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2 years ago

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A local pizza store knows the mean amount of time it takes them to deliver an order is 454545 minutes after the order is placed.

The manager has a new system for processing delivery orders, and they want to test if it changes the mean delivery time. They take a sample of delivery orders and find their mean delivery time is 484848 minutes.

1 answer:

sashaice [31]2 years ago

7 0

Answer:

Difference = 30 303.8 minutes

Step-by-step explanation:

The difference in the mean of the the pizza produces is given by the following:

Later mean - Initial mean

= $484848 - 454545\\= 30 303.8\\$

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Use Pythagorean identities to prove whether ΔLMN is a right, acute, or obtuse triangle. Show all work for full credit.

diamong [38]

Answer: The given triangle LMN is an obtuse-angled triangle.

Step-by-step explanation: We are given to use Pythagorean identities to prove whether ΔLMN is a right, acute, or obtuse triangle.

From the figure, we note that

in ΔLMN, LM = 5 units, MN = 13 units and LN = 14 units.

We know that a triangle with sides a units, b units and c units (a > b, c) is said to be

(i) Right-angled triangle if $b^2+c^2=a^2,$

(ii) Acute-angled triangle if $b^2+c^2>a^2,$

(iii) Obtuse-angled triangle if $b^2+c^2$

For the given triangle LMN, we have

a = 14, b = 13 and c = 5.

So,

$b^2+c^2=13^2+5^2=169+25=194,\\\\a^2=14^2=196.$

Therefore, $b^2+c^2$

Thus, the given triangle LMN is an obtuse-angled triangle.

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2 years ago

Holly bought 23 tickets to the baseball game. She got a group rate that gave her $4 off of the regular ticket price for each tic

sveticcg [70]

Answer:

The regular price of the ticket was $12.

Step-by-step explanation:

Let us call $P$ the regular price of the tickets, and if she had bought tickets at this price, the total cost would have been

$23P$ .

But Holly got $4 off the regular ticket price, that means one ticket cost her

$P-4$

and if she bought 23 tickets it cost her

$23(P-4)$

and we are told this equals $184; therefore we have

$23(P-4)=184$

now we solve this equation the following way:

$23(P-4)=184$

$23P-4(23)=184$

$23P-92=184$

$23P=276$

$\boxed{ P=12}$

Thus, the regular price was $12.

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2 years ago

Read 2 more answers

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.

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

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

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

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2 years ago

To visit his grandmother, Michael takes a motorcycle 3.853.853, point, 85 kilometers and a horse 3.323.323, point, 32 kilometers

liq [111]

Answer: $7.17\ kilometers$

Step-by-step explanation:

<h3> The exercise is: "To visit his grandmother, Michael takes a motorcycle 3.85 kilometers and a horse 3.32 kilometers. In total, the journey takes 50.54 minutes. How many kilometers is Michael's journey in total?"</h3>

To solve this exercise you must pay attention to the data given.

According to the information provided in the exercise, Michael's journey is divided into two parts:

Part 1: $3.85\ kilometers$ (Traveling in a motorcycle)

Part 2: $3.32\ kilometers$ (Traveling in a horse)

Based on the given data, you can conclude that the the total distance in kilometers of Michael's journey to the house to his grandamother, is the sum of those distances ( $3.85\ kilometers$ and $3.32\ kilometers$ )

Therefore, you need to add them in order to solve the exercise.

So, You get that the result is:

$Total=3.85\ kilometers+3.32\ kilometers\\\\Total=7.17\ kilometers$

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2 years ago

Find the cube root of 10 upto 5 signaficant figures by newton raphson method

PSYCHO15rus [73]

Answer: The cube root of 10 is 2.1544 using an Xo value of -0.003723

Step-by-step explanation: The Newton-Raphson is a root finding method and its formula is NR: X=Xo-(f(x)/f'(x). Once you have the equation you also need to find the derivative of that equation before applying the formula. Since the problem stated that X =10, the method was applied to find the best root in order to find the cube root of 10 up to 5 significant figures. The best method is to use a software like Excel that helps you calculate those iterations faster. The root finding for this example was -0.003723.

6 0

2 years ago