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Yakvenalex [24]
2 years ago
13

April is going to the bakery to purchase donuts and cinnamon rolls for the office personnel. She must purchase at least 30 items

. She has collected only $30, so total cost must be no more than $30. If d represents donuts that cost $0.75 each and r represents cinnamon rolls that cost $1.25 each, which system of inequalities can be used to represent the region for the number of donuts and cinnamon rolls April could purchase
Mathematics
1 answer:
evablogger [386]2 years ago
5 0

Answer:

d + r ≥ 30

$0.75d + $1.25r ≤ $30

Step-by-step explanation:

Given the following :

Number of items to purchase = atleast 30

Total cost must be no more than 30

cost of donut (d) = $0.75

Cost of cinnamon (r) = $1.25

Number of donuts and cinnamon to purchase

To total number of items :

Donut + cinnamon ≥ 30

d + r ≥ 30

Cost of items to purchase :

Cost = price per item * number of items

$0.75d + $1.25r ≤ $30

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A four-person committee is chosen from a group of eight boys and six girls. If students are chosen at random, what is the probab
Lapatulllka [165]

Answer: 0.07

Step-by-step explanation:

in the group, we can have only 4 persons.

we have 8 boys, and 6 girls.

We want to find the probability that in the comite we have only boys.

Ok, for the first selection, the probability of selecting a boy is equal to the number of boys divided the total number of the group ( 8 + 6 = 14) this is

p1 = 8/14.

For the second selection we do the same, but we already slected a boy, so now the number of boys is 7, and the total number of posibilities is 13.

p2 = 7/13.

for the third selection we do the same, in this case the probability is

p3 = 6/12

for the fourth selection the probability will be:

p4 = 5/11

The joint probability, of all the events happening at the same time, is equal to the product of the singular probabilities:

P = p1*p2*p3*p4 = (8/14)*(7/13)*(6/12)*(5/11) = 0.07

4 0
2 years ago
Read 2 more answers
Gordon​ Miller's job shop has four work​ areas, A,​ B, C, and D. Distances in feet between centers of the work areas​ are: A B C
andreev551 [17]

Answer: $600,600

Step-by-step explanation:

Total handling cost :

Workpiece moved * cost * distance

Work area A :

-, (5 × 22 × 900), (9 × 22 × 900), (7 × 22 × 500)

-, 99000, 178200, 77000

Work area B:

-, -, (6 × 22 × 500), (8 × 22 × 200)

-, -, 66000, 35200

Work area C:

-, -, -, (11 × 22 × 600)

-,-,-, 145200

Work area D:

-, -, -, -

Total weekly handling cost :

(99000 + 178200 + 77000 + 66000 + 35200 + 145200)

= $600,600

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4 0
2 years ago
Evaluate the line integral by the two following methods. xy dx + x2y3 dy C is counterclockwise around the triangle with vertices
nadezda [96]

Answer:

a)

\frac{2}{3}

b)

\frac{2}{3}

Step-by-step explanation:

a) The first part requires that we use line integral to evaluate directly.

The line integral is

\int_C xydx +  {x}^{2}  {y}^{3} dy

where C is counterclockwise around the triangle with vertices (0, 0), (1, 0), and (1, 2)

The boundary of integration is shown in the attachment.

Our first line integral is

L_1 = \int_ {(0,0)}^{(1,0)} xydx +  {x}^{2}  {y}^{3} dy

The equation of this line is y=0, x varies from 0 to 1.

When we substitute y=0 every becomes zero.

\therefore \: L_1 =0

Our second line integral is

L_2 = \int_ {(1,0)}^{(1,2)} xydx +  {x}^{2}  {y}^{3} dy

The equation of this line is:

x = 0 \implies \: dx = 0

y varies from 1 to 2.

We substitute the boundary and the values to get:

L_2 = \int_ {1}^{2}1 \cdot y(0) +  {1}^{2}   \cdot \: {y}^{3} dy

L_2 = \int_ {1}^2 {y}^{3} dy =  \frac{8}{3}

The 3rd line integral is:

L_3 = \int_ {(1,2)}^{(0,0)} xydx +  {x}^{2}  {y}^{3} dy

The equation of this line is

y = 2x \implies \: dy = 2dx

x varies from 0 to 1.

We substitute to get:

L_3 = \int_ {1}^{0} x \cdot \: 2xdx +  {x}^{2}  {(2x)}^{3}(2 dx)

L_3 = \int_ {1}^{0} 8 {x}^{5}  + 2 {x}^{2} dx  =  - 2

The value of the line integral is

L = L_1 + L_2 + L_3

L = 0 +  \frac{8}{3}  +  - 2 =  \frac{2}{3}

b) The second part requires the use of Green's Theorem to evaluate:

\int_C xydx +  {x}^{2}  {y}^{3} dy

Since C is a closed curve with counterclockwise orientation, we can apply the Green's Theorem.

This is given by:

\int_C \: Pdx +Q  \: dy =  \int \int_ R \: Q_y -  P_x \: dA

\int_C \: xydx + {x}^{2} {y}^{3}   \: dy =  \int \int_ R \: 3 {x}^{2}  {y}^{2}  -  y \: dA

We choose our region of integration parallel to the y-axis.

\int_C \: xydx + {x}^{2} {y}^{3}   \: dy =  \int_ 0^{1} \int_ 0^{2x}  \: 3 {x}^{2}  {y}^{2}  -  y \: dydx

\int_C \: xydx + {x}^{2} {y}^{3}   \: dy =  \int_ 0^{1} \:  {x}^{2}  {y}^{3}  -   \frac{1}{2}  {y}^{2} |_ 0^{2x}  dx

\int_C \: xydx + {x}^{2} {y}^{3}   \: dy =  \int_ 0^{1} \:  8{x}^{5} -  2 {x}^{2}   dx =  \frac{2}{3}

8 0
2 years ago
Which of the following companies offers the greatest total employment compensation? Company A Company B Company C Company D Gros
Sergio039 [100]
Company C hope this helped
7 0
2 years ago
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The table below shows the different times it takes Paula to drive to work each day depending on the rate at which she drives.
faust18 [17]
Speed = distance / time
30 = d / 2.5
30 * 2.5 = d
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40 = d / 1.875
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60 = d / 1.25
60 * 1.25 = d
75 = d

24 = 75 / time
time = 75/24
time = 3.125 hours
7 0
2 years ago
Read 2 more answers
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