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4 years ago

4x^2 - 35x - 99 / x^2 - 5x - 66 Simplify this expression and state any restrictions on the variable

Mathematics

2 answers:

Akimi4 [234]4 years ago

7 0

Answer:

4x+9/x+6

Step-by-step explanation:

arsen [322]4 years ago

6 0

$\frac{4x^{2} - 35x - 99}{x^{2} - 5x - 66} = \frac{4x^2 - 44x + 9x - 99}{x^{2} - 11x + 6x - 66} = \frac{4x(x) - 4x(11) + 9(x) - 9(11)}{x(x) - x(11) + 6(x) - 6(11)} = \frac{4x(x - 11) + 9(x - 11)}{x(x - 11) + 6(x - 11)} = \frac{(4x + 9)(x - 11)}{(x + 6)(x - 11)} = \frac{4x + 9}{x + 6}$

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Round to the nearest whole number 8 5/6

Aleks04 [339]

The rule for rounding is that if the fraction is less than 1/2, we round down; and if the fraction is more than 1/2, we round up.

Because 5/6 is a greater fraction than 1/2, we must round the existing whole number (8), up.

8 5/6 rounded to the nearest whole number is 9.

3 0

3 years ago

Read 2 more answers

function travelSpeed = CalculateTravelSpeed(startX, startY, endX, endY, travelTime) % startX, startY: Starting coordinates % end

Ilia_Sergeevich [38]

Answer:

The functions in Python is as follows:

from math import *

def CalculateTravelSpeed(startX,startY,endX,endY,travelTime):

travelSpeed = EuclideanDist(startX, startY, endX, endY) / travelTime

return travelSpeed

def EuclideanDist(startX, startY, endX, endY):

dist = sqrt((startX - endX)**2 + (startY - endY)**2)

return dist

Step-by-step explanation:

from math import *

This defines the CalculateTravelSpeed function

def CalculateTravelSpeed(startX,startY,endX,endY,travelTime):

This calls the EuclideanDist function to calculate the distance; Next, the speed is calculated

travelSpeed = EuclideanDist(startX, startY, endX, endY) / travelTime

This returns the calculated speed

return travelSpeed

This defines the EuclideanDist function

def EuclideanDist(startX, startY, endX, endY):

This calculates the distance from the given coordinates

dist = sqrt((startX - endX)**2 + (startY - endY)**2)

This returns the calculated distance

return dist

5 0

3 years ago

The probability of the spinner landing on the shaded part is p=1/3. The probability of it landing on an unshaded part is q=2/3 t

raketka [301]

Answer:

The correct answer is 0.5.

Step-by-step explanation:

The probability of a spinner landing on the shaded part follows binomial distribution.

Equation to be used is P(r) = $\left[\begin{array}{ccc}n\\r\end{array}\right]$ × $p^{r}$ × $q^{n-r}$ , where n is the number of times the spinner is spun and r is the number of times the spinner falls on the shaded region.

The probability of the spinner landing on the shaded part is p = $\frac{1}{3}$ . The probability of it landing on the unshaded part is q = $\frac{2}{3}$ .

The spinner is spun n = 3 times.

We need to find the probability of it landing on the shaded part r = 2.

∴ Putting the values in the equation gives,

P(r) = $\left[\begin{array}{ccc}3\\2\end{array}\right]$ × $\frac{1}{2} ^{2}$ × $\frac{2}{3} ^{1}$ = 3 × $\frac{2}{3}$ × $\frac{1}{4}$ = 0.5

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3 years ago

At 5:45 p.m., a jet is located 108 mi due east of a city. A second jet is located 214 mi due north of the city. To the nearest t

Ivan

The answer is 239.7

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4 years ago

Read 2 more answers

When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 55 bat

aleksley [76]

The probability of accepting this shipment is 98%.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here, we have

Almost all such shipments will be accepted because the probability of having a sample with more than 3 defective batteries is very low.

The shipment will be accepted if at most 3 batteries don't meet specifications.

This can be modeled as a binomial distribution, where the sample size is n=55 and the probability of not meeting the specifications of any battery is p=0.02.

The shipment will be accepted if D ≤ 3.

The probability of this event is:

P( D ≤ 3) = P(D=0) + P(D=1) + P(D=2) + P(D=3)

P(D=X) = n!/(x!(n-x)!) pˣ(1-p)ⁿ⁻ˣ

P(D=0) = 55!/(0!(55-0)!) 0.02⁰(1-0.02)⁵⁵⁻⁰ = 1× 1 × 0.32 = 0.32

P(D=1) = 55!/(1!(55-1)!) 0.02¹(1-0.02)⁵⁴ = 54 × 0.02 × 0.33= 0.35

P(D=2) = 55!/(2!(55-2)!) 0.02²(1-0.02)⁵³ = 55 ×27 × 0.0004 × 0.34= 0.20

P(D=3) = 55!/(3!(55-3)!) 0.02³(1-0.02)⁵² = 25740× 0.0000008 × 0.35= 0.07

Then,

P( D ≤ 3) = P(D=0) + P(D=1) + P(D=2) + P(D=3)

P( D ≤ 3) = 0.32 + 0.35 + 0.20 + 0.07

P( D ≤ 3) = 0.98

Hence, the probability of accepting this shipment is 98%.

To learn more about the probability from the given link

brainly.com/question/24756209

#SPJ1

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2 years ago