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2 years ago

The tax rate is 3.9% What is the tax on 42$? Round to the nearest hundredth

1 answer:

7 0

To find the total price, we use this equation:
42 + 0.039(42)
We can make it simpler:
1.039(42)
Multiply:
43.638
Because we're rounding
The total price is $43.64

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A pair of fair dice is cast. what is the probabiliy that the sum of the numbers falling uppermost is 9, given that at least one

WITCHER [35]

If a pair of fair dice is cast, the probability that the sum of the numbers falling uppermost is 9, given that at least one of the numbers falling uppermost is a 3 is given by:

$\frac{P(sum\, of\, 9\, \cup\,3)}{P(3)}$

The number of outcomes of sum of 9 where at last one is 3 is (3, 6) and (6, 3) = 2.

The number of outcomes of last one of the numbers falling uppermost is a 3 is (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (1, 3), (2, 3), (4, 3), (5, 3) and (6, 3) = 11.

Therefore, the probabiliy that the sum of the numbers falling uppermost is 9, given that at least one of the numbers falling uppermost is a 3 is 2 / 11.

5 0

2 years ago

What is the proof the formula for cos(A+B)=cosAcosB-sinAsinB?

brilliants [131]

Given data, cos(A - B) = cosAcosB + sinAsinB
let, A=60' and B=30' ( here the ' sign bears degree) 
L.H.S = cos(A - B) 
=cos (60'-30) ( using value of A and B ) 
=cos30' 
= sqrt3/2 
R.H.S= cosAcosB + sinAsinB 
=cos60' cos30' + sin60' sin30' 
= 1/2* sqrt3/2+ sqrt3/2*1/2 
= sqrt3/4 + sqrt3/4 
=2 sqrt3/4 
= sqrt3/2 
so L.H.S =R.H.S or cos(A - B) = cosAcosB + sinAsinB

8 0

2 years ago

Marginal cost At a certain factory the marginal cost is 3(q-4)^2 dollars per unit when the level of production is q units.

viktelen [127]

Answer:

a.) C(q) = -(1/4)*q^3 + 3q^2 - 12q + OH b.) $170

Step-by-step explanation:

(a) Marginal cost is defined as the decrease or increase in total production cost if output is increased by one more unit. Mathematically:

Marginal cost (MC) = change in total cost/change in quantity

Therefore, to derive the equation for total production cost, we need to integrate the equation of marginal cost with respect to quantity. Thus:

Total cost (C) = Integral [3(q-4)^2] dq = -(1/4)*(q-4)^3 + k

where k is a constant.

The overhead (OH) = C(0) = -(1/4)*(0-4)^3 + k = -16 + k

C(q) = -(1/4)*(q^3 - 12q^2 + 48q - 64) + k = -(1/4)*q^3 + 3q^2 - 12q -16 + k

Thus:

C(q) = -(1/4)*q^3 + 3q^2 - 12q + OH

(b) C(14) = -(1/4)*14^3 + 3*14^2 - 12*14 + 436 = -686 + 588 - 168 + 436 = $170

7 0

2 years ago

The tread life of tires mounted on light-duty trucks follows the normal probability distribution with a population mean of 60,00

valentinak56 [21]

Answer:

0.0013

Step-by-step explanation:

To do this, we need to use a normal distribution table with Z score values, like the one I'm attaching here.

Now, the expression to calculate the Z value is the following:

Z = x - μ / (σ/√n)

Where:

μ: mean

σ: standard deviation

x: value required

n: sample population

Now that we have the data, let's calculate the Z value:

Z = 66,000 - 60,000 / (4000/√4)

Z = 3

Now, let's look at the table to get the value that belongs to this Z score. According to the table, it's 0.0013

Therefore, the likelihood would be 0.0013

3 0

2 years ago

Bill launched a model rocket, and estimated its height h, In feet, after 1 seconds. His results are shown in the table

gizmo_the_mogwai [7]

Answer:

Bill launched a model rocket, and estimated its height h, In feet, after 1 seconds. His results are shown in the table

Time, 1 0 1 2 3 4

Height, h 0 110 190 240 255

Bill's data can be modeled by the function h(t) = -1612 + 128.

Which value is the best prediction for the height of the rocket after 5.5 seconds?

A 150 ft

B. 180 ft

C. 220 ft

D. 250 ft

E 260 ft

0 1

2 years ago