A wagon is being pulled by a handle making a 40° angle with a force of 35 pounds. What amount of force is moving the wagon along level ground? Round to the nearest tenth.

The quadratic equation in standard form is:

[tex]y = 2x^2 - 8x + 6[/tex]

Here we have the quadratic equation:

[tex]y = 2*(x - 2)^2 - 2[/tex]

Here we need to expand the right side, remember:

[tex](a + b)^2 = a^2 + 2ab + b^2[/tex]

Using that, we get:

[tex]y = 2*(x - 2)^2 - 2 = 2*(x^2 - 4x + 4) - 2\\\\y = 2x^2 - 8x + 8 - 2\\\\y = 2x^2 - 8x + 6[/tex]

This is the quadratic equation in standard form.

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Answer:

40%

Step-by-step explanation:

We already have our first value 20 and the second value 8. Let's assume the unknown value is Y which answer we will find out.

As we have all the required values we need, Now we can put them in a simple mathematical formula as below:

Step 1 ⇒ Y = 8/20

By multiplying both numerator and denominator by 100 we will get:

Step 2 ⇒ Y = 8/20 × 100/100 = 40/100

Step 3 ⇒ Y = 40

Finally, we have found the value of Y which is 40 and that is our answer.

Answer:

The correct answer is B, the second option

Step-by-step explanation:

(-2, 5/3)

Solve for the first variable in one of the equations, then substitute the result into the other equation.

Answer: Table D

Step-by-step explanation:

The coefficient of x^2 is -9, the coefficient of x is 7, and the constant is 0, so we know a = -9, b = 7, c = 0.

Thus, table D is the answer.

The probability that among the first 2 songs played ;a) 6% , not unusual b) 40% and c) 48.4%

Probability refers to a possibility that deals with the occurrence of random events.

We have the following information from the statement:

n = 6, r = 2

a)  

P (like both of them) = P (like first song) x P (like second song)

P = 2/6 x 1/5

P = 0.06 = 6%

The probability that among the first 2 songs played and You like both of them is 6%.

b)

P (like neither) = P (not like first song) x P (not like second song)

P = 4/6 x  3/5

P = 0.4 = 40%

c) P (like exactly one of them) = P (first song liked) x P (second song not liked) + P (first song not liked) x P (second song liked)

P = ( 2/6 x 1/5) + (4/6 x  3/5)

P = 0.484 = 48.4%

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The area of the wheel is  31415.9 ft².

The Central angle in degrees is 34.29°

Measure of a central angle in radians is 0.5984 radians

A) The image shows an example of this Ferris wheel.

We are given;

Diameter; d = 200 ft

Radius; r = 100 ft

Number of gondolas = 42

Area of the circle wheel = πr²

Area = π * 100²

Area = 31415.9 ft²

B) Now, the sum of angles in a circle is 360°.

Since there are 42 gondola's, then;

Each angle = 360/42 = 60/7°

The central angle will be an angle with its vertex at the center of a circle and with sides that are radii of the circle. From the image, we see that it covers approximately 4 gondola's. Thus;

Central angle = 4 * 60/7° = 34.29°

C) Central Angle in radians will be converted as 0.5984 rad.

D) Arc length between two gondolas is;

S = rθ

S = 100 * 0.5984

S = 59.84 radians

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Square perimeter =4x cm.

The complete length that a square's edge encompasses is referred to as its perimeter. Any enclosed geometric shape's perimeter may be computed by measuring the space around it.

By calculating the total of all the sides of a square, the perimeter may be determined. The perimeter of a square will be stated as,

The perimeter of square = s + s + s + s

⇒Perimeter of square = 4s, where "s" is the side length of the square.

This is because all edges of a square are equal and each edge measures "s" units.

Mathematically, the formula for calculating a square's perimeter is: Square perimeter, (P) = 4 Side

⇒P= 4x cm

It is concluded that the solution is 4x cm.

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Answer:

y =  4

x = -1

Step-by-step explanation:

4x + 2y = 4     Eq. 1

3x - y = -7       Eq. 2

from the  Eq. 2

3x = y - 7

3x + 7 = y        Eq. 3

Replacing the value of the Eq. 3 in the Eq. 1

4x + 2(3x+7) = 4

4x + (2*3x + 2*7) = 4

4x + (6x + 14) = 4

10x + 14 = 4

10x = 4 - 14

10x = - 10

x = -10/10

x = -1

from the Eq. 3

3x + 7 = y

3*-1 + 7 = y

-3 + 7 = y

4 = y

Check:

from the Eq. 1

4x + 2y = 4

4*-1 + 2*4 = 4

-4 + 8 = 4

Answer:

that makes no sence at all i read it over 3 times and still font understand a word of it

sorry :(

let's name the vertices of the triangle as A B C and D as the image shown above

In triangle ABC

sin 60° = AB/AC

√3/2 = 8√2/ AC

AC = 16√2/√3

In triangle ACD

sin 45° = AC/AD

1/√2 = 16√2/ 3 AD

The base is 60, the part is 40 and the rate is 150%.

The base is the whole quantity or amount that the problem is about.

The part is referred to as the percentage is the portion of the base. The rate is the number with the percentage.

In this case, the base is 60, the part is 40 and the rate is 150%.

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Answer:

80 boys

Step-by-step explanation:

160 total players

50% are boys

50% of 160 is 80

Answer:

130 sq. units

Step-by-step explanation:

Any number multiplied by 10 is the same number with a 0 added at the end.

Answer:

1300

Step-by-step explanation:

1. calculator

2.putreef Iub numbers

3 solve

Step-by-step explanation:

this is first an arithmetic sequence with the first term A1=3(1)+1=4 And the 12th term A12=3(12)+1=37. Then use this formula

S12=12/2 ×(4+37)

=6×41

=246

An equation of Hamid’s revenue by multiplying the book price by the number of copies sold is  x = ny.

The process of equating one thing with another.

Let Hamid’s revenue is $x and the price of book is $y.

If he sold n number of copies.

Then, the general equation will be x = n * y.

Therefore, an equation of Hamid's revenue will be x = ny.

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i) Student A used the property of the power of a power and student B used the definition of power and the property of the product of power with the same base. ii) Both were correct.

In this question we must analyze the procedure used by each student to simplify a power into the form rⁿ:

i) The student A used the property of the power of a power which states that [tex](r^{m})^{n} = r^{m\cdot n}[/tex]. In exchange, the student B used the definition of power and the property of the product of powers with the same base.

ii) Based on the description in i), both students used correct methods of simplifying.

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Answer: 70/29

Step-by-step explanation:

[tex]S=\theta r\\\\35=14.5 \theta\\\\\theta=\frac{35}{14.5}=\boxed{\frac{70}{29}}[/tex]

Answer: [tex]5x^3 - x^2 + 5x+2[/tex]

Step-by-step explanation:

[tex](f+g)(x)=(3x^2 + 5x-2)+(5x^3 - 4x^2 +4)=3x^2 + 5x-2+5x^3 - 4x^2 +4=\boxed{5x^3 - x^2 + 5x+2}[/tex]

Answer:

y = 2

Step-by-step explanation:

Addition Method:

4x - 2y = 6

2x + y = 7

-2(2x + y) = -2(7)

4x - 2y = 6

-4x - 2y = -14

-4y = -8

y = 2

Substitution Method:

4x - 2y = 6

2x + y = 7

-2y = 6 - 4x

2y = 4x - 6

y = 2x - 3

2x + (2x - 3) = 7

4x - 3 = 7

4x = 10

x = 2.5

2(2.5) + y = 7

5 + y = 7

y = 2

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Answer:

Adult: 59 tickets, Student: 642 tickets

Step-by-step explanation:

$5 = ticket per student (s)

$8 = ticket per adult (a)

$3682 = total money made

# of s = 11a-7 (7 less than 11 times the adults)

We can use this information to create a systems of equations.

5s + 8a = 3682

*price of a ticket times the number of students or adults equals total*

where s = 11a-7

Now we substitute in:

5(11a-7) + 8a = 3682

55a - 35 + 8a = 3682

63a - 35 = 3682

63a = 3717

a = 59

so 59 adult tickets were sold, now we can use this information to solve for student tickets.

s = 11(59)-7

s = 642

So 59 adult tickets, and 642 student tickets were sold.

If she arrives by boat;

The distance she needs to row = Lake diameter

Distance = Lake diameter = 2 x Radius

Boat distance = 2 x 2 miles = 4 miles

So;

When moving on foot

The distance that needs to be moved D = Half of the circle circle

∴ D = π × Radius

The distance that needs to be moved D = π × 2 miles = 2π Miles

Arc length = Radius × θ

String length = radius x 2 x sin (θ / 2)

0 ≤ θ ≤ π, 0 ≤ sin (θ / 2) ≤ 1

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The histogram will have a shape that is left-skewed. Then the correct option is B.

A diagram is made up of rectangles whose size is related to a variable's frequency and whose width is comparable to the training sample.

Students in a fitness class each completed a one-mile walk or run. The list shows the time it took each person to complete the mile. Each time is rounded to the nearest half-minute.

5.5, 6, 7, 10, 7.5, 8, 9.5, 9, 8.5, 8, 7, 7.5, 6, 6.5, 5.5

Then the mean will be

Mean = (5.5 + 6 + ..... + 6.5 + 5.5) / 15

Mean = 111.5/12

Mean = 7.4333

Then the median will be

Median = 7.5

The histogram will have a shape that is left-skewed.

Then the correct option is B.

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Answer:

The histogram will have a shape that is left-skewed.

The shape of the histogram can be approximated with a normal curve.

The histogram will show that most of the data is centered between 6 minutes and 9 minutes.

Step-by-step explanation:

B/2, D/4, E/5

The given differential equation is linear with constant coefficients,

[tex]\dfrac{d^2y}{dx^2} - 49y = 0[/tex]

with characteristic equation

[tex]r^2 - 49 = 0[/tex]

and hence characteristic roots [tex]r=\pm7[/tex]. This means the general solution to the ODE is

[tex]y = C_1 e^{7x} + C_2 e^{-7x}[/tex]

In fact, you're given the solution already,

[tex]y = C_1 e^{kx} + C_2 e^{-kx}[/tex]

and you've determined that

[tex]\dfrac{d^2y}{dx^2} = k^2 (C_1 e^{kx} + C_2 e^{-kx}) = k^2 y[/tex]

Comparing this to the given ODE, it's obvious that [tex]k=7[/tex], so you can just replace [tex]k[/tex] with 7 in the given template solution.

Answer:

The golden ratio is a proper term in the field of mathematics, but it finally covers more than the research in the field of mathematics. According to the current literature discussion, we can say that the discovery of the Golden ratio and how it evolved is still a mystery. But studies have shown that the Pythagorean school of ancient Greece in the 6th century BC studied the formation of regular 5-sided and regular 10-sided plots, leading modern mathematicians to conclude that the Pythagorean school had touched on and even mastered some of the rules of the golden ratio and also discovered irrational numbers. It focuses on the relationship from mathematics, to explore the principle of beauty and that beauty is harmony and proportion, according to the proportional relationship can form beautiful patterns, this is actually a digital proportional relations, the line is divided into two parts, a long and a short period of the ratio of the equal to the ratio of length to a long, their proportion is around 1.618:1, This mathematical principle is also embodied in the famous Frederikian sequence, in which everything in this proportion shows the harmony and balance of its internal relations.

In the 4th century BC, the Greek mathematician Eudoxus was the first to systematically study this problem and establish the theory of proportion. Around 300 BC, Euclid absorbed the research results of Eudoxus in writing The Elements of Geometry and further systematically discussed the Golden Section, which became the earliest treatise on the golden Section (i.e. the middle and the end ratio) [5].

After the Middle Ages, the golden ratio was shrouded in mystery. Italian mathematician Luca Pacioli called the middle and the end of the ratio sacred and wrote a book about it. The German astronomer Johannes Kepler called the divine ratio the Golden Ratio. Golden in the 19th century the name only gradually, and the evidence is that German mathematician Martin Ohm (English: Martin Ohm) wrote the second edition of the basic pure mathematics annotation wrote about the interpretation of the golden ratio: "people used to put any straight line along the way will be divided into two parts, the method of known as the golden mean". And in the ninth edition of the Encyclopaedia Britannica, published in 1875, Sully notes: "The interesting, experimental and strong idea put forward by Frederick... proclaimed the supposed superiority of the 'golden Section' in visual proportion." So the Golden Section was already popular. In the 20th century, American mathematician Mark Barr gave it the name Phi. The Golden Section has many interesting properties and has been widely used by humans to make it famous today. The most famous example is the golden ratio or 0.618 method in optimization, which is first proposed in 1953 by Jack Kiefer (English: Jack Kiefer), an American mathematician, and is promoted in China in 1970s.

Answer:

approximately $23,655.91 (rounded to the nearest hundredths place)

Step-by-step explanation:

[tex]22,000=0.93x\\x=23,655.91[/tex]

Explanation:

Add up the given decimal values

0.03+0.14+0.65+0.08 = 0.90

Recall that all of the P(X) values must add to 1 to represent 100% of all possible outcomes. So far we added to 0.90, so we're missing 1 - 0.90 = 0.10

As a check,

0.03+0.14+0.65+0.08 + 0.10 = 1

Let's take this problem step-by-step:

First let's set up the equation for the cost for one week of renting the car

              [tex]charge = 230[/tex]

              [tex]charge = 230 + 0.25x[/tex]

The total cost was 415, therefore:

             [tex]415 =230 + 0.25x\\185 = 0.25x\\x = 740[/tex]

Therefore, you traveled 740 miles

Answer: 740 miles

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Answer:

Using the formula of geometric progression, we get 5.3333333. After rounding off to the nearest hundredth or to the two digit place after the decimal, we get 5.33.

Step-by-step explanation:

Concept: Given expression means that [tex]4(\frac{1}{4} )^{n-1}[/tex] is a series that starts from n = 1 and ends at n = 10. Or we can say that the given expression is a summation from n = 1 to n = 10. This will make a geometric progression. Use the formula of geometric progression to find the answer.

[tex]4(\frac{1}{4})^{0} + 4(\frac{1}{4})^{1} + 4(\frac{1}{4})^{2} +...+ 4(\frac{1}{4})^{10}\\4\frac{-(\frac{1}{4} )^{11} +1}{-\frac{1}{4} +1} \\4\frac{1}{\frac{3}{4} } \\\frac{16}{3} \\5.33333333\\[/tex]

Now, we want the answer to the nearest hundredth. This means that the answer should have two digits after the point.

The answer, to the nearest hundredth is 5.3333333

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The probability that the results indicate a successful market for the product and the product is actually not successful is P=0.77.

Probability refers to a possibility that deals with the occurrence of random events.

Events are given:

S: success

F: failure

MS: market research forecast a success

MF: market research forecast a failure

we have given:

P(S)=0.70

P(F)=0.30

P(S | MS)=0.90

P(F | MS)=0.20

we can derive that P(F | MF)=0.80.

We also can conclude that P(S | MF)=0.10.

We can calculate the probability of having a forecast of a failure,

[tex]P(MF | F) =\dfrac{ P(F | MF)P(F)}{ P(F | MF)P(F) + P(S | MS)P(S) }[/tex]

P (MF | F) = 0.24 / 0.31

P (MF | F) = 0.77

The probability that the results indicate a successful market for the product and the product is actually not successful is P=0.77.

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