c})$

$n (S\cap P^{c} ) = n (S) - n (S \cap P)\\=294-169\\=125$

(d)

The number of shoppers who were not satisfied and did not make a purchase = $n(S^{c}\cap P^{c})$

$n(S^{c}\cap P^{c})=N-n(S\cup P)\\=N-n(P\cup S)\\=428-341\\=87$

6 0

3 years ago

(01.02 LC) simplify -3 1/9 - (-8 1/3) A) -11 1/12 B) -5 2/9 C- 5 2/9 D) 11 1/12

tensa zangetsu [6.8K]

The answers is C 5 2/9

6 0

4 years ago

Let X have the probability mass function P(X = −1) = 1 2 , P(X = 0) = 1 3 , P(X = 1) = 1 6 Calculate E(|X|) using the approaches

Studentka2010 [4]

Answer:

Step-by-step explanation:

From the given information:

Note that the possible values of Y are 0 and 1 because;

y = 0 if X = 0 and y = 1 if X = ±1

∴

$P(Y =0) = P(X = 0) =\dfrac{1}{3}$

$P(Y = 1) = P(X = -1 \ or \ 1) \\ \\ = P(X = -1) + P(X = 1)$

$= \dfrac{1}{2}+ \dfrac{1}{6}$

$=\dfrac{3+1}{6}$

$= \dfrac{2}{3}$

b)

$E(|X|) = \sum |x| P(X=x) = ( 1 \times \dfrac{1}{2}) + ( 0\times \dfrac{1}{3}) + ( 1 \times \dfrac{1}{6})$

$= \dfrac{2}{3}$

7 0

3 years ago

Tasha has a 40-gallon aquarium. If she uses a pint-size container to fill the aquarium, how many times will she have to fill the

quester [9]

Answer:

To fill the aquarium, she will need to fill the container 320 times.

Step-by-step explanation:

This question can be solved using a rule of three.

Each pint has 0.125 gallons.

So each fill of the container contains 0.125 gallons. How many fills are needed for 40 gallons?

1 fill - 0.125 gallons

x fills - 40 gallons

$0.125x = 40$

$x = \frac{40}{0.125}$

$x = 320$

To fill the aquarium, she will need to fill the container 320 times.

6 0

3 years ago

Find the area of quadrilateral ABCD whose vertices are A(1,1) B(7,-3) C(12,2) D(7,21)

sasho [114]

Answer:

The area of quadrilateral ABCD is 139 unit^2.

Step-by-step explanation:

Given:

Quadrilateral ABCD whose vertices are A(1,1) B(7,-3) C(12,2) D(7,21).

Now, to find the area.

The coordinates of the quadrilateral are A(1,1), B(7,-3), C(12,2), D(7,21).

So, to find the area we need to bisect the quadrilateral ABCD and get the triangles ABC and ADC and then calculate their areas:

In Δ ABC:

$A(x_1,y_1)=(1,1)\:,\:B(x_2,y_2)=(7,-3)\:and\:C(x_3,y_3)=(12,2)$

Now, to get the area of triangle ABC:

$Area\,of\,triangle\,=\,\frac{1}{2}\left|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\right|$

$Area\,of\,triangle\,=\,\frac{1}{2}\left|1(-3-2)+(7)(2-1)+12(1--3)\right|$

$Area\,of\,triangle\,=\,\frac{1}{2}\left|1(-5)+(7)(1)+12(4)\right|$

On solving we get:

$Area\,of\,triangle\,=25.$

In Δ ADC:

$A(x_1,y_1)=(1,1)\:,\:D(x_2,y_2)=(7,21)\:and\:C(x_3,y_3)=(12,2)$

Now, to get the area of triangle ADC:

$Area\,of\,triangle\,=\,\frac{1}{2}\left|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\right|$

$Area\,of\,triangle\,=\,\frac{1}{2}\left|1(21-2)+(7)(2-1)+12(1-21)\right|$

On solving it by same process as above we get:

$Area\,of\,triangle\,=114$

Now, to get the area of the quadrilateral we add the areas of the triangles ABC and ADC:

$25+114\\=25+114\\=139\ unit^2$

Therefore, area of quadrilateral ABCD is 139 unit^2.

4 0

3 years ago