Represent the

proportional relationship $2 for 5 ears of

corn and $4 for 10 ears of corn using

another representation.

f(x)=3x+5

f(-2)=3×(-2)+5

= -6+5

=-1

f(-1)=3×(-1)+5

=-3+5

=2

f(0)=3×0+5

=0+5

=5

f(1)=3×1+5

=3+5

=8

f(2)=3×2+5

=6+5

=11

The equation of a circle with center  (1,-2) and radius 2 is ( x - 1 )² + ( y + 2 )² = 4.

The standard form of the circle is x² + y² = r²

Where r is the radius.

h and k is the horizontal and vertical translation which represent the center of the circle..

Hence, the formula is derived from the distance formula where the distance is between the center and every point on the circle is equal to the length of the radius.

( x - h )² + ( y - k )² = r²

Given that;

Center: (1,-2)

Plug the given values into the equation and simplify.

( x - h )² + ( y - k )² = r²

( x - 1 )² + ( y - (-2) )² = 2²

( x - 1 )² + ( y + 2 )² = 2²

( x - 1 )² + ( y + 2 )² = 4

Therefore, the equation of the circle is ( x - 1 )² + ( y + 2 )² = 4

Learn more  about equation of circle here: https://brainly.com/question/29288238

#SPJ1

To find the work done by the force, we need to integrate the product of the force and the distance over the range of x.

Given that the force is F(x) = x^2 * 9.24 N and the distance is x, we have:

Work = ∫ F(x) * dx
     = ∫ (x^2 * 9.24) * dx
     = 9.24 ∫ x^2 dx
     = 9.24 * [x^3 / 3]

Evaluating the integral between the limits of 0 and 6 (since the distance is given as x), we get:

Work = 9.24 * [(6^3 / 3) - (0^3 / 3)]
    = 9.24 * (72)
    = 665.28 Joules

Therefore, the work done by the force is 665.28 Joules.

To find the work done by the force, we need to calculate the integral of the force function with respect to distance. Given the force function F(x) = 6x, and the distance x ∈ [0, 2.9], we can set up the integral as follows:

Work = ∫(6x dx) from 0 to 2.9

To find the integral, we'll apply the power rule for integration:

∫(6x dx) = 3x^2 + C

Now, we need to evaluate the definite integral from 0 to 2.9:

Work = (3 * (2.9)^2) - (3 * (0)^2) = 3 * (8.41) = 25.23 N·m

So, the work done by the force is approximately 25.23 N·m.

Learn more about integration here: brainly.com/question/18125359

#SPJ11

Answer:

#13. line QR is 26.

#14. a) x = 2 b) m = 6

Step-by-step explanation:

13. We can use the Pythagorean therom: a^2 + b^2 = c^2

We will substitue PQ for a and PR for b

10^2 + 24^2  = c^2

100 + 576 = c^2

100 + 576 = 676

Then, we find the square root of 676, which is 26.

14. a) 3(2x -1) = 9

we first use distributive property:

6x - 3 = 9

then we add 3 to both sides to counteract the -3:

6x = 12

we divide both sides by 6 to get x alone:

x = 2

b) 3m - 12 = 6

we add 12 to both sides to counteract the -12:

3m = 18

we divide both sides by 3:

m = 6

Answer:

Step-by-step explanation:  For this question, we need to make a table first.

For which we'll assume values of x and y.

Let the value of x be 0 then y will be 5

if value of x=3 then y=6

hence, we arrive at two points that are satisfying the equation.

Kindly refer to the attachment

another question about similar fashion has been solved on this link:

equation question-https://brainly.com/question/13841596

Answer:

0

Step-by-step explanation:

Total outcomes = 6

Favourable outcomes = 0(As there is no 7 in a dice)

Probability = Favourable Outcome/Total outcomes

=> 0/6

=> 0

The topic that is typically discussed when referring to the need for relative figures as opposed to absolute figures is comparative analysis or relative measures.

Comparative analysis involves comparing data or figures in relation to other data or a reference point, rather than focusing solely on the absolute values. It helps provide context and a better understanding of the data by considering factors such as proportions, ratios, percentages, or changes over time. Relative figures are particularly important when dealing with data that varies significantly in scale or when comparing data across different contexts or populations. By using relative figures, researchers or analysts can gain insights into patterns, trends, and relationships that may not be evident when looking at absolute figures alone.

Know more about comparative analysis here;

https://brainly.com/question/13828476

#SPJ11

If the whole diameter of sphere is 6 inch(means radius is 3 inch) & thickness of material is 1 inch, so the radius of the hollow part should be 2 inch (3-1=2)

The total volume of the ball will be;

= Total volume - Volume of hollow part

= 4/3πr³ - 4/3πr³

= 4/3 × 3.14 × (3)³ - 4/3×3.14×(2)³

= 4 × 3.14 × 9 - 4/3 × 3.14 × 8

= 113.04 - 33.52

= 79.52

If the density of the material is 3.25 g/in3, then the density of 79.52 inch³ should be;

= 79.52 × 3.25

= 258.44 g

Now, if there are 8 spheres in one box, the weight if box will be;

= 258.44 × 8

= 2,067.52 g

_____________________________

Ahh! Finally done with this, if you have any doubt just do ask me :)

The point where marginal cost equals $15 is at the production of the 7th pizza. Therefore, the firm should produce 7 pizzas.

The firm's shut-down price is the price at which the firm is indifferent between producing and shutting down.

Using the table provided, we can calculate the missing values:

Variable Cost:

For 0 pizzas, the variable cost is $0.

For 1 pizza, the variable cost is $10.

For 2 pizzas, the variable cost is $12.

For 3 pizzas, the variable cost is $2.

For 4 pizzas, the variable cost is $1.

For 5 pizzas, the variable cost is $2.

For 6 pizzas, the variable cost is $3.

For 7 pizzas, the variable cost is $13.

For 8 pizzas, the variable cost is $16.

For 9 pizzas, the variable cost is $3.

For 10 pizzas, the variable cost is $6.

For 11 pizzas, the variable cost is $4.

Total Cost: To calculate the total cost, we simply add the variable cost and the fixed cost for each level of output. The fixed cost is not given in the table, so we cannot calculate the total cost.

Average Variable Cost:

To calculate the average variable cost, we divide the variable cost by the level of output. For example, the average variable cost for 1 pizza is $10/1 = $10.

Average Fixed Cost:To calculate the average fixed cost, we divide the fixed cost by the level of output.

Average Total Cost: To calculate the average total cost, we add the average variable cost and the average fixed cost. The firm should produce pizzas up to the point where marginal cost equals marginal revenue.

This is the point where the firm maximizes its profit. From the table, we can see that the marginal cost is increasing as output increases, while the marginal revenue remains constant at $15.

Learn more about variable cost at:

brainly.com/question/26373444

#SPJ1

We prove linear dependent and linear independent vectors as follows:

(a) (i) To prove that the vectors u, v, and w are linearly independent, we need to show that the only solution to the equation au + bv + c*w = 0 is a = b = c = 0. Here, a, b, and c are scalars.

Let's assume that there exist some non-zero values of a, b, and c that satisfy the equation au + bv + c*w = 0. Then we have:

au + bv + cw = a(1,-1,0) + b*(0,1,-2) + c*(2,3,4) = (a + 2c, -a + b + 3c, -2b + 4c) = (0,0,0)

This gives us a system of three linear equations:

a + 2c = 0

-a + b + 3c = 0

-2b + 4c = 0

We can solve this system by using row operations:

The resulting row-echelon form is:

1 0 0 | -4

0 1 0 | 2

0 0 1 | -1

Since the system has a unique solution a = -4, b = 2, and c = -1, we can conclude that the vectors u, v, and w are linearly independent.

(ii) To prove that the vectors u, v, and w are linearly dependent, we need to show that there exist some non-zero values of a, b, and c that satisfy the equation au + bv + c*w = 0.

Let's assume that such values exist. Then we have:

au + bv + cw = a(1,-1,0) + b*(0,1,-2) + c*(2,1,-6) = (a + 2c, -a + b + c, -2b - 6c) = (0,0,0)

This gives us a system of three linear equations:

a + 2c = 0

-a + b + c = 0

-2b - 6c = 0

We can solve this system by using row operations:

The resulting row-echelon form is:

1 0 -2 | 0

0 1 2 | 0

0 0 0 | 0

Since the system has infinitely many solutions (e.g., a = 2t, b = -2t, and c = t for any non-zero scalar t), we can conclude that the vectors u, v, and w are linearly dependent.

(b) The dot product of two vectors u and v is given by u · v = ‖u‖ ‖v‖ cosθ, where θ is the angle between the two vectors. Since ‖u‖ and ‖v‖ are given, the maximum and minimum values of u · v will depend on the angle θ.

The maximum value of cosθ is 1, which occurs when θ = 0°. Therefore, the maximum value of u · v

Know more about linear dependent and independent vectors here:

https://brainly.com/question/30556318

#SPJ11

Answer:

17s+20t

Step-by-step explanation:

A symmetrical distribution of exam scores in a college course indicates that the student's scores are evenly distributed across the entire range of scores. This suggests that about an equal number of students had relatively high and relatively low scores.

Correct answer will be b) About an equal number of students had relatively high and relatively low scores.

And that there is no single group that overwhelmingly outperformed or underperformed the others. Furthermore, it indicates that there were a substantial number of students who achieved high scores, as well as a substantial number who achieved low scores.

This type of even distribution of scores is often seen when students are equally prepared, and when the exam is designed to be neither too difficult nor too simple.

In conclusion, a symmetrical distribution of exam scores suggests that the students were similarly prepared and that the exam was appropriately challenging.

know more about symmetrical distribution here

https://brainly.com/question/28285791#

#SPJ11

Answer:

slope is 2

Step-by-step explanation:

Pick any two points

say point (0,0) and point (2, 4)

to find slope, subtract the x and y coordinates as a fraction.

y on the top, x on the bottom

y/x = (4 -0)/ (2-0) = 4/2 = 2

Answer:

1/10???????????????????????

1)The expression 4x^2-16x+12/x^2-9 is undefined when the denominator, x^2-9, equals zero because division by zero is undefined.

x^2-9 equals zero when x equals 3 or x equals -3. Therefore, the expression is undefined at x = 3 and x = -3. In all other cases, the expression is defined.

2) The given expression is:

(5-2x)/(x+2) + x^2/(x^2-4) - 5

To simplify this expression, we need to first find the LCD (least common denominator) of the two fractions. The denominator of the first fraction is x+2, and the denominator of the second fraction is x^2-4, which can be factored as (x+2)(x-2). So the LCD is (x+2)(x-2). Now we can rewrite the expression with this common denominator:

[(5-2x)(x-2) + x^2(x+2) - 5(x+2)(x-2)] / [(x+2)(x-2)]

Expanding the brackets and simplifying, we get:

(-x^3 - 3x^2 - 3x + 5) / [(x+2)(x-2)]

This expression is undefined when the denominator, (x+2)(x-2), equals zero because division by zero is undefined.

(x+2)(x-2) equals zero when x equals -2 or x equals 2. Therefore, the expression is undefined at x = -2 and x = 2. In all other cases, the expression is defined.

#SPJ1

The shape of the distribution of the number of siblings can vary depending on the specific data set.

However, if we are considering the general case, the most common shape of the distribution is likely to be unimodal and skewed to the right.

This means that the majority of individuals are likely to have fewer siblings,

and as the number of siblings increases,

the frequency of individuals with that number decreases.

The distribution may also have a long tail on the right side,

indicating a few individuals with a significantly larger number of siblings.

However, it is important to note that this is just a general observation, and in specific cases,

the distribution may be different.

To know more about distribution visit:

https://brainly.com/question/33255942

#SPJ11

Answer:

Explanation:

Circumference: 18.84

π: 3.14

18.84 ÷ 3.14

The area of the trapezium ABCD is 1623 square meters.

To find the area of the trapezium ABCD, we need to use the given side lengths and altitude.

The formula for the area of a trapezium is:

Area = (sum of parallel sides) x (altitude) / 2

In this case, the parallel sides are AB and CD, and the altitude is AD. We know that AB = 45 and AD = 41. To find CD, we can use the fact that BC is parallel to AD, so the height of the trapezium splits BC into two segments that are proportional to AD and CD. Let's call the length of CD x. Then we have:

AD/BC = AD/(AB - CD) = 41/(45 - x)

Solving for x, we get:

x= 75 - (45 x 41)/75

= 39

Therefore, CD = 39.

Now we can plug in the values to the formula for the area of a trapezium:

Area = (sum of parallel sides) x (altitude) / 2

= (AB + CD) x AD / 2

= (45 + 39) x 41 / 2

= 1623 square meters

Therefore, the area of the trapezium ABCD is 1623 square meters.

To know more about Area, click here,

brainly.com/question/27683633

#SPJ1

Given:

Use the rules for exponents, according to the steps below.

Step 01: Use The Power Rule for Exponents.

According to this rule:

Then,

Substituting it, we have:

Step 02: Use The Quotient Rule of Exponents.

According to this rule:

Then,

Answer: p⁹.

\(d^5\)

Recall the Law of Exponents:

\(\frac{a^m}{a^n} = a^{m -n}\\\)

Rewriting \(\frac{d^9}{d^4}\\\):

\(\frac{d^9}{d^4} \\ d^{9 -4} \\ d^5\)

Answer:

-3 and -7

Step-by-step explanation:

x^2+10x+21=0

(x+3)(x+7)=0

x=-3

x= -7

Answer: 21 hours

Step-by-step explanation:

i’m not sure how to solve it i just guessed and got it right

Answer:

21

Step-by-step explanation:

a) the expression of P(t) describing the population of crocodiles at any time t is: P(t) = 10 * e\(^{(0.1823t)}\)

b) it would take approximately 4.522 time units (months or years, depending on the unit of t) for the population of crocodiles to reach 30.

a) To determine the expression of P(t) describing the population of crocodiles at any time t, we can use the formula for exponential growth, which states that P(t) = P0 * e\(^{(rt)}\) where P0 is the initial population, r is the growth rate, and t is the time.

Given that the initial population P0 is 10 crocodiles and the population after 6 months is 12 crocodiles, we can use this information to find the value of r.

Using the formula P(t) = P0 * e\(^{(rt)}\) and plugging in the values, we have:

12 = 10 * e\(^{(r * (6/12))}\)

Simplifying further:

12/10 = e\(^{(r/2)}\)

1.2 = e\(^{(r/2)}\)

To find the value of r, we can take the natural logarithm of both sides:

ln(1.2) = r/2

r/2 ≈ 0.1823

Therefore, the expression of P(t) describing the population of crocodiles at any time t is:

P(t) = 10 * e\(^{(0.1823t)}\)

b) To find the population of crocodile species A after 2 years, we substitute t = 2 into the expression we derived in part a:

P(2) = 10 * e\(^{(0.1823 * 2)}\)

P(2) ≈ 10 * e\(^{(0.3646)}\)

P(2) ≈ 10 * 1.4406

P(2) ≈ 14.406

Therefore, the population of crocodile species A after 2 years is approximately 14.406 crocodiles.

c) To determine how long it would take for the population of crocodiles to reach 30, we can set the population P(t) equal to 30 and solve for t in the expression we derived in part a:

30 = 10 * e\(^{(0.1823t)}\)

3 = e\(^{(0.1823t)}\)

Taking the natural logarithm of both sides:

ln(3) = 0.1823t

t = ln(3) / 0.1823

t ≈ 4.522

Therefore, it would take approximately 4.522 time units (months or years, depending on the unit of t) for the population of crocodiles to reach 30.

Learn more about expression at https://brainly.com/question/1859113

#SPJ4

Answer:

This equation has one solution, where x is equal to nine.

Step-by-step explanation:

\(10(x + 4) - 3 = 14x + 1\\10x + 40 - 3 = 14x + 1\\14x - 10x = 40 - 3 - 1\\4x = 36\\x = 9\)

Answer:

0.71428571

Step-by-step explanation:

Answer:5.7

Step-by-step explanation:

The only regular quadrilateral (congruent sides and angles) is the square. A square is a quadrilateral with four congruent sides and four congruent angles, each measuring 90 degrees.

It is also a type of rectangle and a type of rhombus, as it has all the properties of both shapes.Regular polygons are polygons with all sides and angles congruent. In general, a regular polygon with n sides has n congruent sides and n congruent angles. For example, a regular pentagon has five congruent sides and five congruent angles, and a regular hexagon has six congruent sides and six congruent angles.

However, among quadrilaterals, only the square can have all sides and angles congruent, making it the only regular quadrilateral. Other quadrilaterals may have congruent sides or congruent angles, but not both.

To know more about quadrilateral  click here

brainly.com/question/3642328

#SPJ11

The required number of combinations possible is 6 and list has been evaluated below in the answer section.

Given that,
the number cube lands on a number less than 4, then Samone wins 5 tickets. If the number cube lands on a number less than 4 and the coin heads, then Samone wins 20 tickets.
To Create a list to represent the possible outcomes of Samone winning 5 tickets and 20 tickets.

In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In a combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.

Here,
Samone  wins     cube land less than 4     Coin Tossed

5 tickets                 1, 2, 3                             tail, tail, tail
20 tickets                1, 2, 3                            head, head, head

Thus, the required number of combination possible is 6.

Learn more about permutations and combinations here: https://brainly.com/question/2295036
#SPJ1