A social psychologist is interested measuring the effect of the age of the author on the persuasiveness of an opinion about Social Security. 18 research participants read a controversial essay about Social Security. Each participant rated the extent to which he or she agreed with the author (the higher the number, the more the person agreed with the author).

The equilibrium price and quantity for each pair of demand and supply functions are as follows:

a. Q = 10 - 2P

To find the equilibrium, we set the quantity demanded equal to the quantity supplied:

10 - 2P = P

By solving this equation, we can determine the equilibrium price and quantity. Simplifying the equation, we get:

10 = 3P

P = 10/3 ≈ 3.33

Substituting the equilibrium price back into the demand or supply function, we can find the equilibrium quantity:

Q = 10 - 2(10/3) = 10/3 ≈ 3.33

Therefore, the equilibrium price is approximately $3.33, and the equilibrium quantity is also approximately 3.33 units.

b. Q = 1640 - 30P

Setting the quantity demanded equal to the quantity supplied:

1640 - 30P = P

Simplifying the equation, we have:

1640 = 31P

P = 1640/31 ≈ 52.90

Substituting the equilibrium price back into the demand or supply function:

Q = 1640 - 30(1640/31) ≈ 51.61

Hence, the equilibrium price is approximately $52.90, and the equilibrium quantity is approximately 51.61 units.

In summary, for the demand and supply functions given:

a. The equilibrium price is approximately $3.33, and the equilibrium quantity is approximately 3.33 units.

b. The equilibrium price is approximately $52.90, and the equilibrium quantity is approximately 51.61 units.

In the first paragraph, we summarize the steps taken to determine the equilibrium price and quantity for each pair of demand and supply functions. We set the quantity demanded equal to the quantity supplied and solve the resulting equations to find the equilibrium price. Substituting the equilibrium price back into either the demand or supply function allows us to calculate the equilibrium quantity.

In the second paragraph, we provide the specific calculations for each pair of functions. For example, in case a, we set Q = 10 - 2P equal to P and solve for P, which gives us P ≈ 3.33. Substituting this value into the demand or supply function, we find the equilibrium quantity to be approximately 3.33 units. We follow a similar process for case b, setting Q = 1640 - 30P equal to P, solving for P to find P ≈ 52.90, and substituting this value back into the function to determine the equilibrium quantity of approximately 51.61 units.

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Answer:

In Step 1, she multiplied the numerators together and the denominators together.

x=12.50

Step-by-step explanation:

Correct steps

12:30=5:x

Step1:

12/30=5/x

Cross product

Step 2:

12*x=30*5

12x=150

Step3:

x=150/12

x=12.50

In Step 1, she multiplied the numerators together and the denominators together.

Answer:

b on edginuity

Step-by-step explanation:

i got it right

The condition that must be imposed on k1 and k2 so that 22 6. +2,02 is an unbiased estimator of θ.

To prove that 22 6. +2,02 is an unbiased estimator of the parameter θ, we need to show that its expected value is equal to θ, i.e.,

E(22 6. +2,02) = θ.

Using the linearity of the expected value operator, we have:

E(22 6. +2,02) = E(k1Ô1 + k2Ô2)

= k1E(Ô1) + k2E(Ô2)

Since both Ô1 and Ô2 are unbiased estimators of θ, we have:

E(Ô1) = E(Ô2) = θ

Substituting these values in the above equation, we get:

E(22 6. +2,02) = k1θ + k2θ

= (k1 + k2)θ

For 22 6. +2,02 to be an unbiased estimator of θ, the above expression should be equal to θ. Therefore, we must have:

(k1 + k2) = 1

This implies that the constants k1 and k2 must satisfy the constraint:

k1 + k2 = 1

Hence, this is the condition that must be imposed on k1 and k2 so that 22 6. +2,02 is an unbiased estimator of θ.

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Answer:

x = 3.5

Step-by-step explanation:

Given

\(3^{2x-5}\) = 9 , that is

\(3^{2x-5}\) = 3²

Since the bases on both sides are equal, both 3 , then equate the exponents

2x - 5 = 2 ( add 5 to both sides )

2x = 7 ( divide both sides by 2 )

x = 3.5

Answer:

The formula would be

((a+b) / 2)h = area

In this case a is one side of the base (top parralel or bottom line)

And b is the second one (top or bottom)

You can only choose one for each

You add those two up and divide that by 2

Now you multiply it by “h” or height.

Now you have the area

With this query, no effort is necessary. measure the tbsp. of all items.

A great source of both phosphorus and calcium, which are essential for the growth and upkeep of strong, strong teeth and bones, is milk. They lower the chance of developing osteoporosis and suffering broken bones later in life. Milk encourages strong bones.

1. Measure \(8\) tbsp. chocolate sauce and add \(2\frac{1}{2}\) cups of milk.

No work is required for this question. It is a simple instruction to measure out 8 tbsp. of chocolate sauce and add it to \(2\frac{1}{2}\) cups of milk.

2. Start with \(1\frac{3}{4}\) cups of milk and add \(2\frac{1}{2}\) tbsp. chocolate sauce.

No work is required for this question. It is a simple instruction to start with \(1\frac{3}{4}\) cups of milk and add \(2\frac{1}{2}\) tbsp. of chocolate sauce.

3. Add \(3\frac{1}{3}\) tbsp. chocolate sauce to \(1\frac{1}{4}\) cups milk.

No work is required for this question. It is a simple instruction to add  \(3\frac{1}{3}\)tbsp. of chocolate sauce to \(1\frac{1}{4}\) cups of milk.

4. For every 1 cup of milk add \(2\frac{1}{2}\) tbsp. of chocolate sauce.

No work is required for this question. It is a simple instruction to add \(2\frac{1}{2}\) tbsp. of chocolate sauce for every \(1\) cup of milk.

5. Stir \(1\) tbsp. chocolate sauce into \(\frac{2}{3}\) cup milk.

No work is required for this question. It is a simple instruction to stir 1 tbsp. of chocolate sauce into \(\frac{2}{3}\) cup of milk.

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The Critical point and Point of Inflection for the function f(x) = a/(x² + b²) are (0, a/b²) and (b/√3, 3a/4b²) respectively.

The given function is,

f(x) = a/(x² + b²) = a(x² + b²)⁻¹

Differentiating the function with respect to 'x' we get,

f'(x) = -a(x² + b²)⁻²(2x) = -2ax(x² + b²)⁻²

f''(x) = 2a[-2x(x² + b²)⁻³(2x) + (x² + b²)⁻²] = 2a(x² + b²)⁻²[-4x² + (x² + b²)] = 2a(x² + b²)⁻²[ -3x² + b²]

Now, for critical point,

f'(x) = 0 gives

-2ax(x² + b²)⁻² = 0

x = 0

So, at x = 0, f(0) = a/b²

Hence, (0, a/b²) is the critical point.

For point of Inflection,

f''(x) = 0

2a(x² + b²)⁻²[ -3x² + b²] = 0

3x² = b²

x² = b²/3

x = b/√3

So at x = b/√3, f(b/√3) = 3a/4b²

Hence the point of inflection is (b/√3, 3a/4b²).

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Answer:

-2

Step-by-step explanation:

4y - 7 = - 15

4y = -15 + 7

4y = -8

y = - 8 / 4

y = - 2

Divide total price by quantity:

15.60 / 6 = 2.60

Unit price = $2.60

Answer:

5

Step-by-step explanation:

The area of any quadrilateral can be determined by multiplying the length of its base by its height. Since we know the shape here is square, we know that all sides are of equal length. From this we can work backwards by taking the square root of the area to find the length of one side.

The number of different materials that Kat can choose from are 6.

Given that:-

Kat is ordering customized shoes online. She can choose from one material, one color and one sole.

Number of different colors available = 18

Number of different types of soles available = 12

Total number of options available to Kat for her shoes = 1296

We have to find the number of different materials that Kat can choose from.

Let the  number of different materials that Kat can choose from be x.

We know that,

Number of different materials that Kat can choose from = (Number of different colors available)*(Number of different types of soles available)*(number of different materials)

Hence, by simple multiplication, we can write,

1296 = 18*12*x

1296 = 216x

x = 1296/216

x = 6

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Answer:

Solution

verified

Verified by Toppr

Correct option is A)

We first calculate slant height L of the pyramid with base s=10 cm and height 12 cm:

L 2 =H 2 +( 2s )

2

=12

2

+(

2

10

)

2

=12

2

+5

2

=144+25=169

⇒L=

169

=13

The perimeter of the base is P=4s, since it is a square, therefore,

P=4×10=40 cm

The general formula for the lateral surface area of a regular pyramid is LSA=

2

1

Pl where P represents the perimeter of the base and l is the slant height.

Since the perimeter of the pyramid is P=40 cm and the slant height is l=13 cm, therefore, the lateral surface area is:

LSA=

2

1

Pl=

2

1

×40×13=260 cm

2

Now, the area of the base B=s

2

with s=10 cm is:

B=s

2

=10

2

=100 cm

2

The general formula for the total surface area of a regular pyramid is TSA=

2

1

Pl+B where P represents the perimeter of the base, l is the slant height and B is the area of the base.

Since LSA=

2

1

Pl=260 cm

2

and area of the base is B=100 cm

2

, therefore, the total surface area is:

TSA=

2

1

Pl+B=260+100=360 cm

2

Hence, total surface area of the pyramid is 360 cm

2

.

Answer:

In order for a function to be differentiable at a point, it must be continuous at that same point.

General Formulas and Concepts:

Calculus

Continuity

Discontinuities

Differentiation

Step-by-step explanation:

In order for a function to be differentiable, it must be continuous. That means that the function must have a limit that exists and that it should not contain discontinuities.

If the function contains discontinuities, then the function is not continuous at the discontinuities and therefore is not differentiable there.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Answer:

Step-by-step explanation:Okay so first you have to find out if -2 is your growth or y-axis.Your y-axis is when the line hits the up and down graph line.Your -2 is most likely your growth now you need to create a starting point it can be 10 for example then you would subtract 2 from it everytime you place a new dot like (0,10) and then (1,8) and so on.If u make a table the x will be on the left side this is where u will put the number 0,1,2,3.for everytime you make a dot on the graph.

Answer:

48 inches

or

0.8 minutes

Step-by-step explanation:

To find the unit rate of inches per hour, divide 144 by 3.

144÷3=48

You don't need to round because there are no decimals.

To find the time to braid 1 inch, first multiply 3 by 60 (because there are 60 minutes in 1 hour).

3×60=180

Then divide 144 by 180.

144÷180= 0.8

You don't need to round because there are no thousandths.

\(===================================\)

let's find the value of h(2)

we know that

h(r)=5r-5

which means

h of r is 5 times r minus 5

hence

h of 2 is 5 times 2 minus 5

simplify:

h(2)=5(2)-5

h(2)=10-5

h(2)=5

\(==================================\)

Answer:

5

Step-by-step explanation:

h(2)=5r-5

=5×2-5

=10-5

=5

Answer:

they make $19 dollars in profit per sweater

Step-by-step explanation

154/11 is 14. This means that they paid $14 dollars per sweater.

363/11 is 33, meaning that they sold each sweater for $33.

$33 - $14 is $19, thus they made $19 dollars per sweater.

(I could be wrong, though. I tend to make dumb and simple mistakes of simple math, lol)

Answer:

19

Step-by-step explanation:

First Find the difference of the two amounts.

Profit = Sale - Cost

Profit = 363 - 154

Gross Profit = 209

Each sweater sold brings in a profit of 209 / 11  = 19 dollars

So we want to put the number:

on a number line.

Remember that, this number can be expressed as:

-Taking values between 1 and 2 and divide this interval in three parts. The second part will be the location of the number. If we draw:

So the correct answer is A.

Answer:

minimum=1

Q1=3

median=6

Q3=10

maximum=17

The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x  ≥ -6

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

\(f(x) = \sqrt{\frac{1}{3}x + 2\)

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x  ≥ -2

So, we have

x  ≥ -6

Hence, the domain of the function is (d) x  ≥ -6

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Step-by-step explanation:

Remember that in order to find the volume you need to multiply 6.3 x 2.4 x 8.   I don't know for sure but if that is true the answer should be 120.96.  If they ask you to round I think you know how to do that.  

Hope this helps.

Answer:

The answer is x < 4 (or 4>x)

Step-by-step explanation:

We solve the given inequality,

\(3x-3 < 9\\3x < 9+3\\3x < 12\\x < 12/3\\x < 4\)

Hence the answer is x<4 or 4>x

The volume of the solid generated by revolving the region in the first quadrant bounded by the coordinate axes is V = π∫ln 8eˣdx,

The volume of a solid generated by revolving a region about a line is calculated by using the method of slices.

In this case, we have a region in the first quadrant bounded by the coordinate axes, the curve y = eˣ and the line x = ln 8, which is being revolved about the line x = ln 8.

To find the volume of this solid, we need to take slices perpendicular to the line of rotation and calculate the area of each slice.

The volume can then be calculated by multiplying the area of each slice by its corresponding distance from the line of rotation and summing up the results.

The volume of this solid is calculated by the equation

=> V = π∫ln 8eˣdx,

where V is the volume of the solid, x is the distance from the line of rotation, and π is the constant pi

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Answer:

77.5%

Step-by-step explanation:

Add 80 and 75 together: 155

Then divide by 2 because there are 2 #s: 77.5

Add a percent symbol to they're end cause they are all percents: 77.5%

And you have your answer!!!!

Hi there!

Looking at the graph, the first intersection point is clear. The red parabola and  blue line clearing intersect at the point (0, -1).

Find the second intersection point by setting the equations of both graphs equal to each other.

Line: y = 3x - 1

Parabola: y = 4x² - 1

Find another intersection point by setting these two equations equal to each other:

4x² - 1 = 3x - 1

Bring all terms onto one side:

4x² - 3x = 0

Factor out x:

x(4x - 3) = 0

Set 4x - 3 to 0 and solve:

4x - 3 = 0

4x = 3

x = 3/4

Plug in this value of x into an equation to solve for the y-coordinate. Use the linear equation for ease:

y = 3(3/4) - 1

y = 9/4 - 1

y = 5/4

(3/4, 5/4)

Answer:

24.59 m/s

Step-by-step explanation:

Average speed(m/s) = distance travelled(m) / time taken(s)

Distance = 220 miles

220 miles = 354,056 meters

Time taken = 4 hours

4 hours = 14,400 seconds

Average speed = distance travelled / time taken

= 354,056 / 14,400

= 24.59 meter/seconds

= 24.59 m/s

The number of games that will be played in the first round will be 14 games.

It should be noted that the appropriate function to use in this scenario will be:

= (n - 1) × 2

where n = total number of people participating.

Therefore, this will be:

= (n - 1) × 2

= (8 - 1) × 2

= 7 × 2

= 14

Therefore, the number of games that will be played in the first round will be 14 games.

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Answer:

9+1/4g = h

Step-by-step explanation:

consider the other one I used the wrong method.

Answer:

S₂₂ = - 2310

Step-by-step explanation:

the sum to n terms of an arithmetic series is

\(S_{n}\) = \(\frac{n}{2}\) [ 2a₁ + (n - 1)d ]

given a₁ = - 84, d = - 2, n = 22 , then

S₂₂ = \(\frac{22}{2}\) [ (2 × - 84) + (21 × - 2) ]

     = 11 (- 168 - 42)

     = 11 × - 210

     = - 2310