Select the correct answer.
What is the range of g(x) = 3|x-1| - 1
a) (-♾,1)
b) (-1,♾)
c) (1,♾)
d) (-♾,♾)

Sue's statement is incorrect. The decrease in length by 15% and width by 10% does not necessarily result in a 25% decrease in the perimeter of the rectangle.

When the length of the rectangle decreases by 15%, it becomes 60 cm - (15% of 60 cm) = 60 cm - 9 cm = 51 cm. Similarly, when the width decreases by 10%, it becomes 40 cm - (10% of 40 cm) = 40 cm - 4 cm = 36 cm.

The new perimeter of the rectangle can be calculated as 2 * (length + width) = 2 * (51 cm + 36 cm) = 2 * 87 cm = 174 cm.

Comparing this to the original perimeter of 2 * (60 cm + 40 cm) = 2 * 100 cm = 200 cm, we find that the new perimeter is 174 cm, which represents a decrease of (200 cm - 174 cm) / 200 cm ≈ 13%. Therefore, the actual decrease in the perimeter is approximately 13%, not 25% as Sue claimed.


To learn more about perimeter click here: brainly.com/question/7486523

#SPJ11

The surface area of the spherical balloon is 198 cm².

The circumference of a sphere is related to its radius by the formula:

C = 2πr

Given that the circumference of the balloon is 25 cm, we can solve for the radius:

25 = 2πr

Dividing both sides by 2π, we find:

r = 25 / (2π)

To calculate the surface area of a sphere, we use the formula:

A = \(4\pi r^2\)

Substituting the value of r we found:

A = \(4\pi (25 / (2\pi ))^2\)

Simplifying the equation, we get:

\(A = 4\pi (25^2) / (4\pi^2)\)

The π in the numerator and denominator cancels out, and the equation simplifies to:

A = 625 / π

Now, we can calculate the approximate surface area rounded to the nearest centimeter:

A ≈ 625 / 3.14

A ≈ \(198.0918 cm^2\)

Rounding to the nearest centimeter, the approximate surface area of the balloon is \(198 cm^2.\)

Therefore, the answer is C. \(198 cm^2.\)

Learn more about properties of spheres

brainly.com/question/16351667

#SPJ11

A proof competition is held annually by Contradiction Club, with special prizes awarded for first, second, third, and fourth place. If 16 students participate in the competition this year, the awards can be allocated among the students in 120 different ways.

To learn more about Contradiction Club refer to :

https://brainly.com/question/251701

#SPJ4

Answer:

(2, 7) is not an ordered pair for the function.

Step-by-step explanation:

A pair of equations best models the relationship between g and w are  g = w + 8, and g = w - 4 option second is correct.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as linear equation in one variable.

We have :

Variable g is 8 more than variable w, mathematically we can write it as:

g = w + 8  ....(1)

Also, variable g is also 4 less than variable w, mathematically we can write it as:

g = w - 4   ....(2)

The equation (1) and equation (2) are representing the system of linear equation in two variables.

So, we have framed two linear equation, that is:

g = w + 8  and

g = w - 4

Thus, a pair of equations best models the relationship between g and w are g = w + 8, and g = w - 4 option second is correct.

Learn more about the linear equation here:

brainly.com/question/11897796

Answer:

b

Step-by-step explanation:

Therefore, the straight horizontal line labeled f(x) represents where f(x) is equal to 4.

Based on the given information, the function f(x) is represented by the straight horizontal line that crosses the y-axis at (0, 4). The point (0, 4) on the y-axis indicates that when x is 0, the value of f(x) is 4. Since the line is horizontal, it maintains a constant value of 4 for all values of x.

To know more about straight horizontal line,

https://brainly.com/question/16816396

#SPJ11

The variance of a distribution of means of samples of more than one is A) smaller than the original population variance.

When considering the distribution of means of samples, the central limit theorem states that as the sample size increases, the sampling distribution approaches a normal distribution regardless of the shape of the population distribution. Additionally, the standard error of the mean decreases as the sample size increases.

The variance of a population is denoted by σ^2.

The variance of the distribution of sample means, also known as the sampling distribution, is denoted by σ^2/N, where N is the sample size.

As the sample size (N) increases, the denominator increases, leading to a smaller value for the variance of the distribution of sample means (σ^2/N). Thus, the variance of the distribution of means of samples is smaller than the original population variance.

The variance of a distribution of means of samples of more than one is smaller than the original population variance. This is due to the central limit theorem and the decrease in standard error as the sample size increases.

To know more about central limit theorem , visit

https://brainly.com/question/898534

#SPJ11

The required specific energy increases with increasing depth and the water surface profile will be rapidly varied.

To determine the type of water surface profile for different depths in the rectangular channel, we can use the concept of specific energy and Manning's equation.

The specific energy (E) is given by the equation:
E = y + (V² / (2g)) + (Sf * x)

Given values:
Width of the rectangular channel (b) = 2.45 m
Discharge (Q) = 2.83 m³/sec
Bed slope (Sf) = 0.003
Manning's roughness factor (n) = 0.015

For each depth, we can calculate the velocity (V) using Manning's equation and then determine the specific energy (E) using the equation mentioned above.

Depth 1 (y₁ = 1.52 m):

First, let's calculate the velocity (V₁) using Manning's equation:\(V_1 = (1/n) * (R_1^{2/3}) * (S_f^{(1/2)})\)

The hydraulic radius (R₁) can be calculated as:
R₁ = (b * y₁) / (b + 2y₁) = (2.45 * 1.52) / (2.45 + 2 * 1.52) ≈ 0.678 m

Substituting the values
\(V_1= (1/0.015) * (0.678 ^{2/3}) * (0.003^{1/2})\) ≈ 2.81 m/s

Now, let's calculate the specific energy (E₁) using the equation:
E₁ = y₁ + (V₁² / (2g)) + (Sf * x)

Substituting the values:
E₁ = 1.52 + (2.976² / (2 * 9.81)) + (0.003 * x)

The above expression shows, the specific energy increases with increasing depth, and the water surface profile will be rapidly varied.

Learn more about discharge here:
https://brainly.com/question/13105967
#SPJ4

Given question is incomplete, the complete question is:
2.45-m wide rectangular channel with a discharge of 2.83 m³/sec. has a bed slope of 0.003 and Manning's roughness factor of 0.015. What is the type of water surface profile for depths of 1.52 m, whether it is rapidly varied or not?

Answer:

68

Step-by-step explanation:

We can see that the nth term would be the sum of the previous two terms. Continuing this would result in 68.

Answer:

yessir

jimmy jhon

TROOOOOOOOOOOOOOOOOOOOOP

STARING NOW

Answer:

15.25

do 40.75-25.5 i think

Answer:

Ungrouped data

Step-by-step explanation:

The ungrouped data is the data where it has only individual data points that means it does not have a frequency distribution

So according to the given situation

Since it is mentioned that , 4, 10, 3, 3, 4, 7, 4, 6, 5, 11, 9, 5, 7 so this represent the ungrouped date

Answer: are you sure your equation is correct?

Step-by-step explanation:

Answer:

The formula for compound interest is: A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment (the amount Alex has at the end of 7 years)

P = the initial investment (£4000)

r = the annual interest rate (x/100)

n = the number of times interest is compounded per year (let's assume it is compounded annually)

t = the number of years invested (7)

Plugging in the given values and solving for x:

5263.73 = 4000(1 + x/100)^7

So x = ((5263.73/4000)^(1/7))-1*100

x = 6.33% (approximately)

So, the interest rate is 6.33%.

The rotation of the triangle ABC 360 degrees about the y-axis forms a cone

From the question, we understand that the triangle ABC is a right triangle

The vertical cross-section of a cone is a right triangle.

This means that a right triangle can be rotated 360 degrees on one of its legs (opposite or adjacent) to form a cone

Hence, the rotation of the triangle ABC forms a cone

Read more about rotation at:

https://brainly.com/question/13147596

Answer:

Area = 44x - x²/2

Step-by-step explanation:

Given that:

Meter of fencing = 88m

Length of side of rectangle along the river = x

Only one more length is needed since river as been used as one side length of the fence.

Length = x

Width of rectangle = y = 2y (for both sides)

Hence ;

x + 2y = 88 meters

Expressing in terms of y

2y = 88 - x

y = (88 - x) / 2

y = 44 - x/2

Area of rectangle = Length * width

Area = x * y

Area = x * (44 - x/2)

Area = 44x - x²/2

Maximum. Area :

Perimeter = 4s

88 = 4s

s = 88/4 = 22

x = 2(22) = 44 = Length ; y = 22 = width

Maximum area = (22 * 44) = 968m²

The probability that the chosen student eats fish or eggs is 12/26 = 0.4615 or approximately 46.15%

To answer your question, let's first organize the information given:

Total vegetarians: 26
Eat both fish and eggs: 9
Eat eggs but not fish: 3
Eat neither fish nor eggs: 7

We want to find the probability that the chosen vegetarian student eats fish or eggs. To do this, we need to find the total number of vegetarians who eat fish or eggs. Since 9 eat both fish and eggs, and 3 eat eggs but not fish, we can deduce that 9 + 3 = 12 vegetarians eat fish or eggs.

Now, to find the probability, we'll divide the number of vegetarians who eat fish or eggs (12) by the total number of vegetarians (26).

Probability = (Number of vegetarians who eat fish or eggs) / (Total number of vegetarians)
Probability = 12 / 26
Probability ≈ 0.4615

So, the probability that the chosen vegetarian student eats fish or eggs is approximately 0.4615 or 46.15%.

To learn more about probability, click here:

brainly.com/question/30034780

#SPJ11

The population mean, 9,009, 10,585 employees, and 9,009, 10,585 steps are the solution.

A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean," this is the most often used measure of central tendency.

The term "activity tracker" refers to gadgets, including watches and bands, that record your physical activity, such as walking, jogging, and skipping. They only count your steps and inform you of your daily objectives. They are quite useful for tracking blood pressure and other things.

The 95% confidence interval between 9,009 and 10,585 steps was used to estimate the mean number of steps taken by City employees.

The likelihood of the various values may be estimated using the confidence interval. It may be utilised to derive conclusions about the population mean.

To know more about mean visit:

https://brainly.com/question/30094057

#SPJ1

The solution to the equation 2 csc x = 3 csc θ − csc θ sin θ in the range 0 ≤ θ < 2π is:

θ = 7π/6

We can start by manipulating the given equation to express cscθ in terms of cscx:

2 csc x = 3 csc θ − csc θ sin θ

2/cscθ = 3 - sinθ

cscθ/2 = 1/(3 - sinθ)

cscθ = 2/(3 - sinθ)

Now we can use the identity sin²θ + cos²θ = 1 and substitute for cscθ in terms of sinθ:

1/cosθ = 2/(3 - sinθ)

cosθ = (3 - sinθ)/2

Next, we can use the identity sin²θ + cos²θ = 1 to solve for sinθ:

sin²θ + cos²θ = 1

sin²θ + [(3 - sinθ)/2]² = 1

Multiplying both sides by 4, we get:

4sin²θ + (3 - sinθ)² = 4

Expanding and simplifying, we get:

8sin²θ - 6sinθ - 8 = 0

Dividing both sides by 2, we get:

4sin²θ - 3sinθ - 4 = 0

Using the quadratic formula with a = 4, b = -3, and c = -4, we get:

sinθ = [3 ± √(3² - 4(4)(-4))]/(2(4))

sinθ = [3 ± √49]/8

sinθ = (3 ± 7)/8

Since 0 ≤ θ < 2π, we only need to consider the solution sinθ = (3 - 7)/8

= -1/2 corresponds to an angle of 7π/6 in the third quadrant.

To find cosθ, we can use the identity sin²θ + cos²θ = 1:

cosθ = ±√(1 - sin²θ)

Since we are in the third quadrant, we want the value of cosθ to be negative, so we take the negative square root:

cosθ = -√(1 - (-1/2)²)

cosθ = -√(3/4)

cosθ = -√3/2

For similar questions on range

https://brainly.com/question/30389189

#SPJ11

Therefore, the solution to Equation (5) is:

\(V_y(x, y, t) = ± √(m^2 - 5m/q^2) exp(±imV_B t + i sin(y))\)

To solve the given partial differential equations, we will start by solving Equation (4) and then use the solution to solve Equation (5). Let's go through the steps:

Step 1: Solve Equation (4):

We are given the equation:

∂^2V_x/∂t^2 = - (mV_B)^2V_x

To solve this equation, we assume a solution of the form V_x(x, y, t) = V_1 exp(±iω_c t + i sin(y))

Substituting this solution into Equation (4), we get:

\((-ω_c^2) V_1 exp(±iω_c t + i sin(y)) = - (mV_B)^2 V_1 exp(±iω_c t + i sin(y))\)

Dividing both sides by V_1 exp(±iω_c t + i sin(y)), we obtain:

\(-ω_c^2 = - (mV_B)^2\)

Simplifying, we get:

ω_c = ± mV_B

Therefore, the solution to Equation (4) is:

V_x(x, y, t) = V_1 exp(±imV_B t + i sin(y))

Step 2: Solve Equation (5):

We are given the equation:

\(∂^2V_y/∂t^2 = - (m/qz)^2 V_y - 5 V(x, y)\)

Using the solution from Step 1, we have:

V(x, y) = V_1 exp(±imV_B t + i sin(y))

Substituting this into Equation (5), we get:

\((-ω_c^2) V_1 exp(±imV_B t + i sin(y)) = - (m/qz)^2 V_y - 5 V_1 exp(±imV_B t + i sin(y))\)

Dividing both sides by V_1 exp(±imV_B t + i sin(y)), we obtain:

\(-ω_c^2 = - (m/qz)^2 - 5\)

Substituting ω_c = ± mV_B, we have:

\(-(mV_B)^2 = - (m/qz)^2 - 5\)

Simplifying, we get:

\((qz)^2 = m^2 - 5m/q^2\)

Taking the square root, we have:

\(qz = ± √(m^2 - 5m/q^2)\)

Therefore, the solution to Equation (5) is:

\(V_y(x, y, t) = ± √(m^2 - 5m/q^2) exp(±imV_B t + i sin(y))\)

Please note that the given solution in the photograph may have different notations or formatting, but the steps outlined above demonstrate the process to solve the equations and arrive at the solution in terms of V(x, y).

To know more about Equation refer here:

https://brainly.com/question/29657983

#SPJ11

Answer:

Step-by-step explanation:

sin(63°) = x/22

x = 22sin(63°) ≅ 19.6 units

Answer:

7.6

Step-by-step explanation:

m<DBA is 68 degrees

Answer:

21.9 feet

Step-by-step explanation:

The question is incomplete. Here is the complete question.

Vivian is at a fair in Coachella Valley, California. Much of the valley lies below sea level. Vivian has brought along an altimeter to measure her elevation at different places in the valley. Vivian’s first ride was on the Ferris wheel. When she sat on the wheel at its lowest point, her altimeter read -9.6 feet. When she reached the top of the wheel, her altimeter read 12.3 feet.

Is the change in Vivian's elevation from the bottom of the Ferris wheel to the top a positive number or a negative number? Why?

Given parameters

Altimeter of vivian at its lowest point = -9.6 feet

Altimeter of vivian at the top of the wheel = 12.3feet

Note that the sea level is at 0 feet.

change in Vivian's elevation from the bottom of the Ferris wheel to the top is expressed as:

= (12.3-0)+(0-(-9.6))

= 12.3+(0+9.6)

= 12.3+9.6

= 21.9 feet

From the gotten value, it can be seen that the change in Vivian's elevation from the bottom of the Ferris wheel to the top is a positive value.

The value is positive because vivian keeps moving to the top of the wheel (above the sea level). The values above the sea level is always positive.

Answer:Hide Sample Answer

The change in Vivian's elevation is a positive number because her elevation increased as she moved from the bottom of the Ferris wheel to the top.

Step-by-step explanation:Hide Sample Answer

The change in Vivian's elevation is a positive number because her elevation increased as she moved from the bottom of the Ferris wheel to the top.

Answer:

X= 15

Step-by-step explanation:

3x - 15 + 150 = 180

X = 15

The equation of the line would be y = (-3/4)x + 5.

What is the slope-point form of the line?

For the line having slope "m" and the point (x1, y1) the equation of the line passing through the point (x1, y1) having slope 'm' would be

                      y - y1 = m(x - x1)

The given equation is \(y=-\frac{3}{4}x-17\)

The required line is parallel to the given line.

and we know that the slopes of the parallel lines are equal so the slope of the required line would be m = -3/4

And the required line passes through (8, -1)

so by using slope - point form of the line,

      y - (-1) = (-3/4)(x - 8)

      y + 1 = (-3/4)x - (-3/4)8

       y + 1 = (-3/4)x + 24/4

       y = (-3/4)x + (12/2 - 1)

       y = (-3/4)x + 5

Hence, the equation of the line would be y = (-3/4)x + 5.

To learn more about slope - point form of the line, visit:

https://brainly.com/question/24907633

#SPJ1

Answer:

L=55 ft,  W=49 ft

Step-by-step explanation:

W=L-6

perimeter= 2L+2W

208=2(L-6)+2L

L=55

W=55-6

=49

First you will get 4dz

Answer: -84+48i

Step-by-step explanation: This was correct

The solution of the given expression will be 48i - 84.

The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

Given complex expression is (−9−6i)(4−8i). The solution of the expression will be:-

E = (−9−6i)(4−8i).

E = -9 ( 4 - 8i ) -6i ( 4 -8i )

E = -36 + 72i -24i + 48(-1)

E = 48i - 84

Therefore, the solution of the given expression will be 48i - 84.

To know more about an expression follow

https://brainly.com/question/7447962

#SPJ2

Net present value is a measure of profitability. The NPV of an investment is the net cash inflow received over the project's life, less the initial cash outflow, adjusted for the time value of money.

A higher NPV means the project is more lucrative. The profitability index measures the benefit-cost ratio of a project and is calculated by dividing the present value of future cash flows by the initial cash outflow. A profitability index greater than one indicates that the project will be profitable, whereas a profitability index less than one indicates that the project will not be profitable.

Calculation of Net Present Value (NPV) of Project AInitial Outlay = $454,000Net annual cash flows = $68,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project A = PV of net cash flows – Initial OutlayNPV of Project A = 68,000 × 7.63930 – 454,000NPV of Project A = $56,201.85Calculation of Profitability Index of Project AProfitability Index of Project A = Present value of future cash flows / Initial OutlayProfitability Index of Project A = 68,000 × 7.63930 / 454,000Profitability Index of Project A = 1.14

Calculation of Net Present Value (NPV) of Project BInitial Outlay = $300,000Net annual cash flows = $47,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project B = PV of net cash flows – Initial OutlayNPV of Project B = 47,000 × 6.10338 – 300,000NPV of Project B = $37,100.86Calculation of Profitability Index of Project BProfitability Index of Project B = Present value of future cash flows / Initial OutlayProfitability Index of Project B = 47,000 × 6.10338 / 300,000Profitability Index of Project B = 0.96

The NPV and profitability index calculations show that project A is the better investment since it has a higher NPV and profitability index than project B.

To know more about Net present value   visit

https://brainly.com/question/32720837

#SPJ11

If the speed of boat in still water iss 9 mph and takes 1.5 miles to go and come 4 miles uptream and downward then the current of the river is 9.24 mph.

Given that the speed in still water be 9 mph, time to travel 4 miles upstream and downward is 1.5 hours.

We are required to find the speed of current of the river.

let the speed of current be c mph.

Effective speed in downstream=9+c

Effective speed in upstream=9-c

Total time=1.5 hours.

Total distance=4 miles.

Time for upstream stream+ time for downward stream=1.5 hours

2/(9+c)+2/(9-c)=1.5

18-2c+18+2c=1.5(9+c)(9-c)

36=1.5(81-\(c^{2}\))

36=121.5-1.5\(c^{2}\)

1.5\(c^{2}\)=121.5-36

\(c^{2}\)=85.5

c=9.24 mph.

Hence the speed of the current of the river is 9.24 mph.

Learn more about speed at https://brainly.com/question/4931057

#SPJ4