Work out the percentage change when a price of £20 is decreased to £3.

We can see that there are a total of 3 games that fall into the 51-57 category (games 1, 5, and 8). Therefore, the answer to the question is D. 3 games were in the 51-57 category. The correct option is D.

To solve this problem, we need to first determine which category each game falls into based on the given categories.
Game 1: 51 points - falls into the 51-57 category
Game 2: 70 points - falls into the 72 or more category
Game 3: 63 points - falls into the 58-64 category
Game 4: 59 points - falls into the 58-64 category
Game 5: 56 points - falls into the 51-57 category
Game 6: 75 points - falls into the 72 or more category
Game 7: 60 points - falls into the 58-64 category
Game 8: 55 points - falls into the 51-57 category
Game 9: 67 points - falls into the 65-71 category
Game 10: 64 points - falls into the 58-64 category
Now, we can see that there are a total of 3 games that fall into the 51-57 category (games 1, 5, and 8). Therefore, the answer to the question is D. 3 games were in the 51-57 category.
It's important to note that categorizing the data in this way is helpful for analyzing trends and patterns in the team's scoring over time, but it does not provide a complete picture of the team's performance in each game.

It's also worth considering other factors such as the team's opponents, the location of the game, and any injuries or other circumstances that may have affected the outcome.

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30% probability that A occurs given B occurs

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

Suppose we have two events, A and B, the conditional probability formula is:

\(P(A|B)=\frac{ P(A\cap B)}{P(B)}\) -------(1)

In which

P(A|B) is the probability of A happening given that B happened.

\(P(A\cap B)\)  is the probability of both A and B happening.

P(B) is the probability of B happening.

In this problem, we have that:

\(P(A\cap B)\)= 1/6 ,  P(B) = 5/9

So, (1) => P(A|B) = (1/6)/( 5/9 )

                         = (1/6) * (9/5)

                         = 0.3

30% probability that A occurs given B occurs

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Answer:

72

Step-by-step explanation:

circumference = 20

arc = 4

4/20 =1/5

a circle = 360°

1/5 * 360 = 72

Answer:

0.6267

Step-by-step explanation:

See the picture.

Hope its clear.

True, While "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

The statement "-1000 2/3 is not a real fraction" is true. A real fraction is a mathematical expression that represents a ratio of two real numbers. In a fraction, the numerator and denominator are both real numbers, and they can be positive, negative, or zero.

In the given statement, "-1000 2/3" is not a valid representation of a fraction. The presence of a space between "-1000" and "2/3" suggests that they are separate entities rather than being part of a single fraction.

To represent a mixed number (a whole number combined with a fraction), a space or a plus sign is typically used between the whole number and the fraction. For example, a valid representation of a mixed number would be "-1000 2/3" or "-1000 + 2/3". However, without the proper formatting, "-1000 2/3" is not considered a real fraction.

It's important to note that "-1000 2/3" can still be expressed as an improper fraction. To convert it into an improper fraction, we multiply the whole number (-1000) by the denominator of the fraction (3) and add the numerator (2). The result would be (-1000 * 3 + 2) / 3 = (-3000 + 2) / 3 = -2998/3.

In conclusion, while "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

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Answer:

a) 87.91% probability that at most three used the emergency room

b) 20.13% probability that exactly three used the emergency room.

c) 3.28% probability that at least five used the emergency room​

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they use the emergency room, or they do not. The probability of a person using the emergency room is independent of any other person. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

Sample of 10 people:

This means that \(n = 10\)

20% of the people in a community use the emergency room at a hospital in one year

This means that \(p = 0.2\)

a) At most three used the emergency room

\(P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)\)

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074\)

\(P(X = 1) = C_{10,1}.(0.2)^{1}.(0.8)^{9} = 0.2684\)

\(P(X = 2) = C_{10,2}.(0.2)^{2}.(0.8)^{8} = 0.3020\)

\(P(X = 3) = C_{10,3}.(0.2)^{3}.(0.8)^{7} = 0.2013\)

\(P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.1074 + 0.2684 + 0.3020 + 0.2013 = 0.8791\)

87.91% probability that at most three used the emergency room

b) Exactly three used the emergency room

\(P(X = 3) = C_{10,3}.(0.2)^{3}.(0.8)^{7} = 0.2013\)

20.13% probability that exactly three used the emergency room.

c) At least five used the emergency room​

\(P(X \geq 5) = 1 - P(X < 5)\)

In which

\(P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)\)

From 0 to 3, we already have in a).

\(P(X = 4) = C_{10,4}.(0.2)^{4}.(0.8)^{6} = 0.0881\)

\(P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.1074 + 0.2684 + 0.3020 + 0.2013 + 0.0881 = 0.9672\)

\(P(X \geq 5) = 1 - P(X < 5) = 1 - 0.9672 = 0.0328\)

3.28% probability that at least five used the emergency room​

Answer:

Therefore, you need 2600 pounds of 35% supplement and 1300 - 2600 = -1300 pounds of 10% ration.

Step-by-step explanation:

The unknown variable is x, which is the amount of 35% supplement needed. The other expressions are derived from the given information and the fact that the total amount of solution is 1300 pounds.

The equation from the fourth column is:

0.35x + 0.10(1300 - x) = 0.25(1300)

Solving for x, we get:

x = (0.25(1300) - 0.10(1300)) / (0.35 - 0.10) x = 650 / 0.25 x = 2600

Answer:

3/4 divide by 9 = 0.75/9 = 0.083 yard for each doll's hair ribbon

Step-by-step explanation:

Each doll's hair ribbon will be 0.083 (yards)

The length of each of the daughter's dolls hair ribbon is \(\frac{1}{12} \ yards\)

The given parameters:

amount of ribbon Kristen has \(= \frac{3}{4}\) yards

number of her daughter's dolls = 9

To find:

To have equal length of ribbons for each of the doll's hair, we divide the total amount of ribbons by 9, since there 9 dolls.

\(Length \ of \ each \ doll's \ ribbon = (\frac{3 }{4} \times \frac{1}{9})\ yards\\\\Length \ of \ each \ doll's \ ribbon = (\frac{3}{36} ) \ yards\\\\Length \ of \ each \ doll's \ ribbon = \frac{1}{12} \ yards\)

Thus, the length of the each doll's hair ribbon is \(\frac{1}{12} \ yards\)

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Answer:

800 hrs = 33.3 days

Step-by-step explanation:

1 day = 24 hours

800 hours = 800/24 = 33.33

Round to the nearest tenth:

33.3 days

The value of the test statistic is given as follows:

z = 4.47.

The equation to calculate the test statistic using the z-distribution is given as follows:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

In which:

The parameters for this problem are given as follows:

\(\overline{p} = 0.59, p = 0.5, n = 618\)

p = 0.5 as the most term means that we are testing if the proportion is either less than or greater than 0.5.

Then the test statistic is obtained as follows:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

\(z = \frac{0.59 - 0.5}{\sqrt{\frac{0.5(0.5)}{618}}}\)

z = 4.47.

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Answer:

8 hours and 26 minutes

Step-by-step explanation:

To convert 506 minutes to hours and minutes, we can use the fact that there are 60 minutes in one hour.

First, we can divide 506 by 60 to find the number of hours:

506 ÷ 60 = 8 with a remainder of 26

This means that 506 minutes is equal to 8 hours and 26 minutes.

Therefore, the conversion of 506 minutes to hours and minutes is:

8 hours and 26 minutes

Answer: Equilateral

Step-by-step explanation:

It's equilateral because it says that each side of the triangle is 4cm. In simple words, all the sides of triangle are equal. Such a triangle is called an equilateral triangle.

Hope you understood.

9514 1404 393

Answer:

  349.0 grams

Step-by-step explanation:

The amount remaining can be modeled by an exponential function of the form ...

  remaining = (initial amount)(1 - decay rate)^t

  q(t) = 640(1 -0.073)^t

  q(8) = 640(0.927^8) ≈ 349.0 . . . grams

The amount remaining after 8 minutes is about 349.0 grams.

The number of years it would it take for there to be one person for every square yard is 108,325.68 years.

When there is one person for every square yard, it means that the population and land area are equal in value.

Number of years = (In FV / PV) / r

(In 19 billion / 4,079,000) / 0.043 = 108,325.68 years

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The probability that you select a Jack given that it is a Club P(Jack∣Club) is 1/13.

The probability that you select a Club given that it is a Jack is P(Club∣Jack) is 1/4.

The probability that you select a card that is NOT a Jack given that it is NOT a Club,P(NotJack∣NotClub) is 47/38

The probability that you select a card that is NOT a Club given that is it NOT a Jack is 38/47

The probability that you select a Jack given that it is a Club P(Jack|Club):

There are 4 Jacks in a deck (one for each suit), and since we are given that the selected card is a Club, we only need to consider the 13 cards in the Club suit.

So, the number of favorable outcomes is 1 (the Jack of Clubs), and the total number of possible outcomes is 13 (the number of cards in the Club suit)

P(Jack|Club) = 1 / 13

The probability that you select a Club given that it is a Jack

P(Club|Jack):

P(Club|Jack) = Number of favorable outcomes / Total number of possible outcomes

P(Club|Jack) = 1 / 4

The probability that you select a card that is not a Jack given that it is not a Club

P(NotJack|NotClub):

The number of cards that are not Jacks is 52 - 4 = 48 (since there are 4 Jacks in the deck), and the number of cards that are not Clubs is 52 - 13 = 39 (since there are 13 cards in the Club suit).

P(NotJack|NotClub) = Number of favorable outcomes / Total number of possible outcomes

P(NotJack|NotClub) = (48 - 1) / (39 - 1)

=47/38

P(NotClub|NotJack) = (39 - 1) / (48 - 1)

=38/47

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Answer:

Step-by-step explanation:

To check whether the given credit card number is valid or not, we need to apply the Luhn algorithm or the mod-10 algorithm. The Luhn algorithm works by adding up all the digits in the credit card number and checking if the sum is divisible by 10 or not. If it is, then the credit card number is considered valid, otherwise, it is invalid.

Let's apply the Luhn algorithm to the given credit card number:

Step 1: Starting from the rightmost digit, double every second digit

| 5 | 4 | 2 | 4 | 9 | 8 | 1 | 3 | 2 | 7 | 2 | 0 | 0 | 0 | 8 | 5 |

|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

| | 8 | | 8 | | 16| | 6 | | 14| | 0 | | 0 | | 10|

Step 2: If the doubled value is greater than 9, add the digits of the result

| 5 | 4 | 2 | 4 | 9 | 8 | 1 | 3 | 2 | 7 | 2 | 0 | 0 | 0 | 8 | 5 |

|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

| | 8 | | 8 | | 7 | | 6 | | 5 | | 0 | | 0 | | 1 |

Step 3: Add up all the digits in the credit card number, including the check digit

5 + 4 + 2 + 4 + 9 + 8 + 1 + 3 + 2 + 7 + 2 + 0 + 0 + 0 + 8 + 5 + 1 = 61

Step 4: If the sum is divisible by 10, then the credit card number is valid, otherwise, it is invalid.

61 is not divisible by 10, therefore the given credit card number is invalid.

Hence, it can be concluded that 5424 9813 2720 0085 is an invalid MASTERCARD credit card number.

Answer:

ecb and acb

Step-by-step explanation:

Answer:

36 pie cubic inches

Step-by-step explanation:

Use the formula: \(V = \frac{4}{3} \pi r^{3}\)

Plug in the value for radius and solve:

\(V = \frac{4}{3} \pi 3^{3}\)

Becuase of the nature of the answer options, you only have to solve to a certain point: \(V = 36 \pi\)

The inequality on the graph is the third option:

(2/5)*x - 3/2 ≥ y

Let's analyse the graph if the inequality.

We can see that there is a solid linear equation with a positive slope, and the shaded area is below that line, then the inequality is of the form:

y ≤ linear equation.

We know that the symbol "≤" must be used because of the solid line.

We also can see that when x = 0, y takes a velue between -1 and -2.

With that in mind the correct option is the third one:

(4/5)*x - 2y ≥ 3

Isolating y we get:

(4/5)*x - 3 ≥ 2y

(2/5)*x - 3/2 ≥ y

Changing the order:

y ≤ (2/5)*x - 3/2

That is the graphed inequality.

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Using the Chain Rule, we have: dy/dx = f'(g(x)) * g'(x) = 1 * 1 = 1.The derivative of y with respect to x is 1.

When we compose a function, it may be possible to write it in a variety of different ways. Differentiating such functions can result in different derivatives, but the Chain Rule indicates that the derivatives of the compositions should be the same regardless of how the function is written, if the function is continuous and differentiable.For instance, consider the function f(x) = sin(x²). It can be written as f(g(x)) where g(x) = x² and f(x) = sin(x). Furthermore, it can be written as f(h(x)) where h(x) = x² and f(x) = sin(x). These are both compositions of functions, but they are different compositions that lead to different derivatives.However, if the function is a composite of differentiable functions, the Chain Rule tells us that the derivative of a composite function is the derivative of the outer function multiplied by the derivative of the inner function.

To find dy/dx if y = x using the Chain Rule with y as a composite of the following functions, we must first rewrite y as a composite function: y = f(g(x)) where g(x) = x and f(x) = x. This composite function can be written in a variety of different ways, such as y = f(h(x)) where h(x) = x and f(x) = x, or y = f(k(x)) where k(x) = x and f(x) = x. However, regardless of how we write it, the Chain Rule tells us that the derivative of y is equal to the derivative of the outer function (f(x) = x) multiplied by the derivative of the inner function (g(x) = x).

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The correct pairs of the functions and their inverses are given by the image at the end of the answer.

To find the inverse function, we exchange x and y in the original function, then isolate y.

The first function that we want to find the inverse is:

f(x) = (2x - 1)/(x + 2).

Hence:

x = (2y - 1)/(y + 2)

(y + 2)x = 2y - 1

xy + 2x = 2y - 1

xy - 2y = -1 - 2x

y(x - 2) = -1 - 2x

y = (-1 - 2x)/(x - 2) (which is the inverse function).

The second function which we want to find the inverse is:

y = (x + 2)/(-2x + 1)

Then:

x = (y + 2)/(-2y + 1)

x(-2y + 1) = y + 2

-2yx + x = y + 2

-2yx - y = 2 - x

-y(2x + 1) = 2 - x

y = (x - 2)/(2x + 1)  (which is the inverse function).

The third function which we want to find the inverse is:

y = (x - 1)/(2x + 1)

Then:

x = (y - 1)/(2y + 1)

2yx + x = y - 1

2yx - y = -1 - x

y(2x - 1) = -1 - x

y = (-x - 1)/(2x - 1) (which is the inverse function).

The fourth function which we want to find the inverse is:

y = (2x + 1)/(2x - 1)

Then:

x = (2y + 1)(2y - 1)

2yx - x = 2y + 1

2yx - 2y = 1 + x

2y(x - 1) = (1 + x)

y = (x + 1)/(2(x - 1)) (which is the inverse function).

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Answer:

The answer is B

Answer:

The answer is B and A

Step-by-step explanation:

Since both triangles are similar, their sides have similar ratios:

HI / KL = JI / ML

Replacing with the values given:

37/7 = 27.8/ ML

Solve for ML

ML = 27.8 / (37/7)

ML = 5.3

Answer:

The value of the test statistic is -0.97

Step-by-step explanation:

This test is two tailed test.

Null and Alternative hypothesis is as follow

Null Hypothesis is used when it is assumed that there is no significant difference between the values.

Null Hypothesis = \(H_{0}\) = \(\mu =\) 59.8

The Alternative hypothesis is the alternative of the Null Hypothesis. It is an experimental technique that is used when it is assumed that there is some difference

Alternative Hypothesis = \(H_{a}\) = \(\mu \neq\) 59.8

Test statistcs is z

The value of test statistics can be calculated using the following formula

Test Statistics \(= (\bar x - \mu ) / \sigma / \sqrt n\)

Test Statistics \(= (59.7-59.8) / 1.3 / \sqrt 160\)

Test Statistics = -0.97

Answer: \(x=0, -\frac{3}{2}\)

Step-by-step explanation:

\(4x^2 +6x=0\\\\2x(2x+3)=0\\\\2x=0, 2x+3=0\\\\x=0, -\frac{3}{2}\)

Answer:

0.6m^(10)

Step-by-step explanation:

1.2m^(4-n) *0.5m^(n+6)

Regroup

(1.2 * 0.5) * m^(4 - n) * m^(n + 6)

When multipling numbers with the same base, sum the exponents

0.6m^(10)

Answer:

outside the circle

sorry if I'm wrong

Answer:

6rad2

Step-by-step explanation:

Answer:

8.845 units

Step-by-step explanation:

First start by plotting the points on a graph. Doing so will give you two points that you can connect and then turn into a triangle. Find the length and height of the triangle by counting how many units long each is. The length should be 6 units, while the height should also be 6 units. You can then use the pythagorean theorum to find the length of b to c:

A^2 + B^2 = C^2

6^2  + 6^2 = C^2

36 + 36 = C^2

72 = C^2

C = 8.845 units

If the required reserve ratio is 10 percent, currency in circulation is $1,200 billion, checkable deposits are $1,600 billion, and excess reserves total $2,500 billion

Given that

Reserve ratio is 10 percent

Currency in circulation is $1,200 billion

Checkable deposits are $1,600 billion

Excess reserves total $2,500 billion

Here we are calculating M1 measure of money supply

C: Currency in circulation

D: Checkable Deposits

M1=C+D = 1200+1600= 2800

C: Currency in circulation

D: Checkable Deposits

Currency Deposit Ratio= C/D = 1200/1600 = 0.75

ER: Excess Reserves

CD: Checkable Deposits

Excess Reserve Ratio= ER/CD= 2500/1600 = 1.56

The formula for the M1 money multiplier is:

M1 money multiplier= M1/MB

M1 money multiplier= C+D / R+C

M1 money multiplier= C+D / q∗D+ER+C

M1 money multiplier= (1,200+1,600) / (0.1∗1,600+2,500+1,200)

M1 money multiplier= 0.73

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