Which graph represents the solution to the system of inequalities?

y ≥ x – 5

y < –x + 4

Probability: [tex]\( \frac{111}{220} \)[/tex] or approximately 0.5045. Pita has about a 50.45% chance of drawing exactly £2.50.

To find the probability that Pita takes out exactly £2.50, we need to consider the different combinations of coins that would result in that amount.

First, let's calculate the total number of ways Pita can choose 3 coins out of 12:

[tex]\[ \text{Total number of ways} = \binom{12}{3} = \frac{12!}{3!(12-3)!} = \frac{12 \times 11 \times 10}{3 \times 2 \times 1} = 220 \][/tex]

Now, let's determine the combinations that would result in exactly £2.50. She can achieve this in two ways:

1. Selecting two 1 pound coins and one 50p coin.

2. Selecting five 50p coins.

For the first scenario, she can choose 2 out of the 3 1 pound coins and 1 out of the 9 50p coins. This can be calculated as:

[tex]\[ \binom{3}{2} \times \binom{9}{1} = \frac{3!}{2!(3-2)!} \times \frac{9!}{1!(9-1)!} = 3 \times 9 = 27 \][/tex]

For the second scenario, she can choose all 3 coins from the 9 50p coins:

[tex]\[ \binom{9}{3} = \frac{9!}{3!(9-3)!} = \frac{9 \times 8 \times 7}{3 \times 2 \times 1} = 84 \][/tex]

Now, let's add up these two possibilities to find the total number of favorable outcomes:

[tex]\[ \text{Total favorable outcomes} = 27 + 84 = 111 \][/tex]

Finally, we can calculate the probability:

[tex]\[ \text{Probability} = \frac{\text{Total favorable outcomes}}{\text{Total number of ways}} = \frac{111}{220} \][/tex]

[tex]\[ \text{Probability} \approx 0.5045 \][/tex]

So, the probability that Pita takes out exactly £2.50 is approximately 0.5045 or 50.45%.

The probability that Pita takes out exactly £2.50 when selecting 3 coins at random from her bag is approximately 42.27%.

To find the probability that Pita takes out exactly £2.50 when selecting 3 coins at random from her bag, we need to consider the different combinations of coins that would result in this amount.

Pita has 12 coins in total:

- 3 coins worth £1 each

- 9 coins worth 50p each

For a total of £2.50, she would need to select either:

1. Two £1 coins and one 50p coin, or

2. Five 50p coins

Let's calculate the probability for each case:

1. Probability of selecting two £1 coins and one 50p coin:

  - Probability of selecting a £1 coin on the first draw: [tex]\( \frac{3}{12} = \frac{1}{4} \)[/tex]

  - Probability of selecting another £1 coin on the second draw: [tex]\( \frac{2}{11} \)[/tex] (as there are 2 £1 coins left out of 11 total coins)

  - Probability of selecting a 50p coin on the third draw: [tex]\( \frac{9}{10} \)[/tex] (as there are 9 50p coins left out of 10 total coins)

  - Total probability for this case: [tex]\( \frac{1}{4} \times \frac{2}{11} \times \frac{9}{10} \)[/tex]

2. Probability of selecting five 50p coins:

  - Probability of selecting a 50p coin on the first draw: [tex]\( \frac{9}{12} = \frac{3}{4} \)[/tex]

  - Probability of selecting another 50p coin on the second draw: [tex]\( \frac{8}{11} \)[/tex] (as there are 8 50p coins left out of 11 total coins)

  - Probability of selecting another 50p coin on the third draw: [tex]\( \frac{7}{10} \)[/tex] (as there are 7 50p coins left out of 10 total coins)

  - Total probability for this case: [tex]\( \frac{3}{4} \times \frac{8}{11} \times \frac{7}{10} \)[/tex]

Now, we sum up the probabilities for both cases to find the total probability:

[tex]\[ \text{Total probability} = \left( \text{Probability of case 1} \right) + \left( \text{Probability of case 2} \right) \\\[ \text{Total probability} = \left( \frac{1}{4} \times \frac{2}{11} \times \frac{9}{10} \right) + \left( \frac{3}{4} \times \frac{8}{11} \times \frac{7}{10} \right) \][/tex]

Now, let's calculate these probabilities.

First, let's calculate the probability for case 1:

[tex]\[ \text{Probability of selecting two £1 coins and one 50p coin} \\\[ = \frac{1}{4} \times \frac{2}{11} \times \frac{9}{10} \\\[ = \frac{1}{4} \times \frac{18}{110} \\\[ = \frac{9}{220} \][/tex]

Now, let's calculate the probability for case 2:

[tex]\[ \text{Probability of selecting five 50p coins} \\\[ = \frac{3}{4} \times \frac{8}{11} \times \frac{7}{10} \\\[ = \frac{3}{4} \times \frac{56}{110} \\\[ = \frac{42}{110} \][/tex]

Now, let's sum up the probabilities for both cases to find the total probability:

[tex]\[ \text{Total probability} = \frac{9}{220} + \frac{42}{110} \][/tex]

Now, let's calculate the total probability.

[tex]\[ \text{Total probability} = \frac{9}{220} + \frac{42}{110} \][/tex]

First, let's find a common denominator for the fractions:

[tex]\[ \text{Total probability} = \frac{9}{220} + \frac{42 \times 2}{110 \times 2} \\\[ = \frac{9}{220} + \frac{84}{220} \][/tex]

Now, add the fractions:

[tex]\[ \text{Total probability} = \frac{9 + 84}{220} \\\[ = \frac{93}{220} \][/tex]

Now, let's simplify this fraction:

[tex]\[ \text{Total probability} = \frac{93}{220} \][/tex]

To express the probability as a decimal, we divide the numerator by the denominator:

[tex]\[ \text{Total probability} \approx \frac{93}{220} \approx 0.422727 \][/tex]

Now, let's express this probability as a percentage:

[tex]\[ \text{Total probability} \approx 0.422727 \times 100\% \approx 42.27\% \][/tex]

So, the probability that Pita takes out exactly £2.50 when selecting 3 coins at random from her bag is approximately 42.27%.

17.

x = -2 is not a solution of -1 < x < 5 because -2 < -1 (-1 < -2 < 5 FALSE).

18.

m = 5 is a solution of 5 ≤ m because 5 ≤ 5 ( 5 ≤ m → m ≥ 5 greater than 5 or equal 5, 5 is equal 5)

19.

k = 10 is not solution of 2k - 3 < 1 because:

put the value of k to the inequality:

2(10) - 3 < 1

20 - 3 < 1

17 < 1 FALSE

Answer:

$38.40

Step-by-step explanation:

It is right on Plato

James hand is bigger because when you compare decimals you make sure that there's an equal amount of numbers so 0.17 becomes 0.170 and 0.165 stays the same so James's hand is bigger

speed=d/t=200X2/5=80km/hr

d=sXt=13X80/4=260km

865/110=173/22hr=173X60/22=173X30/11=467min

Answer:

Odds against it being striped = 2/3 =0.6667 = 66.67 %

Explanation:

  Total number of billiard balls = 12

  Total number of solid colored balls = 8

  Total number of striped colored balls = 4

  Probability of an outcome = Number of favorable outcome/ Total number of outcome.

   Here total number of outcomes = Total number of billiard balls =  12

   Number of favorable outcomes =Total number of striped colored balls = 4

   Probability of ball being striped = 4/12 = 1/3 =0.333 =33.33 %

 So odds in favor of being striped = 1/3

 Odds against it being striped = 1-1/3 = 2/3 =0.6667 = 66.67 %

The odds against selecting a striped ball from a rack of 12 billiard balls with 4 striped balls is 2 to 1.

In this problem, we are trying to calculate the odds against selecting a striped ball. The total number of balls is 12. Among these, balls numbered 9 through 12, that is exactly 4 balls, have stripes. Hence, we have 8 solid-colored balls and 4 striped balls.

The odds against an event is calculated as the ratio of the number of unsuccessful outcomes to the successful outcomes. In this scenario, an unsuccessful outcome is drawing a striped ball. Hence, the number of unsuccessful outcomes is the number of solid-colored balls which is 8. So, the odds against selecting a striped ball is 8 to 4 or 2 to 1.

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I believe the answer for this question would $be:

$15+$1.50 = $16.50

$25 / $16.50 = 15.45

I believe that he ran 15 - 15.5 laps.

Answer:

average rate =  75- 35 / 6 - 2 = 40/4 = 10

Step-by-step explanation:

This is the same  value if you use other pairs of x and y

the answer is 10, hope this helps

Final answer:

Carl's daily allowance is the square of the date, resulting in amounts that are perfect square numbers like 1, 4, 9, or 100 cents, depending on the day of the month.

Explanation:

Carl earns an allowance in cents equal to the square of the date of the month. Therefore, the number of cents Carl could earn on any given day is the date squared. For example, on the 2nd day of the month, he would earn 22 or 4 cents, and on the 10th day, he would earn 102 or 100 cents. So, any perfect square (1, 4, 9, 16, 25, 36, ... up to the largest square number within a given month) can be an amount Carl earns in a single day.

Let [tex] b [/tex] be the number of three points baskets, and [tex] t [/tex] be the number of three points tries. We are given

[tex] \dfrac{b}{t} = \dfrac{2}{7} \iff 2t=7b [/tex]

Also, we know that the team scored 30 points from three points baskest. Since these baskest are worth 3 points, we have

[tex] 3b=30 \iff b = 10 [/tex]

Now, we also know that [tex] 2t=7b [/tex]. If we plug the known value for b, we can solve for t:

[tex] 2t = 7\cdot 10 \iff 2t = 70 \iff t = 35 [/tex]

A function is increasing if it "points upwards".

Think that you have two inputs [tex] x_1<x_2 [/tex] (think of them as being very close to each other). A function [tex] f [/tex] is increasing if

[tex] f(x_1)<f(x_2) [/tex]

So, smaller input, smaller output.

So:

So, the function is increasing in the third segment, which is delimited by

[tex] -2\leq x \leq 3 [/tex]

This question is based on the increasing function. Therefore,  the correct option is B, [tex]-2\leq x\leq 3[/tex] interval is the function in this graph increasing.

In this question, from the graph we have to observed that over what interval is the function in this graph increasing.

In general, a function is increasing, if graph pointed upwards.

If we have two points [tex]x_1[/tex] and [tex]x_2[/tex] then, we said that function f is increasing if,

[tex]f(x_1) =f(x_2)[/tex].

Therefore, from the given graph it is observed that:

In the first segment on the left, the function is decreasing: if you move with little steps rightwards, the output will get smaller and smaller (the function points to the right bottom).

In the second segment, the line is constant (it's horizontal). This means that even if you consider a larger input, the output remains constant.

In the third segment, the function is increasing. If you consider a larger input, the output will be larger as well: the function points to the top right.

In the fourth segment, the function is decreasing again.

Therefore,  the correct option is B, [tex]-2\leq x\leq 3[/tex] interval is the function in this graph increasing.

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Answer: The upper right corner choice

=======================================================

The idea is that you graph y = x+3 but only when x < 0 (which is everything to the left of the y axis). This line goes through (-3,0) and (0,3). Note the open hole at x = 0 to indicate "do not include this point"

At the same time, you will also graph y = 2x but only if x is 0 or larger. The endpoint here is (0,0) which is a closed circle telling us to include this endpoint. Another point on this line is (1,2).

The corresponding point on the graph of the function -3/4 f(x) when given that (2,8) is on the graph of f(x) is (2, -6), achieved by scaling the y-value by a factor of -3/4.

The question involves finding the corresponding point on the graph of the function -3/4 f(x) given that (2,8) is on the graph of f(x). Since f(x) at x=2 is 8, for the new function -3/4 f(x) at the same x value, the y value will be scaled by a factor of -3/4.

Therefore, we calculate the new y value by multiplying 8 by -3/4, which results in -6. The corresponding point on the graph of the function -3/4 f(x) when x=2 is therefore (2, -6).

We are given statements :  Premise: If the sides of a triangle are all 4 cm, then the triangle is equilateral.

Premise: The triangle is equilateral.

According to law of Detachment : Statement 1: If q, then q.

and Statement 2: p

   Conclusion: q.

According to given reasoning :

p : If the sides of a triangle are all 4 cm.

q :  Then the triangle is equilateral.

Therefore, Statement 1 : If( the sides of a triangle are all 4 cm), then (the triangle is equilateral).

Statement 2:  (the triangle is equilateral).

Conclusion : The sides of the triangle are 4 cm.

Therefore, option B is correct "Law of Detachment".

Answer:

Olivia spent $97.25

Camille spent $175.10

Step-by-step explanation:

Let the amount spent by:

Olivia be x dollars

Camille be 2x - $19.40 dollars

x + 2x - $19.40 = $272.35

3x = $272.35 + $19.40

3x = $291.75

x = $97.25

To find the amount each girl spent, we can use variables to represent the unknown quantities and create a system of equations. By solving the system of equations, we find that Olivia spent $97.25 and Camille spent $175.10.

To solve this problem, let's use variables to represent the unknown quantities. Let x be the amount Olivia spent and y be the amount Camille spent. According to the problem, Camille spent 19.40 less than twice what Olivia spent, so we can write the equation y = 2x - 19.40. The total amount they spent is $272.35, so we can write another equation x + y = 272.35. We now have a system of equations that we can solve to find the values of x and y.

By substituting the value of y in the second equation with the expression for y from the first equation, we get x + (2x - 19.40) = 272.35. Simplifying this equation gives us 3x - 19.40 = 272.35. Adding 19.40 to both sides, we have 3x = 291.75. Dividing both sides by 3 gives us x = 97.25.

Now, we can substitute the value of x back into either of the original equations to find the value of y. Let's use the first equation y = 2x - 19.40. Plugging in x = 97.25, we get y = 2(97.25) - 19.40 = 194.50 - 19.40 = 175.10.

Therefore, Olivia spent $97.25 and Camille spent $175.10.

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$32.50 X .4 = $13, 32.5-13=19.5, 19.5 divided 2 =$9.75

Answer: The combined mass of the quarters is  11.863 g.

Step-by-step explanation:

1. You have the following information given in the problem above:

- The mass of the modern quarter is 5.623 g.

- The mass of the older silver quarter is 6.24 g.

2. Therefore, to calculate the combined mass of the quarters, you only need to add the mass of the modern quarter (5.623 g) and the mass of the older silver quarter is (6.24 g), as you can see below:

Let's  call the combined mass of the quarters [tex]x[/tex]. Then:

[tex]x=5.623g+6.24g\\x=11.863g[/tex]

Answer:

11.863 g

Step-by-step explanation:

because if you add those 2 numbers then it will give you 11.863 g

Answer:

greater than or >

If the triangle is rotated 270° counterclockwise about the origin, the coordinates of A will be at (1, -4)

Given a coordinate (x, y), if the coordinate is rotated 270° counterclockwise about the origin, the resulting coordinates will be at (y, -x)

For the triangle ABC with coordinates (4, 1), B(2, 3), and C(7, 5), if the triangle is rotated 270° counterclockwise about the origin, the resulting coordinate of A will be at:

A' = (1, -4)

If the triangle is rotated 270° counterclockwise about the origin, the coordinates of A will be at (1, -4)

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x - number of miles

[tex]0.19x+75\geq100\qquad|\text{subtract 75 from both sides}\\\\0.19x\geq25\qquad|\text{divide both sides by 0.19}\\\\x\geq132[/tex]

Multiplication and division have the same precedence, binding tighter than addition and subtraction.  Among operators with the same precedence we go left to right.

So the first operation to do is division.   ÷

PEDMAS notwithstanding if your expression depends on the details of the left to right rules, you're better off adding parenthesis to make things clearer.

First of all, you can sum the two terms involving g on the left hand side:

[tex] -6g + 3g + 12 > -18 \iff -3g + 12 > -18 [/tex]

Subtract 12 from both sides:

[tex] -3g > -30 [/tex]

Divide both sides by -3: note that since we're dividing by a negative number, we must invert the inequality sign:

[tex] g< 10 [/tex]

Final answer:

When solving the inequality, we combine like terms, subtract 12 from both sides, and divide by -3, reversing the inequality sign to find that g < 10, hence the correct answer is (c).

Explanation:

To solve the inequality -6g + 3g + 12 > -18, we first combine like terms to simplify the left side of the inequality:

Next, we subtract 12 from both sides of the inequality:

Now we divide by -3, remembering to reverse the inequality sign because we are dividing by a negative number:

Therefore, the correct answer is (c) g < 10.

A number is prime if its only divisors are 1 and the number itself.

Out of your numbers, 36 and 38 are even, and thus divisible by 2, so they aren't prime.

Similarly, 35 ends with 5, so it's divisible by 5, and is not prime.

37 is divisible only by 1 and 37, and thus it's prime.

Out of the numbers listed (36, 37, 35, 38), the number 37 is the only prime number, as it is the only number that has no positive divisors other than 1 and itself.

The question asks which of the listed numbers is a prime number. A prime number is a number greater than 1 that has no positive divisors other than 1 and itself. Therefore, we need to determine if any of the numbers given (36, 37, 35, 38) have divisors other than 1 and themselves.

36 is divisible by 1, 2, 3, 4, 6, 9, 12, 18, and 36, so it is not a prime number.

37 has no divisors other than 1 and itself, making it the prime number in the list.

35 is divisible by 1, 5, 7, and 35, so it is not a prime number.

38 is divisible by 1, 2, 19, and 38, so it is not a prime number.

Therefore, the number 37 is the only prime number from the list provided.

40%

to calculate rate of discount,

[tex]\frac{discount}{original cost}[/tex] × 100%

discount = $60 - $36 = $24

[tex]\frac{24}{60}[/tex] × 100% = 40%

Answer:

it is 40%

Step-by-step explanation:

Answer is B ! Good luck bro

The domain of a graph is the set of input values the graph can take.

The graph that represents y = [x] over the domain -4≤x≤-1 is the 1st graph.

The domain is given as:

[tex]\mathbf{-4 \le x \le -1}[/tex]

The inequalities at -4 and -1 are both "less than or equal to"

In inequalities, "less than or equal to" is represented by a closed circle

This means that, the circles at x = -4 and x =-1 on the graph must be a closed circle.

From the given options, we have the following observations

Hence, the graph that represents y = [x] over the domain -4≤x≤-1 is the 1st graph.

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Answer:

The given function is

  y≥2-2x

Writing this inequality in equation form and then in slope intercept form

  [tex]y=2-2x\\\\2x+y=2\\\\\frac{2x}{2}+\frac{y}{2}=1\\\\ \frac{x}{1}+\frac{y}{2}=1[/tex]

Option D

Graph of a solid line on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A solid line passes through begin ordered pair 1 comma 0 end ordered pair and begin ordered pair 0 comma 2 end ordered pair. The region above the solid line is shaded.

The correct representation of the inequality y≥2−2x is: Graph of a solid line on a coordinate plane. The horizontal x-axis ranges from negative 5 to 5 in increments of 1. The vertical y-axis ranges from negative 5 to 5 in increments of 1. A solid line passes through the ordered pair (0, -2) and (1, 0). The region above the solid line is shaded.

In mathematics and data visualization, a graph is a visual representation of data or mathematical relationships. It typically consists of points (nodes or vertices) connected by lines or curves (edges) that show relationships or connections between the points. Graphs are used to represent various data structures and relationships, such as in graph theory, network analysis, and data plotting.

This representation correctly shows a solid line (not dashed) and shades the region above the line, which indicates the solution to the inequality y ≥ 2 − 2x.

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The land area of Pennsylvania is 44,816 square miles. Rounding it to the nearest hundred gives us 44,800 square miles.

The land area of Pennsylvania is 44,816 square miles. To round this number to the nearest hundred, we look at the digit in the hundreds place. The digit in the hundreds place is 4, so we keep the 4 and change all the digits to the right of it to zeros. Therefore, the land area of Pennsylvania rounded to the nearest hundred is 44,800 square miles.

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