-3(x+ 2y) + 5(3x - y) + y2 for x = 6 and y= 2.

Using the perimeter of a rectangle, the length of wire required is calculated as: 8.4 km.

A rectangle with a length of "l" and a width of "w" has a perimeter which is calculated using the formula below:

Perimeter of rectangle = 2(l + w).

The length of wire required = the perimeter of the island × 3

Length of the island = 0.9 km

Width of the island = 0.5 km

The length of wire required = 2(0.9 + 0.5) × 3

The length of wire required = 2(1.4) × 3

The length of wire required = 2.8 × 3

The length of wire required = 8.4 km.

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The binary equivalent of decimal number 124 expressed in 8 bits is 01111100.

To convert a decimal number to binary, we can use the division method. In this case, we repeatedly divide 124 by 2 and note down the remainder until the quotient becomes 0. Then we read the remainders in reverse order to get the binary equivalent.

124 divided by 2 gives a quotient of 62 and a remainder of 0.

62 divided by 2 gives a quotient of 31 and a remainder of 0.

31 divided by 2 gives a quotient of 15 and a remainder of 1.

15 divided by 2 gives a quotient of 7 and a remainder of 1.

7 divided by 2 gives a quotient of 3 and a remainder of 1.

3 divided by 2 gives a quotient of 1 and a remainder of 1.

1 divided by 2 gives a quotient of 0 and a remainder of 1.

Reading the remainders from bottom to top, we get 01111100 as the binary equivalent of 124 in 8 bits.

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The experimental probability that at least two heads would be gotten is 11 / 25.

The theoretical probability that at least two heads would be gotten is 1/2.

Probability calculates the odds that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

Experimental probability is based on the result of an experiment that has been carried out multiples times.

Experimental probability = number of times at least two heads would be gotten / total number of tosses

( 5 + 6 + 6 + 5)/50 = 22/50 = 11 / 25

Theoretical probability = number of times at least two heads would be gotten / total number of possible outcomes

4 / 8 = 1/2

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Answer: The first one :)

Step-by-step explanation:

The chord length (C) between PC and P is 5.831 cm.

A chord is a straight-line segment that connects two points on a circle. P is a point on the circumference of the circle, while PC is a chord of the circle that passes through P.

Therefore, the chord length (C) between PC and P is equal to half of the length of the chord PC. In other words, we need to find the length of PC and divide it by 2. We can do this using the Pythagorean Theorem since we have a right triangle formed by PC and the diameter of the circle.

Diameter of the circle (AB) = 20 cm

Radius of the circle (OA) = AB/2 = 10 cm

Height of the triangle (OP) = 6 cm

Using the Pythagorean Theorem, we can find the length of PC as follows:

PC² = PO² + OC²PC² = 10² + 6²PC² = 136PC = √136PC ≈ 11.661

Therefore,  is equal to C = PC/2C = 11.661/2C ≈ 5.831 cm.

So, the answer to the question "What is the chord length (C) between PC and P? when the diameter of the circle = 20 cm and the Height of the triangle = 6cm" is 5.831 cm.

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Answer:

Step-by-step explanation:

In each case, square the coordinates of the point and determine whether or not the sum of these squares is 1:

A)  4/9 + 5/9 = 9/9  YES

B)  1 + 1 = 2 NO

C) 3/4 + 1/9 Not equal to 1.  NO

D) 0.64 + 0.36 = 1.00 YES

HENCE OPTION B(1,1) IS CORRECT

What is unit circle?

A unit circle is a circle with a radius of one, as defined by mathematics. The unit circle is a circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane, which is used frequently in trigonometry.

How to solve?

Clearly from the given options (1,1 ) will lie on the circle , Hence option b (1,1) is correct .

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Answer:

0.175438596491

Step-by-step explanation:

I did 14/79.8, btw I counted with my fingers

<3 <3 <3 <3 <3

Age of Mike when he is one and a half times as old as his brother is, 3 years old.

We have,

Mike, six years old, is twice as old as his brother.

Hence,

Mike = 6 years

His brother = 6/2 = 3 years

Condition for when he is one and a half times as old as his brother,

6 + x = 1.5 (x + 3)

Where, x is age of mike when he is one and a half times as old as his brother.

Solve for x,

6 + x = 1.5x + 4.5

1.5x - x = 6 - 4.5

0.5x = 1.5

x = 1.5 / 0.5

x = 3 years

Therefore, Age of Mike when he is one and a half times as old as his brother is, 3 years old.

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a. The volume of the cylinder is 216π cm³  

b. The volume of the cone is 72π cm³

c. The volume of the hemisphere is 144π cm³

The volume of the cylinder is 216π cm³  

Since the hemisphere fits snugly inside the cylinder, and the radius of the cylinder is 6 cm, the radius of the hemisphere equals the radius of the cylinder. Also, the height of the cylinder equals the radius of the hemisphere.

So, the volume of the cylinder V = πr²h where

So, V = πr²h

= πr² × r

= πr³

= π(6 cm)³

= 216π cm³

So, the volume of the cylinder is 216π cm³  

The volume of the cone is 72π cm³  

Since the cone fits snugly inside the same hemisphere, the radius and height of the cone equals the radius of the hemisphere.

So, the volume of the cone V' = πr²h/3 where

So, V' = πr²h/3

= πr² × r/3

= πr³/3

= π(6 cm)³/3

= 216π/3 cm³

= 72π cm³

So, the volume of the cone is 72π cm³  

The volume of the hemisphere is 144π cm³  

Since the volume of hemisphere, V" equals the averages of the volume of the cylinder, V and volume of the cone, V'

So, V" = (V + V')/2

V" = (216π cm³ + 72π cm³)/2

V" = 288π cm³/2

V" = 144π cm³  

So, the volume of the hemisphere is 144π cm³  

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Answer:

Step-by-step explanation:

1/6 ÷ 8

1/6 × 1/8

1/48

for each batch

The initial amount of salt is 20 grams and the rate of change is equal to the difference between the rate at which salt enters the tank and the rate at which it leaves. This is expressed by the equation a'(t) = 1 - (a(t)/150)*3, where a'(t) is the derivative of a(t) with respect to time.

The function a(t) is given by a differential equation, which describes the rate of change of the amount of salt in the tank with respect to time.

To solve the differential equation, we can use separation of variables and integrate both sides with respect to t.

This gives us

ln|a(t)-50| = -3/50*t + C, where C is a constant of integration. Solving for a(t), we get

\(a(t) = 50 + Ce^(-3/50*t).\)

Using the initial condition a(0) = 20, we can solve for the constant C, which is C = -30.

Therefore, the function a(t) is \(a(t) = 50 - 30e^(-3/50*t).\). The function tells us the number of grams of salt in the tank at any given time t.

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Answer: The car travels 97.5 miles in 1.5 hour.

Step-by-step explanation:

Given: A car is traveling down a highway at a constant speed, described by the equation , described by the equation \(d=65t\), where represents the distance, in miles, that the car travels at this speed in t hours.

To find : Number of miles car travel in 1.5 hour.

Simply put t= 1.5 in the given expression , we get

65(1.5)= 97.5

That means , the car travels 97.5 miles in 1.5 hour.

Answer:

Step-by-step explanation:

Multiply through by 7 inorder to clear out the fraction

That's

We have

Multiply the terms in the bracket

That's

2x - 4 = 28x

Subtract 28x from both sides

We have

2x - 28x - 4 = 28 - 28x

Simplify

- 26x = 4

Divide both sides by - 26

That's

We have the final answer as

Hope this helps you

y = 8450(0.7640)ˣ is the equation that will model this situation

The general form of exponential equation is given by:

y = abˣ

Where a is the initial value of the car, b is the depreciation rate and x is the number of years

When x = 0, y = $8450:

y = abˣ

8450 = ab⁰

a = 8450

In 1993, x = 1993 - 1988 = 5 years and y = $2200:

y = abˣ

2200 = 8450b⁵

b⁵ = 2200/8450

b = \(\sqrt[5]{}\)(2200/8450)

b = 0.7640

Thus, the equation that model the situation is y = 8450(0.7640)ˣ

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Answer:

I have a suggestion. There are math apps on google play store or apple app store that can solve this question for you. You'll just take a pic of the question and it will answer it.

Step-by-step explanation:

....... wont let me type the name of the app so I'm gonna code it with the numbers of the alphabets.

13 1 20 8 23 1 25 is a really good one

The approximate value of f(1) using Euler's method with two steps of equal size is 6.636. The range of f for t > 0 is 0 < f(t) < 6.

a. The limiting factor in this logistic differential equation is the carrying capacity, which is 6 in this case. As y approaches 6, the growth rate of y slows down, until it eventually levels off at the carrying capacity.

b. To use Euler's method, we first need to calculate the slope of the solution at t=0. Using the given differential equation, we can find that the slope at t=0 is y(0)/8(6-y(0)) = 8/8(6-8) = -1/6.

Using Euler's method with two steps of equal size, we can approximate f(1) as follows:

f(0.5) = f(0) + (1/2)dy/dx|t=0

= 8 - (1/2)(1/6)*8

= 7.333...

f(1) = f(0.5) + (1/2)dy/dx|t=0.5

= 7.333... - (1/2)(7.333.../8)*(6-7.333...)

= 6.636...

Therefore, the approximate value of f(1) using Euler's method with two steps of equal size is 6.636.

c. The range of f for t > 0 is 0 < f(t) < 6, since the carrying capacity of the logistic equation is 6. As t approaches infinity, f(t) will approach 6, but never exceed it. Additionally, f(t) will never be negative, since it represents a population size. Therefore, the range of f for t > 0 is 0 < f(t) < 6.

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Answer:

Step-by-step explanation:

Given function:

Finding h(-67)

Correct option is B.

Concepts:

Answer: B. 3158

We know:

h(x) = -49x − 125

Finding h(-67)

h(-67) = -49(-67) - 125 = 3283 - 125 = 3158

ANSWER = 3158/B

Answer:

Surface area of the roof of the kennel, including the bottom face is 58.96 ft^2

Step-by-step explanation:

The image is attached below

For the triangular sides of the roof, area is

A = \(\frac{1}{2}bh\)

where b is the base = 4 ft

h is the vertical height = 2.24 ft

A =  \(\frac{1}{2}*4*2.24 =\) 4.48 ft^2

for the two faces we have 2 x 4.48 ft^2 = 8.96 ft^2

For the rectangular sections of the roof, area is

A = \(lh\)

where \(l\) is the length of the rectangle = 5 ft

h is the height of the rectangle = 3 ft

A = 5 x 3 = 15 ft^2

For the two rectangular faces, we have 2 x 15 ft^2 = 30 ft^2

For the bottom face, area is

A = \(lw\)

where \(l\) is the length of the house = 5 ft

w is the width of the house = 4 ft

A = 5 x 4 = 20 ft^2

Surface area of the roof of the dog kennel is

8.96 ft^2 + 30 ft^2 + 20 ft^2 = 58.96 ft^2

Recent research has confirmed the Spillover Hypothesis by demonstrating a favourable association between life and job happiness.

According to the spillover hypothesis, behaviour or affect in a family system might flow immediately from one place or connection to another. Transfer takes place in the same valence, which means that one subsystem's negative affect is connected to another's negative affect, or stress at work spills over and intensifies stress at home. The compensatory hypothesis offers a different perspective by arguing that transfer between family subsystems occurs in the opposite valence, leading a person to seek fulfilment in one relationship or environment in order to make up for shortages in another.

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A square pyramid is a three-dimensional shape that has a total of five faces, hence called a pentahedron.To calculate the volume of a square pyramid, we use the formula: Volume = (1/3) * Base Area * Height

In the given question, we have X (the side length of the square base) = 8 units and Y (the height of the pyramid) = 27 units. First, we need to find the base area of the square pyramid.

Step 1: Find the base area (A)
A = X^2 = 8^2 = 64 square units

Step 2: Calculate the volume (V) of the square pyramid using the formula
V = (1/3) * A * Y = (1/3) * 64 * 27

Step 3: Simplify the expression
V = (64 * 27) / 3 = 1728 / 3 = 576 cubic units

So, the volume of the square pyramid is 576 cubic units.

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Answer:

8

Step-by-step explanation:

8x - 4 = 60

8x = 60 + 4

x = 64/8

x = 8

Answer:

Step-by-step explanation:

( x - 3)²

= x² - 2 * x * 3 + 3²

= x² - 6x + 9

The Latin square that is balanced for residual effects is Latin Square 1.

To determine whether a Latin square is balanced for residual effects, we need to check if the order effects and carryover effects are equal across all rows and columns.

In Latin Square 1:

Order effects: Each treatment appears once in each row and column. Therefore, there are no order effects.

Carryover effects: Each treatment follows every other treatment once in each row and column. Therefore, there are no carryover effects.

Since there are no order or carryover effects in Latin Square 1, it is balanced for residual effects.

In Latin Square 2:

Order effects: Treatment A appears twice in row 1, while treatment D appears twice in row 2. Therefore, there are order effects.

Carryover effects: Treatment C follows treatment A twice in row 3, but only once in row 2. Therefore, there are carryover effects.

Since there are order and carryover effects in Latin Square 2, it is not balanced for residual effects.

Therefore, the Latin square that is balanced for residual effects is Latin Square 1.

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Answer:

no./0=undefined

0/no.=zero

Answer:

yes it is.

Step-by-step explanation:

Answer:

A)113cm^2

Step-by-step explanation:

To exchange $3000 with a 1.5% commission at the given buying rate and selling rate, you would need approximately Rs. 316,680 Nepali currency.

To calculate the amount of Nepali currency (Rs.) required to exchange $3000 with a 1.5% commission, we need to consider the buying rate and the commission rate.

Buying rate of $1 = Rs. 104

Commission rate = 1.5%

First, let's calculate the amount of Nepali currency required without considering the commission:

Amount in Rs. = Amount in $ * Buying rate

Amount in Rs. = $3000 * Rs. 104

Amount in Rs. = Rs. 312,000

let's calculate the commission amount:

Commission = (Commission rate/100) * Amount in Rs.

Commission = (1.5/100) * Rs. 312,000

Commission = Rs. 4,680

Finally, let's calculate the total amount of Nepali currency required, including the commission:

Total amount in Rs. = Amount in Rs. + Commission

Total amount in Rs. = Rs. 312,000 + Rs. 4,680

Total amount in Rs. = Rs. 316,680

Thus, the appropriate answer is approximately Rs. 316,680.

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Answer:

32 times

Step-by-step explanation:

If you can go around 54 times for $12, then you multiply the amount of money you pay by four to get the number of times you can go around the track.

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Answer:

I would say 36 because 54 times 8 is 432 and if you divide that by 12 you get 36.

Step-by-step explanation:

When a linear transformation is done to a nonzero vector in linear algebra, the vector is said to have an eigenvector, or characteristic vector, which only changes by a scalar amount. The scaling factor for the eigenvector is the appropriate eigenvalue, frequently represented as lambda.

When a linear transformation is done to a nonzero vector in linear algebra, the vector is said to have an eigenvector, or characteristic vector, which only changes by a scalar amount. The factor by which the eigenvector is scaled is known as the associated eigenvalue, frequently denoted by.

Hence, characteristic polynomial of A and A^T are the same, therefore their eigenvalues are also same.

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Answer:

\(39.8^{\circ} C\)

Step-by-step explanation:

We are given that the temperature each hour in Elma Texas on October 1 is modelled by the equation

\(t(h)=10cos(15h-10)^{\circ}+30\)

Where h=Hour of the day with 0 meaning midnight

t=Temperature in degree Celsius

We have to find the temperature on October 1.

Substitute h=0

\(t(0)=10cos(15(0)-10)+30\)

\(t(0)=10cos(-10)+30\)

\(t(0)=39.8^{\circ} C\)

Hence, the temperature in Elma on October 1=\(39.8^{\circ} C\)

The ratio of false positives to true positives is 8 over 54.

According to the Question

Results of a strep throat test performed on a sample of 400 ill people are displayed in the table's data. People who have the flu and those who don't are separated into two categories. The patients are then separated into groups based on whether they tested positive or negative for strep throat within each of these categories.

We must first define what a true positive and a false positive are in order to calculate the ratio of false positives to true positives. A patient who tests positive for strep throat but does not actually have the illness is said to have a false positive. The 8% of patients in this instance who tested positive for strep throat but did not have the flu would fall under that category. A patient who tests positive for strep throat and truly has the illness is said to have a true positive. That would be the 54% of patients who tested positive for both the flu and strep throat in this instance.

We divide the percentage of false positives (8%) by the percentage of true positives (54%), which gives us the ratio of false positives to true positives.

As a result, the ratio becomes 8% / 54%, or 8/54.

It's critical to remember that this ratio is dependent on the sample and test performed and may not be the same for different populations or testing methodologies.

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