how to find the total area of a L shape with 8cm, 4cm, 5cm, 8cm, 3cm, 12cm​

let's recall that i⁴ = 1 so then    \(i^{28}\implies i^{4\cdot 7}\implies (i^4)^7\implies (1)^7\implies 1\)

Answer:

\(h'(1) = 23\)

Step-by-step explanation:

Let be \(h(x) = (x^{2}+8)\cdot g(x)\), where \(r(x) = x^{2} + 8\). If both \(r(x)\) and \(g(x)\) are differentiable, then both are also continuous for all x. The derivative for the product of functions is obtained:

\(h'(x) = r'(x) \cdot g(x) + r(x) \cdot g'(x)\)

\(r'(x) = 2\cdot x\)

\(h'(x) = 2\cdot x \cdot g(x) + (x^{2}+8)\cdot g'(x)\)

Given that \(x = 1\), \(g (1) = -2\) and \(g'(1) = 3\), the derivative of \(h(x)\) evaluated in \(x = 1\) is:

\(h'(1) = 2\cdot (1) \cdot (-2) + (1^{2}+8)\cdot (3)\)

\(h'(1) = 23\)

The amount natalya will spend constructing the patio with concrete and brick is $4320, the correct option is D.

We are given that;

The concrete portion of the patio cost=$3 per square

To construct and the brick portion of the patio cost= $6 per square

Now,

The area of a rectangle is given by length times width. The concrete portion of the patio is a rectangle with length 6 cm and width 3 cm. Using the scale, we can convert these to feet:

6 cm = 6 x 4 ft = 24 ft 3 cm = 3 x 4 ft = 12 ft

Therefore, the area of the concrete portion is:

24 ft x 12 ft = 288 ft^2

The brick portion of the patio consists of two identical rectangles with lenth 3 cm and width 6 cm. Using the scale, we can convert these to feet:

3 cm = 3 x 4 ft = 12 ft 6 cm = 6 x 4 ft = 24 ft

Therefore, the area of one brick rectangle is:

12 ft x 24 ft = 288 ft^2

Since there are two brick rectangles, the total area of the brick portion is:

2 x 288 ft^2 = 576 ft^2

Now we can multiply the areas by their costs per square foot to get the costs of each portion:

Concrete cost = $3 x 288 ft^2 = $864 Brick cost = $6 x 576 ft^2 = $3456

The total cost of constructing the patio is the sum of the costs of each portion:

Total cost = $864 + $3456 = $4320

Therefore, by area the answer will be $4320.

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Answer:

4 2/7

Hope this helps and have a nice day!!

Therefore, the answer is A. {5, 5√3, 10}.

The set of values {5, 5√3, 10} could be the side lengths of a 30-60-90 triangle.

In a 30-60-90 triangle, the sides are in a specific ratio. The ratio is 1 : √3 : 2, where the shortest side (opposite the 30-degree angle) has length x, the side opposite the 60-degree angle has length x√3, and the hypotenuse (opposite the 90-degree angle) has length 2x.

Let's check if the given set of values satisfies this ratio:

   If x= 5, then the side opposite the 60-degree angle should be 5√3, and the hypotenuse should be 10. These values match the ratio, so the set {5, 5√3, 10} could be the side lengths of a 30-60-90 triangle.

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The missing pattern behind the sequence 7, 11, 2, 18, -7 is described by the formula \(n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}\), equivalent to the recurrence formula \(a_{n+1} = a_{n} + (-1)^{i+1}\cdot (i + 1)^{2}\).

A sequence is a set of elements which observes at least a defined rule. In this question we see a sequence which follows this rule:

\(n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}\)      (1)

Now we prove that given expression contains the pattern:

n = 0

7

n = 1

7 + (- 1)² · 2² = 7 + 4 = 11

n = 2

7 + (- 1)² · 2² + (- 1)³ · 3² = 11 - 9 = 2

n = 3

7 + (- 1)² · 2² + (- 1)³ · 3² + (- 1)⁴ · 4² = 2 + 16 = 18

n = 4

7 + (- 1)² · 2² + (- 1)³ · 3² + (- 1)⁴ · 4² + (- 1)⁵ · 5² = 18 - 25 = - 7

The missing pattern behind the sequence 7, 11, 2, 18, -7 is described by the formula \(n = 7 + \sum \limits_{i= 1}^{n} (-1)^{i+1}\cdot (i + 1)^{2}\), equivalent to the recurrence formula \(a_{n+1} = a_{n} + (-1)^{i+1}\cdot (i + 1)^{2}\).

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Path A-B-C-E represents the distance traveled, which is 18 meters.

Path A-G-C-E represents the displacement, which is 17 meters.

From the given figure, we can identify the paths and calculate the distance and displacement.

Path A-B-C-E represents the distance traveled, and path A-G-C-E represents the displacement.

Let's calculate the lengths of both paths:

Distance traveled (Path A-B-C-E):

Length of AB = 9m

Length of BC = 3m

Length of CE = 6m

Total distance traveled = Length of AB + Length of BC + Length of CE

= 9m + 3m + 6m

= 18m

Therefore, the distance traveled along path A-B-C-E is 18 meters.

Displacement (Path A-G-C-E):

Length of AG = 5m

Length of GC = 6m

Length of CE = 6m

Total displacement = Length of AG + Length of GC + Length of CE

= 5m + 6m + 6m

= 17m

Therefore, the displacement along path A-G-C-E is 17 meters.

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x | - 8 | - 4 | 2 | 1 | 1/2 | - 1/4 | 0

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

y | - 16/3 | - 8/3 | 4/3 | 2/3 | 1/3 | -1/6 | 0

K = 2/3

The loaded die appears to behave differently from a fair die.Based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

To test the claim that the outcomes of the loaded die are not equally likely, we can use the chi-square goodness-of-fit test. The null hypothesis (H₀) assumes that the outcomes are equally likely, while the alternative hypothesis (H₁) assumes that they are not equally likely.

Step 1: Set up hypotheses

H₀: The outcomes of the die are equally likely.

H₁: The outcomes of the die are not equally likely.

Step 2: Select the significance level

The significance level is given as 0.025, which means we have a two-tailed test and an alpha level of 0.025 for each tail.

Step 3: Compute the test statistic

We calculate the chi-square test statistic using the observed frequencies and the expected frequencies assuming equal probabilities for each outcome.

Expected frequencies (fair die):

1: 200/6 = 33.33

2: 200/6 = 33.33

3: 200/6 = 33.33

4: 200/6 = 33.33

5: 200/6 = 33.33

6: 200/6 = 33.33

Applying the chi-square formula, we get the test statistic:

χ² = ∑((observed - expected)² / expected)

Calculating this value, we get χ² ≈ 13.97.

Step 4: Determine the critical value

Since the significance level is 0.025 and the test is two-tailed, we divide the significance level by 2 to find the critical value associated with each tail. With 5 degrees of freedom (6 categories - 1), the critical value is approximately 11.07.

Step 5: Make a decision

The test statistic (13.97) is greater than the critical value (11.07), which leads us to reject the null hypothesis. Thus, we have evidence to suggest that the outcomes of the loaded die are not equally likely.

The loaded die appears to behave differently from a fair die.

In conclusion, based on the chi-square test, the loaded die does not exhibit equal probabilities for each outcome.

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Answer:

11 m/s

Step-by-step explanation:

In converting from mph to m/s, the appropriate conversion factor must be used which in this case is 0.44704 m/s.

Thus;

If 1mph = 0.44704 m/s

Then 25 mph = 25 × 0.44704 m/s = 11.176 m/s

Answer:

-3/2

Step-by-step explanation:

The standard error for the sample mean exists

\($P(\bar{X} < 0.95)=0.0418=4.18 \%$$\).

Let the value of mean be \($P(\bar{X} < 0.95)$$\)

Normal Distribution, \($\mu=1, \sigma=0.1, n=12$\)

\($P(\bar{X} < 0.95)=$\) Area to the left of 0.95

we convert this to standard normal using

\($z=\frac{\bar{x}-\mu_{\bar{x}}}{\sigma_{\bar{x}}}=\frac{\bar{x}-\mu}{\sigma / \sqrt{n}}$\)

\($z=\frac{0.95-(1)}{0.1 / \sqrt{12}} \approx-1.732051 \approx-1.73$\)

\($P(\bar{X}\) < 0.95) = P(Z < -1.73) = 0.0418 (from z-table)

P(Z < -1.73); in a z-table having area to the left of z, locate -1.7 in the left most column. Move across the row to the right under column 0.03 and get value 0.0418.

\($P(\bar{X} < 0.95)=0.0418=4.18 \%$$\)

Therefore, the standard error for the sample mean exists

\($P(\bar{X} < 0.95)=0.0418=4.18 \%$$\).

The complete question is;

What is the probability that the sample mean will be below 0.95 centimeters?

At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken.

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The decimal calculation for Arturo's is 18.97, Bonnie's is 20.51, Courtney's is 31.42, Dawson's is 35.00.

Measurement is the process of assigning a numerical value to a physical quantity, such as length, weight, temperature, or time. Measurements are used to quantify and compare different aspects of the world around us, and they play a crucial role in many areas of science, engineering, and everyday life.

Measurements can be made using a variety of tools and techniques, ranging from simple rulers and scales to sophisticated scientific instruments. The accuracy and precision of a measurement depend on many factors, including the quality of the measuring instrument, the skill of the person making the measurement, and the conditions under which the measurement is taken.

In order for measurements to be meaningful and useful, they must be expressed in units that are well-defined and universally accepted. The International System of Units (SI) is the most widely used system of units in the world, and it is based on seven fundamental units of measurement, including the meter for length, the kilogram for mass, the second for time, and the kelvin for temperature.

Student           Measurement (yards)    Decimal Calculation

Arturo           6√28                            18.97

Bonnie           8√17                            20.51

Courtney   10π                            31.42

Dawson           3.5√100                    35.00

To calculate the decimals, we can use a calculator to evaluate the square roots and π, and then multiply by the given constant factor, and round the result to the nearest hundredth yard.

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The complete question is:

Answer: none of them are correct

Step-by-step explanation:

BECUASE if it is then it would show it on the nuber line.

Answer:

A

Step-by-step explanation:

Add 3 to each side, there's your answer there.

Step-by-step explanation:

please make it a little bit clear

The answer to all parts is shown below.

1. The most useful statistical instrument to be used with a big number of respondents is a survey questionnaire.

This allows researchers to collect data from a large sample size efficiently and in a standardized manner, ensuring that all respondents are asked the same questions in the same order. Online surveys are particularly useful as they can reach a wider audience and allow for easy data analysis.

2. The process you are referring to is called "expert interviews".

3. This is an example of a survey question that measures a respondent's preference.

4. The changes in characteristics, behavior, and attitudes of the people observed are the focus of observation.

5. Open-ended question.

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The total weight of Rice that Mark buys is given as follows:

2.5 pounds.

The total weight of Rice that Mark buys is obtained applying the proportions in the context of the problem.

The weight of each bag is given as follows:

5/8 pounds = 0.625 pounds.

The number of bags is given as follows:

4 bags.

Hence the total weight of Rice that Mark buys is given as follows:

4 x 0.625 = 2.5 pounds.

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a) The mean of the data-set is of 2.

b) The range of the data-set is of 4 units, which is of around 4.3 MADs.

The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations in the data-set, which is also called the cardinality of the data-set.

The dot plot shows how often each observation appears in the data-set, hence the mean of the data-set is obtained as follows:

Mean = (1 x 0 + 5 x 1 + 3 x 2 + 5 x 3 + 1 x 4)/(1 + 5 + 3 + 5 + 1)

Mean = 2.

The range is the difference between the largest observation and the smallest, hence:

4 - 0 = 4.

4/0.93 = 4.3 MADs.

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Answer:

a-6b-6c-2

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

If 4 out of 10 wore glasses, then 6 out of 10 did not wear classes.  This would be 60% or .6

.6x30 = 18

Answer:

x = -7

x = 5

Step-by-step explanation:

The standard form of quadratic equations is

Ax^2 + Bx + C = 0

The factors need to multiply together to be C and add together to be B.

The two numbers that will multiply together to be -35 and add together to be 2 are -5 & 7.

The factor pairs are (x+7)(x-5). Zero product property means we set each of those factor pairs = 0 and solve.

x + 7 = 0

-7 -7 Subtract 7 from each side to solve

x = -7

x - 5 = 0

+5 +5 Add 5 to each side to solve

x = 5

To solve the equation, factor x²+2x−35 use the formula x² +(a + b) x + ab = (x + a)(x + b). To find a and b, set up a system to be solved.

a + b = 2

ab = −35

Since ab is negative, a and b have opposite signs. Since a+b is positive, the positive number has a greater absolute value than the negative. Show all pairs of integers whose product is −35.

Calculate the sum of each pair.

The solution is the pair that gives sum 2.

Rewrite the factored expression (x + a)(x + b) with the values obtained.

To find solutions to equations, solve x−5=0 and x+7=0.

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Answer:

The equation is:

(1/a)x + (1/b)y + (1/c)z = 1

Step-by-step explanation:

The direction vector between the points (a, 0, 0) and (0, b, 0) is given as:

<0 - a, b - 0, 0 - 0>

<-a, b, 0> .....................(1)

The direction vector between (0, 0, c) and (0, b, 0) is given as:

<0 - 0, b - 0, 0 - c>

= <0, b, -c> .....................(2)

To obtain the direction vector that is normal to the surface of the plane, we take the cross product of (1) and (2).

Doing this, we have:

<-a, b, 0> × <0, b, -c> = <-bc, -ac, -ab>

To find the scalar equation of the plane we can use any of the points that we know. Using (0, b, 0), we have:

(-bc)x + (-ac)y + (-ab)z = (-bc)0 + (-ac)b + (-ab)0

(bc)x + (ac)y + (ab)z = (ac)b

Dividing both sides by abc, we have:

(1/a)x + (1/b)y + (1/c)z = 1

We will call π,  the plane with points P, Q, R  ( the intercepts )

The solution is:

π :  -bc×x + ac×y -ab×z - bac = 0

c) d =   | bac|/√ ( -bc)² + (-ac)² + ( -ab)²

The intercepts  P Q R are three points of the plane, according to that

P ( 0, b, 0 ) intercept with y-axis

Q ( a, 0, 0 ) intercept with x-axis

R ( 0, 0, c ) intercept with  z-axis

We will find the vectors PQ  and  PR both are on the plane

PQ  = [ a, 0, 0 ] - [ 0, b, 0 ]         ⇒     PQ = ( a , -b, 0 )

PR  =  [ 0, 0, c ] - [ 0, b, 0 ]          ⇒     PR = ( 0, -b  c )

The vectorial product of these two vector will give us, one normal vector to the plane.

                        i        j         k

PQ * PR  =     a      -b        0    =   i (-bc)  - j ( ac - 0 ) + k ( -ab - 0)

                       0      -b        c

PQ * PR  = [ -bc,  -ac,  -ab ]

we call this vector n =  [ -bc, -ac, -ab ]

Let´s now find a vector between P,  and a general point T ( x , y , z ) on the plane.

PT = [ x, y, z ] - [ 0, b, 0 ]    ⇒  PT = [ x-0 , y - b , z - 0 ]

PT = [ x, y-b, z ]

Vector PT is perpendicular to vector n, then their dot product must be 0

Then:

PT × n = 0

[ x, y-b, z ] ×   [ -bc, -ac, -ab ] = 0

x × (-bc) + ( y - b )× (ac) + z × (- ab) = 0

-bc×x + ac×y -bac - ab×z = 0

-bc×x + ac×y -ab×z = bac         (1)

Finally,  we got the implicit equation for plane π as:

π :  -bc×x + ac×y -ab×z - bac

c) The distance (d) between the plane and the origin is:

d = | D | / | n |

| n | = √ ( -bc)² + (-ac)² + ( -ab)²

|D| = | bac|     the right side of the equation (1)

Then

d =   | bac|/√ ( -bc)² + (-ac)² + ( -ab)²

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Answer:

23 boxes

Step-by-step explanation:

x=5+9*2

Answer:

23

Step-by-step explanation:

I did this backwards.

Since we know that Sally ended up with 9 boxes of strawberries, and sold half of the remaining strawberries, she must've had 18 boxes. Adding the 5 boxes from the beginning gets us 18+5=23

You also could've wrote an equation.

x=boxes of strawberries

x the total amount of boxes in the beginning of the day

x-5 the 5 boxes she sold

(x-5)/2 half of the remaining boxes sold

(x-5)/2=9 the amount left

The calculated value of the rate of the graph is 0.8

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

The graph

Where, we have

(0, -16) and (20, 0)

The rate of the graph is calculated as

Rate = Change in y/x

using the above as a guide, we have the following:

Rate = (0 + 16)/(20 - 0)

Evaluate

Rate = 0.8

Hence, the rate is 0.8

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The relationship in the figure is a function because each input has only one output to which they are linked

A function is a definition or rule that maps each element in a set of input values to exactly one element in a set output values.

The data in the sets can be presented as follows;

x  \({}\)               f(x)

-1 \({}\)      →         2

0\({}\)        →        2

1\({}\)         →        -3

2\({}\)         →       -2

8\({}\)         →        3

The above table indicates that each x-value has only one f(x) value, which indicates that the relationship s a function. The relationship is still a function with the presence of an f(x) value, 2, having two x values, -1 and 0, as the condition satisfies the definition of a function.

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9514 1404 393

Answer:

  65

Step-by-step explanation:

The six numbers are sequential multiples of 10, so the mean is halfway between the middle two. Halfway between 60 and 70 is 65.

The mean of the 6 numbers is 65.

Answer:

gracias por lo 20 puntos

Step-by-step explanation:

The correct two - way frequency table for the data on High School Students, and the kind of band they want to play at the school dance, is:

                                                     Rap          Rock           Country      Total

Grades 9 - 10                                40              30                55              125

Grades 11 - 12                                60              25                35              120

Total                                              100              55                90             245

Option A is therefore correct.

In a two-way frequency table, there will be totals for both the rows and the columns.

The totals for the rows in this instance are:

Grade 9 - 10 totals :

= 40 + 30 + 55

= 125

Grade 11 - 12 :

= 60 + 25 + 35

= 120

The totals for the columns are:

Rap totals :

= 40 + 60

= 100

Rock :

= 30 + 25

= 55

Country :
= 55 + 35

= 90

Two-way frequency tables allow for us to be able to conclude on the event described by looking at totals from both the columns and the rows. This gives a clearly understanding on preferences and categories.

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Answer:

\(x=-3\\x=6\)

Step-by-step explanation:

We begin with \(x^2-3x-18=0\)

To factor this, we need to look for two things:

Two numbers that add together to get \(-3\) and two numbers that multiply together to get \(-18\).

One method to find the answer is to write out each of the solutions to the multiplication and then check the sum of each of those digits:

The numbers that multiply together to get \(-18\) are:

1 and -18

-1 and 18

2 and -9

-2 and 9

3 and -6

-3 and 6

Now, we can add each of these pairs of digits together to find which one gives us an answer of \(-3\)

\(1+(-18)=-17\\\\-1+18=17\\\\2+(-9)=-7\\\\-2+9=7\\\\3+(-6)=-3\\\\-3+6=3\)

From this, we can see that 3 and -6 gave us the result of -3. This means that these are the two factors.

To get our answer from this, we need to put our answer in the form of \((x+a)(x+b)=0\)

This gives us the factored form of \((x+3)(x-6)=0\)

To solve this equation, we must make either parenthesis equal to zero. This means that our solutions will be

\(x=-3\\x=6\)

By factoring, the solutions to the quadratic equation x² - 3x - 18 = 0 are x = 6 and x = -3.

To solve the quadratic equation x² - 3x - 18 = 0 by factoring, we need to find two binomials that, when multiplied, result in zero. The quadratic equation generally follows the format ax² + bx + c = 0, where a, b, and c are constants.

Here's the step-by-step process for factoring the given equation:

Step 1: Begin with the equation x² - 3x - 18 = 0.

Step 2: Identify two numbers whose product is -18 (the constant term) and whose sum is -3 (the coefficient of the x-term).

We find that the two numbers are -6 and +3 because:

-6 * 3 = -18 (the product of the two numbers is -18)

-6 + 3 = -3 (the sum of the two numbers is -3)

Step 3: Rewrite the middle term (-3x) using -6x and +3x:

x² - 6x + 3x - 18 = 0.

Step 4: Group the terms and factor them by pairs:

(x² - 6x) + (3x - 18) = 0.

Step 5: Factor out the greatest common factor from each group:

x(x - 6) + 3(x - 6) = 0.

Step 6: Notice that both terms have a common factor of (x - 6). Factor it out:

(x - 6)(x + 3) = 0.

Step 7: Apply the zero-product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be zero:

Setting each factor to zero and solving for x:

x - 6 = 0 --> x = 6

x + 3 = 0 --> x = -3

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