Reuben bought 4 CDs that were each the same price. Including sales tax, he paid a total of $44.40. Each CD had a tax of $0.60. What was the price of each CD before tax?

Therefore, the degree of the resulting polynomial is m + n when two polynomials of degree m and n are multiplied together.

What is polynomial?

A polynomial is a mathematical expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Polynomials can have one or more variables and can be of different degrees, which is the highest power of the variable in the polynomial.

Here,

When two polynomials are multiplied, the degree of the resulting polynomial is the sum of the degrees of the original polynomials. In other words, if the degree of the first polynomial is m and the degree of the second polynomial is n, then the degree of their product is m + n.

This can be understood by looking at the product of two terms in each polynomial. Each term in the first polynomial will multiply each term in the second polynomial, so the degree of the resulting term will be the sum of the degrees of the two terms. Since each term in each polynomial has a degree equal to the degree of the polynomial itself, the degree of the resulting term will be the sum of the degrees of the two polynomials, which is m + n.

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Answer:

Step-by-step explanation:

C=2*3.14*r

we have the diameter d=2*r=8.3m

C=8.3*3.14=26.06 m

Answer:

B.   3,158

Step-by-step explanation:

h(x) = -49x − 125

Let x = -67

h(-67) = -49(-67) − 125

          =3283-125

          = 3158

Answer:

Answer B

Step-by-step explanation:

To find the value of h(-67) for the function h(x) = -49x - 125,

we substitute -67 for x in the function and evaluate it.

h ( - 67 ) = - 49 ( - 67 ) - 125

Now we can simplify the expression:

h ( -67 ) = 3283 - 125

h ( -67 ) = 3158

Answer:

ihbuedugefbeubfhiefoeniffiennjdfe

Answer: lost: 0.83 per bought | made: 2.5 per sold

Step-by-step explanation:

5x10 = 50

6/6 = 1

15/6 = 2.5

5/6 = .83

Answer: i think its A

Step-by-step explanation: hope this helped

Answer:

A. (U+V)^2 or (U-V)^2

Step-by-step explanation:

The sine of 0 radians is 0.

In trigonometry, the sine of an angle is defined as the ratio of the length of the side opposite to the angle to the length of the hypotenuse of a right-angled triangle.

When the angle is 0 degrees (or 0 radians), the opposite side has a length of 0, and thus the ratio is also 0. Therefore, the sine of 0 radians is 0.

In a circle with the radius r, the horizontal axis x, and the vertical axis y, 0 is the angle formed by the two sides x and r; r moving counterclockwise is the positive angle.

Note that, the sine function maps an angle to a value which is between -1 and 1, with a periodic nature, meaning that the values repeat in a cycle as the angle increases.

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Answer:

\(x=(b-a)^{3}\)

Step-by-step explanation:

Answer:

x = b³ - 3b²a + 3a²b - a³

Step-by-step explanation:

Given:

\(\sqrt[3]{x} + a = b\)

To determine the value of "x", we need to isolate it. Start out by subtracting "a" both sides. Then, we can cube both sides to remove the cube root. Finally, we can simplify both sides to obtain the value of x.

Subtract "a" both sides to isolate ∛x:

\(\implies \sqrt[3]{x} + a - a = b - a\)

\(\implies \sqrt[3]{x} = b - a\)

Cube both sides to remove the cube root on the L.H.S:

\(\implies (\sqrt[3]{x})^{3} = (b - a)^{3}\)

\(\implies x= (b - a)^{3}\)

Use the formula (a - b)³ = a³ - 3a²b + 3ab² - b³

\(\implies x = b^{3} - 3(b)^{2}(a) + 3(b)(a)^{2} - a^{3}\)

\(\implies \boxed{x = b^{3} - 3b^{2}a + 3a^{2}b - a^{3}}\)

Thus, the value of x is b³ - 3b²a + 3a²b - a³.

Answer:

36%

Step-by-step explanation

Explanation:

To get the percentage of a fraction, we follow these steps:

1- simplify the fraction (get its simplest form)

2- multiply this simplest form by 100%

For the given, we have:

1- the fraction is

We can note that both the numerator and denominator are divisible by 2. Therefore, we can reduce the fraction into

2- Since no further simplification can be applied, therefore, our simplest form is

3- we multiply this simplest form by 100%:

* 100 = 36%

Based on the above:

18 is 36% of 50

Hope this helps :)

Answer:

36%or 0.36

Step-by-step explanation:

hope it help!

The factors of the expression are 2t and (15 - 8t).

We have,

To find the factors of the expression 30t - 16t², we need to factor out the greatest common factor, which is 2t. We can then rewrite the expression as:

30t - 16t² = 2t (15 - 8t)

This is the factored form of the expression, with the factors being 2t, 15, and 8t.

Factor 2t accounts for the common factor of the two terms, while (15 - 8t) represents the remaining difference between the two terms.

Thus,

The factors of the expression are 2t and (15 - 8t).

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Answer:

The correct form for each case is:

Step-by-step explanation:

I'm gonna give you the reason for each case.

a) The original equation is:

Now, we're gonna solve the first part of the equation and comparate:

How you can see, the first part is different from the last number, for this reason, the mistake is the 6, then I change it by the 24.

b) The original equation is:

As the previous exercise, we're gonna solve the first part:

You must know that when you multiply two negative signs, the result is positive.

c) The original equation is:

But, this equation can be made in this form:

How you can see, the first part can't be operated or anything, the one form to operate this is removing the plus sign and operating like a multiply.

1. The measure of AC = 8.4

2. The measure of AC' = 6

3. The measure of C'B' = 12.6

Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other.

Given:

Segment B'C' is parallel to segment BC.

A line splits a triangle's sides in the same proportion if it runs parallel to one side and crosses the other sides at two different spots.

Then,

10/4 = 6/x

x = 2.4

The measure of AC = 2.4

And,

14/8.4 = 21/y

y = 12.6

The measure of C'B' = 12.6

Therefore, all the required values are given above.

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Answer:

Associative property of addition

Step-by-step explanation:

This is the property used here. It states that the sum of three or more quantities will be same regardless of the order in which they are added.

Answer:

Associative Property Is Correct

Step-by-step explanation:

The associative property of Addition states that the Sum of three or more numbers remains the same regardless of how the numbers are grouped.

Answer:

Area is probably around 153.94

Step-by-step explanation:

Answer:

49π or 153.93804

Step-by-step explanation:

The formula for area of a circle is Pi * radius^2. The radius is half of the diameter, so the radius is 7. We then square 7, getting 49, and multiply that by pi, getting us 49π or 153.93804

A number cube is rolled twice. The probability of getting a six on the first roll and then a number less than five on the second roll can be determined by multiplication of the individual probabilities.

The probability of getting a six on the first roll is 1/6, and the probability of getting a number less than five on the second roll is 4/6, or 2/3. To calculate the probability of both events occurring, we will multiply these probabilities.

P(getting 6 on the first roll) = 1/6

P(getting a number less than 5 on the second roll) = 4/6 or 2/3

P(getting 6 on the first roll and a number less than 5 on the second roll) = P(getting 6 on the first roll) × P(getting a number less than 5 on the second roll)

= (1/6) × (2/3)

= 2/18 or 1/9

The probability of getting a six on the first roll and then a number less than five on the second roll is 1/9, or approximately 0.111, or 11.1%.

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Answer:

15/8

Step-by-step explanation:

18/8 - 3/8 = 15/8

Answer:

15/8

Step-by-step explanation:

\(2 \times \frac{1}{4} - \frac{3}{8} \)

First, combine the mixed fraction. 2 (2/1) is equal to 8/4 (multiply by 4/4). This comes out as 9/4.

9/4 - 3/8

Then, we need to multiply the first fraction by 2/2 to get a common denominator

18/8 - 3/8

Since the denominators are the same, we can subtract the numerators, 18 - 3 = 15.

The denominator is kept after doing the subtraction in the numerator. 15/8 is the answer, or 1 7/8 as a mixed fraction

The value of m = -1/6 and b = 3/2.

The given equation of the curve is xy³ + xy = 12.

Now, the equation of the tangent line to the curve at the point (3,1) by using implicit differentiation.

We have dy/dx = (-Fx/Fy) at the point (3,1).

Where Fx = ∂F/∂x

Fx = y³ + 1

Fy = ∂F/∂y

Fy =  3xy² + x.

Now, we have Fx and Fy, and we can calculate dy/dx at the point (3,1).

dy/dx = (-Fx/Fy)

dy/dx = -(y³ + 1)/(3xy^2 + x)

Substituting x = 3 and y = 1, we have

dy/dx = -(1³ + 1)/(3 ×3 × 1 + 3)

dy/dx = -2/12

dy/dx = -1/6

The equation of the tangent line is y = mx + b, where m is the slope of the tangent and b is the y-intercept.

The slope of the tangent is m = -1/6.

Substituting the point (3,1) in the equation of the tangent y = mx + b, we have

1 = (-1/6)(3) + b.

So, b = 3/2. Thus, the equation of the tangent line is y = (-1/6)x + (3/2).

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Answer:

A

Step-by-step explanation:

The solution is Option A. Always

The intersection of two planes contains at lease two points

What is intersection of two planes?

When two planes intersect, they form a line.

The vector equation for the line of intersection is given by

r = r​₀ ​+ tₓ

where r₀​​ is a point on the line

tₓ is the cross product of the normal vectors of the two planes.

The parametric equations for the line of intersection are given by

x = a , y = b and z = c

where a, b and c are the coefficients from the vector equation

r = a (i) + b (j) + c (k)

The line of intersection will be perpendicular to the normal of both the planes

The line of intersection lies on both the planes

Therefore , a line is observed at the intersection of two planes

Hence , the intersection of two planes always contains at least two points and it forms a line

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Answer:

$4/baseball .

Step-by-step explanation:

Here we are given that $24 is paid for 6 baseballs and we need to find out the unit rate of the baseballs . This can be found by using the Unitary Method , as ;

Rate of 6 baseballs is $24

Rate of 1 baseball will be $24/6 = $4

Answer:

It is on floor 2

Step-by-step explanation:

15-18=-3

-3+5=2

hope this helped :)

Answer:

it is on the 2nd floor

Step-by-step explanation: this is because it started at 15, then went down 18: 15-18

     -3

then it went up 5: -3+5  or 5-3

                                to end up at the 2nd floor

Answer:

90

Step-by-step explanation:

7 x 12 + 6

Answer:

  -6

Step-by-step explanation:

You want to know where the line y=6 intersects the graph of h(x) shown as a series of line segments.

The attached graph shows the value of h(x) is 6 for x=-2 (known) and x=-6.

The other input value is -6.

For a normal distribution of the money spent on food per visitor at the san diego zoo, probability that a randomly selected par visitor will spend less than 20 is equals to 0.3488.

There is the money spent on food per visitor at the san diego zoo.

Mean of money = $27.50

Standard deviations= 8

We have to determine the probability that a randomly selected par visitor will spend less than 20, P( X < 20), where X is random variable for spending money. Using the Z-Score formula for normal distribution, \(Z = \frac{X - \mu}{\sigma } \)

where, X --> observed value

μ --> mean

σ --> standard deviations

Substitutes the known values in above formula, \(Z = \frac{20 - 27.50}{8 } \)

\(= \frac{7.50 }{8 } \)

= 0.937

The probability that a randomly selected par visitor will spend less than 20, P( X < 20) = \(P ( \frac{ X - \mu }{\sigma} < \frac {20 - 27.50}{8})\)

= P ( z < 0.937)

Using the Z-distribution table the value of P( z< 0.937) is equals to the 0.3488. So, P( X < 20) = P( z< 0.937) = 0.3488.

Hence, required probability value is 0.3488.

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Answer:

• (a)80 mg

• (c)f(t)=80(0.5)^t

• (d)0.625 mg

Explanation:

Part A

From the point (0, 80), we see that the person took 80 mg of the medicine at the start.

Part B

From the graph:

From points (0,80) and (2,20); and (2,20) and (4,5)

• After 2 hours, the amount of medicine has been reduced by a factor of 1/4.

Therefore, after 1 hour, the amount of medicine is reduced by a factor of 1/2.

The completed table is attached below:

Part C

An exponential function is written in the form:

Since the amount of medicine is halved every 1 hour:

The rate of decrease = 1/2

The starting amount, Ao = 80 mg

Therefore, an equation that defines f is:

Part D

After 7 hours, when t=7

After 7 hours, 0.625 mg of medicine remains in the person's body.

On solving the provided question we can say that - as the probability the result will be either a red- or green-colorblind individual.

A branch of mathematics known as probability measures the possibility of an event happening or a proposition being true. The probability of an occurrence is a number between 0 and 1, where roughly 0 denotes the event's improbability and 1 denotes certainty. A probability is a numerical representation of the possibility or probability that a specific event will take place. Probabilities can alternatively be stated as percentages ranging from 0% to 100%, or as percentages from 0 to 1.

In the US, there are more males than women who are colorblind to red and green  = 0.07adults

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The y-intercept, represented by b, is the constant term, which is 8 in this equation. The y-intercept indicates the point where the line intersects the y-axis. So, the equation Y - X = 8, when simplified and written in slope-intercept form, is Y = X + 8. The slope of the line is 1, and the y-intercept is 8.

To convert the equation Y - X = 8 into slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept, we need to isolate the y variable.

Let's rearrange the equation step by step:

Add X to both sides of the equation to isolate the Y term:

Y - X + X = 8 + X

Y = 8 + X

Rearrange the terms in ascending order:

Y = X + 8

Now the equation is in slope-intercept form. We can see that the coefficient of X (the term multiplied by X) is 1, which represents the slope of the line. In this case, the slope is 1.

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The maximum and minimum values of the length of vector u' are both 6. The length of u' remains constant regardless of the angle of rotation in the xy-plane.

To find the maximum and minimum values of the length of vector u', we need to determine the effect of the rotation on the length of the vector u.

Given that u is a vector with length 6 that starts at the origin and rotates in the xy-plane, we can express u as u = (6cosθ)i + (6sinθ)j, where θ is the angle of rotation.

To find the length of u', we need to differentiate u with respect to θ and find its magnitude. Taking the derivative of u with respect to θ, we get:

u' = (-6sinθ)i + (6cosθ)j

The length of u' can be calculated as √[(-6sinθ)² + (6cosθ)²] = 6√(sin²θ + cos²θ) = 6.

Hence, the length of u' is constant and equal to 6 for all values of θ. Therefore, the maximum and minimum values of the length of u' are both 6, and they occur at all possible angles of rotation in the xy-plane.

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By dividing all possibilities into two sets, the null and alternative hypotheses provide a way to determine if a difference exists between two or more groups.

The null and alternative hypotheses divide all possibilities into two sets. The null hypothesis (H0) is the statement that is assumed to be true unless proven otherwise. This hypothesis is typically the one that states that no difference exists between two or more groups. The alternative hypothesis (H1) is the one that is assumed to be false unless proven otherwise. This hypothesis typically states that there is a difference between two or more groups. The formula for this is H0: μ1 = μ2, and H1: μ1 ≠ μ2, where μ1 and μ2 are the population means for two groups. This formula states that the null hypothesis is that the population means for two groups are equal, and the alternative hypothesis is that the population means for two groups are not equal. Calculating the null and alternative hypotheses is done by first determining the population means for each group. This can be done by taking the average of all the data points in each group. Then, the null hypothesis is set as the population means for the two groups being equal. The alternative hypothesis is set as the population means for the two groups not being equal. By dividing all possibilities into two sets, the null and alternative hypotheses provide a way to determine if a difference exists between two or more groups. This is done by evaluating the population means of each group and determining if they are equal or not.

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The Riemann sum L for the function f(x) = 3 - 2 on the interval (-1,2) consists of six rectangles, each with a height of 3 - 2 and varying widths. The exact value of L6 is 6, and the approximation rounded to one decimal place is 6.0.

The Riemann sum L is a method used to approximate the area under a curve by dividing the interval into subintervals and constructing rectangles with heights determined by the function. In this case, the function f(x) = 3 - 2 is a constant function with a height of 1.

To plot y = f(a), we mark the endpoints of the subintervals and draw rectangles with a height of 1. Since the function is constant, the rectangles will have the same height.

For the interval (-1,2), we divide it into six subintervals of equal width: (-1, -0.5), (-0.5, 0), (0, 0.5), (0.5, 1), (1, 1.5), and (1.5, 2). Each rectangle has a width of 0.5.

The exact value of L6 can be calculated by summing the areas of all six rectangles. Since the height is 1 and the width is 0.5 for all rectangles, each rectangle's area is 0.5 * 1 = 0.5. Therefore, the exact value of L6 is 6 * 0.5 = 6.

The rounded approximation to one decimal place is 6.0, which indicates that the total area under the curve approximated by the Riemann sum is 6 square units.

Based on the plot, we can observe that the rectangles cover the area under the curve. Since the rectangles are all below the curve, Le appears to be an underestimate for the area. This is because the rectangles do not fully capture the curve's shape and may miss some of the area enclosed by the curve.

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Answer:

5%

Step-by-step explanation:

The computation of the two rates of interest is shown below;

The interest  rate for $3,000 be x%

And, for $4,500 the interest rate is (x -2%)

The total interest earned is

= x% of $4,500 + (x - 2)% of $4,500

So, the two rates of interest is

x% of $4,500 + (x - 2)% of $4,500 = $435

30x + 45(x - 2) = $435

30x + 45x - 90 = $43

75x = $25