Which has a unit price of $4.121case?

A. 3 cases for $12.57
B. 4 cases for $16.44
C. 5 cases for $21.25
D. 6 cases for $24.72

Answer:

So the age of Mr.Jones = 39 yrs. |

the age of his wife = 39-4 = 35 yrs.|

and the age his son = 39-31 = 8 yrs.|

Step-by-step explanation:

Let the age of Mr.Jones = x

So, the age of his wife = x-4 (wife is younger by 4 years)

and the age of his son = x-31 (son is younger by 31 years)

Sum of their ages = x + (x-4) + (x-31) = 82

= x + x - 4 + x - 31 = 82 (By removing the brackets)

= 3x - 35 = 82

= 3x = 117 (By adding 35 both the sides)

= x = \(\frac{117}{3}\)= 39

Since the sales representative calls on four hospitals in westchester county, the numbers of ways can he organize his calls is option A: 24  possible ways.

Throughout every stage of the sales process, a sales representative deals directly with customers. They must determine a customer's needs, make a compelling case for pertinent items or services, and guarantee a positive overall experience.

Note that:

For the first call he makes, he has 4 choices.

For the first call he makes, he has  3 choices.

For the first call he makes, he has choices.

For the first call he makes, he has choice.

Solution:

4 x 3 x 2 x 1 = 24 possible combinations.

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See options below

A sales representative calls on four hospitals in Westchester County. It is immaterial what order he calls on them. How many ways can he organize his calls?

24

7

120  

37

The value of cosA/cosB in the right triangle is 1.

The figure in the image is a right triangle, having one of its interior angles at 90 degrees.

From the diagram,

For θ = A:
Adjacent to angle A = 3

Hypotenuse = 4.24

For θ = B:
Adjacent to angle B = 3

Hypotenuse = 4.24

Using trigonometric ratio:

cosine = adjacent / hypotenuse

cosA = adjacent / hypotenuse

cosA = 3/4.24

cosB = adjacent / hypotenuse

cosB = 3/4.24

Now,

cosA/cosB = (3/4.24) / (3/4.24)

cosA/cosB = (3/4.24) × (4.24/3)

cosA/cosB = 1/1

cosA/cosB = 1

Therefore, cosA/cosB has a value of 1.

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Step-by-step explanation:

1:4 bcos u need to divide both sides by 4

To evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

Depending on the powers they possess, many rules of exponents are given.

Law of Multiplication: Exponents should be added while keeping the base constant when multiplying like bases.

Exponents should be multiplied while bases are kept constant when bases are raised by a power of two or more.

Division Rule: When dividing like bases, maintain the base constant and deduct the exponent of the denominator from the exponent of the numerator.

The given value can be written as:

\(8^{\frac{2}{3} } = \sqrt[3]{8^{2} }\)

Hence, to evaluate \(8^{\frac{2}{3} }\) first find the square of 8 and then take the cube root.

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The solution to the inequality is:

x ∈ (-∞, -21].

The correct option is F.

To solve the given inequality, we'll first simplify the expression:

23 < 3x - 3 ≤ -66

To simplify the inequality,

23 < 3x - 3 ≤ -66

Adding 3 to all parts of the inequality:

23 + 3 < 3x - 3 + 3 ≤ -66 + 3

Simplifying:

26 < 3x ≤ -63

Next, divide all parts of the inequality by 3:

26/3 < 3x/3 ≤ -63/3

Simplifying:

8.67 < x ≤ -21

Therefore, the solution to the inequality is:

x ∈ (-∞, -21]

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Let's simplify the expression step by step: Expand the squared term:

(x - 3y)² = (x - 3y)(x - 3y) = x² - 6xy + 9y²

Expand the second term:

3(x + y)(x − 4y) = 3(x² - 4xy + xy - 4y²) = 3(x² - 3xy - 4y²)

Expand the third term:

x(3x + 4y + 3) = 3x² + 4xy + 3x

Now, let's combine all the expanded terms:

(x - 3y)² + 3(x + y)(x − 4y) + x(3x + 4y + 3)

= x² - 6xy + 9y² + 3(x² - 3xy - 4y²) + 3x² + 4xy + 3x

Combining like terms:

= x² + 3x² + 3x² - 6xy - 3xy + 4xy + 9y² - 4y² + 3x

= 7x² - 5xy + 5y² + 3x

The simplified form of the expression is 7x² - 5xy + 5y² + 3x.

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Answer:

I'm not that sure but I really feel like it's 15

The ty plane the hypothesis of theorem are satisfied

The hypothesis of a theorem is a statement or assumption that is made in order to prove a mathematical result.

The hypothesis of the Tychonoff theorem is satisfied in a variety of different spaces, including compact spaces and metrizable spaces.

This theorem is important because it provides a useful tool for understanding the properties of topological spaces, which are spaces that have certain structures that allow for the study of continuous functions and mappings.

In summary, the hypothesis of the Tychonoff theorem is a necessary condition for the theorem to be proven and is satisfied in a variety of different spaces.

Understanding the hypothesis and the spaces in which it is satisfied is crucial for understanding the theorem and its applications in mathematics.

Complete Question:

State where in the ty-plane the hypotheses of Theorem

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The remote interior angles of ∠1 are ∠2 and ∠6.

Corresponding angles in a triangle are those angles which are contained by a congruent pair of sides of two similar (or congruent) triangles.

The remote interior angles of ∠1 is determined by applying the principle of corresponding angles as shown below;

∠1 = ∠2 ( vertical opposite angles are equal )

∠1 = 180 - ∠5 ( corresponding angles  are equal )

180 - ∠5  = ∠ 6 ( vertical opposite angles are equal )

So we can conclude that, ∠1 = ∠6.

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The quadrilateral that has four congruent sides is option D. square. A square is a special type of rectangle and rhombus, characterized by having all four sides of equal length.

A parallelogram (option A) is a quadrilateral with opposite sides that are parallel. While the opposite sides of a parallelogram are congruent, it does not guarantee that all four sides are equal.

A rectangle (option B) is a quadrilateral with four right angles. While opposite sides of a rectangle are congruent, it does not necessarily have four congruent sides unless it is also a square.

A rhombus (option C) is a quadrilateral with all sides of equal length. While a rhombus does have four congruent sides, it is not the only quadrilateral with this property.

Therefore, among the given options, the quadrilateral that has four congruent sides is the square (option D).

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When b is 3, the value of the expression \(2b^3 + 5\) is 59.

To evaluate the expression\(2b^3 + 5\) when b is 3, we substitute the value of b into the expression and perform the necessary calculations.

Given that b = 3, we substitute this value into the expression:

\(2(3)^3 + 5\)

First, we evaluate the exponent, which is 3 raised to the power of 3:

2(27) + 5

Next, we perform the multiplication:

54 + 5

Finally, we add the two terms:

59

Therefore, when b is 3, the value of the expression \(2b^3 + 5\) is 59.

In summary, by substituting b = 3 into the expression \(2b^3 + 5\), we find that the value of the expression is 59.

It's important to note that the provided equation has multiple possible solutions for x, but when b is specifically given as 3, the value of x is approximately 3.78.

It's important to note that in this equation, we substituted the value of b and solved for x, resulting in a specific value for x. However, if we wanted to solve for b given a specific value of x, we would follow the same steps but rearrange the equation accordingly.

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Answer:

Anwer- 9

Step-by-step explanation:

(1+2)2 =6 but since there isnt 6, go for 9.

- Hope this helps a little

The value of a from the given quadratic equation is 9. Therefore, option D is the correct answer.

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

Given that, Nancy found that x=1 is one solution to the quadratic equation (x+2)²=a.

Now, substitute x=1 in the equation (x+2)²=a, that is

(1+2)²=a

a=3²

a=9

Therefore, option D is the correct answer.

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This is an exercise of the Pythagorean Theorem, which establishes that in every right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides, called legs.

This can be expressed mathematically as:

Where "a" and "b" are the lengths of the legs and "c" is the length of the hypotenuse. This theorem is one of the fundamental bases of geometry and has many applications in physics, engineering, and other areas of science.

The Pythagorean Theorem formula is used to calculate the length of an unknown side of a right triangle, as long as the lengths of the other two sides are known. It can also be used to determine if a triangle is right if the lengths of its sides are known.

To calculate the hypotenuse, we will apply the formula:

c = √(a² + b²)

Knowing that:

a = 8cm

b = 15cm

Now we just substitute the data in the formula, and calculate the hypotenuse, then

The hypotenuse C of the triangle is 17 cm.

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Answer:

You forgot to attach the question and the histogram.

Is your question “the interval containing the most movies” ? If yes, then the answer is :

Interval 90-100 minutes

Step-by-step explanation:

A histogram is a chart that is used to represent data in form of bars.

Like every other chart, it consists of both the x and y axis. The y axis contains the frequency or percentage of occurrences while the x axis contains the range or intervals.

To determine the interval with the most occurrences, that is the interval containing most movies, we look for the bar with the most height. The bar that is tallest amongst others has the most movies in its running time.

From the attached histogram, the interval containing the most movies is the 90- 100 minutes interval.

This simply means that from Alex’s record, out of the 50 popular movies, more movies run with the 90-100 minutes interval.

PS: view the attached histogram

Answer:

There are two problems like this, one involving median and the shape.

Here are your answers for both.

Shape is skewed right, this is because it decreases towards the right, like a hill. (C)

Extra info/this part isnt right: It would be skewed left but it isn't because it is not decreasing towards the left like a hill.

The median is between the interval 90-100, because it looks to be the typical number. (A)

Answer:

Is Square Root of 25 Rational or Irrational?  

Step-by-step explanation:

A rational number can be expressed in the form of p/q. Because √25 = 5 and 5 can be written in the form of a fraction 5/1. It proves that √25 is rational.

The answer is:

Work/explanation:

What are rational numbers?

Rational numbers are integers and fractions.

Irrational numbers are numbers that cannot be expressed as fractions, such as π.

Now, \(\bf{\sqrt{25}}\) can be simplified to 5 or -5; both of which are rational numbers.

Answer:

x = 21

Step-by-step explanation:

Answer:

1/3×-6=1

1/3x=1+6

1/3×=7

1/3.3×=7.3

x=21....X is solved

The best statistical method to use for studying the relationship between the income of people living in a neighborhood and the number of sales made at the franchise company's store in that neighborhood would be regression analysis.

Regression analysis would be the best statistical method to use in this situation.

It would help to determine the relationship between the income of people living in a neighborhood and the number of sales made at the franchise company's store in that neighborhood.

The regression analysis would provide a model that would help to predict the expected number of sales based on the income levels of the neighborhood.

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Answer:

The arrow can be broken into a rectangle and a triangle.

And the area of the arrow is 22 ft^2

Step-by-step explanation:

Area of the rectangle:

length • width = 7 • 2 = 14 ft^2

Area of the triangle:

(base • height) / 2

You must add 1 + 2 + 1 in order to get the base which is 4

And to get the height, you must do 11 - 7 = 4 (height)

(4 • 4) / 2 = 8 ft^2

Add both areas together to get the area of the arrow:

14 ft^2 + 8 ft^2 = 22 ft^2

Hope this helps!

Answer:

Step-by-step explanation:

19?

Step-by-step explanation:

a row n adds the number n to the sum (= the first number from the right in row n-1), and therefore also n to the 3rd number from the right of row n-1.

in any case, the first number from the right is the result of

1 + 2 + 3 + 4 + 5 + ... + n-1 + n

that sum is

n(n+1)/2

for the row 20 that is

20×21/2 = 10×21 = 210

the 3rd number from the right in row 20 is then

210 - 2 = 208

Using chebyshev's theorem, 75%  of the observations fall between 1,300 and 1,700

Chebyshev's theorem states that for any distribution, regardless of its shape, at least (1 - 1/k^2) of the observations will fall within k standard deviations of the mean, where k is any positive constant greater than 1.

In this case, we have a mean (μ) of 1,500 and a standard deviation (σ) of 100. To find the percentage of observations that fall between 1,300 and 1,700, we need to determine how many standard deviations away these values are from the mean.

For the lower bound, (1,300 - μ) / σ = (1,300 - 1,500) / 100 = -2 standard deviations.

For the upper bound, (1,700 - μ) / σ = (1,700 - 1,500) / 100 = 2 standard deviations.

Since we are considering the range within 2 standard deviations of the mean, we can apply Chebyshev's theorem.

According to Chebyshev's theorem, at least (1 - 1/k^2) of the observations fall within k standard deviations of the mean. In this case, k = 2.

So, at least (1 - 1/2^2) = 1 - 1/4 = 3/4 = 75% of the observations fall within 2 standard deviations of the mean.

Therefore, using Chebyshev's theorem, we can conclude that at least 75% of the observations will fall between 1,300 and 1,700.

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The surface area of the solid of revolution formed by rotating the bounded region between the curves y = 4x + 3, y = 0, x = 0, and x = 3 about the x-axis is 36π√(17).

To calculate this, we use the formula S = 2π∫[a,b] y√(1 + (dy/dx)²) dx.


The surface area of the solid of revolution formed by rotating the bounded region between the curves y = 4x + 3, y = 0, x = 0, and x = 3 about the x-axis can be calculated using the formula:

S = 2π∫[a,b] y√(1 + (dy/dx)²) dx

In this case, the curves y = 4x + 3 and y = 0 intersect at x = -3/4. However, since the region is bounded between x = 0 and x = 3, we only consider the portion between these limits. Thus, the integral becomes:

S = 2π∫[0,3] (4x + 3)√(1 + (4)²) dx

S = 2π∫[0,3] (4x + 3)√(1 + 16) dx

S = 2π∫[0,3] (4x + 3)√17 dx

To integrate this, we expand the expression inside the square root:

S = 2π∫[0,3] (4x + 3)√17 dx

S = 2π∫[0,3] (4x + 3)√(17) dx

S = 2π∫[0,3] (4x√(17) + 3√(17)) dx

S = 2π∫[0,3] (4√(17)x + 3√(17)) dx

S = 2π[2√(17)x²/2 + 3√(17)x] [0,3]

S = 2π[√(17)x² + 3√(17)x] [0,3]

Evaluating this expression at x = 3 and x = 0 gives:

S = 2π[√(17)(3)² + 3√(17)(3)] - 2π[√(17)(0)² + 3√(17)(0)]

S = 2π[√(17)(9) + 3√(17)(3)] - 2π[0]

S = 2π(9√(17) + 9√(17))

S = 36π√(17)

Therefore, the surface area of the solid of revolution is 36π√(17).

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Let A be a vector and n be a unit vector in a fixed direction. The scalar projection of A onto n can be represented as:

An = A . n = ||A||cos(θ),

where θ is the angle between vectors A and n.

The projection of A onto a plane perpendicular to n can be represented as:

A - (An) = A - (||A||cos(θ))n = ||A||sin(θ)nₜ,

where nₜ is a unit vector perpendicular to n.

Combining these two results, we have:

A = (An) + (A - (An)) = (||A||cos(θ))n + ||A||sin(θ)nₜ

By doing so, it is demonstrated that a vector A may be written as the product of its scalar projection along a unit vector n and its projection onto a plane perpendicular to n. This breakdown of a vector is helpful for looking at its parts from various angles.

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Algorithm is a set of instructions for solving a problem or performing a task, typically designed for a computer to follow.

An algorithm is essentially a step-by-step procedure for solving a problem or accomplishing a specific task. It is used in various fields, including mathematics, computer science, engineering, and many others. In computer science, algorithms are essential for software development and programming, as they provide a systematic approach to designing and implementing complex programs. The process of developing an algorithm typically involves breaking down a problem into smaller sub-problems, identifying the key steps required to solve each sub-problem, and then putting the steps together in the correct order to form a complete solution.

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The researcher should use the confidence interval for a mean, that is, option (b).

As the researcher wants to estimate the length of time that all patients spend in the hospital after having surgery at her hospital, so she should use the estimation, that is, either point or interval.

⇒ The option of hypothesis rules out.

⇒  Both options (c) and (d) are eliminated.

Now, either option (a) or (b) is correct. But we use proportion when after a series of repeated trials, we consider an event a success. This is not the case here, which means the option (a) cannot be correct as well.

So, the researcher should use a Confidence interval for a mean which is option (b).

Therefore, the correct answer is a Confidence interval for a mean, that is, option (b).

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To answer this problem we have to remember that the break even point occur where the revenue function and the cost function have the same value.

Then, this happens when

Pluggin the expressions of our functions and solving for x we have:

Therefore the break even point occurs when x=74000. In this points both functions have value

Answer:

SAS

Step-by-step explanation:

According to the side-angle-side (SAS) rule, if two sides and the angle between them in one triangle are congruent to the corresponding sides and angle in another triangle, then the two triangles are congruent.

Since this is the case with these two triangles, they are congruent by SAS