If p pencils cost c cents, how many pencils can be bought for d dollars? A. (dp)/c B. (100C)/(dp) C. (100cd)/p D. (100dp)/c

The equations given represent parametric equations that define a curve in the Cartesian coordinate system. To plot this curve using the `numpy` and `matplotlib.pyplot` modules in Python, you can follow these steps:

1. Import the required libraries:

```python

import numpy as np

import matplotlib.pyplot as plt

```

2. Define the parameter range `t`:

```python

t = np.linspace(0, 2*np.pi, 1000)  # Specify the range of t values

```

3. Calculate the corresponding `x` and `y` values using the given equations:

```python

x = 16 * np.sin(t)**3

y = 13 * np.cos(t) - 5 * np.cos(2*t) - 2 * np.cos(3*t) - np.cos(4*t)

```

4. Plot the curve:

```python

plt.plot(x, y)

plt.xlabel('x')

plt.ylabel('y')

plt.title('Parametric Curve')

plt.grid(True)

plt.show()

```

Thus, this code will generate a plot of the parametric curve defined by the given equations.

For more details regarding python, visit:

https://brainly.com/question/30391554

#SPJ1

Answer:

25 + 6 = 31

Step-by-step explanation:

Her actual pay is 3262

Her base rate is   2409               Subtract to get the amount over the base

Amount of + 25      853

So how many student more does that amount to?

853 / 136 = 6.27

If you have to round to the nearest integer, the answer is 6.

9514 1404 393

Answer:

  3.5 inches

Step-by-step explanation:

The volume is given by the formula ...

  V = LWH

Filling in the given values, we can solve for the remaining dimension.

  26.46 in³ = (4.2 in)(W)(1.8 in)

  W = 26.46 in²/(7.56 in²) = 3.5 in

The width of the prism is 3.5 inches.

________________________________

Answer:

Explanation:

Multiply height and length of a rectangle then devide to the volume of rectangular prism.

Formula:

Solution:

To double check do the solution of finding volume of rectangular prism.

Formula:

________________________________

Answer:

Purple Circle : 28.27

Yellow Circle : 43.98

Step-by-step explanation:

Radius of Purple Circle : 4.5

2 * π * 4.5 = 28.27

Radius of Yellow Circle : 7

2 * π * 7 = 43.98

Answer:

y = - 3x + 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, 7) and (x₂, y₂ ) = (2, 1) ← 2 points on the line

m = \(\frac{1-7}{2-0}\) = \(\frac{-6}{2}\) = - 3

the line crosses the y- axis at (0, 7 ) ⇒ c = 7

y = - 3x + 7 ← equation of line

The equation of the line in fully simplified slope-intercept form is y = -2.8x + 7

The linear graph represents the given parameter

For the graph, we have the points

(0, 7) and (25, 0)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx + 7

Using the point (2.5, 0) on y = mx + 7, we have

m(2.5) + 7 = 0

2.5m + 7 = 0

Evaluate

m = -2.8

So, we have

y = -2.8x + 7

Hence, the equation of the line in fully simplified slope-intercept form is y = -2.8x + 7

Read more about linear relation at

brainly.com/question/30318449

#SPJ1

Answer: Even though this is kind of late, hope this helps you, and if not any future people!

Y = 2X + -3

Step-by-step explanation:

I always start by getting my equation which is Y = MX + B. M is equal to the slope, and M is equal to the y-int. Then I am going to find the y-int so I can replace the B. To find the y-int you need to look for the point when x is 0. The y-int is -3 (0,-3). Now I will find the slope of this line. You can find the slop by using the equation Y2 - Y1 / X2 - X1 = slope, to find the slope. But an easier way than that is to use RISE / RUN. And in this equation, we rise 2 and run 1 which means the slope is 2 (2/1). The slope is positive as the line goes "uphill". (Look below)

Y = MX + B ➨ Y = MX + -3 ➨ Y = 2X + -3

a) A negative number on the x-axis (-a, b) would move in the left direction by one unit.

To find out why, check point (0, b) on the y-axis and point (-a, b) on the x-axis.

The distance between these two points is a unit, meaning that the point (-a, b) is one unit to the left of the point (0, b).

b) A positive number on the x-axis (+a, b) would move in the right direction by a unit.

Again, let's look at the point (0, b) on the y-axis and the point (+a, b) on the x-axis.

The distance between the two points is also one unit, which means the point (+a, b) is one unit to the right of the point (0, b).

c) A negative number on the y-axis (a, -b) would move in the downward direction by b units.

Assume that point (a, 0) is on the x-axis and point (a, -b) is on the y-axis. The distance between them is b units, which means that the point (a, -b) is b units below the point (a, 0).

d) A positive number on the y-axis (a, +b) would move in the upward direction by b units.

Also, check the point (a, 0) on the x-axis and point (a, +b) on the y-axis. The distance between these two points is b units, which means that the point (a, +b) is b units above the point (a, 0).

A number is a mathematical term used to show the quantity or value of a thing. It can be depicted using numerals, symbols, or words.

Examples include 30, hundred, -8, 6x, "5", 0.67, etc.

Numbers can be Positive - numbers greater than zero, or negative - numbers less than zero.

Learn more about numbers at brainly.com/question/17200227

#SPJ1

Answer:

1 Answer. The bag will yield 13 1/2 containers of sugar.

Step-by-step explanation:

If this helps brainlist me...

Answer:

9 containers

Step-by-step explanation:

containers that hold a pound

9 pounds total

1 pound per container

Since we want the temperature to be less than 8 degrees Fahrenheit, 8 would be the constant that Digby should use in the inequality.

what is inequality ?

An inequality is a mathematical statement that compares two values or expressions using one of the inequality symbols: "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).

To write an inequality for the temperature during a winter day being less than 8 degrees Fahrenheit, we can use the inequality symbol "<" which means "less than."

So, the inequality would be:

Temperature < 8 degrees Fahrenheit

Therefore, Since we want the temperature to be less than 8 degrees Fahrenheit, 8 would be the constant that Digby should use in the inequality.

To learn more about Inequality from given link.

https://brainly.com/question/30228778

#SPJ1

Answer:

A) Vector component for the cruise ship: (0, -22)

B) Vector component for the Gulf Stream: (4, 0)

C) Resultant vector: (4, -22)

D) Resultant velocity: Approximately 22.4 mph (rounded to the nearest tenth)

E) Resultant direction: Approximately -80.5 degrees (rounded to the nearest tenth)

Step-by-step explanation:

To solve this problem, we'll consider the velocities of the cruise ship and the Gulf Stream as vectors and calculate their components and resultant vector. Then we'll find the magnitude (resultant velocity) and direction (resultant direction) of the resultant vector.

Given:

Cruise ship velocity (south): 22 mph

Gulf Stream velocity (east): 4 mph

A) Vector component for the cruise ship:

The cruise ship is traveling south, so its velocity vector is (0, -22).

B) Vector component for the Gulf Stream:

The Gulf Stream is flowing east, so its velocity vector is (4, 0).

C) Resultant vector:

To find the resultant vector, we'll add the two velocity vectors together:

Resultant vector = Cruise ship velocity + Gulf Stream velocity

Resultant vector = (0, -22) + (4, 0)

Resultant vector = (0 + 4, -22 + 0)

Resultant vector = (4, -22)

D) Resultant velocity:

The magnitude of the resultant vector gives us the resultant velocity. We can use the Pythagorean theorem to calculate it:

Resultant velocity = sqrt((x-component)^2 + (y-component)^2)

Resultant velocity = sqrt((4)^2 + (-22)^2)

Resultant velocity = sqrt(16 + 484)

Resultant velocity = sqrt(500)

Resultant velocity ≈ 22.4 mph (rounded to the nearest tenth)

E) Resultant direction:

The direction of the resultant vector can be found using trigonometry. We'll use the inverse tangent function (arctan) to find the angle between the resultant vector and the positive x-axis.

Resultant direction = arctan(y-component / x-component)

Resultant direction = arctan(-22 / 4)

Resultant direction ≈ -1.405 radians or -80.5 degrees (rounded to the nearest tenth)

Therefore, the answers are:

A) Vector component for the cruise ship: (0, -22)

B) Vector component for the Gulf Stream: (4, 0)

C) Resultant vector: (4, -22)

D) Resultant velocity: Approximately 22.4 mph (rounded to the nearest tenth)

E) Resultant direction: Approximately -80.5 degrees (rounded to the nearest tenth)

The mean of a dataset is the sum of all data elements divided by the count of the elements.

The location of the 6th score relative to the mean is 5 points below the mean

Let:

\(\bar x \to\) Mean

\(a \to\) 5 scores

\(b \to\) 6th scores

Given that:

\(n = 6\)

The 5 scores that are 1 above the mean implies that:

\(a = \bar x + 1\)

The mean of a dataset is calculated using:

\(\bar x = \frac{\sum x}{n}\)

So, we have:

\(\bar x =\frac{5a + b}{6}\)

\(\bar x =\frac{5(\bar x + 1) + b}{6}\)

Open brackets

\(\bar x =\frac{5\bar x + 5 + b}{6}\)

Multiply both sides by 6

\(6\bar x =5\bar x + 5 + b\)

Make b the subject

\(b = 6\bar x -5\bar x - 5\)

\(b = \bar x - 5\)

This means that the 6th score is 5 points below the mean

Read more about mean at:

https://brainly.com/question/17060266

Answer:

The fourth vertex needed to create the rectangle is (-7,-25).

Step-by-step explanation:

As per the property of a rectangle, the lengths of the opposite sides of a rectangle are the same.

Let,

point A=(-4,-25)

point B=(-4,-12)

point C=(-7,-12)

Thus, point D or the fourth vertex is (-7,-25).

Refer to the image for a better understanding.

To solve more such questions,

https://brainly.com/question/30343196

The probability that the 4 oldest people in the group were selected is based on combinatorics is 0.00303 or 0.303%.

Given that:

Find how many ways the 4 oldest people can be selected from the group.

Since the 4 oldest people are already determined, there is only 1 way to select them.

To calculate the probability, to determine the total number of ways to select 4 people from the group of 11. This can be found using the combination formula:

Number of ways to choose k items from n items :

C(n,k) = n! / (k!(n-k)!)

Calculate the total number of ways to select 4 people from the group:

Plugging n and k value from given data:

C(11,4 )= 11! / (4!(11-4)!)

On simplifications gives:

C(11, 4) = 330.

Calculate the probability:

Probability = Number of ways 4 oldest people selected / Total number of ways to select 4 people

Plugging the given data:

Probability = 1 / 330

Probability ≈ 0.00303 or 0.303%.

Therefore, the  probability that the 4 oldest people in the group were selected is based on combinatorics is 0.00303 or 0.303%.

Learn more about probabilities here:

https://brainly.com/question/23846068

#SPJ4

Answer: C is the correct answer!I don't feel like explaining. sorry.Please let me know if I am wrong.

Answer:

6

Step-by-step explanation:

You could expand t to 1+1+1+1+1+1 which would give you 6.

Answer:

2+4=6

Step-by-step explanation:

Answer:

a.) each line segment represents a length of 1/8

b.) N = 3/8

c.) -3/8

Step-by-step explanation:

a.) In order to find the interval / length of each line segment, simply count how many line segments there are until you reach one whole integer. Basically, start on one number and count how many sections until the next number.

So for this example, let's start counting from the number 0. From 0 to the next number, 1, there are a total of 8 sections from 0 to 1, so they're each split up into 1/8s.

b.) Count each line as 1/8 from 0 to N to get what N represents. So from 0 to N, there are 3 lines/portions, so N is 3/8 because 1/8 + 1/8 + 1/8 = 3/8

c.) Just put a negative sign in front of N to get the opposite

The circumference and the area of a circle with a radius of 9m is 28.26

The circumference of a circle is its perimeter or distance around it. It is denoted by C in math formulas and has units of distance, such as millimeters (mm), centimeters (cm), meters (m), or inches (in). It is related to the radius, diameter, and pi using the following equations:

Given that:

Circumference of Circle = \(2\pi r\)

\(9x=28.26\)

\(9*3.14=28.26c\)

\(or\) \(28.26c\) ÷ \(\pi(3.14)=9r\)

Therefore, The circumference and the area of a circle with a radius of 9m is 28.26

Learn more about finding the circumference here:

https://brainly.com/question/27447563

Answer:

$63,333.33

Step-by-step explanation:

Divide 1,900,000 by 30 to get $63333.3333....which technically just rounds to $63333.33, and if you want to go further, $63333.

The Domain depends on the value of n.

The Domain is all real numbers if n is ODD.

The Domain is all real numbers if n is EVEN.

Assuming that p(x) is a real-valued function, we can make the following statements about the domain of the function f(x) = n√(p(x)):

The domain of the function f(x) depends on the domain of the function p(x) since we cannot take the square root of a negative number. Therefore, the domain of f(x) is all real numbers x for which p(x) is non-negative (i.e., p(x) ≥ 0).

If n is odd, then the domain of f(x) is still all real numbers x for which p(x) is non-negative since the odd root of a negative number is negative, which is not allowed in the real numbers.

If n is even, then the domain of f(x) is all real numbers x since the even root of a negative number is allowed in the real numbers.

Therefore, the statement "The domain is all real numbers" is not true in general. It depends on the value of n and the domain of p(x).

Learn more about domain here: https://brainly.com/question/26098895

#SPJ1

The binomial variable with mean 17 transformers and standard deviation √2.55 transformers.

In math standard deviation is defined as a measure of how dispersed the data is in relation to the mean.

Here we have know that the good electrical transformers operate at approximate 85% of the total time and 20 electrical transformers are chosen at random.

Here let us assuming the variable is a binomial variable.

Then we have written it as in the following form,

=> Mean = number of samples * probability

And the value of standard deviation is calculated as

=> Standard Deviation = √mean (1 − probability)

Here we know that the value of mean is calculated as,

=> 85% * 20 = 0.85*20 = 17 transformers

Then the value of Standard deviation is calculated as,

=> √mean * (1 − 0.85)

Apply the values on the formula, then we get,

=> √17 * 0.15 =√2.55 transformers.

Hence the random variable is a binomial variable.

To know more about Standard deviation here.

https://brainly.com/question/16555520

#SPJ4

The slope formula is the changes of two y-values over/to the changes of two x-values.

\( \large \boxed{m = \frac{y_2 - y_1}{x_2 - x_1} }\)

Substitute two given points in the formula to find the slope. The m-term represents the slope from y = mx+b.

\(\large{m = \frac{10 - ( - 8)}{2 - 10} } \\ \large{m = \frac{10 + 8}{ - 8} } \\ \large{ m = \frac{18} { - 8} \longrightarrow \frac{9}{ - 4} } \\ \large \boxed{m = - \frac{9}{4} }\)

Answer

Hope this helps and let me know if you have any doubts!

Answer:

m=-9/4

Step-by-step explanation:

Hi there!

The formula for the slope (m) calculated from two points is given as (y2-y1)/(x2-x1), where (x1,y1) and (x2,y2) are points

we are given the two points (2,10) and (10,-8)

to avoid any confusion, let's label the values of the points

x1=2

y1=10

x2=10

y2=-8

now substitute into the formula:

m=(-8-10)/(10-2)

subtract

m=(-18)/(8)

simplify (reduce to lowest terms)

m=-9/4

Hope this helps!

The two types of frequency distributions are Discrete Frequency Distribution and Grouped Frequency Distribution

The two types of frequency distributions are;

When the data consists of discrete, separate values, this sort of distribution is used. It displays the frequency or number of occurrences of each value.

The data is often expressed in a table with two columns: one for distinct values and another for the frequencies of those values.

This distribution is utilized when the data is continuous and has a wide range of values. It entails categorizing the data into intervals or classes and then calculating the frequency of values that fall within each interval.

Learn more about frequency distribution at: https://brainly.com/question/27820465

#SPJ1

Answer:

\(( \frac{1}{3})^{3} \)

Step-by-step explanation:

There are many expressions that can be equivalent to 1/27.

For example, 2/54, 3/81 etc

But I think the expression you are looking for is

\( \frac{1}{27} = \frac{1 \times 1 \times 1}{3 \times 3 \times 3} = \frac{ {1}^{3} }{ {3}^{3} } = ( \frac{1}{3} )^{3} \)

Hope this is helpful

Answer:

(5, 4)

Step-by-step explanation:

(x + 2, y + 3)

(3  + 2, 1 + 3)

(5, 4)

Answer:

B' (5, 4 )

Step-by-step explanation:

the translation rule (x, y ) → (x + 2, y + 3 )

means add 2 to the original x- coordinate and add 3 to the original y- coordinate , then

B (3, 1 ) → B' (3 + 2, 1 + 3 ) → B' (5, 4 )

Answer:

8:15:30

Step-by-step explanation:

8:15:30 a.m hope I helped ;)

The required  exponential function will be F(x)= \(4(0.5)^{x}\)

Hence, Option A is the correct.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

From the assumption graph as shown in attached figure, we can determine that when x = 0  then y = 4.

Also, we can closely observe that the graph represents decay  

exponential function.

The reason is that when the value of x   increases, the graph of the particular function decreases.

But, the rate of decay must be less than 1 for decay exponential function because if it is greater than 1, then it would represent  the exponential growth function.  

Hence, the option B and D should be completely ruled out as these values represent the exponential growth.  

And from graph, it is clear that when  x = 0 then y = 4

The exponential function will be F(x)= \(4(0.5)^{x}\)

To learn more about function visit:

https://brainly.com/question/8892191

#SPJ7

Answer:

a. 0.9375, 0.46875

b. geometric sequence

c. equation: \( 7.5 * (\frac{1}{2})^(n-1)\)

Step-by-step explanation:

a.

The table can be finished as follows:

n t(n)

1 7.5

2 3.75

3. 1.875

4. 0.9375

5 0.46875

b.

The type of sequence is a geometric sequence.

A geometric sequence is a sequence of numbers where the ratio between any two consecutive terms is constant.

In this case, the ratio between any two consecutive terms is 3.75/7.5=½ ,

so the sequence is geometric.

c.

The equation for the sequence is t(n) = 7.5 * (1/2)^n.

This equation can be found by looking at the first term of the sequence (7.5) and the common ratio (1/2).

t(1) = 7.5

t(2) = 7.5 * (1/2) = 3.75

t(3) = 7.5 * (1/2)^2 = 1.875

The equation can also be found by looking at the general formula for a geometric sequence,

which is \(t(n) = a*r^{n-1}\)

In this case,

t(n) =\( 7.5 * (\frac{1}{2})^{n-1}\)

This is the required equation.

Answer:

\(\textsf{a.}\quad \begin{array}{|c|c|c|c|c|c|}\cline{1-6}\vphantom{\dfrac12} n&1&2&3&4&5\\\cline{1-6}\vphantom{\dfrac12}t(n)&7.5&3.75&1.875&0.9375&0.4687\\\cline{1-6}\end{array}\)

\(\textsf{b.} \quad \textsf{Geometric sequence.}\)

\(\textsf{c.} \quad t(n)=7.5(0.5)^{n-1}\)

Step-by-step explanation:

Before we can complete the table, we need to determine if the sequence is arithmetic or geometric.

To determine if a sequence is arithmetic or geometric, examine the pattern of the terms in the sequence.

Calculate the difference between consecutive terms by subtracting one term from the next:

\(t(2)-t(1)=3.75-7.5=-3.75\)

\(t(3)-t(2)=1.875-3.75 = -1,875\)

As the difference is not common, the sequence is not arithmetic.

Calculate the ratio between consecutive terms by dividing one term by the previous term.

\(\dfrac{t(2)}{t(1)}=\dfrac{3.75}{7.5}=0.5\)

\(\dfrac{t(3)}{t(2)}=\dfrac{1.875}{3.75}=0.5\)

As the ratio is common, the sequence is geometric.

To complete the table, multiply the preceding term by the common ratio 0.5 to calculate the next term:

\(t(4)=t(3) \times 0.5=1.875 \times 0.5=0.9375\)

\(t(5)=t(4) \times 0.5=0.9375 \times 0.5=0.46875\)

Therefore, the completed table is:

\(\begin{array}{|c|c|c|c|c|c|}\cline{1-6}\vphantom{\dfrac12} n&1&2&3&4&5\\\cline{1-6}\vphantom{\dfrac12}t(n)&7.5&3.75&1.875&0.9375&0.4687\\\cline{1-6}\end{array}\)

To find an equation for the sequence, use the general form of a geometric sequence:

\(\boxed{\begin{minipage}{5.5 cm}\underline{Geometric sequence}\\\\$a_n=ar^{n-1}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\\phantom{ww}$\bullet$ $r$ is the common ratio.\\\phantom{ww}$\bullet$ $a_n$ is the $n$th term.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}\)

In this case, the first term is the value of t(n) when n = 1, so a = 7.5

We have already calculated the common ratio as being 0.5, so r = 0.5.

Substitute these values into the formula to create an equation for the sequence:

\(t(n)=7.5(0.5)^{n-1}\)