His total bill, with tax, was $7.95. He paid 6 percent sales tax. How much did he pay for the cooler alone without the tax?

Answer: The elimination method is a method for solving a system of equations by eliminating one of the variables. One way to do this is to multiply one equation by a constant and then add or subtract it from the other equation to cancel out one of the variables.

We will start by multiplying the first equation by -1:

x + 2y = 4 ----> -x - 2y = -4

Now we will add the second equation to the modified first equation:

-x - 2y = -4

(x + 3y = 10)

0x + 1y = 6

Now we can solve for y:

y = 6

Now that we know y = 6, we can substitute this back into one of the original equations, for example the first one:

x + 2y = 4

x + 2(6) = 4

x = -8

So the solution to the system of equations is x = -8 and y = 6

Therefore, the solution is (-8,6)

Step-by-step explanation:

The graph of function f is stretched vertically by a scale factor of 3 to create the graph of function g.

The graph of a function is a visual representation of the function's mathematical relationship between inputs and outputs. When a function is said to be "stretched", this means that the graph is being transformed in some way. In this case, the graph of function f is being stretched vertically by a factor of 3 to create the graph of function g. This means that the vertical distance between each point on the graph of function f will be 3 times as great on the graph of function g. For example, if the graph of function f has a point (1,2) then the corresponding point on the graph of function g would be (1, 6). This transformation will change the shape of the graph and the values of the inputs and outputs of the function. The graph of the transformed function g will be wider, taller, and have different values for the inputs and outputs.

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Answer:

x=6

Step-by-step explanation:

hope this helps you with your question

The Work done by a person is 24 x 103 J.

Force ratio is the ratio of two forces. It is often used in the context of mechanics, where a force is the product of mass and acceleration, and is measured in newtons (N).

Velocity ratio, on the other hand, is the ratio of two velocities. It is also used in mechanics and is measured in meters per second (m/s).

Force ratio and velocity ratio are closely related, as they are both used to measure mechanical properties of an object.

Force ratio is used to measure the ratio of two forces acting on an object, while velocity ratio is used to measure the ratio of two velocities.

Both force ratio and velocity ratio can be used to analyze the movement of an object, as well as its response to external forces.

Force ratio and velocity ratio are important concepts in mechanics, as they can help to analyze the dynamics of an object and its behavior over time.

Let M.A. = F1 and V.R. = F2

E = M.A. x 100% V.R.

Substituting the given values,

E = 80 = F1 x 100% F2

Work done by a person = Force x Displacement

= F1 x F2 x 200 kg x 3.0 m

= (80 x 100%) x 200 kg x 3.0 m

= (8 x 103) N x 3.0 m

= 24 x 103 J

Work done by a person = 24 x 103 J

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True, the classic tradeoff between "guns and butter" states that when a society spends more on national defense, it has less to spend on consumer goods to raise the standard of living.

The production possibility curve, which illustrates the concept of opportunity cost, has a famous economic example known as the "guns-and-butter" curve. One must decide how much of each good to create in a hypothetical economy with only two goods.

An economy must decrease its production of butter (food) as it increases its production of firearms (military spending), and vice versa. According to the guns-and-butter curve, you can only acquire something if you offer something else in exchange.

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The answer to this question is -12x+20

Answer:

Step-by-step explanation:

49255-1674.67=47580.33

False. A persuasive speech is a type of public speaking that attempts to convince the audience to adopt a certain viewpoint or take a specific action.

While there are often competing perspectives on issues, a persuasive speech is not the most appropriate way to address them. Instead, a better approach to discussing issues with competing perspectives is to use an informative speech. An informative speech provides an unbiased overview of the issue, presenting both sides fairly and objectively. This allows the audience to develop their own opinion on the matter based on the facts presented. Although a persuasive speech may be used to present a particular point of view, informative speeches are the best tool for discussing issues with multiple perspectives.

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If the terminal point determined by t is in the given quadrant.sin(t), cos(t);  sin(t)= -cos(t) in Quadrant II.

In Quadrant II, the sine function is positive and the cosine function is negative. The sine and cosine functions are related by the Pythagorean identity, which states that sin^2(t) + cos^2(t) = 1.

Since the sine is positive and the cosine is negative in Quadrant II, we can square the sine function and subtract it from 1 to get:

1 - sin^2(t) = cos^2(t)

We can then take the square root of both sides to get:

cos(t) = sqrt(1 - sin^2(t))

And since the cosine is negative in Quadrant II, we can then multiply the equation by -1 to get:

sin(t) = -cos(t)

This equation is only valid in Quadrant II.

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The equation is incorrectly written by the student to find the third side of the triangle.

The right triangle states that if one of the angles of a triangle is a right angle - 90º, the triangle is called a right-angled triangle or a right triangle.

(Hypotenuse)² = (Base)² + (Altitude)²

If the two sides are right angle triangle is 5 units and 13 units and the equation is  5²+13²=c² then the value of c is

c=√25+169

c=13.92 and 13.92 is not an integer number.

so, the equation written by the student to find the third side is incorrect.

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The simple interest rate for Mikhail's investment to grow to $11,500.00 in 20 years is solved to be 10.13%

The rate for the simple interest tis calculated using the formula for simple interest.

The formula is stated as

Simple interest = Principal *  time *  rate / 100

In the problem the give data include

principal = $3,800.00

rate = ?

time = 20 years

simple interest =  $11,500.00 - $3,800.00 = $7700

plugging in the values

Simple interest = Principal *  time *  rate / 100

7700 = 3800 * 20 * r / 100

7700 * 100 = 3800 * 20 * r

770 000 / (3800 * 20 ) = r

r = 10.13%

The interest rate is 10.13%

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The percentage increase in the average price of the piano is 40%.

What is the percentage increase?

To calculate the percentage increase, we use the following formula:

Percentage increase = (New value - Old value) / Old value x 100

In this case, the old value is the average price of the piano in 1991 ($12,500), and the new value is the average price of the piano in 2013 ($17,500). So, we can substitute these values into the formula:

Percentage increase = (17,500 - 12,500) / 12,500 x 100 = 40%

Hence, the percentage increase in the average price of the piano is 40%.

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Answer:

(4x + 5)(4x + 5)

Step-by-step explanation:

4x * 4x = 4x^2, and 5 * 5 = 25. Thus being 4x^2 + 25

The value of x is 17. The solution has been obtained using mid-point theorem of triangle.

What is mid-point theorem of triangle?

The midpoint theorem states, "The line segment of a triangle joining the midpoint of any two sides of the triangle is said to be parallel to its third side and is also half of its length."

Let the triangle be ABC and the line dividing it be PQ

We are given AP = PB and AQ = QC

Now, as per mid-point theorem, PQ is parallel to BC and is also half of its length as the two sides are equal.

Therefore,

x= 34/2

x=17

Hence, the value of x is 17.

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The total surface area is 3994ft sq.

Suppose the base of the pyramid has length = l units, and width = w units.

Surface area of rectangular prism = 2lb +2lh+2bh

Suppose that the height of the pyramid is of h units, then:

[tex]v = \dfrac{l \times w \times h}{3} \: \rm unit^3[/tex]

is the volume of that pyramid.

The base is a rectangle with length = L units, and width = W units, so its area is:

[tex]b = l \times w\: \rm unit^2[/tex]

Given;

Length= 32ft

Breadth= 21ft

Height= 25ft

Now,

Surface area of rectangular prism = 2lb +2lh+2bh

=2*32*21+2*32*25+2*21*25

=1344+1600+1050

=3994

Therefore, the area will be 3994ft sq.

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Answer:

Step-by-step explanation:

a. No, he can't buy 12 packs of baseball cards because 12 packs * $1.70/pack = $20.40, which is more than $20.

b. Yes, he can buy 30 packs of gum because 30 packs * $0.60/pack = $18.00, which is less than or equal to $20.

c. He will still have $6.75 after he buys 5 packs of bouncy balls because $20.00 - (5 packs * $3.15/pack) = $20.00 - $15.75 = $6.75

In the table you provided, you can see the cost of different numbers of packs of baseball cards, gum and bouncy balls. This can help Dante to decide how much to spend on each item and how much he will save.

The equation of variation where y varies jointly as x and the square of z, and where y = 231 when x = 6 and z = 7 is Y= 11/14 xz^2.

The concept that will be used here is variation.

since Y varies jointly with respect to z^2 and x  the we will introduce K which is the proportionality constant, then we have:

Y= Kxz^2.

The we can introduce Y, x and z  to solve for the single unknown and have the answer for the equation of variation.

231=K (6) (7^2)

231=6*49*K

231=(K*294)

231/294=K.

K = 11/14

We can  have Y= 11/14 xz^2 which is the equation of variation.

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complete question:

Find an equation of variation where y varies jointly as x and the square of z, and where y = 231 when x = 6 and z = 7 the equation of varation is y

He travels 2.5 times as farther on Monday than on Tuesday.

The ratio between the distances is obtained applying the proportions in the context of this problem, as the Monday's distance is divided by the Tuesday's distance.

It gives how much farther he traveled on Monday than on Tuesday.

Then the ratio is given as follows:

(5/6)/(1/3) = 15/6 = 2.5.

(the ratio between two amounts is obtained dividing the two amounts).

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Answer:

C. [tex]f(0)=f(2)[/tex]

Step-by-step explanation:

Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) such that f(a) = f(b), then f′(x) = 0 for some x with a ≤ x ≤ b.

The function is not differentiable over [0, 2]. Therefore, the option B is the correct answer.

Rolle's theorem states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) such that f(a) = f(b), then f′(x) = 0 for some x with a ≤ x ≤ b.

The given function is f(x)=x³/3 over [0, 2].

Here, f(0)= 2 and f(2)=2. Hence, according to the Rolle's theorem there should be at least one x for which f'(x)=0.

Now, f'(x)= 3x²/3

0=3x²/3

3x²=0

x²=0

x=0

Therefore, the option B is the correct answer.

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The probabilities are found to be 0.00196 in case- 1  and  

1 / 158753389900  in case - 2.

Note that there are a total of 52 cards in bridge, so by combinations that there are a total of

(13

52)    numbers to deal 13 cards. There are a total of 13 spades, hearts, diamonds and clubs, respectively, so there are

(13

6)   ways to get spades, etc., so that by multiplication principle the probability in we're looking for:

( a )  ( 13      (13      (13      (13

          6)       4)       2)        1)

                      (52

                       13)

      =  1716x715x78x13 / 635013559600

      =  0.00196.

( b)  there are a total of 4 drawings where all 13 cards are are of the same suit, corresponding to a choice of either spades, hearts, diamond, or clubs. Therefore the probability here is given by :

                4 / ( 52       =    4/ 635013559600

                        13)

                                   =    1 / 158753389900 .

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The solution to the product is -18 and the property is negative factors

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

(4)(-0.5)(-3) (-3)

Using the property of negative factors, we have

(4)(-0.5)(3) (3)

Next, we remove the brackets

This gives

4 * -0.5 * 3 * 3

Evaluate the product

-18

Hence, the solution is -18

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The 95% confidence interval for this population proportion is (0.10,0.23).

sample size n = 125

number of people planned to take an extended vacation = 21

sample proportion (p) = 21/125 = 0.168

Confidence level = 0.95

significance level (α) = 1-0.95 = 0.05

Z score = Z(0.05) = 1.96, from the Z table.

confidence interval for a population proportion is-

p±Zα/2 *[tex]\sqrt{\frac{p(1-p)}{n} }[/tex] = 0.168± 1.96[tex]* \sqrt{\frac{0.168(1-0.168)}{125} }[/tex]

                             = 0.168 ± 1.96*0.334

                             = 0.168 ± 0.0655

                              = (0.1025, 0.2335)

                              = (0.10,0.23)

Hence, the confidence interval is  (0.10,0.23).

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The area of the parallelogram is equal to: D. 4 over 25 square foot.

Mathematically, the area of a parallelogram can be calculated by using this formula:

Area of a parallelogram = b × h

Where:

Based on the information provided above, the actual base of the parallelogram is given by:

Actual base of parallelogram = 3/5 - 1/5

Actual base of parallelogram = 2/5 foot.

Substituting the given parameters into the area of a parallelogram formula, we have the following;

Area of a parallelogram = 2/5 × 2/5

Area of a parallelogram = 4/25 square foot.

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The answer to question 1 is not a statistical question. The answer to question 3 is that the notation x-bar ~ n(80,1) means that the set of x-bars is distributed with a bell shape, an average of 80 and a standard deviation of 1.

Question 1: e. secret statisticians code meaning that ohio state graduates are morons.

This is not a statistical question and does not have a correct answer.

Question 2: c. sigma, x-bar, sampling distribution, mu, s, ~, n

The notation for the following (in matching order) is: sigma (standard deviation of a population), x-bar (average of a sample), sampling distribution (a set of sample averages), mu (mean of a population), s (standard deviation of a sample), ~ (is distributed), n (bell shape).

Question 3: b. the set of x-bars is distributed with a bell shape, an average of 80 and a standard deviation of 1.

The notation x-bar ~ n(80,1) means that the set of x-bars is distributed with a bell shape, an average of 80 and a standard deviation of 1.

The answer to question 1 is that it does not have a correct answer as it is not a statistical question. The answer to question 2 is that the notation for the following (in matching order) is: sigma (standard deviation of a population), x-bar (average of a sample), sampling distribution (a set of sample averages), mu (mean of a population), s (standard deviation of a sample), ~ (is distributed), n (bell shape). The answer to question 3 is that the notation x-bar ~ n(80,1) means that the set of x-bars is distributed with a bell shape, an average of 80 and a standard deviation of 1.

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Expanding and simplifying the expression gives:

(3x - 2)² = 9x² - 12x + 4

Here we want to expand and simplify the expression below:

(3x - 2)²

First let's expand that, we can rewrite this as:

(3x - 2)² = (3x - 2)*(3x - 2)

We can distribute that product to get:

(3x - 2)*(3x - 2) = (3x)*(3x) + (3x)*(-2) + (-2)*(3x) + (-2)*(-2)

Now we can keep simplifying this to get:

(3x)*(3x) + (3x)*(-2) + (-2)*(3x) + (-2)*(-2) = 9x² - 6x - 6x + 4

9x² - 6x - 6x + 4 = 9x² - 12x + 4

The simplified expression is:

9x² - 12x + 4

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For a positive angle, the rotation from the initial side to the terminal side takes place in a counter clockwise where as for a negative angle, the rotation takes place in a clockwise.

In math the term angle is defined as a figure in which two rays emerge from a common point and this is called the vertex of the angle and the two rays forming the angle are called its arms or sides.

Here we have to know that the angle which is greater than 180 degrees but less than 360 degrees is called a reflex angle.

Here we need to find the missing term in the given statement.

According to the definition of angle we have know that the rotation is measured from the initial side to the terminal side of the angle.

If it has Positive angles result from counterclockwise rotation, and negative angles result from clockwise rotation.

Here we have know that the angle with its initial side on the x‐axis is said to be in standard position.

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The answer are assuming the information provided, such as cost per visit, co-payments, admission charge etc . The total cost of the Franklin family is $1,865 + $3,650 + $22,025 = $27,540.

Sharon Wilson

a. The amount she paid for the deductible is $2,000.

b. In total co-payments, she paid $9 * $35 + $10 * $50 + $15 * $95 + $2 * $5 + $3 * $10 = $1,085 for physician and specialist visits, physical therapy and pharmacy co-payments.

c. In hospital charges, she paid $240 + $54,860 = $55,100.

d. In total costs, she paid $2,000 + $1,085 + $55,100 = $58,185.

The Franklin family

a. They paid $17 * $75 + $9 * $100 + $4 * $90 = $1,865 for physician and specialist visits and physical therapy.

b. They paid $2 * $1,500 + $350 = $3,650 for emergency room visits and ambulance fees.

c. They paid $350 + $21,675 = $22,025 in hospital charges.

d. The total cost of the Franklin family is $1,865 + $3,650 + $22,025 = $27,540.

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The percent relative average deviation for the data set is 0.30%.

((20.96 - 20.89) + (20.85 - 20.89) + (20.92 - 20.89)) / 3 / 20.89 * 100 = 0.30%

The percent relative average deviation for the given data set can be calculated by first finding the absolute differences between each value and the mean (20.89) then adding those differences together. Once the differences are added, divide that by the mean and multiply by 100. This will give you the percent relative average deviation, which in this case is 0.30%.

The percent relative average deviation for the data set is 0.30%.

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The parabola has a vertex at (7 , -1) has a p-value of -0.5 and it opens downwards.

The axis of symmetry of a parabola is basically perpendicular to the directrix and contains the focus and vertex.  

Thus, the axis of symmetry is the vertical line x = 7.  

The vertex lies halfway between the focus and directrix.  Thus, we can say that the vertex is (7, (6 - 8)/2) = (7, -1)

Due to the fact that the vertex lies above the focus and the directrix is horizontal, then it means that the parabola opens downward.  

Therefore, the focus is (7 - 8)/2 = -0.5 units below the vertex, so, p = -0.5

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The required statistical parameters has been computed as follows:

Range = 17.

Standard deviation, SD = 6.87.

Mathematically, the range of a data set can be calculated by using this formula;

Range = Highest number - Lowest number

Range = 25 - 8

Range = 17.

Mathematically, the mean for these set of data would be calculated by using this formula:

Mean = [F(x)]/n

F(x) = 11 + 8 + 5 + 11 + 25

F(x) = 60.

Mean = 60/5

Mean = 12

Next, we would calculate the standard deviation by using this formula:

SD = √(1/n × ∑(xi - u₁)²)

SD = √(1/5 × (11 - 12)² + (8 - 12)² + (5 - 12)² + (11 - 12)² + (25 - 12)²)

SD = √(1/5 × (1 + 16 + 49 + 1 + 169)

SD = √(1/5 × 236)

Standard deviation, SD = 6.87.

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