Suppose a rumor is spreading at a dance attended by 200 students. The rumor is spreading at a rate that is directly proportional to both the number of students who have heard the rumor and the number of students who have not heard the rumor. Let P be the number of students who have heard the rumor, and let be the time in minutes since the rumor began to spread. (a) Write a differential equation to model this rate of change.

So, Lana gave away 26.32% of he Pokemon cards  to her little brother.

To find the percentage of cards Lana gave away, we can use the formula:(Quantity given away / Total quantity) * 100.

In this case, Lana gave away 125 cards out of her total collection of 475 cards.Plugging these values into the formula, we have:

(125 / 475) * 100 = 0.2632 * 100 = 26.32%.

Lana gave away 26.32% of her Pokemon cards to her little brother.

Alternatively, we can calculate the percentage by subtracting the remaining cards from the total and finding the ratio:

Percentage given away

= (Cards given away / Total cards) * 100

= (125 / 475) * 100

= 26.32%.

For such more questions on Pokemon cards:

https://brainly.com/question/28992229

#SPJ11

Answer:

I think it may be 120 cm

Step-by-step explanation:

A F is 13 using pythagorean theorem on triangle CED and applying the hypotenuse length to A F.

ABC is similar to triangle CED and is dilated by a factor of 3  so the base is 36.

using pythagorean theorem on triangle ABC gets the hypotenuse length of 39 which can be applied to FE

add all the values together

39 + 13 + 15 + 36 +12 +5 = 120

Answer:

x)45

y)45

z)135

Step-by-step explanation:

Step-by-step explanation:

Given:

The rule is telling us to add 7 to the given value of x.

Add 7 to 12.

\(7 + 12 = 19\)

The missing number is 19.

Answer:

i dont now but i thin it is 5

Step-by-step explanation:

A chart or graph that presents grouped data with rectangular bars with lengths proportional to the values that they represent is known as a bar graph.

A bar graph is a way to visually represent data using rectangular bars with lengths proportional to the values that they represent.

The bars can be either vertical or horizontal, depending on the orientation of the graph. The vertical bars are known as a column graph, while the horizontal bars are known as a bar chart.

The purpose of a bar graph is to provide a clear and concise representation of data that is easy to understand and interpret. Bar graphs are commonly used to compare different sets of data or to track changes in data over time.

They can be used to show how a particular variable changes over time or to compare the values of different variables in a single graph.

Bar graphs are easy to read and interpret, making them a popular choice for both simple and complex data sets.

They are widely used in business, science, and education, among other fields, to present information in a clear and concise manner.

To learn more about : graph

https://brainly.com/question/19040584

#SPJ8

Answer:

Slope is -1

Step-by-step explanation:

Slope is always the number before the x in these equations.

(wish I could help you with the graphing- some of the points are: (2,1) (1,2) (3,0) (4,-1) (-1,4) )

(hope this helps!)

If  integral expression that represents the area of R in polar form the area of the region R is ln(2) in polar form.

What is integration?

Integration is a mathematical operation that is the reverse of differentiation. Integration involves finding an antiderivative or indefinite integral of a function.

To find the area of the region R in polar form, we can integrate over the region and use the formula for the area of a sector of a circle.

First, we need to determine the limits of integration for θ. The polar curve r = 4/(1 + sin θ) is defined for 0 ≤ θ ≤ π. At θ = 0, the curve intersects the x-axis at r = 0, and at θ = π, the curve reaches its maximum value of r = 4/2 = 2. Therefore, the limits of integration for θ are 0 to π.

Next, we can find the area of the region R by integrating over the sector of the circle defined by the limits of integration for θ and the maximum value of r:

A = ∫(1/2)r² dθ from θ=0 to θ=π/2 + ∫(1/2)r⇄ dθ from θ=π/2 to θ=π

= 1/2 ∫\(0^{\pi /2}\) (4/(1+sinθ))² dθ + 1/2 ∫π/\(2^\pi\) (4/(1+sinθ))² dθ

We can simplify this expression by using the identity 1 + sin θ = (1/2)(2 + 2sin θ):

A = 1/2 ∫\(0^{\pi/2}\) (16/(2+2sinθ)²) dθ + 1/2 ∫π/\(2^{\pi }\) (16/(2+2sinθ)²) dθ

Next, we can use the substitution u = 2 + 2sin θ, du/dθ = 2cos θ, and dθ = du/2cos θ to simplify the integrals:

A = 1/2 ∫4² (16/u²) (du/2cos θ) + 1/2 ∫\(0^{4}\) (16/u²) (du/2cos θ)

= 1/4 ∫4² (1/cos θ) du + 1/4 ∫0^4 (1/cos θ) du

= 1/4 [ln|2+2sinθ|]0π/2 + 1/4 [ln|2+2sinθ|]π/2π

= 1/4 [ln(2+2) - ln(2-2) + ln(2-2) - ln(2+2)]

= 1/4 ln(16)

= ln(2)

Therefore, the area of the region R is ln(2) in polar form.

To learn more about integration from the given link:

brainly.com/question/18125359

#SPJ1

The number of kilowatt-hours consumed in a week by the 850-Watt window air conditioner that is left on all day is approximately 14.28 kW-hrs.

To calculate the number of kilowatt-hours (kW-hrs) consumed by the air conditioner in a week, we need to consider the power rating of the air conditioner (850 Watts) and the duration it is left on each day.

Power of the air conditioner = 850 Watts

Duration of usage per day = 24 hours (left on all day)

Number of days in a week = 7 days

To calculate the energy consumption, we can use the formula:

Energy (kW-hrs) = Power (kW) * Time (hours)

First, let's convert the power from Watts to kilowatts by dividing it by 1000:

Power (kW) = 850 Watts / 1000 = 0.85 kW

Now we can calculate the energy consumption in a week:

Energy (kW-hrs) = Power (kW) * Time (hours)

Energy (kW-hrs) = 0.85 kW * 24 hours/day * 7 days

Energy (kW-hrs) = 14.28 kW-hrs

Therefore, the number of kilowatt-hours consumed in a week by the 850-Watt window air conditioner that is left on all day is approximately 14.28 kW-hrs.

Learn more about kilowatt-hours here:

https://brainly.com/question/18881835

#SPJ11

The distance between the two towers is 30 meters, and the height of the second tower (Tower B) is 90 meters.

We have two towers. Let's call the first tower Tower A, and the second tower Tower B. The height of Tower A is given as 30 meters. The angle of elevation of the top of Tower A from the foot of Tower B is 60 degrees. The angle of elevation of the top of Tower B from the foot of Tower A is 30 degrees. Our goal is to find the distance between the two towers and the height of Tower B.

In triangle ABC, where A is the foot of Tower A, B is the top of Tower B, and C is the top of Tower A:

tan(30 degrees) = AB / BC

Since tan(30 degrees) = 1 / √3, we can rewrite the equation as:

1 / √3 = AB / BC

Cross-multiplying, we get:

BC = AB * √3

In triangle ABC:

tan(60 degrees) = AC / BC

Since tan(60 degrees) = √3, we can rewrite the equation as:

√3 = AC / BC

Substituting the value of BC from Step 3:

√3 = AC / (AB * √3)

Cross-multiplying, we get:

AC = AB * 3

We have two equations:

BC = AB * √3

AC = AB * 3

Dividing equation 2 by equation 1:

AC / BC = 3 / √3

Simplifying, we get:

√3 = 3 / √3

Cross-multiplying, we get:

3 = 3

Since 3 = 3 is a true statement, we can conclude that the two towers are at the same distance as their heights. Therefore, the distance between the two towers is 30 meters.

Using the value of the distance between the towers (30 meters), we can substitute this value into one of the previous equations to find the height of Tower B. Let's use equation 2:

AC = AB * 3

Substituting AB with the distance (30 meters):

AC = 30 * 3

Simplifying, we find:

AC = 90 meters

Therefore, the height of Tower B is 90 meters.

To know more about distance here

https://brainly.com/question/4199102

#SPJ4

Answer:

d

Step-by-step explanation:

The relationship between △ZVT and △XWU based on a congruence theorem is: D. △ZVT ≅ △XWU by ASA

Recall:

Fromm the information given to us about △ZVT and △XWU, we have the following:

Therefore, the relationship between △ZVT and △XWU based on a congruence theorem is: D. △ZVT ≅ △XWU by ASA

Learn more here:

https://brainly.com/question/23968808

Answer:

-23m-18m^4

Step-by-step explanation:

-10m+2m^4-13m-20m^4

(-10m+-13m)+(2m^4-20m^4)

-23m+-18m^4

-23m-18m^4

If this helps please mark as brainliest

a) The average estimated time for Bill to drive to work when he leaves on time at 6:30 with no red lights and no trains to wait for is approximately -19.9166 minutes. b) The estimated coefficients of REDS and TRAINS in the regression model are 1.3353 (REDS). c) The absolute value of the calculated t-value (-1.7733) is less than the critical t-value (1.9719), we fail to reject the null hypothesis.

a) To find the average estimated time in minutes for Bill to drive to work when he leaves on time at 6:30 and there are no red lights and no trains at the crossroad to wait, we substitute the values into the regression model:

TIME = -19.9166 + 0.3692(DEPART) + 1.3353(REDS) + 2.7548(TRAINS)

Given:

DEPART = 0 (as he leaves on time at 6:30)

REDS = 0 (no red lights)

TRAINS = 0 (no trains to wait for)

Substituting these values:

TIME = -19.9166 + 0.3692(0) + 1.3353(0) + 2.7548(0)

    = -19.9166

Therefore, the average estimated time for Bill to drive to work when he leaves on time at 6:30 with no red lights and no trains to wait for is approximately -19.9166 minutes. However, it's important to note that negative values in this context may not make practical sense, so we should interpret this as Bill arriving approximately 19.92 minutes early to work.

b) The estimated coefficients of REDS and TRAINS in the regression model are:

1.3353 (REDS)

2.7548 (TRAINS)

Interpreting the coefficients:

- The coefficient of REDS (1.3353) suggests that for each additional red light, the estimated time to drive to work increases by approximately 1.3353 minutes, holding all other factors constant.

- The coefficient of TRAINS (2.7548) suggests that for each additional train Bill has to wait for at the crossing, the estimated time to drive to work increases by approximately 2.7548 minutes, holding all other factors constant.

c) To test the hypothesis that each train delays Bill by 3 minutes, we can conduct a hypothesis test.

Null hypothesis (H0): The coefficient of TRAINS is equal to 3 minutes.

Alternative hypothesis (Ha): The coefficient of TRAINS is not equal to 3 minutes.

We can use the t-test to test this hypothesis. The t-value is calculated as:

t-value = (coefficient of TRAINS - hypothesized value) / standard error of coefficient of TRAINS

Given:

Coefficient of TRAINS = 2.7548

Hypothesized value = 3

Standard error of coefficient of TRAINS = 0.1390

t-value = (2.7548 - 3) / 0.1390

       = -0.2465 / 0.1390

       ≈ -1.7733

Using a significance level of 5% (or alpha = 0.05) and looking up the critical value for a two-tailed test, the critical t-value for 230 degrees of freedom is approximately ±1.9719.

Since the absolute value of the calculated t-value (-1.7733) is less than the critical t-value (1.9719), we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that each train delays Bill by 3 minutes.

To know more about hypothesis visit:

brainly.com/question/30404845

#SPJ4

Answer:

67 degrease

Step-by-step explanation:

angle #1 = 23

angle #2 = 90

angle #3 = ?

#1 + #2 + #3 = 180

23 + 90 + ? = 180

180 - (23 + 90) = ?

180 - 113 = ?

? = 67

Area of rectangle = Length * Width

Area of rectangle = 6xy*Width

30x^2y= 6xy *Width

Width =

\(30 {x}^{2} y \div 6xy\\ \\ = 5x\\\)

\(\\ \sf\looparrowright p=0.3r\)

Convert 0.3 to fraction then percent

\(\\ \sf\looparrowright 0.3\)

\(\\ \sf\looparrowright \dfrac{3}{10}\)

\(\\ \sf\looparrowright \dfrac{30}{100}\)

\(\\ \sf\looparrowright 30\%\)

Answer:

Step-by-step explanation:

Given

Find r:

Find the difference:

Convert the difference into percent:

The quantity of substance remains after 850 years is 8.98g if the half life of radioactive radium is 1,599 years.

The time taken by substance to reduce to its half of its initial concentration is called half life period.

We will use the half- life equation N(t)

N e^{(-0.693t) /t½}

Where,

N is the initial sample

t½ is the half life time period of the substance

t2 is the time in years.

N(t) is the reminder quantity after t years .

Given

N = 13g

t = 350 years

t½ = 1599 years

By substituting all the value, we get

N(t) = 13e^(0.693 × 50) / (1599)

= 13e^(- 0.368386)

= 13 × 0.691

= 8.98

Thus, we calculated that the quantity of substance remains after 850 years is 8.98g if the half life of radioactive radium is 1,599 years.

Learn more about half life period:

brainly.com/question/20309144

#SPJ4

The amperage for the given circuit is approximately 2.744 Amperes.

To calculate the amperage (current) for a circuit, we can use Ohm's Law, which states that the current (I) is equal to the voltage (V) divided by the resistance (R).

Given:

Voltage (V) = 277 V

Resistance (R) = 100.959 Ohms

Using Ohm's Law, we can calculate the amperage as follows:

Amperage (I) = Voltage (V) / Resistance (R)

I = 277 V / 100.959 Ohms

I ≈ 2.744 Amperes (rounded to three decimal places)

Therefore, the amperage for the given circuit is approximately 2.744 Amperes.

learn more about "amperage ":- https://brainly.com/question/1100341

#SPJ11

The distribution of Y = -log(U) is exponential with a parameter 1.

Given that U is uniformly distributed on the interval (0, 1). We need to find the distribution of Y=−log(U).

Here, Y is a transformed variable of U.

Now we know the transformation of U into Y, we need to find the inverse transformation of Y into U.

To find the inverse transformation, we need to express U in terms of Y.

\(U = g(Y) = e^(-Y)\)

Let F_Y(y) be the cumulative distribution function (CDF) of Y.

Then, \(F_Y(y) = P(Y ≤ y)\)

For any y < 0,

we have

\(F_Y(y) = P(Y ≤ y)\)

= P(-log(U) ≤ y)

= P(log(U) ≥ -y)

For y ≤ 0,

P(log(U) ≥ -y) = 1

This is because log(U) is a decreasing function of U.

So, if -y ≤ 0, then U takes all the values between 0 and 1, hence the probability is 1.

For y > 0,

\(P(log(U) ≥ -y) = P(U ≤ e^(-y))\)

\(= F_U(e^(-y))\)

Hence,

\(F_Y(y) = F_U(e^(-y))\)

for y > 0

Hence, the cumulative distribution function (CDF) of Y is given by:

F_Y(y) = [0, for y < 0; 1, for y ≥ 0; \(1 - e^(-y)\), for y > 0]

Now, we can find the probability density function (PDF) of Y by differentiating the CDF of Y for y > 0:

\(f_Y(y) = F_Y'(y) = e^(-y)\) for y > 0.

Hence, the PDF of Y is given by:

f_Y(y) = [0, for y < 0;\(e^(-y)\), for y > 0]

Know more about the inverse transformation

https://brainly.com/question/31413924

#SPJ11

The median of the data set given for the tips (in dollars) earned in the last hour by waiters in a Japanese restaurant is determined as: 28.

]The median of any given data set is the data value that lies at the center of the data set when ordered.

Given the data set, 30,17,47,47,26,17,36,31,21,17, order the data set from the least to the greatest:

17, 17, 17, 21, 26, 30, 31, 36, 47, 47

The center or middle of the data set is 28.

Thus, the median of the data set given for the tips (in dollars) earned in the last hour by waiters in a Japanese restaurant is determined as: 28.

Learn more about the median on:

https://brainly.com/question/26177250

#SPJ1

Typically, a score in the top 25th percentile for a student's grade level is considered to be a strong performance, while a score in the bottom 25th percentile may indicate a need for additional support.

The I-Ready Diagnostic is a widely used assessment tool that measures student proficiency in math and reading. It's commonly used in K-12 schools to help teachers and administrators track student progress and identify areas where students may need additional support.

Here's a more detailed explanation: A "good score" on the I-Ready Diagnostic depends on several factors, such as the student's grade level, the state's standards, and the student's past performance.

It's important to note that the I-Ready Diagnostic is designed to provide a snapshot of a student's current skills and understanding, and it should not be used as the sole measure of a student's ability.

A student's score on the I-Ready Diagnostic can change from year to year based on their progress and the new material they are exposed to.

to know more about diagnostic refer here

https://brainly.com/question/12814536#

#SPJ11

Answer:2(3)+4(1)=10,

Step-by-step explanation:

To check if (3,1) is a solution to the system of equations 2x+y=7 and 2x+4y=10, we substitute x=3 and y=1 into the equations and check if the equations hold true.

Answer:

16

Step-by-step explanation:

2/3 of 24 students

2/3 * 24 = 16

Answer:

\(\displaystyle m=8\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Point (-5, -7)

Point (-4, 1)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Answer:

\(m = \frac{y_2 - y_ 1 }{x_2 - x_1 } = \frac{1 - ( - 7)}{ - 4 - ( - 5)} = \frac{1 + 7}{ - 4 + 5} = \frac{8}{1} =8\\\)

8 is the slope of a line that goes through points (-5, -7) and (-4, 1)

Answer:

Example of Property Name of Property 5♢6=6♢5 5•6=6•5 4 ♢ (5 ♢ 6) = (4 ♢ 5) ♢ 6 4 • (5 • 6) ... c c Substitution Property of Equality ⋅ ⋅

Yes it is an example of the Symmetric Property of Equality as the relative position of the multipliers changes while maintaining equality.

Answer:

1/2

D

Step-by-step explanation:

slope = \(\frac{rise}{run}\) = \(\frac{2}{4}\) = \(\frac{1}{2}\)

\(\frac{2}{4}\) = \(\frac{3}{6}\)  Same ratio. Both reduce to \(\frac{1}{2}\)

Answer:

its 21/40

Step-by-step explanation: