Robert is going on a 2-day canoeing trip with his outdoor adventure group. Robert paddled at a constant sped and travels 3/4 of a mile in 15 minutes.
a. Create a table to determine how long it takes Robert to canoe 1 mile.

The relationship between x and y is y = x + 2

From the question, we have the following parameters that can be used in our computation:

(1, 3), (2, 4), (3, 5) and (5, 7)

See attachment for the line

Using the above as a guide, we have the following:

The three other points are (6, 8), (7, 9) and (8, 10)

From the ordered pairs, we can see that

y is the sum of x and 2

This means that

y = x + 2

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Let the width of the path be represented by x.

The total width of the pool and the path would then be 16 + 2x (for the two shorter sides) and 28 + 2x (for the two longer sides).

The area of the pool itself is 16 × 28 = 448 square meters.

The area of the combined pool and path is 864 square meters.

So the area of just the path is:

864 - 448 = 416 square meters

The area of the path can also be expressed as the area of the larger rectangle (16 + 2x) × (28 + 2x) minus the area of the pool (16 × 28).

So we can set up the equation:

(16 + 2x) × (28 + 2x) - 448 = 416

Expanding the left side and simplifying:

4x^2 + 88x - 480 = 0

Dividing by 4:

x^2 + 22x - 120 = 0

Using the quadratic formula:

x = (-22 ± sqrt(22^2 - 4(-120)))/2

x = (-22 ± 26)/2

x = 2 or x = -24

The width of the path cannot be negative, so the width of the path is 2 meters.

The distance between each pair of letters in the word is given by the equation A = 5 inches

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the distance between each pair of letters be A

Now , the equation will be

Let the total distance of the wide banner be = 61 inches

Now , the word is given by { E , A , G , L , E , S }

The number of letters in the word = 6 letters

The width of each letter = 6 inches

So , the total length of all the letters = 6 x 6 = 36 inches

The remaining distance in the wide banner = total distance of the wide banner - total length of all the letters

On simplifying the equation , we get

The remaining distance in the wide banner = 61 - 36

The remaining distance in the wide banner = 25 inches

Now ,

The distance between each pair of letters = remaining distance in the wide banner  / 5 spaces

On simplifying the equation , we get

The distance between each pair of letters A = 25 / 5

The distance between each pair of letters A = 5 inches

Hence , the equation is A = 5 inches

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Answer:The area of a circle can be calculated using the formula:

A = πr²

where A is the area and r is the radius.

Plugging in the given radius of 21 mm, we get:

A = π * 21² = π * 441

A = 441π mm²

To 1 decimal place, 441π can be approximated to 1393.1 mm². So, the area of the circle with a radius of 21 mm is approximately 1393.1 mm² to 1 decimal place.

Step-by-step explanation:

A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

To figure out what fraction of the toys are blue, we need to convert all of the fractions to have a common denominator.

A common denominator consists of two or more fractions that have the same denominator. This makes it easier to perform numeric equations, and to solve them.

Looking at the fractions, we can see that there are 3 fractions, [tex]\frac{1}{8}, \frac{1}{4}[/tex] and [tex]\frac{3}{5}[/tex].

To solve for the common denominator between [tex]\frac{1}{8}[/tex] and [tex]\frac{3}{5}[/tex], we first multiply the denominators, 8 and 5.

We now know that the denominator is going to be 40.

To get the numerators, we can use these equations:

The new fractions look like this:

To easily convert the last fraction ([tex]\frac{1}{4}[/tex]) we can multiply the numerator and denominator by 10.

We multiply by 10 because the denominator, which is 4, can be multiplied by 10 to get our common denominator of 40.

Now, we have our 3 fractions converted to have common denominators.

([tex]\frac{5}{40}, \frac{24}{40}[/tex] and [tex]\frac{10}{40}[/tex])

(Yellow, red, and green)

We can now add these up and see what fraction of blue is remaining.

Therefore, the fraction of blue toys compared to the total amount is [tex]\frac{1}{40}[/tex].

If there are 100 green toys resulting in [tex]\frac{10}{40}[/tex] of all the toys, we can divide 100 by 10 to get the number of blue toys.

We divide by 10 because [tex]\frac{1}{40}[/tex] is only [tex]\frac{1}{10}[/tex] of [tex]\frac{10}{40}[/tex], meaning we divide by 10.

Therefore, there are 10 blue toys.

Answer:

1/4=100

10/40=100

40/40=400

1/8=400/8=50

3/5=400/5*3=240

400-100-50-240=10

10 of the toys are blue

Hope this helped!!

Step-by-step explanation:

For each of the functions, the constant c was determined so that the function would satisfy the conditions of being a pmf for a random variable X, and then a line graph was plotted for each pmf.

a. c = 4 so that f(x) = x/4;

Graph:

x f(x)

1 0.25

2 0.5

3 0.75

4 1

b. c = 1/30 so that f(x) = (1/30)x;

Graph:

x f(x)

1 0.03333

2 0.06667

3 0.1

4 0.13333

5 0.16667

6 0.2

7 0.23333

8 0.26667

9 0.3

10 0.33333

c. c = 1 so that f(x) = (1/4)x;

Graph:

x f(x)

1 0.25

2 0.125

3 0.0625

4 0.03125

d. c = 1/8 so that f(x) = (1/8)(x + 1)²;

Graph:

x f(x)

0 0.125

1 0.25

2 0.375

3 0.5

e. c = n so that f(x) = x/n;

Graph:

x f(x)

1 1/n

2 2/n

3 3/n

... ...

n 1

f. c = 1 so that f(x) = 1/(x + 1) − 1/(x + 2);

Graph:

x f(x)

0 1

1 0

2 −0.5

3 −0.333

4 −0.25

5 −0.2

... ...

For each of the functions, the constant c was determined so that the function would satisfy the conditions of being a pmf for a random variable X, and then a line graph was plotted for each pmf.

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Answer:thwe answer is 8

Step-by-step explanation:

Answer:88

Step-by-step explanation:

Answer: Anand's salary after 10 years working for the company can be calculated as follows:

$60000 + $2000 * 10 = $60000 + $20000 = $80000.

To determine Anand's salary after t years working for the company, we can use the following formula:

$60000 + $2000 * t

So, if t is the number of years he has worked for the company, his salary after t years would be:

$60000 + $2000 * t.

Step-by-step explanation:

The values of the expression following the collection of like terms, rearranging and factoring are presented as follows;

1.1 4·x + 5·a + 3·a + x - 6 = 5·x + 8·a - 6

1.2. 6·a·b + 2·b - 16·a - 2 = 2·(3·a·b + b - 8·a - 1)

1.3. 1024000 : 360000 : 180000 = 256 : 90 : 45

1.4. 150 min : 3 hours = 5 : 6

A mathematical expression comprises of mathematical symbols, numbers and variable, properly arranged to represent a value.

The simplification of the expressions can be presented as follows;

1.1. 4·x + 5·a + 3·a + (x - 6)

The terms in the above expression can be rearranged as follows;

4·x + 5·a + 3·a + (x - 6) = 4·x + x + 5·a + 3·a - 6

4·x + x + 5·a + 3·a - 6 = 5·x + 8·a - 6

Therefore, whereby the expression in the question is; 4·x + 5·a + 3·a + (x - 6), we get;

1.2. Whereby the possible expression in the question is; 6·a·b + 2·b - 16·a + (-2), we get;

The factor common to the terms of the expression 6·a·b + 2·b - 16·a + (-2) is 2. Therefore by factoring the expression, we get;

1.3. 1024000: 360,000 : 180,000

The expression is a ratio of the form a : b : c

Dividing each term in the ratio by 1,000, we get

1024000 ÷ 1000 : 360,000 ÷ 1000 : 180,000 ÷ 1000 = 1024 : 360 : 180

1024000: 360,000 : 180,000 = 1024 : 360 : 180

The common factors of 1024, 360 and 180 are; 1, 2, and 4

Therefore, the GCF of 1024, 360, and 180 is 4

Dividing the terms of the ratio 1024 : 360 : 180 by 4, we get;

1024 ÷ 4 : 360 ÷ 4 : 180 ÷ 4 = 256 : 90 : 45

Therefore;

1.4 150 min : 3 hours

The above ratio can be simplified by rewriting the ratio using unit conversion as follows;

3 hours = 180 minutes, therefore;

150 min : 3 hours = 150 min : 180 min

150 : 180 = 5 : 6

Therefore; 150 min : 180 min = 5 min : 6 min

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The range of the cigarette tax (in cents) for 50 selected states is 62.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

The range of a given set of data is the difference between the largest value and the smallest value.

Given the data shown represent the cigarette tax (in cents) for 50 selected states

70,12,42,45,50,51,60,69,8,40,18

Required; The range

This is calculated as:

Range = highest - lowest

Range = 70 - 8

Range = 62

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a. Point P on the line and the direction vector v of the line can be expressed as P = (x0, y0, z0) + t(a, b, c).

b. The distance from the origin to the line -x=y+1, z=2 is the shortest distance between a point and a line.

Here (x0, y0, z0) is a point on the line and (a, b, c) is the direction vector. To find (x0, y0, z0) and (a, b, c), we need more information about the line.

This formula involves taking the dot product of the direction vector of the line and the difference between a point on the line and the origin. Again, we need more information about the line in order to calculate this distance.

Without more information about line L, it is not possible to find the point P or the distance from the origin to the line.

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The statement that is always correct regarding the multiplication of x and z is given as follows:

The multiplication of x and z is always negative.

The multiplication signal rules is defined by the terms two by two, and the rule is given as follows:

For this problem, we have that x and z have different signs, hence the product is going to be always negative.

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Answer:

2x²+12x-32

Step-by-step explanation:

Answer: 7 is the common factor for ALL of these numbers.

To find the area under the normal distribution between z = -0.30 and z = 0.90, you can use a standard normal distribution table or a calculator with a normal distribution function.

Using a standard normal distribution table:

Look up the area to the left of z = 0.90 in the standard normal distribution table. This will give you a value of 0.8159.

Look up the area to the left of z = -0.30 in the standard normal distribution table. This will give you a value of 0.3821.

Subtract the value from Step 2 from the value from Step 1 to find the area between z = -0.30 and z = 0.90:

Area = 0.8159 - 0.3821 = 0.4338

Using a calculator with a normal distribution function:

Use the normal distribution function on your calculator with a mean of 0 and a standard deviation of 1 to find the area to the left of z = 0.90. This will give you a value of 0.8159.

Use the normal distribution function on your calculator with a mean of 0 and a standard deviation of 1 to find the area to the left of z = -0.30. This will give you a value of 0.3821.

Subtract the value from Step 2 from the value from Step 1 to find the area between z = -0.30 and z = 0.90:

Area = 0.8159 - 0.3821 = 0.4338

Therefore, the area under the normal distribution between z = -0.30 and z = 0.90 is 0.4338.

Due to length restrictions, we kindly invite to see the explanation below to know the complete truth table of the composite proposition.

According to logics, propositions are constructions that contains a truth value and in this question we must complete a truth value of a composite proposition, that is, a combination of simpler proposition.

To complete a this table, we must begin with the most simple proposition and go through propositions with more complexity:

p     q      r       ¬ p      ¬ q      p → q      r ∧ ¬ p      r ∨ ¬ q

T     T      T         F         F         T             F               T

T     T      F         F         F         T             F               F

T     F      T         F         T         F             F               T

F     T      T         T         F         T             T               F

F     F      T         T         T         T             T               T

F     T      F         T         F         T             F               F

F     F      F         T         T         T             F               F

[(p → q) ∨ (r ∧ ¬ p)]       [(p → q) ∨ (r ∧ ¬ p)] → (r ∨ ¬ q)

           T                                          T

           T                                          F

           F                                          T

           T                                          F

           T                                          T

           T                                          F

           T                                          F

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The probability of a defect is 5.7330 x [tex]10^{-5}[/tex] and the number of defects is 5.73.

To calculate the probability of a defect, we need to find the area under the standard normal curve that lies outside of the process control limits of 9.75 ounces and 10.25 ounces. We can use the standard normal distribution table to find this area.

First, we need to standardize the weight limits as follows -

[tex]Z_{lower}[/tex] = (9.75 - 10) / 0.25 = -4

[tex]Z_{upper}[/tex] = (10.25 - 10) / 0.25 = 4

Next, we will find the area under the standard normal curve that lies outside of these limits as follows -

P(Defect) = P(Z < -4) + P(Z > 4)

Using a standard normal distribution table, we can find that P(Z < -4) = 2.8665 x   [tex]10^{-5}[/tex]  and P(Z > 4) = 2.8665 x  [tex]10^{-5}[/tex] .

So, the total probability of a defect is -

P(Defect) = 2.8665 x  [tex]10^{-5}[/tex]  + 2.8665 x  [tex]10^{-5}[/tex]  = 5.7330 x  [tex]10^{-5}[/tex]

Finally, we will find the number of defects for a 1,000-unit production run as follows -

The number of defects = 1000 * 5.7330 x  [tex]10^{-5}[/tex]  = 5.73 (rounded to the nearest whole number).

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Answer:

x=2/3 or x= -3/10

Step-by-step explanation:

30x²-11x-6=0

ax²+bx+c=0

30x²+9x-20x-6=0

3x(10x+3)-2(10x+3)=0

(3x-2)(10x+3)=0

3x-2=0 or 10x+3=0

3x=2 or 10x= -3

x=2/3 or x= -3/10

The number of Gallons of paint that Daniel will need is; 3 gallons

The parameters given are;

Height of each wall = 78 inches = 78/12 = 6.5 ft

Length of wall 1 = 7 ft

Length of wall 2 = 6 ft

Length of wall 3 = 7 ft

Area of wall 1 = 6.5 * 7 = 45.5 sq.ft

Area of wall 2 = 6.5 * 6 = 39 sq.ft

Area of wall 3 = 6.5 * 7 = 45.5 sq.ft

Total area = 45.5 + 45.5 + 39

= 130 sq.ft

1 gallon of paint will cover 300 square feet of wall space

Number of gallons required = 300/130

= 2.3 gallons

Approximating to a whole number gives 3 gallons

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Answer:A tidal wave is a regularly reoccurring shallow water wave caused by effects of the gravitational interactions between the Sun, Moon, and Earth on the ocean.

Strategy-planning activity in which top management envisions different what if scenarios to anticipate plausible futures in order to derive strategic responses is definition of: Scenario planning.

Scenario planning gives company decision-makers the ability to assess reactions, manage for both good and negative possibilities, and establish ranges of prospective outcomes and anticipated implications. Scenario planning is more than simply a financial planning tool; it's an integrated strategy for coping with uncertainty. It includes predicting financial results, calculating cash flow, and devising mitigation actions. But it goes beyond only being a means to identify and reduce risk or prepare for growth scenarios. Planning scenarios involves imagining several futures for an organisation based on various, sometimes positive, sometimes negative, assumptions about market dynamics. Scenario planning is a method pioneered by the United States military, which now conducts exercises looking up to 20 years in advance to direct R&D activities.

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Answer:

0.0588

Step-by-step explanation:

There are 52 cards total in a pack of cards.

There are 13 diamond cards in a pack of card

When the first card is dealt, it is NOT replaced. When the second card is dealt, it is NOT replaced

In probability:

AND = multiplication

  OR = addition

Probability = [tex]\frac{Total number of diamond cards}{Total number of cards}[/tex]

Probability that both friends for diamonds:

First card is DIAMONDS AND second card is DIAMONDS:

= [tex]\frac{13}{52}[/tex]×[tex]\frac{12}{51}[/tex]

= [tex]\frac{156}{2652}[/tex]

= 0.0588 (Rounded off to 3 significant figures)

The number of animals left in the wild after 4 years is approximately 306.

Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.

We are using the concept of compound interest to solve the given problem.

The formula to find the final amount in compound interest is,

A = P (1 + r) ^t

Here P = 400

r = -6.5% = -0.065 (negative sign because the rate is decreasing)

t = 4 years

Substituting the values,

A =400 (1 - 0.065)⁴

  = 305.71 ≈ 306

Hence there will be 306 animals left in the wild after 4 years.

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The total number of toys in Bashir's collection is 160.

A percentage is a number or ratio that can be expressed as a fraction of 100.

Let N represent the total number of toys in Bashir's collection

Since 136 of his toys are on the wall and 15% of the toys are in the display. We can write:

136 + (15% of N) = N

136 + (15/100 * N) = N

136 + 0.15N = N

N - 0.15N = 136

0.85N = 136

N = 136/0.85

N = 160

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Answer:

42

Step-by-step explanation:

6*4+3*6= 42

Answer:

42

Step-by-step explanation:

6*4+3*6=42

Answer: It´s about 14.96 gallons per square foot with 55 square foot area and 2 feet height

Step-by-step explanation:

Answer: Let's call the height of the building "h".

The length of the shadow cast by the building is 5 feet, and the length of the shadow cast by the yardstick is also 5 feet. This means that the ratio of the height of the building to the length of its shadow is the same as the ratio of the height of the yardstick to the length of its shadow.

h / 5 = 1 / 5

Cross-multiplying, we get:

h = 5 * 1 / 5

h = 1

So the building is 1 foot tall.

Step-by-step explanation:

The value of the equation is x = 4 and x = -5 ± √10i

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

( x - 4 ) / ( x + 5 ) + 9 / ( x² + 11x + 30 ) = 1/( x + 6 )

On simplifying the equation , we get

( x - 4 ) / ( x + 5 ) + 9 / ( x + 5 ) ( x + 6 ) = 1/( x + 6 )

Multiply the equation with the LCM , we get

( x - 4 ) ( x + 5 ) ( x + 6 ) + 9 ( x - 5 ) = ( x - 5 ) ( x + 5 )

x³ + 7x² - 14x - 120 + 9x - 45 = x² - 25

Subtracting x² on both sides of the equation , we get

x³+ 6x² - 5x - 165 = -25

Adding 25 on both sides of the equation , we get

x³+ 6x² - 5x - 140 = 0

Hence , the solution to the equation is x = 4 ,  -5 ± √10i

So , the larger solution is x = 4

And , the smaller solution is x = -5 ± √10i

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Answer:

An average of 70.8 miles per hour

Step-by-step explanation: