what is the function header of the following function?

Answer:

A graph has quantity on the x-axis and price on the y-axis. A supply line goes through (10, 25), (20, 30), (30, 35), (40, 40).A graph has quantity on the x-axis and price on the y-axis. A demand line goes through (10, 40), (20, 30), (30, 20), (40, 10). Based on the supply graph and the demand graph shown above, what is the price at the point of equilibrium? a. 20 b. 30 c. 40 d. There is not enough information given to determine the point of equilibrium. Please select the best answer from the choices provided A B C D

At 6% nominal interest, the amount should you receive today is (d) $1600.

The word "total" refers to the addition of numbers or the destruction of something, and a total is a whole or complete sum.

The present value of $2007 received in 5 years can be calculated using the formula:

PV = FV / (1 + r)^t

Where:

PV is the present value

FV is the future value ($2007)

r is the nominal interest rate (6%)

t is the time period (5 years)

So, PV = $2007 / (1 + 0.06)^5 = $1600

Therefore, you should receive $1600 today if you want an equivalent amount.

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Basically in this question we will apply product rule of diffrentiation .

f(t) = 3t (t-6)

f'(t) = (3t)'.(t-6) +(t-6)'.(3t)

f'(t) = 3(1). (t-6) + (1).3t

f'(t) = 3t-18 +3t

Final Answer - f'(t) = 6t -18

Differentiating the given function. f(t) = 3 t (t − 6) gives f'(t) = 6t - 18 using the product rule of differentiation.

Given that, f(t) = 3t.(t-6)

To differentiate the given function we use product rule in order to simplify the differentiation.

Divide the function into two different products and then differentiate :

f(t) = 3t (t-6)

f'(t) = (3t)'.(t-6) +(t-6)'.(3t)

f'(t) = 3(1). (t-6) + (1).3t

f'(t) = 3t-18 +3t               (or)

expand the given f(t) =  3t.(t-6)

                                   = 3t^2 - 18 t

we have , f'(x) = n.x^(n-1)   if    f(x) = x^n

differentiating f(t) = f'(t) = 2(3t) - 18

                                     = 6t - 18

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The ty plane the hypothesis of theorem are satisfied

The hypothesis of a theorem is a statement or assumption that is made in order to prove a mathematical result.

The hypothesis of the Tychonoff theorem is satisfied in a variety of different spaces, including compact spaces and metrizable spaces.

This theorem is important because it provides a useful tool for understanding the properties of topological spaces, which are spaces that have certain structures that allow for the study of continuous functions and mappings.

In summary, the hypothesis of the Tychonoff theorem is a necessary condition for the theorem to be proven and is satisfied in a variety of different spaces.

Understanding the hypothesis and the spaces in which it is satisfied is crucial for understanding the theorem and its applications in mathematics.

Complete Question:

State where in the ty-plane the hypotheses of Theorem

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The measurement of the remaining two sides of the triangle be 4cm and 6cm.

Given :- Perimeter of triangle = 18m.

Area of triangle = √135m².

One side of triangle = 8m.

Triangle  is a plane figure with three straight sides and three angles.

Let the equation be Area of ∆ = 1/2bh

= 1/2 ab sin C = 1/2 bc sin A = 1/2 ca sin B

= √( s(s-a)(s-b)(s-c) ) [ where s = (a + b + c)/2 ]

By using Heron's formula to get the Area of triangle,

s = (Perimeter /2) = (18/2) = 9m.

Putting values now we get :-

√(s(s-a)(s-b)(s-c) ) = √135

substitute the values in the above equation, we get

√[9(9-8)(9-b)(9-c)] = √135

Squaring Both sides we get,

9 × 1 × (9-b)(9-c) = (√135)² = 135

Dividing both sides by 9, we get,

(9-b)(9-c) = 15

81 - 9c - 9b + bc = 15

simplifying the above equation, we get

81 - 9(b + c) + bc = 15

9(b + c) - bc = 81 - 15

9(b + c) - bc = 66 -------- (1).

Also, if Rest two sides are b and c, we get,

→ 8 + b + c = 18

→ (b + c) = 18 - 8 = 10 cm. ------ (2).

Putting value of (2) in (1) , we get,

→ 9 × 10 - bc = 66

simplifying the above equation, we get

→ bc = 90 - 66

→ bc = 24 ------------ (3).

We do Factors of (3), we just have to check now, which satisfy Equation (2) also . (sum of Factors will be 10).

24 = ( 1, 24) , (24, 1), ( 2,12), (12,2) , (3,8) ,(8,3) , (4,6),(6,4)

We can see (4,6) or (6,4) Satisfy the (2).

Therefore, the measurement of the remaining two sides of the triangle be 4cm and 6cm.

The complete question is:

the perimeter of a triangular garden is 18 m. if its area is under root 135 m^2 and one of the tree sides is 8 m, find the remaining two sides

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This is an example of an isosceles triangle. An isosceles triangle is a triangle with two equal sides and two equal angles.

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The population of foxes in the preserve after 42 years will be:

1620 foxes.

The function "y = 60 • 3^t" models the population growth of foxes in a wildlife preserve.

"y" represents the population size, "60" is the initial population size, "3" is the factor by which the population triples, and "t" is the number of 14-year periods that have passed.

In this case, we are told that 42 years have passed, so we can calculate the number of 14-year periods as "t = 42/14 = 3".

Substituting this value of "t" into the function, we get: So, t = 42/14 = 3

Substituting that into the function:

So, after 42 years, the population of foxes in the preserve will have grown to 1620 foxes.

Complete Question:

"A population of 60 foxes in a wildlife preserve triples in size every 14 years. The function y = 60 • 3^x models the population growth, where x is the number of 14-year periods. How many foxes will there be after 42 years?"

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Answer:

$19.20

Step-by-step explanation:

The discount per pound is $0.20, so the cost per pound after the discount is $5.00 - $0.20 = $4.80 per pound.

You want to buy 4 pounds of candy, so the total cost before tax is 4 * $4.80 = $19.20

So, your total cost for 4 pounds of candy will be $19.20.

Answer:

total cost be, excluding tax = $19.20

Step-by-step explanation:

DISCOUNT:  $0.20 x 4 pounds = $ 0.80

Cost of 4 pounds   $5 x4 = $20

      $20 - $0.80 =   $19.20

Answer:

20 miles in 1/2.  That would be 40 miles per hour

Step-by-step explanation:

6 ÷ 1/8 is the same at 6 x 8 = 48

11 ÷1/4 is the same as 11 x 4 = 44

16 x 3/8 is the same as 16 x 8/3 = 42 2/3

20 ÷ 1/2 is the same as 20 x 3 = 40

The break-even point in units can be calculated if the sales price per unit (P) is known. In conclusion, the break-even point in units is an essential calculation that helps companies understand their financial performance and determine the minimum level of sales they need to achieve to cover their costs and start generating a profit.

Break-even point in units = Fixed costs / (P - Variable expenses per unit)

= Fixed costs / (P - Variable expenses / Sales)

The break-even point is a crucial calculation in the field of business and finance, as it represents the level of sales at which a company's expenses and revenue are equal, and there is no profit or loss. In this scenario, Hurst Ltd's break-even point in units can be calculated based on its sales, variable expenses, and fixed costs.

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Answer:

The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. Since the line given in the question is parallel to y = 1/4x + 7, we know that the line has a slope of m = 1/4.

To find the equation of the line that passes through (4,-1), we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1).

Therefore, the equation of the line passing through (4,-1) and parallel to y = 1/4x + 7 is:

y - (-1) = 1/4(x - 4)

y + 1 = 1/4x + 1

This is the equation of a line passing through (4,-1) and parallel to y = 1/4x + 7.

The length of c→ is equal to the sum of the lengths of a→ and b→ when c→ is a perpendicular vector to both a→ and b→, meaning that c→ is at a right angle to both a→ and b→.

This is due to the fact that the length of a vector is equal to the length of the hypotenuse of a right triangle, which is the sum of the lengths of the other two sides (a→ and b→). When c→ is perpendicular to both a→ and b→, the right triangle formed by a→, b→, and c→ is a special type of right triangle called a Pythagorean triangle, in which the length of the hypotenuse (c→) is equal to the sum of the lengths of the other two sides (a→ and b→). Thus, the length of c→ is equal to the sum of the lengths of a→ and b→ when c→ is perpendicular to both a→ and b→.

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a)

P (gold or silver) is 0.20

b)

P (not gold) is 0.95

c)

P (silver or bronze) is 0.70

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Color          gold   silver   bronze  white

Probability 0.05   0.15      0.55     0.25

Now,

The probability that the counter is

a)

P (gold or silver)

= 0.05 + 0.15

= 0.20

b)

P (not gold)

= 1 - 0.05

= 0.95

c)

P (silver or bronze)

= 0.15 + 0.55

= 0.70

Thus,

The probabilities are given above.

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The statement "Almost 25% of the weights for brand B are less than the lowest weight for brand A" is not true concerning the comparison of the bag weights for the two brands, 1st option.

Inequalities are mathematical expressions in which neither side is equal. Unlike equations, we compare two values in inequality. In between, the equal sign is replaced by a less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In comparison to Brand B's box plot display, Brand A's rectangular box, as well as the length of the whiskers, are shorter. As a result, Brand A's bag weights are less variable than Brand B's bag weights.

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The full question is:

Which of the following statements is not true concerning the comparison of the bag weights for the two brands?

Almost 25% of the weights for brand B are less than the lowest weight for brand A.

About 50% of the weights for brand A are within the top 25% of the weights for brand B.

More than 75% of the weights for brand A are within the top 50% of the weights for brand B.

More than 75% of the weights for brand A are higher than the top 25% of the weights for brand B.

The unique property of Pythagorean triplets is the square of the hypotenuse is always equal to the sum of the squares of the perpendicular and base.

In a right-angled triangle, its sides, such as hypotenuse, perpendicular, and base are Pythagorean triplets.

Here,
Pythagorean triplet's unique property is that,
The square of the hypotenuse is always equal to the sum of the squares of the perpendicular and base for a right-angled triangle.
hypotenuse² = perpendicular² + base²

Thus, the unique property of Pythagorean triplets is the square of the hypotenuse is always equal to the sum of the squares of the perpendicular and base.

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Answer:

f(n) = 4n - 6

Step-by-step explanation:

the explicit formula for an arithmetic sequence is

f(n) = f(1) + (n - 1)d

where f(1) is the first term and d the common difference

given the recursive formula

f(n) = f(n - 1) + 4

this allows a term in the sequence to be found by adding the common difference d to the previous term.

here f(1) = - 2 and d = 4 , then explicit formula is

f(n) = - 2 + 4(n - 1) = - 2 + 4n - 4 = 4n - 6

The bolded words represents the verbs in the statement as -

People in church prayed, and an angel woke Peter.

Verbs are words that show an action (sing), occurrence (develop), or state of being (exist).

Given is the statement as -

People in church prayed, and an angel woke Peter.

The verbs in the given statement are {bolded words} -

People in church prayed, and an angel woke Peter.

Therefore, the bolded words represents the verbs in the statement as -

People in church prayed, and an angel woke Peter.

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Answer:

To find the numbers 2001, 2002, 2003, 2004, 2005, and 2006 into the circles so that the sum of the numbers on a side of the triangle is always the same, we can start by finding the average of the numbers:

(2001 + 2002 + 2003 + 2004 + 2005 + 2006) / 6 = (12,016) / 6 = 2004

Next, we can place the numbers around the average so that the sum of the numbers on a side of the triangle is as great as possible:

2004

2006 2005

2003 2002 2001

In this configuration, the sum of the numbers on each side of the triangle is 6021.

Answer:45

Step-by-step explanation: So the total measure of an exterior would be 360 so you divide the number of sides on the polygon be 360 and you get 45. (I hoped that helped.)

Answer:

45 degrees

Step-by-step explanation:

A octagon is 360 degrees total and since there is 8 sides you would do 360/8 which gives you 45 degrees

HOPE THIS HELPS

There are 120 ways that the letters from the word "world" can be arranged

It is the ordered arrangement of members belonging to a set with no repeats.

To solve this problem the formula and the permutation procedure we must use is:

nPr = n! / (n-r)!

Where:

Information about the problem:

Applying the permutation formula we have:

nPr = n! / (n-r)!

5P5 = 5! / (5-5)!

5P5 = 5! / 0!

5P5 = 5*4*3*2 / 1

5P5 = 5*4*3*2

5P5 = 120

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(E) Other

To make 144 slices of cake, Emma will need 18 large eggs.

To solve this problem, we need to know how much 2 dozen is.

So, for every 24 slices of cake, 3 eggs are needed.

To figure out how many slices of cake 1 egg can make, we can divide 24 by 3.

Now, for every 8 slices of cake, 1 egg is needed.

Now, taking 144, we can divide that by 8 to get the number of eggs needed.

Therefore, 18 eggs will be needed to make 144 slices of cake.

The parametric equation x = t^2, y = t + 4, -4 ≤ t ≤ 4 is open at right side.

Therefore the answer is Right.

A parametric equation is a set of equations that describes the position of a point in the xy-plane in terms of a third variable, usually called a parameter. In this case, the parametric equations x = t^2 and y = t + 4 describe the position of a point on the xy-plane in terms of the parameter t.

y = t + 4

So t = y - 4

x = t²

So x = (y - 4)²

This is of the form x = 1(y - 4)²

x = a(y – k)2 +h is the sidewise form of a parabola with vertex (h, k). So this parametric form represents a parabola with vertex (0, 4) open at right side.

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For three fair six-sided dice, the possible sum of the faces rolled can be any digit from 3 to 18.the number of sums will be greater than 16 and the minimum number greater than 16 is 17.

For instance the minimum sum occurs when all three dices shows 1 (i.e. 1 + 1 + 1 = 3) and the maximum sum occurs when all three dces shows 6 (i.e. 6 + 6 + 6 = 18).

Thus, there are 16 possible sums when three six-sided dice are rolled.

Therefore, from the pigeonhole principle, the minimum number of times you must throw three fair six-sided dice to ensure that the same sum is rolled twice is 16 + 1 = 17 times.

The pigeonhole principle states that if n items are put into m containers, with n > m > 0, then at least one container must contain more than one item.

That is for our case, given that there are 16 possible sums when three six-sided dice is rolled, for there to be two same sums, the number of sums will be greater than 16 and the minimum number greater than 16 is 17.

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The scalar projection is 42/13, and the vector projection is 42/169⟨-5,12⟩.

The scalar projection of b onto a can be calculated using the formula [tex]\frac{a.b}{|a|}[/tex], and the vector projection of b onto a can be calculated using the formula [tex]\frac{a.b}{|a|^{2} } .a[/tex]. The formula for finding the magnitude of a is |a| = √c²+d² if a = ⟨c,d⟩.

a = ⟨−5, 12⟩, b = ⟨4, 6⟩

a⋅b = ⟨−5, 12⟩⟨4, 6⟩

= -20 + 72

= 42

|a| = √[(-5)² + (12)²]

= √25 + 144

= √169

= 13

The scalar projection is

[tex]\frac{a.b}{|a|}[/tex] = [⟨−5, 12⟩⟨4, 6⟩]/√[(-5)² + (12)²]

= [-20 + 72]/√25 + 144

= 42/√169

= 42/13

The vector projection is

[tex]\frac{a.b}{|a|^{2} } .a[/tex] = [42/(13)²] ⟨−5, 12⟩

= 42/169⟨−5, 12⟩

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The three possibilities for a linear system, in terms of free variables, rank and nullity, are

Three possibilities for a linear system.

No solution    Signal equation 0 = 1

Infinitely many solutions One or more free variables nullity ≥ 1

Unique solution Zero free variables nullity = 0

No Solution. There is no solution to a system of equations exactly when a signal

equation 0 = 1 occurs during the application of swap, multiply and combination

rules. We report the system inconsistent and announce no solution. Infinitely Many Solutions. The situation of infinitely many solutions occurs when

there is at least one free variable to which an invented symbol, say t1, is assigned.

Since this symbol takes the values −∞ < t1 < ∞, there are an infinity of solutions.

The condition rank less than n can replace a reference to the number of free variables.

Unique Solution. There is a unique solution to a system of equations exactly when

zero free variables are present. This is identical to requiring that the number n of

variables equal the number of lead variables, or rank = n.

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a. 8cm ( AD=BD)

b. 8cm ( BD=BC) , Triangle BCD is equilateral

c. 8 cm ( DC = BD)

d Perimeter of ABCD is AD+DC+BC+AB= 8+8+8+11=35

A triangle is a two-dimensional plane shape formed by three sides in the form of straight lines and has three angles. Besides having 3 sides or ribs and angles, the properties of a triangle have an angle of 180°.

The following are the properties of an equilateral triangle, including:

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Answer:

The graph of the function is a parabolic function graph

Step-by-step explanation:

Formula for a parabolic function: ( x - h )² = 4p ( y - k )

where ( h , k ) is the vertex and ( h , k + p ) is the focus

y is the directrix and y = k – p

The equation of the parabola is also given by the equation

y = ax² + bx + c

where a , b , and c are the three coefficients and the parabola is uniquely identified

Given data ,

Let the graph be represented as A

Now , a parabola is a U-shaped curve that is drawn for a quadratic function, f(x) = ax² + bx + c.

The value of the graph increases and decreases in a format according to the quadratic equation.

So , the graph of the function goes downward when value of a < 0 and the graph of the function goes upward when the value of a > 0

The graph of the parabola is downward (or opens down), when the value of a is less than 0, a < 0. The graph of parabola is upward (or opens up) when the value of a is more than 0, a > 0

Therefore , the graph is a parabolic graph

Hence , The graph of the function is a parabolic function graph

aₙ = 0.20aₙ₋₁ + 200 is the recursive formula for the above sequence.

Therefore, choice A is the right one.

Given:

A holiday tree farm is owned by Mahek.

Currently, the site has 800 trees.

200 saplings are planted together with the 20% of the trees that are harvested and sold each year.

a₁ = 800

The recursive formula is,

aₙ = 0.20aₙ₋₁ + 200

Hence, the correct formula is aₙ = 0.20aₙ₋₁ + 200

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