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OPEN RESPONSE A city parking garage charges $4 to park for up to two hours. After that, an additional charge of $2.50 per hour applies. Write an equation in point-slope form that models the total cost y for parking x hours, where x > 2

The limit of the expression [tex]\lim_{x \to \223} \sqrt{x+2} -\frac{5\\}{x} -23[/tex] when evaluated is -18.22

Limit is a value that a function approaches the output for the given input values.

From the question, we have the following limit expression that can be used in our computation:

[tex]\lim_{x \to \223} \sqrt{x+2} -\frac{5\\}{x} -23[/tex]

To find the limit tends to 23, we substitute 23 for x in the above equation

So, we have the following representation

[tex]\lim_{x \to \223} \sqrt{23+2} -\frac{5\\}{23} -23[/tex]

Evaluate the sum in the expression

[tex]\lim_{x \to \223} \sqrt{25} -\frac{5\\}{23} -23[/tex]

Evaluate the exponent and the fractions

Limit = 5 -5/23 -23

When the expression is evaluated, we have

Limit = -18.2173913043

Approximate

Limit = -18.22

Hence, the solution is -18.22

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4. The probability of drawing 1 pink, 2 yellow and, stripped ball in succession without replacing the ball each time is (7/16) x (1/35) x (1/13) = 1/2540.

5. The probability that we roll a total of five if we are given that the total is less than nine is (1/36) / (4/36) = 1/4.

6. The probability that both cards are 7s is (6/36) x ($5 - $1) + (30/36) x (-$1) = -$0.17.

7. The expected value of the game is a loss of 17 cents per play.

4. The probability of drawing 1 pink ball, 2 yellow balls, and 1 stripped ball in succession is given by the product of the probabilities of drawing each ball without replacement.

The probability of drawing 1 pink ball is 7/16, the probability of drawing 2 yellow balls is (3/15) x (2/14) = 1/35 (because there are 3 yellow balls in the bag out of 15 total balls on the first draw, and 2 yellow balls out of 14 total balls on the second draw), and the probability of drawing 1 stripped ball is 2/13. Therefore, the probability of drawing 1 pink ball, 2 yellow balls, and 1 stripped ball in succession is:

(7/16) x (1/35) x (1/13) = 1/2540

5. If the total is less than nine, then there are only 4 possible outcomes: (1, 4), (2, 3), (3, 2), and (4, 1). The probability of rolling each of these outcomes is 1/36, since each die has 6 equally likely outcomes. The only outcome that adds up to 5 is (1, 4), which has probability 1/36. Therefore, the probability of rolling a total of 5, given that the total is less than nine, is:

(1/36) / (4/36) = 1/4

6. The probability of drawing a 7 on the first card is 4/52, since there are four 7s in a deck of 52 cards. Since the card is replaced, the probability of drawing a 7 on the second card is also 4/52. Therefore, the probability of drawing two 7s in a row is:

(4/52) x (4/52) = 1/169

7. The expected value of the game is the sum of the products of the outcomes and their probabilities. There are 6 x 6 = 36 possible outcomes, each with probability 1/36. Of these outcomes, 6 are winning outcomes (where both dice show the same number), and 30 are losing outcomes. The payout for a winning outcome is $5, and the cost of playing the game is $1. Therefore, the expected value is:

(6/36) x ($5 - $1) + (30/36) x (-$1) = -$0.17

Therefore, the expected value of the game is a loss of 17 cents per play.

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Answer:

22.5 minutes

Step-by-step explanation:

Initially, there were 9 students with 30 minutes to clean up the mess. This means they had a total of 9 · 30 = 270 student minutes to clean up the mess.

After the 3 additional students were added, there were a total of 9 + 3 = 12 students on the clean-up crew.

Now, let's assume the time they need to clean up the mess is "t" minutes. Since the number of students and the time are inversely proportional to the amount of work done, we can set up the following equation based on the idea that the amount of work done is the same before and after the addition of the 3 students:

9 · 30 = 12 · t

Solving for "t":

270 = 12t

t = 270 / 12

t = 22.5

So, the principal should give them approximately 22.5 minutes to complete the job with the new crew of 12 students.

Answer:

zero

Step-by-step explanation:

If a system of equations is graphed as 2 lines, then if the lines intersect, they intersect at one single point, and that point is the solution. There is one solution.

If the lines are parallel and do not intersect, then there is no solution. The number of solutions is zero.

Answer: zero

The inequality form is 4/3<x<11.

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.

The given inequality is log₂(3x-4)<log₂(2x+7)

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form: 4/3<x<11

Interval Notation:(4/3,11)

Therefore, the inequality form is 4/3<x<11.

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Answer: Let's represent the value of car 1 as x. Then, the value of car 2 is 3/4 of x, and the value of car 3 is 4/5 of the value of car 2.

So, we can write the following equations:

x = (3/4) * y

y = (4/5) * z

Where y is the value of car 2, and z is the value of car 3.

Adding all the values, we have:

x + y + z = 1115900

We can substitute the values of y and z in terms of x:

x + (3/4) * x + (4/5) * (3/4) * x = 1115900

Simplifying the expression on the left side, we get:

7/4 * x = 1115900

Finally, dividing both sides by 7/4, we get:

x = 359900

So, the value of car 1 is $359900, the value of car 2 is (3/4) * x = (3/4) * 359900 = 269925, and the value of car 3 is (4/5) * (3/4) * x = (4/5) * (3/4) * 359900 = 213140.

Step-by-step explanation:

Answer: the value of car 1 is $467125, the value of car 2 is $623033.33, and the value of car 3 is $350937.5.

Step-by-step explanation:

Let's call the value of car 1 "x".

From the first ratio, we know that the value of car 2 is 4/3 times greater than the value of car 1, and the value of car 3 is 3/4 times greater than the value of car 1.

So, the value of car 2 is 4/3 * x, and the value of car 3 is 3/4 * x.

From the second ratio, we know that the value of car 2 is 8/5 times greater than the value of car 3.

So, the value of car 2 is 8/5 * (3/4 * x) = 6/5 * x.

The total value of all three cars is $1115900, so we can set up an equation to solve for x:

x + 4/3 * x + 3/4 * x = 1115900

Expanding and simplifying the right side:

x + 4/3 * x + 3/4 * x = 1115900

8/3 * x = 1115900

x = 1115900 * 3 / 8

x = 467125

So, the value of car 1 is $467125, the value of car 2 is $623033.33, and the value of car 3 is $350937.5.

Algebra 1 covers a variety of topics in algebraic mathematics, including linear and quadratic equations, graphing, polynomials, exponents, factoring, rational expressions, inequalities, functions, and data analysis.

Algebra 1 is typically a high school level course that covers a variety of topics in algebraic mathematics. The specific topics covered can vary somewhat depending on the school or district, but some common topics in Algebra 1 include:

1. Linear equations: Solving for unknowns in linear equations and systems of linear equations.

2. Quadratic equations: Solving for unknowns in quadratic equations and understanding their properties.

3. Graphing: Graphing linear and quadratic functions, and understanding their properties such as slope and intercepts.

4. Polynomials: Understanding and manipulating polynomials of different degrees.

5. Exponents: Understanding and working with exponential functions and expressions.

6. Factoring: Factoring polynomials and other algebraic expressions.

7. Rational expressions: Simplifying and manipulating rational expressions, and solving equations involving them.

8. Inequalities: Solving and graphing inequalities, including absolute value inequalities.

9. Functions: Understanding the concept of a function, and working with linear and quadratic functions.

10. Data analysis: Using algebraic methods to analyze and interpret data, including creating and interpreting graphs and tables.

These are some of the main topics that are typically covered in Algebra 1, though the exact curriculum can vary depending on the specific school or district.

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On dividing (3x³ - 2x² + 4x - 3) by (x² + 3x + 3), we get -

h(x) = 3x - 11 + {(28x + 30)/(x² + 3x + 3)}.

An algebraic expression is a combination of terms both constants and variables. For example -

2x + 3y + z

3x + y

Given is to divide (3x³ - 2x² +4x - 3) by (x² + 3x + 3).

Let us assume that -

f(x) = (3x³ - 2x² + 4x - 3)

g(x) = (x² + 3x + 3)

We can write -

h(x) = f(x)/g(x)

h(x) = (3x³ - 2x² + 4x - 3)/(x² + 3x + 3)

h(x) = 3x + {(- 11x² - 5x - 3)/(x² + 3x + 3)}

h(x) = 3x - 11 + {(28x + 30)/(x² + 3x + 3)}

Therefore, on dividing (3x³ - 2x² + 4x - 3) by (x² + 3x + 3), we get -

h(x) = 3x - 11 + {(28x + 30)/(x² + 3x + 3)}.

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We can say that function (C) y = 128(0.5)ˣ will help us to determine the number of teams remaining after x number of rounds.

A relation between a collection of inputs and outputs is known as a function.

A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

Each function has a range, codomain, and domain.

The usual way to refer to a function is as f(x), where x is the input.

One function, many. function onto (Surjective Function) into perform.

The function of a polynomial.

So, by observation we can find out the function:

y = 128(0.5)ˣ

Assume the teams after 1st round:

y = 128(0.5)ˣ

y = 128(0.5)¹

y = 128*0.5

y = 64 (Half od 128)

Therefore, we can say that function (C) y = 128(0.5)ˣ will help us to determine the number of teams remaining after x number of rounds.

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The attachment shows different types of polygons that have 3 more sides then the other.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now depending on these we have following five possibilities:

Case 1: Triangle and hexagon

If first polygon is triangle with three angles, the second will have 6 angles and the second polygon will be hexagon.

Case 2: Quadrilateral and heptagon

If first polygon is quadrilateral with 4 angles, the second will have 4+3 =7 angles and the second polygon will be heptagon.

Case 3: Pentagon and Octagon

If first polygon is pentagon with 5 angles, the second will have 5+3=8 angles and the second polygon will be octagon.

Case 4: Hexagon and Nonagon

If first polygon is hexagon with 6 angles, the second will have 6+3=9 angles and the second polygon will be nonagon.

Case 5: Heptagon and Decagon

If first polygon is Heptagon with 7 angles, the second will have 7+3=10 angles and the second polygon will be decagon.

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Answer:  The formula for finding the area of a triangle is A = 1/2(x1)(y2-y3)+(x2)(y3-y1)+(x3)(y1-y2).

Plugging in the given coordinates, the area of the triangle is:

A = 1/2(-3)(-1-1) + (-2)(1-(-2)) + (1)(-2-(-1))

A = 1/2(-3)(-2)+(-2)(3)+1(-3)

A = -9+6-3

A = 4

Step-by-step explanation:  Step 1: Identify the formula for finding the area of a triangle: A = 1/2(x1)(y2-y3)+(x2)(y3-y1)+(x3)(y1-y2).

Step 2: Plug the given coordinates into the formula: A = 1/2(-3)(-1-1) + (-2)(1-(-2)) + (1)(-2-(-1)).

Step 3: Simplify the equation: A = 1/2(-3)(-2)+(-2)(3)+1(-3).

Step 4: Solve the equation: A = -9+6-3.

Step 5: Find the area of the triangle: A = 4.

Answer:

x=9

Step-by-step explanation:

18/48=x/24

Cross multiply

48x=432

Divide

432/48=9

x=9

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Answer:

5, 18 and 7 respectively

Step-by-step explanation:

4+9+5=18

18+7=35

Answer:The top box is 11 making the middle boxes 15 20

Step-by-step explanation:

4 11 9

4+11  11+9

15 20

15+20

35

The total square centimeters of mirrors covering the lateral surfaces is

171.5 cm².

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface.

Given:

Perpendicular height = 14.3

So, the Surface area of Prism is

= 5 x 10 x 3 + 1/2 x 5 x 4.3 x 2

= 150 + 21.5

= 171.5

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One possible solution is to tutor for 11 hours and clear tables for 5 hours

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

25x + 9y ≥ 270

x + y ≤ 18

Where

x = hours tutoring

y = hours cleaning tables

Next, we plot the graph (see attachment)

One solution from the graph is (11, 5)

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A two-dimensional form having four sides, four vertices, and four angles is referred to as a quadrilateral. Examples are: Trapezium, Parallelogram, Rectangle, Rhombus, Square and Kite.

A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.

The Latin words quadra, which means four, and latus, which means sides, are combined to form the English term quadrilateral. A quadrilateral does not always have to have equal lengths on each of its four sides. As a result, depending on the sides and angles, we might have several sorts of quadrilaterals. Hence a Quadrilateral is of 4 sides, vertices and angles. It consists of 360 degrees.

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Answer:

  $2.21

Step-by-step explanation:

You want to know the savings between using a $10 off coupon and taking a 15% discount, if the tax rate is 10.3%.

The price with the coupon is ...

  $79.99 -10.00 = $69.99

When tax is added, the total becomes ...

  $69.99 × 1.103 ≈ $77.20

The price with the discount is ...

  $79.99 × (1 -0.15) ≈ $67.99

When tax is added, the total becomes ...

  $67.99 × 1.103 ≈ $74.99

The savings by making use of the discount is ...

  $77.20 -74.99 = $2.21

The total savings between the coupon and the discount is $2.21. That is, you save $2.21 more by using the discount instead of the coupon.

__

Additional comment

The question seems a bit ambiguous. The word "or" suggests you cannot use both discounts. If you do, the total amount saved will depend on the order in which they are applied.

You get the best result by taking the $10 off the sale price. Doing that gives you a total savings of about $24.27 off the normal price with tax.

The numbers that can be multiplied by each equation so that when the two equations are added together, the x term is eliminated is: A. –10 times the first equation and 3 times the second equation.

In order to determine the solutions to a system of two linear equations, we would have to evaluate and eliminate each of the variables one after the other, especially by selecting a pair of linear equations at each step and then applying the elimination method.

Given the following system of linear equations:

1/5(x) + 3y/4 = 9                .........equation 1.

2x/3 - 5y/6 = 8          .........equation 2.

In this scenario, the number that should be used to multiply first equation can be calculated by using the following ratio:

Ratio =  -(x-coefficient of second equation)/(x-coefficient of first equation)

Ratio = -(2/3)/(1/5)

Ratio = -10/3

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Answer: 6 square inches

Step-by-step explanation:

Since the pizza is 16 inches and there is 8 slices divide.

16 inches ÷ 8 slices = 2 inches per slice

Each slice is 2 inches.

Since each slice is 2 inches multiply by 3 slices to get how many square inches she ate.

2 inches per slice x 3 slices = 6 square inches

Therefore she ate 6 square inches of pizza.

The answer is: 1 part sample, 9 parts diluent, 1 part of the first dilution, 9 parts diluent, 1 part of the second dilution, 9 parts diluent

When creating a serial dilution, the starting concentration is typically given as a ratio of sample to diluent. For example, a 1/10 dilution would mean that there is one part of sample and nine parts of diluent.

Now when we create a serial dilution from 1/10 to 1/1000, the first dilution will be 1 part sample and 9 parts diluent. The second dilution will be one part of the first dilution and nine parts diluent. The final dilution will be one part of the second dilution and nine parts diluent.

Thus, the answer is:

1 part sample

9 parts diluent

1 part of the first dilution

9 parts diluent

1 part of the second dilution

9 parts diluent

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____ The given question is incorrect, the correct question is given below:

When creating a serial dilution from 1/10 to 1/1000, the first dilution will be _______ part sample and ______ parts diluent. The second dilution will be one part ____ and nine parts _____. The final dilution will be one part _____ and nine parts diluent.

Choices:

1(one)

9(nine)

1/10 dilution

1/100 dilution

1/1000 dilution

diluent

Answer:

Step-by-step explanation:

where is the equation?

Answer:

Step-by-step explanation:

Multiply 4.75 by 2 to find out how much money Maurice gets when finishing 2 chores. $4.75 x 2 = $9.50. So, write $9.50 under 2. For three chores, multiply $4.75 by 3. $4.75 x 3 = $14.25. Write $14.25 under 3.

The count of the ways in which to chose 4 candies from a store that sells 30 candy bars, obtained by the combination formula, are 27405 ways

A mathematical combination, is the ways in which a number of items can be chosen from a set of items, excluding a reference to the order in which the items are selected.

The number of ways k items can be chosen from n items, can be found by using the following combinations formula;

[tex]\binom{n}{k} = \frac{n!}{k!\cdot (n-k)!}[/tex]

Therefore, the number of ways 4 candies can be chosen from a store that sells 30 candy bars can be found by plugging in k = 4, and n = 30 as follows;

[tex]\binom{30}{4} = \frac{30!}{4!\cdot (30-4)!} = 27405[/tex]

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[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"y" varies inversely with }x^2}{y = \cfrac{k}{x^2}}\hspace{5em}\textit{we also know that} \begin{cases} x=4\\ y=\frac{11}{4} \end{cases} \\\\\\ \cfrac{11}{4}=\cfrac{k}{4^2}\implies \cfrac{11}{4}=\cfrac{k}{16}\implies \cfrac{(11)(16)}{4}=k\implies 44=k~\hfill \boxed{y=\cfrac{44}{x^2}} \\\\\\ \textit{when x=2, what's "y"?}\qquad y=\cfrac{44}{2^2}\implies y=\cfrac{44}{4}\implies y=11[/tex]

Answer:

y = 11 when x = 2

Step-by-step explanation:

This is indirect proportionality where:

y ∝ [tex]\frac{1}{x^{2}}[/tex]

This means:

[tex]y_{1} x_{1}^{2} = y_{2}x_{2}^{2}[/tex]

Substitute the following values in the above equation to solve for [tex]y_{2}[/tex]

[tex]y_{1} = \frac{11}{4}[/tex]

[tex]y_{2} = ?[/tex]

[tex]x_{1} = 4[/tex]

[tex]x_{2} = 2[/tex]

= [tex](\frac{11}{4})(4^{2}) = y_{2}(2^{2})[/tex]

= [tex](\frac{11}{4})(16) = y_{2}(4)[/tex]

= [tex]44 = 4y_{2}[/tex]

= [tex]y_{2} =\frac{44}{4}[/tex]

∴ y = 11

Answer:

See explanation

Step-by-step explanation:

40% of the original $54 is $21.60, therefore the pants are $21.60 off of their original price. This makes the pants $32.40.

20% of the new $32.40 is $6.48, therefore the pants are $6.48 off of the 40%-off price. This makes the pants $25.92 for their final price.

Answer:

9.26 tons

Step-by-step explanation:

8400 kilograms is 9.259415 tons and when you round to the nearest hundredth it is 9.26.

The formula for converting pounds (lb) to kilograms (kg) is 1 lb = 0.45359237 kg. To convert from lb to kg, you simply multiply the value in lb by 0.45359237.

For example, to convert 186 lb to kg, you would need to perform the following calculation: 186 lb × 0.45359237 kg/lb = 83.99 kg. Therefore, the answer to the question is that 186 lb is equivalent to 83.99 kg. This can be written in a short form as 186 lb = 83.99 kg. It is important to note that this conversion is based on the International System of Units (SI) and is the most commonly used method for measuring weight. When converting between measurements, it is also important to consider the accuracy of the conversion. In this case, the conversion is accurate to nine decimal places. This means that the result is accurate to within 0.000000001 kg, which is an extremely small amount. As such, this conversion should be suitable for most practical applications.

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