9.
The table shows the number of pools sold by the Allied Pool company over a six month period.
Allied Pool Sales
Month
Number of
Pools Sold
Feb.
11
Mar.
10
Apr.
12
May
16
June
15
July
18


From the above table, what is the range in the number of pools sold during this period?
8 pools

The average speed in laps per minute of Ryan is 2.5 laps per minute

From the question, we have the following parameters that can be used in our computation:

The above can be expressed as

(x, y) = (1, 5) and (3, 10)

The average speed in laps per minute can be calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Rewrite as

Average speed = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (1, 5) and (3, 10)

Substitute the known values in the above equation

So, we have the following equation

Average speed = (10 - 5)/(3 - 1)

Evaluate

Average speed = 2.5

Hence, the average speed is 2.5

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The function f(g) is 8/(8+9x) and the function g(f) is -8x/(x-9).

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are f(x)=x/(x-9) and g(x)= -8/x.

1) f(g)

Here, f(-8/x)= -8/x ÷ (-8/x -9)

= -8/x ÷ (-8-9x)/x

= -8/x × x/(-8-9x)

= 8/(8+9x)

2) g(f)

Now, -8/x/(x-9)

-8x/(x-9)

3) f(f)

Here, f(f) = x/(x-9) ÷ (x/(x-9) -9)

= x/(x-9) ÷ ((x-9x+81)/(x-9))

= x/(x-9) × (x-9)/(-8x+81)

= x/(-8x+81)

4) g(g)

Now, -8/(-8/x)

= 64/x

Therefore, the function f(g) is 8/(8+9x).

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Therefore the table values of which represents a linear function are table 2 and table 3

A linear equation is a first-order (linear) term and a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. A "linear equation of two variables" is what is sometimes referred to here, where y and x are the variables.

Here,

The values shown in table 2 have same constant rate of change of 3 units.

where as,

The values shown in table 3 have same constant rate of change of 5 units.

Therefore the table values of which represents a linear function are table 2 and table 3

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Answer:

x+x+10=90 being Right angle triangle.

2x=90-10

2x=80

x =40

then x+10= 40 + 10

= 50

Answer: 4.8

Step-by-step explanation: By using the intersecting chords theorem, we know that 10 * x = 6 * 8

This simplifies to 10x = 48

After dividing both sides by 10 we get x = 4.8

The equation of line that passes through (-2,-1) and is perpendicular to f(x) = (-1/5)x + 1 is f(x) = 5x + 9.

The slope-intercept form is expressed as;

y = mx + b

Where m is slope and b is the y-intercept.

Given the equation of the graph

f(x) = (-1/5)x + 1

Using the slope intercept, slope m is -1/5

The equation of a perpendicular line to f(x) = (-1/5)x + 1 must have a slope that is the negative reciprocal of the graph.

Slope of perpendicular line = -1 / (-1/5)

Slope of perpendicular line = 5

Plug the slope m = 5 and point (-2,-1) into point-slope formula and simplify.

( y - y₁ ) = m( x - x₁ )

( y - (-1) ) = 5( x - (-2) )

( y + 1 ) = 5( x + 2 )

y + 1 = 5x + 10

y = 5x + 10 - 1

y = 5x + 9

f(x) = 5x + 9

Therefore, the equation of the perpendicular line is f(x) = 5x + 9.

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The equation to represent the height of a glass slab is y=11x+2.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

From the given table, we have (2, 24) and (4, 46).

Substitute (x₁, y₁)=(2, 24) and (x₂, y₂)=(4, 46) in m=(y₂-y₁)/(x₂-x₁)

= (46-24)/(4-2)

= 22/2

= 11

Substitute m=11 and (x, y)=(2, 24) in y=mx+c, we get

24=11(2)+c

c=2

Substitute m=11 and c=2 in y=mx+c, we get

y=11x+2

Therefore, the equation to represent the height of a glass slab is y=11x+2.

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Answer:

Step-by-step explanation:

This is a right triangle that has two equal sides - so it is also isosceles.

It can be solved using Pythagoren Theorem.

a²  +  b²  =  c²

In this case a = b

so:  

6²  +  6²  = c²

36 +  36 =  c²

72  =  c²

[tex]\sqrt{72[/tex]  =  [tex]\sqrt{c^{2} }[/tex]

8.49 = c

round to 8.5

This is the length of the flap.

Answer:

320 pushups

Step-by-step explanation:

16/6= 8/3

8/3*120=32

Answer:

True, 50 tens times hundreds equal 40 tens times 5 hundreds

Step-by-step explanation:

50 tens times 4 hundreds equals to 40 ten times 5

hundreds because if you multiply 50 by 4 hundreds

you'll get 20,000 and if you multiply 40 tens by

hundred it will still give you 20,000

Therefore:

50 × 400 = 40 × 500

20,000 = 20,000

The dimensions of the rectangle are 40 and 18 units respectively

The formula for area is equal to the product of the length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides.

Given here: The length of a rectangle is 4 feet more than twice the width.

Then let the width be x then length is equal to 2x+4 and therefore the perimeter is 2(2x+4+x)=116

                       3x+4      = 58

                             3x    = 54

                               x     = 18

Hence, the dimensions of the rectangle are 40 and 18 units respectively.

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Answer:

49200 rs. so the cost of flooring =246*200=49200 rs

Step-by-step explanation:

we measure the area of veranda by taking width in addition of length and breadth- house area

it means

area of veranda =outer rectangle-inner rectangle

⇒area= (20+3+3)*(15+3+3)-20*15

⇒area=26*21-300

⇒area= 546-300

⇒area=246 m²

Hence , the cost of flooring =246*200=49200 rs.

The trigonometric ratios for the angle x in the triangle are given as follows:

The three trigonometric ratios are defined as follows:

In the right triangle in this problem, we have that d represents the hypotenuse, while the sides relative to angle x are given as follows:

These sides are used along with the definitions of each ratio to give the three trigonometric ratios of angle x.

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Therefore , the solution of he given problem of linear equation comes out to be x = 5.

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.

Here,

Given : 2x-4=6

To prove x =5

Thus,

We have to find the value of x

[tex]= > 2x =10\\= > x =10/2\\= > x =5[/tex]

Therefore , the solution of he given problem of linear equation comes out to be x = 5.

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Answer:

If

f

(

x

)

=

2

x

4

−

3

x

+

3

f(x)=2x

4

−3x+3, then what is the remainder when

f

(

Answer: Let's say,

y = the amount of money Perry will owe his brother after n months.

x = the principal (the initial amount borrowed) = 150

r = the interest rate per month = 7/100 = 0.07

n = number of months.

We know that Interest on a loan is calculated by multiplying the principal by the interest rate.

Therefore, the interest for n months is (0.07*x)*n

So to find the total amount Perry will owe his brother after n months, we need to add the interest to the principal amount.

y = x + interest

y = x + (r*x)n

y = x(1 + rn)

Therefore, the rule in the "y =..." form that will give the amount of money, y, Perry will owe his brother after n months, assuming that he doesn't make any payments is:

y = 150(1 + 0.07*n)

It's worth noting that this formula can be used to calculate the amount he will owe after any number of months by changing the value of n, and It's assuming he doesn't make any payments, meaning if he makes any payments, the total amount he will owe will change.

Step-by-step explanation:

here, on solving  company reduced the size of their percentage  container of dishwashing soap to 4.5 ounces from its original 5 ounce capacity.

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

The initial size was x.

Since 100% - 10% = 90%, 0.9x is 10% smaller than the original size.

90% of the original size is equal to 4.5 ounces,

hence the calculation we use to determine the original size x is:

0.9 x = 4.5 x

= 4.5 / 0. 9 x = 5

The bottle's initial capacity was 5 ounces.

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The width and the length that gives the largest possible areas are 75 meters by 37.5 meters

From the question, we have the following parameters that can be used in our computation:

Number of warehouses = 4

Perimeter of fence = 300 meters

Represent the width with x and the length with y

So, we have the following equations

Area = 4xy

Perimeter = 2(4x + y)

Substitute the known values in the above equation, so, we have the following representation

2(4x + y) = 300

Divide both sides by 2

2x + y = 150

Make y the subject

y = 150 - 2x

Substitute y = 150 - 2x in Area = 4xy

A = 4x(150 - 2x)

This gives

A = 600x - 8x²

Differentiate and set to 0

600 - 16x = 0

So, we have

16x = 600

Divide by 16

x = 37.5

Recall that

y = 150 - 2x

So, we have

y = 150 - 2 x 37.5

Evaluate

y = 75

Hence, the dimensions are 75 meters by 37.5 meters

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Answer: Yes.

Step-by-step explanation: They are in 1:4::1:4

Hope this helps

Answer:

Step-by-step explanation:

Are The Numbers 16,64,18 and 72 In Proportion​?

16 : 64 = 18 : 72

0.25 = 0.25

or

1/4 = 1/4

so your answer is yes

Answer:

Area= 46,000

Permiter= 4,600

Step-by-step explanation:

The formula to find the area of a rectangle is Length(L) times Width(W).

So 2,000(L) times 23 (W)= 46,000.

The formula for perimeter is 2(l+w).

So you're going to go 2,000 + 23 = 2,300 times 2 which equals 4,600.

Hope that helped, have a great day!!

The domain of the function F(x) = 3 [tex]\sqrt{x-2}[/tex] is {x : x ≥ 2 and x is a real number}.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Given function is,

F(x) = 3 [tex]\sqrt{x-2}[/tex]

Domain of this function is all the values of x for which the function is defined.

The expression [tex]\sqrt{x-2}[/tex] is defined only when the value of x - 2 is positive.

x - 2 > 0 ⇒ x > 2

So the function will be defined for all x > 2.

Hence the domain of the function is the set of all x such that x > 2.

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Therefore ,We can see that in equation 1 plunk yields the most lorgs at 30. So the plunk coin is the most valuable.

A mathematical statement known as an equation is created by joining two expressions using the equivalent sign. For instance, 5x - 5 = 25 is an equation. We can find that the variable x has a value of 6  by resolving this equation.

Here,

we need to convert everything to the same unit in order to establish a legitimate comparison when comparing units like inches, feet, and yards. Therefore, we would have to convert everything, for example, to inches. For these five coins, the same concept holds true. Either lorgs, sinds, plunks, harps, or dalts must be used for everything (pick one of those five).

It's equivalent to attempting to change a dollar amount into cents (for example, $1.37 becomes 137 cents). The alternative is to think about it as 1 dollar = 100 cents, 1 quarter = 25 cents, 1 dime = 10 cents, and so on.

The procedures in the various parts below are designed to convert all coinage to lorgs, which will serve as our base unit. Trial and error led me to the conclusion that the lorg coin had the lowest worth, thus I'm striving to obtain everything in lorgs.

The four equations provided are

4 lorgs to a sind

5 dalts x 2 plunks

2 harps from 5 sinds.

3 harps equal 1 plunk.

In that order, I'll refer to them as equations (1) through (4).

One sind equals four logs (1)

5 sinds = 20 lorgs; add 5 to both sides.

2 harps = 20 lorgs; in the equation, swap out "5 sinds" with "2 harps" (3)

1 harp = 10 lorgs; multiply both sides by 2, then write this as an equation (5)

Equation: 1 plunk = 30 lorgs (6)

Each of those equations enables us to determine the lorg value of the coins sind, dalt, harp, and plunk.

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The complete question is : " A nation has five types of coins: sinds, dalts, lorgs, harps, and plunks.1 sind = 4 lorgs ,2 plunks = 5 dalts ,5 sinds = 2 harps , 1 plunk = 3 harps Which coin is the most valuable? a) sindb) daltc) harpd) plunk"

Answer:

Step-by-step explanation: 55

Answer:

yes

Step-by-step explanation:

51 to nearest ten is 50

37 to nearest ten is 40

50 * 40 = 2000

and it's an estimate so yes

Answer:

The table with (-3, 2), (0, 2), etc.

Every input has exactly one output.

Hope this helps :)

Answer:y=(x+3)2−17

Step-by-step explanation: 3,11 5,15

If the probability of s1 = .6 the value above node degree 4 will be 320, as determined by the solution.

The area of mathematics known as probability deals with numerical descriptions about how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

S1 probability = 0.6

F's likelihood is 0.40.

If the probability of S1 is given a value of 0.6, then

Probability of S2 then equals 0.4.

Using the table equation's payoff values as an exception.

EV=Σ

Each decision's expected value is calculated.

EV(Node 8) = 0.6 * 100 + 0.4 * 300

= 180

EV(Node 9) = 0.6 * 400 + 0.4 * 200= 320

We chose the best value for node 4 from nodes 8 and 9.

The ideal option for node 9 is the line complicated branch with EV(node 8) = 180.

The ideal anticipated value is determined to be 320.

Node 4's EV is 320.

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Since matching angles are formed and the equal corners are congruent when a line joins two parallel lines, one of the choices isc=d.

Geometry refers to parallel lines as beams, straight lines that never overlap. Parallel planes are those that never cross each other while occupying the same three-dimensional space. Curves which are equal with each other and keep a predetermined minimum separation from one another must not overlap or intersect. Parallel lines on a plane are those that always have the same distance between them. A parallel line cannot be crossed. Perpendicular lines are those that intersect directly at a 90 degree angle.

Here,

Given :  vertical angles, A = d also represents a solution.

B+d=180 as a result of b+c=180 therefore

B+d=180 as a result of b+c=180 therefore Since a=d, c=d, and b+d=180, the answer is B,C,E.

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The area of the parallelogram is 72 square units. Option B

The formula for calculating the area of a parallelogram is expressed as;

A = bh

Given that;

From the information given, we have that;

Now, substitute the values

x + y = 8 + 4

add the values

x + y = base = 12 units

h = 6 units

Now, substitute the values into the formula, we get;

Area, A = 12(6)

multiply the values

Area, A = 72 square units

Hence, the value is 72 square units

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