Write an equation of the line that is PARALLEL to 12x - 4y = 4 and through the point (-9,-2).

The answer from part A tells us that the trout population was 10 in the first month after it was introduced.

A. P(0) = 740 / (1 + 73e^-0) = 740 / (1 + 73) = 740 / 74 = 10, so the answer is 10.

B. The answer from part A tells us that the trout population was 10 in the first month after it was introduced.

C. To find the number of trout in the lake after 1 year, we need to find P(12): P(12) = 740 / (1 + 73e^-0.07*12) = 740 / (1 + 73e^-0.84) ≈ 490, so the answer is 490.

D. To find the number of trout in the lake after 10 years, we need to find P(120): P(120) = 740 / (1 + 73e^-0.07*120) = 740 / (1 + 73e^-8.4) ≈ 740, so the answer is 740.

E. lim t→∞ P(t) = 740, so the answer is 740.

F. The answer from part E tells us that as the number of months t approaches infinity, the trout population will approach 740. This means that the trout population will eventually stabilize at 740 if no other factors such as predators, disease, or lack of food affect the population.

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Answer:

The transcription of the directions for Lantanoprost 0.005% ophthalmic solution is as follows:

"Sig: ii drops o.u. daily h.s."

This means to use the medication as follows:

"ii drops" = two drops

"o.u." = both eyes

"daily" = once a day

"h.s." = at bedtime (from the Latin "hora somni")

So the complete directions would be:

"Instill two drops in both eyes once a day at bedtime."

The given function y = 4(3/8)^x represents exponential decay.

As x increases, the value of y decreases at an increasingly rapid rate, reflecting the decay behavior of the function.

The given function is y = 4(3/8)^x. To determine if the function represents growth, decay, or neither, we need to examine the base of the exponent, which is (3/8).

When the base of an exponential function is between 0 and 1, such as (3/8) in this case, it represents exponential decay. This is because as the exponent (x) increases, the value of the function decreases.

In the given function, the coefficient 4 multiplied by the decaying exponential term (3/8)^x indicates that the function starts with an initial value of 4 and then exponentially decreases. The term (3/8)^x represents the decay factor, where x determines the extent of decay.

Therefore, we can conclude that the given function, y = 4(3/8)^x, represents exponential decay. As x increases, the value of y decreases at an increasingly rapid rate, reflecting the decay behavior of the function.

In summary, the given function y = 4(3/8)^x represents exponential decay.

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Answer:

$6,000

Step-by-step explanation:

multiply 8000 by .75

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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Answer:

Hope you can understand my handwriting though

Answer:

1. b_ 2. a_ 3. c_ 4. d

Step-by-step explanation:

1 is b mainly because it is marked that way. Your picture doesn't show all of d so not really sure about it, but I used the process of elimination. Picture c is side angle side b/c of the vertical angles.

Answer:

sorry im doing a challenge but i will have someone answer it    

Step-by-step explanation:

If the raffle has 200 tickets total, then about 50 tickets will be in the dining out raffle.

An equation is an expression that shows the relationship between two or more numbers and variables.

From the diagram:

Percentage of dinner out = 65% - 40% = 25%

For 200 total tickets:

Number of dinning out raffle = 25% of 200 = 0.25 * 200 = 50 ticket

If the raffle has 200 tickets total, then about 50 tickets will be in the dining out raffle.

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Answer:

Ed will use 5 more peanut butter  than powdered sugar to make 3 batches of fudge(11-6=5)

Step-by-step explanation:

3 2/3 cups of peanut butter (x)

2 cups of powdered sugar(y)

for every one batch you need 2 cups, and for 3 batches you need 6 cups of powdered sugar(2*3=6)

and  for every batch you need 32/3 cups of peanut butter and for three batches you need (3 2/3 *3)= 11/3 *3=33/3=11 cups of peanut butter to make the fudge

Ed will use 5 more peanut butter  than powdered sugar to make 3 batches of fudge(11-6=5)

The distance between the centers of the two ends circles would be = 60cm.

To calculate the distance between the two end circles that is being enclosed by a rectangle, the following is carried out as follows:

The length of the rectangle = 90cm.

The diameter of the 3 circles = 90/3 = 30cm

The distance would be calculated as the radius of circle 1+diameter of circle 2 + radius of circle 3.

That is;

= 30/2+30+30/2

= 15+30+15

= 60cm

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The expression that is equivalent to the expression 2ˣ⁺⁴ is 16(2ˣ)

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

2ˣ⁺⁴

The above expression is an exponential expression with the following properties

When the above expression is expanded, we have

2ˣ⁺⁴ = 2ˣ * 2⁴

Evaluate the expression 2 exponent 4

So, we have the following representation

2ˣ⁺⁴ = 2ˣ * 16

Rewrite as follows

2ˣ⁺⁴ = 16 * 2ˣ

This gives

2ˣ⁺⁴ = 16(2ˣ)

Hence, the expression that is equivalent to the expression is 16(2ˣ)

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Addison's purple paint will be bluer.

To determine the percent of blue paint in Arturo's mixture, divide the amount of blue paint (11 cups) by the total amount of paint (11 cups + 5 cups) and multiply by 100. This gives you 68.75%.

To determine the percent of blue paint in Addison's mixture, divide the amount of blue paint (8 cups) by the total amount of paint (8 cups + 3 cups) and multiply by 100. This gives you 72.73%. Since 72.73% is greater than 68.75%,

Therefore, the correct answer is as given above. It can then be concluded that Addison's purple paint will be bluer.

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Answer:

Perimeter = 2(L+W)

31 =2(9+w)

31 =18+2W

31-18=2W

13=2W

W=13/2

W=6.5cm

The correct value for z that makes the algebraic expression true is equal to 12

In mathematics, an algebraic expression is an expression which is made up of variables and constants, along with algebraic basic operations such as addition, subtraction, multiplication and division.

we first open the bracket

10 + z - 4 = 18

z + 10 - 4 = 18

z + 6 = 18

subtract 6 from both sides of the equation

z + 6 - 6 = 18 - 6

z = 12

Therefore, 12 is the value of z that makes the algebraic expression true.

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Answer:

D

Step-by-step explanation:

The GCF in answer choice A is 15.

The GCF in answer choice B is none.  

The GCF in answer choice C is 9 since 45 is divisible by 9 and 9 is divisible by itself

D is correct as 55/5 = 11 and cannot be divided anymore.  And 20 is divisible by 5

Answer:

3 pm

Step-by-step explanation:

Because 3x5 = 15 and 5x3=15 so it would be at 3 pm

Answer:

Step-by-step explanation:

Spike gets taken out every 3 hrs meaning he gets taken out at :

6am

9am

12am

3pm

6pm

9pm

Fido gets taken out every 5 hours.

6am

11am

4pm

9pm

Therefore at 9pm, both dogs would get taken out

Answer:

z > -4/5

Step-by-step explanation:

-9 - (2z - 7) > -2z - 6 - 5z

Get rid of the parenthesis

-9 - 2z + 7 > -2z - 6 - 5z

Combine like terms:

       -2 - 2z > -7z - 6

       +2       >       +2

Add 2 to both sides.

 -2z > -7z - 4

 +7z > +7z

Add 7 to both sides.

5z > -4

Divide both sides by 5 to get z.

z > -4/5

---------------------------------

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Answer:

Step-by-step explanation:

Using the pythagorean theorem, we can solve to find C.

a^2 + b^2 = c^2

So it will be 15^2 + 20^2 = c^2

Simplify:

225 + 400 = c^2

625 = c^2

Square root both sides of the equation and you will get:

25 = c

c = 25

(a) The length of the unknown side is 25 yd

For perimeter, just add 20 + 15 + 25

(b) So the perimeter is 60 yd

The formula for area of a triangle is:

Area = (Base x Height) / 2

Now, we can plug in the numbers.

Base = 15

Height = 20

(15 x 20) / 2

300 / 2

= 150

(c) The area of the triangle is 150yd^2

Answer:

miles: 55(36/60) = 55(0.6) = 33 miles

mins: 60(14/17.5) = 60(0.8) = 48 minutes

Total amount of time, in minutes

The total distance, in miles

Step-by-step explanation:

The required distance and time are 47 miles and 84 minutes, respectively.

Speed is measured as the ratio between the distance and time, and the SI unit of speed is m/s.

We know that speed = distance / time

Finding for distance =

55(36/60) = 55(0.6) = 33 miles

Therefore, The total distance, in miles =

= 33 miles + 14 miles

= 47 miles

For Time =

60(14/17.5) = 60(0.8) = 48 minutes

Therefore, Total amount of time, in minutes =

36 minutes + 48 minutes

= 84 minutes

Hence, The required distance and time are 47 miles and 84 minutes, respectively.

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Kira has $19, Boris has $75, and Deshuan has $25.

We will denote as follows:

From information, we can set up equations:

B = 3D (Boris has 3 times what Deshuan has)

D = K + 6 (Deshuan has $6 more than Kira)

K + B + D = 119 (The total amount of money they have is $119)

Substituting equation 2 into equation 1, we have:

B = 3(K + 6)

Substituting equations 1 and 2 into equation 3:

K + 3(K + 6) + (K + 6) = 119

K + 3K + 18 + K + 6 = 119

5K + 24 = 119

5K = 119 - 24

5K = 95

K = 95 / 5

K = 19

Using equation 2, we can find D:

D = K + 6

D = 19 + 6

D = 25

Using equation 1, we can find B:

B = 3D

B = 3 * 25

B = 75.

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Answer:

whats the question?

Step-by-step explanation:

The probability she pulls out a purple piece of candy would be 0.22.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is Sam's fathers collection.

We can write the equations for upstream and downstream as -

x - y = 7/2

x + y = 21/10

Solving the equations graphically -

{x} = 2.8

{y} = 0.7
In still water, the speed would be -

S = 3 - 0.7

S = 2.3 Km/h

Distance peddled upstream -

D = 2.8 x 3.5 = 9.8 Km

Therefore, the speed in still water would be 2.3 Km/h and the distance peddled upstream would be 9.8 Km.

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Maraging (18% Ni) steel has a better tolerance to defects and fracture toughness compared to Medium strength steel.

The tolerance to defects and fracture toughness of a material can be evaluated using its fracture toughness parameter, Kic. The higher the Kic value, the better the material's tolerance to defects and fracture toughness.

To compare the two materials, we can use the concept of critical stress intensity factor (Kic) and factor of safety (FoS). The critical stress intensity factor is the maximum value of stress intensity factor (K) that a material can withstand without fracturing. The factor of safety is the ratio of the maximum allowable stress to the design stress, and it is used to ensure a safety margin in the design.

Assuming that the two materials have the same defect to tolerance ratio, we can calculate the maximum allowable stress for each material using the following formula:

σmax = FoS * Kic / (π * a)

where σmax is the maximum allowable stress, FoS is the factor of safety (assumed to be 2), Kic is the fracture toughness parameter, and a is the size of the defect.

Let's assume a defect size of 1 mm for both materials. Using the values given in the question, we get:

For Maraging (18% Ni) steel:

σmax = 2 * 82 * 10^6 / (π * 1 * 10^-3) = 52.1 GPa

For Medium strength steel:

σmax = 2 * 50 * 10^6 / (π * 1 * 10^-3) = 31.8 GPa

Therefore, Maraging steel has a higher maximum allowable stress, which indicates that it has a better tolerance to defects compared to medium strength steel.

To compare the fracture toughness of the two materials, we can use their respective Kic values. The higher Kic value indicates a better tolerance to defects and fracture toughness.

Comparing the given values, we can see that Maraging (18% Ni) steel has a higher fracture toughness parameter (Kic= 82 MNm-3/2) compared to Medium strength steel (Kic= 50 MNm-3/2).

Therefore, Maraging (18% Ni) steel has a better tolerance to defects and fracture toughness compared to Medium strength steel.

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The exact value of sin(5π/12) is (√6 + √2)/4

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

sin 5pi/12

Express properly

So, we have

sin(5π/12)

Convert the angle to degrees

This gives

sin(5π/12) = sin(5/12 * 180)

Evaluate

sin(5π/12) = sin(75)

The actual value of sin(75) is (√6 + √2)/4

This means that

sin(5π/12) = (√6 + √2)/4

Hence, the exact value of sin(5π/12) is (√6 + √2)/4

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The exact value of sin 5π/12 is (√6 + √2)/4

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Angle in trigonometry can be measured in either degree or radian.

π is a measurement in radian which is equivalent to 180° in degrees.

Therefore:

5π/12 = 5 × 180/12

= 75°

Therefore sin5π/12 = sin75°

sin75 = sin( 45+30) = sin45cos30+ cos 45sin30

= 1/√2 × √3/2 + 1/√2 × 1/2

= √3/2√2 + 1/2√2

= (√3+1)/2√2

rationalizing;

(2√6 + 2√2)/8

dividing through by 2

=(√6 + √2)/4

therefore tan75 =(√6 + √2)/4

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Answer:

64

Step-by-step explanation:

(30+2)2

30*2+2*2

60+4

64

Answer:

B. (30+2)^2

Step-by-step explanation:

(30+2)^2=30^2+2(30)(2)+2^2=900+120+4=1024

32^2=1024. The way to solve without calculator is above.

Hope this helps!

Please mark as brainliest if correct!

answer:

Step-by-step explanation:

1250 plus 0.25 equals 1250.25 plus 1250.25 plus 3200 equals 4450.25 plus 0.10 equals 4450.35

We can conclude that the equation of the circle is (x - 3)² + (y + 6)² = 32, where (3, -6) is the center and 4√2 is the radius. Option 3 and 6 are correct  options.

Based on the information given, we know that circle has its center at the point (3, -6) and a radius of 4√2. We also know that the point (-1, -2) and (4, -0.5) are on the circle.

Using the distance formula, we can confirm that the distance between the center of the circle and each of these points is indeed 4√2.

This equation can be simplified to x² - 6x + y² + 12y + 1 = 0 by expanding and combining like terms. This is the equation of circle , and any point that satisfies this equation will be on the circle. Option 3 and 6 are correct  options.

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