Suppose a supermarket ordered 13 cases of organic vegetable soup with a list price of $18.90 per case and 4 cases of organic baked beans with a list price of $33.50 per case. The wholesaler offered the supermarket a 39% trade discount. (Round your answers to the nearest cent.)


What is the total net amount (in $) the supermarket owes the wholesaler for the order?

The probability of choosing 5 CDs in alphabetical order out of a collection of 23 CDs is approximately 0.00003 or 0.003%.

What is combination?

In mathematics, a combination is a way of selecting objects from a larger group of objects, where the order of selection is not important. A combination is a subset of objects that are chosen from a larger set without regard to the order in which they are selected.

The formula  is given by:

C(n, r) = [tex]\frac{n!}{r!* (n - r)!}[/tex]

The total number of ways to choose 5 CDs from a collection of 23 CDs is given by the combination formula:

C(23, 5) = [tex]\frac{23!}{5!* (23 - 5)!}[/tex]

             = 33649

This means there are 33649 different ways to arrange 5 CDs out of the 23 CDs.

Out of these 33649 ways, only one arrangement is alphabetical. For this to happen, the first CD chosen must be the first one alphabetically, the second CD chosen must be the second one alphabetically, and so on.

The first CD can be any of the 23 CDs. However, once the first CD is chosen, there is only one CD that can be the second one alphabetically, two CDs that can be the third one alphabetically, and so on. Therefore, the probability of choosing 5 CDs in alphabetical order is:

P = 1 / C(23, 5)

P = 1 / 33649

P ≈ 0.00003

So the probability of choosing 5 CDs in alphabetical order out of a collection of 23 CDs is approximately 0.00003 or 0.003%.

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The logarithmic form of the given exponential equation in the question,     4³ = (5x + 4) is Log₄ (5x + 4) = 3.

The exponential-to-logarithmic format is useful because it makes it easy to compute large numeric expressions. Expressions involving exponential multiplication and division can be converted to addition and subtraction by applying logarithms. Logarithmic exponential form is a common means of converting mathematical expressions in one form to another form.

The exponential form aˣ = N is transformed and written logarithmically as LogₐN = x.

The exponential form of a for the exponent of x equal to N is converted to the logarithm of the number N in base a, equal to x.

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Reason:

[tex]\angle 1 = 62^{\circ}[/tex] because of the vertical angles theorem.

Then angle 1 and angle 2 add to 90 degrees (the angles are complementary).

[tex]\angle 1 + \angle 2 = 90\\\\62 + (2x-8) = 90\\\\2x + 54 = 90\\\\2x = 90 - 54\\\\2x = 36\\\\x = 36/2\\\\x = 18\\\\[/tex]

Answer:

x = -3 and x = 1 are the two zeroes of this function. Choose one of them for your answer.

Answer:

M ≈ $933.24

Step-by-step explanation:

To calculate Marcus's monthly payment for financing his car for 5 years at an annual interest rate of 8.5%, we can use the formula for the monthly payment on a loan:

M = P * (r/12) * (1 + r/12)^n / ((1 + r/12)^n - 1)

where:

M is the monthly payment

P is the principal (in this case, $45,000)

r is the annual interest rate (in this case, 8.5%)

n is the number of monthly payments (in this case, 5 years * 12 months/year = 60 monthly payments)

Substituting the given values, we get:

M = $45,000 * (0.085/12) * (1 + 0.085/12)^60 / ((1 + 0.085/12)^60 - 1)

Using a calculator, we get:

M ≈ $933.24

Therefore, Marcus's monthly payment for financing his car for 5 years at an annual interest rate of 8.5% is approximately $933.24.

tan = 1/√3= perpendicular/ base

1/√3 = AB / AC

AB / 6 = 1/√3

AB = 6/√3

Therefore, **x < 7** is the inequality that may be utilized to find x

A mathematical statement known as an inequality compares two expressions using an inequality sign, such as (less than), > (greater than), or (less than or equal to).

For instance, the inequality x + 2 5 signifies that "x + 2 is less than 5".

Let x represent how many days the client paid for pet sitting.

$15 per day plus a $20 fixed service fee equals the total cost of pet sitting.

We are aware that the customer's purchase was under $125. Consequently, we can write:

20 + 15x < 125

Putting this disparity simply:

15x < 105

x < 7

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The weight of the diamonds in each lot is 4.9 pounds.

Here, the fractional idea can be used. A fraction represents a portion of a total. A fraction is a numerical figure that designates a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain value, or an object.

A cargo of half a pound's worth of diamonds was received by a diamond trader. He separated the stones into 4 equal lots and sold them to jewelers so they could be used to make necklaces and rings.

Total shipment = 7/10 pound

number of equal lots = 7

then,   7 x weight = 7/10

weight = 4.9

Therefore, the weight of each lot is 4.9 pounds.

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Answer:

Hm

Step-by-step explanation:

The formula to find the circumference of a circle is:

Circumference = 2πr

Where "r" is the radius of the circle, and "π" (pi) is a mathematical constant approximately equal to 3.14.

Substituting the given value of radius, we get:

Circumference = 2 x π x 6

Circumference = 12π

Circumference ≈ 37.7 cm (rounded to one decimal place)

Therefore, the circumference of a CD that has a radius of 6 centimeters is approximately 37.7 cm.

The expression 8×2 can be used to find the total number of head wraps on the shelf when there are 8 head wraps per shelf and 2 shelves in total, resulting in a total of 16 head wraps.

Expression in mathematics is a combination of symbols and numbers, often using an operation, such as addition, subtraction, multiplication, or division. It can represent a number, a variable, a function, or a mathematical statement. It can also represent a combination of these things. Expressions are used to describe relationships between numbers, variables, and mathematical concepts.

The expression 8×2 can be used to find the total number of head wraps on the shelf when there are 8 head wraps per shelf and there are 2 shelves in total. This expression can be used to calculate the total number of head wraps on the shelves by multiplying 8 (the number of head wraps per shelf) by 2 (the number of shelves). As such, the expression 8×2 can be used to find the total number of head wraps on the shelf when there are 8 head wraps per shelf and 2 shelves in total, resulting in a total of 16 head wraps.

In conclusion, the expression 8x2 can be used to calculate the total number of head wraps on the shelf when there are 8 head wraps per shelf and 2 shelves in total. By multiplying 8 (the number of head wraps per shelf) by 2 (the number of shelves), the total number of head wraps on the shelf can be found, resulting in a total of 16 head wraps.

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Complete questions as follows-
In which situation can the Expression
on 8×2 be used to find the total number of head wraps on the shelf?

To find the specified scalar, we need to first find the dot product of U and V, and then the dot product of U and W, and add these two dot products together:

U·V + U·W

where U·V denotes the dot product of U and V, and U·W denotes the dot product of U and W.

The dot product of two vectors a = (a1, a2) and b = (b1, b2) is given by:

a · b = a1b1 + a2b2

Using this formula, we can find the dot product of U and V:

U · V = (4i - j) · (5i + j) = 4i · 5i + 4i · j - j · 5i - j · j = 20i^2 + (4i · j - 5i · j) - j^2 = 20 + (-i · j) - 1 = 19 - i · j

Next, we can find the dot product of U and W:

U · W = (4i - j) · (i + 6j) = 4i · i + 4i · 6j - j · i - j · 6j = 4i^2 + (4i · 6j - j · i) - 6j^2 = 4 + (24i · j) - 6 = -2 + 24i · j

Now we can substitute these values into the original expression:

U·V + U·W = (19 - i·j) + (-2 + 24i·j) = 17 + 23i·j

Therefore, the specified scalar is 17 + 23i·j.

Answer:

Step-by-step explanation:

just add the two numbers up 576x1 1/2= 864

The function that models the relationship between the number of students enrolled, f(x) and the number of years after 2015, x,  is D. f(x) = 3000(0.98)*.

Mathematically, a function defines a mathematical relationship or an algebraic expression involving one variable (the independent variable) and another variable (the dependent variable).

There are four main types of mathematical functions, including:

The number of students enrolled in 2015 = 3,000

The annual decrease in students enrollment = 2%

Let f(x) the model modeling the relationship between the number of students enrolled and the number of years after 2015.

Let the number of years after 2015 = x.

Thus, the correction function is D. f(x) = 3000(0.98)*.

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Answer:

it would be C

Step-by-step explanation:

Answer: A

Step-by-step explanation: The bluebird Inn is more expensive per night because 475 is greater than 350.

The correct answer is c: Two terms are even, then two terms are odd. This pattern follows the rule of adding 2, so each successive term is an even number followed by an odd number.

Number is a mathematical object used to count, measure and represent a quantity. It is used to symbolize a numerical quantity or value, and is used in various ways in mathematics, science, engineering, finance and other fields. Numbers are also used to represent relationships between objects, such as the number of sides in a triangle or the number of students in a classroom.

This alternating pattern of even and odd terms is a feature of the pattern, with two terms being even followed by two terms being odd. This pattern continues as the terms increase, with the even terms adding 2 and the odd terms adding 2 as well. This pattern is a good way to remember a sequence of numbers and can be used to help understand patterns in mathematics.

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For the given frequency table, (a) 5 (b) 137 (c) lower class boundary is 132.5, and the upper class boundary is 141.5.

What is a frequency table ?

A frequency table is a tabular summary of data showing the frequency (i.e., the number of occurrences) of each category or value in a data set. It usually consists of two columns: one listing the categories or values and the other listing the corresponding frequencies. Frequency tables are commonly used to summarize categorical data, but they can also be used to summarize numerical data by grouping it into intervals or classes.

Now,

(a) The class width is the difference between the upper class limit and the lower class limit. For this frequency distribution, we can see that the class width is the same for each class and is equal to 5.

(b) The class midpoints are found by taking the average of the lower and upper class limits. For the first class, the lower class limit is 135 and the upper class limit is 139. So, the class midpoint is (135 + 139) / 2 = 137.

(c) The class boundaries are found by adding and subtracting half of the class width to the lower and upper class limits. For the first class, the lower class limit is 135 and the upper class limit is 139. The class width is 5, so half of the class width is 2.5. The lower class boundary is 135 - 2.5 = 132.5, and the upper class boundary is 139 + 2.5 = 141.5.

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The value of

m∠GHJ = (3(20°)+50)° = 110°.

m∠GkJ = (4(20°)-10)° = 70°

m∠HJK = (4(20°))° = 80°

What is an angle?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Here, we have

Given: Circle B is shown, with GHJK inscribed in the circle. The m∠GHJ = (3x+50)°, and m∠HJK = (4x)° and mLGK] = (4x-10)°.

we have to find the value of HJK and JHG.

We know that

m∠GHJ + m∠GkJ = 180°

(3x+50)° + (4x-10)° = 180°

7x + 40 = 180°

7x = 140°

x = 20°

Hence, the value of

m∠GHJ = (3(20°)+50)° = 110°.

m∠GkJ = (4(20°)-10)° = 70°

m∠HJK = (4(20°))° = 80°

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The correct answer is: A. Y intercept will be less and X will be less.

A linear function's slope is a gauge of how steep the line is. Between any two points on the line, it is the ratio of the change in the y-coordinate to the change in the x-coordinate. The formula is used to compute it:

slope equals (y2 - y1)/. (x2 - x1)

where any two points on the line (x1, y1) and (x2, y2) are.

The company's expenses will rise once it begins paying a driver at a rate of 0.25 cents per mile, which means its profit will decline. The profit curve on the y-axis will go vertically downward as a result of this. But, because the cost of paying the driver is fixed per mile and has no impact on the profit per mile, the slope of the line—which reflects the profit per mile—will stay the same.

Hence, A. Y intercept will be less and X will be less is correct.

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21 is  the area, measured in square centimeters, of the green shape pictured below.

What is square?

Square, in geometry, a plane figure with four equal sides and four right (90°) angles. A square is a special kind of rectangle (an equilateral one) and a special kind of parallelogram (an equilateral and equiangular one).

the area of a parallelogram, we can split this shape up into a rectangle and two right triangles.

The rectangle:

The rectangle has dimensions of 4 by 3 centimeters therefore the area would be 4*3=12 cm squared

two right triangles:

The area of a triangle is 1/2 base * height, but since there are two triangles it would just be the base times the height. The base is 3 cm and the height is 3 so 3*3=9

Next, we add the two areas together: 12+9 = 21

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Answer:

Step-by-step explanation:

Make a chart.

units                    hours

2                             5

4                             10

6                             15

4) Dane read an average of 400 minutes per week. 5)  Diane will have read 2000 minutes after 5 weeks.

4) The number "0200100300" represents the number of minutes Diane read each week for 3 weeks. To find out how many minutes she read after the first week, we simply look at the first digit, which is "0." This means that Diane did not read any minutes during the first week.

To find out how many minutes she read after the second week, we add the digits in the first two positions, which are "02." This gives us a total of 2 x 60 = 120 minutes.

To find out how many minutes she read after the third week, we add the digits in the first three positions, which are "020." This gives us a total of 20 x 60 = 1200 minutes.

To find out how many minutes she read each week, we simply divide the total number of minutes by the number of weeks, which is 3. So Diane read a total of 1200 minutes in 3 weeks, which means she read an average of 400 minutes per week.

5) If Diane reads the same number of minutes each week, then she will read that same number of minutes after 4 weeks and after 5 weeks. To find out how many minutes she reads after 4 weeks, we can skip count by the same number repeatedly: 400, 800, 1200, 1600. So Diane will have read 1600 minutes after 4 weeks.

Similarly, to find out how many minutes she reads after 5 weeks, we can skip count again by the same number repeatedly: 400, 800, 1200, 1600, 2000. So Diane will have read 2000 minutes after 5 weeks.

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Answer:

Step-by-step explanation: $130-$70 lift = $60/$20 per hour= 3 hours ski time

1.) The probability of rolling two even numbers would be = 1/4

2.) The probability of rolling one even and one odd number = 1/2

3.) The probability of flipping tails on a coin and by rolling a factor of 6 on a six sided die would be = 1/3

To calculate the probability the formula that should be used is given as follows;

probability = possible outcome/sample space

For question 1.):

Sample space when two dice are thrown = 36

possible outcome = (2,2),(2,4),(2,6),(4,2),(4,4),(4,6),(6,2),(6,4),(6,6)= 9

Probability = 9/36 = 1/4

For question 2.)

Sample space when two dice are thrown = 36

possible outcome = 18

probability = 18/36 = 1/2

for question 3.)

Sample space when two dice are thrown = 12

possible outcome = 4

probability = 4/12 = 1/3

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The area of the path is 80 square meters.

Given: A rectangular flower bed measures 10m by 6m. It has a path  2m wide around it.

To Find: The area of the path.

Solution: We need to subtract the area of the inner rectangle from the area of the outer rectangle.

So,

The outer rectangle has dimensions 14m by 10m (adding 2m to each side of the flower bed), so its area is:

A outer = 14m x 10m = 140 m²

Now,

The inner rectangle has dimensions 10m by 6m (the original dimensions of the flower bed), so its area is.

A inner = 10m x 6m = 60 m²

Now,

The area of the path.

A path = A outer - A inner

           = 140 m² - 60 m²

           = 80 m²

Thus, The area of the path is 80 square meters.

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Simplifying this fraction gives us 1/4. The answer is (D) 1/4.

What is arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.

Let's start by finding the fraction of Michelle's patients who are under 12 or over 65. We know that one-third of her patients are under 12, so two-thirds must be 12 or older. Similarly, five-twelfths of her patients are over 65, so seven-twelfths must be 65 or younger.

Now, we want to find the fraction of Michelle's patients who are between 12 and 65. To do this, we need to subtract the fraction of patients who are under 12 or over 65 from 1 (since these are the only two age groups we're considering).

Fraction of patients under 12: 1/3

Fraction of patients over 65: 5/12

Fraction of patients 12 to 65: 1 - 1/3 - 5/12

We can simplify this expression by finding a common denominator:

Fraction of patients 12 to 65: 12/12 - 4/12 - 5/12

Fraction of patients 12 to 65: 3/12

Simplifying this fraction gives us 1/4. Therefore, the answer is (D) 1/4.

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The only equations n + 6 = 12 and 4 • n = 24 have n = 6 as a solution.

An equation is a collection of variables, constants, and mathematical operations like addition, subtraction, multiplication, or division that are balanced by the equal sign. The equation's right-hand side (RHS) is on the right, and its left-hand side (LHS) is on the left.

To check if a given equation has n = 6 as a solution, we simply substitute n = 6 into the equation and see if it is true.

2 + n = 6 : 2 + 6 = 8, not true for n = 6.

n + 6 = 12 : 6 + 6 = 12, true for n = 6.

4 • n = 24 : 4 • 6 = 24, true for n = 6.

n • 3 = 2 : 6 • 3 = 18, not true for n = 6.

Therefore, only the equations n + 6 = 12 and 4 • n = 24 have n = 6 as a solution.

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