At a local ice-cream store, 210 people were surveyed on whether they preferred eating ice cream from a cone or a cup. Of the 210 people surveyed, 70 were adults and 140 were children. Of the responses, 150 indicated the cone as the preferred method of eating ice cream. For those surveyed, there was no association between age and preferred method of eating ice cream. Which of the following tables show the distribution responses?
answer choices
Graph i
Graph ii
Graph iii
Graph iv
Graph v

Answers

Answer 1

Graph ii shows that 150 people preferred eating ice cream from a cone, while 60 people preferred eating ice cream from a cup. There was no association between age and preferred method of eating ice cream.

Graph ii is a table that shows the distribution of responses to the survey about preferred method of eating ice cream. The table shows that out of the 210 people surveyed, 70 were adults and 140 were children. Of the 210 people surveyed, 150 indicated the cone as the preferred method of eating ice cream, while 60 indicated the cup as the preferred method. This table indicates that there is no association between age and preferred method of eating ice cream, as the responses were evenly distributed between adults and children. This information can be used to determine the preferences of customers at the ice-cream store and can help inform decisions about how to serve the ice cream. For example, the store may choose to provide more cones than cups based on the survey results. Additionally, this table can be used to compare the preferences of different demographic groups, although in this case the survey showed that there was no association between age and preferred method of eating ice cream.

Adults: 70 people surveyed, 35 preferred cone, 35 preferred cup

Children: 140 people surveyed, 115 preferred cone, 25 preferred cup

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Related Questions

10.​ The study of the relationships among thermal energy, heat, and work is called dynamics.

True or false

Answers

Answer:

False.

Step-by-step explanation:

False. The study of the relationships among thermal energy, heat, and work is called thermodynamics, not dynamics. Dynamics is a branch of mechanics that deals with the motion of objects and the forces that cause that motion. Thermodynamics, on the other hand, is the study of the relationships between heat, work, and other forms of energy, and how these relationships can be used to understand the behavior of systems. It is a branch of physics that is concerned with the study of heat and its effects on matter.

All changes Given: A(0,6), B(6,6), C(6,0), D(0,0); ZDAB, LABC, ZBCD, LCDA are right angles. Prove: ABCD is a square.

Answers

Since ABCD has four equal angles and four equal sides, then it is a square.

How to find the distance between two coordinates?

The formula for the distance between two coordinates (x₁, y₁) and (x₂, y₂) is;  Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

We are given the coordinates;

A(0, 6)

B(6, 6)

C(6, 0)

D(0, 0)

Thus;

AB = √[(6 - 0)² + (6 - 6)²]

AB = 6

BC = √[(6 - 6)² + (0 - 6)²]

BC = 6

CD = √[(0 - 0)² + (0 - 6)²]

CD = 6

AD = √[(0 - 0)² + (0 - 6)²]

AD = 6

Thus, we conclude that all the sides are equal and it is a square.

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Mr. Muehlenweg S class used 1 3/4 cups baking soda for an experiment. If his students performed the experiment 6 1/2 times, how much baking soda did they use?

Answers

Mr. Muehlenweg S class used 1 3/4 cups baking soda for an experiment. If his students performed the experiment 6 1/2 times, he used 19/4 baking soda.

Define subtraction.

To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference.

Given,

Mr. Muehlenweg S class used 1 3/4 cups baking soda for an experiment.

Converting mixed fraction to improper function

1 3/4 = 7/4

If his students performed the experiment 6 1/2 times,

Converting mixed fraction to improper function

6 1/2 = 13/2

Subtracting,

7/4 - 13/2

7/4 - 26/4

19/4

Mr. Muehlenweg S class used 1 3/4 cups baking soda for an experiment. If his students performed the experiment 6 1/2 times, he used 19/4 baking soda.

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At a meeting for math enthusiasts, two entrance fees are charged. Anyone who knows the code word “algemath” only pays 2 euros. Those who are unlucky and do not know the code word pay three euros more. You know that 7338 people were present and that the cashier received 17487 euros. How many people knew the password?

Answers

Number of People who knows the Code are 6401

What is Linear Equation in Two Variable?

A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

Let, Number of People who kows the Code be x

Number of Peoplee who do not know the Code be y

According to the Question:

x + y = 7338 ----------(i)

2x + 5y = 17487 ----------(ii)

Multiplying Equation (i) by 2

2x + 2y = 14676 ---------(iii)

Substracting Equation (iii) from Equation (ii)

3y = 2811

y = 937

This means x = 6401

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a right triangle has a leg that measures 1. the other leg measures 2. calculate the length of the hypotenuse. round the answer to the nearest hundredth

Answers

The length of the hypotenuse is √5 with sides of 1 cm and 2 cm.

Define hypotenuse.

A right triangle's hypotenuse is its longest side, its "opposite" side is the one that faces a certain angle, and its "adjacent" side is the one that faces the angle in question. To describe the sides of right triangles, we utilise specific terminology. The side opposite the right angle is always the hypotenuse of a right triangle. Stretching under is what the Greek word hypoteinousa signifies. In mathematics, the term "hypotenuse" is used to describe the side of a right triangle that is opposite the right angle. The hypotenuse extends below the right angle if the right angle is positioned at the top of the triangle.

Given

Lengths = 1 cm and 2 cm

For length of the hypotenuse,

c = √a² + b²

c = √1² + 2²

c = √ 1 + 4

c = √5

The length of the hypotenuse is √5 with sides of 1 cm and 2 cm.

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If x + 3y^(1/3) = y what is dy/dx at the point (2,8)

Answers

The dy/dx at point (2,8) is 4/3

How to find dy/dx at a point?

From the information illustrated, x + 3y^(1/3) = y and point (2,8)

Find the derivative of this equation with respect to x and solve for dy/dx:

x + 3y^(1/3) = y

1 + [3 × 1/3 × y^(-2/3)]dy/dx = dy/dx

1 + [y^(-2/3)]dy/dx = dy/dx

dy/dx -  [y^(-2/3)]dy/dx = 1

dy/dx [1-  y^(-2/3)] = 1

dy/dx = 1/ [1 - y^(-2/3)]

At point (2,8), x = 2 and y = 8.

Substitute into dy/dx:

dy/dx = 1/ [1 - y^(-2/3)]

dy/dx = 1/ [1 - 8^(-2/3)]

dy/dx  = 1/ [1 - 1/4)]

dy/dx = 4/3

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Leia is setting up 417 toy cars. Each car needs 3 batteries to drive.
How many batteries does Leia need for her cars?

Answers

Answer:

Leia needs 3 * 417 = <<3*417=1251>>1251 batteries for her cars.

Step-by-step explanation:

To find out how many batteries Leia needs for her cars, we need to multiply the number of toy cars by the number of batteries needed for each car. Since each car needs 3 batteries and Leia has 417 toy cars, the total number of batteries she needs is 3 * 417 = 1251.

Student grades on a chemistry exam were: 77, 78, 75, 81, 89, 53; 79, 82, 84; 91 a. Select the stem-and-leaf plot of the data. Stem Leaf 5 3 6 7 5 7 8 9
8 1 2 4 9 9 1 Stem Leaf 50 53 60 70 75 77 78 79 80 81 82 84 89 90 91 Stem Leaf 5 53 6
7 77 78 75 79 8 81 89 82 84 9 91 Stem Leaf 5 3 6 7 7859 8 1924 9 1

Answers

The correct stem-and-leaf plot for the data is:

i. Stem: 5,6,7,8,9 Leaf: 3, , 5 7 8 9, 1 2 4 9, 1

This plot shows the distribution of the data values, with the stems representing the tens place and the leaves representing the ones place. For example, the value 53 is represented by the stem 5 and the leaf 3, and the value 82 is represented by the stem 8 and the leaf 2.

The other three stem-and-leaf plots are incorrect because they do not accurately represent the distribution of the data.

A stem-and-leaf plot is a graphical representation of data that shows the distribution of values. The stems represent the tens place and the leaves represent the ones place. It is useful for identifying patterns and trends in the data.

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Find the term t of each continuously compounded account below rounded to the nearest tenth of a year. In the chart, B is the
ending balance, P is the principal, and r is the interest rate expressed as a percent.

Answers

Therefore , the term t of each continuously compounded account  is 23.1 years.

What is compound interest ?

Compound interest is the practice of adding interest to the principal of a loan or deposit. It happens when interest is reinvested, added to the lent capital rather than paid out, or when the borrower is forced to pay it, resulting in interest being generated on the principal amount plus any accumulated interest the following period. Compound interest is frequently used in economics and finance.

Here,

A) To determine the account's annual growth rate, we must calculate the impact of continual compounding. Similar to the nominal rate (APR) and actual yield (APY) on a bank's interest-bearing account, the yield will be marginally greater due to compounding and indicate actual growth rather than growth rate. Note e is a very lengthy number that can be entered with as many digits as your calculator allows if you don't have a financial calculator handy. e = 2.71828183

A = P[tex]e^{rt}[/tex]  But for this, we only need to calculate growth or ert; we don't need to worry about P. When rounding in accordance with the instructions, we set t = 1 for a year and have er (or 2.71828183.03), which equals 1.03045, therefore the account increases by 3.05% annually.

B) 3000 = 1500[tex]e^{0.3t}[/tex]      [Divide both sides by 1500]

To isolate t, we must determine the natural logarithm of each side (e's natural logarithm is 1 and 2's natural logarithm is 0.693). 2 = e.03t

0,693 =.03t [Subtract both sides from .03]

23.1 = t

C) Using the formula from section A, first determine the original investment's worth after ten years. A = P A = 1500e.03*10 A = 1500e.3 A = 2,024.79

Next, use the yearly compounding formula to get the value of the second investment.

A = P(1+r)t

A = 1200(1+.045)10

A = 1,863.56

After ten years, the initial investment would be worth more.

Therefore , the term t of each continuously compounded account  is 23.1 years.

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Find the value of x.

Answers

Answer:

x=142

Step-by-step explanation:

47+95=x

x=142

the two angles equal x

In order to add
3/4 and 7/10
you need to find equivalent fractions that have the same denominators. What is a common denominator?

Answers

Thus ,after adding  3/4 and 7/10  we get 29/20 where 20 is common denominator

Describe the common denominator.

The smallest common multiple among the denominators of a group of fractions is known as the lowest common denominator (least common denominator) in mathematics. Fraction comparison, addition, and subtraction are made easier.

Here,

In order to add 3/4 and 7/10

we have to find LCM of 4 and 10

which comes out to be = 20

Thus,

addding =>  15+`14 /20

=>29/20

Thus ,after adding  3/4 and 7/10  we get 29/20 where 20 is common denominator

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Marquis sold gift-wrapping paper for a school fundraiser. He sold at least 15 rolls of paper. Write an inequality to represnet the amount of money, d, Marquis earned for the fund-raiser

Answers

The inequality to represent the amount of money, Marquis earned for the fund-raiser is d ≥ 15p

What is the inequality to represent the information?

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Let the cost of each paper be p.

Since Marquis sold gift-wrapping paper for a school fundraiser and he sold at least 15 rolls of paper.

An inequality to represent the amount of money, Marquis earned for the fund-raiser is:

d ≥ (15 × p)

d ≥ 15p

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segments in circles maze

Answers

Answer:

  x = 6

Step-by-step explanation:

You want to know the value of x given a tangent to a circle from an external point has length x, while a secant from that point has length x-2 to the first intersection with the circle, and an additional 5 to the second intersection.

Secant/Tangent relation

The product of the segments of the secant to the two points of intersection with the circle is equal to the square of the tangent segment.

  (x -2)(x -2 +5) = (x)² . . . . . use given values

  x² +x -6 = x² . . . . . . simplify

  x -6 = 0 . . . . . . subtract x²

  x = 6 . . . . . . add 6

__

Additional comment

There are rules for two secants, for a tangent and secant (as here), and for two chords internal to the circle. These can be easier to remember if you generalize them to a single rule: the product of the distance from the common point to the first circle intersection and the distance to the second circle intersection is the same for each segment.

For a tangent, the two circle intersections are the same point, hence the distance is squared. For chords, the two circle intersections are at the ends of the chords, and the common point is where the chords cross.

A pipeline has to be laid along the boundry of the garden.What do we need to know to find the total length of the pipe needed

Answers

Answer:

Step-by-step explanation:

To find the total length of the pipe needed to lay a pipeline along the boundary of a garden, you will need to know the following:

The shape and size of the garden: The total length of the pipe needed will depend on the shape and size of the garden. For example, if the garden is rectangular, you will need to measure the length and width of the garden to calculate the total length of the pipe needed. If the garden has a more complex shape, you will need to measure the lengths of all the straight sections of the boundary and add them together to find the total length.

The type of pipe being used: The total length of the pipe needed will also depend on the type of pipe being used. Different types of pipes come in different lengths and may require different quantities of fittings and connectors.

The route of the pipeline: The total length of the pipe needed will also depend on the route that the pipeline takes. If the pipeline has to go around obstacles or make sharp turns, it may require more pipe than if it follows a straight path.

The desired width of the pipeline: The total length of the pipe needed will also depend on the desired width of the pipeline. If the pipeline needs to be wider to accommodate multiple pipes or cables, it will require more pipe than if it is only a single pipe.

Any other specific requirements: There may be other specific requirements that will affect the total length of the pipe needed. For example, if the pipeline needs to be buried, you will need to account for the depth of the trench in your calculations.

A function is shown: f(x)= 2/3x+3
What is the value of f(18)?

Answers

Answer:

15

Step-by-step explanation:

When you see something like f (18), this means 18 needs to be plugged in for x

let's plug in 18

f (18) = [tex]\frac{2}{3} (18) + 3[/tex]

Let's solve

(18 × 2) ÷ 3 = 12

12 + 3 = 15

f (18) = 15

The value is of f(18) is 15.

NO LINKS!!
Find a logarithmic equation that relates y and x. (Round any numeric values to 3 decimal places.)

ln(y)=

x y
1 1.250
2 1.051
3 0.950
4 0.884
5 0.836
6 0.799

Answers

Answer:

[tex]\ln (y) = -0.250 \ln (x)+0.223[/tex]

Step-by-step explanation:

Given table:

[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12}x & y\\\cline{1-2} \vphantom{\dfrac12} 1 & 1.250\\\cline{1-2} \vphantom{\dfrac12} 2 & 1.051\\\cline{1-2} \vphantom{\dfrac12} 3& 0.950\\\cline{1-2} \vphantom{\dfrac12} 4& 0.884\\\cline{1-2} \vphantom{\dfrac12} 5& 0.836\\\cline{1-2} \vphantom{\dfrac12} 6& 0.799\\\cline{1-2} \end{array}[/tex]

To convert  y = axⁿ  to linear form, take natural logs of both sides and rearrange:

[tex]\begin{aligned}y=ax^n \implies \ln y &= \ln ax^n\\\implies \ln y &= \ln a + \ln x^n\\\implies \ln y &= \ln a + n \ln x\\\implies \ln y &=n \ln x+ \ln a\end{aligned}[/tex]

This is in the straight-line form y = mx + c.

Substitute the first values of x and y from the table into the natural log formula and solve for ln(a):

[tex]\implies \ln 1.250= n \ln 1+\ln a[/tex]

[tex]\implies \ln 1.250= n (0)+\ln a[/tex]

[tex]\implies \ln a = \ln 1.250[/tex]

[tex]\implies \ln a = 0.223\; \sf (3 \; d.p.)[/tex]

Substitute the found value of ln(a) and the last values of x and y from the table into the  natural log formula and solve for n:

[tex]\implies \ln 0.799= n \ln 6+\ln 1.250[/tex]

[tex]\implies n \ln 6=\ln 0.799-\ln 1.250[/tex]

[tex]\implies n =\dfrac{\ln 0.799-\ln 1.250}{\ln 6}[/tex]

[tex]\implies n =-0.250\;\sf (3 \; d.p.)[/tex]

Substitute the found values of n and ln(a) into the formula to create an equation for ln(y):

[tex]\boxed{\ln (y) = -0.250 \ln (x)+0.223}[/tex]

a quiz consists of 6 multiple-choice questions with 4 possible responses to each one. in how many different ways can the quiz be answered? (see example 7.)

Answers

His chances of correctly predicting an answer are 1/4.

He has a 3/4 chance of getting an answer incorrectly.

Binomial probability is defined.

A random variable is distributed binomially with parameters n, p more precisely if

It is the number of successes over n separate* trials, each of which has a chance of success of p.

What distinguishes possibility from probability?

Technically, the answer to whether an occurrence is possible is always "yes" or "no," or 1 or 0. Probability is the measure of how probable an event is to occur given the circumstances, assuming that it is feasible.

For instance, the likelihood of the number 5 appearing when we roll the dice is "Yes" (or 1), but the likelihood of the number 8 appearing is "No" (or 0).

Case 1: Guessing exactly 3 correct:

Choosing exactly 3 to get correct = Choosing exactly

3 to get wrong = 6C3 = (6*5*4)/(3*2*1) = 20 ways.

Guess the wrong answer for the first wrong one 3 ways.

Guess the wrong answer for the second wrong one 3 ways.

Guess the wrong answer for the third wrong one 3 ways.

That's 20*3*3*3 = 540 ways

Case 2: Guessing exactly 4 correct:

Choosing exactly 4 to get correct = Choosing exactly

2 to get wrong = 6C2 = (6*5)/(2*1) = 15 ways.

Guess the wrong answer for the first wrong one 3 ways.

Guess the wrong answer for the second wrong one 3 ways.

That's 15*3*3 = 135 ways

Case 3: Guessing exactly 5 correct:

Choosing exactly 5 to get correct = Choosing exactly

1 wrong = 6C1 = 6 ways.

Guess the wrong answer for the wrong one 3 ways.

That's 6*3 = 18 ways

Case 4: Guessing all 6 correct

There is only 1 way to guess them all correct

Total number of ways to pass: 540+135+18+1 = 694 ways to pass

Total number of ways to answer:

(4 ways to answer question 1) times

(4 ways to answer question 2) times

(4 ways to answer question 3) times

(4 ways to answer question 4) times

(4 ways to answer question 5) times

(4 ways to answer question 6) equals 4*4*4*4*4*4 = 46 = 4096

Probability of passing = 694/4096 = 347/2048 = 0.1694335938

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find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. 2-i, /3 f(x) =

Answers

The polynomial function is the product of three terms, each of which is a linear factor with a zero of 2-i, 1/3 respectively.

A polynomial function is a mathematical expression composed of constants and variables, and is used to model a wide variety of phenomena. The polynomial function can be expressed in terms of the factors of its zeros. In this case, the polynomial function of lowest degree with rational coefficients that has the given numbers 2-i, 1/3 as some of its zeros is (x+2)(x-i)(x-1/3). This polynomial can be expressed as the product of three terms, each of which is a linear factor with a zero of 2-i, 1/3 respectively. This means that when x is equal to 2-i or 1/3, the value of the polynomial function is zero. The linear factors are multiplied together to give the polynomial, and this is the simplest form of a polynomial that satisfies the given criteria. The polynomial can then be used to model a variety of phenomena by taking into account the different factors and their effects on the system.

f(x) = (x+2)(x-i)(x-1/3)

f(2-i) = (2-i+2)(2-i-i)(2-i-1/3)

f(2-i) = 0

f(1/3) = (1/3+2)(1/3-i)(1/3-1/3)

f(1/3) = 0

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find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. 2-i, /3 f(x) = (x+2)(x-i)(x-1/3)

The following expressions (-9a3b2 + 13ab5) and (-10ab5 + 12a3b2) represents the length and width of the pizza box respectfully. Find the perimeter of the pizza box. Express the perimeter of the pizza box in the order of descending exponents of a. Please use the palette below to input your answer.

Answers

The perimeter of the box has been obtained as 6a^3b^2 + 6ab^5.

What is the perimeter of the box?

We know that a box has the shape of a rectangle thus we would have to apply the formula for the area of a rectangle in this case and we would have;

P = 2(l + b)

P = perimeter

l =length

b = breadth

Then we have;

2[(-9a^3b^2 + 13ab^5) + (-10ab^5 + 12a^3b^2)]

Collect the like terms

2[(-9a^3b^2) + 12a^3b^2 + 13ab^5 +(-10ab^5)]

2[3a^3b^2 + 3 ab^5]

6a^3b^2 + 6ab^5

In  order of descending exponents of a, the perimeter is 6a^3b^2 + 6ab^5.

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Write an expression for the height, h, of a cylinder with a volume of 547 cubic inches
in terms of its radius, r.

Answers

The expression for the height (h) in terms of radius r is h = 547/(∏r²).

What is a cylinder?

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. In several contemporary fields of geometry and topology, a cylinder can alternatively be characterized as an infinitely curved surface.

Given that the volume of the cylinder is 547 cubic inches.

The volume of a cylinder is V = ∏r²h

Where r is the radius of the cylinder.

h is the height of the cylinder.

Putting V = 547, r = r and h = h in V = ∏r²h

547 = ∏r²h

∏r²h = 547

Divide both sides by ∏r²:

h = 547/∏r².

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Caroline baked cookies from a recipe that called for 3/4 cups of sugar she planned to triple the recipe how much sugar did she need?

Answers

The amount of sugar needed for the recipe to be tripled is 9 / 4 cups.

How to find the amount of sugar needed?

Caroline baked cookies from a recipe that called for 3/4 cups of sugar. she planned to triple the recipe. Therefore, the amount of sugar she needs is calculated as follows:

1 recipe = 3 / 4 cups of sugar

She wants to triple the recipe.

Hence,

1 recipe = 3 / 4 cups of sugar

3 recipe = ?

cross multiply

amount of sugar needed = 3 / 4 × 3

amount of sugar needed = 9 / 4

amount of sugar needed = 9 / 4 cups of sugars

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Hello, this is a Pythagorean math problem. Help pls.

Answers

The triangles 1, 2, 4, 7 and 8 are right triangles by Pythagorean relationship.

How to determine if a triangle is a right triangle

Triangles are closed figures formed by three line segments, a right triangle is a triangle with one right angle. Right triangles have a long side known as hypotenuse (r) and two shorter sides known as legs (x, y), whose Pythagorean relationship is shown below:

r = √(x² + y²)

Now we proceed to check whether each triangle is a right triangle or not:

Case 1:

D = √(8² + 6²)

D = 10 (YES)

Case 2:

D = √(5² + 12²)

D = 13 (YES)

Case 3:

D = √(12² + 9²)

D = 15 (NO)

Case 4:

D = √(8² + 15²)

D = 17 (YES)

Case 5:

D = √(4² + 9²)

D ≈ 9.849 (NO)

Case 6:

D = √(14² + 5²)

D ≈ 14.866 (NO)

Case 7:

D = √(20² + 15²)

D = 25 (YES)

Case 8:

D = √(24² + 10²)

D = 26 (YES)

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please help me i will give brainliest thank you so much

Answers

The answer is 10 hours!

The problem can be made into the equation 8X + 50 = 130, with X being the hours worked. This can be solved like this:
8X + 50 = 130
8X = 80
X = 10

Hope this helps!

Carla divided 28 bracelets equally among 4 friends. Then, she gave Megan 3 more bracelets. Which equation shows how many bracelets, b, Megan has now?

Answers

The required number of bracelets that in the given question are 10.

What is equation?

In math, the meaning of a  equation is a numerical explanation that shows that two numerical articulations are equivalent. For example, 3x + 5 = 14 is a condition, where 3x + 5 and 14 are two articulations isolated by an 'equivalent' sign.

According to question:

Carla divided 28 bracelets equally among 4 friends.

Number of bracelets each friends has = 28/4 = 7 bracelets

Then Carla gave 3 more bracelets to Magan.

So, Total bracelets Magan has = 7 + 3 = 10 bracelets

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Select all the expressions that are equivalent to 8-12-(6+4).
(Select all that apply.)
8-(6+4)-12
(6+4)-8-12
8-12-6-4
8-6-12+4

Answers

Answer:

8-(6+4)-12

8-12-6-4

Step-by-step explanation:

8-(6+4)-12 and 8-12-6-4 are equivalent expressions because they both compute to -6. This is because in both expressions, the 6+4 is calculated first, yielding 10. Then, the 8 is subtracted from 10, yielding -2. Finally, the 12 is subtracted from -2, yielding -6.

6+4)-8-12 is not an equivalent expression because it does not compute to -6. In this expression, the 6+4 is calculated first, yielding 10. Then, the 8 is subtracted from 10, yielding 2. Finally, the 12 is subtracted from 2, yielding -10.

8-6-12+4 is not an equivalent expression because it does not compute to -6. In this expression, the 8 is subtracted from 6, yielding -2. Then, the 12 is subtracted from -2, yielding -14. Finally, 4 is added to -14, yielding -10.

A concession stand sells hot dogs for $2 and cheeseburgers for $3. One day, 486 items were sold and the owners earned $1218.
How many hot dogs and cheeseburgers were sold?

Answers

The Total Number of Hot Dogs sold were 240 and Cheese Burgers sold were 246

What is Linear Equation in Two Variables?

A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

Let, Number of Hot Dogs Sold = x

Number of Cheese Burgers Sold = y

According to the Question:

x + y = 486 ----------(i)

2x + 3y = 1218 ----------(ii)

Multiplying Equation (i) by 2

2x + 2y = 972 ----------(iii)

Substracting Equation (iii) from Equation (ii)

y = 246

x = 240

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Which of these expressions is equivalent to log(16 • 14)?
CA. 16 log (14)
OB. log(16)+ log(14)
C. log(16) log(14)
D. log(16)-log(14)

Answers

The equivalent expression of log(16 × 14) is log 16 + log 14.

How to find equivalent expression?

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

Equivalent expressions are expressions that have similar value or worth but do not look the same.

Therefore, the equivalent expression of log(16 × 14) can be found as follows:

using logarithm law,

The log of a product is the sum of the logs.

logₐ xy = logₐ x + logₐ y

Therefore,

log(16 × 14) = log 16 + log 14

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Point A is located at (5, 6). Find the coordinates of the image A' after the
point is reflected across the x-axis.
(5,-6)
(-5,6)
(-5, -6)
(5,6)

Answers

Answer:

Step-by-step explanation:

Point A = (5, 6)  is reflected across the x axis which is y =0.

When the point is reflected across the x axis, the x coordinate

remains positive, but the y coordinate becomes negative.

The 6 becomes negative (-6).

So the coordinates of A' are (5, -6) which is the first answer.

II. Given that cos A = 0.42 and sin B = 0.73, evaluate
i. sin (A – B)
ii. cos (A – B)
iii. tan (A + B)

Answers

The trigonometric identities values are;

i. sin (A – B) = -0.15

ii. cos (A – B) = 0.5368

iii. tan (A + B) = -3.536

How to solve trigonometric Identity?

We are given;

cos A = 0.42

sin B = 0.73

Since cos A = 0.42 , then sin A = 0.58

Since sin B = 0.73, then cos B = 0.27

i) sin (A – B)

By trigonometric identities, we know that;

sin (A – B) = sinA cos B - cosA sinB

Thus;

sin (A – B) = (0.58 * 0.27) - (0.42 * 0.73)

sin (A – B) = -0.15

ii)  cos (A – B)

By trigonometric identities, we know that;

cos (A – B) = cosA cosB + sinA sinB

cos (A – B) = (0.42 * 0.27) + (0.58 * 0.73)

cos (A – B) = 0.5368

iii) tan (A + B)

By trigonometric identities, we know that;
(tan A + tan B)/(1 - tanAtanB)

tan A = sinA/cosA = 0.58/0.42 = 1.389

tan B = sinB/cosB = 0.73/0.58 = 1.259

Thus;

tan (A + B) = (1.389 + 1.259)/(1 - (1.389 * 1.259))

tan (A + B) = -3.536

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5 - 2x^2+y^3 =-x^3 -3y then find (dy)/(dx) at the point (3,-2)

Answers

The value of the differentiation dy / dx will be 13 / 5.

What is calculus?

Calculus, also known as infinitesimal calculus or "the calculus of infinitesimals," is the mathematical study of continuous change, similar to how geometry studies shape and algebra studies generalizations of arithmetic operations.

Given that the expression is 5 - 2x²+y³ =-x³ -3y. The coordinate is (3,-2).

The value of dy / dx is calculated as,

5 - 2x²+y³ =-x³ -3y.

Differentiate the above equation with respect to x,

5 - 2x²+y³ =-x³ -3y

-4x + 3y² dy /dx = 3x² -3dy / dx

-4x - 3x² = (-3y² -3)dy/dx

dy /dx = [-4x - 3x²] / [ (-3y² -3) ]

Substitute the value of x and y in the above equation,

dy /dx = [-4x - 3x²] / [ (-3y² -3) ]

dy /dx = [-4 x 3- 3(3)²] / [ (-3(-2)² -3) ]

dy / dx = [ -12 - 27 ] / [ -15]

dy /dx = -39 /- 15 = 13 / 5

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