The number of students in a chess club decreased from 17 to 10. What is
the percent decrease?
There are 3 answers

To find the y-coordinate of point P on the unit circle, given that its x-coordinate is 5/13, we can utilize the Pythagorean identity for points on the unit circle.

The Pythagorean identity states that for any point (x, y) on the unit circle, the following equation holds true:

x^2 + y^2 = 1

Since we are given the x-coordinate as 5/13, we can substitute this value into the equation and solve for y:

(5/13)^2 + y^2 = 1

25/169 + y^2 = 1

To isolate y^2, we subtract 25/169 from both sides:

y^2 = 1 - 25/169

y^2 = 169/169 - 25/169

y^2 = 144/169

Taking the square root of both sides, we find:

y = ±sqrt(144/169)

Since we are dealing with points on the unit circle, the y-coordinate represents the sine value. Therefore, the y-coordinate of point P is:

y = ±12/13

So, the y-coordinate of point P can be either 12/13 or -12/13.

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The lines through each set of ordered pairs are neither parallel nor perpendicular.

The ordered pairs are given as:

(8, 3) (-2, 5) and (-2, -5) (-1, -10)

Start by calculating the slope (m) using:

m = (y2 - y1)/(x2 - x1)

For the first pair, we have:

m = (5 - 3)/(-2 - 8)

m = -1/5

For the second pair, we have:

m = (-10 + 5)/(-1 + 2)

m = -5

Both slopes are not equal, so they are not parallel

Also, both slopes are not opposite reciprocals, so they are not perpendicular.

Hence, the lines through each set of ordered pairs are neither parallel nor perpendicular.

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Answer:

16383

Step-by-step explanation:

i. After 6 years, the amount in the bank account with annual compounding will be $4,238.51.

ii. After 6 years, the amount in the bank account with quarterly compounding will be $4,243.06.

iii. After 6 years, the amount in the bank account with monthly compounding will be $4,245.97.

iv. After 6 years, the amount in the bank account with continuous compounding will be $4,246.93.

To calculate the future amount in the bank account after 6 years with different compounding frequencies, we can use the formula for compound interest: A =\(P(1 + r/n)^(nt)\), where A is the future amount, P is the principal amount, r is the interest rate, n is the compounding frequency per year, and t is the number of years.

i. With annual compounding: A = \(3000(1 + 0.06/1)^(16)\) = $4,238.51.

ii. With quarterly compounding: A = \(3000(1 + 0.06/4)^(46)\)= $4,243.06.

iii. With monthly compounding: A = \(3000(1 + 0.06/12)^(126)\) = $4,245.97.

iv. With continuous compounding: A = \(3000e^(0.066)\) = $4,246.93 (using the formula A = Pe^(rt) where e is the base of the natural logarithm).

These calculations demonstrate how the compounding frequency affects the growth of the investment over time, with more frequent compounding resulting in slightly higher future amounts.

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Equilibrium is the term refers to coordination, balance, and balance in three dimensional space.

The equilibrium condition of an object exists when Newton's first law is valid. An object is in equilibrium in a reference coordinate system when all external forces (including moments) acting on it are balanced. This means that the net result of all the external forces and moments acting on this object is zero.

There are three types of equilibrium: stable, unstable, and neutral.

Examples of equilibrium in everyday life:

A book kept on a table at rest. A car moving with a constant velocity. A chemical reaction where the rates of forward reaction and backward reaction are the same.

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Answer:

r - 1  + (-1) / (r+5)

Step-by-step explanation:

1) divide r² by r to get r.  write this on top.

2) multiply this r by r + 5 to get r² + 5r

3) subtract ( r² + 5r) from  r² + 4r. this gives answer of -r

4) bring down the -6 from dividend

5) divide -r by r to get -1

6) multiply -1 by r + 5. this gives answer -r - 5

7) subtract (-r - 5) from -r - 6. this gives answer of -1

8) now we cannot divide -1 by r. that means -1 is our remainder.

9) you can confirm this by multiplying out (r + 5) (r - 1) = r² + 4r - 5.

this is 1 more than our original divisor (that was -6)

The correct answer is option a)chi-squared distribution

The chi-squared distribution is a continuous probability distribution that is often used in statistical hypothesis testing, especially in the field of the goodness of fit.

It is a distribution of the sum of squares of k independent standard normal random variables. The degree of freedom, k, determines the shape of the distribution.

The chi-squared distribution is frequently employed in hypothesis testing because of how closely it resembles the normal distribution. A test statistic, such as the t-statistic in a t-test, is used in many hypothesis tests.

The sampling distribution of the test statistic for these hypothesis tests approaches the normal distribution as the sample size, n, rises.

The distribution of real-world observations rarely has a chi-square shape. Chi-square distributions are primarily used for hypothesis testing rather than for characterizing actual distributions.

Therefore, The correct answer is option a)chi-squared distribution

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Because the sample statistic centers around a different value than the population parameter, the sample mean absolute deviation is a biased estimator of the population mean absolute deviation.

Reason Behind a Biased Estimator

The expected value (average) of all the sample absolute deviations must match the population absolute deviation in order for the absolute deviation to function as an unbiased estimator. It does not, however, which makes the values of sample mean absolute deviation behave as a  biased estimator.

Brief Description of Sample Mean Absolute Deviation

The average of the absolute deviations from a central point makes up the average absolute deviation of a data collection. It is a statistical summary of statistical variability or dispersion.

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Answer:

9 R 1

Step-by-step explanation:

73/8 = 9 R 1

we know 8x 9 = 72 so we know we have a remainder of 1

The numeric value of ms within is = 19.

To find the numeric value of ms within:

Given: Swithin = 70, sample size = 17 and number of groups = 3.

So, 17 × 3 = 51

70 - 51 = 19

Therefore, the numeric value of ms within is = 19.

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If volleyball team purchased 15 jackets, 12 pairs of sweatpants for $348 and basketball team purchases 8 jackets , 8 pairs of sweatpants for $200, the the system of equations that represent the situation is (b)  \(15x+12y = 348\) and \(8x+8y = 200\) .

let the number of jackets purchased be = x ;

let the number of pairs of sweatshirts purchased be = y ;

the volley ball team purchased 15 jackets and 12 pairs of sweatpants for $348 ,

that means the equation that represents the situation is :

\(15x+12y = 348\) .

Also given that , the basketball team purchased 8 jackets and 8 pairs of sweatpants for $200 ,

that means the equation that represents the situation is :

\(8x+8y = 200\) .

Therefore , the system of equations are \(15x+12y = 348\) and \(8x+8y = 200\) .

The given question is incomplete , the complete question is

A sports apparel supplier offers teams the option of purchasing extra apparel for players. A volleyball team purchases 15 jackets and 12 pairs of sweatpants for $348. A basketball team purchases 8 jackets and 8 pairs of sweatpants for $200. Let x represent the price of a jacket and let y represent the price of a pair of sweatpants. Which system of equations can be used to find the price of each item ?

(a) 8x + 8y = 200  ;  12x + 15y = 348   ;

(b) 8x + 8y = 200  ; 15x + 12y = 348 ;  

(c) 8x + 8y = 348  ;  12x + 15y = 200 ;  

(d) 8x + 8y = 348 ;  15x + 12y = 200 .

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The statement that best proves that <XWY ≅ <ZYW is that two parallel lines are cut by a transversal, then the alternate interior angles are congruent

To determine the correct statement, we need to know the properties of a parallelogram.

These properties includes;

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The word problems shows that Brianna billed $725.63 for all four sessions last month.

For the first session: 5 hours and 23 minutes = 5 x 4 quarters + 3 quarters = 22 + 0.75 = 22.75 quarters.

For the second session: 4 hours and 12 minutes = 4 x 4 quarters + 3 quarters = 16 + 0.75 = 16.75 quarters.

For the third session: 5 hours and 38 minutes = 5 x 4 quarters + 2 quarters = 20 + 0.5 = 20.5 quarters.

For the fourth session: 1 hour and 49 minutes = 1 x 4 quarters + 2 quarters = 4 + 0.5 = 4.5 quarters.

Total time = 22.75 + 16.75 + 20.5 + 4.5 = 64.5 quarters.

Total bill = 64.5 x $11.25 = $725.63.

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The eye color of people on commercial aircraft flights is not a random variable.

What is random variable?

Random variables are variables that can take on different values based on the outcome of a random event or experiment.

However, eye color is a characteristic of individuals and does not vary randomly within a specific context, such as being on a commercial aircraft flight. Eye color is determined by genetic factors and does not change during a flight or as a result of being on a flight.

Eye color is a categorical variable that represents the color of an individual's eyes, such as blue, green, brown, or hazel. While it is not a random variable in the context of commercial aircraft flights, it can still be observed and recorded as a characteristic of the passengers on the flight.

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Te ratio of the heights of the cones that maximizes the volume of the inner cone is 1/4.

To find the ratio of the heights of the cones that maximizes the volume of the inner cone, we can set up an optimization problem.

Let's denote the height of the outer cone as H and the height of the inner cone as h. We are looking for the ratio h/H that maximizes the volume of the inner cone.

The volume of a right circular cone can be calculated using the formula V = (1/3) * π * r^2 * h, where r is the radius of the base and h is the height.

Given that the vertex of the inner cone touches the center of the base of the outer cone, we can conclude that the radius of the base of the inner cone is half of the radius of the base of the outer cone.

Let's denote the radius of the base of the outer cone as R and the radius of the base of the inner cone as r, where r = R/2.

Since the axes of the cones coincide, the ratio of the heights can be expressed as h/H.

To find the ratio h/H that maximizes the volume of the inner cone, we need to maximize the volume function V(h) with respect to h. So, let's calculate V(h):

V(h) = (1/3) * π * (R/2)^2 * h

     = (1/12) * π * R^2 * h

Given that the volume of the outer cone is 150c * m^3, we have:

(1/3) * π * R^2 * H = 150c * m^3

Simplifying:

R^2 * H = 450c * m^3

Now, let's express H in terms of h using the ratio h/H:

H = (h/H) * H = (h/H) * (12/π) * (150c * m^3)^(1/2)

Substituting this expression for H in the equation R^2 * H = 450c * m^3, we get:

R^2 * [(h/H) * (12/π) * (150c * m^3)^(1/2)] = 450c * m^3

Simplifying:

R^2 * h = 450 * (π/12) * (150c * m^3)^(1/2)

R^2 * h = 450 * (π/12) * 150^(1/2) * c^(1/2) * m^(3/2)

We can see that the right-hand side of the equation is a constant. Let's denote it as K:

R^2 * h = K

Since r = R/2, we have r^2 * h = (R/2)^2 * h = (1/4) * R^2 * h = (1/4) * K.

The volume of the inner cone V(h) = (1/12) * π * r^2 * h = (1/12) * π * (1/4) * K = (π/48) * K.

To maximize the volume of the inner cone, we need to maximize the constant K, which is independent of h. Therefore, the ratio of the heights of the cones that maximizes the volume of the inner cone is h/H = 1/4.

In summary, the ratio of the heights of the cones that maximizes the volume of the inner cone is 1/4.

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Answer:

The answer is 47

The height of a rectangular prism is 8.3 cm.

The area is the space occupied by a two-dimensional flat surface. It is expressed in square units. The surface area of a three-dimensional object is the area occupied by its outer surface.

We have,

Surface Area = 288 square cm

Base length = 4 cm and width = 9 cm

So, SA of rectangular prism

288 = 2(lw+ wh + lh)

144 = (36 + 9h + 4h)

13h = 144- 36

13h = 108

h = 8.30 cm

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Answer:

C

Step-by-step explanation:

The greatest common factor of 8 and 10 is 2

The greatest common factor of a^4 and a^3 is a^3

The binomial whose greatest common factor is 2a³ is 8a⁴ + 10a³.

The largest number among all the common factors of the given numbers is known as the GCF (Greatest Common Factor) of two or more numbers. The greatest integer that may be used to divide two natural numbers x and y without producing any remainders is called their GCF. There are three main methods for calculating GCF: division, multiplication, and prime factorization.

Given the a³ is not common in  A and B they are wrong

C. 8a⁴ + 10a³

common factors of 8 and 10 is 2

so 8a⁴ + 10a³  has factors 2a³

Hence option C is correct.

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Answer:

Answer: y-intercept is (0, -6)

Step-by-step explanation:

\({ \tt{y = 2x - 6}}\)

• For y-intercept, x = 0

\({ \tt{y = 2(0) - 6}} \\ { \tt{y = - 6}}\)

To find the y-intercept we have to put zero intead of x and find the value of y :

y = 2 × ( 0 ) - 6

y = 0 - 6

y = - 6

The function which represent the distance and time is y=6x-17.5.

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Here according to the given data, let us take to points to find linear function then,

\((x_1,y_1)=(0.5,3)\) and \((x_2,y_2)=(1,6)\).

Now using slope formula, m = \(\frac{y_2-y_1}{x_2-x_1}\)

=> Slope m = \(\frac{6-3}{1-0.5} = \frac{3}{0.5}\) = 6

Now using equation formula , \(y-y_1=m(x-x_1)\) then,

=> y-0.5=6(x-3)

=> y-0.5=6x-18

=> y=6x-18+0.5

=> y=6x-17.5

Hence the function which represent the distance and time is y=6x-17.5.

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Answer:

85

Step-by-step explanation:

Answer:

its 85

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

The plane's distance is the hypotenuse of a right triangle with legs of

(50 -20)mi = 30 miles     and     30500 - 18000 = 12500 ft

                             for consistent units  12500ft/5280ft/mile = 2.36742 miles

Now just use Pythagorean theorem

Hypotenuse^2 = leg1^2 + leg2^2

               h^2    = 30^2 + 2.36742^2

                   h = ~ miles 30.093 miles  ( note that the vertical descent distance does not matter much)

    (this is 158 892 feet)

Answer:

560

Step-by-step explanation:

check the attached file, I am a maths expert...kindly check the answer

Answer:

A

Step-by-step explanation:

Answer:

when I finish the test I will tell you the right answerer

Step-by-step explanation:

An ice cream shop has 10 flavors and one can choose 4 different flavors. The question asks for the total number of possible flavor combinations.Therefore, we need to find the number of ways in which 4 flavors can be chosen from 10 flavors.

In such cases where order does not matter and repetitions are not allowed, we can use the formula for combinations which is as follows:C(n, r) = n! / (r! (n - r)!)Where n is the total number of items, r is the number of items being chosen at a time and ! represents the factorial function.

Using this formula we can find the total number of possible flavor combinations. Substituting the values in the above formula, we get:C(10, 4) = 10! / (4! (10 - 4)!)C(10, 4) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)C(10, 4) = 210Hence, there are 210 possible flavor combinations when one can choose 4 different flavors

.Explanation:The formula to be used for this type of question is combination. Combination is the method of selecting objects from a set, typically without replacement (without putting the same item back into the set) and where order does not matter. The formula for combination is given by C(n,r)=n!/(r!(n-r)!).

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Answer:

89%

Step-by-step explanation:

22,250 * 100 = 2,225,000

25,000 * 100 = 2,500,000

2,225,000/2,500,000 = 89/100

=89%

When we have a number followed by the "%" it means that this number is divided in 100 parts, so we can represent it with a fraction as shown below:

In order to determine the percentage of ice cream that was sold, we need to multiply the fraction above by the initial amount they had. This is done below:

They sold 49.14 gallons.

Given:

Speed of car is

Required:

Breaking distance d

Explanation:

We have formula to find the breaking distance

substitute the values

Final answer:

Breaking distance of car at speed 57 kmph with 0.8 friction is 16 m approximately.