I need help with this problem if do thank you a lot

Answer:

6

Step-by-step explanation:

Median is the number in the middle, so 6 is the middle number in the data set.

On that day, 241 adults and 44 children swam at the public pool.

Let's use a system of equations to solve the problem:

From the problem, we know that:

x + y = 285 (the total number of people who swam)

1.25x + 2.5y = 657.5 (the total amount collected in admission fees)

We can use the first equation to solve for x in terms of y:

x = 285 - y

Substituting this expression for x into the second equation, we get:

1.25(285 - y) + 2.5y = 657.5

Expanding and simplifying, we get:

356.25 - 1.25y + 2.5y = 657.5

1.25y = 301.25

y = 241

Substituting this value of y into the equation x + y = 285, we get:

x + 241 = 285

x = 44

Therefore, there were 44 children and 241 adults who swam at the public pool that day.

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After adding the 2 given values the resultant answer is 13.3922 respectively.

One of the four fundamental operations in mathematics is addition, along with subtraction, multiplication, and division.

The entire amount or sum of the two whole numbers is obtained by adding them.

Mathematicians utilize addition as their main arithmetic operation to determine the sum of two or more numbers.

For instance, 7 plus 6 equals 13.

So, add the 2 given values as follows:

= 8.563 + 4.8292

= 13.3922

Therefore, after adding the 2 given values the resultant answer is 13.3922 respectively.

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Answer:

d = √ (4 - (-5))² + (-9 - 2)²

d = √ 9² + (-11)²

d = √81 + 121

d = √202

d ≈ 14.21

Therefore, the distance between (-5, 2) and (4, -9) is approximately 14.21 units. The answer is (C) 14.21.

Step-by-step explanation:

leave thanks

a. The numbers are written as;   -1     7      5     -10   0

b. In the form, Quotient + Reminder/x+ 2

-x⁴ - 7x³ - 5x² - 10 + 0/x + 2

Synthetic division can simply be described as a mathematical method that is used to perform the division operation on algebraic expressions such as  polynomials when the divisor is in the form of linear factor.

The steps in performing the synthetic division are;

From the information given, we have that;

-x⁴ + 5x³ + 19x² - 20 divided by x + 2

Then, we have;

-2)      -1      5      19   0   -20

                 2     -14    -10  20

          -1     7      5     -10   0

Then, we have;

-x⁴ - 7x³ - 5x² - 10

The remainder is 0

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The proof is  the intersection of all subgroups in H is a subgroup of G containing S.

we start by showing that the intersection is a subgroup of G. Let A and B be two subgroups in H.

we define that  A and B contain S which  means that A ∩ B contains S as well, since every element in S is in both A and B. Moreover, A ∩ B is closed under the group operation and inverses, since A and B are subgroups. Therefore, A ∩ B is a subgroup of G.

we go ahead to show that the intersection contains S and it is known that  S is a subset of each subgroup in H, it is also a subset of their intersection. Thus, the intersection of all subgroups in H contains S.

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Mal can make 6 different outfits by selecting one shirt and one pair of pants from her wardrobe.

As per the question, there are 3 options for shirts and 2 options for pants

The total number of outfits is found by multiplying the number of options for the first item (shirts) by the number of options for the second item (pants) because each combination of one shirt and one pair of pants counts as a unique outfit.

Use the multiplication principle of counting: for each shirt, there are 2 different pants to pair with, giving a total of 3 x 2 = 6 possible outfits.

Therefore, she can make 6 different outfits.

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To test the claim that more than one-third of employers have sent an employee home for inappropriate attire, we can set up the following null and alternative hypotheses:

Null hypothesis: p ≤ 1/3

Alternative hypothesis: p > 1/3

where p is the true proportion of all employers who have sent an employee home for inappropriate attire.

We can use the sample proportion, 964/2765 = 0.349, as an estimate of the true proportion p. To test the hypotheses, we can calculate the test statistic z as:

z = (p - 1/3) / sqrt((1/3)*(2/3)/n)

where n is the sample size (2765).

Plugging in the values, we get:

z = (0.349 - 1/3) / sqrt((1/3)*(2/3)/2765) = 4.28

Using a standard normal distribution table or calculator, the P-value for this test is less than 0.0001 (or approximately 0.0000 when rounded to four decimal places), indicating strong evidence against the null hypothesis.

Therefore, we can reject the null hypothesis and conclude that there is convincing evidence to support the claim that more than one-third of employers have sent an employee home for inappropriate attire.

Answer:

1st option will be your answer

Step-by-step explanation:

A figure that correctly shows ΔA'B'C' using the solid line include the following: A. figure A.

In Mathematics and Geometry, a dilation can be defined as a type of transformation which typically changes the size of a geometric shape, but not its shape. This ultimately implies that, the size of the geometric shape would be increased (enlarged) or decreased (reduced) based on the scale factor applied.

In this exercise, we would sketch the image of ABC after a dilation by a scale factor of 2/3 centered at P as shown in the image attached below.

Based on the image (see attachment), we can logically deduce that each vertex is 2/3 times as far from center P as the original vertex and each segment is 2/3 times as long as the original:

Scale factor = AP/A'P = BP/B'P = CP/C'P = 2/3

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Gain on Residual of Right-of-Use Asset ..................................... 1,500.00

The lease is a finance lease since at least one of the classification criteria is met.

*Present value = Lease payments × PV factor for 3 payments at 10% + (asset and liability) Guaranteed residual value × PV factor for single sum at 10%

= ($47,500 × 2.735537) + ($15,000 × 0.751315)

= $129,938.01 + $11,269.73

= $141,207.74

aThe amount of the capital lease obligation is the PV of the lease payments ($129,938.01) plus PV of the amount expected to be paid due to the residual value guarantee ($3,756.58 = $5,000 × 0.751315)

*Adjusted for $0.01 rounding error

3.

2019

Jan. 1 Right-of-Use Asset ...................................................... 133,694.59

Lease Liability ................................................................................ 133,694.59

1 Lease Liability ............................................................. 47,500.00

Cash ................................................................................................ 47,500.00

Dec. 31 Interest Expense ......................................................... 8,619.46

Lease Liability ................................................................................ 8,619.46

31 Maintenance Expense ............................................. 2,500.00

Property Tax Expense ................................................... 1,000.00

Cash ......................................................................................... 3,500.00

31 Amortization Expense ............................................... 44,564.86

Right-of-Use Asset

[133,694.59 ÷ 3] .......................................................................... 44,564.86

2020

Jan. 1 Lease Liability ............................................................. 47,500.00

Cash ................................................................................................ 47,500.00

Dec. 31 Interest Expense ......................................................... 4,731.41

Lease Liability ................................................................................ 4,731.41

31 Insurance Expense .................................................... 2,500.00

Property Tax Expense .................................................... 1,000.00

Cash ................................................................................................ 3,500.00

31 Amortization Expense ............................................... 44,564.86

Right-of-Use Asset ......................................................................... 44,564.86

2021

Jan. 1 Lease Liability ............................................................. 47,500.00

Cash ................................................................................................ 47,500.00

Dec. 31 Interest Expense ......................................................... 454.54

Lease Liability ................................................................................ 454.54

31 Insurance Expense .................................................... 2,500.00

Property Tax Expense .................................................... 1,000.00

Cash ................................................................................................ 3,500.00

31 Amortization Expense ............................................... 44,564.86

Right-of-Use Asset ......................................................................... 44,564.86

31 Lease Liability ............................................................. 5,000.00

Cash ................................................................................................ 3,500.00

Gain on Residual of Right-of-Use Asset ..................................... 1,500.00

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The lateral surface area of the cone is 147.15 ft² and the surface area of the cylinder is 979.68 ft²

To solve this problem, we have to use the formula of lateral surface area of a cone and the surface area of the cylinder which are given as;

In the question given;

Substituting the values into the formulas

a. Lateral surface area of cone = πr√(h² + r²)

LSA = 3.14 * 6 * √(5² + 6²)

LSA = 147.15 ft²

b. Surface area of cylinder = 2πrh + 2πr²

SA = 2 * 3.14 * 6 * 20 + 2 * 3.14 * 6²

SA = 979.68 ft²

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Answer:

1.  (-1, -3)

2.  y = x - 5

Step-by-step explanation:

To find the values of a where the point (a, 3a) is a distance of 5 units from P(2, 1) use the distance formula.

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance Formula}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where:\\ \phantom{ww}$\bullet$ $d$ is the distance between two points. \\\phantom{ww}$\bullet$ $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]

Given values:

Substitute the given values into the distance formula and solve for a:

[tex]\begin{aligned}\sqrt{(a-2)^2+(3a-1)^2}&=5\\(a-2)^2+(3a-1)^2&=25\\a^2-4a+4+9a^2-6a+1&=25\\10a^2-10a-20&=0\\a^2-a-2&=0\\a^2-2a+a-2&=0\\a(a-2)+1(a-2)&=0\\(a+1)(a-2)&=0\\\\a+1&=0 \implies a=-1\\a-2&=0 \implies a=2\end{aligned}[/tex]

Substitute the found values of a into the point coordinate formula, (a, 3a):

[tex]a=-1 \implies (-1,-3)[/tex]

[tex]a=2 \implies (2, 6)[/tex]

As the point is in the third quadrant, this means that the x and y coordinates are negative.

Therefore, the point with coordinates of the form (a, 3a) that is in the third quadrant and is a distance 5 units from P (2, 1) is:

[tex]\large\boxed{(-1, -3)}[/tex]

[tex]\hrulefill[/tex]

The perpendicular bisector of segment AB is the line that passes through the midpoint of AB and is perpendicular to AB.

To find the midpoint of AB, use the midpoint formula.

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Midpoint between two points}\\\\Midpoint $=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the endpoints.\\\end{minipage}}[/tex]

Let (x₁, y₁) = A = (-6, 3)

Let (x₂, y₂) = B = (8, -11)

Substitute the values into the midpoint formula:

[tex]\text{Midpoint of $AB$}=\left(\dfrac{8-6}{2},\dfrac{-11+3}{2}\right)=\left(1,-4\right)[/tex]

Therefore, the midpoint of AB is (1, -4).

To find the slope of AB, use the slope formula.

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-11-3}{8-(-6)}=\dfrac{-14}{14}=-1[/tex]

The slope of a line that is perpendicular to AB is the negative reciprocal of the slope of AB.

Therefore, the slope of the line perpendicular to AB is m = 1.

To determine the equation of the perpendicular bisector of AB that passes through the midpoint of AB and is perpendicular to AB, substitute the found slope, m = 1, and the midpoint (1, -4) into the point-slope formula:

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-(-4)=1(x-1)[/tex]

[tex]\implies y+4=x-1[/tex]

[tex]\implies y=x-5[/tex]

Therefore, the formula that expresses the fact that an arbitrary point P(x, y) is on the perpendicular bisector "l" of segment AB is:

[tex]\large\boxed{y=x-5}[/tex]

Thomas needs to achieve a compound interest rate of approximately 41.4% per year in order to turn R5,000 into R10,000 in two years.

Simple interest and compound interest are the two primary types of interest.

Simple interest does not account for any accumulated interest from prior periods and is computed just on the principal amount of a loan or investment. It can be computed using the following method and is often expressed as a percentage of the principal:

I = P * r * t

If P is the principal, r is the interest rate, and t is the time period, and I is the simple interest.

Compound interest, on the other hand, adds the principle amount to the accrued interest from earlier periods. This indicates that each period's interest is computed using a higher balance than the previous period's balance, resulting in a higher interest rate.

Compound interest is a way to calculate interest that accounts for both the original principal and the interest that has accrued over the course of prior periods. To put it another way, it is the interest that is generated on both the initial investment and the interest that has been accrued over time on that investment.

For instance, if you deposited $1,000 in a savings account with a 5% annual interest rate, you would have received $50 in interest after the first year (5% of $1,000). This $50 would be added to your principal debt using compound interest, resulting in interest being paid on both the initial $1,000 loan and the additional $50 in interest that was accrued the prior year.

Your investment may rise significantly as a result over time.

Compound interest is calculated using the following formula:

A = P(1 + r/n)nt

where A represents the overall sum, P represents the original principal, r represents the yearly interest rate, n represents the number of times the interest is compounded annually, and t represents the passage of time in years.

According to question,

Simple interest and compound interest are the two primary types of interest.

Simple interest does not account for any accumulated interest from prior periods and is computed just on the principal amount of a loan or investment. It can be computed using the following method and is often expressed as a percentage of the principal:

I = P * r * t

If P is the principal, r is the interest rate, and t is the time period, and I is the simple interest.

Compound interest, on the other hand, adds the principle amount to the accrued interest from earlier periods. This indicates that each period's interest is computed using a higher balance than the previous period's balance, resulting in a higher interest rate.

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Sin angle PAQ ≈ 0.6.

The sine ratio in trigonometry is the ratio of the hypotenuse's length to the length of the side that faces an angle in a right triangle. Theta is the angle opposed to the side whose length is the "opposite" side, hence sin(theta) = opposite/hypotenuse. The symbol for it is sin(theta) or just sin(theta). One of the six trigonometric ratios, the sine ratio is frequently employed to resolve issues concerning right triangles and angles.

A square is a regular quadrilateral in which all four sides are of equal length and all four angles are right angles (90 degrees). It can be thought of as a special type of rectangle where the length and width are equal. The area of a square is calculated by multiplying the length of one side by itself, or by squaring the length of one side. The perimeter of a square is calculated by adding the length of all four sides together. Squares have many practical applications, including in construction, geometry, and design.

According to the question

The Pythagorean theorem can be used to determine the length of side AB first:

(BC - PC) = AB2 + BP22 AB 2 equals 4 + (8 - 4) 2 AB 2 equals 16 + 16 AB = 4

In a similar manner, we may determine side AD's length:

BQ² + (CD - QC) + AD² AD² = 4² + (8 - 4)² AD² = 16 + 16

AD = 4√2

The Pythagorean theorem can now be used to determine the diagonal AC's length:

AC2 equals AB2 + BC2 AC2 equals (42) + 82 AC2 equals 32 + 64 AC2 equals 4/6

The Pythagorean theorem can also be used to determine the length of the diagonal BD:

BD2 equals AD2 plus BC2 BD2 equals (42) + 82 BD2 equals 32 + 64

BD = 4√6

We know that APQC is a kite with diagonals AC and BD since a square's diagonals are perpendicular to one another and cut each other in half. As a result, we may calculate that PQ is half as long as diagonal AC:

PQ = AC/2 = (4√6)/2 = 2√6

We may determine the cosine of angle PAQ using the law of cosines:

cos(PAQ) equals (2 * AP * AQ)/(AP * AQ)

Since these numbers can be substituted in because AP = AQ = AB = 42:

cos(PAQ) is equal to (2(32) - (2(6))/2 * 32.

cos(PAQ) equals (64-24)/(64).

sin(PAQ) = 5/8

In order to determine the sine of angle PAQ, we can utilise the Pythagorean identity:

(1 - cos(PAQ)) = sin(PAQ)

(1 - (5/8)) = sin(PAQ)

sin(PAQ) is 0.6.

Sin angle PAQ thus equals 0.6.

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Answer: c=3 m=5

Step-by-step explanation:

c is where it hits the y-axis

c=-3

m=slope, count rise/run = 5/1 = 5    pick points that hit the grid squarely

The equation of the line, represented in the graph is y = 5x +15.

And the value of m is 5 and the value of c is 15.

Use the concept of the equation of line defined as:

A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it.

And the equation the line passing through (x₁ , y₁) and (x₂, y₂):

y -  y₁ = m(x - x₁)

Where the slope of the line,

[tex]m = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

In the figure, it is shown that,

The line is passing through the points:

(0, -3) and (1, 2)

Then the slope of this line is,

[tex]m = \dfrac{2 +3 }{1-0}\\\\m = 5[/tex]

Now the equation of line be,

y - 0 = 5(x + 3)

y = 5x + 15 which  is of the form y = mx  + c

Now after comparing we get,

m = 5 and c = 15

Hence,

The equation of the line is y = 5x + 15:

m = 5 and c = 15

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The estimated total cost for a production volume of 800 units is $7,906.39.

To develop an estimated regression equation, we can use the least squares method to fit a linear equation of the form:

Total Cost = a + b * Production Volume

where a is the intercept and b is the slope of the line. We can use the given data to calculate the values of a and b as follows:

First, calculate the mean of production volume and total cost:

mean(Production Volume) = (400 + 450 + 550 + 600 + 640 + 700 + 750) / 7 = 586.43

mean(Total Cost) = (5000 + 6000 + 6400 + 6900 + 7400 + 8000) / 6 = 6783.33

Next, calculate the sum of squares of deviations:

SSx = Σ(Production Volume - mean(Production Volume))² = 166,950

SSy = Σ(Total Cost - mean(Total Cost))² = 11,223,333

Calculate the sum of cross-deviations:

SSxy = Σ((Production Volume - mean(Production Volume)) * (Total Cost - mean(Total Cost))) = 892,500

Calculate the slope:

b = SSxy / SSx = 892,500 / 166,950 = 5.34

Calculate the intercept:

a = mean(Total Cost) - b * mean(Production Volume) = 6783.33 - 5.34 * 586.43 = 3414.39

Therefore, the estimated regression equation is:

Total Cost = 3414.39 + 5.34 * Production Volume

For example, if the production volume is 800 units, the predicted total cost would be:

Total Cost = 3414.39 + 5.34 * 800 = 7906.39

Therefore, the estimated total cost for a production volume of 800 units is $7,906.39.

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The examples of unit rate are given below and this can be determined by using the definition of unit rate.

The unit rate is nothing but a ratio that represents the rate of something per unit.

Examples  --

1) A car is driving at a speed of 50 kilometers per hour. The 50 km/hr represents the unit rate.

2) The cost of the potatoes is $2 per pound. The $2/pound represents the unit rate.

3) The density of a substance is 4 Kg per liter. The 4kg/lt represents the unit rate.

The correct three equations that can be used to solve for the angle of elevation () from the bottom of the hill to the top of the hill are,

⇒ tan θ = 550 / 3050

⇒ sin θ = 550 / 3600

⇒ cos θ = 3050/ 3600

We have to given that;

A 3,050 foot long road travels directly up a 550 foot tall hill.

Now, We can formulate;

1) In this case, the opposite side is the height of the hill 550 feet and the adjacent side is the length of the road 3,050 feet.

So, the equation becomes;

⇒ tan θ = 550 / 3050

2)  In this case, the opposite side is the height of the hill 550 feet and the hypotenuse is the length of the road plus the height of the hill,

3050 + 550 = 3600 feet

So, the equation becomes;

⇒ sin θ = 550 / 3600

3)  In this case, the adjacent side is the length of the road 3050 feet and the hypotenuse is the length of the road plus the height of the hill,

3050 + 550 = 3600 feet.

So, the equation becomes;

⇒ cos θ = 3050/ 3600

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Answer:

[tex]y=\frac{-7}{2}x+3[/tex]

Step-by-step explanation:

This is currently in standard form, so get it into slope-intercept form instead:

Subtract '7x' from both sides:

[tex]2y=-7x+6[/tex]

Divide by 2 on both sides to isolate the 'y':

[tex]y=\frac{-7}{2}x+3[/tex].

The best decision to purchase a old car is cheaper compare to new car as per the total cost for each scenario over three years.

Compare the total costs of keeping his old car versus buying a new car, Manny needs to consider all the costs involved.

These include the cost of gas, the cost of maintenance and repairs, and the cost of purchasing the new car.

First, calculate the total cost of keeping his old car for three years.

Gas Cost,

Manny drives 190 miles per week,

which is approximately 9,880 miles per year 190 miles x 52 weeks.

With his old car's fuel efficiency of 18 miles per gallon,

He will use approximately 549 gallons of gas per year 9,880 miles ÷ 18 mpg.

At the current gas price of $ 2.9 per gallon, his annual gas cost will be $ 1,593 (549 gallons x $ 2.9 per gallon).

Over three years, his total gas cost will be $ 4,779.

Maintenance and Repairs Cost,

Manny's old car needs an average of $ 770 per year in maintenance and repairs.

Over three years, his total maintenance and repairs cost will be $ 2,310.

Total Cost of Keeping His Old Car,

Adding the gas cost and the maintenance and repairs cost,

Manny's total cost of keeping his old car for three years will be $ 7,089.

Now let's calculate the total cost of buying the new car.

Cost of Purchasing the New Car,

The new car costs $ 6,500, which he will pay over three years.

This works out to a monthly payment of approximately $ 181.94.

Gas Cost,

With the new car's fuel efficiency of 32 miles per gallon,

Manny will use approximately 309 gallons of gas per year (9,880 miles ÷ 32 mpg).

At the current gas price of $ 2.9 per gallon,

His annual gas cost will be $ 897.10 (309 gallons x $ 2.9 per gallon).

Over three years, his total gas cost will be $ 2,691.30.

Maintenance and Repairs Cost,

The new car will only require an average of $ 10 per month for general maintenance.

Over three years, his total maintenance and repairs cost will be $ 360.

Total Cost of Buying the New Car,

Adding the cost of purchasing the new car, the gas cost, and the maintenance and repair cost

= 6500 + 2691.30 + 360

=$9551.30

$9551.3 > $7089

Total cost of new car > Total cost of old car.

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It will cost approximately $2940 to cover the circular region with mud.

The term "cost" in mathematics usually refers to the sum of money or resources needed to acquire or manufacture something.

It can be quantified as a number, frequently in a particular currency.

The formula C = 2r, where r is the circle's radius, determines the circumference of a circle.

In this case, we know that the circumference is about 157 feet, so we can set up an equation:

157 = 2πr

Solving for r, we get:

r = 157 / (2π) ≈ 25

So the radius of the circular region is approximately 25 feet.

The equation A = r² determines a circle's surface area.

Using the radius we just found, we can calculate the area:

A = π(25)² ≈ 1963.5 square feet

The cost to cover 1 square foot with mud is $1.50, so the cost to cover the entire area with mud is:

1963.5 × $1.50 = $2945.25

Rounding to the nearest ten dollars, the cost is:

$2940

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Answer:

D

Step-by-step explanation:

y = -0.04088x^2 + 0.4485x + 1.862

y is the amount of precipitation,

x is the month (1 for January, 2 for February, etc.)

The amount of precipitation from Jan to Dec are listed below

(generated with R language, a handy software)

2.26962 2.59548 2.83958 3.00192 3.08250 3.08132 2.99838 2.83368 2.58722 2.25900 1.84902 1.35728

The month with lowest precipitation is December

Answer:

D) December

Step-by-step explanation:

The given equation to model the monthly precipitation in Phoenix, Arizona is:

[tex]y = -0.04088x^2 + 0.4485x + 1.862[/tex]

where:

To determine the month in which Phoenix received the lowest amount of precipitation, fill in the table by inputting each value of x into the equation. Round the value of y to 2 decimal places.

[tex]\begin{array}{|l|c|c|}\cline{1-3}&x&y\\\cline{1-3}\sf January &1&2.27\\\cline{1-3}\sf February &2&2.60\\\cline{1-3}\sf March &3&2.84\\\cline{1-3}\sf April &4&3.00\\\cline{1-3}\sf May &5&3.08\\\cline{1-3}\sf June &6&3.08\\\cline{1-3}\sf July &7&3.00\\\cline{1-3}\sf August &8&2.83\\\cline{1-3}\sf September &9&2.59\\\cline{1-3}\sf October & 0&2.26\\\cline{1-3}\sf November &11&1.85\\\cline{1-3}\sf December &12&1.36\\\cline{1-3}\end{array}[/tex]

Reading from the table, the month in which Phoenix received the lowest amount of precipitation was December, when only 1.36 inches of precipitation was recorded.

[tex]y=\frac{1}{3}x-4[/tex].

[tex]y=3x+12[/tex]

[tex]x=3y+12[/tex]

[tex]x-12=3y+12-12\\ \\x-12=3y[/tex]

[tex]\frac{x-12}{3} =\frac{3y}{3} \\ \\\frac{x-12}{3} =y[/tex]

[tex]y=\frac{x-12}{3}[/tex]

[tex]y=\frac{x}{3}-\frac{12}{3} \\\\y=\frac{1}{3}x-4[/tex]

Check the attached image to see both of the functions in the cartesian plane and how the domains and ranges are interchanged between each function.

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Learn more about inverses of mathematical functions here:  

https://brainly.com/question/29897264    (Definition of inverse)

https://brainly.com/question/29102418      (Exercise 1)

https://brainly.com/question/28281615      (Exercise 2)

The length of the other two sides in the triangle ABC using Law of Sines is b = 18.1 and c = 14.3.

Given a ΔABC.

Angles are given as, ∠B = 70° and ∠C = 48°.

∠A = 180° - (70° + 48°) = 62°

The sides are given as,

BC = 17

Using law of sines, if a, b and c are sides opposite to the angles A, B and C respectively, then,

a / sin A = b / sin B = c / sin C

Using the law of sines,

17 / Sin (62°) = b / Sin (70°) = c / Sin (48°)

Taking the first two,

17 / Sin (62°) = b / Sin (70°)

b = [17 × Sin (70°)] / Sin (62°)

b = 18.09 ≈ 18.1

Taking the other two,

17 / Sin (62°) = c / Sin (48°)

Solving,

c = 14.308 ≈ 14.3

Hence the lengths are b = 18.1 and c = 14.3.

Learn more about Law of Sines here :

https://brainly.com/question/17289163

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To solve for b and c, we can use the Law of Sines, which states that for any triangle △ABC,

a/sin(∡A) = b/sin(∡B) = c/sin(∡C)

Using this formula, we can write:

b/sin(∡B) = a/sin(∡A)

c/sin(∡C) = a/sin(∡A)

Substituting the given values, we get:

b/sin(70∘) = 17/sin(∡A)

c/sin(48∘) = 17/sin(∡A)

We can solve for sin(∡A) in both equations:

sin(∡A) = 17sin(70∘)/b

sin(∡A) = 17sin(48∘)/c

Setting the two expressions equal to each other, we get:

17sin(70∘)/b = 17sin(48∘)/c

Solving for c, we get:

c = (b*sin(48∘)*17)/(sin(70∘))

To solve for b, we can use the Law of Cosines, which states that for any triangle △ABC,

c^2 = a^2 + b^2 - 2ab*cos(∡C)

Substituting the given values and the value we found for c, we get:

((bsin(48∘)17)/(sin(70∘)))^2 = 17^2 + b^2 - 217b*cos(48∘)

Simplifying and solving for b, we get:

b ≈ 11.28

Substituting this value into the equation we found for c, we get:

c ≈ 14.08

Therefore, b ≈ 11.28 and c ≈ 14.08.

I hope this answer helps you!

BTW is this Khan Academy/Albert.io?

The only solution that satisfies the original equation is x ≈ 17.465. The other solution, x ≈ 1.535, is an extraneous solution.

How to check the equation has extraneous solutions or not?

We need to check if either of these solutions is an extraneous solution, which means it does not satisfy the original equation.

Here given equation,

√(3x - 5) = x - 8

Here we want to isolate the square root on one side and square both sides.

Squaring both side,

√(3x - 5)² = (x - 8)²

expanding the right side

3x - 5 = x² - 16x + 64

bringing all terms to one side)

x² - 19x + 69 = 0

We are solving this quadratic equation using the quadratic formula,

x = [19 ± √(19²- 4(1)(69))] / (2(1))

x = [19 ± √(253)] / 2

x ≈ 1.535 or x ≈ 17.465

Now, we plug each solution back into the original equation and see if we get a true statement.

Checking x ≈ 1.535:

√(3(1.535) - 5) = 1.535 - 8

√(0.605) ≈ -6.465 (not true)

Checking x ≈ 17.465,

√(3(17.465) - 5) = 17.465 - 8

√49.59 ≈ 9.465 (true)

Therefore, the only solution that satisfies the original equation is x ≈ 17.465. The other solution, x ≈ 1.535, is an extraneous solution.

Learn more about extraneous solution here,

https://brainly.com/question/28595231

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Answer:

(1/2)(3 - (-3))(4 - (-5)) = (1/2)(6)(9)

= 27 square units