1/4 Marks
5/17 Marks
Given that f(x) = x2
x2 – 3
9
a) Find f(3)
b) Find f(x)
c) Find f'(11)

Answer:

a) 0.000001 = 0.0001% probability that the shuttle is left with no computer control system on a mission.

b) 3 backup systems are needed.

Step-by-step explanation:

For each system, there are only two possible outcomes. Either it works, or is does not. Systems are independent. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Three separate computer control systems

This means that [tex]n = 3[/tex]

The probability of failure for any one system on any one mission is known to be 0.01.

So the probability of working is:

[tex]p = 1 - 0.01 = 0.99[/tex]

(a) Find the probability that the shuttle is left with no computer control system on a mission. (Enter your answer to six decimal places.)

This is [tex]P(X = 0)[/tex]

So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{3,0}.(0.99)^{0}.(0.01)^{3} = 0.000001[/tex]

0.000001 = 0.0001% probability that the shuttle is left with no computer control system on a mission.

(b) How many backup systems does the space shuttle need if the probability that the shuttle is left with no computer control system on a mission must be 1 over one hundred thousand

This is n for which:

[tex]P(X = 0) < \frac{1}{100000} = 0.00001[/tex]

With 2 backup systems, the probability is lower than this, so lets see if with only two is possible.

We find [tex]P(X = 0)[/tex] when [tex]n = 2[/tex]. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{2,0}.(0.99)^{0}.(0.01)^{2} = 0.0001 > 0.00001[/tex]

So 3 backup systems are needed.

Answer:

4/3

Step-by-step explanation:

Answer:

25 Hours

Step-by-step explanation:

200 computers divided by 8 an hour gives you 25 hours to assemble the computers.

200 ÷ 8 = 25

I hope this helps. ^^

The estimated mean of advertising expenses is $52 million, and the estimated standard deviation is $11.23 million.

To estimate the mean and standard deviation of advertising expenses, we need to calculate the midpoint of each class interval, the product of the midpoint and the frequency, and the squared deviation from the mean.

Here's a table to organize the calculations:

Class Interval (x)     Frequency (f)     Midpoint (x)       fx

25 up to 35                   5                       30                 150

35 up to 45                   10                      40                 400

45 up to 55                   21                      50                1,050

55 up to 65                   16                      60                 960

65 up to 75                   8                        70                  560

To calculate the mean, we need to find the sum of the products of the midpoint and the frequency, divided by the total frequency.

Mean = (fx) / Total Frequency

Mean = (150 + 400 + 1,050 + 960 + 560) / 60

Mean = 3,120 / 60

Mean = 52

Calculate the squared deviation from the mean for each class interval.

(x - mean)² × f

(30 - 52)² × 5 = 484 × 5 = 2,420

(40 - 52)² × 10 = 144 × 10 = 1,440

(50 - 52)² × 21 = 4 × 21 = 84

(60 - 52)² ×  16 = 64 × 16 = 1,024

(70 - 52)² ×  8 = 324 × 8 = 2,592

Calculate the sum of the squared deviations.

Sum of (x - mean)× f = 2,420 + 1,440 + 84 + 1,024 + 2,592

= 7,560

Standard Deviation =√(Sum of (x - mean)² × f / Total Frequency)

Standard Deviation = √(7,560 / 60)

Standard Deviation = √(126)

Standard Deviation = 11.23

Hence, the estimated mean of advertising expenses is approximately $52 million, and the estimated standard deviation is approximately $11.23 million.

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Complete question

Advertising expenses are a significant component of the cost of goods sold. Listed below is a frequency distribution showing the advertising expenditures for 60 manufacturing companies located in the Southwest. Estimate the mean and the standard deviation of advertising expenses. (Round squared deviations to nearest whole number and final answers to 2 decimal places.)

Advertising Expenditure ($ millions)        Number of Companies

25 up to 35                                                                      5

35 up to 45                                                                    10

45 up to 55                                                                    21

55 up to 65                                                                   16

65 up to 75                                                                   8

Total                                                                               60

Answer:

10%

Step-by-step explanation:

first let's write out the problem

0.99 is what percent of 9.90     =        0.99=9.90*x

We need to   what c is so we would do the opposite operation of multiplication, division so we get,

0.99/9.90= .1

now we turn .1 into  percent and get out answer

0.1= 10%

Answer:

Step-by-step explanation:

ahh that's like a math tongue twister  :P

so just remember that when you are given the final amount, as the 0.99 is,  then you want to divide by the total, like this

0.99 / 9.90 =  

we don't really need a calculator for this,  b/c you can see that the answer will come out to a one,  but, where is the decimal, huh

my calculator put the decimal here  0.1

so that's 10% right?  which totally makes sense.. right?    0.99 is 10% of 9.90... just move the decimal one place in the 9.9 to get  .99  see?  so that kinda helps us know where the decimal goes in the answer, if that make sense? The decimal gets moved one place to the  LEFT  of the one, in our answer when we just did the math in our head.

anyway.. leave a comment if you have more questions :)

Answer:

Both have the same y-intercept (-9)

Step-by-step explanation:

✔️Function 1, r = ⅝t - 9, is given in the slope-intercept form, y = mx + b.

b = y-intercept = -9

y-intercept for Function 1 = -9

✔️Function 2, using the table given, the y-intercept is the value of r when t = 0.

Thus, r = -9 when t = 0.

y-intercept for Function 2 = -9

✔️Both functions has the same y-intercept. None is greater than the other.

the burger king sign is a rectangle i had burger king last week

The percentage of 38 that is 23 is = 60.5%

To calculate the percentage of a given quantity, the quantity is taken to be =100%

That is ; 38 = 100%

Therefore, 23 = X

make X the subject of formula,

[tex]x = \frac{23 \times 100}{38} [/tex]

[tex]x = \frac{2300}{35} [/tex]

X = 60.5%

Therefore, 60.5% of 38 is 23.

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Answer:

798 minutes

Step-by-step explanation:

Answer:

[tex](-1,2)[/tex]

Step-by-step explanation:

The vertex of [tex]f(x)=|x|[/tex] is [tex](0,0)[/tex]

The +1 inside the absolute value horizontally shifts the graph 1 unit to the left.

The+2 outside the absolute value vertically shifts the graph 2 units upward.

So, the vertex of the graph of [tex]f(x)=|x+1|+2[/tex] is [tex](-1,2)[/tex]

Answer:

Inequality Form: − 4 √ 2 ≤ x ≤ 4 √ 2 Interval Notation: [ − 4 √ 2 , 4 √ 2 ]

Answer:

-4x ≥ 14

x ≥ -3.5

Graphed (numberline):

<-----------3.5---0------------->

could be x

Answer:

10 minutes.

Step-by-step explanation:

Note the amount of minutes in an hour.

1 hour = 60 minutes.

The system can paint 6 cars in an hour. Divide 60 minutes with 6 cars:

60/6 = 10

Each car takes 10 minutes to get fully painted.

~

Answer:

canopy layer

Step-by-step explanation:

Answer:

arc = 25.29

Step-by-step explanation:

first find the circumference:

C = 2r(Pi) = 2(10)(3.14) = 62.8

since subtended, then we're looking for these opposite angle of 215 degrees:

360 - 215 = 145 degrees

62.8/360 = 0.1744 per degree

0.1744 x 145  = 25.29

Step-by-step explanation:

Given

5c + 9 - 2c - 7

= 3c + 2

Hope it will help :)❤

Step-by-step explanation:

x-3>7 =>

x>10

hope this helps

Answer:

Step-by-step explanation:

surface area of cube = 6×8² = 384 cm²

lateral area of pyramid = surface area of pyramid - base area

= 384 - 8²

= 320 cm²

area of triangular face = 320/4 = 80 = ½(base)(slant height) = ½(8)(slant height)

slant height = 20 cm

The cost of the television Ricardo purchased is A = 0.65t , where t is the initial cost

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage change is the difference between the measured value and the true value , as a percentage of the true value

Percentage change =( (| Measured Value - True Value |) / True Value ) x 100

Given data ,

Let the initial cost of television be = t

Let the percentage of discount on television = 35 %

If the original cost of the television was t dollars, then the sale price would be 65% of the original cost, or 0.65t dollars (since the television is on sale for 35% off).

However, this sale price still includes tax, so we need to subtract the tax from the sale price to get the final cost.

Let's say the tax rate is r (as a decimal), then the final cost would be:

A = 1 - ( 0.35 )t

A = 0.65t

Hence , the expression that represents the final cost of the television that Ricardo purchased is (D) 0.65t

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Answer:

download symbolab or download photo math it gets I covered on most of that your grade should go up

Answer: How to solve equations

Step-by-step explanation:

You have to use Pemdas the order of operations to solve these types of equations.

Parenthesis,Exponents,multiplication,Division,Addition,subtraction.

Multiplication and division fit in a group left to right.

Addition and subtraction come last but depends on which comes first left to right.

Here you first have to use the distributive property.

3(y+5)=39 multiply 3 times y that gives you 3y. Then multiply 3 times 5 that gives you 15 . So, now you have simplified the left side of the equal sign so you have 3y+15=39 now subtract 15 from both sides and you get 3y=24 then you divide both sides by 3 to get y=8. What I just went over you do again and again to solve all these types of equations. Your trying to solve for the variable so you try to get y or m or n or any variable by itself.

Answer:

no.

Step-by-step explanation:

the sum of the two smallest sides of the triangle must be greater than the largest side in order to form a triangle. 2+6<9

Answer:

40.32

Step-by-step explanation

4*1.2=4.8

7*1.2=8.4

8.4*4.8

=40.32

Answer:

0.285714285 nearest thousandth

Answer:

B.  Interquartile range

E. Range

Step-by-step explanation:

When the variability is to be used for comparing the two data sets so the measures that should be considered is range & interquartile range as it shows the difference also it compared the two different data sets

Therefore option B and E is correct

And, the rest of the options are wrong

Answer:

When we have a random function like:

y = f(x)

If there is no clarification, the domain will be the set of all real numbers except the ones that may make a problem.

For example, if there is some value of x such that there is a denominator equal to zero, then that particular value of x is not in the domain of f(x) (because we can not divide by x)

Something similar happens when we have a square root, remember that:

√x

Is a complex number if x < 0.

Then if we have a function like:

y = √x

The domain will be the set of all reals such that x ≥ 0.

Then the procedure to find the domain is to find the inputs that may have problems, and "remove" them from the domain.

For the range, we need to first know the domain, then we can evaluate the function in different points of the domain and see the outputs. Once we know all the outputs, we know the range of the function.

Usually, when working with continuous functions, these may have a global maximum M and a global minimum m, then the range is:

m ≤ Y ≤ M

if not, then the range is the set of all real numbers.