Dale is buying a new stereo for $1,580. If sales tax is 7.2%, how much
will he pay in total?

The true statement about the function is C. function f and function g are not inverse because f{g(x)} = g{f(x)} .

An inverse function or an anti function, which can reverse into another function.In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by 'f' or 'F', then the inverse function is denoted by f-1 or F-1.

now the given functions are,

f(x) = √(2x + 2) and

g(x) = (x^2 -2)/2

Now,

f{g(x)} = f{(x^2 -2)/2}

         = √(2(x^2 -2)/2 + 2)

         = √ x^2 -2 + 2

f{g(x)} = √ x^2

f{g(x)} =  x

Now,

g{f(x)} = g{ √(2x + 2)}

         = (√(2x + 2)^2 -2)/2

         = (2x + 2) -2 /2

         = 2x/2

f{g(x)} = x

Here we see that ,

f{g(x)} = g{f(x)}

Hence f and g are not inverses.

∴The true statement about the function is C. function f and function g are not inverse because f{g(x)} = g{f(x)} .

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ANSWER:

17 inches

STEP-BY-STEP EXPLANATION:

The area of the parallelogram is given by the following formula:

we replace to calculate the value of the height:

Answer:

1/2

Step-by-step explanation:

I got it wrong then it gave me the right answer of 1/2

The fraction of the sweaters that cost $50 or less is 50% is 1/2.

It is the middle value of the given set of numbers after arranging the given set of numbers in order.

We have,

From the box plot,

Median = $50

Now,

Median = $50

This means,

50% of the clothes are above $50 and 50% of the clothes are below $50.

Now,

The fraction of the sweaters that cost $50 or less is 50%.

So,

= 50/100

= 5/10

= 1/2

Thus,

The fraction of the sweaters that cost $50 or less is 50% is 1/2.

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Answer:

as it a cyclic quadrilateral

its opposite sides sum be 180

z/2+z/4+30=180

2z+z/4=150

3z/4=150...z=200

angles...

b=z/2=200/2=100

d=80

e=200-59=141

c=180-141=39

Answer:

After the reverse stock split, Gene will own 120 shares of XYX Corporation.

To calculate the post-split market price per share, we can start by finding the total value of Gene's shares before the split:

Total value before split = 1,200 shares * $1.20 per share = $1,440

Since the reverse stock split is 1 for 10, the total number of shares outstanding will be reduced by a factor of 10, and the price per share will be increased by a factor of 10:

Total value after split = 120 shares * $12.00 per share = $1,440

Therefore, the post-split market price per share is $12.00.

Step-by-step explanation:

Answer:

\(b  =  (q,r , 5q-2\sqrt{26} )\)

Step-by-step explanation:

From the question we are told that

The vector given is  

               \(a = (5,0,-1)\)

  Also  \(comp_a b =  2\)

Generally

       \(comp_a b  =  \frac{a \cdot b}{|a|}\)

Here  \(|a|\) is the magnitude of  a which is mathematically represented as

      \(|a| =  \sqrt{5^2  + 0^2  +(-1)^2 }\)

=>     \(|a| =  \sqrt{26}\)

b is vector which we will assume to have the following parameters

     \(b  =  (q , r , x)\)

So

        \(comp_a b =  \frac{(5,0,-1) \cdot (q,r,x)}{\sqrt{26} } =  2\)

=>     \(\frac{5q + 0 -x}{\sqrt{26} } = 2\)

=>     \(x =  5q-2\sqrt{26}\)

Hence the vector be can be mathematically represented as

      \(b  =  (q,r , 5q-2\sqrt{26} )\)

This means that the vector b is more than one value  since it is made up of variable

This means that if

   \(q = 1\\r=1\\x =1\)

Then

    \(b  =  (1,1,5-2\sqrt{26} )\)

A quantity has magnitude but not position, that's why in this the vector \(b =(0,0, -2\sqrt{26}).\)

If\(a =(5,0,-1)\) Our goal is to determine a vector b that will allow comp to work properly \(_{a}b = 2.\)

Allow the vector to flow naturally  \(b =(x, y,z)\)

Recalling

comp\(_{a}b =\frac{a.b}{|a|}\)

Therefore,

comp \(_{a}b= 2 \\\\\)

\(\to \frac{a.b}{|a|}= 2\\\\\)

\(\to \frac{(5,0,-1)\cdot (x,y,z)}{ |(5,0,-1)|} =2\\\\\to \frac{5x+0-z}{5^2+0+(-1)^2}=2\\\\ \to \frac{5x-z}{\sqrt{26}}= 2 \\\\\to 5x-z = 2\sqrt{26}\\\\ \to z=5x-2\sqrt{26}\\\\\)

As a result, the vector b can be expressed as,

\(\to b =(x,y,z) =(x, y, 5x-2\sqrt{26}) \\\\\)

As a result, this aforementioned form can be found in an endless number of vectors.

One of them is \(b =(0,0, -2\sqrt{26}).\)

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Answer:

35.800

Step-by-step explanation:

The value of 6315 ×41 is 260391.

Multiplication is a method of finding the product of two or more numbers

We have to find the product of 6315 times of forty one

 6351

×     41

_______

    6351

25404+

__________

260391

Hence, the value of 6315 ×41 is 260391.

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Answer:

x=0 or x=2 or x=−4 or x= (7)(2)

Step-by-step explanation:

The length of the second trial will be equal to 2(⁵/₈) miles.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that two bicycle trails were developed in a new housing development. One trail is 3¹/₂ miles long. The other trail is 3/4 as long.

The length of the second trial will be calculated as,

Length =  3/4 x ( 3¹/₂ )

Length = 2(⁵/₈)

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Each piece Measurement of an angle of 120 degrees cut into nine equal lengths with a kerf width of 0.125 would be 14.4583 degrees.

When a particular angle is cut into nine equal parts, the measure of each piece needs to be calculated.

Therefore, it is essential to first calculate the total angle measure and then divide it by the number of parts into which it is being cut.

What is an Angle?

An angle is a geometrical shape that consists of two rays sharing a common endpoint. The common endpoint is known as the vertex, and the two rays are known as the arms of the angle. An angle can be measured in degrees, radians, or gradians. Degrees are the most commonly used unit of measuring angles.How to Calculate Each Piece Measurement of an Angle if Cut into 9 Equal Lengths

To determine each piece measurement of an angle if cut into nine equal lengths, we will need to carry out the following steps:

Step 1: Calculate the total angle measure Suppose the angle being cut into nine equal lengths is an obtuse angle measuring 120 degrees. In that case, the total angle measure will be 120 degrees.

Step 2: Divide the total angle measure by the number of parts into which it is being cut.120 degrees ÷ 9 = 13.3333 degrees

Step 3: Add the kerf width to the piece measurements.0.125 x 9 = 1.125 degrees13.3333 + 1.125 = 14.4583 degrees

Therefore, each piece measurement of an angle of 120 degrees cut into nine equal lengths with a kerf width of 0.125 would be 14.4583 degrees.

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The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.

To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.

The slope of a line can be found using the formula:

slope = (change in y) / (change in x)

For the line containing (1,2) and (5,3), the slope is:

slope1 = (3 - 2) / (5 - 1) = 1 / 4

To find the slope of the line containing (x,4) and (3,0), we use the same formula:

slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.

So, we can set up the equation:

-1 / (1/4) = -4 / (3 - x)

Simplifying this equation:

-4 = -4 / (3 - x)

To remove the fraction, we can multiply both sides by (3 - x):

-4(3 - x) = -4

Expanding and simplifying:

-12 + 4x = -4

Adding 12 to both sides:

4x = 8

Dividing both sides by 4:

x = 2

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Answer: 0.220

Step-by-step explanation:

    First, we will find the total amount of regular or heavy smokers.

         163 regular + 78 heavy = 241 total for these groups

    Next, we will divide this by the total number to find the probability the person selected will be a regular or heavy smoker.

         \(\displaystyle \frac{\text{Outcome we are discussing}}{\text{Total number}} =\frac{241}{1,096} = 0.220\)

Answer:

c

Step-by-step explanation:

(163 + 78) : 1096 = 241 : 1096 =

= 0.219890511 = 0.220

3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

To express 3 1/2 cups as a multiplication expression using the unit "1 cup" as a factor, you can write it as:

3 1/2 cups = (3 + 1/2) cups = 3 cups + 1/2 cup

Since there are 1 cup in each term, we can rewrite it as:

3 cups + (1/2) cup

Now, we can express each term as a multiplication expression:

3 cups = 3 * 1 cup = 3

(1/2) cup = (1/2) * 1 cup = 1/2

Putting it all together, the multiplication expression is:

3 * 1 cup + (1/2) * 1 cup = 3 + 1/2

Therefore, 3 1/2 cups can be expressed as the multiplication expression: 3 + 1/2.

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Answer: The answer for the second one is solid figure

Step-by-step explanation: In geometry, three-dimensional shapes are solid figures.

a. The graph represents a proportional relationship.

b. The graph does not represent a proportional relationship.

c. The graph does not represent a proportional relationship.

d. The graph represents a proportional relationship.

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

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

y = kx.

Hence graphs a and d represent proportional relationship, as they have intercepts at the origin.

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Answer:

infinite

Step-by-step explanation:

multiply and you see

3x+6=3x+6

Answer:

£500

Step-by-step explanation:

ratio of money = 3 : 1 = 3x : x ( x is a multiplier )

winner receives £250 more than the runner up, that is

3x = x + 250 ( subtract x from both sides )

2x = 250 ( divide both sides by 2 )

x = 125

total prize money = 3x + x = 4x = 4 × 125 = £500

The vertices of the feasible region is (4, 3)

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

x + y ≤ 7

x - 2y ≤ -2

x ≥ 0

y ≥ 0

Express as equations

So, we have

x + y = 7

x - 2y = -2

Subtract the equations

3y = 9

So, we have

y = 3

Next, we have

x + 3 = 7

This gives

x = 4

Hence, the vertex of the feasible region is (4, 3)

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Answer:

Y=5

Step-by-step explanation:

Hope this helps. :)

Answer:

120

Step-by-step explanation:

You have 15 inches and 1 and 8 devide 15 multiply 1 and 8

Answer:960? correct for me!

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

the answer is d because it's a closed circle

Answer:

7. \((f+g)(x) = 6x - 2\)

8. \((f-g)(x) = 2x + 8\)

Step-by-step explanation:

We are given two function, f(x) and g(x).

We want to find their addition and their subtraction, and we do this combining like terms.

The functions are:

\(f(x) = 4x + 3\)

\(g(x) = 2x - 5\)

7. Find (f+9) (x)

\(4x + 3 + 2x - 5 = 4x + 2x + 3 - 5 = 6x - 2\)

So

\((f+g)(x) = 6x - 2\)

8. Find (f - g) (x)

\(4x + 3 - (2x - 5) = 4x + 3 - 2x + 5 = 4x - 2x + 3 + 5 = 2x + 8\)

So

\((f-g)(x) = 2x + 8\)

This means that the football’s height when it was kicked 41 yards away was -1.762 yards.

A yard is a unit of length measurement in the imperial and US customary systems of measurement. It is equal to 3 feet or 36 inches.

The equation given is a parabolic equation which models the path of the football. It is a quadratic equation in the form of y = ax² + bx + c, where a, b, and c are coefficients that determine the shape of the path. The coefficient a represents the rate of change in the football’s height as it moves away from the punter. In this equation, a is -0.035, which indicates that the football’s height decreases as it moves away from the punter. The coefficient b indicates the rate of change in the football’s height as it moves back toward the punter, and in this equation, b is 1.4, which means that the football’s height increases as it moves back towards the punter. Finally, the coefficient c is 1, which indicates the height of the football when it is kicked.

In this case, the football was kicked 41 yards, so plugging x = 41 into the equation gives us y = -0.035(41²) + 1.4(41) + 1 = -1.762.

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Answer:

2(x-y)

Step-by-step explanation:

x-y is the difference between x and y

then you multiply this term by 2

====================================================

Explanation:

Utility is another way of saying happiness more or less. Marginal utility is getting that extra bit of satisfaction from buying/consuming one additional item. Saying the marginal utility is diminishing but not negative, means we have an increasing utility curve that has its rate of increase slow down. An example would be a log curve.

Inflation can be thought of as an expense. For example, if it costs $1 to get a loaf of bread one year, and then next year that cost jumps to $1.50 for that same loaf of bread, then the worker has effectively lost 50 cents on their paycheck. Zero inflation means there isn't any such expense. So in a way, this is like getting a raise.

Being paid more due to higher labor costs means that the worker gets even more money on top of the bonus money saved from zero inflation. These two aspects would provide a lot of incentive for the person to work more hours. Of course, there would be a point in which the marginal utility is far too small. In other words, the amount of additional money earned isn't worth the additional time spent working. This is likely when the worker would take time off, seek out a raise, or find some other job.

Answer:

Mean = 53.

Step-by-step explanation:

The median is the middle value so the 3 cards are

36, 46, x       where x is to be found.

The range is 41, so:

x - 36 = 41

x = 41 + 36

x = 77.

Therefore, the mean is

(36+46+77) / 3

= 159/3

= 53.

\((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

We can use the rules of exponents and simplify the terms with the same base.

Dividing the coefficients: 21 / 7 = 3.

For the variables, you subtract the exponents: \(a^6 / a^3 = a^(^6^-^3^) = a^3.\)

Similarly,\(b^5 / b = b^(5-1) = b^4\).

Putting it all together, the simplified expression is:

\(3a^3b^4.\)

Therefore, \((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)

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