$80 at q $100 at qlet q represent the quantity of output and suppose the price of the good is $125 then the marginal revenue is

The quadratic formula will give us the coordinates of the points of intersection of a line and a quadratic only when the value of the discriminant b^2 - 4ac is either positive or zero .

Given :

the quadratic formula will give us the coordinates of the points of intersection of a line and a quadratic only when the value of the discriminant, is .

Quadratic equation :

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0.

Formula :

= -b ± [tex]\sqrt{b^2 - 4ac / 2a}[/tex]

Discriminant = b^2 - 4ac

if b^2 - 4ac = 0 or positive value then only the formula give us the coordinates of the points of intersection of a line .

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Answer:

148 degrees

Step-by-step explanation:

b/c a line is 180 degrees and the angle given is 32 so 180- 32= 148

and the line is bisected at point p so it is 148 because of alternate interior angles.

The coordinate of the parabola's focus in the following equation, x2=6y, is (0,3/2)

What are Directrix and Focus?

What are a parabola's focus and directrix? Typically speaking, parabolas are the graphs of quadratic functions. They can alternatively be thought of as the collection of all points whose separation from the focus is the same as their separation from a certain line (the directrix).

What are the focus's coordinates?

The focus's coordinates f(0,a)

The equation that we have given is

x^2 = 6y

We are aware that the parabola's general equation is,

x^2 = 4ay

The axis of symmetry is a line that splits the parabola in half and runs through the focus.

We must ascertain the worth of

6y = 4ay

6 = 4a

a = 6/4 = 3/2

The focus' coordinate (0,3/2) is as a result.

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Answer:

No, Franco's calculation is incorrect.

Step-by-step explanation:

No, Franco's calculation is incorrect. The correct answer is 9.37 x 0.1 = 0.937.

When multiplying a decimal number by a decimal number, the decimal point in the product should be placed so that the number of decimal places in the product is equal to the sum of the number of decimal places in the factors. In this case, the number 9.37 has two decimal places, and the number 0.1 has one decimal place. Therefore, the product of 9.37 x 0.1 should have a total of 2 + 1 = 3 decimal places.

To obtain the correct answer, we need to multiply 9.37 x 0.1 using standard long multiplication:

Copy code

9.37

x 0.1

0.937

Therefore, the correct answer is 0.937, not 93.7 as Franco stated.

Answer:

No. This is incorrect.

Step-by-step explanation:

9.37 × 1 = 9.37

Times by 1 the number stays the same.

If you multiply by 0.1 the decimal will move one place and the 9.37 should get smaller! The sentence in the problem shows 93.7 which is bigger.

9.37 × 10 = 93.7

9.37 × 0.1 = 0.937

Mathematically, the balance on Howard Gessner's American Express card on September 1 is $360.63.

The ending balance on September 1 is determined using the mathematical operations of addition, subtraction, and multiplication (for the finance charge).

The finance charge is the interest and other fees paid for borrowing credit.

The finance charge is always based on a percentage, called the annual or monthly percentage rate (APR or MPR).

In this situation, the monthly percentage rate is applied to the unpaid balance (multiplication) at the end of August, to determine the finance charge, which is added to the unpaid balance to compute the September 1 balance.

August 1 Balance =        $543.27

Purchases                        201.25

Returns                            (89.22)

Payments                      (300.00)

Unpaid balance           $355.30

Finance charge                  5.33 ($355.30 x 1.5%)

September 1 Balance $360.63

Thus, using mathematical operations, the balance on September 1 is $360.63.

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Answer:

x = 3+y

Step-by-step explanation:

is your ans .................

Answer:

Factored form is (x - 5) (x² + 5x + 25)

Step-by-step explanation:

You can get the factors directly by using the formula for a³ - b³.

Between x=-1 and x=1, the average rate of change is 1.

It represents the average change in the function's per-unit value during that time period. Calculating the average rate of change is very helpful for tracking changes in measurable parameters like average speed or average velocity. As the slope of the straight line that links the two spots, the average rate of change between the two points is determined. Use the formula:

(f(b)-f(a))/(b-a) to get the average rate of change of f(x) between x=a and x=b.

Given line in the figure passes through the points A(4, 0), B(-1, -5)

Let the  equation of the line be:

y=mx+ c

Slope m=(-5-0)/(-1-4)

m=1

Therefore, y=x+ c

It passes through (4, 0)

y+ c=0

c=-4

y=x-4=f(x)

f(-1)= -1-4=-5

f(1)= 1-4=-3

The average rate of change=(f(b)-f(a))/(b-a)

=(f(1)-f(-1))/1-(-1)

= -3-(-5)/(1+1)

=2/2

=1

Therefore, Between x=-1 and x=1, the average rate of change is 1.

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Answer:

A

Step-by-step explanation:

The answer is option A

Hope this helps :)

Since Amy's rent is 60 percent of the budget for Rent, Utilities, and Food, she will have $853 to spend on entertainment each month.

The total budget for rent, utilities, and food for nine months is given as $12,798.

Using the mathematical operation of multiplication, the proportion that belongs to rent alone is $7,678.80, representing 60%.

This rental proportion is divided by 9 to determine the monthly budget for rent, which will then be spent on entertainment.

The total budget for rent, utilities, and food for nine months = $12,798

The percentage of the budget for rent = 60%

The amount for rent for nine months = $7,678.80 ($12,798 x 60%)

The monthly rent amount is $853.20 ($7,678.80/9)

Thus, we can conclude that Amy will spend $853 monthly on entertainment if she saves the rent budget.

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The percentage of the rent to the total rent, utilities, and food budget is 60%.

Rounding to seven decimal places, the probability that one individual would be selected by all witnesses is 0.0000128.

Six different witnesses chose the same individual from a lineup in a homicide case. There were 5 guys in the lineup. The likelihood that each of the six witnesses would choose the same person if the identifications were done based just on guesswork.

P = 1 ÷ 5 is the likelihood that a witness will choose a certain individual at random.

The likelihood that all seven witnesses would select the same subject is P = [tex](\frac{1}{5})^{7}[/tex]= 0.0000128.

Simply put, the probability is the likelihood that something will occur. We can discuss the probabilities of different outcomes to determine how likely they are if we are unclear about how an event will turn out.

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Answer:

[tex]x = -2[/tex]

Step-by-step explanation:

[tex]\textsf {Square both sides:}\\\\(\sqrt{3x+12} )^2 = 3x + 12\\\\(\sqrt{x+8} )^2 = x + 8[/tex]

(The square of the square root of a value is the value itself

[tex](\sqrt{x} )^2 \;is\;x[/tex])

The original identity then becomes
[tex]3x + 12 = x + 8\\\\3x - x = 8 - 12\\\\2x = -4\\\\x = -4/2\\\\x = -2[/tex]

Answer: 6,250

Step-by-step explanation: As the equation states there are 25 boxes with 250 packs of ketchup take the 25 boxes and multiply the 250 packets

250x25=6,250

Answer:

X=54

Step-by-step explanation:

equate both the equations since angles of opposite sides are equal

2x+2=3x-52

3x-2x= 52+2

x=54

answer:

x=54

Step-by-step explanation:

2x+2=3x-52

move the 2x to 3x because x can't be negative

and add 52 to 2 so x=54

Answer:

Do u like m&m because I do

The area of each section is 3/4 square feet. To solve the give question use division operation.

What is mixed fraction?

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder.

Given that the area of the garden is [tex]5\frac{1}{4}[/tex] square feet.

Now convert the mixed fraction with improper fraction:

[tex]5\frac{1}{4}[/tex] = [(5×4) + 1]/4

[tex]5\frac{1}{4}[/tex] = 21/4

We have to divide the area 7 equal area.

Thus divide 21/4 by 7.

21/4 ÷ 7

To convert the division sign into multiplication sign, take the reciprocal of 7:

21/4 × 1/7

= (21 × 1)/(4 × 7)

Divide the denominator and numerator by 7:

= 3/4

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The Local maxima and minima will be at X = 0 , 4 , -5 and point of inflation will be at [tex]\frac{(-1 + \sqrt{61})}{3},[/tex] [tex]\frac{(-1 - \sqrt{61})}{3}[/tex].

The curve of a function has peaks and troughs called maxima and minima. A function may have any number of peaks and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph. Maxima will be the curve's highest point within the specified range, while minima will be its lowest.

Extrema is the result of maxima and minima combined. The graph in the graphic below shows several peaks and falls. We obtain the function's maximum and lowest values at x = a and 0 respectively, and at x = b and c respectively. The valleys are the minima and all the peaks are the maximum.

The peaks and minima of the function that appear in a certain interval are known as local maxima and minima. The value of a function at a place in a certain interval for which the values of the function near that point are always smaller than the value of the function at that point would be considered a local maximum. Local minima, on the other hand, would be the value of the function at a location where the values of the function nearby are higher than the value of the function at that location.

When the concavity of a function's graph (or picture) changes, a point of inflection is identified. We need to determine where the second derivative of the function switches from negative to positive, or vice versa, in order to determine this in algebra. So, we calculate the provided function's second derivative.

The fuction is :

[tex]3x^{4} + 4x^{3} -120x^{2} + 120[/tex]

So for local Maxima and minima first derivatives should be zero

Therefore,

[tex]\frac{d}{dx}\\[/tex] ([tex]3x^{4} + 4x^{3} -120x^{2} + 120[/tex] ) = 0

⇒ [tex]12x^{3} + 12x^{2} - 240x = 0[/tex]

⇒ [tex]x^{3} + x^{2} - 20x = 0[/tex]

⇒[tex]x(x^{2} + x - 20) = 0 \\[/tex]

⇒x(x-4)(x+5) = 0

For x = 0, 4 , -5 there is a local maxima or minima.

Now for Point of Inflation second derivative is zero

Therefore,

[tex]\frac{d^{2} }{dx^{2} }[/tex] ( [tex]3x^{4} + 4x^{3} -120x^{2} + 120[/tex]) = 0

⇒  [tex]\frac{d}{dx}[/tex][tex]12x^{3} + 12x^{2} - 240x = 0[/tex]

⇒ [tex]36x^{2} + 24x - 240 = 0[/tex]

⇒[tex]3x^{2} + 2x - 20 = 0[/tex]

⇒ x = [tex]\frac{(-1 + \sqrt{61})}{3},[/tex] [tex]\frac{(-1 - \sqrt{61})}{3}[/tex]

So the point of inflations are [tex]\frac{(-1 + \sqrt{61})}{3},[/tex] [tex]\frac{(-1 - \sqrt{61})}{3}[/tex].

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Answer: x=22

Step-by-step explanation:

Based on the given figure, we can tell that 2x and 44 are vertical angles. Vertical angles are congruent to each other, so we can set them equal to each other.

2x=44           [divide both sides by 2]

x=22

Therefore, x=22.

The greatest number of snack bags is 10.

The largest of all the common factors between two or more numbers is known as the Highest Common Factor (HCF). It is also known as the Greatest Common Element (GCF).

HCF is a fundamental method that allows you to equally distribute items throughout a group or set.

We can use the idea of HCF to determine the same when you are organizing a party and want to make sure that nothing is wasted or you require a proper calculation.

Here we have

Number of carrots = 75

Number of celery sticks = 40

Here we are making snack bags such that each bag contains the same combination of carrot and celery sticks.

To find the greatest number of snack bags we need to find HCF of 70 and 40 as given below

Write given numbers as the product of prime numbers

=> 70 = 2 × 5 × 7

=> 40 = 2 × 2 × 2 × 5  

List out the common factors

=> 2 × 5  

=> HCF (70, 40) = 10

Therefore,

The greatest number of snack bags is 10.

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The probability of those that favors building the health center is 0.196

The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event. The formula for probability is given by; P(E) = Number of Favorable Outcomes/Number of total outcomes.

In a recent survey, 70% of the community favored building a health center in their neighborhood. If 14 citizens are chosen, find the probability that exactly 8 of them favor the building of the health center.

According to the scenario, 70% of the community favoured in building a health centre.

Hence , p=0.7.

In order to find the probability, binomial theorem will be used as follows :

= 0.196

Hence, The probability is 0.196

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After using trigonometric function the value of to the nearest tenth digit is 11.11

What is Trigonometric function ?

Trigonometric functions are mathematical functions that are used to describe relationships between certain angles and lengths in a triangle. They are based on the ratios of the sides of a right triangle and are used in a variety of applications including surveying, navigation, engineering, and physics. Trigonometric functions are commonly referred to as sine, cosine, tangent, cotangent, secant, and cosecant. Each of these functions can be used to calculate the angle of a triangle, the length of the sides, or the area of the triangle.

Function of Sine

The ratio of the opposing side's length to the hypotenuse is known as an angle's sine function.
Sin a =Opp/Hypot = CB/CA

Cos Function
The cosine of an angle is the ratio of the neighbouring side's length to the hypotenuse's length.
Adjacent/Hypotenuse = AB/CA is the cosine of.

Functional Tan
The ratio of the lengths of the adjacent and opposing sides is known as the tangent function. It should be noted that the ratio of sine and cosine to the tan may also be used to express the tan.
Tan a = Opposite/Adjacent = CB/BA
In terms of sine and cos, tan is also equivalent to:
Tan = cos a/sin a
Sin 46° = 8/x
x = 8/Sin 46°
x= 8/0.72
x=11.11

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For sketching the graph we need to know the coordinate of the vector which are r(1) = ⟨−1, 2⟩, r′(1) = ⟨1, 2⟩

Given:-

x = t − 2,

y = t² + 1 ⇒ t = x + 2

⇒ y = (x + 2)2 + 1

⇒ y = x² + 4x + 5

For find r′(t) we have to ,

r′(t) = ⟨1, 2t⟩

To sketch the position vector r(t) and the tangent vector r′(t) for t = 1.

r(1) = ⟨−1, 2⟩, r′(1) = ⟨1, 2⟩

See the above figure. The red vector is r(1) and the blue one is r′(1)

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The multiplications, applying the associative property, are given as follows:

1. (5 x 2) x 3 = 10 x 3 = 30.

2. 4 x (3 x 3) = 4 x 9 = 36.

3. (6 x 1) x 4 = 6 x 4 = 24.

4. 5 x (2 x 4) = 5 x 8 = 40.

5. (2 x 2) x 8 = 4 x 8 = 32.

6. 3 x (2 x 2) = 3 x 4 = 12.

7. (4 x 2) x 4 = 8 x 4 = 32.

8. 6 x (3 x 3) = 6 x 9 = 54.

The associative property of multiplication defines that the order in which the factors are multuiplied does not change the product.

In this problem, we have to consider that the parenthesis gives the precedence of the factors, meaning that the terms inside the parenthesis are multiplied first, and their result should be placed on the blanks below the parenthesis.

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Answer:

A and B

Step-by-step explanation:

actually the 180° rotation does the same as the reflection over the x-axis and then the reflection over the y-axis.

Answer:

There are 3 blue fish in the aquarium.

Step-by-step explanation:

Let the total number of fish be denoted by T, total number of blue fish be B and total number of red fish be R

We can write, T = B + R

Since the aquarium has one fewer redfish than blue fish, R = B - 1

So,

T = B + (B - 1) = 2B - 1

As 60% of total fish is blue, we can write

60% of T = B

or, (60/100) x T = B

or, 3/5 x T = B

or, 3/5 x (2B - 1) = B

or, 6B - 3 = 5B

or, 6B - 5B = 3

or B = 3

Therefore, there are 3 blue fish in the aquarium.

No. of red fish, R = B - 1 = 3 - 1 = 2

The value of the Test statistic =z=-1.67

We have the value of sigma = 6, n = 260

In a hypothesis test, a test statistic—a random variable—is computed from sample data. To decide whether to reject the null hypothesis, you can utilize test statistics. Your results are compared to what would be anticipated under the null hypothesis by the test statistic. The p-value is computed using the test statistic.

Now using the formula of Test static

Test statistic will be:  [tex]\mathrm{z}=\frac{\overline{\mathrm{x}}-\mu}{\frac{\sigma}{\sqrt{\mathrm{n}}}}\\[/tex]

Where, n = total number of sample = 100

[tex]\bar x[/tex] = mean of the given data

[tex]\mu[/tex] = total number of hours taken to receive a basic driving licence.

So, putting the value given in the question,

We will get the value of test static as:

[tex]=\frac{99-100}{\frac{6}{\sqrt{260}}}=-1.67[/tex]

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We are given that [tex]\overline\lambda[/tex] is in the point spectrum and we are to prove that the conjugate is the union of the point and residual spectra of the adjoint.

If [tex]\overline\lambda[/tex] ∈ σp(T∗), then T∗v = [tex]\overline\lambda[/tex]v for some v ∈ D(T∗).

Hence, for all u ∈ D(T) we have -

⟨Tu,v⟩ = ⟨u,T∗v⟩ = ⟨u,[tex]\overline\lambda[/tex]⟩ = λ⟨u,v⟩,

⟨(T−λ)u,v⟩ = 0, for all u ∈ D(T)

If λ ∈ σp(T∗), then T∗v = [tex]\overline\lambda[/tex]v for some v∈D(T∗).

Hence, for all u∈D(T), we have ⟨Tu,v⟩=⟨u,T∗v⟩=⟨u,[tex]\overline\lambda[/tex]v⟩=λ⟨u,v⟩,

and therefore,

⟨(T−λ)u,v⟩=0, for all u∈D(T)

i.e. the range of T−λ is not dense and we will have λ ∈ σr(T) ∪ σp(T).

Hence, proved.

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Answer: The degree of a polynomial is the highest exponent of the variable in the polynomial. The leading coefficient of a polynomial is the coefficient of the term with the highest degree.

In the expression "n + 8", the highest degree of the variable is 1 and the coefficient of the term with the highest degree is 1. Therefore, the degree of the polynomial is 1 and the leading coefficient is 1.

So, the degree of the polynomial is 1 and the leading coefficient is 1.

Note: If the expression had included terms with higher degrees of the variable, such as "n^2 + 3n + 8", the degree of the polynomial would have been 2 and the leading coefficient would have been 1.