write a mathematical sentence which relates to a real life scenario in business

Answer:

Calculate the arc length according to the formula above: L = r * θ = 15 * π/4 = 11.78 cm. Calculate the area of a sector: A = r² * θ / 2 = 15² * π/4 / 2 = 88.36 cm².

Step-by-step explanation:

The answer to this question is 0.6826, or 68.26%. To calculate this probability, we need to use the z-score formula.

The z-score formula is a statistical measurement that is used to identify how far a raw score is from the mean score of a population. It is calculated by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation.

This formula allows us to convert a given value into a standardized score relative to the mean and standard deviation of the normal distribution. In this case, the z-score for 27.42 is -1 and the z-score for 34.08 is 1.

We can then use the cumulative normal distribution function to calculate the probability of x being between 27.42 and 34.08. This function allows us to calculate the area under the normal distribution curve between two given points. Since the normal distribution is symmetrical, the area under the curve between -1 and 1 is 0.6826 or 68.26%. This is the probability of x being between 27.42 and 34.08.

To summarize, in order to calculate the probability of x being between 27.42 and 34.08, we need to calculate the z-scores of these two values and then use the cumulative normal distribution function to calculate the area under the curve between the two z-scores. The area under the curve between -1 and 1 is 0.6826 or 68.26%, which is the probability of x being between 27.42 and 34.08.

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Answer:

(−∞,∞)

Step-by-step explanation:

The correct statement regarding whether (8, √17) lies on the circle is given as follows:

Yes, the distance from the origin to the point (8,√17) is 9 units.

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle that pass through the center. Hence, the diameter’s length is twice the radius length.

The parameters for this circle are given as follows:

Hence the equation is given as follows:

x² + y² = 81.

For point (8, √17), we have that:

8² + (√17)² = 81

64 + 17 = 81

81 = 81.

Hence the point lies on the circle.

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The 9th term of the sequence is approximately 30.234.

In mathematics, a sequence is an ordered list of numbers or other mathematical objects, such as functions, matrices, or vectors. Each member of the sequence is called a term, and the position of each term in the sequence is identified by its index or subscript.

Looking at the given terms, we can observe that each term is less than the previous term and the difference between consecutive terms is decreasing. Therefore, the sequence is decreasing and the difference between consecutive terms is decreasing by a factor of 2 each time.

Using this pattern, we can find the common difference between consecutive terms as follows:

60 - 80 = -20

45 - 60 = -15

We see that the difference between consecutive terms decreases by a factor of 2 each time. Therefore, the next difference would be:

-15 / 2 = -7.5

So, the next term would be:

45 - 7.5 = 37.5

We can continue this pattern to find the 9th term as follows:

Term 1: 80

Term 2: 60

Term 3: 45

Term 4: 37.5

Term 5: 33.75

Term 6: 31.875

Term 7: 30.9375

Term 8: 30.46875

Term 9: 30.234375

Therefore, the 9th term of the sequence is approximately 30.234.

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Answer:

Step-by-step explanation:

To find the critical points of the function f(x,y), we need to find all points where both partial derivatives ∂f/∂x and ∂f/∂y are equal to zero.

We first find ∂f/∂x by differentiating f(x,y) with respect to x and treating y as a constant:

∂f/∂x = 4x + 2y + 2

We then find ∂f/∂y by differentiating f(x,y) with respect to y and treating x as a constant:

∂f/∂y = 2x + 2y

To find the critical points, we need to solve the following system of equations simultaneously:

4x + 2y + 2 = 0

2x + 2y = 0

We can solve the second equation for y:

2y = -2x

y = -x

Substituting this into the first equation, we get:

4x + 2(-x) + 2 = 0

2x + 2 = 0

2x = -2

x = -1

Substituting x = -1 into y = -x, we get:

y = -(-1) = 1

Therefore, the critical point is (-1,1).

To verify that this point is a minimum, we can use the second partial derivative test. We first find the second partial derivatives:

∂²f/∂x² = 4

∂²f/∂y² = 2

∂²f/∂x∂y = 2

The discriminant of the Hessian matrix is:

∂²f/∂x² * ∂²f/∂y² - (∂²f/∂x∂y)² = (42) - (22) = 4

Since the discriminant is positive and the second partial derivative with respect to x is positive, the critical point (-1,1) is a local minimum.

Therefore, the point (-1,1) is the only critical point of the function f(x,y), and it is a local minimum.

According to given information, A is 50 years old and B is 10 years old.

In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that can be evaluated to produce a numerical result or a value.

Let's use algebra to solve the problem.

Let A's current age be x, and B's current age be y.

From the problem, we know that:

x = 5y (A is five times as old as B)

x + 10 = 3(y + 10) (After 10 years, A will be 3 times as old as B)

We can use the first equation to substitute x in the second equation:

5y + 10 = 3(y + 10)

Simplifying this equation gives:

5y + 10 = 3y + 30

2y = 20

y = 10

So B is currently 10 years old. We can use the first equation to find A's current age:

x =5y = 5(10) = 50

So A is currently 50 years old.

Therefore, according to given information, A is 50 years old and B is 10 years old.

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If the rope is to be doubled or tripled up around the perimeter of each site, the actual amount of rope needed will be greater than 315 meters.

Amount is a term used to describe the total of something. It can refer to a quantity of money, a number of items, or a measure of any other type of resource. Amounts are typically expressed as a numerical value, and they can be represented in different units depending on the type of resource. For example, an amount of money could be expressed in dollars, whereas an amount of time could be expressed in hours.

To calculate the amount of rope needed for both sites, we will first need to calculate the perimeter of each site. The perimeter of Site A is 180 meters (60 + 40 + 40 + 40) and the perimeter of Site B is 135 meters (45 + 45 + 45).

To calculate the total amount of rope needed for both sites, we will need to add the two perimeters together. The total amount of rope needed for both sites is 315 meters (180 + 135).

It is important to note that 315 meters of rope is the minimum needed to rope off both sites. Depending on the desired spacing between the rope and the sites, the actual amount of rope needed may be greater than 315 meters.  Additionally, if the rope is to be doubled or tripled up around the perimeter of each site, the actual amount of rope needed will be greater than 315 meters.

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If the rope is to be doubled or tripled up around the perimeter of each site, the actual amount of rope needed will be greater than 315 meters.

Amount is a term used to describe the total of something. It can refer to a quantity of money, a number of items, or a measure of any other type of resource. Amounts are typically expressed as a numerical value, and they can be represented in different units depending on the type of resource. For example, an amount of money could be expressed in dollars, whereas an amount of time could be expressed in hours.

To calculate the amount of rope needed for both sites, we will first need to calculate the perimeter of each site. The perimeter of Site A is 180 meters (60 + 40 + 40 + 40) and the perimeter of Site B is 135 meters (45 + 45 + 45).

To calculate the total amount of rope needed for both sites, we will need to add the two perimeters together. The total amount of rope needed for both sites is 315 meters (180 + 135).

It is important to note that 315 meters of rope is the minimum needed to rope off both sites. Depending on the desired spacing between the rope and the sites, the actual amount of rope needed may be greater than 315 meters.  Additionally, if the rope is to be doubled or tripled up around the perimeter of each site, the actual amount of rope needed will be greater than 315 meters.

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Answer:

the answer is D

both lines intersect at (2, -3)

hope this helps <3

Answer:

you need to put the answers down

Step-by-step explanation:

.

Answer:6

Step-by-step explanation:

[tex]\frac{a^{b} }{a^{c}} =a^{b-c} \\a^{b} *a^{c} =a^{b+c}\\ \frac{(-4)^{10}}{(-4)^{n}}=(-4)^{2}*(-4)^{2} \\(-4)^{10-n}=(-4)^{4}\\ 10-n=4\\ -n=-6\\n=6[/tex]

Answer:

n = 6

Step-by-step explanation:

[tex]\frac{(-4)^{10}}{(-4)^{n}} =(-4)^{2}*(-4)^{2}\\\\\frac{(-4)^{10}}{(-4)^{n}} =(-4)^{2+2}\\\\\frac{(-4)^{10}}{(-4)^{n}} =(-4)^{4}[/tex]

If they have the same base which is -4 we can either add or subtracting the exponent.

Add the exponenet when multiplying.

Subtract the exponent when dividing.

[tex](-4)^{10-n}=(-4)^4\\\\10-n=4\\10=4+n\\n= 6[/tex]

[tex]\frac{(-4)^{10}}{(-4)^{6}}=(-4)^{10-6}=(-4)^4[/tex]

1- 58000

2- 232000

3- 1245.43

4- 506354.8

The total surface area of a cylinder with a height that was two times greater than its radius is 6πr²

The total surface area of a cylinder is the region occupied by the cylinder. It is given by A = 2πr(r + h) where

Since we want to find which student found the total surface area of a cylinder with a height that was two times greater than its radius.

We proceed as follows.

Since we have that the height that was two times greater than its radius. So, for that cylinder, h = 2r

So, to find the surface area, we substitute the values of the variables into the equation for the total surface area.

So,  A = 2πr(r + h)

Given that h = 2r, we have that

A = 2πr(r + h)

A = 2πr(r + 2r)

A = 2πr(3r)

A = 6πr²

So, the area is 6πr²

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Answer:

The 440-yd race is longer than the 400-m race by 2.336 meters.

Step-by-step explanation:

We can convert the distance of the 440-yd race to meters using the conversion factor 1 yd = 0.9144 m:

440 yd = 440 x 0.9144 m/yd = 402.336 m

Therefore, the 440-yd race is 402.336 meters long.

On the other hand, the 400-m race is already in meters.

Comparing the two distances, we can see that the 440-yd race is longer than the 400-m race.

To find out by how much longer, we can subtract the length of the 400-m race from the length of the 440-yd race:

402.336 m - 400 m = 2.336 m

Therefore, the 440-yd race is longer than the 400-m race by 2.336 meters.

The time needed for the sample size to double is given as follows:

26.3 hours.

The exponential function that models the sample size after t hours is given as follows:

y(t) = y(0)e^(0.0264t).

The parameter y(0) represents the initial population, hence when the population is doubled, we have that:

y(t) = 2y(0).

Then we must solve the exponential function for the variable t, applying the natural logarithm, which is the inverse of the exponential, as follows:

2y(0) = y(0)e^(0.0264t).

e^(0.0264t) = 2

0.0264t = ln(2)

t = ln(2)/0.0264

t = 26.3 hours.

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Answer: 15.54 degrees.

Step-by-step explanation:

To find the average temperature, we need to add up all the temperatures and then divide by the number of days:

Average temperature = (14.6 + 15.2 + 15.8 + 16.1) / 5

= 77.7 / 5

= 15.54

Therefore, the average temperature over the 5 consecutive days in October is approximately 15.54 degrees.

The pressure οn the grοund when the blοck exerts a fοrce οf 7 Nm is [tex]175 nm^{-2[/tex].

First, we need tο cοnvert the area οf the blοck's base frοm square meters tο square nanοmeters, since the fοrce is given in newtοn-meters (N m) and we want tο find the pressure in newtοn-meters-squared ([tex]N/m^2[/tex] οr[tex]Nm^{-2[/tex]):

[tex]0.04 m^2 = 0.04 \times 10^18 nm^2 (since 1 m = 10^9 nm)[/tex]

Next, we can use the fοrmula fοr pressure, which is:

pressure = fοrce/area

Substituting the given values, we get:

[tex]pressure = 7 N m / 0.04\times 10^{18} nm^2[/tex]

Simplifying this expressiοn, we get:

[tex]pressure = (7 / 0.04) \times 10^{(-9)} N/nm^2[/tex]

[tex]pressure = 175 \times 10^{(-9)} N/nm{^2[/tex]

[tex]pressure = 175 nm^{-2[/tex]

Therefοre, the pressure οn the grοund when the blοck exerts a fοrce οf 7 Nm is[tex]175 nm^{-2[/tex].

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Correct option is B, modification that can be made to this loan to make it a viable option, given Giselle's situation Change the interest to 5.5%.

Giselle may either lower the interest rate to 5.5% or increase the down payment to 18% down in order to make the 20% down, 30-year fixed loan option financially feasible. Giselle's maximum monthly payment of $746.50 is exceeded by the monthly payment for the current loan option. The monthly payment would rise if the loan was shortened to 15 years, rendering it unprofitable. As a result, Giselle should choose a mortgage with a lower interest rate or put more money down in order to bring the monthly payment within her means.

Given Giselle's circumstances, the modification that may be made to this loan to make it an attractive alternative is to raise the interest rate to 5.5%.

Changes to the loan that will be made:

Price of acquisition: $163,000

Monthly income equals $2,986

25% of people are unwilling to spend money.

$33,000 is the down payment.

20% decline rate

Analysis

163,000 less $33,000 is the balance of the loan.

Amount remaining on loan is $130,000.

Condo loan balance = $163,000.20

Condo loan balance = $32,600

Down rate increase equals $163,000 x 20.25%

A higher down payment equals $33,007.50

The optimal solution, based on the research above, is to change the interest rate to 5.5% because it will result in a lower overall payment cost and make the loan amount a viable option.

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So the equation for the distance from the center of the habitat to the point (x, y) is: Distance = √[(x - x1)² + (y - y1)²].

A coordinate is a number that indicates the position of a point in a space or plane. In mathematics, we often use a coordinate system to represent points and their positions. A coordinate system is a system that uses one or more numbers or coordinates to uniquely determine the position of a point or an object in a space or plane. The most common coordinate system is the Cartesian coordinate system, which is named after the mathematician René Descartes. In the Cartesian coordinate system, each point is represented by an ordered pair of numbers (x, y), where x is the horizontal coordinate or abscissa, and y is the vertical coordinate or ordinate. The point (0, 0) is called the origin, and it represents the point where the x and y axes intersect. Coordinates can also be expressed in three or more dimensions, using three or more numbers. In three-dimensional space, the coordinates of a point are represented by an ordered triple (x, y, z), where x, y, and z are the horizontal, vertical, and depth coordinates, respectively.

Here,

The distance formula is used to find the distance between two points in a coordinate plane. In this case, we are finding the distance from the center of the habitat (x1, y1) to the point (x2, y2), so the formula becomes:

=√[(x2 - x1)² + (y2 - y1)²]

Substituting the coordinates of the given point (x, y), we get:

=√[(x - x1)² + (y - y1)²]

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Answer:

Step-by-step explanation:

ntroduction to standard deviation

Standard deviation measures the spread of a data distribution. The more spread out a data distribution is, the greater its standard deviation.

For example, the blue distribution on bottom has a greater standard deviation (SD) than the green distribution on top:

Step-by-step explanation:

To calculate the amount of money in the account at the end of 4 years, we can use the formula for simple interest:

I = P * r * t

Where:

I = Interest earned

P = Principal amount (initial deposit)

r = Annual interest rate (as a decimal)

t = Time period (in years)

Plugging in the given values, we get:

I = $50,000 * 0.025 * 4

I = $5,000

This means that over the course of 4 years, the account will earn $5,000 in interest.

To find the total amount in the account at the end of 4 years, we simply add the interest earned to the initial deposit:

Total amount = $50,000 + $5,000

Total amount = $55,000

Therefore, at the end of 4 years, there will be $55,000 in the account if you deposit $50,000 into a bank account that earns 2.5% simple interest annually.

The null hypothesis for this study is that there is no significant difference in stress levels between the untreated population and the sample of students who were taught mindfulness meditation.

The null hypothesis states that the mindfulness meditation has no effect on the stress levels of the students.

In terms of the mean stress level (μ), the null hypothesis can be expressed as:

H₀: μ = 30

This means that under the null hypothesis, the mean stress level of the students who were taught mindfulness meditation is equal to the mean stress level of the untreated population (μ = 30).

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Answer:

Answer is B

Step-by-step explanation:

Multiply by 15 on both sides, subtract by 10 on both sides, and divide by 5 on both sides to get x=10

In summary, a change in a value in a data set can have varying impacts on the measures of central tendency and dispersion, depending on the value that was changed and its relationship to the other values in the data set.

Why it is?

The measures of central tendency, such as mean, median, and mode, and the measure of dispersion, range, can be impacted by a change in a value in a data set.

Mean: The mean is calculated by adding all the values in a data set and then dividing by the total number of values. If a value in the data set changes, the sum of the values will change, and thus the mean will also change. The impact of the change on the mean will depend on the value that was changed and how much it differs from the other values in the data set.

Median: The median is the middle value in a data set, when the values are arranged in order. If a value in the data set changes, the position of the median may change, depending on where the new value falls in the order of the values.

Mode: The mode is the value that appears most frequently in a data set. If a value in the data set changes, the mode may change, depending on whether the new value becomes the most frequent value or not.

Range: The range is the difference between the highest and lowest values in a data set. If a value in the data set changes, the range may change, depending on how much the new value differs from the highest or lowest value in the data set.

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Answ

Step-by-step explanation:

x is equal to -9/2

Answer:

To use the distributive property to solve 99 x 3, we can write it as:

99 x 3 = (90 + 9) x 3 (decomposing 99 as 90 + 9)

= 90 x 3 + 9 x 3 (using distributive property)

= 270 + 27

= 297

Therefore, 99 times 3 using the distributive property equals 297.

Step-by-step explanation:

Answer:

A fully loaded and fueled spacecraft weighing 5.1 million pounds is equivalent to 2550 US tons

Step-by-step explanation:

Answer:

c. 0.29

Step-by-step explanation:

edge

Answer:

B. linear

Step-by-step explanation:

x     y

0     9

1      9 + 8

2      9 + 2(8)

3      9 + 3(8)

4      9 + 4(8)

=> linear function

The area of the circle shown above is equal to: A. 1,520.5 cm².

Mathematically, the area of a circle can be calculated by using the following mathematical expression:

Area of a circle, A = πr²

Where:

r represents the radius of a circle.

By substituting the radius into the formula for the area of a circle, we have the following;

Area of a circle, A = πr²

Area of a circle, A = 3.14 × 22²

Area of a circle, A = 1,520.5 cm².

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