Find the distance between the points ( 1, 4 ) and ( -2, -1 )​

The percentage increase in the diameter of the drain pipe necessary to enable it to carry 60 litres per second is  28.87%.

Given that the carrying capacity is directly proportional to the area, we can write:

C1 ∝ A1 = πr₁²

Since the carrying capacity is directly proportional to the area, we have:

C2 ∝ A2 = πr₂²

To find the percentage increase in diameter, we need to find the ratio of the increased area to the initial area and then express it as a percentage. Let's calculate this ratio:

(A2 - A1) / A1 = (πr₂² - πr₁²) / (πr₁²) = (r₂² - r₁²) / r₁²

We can also express the ratio of the increased carrying capacity to the initial carrying capacity:

(C2 - C1) / C1 = (60 - 36) / 36 = 24 / 36 = 2 / 3

Since the area and the carrying capacity are directly proportional, the ratios should be equal:

(r₂² - r₁²) / r₁² = 2 / 3

Now, let's substitute r = D/2 in the equation:

((D₂/2)² - (D₁/2)²) / (D₁/2)² = 2 / 3

(D₂² - D₁²) / D₁² = 2 / 3

Cross-multiplying:

3(D₂² - D₁²) = 2D₁²

3D₂² - 3D₁² = 2D₁²

3D₂² = 5D₁²

Dividing by D₁²:

3(D₂² / D₁²) = 5

(D₂² / D₁²) = 5 / 3

Taking the square root of both sides:

D₂ / D₁ = √(5/3)

To find the percentage increase in diameter, we subtract 1 from the ratio and express it as a percentage:

Percentage increase = (D₂ / D₁ - 1) × 100

Percentage increase = (√(5/3) - 1) × 100

Percentage increase = 28.87%

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The normal distribution curve gives useful information regarding the distribution of students' grades, such as the average grade, the dispersion of grades, the likelihood of receiving a specific grade, and the presence of any outliers.

The normal distribution curve generated by the educator offers multiple insights into the distribution of academic achievement among her pupils. The analysis of the curve yields various informative data such as:

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C) The lines g and g' are parallel and E'(-2,0) and F'(0, 1)

1) Let's locate points E and F.

E (0,2) and F( -4,0)

Given that line was dilated by a scale factor k = 1/2 about the origin we can state the following

• The line segment g' is shorter, half of g.

• Points E'(0,1) and F'(0,1)

3) Examining the answers we can state:

The lines g and g' are parallel and E'(-2,0) and F'(0, 1)

The probability that calls to exactly two randomly selected households will both go unanswered is 0.1849

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

Probabiity of answering, p = 57%

This means that the probability that no one answers the call is

q = 1 - 57%

Evaluate

q = 43%

So, the probability that both calls will go unanswered is

P = q²

This gives

P = (43%)²

Evaluate

P = 0.1849

Hence, the probability is 0.1849

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In calculus, dx is a symbol used to represent a small change or increment in the variable x.

It is commonly used in derivative and integral expressions to indicate the variable of differentiation or integration.

For example, if we have the function f(x) and want to find its derivative, we would write it as df/dx, which represents the change in f with respect to the change in x.

Similarly, if we want to find the integral of a function g(x), we would write it as ∫g(x)dx, which represents the sum of all the small changes in g(x) multiplied by the corresponding small changes in x.

In short, dx is used to indicate the variable of differentiation or integration in calculus.

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By writing and solving a system of equations we will find that the number is 56

So we can write a two-digit number as:

a*10 + b

Where the two digits are a and b.

Here we must have:

a + b = 11

The reversed number is:

b*10 + a

Then we can write the equation:

b*10 + a - a*10 - b = 9

b*9 - a*9 = 9

Then we have a system of two equations:

a + b = 11

b*9 - a*9 = 9

We can divide both sides of the second equation by 9 to get:

b - a = 1

Now we can isolate b to get:

b = 1 + a

Now we can replace this in the other equation.

a + b = a + (1 + a) = 11

2a + 1 = 11

2a = 11 - 1  = 10

a = 10/2 = 5

Now we have the value of a, and we know that:

b = 1 + a = 1 + 5  = 6

Then the two-digit number is:

a*10 + b = 5*10 + 6 = 56

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Given: Jamal is x years old.

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━

And, his mother is 28 years older than Jamal.

Then, age of Jamal's mother is = (x + 28)

⠀⠀⠀

⠀⠀⠀

\(:\implies\sf Jamal's\: uncle\:age = (Jamal's mother age)\\\\\\ :\implies\sf Jamal's\: uncle\:age = 2(x + 28)\\\\\\ :\implies{\underline{\boxed{\pmb{\frak{\purple{Jamal's\: uncle\:age = 2x + 56}}}}}}\:\bigstar\\\\\)

\(\therefore\:{\underline{\sf{Hence,\:the\:expression\:that\: represents\: Jamal's\: uncle \:age\:is\: {\pmb{2x + 36}}.}}}\)

The Alternating Series Test (AST) is used to determine if a series is convergent or divergent. It assumes that the terms alternate in sign and are monotonically decreasing in magnitude, and if lim_(n)a_n = 0, then the series is convergent. The series is given in the general formula for the AST, and the absolute value of each term is equal to the corresponding term.

The series for convergence or divergence using the alternating series test is given below:

[infinity] (−1)n 2nn n! n = 1

The general formula for the alternating series test is as follows. Assume that a series [a_n]_(n=1)^(∞) is defined such that the terms alternate in sign and are monotonically decreasing in magnitude.

If lim_(n→∞)△a_n = 0, where △a_n denotes the nth term of the series,

then the alternating series [a_n]_(n=1)^(∞) is convergent. We must evaluate if the alternating series is monotonically decreasing and if the absolute value of each term of the series is decreasing as well. If both conditions are met, we may apply the Alternating Series Test (AST). Let's take a look at the given series below:(-1)^n(2^n)/(n!) for n = 1 to infinity The series is given in the general formula for the AST. Because the series is already in the right form, we do not need to test it first.

The terms of the sequence decrease since (n+1)!/(n!) = (n+1), which is a positive number. Furthermore, since (n+1) > n for any natural number n, the sequence decreases monotonically. When we take the absolute value of each term in the series, it is equal to the corresponding term since all terms are positive.

Therefore, the series is convergent according to the Alternating Series Test.

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Answer:

16. 1/2

17. 3/4

18. 1/3

19. 1/4

20. 2/3

21. 1/7

22. 1/4

23. 1/7

Answer:

16. 1/2 or 1 over 2

17. 3/4 or 3 over 4

18. 1/3 or 1 over 3

19. 1/4 of 1 over 4

20. 2/3 or 2 over 3

21. 1/7 or 1 over 7

22. 1/4 or 1 over 4

23. 1/7 or 1 over 7

Please Brainliest would be much appreciated

Answer:

177.008in^3

Step-by-step explanation:

Given data

Height= 10.4in

Lenght= 7.4in

Width= 2.3in

The expression for the volume of a box is given as

Volume= Length*width*Height

Volume= 10.4*7.4*2.3

Volume= 177.008 in^3

Hence the volume is 177.008in^3

The solution of units problem is   Suzy has 5 toy trucks by using the equation 15 = 3 * Suzy's number of toy trucks

According to the given information:

If Patricia has 3 times as many toy trucks as Suzy, we can set up an equation where:

Patricia's number of toy trucks = 3 * Suzy's number of toy trucks

We know that Patricia has 15 toy trucks, so we can substitute that value into the equation:

15 = 3 * Suzy's number of toy trucks

Now we can solve for Suzy's number of toy trucks:

Suzy's number of toy trucks = 15 / 3

Suzy's number of toy trucks = 5

Therefore, Suzy has 5 toy trucks.

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Time-series plots are used for several reasons:

B. Time-series plots are used to identify any outliers in the data.

C. Time-series plots are used to identify trends in the data over time.

D. Time-series plots are used to present the relative frequency of the data in each interval or category.

First, we need to know that quantitative variable is required when drawing a time-series plot.

We need to also know that data points are graphically represented as time-series plots, with the variable of interest drawn on the y-axis and time commonly depicted on the x-axis. They demonstrate the variable's evolution over time.

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Answer:

y = 3x + 20

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 )

y = 3x + 5 ← is in slope- intercept form

with slope m = 3

• Parallel lines have equal slopes , then

y = 3x + c ← is the partial equation

to find c substitute (- 8, - 4 ) into the partial equation

- 4 = - 24 + c ⇒ c = - 4 + 24 = 20

y = 3x + 20 ← equation of parallel line

Answer:

Step-by-step explanation: From the given point,

The line is: -8x-4y=0

           viz, 2x+y=0

Answer:

Real, Rational

Step-by-step explanation:

The Set of integers includes zero, positive and negative numbers (not fractions)

Whole numbers include only zero and positive numbers.

Irrational numbers can't be expressed as a fraction; in fact, it's an infinite decimal.

So 0/3 is real and rational. Hope it helps!

Answer:

50,000

Step-by-step explanation:

10*5,000=50,000

Answer: 50,000

Step-by-step explanation:

10× 5,000= 50,000

Or

Just add one zero to 5,000 :)

Hope this helps :)

Okay, it seems like you want to analyze a sample of 16 babies based on their weight.

The information you provided states that the Center for Disease Control and Prevention reports that 25% of baby boys aged 6-8 months in the United States weigh more than 20 pounds.

However, you haven't mentioned the specific question or analysis you want to perform on the sample. Could you please clarify what you would like to know or do with the given information?

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\({\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}\)

\( \star \: \tt \cot \theta = \dfrac{7}{8} \)

\( {\large{\textsf{\textbf{\underline{\underline{To \: Evaluate :}}}}}}\)

\( \star \: \tt \dfrac{(1 + \sin \theta)(1 - \sin \theta) }{(1 + \cos \theta) (1 - \cos \theta) }\)

\({\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}\)

Consider a \(\triangle\) ABC right angled at C and \(\sf \angle \: B = \theta \)

Then,

‣ Base [B] = BC

‣ Perpendicular [P] = AC

‣ Hypotenuse [H] = AB

\( \therefore \tt \cot \theta = \dfrac{Base}{ Perpendicular} = \dfrac{BC}{AC} = \dfrac{7}{8}\)

Let,

Base = 7k and Perpendicular = 8k, where k is any positive integer

In \(\triangle\) ABC, H² = B² + P² by Pythagoras theorem

\( \longrightarrow \tt {AB}^{2} = {BC}^{2} + {AC}^{2} \)

\( \longrightarrow \tt {AB}^{2} = {(7k)}^{2} + {(8k)}^{2} \)

\(\longrightarrow \tt {AB}^{2} = 49{k}^{2} + 64{k}^{2} \)

\(\longrightarrow \tt {AB}^{2} = 113{k}^{2} \)

\(\longrightarrow \tt AB = \sqrt{113 {k}^{2} } \)

\(\longrightarrow \tt AB = \red{ \sqrt{113} \: k}\)

Calculating Sin \(\sf \theta \)

\( \longrightarrow \tt \sin \theta = \dfrac{Perpendicular}{Hypotenuse}\)

\( \longrightarrow \tt \sin \theta = \dfrac{AC}{AB}\)

\(\longrightarrow \tt \sin \theta = \dfrac{8 \cancel{k}}{ \sqrt{113} \: \cancel{ k } }\)

\(\longrightarrow \tt \sin \theta = \purple{ \dfrac{8}{ \sqrt{113} } }\)

Calculating Cos \(\sf \theta \)

\( \longrightarrow \tt \cos \theta = \dfrac{Base}{Hypotenuse}\)

\( \longrightarrow \tt \cos \theta = \dfrac{BC}{ AB} \)

\( \longrightarrow \tt \cos \theta = \dfrac{7 \cancel{k}}{ \sqrt{113} \: \cancel{k } }\)

\(\longrightarrow \tt \cos \theta = \purple{ \dfrac{7}{ \sqrt{113} } }\)

Solving the given expression :-

\( \longrightarrow \: \tt \dfrac{(1 + \sin \theta)(1 - \sin \theta) }{(1 + \cos \theta) (1 - \cos \theta) } \)

Putting,

• Sin \(\sf \theta \) = \(\dfrac{8}{ \sqrt{113} }\)

• Cos \(\sf \theta \) = \(\dfrac{7}{ \sqrt{113} }\)

\( \longrightarrow \: \tt \dfrac{ \bigg(1 + \dfrac{8}{ \sqrt{133}} \bigg) \bigg(1 - \dfrac{8}{ \sqrt{133}} \bigg) }{\bigg(1 + \dfrac{7}{ \sqrt{133}} \bigg) \bigg(1 - \dfrac{7}{ \sqrt{133}} \bigg)} \)

Using (a + b ) (a - b ) = a² - b²

\(\longrightarrow \: \tt \dfrac{ { \bigg(1 \bigg)}^{2} - { \bigg( \dfrac{8}{ \sqrt{133} } \bigg)}^{2} }{ { \bigg(1 \bigg)}^{2} - { \bigg( \dfrac{7}{ \sqrt{133} } \bigg)}^{2} } \)

\(\longrightarrow \: \tt \dfrac{1 - \dfrac{64}{113} }{ 1 - \dfrac{49}{113} } \)

\(\longrightarrow \: \tt \dfrac{ \dfrac{113 - 64}{113} }{ \dfrac{113 - 49}{113} } \)

\(\longrightarrow \: \tt { \dfrac { \dfrac{49}{113} }{ \dfrac{64}{113} } }\)

\(\longrightarrow \: \tt { \dfrac{49}{113} }÷{ \dfrac{64}{113} }\)

\(\longrightarrow \: \tt \dfrac{49}{ \cancel{113}} \times \dfrac{ \cancel{113}}{64} \)

\(\longrightarrow \: \tt \dfrac{49}{64} \)

\(\qquad \: \therefore \: \tt \dfrac{(1 + \sin \theta)(1 - \sin \theta) }{(1 + \cos \theta) (1 - \cos \theta) } = \pink{\dfrac{49}{64} }\)

\(\begin{gathered} {\underline{\rule{300pt}{4pt}}} \end{gathered} \)

\( {\large{\textsf{\textbf{\underline{\underline{We \: know :}}}}}}\)

✧ Basic Formulas of Trigonometry is given by :-

\(\begin{gathered}\begin{gathered}\boxed { \begin{array}{c c} \\ \bigstar \: \sf{ In \:a \:Right \:Angled \: Triangle :} \\ \\ \sf {\star Sin \theta = \dfrac{Perpendicular}{Hypotenuse}} \\\\ \sf{ \star \cos \theta = \dfrac{ Base }{Hypotenuse}}\\\\ \sf{\star \tan \theta = \dfrac{Perpendicular}{Base}}\\\\ \sf{\star \cosec \theta = \dfrac{Hypotenuse}{Perpendicular}} \\\\ \sf{\star \sec \theta = \dfrac{Hypotenuse}{Base}}\\\\ \sf{\star \cot \theta = \dfrac{Base}{Perpendicular}} \end{array}}\\\end{gathered} \end{gathered}\)

\({\large{\textsf{\textbf{\underline{\underline{Note :}}}}}}\)

✧ Figure in attachment

\(\begin{gathered} {\underline{\rule{200pt}{1pt}}} \end{gathered} \)

We can see here that:

A cube is a three-dimensional geometric shape that has six square faces, all of which are congruent (equal in size) and perpendicular to each other. It is a special type of rectangular prism where all edges have the same length, and all angles are right angles (90 degrees).

Cubes are commonly encountered in everyday life, such as dice, boxes, and Rubik's Cube puzzles. They have precise and uniform geometry, making them useful in various mathematical and engineering applications.

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Answer:

98765

Step-by-step explanation:

Answer:

Step-by-step explanation:

180-68=112

1= 68

2=112

Answer:

Step-by-step explanation:

For a point to be a solution to a system of inequalities, the points must make the signs of the inequalities true.

For example, the points must give results like 2<3 or 0>-2, these are true solutions. If the points gives 1>2, then that point is not a solution.

Answer:

A decimal number is a number that has two parts, the whole and the fractional. These parts are divided by a decimal point. For example: 7.45 or 102.7 are decimal numbers.

Answer:

8+2x=18

x=______

10x+4=44

x=_____

To find the values of sin D, sin E, cos D, and cos E, we need additional information such as the measures of angles D and E or the lengths of the sides of the triangle.

However, based on the information you provided (9, 12, 15), we can make some assumptions.

If we assume that the triangle is a right triangle, with side lengths of 9, 12, and 15, we can use the Pythagorean theorem to find the missing side lengths. The side lengths satisfy the Pythagorean theorem: 9^2 + 12^2 = 15^2.

Using these assumptions, we can calculate the values of sin D, sin E, cos D, and cos E. Since angle D is opposite side 9 and angle E is opposite side 12, we have:

sin D = 9/15 = 3/5

sin E = 12/15 = 4/5

cos D = 12/15 = 4/5

cos E = 9/15 = 3/5

Please note that these values are based on the assumption of a right triangle with side lengths of 9, 12, and 15.

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Complete question: Find Sin D, Sin E, Cos D, And Cos E. Write Each Answer As A Fraction In Simplest Form. 9 12 15 E Sin D = Sin E= Cos D= Cos E.

The farmer would have made a profit of 5% if he had sold the goat for 2100 shillings.

Let's use the given terms and find out the percentage profit if the farmer had sold the goat for 2100 shillings.
Calculate the cost price of the goat
We know that the farmer made a loss of 28% by selling the goat for 1440 shillings. Let's represent the cost price as "CP".

We can write the equation:
\(CP \times  (1 - loss% ) = selling price (SP)\)
\(CP \times  (1 - 0.28) = 1440\)
Solve for CP
\(CP \times 0.72 = 1440\)
CP = 1440 / 0.72
CP = 2000 shillings
Calculate the percentage profit
Now we want to find out the percentage profit if the farmer had sold the goat for 2100 shillings.

We can write the equation:
\((SP_{new - CP)} / CP \times  100 = profit\)
\((2100 - 2000) / 2000 \times  100 = profit%\)
\(100 / 2000 \times  100 = profit%\)
5% = profit%.

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Answer:

p = 16

Step-by-step explanation:

Given p is directly proportional to (q + 2)² then the equation relating them is

p = k(q + 2)² ← k is the constant of proportion

To find k use the condition when q = 1, p = 1

1 = k(1 + 2)² = k × 3² = 9k ( divide both sides by 9 )

\(\frac{1}{9}\) = k

p = \(\frac{1}{9}\) (q + 2)² ← equation of proportion

When q = 10 , then

p = \(\frac{1}{9}\) × (10 + 2)² = \(\frac{1}{9}\) × 12² = \(\frac{1}{9}\) × 144 = 16

Answer: I think it’s the 4th one

Step-by-step explanation:

Answer:

2nd one

Step-by-step explanation:

Shaded below means less than

There are infinitely many solutions to an equation with two variables.

We know that an equation is a mathematical statement that contains equal symbol between two mathematical expressions.

In this question need to solve  an equation with x and y in one equation.

Consider an equation with two variables: 5x + y = 8

If we solve given equation for x then it would be,

5x + y = 8

5x + y - y = 8 - y

5x/5 = (8 - y)/5

x = (8 - y)/5

for any arbitrary real value value of y we can find the value of x.

This means there are infinitely many solutions.

If we solve given equation for y then it would be,

5x + y = 8

5x + y - 5x = 8 - 5x

y = 8 - 5x

for any arbitrary real value value of x we can find the value of y.

Therefore, an equation with two variables has infinitely many solutions.

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Answer:

B=3

Step-by-step explanation:

30/3=10

the inequality wanted some  thing equal or grater so 30/3=10

Answer:

Look at the image I attached to my response.

Step-by-step explanation:

For proof #3, I did it according to the way I was taught how to do proofs in my state/school, so what you wrote could be correct.