What is the circumference of a circle with a radius of 94. 2 using 3. 14 for pi

The population in 2020 is given as follows:

255,323.

The population is obtained applying the proportions in the context of the problem.

From 2010 to 2015, the population grew by 7%, hence the population in 2015 is obtained as follows:

246000 x 1.07 = 263220.

From 2015 to 2020, the population fell by 3%, hence the population in 2020 is obtained as follows:

0.97 x 263220 = 255,323.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

The wave has:

Period = 3.5 seconds

Frequency = 1/3.5 = 0.29

Amplitude = 42 - 26 = 16 cm

We have,

Period:

The period of a wave refers to the time it takes for one complete cycle of the wave to occur.

T = 1 / f where f represents the frequency.

Frequency:

The frequency of a wave represents the number of complete cycles or oscillations of the wave that occur in a given time period.

f = 1 / T where T represents the period.

Amplitude:

The amplitude of a wave refers to the maximum displacement or distance from the equilibrium position of a particle in the wave.

Now,

The wave has:

Period = 3.5 seconds

Frequency = 1/3.5 = 0.29

Amplitude = 42 - 26 = 16 cm

Thus,

Period = 3.5 seconds

Frequency = 1/3.5 = 0.29

Amplitude = 42 - 26 = 16 cm

Learn more about Wave Graph here:

https://brainly.com/question/29142985

#SPJ1

The properties used in the given steps include the multiplication property of equality, addition property of equality, subtraction property of equality, and division property of equality.

The steps taken to solve the system of equations and the properties used are as follows:

1.Step 1: 2a + 7b = 0; 3a − 5b = 31

No specific property is used.

Step 2: 10a + 35b = 0; 21a − 35b = 217

Multiplication property of equality: Both sides of the equations are multiplied by 5 and 7 to eliminate coefficients and simplify the expressions.

Step 3: 31a = 217

Addition property of equality

Step 4: a = 7

Division property of equality as both sides are divided by 31 to solve for a.

2. Step 1: 2(7) + 7b = 0

Simplify: the expression is simplified by multiplying 2 and 7 to obtain 14.

Step 2: 14 + 7b = 0

Simplify

Step 3: 7b = −14

Simplify: the equation is simplified by subtracting 14 from both sides.

Step 4: b = −2

Division property of equality: both sides of the equation are divided by the coefficient of 'b' (7) to solve for 'b'.

Learn more about the multiplication property of equality at: https://brainly.com/question/24675477

#SPJ1

The given differential equation is dp/dt = 8√(pt), where p is a function of t. To solve this differential equation,

we need to separate the variables and integrate both sides.

dp/√(p) = 8√(t) dt

Integrating both sides, we get:

2√(p) = 8/3 t^(3/2) + C, where C is the constant of integration.

To find the value of the constant C, we use the initial condition p(1) = 7. Substituting t = 1 and p = 7, we get:

2√(7) = 8/3 (1)^(3/2) + C

Simplifying this equation, we get:

C = 2√(7) - 8/3

Therefore, the solution of the differential equation that satisfies the given initial condition is:

2√(p) = 8/3 t^(3/2) + 2√(7) - 8/3

Simplifying this equation, we get:

√(p) = 4/3 t^(3/4) + √(7) - 4/3

Squaring both sides, we get:

p = (16/9)t^(3/2) + (8/3)√(7)t^(3/4) + 7 - (16/3)√(7)t^(3/4) + (7/9)

Hence, the solution of the differential equation with the given initial condition is p = (16/9)t^(3/2) + (8/3)√(7)t^(3/4) - (16/3)√(7)t^(3/4) + (70/9).

Learn more about integrating here: brainly.com/question/31744185

#SPJ11

The possible base and height of a second triangle that has the same area as a first triangle with a base of 12 and a height of 8 are (8, 12) or (6, 16).

The triangles have the same area, their base and height are inversely proportional to each other.

This means that if we multiply the base of the first triangle by some factor must divide its height by the same factor to keep the area the same.

Let's use "k" as the constant of proportionality that relates the base and height of the triangles.

Then, we can write:

base₁ × height₁ = base₂ × height₂

The subscripts 1 and 2 refer to the first and second triangles respectively.

The base and height of the first triangle so we can substitute those values:

12 × 8 = base₂ × height₂

Simplifying, we get:

96 = base₂ × height₂

Now, since the base and height are inversely proportional can choose any pair of values that multiply to 96.

The base of the second triangle is 8 then its height must be:

height₂ = 96 / base₂

= 96 / 8

= 12

Alternatively, if the base of the second triangle is 6, then its height must be:

height₂ = 96 / base₂

= 96 / 6

= 16

For similar questions on triangle

https://brainly.com/question/17335144
#SPJ11

The central angle is solved and wheel turns while the car travels 2 meters is 5.5556 radians, and while the car travels 5 meters, it is 13.8889 radians

Given data ,

To find the angle (in radians) that the wheel turns while the car travels a given distance, we can use the formula:

Angle (in radians) = Distance / Radius

a)

For a distance of 2 meters (200 cm):

Angle (in radians) = 200 cm / 36 cm

Angle (in radians) = 5.5556 radians

b)

For a distance of 5 meters:

Angle (in radians) = 500 cm / 36 cm

Angle (in radians) = 13.8889 radians

Hence , the angle (in radians) that the wheel turns while the car travels 2 meters is approximately 5.5556 radians, and while the car travels 5 meters, it is approximately 13.8889 radians

To learn more about central angle click :

https://brainly.com/question/11877137

#SPJ1

a) An unbiased estimator for λ is [tex]\hat{\lambda}=\frac{1}{n}\sum Y_i[/tex]

b) E(C) = 4λ - λ²

c) [tex]\hat{C}=4\hat{\lambda}-(\hat{\lambda})^2[/tex] is an unbiased estimator of E(C).

(a) To find an unbiased estimator for λ, we can use the sample mean. The sample mean is an unbiased estimator for the population mean of a Poisson distribution.

Therefore, an unbiased estimator for λ is:

[tex]\hat{\lambda}=\frac{1}{n}\sum Y_i[/tex]

where n is the sample size and [tex]\sum Y_i[/tex] is the sum of the observed breakdowns.

(b) The weekly cost of repairing the breakdowns is given by C = -3Y + Y². To find the expected value of C, we need to compute E(C).

E(C) = E(-3Y + Y²)

Using linearity of expectation, we can split this into two parts:

E(C) = E(-3Y) + E(Y²)

Since Y follows a Poisson distribution with mean λ, we know that E(Y) = λ.

E(C) = -3E(Y) + E(Y²)

The second term E(Y²) can be computed using the variance of Y.

Var(Y) = λ

E(Y²) = Var(Y) + (E(Y))²

= λ + λ²

= λ(1 + λ)

Substituting this back into E(C):

E(C) = -3E(Y) + E(Y²)

= -3λ + λ(1 + λ)

= λ + λ² - 3λ

= λ² - 2λ

E(C) = 4λ - λ²

Therefore, E(C) = 4λ - λ²

(c) To find an unbiased estimator of E(C), we need to find a function of Y₁, Y₂, ..., Yₙ that is an unbiased estimator of E(C). Let's call this estimator [tex]\hat{C}[/tex].

[tex]\hat{C}=4\hat{\lambda}-(\hat{\lambda})^2[/tex]

Since [tex]\hat{\lambda}[/tex] is an unbiased estimator of λ (as derived in part (a)), [tex]\hat{C}[/tex] is an unbiased estimator of E(C).

Therefore, [tex]\hat{C}=4\hat{\lambda}-(\hat{\lambda})^2[/tex] is an unbiased estimator of E(C).

Learn more about Unbiased estimator here

https://brainly.com/question/32063886

#SPJ4

The probability that the mean weight of a 24-bag case of potato chips is below 10 ounces is approximately 0.

Here,

Let X = weight of potato chips in medium size bag.

The random variable X follows a Normal distribution with mean, μ = 10.2 ounces and standard deviation, σ = 0.12 ounces.

A sample of n = 24 bags of chips is selected.

Compute the probability that the mean weight of these 24 bags is less than 10 ounces as follows:

P (X < 0) = 1 - P(Z < 8.16)

            ≈ 0

Thus, the probability that the mean weight of a 24-bag case of potato chips is below 10 ounces is approximately 0.

Read more on probability Brainly.com -

https://brainly.com/question/14973333

#SPJ1

complete question:

The weight of potato chips in a medium-size bag is stated to be 10 ounces the amount that the packaging machine puts in these bags is believed to have a normal model with mean 10.2 and standard deviation 0.12 ounces. What's the probability that the mean weight of a 24-bag case of potato chips is below 10 ounces?

This is because when there is no correlation, the variation in y cannot be explained by the variation in x, leaving a lot of room for error. the error variance for the linear model

a) If the correlation between x and y is 1, it means that the two variables have a perfect positive linear relationship. In this case, the error variance for the linear model would be 0. This is because when there is a perfect correlation, all the variation in y can be explained by the variation in x, leaving no room for error. Therefore, the error variance would be 0.

b) If the bet correlation ween x and y is 0, it means that the two variables have no linear relationship. In this case, the error variance for the linear model would be the sum of the variances of x and y. This is because when there is no correlation, the variation in y cannot be explained by the variation in x, leaving a lot of room for error. Therefore, the error variance would be the sum of the variances of x and y, which is 49+4=53.

a) If the correlation between x and y is 1, the value of the error variance for your linear model would be 0. This is because a correlation of 1 indicates a perfect positive linear relationship between x and y, meaning there is no error or deviation from the predicted values of y based on the linear model.

b) If the correlation between x and y is 0, the value of the error variance would be equal to the variance of y. This is because a correlation of 0 indicates that there is no linear relationship between x and y, meaning that the linear model provides no predictive value for y. In this case, the error variance is equal to the variance of y, which can be calculated by squaring the standard deviation of y (2^2 = 4).

learn more about  correlation here : https://brainly.com/question/22085260

#SPJ11

The range of y when x belongs to the set of real numbers is

y ≥ -4

To find the range of y when x belongs to the set of real numbers, we can consider the shape of the graph of the function

y = x² - 2x - 3.

Plotting the graph shows that the graphs opens upward and the parabola opens upward and the range of y is all real numbers greater than or equal to the y coordinate of the minimum point.

In this case, the range is y ≥ -4.

Learn more about parabola at

https://brainly.com/question/29635857

#SPJ1

The set of parametric equations for the line y = 3x - 2, with t = 0 at the point (2,4), is x = t + 2, y = 3t + 4.

We can use the point-slope form of a line to find the parametric equations:

y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope of the line.

The slope of the line y = 3x - 2 is 3, so we have:

y - 4 = 3(x - 2)

Simplifying, we get:

y = 3x - 2

We can rewrite this as a set of parametric equations:

x = t + 2

y = 3t + 4

So the set of parametric equations for the line y = 3x - 2, with t = 0 at the point (2,4), is:

x = t + 2, y = 3t + 4.

Learn more about parametric equations here

https://brainly.com/question/30451972

#SPJ11

The median would be a better measure of central tendency than the mean in representing the number of accidents an average person in this survey had over a 10-year period

In statistics, the mean and median are measures of central tendency used to describe a set of data. The mean is the average of a set of numbers, while the median is the middle value when a set of numbers is arranged in order. In this essay,

To determine which measure, the mean or median, better represents the number of accidents an average person in a survey had over a 10-year period, we need to understand the difference between these two measures of central tendency.

The mean is calculated by adding up all the numbers in a set and dividing by the total number of values in the set. It is a useful measure when the data is normally distributed and there are no extreme values that could skew the result. However, when there are extreme values or outliers, the mean can be significantly affected.

The median is the middle value of a set of numbers arranged in order. It is not affected by extreme values, making it a more robust measure of central tendency than the mean. However, it is not always an accurate representation of the data, especially when the data is skewed.

In the context of a survey about the number of accidents people had over a 10-year period, it is possible that some people may have had many accidents while others may have had none. This suggests that the data may be skewed, with some extreme values.

In such a scenario, the median would be a better measure of central tendency than the mean because it is not affected by extreme values. The median would represent the number of accidents that the person in the middle of the group had, which would be a more accurate representation of the typical experience of a person in the survey.

To know more about Mean, Median here

https://brainly.com/question/30891252

#SPJ4

The graphical representation that would be best to display the data is given as follows:

Histogram.

An histogram is a graph that shows the number of times each element of x was observed.

The four types of products are given as follows:

Each of these item would represent a bin, and the values of each bin are given as follows:

More can be learned about histograms at brainly.com/question/25983327

The distance from the Earth to the Sun is approximately 412 million km.

To find the distance from the Earth to the Sun and calculate the remaining information, we can utilize basic trigonometry principles and the given distances.

Let's denote the distance from the Earth to the Sun as "x" (unknown), the distance from the Sun to the Moon as "y" (150 million km), and the distance from the Moon to the Earth as "z" (384 million km).

To determine the missing side lengths and angle measures, we can use the concept of right-angled triangles.

First, let's consider the triangle formed by the Moon, Earth, and Sun. The side lengths and angle measures are as follows:

Side lengths:

Moon to Earth (z) = 384 million km

Earth to Sun (x) = unknown (to be determined)

Sun to Moon (y) = 150 million km

Angle measures:

Angle at Moon (θ1) = 90 degrees (perpendicular angle)

Angle at Earth (θ2) = unknown (to be determined)

Angle at Sun (θ3) = 90 degrees (perpendicular angle)

Next, let's examine the triangle formed by the Earth, Sun, and Moon. The side lengths and angle measures in this triangle are:

Side lengths:

Earth to Moon (z) = 384 million km

Moon to Sun (y) = 150 million km

Sun to Earth (x) = unknown (to be determined)

Angle measures:

Angle at Earth (θ4) = 90 degrees (perpendicular angle)

Angle at Sun (θ5) = unknown (to be determined)

Angle at Moon (θ6) = 90 degrees (perpendicular angle)

To find the distance from the Earth to the Sun (x), we can use the Pythagorean theorem on the triangle involving the Moon, Earth, and Sun:

[tex]x^2 = z^2 + y^2[/tex]

[tex]x^2[/tex] [tex]= (384 million km)^2 + (150 million km)^2[/tex]

[tex]x^2[/tex] [tex]= 147,456,000,000,000 km^2 + 22,500,000,000,000 km^2[/tex]

[tex]x^2[/tex] [tex]= 169,956,000,000,000 km^2[/tex]

Taking the square root of both sides:

x ≈  [tex]\sqrt(169,956,000,000,000 km^2)[/tex]

x ≈ 412 million km (approximately)

Therefore, the distance from the Earth to the Sun is approximately 412 million km.

For the trigonometric functions, we can calculate them for the angles θ2 and θ5.

Trig functions for the angle from Moon, Earth, Sun (θ2):

sin(θ2) = Opposite/Hypotenuse = z/y = 384 million km / 150 million km

cos(θ2) = Adjacent/Hypotenuse = x/y = 412 million km / 150 million km

tan(θ2) = Opposite/Adjacent = z/x = 384 million km / 412 million km

csc(θ2) = 1/sin(θ2)

sec(θ2) = 1/cos(θ2)

cot(θ2) = 1/tan(θ2)

Trig functions for the angle from Earth, Sun, Moon (θ5):

sin(θ5) = Opposite/Hypotenuse = y/x = 150 million km / 412 million km

cos(θ5) = Adjacent/Hypotenuse = z/x = 384 million km / 412 million km

tan(θ5) = Opposite/Adjacent = y/z = 150 million km / 384 million km

csc(θ5) = 1/sin(θ5)

sec(θ5) = 1/cos(θ5)

cot(θ5) = 1/tan(θ5)

Please note that the trigonometric functions can be calculated using a calculator or software capable of performing trigonometric calculations.

For more such questions on  distance

https://brainly.com/question/30395212

#SPJ8

Answer:

c

Step-by-step explanation:

y=x-10 is the equation of the line.

We can use the point-slope form of a linear equation to find the equation of the line that passes through two given points.

First, we need to find the slope of the line:

slope = (change in y) / (change in x) = (0 - (-8)) / (-6 - 2) = 8 / 8 = 1

Now we can use one of the given points, say (2, -8), and the slope, m = 1, to write the equation of the line in the point-slope form:

y - y1 = m(x - x1)

y - (-8) = 1(x - 2)

y + 8 = x - 2

y = x - 10

Therefore, an equation of the line that passes through the points (2, -8) and (-6, 0) is y = x - 10.

Learn more about Linear equations here:

https://brainly.com/question/11897796

#SPJ1

All the correct statements are,

⇒ the absolute value a number is from 0 on a number line

⇒ The additive inverse of a number

⇒ Horizontal left and right

⇒ An integer number or its opposite

⇒ Straight vertical and down

⇒ A set of two opposite numbers that equal zero when combined.

We have to given that;

To fill the blanks in all the statement.

Hence, We get;

We know that;

⇒ The absolute value a number is from 0 on a number line

⇒ The additive inverse of a number

⇒ Horizontal left and right

⇒ An integer number or its opposite

⇒ Straight vertical and down

⇒ A set of two opposite numbers that equal zero when combined.

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ1

The value of the measure of Arc CDE is,

⇒ Arc CDE = 128 degree

Since, An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Here, A circle is shown in figure.

And, By circle we have;

The measure of Arc CDE is,

⇒ Arc CDE = 128 degree

Thus, The value of the measure of Arc CDE is,

⇒ Arc CDE = 128 degree

Learn more about the angle visit:;

https://brainly.com/question/25716982

#SPJ1

The 80s series of nasal consonants, including /m/, /n/, and /ŋ/, is the best option for testing for hyponasality. These consonants require adequate nasal resonance for accurate articulation, making them effective for identifying individuals with this speech disorder. Option D is correct.

Hyponasality is a speech disorder characterized by reduced nasal resonance during speech production. To test for hyponasality, a series of nasal consonants can be used, as they require appropriate nasal resonance for accurate articulation.

Among the options given, the best series of numbers to use when testing for hyponasality is the 80s. This series includes nasal consonants that are commonly used in the English language, and their production requires adequate nasal resonance. The nasal consonants in the 80s series include /m/, /n/, and /ŋ/, which are produced with varying degrees of nasal airflow.

/m/ is a bilabial nasal consonant, which requires the closure of the lips and the lowering of the velum to allow air to flow through the nasal cavity. /n/ is an alveolar nasal consonant, which requires the tongue to contact the alveolar ridge while the velum is lowered. /ŋ/ is a velar nasal consonant, which requires the back of the tongue to contact the soft palate while the velum is lowered.

Using the 80s series of numbers to test for hyponasality can help identify individuals who have difficulty producing nasal consonants correctly due to reduced nasal resonance. This information can be used to develop appropriate speech therapy interventions to help improve nasal resonance and overall speech production.

To learn more about hyponasality

https://brainly.com/question/31662331

#SPJ4

Complete question:

What is the recommended series of numbers to use for testing hyponasality?

a) 50s,

b) 60s,

c) 70s,

d) 80s,

e) 90s

Yes, this equation M=45−7. 5d is useful to calculate the number of miles left after each day.

On the 6th day they cover 45 miles.

Plan to cover distance by hiking club to hike = 45 mile

Per day hiking = 7.5 miles

The equation M = 45 - 7.5d represents the number of miles remaining to hike after each day of hiking,

where M is the number of miles remaining and d is the number of days of hiking.

Let us use this equation to calculate the number of miles remaining after each day of hiking.

For Day 1,

d = 1

M = 45 - 7.5(1)

    = 45 - 7.5

    = 37.5 miles remaining

For Day 2,

d = 2

M = 45 - 7.5(2)

   = 45 - 15

   = 30 miles remaining

For Day 3,

d = 3

M = 45 - 7.5(3)

   = 45 - 22.5

   = 22.5 miles remaining

And so on...

For Day 4,

d = 4

M = 45 - 7.5(4)

   = 45 - 30

   = 15 miles remaining

For Day 5,

d = 5

M = 45 - 7.5(5)

   = 45 - 37.5

   = 7.5 miles remaining

For Day 6,

d = 6

M = 45 - 7.5(6)

   = 45 - 45

   = 0 miles remaining

By continuing the pattern it is easy to calculate the number of miles remaining .

After each day of hiking until the remaining miles reach 0, indicating the completion of the 45-mile hike.

Therefore, this equation help us to calculate the number of miles remaining.

learn more about miles here

brainly.com/question/32055562

#SPJ4

The area of the shaded region is 113.04 square yards in the ring

The formula to calculate the area of a circle is:

Area = π × (radius²)

For the outer circle:

Area of outer circle = π × (10 yd)² = π100 yd²

For the inner circle:

Area of inner circle = π × (8 yd)^2 = π × 64 yd²

To find the area of the shaded region

we subtract the area of the inner circle from the area of the outer circle:

Area of shaded region = Area of outer circle - Area of inner circle

Area of shaded region = π × 100 yd² - π ×64 yd²

Area of shaded region = π × (100 yd²- 64 yd²

Area of shaded region = π × 36 yd²

Area of shaded region = 3.14 × 36 yd²

Area of shaded region = 113.04 yd^2

Therefore, the area of the shaded region is 113.04 square yards.

To learn more on Circles click:

https://brainly.com/question/11833983

#SPJ1

The correct option is option 5: monetary policy affects interest rates but no change in investment spending results when the LM-curve is vertical.

The LM curve represents the relationship between the interest rate and the level of income or output in an economy, assuming a fixed money supply. When the LM curve is vertical, it means that the central bank has fixed the money supply and is targeting a specific interest rate. In this case, changes in income or output do not affect the interest rate.

Option 1 is incorrect because the monetary policy multiplier can still be nonzero even when the LM curve is vertical. The multiplier refers to the effect of changes in monetary policy on income or output, and it depends on other factors such as the slope of the aggregate demand curve.

Option 2 is incorrect because when the LM curve is vertical, fiscal policy does not have a maximum effect on income. Fiscal policy refers to the use of government spending and taxation to influence the level of economic activity. In this case, changes in fiscal policy would not have a significant impact on income because the interest rate is fixed.

Option 3 is incorrect because when the LM curve is vertical, monetary policy has no effect on income. Fiscal policy would also have limited effectiveness since changes in government spending or taxation would not have a significant impact on interest rates.

Option 4 is incorrect because fiscal policy's impact on interest rates can still affect investment even when the LM curve is vertical. When fiscal policy influences interest rates, it can affect the cost of borrowing and, consequently, investment decisions.

To know more about LM-curve,

https://brainly.com/question/22683083

#SPJ11

The area of the hub cap, with a circumference of 78.00 centimeters, is approximately 483.62 square centimeters.

To find the area of the hub cap, we need to know the radius of the hub cap. We can use the formula for the circumference of a circle to find the radius, and then use the formula for the area of a circle to calculate the area.

The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius. In this case, the circumference is given as 78.00 centimeters. Plugging in the values, we have:

78.00 = 2πr

To find the radius, we can solve for r:

r = 78.00 / (2π) ≈ 12.42 centimeters

Now that we have the radius, we can find the area using the formula A = πr^2:

A = π(12.42)^2 ≈ 483.62 square centimeters

Therefore, the area of the hub cap is approximately 483.62 square centimeters.

If the circumference of the hub cap were smaller, it would mean the radius would be smaller as well. As the radius decreases, the area of the hub cap would also decrease.

This is because the area of a circle is directly proportional to the square of its radius. So, a smaller circumference would result in a smaller area.

For more such question on circumference. visit :

https://brainly.com/question/27447563

#SPJ8

Thus,  the rate per period (i) is 0.02675 or 2.675%, and the number of periods (n) is 40.

For this problem, we can use the formula for the present value of annuity:
PV = PMT * ((1 - (1 + i)^(-n)) / i)

Where PV is the present value of the loan, PMT is the quarterly payment, i is the rate per quarter, and n is the total number of quarters.

We know that the quarterly payment is $1000 and the annual rate is 10.7%, compounded quarterly. To find the quarterly rate, we need to divide the annual rate by 4 (since there are 4 quarters in a year):
i = 10.7% / 4 = 0.02675

Next, we need to find the total number of quarters, which is 10 years * 4 quarters per year = 40 quarters:
n = 40

Now we can solve for the present value of the loan:
PV = $1000 * ((1 - (1 + 0.02675)^(-40)) / 0.02675) = $70,401.41

So the rate per period (i) is 0.02675 or 2.675%, and the number of periods (n) is 40.

Know more about the  present value of annuity

https://brainly.com/question/25792915

#SPJ11

Answer:

Step-by-step explanation:

The points on a circle can be determines by the equation of a circle

The point (-11,2) is not on the circle

How to determine the position of the point

The equation of a circle is represented as:

Where:

Center = (a,b)

Radius = r

The radius of the circle is 5, and the center is (-7,4).

So, we have:

The point is given as:

(x,y) = (-11,2)

So, we have:

Evaluate the exponents

Evaluate the sum

The above equation is not true.

Hence, the point (-11,2) is not on the circle

Read more about circle equations at:

brainly.com/question/1559324

a) The scale factor from shape A to shape B is given as follows: 4/5.

b) The value of t is given as follows: t = 5.6.

Similar triangles are triangles that share these two features listed as follows:

The concepts relating to similar shapes shape can be extended to any, hence the proportional relationship is given as follows:

5/4 = 7/t = 15/12.

Hence the value of t is obtained as follows:

5/4 = 7/t

5t = 28

t = 28/5

t = 5.6.

More can be learned about similar triangles at brainly.com/question/14285697

#SPJ1

After analysing the given data we conclude that the height of the streetlight is 29.4 feet, under the condition that a six-foot man places a 15 foot shadow. At the same time a streetlight casts an 80-foot shadow.

Now Let us consider the height of the streetlight "h".
The given angle of elevation is 52.5 degrees. This projects that the angle between the horizontal line and the line of sight to the top of the streetlight is 52.5 degrees.
We can apply the tangent function to evaluate h. tan(52.5) = h/20.
Evaluating  for h, we get h = 20 × tan(52.5) = 29.4 feet (rounded to one decimal place).
Therefore, the height of the streetlight is approximately 29.4 feet.
To learn more about tangent function
https://brainly.com/question/30162652
#SPJ1
The complete question is
A six-foot man casts a 15 foot shadow. At the same time a streetlight casts an 80-foot shadow.
The same six-foot tall man wants to indirectly measure the streetlight in screen 3. But it is a cloudy day and there are no shadows. So holding his phone by his eye, he uses the "level" feature on the Measure app to sight the top of the streetlight. Standing 20 feet away he finds an angle of elevation of 52.5 degrees.
Write and solve an equation to determine the height of the streetlight.

The relative rate of change f′(t)/f(t) at t=1 can be found by first calculating the derivative of the function f(t) and evaluating it at t=1.

f(t) = ln(t^2 - 1)

f'(t) = 2t / (t^2 - 1)

f'(1) = 2 / (1^2 - 1) = 1

Next, we can evaluate f(1) and use the formula for relative rate of change:

f(1) = ln(1^2 - 1) = ln(0) = undefined

Therefore, the relative rate of change f′(1)/f(1) cannot be calculated.

The function f(t) is undefined at t=1 because ln(0) is undefined. This means that we cannot calculate the value of f(1) and hence, cannot determine the relative rate of change f′(1)/f(1).

This is an example of a situation where the relative rate of change cannot be determined due to the function being undefined or having a singularity at the point of interest.

It is important to be aware of such situations when dealing with calculus and to check for any potential issues with the function or point of interest before attempting to calculate the relative rate of change.

To know more about derivative click here

brainly.com/question/29096174

#SPJ11

Without additional information about the distribution of costs, it is impossible to determine the probability that the cost will be less than $240.

To calculate a probability, we need to know the distribution of the data. For example, if the costs followed a normal distribution with a mean of $200 and a standard deviation of $20, we could use a standard normal table or a calculator to find the probability that a randomly selected cost is less than $240.

However, if we do not have information about the distribution of the costs, we cannot calculate a precise probability. In this case, we could make some assumptions about the distribution based on past data or expert opinion and use those assumptions to estimate the probability.

For example, if we know that costs tend to be positively skewed, we might assume that the distribution is lognormal and use that assumption to estimate the probability. Alternatively, we could use a non-parametric method like bootstrapping to estimate the probability based on a sample of observed costs.

Ultimately, the accuracy of any estimate will depend on the quality of the assumptions and the amount of data available.

Learn more about information here: brainly.com/question/30350623

#SPJ11