By using the knowledge acquired about proportional relationships, solve the following questions.
Does it represents a proportional relationship?
find the constant of proportionality (K=Y/X)
give the equation that represents the relationship (Y=K*X)

The simplified answer is 6.01* 10^6.

Any number that we can write as a decimal number, between 1.0 and 10.0, multiplied by a power of 10, is said to be in standard form.

Given:

(4.1 x 10^5) + (5.6 x 10^6)

Solving further

4.1 * 10^5 + 5.6 * 10^6

4.1* 10^5 + 5.6*10*10^5

4.1* 10^5 + 56*10^5

(4.1 + 56 ) * 10^5

60.1* 10^5

6.01* 10^6

Hence, the simplified answer is 6.01* 10^6

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a)0.250

b)0.606

In the given question , we observe that

at Elmo's an old-fashioned barber shop in Melbourne, Florida ,66% of all customers  get a haircut ,49% get a save and 40% get both.

Probability is simply how likely something is to happen.

Whenever we are unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

The best example for understanding probability is flipping a coin:

There are two possible outcomes—heads or tails.

Independent event:

If two events, A and B are independent then the joint probability is

P(A and B)=P(A∩B)=P(A)P(B)

For example, if two coins are flipped, then the chance of both being heads is 1/2*1/2=1/4

probabilities of different events are:

P(Haircut)=66%=66/100=0.66

P(Shave)=49%=49/100=0.49

P(both)=40%=40/100=0.40

a) we have to find the probability that a randomly selected person doesn't get a shave and doesn't get a haircut.

P(no haircut ∩ no shave)=1-P(haircut ∪ shave)

                                        =1-[P(haircut)+P(shave)-P(both)]

                                         =1-[0.66+0.49-0.40]

                                         =1-0.75

                                         =0.250

b) we have to find the probability that a randomly selected person gets a shave, given that they get a haircut.

P(Shave/Haircut)=P(Both)/P(Haircut)

                           =0.40/0.66

                           =0.606

Hence, final answer is

a) the probability that a randomly selected person doesn't get a shave and doesn't get a haircut=0.250

b)the probability that a randomly selected person gets a shave, given that they get a haircut=0.606

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The standard deviation of both sets of data is the same, at 3.67,and adding the same constant c to each data value results in the standard deviation remaining the same.

Define Standard deviation?

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.

We have a data set:

14, 12, 16, 8, 6

As we know the standard deviation formula is :

               σ = √[∑(xi-X)/n]

σ = population standard deviation

Here ,

xi = value from the data set

X = mean of the data set

n = number of observation in data set.

X = (14+12+16+8+6)/5

X = 56/5

Where,   n = 5

After calculating the standard deviation will be:

σ = 11.2

Add 8 to each data value to get the new data set 14, 12, 16, 8, 6.

We can write,

14+8=22

12+8=20

16+8=24

8+8=16

6+8=14

Then,      

New data set is   ⇒  22,20,24,16,14

New standard deviation:

σ(new) = 11.2

Since both sets of data have the same standard deviation, we can conclude that adding a constant to each data value has no effect on the standard deviation.

Adding the same constant c to each data value results in the standard deviation remaining the same.

Thus, the standard deviation of both the data are the same which is 11.2 and adding the same constant c to each data value results in the standard deviation remaining the same.

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A basketball team sells tickets that cost $10 $20 or VIP seats, $30.

The no. of three types of tickets = x, y, z

;

The team has sold 492 tickets over all.

x + y + z = 492

:

It has sold 177 more $20 tickets than $10 tickets.

y = x + 177

:

The total sales are $8580.

10x + 20y + 30z = 8580

:

How Many tickets of each kind have been sold?

:

Replace (x+177) for y in the 1st and 3rd equations

x + (177+x) + z = 492

2x + z = 492 - 177

2x + z = 315

and

10x + 20(x+177) + 30z = 8580

10x + 20x + 3540 + 30z = 8580

30x + 30z = 8580 - 3540

30x + 30z = 5040

Simplify, divide equation by 30

x + z = 168

:

Using these two equations for elimination

2x + z = 315

x + z = 168

---------------subtracting eliminates z

x = 147 ea $10 tickets sold

:

y = 147 + 177

y = 324 ea $20 tickets sold

;

Find z using the 1st equation

147 + 324 + z = 492

471 + z = 492

z = 492 - 471

:

Check solution in the $$ equation

10(147) + 20(324) + 30(21) =

1470 + 6480 + 630 = 8580; confirms our solutions

The number of $10 tickets sold is 1094.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Number of $10 tickets = x

Number of $20 tickets = x + 158

Number of $30 tickets = y

Total tickets = 3227

Total sales = $62410

We can make two equations.

x + (x + 158) + y = 3227

2x + y = 3227 - 158

2x + y = 3069 ____(1)

10x + 20(x + 158) + 30y = 62410

10x + 20x + 3160 + 30y = 62410

30x + 30y = 62410 - 3160

30x + 30y = 59250

30 (x + y) = 59240

x + y = 1975 ____(2)

From (1) and (2).

 2x + y = 3069

 x + y = 1975  

(-)   (-)    (-)      

x = 3069 - 1975

x = 1094

And,

Substituting x = 1094 in (2)

x + y = 1975

y = 1975 - x

y = 1975 - 1094

y = 881

The number of $10 tickets.

= x

=1094

Thus,

The number of $10 tickets is 1094.

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For the given coordinates, The equation of line is x - 3y + 8 =0

The equation of line is given by -

y − y 1 = m ( x − x 1 )

here x1,y1 = (1,-5)

m = x2 - x1/ y2 - y1

m = 4-1/4+5

m = 3/9

m = 1/3

y - 1 = 1/3 (x +5)

3y - 3 = x + 5

x - 3y = -8

x - 3y + 8 =0

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Answer:

it would be C

Step-by-step explanation:

because youd multiply the weeks by the total money made per day and subtract it by the amount the bike costs to see if you made enough

The Domain is [0, ∞) and range is (0, ∞)

An exponential function is a mathematical function of the following form: f ( x ) = [tex]a^{x}[/tex]. where x is a variable, and a is a constant called the base of the function.

Given:

After taking a dose of medication, the amount of medicine remaining in a person's bloodstream, in milligrams, after x hours can be modeled by the function

f(x)=110[tex](0.91)^{x}[/tex]

as, the general form of exponential function is

f(x)= [tex](ab)^{x}[/tex]

where  a is the initial value, 0<b<1 is decay factor and b>1 is growth factor.

Now comparing with main function we have 110 is the initial value and 0.91 is the decay factor.

As,  exponential function is defined for all real values of x but the time cannot be negative.

so, Domain: [0, ∞)

and, [tex](0.91)^{x}[/tex]>0

so,  110[tex](0.91)^{x}[/tex]>0

Then the range is (0, ∞)

Hence, the Domain: [0, ∞) and range is (0, ∞)

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Answer: ?

comfusing

Step-by-step explanation:

The amount of profit each of them received $49625 and $36625 respectively

To solve the problem, we need to write a system of equations.

Let

Given that a profit of $86,250 was shared by the two partners of a business, we have that

x + y = 86,250 (1)

Also, since one partner received $13,000 more than the other, we have that

x - y = 13,000  (2)

We now solve for x and y in the system of equations

x + y = 86,250 (1)

x - y = 13,000  (2)

Adding equations (1) and (2), we have

x + y = 86,250 (1)

+

x - y = 13,000  (2)

2x = 99250

x = 99250/2

x = $49625

From equation (2) y = x - 13000

Substituting x into the equation, we have

y = x - 13000

= 49625 - 13000

= $36625

Since x = $49625 and y = $36625,

So, the amount of profit each of them received $49625 and $36625 respectively

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The inverse of the conditional statement w = v is the same as ~w = ~v

This is the term that is used to refer to the statement that is written in mathematics as well as in logic that tells us the negation of the hypothesis that has been made in a statement and the conclusion that has been made as well of that statement.

For instance when we say that it is snowing, the opposite would be it is not snowing.

Hence the way that we would be able to write the statement that we have here would be same as ~w = ~v

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Answer:

It's both an A. P and a G. P series.

Step-by-step explanation:

Let's prove using A.P with a common difference (d) = 13

Let's say we want to find the second number

a + (n - 1)d

a = 13, n = 4, d = 13

.: S2= 13 + ( 2- 1)13

S2= 13 + (1) 13

S2= 13 + 13 = 26

Let's show using a G. P series.

S2 = arⁿ—¹

S2 = 13 × 2²—¹

S2 = 13 × 2¹

S2 = 13 × 2 = 26

N'O' does not pass through point M.

NO and N'O' both have the same slopes.

A closed polygonal chain made up of a finite number of straight line segments defines a polygon as a planar figure. A polygon is a region that is bounded by a bounding circuit, a bounding plane, or both. A polygonal circuit's segments are referred to as its edges or sides.

Every point will be 5.4 times farther away from point M after dilation by a factor of 5.4 around that point. (The only point that stays put is point M.) If a line didn't cross point M before the dilation, it won't cross point M after the dilation.

Point M is not traversed by segment N'O'.

Only the distances from the dilation center are altered by dilation. Angles or orientation are unaffected.

NO and N'O' both have the same slopes.

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Answer:

 the value of cos(x) is ±√3/2 and tan(x) is ±1/√3.

Step-by-step explanation:

Answer:

She has 12 oranges left

Step-by-step explanation:

convert 3/5 to a decimal

3÷5=0.6

then multiply that by 20

0.6*20=12

The explanation for the reason why the graph is not a function is: It is not a function because the graph has two different y-values for a single x-value.

A graph is a function when there are exactly one y-value for every x-value that is plotted on the graph.

This implies that, no single x-value can have two different y-values in a graph that represents a function. If there are two different y-values for a single x-value, then the graph is not a function.

In the graph given below, the x-value, 4, has two different y-values, -2 and 4. This makes the graph not a function.

Therefore, the explanation for the reason why the graph is not a function is: It is not a function because the graph has two different y-values for a single x-value.

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Answer:

Step-by-step explanation:

It is not a function because there are two different y-values for a single x-value.

The range of the function is (11, -4, 29}.

What is the range of a function?

The set of all a function's outputs is its range. In the function, f : A→B, A is the domain and B is the co-domain. The range is then created by this function's output. "Set of even natural numbers" defines the range. The mapped elements of the co-domain are referred to as the images, while domain elements are referred to as pre-images. The set of all images representing the domain's elements, or the set of all its outputs, defines the range of the function f in this case.

The range in this case is (11, -4, 29}.

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The total cost for 4 tickets,  2 popcorns, and 1 bottled water is $46.25

Here we know that:

Then the cost of 4 tickets,  2 popcorns, and 1 bottled water is given by the expression:

4*$9.75 + 2*$6.25 + 1*$4.75

Solving this expression we will get that the total cost is:

C = 4*$9.75 + 2*$6.25 + 1*$4.75 = $46.25

We can conclude that the total cost for 4 tickets,  2 popcorns, and 1 bottled water is $46.25.

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Based on the fact that the vehicle's fuel efficiency is not less than 35 miles per gallon, using f to represent the vehicle's fuel efficiency gives f ≥ 35.

The fuel efficiency of the vehicle is no less than 35 miles per gallon. This means that the fuel efficiency is either 35 miles per gallon, or greater than 35 miles per gallon.

Assuming f is meant to represent this fuel efficiency of a vehicle, this means that f can be shown as being either greater than, or equal to 35 miles per gallon.

A representation of this would be:
f ≥ 35

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Answer:

-1/12

Step-by-step explanation:

-⅓ + ¼

= (-4 + 3)/12

= -1/12

[tex]cats = \frac{90}{2 + 7} \times 2 = 20 \: cats[/tex]

The speed of the​ current will be 8.89 miles per hour.

Given that,

The constant speed of motorboat = x = 48 miles per hour

And,

The Time taken by boat to make the upstream trip = 19/60 hour

And,

The Time taken by boat to make the return trip = 13/60 hour

Now,

According to the question,

Let,

The speed of the current = y  miles per hour

And,

The total distance covered = z miles

And,

We know that,

Speed = Distance/Time

So,

For the upstream trip,

x - y = z/(19/60),

So,

z = (x-y) * (19/60)     .....(i)

And,

For downstream trip

x + y = z/(13/60)

So,

z = (x + y) * (13/60)     .....(ii)

From equations (i) and (ii),

We get,

(x - y) * (19/60) = (x + y) * (13/60)

i.e.

(48 - y) * (0.32) = (48 + y) * (0.22)

On solving we get,

15.36 - 0.32y = 10.56 + 0.22y

We get,

0.54y = 4.8

y = 4.8/0.54 = 8.89 miles per hour

So,

The speed of current = 8.89 miles per hour

Hence we can say that the speed of the​ current will be 8.89 miles per hour.

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the difference quotient for the given function is 2.

For any function f(x), we define the difference quotient as:

( f(x + h) - f(x))/h

And we take the limit as h tends to zero.

Here our function is:

f(x) = 2x + 4

Replacing it in the difference quotient we get:

(2*(x + h) + 4 - 2x - 4)/h = ( 2x + 2h + 4 - 2x - 4)/h = 2h/h = 2

So we conclude that the difference quotient for the given function is 2.

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Answer:

75=8x-5x

75=3x

75/3=x

x=25 answer

Answer:

27

Step-by-step explanation:

-2x+3(y-5x)-x --- distribute the parenthesis

-2x+3y-15x-x --- evaluate by combining similar terms

3y-18x --- plug in -1 for x and 3 for y

3(3)-18(-1) --- evaluate

9+18 --- evaluate

27

Answer:

27

Step-by-step explanation:

-2(-1)+3{3-5(-1)}-1(-1)

2+3(3+5)+1

2+3(8)+1

2+24+1

=27

Answer:

30% x 350000 + 105000

Step-by-step explanation:

30

100

(350000)

=(

30

100

)(

350000

1

)

=(

3

10

)(

350000

1

)

=

(3)(350000)

(10)(1)

=

1050000

10

=105000

I suppose you're given [tex]f(x) = x^2 + 2[/tex], which would mean [tex]f^{-1}(x) = \sqrt{x-2}[/tex]. Then

[tex]f^{-1}(f(x)) = f^{-1}(x^2 + 2)[/tex]

and

[tex]f^{-1}(x) = \sqrt{x - 2} \implies f^{-1}(x^2+2) = \sqrt{(x^2+2) - 2}[/tex].

You should have [tex]x^2+2[/tex] where you wrote [tex]x+2[/tex]. This then simplifies to [tex]\sqrt{x^2} = x[/tex] (as long as [tex]x\ge0[/tex]).

Answer:

3 packages

Step-by-step explanation:

64/23 = 2 18/23, so 3 packages will be needed.

Alternately, 23 + 23 = 46, and 64 - 46 = 18.

So 2 packages will not be enough; 3 packages will do.

The equation which results from the transformation of the equation given; y = x in the task content is; y = (1/11)x.

It follows from the task content that the resulting equation from the transformation of the graph of y =x after a vertical compression by a factor of 1/11 as given in the task content is to be determined.

On this note, since the compression is vertical, the resulting vertical component is; (1/11)• y.

Hence, the resulting graph upon compression is; (1/11)• y.

Ultimately, the resulting graph upon the vertical compression is; y = (1/11) x.

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Laurie is talking about numbers which are lesser than 1 as their square root is the perfect example.

We are given that:

Ishmael claims:

the square root of a number is always less than the number under the radical symbol.

Laurie claims:

there are lots of numbers whose square root is larger than the number and the radical.

Laurie can convince Ishmael by giving examples like 1/4 whose square root is 1/2 which is greater than 1/2.

Another number is 1/9 whose square root is 1/3.

Therefore, Laurie is talking about numbers which are lesser than 1 as their square root is the perfect example.

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