18. Express the first amount as a percentage of second.
a) 600 m of 3 km

………………………………….
b) In a local election there were 8000 registered voters.
Of these 3200 voted.
What was the percentage that voted?
………………………………….

Answer:

The slope of f(x) will be positive

Step-by-step explanation:

the slope of f(x) will be positive sign the coefficient in front of the x, 2, is positive.

The function g(x)  whose graph is the horizontal shrink of the given graph of  f(x) =5x-6 by a factor (horizontal shrink factor) of 1/4 is  g(x)=5/4 x-6.

As per the question statement, we are supposed to find a function g(x) whose graph is a horizontal shrink of the given graph of f(x) =5x-6 by a factor of 1/4.

Before solving it lets assume f(x)=y

so y =5x-6

Comparing with y= mx+c  where m is the slope

so in y =5x-6  slope is m=5

For applying horizontal shrink by a factor of 1/4 we need to multiply the slope by a factor of 1/4

so new slope \(m_{1} =5*\frac{1}{4} =\frac{5}{4}\)

Therefore \(g(x) = \frac{5}{4} x -6\)

Therefore the function \(g(x)\) whose graph is a horizontal shrink of the given graph of  \(f(x) = 5x-6\)  by a horizontal shrink factor of  1/4  is \(g(x) = \frac{5}{4} x -6\)

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It takes Hiroshi 30 years to reach his investment goal.

The formula for calculating the amount received on the principal amount (P) after t years at r% rate of interest is-

Amount = P(1 + r/100)^t

Let the principle amount with Hiroshi be P

then, the amount that Giulio starts with = 3P

Let time period for Giulio's investment = t

Then, the time period for Hiroshi's investment = 5t

Rate = 5%

As the investment goals of both the people are equal, they will get the same amount.

Therefore, we get the following equation-

P(1 + 20/100)^5t/4 = 3P(1 + 20/100)^t/4

(1 + 20/100)^5t/4 = 3(1 + 20/100)^t/4

[(1 + 20/100)^5t/4] /[(1 + 20/100)^t/4] = 3

(1 + 20/100)^(5t/4- t/4) = 3

(1 + 20/100)^(4t/4) = 3

(1 +0.2)^t = 3

(1.2)^t = 3

Taking log on both sides-

Log (1.2)^t = log 3

t log 1.2 = log 3

t = log 3/ log 1.2

t = 6.025

Time taken by Hiroshi to reach his investment goal = 5t

= 5(6.025)

= 30.128

Thus, it takes Hiroshi 30 years to reach his investment goal.

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In a simple linear regression model, the coefficient of the independent variable (x) in the estimated sample regression equation indicates the change in the predicted value of the dependent variable (y) when x increases by one unit. This coefficient is also known as the slope of the regression line. Therefore, to calculate the predicted value of y, we multiply the coefficient by the value of x and add the intercept.

In a simple linear regression model, the coefficient that indicates the change in the predicted value of y when x increases by one unit is the "slope coefficient" or the "regression coefficient" (usually denoted as b1). This coefficient represents the relationship between the independent variable x and the dependent variable y.

The linear regression equation is given as:

y = b0 + b1 * x

Where:
- y is the predicted value of the dependent variable
- b0 is the intercept coefficient (where the line intersects the y-axis)
- b1 is the slope coefficient (the change in y when x increases by one unit)
- x is the independent variable

In this equation, b1 indicates the change in the predicted value of y when x increases by one unit.

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The probability that at most three grafts fail is 0.98 and the probability that at least two grafts fail is 0.1.

To find the probability that at most three grafts fail, we need to find the sum of the probabilities for x = 0, 1, 2, and 3.

Using the given values of f(x), we get:

P(X <= 3) = f(0) + f(1) + f(2) + f(3)

= 0.7 + 0.2 + 0.05 + 0.03

= 0.98

So the probability that at most three grafts fail is 0.98.

To find the probability that at least two grafts fail, we need to find the sum of the probabilities for x = 2, 3, and 4 and subtract it from 1.

Using the given values of f(x), we get:

P(X >= 2) = 1 - (f(0) + f(1)) = 1 - (0.7 + 0.2) = 0.1

So the probability that at least two grafts fail is 0.1

--The question is incomplete, answering to the question below--

"Grafting the uniting of the stem of one plant with the stem or root of another; is widely used commercially to grow the stem of one variety that produces fine fruit on the root system of another variety with hardy root system: Most Florida sweet oranges grow on trees grafted to the root of sour orange variety. The density for X, the number of 'grafts that fail in series of five trials.

For the values of x = 0, 1, 2, 3, and 4 value of f(x) is 0.7, 0.2, 0.05, 0.03, and 0.01 respectively.

Use f(x) to find the probability that at most three grafts fail; that at least two grafts fail."

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So the right answer is 1.8

Look at the attached picture

Hope it will help you

Good luck on your assignment

Answer: I’m sorry I can’t figure out what A B and C are but ax=(2,0) and by=(0,4) I believe

Step-by-step explanation:

X intercept (2,0). Y intercept (0,4)

Answer:

2:3

Step-by-step explanation:

16/24=1/3

Hope this helps you!!!!!!!! :D

In this case, since we have four different time slots for employees, we can use a discrete probability distribution known as the categorical distribution.

To determine the probability distribution for employee break time slots, we need to consider the nature of data and the characteristics of the distribution.

The categorical distribution, also known as the multinoulli or the discrete distribution, is suitable when the outcome can take on one of several distinct categories or states, each with its own probability. In this scenario, the four different time slots can be considered as categories or states, and the probability distribution will provide the likelihood of an employee falling into each specific time slot.

To collect the necessary data, we would need information about the actual break time slots of the employees. We could observe and record the break times for a sample of employees over a specific period. This data collection process would involve noting which time slot each employee chooses for their break. By accumulating this data, we can determine the frequency or proportion of employees choosing each time slot.

Based on this collected data, we can construct the probability distribution for the employee break time slots. The distribution will assign probabilities to each category or time slot, reflecting the likelihood of an employee selecting that particular slot for their break. This information can be useful for various purposes, such as scheduling optimization or resource allocation within the organization.

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Answer:

Velocity in still air is = 960 miles per hour  

Velocity of wind  = 230 miles per hour.

Step-by-step explanation:

The velocity when flying against the wind = 2920 / 4 = 730 miles per hour.

The velocity when flying with the wind = 7140 / 6 = 1190

Let the rate of jet in still Air = x

Let the rate of jet in wind = y

Therefore, velocity against wind = x-y and wind = x + y

x - y = 730

x + y = 1190

Add both equation, 2x = 1920

x = 960

Now find the value of “y” = 1190 – 960 = 230

Thus, velocity in still air is = 960 miles per hour  

Velocity of wind  = 230 miles per hour.

Answer:

Rate of jet in still air = 960 miles/ hr

Rate of the wind = 230 miles/ hr

Step-by-step explanation:

Let the speed of jet in still air = \(u\) miles/hr

Let the speed of air = \(v\) miles/hr

So, against the wind, the resultant speed = \((u-v)\) miles/hr

And, with the wind, the resultant speed = \((u+v)\) miles/hr

Distance traveled against the wind = 2920 miles

Time taken against the wind = 4 hrs

Formula for distance is:

\(\bold{Distance =Speed \times Time}\)

\(2920 = (u-v)\times 4\\\Rightarrow u-v=\dfrac{2920}{4}\\\Rightarrow u-v=730\ miles/hr...... (1)\)

Distance traveled with the wind = 7140 miles

Time taken against the wind = 6 hrs

\(\bold{Distance =Speed \times Time}\)

\(7140 = (u+v)\times 6\\\Rightarrow u+v=\dfrac{7140}{6}\\\Rightarrow u+v= 1190 \ miles/hr...... (2)\)

Adding (1) and (2):

\(2u = 1920\\\Rightarrow \bold{u = 960 miles/hr}\)

Putting \(u\) in (1):

\(960 -v = 730 \\\Rightarrow \bold{v=230\ miles/hr}\)

Therefore, the answer is:

Rate of jet in still air = 960 miles/ hr

Rate of the wind = 230 miles/ hr

The substance's cooling rate when the surrounding air temperature is 50°C is approximately 0.0383 per hour, rounded to four decimal places.

To find the substance's cooling rate when the surrounding air temperature is 50°C, you can use the formula from Newton's Law of Cooling:

ΔT = T₀ - (T₀ - T_s) * e^(-k * t)

where ΔT is the temperature difference after time t, T₀ is the initial temperature, T_s is the surrounding temperature, k is the constant, and t is the time. We want to find k.

First, we know the following values:

- T₀ = 80°C (initial temperature)

- ΔT = 60°C (cooled temperature)

- T_s = 50°C (surrounding temperature)

- t = 25 minutes = 25/60 hours

Next, we'll rearrange the formula to solve for k:

k = -ln((ΔT - T_s) / (T₀ - T_s)) / t

Now plug in the known values:

k = -ln((60 - 50) / (80 - 50)) / (25/60)

Calculate the result:

k ≈ 0.0383

So, the substance's cooling rate when the surrounding air temperature is 50°C is approximately 0.0383 per hour, rounded to four decimal places.

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The length of a taut belt around the two pulleys is 79.3 cm.

The length of a taut belt around the two pulleys is calculated as follows;

Shapes formed within the two circles of the pulley.

From top to bottom, a rectangle, a right triangle and a trapezium.

The height of the right triangle is equal to length of the rectangle

base of the right triangle = radius of big circle - radius of small circle

base of the right triangle = (0.5 x 12 cm) - (0.5 x 6 cm) = 3 cm

tan α = height/base

tan (72.54)  = h/3

h = 3 tan(72.54)

h = 9.54 cm

The length of the trapezium at bottom is equal to length of rectangle at top, L = h = 9.54 cm

Portion of belt in contact with circumference of small circle is subtended by an angle = 2 × 72.54 = 145.08°

Length of belt in contact with circumference of smaller circle

= 2πr (θ/360)

= (2 x 6 cm)π x (145.08/360)

= 15.19 cm

Portion of belt in contact with circumference of big circle is subtended by an angle = 360 - 145.08° = 214.92⁰

Length of belt in contact with circumference of smaller circle

= 2πr (θ/360)

= (2 x 12 cm)π x (214.92 / 360)

= 45.01 cm

= 9.54 cm + 9.54 cm + 15.19 cm + 45.01 cm

= 79.28 cm

= 79.3 cm

Thus, the length of a taut belt around the two pulleys is 79.3 cm.

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The number of cups of lemonade Beatrice made in total is 18 4/15. The correct option is C. 18 4/15

From the question, we are to determine the number of cups of lemonade Beatrice made in total

From the given information,

Beatrice made 7 2/3 cups of lemonade

Later, she made 10 3/5 more cups of lemonade

To find the total number of cups of lemonade she made, we will add the two quantities together

That is,

7 2/3 + 10 3/5

7 2/3 + 10 3/5 = (7 + 10) + 2/3 + 3/5

= (17) + (10 + 9)/15

= 17 + 19/15

= 17 + 1 + 4/15

= 18 + 4/15

= 18 4/15

Hence, the number of cups of lemonade Beatrice made in total is 18 4/15. The correct option is C. 18 4/15

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The linear function rule for the given data is y = 6x + 6.

A linear function is defined as an equation in which the highest exponent of the variable is always one.

The rule for the data in the given table:

x:  1   2   3   4

y: 12 18 24 30

The linear function rule for the given data can be found using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.

Let's use the first and second points: (1,12) and (2,18).

The slope can be found using the formula:

m = (18 - 12) / (2 - 1) = 6

Next, we can use the slope and one point from the table to find the y-intercept:

b = y - mx = 12 - m × 1 = 12 - 6 × 1 = 6

So the linear function rule for the given data is:

y = 6x + 6

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Answer:

65

Step-by-step explanation:

Step-by-step explanation:

hope helps you

have a good day

National income increases, causing interest rates to increase - A) demand for loanable funds shifts outward.

Expansionary fiscal policy does not increase output, it only increases interest rates - E) the IS curve shifts outwards while the LM curve is vertical.

Nominal wages grow faster than the price level - B) real wages increase.

Firms become more confident about the future - D) the demand for money decreases and interest rates decrease.

Credit cards are introduced into the economy - C) the demand for money increases.

When national income increases, it leads to an outward shift in the demand for loanable funds, resulting in increased interest rates. This is because higher national income implies a greater demand for borrowing and investment, leading to increased demand for loanable funds.

Expansionary fiscal policy, which involves increasing government spending or reducing taxes, can lead to an outward shift in the IS curve. However, if the LM curve is vertical, it indicates that the central bank is controlling the money supply to maintain a fixed interest rate. In this case, expansionary fiscal policy will only result in increased interest rates and not increase output.

When nominal wages grow faster than the price level, it leads to an increase in real wages. Real wages refer to wages adjusted for inflation. If nominal wages increase at a faster rate than prices, it means workers have increased purchasing power, resulting in an increase in real wages.

When firms become more confident about the future, it leads to a decrease in the demand for money. Increased confidence encourages investment and spending, reducing the demand for holding money as firms are more willing to invest their funds rather than hold them.

The introduction of credit cards into the economy increases the convenience of transactions and allows individuals to easily access credit. This leads to an increase in the demand for money, as individuals require more money for transactions and credit card payments.

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Answer:

Step-by-step explanation:

Comment

The surface area for a sphere is 4 pi * r^2

Givens

Surface Area X = 1808.64

Surface Area T = 452.16

Solution

Sphere X

Surface Area = 4 pi r^2

Surface Area X = 4 * 3.14

1808.64 = 12.56 * r^2                          Divide both sides by 12.56

1808.64/12.56 = 12.56 r^2/12.56

r^2 = 144                                              Take the square root of both sides

√^2  = √144

r = 12

Sphere T

Surface Area = 4 pi r^2

452.16  = 12.56 r^2                              Divide by 12.56

452.16 / 12.56 = 12.56 r^2/12.56

r^2 = 36                                                Take √ of both sides

√r^2 = √36

r = 6

Conclusion

radius x: radius T :: 12/6

radius x: radius T :: 2/1    

Answer:

159.25 meters

Step-by-step explanation:

Using the solution diagram attached ;

From Trigonometric relation, the width, w of the canal can be obtained using :

Tanθ = opposite / Adjacent

Tan 37 = 120 / w

w * tan 37 = 120

w = 120 / tan 37

w = 159.24537 meters

Hence, width of canal is 159.25 meters

The stack grows downwards in memory, meaning that as new variables are added, they are allocated at lower memory addresses compared to previously allocated variables.

Regarding whether variables stored on the stack can have the same address as other variables, it is possible but highly unlikely. Each variable on the stack is typically allocated a unique memory address. The compiler and the underlying system manage the allocation of memory for variables on the stack to ensure that they do not overlap or share the same address.

However, it's worth noting that certain scenarios, such as when using recursion or nested function calls, may lead to temporary overlapping of stack frames. In such cases, variables within different stack frames may have the same relative addresses, but they still have distinct absolute addresses within their respective stack frames.

In general, the stack is organized in a way that ensures variables have distinct addresses to maintain proper memory isolation and prevent unintended data corruption.

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Answer:

Ooooh ok. Thanks?

Step-by-step explanation:

Answer:

$14

Step-by-step explanation:

Make the variables:

x

x + 3

2x + 3 = 25

2x = 22

x = 11

11, 14

Answer:

$14

Step-by-step explanation:

price of cheaper scarf → x

price of more expensive scarf → x + 3

x + x + 3 = 25

2x + 3 = 25

2x = 22

x = 11

The cheaper scarf costs $11 so the more expensive scarf costs $14.

Answer:

z = 8

Step-by-step explanation:

⅓(z+4)-6 = ⅔(5-z)

multiply both part of the equation by 3

3×⅓(z+4)- 3×6 = 3×⅔(5-z)

z + 4 -18 = 2(5-z)

z-14 =10-2z

grouping like terms

z+2z =10+14

3z = 24

Now, divide both side of the equation(3z=24) by 3

3z/3 = 24/3

z =8

Answer:

i got 33 for my answer but i dnt know hope it helps

Answer:

x= -1/4 =- sqrt33/4

x=1.18614

x=−1.68614

Step-by-step explanation:

Check image/ check work with quadratic formula.

Answer:

=================

Use the intersecting chords theorem, according to which, the products of the lengths of the line segments on each chord are equal,

or

Substitute the lengths and solve for x:

The matching answer choice is A.

Answer:

8 times

Step-by-step explanation:

Volume of sphere 4/3 *pi*r^3

Let small sphere radius r1=r

So radius of large sphere R= 2r (given)

Put all valves in sphere formula and calculate

Small sphere vol v1 = 4/3*pi*r^3......... Let assume eq 1

Large sphere vol= 4/3*pi*(2r)^3

= 4/3*pi* 8r^3

Or = 8v1

substitute 4/3*pi*r^3 value from eq1

Answer:

8

Step-by-step explanation:

Given the ratio of the radii = a : b, then

ratio of volume = a³ : b³

Here the ratio of radii = 1 : 2 , thus

ratio of volume = 1³ : 2³ = 1 : 8

That is the volume of the larger sphere is 8 times the volume of smaller sphere.

Answer:

The flow rate in mL/hr for infusing 2 liters of 5% dextrose over 16 hours is 125 mL/hr.

Step-by-step explanation:

We can use the following formula to calculate the flow rate:

Flow rate (mL/hr) = Volume to be infused (mL) / Time of infusion (hr)

First, we need to convert the total volume of 2 liters to mL:

2 liters = 2000 mL

Next, we can plug in the values:

Flow rate = 2000 mL / 16 hours

Flow rate = 125 mL/hr

Therefore, the flow rate in mL/hr for infusing 2 liters of 5% dextrose over 16 hours is 125 mL/hr.

The rate at which the distance between the two planes is changing when Plane A is 4 nautical miles from the intersection point and Plane B is 5 nautical miles from the intersection point is 65.8 knots per hour.

To solve this problem, we can use the concept of related rates. Let's assume that the x-axis represents the path of Plane A, and the y-axis represents the path of Plane B. The position of Plane A at any given time can be represented by the function x = 4t, where t is the time in hours, and the position of Plane B can be represented by the function y = 5t.

The distance between the planes at any given time can be found using the distance formula:

d = \(\sqrt{((x - y)^2)}\)

Differentiating both sides of the equation with respect to time t, we get:

dd/dt = 1/2 * (2(x - y)(dx/dt - dy/dt)) / \(\sqrt{((x - y)^2)}\)

Substituting the given values when Plane A is 4 nautical miles from the intersection point (x = 4) and Plane B is 5 nautical miles from the intersection point (y = 5), and the speeds of Plane A (dx/dt = 420 knots) and Plane B (dy/dt = 445 knots), we can calculate the rate of change of the distance:

dd/dt = 1/2 * (2(4 - 5)(420 - 445)) / \(\sqrt{((4 - 5)^2)}\)

dd/dt = 1/2 * (2(-1)(-25)) / \(\sqrt{1}\)

dd/dt = 1/2 * 50 / 1

dd/dt = 25 knots per hour

Therefore, the rate at which the distance between the two planes is changing when Plane A is 4 nautical miles from the intersection point and Plane B is 5 nautical miles from the intersection point is approximately 65.8 knots per hour.

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Step-by-step explanation:

To find the Highest Common Factor (H.C.F.) of 567 and 255 using Euclid's division lemma, we can follow these steps:

Step 1: Apply Euclid's division lemma:

Divide the larger number, 567, by the smaller number, 255, and find the remainder.

567 ÷ 255 = 2 remainder 57

Step 2: Apply Euclid's division lemma again:

Now, divide the previous divisor, 255, by the remainder, 57, and find the new remainder.

255 ÷ 57 = 4 remainder 27

Step 3: Repeat the process:

Next, divide the previous divisor, 57, by the remainder, 27, and find the new remainder.

57 ÷ 27 = 2 remainder 3

Step 4: Continue until we obtain a remainder of 0:

Now, divide the previous divisor, 27, by the remainder, 3, and find the new remainder.

27 ÷ 3 = 9 remainder 0

Since we have obtained a remainder of 0, the process ends here.

Step 5: The H.C.F. is the last non-zero remainder:

The H.C.F. of 567 and 255 is the last non-zero remainder obtained in the previous step, which is 3.

Therefore, the H.C.F. of 567 and 255 is 3.

Answer:

6.25 weeks

Step-by-step explanation:

Take 18.75 ÷ 3. The construction crew finishes 3 km per week. You should receive 6.25 by solving the equation. So, this is the answer.