Find the equation of the line through the points (8, 1) and (10, 11).

The perimeter of the rectangle of dimension 1.5 × 10² feet by 1.35 × 10³ feet will be 3,000 feet.

Let W be the rectangle's width and L its length.

The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be given as,

Perimeter of the rectangle = 2(L + W) units

The components of a school building are 1.5 × 10² feet by 1.35 × 10³ feet.

Then the perimeter of the rectangle will be given as,

P = 2(1.5 × 10² + 1.35 × 10³)

Simplify the equation, then we have

P = 2(1.5 × 10² + 1.35 × 10³)

P = 2(150 + 1350)

P = 2(1500)

P = 3000 feet

The edge of the square shape of aspect 1.5 × 10² feet by 1.35 × 10³ feet will be 3,000 feet.

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a) two representatives be picked in 5850 ways so that one is a mathematics major and the other is a computer science major. b) one representative be picked in 343 ways who is either a mathematics major or a computer science major.

Product Rule: If one event occurs in m ways and a second event occurs in n ways, the number of ways the two events occur in the sequence is m×n ways.

Sum Rule: If an event occurs either in m ways or in n ways (non-overlapping), the number of ways the event can occur is m+n ways.

according to the question,

Mathematics majors =18 and Computer science majors = 325

A. We need to use the product rule because the first event is picking up a Mathematics major and the second event is picking up a computer science major.

= 18 x 325

= 5850

B. Here sum rule is applicable because the event is picking up a mathematics major or a computer science major.

= 18 + 325

= 343

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(complete question)

there are 18 mathematics majors and 325 computer science majors at a college. a) in how many ways can two representatives be picked so that one is a mathematics major and the other is a computer science major? b) in how many ways can one representative be picked who is either a mathematics major or a computer science major.

Answer: 7.8 !!!!!!!!

:)

Properties of Special right angled triangle,

a) If the leg of a 45°-45°-90° right triangle is x units, then the length of hypotenuse is x√2 units.

b) If a 30°-60°-90° right triangle the hypotenuse is twice the shorter leg, then longer leg is √3 times the shorter leg.

We have to discuss properties of special Right Triangles :

a) Properties of 45°-45°-90° Triangles : The sides of a 45°-45°-90° right triangle have a special relationship.

Example 1: If the leg of a 45°-45°-90° right triangle is x units, show that the hypotenuse is x√2 units.

Using the Pythagorean Theorem with

a = b = x, then c² = a² + b²

=> c² = x² + x²

=> c² = 2x²

=> c = √2x²

=> c = x√2

Thus, hypotenuse is x√2 units.

b) The sides of a 30°-60°-90° right triangle also have a special relationship.

Example 1: In a 30°-60°-90° right triangle the hypotenuse is twice the shorter leg. Show that the longer leg is √3 times the shorter leg.

∆MNQ is a 30°-60°-90° right triangle, and the length of the hypotenuse MN is two times the length of the shorter side NQ. Use the Pythagorean Theorem, c² = a²+ b²

let length of shorter side of ∆MNQ, NQ= x units, so, length of hypotenuse,MN = 2x

=> MN² = NQ² + MQ²

=> MQ² = MN² - NQ²

=> MQ² = (2x)² - x²

=> MQ² = 4x² - x² = 3x²

=> MQ = √3x²

=> MQ = √3 x = √3 NQ

So, longer side of right angled triangle is √3 times the short side.

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Complete question:

8-3 study guide and intervention special right triangles

a) Properties of 45°-45°-90° Triangles

b) Properties of 30°-60°-90° Triangles

Answer: \(b < 28.12\)

Step-by-step explanation:

\(\frac{b}{-3.8} > -7.4\\\\b < (-7.4)(-3.8)=28.12\)

Answer: C) 15 cm, D) 10 cm

Step-by-step explanation:

Let's use the scale to convert the measurements on the drawing to real-life measurements in feet:

3 cm on the drawing = 4 feet in real life

To determine which lines on the drawing would be greater than 12 feet in real life, we need to find the lines on the drawing that correspond to more than 12 feet in real life.

For each line on the drawing, we can convert its length to feet using the scale:

A) 12 cm = (12/3) * 4 = 16 feet

B) 6 cm = (6/3) * 4 = 8 feet

C) 15 cm = (15/3) * 4 = 20 feet

D) 10 cm = (10/3) * 4 = 13.33 feet

Therefore, the lines that are greater than 12 feet in real life are C) 15 cm and D) 10 cm.

Answer:

C + D

Step-by-step explanation:

Answer:

4x -4 < 10 (add 4 to both sides)

4x < 14 (divide each side by 4)

x < 3.5

Answer:

x< 7/2

Step-by-step explanation:

add for to both sides

divide by four

simplify 14/4

Answer:

heres the graph

Step-by-step explanation:

Consider that in slope-intercept form the equation of a line is given by:

y = mx + b

where m is the slope and b the y-intercept.

Then, solve for y the given equation, as follow:

2x - 3y = -6 subtract 2x both sides

-3y = -2x - 6 divide by -3 both sides

y = 2/3 x + 2

The previous result is the equation is slope-intercept form.

The graph the previous equation, use the a pair of values for x and placed them in the coordinate system, after this, draw a straigh line which crosses the two points, as follow:

where we have use the values of x = -3 and x = 0 and the results for y are:

y = 2/3 (-3) + 2 = - 2 + 2 = 0

y = 2/3(0) + 2 = 2

Which correspond to the shown points (-3,0) and (0,2)

Answer:

Go to the nether

Step-by-step explanation:

Go to the nether and make sure you have a shield and a fire resistance potion  and make sure you have a bow to shoot them while they fly also make sure you have a good sword and armor cuz the nether is dangerous

A) when the diameter of the balloon is 1.2 feet, the diameter is increasing at a rate of approximately 0.853 feet per minute .

B) when the top of the ladder is 12 feet above the ground, the foot of the ladder is moving away from the wall at a rate of approximately 0.8817 ft/s.

To find the rate at which the diameter of the balloon is increasing, we can use the relationship between the volume and the diameter of a sphere. The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere. Since the diameter is twice the radius, we have d = 2r.

Given that the volume is increasing at a rate of 2.4 cubic feet per minute, we can differentiate the volume equation with respect to time t to find the rate of change of volume with respect to time:

dV/dt = (4/3)π(3r²)(dr/dt)

Since we are interested in finding the rate at which the diameter (d) is increasing, we substitute dr/dt with dd/dt:

dV/dt = (4/3)π(3r²)(dd/dt)

We also know that r = d/2, so we substitute it into the equation:

dV/dt = (4/3)π(3(d/2)²)(dd/dt)

= (4/3)π(3/4)d²(dd/dt)

= πd²(dd/dt)

Now we can substitute the given values: d = 1.2 ft and dV/dt = 2.4 ft³/min:

2.4 = π(1.2)²(dd/dt)

Solving for dd/dt, we have:

dd/dt = 2.4 / (π(1.2)²)

dd/dt ≈ 0.853 ft/min

Therefore, when the diameter of the balloon is 1.2 feet, the diameter is increasing at a rate of approximately 0.853 feet per minute.

For the second question, we can use similar reasoning. Let h represent the height of the ladder, x represent the distance from the foot of the ladder to the wall, and θ represent the angle between the ladder and the ground.

We have the equation:

x² + h² = 16²

Differentiating both sides with respect to time t, we get:

2x(dx/dt) + 2h(dh/dt) = 0

We are given that dx/dt = 2 ft/s and want to find dh/dt when h = 12 ft.

Using the Pythagorean theorem, we can find x when h = 12:

x² + 12² = 16²

x² + 144 = 256

x² = 256 - 144

x² = 112

x = √112 ≈ 10.58 ft

Substituting the values into the differentiation equation:

2(10.58)(2) + 2(12)(dh/dt) = 0

21.16 + 24(dh/dt) = 0

24(dh/dt) = -21.16

dh/dt = -21.16 / 24

dh/dt ≈ -0.8817 ft/s

Therefore, when the top of the ladder is 12 feet above the ground, the foot of the ladder is moving away from the wall at a rate of approximately 0.8817 ft/s.

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One of Pryor's 10 Laws of shaping is D. Train one behavior at a time is one of Pryor's 10 Laws of shaping. This law emphasizes the importance of focusing on one behavior at a time when shaping behavior.

By doing so, the trainer can avoid confusing the animal and can more effectively reinforce the desired behavior. This law also helps the trainer to break down complex behaviors into smaller, more manageable parts, which can then be shaped individually.

According to Karen Pryor's 10 Laws of Shaping, one of the key principles is to train one behavior at a time. This is important because it helps the learner to focus on mastering a specific behavior without getting overwhelmed or confused by multiple tasks.

By concentrating on one behavior at a time, the trainer can provide clear, consistent reinforcement and feedback, which increases the likelihood of successfully shaping the desired behavior.

Overall, following this law can lead to more successful shaping and training outcomes.

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Among the provided options, Pryor's 10 Laws of Shaping suggests training one behavior at a time. This technique avoids confusion and ensures reliable behavior is established before moving to the next behavior.

According to Pryor's 10 Laws of Shaping, among the given options, the correct answer is: Train one behavior at a time. This rule focuses on the fact that trying to shape multiple behaviors simultaneously can often lead to confusion for the individual or animal being trained. Instead, it's more effective to focus on one behavior at a time, reinforcing each successful approximation towards the target behavior before moving on to the next. The goal is to build a strong, reliable behavior before adding complexity or new behaviors.

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Answer:

Step-by-step explanation:

A=2(10)12+2(10)9+9(12)

A=240+180+108

A=528 in^2

Answer:

There is only one way to obtain a sum of 12 when rolling two standard six-sided dice, which is to get a 6 on both dice.

The probability of rolling a 6 on one die is 1/6. Therefore, the probability of rolling a 6 on both dice is:

P(D1 = 6 and D2 = 6) = P(D1 = 6) x P(D2 = 6) = 1/6 x 1/6 = 1/36

Therefore, the probability of rolling a sum of 12 with two standard six-sided dice is 1/36.

P(D1 + D2 = 12) = 1/36

IF THIS HELPS, CAN YOU PLEASE GIVE MY ANSWER BRAINLIEST?:)

Answer:

47.88milliliters

Step-by-step explanation:

Given data

Total amount of the solution=  342 milliliters

14% is acid

Hence the amount of acid

=14/100* 342

=0.14* 342

=47.88milliliters

Therefore there are 47.88milliliters of acid

Answer:

Step-by-step explanation:

We can make an equation for this with our unknown number equal to x.

x - 13 = -2

x - 13 + 13 = -2 + 13

x = 11

11 is your answer

Answer: yes, the transformation is a dilation.

Answer:

410 Miles per Hour

Step-by-step explanation:

If the plane flew 1640 miles in 4 hours, we divide the distance by time to get how far it flew in just 1 hour.

The actual APR is not equal to advertised APR of 8%, thus it does not verify and the advertised APR is incorrect.

Price of used car bought by Stan Loll = $9,500

Down payment = 10%

Rate of Interest = 7.8%

Time = 4 years

Add-on rate = 8%

We can calculate the loan amount as follows;

Loan amount = Total price of car - Down payment

= $9,500 - 0.10 × $9,500

= $9,500 - $950

= $8,550

Now we can use this loan amount and other values to calculate monthly payment. We know,

Add-on rate = (Interest paid over the loan period) / Loan amount×100Let interest paid over the loan period be I, then

I = Add-on rate × Loan amount/100

= (8 × 8,550)/100

= $684

Using I, we can calculate the total amount repaid over the loan period.

Total amount = Loan amount + Interest

= $8,550 + $684

= $9,234

Now, monthly payment can be calculated as

Total amount / number of months= $9,234 / (4 × 12) = $192.625 ≈ $192.63

Therefore, the monthly payment is $192.63.

Verify the APR

Let the actual APR be A. Then we have;

A = 2 × (Interest rate per month) × (Loan amount / Total amount)× 100

We know that the Interest rate per month = 7.8 / 12= 0.65%

We can calculate Loan amount / Total amount as;

Loan amount / Total amount= 8,550 / 9,234= 0.9269

Now, substituting these values in above equation for A,

A = 2 × 0.65 × 0.9269 × 100= 120.44% ≈ 120.43%

Actual APR = 120.43%

Since the actual APR is not equal to advertised APR of 8%, it does not verify and the advertised APR is incorrect.

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The inverse of the function f(x) = 12x + 4 is y = (x - 4) / 12.

An inverse function or an anti function is defined as a function, which can reverse into another function.

The given function is,

f(x) = 12x + 4

Now, to find inverse function

Let y =  f(x) = 12x + 4

⇒ y = 12x + 4

Switch x and y we get,

x = 12y + 4

Solve for y

12y = x - 4

⇒ y = (x - 4) / 12

this is the required inverse function.

Thus, the inverse of the function f(x) = 12x + 4 is y = (x - 4) / 12.

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Answer:

x = 11

Step-by-step explanation:

We know that the answer we will get will be the same as BD because BD and AC are congrudent, meaning that they are exactly equal shape and size. To find 'x' our equation would be: 29 = 3x - 4. To figure this out we just add 29 and 4 which gives us 33 and then divide that by 3 which gives us 11 (our answer)

Graph C could represent a cubic function. Graphs A, B, and D do not represent a cubic function.

A cubic function is a polynomial function of degree 3, meaning it has the highest exponent of x as 3. In Graph C, the curve exhibits a smooth, "S"-shaped appearance with both positive and negative values of y, indicating it could represent a cubic function.

Graph A shows a linear function with a constant slope, which is not characteristic of a cubic function. Graph B shows an exponential growth function, characterized by a steep upward curve, which is also not representative of a cubic function. Graph D shows a quadratic function, which has a maximum or minimum point but lacks the "S"-shaped curve typically associated with a cubic function.

In conclusion, Graph C is the most likely representation of a cubic function among the options provided.

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However, the complete question should include a reference to the question:

Answer:

Graph C is the correct answer.

The Feasible region's vertices are as follows.

(24,12)(0,36)

A vertex in geometry is the intersection of two or more curves, lines, or edges. Vertices are frequently represented by the letters P, Q, R, or S. The intersection of two lines to form an angle, as well as the corners of polygons and polyhedra, are vertices according to this definition.

He desires at least two times as many flowering plants as non-flowering ones.

the amount of blossoming plants be  = x

the number of non-flowering plants be. = y

The question states

Assuming the following circumstance, inequality is:

x ≥ 2y = 0   ..............(1)

Additionally, the inequality must be reflected by at least as many flowers in the garden as:

x + 2y ≥36 .................(2)

The price of x blooming plants will be. = 8x

the cost of y nonflowering plants be = 9y

Additionally, in order to prevent inequality, he must reduce costs.

the lowest price

Now,

Ones that meet the requirements (1) and are feasible (2).

In order to overcome constraints (1) and (2), we get

using equation (1)'s value as the value for equation (2)

                             2y + y = 36

                                     3y = 36

                                     y = 36/3

                                      y = 12

then

                                   x = 24

With Equation (1) & (1) once more solved, we obtain x = 0 & y = 36.

Hence,

The Feasible region's vertices are as follows.

(24,12)(0,36)

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Answer:

d

Step-by-step explanation:

on edge

Answer:

24

Step-by-step explanation:

Answer:

-31

Step-by-step explanation:

\(-38-16-(-23) \\ \\ =-38-16+23 \\ \\ =-54+23 \\ \\ =-31\)

The true statement is that (b) The limit \(\lim_{x \to 0} f(x)\) does not exist because there is an open circle at (0, 4).

From the graph of the function (see attachment), we have the following highlight:

There is an open circle at point (0,4), the maximum point of the function f(x) and when x = 0

When there is an open circle in the graph at x = 0, then the function has no limit at this point

This is so because the value is exclusive of the function values

Hence, the limit \(\lim_{x \to 0} f(x)\) does not exist because there is an open circle at (0, 4).

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Answer:

C - The limit Limit of f (x) as x approaches 0 = 4 because both the left-hand and right-hand limits equal 4.

Step-by-step explanation:

Precalc Edge 2023

Answer:

Therefore, based on the given scatter plot, the set of numbers that matches the points is C. 8,9,8,10,8,11.

Step-by-step explanation:

The scatter plot shown represents a set of nine points on a coordinate plane. Each point consists of an x-coordinate and a y-coordinate. To determine which set of numbers corresponds to the scatter plot, we need to analyze the pattern in the given points.

Looking at the scatter plot, we observe that the x-coordinates range from 0 to 10 with an increment of 1, while the y-coordinates seem to vary.

Now let's examine the given answer choices:

A. .4,4,5,5,6,6

B. .4,10,4,11,4,12

C. 8,9,8,10,8,11

D. 10,10,10,11,10,12

Set C (8,9,8,10,8,11) among these answer choices matches the pattern observed in the scatter plot. The x-coordinates in the scatter plot range from 0 to 10, and the y-coordinates correspond to the numbers provided in set C.

Therefore, based on the given scatter plot, the set of numbers that matches the points is C.

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Answer:

A

Step-by-step explanation:

Using the sine ratio in the right triangle

sin ? = \(\frac{opposite}{hypotenuse}\) = \(\frac{26}{29}\) , then

? = \(sin^{-1}\) (\(\frac{26}{29}\) ) ≈ 64° ( to the nearest degree ) → A

Answer:

A

Step-by-step explanation:

\(Sin X = \dfrac{Opposite}{hypotenuse}\\\\Sin \ X =\dfrac{26}{29}\\\\X = Sin^{-1} \ (0.8965)\\\\x = 63.7\)

x = 64

Answer: 21 hours

Step-by-step explanation:

i’m not sure how to solve it i just guessed and got it right

Answer:

21

Step-by-step explanation: