The following is a stem-and-leaf display representing the amount of gasoline purchased, in gallons (with leaves in tenths of gallons), for a sample of 25 cars that use a particular service station on the New Jersey Turnpike: 9 147 10 02238 11 125566777 12 223489 13 02 (a) Construct an ordered array. (b) Which of these two displays seems to provide more information? Discuss

To prove that (4x - 5)^2 - 5x(3x - 8) is positive for all values of x, we can start by expanding the expression:

(4x - 5)^2 - 5x(3x - 8) = 16x^2 - 40x + 25 - 15x^2 + 40x = -14x^2 + 80x - 25

Now, we can complete the square to find that this expression is always positive:

-14x^2 + 80x - 25 = (-14x^2 + 80x) - 25

= (-14x^2 + 80x + (80/2)^2 - (80/2)^2) - 25

= (-14x + 40)^2 - 25 - 40^2 + 40^2

= 15^2 - 25

= (15 - 5)(15 + 5)

= 10(20)

= 200

Since this expression is equal to 200, which is a positive number, we can conclude that (4x - 5)^2 - 5x(3x - 8) is positive for all values of x.

Answer:

37

Hope this helps :)

Answer:

60 × 40 = 2,400

I hope this helped.

Answer: 2400 people would come in 40 days

Step-by-step explanation:

If 60 people came on 1 day, that is the unit rate

60 to 1

So, just multiply 1 by 40 and 60 by 40

2400 to 40

Therefore, 2400 is the answer

The dot plot in option E is correct.

What is sample size?

Choosing the number of observations or replicates to include in a statistical sample is the process of determining sample size. Any empirical study whose objective is to draw conclusions about a population from a sample must take the sample size into consideration.

Finding your sample size in five steps

Clarify the term "population size" or "people"

Specify your error margin.

Decide how confident you are.

Calculate the expected variance.

Decide on the sample size.

As long as it doesn't go over 1,000, 10% of the population serves as a good maximum sample size.

The dot plot in option E is correct.

Because we conduct 50 trials, dot plot should have 50 points, one point per each trial.

On X axis, we take no. of successes out of 10.

Hence it having 0 to 10 numbering.  

Hence, the dot plot in option E is correct.

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The two lines intersect at (-3,-5) and thus a common solution.

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

Given here, the system of linear equations as  Y=4x+7 and 2=x-y

On solving these two equations we get that the two lines intersect at (-3,-5) and thus a common solution.

The two equations are plotted in the attachment below.

Hence, The two lines intersect at (-3,-5) and thus a common solution.

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Answer:

d. y=8x

Step-by-step explanation:

since y = the number of legs and spiders = x

each spider has 8 legs

so y = 8*x

which is y=8x

After a work out, the simplest form of e:g is 3:10.

Ratio is an expression which shows the relationship between two numbers or variables. It can generally be expressed in two forms, viz; a:b or a/ b.

To work out the simplest form of e:g as required in the question,

e/ f = 2/ 5

2f = 5e ........... 1

f/g = 3/ 4

3g = 4f ........... 2

From equation 1,

f = 5e/2

substitute the value of f in equation 2

3g = 4(5e/2)

3g = 10e

Therefore, e:g is given as;

3/ 10 = e/ g

3:10 = e: g

Thus in its simplest form, e:g = 3:10

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A polynomial in which the degrees of all the variables is 0 is called a zero degree polynomial .

The zeros of a polynomial p(x) are all the x-values that make the polynomial equal to zero.

For example- 6 x 0 , − 9 a 0.

Polynomial

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division .

Degree of polynomial

The degree of a polynomial is defined as the highest exponent of a monomial within a polynomial. Thus, a polynomial equation having one variable which has the largest exponent is called a degree of the polynomial .

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Probability that the calendar turned to month of May or June is 1/6.

Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.

The value of probability will be always in the range from 0 to 1.

Total number of months = 12

Suppose that a calendar is turned.

Probability that the calendar turned to month of May = 1/12

Probability that the calendar turned to month of June = 1/12

Probability that the calendar turned to month of May or June = 1/12 + 1/12

                                                                                                      = 2/12

                                                                                                      = 1/6

Hence the probability that the calendar turned to month of May or June is 1/6.

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The scientific notation to express the mass of 60 cows is 2.46 × 10⁴ kg. It is determined after multiplying the mass of one cow by the number of cows.

Scientific notation is a way of expressing very small or very large numbers in a simpler form.

In scientific notation, the number is written as

a.b × 10ⁿ

Where

If the mass of one cow is 410 kg, find the mass of 60 cows in scientific notation!

The mass of 60 cows would be

= number of cows × mass of one cow

= 60 × 410 kg

= 24,600 kg

In scientific notation, it is

24,600 kg = 2.46 × 10,000

24,600 kg = 2.46 × 10⁴ kg

Hence, the mass of 60 cows in scientific notation is 2.46 × 10⁴ kg.

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The answers to these partial divisions add up to 30 + 2 = 32, or 192/6. We can calculate the solution by dividing 32 by 100, or 0.32, to get 1.92/6.

The formula for computing 1.92 divided by 6 is 1.92 multiplied by 100, divided by 100, and then multiplied by 1.92. There are 18 tenths and 12 ones in 1.92*100 = 192, which is the result. Due to the fact that both 18 and 12 are multiples of 6, this representation is practical.

Then, we can divide 18 tenths by six to get three tenths (30), and we can divide 12 ones by six to get two ones (2). 30 + 2 = 32, or 192/6, is the result of adding the answers to these partial divisions. To get 1.92/6, divide 32 by 100, which is 0.32, and that gives us the answer.

The complete question is:

Janice is dividing 1.92 divided by 6. Why does she exchange the place value blocks shown for 18 tenths and 12 ones ?​

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The answers to these partial divisions add up to 30 + 2 = 32, or 192/6. We can calculate the solution by dividing 32 by 100, or 0.32, to get 1.92/6.

The formula for computing 1.92 divided by 6 is 1.92 multiplied by 100, divided by 100, and then multiplied by 1.92. There are 18 tenths and 12 ones in 1.92*100 = 192, which is the result. Due to the fact that both 18 and 12 are multiples of 6, this representation is practical.

Then, we can divide 18 tenths by six to get three tenths (30), and we can divide 12 ones by six to get two ones (2). 30 + 2 = 32, or 192/6, is the result of adding the answers to these partial divisions. To get 1.92/6, divide 32 by 100, which is 0.32, and that gives us the answer.

The complete question is:

Janice is dividing 1.92 divided by 6. Why does she exchange the place value blocks shown for 18 tenths and 12 ones ?​

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The height in feet of its replica at this park, rounded to the nearest whole number is 14 feet.

Distance is the measurement of an object's horizontal distance from a specific location, whereas height is the measurement of an object's height in the vertical direction.

Since the heights of real buildings are 1:10 times higher than those of model buildings, this is evident. We also know that the actual height of the US Capitol is 289 feet, so we divide that figure by 20 to determine the model's height. That amounts to 14.45, rounding to 14. Thus, the duplicate is 14 feet, rounded up to the nearest whole number.

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Answer:

option D is correct

5.7+x=-3.5

x= -3.5-5.7

Answer:

D

Step-by-step explanation:

5.7 + x = - 3.5 ( subtract 5.7 from both sides )

x = - 3.5 - 5.7 ( x = - 9.2 )

The shorter side should be 200 ft and the longer side should be 200 ft. This would give the garden the greatest possible area of 40,000 square-feet.

1. The area of a rectangle can be calculated by multiplying the length and width together.

A = L * W

2. We know that the total amount of fencing is 400 ft.

3. We also know that one side of the garden is a river and so it doesn't require fencing.

4. Therefore, the remaining fencing must be divided equally between the two other sides of the garden (200 ft per side).

5. We now know that the length and width of the garden are both 200 ft.

6. Plugging these values into the area equation, we get:

A = 200 ft * 200 ft = 40,000 sqft

7. Therefore, the greatest possible area of the garden is 40,000 square-feet..

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Based on the information provided, Qamar will have enough lacquer to cover the floor and 24 square feet will be left over.

Based on the information given, Qamar has 600 square feet.

To calculate the total lacquer Qamar needs, it is necessary to calculate the area of the floor that has to be covered. In the case of a parallelogram, the area can be calculated using the following formula:

Now, if the total of material available is 600 feet, it can be concluded there is enough material to cover this floor. Let's calculate the lacquer left over:

Note: This question is incomplete; here is the missing information:

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Answer:

12.

Step-by-step explanation:

right!!

Inversely proportional graphs are reciprocal graphs consisting of one smooth curve in the first quadrant only.

When one quantity grows, the other quantity decreases, and vice versa, this is known as an inverse proportion. Indirect proportion is another name for inverse proportion.

Consider a task like painting a fence as an illustration. The amount of time it takes to complete the task lowers as the number of employees rises. The amount of time it takes to complete the task grows as the number of workers reduces.

If y  is inversely proportional to x then we write y = 1/x

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Answer:

  -4/17

Step-by-step explanation:

You want the slope of the line described by the equation 20x +85y = 120.

Putting the equation in slope-intercept form by solving for y gives ...

  20x +85y = 120

  85y = -20x +120

  y = -20/85x +120/85

  y = -4/17x +24/17

The slope is the coefficient of x: -4/17.

The rate of change is -4/17.

Answer: 19

Step-by-step explanation:

56-13=43

43-24=19

Answer: 19

Step-by-step explanation: 13 + 24 = 37

so (56 - 37 = 19)

The water level is rising at a rate of 0.5tf² /min*ft². This is in cubic feet per minute per square feet, if you want to express this in terms of height, you will have to convert the units

To find out how fast the water level is rising, we need to use the concept of volume flow rate. Volume flow rate is the volume of fluid that passes through a given surface per unit of time. In this case, the volume flow rate is given as 3tf^3/min.

Since the base of the tank is a rectangle with dimensions 2x3 ft, we can find the area of the base by multiplying the length and width:

2 ft * 3 ft = 6 ft^2

To find the rate of change of the water level, we need to divide the volume flow rate by the area of the base.

3tf^3/min / 6 ft^2 = 0.5tf^3/min*ft^2

So the water level is rising at a rate of 0.5tf^3/min*ft^2

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By setting up the equation and solving we get the positive number is 2/5.

A positive number is a number greater than zero. In mathematical terms, it is a number that is greater than zero on the number line. Positive numbers are often represented with a "+" sign in front of them, but this is not always necessary as the positive sign is the default and is usually omitted.

An equation is a mathematical statement that asserts the equality of two expressions. It is a statement that asserts that the two expressions on either side of the "=" sign are equal and have the same value. The expressions on either side of the "=" sign are called the left-hand side (LHS) and the right-hand side (RHS) of the equation.

For example:

2x + 3 = 7

x(2x+x/2)=x

2x^2+x^2/2=x

5x^2/2=x

5x^2=2x

5x=2

x=2/5

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The midpoint of the x-intercepts of f(x) = (x - 4)(x + 4) is (0, 0).

The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.

A compass and straightedge setup can be used to locate the midpoint of the line segment they determine given two points of interest. By initially building a lens out of circular arcs with equal radii centered at the two endpoints and joining the cusps of the lens, one can determine the midpoint of a line segment immersed in a plane. The midpoint of the segment is then the place where the line joining the cusps intersects the segment.

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A positive second derivative means that the solution curve is concave up. Therefore, all solution curves for the given differential equation in Quadrant II are concave up.

(b) To find the second derivative of y with respect to x, we can use the chain rule. Since y is a function of x, we have [tex]dy/dx = f(x) and d^2y/dx^2 = d/dx(dy/dx) = d/dx(f(x)) = f'(x).[/tex]

To find f'(x), we can use the product rule and the given differential equation:

[tex]f'(x) = d/dx(xy^4) = y^4 + xy^4dy/dx = y^4 + xy^4f(x)[/tex]

Now, to determine the concavity of the solution curves, we need to find the sign of f'(x).

In Quadrant II, x and y are both positive, so [tex]x*y^4[/tex] is positive. Therefore, f'(x) is positive as well.

A positive second derivative means that the solution curve is concave up. Therefore, all solution curves for the given differential equation in Quadrant II are concave up.

(c) To find a particular solution to the differential equation with the given initial condition, we can use separation of variables.

The equation can be rewritten as [tex]dy/y^4 = x dx[/tex]

Integrating both sides gives:

[tex]\int\limits^ {} \,dy/y^4 = \int\limits^ {} \, dx* dx\\-1/y^3 = (x^2)/2 + C\\y^3 = -1/(x^2/2 + C)\\y = (-1/(x^2/2 + C))^(1/3)[/tex]

Using the initial condition f(4) = -1, we can find the value of C:

[tex](-1) = (-1/(4^2/2 + C))^(1/3)\\(-1)^3 = -1/(4^2/2 + C)\\-1 = -1/(16/2 + C)\\C = 15/2[/tex]

So the particular solution is:

[tex]y = (-1/(x^2/2 + 15/2))^(1/3)[/tex]

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Complete question is: Consider the differential equation dy/dx=xy^4.

(b) Find ⅆ2yⅆx2 in terms of x and y. Determine the concavity of all solution curves for the given differential equation in Quadrant II. Give a reason for your answer.

(c) Find the particular solution y=f(x) to the given differential equation with initial condition f(4)=−1.

Therefore, if the cafeteria sells all of the pancakes made for 75 people, they will make $525.

The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. How to determine the value of one pen, for instance, if the cost of 40 pens is Rs. 400. The unitary method can be used to complete it.

Two quantities are compared to form a ratio. An equality of two ratios is a percentage. How to format a ratio Analyze the ratio to see whether it is part to part or part to whole. Calculate the whole and the pieces as necessary.

If the cafeteria sells all of the pancakes made for 75 people, and the original recipe makes 14 pancakes, they would need to make 1475 = 1050 pancakes.

If they charge $0.50 per pancake and they sell all 1050 pancakes, they would make 1050$0.50 = $525.

Therefore, if the cafeteria sells all of the pancakes made for 75 people, they will make $525.

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on solving the provided question, we can say that - the graphs which is shown as the straight line graph.

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

here,

then line which is drawn is straright,

so the graph is straight .

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Answer:

68

Step-by-step explanation:

25% of a number is 20, where the number is 80 because 25% times 4 is 100% and 20 times 4 is 80.

We can check by doing 60% of 80 to see if it is 48. Instead of 60%, we can do 10% of 80, which is 8. Since we divided by 6, we multiply 8 by 6 which is 48.

Since we know 80 is the number, we have to find 85% of 80. First, let's find 5% of 80, which is 4 since 4 x 20 is 80 and 5% x 20 is 100%. Now, 85 divided by 5 is 17, let's multiply 17 by 4 to get 85% of 80. 17 x 4 is 68 which is 85% of 80.

Answer:

2.7n + 6.6 or 6.6 + 2.7n

Step-by-step explanation:

Algebraic Expressions are just like Numerical Expressions but instead of numbers, alphabets are used, these alphabets can also be used as variables. (BODMAS rule applies to Algebraic Expressions as well.)

Eg. 45x + 31x(2) = 45x + 62x = 107x

Given from the question:

[tex]0.3(9n + 22) \\ = 2.7n + 6.6 \: or \: 6.6 + 2.7n[/tex]

Solved equation is, x = 4/3 + 2y/3

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.

here we have,

Write equation

6x - 4y = 8

Then,

Solve for x

Add 4y to both sides: 6x = 8 + 4y

Divide both sides by 6: x = 8/6 + 4y/6

Simplify: x = 4/3 + 2y/3

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Following are the mathematical operations for the numerics.

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands.

In mathematics, addition, subtraction, multiplication, division, and modular forms are the five basic operations.

Calculating a value using operands and a math operator is referred to as performing a mathematical "operation." The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers. Image: The basic mathematical operation symbols. A set of numbers and operations make up a mathematical expression.

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