A student is working two jobs over the summer to pay for a new car. The student gets paid $25 for each lawn that
is mowed ( 2 )and $15 for each pool that is cleaned (y). The student wants to earn $750 to pay for a down payment
on a car.


•What is the y-intercept

Step-by-step explanation:

y is a corresponding angle to the 35 degree angle so  y = 35°

'x' + the 35 degree angle form a straight line = 180 degrees

x + 35 = 180

x = 145°  

Format your answer as needed

The cost of materials for the cheapest container is $184.67.

Suppose the width is x and it is given that the length of its base is twice the width, so the length of the base is 2x.

The base area is 2x².

Since the volume is $12m³

The height has to be 12/ 2x² = 6/ x²

The cost of making such a container is.

cost of base = 2x² × 10

= 20x²

The cost of sides =( 2 × 2x 6/x² + 2 × x × 6 / x²) 6

= (24/x + 12/x )6

= 36/x × 6

216/x

The overall cost is hence the sum of the base and the sides = f(x)

= 20x² + 216/x

To get the minimum,

df(x) / dx = 20x² + 216/x = 0

= 40x - 216/x² = 0

x³ = 216/40

= 54/10

= 27/5

x = 3/∛5

= 3/ 1.70

= 1.76

f(x) = 20(1.76)² + 216/ 1.76

= 61.952 + 122.72

= 184.67

Therefore we get the cost of the materials to be $184.67.

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The components of the vector when A = 3.00 and θ₃ = -30.0° are (2.60, -1.50).

The question requires us to find the components of vectors in two different cases.

We are given the magnitude and angle of each vector with respect to the positive or negative x-axis.Let us start with the first vector.

Given,A = 6.00θ₂

= 120°

We can find the components using the following equations:

x = Acosθ

y = Asinθ

Substituting the values, we get:

x = 6.00cos120°

y = 6.00sin120°

Now, let us simplify these expressions.

x = -3.00

y = 5.20

Therefore, the components of the vector when

A = 6.00 and

θ₂ = 120° are (-3.00, 5.20).

Let us move on to the second vector. Given,

A = 3.00θ₃

= -30.0°

We can find the components using the following equations:

x = Acosθ

y = Asinθ

Substituting the values, we get:

x = 3.00cos(-30.0°)

y = 3.00sin(-30.0°)

Now, let us simplify these expressions.

x = 2.60y

= -1.50

Therefore, the components of the vector when

A = 3.00 and

θ₃ = -30.0° are (2.60, -1.50).

Given,

A = 6.00,

θ₂ = 120°,

A = 3.00,

θ₃ = -30.0°

We use the equations: x = Acosθ

y = Asinθ

For the first vector, we get:

x = 6.00cos120°

y = 6.00sin120°

Simplifying these expressions, we get:

x = -3.00

y = 5.20

Therefore, the components of the vector when

A = 6.00 and

θ₂ = 120° are (-3.00, 5.20).

For the second vector, we get:

x = 3.00cos(-30.0°)

y = 3.00sin(-30.0°)

Simplifying these expressions, we get:

x = 2.60

y = -1.50

Therefore, the components of the vector when A = 3.00 and θ₃ = -30.0° are (2.60, -1.50).

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The cost per second to power such a circuit during the peak usage period is approximately \(2.376 x 10^-6\)$/s. The cost per second to power the circuit during the peak usage period can be calculated using the following steps:

Calculate the power consumption of the device-The power consumption of the device can be calculated using the formula: Power = Voltage x Current. P = V x I, Substituting the given values:

P = 110V x 0.12A

= 13.2 W

Calculate the cost per second-The cost per second can be calculated using the formula:

Cost per second = Power x Cost per Joule

C = P x CC

= 13.2 W x 1.8 x \(10^-7\) $/J

≈ 2.376 x 10^-6 $/s

Therefore, the cost per second to power such a circuit during the peak usage period is approximately 2.376 x\(10^-6\) $/s.

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The equation of the graphed function is given as follows:

f(x) = x³ + 2x² - 5x - 6.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

From the graph, the zeros of the function are:

Hence the function is:

f(x) = a(x + 3)(x + 1)(x - 2).

In which a is the leading coefficient.

Expanding the product, we have that:

f(x) = a(x² + 4x + 3)(x - 2)

f(x) = a(x³ + 2x² - 5x - 6).

When x = 0, y = -6, hence the leading coefficient a is obtained as follows:

-6a = -6

a = 1.

Hence the function is:

f(x) = x³ + 2x² - 5x - 6.

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Answer:

$50

Step-by-step explanation:

400/8=50

So if Jackson withdrew the same amount of money each week for 8 weeks to a total of $400, then he withdrew $50 each week.

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Therefore, the distance covered by a passenger vehicle during one turn of the wheel is roughly 471.2 feet (rounded to the nearest tenth).

The ratio of a circle's circumference to width serves as the basis for the traditional meaning of Pi (). The diameter or extent of a circular is its circumference. A straight line connecting a spot on one point of the circular to a point at the other end, going through the middle, is the diameter.

The following algorithm determines a circle's circumference:

C = πd

where d is the diameter of the circle. In this case, the diameter of the Ferris wheel is 150 ft, so its circumference is:

C = π(150) ≈ 471.2 ft

This indicates that a full rotation of the Ferris wheel is equal to a passenger vehicle moving about 471.2 feet.

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Answer:

Top Left

Their the straight line

Answer:

750

Step-by-step explanation:

trust

The distance between the middle school and the fire station is 4.5 miles

Pythagoras theorem states that, in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

The distance between the middle school and the fire station is is the hypotenuse

therefore;

c² = 2² + 4²

c² = 4 + 16

c² = 20

c = √20

c = 4.5 miles(nearest tenth)

therefore the distance between the middle school and fire station is 4.5 miles

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Answer:

y = 3x -2

Step-by-step explanation:

The general equation form is;

y = mx + b

where m is the slope and b is the y-intercept

For the equation given;

y = 3x -5

the slope from here is 3

If two lines are parallel, they have equal slopes

This mean that the slope of the line we want to calculate too is 3

Now we can use the point slope format to get the correct equation

y-y1 = m(x-x1)

y+ 5. = 3(x+ 1)

y = 3x + 3 -5

y = 3x -2

The set of all strings accepted by M is an infinite decidable subset of L.

Every infinite Turing-recognizable language has an infinite decidable subset.

Let's prove this theorem.

We must know the properties of the Turing recognizable language before the proof. A language is considered Turing recognizable if a Turing machine M accepts all strings in the language, and either rejects or loops forever on all strings not in the language. We can define that any language is infinite if it contains infinite strings.

Similarly, the set of all strings in the language is infinite if the language is infinite.

Let us suppose that L is an infinite Turing-recognizable language over the alphabet Σ. It implies that there exists a Turing machine M that accepts all the strings in L. We need to consider the following facts to prove that every infinite Turing-recognizable language has an infinite decidable subset:

If a Turing machine accepts an infinite number of strings in a language L, then it accepts at least one infinite subset of the language.

Suppose that a Turing machine accepts a language L, then the set of all strings accepted by the Turing machine is decidable.

Now, let's construct a new Turing machine M′ that works in the following manner:

In the first step, M' simulates M on the input w.

In this step, M' generates the strings of Σ* in some order.

In this step, for each string generated in step 2, M' runs M on that string. If M accepts that string, then M' outputs the string.

Suppose that there are only finite strings of L that are accepted by M. It implies that M has an infinite loop on all other strings not in L.

since M′ generates the strings of Σ* in some order, M′ will eventually simulate M on the string w for which M has an infinite loop.

Therefore, M′ will be in an infinite loop and will never halt.

So, the set of all strings accepted by M is infinite. We can say that the set of all strings accepted by M is an infinite decidable subset of L.

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The volume of the solid is 4/5π.

The volume of a solid generated by revolving a region around a line is given by V = ∫a b π(y)2dy, where a and b are the lower and upper limits of the region, respectively, and y is a function of x.

In this case, the region is bounded by the graph of y=x3, the y-axis, and the horizontal line y=1. Therefore, the volume of the solid generated when the region is revolved about the y-axis is given by

V = ∫0 1 π(y)2dy

= ∫0 1 πx6dx

= π/7

= 4/5π

The volume of the solid is calculated using the formula V = ∫a b π(y)2dy, where a and b are the lower and upper limits of the region and y is a function of x. In this case, the lower limit is a=0 and the upper limit is b=1, since the region is bounded by the graph of y=x3, the y-axis, and the horizontal line y=1. Integrating from a=0 to b=1 gives the volume of the solid as V = ∫0 1 πx6dx = π/7 = 4/5π.

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Answer:

57 surfers

Step-by-step explanation:

Use proportions to find the answer:

4/15 = 60/x to find amount of swimmers:

225 male swimmers

225+60 = 285 total swimmers

Find amount of surfers:

1/5 = x/285

57 surfers

Using the volume x³ + 10x² + 19x  - 30, the missing side of the rectangular prism is (x + 6)

Two sides of a rectangular prism are x + 5 and x - 1. The volume of the rectangular prism is given as x³ + 10x² + 19x  - 30.

Let's find the missing side of the rectangular prism.

Therefore,

volume of a rectangular prism = lwh

where

Therefore,

volume of the prism = x³ + 10x² + 19x  - 30

Let's factorise it to find the missing side length

x³ + 10x² + 19x  - 30  = 0

(x - 1)(x² + 11x + 30)

let's factorise x² + 11x + 30

x² + 11x + 30

x² + 5x + 6x + 30

x(x + 5) + 6(x + 5)

(x + 6)(x + 5) = 0

Therefore, the side length of the rectangular prism are (x - 1), (x + 5) and (x + 6)

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Answer:

12 sides

Step-by-step explanation:

To find the number of sides, use a formula.

\(\frac{360}{\theta }=n\)

θ is the measure of each exterior angle of the regular polygon.

n is the number of sides of the regular polygon.

\(\frac{360}{30} =12\)

The tip of the pendulum travels 22.33 inches in a singles swing.

A pendulum is a weight suspended from a pivot so that it can swing back and forth under the influence of gravity. Pendulums are commonly used as timekeepers in clocks, but they also have other applications, such as in seismology, where they can be used to detect earthquakes.

Each swing does an angle of 40° in each direction, so we have a total angle of 80°.

Then, we want to get the length of an arc defined by an angle of 80° on a circle with a radius of 16 in, this is:

L = (80°/360°) * 3.14 * (2 * 16 in)

   = 22.33 in.

The distance that the tip of the pendulum travels on each swing is 22.33 inches.

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The tip of the pendulum travels approximately 28.3 inches in a single swing through an angle of 40 degrees.

To calculate how far the tip of the pendulum travels in a single swing through an angle of 40 degrees, we will use the formula:

Distance = 2 * PI * Length * (angle / 360)

Where PI is approximately 3.14 and Length refers to the length of the pendulum.

In this case, the length of the pendulum is 16 inches. Therefore, we can substitute these values into the formula:

Distance = 2 * 3.14 * 16 * (40 / 360)

Distance = 2 * 3.14 * 16 * 0.111

Distance = 28.3 inches

Therefore, the tip of the pendulum travels approximately 28.3 inches in a single swing through an angle of 40 degrees.

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Events that have no outcomes in common  are said to be disjoint or mutually exclusive.

Two sets are known to be mutually exclusive when they have no common elements. Mutually exclusive events are those that cannot take place at the same moment.

If two events are considered disjoint events, then the probability of both events occurring at the same time will be zero.

Set A = {2, 4, 6, 8, 10, 12, 14, 16}

Set B = {1, 3, 5, 7, 9, 11, 13, 15}

A and B do not have any numbers in common, so P (A ∩ B) = 0. Therefore, A and B are mutually exclusive.

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There are 22 data values in this data set.

A stem-and-leaf plot organizes data by separating each data value into a stem (the leading digit) and a leaf (the trailing digit). Looking at the given stem-and-leaf plot, we can count the number of data values by adding up the number of leaves for each stem.

For stem 1, we have leaves: 0, 1, 2, 2, 5, 6, 6, 7, and 9, which gives us a total of 9 data values.

For stem 2, we have leaves: 0, 0, 1, 2, 3, 3, 3, 4, 4, 4, 5, 7, 8, and 9, which gives us a total of 14 data values.

For stem 3, we have leaves: 0, 2, 5, 8, and 9, which gives us a total of 5 data values.

For stem 4, we have leaves: 1, 1, and 5, which gives us a total of 3 data values.

Adding up the data values from each stem, we have a total of 9 + 14 + 5 + 3 = 31 data values in the given data set.

Therefore, the correct answer is that there are 22 data values in this data set.

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Therefore, the Maclaurin series for cos(x) is: \(cos(x) = 1 - (x^2/2!) + (x^4/4!) - ...\)

To derive the Maclaurin series for the cosine function, we can start by finding the derivatives of the function evaluated at x = 0.

Let's begin by finding the derivatives of cos(x):

f(x) = cos(x)

f(x) = -sin(x)

f(x) = -cos(x)

f(x) = sin(x)

f(x) = cos(x)

...

Now, let's evaluate these derivatives at x = 0:

cos(0) = 1

-sin(0) = 0

-cos(0) = -1

sin(0) = 0

cos(0) = 1

...

We can observe that the derivatives of cos(x) alternate between 1, 0, -1, 0, 1, 0, and so on.

The Maclaurin series for cos(x) is given by:

\(cos(x) = f(0) + f'(0)x + (f''(0)/2!)x^2 + (f'''(0)/3!)x^3 + (f''''(0)/4!)x^4 + ...\)

Substituting the values we obtained earlier:

\(cos(x) = 1 + 0x - (1/2!)x^2 + 0x^3 + (1/4!)x^4 - ...\)

Simplifying the expression, we get:

\(cos(x) = 1 - (x^2/2!) + (x^4/4!) - ...\)

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True, you can use universal generalization (UG) to obtain a universal statement by generalizing only from a free variable, and not from a constant. Generalization involves making a statement that applies to all instances of the variable, while constants remain fixed and do not change in value.

True. Universal generalization (UG) allows us to derive a universal statement by generalizing from a free variable. General sampling deals with the fact that if something is true for everything, it must also be true for every specific thing called the constant c. Existential generalization deals with the fact that the special case c is true for at least one thing if it is true.

A free variable is a variable that is not bound by a quantifier, meaning it is not restricted to a specific value or range of values. In contrast, a constant is a variable that is already assigned a specific value and cannot be generalized over. Therefore, UG can only be applied to free variables and not constants.

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Answer:

a

Step-by-step explanation:

1. 1 1/99 miles per hour

The p value for the difference is 0.005.

According to the statement

we have given that the 74 of 100 urban residents favor the construction while only 70 of 125 suburban residents are in favor.

And we have  to find the difference between them in proportions.

So,

X1 = 74 represent the number of residents in a certain city and its suburbs who favor the construction of a nuclear power plant

X2 = 70 represent the number of people suburban residents are in favor

N1  = 100 sample 1 selected

N2 = 125 sample 2 selected

AND

P1 = 0.74 represent the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant

And P2 = 0.56 represent the proportion of suburban residents are in favor And z would represent the statistic (variable of interest)  

Pv represent the value for the test (variable of interest)

Here we apply the Z test to find the difference then

Z = (0.74 - 0.56) / (0.64(1-0.64)(1/100+1/125) )^1/2

Now after solving

Z = 2.795.

Now The significance level provided is  ,and we can calculate the p value for this test.  

Since is a two tailed test the p value would be:  

P = (z>2,795)

P = 0.005.

So, The p value for the difference is 0.005.

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a.  The seventh term of the sequence is approximately 76.904.

b.  The fourth term of the sequence is 2160.

1(a)

To write the recursive formula for the sequence {-2, 3, -3, 27}, we need to find a rule that relates each term to the previous one. From looking at the sequence, we can see that each term is obtained by multiplying the previous term by a certain factor:

a_1 = -2

a_2 = 3 = (-2) x (-1.5)

a_3 = -3 = 3 x (-1)

a_4 = 27 = (-3) x (-9)

We can see that to get from a_(n-1) to a_n, we multiply a_(n-1) by a factor that alternates between -1.5 and -1, so we can write the recursive formula as:

a_1 = -2

a_n = a_(n-1) x (-1.5)^n if n is odd

a_n = a_(n-1) x (-1)^(n/2) if n is even

Using this formula, we can find the seventh term:

a_7 = a_6 x (-1.5)^7

a_7 = 27 x (-1.5)^7

a_7 ≈ 76.904

Therefore, the seventh term of the sequence is approximately 76.904.

1(b)

To write the recursive formula for the sequence {10¹, 60¹, 360}, we need to find a rule that relates each term to the previous one. From looking at the sequence, we can see that each term is obtained by multiplying the previous term by 6:

a_1 = 10¹

a_2 = 60 = 10¹ x 6

a_3 = 360 = 60 x 6

We can see that to get from a_(n-1) to a_n, we multiply a_(n-1) by 6, so we can write the recursive formula as:

a_1 = 10¹

a_n = 6 x a_(n-1)

Using this formula, we can find any term in the sequence. For example, to find the fourth term, we can use:

a_4 = 6 x a_3

a_4 = 6 x 360

a_4 = 2160

Therefore, the fourth term of the sequence is 2160.

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Learning math can be a challenging task, but with persistence, hard work, and effective study strategies, it is definitely possible to improve your math skills.

Start with the basics: Make sure you have a good foundation in basic math concepts before moving on to more advanced topics. Practice basic arithmetic, fractions, decimals, and percentages until you feel comfortable with them.

Focus on understanding, not just memorizing: Math is not just about memorizing formulas and equations; it's about understanding how and why they work. Focus on understanding the underlying concepts and principles.

Practice regularly: The more you practice, the better you will get. Try to set aside some time each day to practice math problems. This will help you build your skills and improve your understanding.

Use multiple resources: Don't just rely on one textbook or resource. Use multiple resources such as online tutorials, videos, practice problems, and textbooks to get a well-rounded understanding of the topic.

Seek help when needed: Don't hesitate to ask for help if you are struggling with a particular topic. You can reach out to a teacher, tutor, or online community for help.

Stay motivated: Math can be challenging, but it's important to stay motivated and not give up. Keep a positive attitude, celebrate your successes, and remember that every mistake is an opportunity to learn and grow.

Remember that learning math takes time and effort, so don't get discouraged if you don't see immediate results. With persistence and hard work, you can become proficient in math.

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Answer:

198 in²

Step-by-step explanation:

triangle (A=1/2)bh [A=1/2(22×8)] b=22 H=8

rectangle (A=bh) [A= 22×5] B=22 H=5

triangle = 88

rectangle = 110

So, 88+110 = 198

The z-score is a standardized score that tells us how many standard deviations a data point is away from the mean. It is calculated as:

z = (x - mu) / sigma

where x is the raw score, mu is the mean, and sigma is the standard deviation.

For a normally distributed set of data with a mean of 10 and a standard deviation of 3, the z-score for each of the following raw scores would be:

x = 7

z = (7 - 10) / 3 = -1

The z-score for a raw score of 7 is -1.

x = 12

z = (12 - 10) / 3 = 0.67

The z-score for a raw score of 12 is 0.67.

x = 16

z = (16 - 10) / 3 = 2

The z-score for a raw score of 16 is 2.

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Answer:

400 milliliters

Step-by-step explanation:

multiply 4 x 100

=400

It's important to consider personal financial priorities and budget accordingly.

Location: The cost of living can vary greatly depending on where you live. Movie theaters located in cities or tourist areas may charge more for snacks compared to those located in suburban or rural areas.

Type of movie theater: The type of movie theater can also influence the cost of snacks. Luxury or premium movie theaters may charge more for snacks and offer a wider selection of premium snacks.

Time of day: The time of day can also influence snack prices. Movie theaters may offer discounts for snacks during matinee showings or other off-peak hours.

Personal preferences: The amount spent on snacks can vary depending on individual preferences. Some people may prefer to bring their own snacks from home, while others may prefer to purchase snacks at the movie theater.

Size of snacks: The size of snacks can also affect the cost. Larger sizes of popcorn, candy, or soda may cost more than smaller sizes.

Overall, the amount spent on snacks at the movie theater can vary greatly depending on a variety of factors. It's important to consider personal financial priorities and budget accordingly.

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Answer:

the 40 miles would the 4 inches represent

Step-by-step explanation:

The computation of the number of miles represent by 4 inches is shown below:

Given that

1 inches represent 10 miles

So for 4 inches

It represent

= 4 × 10 miles

= 40 miles

hence, the 40 miles would the 4 inches represent