This table on a package of dog food tells how much to feed a dog, depending on its weight.  Weight of Dog (pounds)153045 Amount of Food (scoops)246 The amount of food in scoops (s) is related to the weight of the dog in pounds (p) by the equation s = kp. What is k?​

Answer:

See attached photo!

Step-by-step explanation:

The constant of proportionality is a crucial aspect of a proportional relationship, as it tells us how much one variable changes in relation to the other. It can be calculated from the equation of the relationship, or from the slope of the graph if it is a linear relationship.

A proportional relationship is a mathematical equation that expresses two variables that are in proportion to one another. In this type of relationship, if one variable is multiplied by a certain constant factor, then the other variable will be multiplied by the same constant factor. For example, if the cost of 3 books is $15, then the cost of 6 books will be $30. In this case, the number of books and the cost of the books are in proportion to one another.

The constant of proportionality is the constant factor by which the two variables are multiplied to obtain each other. In other words, it is the ratio between the two variables that remain constant in a proportional relationship. It can be represented by the letter k, and is calculated by dividing one variable by the other.

To find the constant of proportionality from a graph, we need to look at the slope of the line. The slope is the ratio between the change in the y-values and the change in the x-values, which is also known as the rise over run. If the graph shows a proportional relationship, then the slope will remain constant throughout the graph.

For example, if the graph shows the relationship between the number of hours worked and the amount of money earned, and the slope is 10, then the constant of proportionality is 10. This means that for every hour worked, the person earns $10. The equation for this proportional relationship can be written as y = 10x, where y represents the amount of money earned and x represents the number of hours worked.

In conclusion, the constant of proportionality is a crucial aspect of a proportional relationship, as it tells us how much one variable changes in relation to the other. It can be calculated from the equation of the relationship, or from the slope of the graph if it is a linear relationship.

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The impact on Carns Company's income from eliminating the Small Tools Division would be a decrease of $1,209,000.

To determine the impact on Carns Company's income from eliminating the Small Tools Division, we need to consider the avoidable costs associated with the division.

The avoidable costs include all of the variable costs of the division and a portion of the fixed costs that are specifically related to the Small Tools Division. In this case, the variable costs of the division are $1,295,000, and $119,000 of the fixed costs are avoidable.

To calculate the impact on income, we subtract the avoidable costs from the loss reported by the division:

Impact on income = Loss - Avoidable costs

Impact on income = $205,000 - ($1,295,000 + $119,000)

Impact on income = $205,000 - $1,414,000

Impact on income = -$1,209,000

The negative sign indicates a decrease in income.

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Answer:

1 answer

Answer:lower bound = 147.5gupper bound = 152.5gStep-by-step explanation:if you were rounding a single digit number to the nearest 5, ...

Step-by-step explanation:

The required permutation of the letters of the word coefficient provided that all words start with coe is equals to 40,320.

The number of permutations of the letters of  word coefficient

With the condition that all words start with 'coe'.

Since we are given that the first three letters must be "coe",

Required to permute the remaining 8 letters.

The number of permutations of 8 letters can be found,

Using the formula for permutations of n distinct objects, which is,

P(n) = n!

where n is the number of objects.

Since the first three letters are fixed as 'coe',

The order of these letters is not counted in the permutation.

So, the number of permutations of the 8 remaining letters is,

⇒P(8) = 8!

⇒P(8) = 40,320

Therefore, the total number of permutations of the letters in the word 'coefficient' that start with 'coe' is P(8) = 40,320.

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The estimated mean daily methadone dosage for the patients is approximately 54.9 milligrams.

Llet's find the midpoint for each data class. The midpoint is calculated by averaging the lower and upper limits of each class interval.

Midpoint of 0 to 49: (0 + 49) / 2 = 24.5

Midpoint of 50 to 99: (50 + 99) / 2 = 74.5

Midpoint of 100 to 149: (100 + 149) / 2 = 124.5

Midpoint of 150 to 199: (150 + 199) / 2 = 174.5

Midpoint of 200 to 249: (200 + 249) / 2 = 224.5

Next, we calculate the weighted average by multiplying each midpoint by its corresponding frequency, summing up the products, and dividing by the total frequency.

Weighted average = (24.5 * 4 + 74.5 * 9 + 124.5 * 11 + 174.5 * 5 + 224.5 * 2) / (4 + 9 + 11 + 5 + 2)

Weighted average = 1702.5 / 31

Weighted average ≈ 54.9

Therefore, the estimated mean daily methadone dosage for the patients is approximately 54.9 milligrams.

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The given scenario, where a sample of teen drivers at a high school is surveyed about their engagement in the illegal activity of texting while driving, is an example of Selection bias. Option C

Selection bias occurs when the process of selecting participants for a study or survey is not random or representative of the entire population.

In this case, the sample consists only of teen drivers at a high school, which may not accurately represent all teen drivers in the broader population. The sample is limited to a specific group, which can introduce bias and affect the generalizability of the results to the wider population of teen drivers.

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44.44% or 4/9

percentage

200/450=.444...

.444x100=44.44%

fraction

200/450 is simplified to 4/9

Answer:

~ probability of 4/9 ~

Step-by-step explanation:

1. Here we can see that 1 box ⇒ I car, so the cars are equal to the boxes (450 boxes, 450 cars)

2. As this is true, to determine the probability a cereal box has a blue car in it, out of the 450 cereal boxes there are 200 blue cars, in a fraction expressed as such: 200/450

3. This value can be simplified through simple algebra, to be: probability of 4/9, which was computed through division of 50 on 200 and 450

Step-by-step explanation:

C = root of 7^2 + 4^2

= 8.06

Ans = A

Both f(x) and g(x) have one x-intercept at x = -1/3.

Theorem A states that for a cubic function of the form f(x) = x^3 + x + b, with b > 1, the function f has exactly one x-intercept. Using Theorem B, we can conclude that for any nonzero real number k, the function g(x) = kf(x) = kx^3 + kx + bk also has exactly one x-intercept.

For example, if f(x) = x^3 + x + 5 and k = 2, then g(x) = 2x^3 + 2x + 10. Both f(x) and g(x) have exactly one x-intercept. This can be shown by solving the quadratic equation formed by setting f(x) = 0 or g(x) = 0. Doing this yields x = -1/3. Therefore, both f(x) and g(x) have one x-intercept at x = -1/3.4

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Answer:

2500×100/2×450

25/2×450

25/900=

36

Answer:

6610

Step-by-step explanation:

We have tan(X) = opposite/ adjacent

tan(QBP) = PQ/BQ

tan(35) = PQ/BQ    ---eq(1)

tan(QAP) = PQ/AQ

tan(20) = \(\frac{PQ}{AB +BQ}\)

\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)

230*tan(20) + PQ*tan(20)*tan(35) = PQ

⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)

⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]

\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)

\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)

PQ = 110.4

≈110

Height above sea level = 6500 + PQ

6500 + 110

= 6610

The slope of a horizontal line is always zero.

What is slope?

The slope of a line is a measure of how steep the line is. It represents the rate at which the y-coordinate of the line changes with respect to the x-coordinate. Symbolically, it is represented by the letter m, and can be calculated using the following formula:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are any two points on the line.

The slope of a horizontal line is always zero. This is because a horizontal line has the same y-coordinate at every point, and therefore, there is no change in the y-coordinate for any change in the x-coordinate.

By definition, the slope of a line is the change in y divided by the change in x. In the case of a horizontal line, the change in y is always zero, since the y-coordinate does not change. So, no matter what value of x you choose, the slope of a horizontal line will always be:

slope = change in y / change in x = 0 / (any non-zero value of x) = 0

So, the slope of a horizontal line is always zero.

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I solved it using my calculator but you can also solve the matrix by hand.

The amount of the loan was $1600.

Given that the Luz an Amity owe $600 interest on a loan after 5 years. The rate of simple interest was 7.5%. We need to find the amount of the loan.

So,

SI = principal × rate × time / 100

Therefore,

600 = principal × 5 × 7.5 / 100

60000 = principal × 37.5

Principal = 60000 / 37.5

Principal = 1600

Hence the amount of the loan was $1600.

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Answer:

64cm³

Step-by-step explanation:

( 4 x 4 x 4) cm x cm x cm

The two prime numbers that add up to 100005, based on the properties of prime numbers would be 2 and 100003.

To find the two prime numbers, the relevant relationship would be  the Goldbach's Conjecture. This posits that every even number greater than 2 can be expressed as the sum of two prime numbers.

So, to write an odd number as the sum of two prime numbers, one of the prime numbers has to be 2 because we know that 2 is the only even prime number.

The other number would therefore be:

= 100005 - 2

= 100003

100003 is a prime number so the two prime numbers are 2 and 100003.

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Answer:

384

Step-by-step explanation:

A=\(6_{2}\)a=6·82=384

Answer:

Part A: $212 Part B: 25 miles

Step-by-step explanation:

f(x)=Total amount earned

x=miles walked

Part A:

f(x)=8x+100

f(14)=8(14)+100

f(14)=212

$212

Part B:

f(x)=8x+100

300=8x+100

-100      -100

200=8x

 8     8

25=x

25 miles

Answer:

x>-3

Step-by-step explanation:

Answer:

x > 3

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The correct answer is A

Answer: 20%

Step-by-step explanation: Annual depreciation = $2,600 * 12 = $31,200

Annual depreciation rate = Annual depreciation /Depreciable costs

= $31,200 / ($188,000 - $32,000)

= 20%

Answer:

55

Step-by-step explanation:

The perimeter of a triangle with vertices A(–3, 5), B(–3, 2), and C(1, 2) is 12 units

Given: the coordinates of the vertices of the triangle as A(–3, 5), B(–3, 2), and C(1, 2).

We can find the perimeter of the triangle by finding the distance between the vertices and we will then sum distances to get the perimeter

The formula for finding the distance between the two points is given by d=√((x2 – x1)² + (y2 – y1)²)

Distance between  vertices A(–3, 5) and B(–3, 2):

d=√((x2 – x1)² + (y2 – y1)²)

where x1 = -3, y1 = 5 and x2 = -3, y2 = 2

d = √((-3 – (-3))² + (2 – 5)²)  

   = √((0)² + (–3 )²) =   √9 = 3

Distance between  vertices A(–3, 5) and  C(1, 2):

d=√((x2 – x1)² + (y2 – y1)²)

where x1 = -3, y1 = 5 and x2 = 1, y2 = 2

d = √((1 – (-3))² + (2 – 5)²)  

  = √((4)² + (–3 )²)

  = √(16+9)  = √25 = 5

Distance between  vertices  B(–3, 2) and  C(1, 2):

d=√((x2 – x1)² + (y2 – y1)²)

where x1 = -3, y1 = 2 and x2 = 1, y2 = 2

d = √((1 – (-3))² + (2 – 2)²)  

  = √((4)² + (0 )²)

  = √16 = 4

Perimeter = 3 + 5 + 4 = 12 units

Therefore, the perimeter of the triangle is 12 units

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Answer:20

Step-by-step explanation:this is wrong

Answer:

40

Step-by-step explanation:

subtract median of dogs and median of cats

The walkway is 11 feet 6 inches long.

To find the length of the walkway, we need to add the lengths of the two boards.

The first board is 6 feet 11 inches long, which can be written as 6 + 11/12 feet using the fact that there are 12 inches in a foot.

The second board is 5 feet 7 inches long, which can be written as 5 + 7/12 feet.

Now we can add the lengths of the two boards:

6 + 11/12 feet + 5 + 7/12 feet

= 11 + 6/12 feet

=11 + 1/2 feet

Therefore, the walkway is 11 feet 6 inches long.

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Answer:

  y = -5/2x +1

Step-by-step explanation:

You want the slope-intercept form equation for the line through the point (-2, 6) that is parallel to 5x +2y = -4.

The equation of a parallel line can be the same as the given equation, except for the constant. The new constant can be found by substituting the given point coordinates:

  5(-2) +2(6) = c

  -10 +12 = c

  2 = c

Now we know the equation of the parallel line can be written as ...

  5x +2y = 2

Solving for y puts this in slope-intercept form:

  2y = -5x +2 . . . . . . . . subtract 5x

  y = -5/2x +1 . . . . . . . . divide by 2

We don't know what your boxes look like, but we can separate the numbers to make it look like this:

  \(\boxed{y=\dfrac{-5}{2}x+1}\)

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