Mamadou spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 7325 feet. Mamadou initially measures an angle of elevation of 15 degrees to the plane at point A. At some later time, he measures an angle of elevation of 42 degrees to the plane at point BB. Find the distance the plane traveled from point AA to point BB. Round your answer to the nearest foot if necessary.

Answer:

75

Step-by-step explanation:

15 + 2 × 30

Answer:

1320 seats.

Step-by-step explanation:

The given scenario can be modeled as an arithmetic series.

[tex]\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of an arithmetic series}\\\\$S_n=\dfrac{1}{2}n[2a+(n-1)d]$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $d$ is the common difference.\\ \phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

The first term is the number of seats in the front row.

Given that the number of seats in a row increases by 2 with each successive row, the common difference is 2.

The nth term is 30 since there are 30 rows in the theater.

Therefore:

Substitute the values into the arithmetic series formula and solve:

[tex]\implies S_{30}=\dfrac{1}{2}(30)[2(15)+(30-1)2][/tex]

[tex]\implies S_{30}=15[30+(29)2][/tex]

[tex]\implies S_{30}=15[30+58][/tex]

[tex]\implies S_{30}=15[88][/tex]

[tex]\implies S_{30}=1320[/tex]

Therefore, the total seating capacity of the theater is 1320 seats.

Check below, please

1) The way to tackle this problem, is by dividing those numerators by the denominators so we can get the decimal form of each fraction, and count the marks to plot them.

2) Let's divide them:

So now, we can plot them:

Thus, this the answer.

The volume of the given rectangular prism is V = 5x⁵ + 4x⁴ + x³ cubic units.

What is the volume of the rectangular prism?
Four rectangular faces and two parallel rectangular bases make up a rectangular prism. We are aware that a rectangular prism's cross section is a rectangle. The term "Cuboid" is another name for the rectangular prism.
Therefore, the following formula is provided to determine a rectangular prism's volume: Volume = l*b*h cubic units.

Given, the length of the rectangular prism = l = x
Also, the width of the rectangular prism = w = x²
Again, the height of the rectangular prism = h = 5x² + 4x + 1
Volume of the rectangular prism = l*w*h = x*(x²)*(5x² + 4x + 1)
= x³(5x² + 4x + 1) = 5x⁵ + 4x⁴ + x³
Thus, the volume of the given rectangular prism is V = 5x⁵ + 4x⁴ + x³ cubic units.

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The third option is the correct method that solves for the variable r in the equation

Given the equation: 3/8r+ 2 = 14

Subtract 2 from both sides:

3/8r = 12

Multiply both sides by 8:

3r = 12 x 8

3r = 96

Divide both sides by 3:

r = 96/3 = 32

Therefore, the method that solve the variable r in the equation correctly is the third option.

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If the baseball diamond at a playground is a square with sides that measure 80 feet. About how long would a straight line be from home plate to second base is: B.113.1 feet.

Given data

Sides measure in feet = 80 feet.

Since the  diagonal tend to forms the hypotenuse of a right triangle with both sides of 80 feet

Hence,

Using the Pythagoreans theorem to determine the distance

(80)² + (80)² = x²

6400 + 6400 = x²

x² = 12,800

x = √ 12,800

x = 113.1 feet

Therefore the correct option is B.

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The equation that represents the total amount of money Papi's made selling pizzas on Saturday is (39 x $9.99) + (62 x $11.99) + (83 x $13.99)

Equation:

An equation is the mathematical statement which is made up of two expressions connected by an equal sign.

For example, 3x – 2 = 16 is an equation.

Given,

There are three types of pizza varieties are small, medium and large. And the price of them are $9.99, $11.99 and $13.99 respectively.

On Saturday, Papi's sold 39 small pizzas, 62 medium pizzas, and 83 large pizzas.

So, we have to write the equation for the total amount of money Papi's made selling pizzas on Saturday.

To calculate the price of the pizza we have to multiply it by the number of items sold by the cost.

So, the equation to calculate the cost of pizza,

=> number of items sold x cost.

Here we have to write the equation for three types and we have to find the total cost for it,

So, the equation is looks like,

=> (39 x $9.99) + (62 x $11.99) + (83 x $13.99)

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The student needs a minimum score of 956 to stay in the top 15% of the normal distribution.

Normal distributions are fundamental to statistics because they are widely used in the social and natural sciences to represent real-valued regressors with uncertain distributions.

Now top 15%

Therefore P=0.15

P(X<x) = 1 -0.15 = 0.85

Z-score = 1.04

Now we know that

z=(x-μ)/σ

Solving we get :

1.04 = (x - 800)/150

or, x = 956

hence the minimum score is 956.

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The angle does a 3.8 meter ladder make with the ground if it reaches 2.1 meter up the wall is 33.54 degrees and the distance between the foot of the ladder and the wall is 3.16 meters

The length of the ladder = 3.8 meter

The length of wall = 2.1 meter

Draw the figure using the measurements

We have to use the trigonometric function

The angle that a ladder make with the ground

sin θ = Opposite side / Hypotenuse

sin θ = 2.1/3.8

θ = 33.54 degrees

The distance from the foot of the ladder from the wall

cos θ = Adjacent side / Hypotenuse

cos 33.54 = Adjacent side / 3.8

Adjacent side = 3.8 × cos 33.54

= 3.16 meters

Hence, the angle does a 3.8 meter ladder make with the ground if it reaches 2.1 meter up the wall is 33.54 degrees and the distance between the foot of the ladder and the wall is 3.16 meters

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Answer:

x-intercept (-2,0)

y-intercept (0,-3)

Step-by-step explanation:

to find the x-intercept we set y=0

so 3x=-6

x=-2

to find the y-intercept we set x=0

so 2y=-6

y=-3

Answer:

324 miles

Step-by-step explanation:

Set up a proportion

243

12

=

x

16

Cross multiply

12

x

=

3888

x=324 miles

Step-by-step explanation:

Write 98 as the product of prime factors. Write the prime factors in ascending order.​

2 × 7 × 7

2 × 7 × 7 = 98

Answer: 2×7×7

Step-by-step explanation: 98= 2×7×7

Lets first know about what is prime factor :- A factor which is a Prime number and not a composite number.

prime factor in ascending order = 2,7

hence the required product of prime factor is 2×7×7 or 2×[tex]7^{2}[/tex]

(1) The system of inequalities that can be used to represent this situation is 1.25x + 2y > 375  and x+y ≤ 500 .

(2) The least number of chocolate covered almonds that must be sold to cover the cost of attending Beta convention is 126 .

In the question ,

Part(1)

let the number of chocolates be "x" .

let the number of chocolates with covered almonds be "y"

price of each chocolate bar = $1.25

price of each chocolate covered almonds = $2

Beta club needs more than $375

So , according to the question

1.25x + 2y > 375

and also the students can sell up to 500 bars and covered almonds altogether.

So , x+y ≤ 500 .

Part(2)

Given , the club sells 100 chocolate bars.

substituting x= 100 in the inequality 1.25x + 2y > 375  , we get

1.25(100) + 2y > 375

125 + 2y > 375

2y > 375-125

2y > 250

y > 125

least number of chocolate covered almonds to be sold is 126 .

Therefore , (1) The system of inequalities that can be used to represent this situation is 1.25x + 2y > 375  and x+y ≤ 500 .

(2) The least number of chocolate covered almonds that must be sold to cover the cost of attending Beta convention is 126 .

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The given calculation, -3+1-7- (-4)+10, can be rewritten as (1+4) so that it only involves addition and the result is 5.

According to the question,

We have the following expression:

-3+1-7- (-4)+10

Now, we have to remove all the negative signs from this expression.

So, we will first solve this expression to the step where we have only addition.

Now, we know that the multiplication of two negative integers is always positive.

-3+1-7+4+10

Adding the numbers with the negative sign:

-10+10+1+4

1+4

5

Hence, -3+1-7- (-4)+10 can be rewritten as (1+4) so that it only involves addition and the result is 5.

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A parabola with focus of (-5, -1) and a directrix of y=7 has the equation of the parabola as: (x + 5)² =  8 (y - 3)

Quadratic equation = parabolic equation, when the directrix is at y direction is of the form:

(x - h)² =  4P (y - k)

OR

standard vertex form, y = a(x - h)² + k     where a = 1/4p

The focus

F (h, k + p) = (-5,-1)

h = -5

k + p = -1

P in this problem, is the midpoint between the focus and the directrix

P = (-1 - 7) / 2 = -4

p = -4

the vertex

v(h, k)

h = -5

k + p = -1, k = 3

v(h, k) = v(-5, 3)

substitution of the values into the equation gives

(x - h)² =  4P (y - k)

(x - -5)² =  4 * 2 (y - 3)

(x + 5)² =  8 (y - 3)

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Answer:

Below in bold.

Step-by-step explanation:

s(t) = -16t² - 12t + 300

v(t) = ds/ dt = -32t - 12

At time t:

velocity = -32(4) - 12 = -140 ft/s.

The binomials  5x-2yz are a factor of this expression

25x^2-4y^2z^2

This is further explained below.

Generally, A binomial is a kind of polynomial that is used in algebra and is defined as the sum of two terms, each of which is a monomial.

After monomials, this is the sort of sparse polynomial that is the easiest to understand.

The word "binomial" refers to an algebraic expression that consists of just two different terms. This is a polynomial with two terms.

25 x^2-4 y^2 z^2

Rewrite 25 x^2 as (5 x)^2.

(5 x)^2-4 y^2 z^2

Rewrite 4 y^2 z^2 as (2 y z)^2.

(5 x)^2-(2 y z)^2

Since both terms are perfect squares, factor using the difference of squares formula, a^2-b^2=(a+b)(a-b) where a=5 x and b=2 y z.

(5 x+2 y z)(5 x-(2 y z))

Simplify.

(5 x+2 y z)(5 x-2 y z)

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Based on the dimensions of the shape, the area of the figure can be found to be 215 ft².

To find the area of the figure, you can divide the shape into two different shapes and then find the area of those shapes, and then sum them up to find the area of the entire figure.

As shown in the attached photo, you can divide the figure into two rectangles with the dimensions:

The areas are:

= 15 x 12

= 180 ft²

Second rectangle:

= 7 x 5

= 35ft²

The area of the figure is:

= 35 + 180

= 215 ft²

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The scientist was 83.5 feet below sea level while studying ocean life.

Given that:-

Distance the scientist ascended after studying the ocean life = 61.9 feet

Distance below sea level the scientist is after ascending = 21.6 feet

We have to find the distance by which the scientist was below sea level while studying the ocean life.

We know that,

Distance by which the scientist was below sea level while studying the ocean life = Distance the scientist ascended after studying the ocean life + Distance below sea level the scientist is after ascending

Hence, we can write,

Distance by which the scientist was below sea level while studying the ocean life = 61.9 + 21.6 = 83.5 feet.

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Answer:

5e?

Step-by-step explanation:

so if i help let me know this please

[tex]22e - 5e - 8e - 4e = 5e[/tex]

The equivalent expression of the expression given as [tex]\frac{\frac{3}{x - 2} - 5}{2 - \frac{4}{x - 2}}[/tex] is (13 - 5x)/(2x - 8)

From the question, the expression is given as

[tex]\frac{\frac{3}{x - 2} - 5}{2 - \frac{4}{x - 2}}[/tex]

Take the LCM of the fractions in the above expression

So, we have

[tex]\frac{\frac{3 - 5x + 10}{x - 2}}{\frac{2x - 4 - 4}{x - 2}}[/tex]

Evaluate the like terms of the expressions

So, we have

[tex]\frac{\frac{13 - 5x}{x - 2}}{\frac{2x - 8}{x - 2}}[/tex]

Divide the common factor x -2 in the expression

So, we have

[tex]\frac{13 - 5x}{2x - 8}[/tex]

Rewrite as

(13 - 5x)/(2x - 8)

The expression cannot be further simplified

Hence, the solution is (13 - 5x)/(2x - 8)

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The required correct answer is,

The area under P2 is 1, the area under P1 depends on the standard deviation of the dataset

i.e., Option d. is correct.

What is density curve ?

A density curve is a curve that illustrates the general shape of a data distribution. It is always above the x-axis; the area beneath it is always equal to one whole; the area beneath shows the percentage of all observations that fall in a given range. It is statistically easier to deal with a smooth curve than a histogram.

The bell-shaped density curve, which symbolizes the normal distribution, is the most well-known.

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The equation of the line is y = x - 8 which passes through the point  (13,5) with slope 1.

We have to determine the equation of a line that passes through the point (13,5) with slope 1.

The slope of a line is defined as the angle of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

Let the required line would be as

⇒ y - y₁ = m (x - x₁ )

The required line passes through the point (13, 5)

Here x₁ = 13 and y₁ = 5 and m = 1

Substituting these inputs into the above equation obtains the line equation.

⇒ y - 5 = (1)(x - 13)

⇒ y - 5 = (x - 13)

⇒ y = x - 13 + 5

⇒ y = x - 8

Thus, the equation of the line is y = x - 8 which passes through the point (13,5) with slope 1.

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Step-by-step explanation:

you don't a type your question. so if it correct i will be happy to help you

Rate of change of x with respect to [tex]\alpha[/tex] when [tex]\alpha =\frac{\pi }{3}[/tex] is 5ft/s.

Since the ladder is 10ft long resting against a vertical wall.

Let the angle between the top of the ladder and the wall is [tex]\alpha[/tex] .

And let the distance from the bottom of the ladder to the wall is x.

Thus we need to find the rate of change of x with respect to [tex]\alpha[/tex]  when [tex]\alpha =\frac{\pi }{3}[/tex]

Consider L to be the length of the ladder.

Then, L = 10ft

Thus, we get the relation between the angle and distance x i.e.

x = L [tex]\sin \alpha[/tex]

On differentiating the above equation,

[tex]\frac{dx}{dt} =L \cos \alpha[/tex]

Now after putting the values [tex]\alpha =\frac{\pi }{3}[/tex] in above equation, we get,

[tex]=(10)\cos(\frac{\pi }{3} )=(10)(\frac{1}{2} )=5[/tex]

Therefore, [tex]\frac{dx}{dt} =5[/tex] ft/s

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Answer:

10

Step-by-step explanation:

Right angles add up to 90

5x + 4x = 90

9x = 90  Divide both sides by 9

x = 10