big bobs bakery charges $9 for 1/2 dozen donuts. what is the price per dozen?

Answer/Step-by-step explanation:

The first equation is confusing so I'll solve both ways:

Addition

1. -4x + 2y = -12

   4x + 8y = -24

-----------------------------

            10y = -36

          ÷10      ÷10

        --------------------

              y = -3.6

4x + 8y = -24

4x + 8(-3.6) = -24

4x - 28.8 = -24

     +28.8    +28.8

-----------------------------

      4x = 4.8

    ÷4     ÷4

---------------------

   x = 1.2

If the first equation is subtraction this is the solution:

2. -4x - 2y = -12

   4x + 8y = -24

 ------------------------

            6y = -36

           ÷6      ÷6

         -------------------

                y = -6

4x + 8y = -24

4x + 8(-6) = -24

4x - 48 = -24

     +48    +48

---------------------

4x = 24

÷4   ÷4

-----------------

x = 6

(6, -6)

I hope this helps!

The control limits that include 90% of the sample means be,

(24.9671 , 25.0329).

Given, twenty-five engine mounts are sampled each day and found to have an average width of 2 inches, with a standard deviation of 0.1 inches.

we have to find the confidence interval under confidence of 90%.

As, Mean = 2 and Standard Deviation = 0.1

Subtract 1 from your sample size. 25 – 1 = 24. This gives you degrees of freedom.

Subtract the confidence level from 1, then divide by two.

(1 – 0.9) / 2 = 0.05

For 24 degrees of freedom (df) and α = 0.05, the result is 1.645.

Divide your sample standard deviation by the square root of your sample size.

0.1 / √(25) = 0.02

Now, 0.02 × 1.645 = 0.0329

The lower end of the range

25 – 0.0329 = 24.9671

The upper end of the range

25 + 0.0329 = 25.0329

Hence, the confidence interval be, (24.9671 , 25.0329)

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The required number of sessions is obtained as 2.

A linear equation can be balanced by adding or subtracting the same number on both sides of the equality sign. Similarly, multiplication and division is also possible with the same numbers.

Suppose the number of sessions be x.

Then, the expression for the training cost as per the first plan is given as 41 + 83x.

And, for the another plan it is 43x + 82.

As per the question both the expressions has to be equated for the same cost as follows,

43 + 82x = 41 + 83x

=> 43 - 41 = 83x - 82x

=> x = 2

Hence, the number of sessions for both the plans to have same cost is 2.

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The probability that a randomly selected student scored between 70 and 84 is 0.8351

Probability is simply how likely something is to happen.

Whenever we’re unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

given that:

mean = 80

standard deviation = 4

now we need to find the probability of students scored between 70 and 84

P(70<X<84) = P(X<84) - P(X>70)

                   = P(Z<(84-80)/4)-P(Z>(70-80)/4)

                   =P(Z<1) - P(Z>-2.5)

                   = 0.8413-0.0062

                   = 0.8351

the probability that a randomly selected student scored between 70 and 84 is 0.8351

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The Slope of the line that passes through the points (1, 4) and (1, -3) is Undefined.

If we are provided with two points (x₁, y₁) and (x₂, y₂) then the formula of finding the slope between these points is expressed as

m = (y₂ - y₁)/(x₂ - x₁)

where m is the slope between the points, y₂ - y₁ is difference between the y coordinates and x₂ - x₁ is the difference between the x coordinates.

Now the points are (1, 4) and (1, -3), so the difference between the coordinates is expressed as

y₂ - y₁ = -3 - 4

y₂ - y₁ = -7

x₂ - x₁ = 1 -1

x₂ - x₁ = 0

Now the slope will be

m = -7/0

Since, we have zero in the denominator and any number divided by zero is undefined so the slope is undefined.

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Complete Question:

What is the slope of the line that passes through (1, 4) and (1, -3)?

Answer:

Step-by-step explanation:

I'm sorry if I'm wrong I think its 0.62 or 30.

Answer: A

Step-by-step explanation:

I graphed it using my graphing calculator. the maximum point is -2, 9. f(x) means y so graphing just requires you to type the equation into a calculator and replace the f(x) with y. sorry if that doesnt make sense. no money

Answer:

what was the original cost of the lunch before they added the tip?

Answer:

Just as geometry has rules, definitions, postulates, and theorems that help with problem-solving and understanding the relationships of shapes and solids, the Bible provides a similar guide for living a Christian life. The Bible contains a set of principles and teachings that serve as a foundation for Christian beliefs and values. These principles and teachings help Christians to understand the nature of God and their relationship with him, as well as the principles for living a moral and virtuous life.

In the same way that geometry relies on deductive reasoning to draw conclusions and make predictions, Christians use their knowledge of the Bible to make decisions and navigate the challenges of daily life. The Bible provides guidance on a wide range of topics, including relationships, work, ethics, and personal growth, helping Christians to make wise choices and avoid pitfalls.

Additionally, just as geometry helps us to understand the spatial relationships of objects, the Bible helps us to understand our place in the world and our relationship with others. The Bible teaches us about the importance of love, compassion, and forgiveness, and helps us to see the value and worth of every human being.

Overall, the Bible serves as a guide for living a Christian life, providing principles, teachings, and guidance that help us to understand God, ourselves, and our relationships with others.

Step-by-step explanation:

Answer:

yes...........s..s.s..s..s..,...

The artist should sell at least 200 paintings for the profit of $60,000.

Profit is the money you have left after paying for business expenses.

Given that, An artist makes a profit of (500p-p²) dollars from selling p paintings.

Establishing the equation, we have,

500p-p² = 60,000

p²-500p+60,000 = 0

Factorizing to find p,

p²-200p-300p+60,000 = 0

p(p-200)-300(p-200) = 0

(p-200)(p-300) = 0

p = 200 or p = 300

Since, the question is asking for least number of paintings so, we'll consider 200 paintings.

Hence, The artist should sell at least 200 paintings for the profit of $60,000.

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Conceptual Learning involves students engaged in quality learning experiences based around key concepts and central ideas rather than using the more traditional method of focusing on learning on topics.

Example of Conceptual Learning

A student with a conceptual understanding of decimals may readily work with fractions, percentages, and ratios. Students who just have traditional knowledge, on the other hand, may struggle to cope because they will have to recollect the information as different concepts.

Conceptual learning encourages active participation since it requires students to participate actively in the process, whereas traditional types of learning require the teacher to explain information

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the find the probability of having two boys or two girls will be 50%

What is probability ?

The probability formula can be used to calculate the likelihood of an event by simply dividing the favorable number of possibilities by the total number of options. The likelihood of an occurrence might vary from 0 to 1 because the favourable number of outcomes can never be greater than all possible outcomes.

For two genders and three children, there are a total of 2³=8 potential combinations.

There are (GGG, GGB, BGG, GBG) = 4 pairs where at least two of the children are female.

As a result, there is a 4/8 = 1/2 chance that the family of three children will include at least two girls.

Hence the find the probability of having two boys or two girls will be 50%.

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So, when the box has a square base with 4.8 feet on each side and a height of 40.41 feet, then cost will be at its lowest.

When referring to a specific mathematical item that serves as a building block, the word "basis" in mathematics is employed. The notions of a number system in which numbers are represented by digits and a numerical system in which logarithms were defined are the ones that are most frequently utilized.

V=x2×y931=x2y=93x2

Given that the square foot price for the bottom is 15 cents, the top is 10 cents, and the sides are 1.5 cents

Therefore, total cost

C=15x2+10x2+(1.5xy)

C=25x2+6xyC(x)=2x2+6x×931x2C(x)=25x2+5586x

Upon separating it from x, we obtain,

C′(x)=50x−5586x2

We obtain 50x5586x2=0x3=5586 when equating with zero.

50x=4.8ft

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Answer: 216 cm^2

Step-by-step explanation:

The equation finds the area of the cube is

6 * S^2

6 (6^2) = 216 cm^2

To solve a one-step equation, you need to do the opposite operation on both sides of the equation to isolate the variable .To solve a two-step equation, you need to do two operations on both sides of the equation to isolate the variable

1. One-Step Equation: To solve a one-step equation, you need to do the opposite operation on both sides of the equation to isolate the variable. For example:

2x + 5 = 11

To solve, subtract 5 from both sides:

2x = 6

Divide both sides by 2:

x = 3

2. Two-Step Equation: To solve a two-step equation, you need to do two operations on both sides of the equation to isolate the variable. For example:

2x + 5 = 11

2x = 6

Next, divide both sides by 2:

x = 3

3. Three-Step Equation: To solve a three-step equation, you need to do three operations on both sides of the equation to isolate the variable. For example:

2x + 5 = 11

2x = 6

Next, divide both sides by 2:

x = 3

Finally, multiply both sides by 3:

3x = 9

Therefore, the solution is x = 3.

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Answer:

A

Step-by-step explanation:

The required probability that she'll use a cab exactly one time is  4/9.

probability is a part of math that arrangements with figuring out the probability of the event of an occasion.

Elizabeth lives in San Francisco and works in Mountain View.

In the first part of the day she has 3 transportation choices  (bus, cab, train) to work, and at night she has similar 3 options for her outing home.

All transportation  (bus, cab, train) are comparably liable to be chosen, and 1 of them should be chosen in the first part of the day and night, so we get:

P (bus) = P (taxi) = P (train) = 1/3.

We additionally have P(no taxi in night) = P(no taxi at morning) = 2/3

Presently, P(using taxi precisely once) = P(cab at morning and no taxi at night) + P(no taxi at morning and taxi at night)

= P(cab, no taxi) + P(no taxi, taxi)

= 1/3 × 2/3 + 2/3 × 1/3

= 2/9 + 2/9

= 4/9

Consequently, the probability that Elizabeth utilizes a taxi just once is 4/9.

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The tangent planes to the surface are described by the equation "6x + 12y + 48z - 210 = 0" (3, 4, 3).

In this instance, the equation yields the parametrized surface "r(t) = (t², [tex]t^3[/tex], [tex]t^4[/tex]). On the surface, the issue that interests us is (3, 4, 3).

We may use the partial derivative concept to obtain the second derivative of the surface at points (3, 4, 3). Regardless of whether a change in the parameterization approaches zero, the time derivative of the parameter value of a variable serves as the upper estimate of the differentiating quotient.

[(r(3 + h) - r(3)) / h] as h approaches 0

For the x-coordinate of the surface, this limit is given by

[((3 + h)² - 3²) / h] as h approaches 0

which simplifies to

[(9 + 6h + h² - 9) / h] as h approaches 0

which simplifies to

[6h + h²] as h approaches 0

Since h is approaching 0, h2 is approaching it faster than h. As h approaches 0, the limit changes from 0 to 6, and the number of h2 decreases relative to the value of 6h.

Thus, the partial derivative of the x-coordinate of the surface concerning the time at the coordinates (3, 4, 3) is 6.

As a result, the vector is the normal vector to the ground at the location (3, 4, 3). (6, 12, 48). 6x + 12y + 48z + d = 0 is the equation of the tangent planes to the ground at this position.

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The probability that on any given day the office receives exactly 3 calls is 0.0076.

What is probability?

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Here, we let

Let X be the number of calls received in an office per day.

X≈Poison(λ=10)

P(X = x) = e^(-λ)λˣ/x!; x = 0, 1, 2.....

= 0, otherwise

The probability that on any given day the office receives exactly 3 calls: 0.0076

P(X = 3) = e^(-10)10³/3!

P(X=3) = 0.0076

Hence, the probability that on any given day the office receives exactly 3 calls is 0.0076.

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The required f(x) values are  5, 1 , -1 , -3

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

f(x)= -2x+1

Substitute the values for x and find the value of f(x)

For x= -2:

f(x)= -2(-2)+1

    = 5

For x= 0:

f(x)= -2(0)+1

    = 1

For x= 1:

f(x)= -2(1)+1

    = -1

For x= -2:

f(x)= -2(2)+1

    = -3

The required f(x) values are  5, 1 , -1 , -3

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The graph that represents the given situation is graph (A). (Refer to the graph attached below)

The set of ordered pairs is the graph of a function f in mathematics, where these pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical case when x and f(x) are real numbers.

To create a graph is to make a diagram that shows the relationship between two or more things.

So, we know that:

The bathtub is filling at a constant rate.

When the tap was closed, the water drained out.

Then again, the tap was open for the water to come out at a constant rate.

So, the correct graph that resembles these lines is a graph (A).

Therefore, the graph that represents the given situation is a graph (A). (Refer to the graph attached below)

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It is ''True'' that leagues with larger standard deviation values are more competitively balanced than other leagues.

The standard deviation is a measure of how widely distributed or how much values vary. The expected value occurs when the standard deviation is low, which increases the likelihood that the values will fall within a small range. When the standard deviation is high, on the other hand, the expected value occurs when the values are closer to the mean.

Lets take an example to understand Standard deviation

Let's say the entire target population is comprised of eight students in a specific class. By subtracting the average of the values' squared deviations from it, one can calculate the population standard deviation for a finite set of numbers.

Eight of the following values represent the marks of an eight-student class (or a statistical population):

2,4,4,5,5,5,7,8

These eight data points have the mean (average) of 6;

[tex]\frac{2+4+4+5+5+5+7+8}{8}[/tex] =  [tex]\frac{40}{8}[/tex]

=  5  

First, calculate the deviations of each data point from the mean, and square the result of each:

[tex](2-5)^{2} =[/tex] [tex](-3)^{2}[/tex] = 9                          [tex](5-5)^{2} =[/tex]  [tex]0^{2}[/tex]     = 0

[tex](4-5)^{2} =[/tex] [tex](-1)^{2}[/tex] = 1                           [tex](5-5)^{2} =[/tex]  [tex]0^{2}[/tex]     = 0

[tex](4-5)^{2} =[/tex] [tex](-1)^{2}[/tex] = 1                           [tex](7-5)^{2} =[/tex] [tex]2^{2}[/tex]      = 4

[tex](5-5)^{2} =[/tex]  [tex]0^{2}[/tex]     = 0                           [tex](8-5)^{2} =[/tex] [tex]3^{2}[/tex]      = 9.

The variance is the mean of these values:

[tex](sigma)^{2}[/tex] =  [tex]\frac{9+1+1+0+0+0+4+9}{8}[/tex] =  [tex]\frac{24}{8}[/tex] = 3

and the population standard deviation is equal to the square root of the variance:

sigma = √3 = 1.732

This formula is valid only if the eight values with which we began form the complete population.

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47

Cuando dividas 752 por 16 obtendrias 47.

The value of x for a given expression 4x + 3 = 9 is equal to -1.415.

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 the expression is 4x + 3 = 9. The value of x will be calculated as,

log(4)⁹= x + 3

log9 / log4 = x + 3

0.95424425 / 0.6020599 = x + 3

1.584962725 -3 = x + 3 - 3

x = -1.415037275

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The true statements regarding the trigonometric functions are given as follows:

The three trigonometric functions are defined as follows:

The statements are described as follows:

The remaining statements are true.

The statements are given by the image shown at the end of the answer.

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Answer:

- 1/2 × 8 = -4

-1/2 × -2 = 1

- 1/2 × 6/7 = - 3/7

-4 + 1 - 3/7x

-3-3/7x

The Rational number are 7/3, 8 and 72/8.

What is Rational Number?

Numbers that may be expressed in the form p/q, where p and q are integers and q0, are considered rational numbers. Because fractions cannot have a negative numerator or denominator, they differ from rational numbers in this respect. Because of this, the numerator and denominator of a fraction are whole numbers (denominator 0), unlike in the case of rational numbers, when they are both integers.

So to convert a fractional to reduce form we have to divide by 10 to power how many digits thereafter decimal point, and make sure that the numerator or denominator doesn't have commonly divisible.

√5 is not rational.

7/3 is rational

√17 is not rational

√64 = 8 is rational

72/8 is rational

Hence, The Rational number are 7/3, 8 and 72/8.

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The mean of the quantitative variable of interest in the population is called the mean.

For the purposes of data collection and analysis in statistics and other fields of mathematics, a population is a distinct group of people, animals, or things that can be recognized from one another. In order to learn more about a large population, data is often gathered from a sample.

As an example, inquire about the primary occupation of 100 people chosen at random during a football game. All 100 members of your sample make up the population at that match. The population will always equal the larger of the sample size and the total population. The population is used to refer to the overall population being studied. The illustration's population is representative of the student body at the high school under examination.

Therefore, the mean of the quantitative variable of interest in the population is called the mean.

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