This is my last ONE I HAVE TO ANSWER HELP ME

We will have that Sarah's function is the correct one, since each hour she will get $9, then when we multiply will give us the amount of money she makes in the number of hours.

H = 9h

Answer:

x = 50

Step-by-step explanation:

The sum of all interior angles of a quadrilateral is always 360°.

Step 1: Set up equation

x + 10 + 3x + 2x + x = 360

Step 2: Solve for x

The weighted mean cost of a haircut for Malachi is $15.67, divided by the total number of haircuts, which comes to 6, to yield a total cost of $94.00.

We must compute the total cost of all haircuts and divide it by the total number of haircuts in order to determine the weighted mean price of a haircut for Malachi. The expense of each haircut must be weighed according to the frequency with which it occurred, though, because they varied in price.

To begin, let's figure out how much each haircut will cost overall:

2 haircuts at $12.00 each = $24.00

3 haircuts at $15.00 each = $45.00

1 haircut at $25.00 = $25.00

Total cost = $24.00 + $45.00 + $25.00 = $94.00

Next, We must determine the total number of cuts:

2 haircuts + 3 haircuts + 1 haircut = 6 haircuts

Finally, The weighted mean cost of a haircut can be determined by dividing the total cost by the total number of haircuts:

The weighted mean cost of a haircut = Total cost / Total number of haircuts

= $94.00 / 6 haircuts

= $15.67 per haircut (rounded to the nearest cent)

Therefore, Malachi's weighted mean haircut expense is $ 15.67 , divided by the total number of haircuts, which comes to 6, to yield a total cost of $94.00.

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Answer:

-4 and 4.

Step-by-step explanation:

they are both the same distance away from zero on a number line so they cancel out to equal 0

Answer:

4

Step-by-step explanation:

4-4=0 we know that for the number to be zero it has to subtract the opiset of itself such a 4 and -4

Answer:

70%

Step-by-step explanation:

The fraction of the game won is 14/20

Percent means out of 100

14/20 * 5/5 = 70/100

The percent is 70%

Answer:

Step-by-step explanation:

Since 1cm=10mm

(big to small multiply, small to big divide)

3579/10=357.9

so 1.1 cm or 11 mm

The resort has set clear guidelines for rowboat rentals, including a limit of four people per boat and a maximum weight capacity of 800 pounds. These rules help to provide a safe and enjoyable experience for customers using the rowboats.

The summer resort has a policy that restricts the number of people allowed in each rowboat to four. Additionally, each boat is designed to hold a maximum weight capacity of 800 pounds. This policy is likely in place to ensure the safety of the guests and to prevent any accidents or mishaps on the water. In terms of pricing and availability, it's possible that the resort may offer different rental options depending on the size of the party or the length of time they wish to rent the boat for.

It's important for customers to adhere to the rules and regulations set forth by the resort to ensure a fun and safe experience for all. The summer resort rents rowboats to customers with a maximum capacity of four people per boat. This is to ensure the safety and comfort of the customers using the boats. Each rowboat is designed to hold no more than 800 pounds in total weight. This weight limit is put in place to maintain the boat's stability and prevent any accidents from occurring due to overloading.

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The fraction of the cake that was ron's pieces is 1/5.

Ratio demonstrates how many times one number can fit into another number. Ratios contrast two numbers by ordinarily dividing them. A/B will be the formula if one is comparing one data point (A) to another data point (B).

Since Mrs Jones gave 1/5 of a cake to her neighbour, the remaining fraction will be:

= 1 - 1/5

= 4/5

The fraction of the cake that was ron's pieces will be:

= 2/(1+3+4) × 4/5

= 2/8 × 4/5

= 8/40

= 1/5

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Answer:

2 linear equations can only have 1 solution.

Step-by-step explanation:

⭐ What is a linear equation?

⭐What does "solution" mean?

Thus, when 2 linear equations intersect, they can only have 1 solution, because straight lines can only meet at 1 point.

Answer:

Step-by-step explanation:

bearing is the angle which a line makes with the north.

Answer: $3.50

Step-by-step explanation:

He came home with $3.00.

He gave Rene $1.50 which means that $1.50 was deducted from his money.

Pedro gave him $1.00 which added to his money.

Money he had therefore was:

= 3 + 1.50 - 1

= $3.50

Answer:

f(-4)=85

Step-by-step explanation:

Given function

f(x)= 2x^2-10x+13

Now put x= -4, We get

f(-4)=2(-4)^2-10(-4)+13

f(-4)=2(16)+40+13

f(-4)=32+53

f(-4)=85

Therefore, we can order the integrals as follows, from smallest to largest:

a: ∫80f(x)dx (interval [3, 0], negative values, short length)

b: ∫30f(x)dx (interval [0, 5], positive values, longer length)

d: ∫50f(x)dx (interval [0, 5] and part of [5, 8], positive values, longest length)

c: ∫85f(x)dx (interval [5, 8], positive values, short length)

However, we can compare the given intervals in terms of their length and the position of the function on those intervals to determine the order of the integrals. From left to right, the intervals and their approximate lengths are:

Interval [3, 0]: length 3

Interval [0, 5]: length 5

Interval [5, 8]: length 3

Now we need to examine the position of the function on each interval. From the graph, we can see that the function is negative on the interval [3, 0] and positive on the intervals [0, 5] and [5, 8].

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Complete question:

For the function f whose graph is given below, list the following quantities in increasing order, from smallest to largest.

a: ∫80f(x)dx

b: ∫30f(x)dx

c: ∫85f(x)dxd: ∫50f(x)dx

Answer:

Step-by-step explanation:

Answer:

The correct answer is $6,373.02.

We can use the formula for present value of an annuity:

PV = PMT x ((1 - (1 + r/n)^(-n*t)) / (r/n))

Where PV is the present value, PMT is the monthly payment, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

Plugging in the values, we get:

PV = 300 x ((1 - (1 + 0.12/12)^(-12*2)) / (0.12/12))

PV = $6,373.02

Therefore, the present value of Maria's investment is $6,373.02.

The measure of arc BC is 720 times the measure of angle BAC.

Given that AC is the diameter of the circle and AB is a chord with a length of 16 units, we need to find BC (the length of the other chord) and mBC (the measure of angle BAC).

To find BC, we can use the property of chords in a circle. If two chords intersect within a circle, the products of their segments are equal. In this case, since AB = BC = 16 units, the product of their segments will be:

AB * BC = AC * CE

16 * BC = 2 * r * CE (AC is the diameter, so its length is twice the radius)

Since the area of the circle is given as 289 square units, we can find the radius (r) using the formula for the area of a circle:

Area = π * r^2

289 = π * r^2

r^2 = 289 / π

r = √(289 / π)

Now, we can substitute the known values into the equation for the product of the segments:

16 * BC = 2 * √(289 / π) * CEBC = (√(289 / π) * CE) / 8

To find mBC, we can use the properties of angles in a circle. The angle subtended by an arc at the center of a circle is double the angle subtended by the same arc at any point on the circumference. Since AC is a diameter, angle BAC is a right angle. Therefore, mBC will be half the measure of the arc BC.

mBC = 0.5 * m(arc BC)

To find the measure of the arc BC, we need to find its length. The length of an arc is determined by the ratio of the arc angle to the total angle of the circle (360 degrees). Since mBC is half the arc angle, we can write:

arc BC = (mBC / 0.5) * 360

arc BC = 720 * mBC

Therefore, the length of the arc BC equals 720 times the length of the angle BAC.

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Answer:

12x - 6

Step-by-step explanation:

\( \rm \: 4 + 5(3x - 2) - 3x\)

\( \rm \: = 4 + 15x - 10 - 3x \: \sf (distribute \: the \: 5)\)

\( \rm= 12x - 6 \: \sf (combine \: like \: terms)\)

\( \rm= 6(2x - 1) \: \sf (factor \: out \: a \: 6)\)

\( \rm \: = 6(2x) - 6(1) \: \sf (distribute \: the \: 6)\)

\( \rm \:= 12x - 6 \: \sf (simplify)\)

Answer:

As the sample size increases, the variability decreases.

Step-by-step explanation:

The actual departures from the mean are used to quantify variability. The variance would be lower the fewer the deviations.

By using the central limit theorem, we can determine that the sample mean for random samples of size n follows a normal distribution.

The standard deviation of the X bar will be \(\frac{s}{\sqrt{n} }\).

where s is the sample's variance's square root.

As a result, we discover that the standard deviation, or variability, is inversely proportional to the square root of the sample size. Therefore, standard error lowers as sample size grows. The variability falls off as sample size rises.

The product of r and s to the fourth power is written as

In math, the term exponent refers to the number of times a certain number multiplies it self.

The number that is being multiplies is referred to as the base number while the number of times it multiplies itself is the exponents

In the problem, the multiplication of r and s is done as follows

= r * s

= rs

In this case, the base number is rs and raise to the fourth power implies that rs multiplies it self four times

= rs * rs * rs * rs

= (rs)⁴

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Answer:

(rs)^4

Step-by-step explanation:

The number of pounds of candy that sells for $0.79 per lb that  must be mixed with candy that sells for $1.35 per lb to obtain 8 tons of a mixture that should sell for $335 per ton is 580 pounds

Take x as the number of pounds of candy that sells for $0.79 per lb, and y as the number of pounds of candy that sells for $1.35 per lb.

x + y = 8 (i.e total amount of candy to be mixed)

0.79x + 1.35y = 335 (desired selling price per ton)

solve for x

y = 8 - x

0.79x + 1.35(8 - x) = 335

0.79x + 10.8 - 1.35x = 335

-0.56x = 324.2

x = 579.64

Thus x ≈ 580 to the nearest pound

Hence, about 580 pounds of candy that sells for $0.79 per lb must be mixed with candy that sells for $1.35 per lb to obtain 8 tons of a mixture that should sell for $335 per ton.

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9514 1404 393

Answer:

  59.8 cm

Step-by-step explanation:

The length of arc ABC is ...

  s = rθ

  s = (9 cm)(220/180π) = 11π cm ≈ 34.558 cm

The length of segment CD is 9 cm less than the length of segment OD. OD can be found using the law of sines.

  OD/sin(A) = AD/sin(O)

  OD = AD·sin(A)/sin(O) = (21 cm)sin(24°)/sin(140°) ≈ 13.288 cm

Then the length of CD is ...

  CD = OD -9 cm = (13.288 cm) -(9 cm) = 4.288 cm

The perimeter is the sum of the segment and arc lengths:

  P = ABC + CD +AD

  P = 34.558 cm + 4.288 cm + 21 cm = 59.846 cm

The perimeter of the shape is about 59.8 cm.

Answer:

1) \(x^{2/3}\)

\(3\) → index

\(\sqrt[3]{x^{2} }\)

\(Index: 3\)

----------------

2) \(7^{5/4}\)

\(=\sqrt[4]{7^{5} }\)

\(=(\sqrt[4]{7})^{5}\)

----------------

3) \(\sqrt[7]{2^{3} }\)

\(=(2^{3} )^{1/7}\)  \([\sqrt[x]{n} =n^{1/n} ]\)

\(=2^{3/7}\)

----------------

3) \(\sqrt[12]{8^{4} }\)

\(y=(8^{4} )^{1/12}\)

\(y=(8)^{1/3}\)

\(y=(2)^{3\times 1/3}\)

\(y=2\)

------------------

4) \(128^{3/7}\)

\(=\sqrt[7]{2\times 2\times2\times 2\times 2\times2\times 2}\)

\(=(2)^{3}\)

\(=8\)

----------------------

OAmalOHopeO

The given equation is:

√(x + 7) + 3x - 2 = 1

To solve for x, we can isolate the square root term on one side of the equation and square both sides to eliminate the square root:

√(x + 7) + 3x - 2 = 1

√(x + 7) = 1 - 3x + 2

√(x + 7) = -3x + 3

(x + 7) = (-3x + 3)^2

x + 7 = 9x^2 - 18x + 9

9x^2 - 19x + 2 = 0

Now we can use the quadratic formula to solve for x:

x = (-b ± √(b^2 - 4ac)) / 2a

Where a = 9, b = -19, and c = 2.

Plugging in the values, we get:

x = (-(-19) ± √((-19)^2 - 4(9)(2))) / 2(9)

x = (19 ± √205) / 18

So the solutions for x are:

x = (19 + √205) / 18 or x = (19 - √205) / 18

These are both irrational numbers, so we cannot simplify them further. Therefore, the value of x that satisfies the equation √(x + 7) + 3x - 2 = 1 is either (19 + √205) / 18 or (19 - √205) / 18.

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The Fourier series representation of the 2π periodic signal f(x) = x for 0 < x < π is (π/4) + Σ[(-1/n) \((-1)^n\) sin(nω₀x)].

To determine the Fourier series representation of the periodic signal f(x) = x for 0 < x < π with a period of 2π, we can use the following steps:

Determine the coefficients a₀, aₙ, and bₙ:

a₀ = (1/π) ∫[0,π] f(x) dx

= (1/π) ∫[0,π] x dx

= (1/π) [x²/2] ∣ [0,π]

= (1/π) [(π²/2) - (0²/2)]

= π/2

aₙ = (1/π) ∫[0,π] f(x) cos(nω₀x) dx

= (1/π) ∫[0,π] x cos(nω₀x) dx

bₙ = (1/π) ∫[0,π] f(x) sin(nω₀x) dx

= (1/π) ∫[0,π] x sin(nω₀x) dx

Simplify and evaluate the integrals:

For aₙ:

aₙ = (1/π) ∫[0,π] x cos(nω₀x) dx

For bₙ:

bₙ = (1/π) ∫[0,π] x sin(nω₀x) dx

Write the Fourier series representation:

f(x) = a₀/2 + Σ[aₙcos(nω₀x) + bₙsin(nω₀x)]

where Σ represents the summation from n = 1 to ∞.

To evaluate the integrals for aₙ and bₙ and determine the specific values of the coefficients, let's calculate them step by step:

For aₙ:

aₙ = (1/π) ∫[0,π] x cos(nω₀x) dx

Using integration by parts, we have:

u = x (derivative = 1)

dv = cos(nω₀x) dx (integral = (1/nω₀) sin(nω₀x))

Applying the integration by parts formula, we get:

∫ u dv = uv - ∫ v du

Plugging in the values, we have:

aₙ = (1/π) [x (1/nω₀) sin(nω₀x) - ∫ (1/nω₀) sin(nω₀x) dx]

= (1/π) [x (1/nω₀) sin(nω₀x) + (1/nω₀)² cos(nω₀x)] ∣ [0,π]

= (1/π) [(π/nω₀) sin(nω₀π) + (1/nω₀)² cos(nω₀π) - (0/nω₀) sin(nω₀(0)) - (1/nω₀)² cos(nω₀(0))]

= (1/π) [(π/nω₀) sin(nπ) + (1/nω₀)² cos(nπ) - 0 - (1/nω₀)² cos(0)]

= (1/π) [(π/nω₀) sin(nπ) + (1/nω₀)² - (1/nω₀)²]

= (1/π) [(π/nω₀) sin(nπ)]

= (1/n) sin(nπ)

= 0 (since sin(nπ) = 0 for n ≠ 0)

For bₙ:

bₙ = (1/π) ∫[0,π] x sin(nω₀x) dx

Using integration by parts, we have:

u = x (derivative = 1)

dv = sin(nω₀x) dx (integral = (-1/nω₀) cos(nω₀x))

Applying the integration by parts formula, we get:

∫ u dv = uv - ∫ v du

Plugging in the values, we have:

bₙ = (1/π) [x (-1/nω₀) cos(nω₀x) - ∫ (-1/nω₀) cos(nω₀x) dx]

= (1/π) [-x (1/nω₀) cos(nω₀x) + (1/nω₀)² sin(nω₀x)] ∣ [0,π]

= (1/π) [-π (1/nω₀) cos(nω₀π) + (1/nω₀)² sin(nω₀π) - (0 (1/nω₀) cos(nω₀(0)) - (1/nω₀)² sin(nω₀(0)))]

= (1/π) [-π (1/nω₀) cos(nπ) + (1/nω₀)² sin(nπ)]

= (1/π) [-π (1/nω₀) \((-1)^n\) + 0]

= (-1/n) \((-1)^n\)

Now, we can write the complete Fourier series representation:

f(x) = a₀/2 + Σ[aₙcos(nω₀x) + bₙsin(nω₀x)]

Since a₀ = π/2 and aₙ = 0 for n ≠ 0, and bₙ = (-1/n) \((-1)^n\), the Fourier series representation becomes:

f(x) = (π/4) + Σ[(-1/n) \((-1)^n\) sin(nω₀x)]

where Σ represents the summation from n = 1 to ∞.

This is the complete Fourier series representation of the given 2π periodic signal f(x) = x for 0 < x < π.

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The question is -

Determine the Fourier series representation for the 2n periodic signal defined below:

f(x) = x, 0 < x < π

Answer:

c = 25

Step-by-step explanation:

First, you can divide by 18 on both sides:

18 (c - 19) = 108

÷ 18             ÷18

c - 19 = 6

To isolate the variable c, you can add 19 on both sides:

c - 19 = 6

  +19   +19

c = 25

Answer:

c= 25

Step-by-step explanation:

108/18 = 6

6 +19 = 25

Answer:

-3.5

Step-by-step explanation:

2x-8+3x=5x-8

5x-8=(2x+5)(x-7)-13

5x-8=2x+5+x-7-13

5x-8=3x-15

5x=3x-7

2x/2=-7/2

x=-3.5

Answer:

x=50

Step-by-step explanation:

the opposite angle is always equal to the angle next to it

Answer: The cone has a larger volume.

Step-by-step explanation:

Volume of a cone = ⅓πr²h

where, radius = 5cm

height = 10cm

Volume = ⅓ × 3.142 × 5² × 10

Volume of cone = 261.83cm³

Volume of square pyramid = A(h/3)

where, A = 10 × 10 = 100cm²

Volume = 100 × (5/3)

Volume of square pyramid = 166.67cm³

Therefore, the cone has a larger volume.

The table and the graph are given below.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

Flat fee = $75

Fees per hour = $25

We can make an equation for x number of hours.

y = 25x + 75

Now,

Table:

Hours        Process          Cost

0              25 x 0 + 75        75

1               25 x 1 + 75         100

2              50 + 75             125

3              75 + 75             150

4              100 + 75           175

The graph of the equation y = 25x + 75 is given below.

Thus,

The table and the graph are given above.

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