x^2 − 15 = 1 please help

Answer: X PLUS 14

Step-by-step explanation:

The standard form of the given numbers is 207360 × 10¹⁷.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

Given the numbers is  (5 x 1,000,000) (6 x 100,000) (4 x 10,000) (8 x 1,000) (3 x 100) (2 x 10) (4 x 0.1) (9 x 0.001)

Now standard form means we need to write the exponents form.

So,

5 x 6 x 4 x 8 x 3 x 2 x 4 x 9 = 207360

And

1,000,000 x  100000 x 10000 x 1000 x 100 x 10 x 0.1 x 0.001 = 10¹⁷

So, combine 207360 x  10¹⁷

Hence "The standard form of the given numbers is 207360 × 10¹⁷".

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Answer:

the second one

Step-by-step explanation:

The equation presented in this problem has a solution, as the graphs of the two sides of the equality intersect each other.

The equations that compose the system in this problem are given as follows:

We solve the system graphically, hence the solution is given by the point of intersection of the graphs of the two functions.

From the image given at the end of the answer, the system has a solution, which is given as follows:

(7.528, -11.646).

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Answer:

12/6 simplified to lowest terms is 2/1.

Step-by-step explanation:

Divide both the numerator and denominator by the HCF

12 ÷ 6

6 ÷ 6

Reduced fraction:

12/6 simplified to lowest terms is 2/1.

Answer: 2:1

Step-by-step explanation:

12:6

Both left and right can be divided by 6, like a fraction, reduce.

= 2:1

Answer:

graph

Step-by-step explanation:

You would start at -2 then you would go down 3 and right 1, and then you keep doing it until you have no more graph.

Function notation is a way of representing mathematical functions using symbols. In function notation, a function is represented by a single letter, such as "f" or "g," followed by a set of input values in parentheses. For example, f(x) represents a function of x, where the value of f for a given x can be found by evaluating the function.

Function notation is commonly used in mathematics to simplify expressions and make it easier to understand mathematical relationships between variables.

The following function notations represent the following given conditions:

a) N(5) represents the population of Miami 5 years after 1990.

b) N(9) represents the population of Miami 9 years after 1990, or in the year 1999.

c) N(1997) + 45,000 represents the population of Miami which is 45,000 more than the population in 1997.

d) N(1990 + k) represents the population of Miami k years after 1990.

e) N(1998) - N(1995) represents the change in the population of Miami from 1995 to 1998.

f) N(11) - N(7) represents the change in the population of Miami from 7 years after 1990 to 11 years after 1990.

g) N(2008) = 431,200 represents the population of Miami in 2008 as being 431,200.

h) The solution of the equation N(t) = 412,000 represents the year (or years) when the population of Miami was 412,000.

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The estimate of the median number of science homework problems is more likely to be accurate, based on the given information about the median and IQR.

The median and IQR (Interquartile Range) provide information about the central tendency and spread of a set of data, respectively. The fact that the median number of science homework problems is 5 and the IQR is 2 with the middle 50% of the data falling between 4 and 6 problems. This indicates that the data is not highly skewed or influenced by outliers.

In contrast, the fact that the median number of Spanish homework problems is 10 and the IQR is 1 with the middle 50% of the data falling between 9 and 11 problems. This indicates that the data is highly skewed and that even small deviations from the median can have a large impact on the IQR.

Therefore, the estimate of the median number of science homework problems is more likely to be accurate than the estimate of the median number of Spanish homework problems, because the science homework data appears to be more consistent and less influenced by outliers or extreme values.

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____The given question is incorrect, the correct question is given below:

The science teacher gives daily homework. For a random sample of days throughout the year, the median number of problems is 5 and the IQR is 2 . The Spanish teacher also gives daily homework. For a random sample of days throughout the year, the median number of problems is 10 and the IQR is 1 . If you estimate the median number of science homework problems to be 5 and the median number of Spanish problems to be 10, which is more likely to be accurate? Explain your reasoning.

Answer:

(a) 2 degree celsius per hour

(b) 3 degree celsius per hour.

Step-by-step explanation:

From the question,

(a) Avearge rate of rise in temperature per hour(T') = Rise in temperature(T)/Time required for the rise(t).

T' = T/t.................... Euqation 1

Rise in temperature (T) = 4 degree celsius, t = 10.00 am to noon = 2 hours.

Substitute into equation 1

T' = 4/2

T' = 2 degree celsius per hour.

(b) Also,

Average rate of fall in temperature per hour (T') = Fall in temperature (T)/Time(t)

T' = T/t

Given: T = 6 degree celsius, t = 3:00 pm to 5:00 pm = 2 hours

T' = 6/2

T' = 3 degree celsius per hour

Answer:

I believe the answer to be 61

Step-by-step explanation:

180-58=122

122÷2=61

Answer:

-160

Step-by-step explanation:

All you have to do is substitute -2 for all values of x!

Is that last x raised to the power of 4 (looks like \(x^4\))?

If so, the equation is:

\(f(-2)=2(-2-3)(-2)^4\)

2(-5)(16)

-10(16)

-160

We have two right-angled triangles that share a common side, with side lengths 6 and 10. Let's label the sides of the triangles as follows:

Triangle 1:

Side adjacent to the right angle: 6 (let's call it 'a')

Side opposite to the right angle: x (let's call it 'b')

Triangle 2:

Side adjacent to the right angle: x (let's call it 'c')

Side opposite to the right angle: 10 (let's call it 'd')

Using the Pythagorean theorem, we can write the following equations for each triangle:

Triangle 1:\(a^2 + b^2 = 6^2\)

Triangle 2: \(c^2 + d^2 = 10^2\)

Since the triangles share a common side, we know that b = c. Therefore, we can rewrite the equations as:

\(a^2 + b^2 = 6^2\\b^2 + d^2 = 10^2\)

Substituting b = c, we get:

\(a^2 + c^2 = 6^2\\c^2 + d^2 = 10^2\)

Now, let's add these two equations together:

\(a^2 + c^2 + c^2 + d^2 = 6^2 + 10^2\\a^2 + 2c^2 + d^2 = 36 + 100\\a^2 + 2c^2 + d^2 = 136\)

Since a^2 + 2c^2 + d^2 is equal to 136, we can conclude that x (b or c) is between 11 and 12

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The answer to the researcher's question would be affected by the perceived lack of anonymity.

The perceived lack of anonymity refers to a situation where individuals feel that their responses or actions may not remain confidential or anonymous. In the given scenario, the researcher is asking people to stop and chat as they are leaving the restaurant. This method of data collection may create a perceived lack of anonymity, which can significantly impact the responses obtained from the individuals.

When people feel that their responses are not anonymous, they might be hesitant to provide honest or accurate information. They may feel pressured to provide socially desirable answers or modify their responses to fit societal expectations. In the case of tipping at a restaurant, individuals might feel judged or scrutinized based on their tipping behavior, leading to biased or inaccurate responses.

This perceived lack of anonymity can introduce response bias into the study. People might be less inclined to disclose their actual tipping amounts, resulting in underreported or distorted data. This bias can affect the accuracy and representativeness of the findings and lead to misleading conclusions about the average tipping behavior.

To minimize the impact of perceived lack of anonymity, researchers often employ methods that ensure privacy and confidentiality. For example, anonymous surveys or questionnaires can be used to collect data on tipping habits, allowing individuals to provide their responses without the fear of being identified or judged. Alternatively, researchers can collect data through indirect methods, such as observing tipping behavior without directly interacting with the individuals involved.

In summary, the researcher's approach of stopping and chatting with people as they leave the restaurant creates a perceived lack of anonymity, which can introduce bias into the study. To obtain more accurate and reliable data on average tipping amounts, it is essential to ensure privacy and anonymity in data collection methods.

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Using monthly payment formula, the Smith Family's total monthly payment is approximately $2,360.99.

To calculate the total monthly payment for the Smith Family, we need to consider the mortgage payment, insurance, property tax, and HOA fees.

1. Mortgage Payment:

The loan amount is the house price minus the down payment:

$350,000 - $70,000 = $280,000.

To calculate the monthly mortgage payment, we need to determine the interest rate and loan term. Since you mentioned it's a 15-year loan, we'll assume an interest rate of 4% (which can vary depending on market conditions and the borrower's credit).

We can use a mortgage calculator formula to calculate the monthly payment:

M = P [i(1 + i)ⁿ] / [(1 + i)ⁿ⁻¹]

Where:

M = Monthly mortgage payment

P = Loan amount

i = Monthly interest rate

n = Number of months

The monthly interest rate is the annual interest rate divided by 12, and the loan term is 15 years, which is 180 months.

i = 4% / 12 = 0.00333 (monthly interest rate)

n = 180 (loan term in months)

Plugging in the values into the formula:

M = $280,000 [0.00333(1 + 0.00333)¹⁸⁰] / [(1 + 0.00333)¹⁸⁰⁻¹]

Using a calculator, the monthly mortgage payment comes out to be approximately $2,014.99.

2. Insurance:

The monthly insurance payment is given as $66.

3. Property Tax:

The monthly property tax payment is given as $230.

4. HOA Fees:

The HOA fees are stated as $600 per year. To convert this to a monthly payment, we divide by 12 (months in a year): $600 / 12 = $50 per month.

Now, let's add up all these expenses:

Mortgage payment: $2,014.99

Insurance: $66

Property tax: $230

HOA fees: $50

Total monthly payment = Mortgage payment + Insurance + Property tax + HOA fees

Total monthly payment = $2,014.99 + $66 + $230 + $50

Total monthly payment = $2,360.99

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Answer:

Step-by-step explanation:

The relationship between magnitude (M) and intensity (I) of an earthquake is given by:

I ~ 10^(1.5M + 4.8)

We can use this relationship to compare the intensities of the two earthquakes:

I1/I2 = (10^(1.5M1 + 4.8))/(10^(1.5M2 + 4.8))

= 10^(1.5(M1 - M2))

Substituting the given magnitudes, we get:

I1/I2 = 10^(1.5(8.6 - 8.2))

= 10^(1.5(0.4))

≈ 2.24

Therefore, the intensity of the first earthquake was approximately 2.24 times greater than the intensity of the second earthquake.

Answer:

The equation for your graph is Y=2x+1

Answer:

derivative on r^2 with respect to r

one time derivative is 2r

second time derivative is 2

third time derivative is 0

The coefficient of multiple determination is B. 0.1225

The coefficient of multiple correlation is a measure of the linear relationship between multiple independent variables and a dependent variable. It ranges from -1 to 1, where 1 indicates a perfect positive relationship, -1 indicates a perfect negative relationship, and 0 indicates no relationship.

The coefficient of multiple determination, also known as R-squared, represents the proportion of the variance in the dependent variable that can be explained by the independent variables in a multiple regression model.

To find the coefficient of multiple determination, we square the coefficient of multiple correlation. In this case, since the coefficient of multiple correlation is 0.35, we square it to get the coefficient of multiple determination.

\( 0.35^2 = 0.1225 \)

So, the coefficient of multiple determination is approximately 0.1225.

Now, let's check which option from the given choices is the closest to 0.1225:

a. 0.10
b. 0.12
c. 0.14
d. 0.16

Based on our calculation, the coefficient of multiple determination is approximately 0.1225, which is closest to option b. Therefore, the correct answer is b. \( 0.12 \).

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The differences between clay that has been too consolidated and clay that has been usually consolidated are listed below.

What are they?

Normally consolidated clay

Over-consolidated clay

The rate of consolidation is rapid.

The rate of consolidation is slow.

Highest value of void ratio.

Lowest value of void ratio.

More compressible.

Less compressible.

Higher water content and swelling potential.

Lower water content and swelling potential.

Higher permeability.

Lower permeability.

The OCR is equal to 1.

The OCR is greater than 1.

b) A pile foundation would be the most suitable foundation type for the construction of a 20-storey apartment in Cyberjaya, Selangor, underlaid with 15m depth of clayey silts of a very high-water table.

The following are the reasons for this selection of a pile foundation:

Reason 1: Pile foundations are suitable for use in soft soil conditions such as clayey silts. Pile foundations are suitable for soil types with low bearing capacity and high settlement rate.

A pile foundation transfers the load of the structure to a stronger layer beneath the soil, preventing excessive settlement and maintaining stability.

Reason 2: Pile foundations may be installed to reach the required soil depth. Pile foundations are used to transfer load through poor soil to stronger strata beneath the soil.

They are installed by drilling or driving into the ground until they reach a layer of soil or rock with adequate strength.

Since the proposed area has a high-water table, pile foundations are also ideal for use in such conditions because they can be extended through water to the underlying stronger strata.

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Normally consolidated clay has experienced a maximum effective past pressure equal to or less than the existing overburden pressure, while over consolidated clay has experienced a greater past pressure. For an apartment in Cyberjaya with clayey silts and a high water table, a suitable foundation type would be pile foundations due to their ability to handle poor load-bearing capacity and resist the upward pressure from groundwater.

a) Normally consolidated clay and over consolidated clay are two types of clay soils with different characteristics.

Normally consolidated clay refers to clay that has experienced a maximum effective past pressure that is equal to or less than the existing effective overburden pressure at the time of sampling. This means that the clay has undergone natural or human-induced processes that have caused a reduction in effective pressure in the field. As a result, normally consolidated clay tends to have relatively predictable and consistent behavior under loading. When subjected to additional loading, the normally consolidated clay will continue to consolidate and settle gradually over time.

On the other hand, over consolidated clay refers to clay that has experienced a maximum effective past pressure that is greater than the existing effective overburden pressure at the time of sampling. This means that the clay has undergone natural or human-induced processes that have caused the clay to be subjected to higher pressures in the past. As a result, over consolidated clay tends to be more compact and dense compared to normally consolidated clay. It also exhibits higher strength and stiffness due to the previous higher pressures it has experienced.

b) Based on the given situation of developing a 20-storey apartment in Cyberjaya, Selangor, with a 15m depth of clayey silts of very high-water table, a suitable foundation type would be a pile foundation.

Two valid reasons to support this judgment are:

1. Load-bearing capacity: Pile foundations are commonly used in areas with weak or compressible soils, such as clayey silts. By driving piles deep into the ground, the foundation can transfer the load of the structure to a more stable layer of soil or rock below. In this case, the 15m depth of clayey silts suggests the need for a deep foundation to ensure adequate load-bearing capacity.

2. Water table considerations: The presence of a very high-water table indicates the potential for saturated soil conditions. Pile foundations can be designed to withstand the effects of groundwater and minimize settlement caused by water infiltration. By utilizing piles, the foundation can be elevated above the water table, reducing the risk of instability and potential damage to the structure.

Overall, a pile foundation would be a suitable choice for the proposed apartment building in Cyberjaya, Selangor, due to its ability to provide adequate load-bearing capacity and address the challenges posed by the high-water table and clayey silts.

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The area of a disk of radius r is given by the formula, A = πr²Given that the radius of the disk is r = 9 - 9x²We can substitute r in the formula to find the cross-sectional area of the disk.

A = πr²A

= π(9 - 9x²)²

A = π(81 - 162x² + 81x⁴)

A = 81π - 162πx² + 81πx⁴

The cross-sectional area of the disk is given by 81π - 162πx² + 81πx⁴.

The function y = 9 - 9x² intersects the x-axis at the following values of x: When y = 0, we have

0 = 9 - 9x²

9x² = 9

x² = 1

x = ± √1

x = ± 1

The function intersects the x-axis at the values -1 and 1. Hence, the smaller value is -1 and the larger value is 1.

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Answer:

9/14 cups of water.

Step-by-step explanation:

2/3 juice for each   3/7 of water

1      ............................ 3/7 / 2/3 water

= 3/7 * 3/2

= 9/14.

The function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1 and the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

To analyze the provided pseudo code for matrix multiplication and determine the function T(n) in terms of the number of operations, we need to examine the code and count the number of operations performed.

The pseudo code for matrix multiplication may look something like this:

```

MatrixMultiplication(A, B):

   n = size of matrix A

   C = empty matrix of size n x n

   for i = 1 to n do:

       for j = 1 to n do:

           sum = 0

           for k = 1 to n do:

               sum = sum + A[i][k] * B[k][j]

           C[i][j] = sum

   return C

```

Let's break down the number of operations step by step:

1. Assigning the size of matrix A to variable n: 1 operation

2. Initializing an empty matrix C of size n x n: n^2 operations (for creating n x n elements)

3. Outer loop: for i = 1 to n

- Incrementing i: n operations  

- Inner loop: for j = 1 to n

- Incrementing j: n^2 operations (since it is nested inside the outer loop)

- Initializing sum to 0: n^2 operations

- Innermost loop: for k = 1 to n

- Incrementing k: n^3 operations (since it is nested inside both the outer and inner loops)

- Performing the multiplication and addition: n^3 operations

- Assigning the result to C[i][j]: n^2 operations

- Assigning the value of sum to C[i][j]: n^2 operations

Total operations:

1 + n^2 + n + n^2 + n^3 + n^3 + n^2 + n^2 = 2n^3 + 3n^2 + 2n + 1

Therefore, the function T(n) in terms of the number of operations is:

T(n) = 2n^3 + 3n^2 + 2n + 1

To determine the asymptotic (big O) complexity of the algorithm, we focus on the dominant term as n approaches infinity.

In this case, the dominant term is 2n^3. Hence, the asymptotic complexity of the matrix multiplication algorithm is O(n^3).

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Answer:

\(86.666666666666....\)

its 86.6 with the 0.6 recurring

The answer has a line on it

Answer:

  34 square units

Step-by-step explanation:

You want the area of the triangle with vertices X(6, 8), Y(3, 3), and Z(13, -3).

There are several ways the area of a triangle can be calculated from the coordinates of the vertices. One relatively easy method is to find half the absolute value of the sum of the determinants of adjacent pairs of points.

This calculation is shown in the second attachment.

The area of ∆XYZ is 34 square units.

A slope calculation will tell you side XY is perpendicular to side YZ. This means you can find the area from the lengths of these two sides. The distance formula can tell you the lengths.

  XY = √((3 -6)² +(3 -8)²) = √(9 +25) = √34

  YZ = √((13 -3)² +(-3 -3)²) = √(100 +36) = 2√34

 Area = 1/2bh = (1/2)(√34)(2√34) = 34 . . . . square units

Pick's theorem tells you the area of a polygon with vertices on grid points can be found by counting the grid points on the boundary and interior to the boundary.

  A = i + (b/2) -1

This triangle has the three given vertices on grid points, along with point (8, 0), which is the midpoint of YZ. There are 33 interior points, so the area is ...

  A  = 33 +(4/2) -1 = 34 . . . . square units

The length of XZ is ...

  XZ = √((13 -6)² +(-3 -8)²) = √(49 +121) = √170

Heron's formula tells you the area is given by ...

  A = √(s(s -a)(s -b)(s -c)) . . . . . . where s = (a+b+c)/2, the semiperimeter

The third attachment shows this calculation gives an area of 34 square units.

__

Additional comments

The slope calculation tells you the slope of XY is ...

  m = (y2 -y1)/(x2 -x1) = -5/-3 = 5/3

and the slope of YZ is ...

  m = -6/10 = -3/5 . . . . . . . . the opposite reciprocal of the slope of XY

Hence these sides are perpendicular, as we noted above.

We like Pick's theorem for finding the areas of small figures with irrational side lengths (such as this one). It just involves counting, which is often easier than using a bunch of different formulas for slope or length.

The determinant formula is easy to compute, but tedious to enter on a calculator. It is much easier to program a spreadsheet for this. As with Pick's theorem, the method applies to a polygon with any number of vertices.

  \(\left|\begin{array}{cc}a&b\\c&d\end{array}\right|=ad-bc\)

In these 2×2 matrices, the coordinates can be listed in rows or in columns. It makes no difference to the calculation. The key is to work in one direction around the figure. (Here, we went CCW.)

The triangle is drawn in the first attachment. The geometry program that drew it also calculated its area to be 34 square units.

You may have noticed that the "determinant" method and Pick's theorem guarantee that the area of any polygon with integer coordinates will be an integer multiple of 1/2 square unit. That is, it will never be irrational. (You might not see that using Heron's formula.)

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The above function should be used to complete the table based on the given domain as follows;

x         0      1     2     3    4    

f(x)      -6     -5   -3     1    9

In order to use the given exponential function to complete the table, we would have to substitute each of the values of x (x-values or input values) into the exponential function and then evaluate as follows;

When the value of x is 0, the exponential function is given by;

f(x) = 2^x - 7

f(0) = 2^0 - 7

f(0) = 1 - 7

f(0) = -6.

When the value of x is 1, the exponential function is given by;

f(x) = 2^x - 7

f(1) = 2^1 - 7

f(1) = 2 - 7

f(1) = -5.

When the value of x is 2, the exponential function is given by;

f(x) = 2^x - 7

f(2) = 2^2 - 7

f(2) = 4 - 7

f(2) = -3.

When the value of x is 3, the exponential function is given by;

f(x) = 2^x - 7

f(3) = 2^3 - 7

f(3) = 8 - 7

f(3) = 1.

When the value of x is 4, the exponential function is given by;

f(x) = 2^x - 7

f(4) = 2^4 - 7

f(4) = 16 - 7

f(4) = 9.

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Answer:

Step-by-step explanation:

this app is useless don't use it for math probs it doesn't help at all just stay on your work hoped this helped