What is the equation of a line perpendicular to 3x+ 4y =12and passes thru the point (3,2)? Write the equation in slope-intercept form (y=mx+b)

31.41 feet of fence to you need to go around the building.

What is circumference of a circle?

The measurement of the circle's boundaries is called as the circumference or perimeter of the circle. whereas the circumference of a circle determines the space it occupies. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units like cm or unit m are typically used to measure it. The circle's radius is considered while calculating the circumference of the circle using the formula. As a result, in order to calculate the circle's perimeter, we must know the radius or diameter value.

The radius of the circle given is = 50/2 feet.

So the clearance of 20 feet will be there all way.

So total effective radius will be 25-20 5 feet.

the circumference is 2πr = 2*π*5 = 31.41 feet

Hence, 31.41 feet of fence to you need to go around the building.

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The dimensions of a right circular cylinder of maximum volume are

[tex]5\sqrt{6}[/tex] and [tex]10\sqrt{3}[/tex].

Given the radius of sphere is 15 cm.

Let's assume radius of right circular cylinder = r

height of right circular cylinder = h.

Since the cylinder is inscribed in the sphere, their centers will coincide. As a result, the height is divided into two equal portions from the sphere's center. Therefore, we can apply Pythagoras' Theorem to get the cylinder's half-height in terms of radius.

[tex]R^2 = r^2 + (h/2)^2.[/tex]

[tex]r^2 = R^2 - h^2/4.[/tex]

Volume of cylinder = [tex]\pi*r^2*h.[/tex]

Now we can substitute value of [tex]r^2[/tex] in volume of cylinder.

V =  [tex]\pi*( R^2 - h^2/4)*h[/tex]

taking  R = 15 .

V = [tex]\pi*(225 - h^2/4)*h[/tex]

V = [tex]\pi*225*h - \pi*h^3/4[/tex]

For maximum volume we have to do derivative of volume  = 0

derivative with respect to h.

V' = [tex]\pi*225 - 3*\pi*h^2/4[/tex]

V' = 0

[tex]\pi*225 - 3*\pi*h^2/4[/tex]= 0

[tex]3*h^2/4 = 225[/tex]

[tex]h^2 = 75*4.[/tex]

h = 10[tex]\sqrt{3}[/tex]

put the value of h in [tex]r^2 = 225 - h^2/4[/tex]

[tex]r^2[/tex] = 225 - (300/4)

[tex]r^2[/tex] = 150

r = [tex]\sqrt{150}[/tex]

r = 5[tex]\sqrt{6}[/tex].

So the dimensions of a right circular cylinder are 10[tex]\sqrt{3}[/tex] and 5[tex]\sqrt{6}[/tex].

Given Question is incomplete, Complete Question here:

find the dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 15 cm. what is the maximum​ volume?

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Answer:

10

Step-by-step explanation:

if u got up 10 from (9,-2) you will get to (9,8)

The value of x from the given five integers is 34.

Here we have to find the value of x.

Data given:

Five positive number = 31, 58, 98, x, x

The mean is 1.5 times the mode.

Mean = (31 + 58 + 98 + x + x) / 5

         = (187 + 2x) / 5

Mode = x

As the mean is 1.5 times the mode so from this we have:

mean = 1.5 × mode

(187 + 2x)/ 5 = 1.5x

187 + 2x = 7.5x

5.5x = 187

x = 34

Therefore the value of x is 34.

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Answer: A and C is incorrect, the middle is 14. The minimum is 13. The max is 16.

Step-by-step explanation: B is correct

there is no 12

The magnetic moment of an octahedral complex with CFSE=0.8Δo and weak field ligands can take the form of Q.

The Crystal Field Stabilization Energy for a (d3 metal in both forms must be determined in order to provide an answer. The chosen geometry will be the one with the greatest stabilization. The Crystal Field Stabilization Energy is therefore CFSE = -0.8 x 4/9 Δo = -0.355 Δo for tetrahedral d3.

The octahedral d7 complex [Co(CN)64-] is also CN—a strong field ligand. Because of its (t2g)6(eg)1 orbital occupancy, it possesses one unpaired electron. The CFSE in this instance is −(6)(25)ΔO+(1)(35)ΔO+P=−95ΔO+P.

The [Ti(H2O)6]3+ complex's crystal field stabilization energy (CFSE), measured in kJ/mol. The first absorption maximum for the transition, according to CFT, is at 20,3000 cm-1.

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f-1(x)=1\5x-11

Step-by-step explanation:

The relation that is a function is the graph (d)

From the question, we have the graphs to represent the given parameters that can be used in our computation

We are to find out which of them represents a function

For a graph to represent a function, the graph must pass the vertical line test

This means that a line drawn from the x-axis must touch the graph at most once

So, we draw these lines  and attach the graphs (see attachment)

The graph that pass the vertical line test is graph d

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The slope (-8) of the linear equation that is represented by the table, is the amount Austin pays each week, which is $8.

A linear equation which is given as y = mx + b, has a slope value which represents the change in y over a change in x and is given by the value of m in the linear equation.

If a table is said to represent a linear equation, the slope of the linear equation, which can also be called the unit rate, can be found by using two pairs of values from the table to calculate the change in y over the change in x.

Given that the table above represents a linear equation where L is dependent on the value of t, it means that slope of the linear equation represents the amount Austin paid back each week.

Find the slope using two points, (2, 24) and (4, 8):

Slope (m) = (24 - 8) / (2 - 4)

m = 16/-2

m = -8

Therefore, this means that Austin pays $8 every week.

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Answer: 2y4 + 4y2

Step-by-step explanation:

2y3 + 4y2

2y4 + 4y2✔

1/2y3 + 1y2

1/2y4 + 4y2

Out of the 15 people the probability that none of the patients will experience dizziness is approximately 0.206 .

10% of the people experiences dizziness.

Probability that a random patient experiences dizziness = 0.1

Probability that the person does not experience dizziness = 0.9

Now this is in the form of a binomial distribution such that the probability is given by:

Sample = 15

P = 0.1

P' =0.9

Required probability :

= ¹⁵C₀ × P⁰ × P'¹⁵ (binomial distribution)

= 1 × 0.1⁰ × 0.9¹⁵

= 0.20589...

≈ 0.206

Hence the required probability is approximately 0.206 .

The binomial distribution is often used to predict the number of further successes in either a sample of size n drawn under replacement from either a population of size n.

If the sampling is carried out without replacement, the drawings are not independent, hence the resulting distribution is a hypergeometric one rather than a binomial one.

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This study can be best described as Controlled Placebo Experiment

What is a Controlled Placebo Experiment?

A controlled placebo experiment is a type of research method that is used to check the effectiveness of a drug in a patient. This is done by selecting a sample group, then randomly divide the two group into a placebo group (this are the group that will receive the drug treatment ) and the controlled group (these are the group that will receive a colored mixture that looks like the drug, but does not have any effect). Without the groups knowledge about the real drugs and the colored mixture, but are followed up and tested.

According to the given question:

This is a controlled placebo experiment, because 400 student has been chosen as the sample, and are divided into a placebo group and a controlled group, to check the effectiveness of a drug on their memory.

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The value of f(t) are 48000, 52200, 54300, 56400, and g(t) are 48000, 49776, 51617.71, and 53527.56.

She was given a starting wage of $48,000 from Company A, with annual raises of $2100.

The formula for Company A is

f(t) = 48000 + 2100t

She was given a starting wage of $48,000 from Company B, with an annual rise of 3.7%.

The formula for Company B is

g(t) = 48000 × [tex](1 + 0.037)^t[/tex]

The value of f(t) and g(t),

t ------- f(t) ------- g(t)

0 ----- 48000 ----- 48000

1 ------ 52200 ----- 49776

2 ----- 54300 ----- 51617.71

3 ----- 56400 ----- 53527.56

The graphical representation of both the linear equations of company A and company B.

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There are 0 lines, 1 regions, and no line junctions. There are always k+1k+1 regions and kk intersections added whenever a line is added and crosses k other lines.

Another perspective is that k+1k+1 areas are added for each line and k intersections added (the number of added lines and intersections).Consequently, the total number of regions is 1 plus the sum of the number of lines and junctions.The number of intersections is 1 + the number of lines. There are (n2) (n2) crossovers with nn lines (if no two lines are parallel and no three lines are coincident). Therefore, there are (n2) +n+1=n(n1)/2+n+1=n2+n+2/2 areas instead of (n2) +n+1=n(n1)/2+n+1=n2+n+2/2).

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Answer:

false

Step-by-step explanation:

7*3 / 4 = 7

21 / 4 = 7

5.25 ≠ 7

Could you please give me brainliest? Thanks!

Answer:

5 chairs per table.

Step-by-step explanation:

The random sample study's standard error, which measures the energy usage in a major metropolis, is 0.275.

The formula used to compute standard error is as follows:

standard error = standard deviation / √sample size

For  the data given in question-

Thus,

Standard error = 4.68 / 17

Standard error  = 0.275

Thus, the standard error for the mean of the sample is found as 0.275.

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Answer: Y=2

Step-by-step explanation:

The given command  "select cname from customer where age < 30 and age > 40" will produce 4 rows according to the database table.

A database in computing is a structured collection of data that is electronically accessible and stored. Large databases are housed on computer clusters or cloud storage, whilst small databases can be kept on a file system. A database is a collection of data that has been organized to make it simple to maintain and update. Data records or files containing information, including as sales transactions, customer information, financial data, and product information, are often aggregated and stored in computer databases. A database is a planned gathering of data. They enable the manipulation and storage of data electronically. Data administration is made simple by databases. Let's use a database as an example. A database is used to store information about people, their phone numbers, and other contact information in an online telephone directory.

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If Noah earns £160 a week and pays £55 in tax, he has £160 - £55 = £160-£55 = £105 to spend.

Subtraction is a mathematical procedure that includes subtracting one number from another. For example, if we have five apples and subtract three of them, we are left with two apples. Beginning with the bigger number and deducting the smaller number from it is how subtraction is done. Subtraction is denoted by the minus symbol (-). A difference is the outcome of a subtractive operation.

We may better grasp how to solve issues requiring the removal of one or more elements from a set by understanding the fundamental mathematical formula of subtraction. It is employed in many different scenarios, such as when we need to subtract incomes on a regular basis.

How to solve?

The formula for the money Noah has to spend each week is m = w - t.

£160 - £55 = £160 - £55 = £105

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The probability of three people who share the same birthday is 0.6459.

Let us consider that A₀ be the event that everyone in the room has a distinct birthday. Let Ai be the event that pairs of people share a birthday. Then the probability we are interested in is

P(at lest three people share a birthday) = 1 - P(A₀) - ∑ P(Ai)

where there are n people in the lecture hall.

First we note that P(A₀) is in the book and is

P(A₀) = (365Cn)n!/365^n.

Now we will compute P(Ai).

For i = 1,

P(A₁) = (365) × [tex]\frac{(nC2)(365-1Cn-2)(n-2)!}{365^{n} }[/tex]

For i = 2,

P(A₂) = [tex]\frac{(365C2)(nC2)(n-2C2)(365-2Cn-4)(n-4)!}{365^{n} }[/tex]

This generalizes for i pairs of people sharing i distinct birthdays

P(Ai) = (365Ci)πj=1toi(n-2j+2C2)(365-iCn-2i)(n-2i)!/([tex]365^{n}[/tex])

Substituting all values into the equation and putting in n = 100, we can compute a value for this probability.

Therefore we get,

P(at least 3 people share a birthday)0.6459.

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The Residual is defined as the difference between the actual and predicted, or fitted values of the response variable. This statement is true.

Linear regression is a statistical tool that determines how well a straight line fits a set of paired data. The straight line that best fits that data is called the least squares regression line. This line can be used in a number of ways. One of these uses is to estimate the value of a response variable for a given value of an explanatory variable. Related to this idea is that of a residual.

Residuals are obtained by performing subtraction. All that we must do is to subtract the predicted value of y from the observed value of y for a particular x. The result is called a residual.

The formula for residuals is straightforward:

Residual = observed y – predicted y

It is important to note that the predicted value comes from our regression line. The observed value comes from our data set.

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Answer:

multiplication property of equality

We have proven that no two events a and b can be independent unless either a or b is the whole sample space or the empty set below.

A sample space can be defined as the set of all possible outcomes of any experiment.

We are already aware that the outcomes of this die are going to be (1,2,3,..p). If we have a pair of proper events A, B which are independent, this would mean that = A∩B={∅}  (i)

This is a contradiction. So, now we suppose that = A∩B=C, for some proper event C (ii)

Using the values of (i) and (ii), we get -

= |C|p=P(A∩B)=P(A)P(B)=|A||B|p2.

= p|C|=|A||B|.

From this, we understand that neither A nor B are going to be full spaces and hence, no two events a and b are independent and 0<|A|<p and 0<|B|<p. Since |C| is also going to be less than 0 and p is prime, p divides either |A| or |B|.  if p was not prime (say, p=4), then you would only need the factors of p to divide either |A|,|B|, so, it becomes necessary for p to be a prime number. Hence, proved.

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Expression a⁶ + b⁶ = (a² + b²)(a⁴ - a²b² + b⁴)   is an identity, by left-hand term and right-hand term property.

An algebraic expression is consists of variables, numbers with various mathematical operations,

The given expression is,

a⁶ + b⁶ = (a² + b²)(a⁴ - a²b² + b⁴)  

To prove that the given expression is an identity,

Solve left-hand term,

Substitute a² = x, b² = y

a⁶ + b⁶

= x³ + y³

Use formula x³ + y³ = (x + y)(x²  - x y + y²)

= (x + y)(x²  - x y + y²)

Again substitute x = a², y = b², expression will be,

= (a² + b²)(a⁴ - a²b² + b⁴)  

Hence, a⁶ + b⁶ =  (a² + b²)(a⁴ - a²b² + b⁴)  

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The mistake are shown below and the correct steps are shown below.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 6 (8 - 3x) = - 3 (9x - 1) + 60

And, All the steps are;

⇒ 6 (8 - 3x ) = - 3 (9x - 1 ) + 60

⇒ 54 - 18x = −27x − 3 + 60

⇒ 54 - 18x = −27x + 57

⇒ -18x = -27x + 3

⇒ 9x = 3

⇒ x= 1/3

Now,

Since, The expression is,

⇒ 6 (8 - 3x) = - 3 (9x - 1) + 60

Cleary, In the second step 2; your partner doing mistake.

So, All the correct steps are;

⇒ 6 (8 - 3x) = - 3 (9x - 1) + 60

⇒ 48 - 18x = - 27x + 3 + 60

⇒ 48 - 18x = - 27x + 63

⇒ 27x - 18x = 63 - 48

⇒ 9x = 15

⇒ x = 15/9

⇒ x = 5/3

Thus, The correct value is;

⇒ x = 5/3

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the minimum number of american adults that they need to survey to ensure that the error bound is 16,867 with sample size

The sample size of a study is the number of subjects or observations that are included.Two statistical properties are influenced by the sample size: 1) The accuracy of our estimates, and 2) The ability to draw conclusions from the study.

The minimum sample size required to get a 95% confidence interval with an error bound of 0.01 is 16,867. This can be calculated using the formula:

n = (1.96 / 0.01)2 = 16,867.

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Adjacent angles of a parallelogram are supplementary.

[tex]x+2x=180 \\ \\ 3x=180 \\ \\ x=\boxed{60}[/tex]

The height of the triangle would be 5.63 cm.

What is the area of the triangle?

For a given triangle of height 'h' and the base is 'b' then the area of the triangle is

            A = 1/2 Base * Height

Given data:

          Base of the triangle = 2*height of the triangle + 4

                      b = 2h + 4

Area = 43 square centimeters

By using the area of the triangle,

        A = 1/2 *b * h

    43 = 1/2(2h + 4)*h

    86 = 2h²+4h

Simplifying this, we get

        h² + 2h - 43 = 0

Solving this, we get

h = 5.63 and h = -7.63

Height cannot be a negative value so h = 5.63

Hence, the height of the triangle would be 5.63 cm.

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