The gas mileages​ (in miles per​ gallon) for cars are shown in the frequency distribution. Approximate the mean of the frequency distribution.
Gas Mileage
​(in miles per​ gallon)
Frequency

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Part 1
The approximate mean of the frequency distribution is

enter your response here.

Step-by-step explanation:

To find the probability of an advertising firm selected at random having under $1 million or $1 million to $20 million in income after taxes, we need to add the number of firms in each of these two categories and divide the result by the total number of firms.

Number of firms with under $1 million in income after taxes = 95

Number of firms with $1 million to $20 million in income after taxes = 74

Total number of firms = 95 + 74 + 31 = 200

Therefore, the probability of an advertising firm selected at random having under $1 million or $1 million to $20 million in income after taxes is:

(95 + 74) / 200 = 0.845

So the probability is 0.845 or 84.5%.

The measure of the angle x is 70.53 degrees

It is important to know that trigonometric identities are defined as equalities that relate to different trigonometric functions and also holds true for any value of the variable that is in the domain.

There are different trigonometric identities namely;

The ratio for the identity cosine is;

cos θ = adjacent/hypotenuse

substitute the values, we get;

cos x = 4/12

divide the values

cos x = 0. 3333

Take the inverse cosine of the values

x = 70. 53 degrees

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If a sum of money put out a compound interest increased by Rs. 180 at the end first year and Rs. 188 10 at the end of second year. The rate is 4.5% and the sum is $4,000.

Let the sum of money be x.

After the first year, the amount becomes x+180.

After the second year, the amount becomes (x+180)+188.10 = x+368.10.

Let the rate of interest be r, expressed as a decimal.

Then, using the formula for compound interest, we have:

(x+180) = x(1+r)

(x+368.10) = (x+180)(1+r) = x(1+r)² + 180(1+r)

Subtracting the first equation from the second, we get:

188.10 = x(1+r)² - x(1+r) + 180(1+r)

8.10 = x(r+r²) + 180r

Simplifying this equation, we get a quadratic in r:

r² + r(180/x) - 8.1/x = 0

Using the quadratic formula, we can solve for r:

r = [-180/x ± sqrt((180/x)² + 4(8.1/x))]/2

r = [-180/x ± sqrt((32400/x²) + (32.4/x))]/2

r = (-90/x) ± sqrt((8100/x²) + (8.1/x))

Since r must be positive (since the amount increased), we take the positive root:

r = (-90/x) + sqrt((8100/x²) + (8.1/x))

Substituting the given values of the increase and solving for x, we get:

180 = x[(1+(-90/x)+sqrt((8100/x²)+(8.1/x))) - 1]

180 = x(-90/x + sqrt((8100/x²)+(8.1/x)))

180 = -90 + xsqrt((8100 + 8.1x)/x³)

270 = xsqrt((8100 + 8.1x)/x³)

72900 + 729. x = 729. x²

x² - x(100.1) + 720000 = 0

(x-400)(x-1800) = 0

x = 400 or x = 1800

Since x cannot be negative, we take x = 400.

To find the rate of interest, we use the first equation:

x+180 = x(1+r)

180 = x*r

r = 180/x

r = 180/ 400

r  = 0.45 = 4.5% per annum.

Therefore, the sum of money is Rs. 4,000.

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Using a calculatοr οr spreadsheet, we can find that x is apprοximately 3.977 after several iteratiοns.

We can use trial and errοr οr iterative methοd tο find the value οf x.

Trial and Errοr Methοd is a prοblem-sοlving strategy that invοlves testing variοus sοlutiοns until the cοrrect οne is fοund. It is a simple but time-cοnsuming apprοach that invοlves attempting different sοlutiοns and checking their οutcοmes until the desired result is achieved. This methοd is οften used when there is nο clear οr οbviοus sοlutiοn tο a prοblem, and it requires patience, persistence, and the ability tο learn frοm mistakes.

Trial and Errοr Methοd:

We can substitute different values οf x intο the equatiοn until we get a value that is very clοse tο 2.

Using the calculatοr and by trial and errοr, we can find that x is apprοximately 3.977.

Iterative Methοd:

We can use an iterative methοd tο find the value οf x that satisfies the equatiοn. The iterative fοrmula fοr this prοblem is:

x_{n+1} = lοg[tex](2 + 1.5(0.55)^{x_n})[/tex] / lοg(0.55)

where x_n is the nth apprοximatiοn οf x.

Starting with x_0 = 3, we can use this fοrmula tο get better and better apprοximatiοns οf x. Using a calculatοr οr spreadsheet, we can find that x is apprοximately 3.977 after several iteratiοns.

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Answer:

The decision of whether Gavin should take culinary as his shop class at the vocational school depends on his personal goals and priorities.

If Gavin is seriously considering a culinary career as a chef, then taking culinary classes at the vocational school could provide him with valuable skills and knowledge that could help him achieve his career goals. In this case, he should prioritize his personal goals over his friends' plans and choose the vocational school option.

On the other hand, if Gavin is not sure about his career goals and values spending time with his friends, then he may want to choose a different shop class that is offered at his high school. It is important to note that culinary skills can be learned outside of school as well, through internships, volunteering, or cooking at home.

Ultimately, Gavin should weigh his personal goals and priorities against the potential benefits and drawbacks of each option and make a decision that is best for him.

The value of x is obtained as 37.49°. The solution has been obtained by using the concept of trigonometry.

What is trigonometry?

The study of the sides, angles, and connections of the right-angle triangle is known as trigonometry which is a branch of mathematics.

In the figure, we are given length of perpendicular as 14 and length of  hypotenuse as 23.

We are also given an angle 'x'

We know that sin theta = [tex]\frac{opposite side}{hypotenuse}[/tex]

Here, theta = x

Using this, we get

⇒ sin x = [tex]\frac{14}{23}[/tex]

⇒ x = [tex]sin^{-1} (\frac{14}{23})[/tex]

⇒ x = 37.49°

Hence, the value of x is obtained to be 37.49°.

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The allusion represents a symbol of strength and power, as the Colossus of Rhodes was a giant statue made of bronze that was built to commemorate the island's successful resistance to a siege.

Allusion is a figure of speech that makes a reference to a person, place, thing, event, or idea from history, literature, mythology, or another source. It is used to create an implied comparison without explicitly stating it. Allusions can be used to express feelings, suggest ideas, or draw attention to a certain concept. An allusion can be subtle, humorous, or even ironic. Allusions can also add depth and complexity to a piece of writing, or draw attention to a specific idea or point.

The statue is meant to represent the strength and power of the island, and its ability to protect itself from outside forces.

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The credit card's outstanding amount is [tex]4875[/tex], the new interest rate is [tex]75[/tex], as well as the buying power is [tex]50[/tex] after paying the required minimum payment of [tex]125[/tex].

The urge to become interested with something, give it your whole attention, and learn more about it My entire life, astronomy has captivated me. He never seems to be concerned about his children.

You pay the interest on almost any loans and bank debt of money. The proportion of the loan balance used by lenders to compute interest. Clients who lend money can earn interest

We determine the monthly interest charge,

Interest charge = (1.5% per month) [tex]*[/tex] (5000 unpaid balance)

Interest charge [tex]= 75[/tex]

The new overdue debt is obtained by deducting the minimum monthly payment from the original unpaid balance:

Unpaid balance [tex]= 5000 - 125[/tex]

Unpaid balance [tex]= 4875[/tex]

we add the interest charge to the new unpaid balance to get the new balance:

New balance [tex]= 4875 + 75[/tex]

New balance [tex]= 4950[/tex]

Lastly, we may determine the purchasing power by deducting the new balance from the credit limit:

Purchasing power [tex]= 5000 - 4950[/tex]

Purchasing power [tex]= 50[/tex]

Therefore the unpaid balance on the credit card is [tex]4875[/tex], the new interest charge is [tex]75[/tex], and the purchasing power is [tex]50[/tex].

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In response to the query, we can state that As a result, the following is equation the system of equations' solution: x = 8 \sy = -7

An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.

We can use the substitution or elimination methods to find the values of x and y in this system of equations. We shall apply the elimination approach in this case:

-3y - 4x = -11 (equation 1) (equation 1)

3y - 5x = -61 (equation 2) (equation 2)

By combining equations 1 and 2, we may remove the y variable:

-3y -4x + 3y - 5x = -11 - 61

Streamlining the left side:

-9x = -72

-9 divided by both sides:

x = 8

Knowing that x = 8 allows us to solve for y by introducing this number into either equation. Consider using equation 1:

-3y - 4(8) = -11

Simplifying:

-3y - 32 = -11

32 more on both sides:

-3y = 21

By -3, divide both sides:

y = -7

As a result, the following is the system of equations' solution:

x = 8 \sy = -7

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A bottle of orange juice contains 64 fluid ounces. The percent of bottle of orange juice is water is 75% and there are 48 cups of orange juice are there in bottles.

Percentage:

In mathematics, a percentage is a number or a ratio that can be expressed as a fraction of 100. If we need to calculate a percentage of a number, we divide the number by a whole number and multiply by 100. So , percent means one hundredth and the word percent means every 100th. It is represented by the symbol "%".

Using this formula

Percentage = Ounces of water/Ounce bottle of orange juice

Where:

Ounces of water = 48 ounces

Ounce bottle of orange juice = 64 ounce

Let plug in the formula

Percentage = 48/64

Percentage = 0.75×100

Percentage = 75%

Therefore,

the percent of bottle of orange juice is water is 75%.

Complete Question:

A bottle of orange juice contains 64 fluid ounces. how many cups of orange juice are in three bottles. What percent of bottle of orange juice is water

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Answer:

the percent of bottle of orange juice is water is 75%.

Step-by-step explanation:

The translations that would map Figure F onto Figure G are given as follows:

A translation right 4 units and up 3 units.

A translation happens when either a figure or a function are moved horizontally or vertically on the coordinate plane.

The four translation rules for coordinates are defined as follows:

The rule applied to the coordinates of each point on the figure F to obtain Figure G is given as follows:

(x,y) -> (x + 4, y + 3).

Hence the translation is defined as follows:

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According to the information, the correct order of the steps would be: 5, 2, 3, 6, 7, 4, 1.

To properly organize the steps we must read each one of them and identify the procedure they are describing. In this case, they are describing the procedure for cooking a fried food. According to the above, the steps to follow would be:

5. Wash your hands.

2. Take strips out of the freezer and put a maximum of 15 into a basket. Lower the basket into preheated oil.

3. Start the strip' timer by pressing the button on the front of the fryer.

6. When the timer sounds, shake the basket once during cooking without removing the basket from the oil.

7. When the timer sounds, remove the basket from the fryer and drain well.

4. Hold food in warming drawer or cabinet. Press the strips' hold timer button on the cabinet timer.

1. Use tongs to place strips in the package (3 for a small order, 5 for a large order).

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One example of a graph that satisfies these properties is a cubic polynomial with the equation y=ax³+bx²+cx+d.

A cubic polynomial is a mathematical expression composed of terms that are raised to the third power. It is written as ax³ + bx² + cx + d, where a, b, c and d are constants and x is a variable. Cubic polynomials are used in many applications, such as approximating functions, solving equations, and finding the roots of polynomials. They can also be used to model physical phenomena, such as the motion of objects.

This graph will have a positive second derivative on the intervals (-infinity, -2) and (4, infinity). At the points -2, -1, 1, 2, and 3, the second derivative will be zero, the first derivative will be zero at -1, 1, and 3, and the function will be zero at 1.

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Answer:

262609375 is the answer.

Statistical scores and rankings in school can be useful for a variety of purposes, such as measuring academic performance, making admissions decisions, and providing feedback for improvement.

The usefulness of statistical scores or rankings in school can vary depending on the context and purpose of their use.

GPA (Grade Point Average) is a common metric used to measure a student's academic performance over time. It is calculated by assigning numerical values to letter grades and averaging them. GPA can be useful for college admissions, scholarships, and job applications, as it provides a quick snapshot of a student's overall academic performance.

SAT and ACT scores are standardized tests used by colleges and universities as part of their admissions process. These scores are designed to measure a student's readiness for college-level work and are often used in combination with other factors, such as GPA and extracurricular activities, to make admissions decisions.

Test scores, such as those from quizzes, exams, or assignments, provide feedback to both students and teachers about the effectiveness of their teaching and learning strategies. These scores can be useful in identifying areas where a student may need additional support or where a teacher may need to adjust their teaching methods.

Class ranking compares a student's academic performance to their peers in the same graduating class. This ranking can be useful for college admissions and scholarships, as it provides a way to differentiate between students with similar GPAs.

Overall, statistical scores and rankings in school can be useful for a variety of purposes, such as measuring academic performance, making admissions decisions, and providing feedback for improvement. However, it is important to keep in mind that these scores should be viewed as one piece of information among many and should not be relied upon as the sole indicator of a student's abilities or potential.

[tex]$$\textbf{Formula:}$$[/tex]

[tex]GPA = \frac{\sum_{i=1}^n (credit_i \times grade_i)}{\sum_{i=1}^n credit_i}[/tex]

SAT and ACT scores = Combination of scores from various sections of the test

Class ranking = Student's position in the graduating class based on their GPA or other academic performance metrics

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Complete Question:

People use data and statistics to help them make important policy decisions, to identify

problems in an organization, and to predict outcomes. In this unit, you studied various

ways to analyze and represent data sets to determine how to best interpret the data.

You also learned how to critically examine the data and account for outside factors that

may influence the patterns you see in the data.

Think about the many statistical scores or rankings you receive in school, such as GPA,

SAT and ACT scores, test scores, and class ranking. Describe the usefulness and

limitations of these pieces of data in defining who you are as a person or as a student.

In what ways do they help give a clear picture? What are they not conveying?

Answer: X = 12, Y = 60°

Step-by-step explanation:

We are given a parallelogram. We know one degree measure, and one given side. To find X, create an equation, x + 3 = 15. Solve. X = 12. Since this is a parallelogram, Y must equal 60°, since parallelograms have two sets of equal degree measures.

Answer:

Step-by-step explanation:

The line contains the points (0,3) and (6,11).

first find the slope with slope formula.
m=(11-3)/(6-3)

=8/2

=4.

you know the y-intercept is 3, so use slope-intercept form

y=4x+3

The root(s) of f (x) are

6 with multiplicity 2

-2 with multiplicity 2.

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

We are given to find the roots of the following polynomial function :

f (x) = (x- 6)²(x + 2)²

We know that

the roots of a polynomial f(x) are given by the equation f(x) = 0.

Therefore, the roots of the given polynomial are given by

(x- 6)² =0 => x =6,6

(x + 2)² =0 , x =-2, -2

Thus, the required roots are

6 with multiplicity 2 and -2 with multiplicity 2.

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We can conclude after answering the provided question that We can estimate that a 3 would be rolled probability 71 times after 200 rolls if we round off to the nearest integer.

Probability is a way of measuring of how likely an event is to occur. It is represented by a number respectively 0 and 1, with 0 representing an unlikely event and 1 representing an unavoidable event. Switching a valid coin and coin flips has such a probability of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails). Probability theory is a branch of mathematics that studies random events instead than their properties. It is applied in many fields, including facts and figures, finance, science, and construction.

Based on the information provided, the estimated probability of rolling a 3 can be calculated as follows:

8/20 = 0.4 for 20 rolls

18/50 = 0.36 for 50 rolls

For 100 rolls: 30/100 = 0.3

We can take the average of these values to get the best estimate:

(0.4 + 0.36+ 0.3) / 3 = 0.3533

As a result, the best estimate of the likelihood of rolling a 3 is 0.3533.

We can estimate the number of times a 3 would be rolled after 200 rolls using this probability as:

The number of times a 3 would be rolled equals the probability of rolling a 3 multiplied by the number of rolls.

= 0.3533 x 200

= 70.66

We can estimate that a 3 would be rolled approximately 71 times after 200 rolls if we round off to the nearest integer.

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An exponential function showing the relationship between y and t is:

y(t) = 1500(e)^(-0.0425t)

The general form of expression of an exponential growth function is:

y = P(e)^(rt)

where;

y is the Amount you want the account/price/population/etc. to equal

P is the principal, or the amount you start with.

e is a specific irrational number approximately 2.718.

We are given:

In 2004, a forest covered an area of 1500 km². Thus:

y(0) = 1500 km²

r = -4.25% = -0.0425

y(t) = P(e)^(rt)

Thus:

A = y(0) = 1500

Thus:

y(t) = 1500(e)^(-0.0425t)

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Answer:

Step-by-step explanation:

1. (0,5) or A

2.(2,5) or B

The ratiο οf bοοks in οther languages tο the rest οf the bοοks in the library is 204 : 1505.

A ratiο is a way οf cοmparing twο quantities by expressing the relatiοnship between them in terms οf their relative sizes. It is usually written in the fοrm οf a fractiοn οr using a cοlοn (:).

The tοtal number οf bοοks in the library is:

12345 + 7842 + 32178 + 7116 = 59481

The tοtal number οf bοοks in languages οther than English, French, and Arabic is:

7116

The ratiο οf bοοks in οther languages tο the rest οf the bοοks in the library is:

7116 : (59481 - 7116) = 7116 : 52365

Simplifying this ratiο by dividing bοth numbers by their greatest cοmmοn factοr gives:

7116 : 52365 = 204 : 1505

Therefοre, the ratiο οf bοοks in οther languages tο the rest οf the bοοks in the library is 204 : 1505.

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So the correct option is (d), for that we have know little bit about graph because graph is helpful to represent points.

A diagram that depicts the relationship between two variables, usually (generally)  measured along opposite axes in a pair, is used.

We have that means given,

[tex]\frac{x^{2} +10x+16}{x-3} > 0[/tex]

[tex]\frac{(x+2)(x+8)}{x-3} > 0[/tex]

So,

(a). (x +2) >0                                      

(x +8) > 0                        

[tex](x - 3) > 0 \implies x > 3[/tex]

(b). (x +2) < 0

(x +8) < 0

[tex](x - 3) > 0 \implies No\ Solution[/tex]

(c). (x +2) > 0

(x +8) < 0

[tex](x - 3) < 0 \implies No \ Solution[/tex]

(d). (x +2) < 0

(x +8) > 0

[tex](x - 3) < 0 \implies -8 < x < -2.[/tex]

[tex]So, -8 < x < -2 \ or\ x > 3[/tex]

Therefore the 4th graph is right.

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Answer:

5 by 2, 13 by 4, and 6 by 6.

The pool at Philip and Laura's home is therefore 5 x 2 x 13 x 6 square feet in size.

Step-by-step explanation:

We must multiply the pool's length by its breadth to determine its area. The formula f(x) = (x-3)(5x+2) yields the length and width, so:

Size equals (x-3) feet

Size is (5x+2) feet wide.

Length times Width equals (x-3) times (5x+2) square feet.

Increasing the brackets results in:

Area: 5 by 2, 13 by 4, and 6 by 6.

The pool at Philip and Laura's home is therefore 5 x 2 x 13 x 6 square feet in size.

At the relative extremum

What is a relative extremum?

A relative extremum is a relative minimum or maximum of a function.

Since the function F(x) = 2ax² + bx + 3 has a relative extremum at the point (-1,2). This implies that dF(x)/dx = 0 at the extremum.

So, F(x) = 2ax² + bx + 3

dF(x)/dx = d(2ax² + bx + 3)/dx

= d2ax²/dx + dbx/dx + d3/dx

= 4ax + b

dF(x)/dx = 0

⇒ 4ax + b = 0

⇒b = -4ax at x = -1

b = -4a(-1)

= 4a

Since the function F(x) = 2ax² + bx + 3 has a relative extremum at the point (-1,2), we have that

F(-1) = 2a(-1)² + b(-1) + 3

= 2a - b + 3

F(-1) = 2

⇒2a - b + 3 = 2

⇒2a - b = 2 - 3

2a - b = -1

Now, b = 4a

So,  substituting b into the equation, we have that

2a - b = -1

2a - 4a = -1

-2a = -1

a = -1/-2

a = 1/2

So, b = 4a

= 4(1/2)

= 2

So,

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Answer:

what do you want to ask dear?

Step-by-step explanation:

For the rectangle given the correct option is B) HL.

What is a rectangle?

A quadrilateral with parallel sides that are equivalent to one another and four equal vertices is known as a rectangle. It is also known as an equiangular rectangle for this reason.

A rectangle is given with parallel sides equal.

Two opposite angles are 90°.

A diagonal is drawn.

The given information describes a rectangle, which is a special case of a parallelogram with all angles equal to 90°.

In a rectangle, the diagonals are congruent and bisect each other.

Therefore, the correct option is (HL) hypotenuse-leg, which is a special case of the congruence rule for right triangles.

If we consider the right triangle formed by one of the diagonals and one of the sides of the rectangle, we can see that we have a right triangle with hypotenuse equal to the diagonal and leg equal to one of the sides of the rectangle.

Since the diagonals are congruent and the sides of the rectangle are equal, we have a case of HL congruence.

Option (a) AAS (angle-angle-side) and option (c) SSS (side-side-side) do not apply to this situation since we only have information about one side and one diagonal of the rectangle.

Option (d) "Not equal and congruent" is not a valid answer choice as congruent objects, by definition, must be equal.

Therefore, option B is the correct answer.

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Answer:

The normal distribution has the same mean as the original distribution and a variance that equals the original variance divided by, the sample size.

Step-by-step explanation: