An airplane cruises at an altitude of 35,000 feet. It begins its descent at a rate of 1,200 feet per minute. Find a linear model in the form h(t)=mt+b where h represents the altitude of the plane, in feet, after t minutes into its descent.

Answer:

0 = 0 means that there are infinite solutions.

Step-by-step explanation:

Equation is -5(-4+2n)=-10(n-2)

1. Distribute the -5 and -10

20 -10n = -10n + 20

2. Subtract 20 from one side to the other to get only 1 variable on 1 side.

-10n = -10n

3. divide -10 to separate the variable from the constant.

n = n

This means there are infinite solutions.

Answer:

c=30

Step-by-step explanation:

Inverse: 22 + 8 = 30

c = 30

Answer:

c = 30

Step-by-step explanation:

Step 1: Add 8 to both sides.

Step 2: Check if solution is correct.

Therefore, the answer is c = 30.

(a) 6/245 is the probability that you and your friend joe are among the chosen.

(b) 68/245 the probability that you or your friend joe are among the chosen.

Q5. 0.5372 is the probability that i have chosen bag 1.

(a) The probability of you being chosen is 15/50, or 3/10.

Once you are chosen, there are 49 students left in the class, including Joe. The probability of Joe being chosen from the remaining 49 students is 14/49.

So the probability of both you and Joe being chosen is:

(3/10) x (14/49) = 6/245

(b) The probability of either you or Joe being chosen is the probability of you being chosen plus the probability of Joe being chosen, minus the probability of both of you being chosen (because we don't want to count that twice):

(3/10) + (14/49) - (6/245) = 68/245

Q.5

Let A be the event that bag 1 is chosen and B be the event that exactly 2 red marbles are chosen.

We want to find P(A|B), the probability that bag 1 is chosen given that exactly 2 red marbles are chosen.

Using Bayes' theorem, we have:

P(A|B) = P(B|A) x P(A) / P(B)

P(A) is the probability of choosing bag 1, which is 1/2.

P(B|A) is the probability of getting exactly 2 red marbles given that bag 1 is chosen.

This can be calculated using the hypergeometric distribution:

P(B|A) = (10 choose 3) x (6 choose 2) / (16 choose 5) = 0.2616

P(B) is the overall probability of getting exactly 2 red marbles, which can be found by using the law of total probability:

P(B) = P(B|A) x P(A) + P(B|not A) x P(not A)

where P(not A) = 1 - P(A) = 1/2.

P(B|not A) is the probability of getting exactly 2 red marbles given that bag 2 is chosen.

This can also be calculated using the hypergeometric distribution:

P(B|not A) = (15 choose 3) x (6 choose 2) / (21 choose 5) = 0.2249

So we have:

P(B) = 0.2616 x 1/2 + 0.2249 x 1/2 = 0.2432

Finally, we can plug all of these values into Bayes' theorem to find P(A|B):

P(A|B) = 0.2616 x 1/2 / 0.2432 = 0.5372

So, the probability that bag 1 was chosen given that exactly 2 red marbles were chosen is approximately 0.5372.

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Answer:

100\(\pi\) cubic cm

Step-by-step explanation:

The volume of a cone can be represented by the formula \(\frac{1}{3} \pi r^{2} h\). Since we know the radius is 5, all we need to find id the height. To do that, we can use the Pythagorean theorem, and see that the height is equal to 12. Plugging the numbers into the formula gives us:

\(V =\frac{1}{3} \pi (5^{2}) (12)\)

\(V = 100\pi\)

HOPE THIS HELPED! :)

Answer:

B. Irrational

Step-by-step explanation:

The √14 = 3.74 recurring. This isn't an integer and therefore can't be written as a fraction. Therefore it's an irrational number.

Whereas, if it was √16 which equals 4, the answer would be rational as it is an integer which can be written as a fraction such as 4/1 or 8/2 etc.

Answer:

43.6 mm²

Step-by-step explanation:

Answer:

55% of the students surveyed said their favorite color was blue

Step-by-step explanation:

\(\frac{209}{380}\) as a percent = 55%, or 0.55 in decimal form.

The  expression represents the total surface area of the prism is

2 (5 * 7) + 2 (4 * 7) +  2  (4 * 5)

The term "TSA" stands for "Total Surface Area" of a prism. The Total Surface Area represents the  sum of the areas of all the faces (including the bases) of the prism.

for the rectangular prism, the Total Surface Area can be calculated using the formula:

TSA = 2lw + 2lh + 2wh

where

l = 5

w = 4

h = 7

plugging in the values gives

TSA = 2 (5 * 7) + 2 (4 * 7) +  2  (4 * 5)

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Answer:

\(\frac{9}{28}\)

Step-by-step explanation:

Given expression:

 Find the quotient;

                      =      \(\frac{2}{7}\)  ÷ \(\frac{8}{9}\)

Now, let us solve the problem;

          the division sign will invert  \(\frac{8}{9}\);

                     =    \(\frac{2}{7}\)  x \(\frac{9}{8}\)

                               2 will go in 8

                   = \(\frac{1}{7}\) x \(\frac{9}{4}\)

                   = \(\frac{9}{28}\)

We can expand

\(f(x,y,z) = xy\ln(yz) = xy \ln(y) + xy\ln(z)\)

Then using the product and chain rules,

\(\dfrac{\partial f}{\partial x} = y\ln(y) + y\ln(z) + \boxed{y\ln(yz)}\)

\(\dfrac{\partial f}{\partial y} = x\ln(y) + \dfrac{xy}y + x\ln(z) = \boxed{x\ln(yz) + x}\)

\(\dfrac{\partial f}{\partial z} = \boxed{\dfrac{xy}z}\)

Step-by-step explanation:

√2x² + 7x +√2=0

2x + 7x + √ 2 =0

√2=9x

x = o.15713484

Because EF = GH = 4, EF≅GH, Because these are vertical line segments, their are slope undefined and they are parallel. EF and GH are opposite sides that are equal and parallel. So, EFGH is a parallelogram by the definition of a parallelogram.

What is a parallelogram?

A parallelogram is a simple quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposite or facing sides are equal in length, and its opposite angles are equal in size.

Given that E(-3,0), F(-3,4), G(3,-1),H(3,-5)

The quadrilateral is attached below.

The distance between two points (x₁, y₁) and (x₂, y₂) is √[(x₂ - x₁)² + (y₂ - y₁)²].

The length of EF is √[(-3 -(-3))² + (4- 0)²] = √4² = 4

The length of GH is √[(3 -3)² + (-1- (-5))²] = √4² = 4

Therefore, EF = GH = 4

The line segments are congruent.

The line segments are vertical, thus the slope of the line is undefined.

If opposite sides are equal and parallel, then the quadrilateral is a parallelogram.

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Answer: $25.90

Step-by-step explanation:

We will have x as the youngest son's share, (the youngests son's share is the basis)

(x + 4.30) as the eldest son's share, (the eldest received 4.30 more than the youngest)

(x - 7.80) as the second son's share, (the second received 7.80 less than the youngest)

and 64.90 as their share altogether.

To find the youngest son's share:

(x) + (x + 4.30) + (x - 7.80) = 64.90

x + x + 4.30 + x - 7.80 = 64.90

x + x + x = 64.90 - 4.30 + 7.80 (group all of the like terms together. variables with variables, numbers with numbers. 4.30 became negative since it was moved to the other side, the same happened with 7.80 since it was a negative, it became a positive when it moved to another side)

Solve...

x + x + x = 64.90 - 4.30 + 7.80

3x = 68.40 (divide both sides by 3)

\(\frac{3x}{3} = \frac{68.40}{3}\)  

x = 22.80

(The youngest son's share is $22.80)

To get the eldest son's share:

x + 4.30 (substitute x since it has already been solved)

22.80 + 4.30 = 27.10

The eldest son's share is $27.10

The width cannot be negative, the width of the walkway is 6 feet. The total area of the garden and the walkway is given as 648 square feet. We know the area of the garden is length multiplied by width, which in this case is 12 feet by 15 feet, so the garden area is\(12 \times 15 = 180\) square feet.

To find the area of the walkway, we subtract the garden area from the total area. Therefore, the area of the walkway is 648 - 180 = 468 square feet.

The walkway surrounds the garden on all sides, so its length and width will be greater than the corresponding dimensions of the garden.

To calculate the width of the walkway, we can use the formula for the area of a rectangle, which is length multiplied by width. In this case, the length is 12 + 2x (twice the width of the walkway) and the width is 15 + 2x.

So, we have the equation\((12 + 2x) \times (15 + 2x) = 468\).

Expanding and rearranging the equation, we get\(4x^2 + 54x - 228 = 0.\)

Solving this quadratic equation using factoring, completing the square, or the quadratic formula, we find that x = 6 or x = -9/2.

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Answer:\(5^{3}\)

Step-by-step explanation:

Answer:

-5 to the forth power

Step-by-step explanation:

The solution to the system of equations is 6x – 2y = -14 with x = -4 and y = -5

4x – 3y = -31

To find x or method, you must first make one of the words the same so that they may cancel out.

To determine the x terms, we will make the y terms the same in this example.

To do so, multiply the first equation by three, yielding:

18x – 6y = - 42

And multiply the second equation by two to get:

8x – 6y = - 62

Now that we have the y terms, you may cancel them out.

You now have the following two equations:

18x = -42

8x = -62

The next step is to combine them, since the preceding – and – form a +.

This implies that you are left with one equation

26x = -104

Now divide by 26 on each side to get:

x = -4

As you have x, you substitute it into one of the ORIGINAL equations.

6x – 2y = -14

Substitute x in:

6(-4) – 2y = -14

-24 – 2y = -14

Add 24 on each side to get:

-2y = 10

y = -5

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Answer:

neither of them are

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

the answer is vertical angles are angles that are opposite from each other

With the help of percentage increase information, we conclude that,  Americans spent approximately $1,141.31 on summer vacation in 2014.

What is percenatge increase?

Percentage increase is a measure of how much a value has increased in comparison to the original value, expressed as a percentage.

To find what Americans spent in 2014, we need to use the percentage increase and the 2015 amount.

Let X be the amount spent in 2014.

We know that the increase from 2014 to 2015 is 3.4%, which can be expressed as:

3.4% = 0.034 (as a decimal)

We also know that the amount spent in 2015 is $1,180.

Using this information, we can set up an equation:

X + 0.034X = 1180

Simplifying the left side:

1.034X = 1180

Dividing both sides by 1.034:

X = 1141.31

So Americans spent approximately $1,141.31 on summer vacation in 2014.

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Answer:

15-18

Step-by-step explanation:

The IQR is the middle 50% of a set of numbers

There are 8 numbers, so its the middle 4

The middle 4 consists of 15,15,16,18

The range is 15-18

Answer: 0.35

Step-by-step explanation:

Times 7 = 2. 45kg

The value of x is 21

The other angles are 63°, 117°, 63°, 117°

Given:

The angles of a parallelogram ABCD are

∠A = 3x°

∠B = (5x+12)°

To find:

The value of x

Parallelogram ABCD,

∠A and ∠B are two adjacent sides

Properties of a parallelograms

Two opposite sides are parallelogram are equal and parallel to each other.

So, the adjacent sides are supplementary angles i.e. sum is 180°.

The opposite angles are equal.

Now,

∠A + ∠B = 180°

⇒ 3x + (5x + 12) = 180

⇒ 3x + 5x + 12 = 180

⇒ 8x + 12 = 180

⇒ 8x = 180 - 12

⇒ 8x = 168

⇒ x = 168 ÷ 8

⇒ x = 21

Thus,

The value of x = 21

The angles are

∠A = 3x = 3 * 21 = 63°

∠B = (5x + 12) = (5 * 21 + 12) = 105 + 12 = 117°

As opposite angles are equal so

∠A = ∠C = 63°

∠B = ∠D = 117°

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Answer:

To one decimal place,

y = 16.3 m

Step-by-step explanation:

Using SOHCAHTOA,

In this case we need to use CAH,

WE know the angle = 25 and the hypotenuse H = 18,

so,

y = adjacent

\(cos(angle) = y/H\\y = (18)(cos(25))\\y = 16.3135\\y = 16.3\)

Answer: 16.3 in.

Step-by-step explanation:

use SOH CAH TOA

cos x = adj/hyp

cos 25  = y/18

18 cos 25  = y

y= 16.3

Answer:

Step-by-step explanation:

0.01 is the largest decimal in the pair of 0.01 and 0.005

Answer:

So first subtract 14 from 32

That means that -6y+4y = 18

Simplify the left side 4-6=-2

-2y = 18

Divide by -2

-9 = y

Step-by-step explanation:

Answer:

-9

Step-by-step explanation:

-6y+14+4y=32

Combine like terms

-2y +14 = 32

Subtract 14 from each side

-2y +14-14 = 32-14

-2y =18

Divide each side by -2

-2y/-2 = 18/-2

y = -9

Answer:

The said friend's grade in Professor Ivy's class is 85.7.

Step-by-step explanation:

Assuming the question asks for your friend's grade in Professor Ivy's class.

0.05(95) + 0.25(89) + 0.25(80) + 0.45(86) = 85.7

Answer:

\(9x^2+14x+1\)

Step-by-step explanation:

Hey there!

In order to find the answer to this problem, we must first form an equation; then we can solve/simplify it further

Our Equation:

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

\((9x^2+5x+8)+(9x-7)\)

1. Distribute the positive sign: positive and positive make positive, positive and negative make negative, negative and negative make positive

\(9x^2+5x+8+9x-7\)

2. Combine like terms in each parenthesis: This means combining the x values and the constants.

\(9x^2+14x+1\)

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

This means that when you add the two given values, the answer you get is: \(9x^2+14x+1\)

Answer:

nice

Step-by-step explanation:

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