Essay Question.
You are purchasing a new car. In order to determine which car will provide maximum savings, you’ve researched miles per gallon (mpg) ratings of cars. If gas is $3.45 per gallon and you drive an average of 18,000 miles per year, the following rational equation is given:

The exact value of cos(θ/2) is:

[tex]cos(\frac{\theta }{2}) = \right-\sqrt{\frac{1}{122} }[/tex]

To find the exact value of cos(θ/2), we can use the half-angle formula for cosine:

[tex]cos(\frac{\theta }{2}) = \right\pm\sqrt{\frac{1+cos\theta}{2} }[/tex]

First, let's find the value of cos(θ) using the given information about θ:

Given:

tan(θ) = 11/60

θ lies in the 3rd quadrant (π < θ < 3π/2)

In the 3rd quadrant, both sin(θ) and cos(θ) are negative.

tan(θ) = opposite/adjacent

Also, in the 3rd quadrant, both opposite and adjacent are negative.

Thus,

opposite = -11

adjacent = -60

hypotenuse = √[(-60)² + (-11)²]   (Pythagoras theorem)

hypotenuse = 61

cos(θ) = adjacent/hypotenuse

cos(θ) = -60/61

Finally, we can substitute these values into the half-angle formula for cosine:

[tex]cos(\frac{\theta }{2}) = \right\pm\sqrt{\frac{1+(\frac{-60}{61})}{2} }[/tex]

[tex]cos(\frac{\theta }{2}) = \right\pm\sqrt{\frac{\frac{1}{61} }{2} }[/tex]

[tex]cos(\frac{\theta }{2}) = \right\pm\sqrt{\frac{1}{122} }[/tex]

Since the cos(θ/2) is negative. Therefore, the exact value of cos(θ/2) is:

[tex]cos(\frac{\theta }{2}) = \right-\sqrt{\frac{1}{122} }[/tex]

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[tex]2x^2-10x=0\\2x(x-5)=0\\2x=0 \vee x-5=0\\x=0 \vee x=5[/tex]

Answer:

Here

2x^2 - 10x = 0

2x^2 = 0 + 10x

2x^2 = 10x

x^2 = 10x ÷ 2

x^2 = 5x

2x^2 - 10x = 0

x^2 - 5x = 0

Step-by-step explanation:

first find the value of x and then put the value and slove

The measure of unknown angle of triangle is 28.2°.

From the given triangle, we have sides 11 units, 12 units and 20 units.

The law of cosine states that the square of any one side of a triangle is equal to the difference between the sum of squares of the other two sides and double the product of other sides and cosine angle included between them. The law of cosine states that: a² = b² + c² − 2bc·cosA.

Here, 11²=12²+20²-2×12×20·cosA

121=144+400-480·cosA

121=544-480·cosA

121-544=-480·cosA

-423=-480·cosA

cosA= 423/480

cosA= 0.88125

A=28.2°

Therefore, the measure of unknown angle of triangle is 28.2°.

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The measure of the marked central angle for the given circle is 160°.

Given a part of a circle.

This part is 4/9 of the full circle.

We have to find the marked central angle.

We know that,

Total circle can be represented as,

Total circle = 360°

Since the given figure is 4/9 part of the total circle, the marked central angle will be 4/9 of the total central angle.

Marked central angle = 4/9 × 360

                                    = 160°

Hence the marked central angle is 160°.

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The percentage is 26%, so the number is 26.

Here we know that the x% of the number 800,000 is equal to 208,000.

Remember that the x% of a number N, is given by the product:

(x%/100%)*N

So in this case we can solve the equation:

(x%/100%)*800,000 = 208,000

Solving that equation for the percentage, we will get:

x% = 100%*(208,000/800,000)

x% = 26%

That is the missing number.

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The area of the composite figures are:

The total area of Shape A is = 115.5 in²

and, total area of Shape B is = 51ft².

Here, we have,

from the given diagram we get,

Shape A.)

Part 1: it is a rectangle,

l= 13 and w = 7

so, area = 91 in²

Part 2: it is a triangle,

b = 7 and h = 7

so, area = 1/2 *7 * 7 = 24.5 in²

So, The total area of Shape A is = 115.5 in²

now, Shape B.)

part 1 : it is a rectangle,

l=4 and w = 6

so, area = 24 ft²

part2: it is a square,

side = 3

so, area = 9 ft²

part 3: it is a trapezium,

a = 6, b = 3, h =4

so, area = 1/2 * (6+3) * 4 = 18ft²

So, total area of Shape B is = 51ft².

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the answer to this question is

m=1

Answer: y<-x+3

Step-by-step explanation:

Slope-Intercept Form formula is y=mx+b.

1. Rearrange the variables (subtract x).  x+y<3  --> y<-x+3.

2. y<-x+3 is the final answer!

Very Simple!

Please vote me brainliest! Thanks!

The probabilities of getting eagles in different quantities, given the number of coins would be:

There are 8 possible outcomes when tossing 3 coins: HHH, HHT, HTH, THH, TTH, THT, HTT, TTT.

The probability of getting 2 eagles is 3/8 because the ways of getting eagles HHH, HHT, and HTH.

The probability of getting at least 1 eagle is 7 / 8. There are 7 ways to get at least 1 eagle: HHH, HHT, HTH, THH, TTH, THT, and HTT.

The probability of getting no eagles is 1/8 / . There is only 1 way to get no eagles: TTT.

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The relationship between Calorie and weight is very weak and insignificant.

Comparing the relationship between Calorie and Weight using the correlation coefficient, the coefficient value obtained is 0.0086 which is very weak.

There is no obvious pattern linking an increase in calorie to Weight or decrease in association between the two variables.

Therefore, we can conclude that a very weak and insignificant relationship exists between Calorie and weight for the given data.

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Altogether they have 85 marbles.

Given,

Randy's marbles = 50

Randy's marbles is 5/2 of Andy's marbles.

Randy's marbles is 10/3 of Peter's marbles.

Now form the linear equations,

Let Andy has x marbles.

So,

5/2 × x = 50

x = 20

Andy's marbles = 50

Let Peter has y marbles.

So,

10/3 × y = 50

y = 15

Peter's marbles = 15

Thus total marbles of Randy , Andy , Peter is 85.

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Answer:

85 marbles

Step-by-step explanation:

Andy has 20

Randy has 50

Peter has 15

Answer:L*W

Step-by-step explanation:

if you look at the pattern you will see that

Option C is the table of values representing a proportional relationship in the context of this problem.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

For item c, we have that the output is equals to the input, hence the proportional relationship is given as follows:

y = x.

The problem asks for which table represents a proportional relationship.

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Answer:

Arc EG = 23.21 units

Step-by-step explanation:

Arc length:

Arc length could be found by the below mentioned formula.

         [tex]\boxed{\bf Arc \ length =\dfrac{\theta }{180}*\pi r}[/tex]

r - radius of circle = 19 units

Ф - central angle of arc = 70°

                             [tex]\sf arc \ EG = \dfrac{70}{180}*3.14*19\\\\[/tex]

                                         = 23.21 units

The expression x²x²x²√x when evaluated is [tex]x^{6\frac{1}{2}}[/tex]

From the question, we have the following parameters that can be used in our computation:

x²x²x²√x

The above expression can be evaluated using the law of indices

Using the above as a guide, we have the following:

x²x²x²√x = x⁶√x

So, we have

x²x²x²√x = x⁶ * √x

When evaluated, we have

x²x²x²√x =  [tex]x^{6\frac{1}{2}}[/tex]

Hence, the expression when evaluated is [tex]x^{6\frac{1}{2}}[/tex]

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Complete question

Evaluate x²x²x²√x

Answer:

Table B was created using the equation y = 4x-1.

Explanation:

The equation y = 4x-1 means that for any given value of x, the corresponding value of y can be found by multiplying x by 4 and then subtracting 1.

Table B shows input values of x and output values of y that are consistent with this equation. For example, when x = 3, y = 11 (4 * 3 - 1), and when x = 4, y = 15 (4 * 4 - 1), and so on.

Therefore, we can conclude that Table B was created using the equation y = 4x-1.

The minimum y-value of g(x) is -3 and g(x) has the smallest possible y-value.

The function  f(x) = 32 - 3 is a constant function, as there is no variable term involving x. It simplifies to f(x) = 29.

Regardless of the value of x, the function f(x) will always have a y-value of 29.

Therefore, option A is incorrect because there is no minimum y-value for f(x); it is a constant.

g(x) = 7x² - 3 is a quadratic function in the form of ax² + bx + c, where a = 7, b = 0, and c = -3.

The coefficient a (7) is positive, indicating that the parabola opens upward.

Since there is no linear term (bx), the vertex of the parabola is located at the point (0, -3), which corresponds to the minimum y-value of the function.

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Answer:

One method that a person can use to send money to another person who does not have a bank account is through a money transfer service like Western Union or MoneyGram. These services allow individuals to send money to recipients who can then collect it in cash from designated locations. The sender can visit a local agent or use an online platform to initiate the transfer, providing the recipient's name and other required details. The recipient can then go to a nearby agent location with proper identification to receive the cash. This method provides a convenient way to send money to individuals who may not have access to traditional banking services.

Step-by-step explanation:

Person 1 takes money out of wallet, gives money to person 2.

BOOM!

floor plan => It is the scale drawing that show the relationship between rooms, spaces, and physical features viewed from the above

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The GDP at FC from the following data: GDP at MP = Rs. 2,000 billion Indirect taxes = Rs. 300 billion Subsidies = Rs. 100 billion​ is: Rs. 1,800 billion.

Using this formula to determine the GDP at FC

GDP at FC = GDP at MP - Indirect taxes + Subsidies

Where:

GDP at MP (Market Price) = Rs. 2,000 billion

Indirect taxes = Rs. 300 billion

Subsidies = Rs. 100 billion

Let plug in the formula

GDP at FC = 2,000 billion - 300 billion + 100 billion

GDP at FC = 1,800 billion

Therefore the GDP at factor cost (FC) is Rs. 1,800 billion.

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The value of the missing segment n using the product of intersecting chord theorem is 14cm

The product of the segments of two intersecting chords are equal.

The segments of the chords ;

Chord 1 = 4 and n

Chord 2 = 7 and 8

The principle can be related Mathematically thus ;

4 × n = 7 × 8

4n = 56

Divide both sides by 4

4n/4 = 56/4

n = 14

Therefore, the value of n in the question is 14cm

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Answer:

To calculate Mr. Chi's total tax bill, we need to find the amount of sales tax charged by each entity and add them together.

The state sales tax on the sale of a house is 3.2%, which means Mr. Chi will owe 0.032 x $289,300 = $9,267.20 in state sales tax.

The county sales tax on the sale of a house is 2.6%, which means Mr. Chi will owe 0.026 x $289,300 = $7,520.80 in county sales tax.

The city sales tax on the sale of a house is 1.8%, which means Mr. Chi will owe 0.018 x $289,300 = $5,207.40 in city sales tax.

Therefore, Mr. Chi's total tax bill will be $9,267.20 + $7,520.80 + $5,207.40 = $21,995.40.

AnswerTherefore, Jennifer traveled for 2 hours.

Step-by-step explanation:

Let x be the time Jennifer traveled.

Kristin traveled for 2 hours at 33 km/h, so she had traveled 66 km when Jennifer started traveling.

After x hours, Jennifer had traveled 45x km.

The total distance between them was 156 km.

So, we have:

66 km + 45x km = 156 km

Simplifying the equation, we get:

45x km = 90 km

x = 2 hours

Therefore, Jennifer traveled for 2 hours.

Por lo tanto, la parcela mide 18 metros de largo y 12 metros de ancho.

Llamemos "largo" (L) a una de las dimensiones de la parcela y "ancho" (A) a la otra dimensión.

Según la información dada, sabemos que la suma del largo y el ancho es de 30 metros:

L + A = 30 ---(1)

También se nos dice que la diferencia entre el largo y el ancho es de 6 metros:

L - A = 6 ---(2)

Podemos resolver este sistema de ecuaciones utilizando el método de sustitución o de eliminación. En este caso, resolveremos utilizando el método de sustitución.

De la ecuación (2), podemos despejar L en términos de A:

L = A + 6

Sustituyendo este valor de L en la ecuación (1), obtenemos:

(A + 6) + A = 30

2A + 6 = 30

Restamos 6 de ambos lados de la ecuación:

2A = 30 - 6

2A = 24

Dividimos ambos lados de la ecuación por 2:

A = 12

Ahora que conocemos el valor de A, podemos encontrar el valor de L sustituyendo en la ecuación (2):

L = A + 6

L = 12 + 6

L = 18

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Answer:

76.5 hours

(If you like this answer i would appreciate if u give brainliest but otherwise, i hope this helped ^^)

Step-by-step explanation:

Part 1 of 2:

(a) The equation that describes Winona's total take-home pay, P, in terms of the number of hours, x, worked at the first job and the number of hours, y, worked at the second job can be written as:

P = (10x) + (9.25y + 0.7 * 9.25y) - 0.2[(10x) + (9.25y + 0.7 * 9.25y)]

Simplifying the equation:

P = 10x + 9.25y + 0.7 * 9.25y - 0.2(10x + 9.25y + 0.7 * 9.25y)

Part 2 of 2:

(b) If Winona is committed to working 30 hours per week at the first job, let's assume x = 30. We need to find the number of hours per week, y, she would need to work at the second job to reach a biweekly take-home pay of $800.

Using the simplified equation from part (a), we substitute x = 30 and solve for y:

800 = (10 * 30) + (9.25y + 0.7 * 9.25y) - 0.2[(10 * 30) + (9.25y + 0.7 * 9.25y)]

800 = 300 + (9.25y + 0.7 * 9.25y) - 0.2(300 + (9.25y + 0.7 * 9.25y))

Now, we can solve for y:

800 = 300 + 9.25y + 0.7 * 9.25y - 0.2(300 + 9.25y + 0.7 * 9.25y)

Simplify the equation:

800 = 300 + 9.25y + 0.7 * 9.25y - 0.2 * 300 - 0.2 * 9.25y - 0.2 * 0.7 * 9.25y

Combine like terms:

800 = 300 - 60 + 9.25y - 1.85y - 0.1295y

800 = 240 + 7.32y

Subtract 240 from both sides:

560 = 7.32y

Divide both sides by 7.32:

y ≈ 76.5

Therefore, Winona would need to work approximately 76.5 hours per week at her second job to reach a biweekly take-home pay of $800.

Answer:

To summarize:

√3 - 6x: Domain is all real numbers (-∞, +∞).

√13 - (13 - 2x): Domain is all real numbers (-∞, +∞).

1/√x - 2: Domain is all real numbers except x = 0, represented as (-∞, 0) U (0, +∞).

Step-by-step explanation:

To find the domain of each expression, we need to identify any restrictions or limitations on the variables that would result in undefined values.

√3 - 6x:

Since square roots are defined for non-negative numbers, the expression is defined as long as the value inside the square root (√3) is non-negative. The square root of 3 is a positive value, so there are no restrictions on the domain of this expression. Therefore, the domain is all real numbers (-∞, +∞).

√13 - (13 - 2x):

Similar to the previous expression, the square root (√13) is defined for non-negative values. However, we also need to consider the expression (13 - 2x) inside the parentheses. This expression does not have any limitations since it is defined for all real numbers. Therefore, the domain of this expression is all real numbers (-∞, +∞).

1/√x - 2:

For this expression, we need to consider both the square root (√x) and the denominator (1/√x). The square root (√x) is defined for non-negative values of x. However, the denominator 1/√x will become undefined if the value of x is zero because division by zero is undefined. Therefore, we need to exclude x = 0 from the domain. For all other non-zero values of x, the expression is defined. Therefore, the domain of this expression is all real numbers except x = 0, represented as (-∞, 0) U (0, +∞).

Answer:

Hope this saved you ^^

Step-by-step explanation:

To determine the number of babies we can expect among the next 12 children to enroll, we need to calculate the proportion of babies based on the current enrollment data.

Out of the total enrollment so far, there are 3 babies and 6 children of other ages, making a total of 9 children.

Proportion of babies = (Number of babies / Total number of children) = 3 / 9 = 1/3

Now, to estimate the number of babies among the next 12 children, we multiply the proportion of babies by the total number of children to be enrolled:

Number of babies expected = Proportion of babies * Total number of children to enroll

Number of babies expected = (1/3) * 12 = 4

Therefore, based on the current enrollment data, we can expect approximately 4 out of the next 12 children to be babies.

Answer:

Θ ≈ 103°

Step-by-step explanation:

using the Cosine rule in Δ ABC

cosB = [tex]\frac{a^2+c^2-b^2}{2ac}[/tex]

where a is the side opposite ∠ A , b the side opposite ∠ B and c the side opposite ∠ C

here a = 42 , b = 78 and c = 57 , then

cos B = [tex]\frac{42^2+57^2-78^2}{2(42)(57)}[/tex]

          = [tex]\frac{1764+3249-6084}{4788}[/tex]

          = [tex]\frac{5013-6084}{4788}[/tex]

         = [tex]\frac{-1071}{4788}[/tex] , then

B = Θ = [tex]cos^{-1}[/tex] ( - [tex]\frac{1071}{4788}[/tex] ) ≈ 103° ( to the nearest degree )

The statement "The cup of flour has a mass of exactly 121.8 grams" is not true.

Since the baking scale measures mass to the tenth of a gram, it means it can measure values such as 121.7 grams, 121.8 grams, and 121.9 grams. However, it does not have the capability to measure beyond the tenths place, so it cannot determine whether the exact mass of the cup of flour is exactly 121.8 grams. Therefore, the statement claiming an exact mass is not true.

The other statements are all true:

[tex]\huge{\mathcal{\colorbox{black}{\textcolor{lime}{\textsf{I hope this helps !}}}}}[/tex]

♥️ [tex]\large{\textcolor{red}{\underline{\texttt{SUMIT ROY (:}}}}[/tex]

Answer:

Step-by-step explanation:

A baking scale measures mass to the tenth of a gram, up to 650 grams. A cup of flour is placed on the scale and results in a measure of 121.8 grams. [ Which of the following statements is not true? a.The exact mass of the cup of flour must be between 121.7 and 121.9 grams.