You have $30 to buy baseball cards. Each pack of cards costs $5. Write and solve an
inequality that represents the numbers of packs of baseball cards you can buy and
still have at least 40% of your money left.

divide cost by quantity. The lowest rate is the best buy:

26/8 = 3.25 each

30/5 = 6.00 each

15/4 = 3.75 each

39/12 = 3.25 each

45/10 = 4.50 each

The 8 for 26 and the 12 for 39 are both the same price each and are the better buys.

Given :

A mountain climber started his climb at 50 feet above see level .

He then raised 3 feet to rest in his cot to make his final 10 feet climb down.

To Find :

An expression to find his position relative to his final position.

Solution :

Let , final position is h .

h is given by :

\(h=\text{(Initial position)-(initial descended)+(height raised to rest)-(final descended)}\\\\h=50 -28 +3-10\ feet\\\\h=15\ feet\)

So , his final position is 15 feet .

Hence , this is the required solution .

Answer:

42m

Step-by-step explanation:

Let's call the rectangle ABCD. Since this is a rectangle, the triangles inside this rectangle (ΔACD and ΔABD) are both right triangles because of the definition of a rectangle. In addition, AB = CD and AC = BD because of the definition of a rectangle. Since AD = 15 (The Diagonal), you can say that because of Pythagorean Triples that AC = 9 and CD = 12 (3 : 4 : 5 = 9 : 12 : 15). Since we stated that AB = CD and AC = BD, we can say that the perimeter of ABCD is equal to 9 + 9 + 12 + 12. 9 + 9 + 12 + 12 is equal to 42.

Therefore: Perimeter of ABCD = 42

The point that should an open circle be drawn exists (0, 0).

The first equation in the system is f(x) = -x, for x < 0.  

This means when x=0, f(x) = f(0) = 0.

Since we have the inequality x<0, this means at the point (0, 0),

the point will be open and not filled in.

Therefore, the correct answer is option b) (0, 0).

The complete question is:

The function f(x) is to be graphed on a coordinate plane

At what point should an open circle be drawn?

a) (–1, 0)

b) (0, 0)

c) (0, 1)

d) (1, 0)

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Answer

This should be it, ask me for any concerns that you may have

The integral to find the volume V is then:

V = ∫[0 to L] 144 dx

What is volume of the solid?

The volume of a solid is a measure of how much area of ​​space an object occupies. It is measured by the number of unit cubes needed to fill the body. It is decided by counting the unit cubes in the solid.

To find the volume of a solid, we need to consider parallel cross-sections perpendicular to the x-axis. Since these cross-sections are square, each square cross-section will have the same area throughout the body.

Consider a representative square cross-section at a given x-coordinate. The length of each side of this square will be equal to the diameter of the corresponding circular disc at this x-coordinate. Since the radius of a circular disk is given as 6, the diameter will be twice the radius, which is 12.

Therefore, the area of ​​a square cross-section at any coordinate is x (12)^2 = 144 square units.

To find the volume of a body, we must integrate the areas of all these square cross-sections over the range of values ​​of x that the body occupies. Since no specific range is mentioned in the information provided, I will assume that the body extends from x = 0 to x = L, where L is the length of the body along the x-axis.

The integral to find the volume V is then:

V = ∫[0 to L] 144 dx

Note: dx represents an infinitesimal change in x.

Note that this integral is just a setup and the actual evaluation of the integral is not required in the question.

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Answer:

I would say Jessica

Step-by-step explanation:

Because Mia's grade dropped by 4% and Jessica's grade increased by 5%

1% difference in the grades

The two expressions are:

The greatest common factor of the two expressions is found below:

The greatest common factor of the two expressions is 4x²u⁴

Answer:

3

Step-by-step explanation:

when two lines are parallel, they have the same slope

you can find slop by changing the equation to slope intercept form (y=mx+b), m being the slope

slopes:

1. -2

2. -1/2

3. 2

4. 1/2

Answer:

3. y-2x=-8

Step-by-step explanation:

solution of the inequality is r>4/3.

An inequality is a mathematical statement that compares two values or expressions, indicating that one is greater than, less than, or not equal to the other. Inequalities are expressed using symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

Inequalities can also involve variables, and solutions to such inequalities are the sets of values of the variable that make the inequality true. For example, the inequality 2x + 3 < 7 states that 2x + 3 is less than 7, and solving for x gives the solution x < 2.

Given inequality

2>6-3r

Solving the inequality

2-6>-3r

-4>-3r

r>4/3

Hence, solution of the inequality is r>4/3

Image of the inequality is attached below.

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The importance of destroyers is given. The destroyer serves as the battleship's night watchman.

Designed to accompany larger ships in a fleet, convoy, or battle group to defend them against powerful, close-range attacks, destroyers are swift, maneuverable, long-endurance warships.

A destroyer is a quick, nimble, long-endurance warship that is designed to accompany bigger ships in a fleet, convoy, or battle group and protect them against strong, close-range assaults.

The destroyer serves as the battleship's night watchman, and the number required to keep it safe relies directly on the number of assault torpedo vessels that may be used by a potential opponent.

Battleships are significantly slower and less adaptable than destroyers, which are also far less expensive to build and operate.

You may construct more than ten destroyers for the price of one battleship.

Destroyers may work alone or as a team with Expeditionary Strike Groups, Surface Action Groups, and Carrier Strike Groups.

Therefore, the destroyers are important for any naval army.

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There are a total of 273 ways of ascending the grand staircase using the same rules as the priestess.

A combination is a selection of all or a portion of a group of items, regardless of the sequence in which the items are chosen.

A).;

The priestess has to ascend a flight of 5 steps each day, and she can do so by taking one or two steps at a time.

Let's consider the possible combinations of steps she can take:

1-1-1-1-1

1-1-1-2

1-1-2-1

1-2-1-1

2-1-1-1

1-2-2

2-1-2

2-2-1

There are 8 possible ways of ascending the 5 steps, which means the priestess can ascend the steps in a different way each day for a week.

B) The grand staircase has 13 steps, and the priest wants to know if he can climb it in a different way each day for a year using the same rules as the priestess.

Let's consider the number of possible combinations of steps the priest can take:

If he takes 1 step at a time, he can climb the staircase in 1 way (all 1s).

If he takes 2 steps at a time, he can climb the staircase in 1 way (all 2s).

If he takes 3 steps at a time, he can climb the staircase in 2 ways (1-1-1-1-1-1-1-1-1-1-1-1-1 and 1-1-1-1-1-1-1-1-1-2-2-2).

If he takes 4 steps at a time, he can climb the staircase in 4 ways (1-1-1-1-1-1-1-1-2-2-2-2 and three other combinations).

If he takes 5 steps at a time, he can climb the staircase in 6 ways.

If he takes 6 steps at a time, he can climb the staircase in 10 ways.

If he takes 7 steps at a time, he can climb the staircase in 14 ways.

If he takes 8 steps at a time, he can climb the staircase in 21 ways.

If he takes 9 steps at a time, he can climb the staircase in 29 ways.

If he takes 10 steps at a time, he can climb the staircase in 41 ways.

If he takes 11 steps at a time, he can climb the staircase in 55 ways.

If he takes 12 steps at a time, he can climb the staircase in 76 ways.

If he takes 13 steps at a time, he can climb the staircase in 1 way (all 13s).

Therefore, there are a total of 273 ways of ascending the grand staircase.

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Answer:28

Step-by-step explanation:

Break it up! 6x3 is 18. Then 18 + 10 is 28 :P

Hope this helps :D

Answer:

Here,

SP with VAT = Rs. 99000

Discount = 10%

VAT = 10%

Discount Amount =?

VAT Amount = ?

We know,

SP = "100" /"100 + v% "  × SP with VAT    

 = "100" /"100 + 10 "  × 99000    

= "100" /"110 "  × 99000      

= Rs. 90000 ∴   VAT Amount = SP with VAT – SP    

= Rs. 99000 – 90000    

= Rs. 9000 Again,  MP = "100" /"100 – d% "  × SP      

=  "100" /"100 – 10 "  × 90000      

=  "100" /"90"  × 90000      

= Rs. 100000

∴   Discount Amount = MP – SP          

= Rs. 100000 – 90000          

= Rs. 10000

Step-by-step explanation:

Here is the list of all formulas on MP, Discount, SP, and VAT.

1. Discount Amount = Discount % of MP    

2. Discount % = (Discount Amount)/MP  ×100%      

3. SP = MP – Discount Amount    

4. SP = (100 - d%)/(100 )  × MP    

5. MP = 100/(100 - d% )  × SP  

 6. VAT amount = VAT percent of SP    

7. VAT percent = (VAT Amount)/SP  ×100%  

 8. SP with VAT = SP + VAT amount    

9. SP with VAT = (100 + v%)/(100 )  × SP    

10. SP = 100/(100 + v% )  × SP with VAT  

 11. MP = (100 × 100)/((100 - d%)(100 + v%))  × SP with VAT    

12. SP with VAT = ((100 - d%)(100 + v%))/(100 × 100)  × MP

Answer: 700

Step-by-step explanation:

Answer:

700

Step-by-step explanation:

copy and paste

The gradient field F = ∇Φ for the potential function Φ(x, y, z) = ln(2x^2 + y^2 + z^2) is given by F(x, y, z) = (4x / (2x^2 + y^2 + z^2), 2y / (2x^2 + y^2 + z^2), 2z / (2x^2 + y^2 + z^2)).

To find the gradient field F = ∇Φ, we need to take the partial derivatives of the potential function Φ(x, y, z) = ln(2x^2 + y^2 + z^2) with respect to each variable x, y, and z.

Taking the partial derivative with respect to x, we get:

∂Φ/∂x = (4x) / (2x^2 + y^2 + z^2)

Similarly, taking the partial derivative with respect to y, we have:

∂Φ/∂y = (2y) / (2x^2 + y^2 + z^2)

And taking the partial derivative with respect to z, we obtain:

∂Φ/∂z = (2z) / (2x^2 + y^2 + z^2)

Combining these partial derivatives, we have the gradient field F = ∇Φ:

F(x, y, z) = (4x / (2x^2 + y^2 + z^2), 2y / (2x^2 + y^2 + z^2), 2z / (2x^2 + y^2 + z^2))

Therefore, the gradient field for the given potential function is F(x, y, z) = (4x / (2x^2 + y^2 + z^2), 2y / (2x^2 + y^2 + z^2), 2z / (2x^2 + y^2 + z^2)).

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The quantitative variables that can be identified from the problem are Median age of town, Average weekly sales, and Median income of town.

The units for Median age of town is years, Average weekly sales is dollars, and Median income of town is dollars.The remaining options City, Whether or not the store sells liquor, Type of food, and Town area have not specified the units and therefore are not quantitative variables. Quantitative variables are variables that are measured on a numerical scale. The problem in this question provides a list of options and asks to select the options that identify quantitative variables and specify their units. The following quantitative variables can be identified from the problem:Median age of town: Median age of town is a quantitative variable since it is measured in years. The median age of the town is the middle value of the ages of the population of the town. The unit for median age is years since it is a numerical scale that represents the age of the population in years.Average weekly sales: Average weekly sales is a quantitative variable since it is measured in dollars. The average weekly sales represent the mean sales of a store over a week, which can be calculated by dividing the total sales by seven. The unit for average weekly sales is dollars since it is a numerical scale that represents the currency value of sales.Median income of town: Median income of town is a quantitative variable since it is measured in dollars. The median income of the town is the middle value of the income of the population of the town. The unit for median income is dollars since it is a numerical scale that represents the income value of the population.

The units of quantitative variables are essential as they provide a measure of the scale of the variable. In this problem, the quantitative variables identified were Median age of town, Average weekly sales, and Median income of town. The units of these variables are years, dollars, and dollars, respectively. The remaining options do not specify the units and hence cannot be classified as quantitative variables.

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Answer:

This gives us a square with an area of 225 square units.

Step-by-step explanation:

To find the dimensions of the rectangle with the largest area for a given perimeter of 60, we need to use the formula for the perimeter of a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.

In this case, we know that P = 60, so we can write:

60 = 2l + 2w

Simplifying this equation, we get:

30 = l + w

To find the largest area of the rectangle, we need to maximize the product of the length and the width, which is the formula for the area of a rectangle, A = lw.

We can solve for one variable in terms of the other using the equation above. For example, we can write:

w = 30 - l

Substituting this expression for w into the formula for the area, we get:

A = l(30 - l)

Expanding and simplifying this expression, we get:

A = 30l - l^2

This is a quadratic equation in l, which has a maximum value when l is halfway between the roots. We can find the roots using the quadratic formula:

l = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = -1, b = 30, and c = 0, so we get:

l = (-30 ± sqrt(30^2 - 4(-1)(0))) / 2(-1)

Simplifying, we get:

l = (-30 ± sqrt(900)) / -2

l = (-30 ± 30) / -2

So the roots are l = 0 and l = 30. We want the smaller value first, so we take l = 0 and find w = 30. This would give us a rectangle with zero area, so it is not a valid solution.

The other root is l = 30, which gives us w = 0. Again, this is not a valid solution because we need both dimensions to be positive.

Therefore, the dimensions of the rectangle with the largest area for a perimeter of 60 are:

l = 15 and w = 15

This gives us a square with an area of 225 square units.

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The distance bewteen the points (-3,5) and (3,1) in a simple radical form is 2√13.

The distance formula used in finding the distance between two points is expressed as;

d = √( ( x₂ - x₁ )² + ( y₂ - y₁ )² )

From the graph;

Point A: (-3,5)

x₁ = -3

y₁ = 5

Point B: (3,1)

x₂ = 3

y₂ = 1

Plug the given values into the distance formula and simplify.

\(d = \sqrt{( x_2 - x_1)^2 + (y_2 -y_1 )^2} \\\\d = \sqrt{( 3-(-3))^2 + (1 -5)^2} \\\\d = \sqrt{( 3+ 3)^2 + (1 -5)^2} \\\\d = \sqrt{( 6)^2 + (-4)^2} \\\\d = \sqrt{36 + 16} \\\\d = \sqrt{52}\\\\d = 2\sqrt{13}\)

Therefore, the distance between the points is 2√13.

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The correct system of equations is A. x+y=1212 and x-y=518.

Let us assume the two numbers to be x and y. Based on the first statement, the equation will be:

x + y = 1212

Based on the second statement, the equation will be:

x - y = 518

Using the equation to find the value of x and y

Adding these two equations. We get -

2x = 1730

x = 1730 ÷ 2

Performing division

x = 865

Keeping the value of x in first equation to find the value of y

y = 1212 - 865

Performing subtraction

y = 347

Thus, the system of equations that can solve this problem are: x+y=1212 and x-y=518.

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The complete question is attached in figure.

Answer:

Step-by-step explanation:

Finding an equation of a line can be condensed into 2 easy steps.  Step one is to establish the basic form of the equation, including it's slope.  

1)  Lets use y=mx + b as the basic form, where m is the slope and b is the y-intercept (the value of y when x is zero).  We are told the line is parallel to y = 3x - 1, which is a line with a slope (m) of 3.  Parallel lines have the same slope, so our kline will also have a slope of 3, bringing us to:

   y = 3x + b.

2)  The second step is finding the value of b.  We are told the line must go through point (1,5), so we need a value of b that will shift the line to (1,5).  Easy:  just enter this point in the equation we have so far:  y = 3x + b:

y = 3x + b

5 = 3*(1) + b for point (1,5)

b = 2

The equation becomes y = 3x + 2

See the attached graph.  [Extra credit]

The lines are parallel, and the y-intercept for the second line (b) is (0,2).

Answer:

himself: grandmother: neighbor: total

3                       3                   6           12

Step-by-step explanation:

himself: grandmother: neighbor: total

1                  1                     2             4

The total lbs is 12

12/4 = 3

Multiply each by 3

himself: grandmother: neighbor: total

1*3                  1*3                 2*3        4*3

3                       3                   6           12

The answer to this question is:

One of the angle = 25.5° and other angle = 114.5°

Let us assume that one of the angle be x.

Then according to the question, other angle will be 5x - 13

Given that the sum of both the angles is 140°.

So,  x + (5x-13) = 140

      x + 5x - 13 = 140

      6x - 13 = 140

      6x = 140 + 13

      6x = 153

        x = 153/6

        x = 25.5°

One angle = 25.5°

Other angle = 5x - 13 = 5(25.5) - 13

                                  = 127.5 - 13

                                  = 114.5°

Therefore, one of the angle = 25.5° and other angle = 114.5°

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The calculation \((9.04-8.23+21.954+81.0) \times 3.1416\) would have 4 significant figures.



To determine the number of significant figures in a calculation, we follow the rules for significant figures:

1. Addition and subtraction: The result should have the same number of decimal places as the measurement with the fewest decimal places.
2. Multiplication and division: The result should have the same number of significant figures as the measurement with the fewest significant figures.

Let's break down the calculation step by step:
\(9.04-8.23+21.954+81.0\) yields \(104.764\).

Now, multiplying this result by \(3.1416\) gives \(329.5719744\).

The measurement with the fewest significant figures in the calculation is \(3.1416\), which has 5 significant figures.

According to the rule for multiplication and division, the result should have the same number of significant figures as the measurement with the fewest significant figures. Hence, the result, \(329.5719744\), will be rounded to 4 significant figures.

Therefore, the calculation \((9.04-8.23+21.954+81.0) \times 3.1416\) would have 4 significant figures.

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Answer:

segment a = 12

Step-by-step

2 transversal lines will create similar figures. this means that by doing

a/20= 9/15, you can calculate the length of segment a since they will be similar

The approximate 95% confidence interval for the proportion of coworkers who have received this year's flu vaccine is (0.339, 0.501). Based on this information, it is true that 95% of the coworkers fall within the interval (0.339, 0.501), and we can be 95% confident that the proportion of coworkers who have received the vaccine is between 33.9% and 50.1%. However, it is false to say that there is a 95% chance that a randomly selected coworker has received the vaccine or that there is a 42% chance for a randomly selected coworker to have received the vaccine.

The approximate 95% confidence interval for the proportion of coworkers who have received this year's flu vaccine is (0.339, 0.501). Based on this information, we can determine which of the following statements are true:

a) 95% of the coworkers fall in the interval (0.339, 0.501).

This statement is true. The 95% confidence interval represents the range of values within which we can be 95% confident that the true proportion of coworkers who have received the flu vaccine lies. Therefore, we can say that 95% of the coworkers fall within the interval (0.339, 0.501).

b) We are 95% confident that the proportion of coworkers who have received this year's flu vaccine is between 33.9% and 50.1%.

This statement is true. The 95% confidence interval (0.339, 0.501) provides us with a range of values within which we can be 95% confident that the true proportion of coworkers who have received the flu vaccine lies. Therefore, we can say that we are 95% confident that the proportion of coworkers who have received the vaccine is between 33.9% and 50.1%.

c) There is a 95% chance that a randomly selected coworker has received the vaccine.

This statement is false. The 95% confidence interval does not represent a probability or chance for an individual coworker. It provides a range of values within which we can be 95% confident that the true proportion of coworkers who have received the flu vaccine lies. It does not give information about the likelihood of an individual coworker receiving the vaccine.

d) There is a 42% chance that a randomly selected coworker has received the vaccine.

This statement is false. The 42% represents the proportion of coworkers in the survey who have received the flu vaccine, but it does not represent the chance or probability for a randomly selected coworker to have received the vaccine. The 42% is a point estimate, not a probability.

e) We are 95% confident that between 33.9% and 50.1% of the samples will have a proportion near 42%.

This statement is false. The confidence interval (0.339, 0.501) does not directly provide information about the proportion of samples that will have a proportion near 42%. The confidence interval represents the range of values within which we can be 95% confident that the true proportion of coworkers who have received the flu vaccine lies, but it does not specifically address the proportion of samples near 42%.

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Grace usually does 221 performances each year

last year , she does +10 perfromances

to calculate total number of performances in year Y

we will add ( 221 + 10)= 231

therefore, grace completed 231 performances last year

Answer:231

Step-by-step explanation:

just add 10

The area of Kimberly's wall hanging will be 32 square units.

Given that:

Points, A(1, 5), B(1, 9), C(7, 9), D(7, 5), E(5, 3), and F(3, 3)

The area of a two-dimensional figure is the area that its perimeter encloses. The quantity of unit squares that occupy a closed figure's surface is its region.

The polygon is shown in the graph below.

The area of the polygon is given as,

A = Area of rectangle + Area of trapezium

A = 4 x 6 + 1/2 x (6 + 2) x 2

A = 24 + 8

A = 32 square units

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