There are fewer than 30 students in the A-level mathematics class. One half of them
play the piano, one quarter play hockey and one seventh are in the school play.
How many of the students play hockey?

Answer:

Step-by-step explanation:

im sorry cant help but i hope you have a gate day heres a quote "you can do any thing if you believe you can achieve so go go go!!!!!

The mean value of the sample is 89.

Standard deviation = 13.

We are given that a value of 128 has a z-score of 3.

Use the formula for z-score:

z = (x - μ) / σ

where:

x is the value of interest (in this case, x = 128)

μ is the mean of the sample

σ is the standard deviation of the sample

mean = x - z-score * standard deviation

mean = 128 - 3 * 13

mean = 89

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The correct APA style for the statistical conclusion that Dr. Tebbetts should make is option B. z(N=50) = 2.27, p > .05.

Here's why:

Dr. Tebbetts is testing whether the mean creativity score of people who read fantasy novels is significantly different from the established average of 25 on the Alternate Uses Test. He gathered a sample of 50 participants and found that their mean creativity score was 33.

Since the population standard deviation is known, we can use a z-test to test the hypothesis.

The formula for the z-test is:

z = (sample mean - population mean) / (population standard deviation / sqrt(sample size))

Substituting the values given in the problem, we get:

z = (33 - 25) / (10 / sqrt(50))

z = 2.83

The critical value of z for a two-tailed test at alpha level 0.05 is 1.96. Since our calculated z-value is greater than the critical value, we reject the null hypothesis and conclude that people who read fantasy novels have higher personal creativity as measured by the Alternate Uses Test.

The correct APA style for reporting this conclusion is:

z(N=50) = 2.27, p > .05, indicating that people who read fantasy novels have significantly higher personal creativity as measured by the Alternate Uses Test compared to the established average.

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Answer:

3

Step-by-step explanation:

Mark two points from the graph

(-1 , 0)  & (0 , 3)

\(Gradient = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\\\=\dfrac{3-0}{0-[-1]}=\dfrac{3}{0+1}\\\\\\=\dfrac{3}{1}\\\\\\=3\)

Answer:

40

Step-by-step explanation:

Let's call blueberries, raspberries, grapes and cherries b, r, g, and c respectively. We can write:

b + r + g + c = 280 (1)

r = 2b (2)

g = 3c (3)

c = 4r (4)

We can plug (2) into (1) to get b + 2b + g + c = 280. Then, we can re-write (4) into r = c / 4 and plug that into (2) which gets us c / 4 = 2b, and when we re-write that we get c = 8b (5). Let's plug that into (1) to get b + 2b + g + 8b = 280. Next, we'll re-write (3) to get g / 3 = c, and we can plug that into (5) to get g / 3 = 8b so then g = 24b and plug that into (1) to get b + 2b + 24b + 8b = 280 → 35b = 280 → b = 8. We can plug this into (5) to get c = 8 * 5 = 40. Hope this helps!

Answer:

41.5675675676km/hour or 41.57km/hour

Step-by-step explanation:

158÷3.7=41.5675675676  or 41.57

The cost price of the article is 160,000$

A woman old an article for 200,000.00$ and made a profit of 25%

The financial gain a business has when revenue exceeds costs and expenses is frequently referred to as profit.

The formula Profit = Selling Price - Cost Price can be used to determine the profit when the selling price and the cost price of a product are known. The formula for calculating profit percentage is then applied, which is profit percentage = (profit/cost price) x 100.

X  x 25/100 + X = 200,000

25X/100 + X =200,000

X= 200,000-25X/100

X= (20,000,000-25X) / 100

100X = 20,000,000-25X

125X = 20,000,000

X = 160000

cost + 25% of cost = 200,000

cost (1+25/100)= 200,000

cost (1+1/4)=200,000

cost (5/4)=200,000

cost=200,000x(4/5)

=40000x4

= 160,000

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Area Principle. In a statistical display, each data value should be represented by the same amount of area. Bar chart (Relative Frequency Bar Chart)

Using rectangular bars with heights or lengths proportional to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.

Using rectangular bars with heights or lengths proportional to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.

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Rolle's theorem:

If a function \(f\) is continuous on the closed interval \( [a, b] \) and differentiable on the open interval \((a,b)\) such that \(f(a) = f(b)\), then [tex)f′(x) = 0\) for some \(x\) with \( a \leq x \leq b\).

Tangent:

A tangent is parallel to the x-axis if the slope of the tangent is 0. So, using Rolle's theorem, if we consider \(x=-\pi/2\) and \(x=\pi/2\), then \(f(-\pi/2)=f(\pi/2)=-1\).

Since \(f(x)\) is continuous on \([-\pi/2, \pi/2]\) and differentiable on \((-\pi/2, \pi/2)\), \(f'(x)=0\) for some \(-\pi/2 \leq x \leq \pi/2\), and thus there is a point in this interval which is parallel to the x-axis.

Answer:

the third one

Step-by-step explanation:

rational numbers have an end while irrational don't

The x is a specific value that the variable can take on.

A random variable is a variable that has a numerical value, which is determined by the result of a random experiment. The numerical value is determined by a set of probabilities, which are associated with each possible outcome of the experiment. Random variables can be classified as discrete or continuous, depending on the type of outcomes that they can have. Examples of random variables include the number of heads in a series of coin tosses, the time until a traffic light changes from red to green, and the height of a randomly selected person.The randomness of a random variable comes from the fact that the outcome of the experiment that it represents is uncertain. The uncertainty arises because the experiment is subject to the effects of chance, rather than being completely determined by fixed physical laws or other deterministic factors. Because of this, it is not possible to predict with certainty what the value of a random variable will be, even if we know the probabilities associated with each possible outcome.There are many different notations that can be used to represent random variables, depending on the context and the preferences of the person using the notation. Some of the most common notations include X, Y, and Z, as well as Greek letters such as µ, σ, and ρ. When a random variable is discrete, it is often represented using a probability mass function, which is denoted by P(X=x), where x is a specific value that the variable can take on. When a random variable is continuous, it is often represented using a probability density function, which is denoted by f(x), where x is a specific value that the variable can take on.

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Answer:

156

Step-by-step explanation:

The probability that all adjacent points differ in color is given as follows:

1/10. (second option).

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For the total outcomes, we have an arrangement of 6 elements, due to the six points, with 3 and 3 repetitions, as 3 are green and 3 are red, hence the number of total outcomes is calculated as follows:

\(T = A_6^{3,3} = \frac{6!}{3!3!} = 20\)

For the desired outcomes, there are two, given as follows:

This means that the probability that all adjacent points differ in color is calculated as follows:

p = 2/20 = 1/10.

Hence the second option is the correct option.

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Answer:

Chris' initial investment is $5000. The interest rate is 2% quarterly for 4 years.

Step-by-step explanation:

The lateral surface area of a rectangular prism has length, breadth, and height is 3cm, 3cm, and 2cm is 36cm sq.

A rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces.

The lateral surface area of this rectangular prism = 2( l + b) h

It is given that length, breadth and height are 3cm, 3cm and 2cm.

The lateral surface area of this rectangular prism = 2( l + b) h

= 2 (3+3) 2

= 4 × 9

= 36cm sq.

Hence, the lateral surface area of this rectangular prism is 36cm sq.

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Answer:

39 ig

Step-by-step explanation:

The cumulative frequency column indicates the percent of scores at or below a given value.

In Mathematics and Statistics, a frequency table can be used for the graphical representation of the frequencies or relative frequencies that are associated with a categorical variable.

In Mathematics and Statistics, the cumulative frequency of a data set can be calculated by adding each frequency from a frequency distribution table to the sum of the preceding frequency.

In conclusion, we can logically deduce that the percentage of scores at and/or below a specific (given) value is indicated by the cumulative frequency.

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Complete Question:

The cumulative frequency column indicates the percent of scores ______ a given value.

at or below

at or above

greater than less than.

The correct option is A, equilibrium price increases from $6 to $8.

In economics, equilibrium is a state in which the supply and demand for a product or service are balanced, resulting in a stable price. This can occur in a free market, where the price of a good or service is determined by the interaction of buyers and sellers.

Overall, equilibrium is a fundamental concept in many different fields, representing a state of balance or stability in a system or situation.

If the demand schedule changes from D2 to D1, then the demand curve shifts to the left. As a result, the new equilibrium point will be where the new demand curve (D1) intersects with the supply curve (S1).

From the table, we can see that the new equilibrium point is at a price of $8 and a quantity of 15. Therefore, the equilibrium price increases from $6 to $8, but the equilibrium quantity decreases from 15 to 13.

So the correct answer is: equilibrium price increases from $6 to $8.

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The value of the angle x using trigonometric ratio is: x = 53.13°

Some of the trigonometric ratios in mathematics based on a right angle triangle are:

Sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

Similarly:

cot x = 1/tan x

sec x = 1/cos x

cosec x = 1/sin x

We are given that:

sin x = 12/15

Thus:

x = sin⁻¹(12/15)

x = 53.13°

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Answer:

Look at step by step

Step-by-step explanation:

i is √-1 So A√B = √98

If both A and B must be more than 1 and has to be an integer, with a little guessing, we can get that A = 7 and B = 2, but other requirements and there will be too many possible solutions

Answer:

3, -6, 0, -9, 6

Step-by-step explanation:

Select the numbers below that are part of the domain of the function. (3, 0); (-6, -5); (0,-3) ; (-9, 7) ; (6, 4

The domains are independent variables in Mathematical equations. They are the variables that determine the range of any Mathematical equations.

From the series of numbers given above, the domains are:

3, -6, 0, -9, 6

The unbiased estimator for \( \sigma^{2} \) for the given model is \( S^{2} \), where \( S^{2} \) represents the sample variance.

To find an unbiased estimator for \( \sigma^{2} \), we can use the sample variance formula. The sample variance is defined as the average of the squared differences between each data point and the sample mean. Mathematically, the sample variance is calculated as:

\[ S^{2} = \frac{1}{n-1} \sum_{i=1}^{n}(x_{i}-\overline{x})^{2} \]

where \( n \) is the sample size, \( x_{i} \) represents each data point, and \( \overline{x} \) is the sample mean.

It can be proven that \( S^{2} \) is an unbiased estimator for \( \sigma^{2} \), meaning that on average, it gives an estimate that is equal to the true population variance \( \sigma^{2} \). The denominator \( n-1 \) in the formula corrects for the bias and ensures that the estimator is unbiased.

Therefore, in the given model, the unbiased estimator for \( \sigma^{2} \) is \( S^{2} \), which is calculated using the sample variance formula with \( n-1 \) as the denominator.

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Answer:

⁴/2

Step-by-step explanation:

because is I solveng to be a good

brainliest me

Answer:

Common ratio is - 4 / 2.

Step-by-step explanation:

Sequence = - 2, 4, - 8, 16, - 32, ....

Let the terms be " a ".

Here,

a1 = 2

a2 = 4

a3 = - 8

a4 = 16

a5 = - 32

Let the common ratio be " r ".

r1 = a2 / a1

= 4 / - 2

r1 = - 2

r2 = a3 / a2

= - 8 / 4

r2 = - 2

r3 = a4 / a3

= 16 / - 8

r3 = - 2

r4 = a5 / q4

= - 32 / 16

r4 = - 2

Since, the common ratios are same,

Therefore, r = - 2

- 4 / 2 = - 2

So, - 2 can also be written as - 4 / 2.

Hence,

r = - 4 / 2

Finally,

Common ratio ( r ) = - 4 / 2

The given series is ∑((-1)^n(x - 6)^n)/(4n + 1) from n = 0 to infinity. The radius of convergence, R, is 1 and the interval of convergence is (5, 7) in interval notation.

To find the radius of convergence, R, we can use the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms of a series is L, then the series converges if L is less than 1 and diverges if L is greater than 1.

Let's apply the ratio test to the given series:

L = lim(n→∞) |((-1)^(n+1)(x - 6)^(n+1))/(4(n+1) + 1)| / |((-1)^n(x - 6)^n)/(4n + 1)|

Simplifying the expression inside the limit, we have:

L = lim(n→∞) |(-1)^(n+1)(x - 6)^(n+1)(4n + 1)| / |((-1)^n(x - 6)^n)(4n + 1)|

Simplifying further, we get:

L = lim(n→∞) |(x - 6)(4n + 1)/(4n + 5)|

Taking the limit as n approaches infinity, we find:

L = |(x - 6)|/1 = |x - 6|

For the series to converge, we need L < 1, so |x - 6| < 1. This means that the radius of convergence, R, is 1.

To find the interval of convergence, I, we consider the endpoints of the interval. Since |x - 6| < 1, we have -1 < x - 6 < 1. Adding 6 to all sides of the inequality, we get 5 < x < 7.

Therefore, the interval of convergence is (5, 7) in interval notation.

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Step-by-step explanation:

the answer is

1 C

2 D

3 F

4 B

5 E

6 A

The capture-recapture method is commonly used to estimate population sizes in situations where direct counting is not feasible. By marking a portion of the population and then recapturing some marked individuals in a subsequent sample, we can make inferences about the entire population size. In this case, by comparing the proportion of marked salmon in the second sample to the known number of marked salmon in the first sample, we can estimate the total population size to be 300 salmon.

Let's calculate the population size step-by-step:

1. Determine the proportion of marked salmon in the second sample:
  - In the first sample, 280 salmon were marked and released.
  - In the second sample, 60 salmon were recaptured and marked.
  - The proportion of marked salmon in the second sample is 60/300 = 0.2 (or 20%).

2. Use the proportion to estimate the population size:
  - Let N be the population size.
  - The proportion of marked salmon in the entire population is assumed to be the same as in the second sample (0.2).
  - Setting up a proportion, we have: 0.2 = 60/N.
  - Cross-multiplying gives us: 0.2N = 60.
  - Dividing both sides by 0.2 gives us: N = 60/0.2 = 300.

Based on the capture-recapture method, the estimated population size of salmon in this stream is 300.

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Answer: Choice C

The angle opposite N is going to involve endpoints other than N. So it will involve point I and point M to form segment IM.

Given that John climbs a height of \($(x + 5)$\) miles in \($(x - 1)$\) hours and Jane climbs a height of \($(x + 11)$\) miles in \($(x + 1)$\) hours. We know that the distance covered by both John and Jane are equal.

Distance covered by John = Distance covered by Jane

Therefore, \($(x + 5) = (x + 11)$\)

Thus, x = 6

Now, we need to find the speed of both, which is given by the formulae:

Speed = Distance / Time

So, speed of John = \($(x + 5) / (x - 1)$\) Speed of John =\($11 / 5$\) mph

Similarly, speed of Jane = \($(x + 11) / (x + 1)$\)

Speed of Jane = \($17 / 7$\) mph

Since both have to be equal, Speed of John = Speed of Jane Therefore,

\($(x + 5) / (x - 1) = (x + 11) / (x + 1)$\)

Solving this equation we get ,x = 2Speed of John = \($7 / 3$\) mph

Speed of Jane = \($7 / 3$\) mph

Thus, their speed was \($7 / 3$\) mph.

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If AD = 2x + 4 and CD = 4x - 4, and they share point D, then x must be equal to 4.

An equatiοn is a mathematical statement that indicates that twο expressiοns are equal.

Hοwever, we can use the fact that they share pοint D tο set them equal tο each οther and sοlve fοr x:

AD = CD

2x + 4 = 4x - 4

Collecting like terms:

2x - 4x = -4 - 4

-2x = -8

Dividing both sides by -2:

x = 4

Hence, if AD = 2x + 4 and CD = 4x - 4, and they share point D, then x must be equal to 4.

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Answer:

b

Step-by-step explanation:

Answer:

x < -0

Step-by-step explanation:

Note that y is increasing on the interval (-3, 0).  We could generalize this to:

x < -0 (Answer C)