Last year there were 30 students in the Chess Club. If the number of students in the Rubik's Cube Club was 20% greater than the number of students in the Chess Club, how many students were in the Rubik's Cube Club?

A. 30
B. 42
C. 36
D. 58 ​

Answer:

Given equation of motion of a particle is,

To find the velocity function of t, value of t when the velocity is zero and acceleration of the particle.

Explanation:

we know that, velocity of a particle is rate of change of the object’s position with respect to a frame of reference and time.

we get,

Substitute for s(t), we get

Differenting we get,

Required velocity function is,

when velocity equal to 0, we get

Dividing by 12, we get

we get,

Taking (t+4) as common we get,

we get,

The values of t are,

t=-4 and t=-2

To find acceleration of a particle.

we know that,

Acceleration a(t) is the rate at which velocity (speed) is changing.

we get,

Substitute v(t), we get,

we get,

The acceleration of a particle is,

The shipping and handling that Danny pay is $145.35.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent.

In this case, Danny buys a couch priced at $765. Shipping and handling area an additional 19% of the price.

The amount will be:

= (19% × $765)

= $145.35

The fee is #145.35.

Learn more about percentages on:

brainly.com/question/24877689

#SPJ1

Answer: $300

Step-by-step explanation:

To calculate the total revenue from selling oranges, we need to multiply the amount of oranges sold by the price per pound.

In this case, we sold 100 pounds of oranges at $3 per pound. So, the total revenue for that day is:

Total revenue = Amount of oranges sold × Price per pound

Total revenue = 100 pounds × $3

Total revenue = $300

Answer:

-6/-2=3   (the answer is 3)

Step-by-step explanation:

Change in y/ Change in x. How you do it: -6-0/2-4=-6/-2=3

Hope this helped :)

The correct answer is B) Point S is between point R and point T.

We know that RS = 7, which means the distance between points R and S is 7 units.
We also know that RT - 5, which means the distance between points R and T is 5 units more than the distance between points R and S.
Lastly, ST = 12, which means the distance between points S and T is 12 units.

To determine the relationship between the points, we can compare the distances RS, RT, and ST.

If R is between S and T, then the distance RS plus the distance ST should equal the distance RT.
In this case, 7 + 12 = 19. However, we are given that RT - 5, not RT. Therefore, R cannot be between S and T.

If S is between R and T, then the distance RS plus the distance ST should equal the distance RT.
In this case, 7 + 12 = 19, which is equal to RT. Therefore, the relationship between points R, S, and T is that point S is between point R and point T.

Therefore, the correct answer is B) Point S is between point R and point T.

Learn more on point here:

brainly.com/question/32083389

#SPJ11

The new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees are approximately (4.993, 2.048).

To find the new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees, we can use the rotation formula:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

Where (x, y) are the original coordinates, (x', y') are the new coordinates after rotation, and theta is the angle of rotation in radians.

Converting the angle of rotation from degrees to radians:

theta = 5 degrees * (pi/180) ≈ 0.08727 radians

Plugging in the values into the rotation formula:

x' = 5 * cos(0.08727) - 2 * sin(0.08727)

y' = 5 * sin(0.08727) + 2 * cos(0.08727)

Evaluating the trigonometric functions and simplifying:

x' ≈ 4.993

y' ≈ 2.048

KLnow more about coordinates here;

https://brainly.com/question/32836021

#SPJ11

The evaluated expression in scientific notation is 1.33 x 10⁰.

To evaluate the expression 7.87 x 10⁻¹ + 0.543 in scientific notation, we need to perform the addition first and then convert the result into scientific notation.

Adding 7.87 x 10⁻¹ and 0.543:

7.87 x 10⁻¹ + 0.543 = 0.787 + 0.543

= 1.33

Now, let's express 1.33 in scientific notation.

In scientific notation, a number is written as a decimal between 1 and 10, multiplied by a power of 10.

To represent 1.33 in this format, we need to determine the appropriate exponent of 10.

Since 1.33 is greater than 1 and less than 10, we can write it as:

1.33 = 1.33 x 10⁰

The exponent of 10 represents the number of places the decimal point must be moved to obtain the original value.

The exponent is 0, the decimal point remains in its original position.

Thus, 1.33 x 10⁰ is equivalent to 1.33.

The expression 7.87 x 10⁻¹+ 0.543, when evaluated and expressed in scientific notation, is equal to 1.33 x 10⁰ or simply 1.33.

For similar questions on scientific notation

https://brainly.com/question/1767229

#SPJ11

Answer:

2=90°

1= 180-(90+48)=42°

3=48°

The amount the college senior will have to pay in one year, given the interest charge and the amount paid, is $ 1, 408. 80

To find the amount, you need to use the future value formula. This would show the amount the college senior would pay in a year given what they spent on the credit card.

The monthly rate is:

= 25 % / 12

= 25 / 12 %

The amount the college senior will pay is:

= 1, 100 x ( 1 + 25 / 12 % ) ¹²

= $ 1, 408. 80

Note : The brackets are raised to the power of 12 because of the number of months in a year which is the amount of time till the college senior pays back.

Find out more on credit card interest at https://brainly.com/question/28800758

#SPJ1

False. When linearizing exponential data using logarithms, the data will become linear and the r²-value of the regression line will likely increase.

The logarithm transformation of the data will help to better fit the data with a linear regression line, since linear regression is used to fit linear data. Therefore, the use of logarithms can actually increase the r²-value of the regression line, not decrease it.

It is important to note that the r²-value does not necessarily indicate the accuracy of the model, but rather how well the model fits the data.

Learn more about logarithms:

https://brainly.com/question/25710806

#SPJ4

The surface area of the rectangular prism figure is S = 838 cm²

Given data ,

The formula for the surface area of a prism is SA=2B+ph, where B, is the area of the base, p represents the perimeter of the base, and h stands for the height of the prism

Surface Area of the prism = 2B + ph

So, the value of S is given by

The heights of the prism is represented as 7cm.

S = ( 11 x 20 ) + ( 7 x 20 ) + ( 4 x 20 ) + 2( 5 x 7 ) + 2( 6 x 4 ) + ( 6 x 20 ) + ( 5 x 20 ) + ( 3 x 20 )

On simplifying the equation , we get

S = 220 + 140 + 80 + 70 + 48 + 120 + 100 + 60

S = 838 cm²

Therefore , the value of S is 838 cm²

Hence , the surface area is S = 838 cm²

To learn more about surface area of prism click :

https://brainly.com/question/9183590

#SPJ1

Let's find the equations of the lines first

1. y=-2x+3

2. y=x+3

Then let's see which one is right

When x = 32 and y = 25, the value of z is calculated as 3200 using the given expression.

According to the following expression, the value of z when x = 32 and y = 25 is:

[z = (x+y)² - (x-y)²]

Substitute the given values of x and y:

\(\[\begin{aligned}z &= (32+25)^2 - (32-25)^2 \\ &= 57^2 - 7^2 \\ &= 3249 - 49 \\ &= \boxed{3200}\end{aligned}\]\)

Therefore, the value of z when x = 32 and y = 25 is \(\(\boxed{3200}\)\).

To know more about expression, refer to the link below:

https://brainly.com/question/28170201#

#SPJ11

Complete Question:

Answer:

A=πr2

Step-by-step explanation:

radius is half a circle and pi is 3.14

When comparing two data sets, the best measure of the center depends on the nature of the data and the specific context of the comparison. There are several measures of central tendency commonly used, each with its own advantages and limitations. The choice of measure depends on the characteristics of the data and the goals of the analysis.

Mean: The mean, also known as the average, is calculated by summing all the values in a data set and dividing by the total number of observations. It is often used when the data is numeric and symmetrically distributed. The mean is sensitive to extreme values and outliers.

Median: The median is the middle value in a data set when it is ordered from least to greatest. It is not affected by extreme values or outliers and is often used when the data is skewed or contains outliers. The median is especially useful when the distribution of the data is not symmetric.

Mode: The mode is the value that appears most frequently in a data set. It is useful for categorical or discrete data and can also be used for numeric data. The mode is often used to identify the most common category or response.

The best measure of center depends on the specific characteristics of the data and the objectives of the analysis. It is often recommended to consider multiple measures of center to gain a more complete understanding of the data.

Learn more about: measure

brainly.com/question/28913275

#SPJ11

The values for p and q in the equation (x² - 6x + 9 = 49) transformed into (x - p)² = q are p = 3 and q = 40, so the answer is option A: -3 and 40.

An equation is a mathematical statement that shows that two expressions are equal. It consists of variables, constants, and mathematical operators such as addition, subtraction, multiplication, and division. Equations are used to solve problems and find unknown values of variables.

In the given question,

To transform the equation x² - 6x + 9 = 49 into the equation (x - p)² = q, we can first subtract 49 from both sides to get:

x² - 6x - 40 = 0

Next, we complete the square by adding (6/2)² = 9 to both sides:

x² - 6x + 9 - 40 + 9 = 0 + 9

(x - 3)² - 22 = 0

Now we can see that p = 3 and q = 22.

Therefore, the answer is D) 3 and 49.

To know more about equation and expression, visit:

https://brainly.com/question/10708415

#SPJ1

The probability is 0.0132.

Here we have mean and standard deviations for air samples from large cities.

According to large samples, the law sample average calculated from large samples is approximately equal to the population average.  

As here sample is taken from a large city, the sample is considered a large sample. Hence mean is approximately equal to the population mean. Also, it is considered a random sample is representative of the population and the sample standard deviation is approximate to the population standard deviation. Hence we can say that carbon monoxide concentrations in air samples from this city are normally distributed.

So here we have

μ = 12

σ = 9 , n = 100

Hence here we need to find,

= p (x > 14)

= p((x-μ /(σ/√n)) > 14-12/9/√100)

= p ( z > 2.22 )

= 1 - p ( z < 2.22 )

= 1 - 0.9868 (using excel formula = norm.s.dist(2.22,1))

= 0.0132

To learn more about standard deviation, and probability,

https://brainly.com/question/13905583

#SPJ4

If a categorical independent variable contains 4 categories, then four dummy variables will be needed to uniquely represent these categories. a. 1 b. 2 c. 3 d. 4

How many dummy variables are needed to represent the categorical variable?

We need 1 less dummy variable than outcomes for the categorical variable.

categorical variable has 2 outcomes

So, we need 2-1 = 1 dummy variable.

Note: If our categorical variable had 5 outcomes, we would need 5-1 = 4 dummy variables.

b. Write the multiple regression equation relating the dependent variable to the independent variables.

Note: Depending your your professor, this can be written one of the following ways...

yhat = a + b1 x1 + bx2

yhat = b0 + b1 x1 + b2 x2

yhat = beta0hat + beta1hat x1 + betahat2 x2

where x1 is the ratio variable

and x2 is the dummy variable

c. Interpret the meaning of the coefficients in the regression equation.

b0 = the predicted value of y when x1 and x2 both equal 0.

b1 = the change in y when x1 increases by 1 unit holding x2 constant.

b2 = the predicted difference in y between the two possible outcomes of the categorical variable holding x1 constant

learn more about of variable here

https://brainly.com/question/14454720

#SPJ4

Using the Runge-Kutta method of second order, the approximate value of y when x = 0.02 is is 1.0203045100525125.

To apply the Runge-Kutta method of second order to approximate the value of y when x = 0.02, we can follow these steps:

\(y' = x^2 + y\)

y(0) = 1

h = 0.01 (step size)

x = 0.02 (desired x-value)

The general formula for the second-order Runge-Kutta method is:

y(i+1) = y(i) + (k1 + k2)/2

where

k1 = h * f(x(i), y(i))

k2 = h * f(x(i) + h, y(i) + k1)

Let's calculate the values step by step:

Set x(0) = 0, y(0) = 1.

k1 = h * f(x(0), y(0))

\(= 0.01 * (0^2 + 1)\)

  = 0.01

k2 = h * f(x(0) + h, y(0) + k1)

\(= 0.01 * ((0 + 0.01)^2 + 1 + 0.01)\)

  = 0.01 * (0.0001 + 1.01)

  = 0.010101

y(1) = y(0) + (k1 + k2)/2

    = 1 + (0.01 + 0.010101)/2

    = 1 + 0.020101/2

    = 1.0100505

Let's perform the calculations iteratively:

Iteration 1:

x = 0.01

y = 1.0100505 (from Step 4)

Iteration 2:

Now we need to repeat steps 2-4 with the new x and y values:

k1 = h * f(x(1), y(1))

\(= 0.01 * (0.01^2 + 1.0100505)\)

  = 0.0102010050025

k2 = h * f(x(1) + h, y(1) + k1)

\(= 0.01 * ((0.01 + 0.01)^2 + 1.0100505 + 0.0102010050025)\)

  = 0.010307015102525

y(2) = y(1) + (k1 + k2)/2

    = 1.0100505 + (0.0102010050025 + 0.010307015102525)/2

    = 1.0203045100525125

After the second iteration, when x = 0.02,

we obtain y ≈ 1.0203045100525125.

Therefore, the approximate value of y when x = 0.02 using the Runge-Kutta method of second order is 1.0203045100525125.

Learn more about Runge-Kutta method

brainly.com/question/30267790

#SPJ11

Using the concept of GCF, the number of people she can feed is 12.

To find the number of people Betty can feed, we should find the GCF of 24 and 36.

The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of two numbers, we can use a factor tree or the Euclidean algorithm.

\(24 = 2 * 2 * 2 * 3\\36 = 2 * 2 * 3 * 3\\GCF = 2 * 2 * 3 = 12\)

GCF(24, 36) = GCF(36, 24 - 12) = GCF(36, 12) = 12

The greatest common factor of 24 and 36 is 12

Learn more on GCF here;

https://brainly.com/question/9703976

#SPJ1

Answer: · D'(-25,-10) E'(-25,15) F'(10,15)

Answer:

o D'(-25,-10) E'(-25,15) F'(10,15)

Step-by-step explanation:

In dilations, the scale factor is how many times larger than the new image will be.

Great, that explains a lot.

In other words, multiply the x and y-coordinate by the scale factor.

In this case, the scale factor is 5.

D(-5,-2)

-5 ⋅ 5 = -25

-2 ⋅ 5 = -10

E(-5,3)

-5 ⋅ 5 = -25

3 ⋅ 5 = 15

F(2,3)

2 ⋅ 5 = 10

3 ⋅ 5 = 15

Therefore, the new coordinates are:

D' (-25,-10)

E' (-25,15)

F' (10,15)

Answer:

Step-by-step explanation: 5/6 - 1/2= 2/6 = 1/3

The given function is:
f(x)={2x+9,44−25​x,​ for x≤5 for x>5​
We need to find the area under the graph of f over the interval [3,6].

Here, we have two different functions for two different intervals:
\(For x ≤ 5, f(x) = 2x + 9For x > 5, f(x) = 44 - 25xFor x ∈ [3, 5],\)
we have\(f(x) = 2x + 9For x ∈ [5, 6], we have f(x) = 44 - 25x\)

we have to find the areas separately for x ∈ [3, 5] and x ∈ [5, 6].For x ∈ [3, 5]:

We need to integrate the function\(f(x) = 2x + 9\)within the interval [3, 5].
We have: \(A = ∫f(x) dx = ∫(2x + 9) dx\)[over the interval \(x ∈ [3, 5]]= [x² + 9x] from x = 3 to x = 5\),
\([(5)² + 9(5)] - [(3)² + 9(3)]= 40\)

area under the graph of f(x) over the interval \(x ∈ [3, 5] is 40.For x ∈ [5, 6]:\)
We need to integrate the function\(f(x) = 44 - 25x\) within the interval [5, 6].
We have:\(A = ∫f(x) dx = ∫(44 - 25x) dx\)[over the interval \(x ∈ [5, 6]]= [44x - (25/2)x²] from x = 5 to x = 6\),
\([44(6) - (25/2)(6)²] - [44(5) - (25/2)(5)²]= 8.5\)

Therefore, area under the graph of f(x) over the interval x ∈ [5, 6] is 8.5.
Therefore, the area under the graph of f over the interval [3, 6] is:
\(A = Area for x ∈ [3, 5] + Area for x ∈ [5, 6]= 40 + 8.5= 48.5\)
the area under the graph of f over the interval [3, 6] is 48.5 square units.

To know more about integrate visit:-

https://brainly.com/question/31744185

#SPJ11

Answer:

D. 60

Step-by-step explanation:

Height = constant / width

30 = c / 2

2* 30 = 60

c = 60

12 = c / 5

12 * 5 = 60

c = 60

10 = c / 6

10 * 6 = 60

c = 60

Answer:

Distribute

Subtract   two from both sides of the equation

Simplify

and that's your solution

which should be t=4

Step-by-step explanation:

The price of the house (y) is directly proportional to the total area of the house (x), you can express the relationship between both variables as follows:

Where "k" is the constant of proportionality.

To determine the price of a house that has 2,000 ft², the first step is to determine the value of the constant of proportionality between both variables. For this, we have to use the known price and size of the house:

-The house has 1,500 ft² → this is the value of x

-The house costs $300,000 → this is the value of y

You can express the relationship as:

To calculate the value of k, you have to divide both sides by 1,500ft²

The constant of proportionality is 200$/ft², this value indicates that the price of the house increases $200 for every additional square foot.

Now that we know the value of the constant of proportionality we can calculate the price of a 2,000ft² house:

For x=2,000ft²

The price of a 2,000ft² is $400,000

The probability that a hand of seven cards drawn at random from a standard 52 card deck contains four cards of one kind and three of another kind is 0.000233.

To calculate the probability of drawing a hand of seven cards containing four cards of one kind and three of another kind, we first need to determine the number of ways we can form such a hand. T

here are 13 ranks of cards in a standard deck, and we need to choose two of them: one for the four cards and one for the three cards. We can do this in 13 choose 2 ways: C(13,2) = 78

Once we have chosen the two ranks, we need to select four cards of one rank and three cards of the other rank. For the first rank, there are C(4,4) = 1 ways to choose four cards, and for the second rank, there are C(4,3) = 4 ways to choose three cards. So the total number of ways to form the desired hand is: 78 * 1 * 4 = 312

Finally, we need to divide this by the total number of possible seven-card hands, which is C(52,7): C(52,7) = 133,784,560 So the probability of drawing a hand of seven cards containing four cards of one kind and three of another kind is: 312 / 133,784,560 ≈ 0.000233

Visit here to learn more about Probability:

brainly.com/question/13604758

#SPJ11

The equations that has a leading coefficient of 3, and a constant of -2 are:

0 = 3x² + 2x – 2

0 = –3x + 3x² – 2

0 = –1x – 2 + 3x²

A leading coefficient is the term that has the highest degree in a polynomial expression.

A constant is a term that has only numbers and contains no variable.

We are given the following equations:

The first, third, and last equations each has a leading coefficient of 3 and a constant of -2.

Therefore, the equations that has a leading coefficient of 3, and a constant of -2 are:

0 = 3x² + 2x – 2

0 = –3x + 3x² – 2

0 = –1x – 2 + 3x²

Learn more about leading coefficient on:

https://brainly.com/question/99237