hil spent $21 of his $115 pocket money on eating out for one meal. What percent of Phil's pocket money did he spend on eating out for one meal? Round your answer to the nearest hundredth.

Answer:

Below

Step-by-step explanation:

x^2 -x + 1      Use Quadratic Formula    a = 1    b = -1    c = 1

  to find zeroes   1/2 ±  i sqrt(3) / 3

Sooo.... Not sure you could find it by factoring:

         (x -1/2 +i sqrt(3) /2) (x - 1/2 - i sqrt (3)/2)    would be hard to see !!

√9 - 3x⁄x + 4x2 - x3⁄2 + y2 - 2xy + 2⁄2 + 9 - x2⁄2 from 0 to √9

To find the area bounded by the given functions, we will need to solve the following integrals:

1. Integral of √9 - 3x⁄x from 0 to √9
2. Integral of 4x2 - x3⁄2 from 0 to √9
3. Integral of y2 - 2xy + 2⁄2 from 0 to √9
4. Integral of 9 - x2⁄2 from 0 to √9

The area bounded by the given functions is then equal to the sum of the four integrals, or:

Area = √9 - 3x⁄x + 4x2 - x3⁄2 + y2 - 2xy + 2⁄2 + 9 - x2⁄2 from 0 to √9

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Answer- 1:8

The original length of the board was 32 inches. Since it reduced we can divide 32 into 4. 32/4 is 8. This means that the scale factor of the dilation  is 1:8. 32 is 8/1 of 4, so that means in ratio 1 whole is divided into 8 parts, hence 1:8.

I hope this helped and Good Luck <3!!!

The number of servings that a 1.5 liter (1500ml) bottle of soda will make is 6 servings of 0.25 liter (250ml).

To find the number of servings, you can divide the total volume of the bottle by the volume of each serving.
Step-by-step explanation:
1. Convert the volume of the bottle to milliliters: 1.5 liters = 1500 milliliters
2. Convert the volume of each serving to milliliters: 0.25 liters = 250 milliliters
3. Divide the total volume of the bottle by the volume of each serving: 1500 milliliters / 250 milliliters = 6 servings
Therefore, a 1.5 liter (1500ml) bottle of soda will make about 6 servings of 0.25 liter (250ml).

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Jody needs to walk 3.5 miles on Sunday to reach her goal.

What is Multiplication?

Multiplication is a mathematical operation that combines two or more numbers to produce a result called the product. It is a repeated addition of the same number.

To reach her goal of 25 miles per week, Jody would have already walked a total of:

4.5 miles/day x 4 days = 18 miles

3.5 miles on Saturday = 3.5 miles

The total distance walked from Monday to Saturday is:

18 + 3.5 = 21.5 miles

To reach her goal of 25 miles per week, she needs to walk an additional:

25 - 21.5 = 3.5 miles

Therefore, Jody needs to walk 3.5 miles on Sunday to reach her goal.

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No, (-1,9) is not a solution to the inequality 2x+y<-3.

Inequality is when something is not equal in terms of rights, resources, opportunities or outcomes between different groups or individuals.

To determine if a point is a solution to an inequality, we can plug in the x and y values of the point into the inequality and see if it is true.

In this case, we plug in x=-1 and y=9 into the inequality:

2(-1)+9<-3

Simplify:

-2+9<-3

7<-3

This is not true, so (-1,9) is not a solution to the inequality.

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The linear velocity of the bicycle is approximately 6.68 miles per hour.

a) The angular velocity of the wheel can be found by using the formula:
ω = v / r
where ω is the angular velocity, v is the linear velocity, and r is the radius of the wheel.
In this case, v = 115 m/sec and r = (8 cm / 2) = 4 cm = 0.04 m.
So, the angular velocity of the wheel is:
ω = (115 m/sec) / (0.04 m) = 2875 radian per second.

b) The linear velocity of the bicycle can be found by using the formula:
v = ω * r
where v is the linear velocity, ω is the angular velocity, and r is the radius of the wheel.
In this case, ω = 125 revolutions per minute = (125 * 2π) / 60 = 13.09 radian per second and r = (18 inches / 2) = 9 inches = 0.75 feet.
So, the linear velocity of the bicycle is:
v = (13.09 radian per second) * (0.75 feet) = 9.82 feet per second.
To convert this to miles per hour, we can use the conversion factor 5280 feet = 1 mile:
v = (9.82 feet per second) * (60 seconds / 1 minute) * (60 minutes / 1 hour) * (1 mile / 5280 feet) = 6.68 miles per hour.
So, the linear velocity of the bicycle is approximately 6.68 miles per hour.

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Answer:

2/10

Step-by-step explanation:

7/ 10 of the distance on Saturday

Remaining distance is 3/10

2/3 of remaining distance is 2/3 x 3/10 = 2/10

Saturday 7/10

Sunday 2/10

We have the following response after answering the given question: function Hence, the quarterly growth rate is almost 4.08%.

Mathematicians research numbers, their variants, equations, forms, and related structures, as well as possible locations for these things. The relationship between a group of inputs, each of which has a corresponding output, is referred to as a function. Every input contributes to a single, distinct output in a connection between inputs and outputs known as a function. A domain, codomain, or scope is assigned to each function. Often, functions are denoted with the letter f. (x). The key is an x. There are four main categories of accessible functions: on functions, one-to-one capabilities, so many capabilities, in capabilities, and on functions.

[tex]P(t) = P0 * e^(rt) (rt)[/tex]

Where q is the quarterly rate of increase, [tex]q = (1 + r)(1/4) - 1.[/tex]

[tex]q = (1 + 0.17)^(1/4) - 1 ≈ 0.0408\sP(t) = 1100 * e^(0.17t) (0.17t)[/tex]

Q is equal to round[tex]((1 + 0.17 ** (1/4) - 1, 4)[/tex]

P0 = 1100

math.log(1 + q) = r

(q * 100, 2)

4.08 P(t) = P0 * e(rt), where r is the natural logarithm's base and P0 is the beginning population (approximately 2.71828).

Where q is the quarterly rate of increase, q = (1 + r)(1/4) - 1.

[tex]q = (1 + 0.17)^(1/4) - 1 ≈ 0.0408\sP(t) = 1100 * e^(0.17t) (0.17t)[/tex]

We may convert the quarterly growth rate to a percentage and round to the closest hundredth of a percent to get the percentage rate of change every quarter:

(q * 100, 2)

4.08

Hence, the quarterly growth rate is almost 4.08%.

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The velocity of the pendulum is approximately -2.45 inches/second.

The acceleration of the pendulum is approximately 5.13 inches/second².

To find the velocity and acceleration of the pendulum, we need to find the first and second derivatives of the function d(t).

a. The velocity of the pendulum is given by the first derivative of the function d(t):

v(t) = d'(t) = 7 * (π/3) * cos(πt/3 - 2)

To find the velocity at t = 6 seconds, we simply plug in 6 for t:

v(6) = 7 * (π/3) * cos(π(6)/3 - 2) = 7 * (π/3) * cos(4) ≈ -2.45 inches/second

So the velocity of the pendulum at 6 seconds is approximately -2.45 inches/second.

b. The acceleration of the pendulum is given by the second derivative of the function d(t):

a(t) = d''(t) = -7 * (π/3)² * sin(πt/3 - 2)

To find the acceleration at t = 6 seconds, we simply plug in 6 for t:

a(6) = -7 * (π/3)² * sin(π(6)/3 - 2) = -7 * (π/3)² * sin(4) ≈ 5.13 inches/second²

So the acceleration of the pendulum at 6 seconds is approximately 5.13 inches/second².

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It will take approximately 13.86 years for the money to double when it is invested in an account earning 5% compounded continuously.

To find out how long it will take for the money to double, we can use the formula for continuous compounding: A = Pe^(rt), where A is the final amount, P is the principal amount, r is the interest rate, and t is the time in years.

We are given that P = $50,000, r = 5%, and A = 2P = $100,000. We need to solve for t.

Plugging in the given values, we get:

$100,000 = $50,000e^(0.05t)

Dividing both sides by $50,000, we get:

2 = e^(0.05t)

Taking the natural logarithm of both sides, we get:

ln(2) = 0.05t

Solving for t, we get:

t = ln(2)/0.05

t ≈ 13.86 years

Therefore, it will take approximately 13.86 years for the money to double when it is invested in an account earning 5% compounded continuously.

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Below is the exact match for public good or service of Local Government and Federal Government.

Goods and services are two distinct types of economic products that are exchanged in the marketplace.

Goods are tangible, physical products that can be seen, touched, and stored. They are typically manufactured or produced and can be traded in the marketplace.

Services are usually produced and consumed simultaneously and involve an activity performed by one person or group for the benefit of another. Examples of services include healthcare, education, transportation, banking, consulting, and entertainment.

Local Government                                Federal Government

Sewage system                                    Financial aid for college

Traffic light                                            Internal Revenue Service (IRS)

Hospitals                                               Hospitals  

                                                              Currency

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The original value of the oranges is 143.75.

A percentage is a number or a ratio that is expressed as a fraction of 100 i.e. out of 100.

In formula, x% of amount y = y*(x/100)

Given :

Tax paid by Rekha : 15%

Final Price paid by Rekha : 165.31

Let the original price of the oranges = x

The additional tax amount on oranges

           = 15% of original price of x

           = 15 * x / 100

           = 0.15 x

Total price paid by Rekha = Original price of orange + Tax amount

165.31 = x + 0.15x

165.31 = (1 + 0.15)x

165.31 = 1.15x

x = 165.31/1.15

x = 143.75

Thus, the original value of the oranges is 143.75.

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The number representing the 6th grader participated in the field event is 120

A sample space is a collection or a set of possible outcomes of a random experiment.

The sample space is represented using the symbol, “S”. The subset of possible outcomes of an experiment is called events.

Given is a graph, showing the number of class students taking parts in different events,

We need to find the number of the 6th graders who participated in field event.

The sample size is 20 for who participated in field event, that means one unit is representing 20 participants

The sample number for 6th graders who participated in field event = 6

That means, the total number of the 6th graders who participated in field event = 20 x 6 = 120

Hence, the number representing the 6th grader participated in the field event is 120

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In interval notation, the domain and range of the function are:
Domain: (-∞, ∞)
Range: [1, ∞)

The domain of a function is the set of all possible values of x that can be plugged into the function. The range of a function is the set of all possible values of f(x) that can be obtained by plugging in values of x into the function.

For the given function f(x) = 9x² + 1, the domain is all real numbers, because any value of x can be plugged into the function. Therefore, the domain is (-∞, ∞).

The range of the function is the set of all possible values of f(x) that can be obtained by plugging in values of x into the function. Since the function is a quadratic with a positive leading coefficient (9), the graph of the function will be a parabola that opens upward. The minimum value of the function will occur at the vertex of the parabola, which is (0, 1). Therefore, the range of the function is [1, ∞).

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The value of a is 20, b is 40, c is 10 and d is 10√3

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

By using sine function we find the value of a

sin 45=a/20√2

1/√2 = a/20√2

20√2=a√2

a=20

Now let us find c

cos 45=c/(20√2)

1/√2×20/√2=c

10=c

sin30=a/b

1/2=20/b

b=40

Now we have to find d by cosine function

cos30=d/a

√3/2=d/20

d=10√3

Hence, the value of a is 20, b is 40, c is 10 and d is 10√3

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Answer:6

Step-by-step explanation:

the perimeter of the orange square is 18

4+4+5+5=18

3+3=6

18-6=12

12/2=6

6+6=12

3+3=6

6+12=18

18=18

Answer: [tex]x^{2}[/tex]+2x-5

Step-by-step explanation:

(g+f)(x) = g(x)+f(x)

g(x) = 2x-2

f(x) = [tex]x^{2}[/tex]-3

g(x)+f(x) = (2x-2) + ([tex]x^{2}[/tex]-3)

g(x)+f(x) =  [tex]x^{2}[/tex]+2x-5

427.

The proof for the question is as follows:

A(n) is the arithmetic mean of the (positive) factors of n.

We want to find the n for which A(n) = 124.

Let F be the set of (positive) factors of n, and let f1, f2,..., fm be the elements of F.

The arithmetic mean of F is defined as A(n) = (f1 + f2 + ... + fm)/m.

Now, we have A(n) = 124. So, 124 = (f1 + f2 + ... + fm)/m.

Therefore, 124m = f1 + f2 + ... + fm.

This implies that f1 + f2 + ... + fm = 124m = 427.

Thus, n = 427.

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The total mass of the chain is approximately 76.82 kg

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a² + b² = c².

We can use the Pythagorean theorem to solve this problem. According to the diagram, we have:

n² = 36² + 23²

n² = 1296 + 529

n² = 1825

n = √(1825) ≈ 42.68

So the length of the chain is approximately 42.7 meters (rounded to 1 decimal place).

To find the total mass of the chain, we can multiply the length by the mass per meter:

mass = 42.68 x 1.8 ≈ 76.82

Therefore, the total mass of the chain is approximately 76.82 kg (rounded to the nearest kilogram).

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The required value of a + b is 35.

The area of the shadow can be calculated by finding the area of the regular hexagon. The formula for the area of a regular hexagon is:

    A = (3√3)/2 * s^2,

where s is the length of one side of the hexagon.

Since the cube is balanced on one of its vertices, the length of one side of the hexagon is equal to the length of one edge of the cube, which is 8.  Therefore, the area of the shadow is A = (3√3)/2 * 8^2 = 64√3/2 = 32√3.

The value of a is 32 and the value of b is 3, so the value of a + b is 32 + 3 = 35. Therefore, the answer is 35.

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Step-by-step explanation:

So, let's say that we have 5/20. 5 and 20 can divide by a similar number (5) so you divide each variable by 5. in the end, you get 1/4.

Maxine's projected ending cash balance is $1,900.

What is the basic arithmetic operations?

The basic arithmetic operations are addition, subtraction, multiplication, and division.

Maxine's projected cash inflow from 20 sessions at $70 per session is:

20 sessions x $70/session = $1400

Her total projected cash inflow is therefore $1400.

Her projected cash outflow is $900 for rent and $600 for supplies, for a total of:

$900 + $600 = $1500

Her beginning cash balance is $2,000.

To calculate her projected ending cash balance, we need to subtract her projected cash outflow from her projected cash inflow and add her beginning cash balance:

Projected ending cash balance = Beginning cash balance + Projected cash inflow - Projected cash outflow

Projected ending cash balance = $2,000 + $1,400 - $1,500

Projected ending cash balance = $1,900

Therefore, Maxine's projected ending cash balance is $1,900.

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A 12-ft high flagpole is standing vertically at the edge of the roof of a building with angle of elevation of 78°50'.  The height of the building is 312.2 ft (option c)

To find the height of the building, we can use the tangent function of the angle of elevation. The tangent function relates the opposite side (height of the building + flagpole) to the adjacent side (distance from the base of the building) of a right triangle.

The angle of elevation is given as 78° and 50'. We can convert this to decimal form by dividing the minutes by 60:

78° + (50'/60) = 78.833°

Let H = height of the building + height of the flagpole

Then,

tan(78.833°) = opposite/adjacent
tan(78.833°) = H/64 ft
H = 64 ft * tan(78.833°)
H = 324.2 ft

Therefore,

the height of the building = H - 12

                                            = 324.2 - 12 = 312.2 ft (option c)

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Answer: 55

Step-by-step explanation: 13 -7 = 16. 16/2 = 8. 8 + 7 = 15. 8 X 5 = 40

Answer:

z=5/138

Step-by-step explanation:

15 1/3z=5

46/3z=5

3z=5/46

z=5/138

The solution to the given system of equations, 3x+2y=4; 2x−3y=7 is (2, -1).

To solve the given system of equations graphically, we need to first graph each equation on the same coordinate plane and then find the point of intersection.

The first equation is 3x+2y=4. We can rearrange this equation to get y in terms of x:
2y = -3x + 4
y = (-3/2)x + 2

The second equation is 2x−3y=7. We can also rearrange this equation to get y in terms of x:
3y = 2x - 7
y = (2/3)x - (7/3)

Now we can graph both equations on the same coordinate plane. The first equation has a y-intercept of 2 and a slope of -3/2, while the second equation has a y-intercept of -7/3 and a slope of 2/3.

After graphing both equations, we can see that they intersect at the point (2, -1). This means that the solution to the system of equations is x = 2 and y = -1.

Therefore, the solution to the given system of equations is (2, -1).

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Box plot of the given data for the scores of the statistics is represented by minimum value = 51, maximum value = 93, Median = 75, lower quartile = 67 and upper quartile = 87.

Box plot is attached.

Scores of the statistics test  is equal to

83,72,91,73,74,51,62,52,76,93

Arrange the scores into ascending order we get,

51, 52, 62, 72, 73, 74, 76, 83, 91, 93

Minimum value = 51

Maximum value = 93.

Median= Average of the two middle values.

Two middle values are 74 and 76

Median

= (74 + 76) / 2

= 75

Lower quartile = Median of the lower half of the data

Upper quartile = Median of the upper half of the data

Lower half= 51, 52, 62, 72, 73

Upper half = 76, 83, 91, 93

Lower quartile

= (62 + 72) / 2

= 67

Upper quartile

= (83 + 91) / 2

= 87

Constructed box plot is attached.

Therefore, to construct box plot minimum value = 51, maximum value = 93, Median = 75, lower quartile = 67 and upper quartile = 87 for the given test scores.

Box plot is attached.

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To run 6 miles it takes 2880 seconds of time.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Given that, a runner records his rate of speed along the first mile of a 6 mile path that winds through the park.

We know that, speed =Distance/Time

Here, Distance= 1/4 mile and time=120 seconds

Speed = 1/4 ÷120 =1/480 miles per seconds

Time taken to run 6 miles

We know that, Time =Distance/Speed

Time = 6 ÷ 1/480

= 6×480

= 2880 seconds

Therefore, to complete 6 miles it takes 2880 seconds.

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Factored form of 3[tex]z^{2}[/tex] + 20z - 7 is (3z - 5)(z - 2)(3z - 7)

Yes, factoring a quadratic with a leading coefficient is possible. The leading coefficient of your polynomial is 3. To factor this quadratic, use the following steps:

1. Divide the leading coefficient (3) into the constant term (-7). This will give you a quotient of -7/3 and a remainder of 1.

2. Create two terms that multiply together to give -7/3 and add to 20/3. In this case, the two terms are -4/3 and -5/3.

3. Write the quadratic as a product of two binomials.

3[tex]z^{2}[/tex] + 20z - 7

= 3[tex]z^{2}[/tex] + (4/3)(-3z) + (5/3)(-3z) - 7

= 3[tex]z^{2}[/tex] - 9z - 4z - 7 = 3[tex]z^{2}[/tex] - 13z - 7

4. Factor the binomials by grouping.

3[tex]z^{2}[/tex] - 13z - 7 = (3[tex]z^{2}[/tex] - 10z) - (3z - 7)

5. Factor each binomial.

(3[tex]z^{2}[/tex] - 10z) = (3z - 5)(z - 2)

(3z - 7) = (3z - 7)(1)

Therefore, the factored form of 3[tex]z^{2}[/tex] + 20z - 7 is (3z - 5)(z - 2)(3z - 7).

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