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9514 1404 393

Answer:

  √34 ≈ 5.831

Step-by-step explanation:

The distance (d) between point (x, y) and the line ax +by +c = 0 is given by ...

  d = |ax +by +c|/√(a²+b²)

Using the given values, the distance is ...

  d = |3(6) +5(3) +1|/√(3² +5²) = 34/√34

  d = √34

The distance between the point and the line is √34 ≈ 5.831 units.

_____

The graph confirms this result by showing the line is tangent to a circle with radius √34 centered on (6, 3).

(1) 6 students read all three courses.

(II) 37 students read only one course.

(III) 77 students read exactly two courses.

(IV) 73 students read Accountancy irrespective of Sociology or French.

Let A represent the number of students reading Accountancy, S represent the number of students reading Sociology, and F represent the number of students reading French.

Let X be the number of students reading all three.

From the information given:

A ∩ S = 19

A + S - 27 = 120 - 53 + 19 = 86 (number of students reading Accountancy or Sociology but not French)

S - A - X = 27

S + F - X = 53

F - X = 19

A - X = 86 - 19 = 67

Total = A + S + F - (A ∩ S) - (A ∩ F) - (S ∩ F) + X = 120

Solving, we get X = 6, A = 73, S = 52, F = 25.

(1) 6 students read all three courses.

(II) 37 students read only one course.

(III) 77 students read exactly two courses.

(IV) 73 students read Accountancy irrespective of Sociology or French.

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Answer:

none of the answers are correct because 2 and 5 are across      

( don't know how to explain it) and they have to be the same

Answer:

Angle × = 23°

Step-by-step explanation:

All angles of a triangle are always equal to 180°.

So, we got the measurements of two angles already.

One is 67° and the other is 90° (right angle).

So, (67 + 90) + Angle × = 180°

157 + Angle × = 180°

Transpose 157 to the side if 180°.

Angle × = 180 - 157

Angle × = 23°

Hope it helps!

The time that David left the money in the account would be = 4 years

An earned interest is the amount of money that is regularly paid to an individual who invested a specific amount of money for a stipulated period of time.

The principal amount(p)= $300

The time (T)= X

The rate of interest yield (R)= 5 %

Simple interest( SI)= $ 60

Using the formula;

SI = P×T×R/100

Make T the subject of formula;

T = SI×100/P*R

T= 60×100/300×5

T= 6000/1500

T = 4 years.

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Answer:

303 mi

Step-by-step explanation:

18 (24) = 432

9 (16) = 144 - 15 = 129

432 - 129 = 303 mi

Hope this helps！

Answer:

Area of the shaded region = 303 mi²

Step-by-step explanation:

Area of the shaded region : ( 4 * 8  ) + (5 * 11 ) + ( 24 * 9 ) = 303 mi²

The total amount to each person end up paying $20.54.

To find the total amount each person will pay, first calculate the 20% tip on the total bill and then divide the sum by the number of people.

To split the bill evenly among Raphael and his four friends, we first need to find the total cost including the 20% tip.

The tip is 20% of the original bill, which is equivalent to 0.20 x $85.60 = $17.12.

Therefore, the total cost of the bill with the tip is $85.60 + $17.12 = $102.72.

To split this evenly among the five people, we divide by 5:

$102.72 ÷ 5 = $20.54

So each person will end up paying $20.54.

20% of $85.60 is ($85.60 * 0.20) = $17.12

Add the tip to the total bill:

$85.60 + $17.12 = $102.72

Divide the total amount by the number of people (5): $102.72 / 5 = $20.54

Therefore, the answer is B. $20.54.

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Answer:

\(135^\circ\)

Step-by-step explanation:

Given that, a regular octagon is to be constructed.

To find:

Each angle in the octagon = ?

Solution:

We know that a regular triangle (polygon with 3 sides) has an interior angle of \(60^\circ\).

And a regular quadrilateral (square) has an interior angle of \(90^\circ\).

Therefore, formula for interior angle of a regular polygon with \(n\) number of sides can be given as:

\(\dfrac{n-2}{n}\times 180^\circ\)

For an octagon, we have \(n=8\).

Value of Interior angle in a regular octagon:

\(\dfrac{8-2}{8}\times 180^\circ=\dfrac{6}{8}\times 180^\circ=\bold{135^\circ}\)

Kindly refer to the attached image for the angle of \(135^\circ\)

Answer:

The answer is 20

Step-by-step explanation:

Solve paranthese first then sqrt your answer then add the remainig

Hey there!

GUIDE:

- means difference which also means “subtract”/“subtraction”.

+ means sum which also means “add”/“addition”.

÷ means quotient which also means “divide”/“division”.
× means product which also means “multiply”/“multiplication”.

= means which also means “is” or “equivalent to”.
a - z (any letter of the alphabet) is known as your “variable”

MET the ANSWER

“The SUM of 4 & k” or “The SUM of k and 4”

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

97

Step-by-step explanation:

48 ( 2 )

= 48 x 2

= 96

48 ( 2 ) + 1

= 96 + 1

= 97

Answer:

97

Step-by-step explanation:

Given the following question:

\(48(2)+1\)

In order to find the answer, we apply the rule where 48(2) = 48 × 2

\(48(2)+1\)
\(48(2)=48\times2\)
\(48\times2=96\)
\(96+1\)
\(96+1=97\)
\(=97\)

Hope this helps.

Answer:

41 1/4 turns

Step-by-step explanation:

create a proportion:

turns / inches = turns / inches

't' = turns

16.5 / 1 = t / 2.5

cross-multiply to get:

t = 41.25 or 41 1/4

Answer:

3x^2+x-2

Step-by-step explanation:

Answer:

\(\displaystyle y=-\frac{4}{13}x+\frac{2}{13}\)

Step-by-step explanation:

Median of a Triangle

The median of a triangle is a line segment joining a vertex to the midpoint of the opposite side.

We have a triangle formed by the points A(-9,-4), B(-3.8), and C(7.-2).

The median from vertex C must pass through the midpoint of the segment AB. First, find that midpoint:

The midpoint (xm,ym) is calculated as follows:

\(\displaystyle x_m=\frac{x_1+x_2}{2}=\frac{-3-9}{2}=-6\)

\(\displaystyle y_m=\frac{-4+8}{2}=2\)

Midpoint AB=(-6,2). This point and C(7,-2) form the required median.

The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:

\(\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\)

\(\displaystyle y-2=\frac{-2-2}{7+6}(x+6)\)

\(\displaystyle y-2=-\frac{-4}{13}(x+6)\)

Operating:

\(\displaystyle y-2=-\frac{4}{13}.x-\frac{4}{13}.6\)

\(\displaystyle y=-\frac{4}{13}.x-\frac{24}{13}+2\)

\(\mathbf{\displaystyle y=-\frac{-4}{13}x+\frac{2}{13}}\)

Answer:

42,40,58

Step-by-step explanation:

Answer:

Ask away by typing or recording your messageAdam, Ben and Carly work out the mean of their ages.Adam is 4 years older than the mean. Ben is 1 year younger than the mean.Is Carly older or younger than the mean?By how many years?Let's start by finding the mean of their ages. We can do this by adding their ages and dividing by the number of people: Mean = (Adam's age + Ben's age + Carly's age) / 3 Let's call the mean "M" for now. We can use this to create two equations based on the information given: Adam = M + 4 Ben = M - 1 We can substitute these equations into the mean equation to get: M = (M + 4 + M - 1 + Carly's age) / 3 Simplifying this equation gives us: 3M = 2M + 3 + Carly's age Carly's age = M - 3 So Carly's age is younger than the mean by 3 years.Hey ✋, are you still around? anything else on your mind?To the nearest tenth of a second, how long after the pebble falls will it hit the ground?sTo answer this question, we need to know the height from which the pebble was dropped. We can use the formula: time = sqrt(2 * height / acceleration due to gravity) Assuming the pebble was dropped from a height of 10 meters, and taking the acceleration due to gravity as 9.8 m/s^2, we get: time = sqrt(2 * 10 / 9.8) = 1.43 seconds (to two decimal places) Therefore, the pebble will hit the ground approximately 1.43 seconds after it was dropped.

0 / 350

Answer:

i dont know what you want but exact form is 983/243

decimal form is 4.04526748

mixed form 4 \(\frac{11}{243}\)

Step-by-step explanation:

3x - 14 here, 2x + 10 here. Consequently, X has a value of 14. In algebra, the letter "x" is frequently used to denote a value that is still unknown. It is referred to as a "variable" or "unknown" at times.

In algebra, the letter "x" is frequently used to denote a value that is still unknown. The term "variable" or "unknown" is used to describe it. x in x+2=7 is a variable. Not only can a variable be "y," "w," or any other letter, name, or symbol, it can also be "x." Examine: Variable

Bring the variable to one side of the equation, and then move all the other values to the other side by performing arithmetic operations on both sides of the equation to find the value of x. To determine the answer, simplify the values.

An experiment's independent variable is a variable that stands in for a variable that is being altered. In equations, the independent variable is frequently denoted by the variable x. X is the variable here.

\($$3 x-14-(2 x)=0$$\\\)

We shift every term to the left:

\($3 x-14-(2 x)=0$\)

We combine all the numbers and all the variables.

\($$x-14=0$$\)

All terms containing x are shifted to the left, and all other terms are shifted to the right.

\($$x=14$$\)

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The polar form of the rectangular coordinates (-√√2, -√2) is (2√(1 + √2), 15π/28)

To convert the rectangular coordinates (-√√2, -√2) into polar form, we first need to find the value of r (the radius) and θ (the angle).

r = √((-√√2)^2 + (-√2)^2) = √(2 + 2√2) = 2√(1 + √2)

To find the value of θ, we can use the following formula:

θ = atan(y/x)

where atan is the inverse tangent function, and (x, y) are the rectangular coordinates.

θ = atan(-√2/(-√√2)) = atan(√2) = π/4 radians

However, we need to express the angle in terms of 7 over the interval 0 ≤ θ < 2π/7, with a positive value of r.

To do this, we can add a multiple of 2π/7 to the value of θ until we get an angle in the desired interval.

θ = π/4 + 2π/7 = (7π + 8π)/28 = 15π/28 radians

So the polar form of the rectangular coordinates (-√√2, -√2) is:

(2√(1 + √2), 15π/28)

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Answer:

i have a class now but i will get in trouble sry

Step-by-step explanation:

Answer:

Meeting ID: 851 5556 0217

Step-by-step explanation:

i hate school proceed as you wish good sir! :)

meeting starts at 11:10 btw

Answer:

The  95% confidence interval is  \(98.27 < \mu < 102.53\)

This interval means that there 95% confidence that the true mean is within this interval  

Yes i would agree with my friend because the lower and the upper limit 95% confidence interval for mean points scored at home is greater than 98 points

Step-by-step explanation:

From the question we are told that

   The  sample size is  n =  20

   The  sample mean is  \(\mu = 100.4\)

     The standard deviation is  \(\sigma = 4.86\)

Given that the confidence level is  95% then the level of significance is mathematically evaluated as

                \(\alpha = 100 - 95\)

               \(\alpha = 5\%\)

                \(\alpha = 0.05\)

Next we obtain the critical value of \(\frac{ \alpha }{2}\) from the normal distribution table, the value is  

           \(Z_{\frac{ \alpha }{2} } = 1.96\)

Generally the margin of error is mathematically represented as

           \(E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{ \sqrt{n} }\)

substituting values

            \(E = 1.96 * \frac{ 4.86 }{ \sqrt{20 } }\)

           \(E = 2.13\)

The  95% confidence interval is  mathematically represented as

          \(\= x - E < \mu < \= x + E\)

substituting values

         \(100.4 - 2.13 < \mu < 100.4 + 2.13\)

          \(98.27 < \mu < 102.53\)

Answer:

-64

Step-by-step explanation:

By looking at the numbers, we can identify that this is a geometric sequence and the ratio would be 2. The formula to find the nth term in a geometric series is:

\(t *r^{n-1}\)

where t is the first term and r is the ratio. We can substitute in the information we know:

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

We are looking for the eighth term, so we substitute 8 where n is:

\(-\frac{1}{2}*2^{8-1}\)

We can simplify:

\(-\frac{1}{2}*2^7\)

\(-2^6\)

\(-64\)

Answer:

This function has a local minimum at x = 10 with output value -693

and a local maximum at x = 1 with output value 36.

Step-by-step explanation:

see attached desmos graph.

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Answer:

Already simplified

Step-by-step explanation:

Answer:

Step-by-step explanation:

its preety simple you just have to divide 3/10 and 1/8 and you will get your two answers

Answer:

x=1

Step-by-step explanation:

2x+6x-x=7

7x=7

x=1

...............

The expression equivalent to 2x + 7 + 6x - x is 7(x + 1).

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

2x + 7 + 6x - x

Combine like terms.

2x + 6x - x + 7

7x + 7

7(x + 1)

Thus,

The equivalent expression is 7(x + 1).

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Answer:

(a)7.185

(b)0.000371

(c) 0.019

(d)Sample variance and Sample standard deviation

Step-by-step explanation:

We are given the following sample data.

7.15, 7.20, 7.18, 7.19, 7.21, 7.20, 7.17, 7.18.

(a) Calculate the sample mean. Round your answer to 3 decimal places.

The formula for sample mean =

Sum of terms/Number of terms

= 7.15 + 7.20+ 7.18+7.19+7.21+7.20+7.17+ 7.18/8

= 57.48/8

= 7.185

(b) Calculate the sample variance. Round your answer to 6 decimal places.

The formula for sample Variance =

(x - mean)²/n - 1

n = 8

Sample variance = (7.15 - 7.185)² + (7.20-

7.185)²+ (7.18 -7.185)² + (7.19 -7.185)² + (7.21 - 7.185)² + (7.20 - 7.185)² + (7.17 - 7.185)² + (7.18 - 7.185)² /8 - 1

= 0.001225 + 0.000225+ 0.000025+ 0.000025 + 0.000625 + 0.000225 + 0.000225 + 0.000025/7

= 0.0026/7

= 0.000371428571

Approximately to 6 decimal places = 0.000371

(c) Calculate the sample standard deviation. Round your answer to 3 decimal places.

The formula for Sample Standard Deviation = √Sample variance

= √0.000371428571

= 0.01927248223

To 3 decimal places = 0.019

(d) Which of the following are potential major sources of variability in the experiment

Sample variance

Sample standard deviation

The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.

Answer:

x=3.5

Step-by-step explanation:

Seven divided by Two equals three, and a half.

Answer:14

Step-by-step explanation:do 2*7=14