in exercises 47 and 48, find an equation for (a) the tangent to the curve at p and (b) the horizontal tangent to the curve at q

Answer:

The unit circle has many different angles that each have a corresponding point on the circle. The coordinates of each point give us a way to find the tangent of each angle. The tangent of an angle is equal to the y-coordinate divided by the x-coordinate.

The value of standard deviation of the stock returns is 10.246%.

The variance or dispersion of a group of data points is measured by standard deviation. Finding the square root of the variance, which is the sum of the squared deviations between each data point and the mean, is how it is determined. In statistics, the term "standard deviation" is used to characterise the distribution of a data collection and to estimate the probability of certain outcomes or events.

The standard deviation is determined using the formula:

√(V).

The mean of the given data is:

(−12 + 10 + 5 − 7 + 3) / 5 = −0.2%

Now, the variance is:

Variance = [ (−12 − (−0.2))² + (10 − (−0.2))² + (5 − (−0.2))² + (−7 − (−0.2))² + (3 − (−0.2))² ] / 5

Variance = 104.96

Now, for standard deviation:

Standard deviation = √(104.96) = 10.246%

Hence, the value of standard deviation of the stock returns is 10.246%.

Learn more about standard deviation here:

https://brainly.com/question/29088233

#SPJ1

Answer:

Step-by-step explanation:

Question 1

Part A:

To predict the number of times Harris will spin a sum less than 10, we need to find the probability of getting a sum less than 10 and multiply it by the total number of spins, which is 500.

The possible outcomes of the first spinner are 1, 2, and 3, and the possible outcomes of the second spinner are 4, 5, 6, 7, and 8. The minimum sum we can get is 1+4=5, and the maximum sum we can get is 3+8=11.

To get a sum less than 10, we can get:

1+4=5

1+5=6

1+6=7

1+7=8

1+8=9

2+4=6

2+5=7

2+6=8

2+7=9

3+4=7

3+5=8

3+6=9

There are 12 possible outcomes that result in a sum less than 10. So the probability of getting a sum less than 10 is 12/15, or 4/5.

To find the number of times Harris will spin a sum less than 10, we can use the equation:

probability of getting a sum less than 10 × total number of spins = x

So the equation that can be solved to predict the number of times Harris will spin a sum less than 10 is:

C) 12/15 = x/500

Part B:

To find the number of times Harris should expect to spin a sum that is 10 or greater, we can subtract the number of times he will spin a sum less than 10 from the total number of spins:

total number of spins - number of times he will spin a sum less than 10 = number of times he should expect to spin a sum that is 10 or greater

Substituting the values, we get:

500 - (12/15 × 500) = 500 - 400 = 100

So Harris should expect to spin a sum that is 10 or greater 100 times.

(a) Experimental probability (5 or 8) = 0.193

(b) Theoretical probability (5 or 8) = 0.200

(c) As the number of trials increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.

Probability is the likelihood of a desired event happening.

Experimental probability is a probability that relies mainly on a series of experiments.

Theoretical probability is the theory behind probability. To find the probability of an event, an experiment is not required. Instead, we should know about the situation to find the probability of an event occurring.

(a) From these results, the experimental probability of getting a 5 or 8 will be:

Experimental probability (5 or 8) = P(5) + P(8)

Experimental probability (5 or 8) = (15/150) + (14/150)

Experimental probability (5 or 8) = 29/150

Experimental probability (5 or 8) = 0.193

(b) The theoretical probability of getting a 5 or 8 will be:

0,1, 2, 3, 4, 5, 6, 7, 8, 9

Theoretical probability (5 or 8) = P(5) + P(8)

Theoretical probability (5 or 8) = (1/10) + (1/10)

Theoretical probability (5 or 8) = 2/10

Theoretical probability (5 or 8) = 0.200

(c) As the number of trials increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.

Learn more about probability on:

brainly.com/question/251701

#SPJ1

Answer:

Step-by-step explanation:

The Dcpromo wizard will guide you through e. All of the above installation scenarios

A utility in Active Directory called DCPromo (Domain Controller Promoter) installs and uninstalls Active Directory Domain Services and promotes domain controllers. Since Windows 2000, every version of Windows Server contains DCPromo, which creates forests and domains in Active Directory. It works with Windows Server and houses all network resources as a centralised security management solution.

The functionality aids in building a completely new forest structure. It allows for both the addition of a new domain tree to an existing forest and the addition of a child domain to an existing domain. Additionally, it degrades the domain controllers and ultimately deletes a domain or forest.

Complete Question:

The dcpromo wizard will guide you through which of the following installation scenarios? [check all that apply]

Creating an entirely new forest structure.

Adding a child domain to an existing domain.

Adding a new domain tree to an existing forest.

Demoting domain controllers and eventually removing a domain or forest

All of the above

Read more about Dcpromo on:

https://brainly.com/question/9473585

#SPJ4

The appropriate inference from the data is (B) Since [tex]20%[/tex] of this group read below grade level, we cannot draw any generalizations about the population. Thus, option B is correct.

A representative sample is a subset of data, often drawn from a wider population, that can show qualities that are similar.

Because the data produced contains more manageable, smaller representations of the larger group, representative sampling aids in the analysis of bigger groups.

Although the sample may be representative of seventh-grade American students, it is not necessarily representative of all seventh-graders or all American children. Hence, without additional data or research, we cannot extrapolate the sample's results to the overall population.

Therefore, 20%20, percent of all American students in seventh grade were reading below grade level.

Learn more about sample here:

https://brainly.com/question/30333799

#SPJ1

Answer:

Traffic signs are regulated by the Manual on Uniform Traffic Control Devices (MUTCD). The perimeter of a rectangular traffic sign is 126 inches. Also, its length is 9 inches longer than its widthFind the dimensions of this sign.

Step-by-step explanation:

Let's say the width of the sign is x inches. Then, according to the problem, the length of the sign is 9 inches longer than the width, which means the length is x + 9 inches.

The perimeter of a rectangle can be found by adding up the length of all its sides. For this sign, the perimeter is given as 126 inches. So we can set up an equation:

2(length + width) = 126

Substituting the expressions for length and width in terms of x, we get:

2(x + x + 9) = 126

Simplifying and solving for x:

2(2x + 9) = 126

4x + 18 = 126

4x = 108

x = 27

So the width of the sign is 27 inches, and the length is 9 inches longer, or 36 inches. Therefore, the dimensions of the sign are 27 inches by 36 inches.

(a) The country will first experience shortages of food in approximately 26.6 years

(b) If the country doubled its initial food supply and maintained a constant rate of increase in the supply, shortages would still occur in approximately 38 years.

(c) If the country doubled the rate at which its food supply increases, in addition to doubling its initial food supply, shortages would still occur in approximately 55.4 years.

a. Let P(t) be the population of the country at time t (in years), and F(t) be the food supply of the country at time t.

We know that P(0) = 4 million, and P'(t) = 0.05P(t), which means that the population is increasing by 5% per year.

We also know that F(0) = 8 million, and F'(t) = 0.25 million, which means that the food supply is increasing by 0.25 million people per year.

When the food supply is just enough to feed the population, we have P(t) = F(t), so we can solve for t as follows:

4 million x (1 + 0.05)^t = 8 million + 0.25 million x t

[tex]4(1 + 0.05)^t = 8 + 0.25t\\\\t \approx 26.6 \ years[/tex]

b. If the country doubled its initial food supply, then F(0) = 16 million. We can use the same equation as before and solve for t:

4 million x  (1 + 0.05)^t = 16 million + 0.25 million x t

[tex]4(1 + 0.05)^t = 16 + 0.25t\\\\t \approx 38 \ years[/tex]

c. If the country doubled the rate at which its food supply increases and doubled its initial food supply, then we have F(0) = 16 million and F'(t) = 0.5 million. Using the same equation as before, we get:

4 million x  (1 + 0.05)^t = 32 million + 0.5 million x t

[tex]4(1 + 0.05)^t = 32 + 0.5t\\\\t \approx 55.4 \ years[/tex]

Learn more about rate of food supply here: https://brainly.com/question/30848751

#SPJ1

Answer: x = 5 and x = 1.

Step-by-step explanation:

To solve fg(x) = gf(x), we need to find the expressions for fg(x) and gf(x) and then set them equal to each other.

fg(x) = f(g(x)) = f(x² + 2) = 2(x² + 2) - 3 = 2x² + 1

gf(x) = g(f(x)) = g(2x - 3) = (2x - 3)² + 2 = 4x² - 12x + 11

Now we set fg(x) equal to gf(x) and solve for x:

2x² + 1 = 4x² - 12x + 11

2x² - 12x + 10 = 0

Dividing both sides by 2 gives:

x² - 6x + 5 = 0

This quadratic equation factors as:

(x - 5)(x - 1) = 0

So the solutions are x = 5 and x = 1.

Therefore, the solutions to fg(x) = gf(x) are x = 5 and x = 1.

Answer:

56

90

56

Step-by-step explanation:

easy easy lol.

aaaaa

Let X and Y be independent random variables, uniformly distributed in the interval [0, 1 ]. The CDF of X - Y is FZ(z) = (1/2)(1+z)^2 for -1 ≤ z ≤ 0, 1 - (1/2)(1-z)^2 for 0 ≤ z ≤ 1, 0 for z < -1 or z > 1. The PDF of X - Y is fZ(z) = z + 1 for -1 < z < 0, 1 - z for 0 < z < 1, 0 otherwise.

To find the CDF of X - Y, we first note that the range of X - Y is [0, 1]. Let Z = X - Y, then:

FZ(z) = P(Z ≤ z) = P(X - Y ≤ z)

We can write this as an integral over the joint distribution of X and Y:

FZ(z) = ∫∫[X - Y ≤ z] fXY(x, y) dx dy

Since X and Y are independent, the joint distribution is simply the product of their marginal distributions:

fXY(x, y) = fX(x) fY(y) = 1 * 1 = 1

for 0 ≤ x, y ≤ 1.

Thus, we have:

FZ(z) = ∫∫[X - Y ≤ z] dx dy

= ∫∫[Y ≤ X - z] dx dy

= ∫0^1 ∫0^(x-z) 1 dy dx + ∫0^1 ∫(x-z)^1 1 dy dx

= ∫0^(1+z) (1-z) dx

= (1/2)(1+z)^2 for -1 ≤ z ≤ 0

= 1 - (1/2)(1-z)^2 for 0 ≤ z ≤ 1

Therefore, the CDF of X - Y is:

FZ(z) =

(1/2)(1+z)^2 for -1 ≤ z ≤ 0

1 - (1/2)(1-z)^2 for 0 ≤ z ≤ 1

0 for z < -1 or z > 1

To find the PDF of X - Y, we differentiate the CDF:

fZ(z) = dFZ(z)/dz =

z + 1 for -1 < z < 0

1 - z for 0 < z < 1

0 otherwise

Therefore, the PDF of X - Y is:

fZ(z) =

z + 1 for -1 < z < 0

1 - z for 0 < z < 1

0 otherwise

To know more about CDF and PDF:

https://brainly.com/question/31140093

#SPJ4

Answer:The specific heat of a substance is defined as the amount of heat required to raise the temperature of one gram of the substance by one degree Celsius (or Kelvin).

To find the specific heat of the unknown substance, we can use the following equation:

Q = m x c x ΔT

where Q is the heat gained or lost, m is the mass of the substance, c is its specific heat, and ΔT is the change in temperature.

In this problem, we know the mass and initial and final temperatures of both the unknown substance and the water, as well as the specific heat of water. We can use this information to calculate the heat gained by the water, which must be equal to the heat lost by the unknown substance:

Heat gained by water = Heat lost by unknown substance

m(water) x c(water) x ΔT(water) = m(substance) x c(substance) x ΔT(substance)

We can plug in the values we know and solve for the specific heat of the unknown substance:

m(water) = 75.0 g

c(water) = 4.18 J/g°C

ΔT(water) = 27.1 °C - 20.00 °C = 7.1 °C

m(substance) = 100.0 g

ΔT(substance) = 200.0 °C - 27.1 °C = 172.9 °C

75.0 g x 4.18 J/g°C x 7.1 °C = 100.0 g x c(substance) x 172.9 °C

Simplifying this equation, we get:

c(substance) = (75.0 g x 4.18 J/g°C x 7.1 °C) / (100.0 g x 172.9 °C)

c(substance) = 0.197 J/g°C

Therefore, the specific heat of the unknown substance is 0.197 J/g°C.

Step-by-step explanation:

Answer:

The specific heat of the unknown substance is 0.39 J/g°C.

Step-by-step explanation:

To solve this problem, we can use the principle of conservation of energy, which states that the heat lost by the unknown substance is equal to the heat gained by the water and the calorimeter. We can express this principle mathematically as:

Q_lost = Q_gained

where Q_lost is the heat lost by the unknown substance, and Q_gained is the heat gained by the water and calorimeter.

We can calculate Q_lost using the formula:

Q_lost = m × c × ΔT

where m is the mass of the unknown substance, c is its specific heat, and ΔT is the change in temperature it undergoes.

We can calculate Q_gained using the formula:

Q_gained = (m_water + m_calorimeter) × c_water × ΔT

where m_water is the mass of the water, m_calorimeter is the mass of the calorimeter, c_water is the specific heat of water, and ΔT is the change in temperature of the water and calorimeter.

Since the system reaches an equilibrium temperature, we can set Q_lost equal to Q_gained and solve for the specific heat of the unknown substance (c).

Here's the calculation:

Q_lost = Q_gained

m × c × ΔT = (m_water + m_calorimeter) × c_water × ΔT

100.0 g × c × (200.0 °C - 27.1 °C) = (75.0 g + 75.0 g) × 4.18 J/g°C × (27.1 °C - 20.00 °C)

Simplifying:

c = [(75.0 g + 75.0 g) × 4.18 J/g°C × (27.1 °C - 20.00 °C)] / (100.0 g × (200.0 °C - 27.1 °C))

c = 0.39 J/g°C

Therefore, the specific heat of the unknown substance is 0.39 J/g°C.

As a result, the probability that the average battery life exceeds 553.9 minutes is 0.0262 (or 2.62%). The answer, rounded to four decimal places, is 0.0262.

Probability serves as an indicator of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing an unlikely event and 1 representing an unavoidable event. Switching a fair coin and coin flips has a probability of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails). Probability theory is a branch of mathematics that studies happenings rather than their properties. It is applied in many fields, including statistics, fund, science, and engineering.

The central limit theorem can be used to approximate the sample mean distribution as a normal distribution with a mean of the population mean and a standard deviation of the population standard deviation divided by the square root of the sample size.

The standard error of the mean (SE) is calculated as follows:

SE = σ/√n

Where n is the sample size and is the population standard deviation.

SE = 83/√160 = 6.575

Z = (X - μ) / SE

Where X represents the sample mean, is the population mean, and SE represents the standard error of the mean.

Z = (553.9 - 541) / 6.575 = 1.94

As a result, the probability that the average battery life exceeds 553.9 minutes is 0.0262 (or 2.62%). The answer, rounded to four decimal places, is 0.0262.

To know more about probability visit:

https://brainly.com/question/11234923

#SPJ1

Therefore , the solution of the given problem of function comes out to be  the zeros of the function y = x² + x - 2 are x = -2 and x = 1, and the polynomial in factored form is y = (x + 2)(x - 1).

All of the subjects, including actual and fictitious locales and arithmetic variable design, will be covered in the midterm exam questions. a schematic illustrating the connections between various components that work together to produce the same outcome. A service is made up of many unique parts that work together to produce unique outcomes for each input. Every postbox has a specific location that could serve as a refuge.

Here,

We can draw points for different values of x and y to graph the function => y = x² + x- 2:

|x| |y=x²+x-2|

|---|-----------|

|-3 | 4 |

|-2 | 0 |

|-1 | -2 |

|0 | -2 |

|1 | 0 |

|2 | 6 |

|3 | 12 |

We can use the elements in the table above to plot them on a graph and link them to create a parabolic shape.

We can search for the values of x where the function y = 0 to determine the function's zeros.

Using the zeros we discovered, we can recast the function as the polynomial in factored form is:

=> y = (x + 2)(x - 1)

Therefore, the zeros of the function y = x² + x - 2 are x = -2 and x = 1, and the polynomial in factored form is y = (x + 2)(x - 1).

To know more about function visit:

https://brainly.com/question/28193995

#SPJ1

The specific heat of water is [tex]+41840J . mol^{-1}[/tex].

The following formula is used to determine how much heat a substance absorbs or releases during a heat exchange between two bodies, Calculate the value of q.

Q = m.s.t

Where,

Q is equal to how much heat is received or emitted.

m = The substance's mass

t = Temperature change

s = The substance's specific heat

The starting temperature in this dissolve is,

[tex]T_{i}[/tex] = 25.00°C

(25.00 + 273.00) K

= 298.00 K

Final temperature in this dissolving is,

[tex]T_{f}[/tex] = 23.36°C

= (23.36 + 273.00) K

Specific Water's heat is, [tex]4.184\frac{J}{g.K}[/tex]

In this issue, the heat that water releases are,

[tex]Q_{released} = 50.0g*4.184\frac{J}{g.K} * (298.00 - 296.36)K[/tex]

= 343.088J

2) Molar Mass of KClO₃ is [tex]122.55g mol^{-1}[/tex]

As a result, number of moles of KClO₃ present in 1g sample is,

[tex]\frac{1.00g}{122,55g/mol} = 0.0082mols[/tex]

Hence, the standard enthalpy change of the dissolving process is determined as follows:

Δ[tex]H^{o} = +\frac{343.088J}{0.0082mol} \\= +41840J . mol^{-1}[/tex]

The plus symbol (+) denotes the absorption of heat during the dissolving phase.

Learn more about enthalpy here:

https://brainly.com/question/13996238

#SPJ4

Complete Question:

When 1.00 g potassium chlorate (KCIO₃) is dissolved in 50.0 g water in a Styrofoam calorimeter of negligible heat capacity, the temperature decreases from 25.00°C to 23.36°C. Calculate q for the water and AH° for the process. KCIO: (s) → K* (aq) + CIO (aq) The specific heat of water is 4.184 J K-1 g¯!.

The discount rate that should be applied to a new project's cash flows is the Weighted Average Cost of Capital (WACC). To calculate WACC, you need to first calculate the cost of debt. This is done by taking the face value of the bonds ($1000) multiplied by the coupon rate (8%) multiplied by (1 - the tax rate (26%)), which equals 5.92%. The cost of debt is then calculated by taking the market value of the debt (6,380 x $1,000 x 99.1%) and dividing this by the total market value of the debt plus the market value of the equity (6,380 x $1,000 x 99.1% + 76,650 x $50 + 14,250 x $80), which equals 5.22%.

Next, you need to calculate the cost of equity using the Capital Asset Pricing Model (CAPM). This is done by taking the risk-free rate (3.21%) plus the market risk premium (9.79%) multiplied by the firm's beta (1.47), which equals 17.18%.

The WACC is then calculated by taking the cost of equity multiplied by the proportion of equity (76,650 x $50 + 14,250 x $80 divided by the total market value of the debt plus the market value of the equity) plus the cost of debt multiplied by the proportion of debt (6,380 x $1,000

Answer:

0 and 180 degrees.

Step-by-step explanation:

We can start by using a trigonometric identity to rewrite sin2x in terms of cos2x:

sin2x = 1 - cos2x

Substituting this into the given equation, we get:

cos2x = 1 + (1 - cos2x)

Simplifying this equation, we get:

2cos2x = 2

Dividing both sides by 2, we get:

cos2x = 1

Solving for x, we get:

2x = 0°, 360°x = 0°, 180°

Therefore, the solutions to the equation cos2x = 1 + sin2x in the interval 0° ≤ x ≤ 360° are x = 0° and x = 180°.

Please hit brainliest if this helped! If you have any questions, please comment below!

The probability of spinning a slice that is not yellow is equal to the total number of non-yellow slices divided by the total number of slices.

Total number of non-yellow slices = 9 (3 red + 5 blue)

Total number of slices = 12

Therefore, the probability of spinning a slice that is not yellow is 9/12 or 75%.

A parabola with a vertex at (1,3) and an opening downhill is depicted by the equation.

A parabola is an equation of a curve with a spot on it that is equally spaced from a fixed point and a fixed line.

In mathematics, a parabola is a roughly U-shaped, mirror-symmetrical plane circle. The same curves can be defined by a number of apparently unrelated mathematical descriptions, which all correspond to it. A point and a line can be used to depict a parabola.

Equation given: 3x² - 6x + 4y - 9 = 0. When the given equation's graph is plotted, it is discovered that the parabola that is created is opened downward and has a vertex at the spot. ( 1,3). The graph and the following response are attached.

The equation that depicts a parabola with a vertex at (1,3) opening downward is option C, making it the right choice.

To know more about parabola follow

brainly.com/question/4061870

#SPJ1

Answer:

Parabola with a vertex at (1, 3) opening downward.

Step-by-step explanation:

If we total up the dots plot for 3, 4, and 5 pets, we find that 3 people have 2 pets at home, 10 individuals have at least 3 pets at home.

The fact that dogs are the most common pet in the world shouldn't be shocking. There is a reason why there are tens of millions of dogs living in the United States alone, which is why some people say that dogs are a man's greatest friend. Around the world, at least one dog is kept in one-third of all households.

A fully domesticated animal kept constitutes a "household pet." a pet kept by you for personal company, like a dog, cat, reptile, bird, or mouse. Any kind of horse, cow, pig, sheep, goat, chicken, turkey, other captive fur-bearing animal is not considered a household pet, nor is any animal that is typically kept for food or profit.

To know more about dots plot visit:-

https://brainly.com/question/22068145

#SPJ1

The total number of people with pets at home is 11, which is the sum of the heights of the columns.

What is equation?

A math equation is a method that links two claims and represents equivalence using the equals sign (=). An equation is a mathematical statement that establishes the equivalence of two mathematical expressions in algebra.

Based on the given dot plot, we can answer the following questions:

How many people have 2 pets at home?

Answer: Two people have 2 pets at home, as indicated by the two dots in the second column.

How many people have at least 3 pets at home?

Answer: Six people have at least 3 pets at home, as indicated by the dots in the third column and beyond.

How many more people have 2 pets than 5 pets?

Answer: There are no dots in the last column, which represents 5 pets. Therefore, the difference between the number of people with 2 pets and those with 5 pets is 2 - 0 = 2.

How many people have less than 3 pets at home?

Answer: Three people have less than 3 pets at home, as indicated by the dots in the first two columns.

Therefore, the total number of people with pets at home is 11, which is the sum of the heights of the columns.

To know more about equation fro the given link:

brainly.com/question/649785

#SPJ1

The returned value would be 70 which is the missing value in the data set. Hence, option D is correct. We have some X values; we called these numeric inputs and some Y value that we are trying to predict.

This set of data would yield a result of 70 if a median imputer were run on it. In regression, we have some X values that are referred to as independent variables and some Y values that are referred to as dependent variables (this is the variable we are trying to predict). Several Y values are possible, but they are uncommon.

Learning a function that can predict Y given X is the fundamental concept behind a regression. Depending on the data, the function may be linear or non-linear.

To know more about data set, refer:

https://brainly.com/question/11284607

#SPJ4

Complete question is:

Imagine X in the below is a missing value. If I were to run a median imputer on this set of data. What would the returned value be? 50 , 60 , 70 , 80 , 100 , 60 , 5000 , x (It's okay to have to look up how to do this!)

50

An error

80

70

100

The basic idea of a regression is very simple. We have some X values, we called these ______ and some Y value (this is the variable we are trying to _______.

We could have multiple Y values, but that is not but that is not re-ordered ordinals intercepts features numeric inputs.

Thus, the rectangular fence has a 15-meter width.

We must determine the fence's length. The equation A=lw, where l seems to be the length & w is the width, determines the surface area A of a rectangle.

Let the variable "w" stand in for the rectangular fence's width.

We are aware that the fence's perimeter measures 54 metres in total.

Since a rectangle's opposite sides are identical in length and the fence contains four sides, we may write the following equation to get the perimeter:

(Length + Width)2 = the perimeter

Inputting the values provided yields:

54 = 2(12 + w)

After simplifying and finding "w," we arrive at:

54 = 24 + 2w

2w = 30

w = 15

Hence, the rectangular fence's width is 15 meters.

To know more about rectangular fence visit:

https://brainly.com/question/29258857

#SPJ1

Answer:

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

Find the prime factors of 1352:

We need another factor of 2 as a minimum added in order to have even number of same factors:

Hence we need to multiply the given number by 2.

Answer:

N and E is 90 degrees

N and S is 180 degrees

N and W is 90 degrees

The area of the enlarged logo will be 9 times larger than the original logo.

When an object is enlarged or scaled up how does it area change ?

When an object is enlarged or scaled up by a factor of [tex]k[/tex], both its length and width are multiplied by [tex]k[/tex]. Therefore, the new length is [tex]k[/tex] times the original length, and the new width is [tex]k[/tex] times the original width.

The area of the new object is the product of the new length and width, which is ([tex]k[/tex] times the original length) multiplied by ([tex]k[/tex] times the original width), or [tex]k^2[/tex] times the original area.

Therefore, the area of an object increases by a factor of [tex]k^2[/tex] when the object is enlarged or scaled up by a factor of [tex]k[/tex].

Calculating how many times larger the area of the enlarged logo will be :

The original logo has dimensions of 3 inches by 5 inches, so its area is 3 x 5 = 15 square inches.

Mr. James wants to enlarge the logo so that the dimensions are 3 times larger than the original. This means the new dimensions will be 9 inches by 15 inches.

To determine how many times larger the area of the enlarged logo will be, we need to compare the areas of the original logo and the enlarged logo. The area of the enlarged logo is 9 x 15 = 135 square inches.

To find out how many times larger the area of the enlarged logo is compared to the original logo, we divide the area of the enlarged logo by the area of the original logo:

135 square inches ÷ 15 square inches = 9

Therefore, the area of the enlarged logo will be 9 times larger than the area of the original logo.

To know more about area visit :

brainly.com/question/27683633

#SPJ1

Answer: The width of the rectangular window is 53 cm.

Step-by-step explanation:

We know that the area of a rectangle is given by the formula:

Area = Length x Width

Substituting the given values, we have:

3816 cm² = 72 cm x Width

To solve for the width, we can divide both sides by 72 cm:

Width = 3816 cm² ÷ 72 cm

Width = 53 cm

Therefore, the width of the rectangular window is 53 cm.

Rumiya's total earnings can be represented by the inequality: [tex]85000 + 0.1x > 100000[/tex] and she would need to make sales of at least $150,000 to earn over $100,000 for the year.

What do you mean by commission and inequality ?

A commission is a percentage of sales that a salesperson earns on top of their base salary. In this case, Rumiya earns a 10% commission on sales she makes for the year. An inequality is a statement that compares two values, indicating whether one is greater than, less than, or equal to the other. It is used to represent that Rumiya needs to make sales that exceed a certain amount in order to earn a desired amount.

Finding the minimum amount of sales :

Rumiya's total earnings for the year will be the sum of her base salary and commission on sales. We can represent this as an inequality:

[tex]85000 + 0.1x > 100000[/tex]

To solve for [tex]x[/tex], we first need to isolate the variable on one side of the inequality. We can do this by subtracting 85000 from both sides:

[tex]0.1x > 15000[/tex]

Next, we can solve for [tex]x[/tex] by dividing both sides by 0.1:

[tex]x > 150000[/tex]

Therefore, Rumiya would need to make sales of at least $150,000 to earn over $100,000 for the year. This means that her commission on these sales would be $15,000 (10% of $150,000).

To know more about sales visit :

brainly.com/question/29442509

#SPJ1