Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 14 gallons of fuel, the airplane weighs 2091 pounds. When carrying 48 gallons of fuel, it weighs 2312 pounds. How much does the airplane weigh if it is carrying 52 gallons of fuel?

The objective function that can be used to maximize the profit is Profit = 15a + 8b

Let a is the number of units of product A and b is the number of units of product B.

Profit = 15a + 8b

This function represents the total profit earned by producing a units of product A and b units of product B

Given that the profit per unit of product A is $15 and the profit per unit of product B is $8.

To maximize the profit, we would need to find the values of a and b that satisfy the constraints given in the problem and maximize the value of the objective function

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The single transformation that maps shape A to shape B is: Reflection about the line x = -2

There are different ways of carrying out transformation of objects and they are:

Reflection whereby  all the points of an object are reflected or flipped on a line called the axis of reflection or line of reflection

Rotation whereby all points are rotated about a point.

Dilation where the object is reduced or increased by a scale factor.

Translation where the object is moved from one point to another.

Looking at the given image, we can tell that this denotes a reflection because it is the exact same shape and looks like a mirror image which was reflected over the line x = -2

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If given trigonometric functions of θ are tan θ= -3/5, sec θ>0, the exact value of sin θ is 3/√(34).

To find the value of sin θ, we can use the Pythagorean identity: sin²θ + cos²θ = 1.

First, we need to find the value of cos θ. We know that sec θ = 1/cos θ and sec θ > 0, which means that cos θ > 0. Therefore, we can use the identity: tan²θ + 1 = sec²θ to find the value of cos θ.

tan θ = -3/5

tan²θ = 9/25

sec²θ = tan²θ + 1 = 34/25

cos²θ = 1/sec²θ = 25/34

cos θ = √(25/34) = 5/√(34)

Now, we can use the Pythagorean identity to find sin θ:

sin²θ + cos²θ = 1

sin²θ = 1 - cos²θ

sin²θ = 1 - 25/34

sin²θ = 9/34

sin θ = √(9/34) = 3/√(34)

In trigonometry, the six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) are used to relate the angles of a triangle to its sides. The sine function is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In other words, sin θ = opposite/hypotenuse.

Knowing the value of sin θ is important because it allows us to calculate the values of the other trigonometric functions. For example, cosine is defined as the ratio of the length of the adjacent side to the length of the hypotenuse, so we needed to find the value of cos θ to calculate sin θ.

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After considering all the given options we conclude that the number is atleast 21 and the less than 25, which is Option C.

It is given to us that two events are independent if they take place then one event does not trigger the probability of the other event.

Now if the taking place of a certain event triggers the other event then it is referred as dependent

For the given case, we have four events A, B, Q and L.

A = the state when the given number is At least 21

B = is the sate when the given number is Between 12 and 25

Q = is the sate when the given number is Odd

L = is the state when the given number is a Less than 25

It is clearly visible that events A and L are independent due to the number being at least 21, it doesn't affect whether it's less than 25 or not. So, events B and Q are independent because if we know that a number is between 12 and 25, it doesn't affect whether it's odd or not.

Hence, option C) A and L is correct.

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The complete question is

S = [10, 11, 13, 19, 21, 23, 29, 30]

A = The number is At least 21

B= the number is Between 12 and 25

Q = number is Odd

L= number is a Less than 25

Which events are independent.

Question options:

A) A and B

B) A and O

C) A and L

D) Band O

E) Land B

F) Land O

G) None of the 2 events are independent

Answer:

Option D.   [tex]g(x)=5(0.8)^{x}+2[/tex]

Step-by-step explanation:

Main concepts

Concept 1: identifying horizontal asymptote

Concept 2: assuring decreasing exponential function

Concept 1. identifying horizontal asymptote

Any exponential function of the form [tex]y=a*b^x[/tex] has a horizontal asymptote on the x-axis.  A constant (positive or negative) added to the end of the exponential expression will shift the graph of the exponential function up (if positive) or down (if negative) the number of units equal to the magnitude of the number.  Since the original function f(x) has a "+2" at the end, it has been shifted up 2 units.  Thus, we can eliminate answers A and C from feasible answers since they each shift the exponential function up 3 units, not 2.

Concept 2. assuring decreasing exponential function

Exponential functions of the form [tex]y=a*b^x[/tex] increase or decrease based on the value of "b".

Observe that the graph of the function f(x) is decreasing, and the value of b=0.5.

To ensure that g(x) also decreases, the b-value must be between 0 and 1, which eliminates option B.

Option D is the correct answer because the value of "b" is between 0 and 1 (making the graph of the function a decreasing exponential), and the number added at the end is "+2", causing the horizontal asymptote to be at a height of positive 2.

Answer:

Step-by-step explanation:

Law of sines states that the lengths of the sides of a triangle are proportional to the sines of the corresponding angles.

sinM/17 = sinx/10

sin M = .94551

.94551/17 = sin x /10

cross mulitply and then divide.

.954551 · 10/17 = sin x

9.4555/17 = .5562

sin inverse is 33.793 ° or rounded to 33.8°

Answer: ⬇️

Step-by-step explanation:

Given, u=(2,4,−5) and v=(1,−6,9).Now,3u−5v=3(2,4,−5)−5(1,−6,9)=(1,42,−60).

If a spinner divided into three equal sections marked A A and Z is spun 570 times .  The number of  times it will be expected to land on an A is 380 times.

Since the spinner has three equal sections in which two of them are marked A.  The probability of landing on an A in a single spin will be 2/3  while the probability of landing on Z  will be 1/3.

So,

Expected number of time E(A) =Number of spins x Probability of landing on A

Expected number of time E(A) = 570 x (2/3)

Expected number of time E(A)  = 380

Therefore the Expected number of time E(A) is 380 times.

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Using a linear equation, the minutes it would take both pipes to drain the swimming pool that holds 450,000 liters is 90 minutes.

A linear equation is an equation of a straight line written in the form of y = mx +b, where m is the slope.

The quantity of water the swimming pool holds = 450,000 liters

The drainage time of Pipe A working alone = 150 minutes

Drainage rate of Pipe A = 3,000 liters per minute (450,000 ÷ 150)

The drainage time of Pipe B working alone = 225 minutes

Drainage rate of Pipe B = 2,000 liters per minute (450,000 ÷ 225)

The drainage rate of the combined pipes = 5,000 liters per minute (3,000 + 2,000)

Let the number of minutes for both pipes to drain the pool = x

Therefore, the linear equation is 5,000x = 450,000

x = 90 minutes (450,000 ÷ 5,000)

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The probability that event A or B takes place is P ( A ∪ B ) = 6/17

Given data ,

Let the probability that event A or B takes place is P ( A ∪ B )

Now , the probability of A is P ( A ) = 2/17

And , the probability of B is P ( B ) = 4/17

where P ( A ∩ B ) = 0

On simplifying the equation , we get

P ( A ∪ B ) = P ( A ) + P ( B ) - P ( A ∩ B )

So , P ( A ∪ B ) = 2/17 + 4/17

P ( A ∪ B ) = 6/17

Hence , the probability is 6/17

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Answer:

Compound Interest Formula: A = P (1 + R/100)^t

A = 1000 (1 + 10/100)^10

A = $2593.74

Please mark my answer as Brainliest if you found it helpful.

Answer:

Step-by-step explanation:

Answer:

-13n + 5

Step-by-step explanation:

Give:

– 7n + –3 – 6n + 3 + 5

To Find:

simplify

Explanation:

– 7n + –3 – 6n + 3 + 5

= (-7n - 6n) + (-3 + 3 + 5)

=  - 13n + 0 + 5

= -13n + 5

Final Answer:

-13n + 5

To represent z+9=14, we can start by subtracting 9 from both sides of the equation:

z + 9 - 9 = 14 - 9

Simplifying the left side of the equation gives:

z = 5

Therefore, the solution to the equation z+9=14 is z=5.

Using two column proof we have been able to show that AB ║ EC

by definition of alternate interior angles

A two-column proof is defined as a two-column table labeled with statements on the left-hand side and reasons on the right-hand side.

The two column proof of the given diagram is as follows:

Statement 1: ΔADE is an Isosceles Triangle

Reason 1: Given

Statement 2: ∠DEA ≅ ∠DAE

Reason 2: Properties of Isosceles Triangles

Statement 3: ∠ADE = 20°

Reason 3: Sum of angles in a triangle

Statement 4: ∠BAD ≅ ∠EDA

Reason 4: Congruent Angles

Statement 5: ∠BAD and ∠EDA are alternate angles

Reason 5: Alternate angles are congruent

Statement 6: AB ║ EC

Reason 6: Definition of alternate interior angles

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Answer:

B

Step-by-step explanation:

Lateral surface contains B,C and D (because A and E are bases)

A (lateral surface area) = 70 + 70 + 56 = 196 cm^2

Answer: 100.48 cubic feet

Step-by-step explanation:

The total amount in the acount in 5 years is approximately $13,321.76.

The formula accrued amount in a compounded interest is expressed as;

[tex]A = P( 1 + \frac{r}{n} )^{n*t}[/tex]

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given that:

First, convert R as a percent to r as a decimal

r = R/100

r = 5.75/100

r = 0.0575

Plug the given values into the above formula and solve for A.

[tex]A = P( 1 + \frac{r}{n} )^{n*t}\\\\A = 10000( 1 + \frac{0.0575}{12} )^{(12*5)}\\[/tex]

A = $13,321.76

Therefore, the accrued amount is $13,321.76.

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Answer:

Earned = 25 + 18h

Earned = 151

Step-by-step explanation:

The amount earned is the travel time plus the amount per hour times the hours

Earned = 25 + 18h

She works 7 hours

Earned = 25 + 18*7

Earned = 25 + 126

Earned = 151

Since BD is the perpendicular bisector of AC, then AB = BC, which implies 2x - 8 = 5x - 17.

Solving for x, we have:

3(2x - 8) = 4425

6x - 24 = 4425

6x = 4451

x = 741.83

Rounding to the nearest whole number, we have x = 742.

Therefore, x = 742.

The measure of angle IHE is 23°.

Since DF and GI are parallel, we know that angle HJF is congruent to angle GHJ. Therefore, we have:

mHJF = mGHJ = 134°

We can now use this information to find the measure of angle IHE. To do this, we need to use the fact that the sum of the angles in a straight line is 180°. Since H, J, F, and I lie on a straight line, we have:

mHJF + mFJI + mIHE = 180°

Substituting the values we know, we get:

134° + mFJI + mIHE = 180°

Simplifying the equation, we get:

mFJI + mIHE = 46°

We still need to find the measure of angle FJI. To do this, we can use the fact that the angles in a triangle add up to 180°. Triangle GHJ is a straight line, so its angles add up to 180°. Therefore, we have:

mGHJ + mHJF + mFJI = 180°

Substituting the values we know, we get:

134° + mFJI + mFJI = 180°

Simplifying the equation, we get:

2mFJI = 46°

Dividing both sides by 2, we get:

mFJI = 23°

Finally, we can substitute this value back into our earlier equation to find the measure of angle IHE:

mFJI + mIHE = 46°

23° + mIHE = 46°

Subtracting 23° from both sides, we get:

mIHE = 23°

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Complete Question:

If DF and GI are parallel lines and mGHJ = 134°, what is mIHE?

Answer:

430

Step-by-step explanation:

Let's call the price of the television set before taxes "x".

The total cost including tax is $451.50, which is equal to x plus 5% of x (the tax). In other words:

x + 0.05x = $451.50

Simplifying the left side by factoring out x, we get:

1.05x = $451.50

Dividing both sides by 1.05, we get:

x = $430

Therefore, the price of the television set before taxes was $430.

The percent of the area that is not covered is 80 percent

In mathematics area is defined as the absolute or total space that an object or shape occupies. It is usually measured using centimeters, cm ² square or the use of meter square m ².

area of tent

= (10 - 0) * (6 - (-3))

= 90

The area of the campsite would be:

(25 - (-5) x (10 - (-5))

= 450

Then the area would be 450 - 90

= 360

the percentage that is not covered by tent = 360 / 450 x 100

= 80 percent

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The caloric content for ice cream C is 250 calories while the caloric content for ice cream B is 270 calories.

To determine the caloric content, we will assign algebraic notations to each of the dessert types.

1 Icecream + 2 Blueberry pie =   790 calories

3 icecream + 2 Blueberry pie = 1290 calories

Now the first equation will be subtracted from the second equation as follows:

2 icecream = 500 calories

So, 1 ice cream is 250 calories.

Also, since, 1 icecream serving equals 250 calories, 2 Blueberry pies = 790 - 250 = 540 calories, and 1 Blueberry pie equals 270 calories.

Complete question:

Johnny's cafe serves desserts. One serving of ice cream and two servings of blueberry pie provides 790 calories. Three servings of ice cream and two servings of blueberry pie provides 1290 calories. Find the caloric content of each item.

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If population of rabbits is increasing at a rate of 1.5% per month, after 10 months, there will be approximately 71 rabbits in the population.

To solve this problem, we need to use the formula for exponential growth:

A = P(1 + r)ᵗ

where A is the final amount, P is the initial amount, r is the growth rate as a decimal, and t is the time period. In this case, we have P = 60, r = 0.015 (1.5% expressed as a decimal), and t = 10.

Plugging these values into the formula, we get:

A = 60(1 + 0.015)¹⁰

A ≈ 71

t's important to round to the nearest whole, so we can't be exact, but we know the answer will be somewhere between 70 and 72 rabbits.

Exponential growth is a model that assumes continuous growth over time, which may not be entirely accurate in real-world scenarios.

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Answer:

270

Step-by-step explanation:

I am showing my mental math, hope this helps you:

45 x 6 is the same as 4 x 6 = 10s place value and 5 x 6 = 1s place value:

4 x 6 = 24

5 x 6 = 30

Therefore, the answer is:

2 (4 + 3) 0

270

The value of the expression 45 x 6 is 270.

We have,

To calculate the product of 45 multiplied by 6, you can follow these steps:

- Start by multiplying the units digits of the two numbers: 5 x 6 = 30.

- Write down the units digit of the result, which is 0, and carry over the tens digit, which is 3.

- Multiply the tens digit of the first number by the second number: 4 x 6 = 24.

- Add the carried-over value from step 2 to this result: 24 + 3 = 27.

- Write down the tens digit of the result, which is 7, and carry over the hundreds digit, which is 2.

- Multiply the hundred digit of the first number by the second number: 4 x 6 = 24.

- Add the carried-over value from step 5 to this result: 24 + 2 = 26.

- Write down the hundred digit of the result, which is 6.

- Combine the hundreds, tens, and units digits together: 6, 7, 0.

- The final product of 45 multiplied by 6 is 270.

So, 45 x 6 = 270.

Thus,

The value of the expression 45 x 6 is 270.

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