a) Given f(x)= √x-3, g(x)= 2/x-1, h(x)= x +7. Find xg h X-1' Domain of f(x) (2 marks) ii) g.h and its domain (3 marks)

The future value of the fund on January 1, 2018, just after the third deposit, is approximately $47,986.47.

To find the future value of the fund on January 1, 2018, just after the third deposit, we can use the compound interest formula:

\(FV = P(1 + r/n)^{nt}\)

Where:

FV = Future Value

P = Principal amount (initial investment)

r = Annual interest rate (expressed as a decimal)

n = Number of times the interest is compounded per year

t = Number of years

Let's calculate the future value step by step:

First deposit:

P = $16000

r = 7.2% = 0.072 (as a decimal)

n = 12 (compounded monthly)

t = 4.333 years (from September 1, 2010, to March 1, 2015)

\(FV_1 = 16000(1 + 0.072/12)^{(12*4.333)}\\= 16000(1 + 0.006)^{52}\\= 16000(1.006)^{52}\\= 20,296.43\)

Second deposit:

P = $13000

r = 7.2% = 0.072 (as a decimal)

n = 12 (compounded monthly)

t = 2.917 years (from March 1, 2015, to January 1, 2018)

\(FV_2 = 13000(1 + 0.072/12)^{(12*2.917)}\\= 13000(1 + 0.006)^{35}\\= 15,618.04\)

Third deposit:

P = $12000

r = 7.2% = 0.072 (as a decimal)

n = 12 (compounded monthly)

t = 0.084 years (from January 1, 2018, to January 1, 2018)

\(FV3 = 12000(1 + 0.072/12)^{(12*0.084)}\\= 12000(1 + 0.006)\\= $12,072.00\\\)

Adding up the future values:

\(Total FV = FV_1 + FV_2 + FV_3\)

= $20,296.43 + $15,618.04 + $12,072.00

≈ $47,986.47

Therefore, the future value of the fund on January 1, 2018, just after the third deposit, is approximately $47,986.47.

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Given:

The set of ordered pairs.

To find:

Which set of ordered pairs represents a function?

Solution:

A set of ordered pairs represents a function, if there exist unique output value for each input value.

In option A,

{(2, 9), (5, 9), (1, -6), (-5, 5)}

It is a function because all input has unique outputs.

In option B,

{(6, 6), (6, 8), (-8, -7), (-3, -8)}

For x=6, there exist two outputs y=6 and y=8. So, it is not a function.

In option C,

{(1, 8), (9, -3), (7, -4), (7, -6)}

For x=7, there exist two outputs y=-4 and y=-6. So, it is not a function.

In option D,

{(-5, -1), (-3, -7), (-5, 3), (-7, -4)}

For x=-5, there exist two outputs y=-1 and y=3. So, it is not a function.

Therefore, the correct option is A.

From the given option, the  set of ordered pairs that represents a function is {(2, 9), (5, 9), (1, -6), (-5, 5)\}

A coordinate is known to represents a function if all the domain values have a unique value in the codomain.

The x-coordinate point should not be repeated for the coordinate to be a function, otherwise it is not a function.

From the given option, the  set of ordered pairs that represents a function is {(2, 9), (5, 9), (1, -6), (-5, 5)\}

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Considering the given tree diagram, there is a 0.5 = 50% probability of an investor choosing either stocks or bonds from portfolio C.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

At each node, the sum of the probabilities is of 1, hence:

0.2 + 0.3 + Z = 1.

Z = 0.5.

There is a 0.5 = 50% probability of an investor choosing either stocks or bonds from portfolio C.

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Answer:

\(y = -\frac{5}{3}x-7\)

Step-by-step explanation:

We are given three coordinates. First, we have to find the slope. We can do this by counting the slope of two points which we will do for simplicity's sake.

\(\frac{rise}{run}\) gives us \(-\frac{5}{3}\) which we will use as the slope.

Looking at the graph, the y intercept of the equation is -7, so our equation would be \(y=-\frac{5}{3}x-7\)

Answer:

Step-by-step explanation:

Fraction: 3/10 decimal: 0.30

Answer:

Fraction: 3/10; Decimal: 0.3

Step-by-step explanation:

A). When trying to find the fraction of percent, the denominator is always 100 since the word percent itself states "per-cent," meaning per 100 as a cent can go up to a maximum of 100 before being converted into a dollar. Therefore, the fraction then becomes 30/100, however, we need to simplify it as stated by the question and we can easily do that by canceling out one zero on the numerator and the denominator, giving us the simplified fraction of 3/10.

B). Now, to find the decimal, we just have to divide the numerator by the denominator and dividing 3 by 10 gives us a decimal of 0.3. This decimal has already been rounded to the nearest hundredth since it is in the tenths place, so thus, there is a continuation of zeroes after the 3 infinitely. Therefore, the decimal rounded to the nearest hundredth is 0.3.

Hope this helped!  :D

Answer:

106

Step-by-step explanation:

3^4=81

5·5=25

81+25=106

Step-by-step explanation:

Perimeter = 5.2cm + 7.8 cm + 4cm = 17 cm

Answer:

12

Step-by-step explanation:

122

Answer:

25

Step-by-step explanation:

The number that could be divided up either into bags of 18 marbles or into bags of 42 marbles is 126.

The number that could be divided up either into bags of 18 marbles or into bags of 42 marbles, with no marbles left over in each case, is the lowest common multiple between these two numbers.

By decomposing these numbers as a product of primes, we get:

18 = 2*3*3

42 = 2*3*7

Notice that the first two prime factors are the same, but the third one changes. To get the first common multiple, we need to multiply both numbers by the third factor (the different one) of the other.

We will get:

18*7 = 126

42*3 = 126

Then 126 is the smallest number that can be divided by 18 and 42.

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The proababilities are: i) P(Aᶜ) = 0.6, ii) P(Bᶜ) = 0.4

iii) Probability that exactly one of the events A, B occurs = 0.7

Let A and B be any two disjoint events such that P(A) = 0.4 and P(A ∪ B) = 0.7. We need to find the following probabilities:

i) P(Aᶜ): This is the probability of the complement of event A, which represents the probability of not A occurring. Since A and B are disjoint, Aᶜ and B are mutually exclusive and their union covers the entire sample space.

Therefore, P(Aᶜ) = P(B) = 1 - P(A) = 1 - 0.4 = 0.6.

ii) P(Bᶜ): This is the probability of the complement of event B, which represents the probability of not B occurring. Since A and B are disjoint, Bᶜ and A are mutually exclusive and their union covers the entire sample space.

Therefore, P(Bᶜ) = P(A) = 0.4.

iii) Probability that exactly one of the events A, B occurs: This can be calculated by subtracting the probability of both events occurring (P(A ∩ B)) from the probability of their union (P(A ∪ B)).

Since A and B are disjoint, P(A ∩ B) = 0.

Therefore, the probability that exactly one of the events A, B occurs is P(A ∪ B) - P(A ∩ B) = P(A ∪ B) = 0.7.

To summarize:

i) P(Aᶜ) = 0.6

ii) P(Bᶜ) = 0.4

iii) Probability that exactly one of the events A, B occurs = 0.7

Note: The provided values of P(A), P(A ∪ B), and the disjoint nature of A and B are used to derive the above probabilities.

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Answer:

60 ft³

Step-by-step explanation:

Concepts

The volume of any prism is represented as Bh, where B = Area of the Base and h = height of the prism.

Application

In this case, we're given the area of the base as five feet² and the height as 12 feet. Now, we just multiply these two numbers to get the volume.

Solution

Answer:

I think Linear but i am not sure

Step-by-step explanation:

A linear function is a function with standard form y = mx + b, where m is the slope and b is the y-intercept, and whose graph looks like a straight line. There are other functions whose graph is not a straight line. These functions are known as nonlinear functions and they come in many different forms.

Answer:

x = 5

Step-by-step explanation:

f(x) = -17.1 means that the number you inputted for x gave an output of -17.1.  We see from the table that when x = 5, f(x) = -17.1.  

The area of the regular pentagon is 252.7m²

The formula that is used for calculating the area of a regular pentagon is expressed with the equation;

A = 5/2 x s x a

where the parameters are;

Apothem is the line from the center of the pentagon to a side, intersecting the side at 90 degrees right angle.

apothem,a = s/2 tan (180/n)

Substitute the values

Apothem, a = 7.6/2 tan 16

a = 7.6/0.57 = 13.3m

Substitute the values, we get;

Area = 5/2 × 7.6 × 13.3

Multiply the values, we have;

Area = 505. 4/2

Divide the values, we get;

Area = 252.7 m²

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8x + y = 21 (1)

22x - 2y = 34 (2)

To solve this system of the equation we will use the elimination method

Since y has opposite signs, then we will make their coefficients equal and add the equations

Multiply equation (1) by 2 to eleminate y

2(8x) + 2(y) = 2(21)

16x + 2y = 42 (3)

Now add equations (2) and (3)

(22x + 16x) + (2y - 2y) = (34 + 42)

38x + 0 = 76

38x = 76

Divide both sides by 38 to find x

x = 2

Now let us find y

Substitute the value of x in equation (1) or (2) to find y

I will substitute it in (1)

8(2) + y = 21

16 + y = 21

Subtract 16 from both sides to find y

16 - 16 + y = 21 - 16

y = 5

The solution of the system of equation is (2, 5)

Therefore, the average lateness using the earliest due date criterion is 2. The corect option is not one of the given options (A, B, C, or D).

To calculate the average lateness using the earliest due date criterion, we need to first determine the sequence in which the jobs should be processed. The earliest due date (EDD) criterion schedules jobs in the order of increasing due dates, so we will arrange the jobs in this order:

c, a, e, b, d

The table below shows the processing time, due date, and completion time of each job, as well as the lateness (completion time - due date) for each job:

Job Processing Time Due Date Completion Time Lateness

c 4 4 4 0

a 2 7 6 -1

e 5 15 11 -4

b 8 16 19 3

d 10 17 29 12

To calculate the average lateness, we add up the lateness values for all jobs and divide by the total number of jobs:

Average lateness = (0 + (-1) + (-4) + 3 + 12) / 5

= 2

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Answer:

2/3

Step-by-step explanation:

To write 10/15 in simplest form we have to:

Find the GCD (Greater common divisor)  of numerator and denominator

⇒ GCD of 10 and 15 is 5

Now, Divide both the numerator and denominator by the GCD

10 ÷ 5 = 2

15 ÷ 5 = 3

Numerator = 2

Denominator = 3

Therefore, 10/15 simplified to lowest terms is 2/3.

Kavinsky

Answer: The answer is 341 degress

Step-by-step explanation:

Answer:

73

Step-by-step explanation:

180-107=73

Answer:

Each oven is discounted by $40

Step-by-step explanation:

Total discount for 12 ovens is $480, so:

$480/12 = $40

$40 discount per oven.

Given:

If AB = 0,

Then it is not necessary that A=0 or B=0

To prove this, we consider an example:

Let n=m = p =2

Then AB is given as:

Clearly AB= 0 but A,B not equals to zero.

Hence, the given statement is not true.

Hence, the answer is false.

21 + (36 + 0 + 19) Equals 76.

A final result is obtained by adding two or more integers together. Commutative, associative, distributive, and additive identity are the four major characteristics of b. b means that even if the order changes, the addition result will remain the same.

Equation to be used: 21 + (36 + 0 + 19)

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I understand that the you are looking for is :

Several properties are used to evaluate this expression. Identify the property used in each step.

21 + (36 + 0 + 19)

21 + (36 + 19):

21 + (19 + 36):

(21 + 19) + 36:

40 + 36

76

Answer:

The player will be more likely to wear a yellow jersey because P(yellow) is more tha P(white).

Step-by-step explanation:

Get rid of the 0s. 35 is more than 20, therefore 0.35 will also be more than 0.20.

Hope this helps!

Answer:

Step-by-step explanation:

Since segment P A bisects angle A P B, we know that angle A P C measures 90 degrees. Therefore, segment C P is the radius of the circle.

We can use the Pythagorean theorem to find the length of segment A P:

AP^2 + CP^2 = AC^2

AP^2 + CP^2 = (2CP)^2 (since AC is the diameter of the circle)

AP^2 = 4CP^2 - CP^2 = 3CP^2

AP = CP * sqrt(3)

We know that CP is 4 feet, so:

AP = 4 * sqrt(3) feet

The arc length of a circle is given by:

arc length = (angle/360) * 2 * pi * radius

The angle of arc A B C is 360 - 45 = 315 degrees. The radius of the circle is CP = 4 feet. Substituting these values into the formula, we get:

arc length = (315/360) * 2 * pi * 4 feet

arc length = 3.5 * pi feet

Rounding to the nearest hundredth, the arc length is approximately 10.99 feet.

The value of radius of a right circular cylinder is 1,248 in for which the minimum surface area is obtained.

Volume of the  right circular cylinder be;

v(c) = 12 in³ =  π*r²*h    

In which, h is the height of the cylinder,

Then , h  =  12 / π*r²

Surface area of a right circular cylinder is:

S = area of base and top  + lateral area

S(A)  =  2*π*r²  + 2*π*r*h  ....eq 1

Put value of 'h' in equation (1)

S(r)  =  2*π*r² +   2*π*r*  ( 12 / π*r²)

S(r)  =  2*π*r² + 24 /r

Differentiate both sides,

S´(r)  =  4*π*r -  24 /r²

Put , S´(r)  = 0 to get the critical points.

4*π*r -  24 /r²  =  0

π*r - 6/r² = 0

π*r³ - 6  = 0

r³   =  1,91    

r = 1,248 in    

Check for the minimum surface area for r = 1,248 in.

Find the second derivative,

S´´(r)  =  4*π  +  48/r³    

S´´(r)  will always be positive.

Thus,  the minimum surface area S  is for   r = 1,248 in.

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The ordered pairs (21, 0) and (6, -4) are the solutions to the given inequality.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is y<2/7x-5.

Here,

Put (x, y)=(21, 0) in the given inequality, we get

0<2/7(21)-5

0<1

So, it is solution

Put (x, y)=(6, -4) in the given inequality, we get

-4<2/7(6)-5

-4<12/7-5

-4<1.7-5

-4<-3.3

So, it is solution

Put (x, y)=(0, -5) in the given inequality, we get

-5<2/7(0)-5

-5<-5

Which is not true, it is not a solution

Put (x, y)=(7, -3) in the given inequality, we get

-3<2/7(7)-5

-3<-3

Which is not true, it is not a solution

Therefore, the ordered pairs (21, 0) and (6, -4) are the solutions to the given inequality.

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For a one-tailed test with a 0.05 level of significance, the critical z statistic is 1.645, but the critical t statistic is 1.96. The statement is false.

The statement is incorrect. For a one-tailed test with a 0.05 level of significance, the critical z statistic is indeed 1.645. However, the critical t statistic value depends on the degrees of freedom (df), which is not provided in the statement. The 1.96 value mentioned is actually the critical z statistic for a two-tailed test with a 0.05 level of significance.

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