A professional gamer is preparing for a tournament. in his game he averaged a score of 534 points, every day, for 5 days. then, for the next 3 days he scored a total of 1827 points. finally in another 4 days he averaged a score of 516 points each day. in 12 days how many points in total did this gamer get

Step-by-step explanation:

E=29

G = 180-29-107= 44

F = 180-29-29 = 122

H = 180-29-29 = 122

S = 180-107 = 73

M = 107

C = 73

D = 107

T = 73

B = 107

N = 73

K = 44

A = 360-44-44-107 = 165

O = 180-44 = 136

P = 44

J= 136

The p-value of a test of significance is calculated assuming that the null hypothesis is true. Option c. the null hypothesis is true is the correct choice for the assumption made in calculating the p-value.

The p-value represents the probability of obtaining the observed test statistic or a more extreme value, assuming that the null hypothesis is true. It provides evidence against the null hypothesis and helps determine the level of statistical significance. Therefore, option c. the null hypothesis is true is the correct choice when considering the assumptions made in calculating the p-value.

In hypothesis testing, the p-value is a crucial measure that indicates the strength of evidence against the null hypothesis. It represents the probability of observing the test statistic or a more extreme value, assuming that the null hypothesis is true. The p-value allows us to determine the level of statistical significance and decide whether to reject or fail to reject the null hypothesis.

By assuming the null hypothesis is true, we calculate the p-value based on the observed data and the test statistic. The p-value is then compared to a predetermined significance level (commonly set at 0.05) to make a decision regarding the null hypothesis. Option a. a significance level of 0.05 refers to the predetermined threshold at which we decide to reject or fail to reject the null hypothesis, but it is not directly related to the assumption made when calculating the p-value.

Option b. the alternative hypothesis being true is the opposite scenario to the null hypothesis, and it is not the assumption made when calculating the p-value. Option d. making no assumptions about which hypothesis is true would result in a lack of basis for the p-value calculation and would hinder the interpretation of the test's significance. Therefore, option c. the null hypothesis is true is the correct choice for the assumption made in calculating the p-value.

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The equation needed to calculate the compound interest is \(A = P(1 +\frac{r}{n} )^{nt}\)

The value of the account after ten years is $9347.62 .

If the account is left alone for 20 years, the amount of interest earned is $6942.76

The compound interest formula is represented as follows;

\(A = P(1 +\frac{r}{n} )^{nt}\)

where

Therefore,

where

r = 3.7% = 3.7 / 100 = 0.037

n = 1

t = 10

P = $6500

Hence,

\(A = 6500(1+\frac{0.037}{1} )^{1(10)}\)

\(A = 6500(1.037)^{10}\)

\(A = 6500(1.43809495884)\)

A = 9347.61723247

A = $9347.62

The value of the account after ten years is $9347.62

Interest = 9347.62  - 6500 = 2847.62 dollars

When it is 20 years.

r = 3.7% = 3.7 / 100 = 0.037

n = 1

t = 20

P = $6500

Hence,

\(A = 6500(1+\frac{0.037}{1} )^{1(20)}\)

\(A = 6500(2.06811711064)\)

A = 13442.7612192

A = $13442.76

Interest = 13442.76 - 6500 = 6942.76 dollars

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Answer:

90% percent of the computers are working.

Step-by-step explanation:

3/30 of the computers don't work and we can simplify this

1/10 or 10% Subtract 10% from 100%

90% are working computers.

Answer:

x= 72

Step-by-step explanation:

- move 9 to the right.

- when a number moves to the other side, their sign changes.

- in this case, 9 multiplies by 8.

- thus 9 x 8 equals to 72.

Answer:

x=0

Step-by-step explanation:

1.Subtract 8x from both sides

2.Simplify the expression

3.Divide both sides by the same factor

4.Cancel terms that are in both the numerator and denominator

Answer: x=0

Answer:

-20

Step-by-step explanation:

solve x

4x=24-4+5x

-20=x

Answer:

x = -20

Step-by-step explanation:

-3x + 7x = 24 + 5x - 4

4x = 20 + 5x

0 = 20 + x

x = -20

The situation that would best be represented by an inverse variation function is (c) The area of a circle as a function of the radius.

An inverse variation function is a mathematical relationship where one variable increases as the other variable decreases, and vice versa. It can be represented by an equation of the form y = k/x, where k is a constant.

Out of the options provided, the situation that would best be represented by an inverse variation function is

c) The area of a circle as a function of the radius.

This is because the area of a circle is given by the formula A = πr^2, where r is the radius. As the radius increases, the area of the circle also increases, but not in a linear way. Instead, the area increases at a decreasing rate. This is an example of inverse variation, where the area (y) increases as the radius (x) decreases, and vice versa. The constant k in this case is π.

Option a) Total cost as a function of the number of items purchased, option b) Distance travelled as a function of speed, and option d) Time it takes to finish a race as a function of the runner's speed, do not represent inverse variation functions.

Therefore, the correct option is (c) The area of a circle as a function of the radius.

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The lines x - y = 2 and y = x - 1 are related as they are equations of two different lines that intersect at a single point. This is not a valid equation, indicating that the lines are parallel and do not intersect.

The equation x - y = 2 can be rewritten as y = x - 2, which represents a line with a slope of 1 and a y-intercept of -2. On the other hand, the equation y = x - 1 represents a line with the same slope of 1 but a y-intercept of -1.

When we compare the two equations, we can see that they have the same slope, indicating that the lines are not parallel. The lines intersect at a point where their y-coordinates are equal. To find the point of intersection, we can set the two equations equal to each other:

x - 2 = x - 1

By canceling out the x terms, we find:

-2 = -1

This is not a valid equation, indicating that the lines are parallel and do not intersect. Therefore, the two lines x - y = 2 and y = x - 1 are actually parallel lines and do not have a common point of intersection.

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The value of the union of sets A and B is, P(A ∪ B) is 0.64.

The union of two sets means the total elements in both the sets combined.

Given: sets P(A) = 0.38, P(B) = 0.83, and  intersection P(A ∩ B) = 0.57

We need to find the union of P(A ∪ B).

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Let us substitute the given values in the formula.

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

=0.38+0.83-0.57

=1.21-0.57

=0.64

Therefore, the value of union of sets P(A ∪ B) is 0.64.

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The lower bound for the 95% confidence interval for the proportion of Android users who plan to get another Android phone is 0.463 .

It can be evaluated applying the formula

Lower Bound = Sample Proportion - Z-Score × Standard Error

Here

Sample Proportion
= 200/371 = 0.539

Z-Score = 1.96 (for a 95% confidence interval)

Standard Error = √[(Sample Proportion * (1 - Sample Proportion)) / Sample Size]
= √[(0.539 × (1 - 0.539)) / 371]
= 0.045
Therefore,

Lower Bound = 0.539 - 1.96 × 0.045 = 0.463
A confidence interval is a known as the specified range of values that is prone to contain an unknown population area with a certain degree of confidence.

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Step 1

Find the equation of both lines using

Where,

Hence,

For the second line we will have

Step 2

Hence expressed the graphed solution as a piecewise function

Answer:

C. C and E

Step-by-step explanation:

The solutions for a system of equations is the point of intersection of the two graphs of those equations. Here, there are two points of intersection, that is, two points where the graphs cross. The graphs cross at point C and point E.

C and E are the solutions to this system.

The value of r'(1) and s'(4) is 0 that can be interpreted with the help of the graph that is given in the question.

Derivative in mathematics, the rate of change of a characteristic with recognize to a variable. Derivatives are essential to the answer of troubles in calculus and differential equations. The essence of calculus is the by-product. The by-product is the immediately price of extrade of a characteristic with recognize to certainly considered one among its variables. This is equal to locating the slope of the tangent line to the characteristic at a point

\(r(x) = f(g(x))\)therefore the derivative of r is given by \(r'(x) = f'g(x)\times g'(x)\)

\(r'(1) = f'(g(1))\times g'(1)\) from the graphs

r'(1) = f'4 \times g'1 = (5/4) \times(0) = 0

Similarly s'(1) = g'(f(1))\times f'(1) from the graphs

 f(1)=1.5, f'(1)

=\dfrac{ (3-0)}{(0-2)}

= -3/2 , g'(3/2) = 0

s'(4) = g'(3/2) \times f'(4) = 0(-1.5) = 0

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Complete question:

let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. find r'(1) and s'(4).

Answer :

\(p = 169\)

a. The volume of the solid is 24 cubic units.

b. The volume of the solid is 4π cubic units.

a. Volume = Area of Base * Height

The base is a right triangle with base length of 3 units and height of 4 units. The area of the base can be calculated as:

Area of Base = (1/2) * base * height

= (1/2) * 3 * 4

= 6 square units

The height of the solid is 4 units.

Volume = Area of Base * Height

= 6 * 4

= 24 cubic units

b) Any cross section of the solid, taken parallel to the y-axis and perpendicular to the x-axis, is a semicircle.

Volume = (1/2) * π * radius² × height

Volume = (1/2) * (1/2) * π * 2² * 4

= (1/4) * π * 4 * 4

= π * 4

Therefore, the volume of the solid is 4π cubic units.

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The output obtained after executing the java code snippet,

double bottles;

double bottleVolume = bottles * 2;

System.out.printIn(bottleVolume);

will throw an error that bottle variable might not have been initialized.

As per the question statement, we are provided with a java code snippet, which goes as:

double bottles;

double bottleVolume = bottles * 2;

System.out.printIn(bottleVolume);

We are required to determine the output, that we will obtain on executing the above mentioned code.

That is, on executing the code

double bottles;

double bottleVolume = bottles * 2;

System.out.printIn(bottleVolume);

We will obtain an error that bottle variable might not have been initialized because we are using the variable bottle without initializing.

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Answer:

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

2000(x-3)=6000

divide both sides by 2000 to cancel it

x-3=3

add (+3) to both sides to cancel the -3

x=6

The sum of the given Fourier sine series is equal to (1/π) * ∫[0 to π] |f(x)|² dx, where f(x) = x.

to find the sum of the given series using Parseval's identity, we need to follow these steps:

a) For the series ∑[n=1 to ∞] n²/1², we will use the Fourier sine series for f(x)

= x on 0≤x≤π.

Step 1: Express f(x) as an odd function by extending it to the interval [-π, π] with f(-x) = -f(x).
Since f(x) = x is already an odd function, we don't need to extend it.

Step 2: Calculate the Fourier coefficients of the odd extension.
The Fourier sine series coefficients for an odd function are given by:
b_n = (2/π) * ∫[0 to π] f(x) * sin(n*x) dx

For f(x) = x, the Fourier sine series coefficients are:

b_n = (2/π) * ∫[0 to π] x * sin(n*x) dx

Step 3: Calculate the sum of the series using Parseval's identity.
Parseval's identity states that for a function f(x) with its Fourier series coefficients b_n, the sum of the series can be found using the formula:
∑[n=1 to ∞] |b_n|²= (1/π) * ∫[0 to π] |f(x)|² dx

In our case, we have:
∑[n=1 to ∞] n²/1² = ∑[n=1 to ∞] |b_n|²

Therefore, the sum of the series is equal to:
(1/π) * ∫[0 to π] |f(x)|² dx

= (1/π) * ∫[0 to π] x² dx

b) For the series ∑[k=1 to ∞] (2k+1)⁴/1², we will use the Fourier cosine series for f(x)

= x on 0≤x≤π.

Step 1: Express f(x) as an even function by extending it to the interval [-π, π] with f(-x) = f(x).
Since f(x) = x is already an even function, we don't need to extend it.

Step 2: Calculate the Fourier coefficients of the even extension.
The Fourier cosine series coefficients for an even function are given by:
a_0 = (1/π) * ∫[0 to π] f(x) dx

a_n = (2/π) * ∫[0 to π] f(x) * cos(n*x) dx

For f(x) = x, the Fourier cosine series coefficients are:
a_0 = (1/π) * ∫[0 to π] x dx
a_n = (2/π) * ∫[0 to π] x * cos(n*x) dx

Step 3: Calculate the sum of the series using Parseval's identity.
Parseval's identity states that for a function f(x) with its Fourier series coefficients a_n, the sum of the series can be found using the formula:

∑[n=0 to∞] |a_n|²= (1/π) * ∫[0 to π] |f(x)|² dx

In our case, we have:
∑[k=1 to ∞] (2k+1)⁴/1² = ∑[n=0 to ∞] |a_n|²

Therefore, the sum of the series is equal to:
(1/π) * ∫[0 to π] |f(x)|² dx = (1/π) * ∫[0 to π] x² dx

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Answer:

THATS MADDDD CAPPPP U NEED 25 POINTS OF THE QUESTION FOR BRAINLIEST

The limit of the function f(x) as x approaches 3 is 1, and the limit of the function g(x) as x approaches 3 is 8.

Given that \(\(\lim_{{x \to 3}} f(x) = 1\)\) and \(\(\lim_{{x \to 3}} g(x) = 8\)\), we can evaluate the limits as follows:

\(\[\lim_{{x \to 3}} (f(x) + g(x)) = \lim_{{x \to 3}} f(x) + \lim_{{x \to 3}} g(x) = 1 + 8 = 9.\]\)

This is known as the limit addition property, which states that the limit of the sum of two functions is equal to the sum of their individual limits if both limits exist.

Similarly, we can evaluate the limit of the product of f(x) and g(x):

\(\[\lim_{{x \to 3}} (f(x) \cdot g(x)) = \lim_{{x \to 3}} f(x) \cdot \lim_{{x \to 3}} g(x) = 1 \cdot 8 = 8.\]\)

This is known as the limit multiplication property, which states that the limit of the product of two functions is equal to the product of their individual limits if both limits exist.

In conclusion, the limit of the sum of f(x) and g(x) as x approaches 3 is 9, and the limit of the product of f(x) and g(x) as x approaches 3 is 8.

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Answer:

3

Step-by-step explanation:

because 3 square 3 gives 27

Answer:

In general, those students that studied scored much higher than those students that did not study.

Step-by-step explanation:

Hope this helps.

The median of the group that did not study is less than 80.

also

In general, those students that studied scored much higher than those students that did not study.

Answer:

8x+16

7x-9

_____

15x+7

Step-by-step explanation:

Add or subtract like terms

Answer:

15x+7

No step I did it

The fraction, \(4\frac{7}{5}\) as a mixed number can be written as, 5 whole and \(\frac{2}{5}\).

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

A mixed number is a representation of both a whole number and a legal fraction. In most cases, it denotes a number that falls between any two whole numbers.

Given, A fraction \(4\frac{7}{5}\),

Now, \(4\frac{7}{5}\) = \(4 + 1\frac{2}{5}\).

= \(5 \frac{2}{5}\).

This can be written as a whole number 5 and a proper fraction \(\frac{2}{5}\).

Q. Write \(4\frac{7}{5}\) as a mixed number.

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Answer:

B

Step-by-step explanation:

4÷2=2

14÷2=7

making it a equal ratio

Answer:

Step-by-step explanation:

Hey ! I beleive this is the answer: 27.5/100=.275

The correct null and alternative hypotheses for Becky's one-proportion hypothesis test are H0: p = 0.5 and Ha: p ≠ 0.5 (The true proportion of heads is different from 50%).

This represents a two-tailed test because the alternative hypothesis (Ha) includes the "≠" symbol, indicating that the true proportion of heads could be either greater than or less than 50%.

In this case, Becky conducted a coin flip experiment, where she flipped the coin 30 times and obtained 18 heads. By comparing the observed proportion (18/30 = 0.6) to the hypothesized proportion of 0.5 (50%), she wants to determine if there is evidence to suggest that the coin is biased and not coming up heads or tails in a truly random fashion.

To perform the hypothesis test, she will calculate the test statistic (Z) and compare it to the critical value(s) corresponding to her chosen significance level of 5%. If the test statistic falls in the rejection region, she would reject the null hypothesis and conclude that there is evidence to suggest that the true proportion of heads is different from 50%.

Therefore, by using the correct null and alternative hypotheses, Becky can proceed with her hypothesis test accurately and draw valid conclusions regarding the randomness of her coin flips.

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