20k + 5 = 5k + 65 know the answer

General rules people unconsciously follow in estimating probabilities are known as heuristic.

According to the statement

we have to explain all about the term by which people unconsciously follow in estimating probabilities.

So, For this purpose, we know that the

A heuristic, or heuristic technique, is any approach to problem-solving that uses a practical method or various shortcuts in order to produce solutions that may not be optimal but are sufficient given a limited time frame or deadline.

By this way, we solve the probabilities without any formula of probability.

In other words it is a method which solves the every problem without any formula.

So, General rules people unconsciously follow in estimating probabilities are known as heuristic.

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The answer is approximately 872 juniors scored at least 74 on the test. To find out how many juniors scored at least 74 on the test, we need to calculate the area under the normal distribution curve to the right of 74. This area represents the percentage of students who scored at least 74 on the test.

Using a standard normal distribution table or calculator, we can find that the z-score for 74 is 0. To find the area to the right of 0, we look up the corresponding area in the table or use a calculator. The area to the right of 0 is 0.5, or 50%.

Since we know that the scores are normally distributed with a mean of 74 and a standard deviation of 8, we can use the z-score formula to find the number of students who scored at least 74:

z = (x - mu) / sigma

where x is the score we want to find the number of students for, mu is the mean, sigma is the standard deviation, and z is the corresponding z-score.

Plugging in the values, we get:

z = (74 - 74) / 8 = 0

This means that the number of students who scored at least 74 on the test is equal to 50% of the total number of students, or:

50% of 1744 = 872

Therefore, approximately 872 juniors scored at least 74 on the test.

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Answer:

B) Sometimes

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

\(12 + \frac{24}{4} \\ = 12 + 6 \\ = 18\)

Answer:

18 ( or 9 )

Step-by-step explanation:

Given

p + \(\frac{q}{4}\) ← substitute p = 12 and q = 24 into the expression

= 12 + \(\frac{24}{4}\)

= 12 + 6

= 18

If the expression is meant to be

\(\frac{p+q}{4}\) , then

\(\frac{12+24}{4}\)

= \(\frac{36}{4}\)

= 9

Answer: 2 + 0.7 + 0.06

Step-by-step explanation:

Expanded form is a method of writing numbers in such a way that the mathematics value of their individual digits would be shown.

Therefore, 2.76 inches in expanded form would be:

= 2 + 0.7 + 0.06

The above shows the units value, tenths value and the hundredths value of the number.

Answer:

Step-by-step explanation:

for T and T'   it's going to be  ( 2 , -1)   you switched them  the x, and y

W and W'  is  ( 0, 3)  as the other person said

The prove of ∠1 equal to ∠2 is shown below.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

⇒ AB = AC, AD = AE and DC = EB

Now,

In ΔDBC and ΔEBC;

⇒ DC = EB   (Given)   ..(i)

Since,  AB = AC

So, the ΔABC is a isosceles triangle.

Hence, ∠DBC = ∠ ECB   ..(ii)

Here,  AB = AC and AD = AE

So, BD = EC   ..(iii)

Hence, By the condition (i), (ii) and (iii);

By SAS condition,

⇒ ΔDBC ≅ ΔEBC

Hence, We get;

⇒ ∠1 = ∠2

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Answer:

64 poles

Step-by-step explanation:

Given the question :

Fence posts are erected 5m apart (with a post at each corner) to support fencing round a rectangular field. If the field measures 100m by 60m, how many posts are needed?

Dimension of rectangular field = 100m by 60m

Length = 100m ; breadth = 60m

Since it is erected around the corners of the field, we need to calculate the entire perimeter of the rectangular field.

Perimeter of a rectangle : 2( length + breadth)

Perimeter = 2(100 +60) = 2(160) = 320m

Since the posts are erected 5m apart, the number of post needed will be :

Perimeter / 5

= 320 / 5

= 64 poles

In order to estimate the coefficients of linear regression equations that explain the connection between one or more independent quantitative variables and a dependent variable, researchers frequently use the ordinary least squares regression (OLS) method (simple or multiple linear regression), this is ordinary about it.

Because it is the smallest sum of squares of errors, also known as the "variance," the term "least squares" is employed. In a regression analysis, independent variables are shown on the horizontal x-axis and dependent variables are shown on the vertical y-axis.

A linear regression approach that is used to estimate a model's unknown parameters is known as the ordinary least squares (OLS) method.

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Aya can make 14 mats of 1 foot long.

Division is one of the fundamental arithmetic operation, which is performed to get equal parts of any number given, or finding how many equal parts can be made. It is represented by the symbol "÷" or sometimes "/"

Given that, Aya has 14\(\frac{2}{5}\) feet of chain. She wants to make pieces foot long mat.

Let can make x mats out of the given chain, since each mat is 1 foot long, so,

1×x =  14\(\frac{2}{5}\)

x = 72/5

x = 14.4

x ≈ 14

Hence, She can make 14 mats out of the given chain.

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The value of a and b are 1 and -8 respectively.

Quadratic expressions are polynomial expressions of second degree.

The general form of a quadratic expression is ax² + b x + c.

The given quadratic expression is x² + 2x - 7.

We have to write this in the form (x + a)² + b.

We have the algebraic identity a² + 2ab + b² = (a + b)²

x² + 2x - 7 = x² + 2x - 7 + 1 - 1

                 = (x² + 2x + 1) - 7 - 1

                 = (x + 1)² - 8, which is in the form (x + a)² + b.

a = 1 and b = -8

Hence the value of a is 1 and the value of b is -8.

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Answer:

See Attached

Step-by-step explanation:

Answer:

sides 1 and 2 are 150 m. Side 3 is 270m

Step-by-step explanation:

perimeter = 570 m

sides 1 and 2 = x

side 3 = 2x-30

permeter = side+side+side

570=x+x+2x-30

600=4x

x = 150

Answer:

8,024,832

Step-by-step explanation:

To solve the expression 27 × 18 × 3 × 43 × 128, you can follow these steps:

Start by solving the first two numbers:

Then, multiply the result by the next number:

Continue multiplying by the next number:

Finally, multiply by the last number:

Therefore, the final result of 27x18x3x43x128 is 8024832.

The global maximum and minimum values of f(x, y) subject to the constraint x^2 + y^2 = 80 are both approximately 15.314, and they occur at the points (2√5, -4√5) and (-2√5, 4√5), respectively.

To use Lagrange multipliers, we need to define the Lagrangian function as follows:

L(x, y, λ) = f(x, y) - λg(x, y)

where g(x, y) is the constraint function, which in this case is g(x, y) = x^2 + y^2 - 80.

So, we have:

L(x, y, λ) = (x - 1)^2 + (y + 2)^2 - λ(x^2 + y^2 - 80)

Next, we need to find the partial derivatives of L with respect to x, y, and λ, and set them equal to 0:

∂L/∂x = 2(x - 1) - 2λx = 0

∂L/∂y = 2(y + 2) - 2λy = 0

∂L/∂λ = x^2 + y^2 - 80 = 0

Simplifying the first two equations, we get:

x(1 - λ) = 1

y(1 - λ) = -2

Dividing these two equations, we get:

x/y = 1/-2 => x = -y/2

Substituting this into the constraint equation, we get:

(y/2)^2 + y^2 = 80 => 5y^2 = 320 => y = ±4√5

Substituting this back into x = -y/2, we get:

x = ∓2√5

So, the critical points are (2√5, -4√5) and (-2√5, 4√5).

To determine whether these are maximum or minimum values, we need to compute the second partial derivatives of L:

∂^2L/∂x^2 = 2 - 2λ

∂^2L/∂y^2 = 2 - 2λ

∂^2L/∂x∂y = 0

At the critical points, we have λ = 1/5, so:

∂^2L/∂x^2 = -2/5 < 0, so (2√5, -4√5) is a local maximum.

∂^2L/∂y^2 = -2/5 < 0, so (-2√5, 4√5) is a local maximum.

To determine whether these are global maximum or minimum values, we need to compare the values of L at these critical points and at the endpoints of the constraint region:

L(2√5, -4√5) ≈ 15.314

L(-2√5, 4√5) ≈ 15.314

L(4√2, 0) = 18

L(-4√2, 0) = 18

So, the global maximum and minimum values of f(x, y) subject to the constraint x^2 + y^2 = 80 are both approximately 15.314, and they occur at the points (2√5, -4√5) and (-2√5, 4√5), respectively.

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Let's assume that the width of the poster is "x" inches.

According to the problem, the length of the poster is 10 more inches than three times its width. So, the length is (3x + 10) inches.

The area of a rectangle is given by the formula A = length x width. We are given that the area of the poster is 88 square inches. So, we can write:

(3x + 10) x x = 88

Simplifying the above equation, we get:

3x^2 + 10x - 88 = 0

We can solve this quadratic equation by factoring or using the quadratic formula. Let's use the quadratic formula:

x = [-b ± sqrt(b^2 - 4ac)] / 2a

where a = 3, b = 10, and c = -88

Plugging in the values, we get:

x = [-10 ± sqrt(10^2 - 4(3)(-88))] / 2(3)

x = [-10 ± sqrt(1000)] / 6

x = [-10 ± 31.62] / 6

x = 3.27 or x = -8.94

Since the width cannot be negative, we ignore the negative solution. Therefore, the width of the poster is approximately 3.27 inches.

Using this value, we can find the length:

length = 3x + 10 = 3(3.27) + 10 = 19.81 inches (rounded to two decimal places)

Therefore, the dimensions of the poster are approximately 3.27 inches by 19.81 inches.

Answer:

It's just 22

Step-by-step explanation:

22

The average rate of change between hour 4 and hour 8 is equal to the  average rate of change between hour 0 and hour 4.

Function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given,

The function f(x)=80(1.5)x

where x is the time in hours

Then,

f(4)=80(1.5)4=480

f(8)=80(1.5)8=960

f(0)=80(1.5)0=0

Then the average rate of change between 4 and 8 hours =\(\frac{960-480}{4}\)

=120 units per hour

The average rate of change between 0 and 4 hours=\(\frac{480-0}{4}\)

=120 units per hour

Hence, the average rate of change between hour 4 and hour 8 is equal to the  average rate of change between hour 0 and hour 4.

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Answer:

Below

Step-by-step explanation:

The end behavior of a function is how it grows when it reaches both plus and - infinity.

To do that we will calculate:

● lim h(x) x=> +infinity = lim-4x+4 x=> +inf = lim -4x x=> +inf

-4 is negative so the limit will be -infinity

● lim (-4x+4) x=> -inf = lim (-4x) x=> -inf

-4 is negative, x is negative then -4x is positive. So the limit will be + inf

Answer:

His total cost is $564.68

Step-by-step explanation:

333.75 + 134.87 + 67.89 = 536.51

536.51 x 0.0525 = 28.17

536.51 + 28.17 = 564.68

The labor cost percentage for next Friday at Fawlty Towers would be approximately 0.63%, which is closest to the option a. 0.05%.

To calculate the labor cost percentage for next Friday at the Fawlty Towers, we need to consider the number of rooms, the time required to clean each room, the number of working hours, the labor rate, and the occupancy rate. Here are the steps to determine the labor cost percentage:

Calculate the number of rooms to be cleaned. If the hotel has 1000 rooms and the occupancy rate for next Friday is 80%, then the number of occupied rooms would be 1000 * 0.8 = 800 rooms.

Calculate the total time required to clean the rooms. Since each room attendant is allocated 30 minutes per room, the total time required would be 800 rooms * 30 minutes = 24,000 minutes.

Convert the total cleaning time to hours. Since there are 60 minutes in an hour, the total cleaning time would be 24,000 minutes / 60 = 400 hours.

Calculate the total labor cost. Each room attendant works 8 hours per day, so for 400 hours, the hotel would require 400 hours / 8 hours = 50 room attendants. Considering their hourly rate of $15, the total labor cost would be 50 room attendants * $15/hour = $750.

Calculate the total revenue. The Average Daily Rate (ADR) is expected to be $150, and with an occupancy rate of 80%, the total revenue would be 800 rooms * $150/room = $120,000.

Calculate the labor cost percentage. Divide the total labor cost ($750) by the total revenue ($120,000) and multiply by 100 to get the percentage: ($750 / $120,000) * 100 = 0.625%.

Therefore, the labor cost percentage for next Friday at Fawlty Towers would be approximately 0.63%, which is closest to the option 0.05%.

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The Fawlty Towers is a Nuxury 1000 room hotel catering to business executives. The occupancy for nad Friday is expected to be 80% Room attendants are allocated 30 minutes to clean each room Room attendants work 8 hours per day at a rate of $15/hour. ADR is expected to be $150 What would the labour cost percentage be for next Friday assuming everything stays the same?

a. 0.05%

b. 5.00%

c. 20.00%

d. 0.20%

Answer:

There are no reflectional symmetries.

Step-by-step explanation:

Hi there, a reflectional symmetry requires the reflection to mirror that of the figure being reflected. To put it in simpler terms, it should look exactly the same if you put one half right next to a mirror.

I hope this clears up things a bit.

The required, latter F does not have reflectional symmetries.

Reflection symmetry is a type of symmetry where a figure is reflected across a line, called the line of symmetry, and the resulting figure is identical to the original. In other words, if you were to fold the figure along its line of symmetry, the two halves would match up perfectly.

Since we have given the figure of latter F, which does not have reflectional symmetries.

It's important to note that not all letters have reflectional symmetry, but the letter "F" is one example of a letter that does have this type of symmetry.

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The claim that a drug is effective at 1% is not sufficiently supported by the available data.

Participant 1 2 3 4 5 6

Before 185 220 190 158 227 211

After 175 215 195 155 230 207

Difference = Before - After = 10 5 -5 3  -3 4

Participant 7 8 9 10 11 12

Before 260 156 201 300 180 270

After 258 159 201 290 172 272

Difference = Before - After = 2 -3 0 10  8 -2

Participant 13 14 15 16 17 18

Before 293 183 205 151 291 166

After 290 185 200 146 287 166

Difference = Before - After = -7 -2 5 5  4 0

Hypothesis :

H0 : μd = 0

H0 : μd ≠ 0

10+5-5+3-3+4+2-3+10+8-2+3-2+5+5+4+0 = 44

The mean of d, \(d`\) = Σd / n = 44 / 18 = 2.44

The standard deviation, S.d = 4.45 (using calculator)

The test statistic, T : \(d`\) / (S.d/√n)

T = 2.44 / (4.45/√18)

T = 2.44 / 1.0488750

T = 2.326

Degree of freedom, df = n - 1 ; 18 - 1 = 17

P value = 0.0326

α = 0.01

Since P value < α ; we fail to reject H0

So the claim that a drug is effective at 1% is not sufficiently supported by the available data.

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Answer:

73

Step-by-step explanation:

17+90+C=180 since it is a straight angle and yeah.

17+90=107+c=180

180-107=73

The value of x is either 3 or -5 based on the distance formula.

What is a co-ordinate system?

In pure mathematics, a coordinate system could be a system that uses one or additional numbers, or coordinates, to uniquely confirm the position of the points or different geometric components on a manifold like euclidean space.

Main body:

according to question

Given points A(-1,4) and B(x,7)

Also AB = 5 cm

Formula of distance = \(\sqrt{(y1-y2)^{2}+(x1 -x2)^{2} }\)

here by using points ,

5 = \(\sqrt{(x+1)^{2} +(7-4)^{2} }\)

taking square on both side ,'

25 = \((x+1)^{2} +3^{2}\)

25-9 = (x+1)²

16 = (x+1)²

taking square root on both sides,

x+1= ±4

x = 4-1 = 3                                  or              x = -4-1 = -5

Hence value of x is either 3 or -5.

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In mutually exclusive data, you cannot find any overlap or intersection between the categories or events being analyzed.

This means that the occurrence of one event or category precludes the occurrence of the other. On the other hand, in dependent data, the occurrence of one event or category may have an effect on the occurrence of the other, and thus, they are not completely independent or separate. Therefore, in both cases, you cannot find any shared or common outcomes or occurrences between the categories or events being analyzed.

You cannot find a direct correlation or causal relationship between mutually exclusive or dependent data. In mutually exclusive events, the occurrence of one event prevents the occurrence of the other, meaning they cannot happen at the same time. In dependent events, the probability of one event happening is influenced by the outcome of a previous event. Due to these characteristics, it is not possible to establish a direct correlation or causal relationship between such events.

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The coefficient of\(x^{k} y^{n-k}\) in the expansion of (xy)ⁿ is C(n, k), which is the binomial coefficient for choosing k elements out of n.

To find the coefficient of a specific term in the expansion of a binomial raised to a power, you can use the binomial theorem. In this case, we want to find the coefficient of the term with the term with \(x^{k} y^{n-k}\).

The binomial theorem states that for any real numbers a and b, and a non-negative integer n, the expansion of (a + b)ⁿ can be written as:

(a + b)ⁿ = C(n, 0) ×aⁿ ×b⁰ + C(n, 1) × \(a^{n-1}\)× b¹ + C(n, 2)× \(a^{n-2}\) ×b² + ... + C(n, n-1) ×a¹ × \(b^{n-1}\) + C(n, n) × a⁰ × bⁿ

where C(n, k) represents the binomial coefficient, which is given by:

C(n, k) = n! / (k! × (n - k)!)

In this case, we have (xy)ⁿ, so a = x, b = y, and we're looking for the term with \(x^{k} y^{n-k}\), which corresponds to the term with C(n, k) × \(a^{k}\) × \(b^{n-k}\). Therefore, the coefficient of \(x^{k} y^{n-k}\) in the expansion of (xy)ⁿ is given by C(n, k).

Therefore, the coefficient of\(x^{k} y^{n-k}\) in the expansion of (xy)ⁿ is C(n, k), which is the binomial coefficient for choosing k elements out of n.

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Answer:

y = -x - 1

Step-by-step explanation:

-2y=-x+2

y—x-1

The optimal values of these parameters are:

a. β₁ = 0

b. β₂ = 0

The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:

SSE = 382 + 681 + 382 + 18β1β2

Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.

Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0

Now, we need to find the partial derivative of SSE with respect to β1.

∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0

Therefore, we obtain the optimal value of β2 as 0.

Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0

Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.

Thus, the optimal values of β1 and β2 are 0 and 0, respectively.

Therefore, the answers are: a. β₁ = 0 b. β₂ = 0

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