ABCD is a rhombus with A(-3; 8) and C(5 ; -4). The diagonals of ABCD bisect each other at M. The point E(6; 1) lies on BC. 3.1 3.2 3.3 3.4 A(-3; 8) P D 0 O M TR S B E(6; 1) C(5 ; - 4) Calculate the coordinates of M. Calculate the gradient of BC. Determine the equation of the line AD in the form y = mx + c. Determine the size of 0, that is BAC. Show ALL calculations. T (2 (2 (3 [13​

The line plot, histogram, and box plot provide different visual representations of the reading time data. By analyzing these plots, we can observe the distribution and characteristics of the data, such as central tendency, spread, and outliers.

Line Plot:

A line plot displays data points on a number line, representing the frequency or count of each value.

In this case, the line plot will show the minutes spent reading on the x-axis and the count of students on the y-axis.

For the given data, the line plot will show 10, 20, 30, 40, and 60 on the x-axis, with the corresponding counts displayed above each value.

Histogram:

A histogram displays data distribution by dividing the range of values into intervals or bins and representing the frequency of values falling into each bin.

The histogram will have the minutes spent reading on the x-axis and the count or frequency of students on the y-axis.

The intervals will be 10-19, 20-29, 30-39, 40-49, and 50-59, with the last interval being 60+.

The height of each bar in the histogram will represent the number of students falling into each interval.

Box Plot:

A box plot (also known as a box-and-whisker plot) provides a visual representation of the distribution of data, including measures of central tendency and variability.

The box plot will show a horizontal line inside a box, with whiskers extending from the box, and possibly individual data points beyond the whiskers.

The box will represent the interquartile range (IQR), showing the middle 50% of the data.

The line within the box will represent the median value.

The whiskers will indicate the minimum and maximum values, excluding outliers.

By analyzing these plots, you can observe the central tendency, spread, and distribution of the reading time data. For example, you can identify any outliers, notice the most common reading durations, and observe any patterns or trends within the dataset.

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Answer:

18A324 units

Step-by-step explanation:

The volume of a sphere is given by where r is  given: The raduis of sphere =24 units  

Then the volume of the given sphere will be

Hence, the volume of given sphere

The domain restrictions for (f/g)(x) are (c) x = 0, 6

From the question, we have the following parameters that can be used in our computation:

f(x) = x² - 5x - 6

g(x) = x² - 6x

The composite function (f/g)(x) is calculated as

(f/g)(x) = f(x)/g(x)

substitute the known values in the above equation, so, we have the following representation

(f/g)(x) = (x² - 5x - 6 )/(x² - 6x)

For the domain restriction, we have

x² - 6x = 0

When solved, we have

x =  6 or x = 0

Hence, the domain restrictions for (f/g)(x) are (c) x = 0, 6

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Question

Given f(x) = x² - 5x - 6 and g(x) = x² - 6x, what are the domain restrictions

for (f/g)(x)?

A) x = +6

B) x = 0

C) x = 0,6

D) x = -2,6

Answer:

1)  H0 :  σ₁ ²≥ σ₂²;   Ha:  σ₁² < σ₂²

2)  χ²= 43.52

3) The critical region is χ²≤ 5.23

4) Reject the alternate hypothesis.

5) We conclude that the alternate hypothesis is false and accept the null hypothesis.

Step-by-step explanation:

The claim is that it fills bottle with a lower variation which is the alternate hypothesis

1)  Ha:  σ₁² < σ₂² where  σ₁² is the variation of the new machine and σ₂² is the variation of the old machine.

The null hypothesis is opposite of alternate hypothesis H0 :  σ₁ ²≥ σ₂²

2) The test statistic is χ²= ns²/σ ² which under H0 has  χ² distribution with n-1 degrees of freedom assuming the population is normal.

The calculated χ²= ns²/σ ² = 68( 0.12)²/ (0.15)²=0.9792/0.0225= 43.52

3) The critical region is entirely in the left tail. χ²≤χ²( 0.99)(15)= 5.23

4) The alternate hypothesis is false hence reject it.

5) The calculated χ²=  43.52 does not lie in the critical region χ²≤ 5.23 therefore H0 is accepted and concluded that new machine does not fill bottles with a lower variation.

5 × (10 + 7) = (5 × 10) + (5 ×7) whole number property is represented by

distributive property of multiplication.

As given in the question,

Given number : 5 × (10 + 7) = (5 × 10) + (5 ×7)

Here whole number 5 is first multiplied to addend 10 and then whole number 5 is multiplied to addend 7.

Then, their products are added.

This is represented by property of  Distributive Property of Multiplication.

Therefore,5 × (10 + 7) = (5 × 10) + (5 ×7) whole number property is represented by distributive property of multiplication.

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Answer:

Distributive Property of Multiplication

Step-by-step explanation:

The Distributive Property of Multiplication states that multiplying a number by a group of numbers added together is the same as multiplying each number separately:

\(\large\text{$a(b + c) = ab + ac$}\)

Therefore, applying the Distributive Property of Multiplication to the given expression:

⇒ 5 × (10 + 7) = 5(10) + 5(7)

--------------------------------------------------------------------------------------------

Here are the definitions of the other properties for information purposes:

Associative Property of Multiplication

The grouping of numbers by parentheses in a different way does not affect their product.

\(\large\text{$(a \times b) \times c = a \times (b \times c) = (a \times c) \times b$}\)

Identity Property of Multiplication

This property is also known as the identity property of one.

Multiplying any number by 1 does not change the number, i.e. the number keeps its identity.

\(\large\text{$a \times 1 = a = 1 \times a$}\)

Commutative Property of Multiplication

Changing the order or position of two numbers does not change the end result.

\(\large\text{$a \times b = b \times a$}\)

Step-by-step explanation:

3. Let P(t) be the number of people infected by the virus at time t (in days). We can model the situation with the following exponential function:

P(t) = 400 * 1.25^t

Here, 400 represents the initial number of infected people, and 1.25 represents the growth factor, since the virus is spreading to 25% more people each day.

To find the number of people infected after t days, we can substitute t = (log(3000) - log(400)) / log(1.25) into the equation:

P(t) = 400 * 1.25^t

P(t) = 400 * 1.25^((log(3000) - log(400)) / log(1.25))

P(t) ≈ 2,343

Therefore, approximately 2,343 people are infected when the total number of infections reaches 3000.

4. Let P(t) be the population of the town at time t (in years). We can model the situation with the following exponential function:

P(t) = 10,800 * 0.975^t

Here, 10,800 represents the initial population in 2002, and 0.975 represents the decay factor, since the population is decreasing at a rate of 2.5% each year.

To find when the population reaches half the 2002 value, we can set P(t) = 5,400 and solve for t:

5,400 = 10,800 * 0.975^t

0.5 = 0.975^t

log(0.5) = t * log(0.975)

t ≈ 28.2

Therefore, the population will reach half the 2002 value in approximately 28.2 years, which corresponds to the year 2030.

Answer:

3) 9.03 days

4)  27.38 years

Step-by-step explanation:

To model the spread of the virus over time, we can use an exponential function in the form:

\(\large\boxed{P(t) = P_0(1 + r)^t}\)

where:

Given the virus has infected 400 people in the town and is spreading to 25% more people each day:

Substitute these values into the formula to create a function for P in terms of t:

\(P(t) = 400(1 + 0.25)^t\)

\(P(t) = 400(1.25)^t\)

To find how many days it will take for 3000 people to be infected, set P(t) equal to 3000 and solve for t:

\(\begin{aligned}P(t)&=3000\\\implies 400(1.25)^t&=3000\\(1.25)^t&=7.5 \\\ln (1.25)^t&=\ln(7.5)\\t \ln (1.25)&=\ln(7.5)\\t &=\dfrac{\ln(7.5)}{\ln (1.25)}\\t&=9.02962693...\end{aligned}\)

Therefore, it will take approximately 9.03 days for the virus to infect 3000 people, assuming the daily growth rate remains constant at 25%.

Note: After 9 days, 2980 people would be infected. After 10 days, 3725 people would be infected.

\(\hrulefill\)

To model the population of the town over time, we can use an exponential function in the form:

\(\large\boxed{P(t) = P_0(1 - r)^t}\)

where:

Given the initial population was 10,800 and the population has decreased at a rate of 2.5% each year:

Substitute these values into the formula to create a function for P in terms of t:

\(P(t) = 10800(1 -0.025)^t\)

\(P(t) = 10800(0.975)^t\)

To find how many days it will take for the population to halve, set P(t) equal to 5400 and solve for t:

\(\begin{aligned}P(t)&=5400\\\implies 10800(0.975)^t&=5400\\(0.975)^t&=0.5 \\\ln (0.975)^t&=\ln(0.5)\\t \ln (0.975)&=\ln(0.5)\\t &=\dfrac{\ln(0.5)}{\ln (0.975)}\\t&=27.3778512...\end{aligned}\)

Therefore, it will take approximately 27.38 years for the population to reach half the 2002 value, assuming the annual decay rate remains constant at 2.5%.

Answer:

Step-by-step explanation:

Parallel to y=3x-4 and contains the point (4,5)

if it is to be parallel it has to have the same slope

now to put the point in and solve for b

5 = 3(4) + b

5 = 12 + b

minus 12 from each side

-7=b

so your equation will be....

y = 3x - 7

Remember that

In order to find a coterminal angle or angles of the given angle, simply add or subtract 360 degrees of the terminal angle as many times as possible

Part a

we have

65 degrees

so

65+360=425 degrees

65-360=-295 degrees

Part B

we have

-125 degrees

so

-125+360=235 degrees

-125-360=-485 degrees

Answer:

first four terms are 2, 7, 12, 17

Step-by-step explanation:

use this formula:  \(a_{n}\) = \(a_{1}\) + (n - 1)· d

where 'n' equals the position in the sequence the term is in and 'd' is the common difference

if \(a_{1}\) = 2 and d = 5 are given, plug those into formula

\(a_{1}\) = 2

\(a_{2}\) = 2 + (2 - 1)·5 = 2+5 = 7

\(a_{3}\) = 2 + (3 - 1)·5 = 2+2(5) = 12

\(a_{4}\) = 2+(4 - 1)·5 = 2+3(5) = 17

The first four terms of the arithmetic sequence are 2, 7, 12, and 17.

It is a sequence where the difference between each consecutive term is the same.

We have,

First term = 2

Common difference = 5

First term = 2

Second term = 2 + 5 = 7

Third term = 7 + 5 = 12

Third term = 12 + 5 = 17

Thus,

The first four terms of the arithmetic sequence are 2, 7, 12, and 17.

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Answer:

f(x) = -5/9x - 11/9

Step-by-step explanation:

Consider f(x) = y

so if x = -4 => y = 1 and x = 5 => y = -4

so (-4,1) and (5,-4) should be on the same linear equation

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

m = (-4 - 1)/(5 -  -4) = (-5)/(9) = -5/9

y = mx + b

given m = -5/9, x = -4, y = 1

1 = -5/9(-4) + b

b = 1 - 20/9

b = 9/9 - 20/9 = -11/9

so y = -5/9x - 11/9

or f(x) = -5/9x - 11/9

Answer:

-11

Step-by-step explanation:

6x + 3 = 5x – 8

x + 3 = -8

x = -11

The rectangle's circumference is 27+ (3/2) fee and one of its sides is a semicircle.

We can start by finding the perimeter of the rectangle, which is simply the sum of the lengths of all four sides:

Perimeter of rectangle = 2(length + width) = 2(12 + 3) = 30 feet

Next, we need to find the perimeter of the semicircle.

The diameter of the semicircle is equal to the width of the rectangle, which is 3 feet. The formula for the perimeter of a semicircle is:

Perimeter of semicircle = (π/2) x diameter + diameter

Plugging in the values, we get:

Perimeter of semicircle = (π/2) x 3 + 3 = (3/2)π + 3

Now, we can add the perimeter of the semicircle to the perimeter of the rectangle to get the total perimeter:

Total perimeter = Perimeter of rectangle + Perimeter of the semicircle- 2*diameter of the semicircle

= 30 + (3/2)π + 3 - 3*2

= 27+ (3/2)π

Therefore, the perimeter of the rectangle with a semicircle on one side is 27+ (3/2)π feet, or approximately 31.71 feet (rounded to two decimal places).

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The equation has a solution of x= 3/4 will be B. 8x = 6

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

In this case, the value of x in 3x = 6 will be:

x = 6 / 3

x = 2

The value of x in 8x = 6 will be:

x = 6 / 8

x = 3 / 4

The value of x in 4x = 2 will be:

x = 2/4

x = 1/2

The value of x in 3x = 15 will be:

x = 15 / 3

x = 5

The correct option is B.

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Complete question

Which equation has a solution of x= 3/4?

A. 3x = 6

B. 8x = 6

C. 4x = 2

D. 3x = 15

The solution to the inequality x^3 + x^2 ≤ 10x - 8 is x ≤ -2 or -1 ≤ x ≤ 1.

To find the solution to the inequality x^3 + x^2 ≤ 10x - 8, we need to determine the values of x that satisfy this inequality. Let's break down the problem step by step.

First, let's bring all terms to one side of the inequality to get a cubic equation: x^3 + x^2 - 10x + 8 ≤ 0.

To solve this inequality, we can employ various methods, such as graphing, factoring, or using calculus. However, since the degree of the polynomial is relatively low, we can use a simpler approach.

We start by finding the critical points where the polynomial changes its behavior. To do this, we set the equation equal to zero: x^3 + x^2 - 10x + 8 = 0.

Next, we can use synthetic division or long division to find the factors of the polynomial. By performing this calculation, we find that x = -2 is a factor. Using synthetic division again, we can divide the polynomial by (x + 2) to obtain a quadratic equation: (x + 2)(x^2 - x + 4) = 0.

Setting each factor equal to zero gives us two additional solutions: x = 1 ± √15i. However, since we are dealing with a real-valued inequality, we only consider the real solutions. Therefore, x = -2 is the only real root.

Now, we have identified the critical point x = -2. We can plot this on a number line and choose test points within each interval to determine if they satisfy the inequality. By evaluating the inequality for these test points, we find that the solution is x ≤ -2 or -1 ≤ x ≤ 1.

To summarize, the solution to the inequality x^3 + x^2 ≤ 10x - 8 is x ≤ -2 or -1 ≤ x ≤ 1.

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Answer: 1.5625

Step-by-step explanation: just a calculator

Answer:

1.5625

Step-by-step explanation:

Answer:

It has to be x - 9= 27

so it can be x=36

Answer: The answer to your question is C. Brainliest?

Step-by-step explanation:

For the first square, we can multiply both the numerator and denominator by 5 to get an equivalent fraction with a denominator of 60:

2/12 = (2 x 5) / (12 x 5) = 10/60

For the second square, we can multiply both the numerator and denominator by 4 to get an equivalent fraction with a denominator of 60:

2/15 = (2 x 4) / (15 x 4) = 8/60

Now, we can add the two fractions:

10/60 + 8/60 = 18/60

Simplifying this fraction by dividing both numerator and denominator by 6, we get:

18/60 = 3/10

Therefore, the total shaded area in the diagram is 3/10 or 0.3 in decimal form.

The answer is C. 0.3.

Answer:

1.5 hours

Step-by-step explanation:

Number of miles = 25 miles

Average speed = 7.4 miles per hour

Break after 13.9 miles

How many more hours does he run

Speed = distance / time

Total time for 25 miles :

Time = distance / speed

Time = 25 / 7.4

Time = 3.378 hours

Total time to cover 13.9 miles :

Time = 13.9 / 7.4

Time = 3.378 hours

Time = 1.878 hours

Difference = (3.378 - 1.878) hours = 1.5 hours

Hence, he to ran for 1.5 hours after taking a break

The total time required for the 25 miles run is 3.378 hours and he will run for 1.5 hours after the break.

Given information:

Roberto runs 25 miles.

The average speed is 7.4 miles per hour.

He takes a break after 13.9 miles.

Now, speed is defined as the ratio of distance and time.

So, the time taken by him to run first 13.9 miles will be,

\(s=\dfrac{d}{t}\\7.4=\dfrac{13.9}{t_1}\\t_1=1.878\)

So, he ran for 1.878 hours to cover 13.9 miles.

Now, the total time of the 25 miles run will be,

\(T=\dfrac{25}{7.4}\\T=3.378\)

So, the total time of the run is 3.378 hours.

After the break, he will run for 3.378-1.878 hours = 1.5 hours.

Therefore, the total time required for the 25 miles run is 3.378 hours and he will run for 1.5 hours after the break.

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The value of the angle B from the trigonometric ratios is 53.13 degrees

The Pythagorean theorem is a powerful tool for solving various problems involving right triangles. It allows us to find the length of a missing side in a right triangle when the lengths of the other two sides are known. It is also used to identify whether a triangle is a right triangle or not.

We have that;

TanB = 4/3

B= Tan-1(4/3)

B = 53.13 degrees

Hence we are going to have by the use of tan that the angle is 53.1 degrees

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Answer:

the answer is 360%

Step-by-step explanation:

babc ahx

Okay, here we have this:

Considering the provided equation, we are going to solve the system using an augmented matrix and Gauss-Jordan Elimination. So we obtain the following:

Finally we obtain that the solution to the system is:

Answer:

There are 0

Step-by-step explanation:

Absolute value is the positive distance a number is away from 0, so no value of x will make the equation true

Answer:

A 0

Step-by-step explanation:

There are no solutions. Because the absolute value always returns a positive value, there are no solutions to this equation.

If x is negative, the answer will be positive. If x is positive the answer will still be positive. No value of x will give a value of -4. So there is no solution.

Answer:

1.63 lb

Step-by-step explanation:

1.625 \|\ the five would round the two up to a three

1.63

The probability of randomly picking a school or library-related issue from the ballot is 9/19 or approximately 0.474 (rounded to three decimal places).

To determine the probability of a randomly picked issue being school or library related, you'll need to consider the total number of issues and the number of school and library issues combined.

There are 7 school-related issues, 10 ordinance-related issues, and 2 library-related issues, making a total of 19 issues on the ballot. To find the probability of picking a school or library issue, combine the number of school and library issues: 7 + 2 = 9.

Now, divide the number of school and library issues (9) by the total number of issues (19): 9/19.

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Answer:

8 boxes of donuts

Step-by-step explanation:

72$ /9$ = 8 boxes of donuts

The institution from the industrial revolution is the national institute of space and technology. Hence, option B is correct.

Agrarian and handcraft economies were replaced by industrialized and machine production during the Industrial Revolution in modern history. New modes of living and working were made possible by these technical advancements, which profoundly altered society.

In the 18th century, this practice started in Britain and then extended to other regions of the world. The English economics professor Arnold Toynbee (1852–83), who originally used the word to characterize Britain's economic growth from 1760 to 1840, although it had been used by French writers earlier.

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