Expression equivalent to a^2-144b^2

The resolution of the human eye is ultimately limited by the pupil diameter.

When the pupil diameter is 2.18mm, the smallest diameter spot the eye can produce on the retina is determined by the diffraction limit, which can be calculated using the formula:

θ = 1.22 * (λ / D)

where θ is the angular resolution, λ is the wavelength of light (typically around 550 nm for the visible spectrum), and D is the pupil diameter (2.18mm in this case). To find the smallest diameter spot on the retina, you would need to multiply the angular resolution by the distance from the lens to the retina (approximately 17mm for an average human eye).

However, the information provided is insufficient to calculate the exact smallest diameter spot. Additionally, factors like the density of photoreceptor cells in the retina also play a role in determining the resolution of the eye.

To learn more about wavelength visit;

https://brainly.com/question/31143857

#SPJ11

The yellow car travel before it catches up with the red car in 1.2 hour

Let the speed of the car be x

A red car and a blue car are traveling at the same speed

A red car travels for 3 hours

A blue car travels for 3.5 hour

Distance travelled by red car = 3x

Distance travelled by blue car = 3.5x

3.5x = 3x + 25

0.5x = 25

x = 50 mph

Speed of car = 50 mph

Speed of yellow car = 50 + 10

Speed of yellow car = 60 mph

Time = y + 12/60

Distance travelled by red car = Distance travelled by yellow car

50(y) = 60 (y - 12/60)

50y = 60y - 12

-10y = -12

y = 1.2

To know more about travel click here :

https://brainly.com/question/18090388

#SPJ4

Answer:

C 4 glasses

I took the thing

Answer:

500 minutes= 8.33 hr

Step-by-step explanation:

The number of hours that he works will be 8 hours and 20 minutes.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Jude arrived at work at 7:55 am and left at 4:15 pm.

Convert the time into 24 hours system. Then we have

4:15 pm = 16: 15

7:55 am = 7: 55

Then the number of hours is given as,

    16: 15

  -  7: 55

     8: 20

Then the number of hours that he works will be 8 hours and 20 minutes.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ2

Answer:

6 *18

Step-by-step explanation:

Answer:

96π mm^3

Step-by-step explanation:

πr^2*h = formula

π4^2*6 = 16π(6) = 96π mm^3

Answer:

\(\Longrightarrow: \boxed{\sf{96\pi }}\)

Step-by-step explanation:

You must use the volume of this cylinder formula to solve the volume of this cylinder.

Volume of this cylinder formula:

\(\Longrightarrow: \sf{\pi r^2*h}\)

\(\Longrightarrow\sf{\pi 4^2*6}\)

Use the order of operations.

PEMDAS stands for:

First, solve exponents.

4²=4*4=16

16*6

Multiply.

16*6=96

\(\Longrightarrow: \boxed{\sf{96\pi}}\)

I hope this helps! Let me know if you have any questions.

2.8x+8.7

Step-by-step explanation:

-2.1x+3.7+5+4.9x

=2.8x+8.7

Answer:

Step-by-step explanation:

Area of rectangle = length * width

Area of rectangle = 55x⁶ + 22x⁴

                             = 5*11*x⁶ + 2 *11*x⁴

                             = 11x⁴*(5x² + 2)

width = 11x⁴

So, length = 5x² + 2

Answer:

184

Step-by-step explanation:

The modified Reynolds analogy, also known as the Chilton-Colburn analogy, is expressed mathematically as Nu = f * Re^m * Pr^n. It relates the convective heat transfer coefficient (h) to the skin friction coefficient (Cf) in fluid flow. This equation is widely used in heat transfer analysis and design applications involving forced convection.

The modified Reynolds analogy is a useful tool in heat transfer analysis, especially for situations involving forced convection. It provides a correlation between the heat transfer and fluid flow characteristics. The Nusselt number (Nu) represents the ratio of convective heat transfer to conductive heat transfer, while the Reynolds number (Re) characterizes the flow regime. The Prandtl number (Pr) relates the momentum diffusivity to the thermal diffusivity of the fluid.

The equation incorporates the friction factor (f) to account for the energy dissipation due to fluid flow. The values of the constants m and n depend on the flow conditions and geometry, and they are determined experimentally or by empirical correlations. The modified Reynolds analogy is widely used in engineering calculations and design of heat exchangers, cooling systems, and other applications involving heat transfer in fluid flow.

Learn more about Prandtl number here:

https://brainly.com/question/32353670

#SPJ11

Answer:

9

Step-by-step explanation:

1. Just input the x value with -180:

24 (+) -180 / 12 = answer

2. Follow PEMDAS to solve, which in this case division comes before addition:

24 + (-180 / 12)

24 + (-15)

3. Addition

24 + (-15) or 24 - 15

= 9

Therefore, 24 (+) -180 / 12 equals 9.

Answer:

Step-by-step explanation:

x^2 - 6x = -156    Next step is:

x^2 - 6x + (-3)^2 = -156 + (-3)^2

The amount of commission amount that  Shayna make on the 3 sales is $5,040.

First step is to calculate the commission she makes on total sales over $83,000.

Sales commission=18%×$83,000

Sales commission=$14,940

Second step is to calculate the commission she makes If she sold 3 vehicles in 1 day at $37,000

Sales commission=(3×$37,000)×18%

Sales commission=$111,000×18%

Sales commission=$19,980

Third step is to calculate the he commission she makes on the 3 sales

Sales commission=$19,980-$14,940

Sales commission=$5,040

Inconclusion the amount of commission amount that  Shayna make on the 3 sales is $5,040.

Learn more here:

https://brainly.com/question/14065593

Answer:

please mark my answer brainliest

Step-by-step explanation:

the answer will be...9in square +25in square +24 in square.....=58 in square.....that is ur answer...find individual areas then sum up

Answer:

-4 and 7 is really your answer

Slope formula: y2-y1/x2-x1

We can use the points given to solve for the slope.

7-8/3-5

-1/-2

1/2

Best of Luck!

Answer:

(0,2)

Step-by-step explanation:

The equations must be derived from the graph:

First, find the slope of f(x):

\(m=\frac{y_2-y_1}{x_2-x_1}\) let \((x_1,y_1)=(-3,3)\) and \((x_2,y_2)=(3,1)\)

\(m=\frac{(1)-(3)}{(3)-(-3)}\\m=\frac{-2}{6}\\m=-\frac{1}{3}\)

Then use \(y-y_1=m(x-x_1)\)

\(y-3=-\frac{1}{3}[x-(-3)]\\y-3=-\frac{1}{3}x-1\\y=-\frac{1}{3}x+2\\f(x)=-\frac{1}{3}x+2\)

For g(x), let:

\((x_1,y_1)=(-3,0)\\(x_2,y_2)=(0,2)\)

\(m=\frac{(2)-(0)}{(0)-(-3)}\\m=\frac{2}{3}\)

\(y-0=\frac{2}{3}[x-(-3)]\\y=\frac{2}{3}x+2\\g(x)=\frac{2}{3}x+2\)

Now, to solve for x, allow the two expressions written in terms of x equal each other.

\(-\frac{1}{3}x+2=\frac{2}{3}x+2\\(-\frac{1}{3}x+2)+\frac{1}{3}x=(\frac{2}{3}x+2)+\frac{1}{3}x\\2=x+2\\(2)-2=(x+2)-2\\x=0\)

To solve for y, substitute 0 for x in f(x):

\(y=-\frac{1}{3}x+2\\y=-\frac{1}{3}(0)+2\\y=0+2\\y=2\)

So, the solution to this system of equations would be the ordered pair (0,2).  This solution is seen on the graph as the intersection of the two lines.

The approximate chi-square value for this study is 10.84.

In a brand awareness study involving 35 males and 35 females, 25 males and 15 females identified the brand correctly.

To find the chi-square value, we need to create a contingency table and apply the chi-square formula. Here's a quick breakdown of the process:

1. Create a contingency table:
       Males    Females
Correct    25          15
Incorrect  10          20

2. Calculate row and column totals:
       Males    Females    Total
Correct    25          15          40
Incorrect  10          20          30
Total         35          35          70

3. Find the expected frequencies for each cell by multiplying row and column totals and dividing by the overall total (for example, for the 'Correct Males' cell, multiply 40*35 and divide by 70):
       Males    Females
Correct    20          20
Incorrect  15          15

4. Apply the chi-square formula: Χ² = Σ[(Observed-Expected)²/Expected]
Χ² = [(25-20)²/20] + [(15-20)²/20] + [(10-15)²/15] + [(20-15)²/15]
Χ² ≈ 5 + 2.5 + 1.67 + 1.67
Χ² ≈ 10.84

To learn more about chi-square click here

brainly.com/question/31433366

#SPJ11

Answer:

5c + 50.00

Step-by-step explanation:

To represent the total amount spent, we can sum up the cost of the 5 videos, the DVD, and the CD. Let's assume the cost of the videos is represented by the variable "v."

Total amount spent = Cost of 5 videos + Cost of DVD + Cost of CD

Since each video costs "c" dollars, the cost of 5 videos is 5c.

Therefore, the expression in simplest form representing the total amount spent is:

Total amount spent = 5c + 30.00 + 20.00

Simplifying further:

Total amount spent = 5c + 50.00

Based on the given data, it seems that both the polysilicon doping level and anneal temperature can affect the base current.

To visually interpret the data, we can create a scatter plot with the polysilicon doping level on the x-axis and the base current on the y-axis, with different colors or symbols representing the different anneal temperatures. We can also create a similar plot with the anneal temperature on the x-axis and the base current on the y-axis, with different colors or symbols representing the different polysilicon doping levels.

To analyze the model, we can examine the residuals to see if they are randomly distributed around zero, indicating that the model is a good fit for the data. If the residuals show a pattern, it may suggest that the model is not a good fit.

Assuming a linear model, we can estimate the parameters using regression analysis. The model could be of the form:

Base current = β0 + β1(doping level) + β2(anneal temperature) + ε

where β0 is the intercept, β1 is the coefficient for doping level, β2 is the coefficient for anneal temperature, and ε is the error term.

Once we have estimated the parameters, we can plot the response surface to see how the base current changes as a function of both the doping level and annealing temperature. This will give us a better understanding of the relationship between these variables and the response variable.

Learn more about doping here:

https://brainly.com/question/23867172

#SPJ11

10. Assume x in both sets (A-C) n (C-B) and derive contradiction to prove empty set.
11. (a) Prove identity (∀x)[a(x) ∨ b(x)] = (∀x)[a(x) ∨ (b(x) ∧ ¬a(x))]. (b) Prove (AUB) CC = (A ≤ C) A (BCC) using set theory.
12. (a) Prove empty set for BOCCA (C-A) n (BA) by contradiction. (b) Show (AUB) - (An B) = A → B is invalid with counterexample.

10. To show (A-C) n (C-B) = Ø, assume x belongs to both. Then x belongs to (A∩C)-B, which contradicts x not belonging to B.
11. (a) (∀x)[a(x) ∨ b(x)] = (∀x)[a(x) ∨ (b(x) ∧ ¬a(x))]. Distribute universal quantifier and use distributive property.
(b) (AUB) CC = (A ≤ C) A (BCC). Use set theory laws and definitions to show equivalence.
12. (a) BOCCA (C-A) n (BA) is empty. Assume it's not empty and derive a contradiction.
(b) (AUB) - (An B) = A → B is empty. Invalid. Counterexample: A={1}, B={2}, AUB={1,2}, AnB=Ø, LHS={1,2}, but A→B is not empty.

To know more about set theory, visit:
brainly.com/question/30705181
#SPJ11

Answer:

1. 1.925 Liters

2.  0.075 Liters  less than the 2 Liter of special drink

Step-by-step explanation:

Step 1

Quantity of lemon juice = 0.375 Liters

Quantity of cranberry juice = 0.35 liters

Quantityof water = 1.2liters

Total Quantity of  Special drink = 0.375 L+ 0.35L + 1.2 L= 1.925 Liters

Step 2

But since she wanted to make 2 Liters of the special drink she will have

2 Lter - 1.925L= 0.075Liters  less than the initial 2 Liter of special drink planned.

Answer:

a. 1.925 litres

b. 0.075 litres less

Step-by-step explanation:

a. How much of the special drink can she make?

To find out the quantity of juice produced, add the component juice quantities and the water:

= 0.375 + 0.35 + 1.2

= 1.925 litres

b. How much more or less than 2 litres will she have?

= 2 - 1.925

= 0.075 litres less

To make the fractions 5/24 and 5/8 equivalent, the common denominator of 24 is used. The numerator of the second fraction, 5, is adjusted by multiplying it by the ratio of the denominators, resulting in the equivalent fractions 5/24 and 5/3.

To make the two fractions equivalent, we need to find a common denominator.

The denominator of the first fraction is 24, while the denominator of the second fraction is 8. To find a common denominator, we need to find the least common multiple (LCM) of 24 and 8, which is 24.

Since the denominator of the first fraction is already 24, we don't need to make any changes to it. However, we need to adjust the numerator of the second fraction to maintain equivalence.

To do this, we divide the denominator of the second fraction (8) by the denominator of the first fraction (24) and multiply the result by the numerator of the second fraction (5).

(8 ÷ 24) × 5 = (1/3) × 5 = 5/3

Therefore, the equivalent fractions are 5/24 and 5/3. The common denominator is 24, and both fractions have the same numerator, which is 5.

To know more about fractions refer here:

https://brainly.com/question/29766013#

#SPJ11

Answer:

What is the probability of a sample mean?

The Probability of a Sample Mean The Probability of a Sample Mean We saw in the previous section that if we take samples, the distribution of the sample means will be approximately normal. This will hold true even when the underlying population is not normally distributed, provided we take samples of n=30 or greater.p-by-step

The equivalent expression for 1.5 cubed over 1.3 raised to the fourth power all raised to the power of negative six is 1.5 to the eighteenth power over 1.3 to the twenty-fourth power.

Here are the steps to simplify the expression:

Apply the negative power rule: (1.5 cubed over 1.3 raised to the fourth power) raised to the power of negative six is equal to (1.3 raised to the fourth power over 1.5 cubed) raised to the power of six.

Apply the power of a quotient rule: (1.3 raised to the fourth power over 1.5 cubed) raised to the power of six is equal to (1.3 raised to the fourth power)⁶ / (1.5 cubed)⁶.

Apply the power of a power rule: (1.3 raised to the fourth power)⁶ is equal to 1.3(⁴*⁶) = 1.3²⁴.

Apply the power of a power rule: (1.5 cubed)⁶ is equal to 1.5(³*⁶) = 1.5¹⁸.

Therefore, the equivalent expression is 1.5¹⁸ / 1.3²⁴.

Learn more about expressions on

https://brainly.com/question/1859113

#SPJ4

Answer:

12 1/2

Step-by-step explanation:

Answer:

25/2.... DON'T WORRY... I AM CORRECT

Also if i can, could I have brainliest...

A line chart is the best chart to show trends over time. It shows trends and data variables clearly.

In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.  

The points on the graph often represent the relationship between two or more things.

We can deduce that a line chart is the best chart to show trends over time as it shows trends and data variables clearly and also assists readers with making predictions for the future. However, for a data set comparison being useful, you must use the same scale on both axes.

Learn more about graphs here: https://brainly.com/question/19040584

#SPJ1