Mt. Vesuvius has an altitude of 3000 feet. A person stands 120 feet away from the base of the volcano. What is the angle of elevation from the person on the ground to the top of the volcano?

The expression [tex]\(24x + 36y\)[/tex] represents the total cost of Coach Martinez's order for 12 team members, where [tex]\(x\)[/tex] is the cost of each pair of shorts and [tex]\(y\)[/tex] is the cost of each shirt.

The total cost [tex](\(C\))[/tex] of Coach Martinez's order can be represented by the expression:

[tex]\[ C = \text{Cost of shorts} + \text{Cost of shirts} \][/tex]

Since Coach Martinez is ordering 2 pairs of shorts and 3 shirts for each player, and there are 12 members on the team, the expression for the total cost is:

[tex]\[ C = 12 \cdot (2x) + 12 \cdot (3y) \][/tex]

Simplify this expression to get the total cost:

[tex]\[ C = 24x + 36y \][/tex]

Therefore, the expression [tex]\(24x + 36y\)[/tex] represents the total cost of Coach Martinez's order for 12 team members, where [tex]\(x\)[/tex] is the cost of each pair of shorts and [tex]\(y\)[/tex] is the cost of each shirt.

Answer:

The answer is b and d.

Step-by-step explanation:

Answer: P(x≥4) = 0.337

Step-by-step explanation: p = probability of getting head = 0.6, probability of not getting head = q = 1 - 0.6 =0.4

n = number of times experiment was performed = 5

We are to find

P(x≥4) = 1 - P(x≤3)

We can get the value of P(x≤3) using a cumulative binomial probability table.

P(x≤3) = 0.663

P(x≥4) = 1 - 0.663

P(x≥4) = 0.337

Answer:

Length=96 feet

Width=70 feet

Step-by-step explanation:

Let the length = l

The width 26 feet less than its length=l-26

Perimeter of the giant rectangular movie screen= 332 feet

Perimeter of a rectangle = 2(L+W)

332=2(l+l-26)

332=2(2l-26)

Expanding the brackets

332=4l-52

4l=332+52

4l=384

l=384/4=96

The Length of the giant rectangular movie screen is 96 feet.

The Width, W=l-26=96-26=70 feet

The dimensions of the screen are: [tex]Length: 96\ feet[/tex] and [tex]Width: 70\ feet[/tex]

To find the dimensions of the IMAX screen, we need to set up a system of equations based on the given information. Let's denote the length of the screen by [tex]\( L \)[/tex] and the width by [tex]\( W \)[/tex].

Given:

1. The width is [tex]26 \ feet[/tex] less than the length: [tex]\( W = L - 26 \)[/tex]

2. The perimeter of the rectangle is [tex]332\ feet: \( 2L + 2W = 332 \)[/tex]

First, we can simplify the perimeter equation:

[tex]\[2L + 2W = 332\][/tex]

Divide both sides by [tex]2[/tex]

[tex]\[L + W = 166\][/tex]

Now, substitute the expression for [tex]\( W \)[/tex] from the first equation into the simplified perimeter equation:

[tex]\[L + (L - 26) = 166\][/tex]

Combine like terms:

[tex]\[2L - 26 = 166\][/tex]

Add 26 to both sides:

[tex]\[2L = 192\][/tex]

Divide both sides by [tex]2[/tex]

[tex]\[L = 96\][/tex]

Now that we have the length, we can find the width using the equation [tex]W = L - 26 \)[/tex]

[tex]\[W = 96 - 26 = 70\][/tex]

Answer:

[tex]a_1 = 5,\\a_n =4 a_{n-1}[/tex]

Step-by-step explanation:

The first term of the geometric sequence is

[tex]a_1 =5[/tex].

The common ratio between the consecutive terms is

[tex]\dfrac{20}{5} = 4,[/tex]

[tex]\dfrac{80}{20} = 4;[/tex]

therefore, we see that the nth term is found by

[tex]a_n =4 a_{n-1}[/tex]

Thus, the recursive formula for the geometric sequence is

[tex]a_1 = 5,\\a_n =4 a_{n-1}.[/tex]

The recursive formula for finding the nth term of a geometric sequence is a_n = a_1 * r^(n-1), where a_n represents the nth term, a_1 is the first term, and r is the common ratio. In this case, the given sequence is 5, 20, 80. The recursive formula for this sequence is a_1 = 5 and a_n = 4 * a_(n-1).

The recursive formula for finding the nth term of a geometric sequence is given by: an = a1 * r(n-1) where an represents the nth term, a1 is the first term, and r is the common ratio. In this case, the given sequence is 5, 20, 80, ...

Since the first term is 5, and the common ratio between terms is 4, the recursive formula for this sequence is: a1 = 5 and an = 4 * an-1.

Answer:

360 mg.

Step-by-step explanation:

The medicine has a decay rate of 40% in 25 hours, which means after 24 hours its amount will be 100% - 40% = 60% it's original value.

Let us call [tex]t[/tex] the number of hours passed and [tex]d[/tex] the number of 24-hours passed, then we know that

[tex]t = 24d[/tex].

Now, the amount [tex]c[/tex] of medicine left after time [tex]d[/tex] (dth 24-hour) will be

[tex]c = 1000(0.6)^d[/tex]

and since [tex]t =24d[/tex], we have

[tex]$\boxed{c = 1000(0.6)^{\frac{t}{24} }}$[/tex]

We now use this equation to find the final amount after [tex]t =48 hours[/tex]:

[tex]c = 1000(0.6)^{\frac{48}{24} }[/tex]

[tex]c = 1000(0.6)^2 }[/tex]

[tex]\boxed{c =360mg}[/tex]

Final answer:

An appeal to authority is using an expert's statement to support a conclusion, which is valid when the statement is within the expert's field. The authority should be able to provide support for the claim, and the appeal should not be based on the authority's position alone. The fallacy of false authority arises when an individual is not actually an expert in the subject matter they are discussing.

Explanation:

The term appeal to authority or argumentum ad verecundiam involves using the statement of an expert to support a conclusion. However, not every appeal to an authority is valid. A key point is that the statement must fall within the expert's range of expertise. For example, a Nobel Laureate in Economics would not be a qualified authority on medical issues unless their advice pertains to economic factors of medicine.

An argument from authority becomes fallacious when the cited authority is not an expert in the relevant field. Moreover, the authority's position should not be the sole foundation for a conclusion; the authority must be able to provide independent support for the conclusion. When an appeal to authority is appropriate, it means that the person being cited is a recognized expert and is knowledgeable and credible in the area under discussion, such as a doctor when it comes to medical issues or a lawyer in legal matters.

Answer:

The probability associated with the range lethal morphine blood levels is 0.9902.

Step-by-step explanation:

Let X = lethal blood concentration of morphine.

The random variable X is normally distributed with parameter μ = 2.5 μg/ mL and σ = 0.95 μg/ mL.

Compute the probability of X within the range 0.05 to 4.95 μg/ mL as follows:

[tex]P(0.05<X<4.95)=P(\frac{0.05-2.5}{0.95}<\frac{X-\mu}{\sigma}<\frac{4.95-2.5}{0.95})\\=P(-2.58<Z<2.58)\\=P(Z<2.58)-P(Z<-2.58)\\=P(Z<2.58)-[1-P(Z<2.58)]\\=2P(Z<2.58)-1\\=(2\times0.9951)-1\\=0.9902[/tex]

*Use a z-table for the probability.

Thus, the probability associated with the range lethal morphine blood levels is 0.9902.

Using the properties of the normal distribution, we calculate the probability associated with the lethal morphine blood levels range of 0.05 to 4.95 µg/mL is essentially 1.0 (100%), meaning a lethal concentration is almost certain to fall within this range.

To calculate the probability associated with the range of lethal morphine blood levels, we need to use the properties of the normal distribution. The mean (μ) lethal concentration is 2.5 µg/mL and the standard deviation (σ) is 0.95 µg/mL. We are examining the range 0.05 to 4.95 µg/mL.

First, we calculate the z-scores for both the lower limit (0.05 µg/mL) and the upper limit (4.95 µg/mL) of the range using the formula:

Z = (X - μ) / σ

For the lower limit:

Zlower = (0.05 - 2.5) / 0.95 ≈ -2.58

For the upper limit:

Zupper = (4.95 - 2.5) / 0.95 ≈ 2.58

Using a standard normal distribution table, we find the corresponding probabilities for both z-scores. Since the z-scores are symmetrical about the mean, the probability for both is the same. Thus, the probability up to Zlower is about 0.495 (adjusted from table values), and the probability up to Zupper is also about 0.495.

To find the probability within the range, we subtract the probability of the lower limit from the upper limit:

P(0.05 µg/mL < X < 4.95 µg/mL) = P(Zupper) - P(Zlower)

P(0.05 µg/mL < X < 4.95 µg/mL) ≈ 0.495 - (1 - 0.495) = 0.495 - 0.505 = -0.01

The negligible negative value suggests an error, likely due to rounding issues when looking up z-scores in the standard normal distribution table. Correctly, the total area under the curve, which corresponds to the probability of the range, should be virtually 1.0 (or 100%) since both z-scores are quite extreme (far in the tails of the distribution).

Therefore, practically, the probability associated with the given range of lethal morphine blood levels is essentially 1.0 (or 100%), meaning it is almost certain that a lethal concentration falls within this range.

Answer:

The vertex is the point (6,-31)

Step-by-step explanation:

we have

[tex]f(x)=x^2-12x+5[/tex]

This is a vertical parabola open upward

The vertex represent a minimum

Convert to vertex form

Complete the square

[tex]f(x)=(x^2-12x+6^2)+5-6^2[/tex]

[tex]f(x)=(x^2-12x+36)-31[/tex]

Rewrite as perfect squares

[tex]f(x)=(x-6)^2-31[/tex] -----> equation in vertex form

therefore

The vertex is the point (6,-31)

Answer:

The answer to your question is 224 π in³

Step-by-step explanation:

Data

Cylinder                      Cone

height = 12 in              height = 6 in

radius = 4 in                radius = 4 in

Volume = x                 Volume = y

Process

1.- Calculate the volume of the Cylinder

V = πr²h

V =  π (4)²(12)

V =  π(16)(12)

V = 192 π

2.- Calculate the volume of the Cone

V = 1/3  πr²h

V = 1/3  π(4)²(6)

V = 1/3  π(16)(6)

V = 96/3  π

V = 32 π

3.- Calculate the volume of the head

Volume = 192 π + 32 π

Volume = 224 π in³

Answer:

The answer to your question is 224 π in³

Step-by-step explanation:

Answer:

[tex] Y(t)= 475 (1.076)^t [/tex]

Where Y(t) represent the average annual per capita health care costs

475 represent the initial amount for the average annual per capita health care costs

t represent the number of years since 1970

And 1.076 represent the growth factor given by:

[tex] 1+r = 1.076[/tex]

And solving for r we got:

[tex] r = 1.076-1 =0.076[/tex]

So for this case we can say that the value 1.076 represent the growth factor.

Step-by-step explanation:

For this case we have the following model given:

[tex] Y(t)= 475 (1.076)^t [/tex]

Where Y(t) represent the average annual per capita health care costs

475 represent the initial amount for the average annual per capita health care costs

t represent the number of years since 1970

And 1.076 represent the growth factor given by:

[tex] 1+r = 1.076[/tex]

And solving for r we got:

[tex] r = 1.076-1 =0.076[/tex]

So for this case we can say that the value 1.076 represent the growth factor.

Final answer:

In the provided expression, 1.076 represents the annual growth factor of US health care costs, indicating an annual increase of 7.6% since 1970.

Explanation:

The expression 475 * 1.076 ^ t represents the average annual per capita health care costs in the US as a function of the number of years since 1970. Here, 1.076 signifies the annual growth factor of the costs, which means health care costs have been increasing by 7.6% each year since 1970. This exponential function captures the trend of increasing health care expenditure, which plays a significant role in the nation's economy, consuming a larger share of the Gross Domestic Product (GDP) over time.

Answer: the area of the shaded region is 72.96 ft²

Step-by-step explanation:

The formula for determining the area of a circle is expressed as

Area = πr²

Where

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

Diameter of circle = 16 feet

Radius = diameter/2 = 16/2 = 8 feet

Area of circle = 3.14 × 8² = 200.96ft²

The sides of the square are equal. To determine the length of each side of the square, L, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

Therefore,

16² = L² + L²

256 = 2L²

L² = 256/2 = 128

L = √128 ft

Area of the square is

L² = (√128)²

Area = 128 ft²

Area of shaded region is

200.96 - 128 = 72.96 ft²

Answer:

Vol=[tex]450,000m^3[/tex]

Step-by-step explanation:

Volume of rectangular prism is obtained using the formula:

[tex]V=whl\\w-width\\h-height\\l-length[/tex]

Dimensions of shipping containers is given as:

[tex]w=2.5m\\h=2.5m\\l=6m\\[/tex]

To obtain the volume of the cargo ship, we need to calculate the volume of 1 unit of a shipping container then multiply it by the number of containers the ship can carry.

let n be the number of containers ship can carry.

[tex]V_c=whl\\V_c=2.5m\times2.5m\times6m\\V_c=37.5m^3\\[/tex]

Volume of ship,[tex]V_s[/tex]

[tex]V_s=nV_c[/tex]

But n=12000

[tex]V_s=12000\times37.5m^3\\=450,000m^3[/tex]

Answer:

Rank (in order of decreasing strength):

HZ

HX

HY

Step-by-step explanation:

The Stronger the base the weaker its conjugate acid.

The strongest base is Y-, then the weakest conjugate acid is HY.

The weakest base is Z-, then the strongest conjugate acid is HZ.

Between them is the pair composed by X- and HX

Answer: 60°

Step-by-step explanation:

When a figure has a rotational symmetry, it maps onto itself under rotation about a point at the centre.

When an hexagon rotate onto itself,

the vertices must cover to vertices and from sides to sides. There are six angles in a hexagon and the sum of the angles is 360°. Therefore, each angle has a measure of 360°/6 is equal to 60°.

Rotating subsequently by 60 degree will rotate a hexagon onto itself. A hexagon has 6 rotations, that is, a hexagon has a rotational symmetry of 6 and at angle 60°, the hexagon will rotate onto itself.

Answer:

[tex]1\frac{1}{4} \ cups \ of \ juice[/tex] ,[tex]2\frac{2}{3}\ cups \ of \ juice[/tex]

Step-by-step explanation:

Given:

Number of people in a group = 4

Each person gets cup of juice = [tex]\frac{1}{3}[/tex]

Question asked:

How much tomato juice is needed for a group of four people ?

How much tomato juice is needed if they each get 2/3 cup of juice ?

Solution:

Unitary method:

In case of each person gets [tex]\frac{1}{3}[/tex] up of juice.

1 person gets cup of juice = [tex]\frac{1}{3}[/tex]

4 persons gets cup of juice = [tex]\frac{1}{3} \times4=\frac{4}{3} =1\frac{1}{3} \ cup \ of\ juice[/tex]

Therefore, [tex]1\frac{1}{4} \ cups \ of \ juice[/tex] is needed for a group of four people.

In case of each person gets [tex]\frac{2}{3}[/tex] cup of juice.

1 person gets cup of juice = [tex]\frac{2}{3}[/tex]

4 persons gets cup of juice = [tex]\frac{2}{3}\times4=\frac{8}{3} =2\frac{2}{3} \ cups\ of \ juice[/tex]

Thus, [tex]2\frac{2}{3}[/tex] cups of tomato juice is needed if they each get [tex]\frac{2}{3}[/tex] cup of juice.

Final answer:

To compute the needed tomato juice for four people with varying cup quantities, multiply the cup amount by the number of people.

Explanation:

To find out how much tomato juice is needed for four people if each person gets 1/3 cup, you would multiply 1/3 cup by 4 people:

1/3 cup x 4 people = 4/3 = 1 1/3 cups of tomato juice

If each person gets 2/3 cup of juice, you would multiply 2/3 cup by 4 people:

2/3 cup x 4 people = 8/3 = 2 2/3 cups of tomato juice

Answer:

P[X=3,Y=3] = 0.0416

Step-by-step explanation:

Solution:

- X is the RV denoting the no. of customers in line.

- Y is the sum of Customers C.

- Where no. of Customers C's to be summed is equal to the X value.

- Since both events are independent we have:

                         P[X=3,Y=3] = P[X=3]*P[Y=3/X=3]

              P[X=3].P[Y=3/X=3] = P[X=3]*P[C1+C2+C3=3/X=3]

        P[X=3]*P[C1+C2+C3=3/X=3] = P[X=3]*P[C1=1,C2=1,C3=1]        

              P[X=3]*P[C1=1,C2=1,C3=1]  = P[X=3]*(P[C=1]^3)

- Thus, we have:

                        P[X=3,Y=3] = P[X=3]*(P[C=1]^3) = 0.25*(0.55)^3

                        P[X=3,Y=3] = 0.0416

Answer:

The iron will need 10 amps

Step-by-step explanation:

The extension cord can support uptown 8 amps.

The iron has a 1200watts labelled on it

Converting watts to amps by dividing by 120 gives:

1200watts/120 =10 amps

The iron is 10amps

Answer:

18.6 (C)

Step-by-step explanation:

(I am assuming) it is a parallelogram, meaning that  R to the center = 1/2 (QR).

9.3 *2=QR, meaning that 18.6 is the answer.

Answer:

Consider two representations. Representation A is abstract and bears no systematic relationship to what it represents, whereas Representation B shares some features of what it represents. Representation A is a **symbolic representation** and Representation B is an **analogical representation**.

Step-by-step explanation:

Symbolic representation as it sounds, uses visual symbols to represent variable/data. This form of representation doesn't need an explanation or a relationship between the symbol and what it is representing. There are numerous examples of these all over Mathematics and Physics. For example, Angular speed is represented by ω; there isn't a direct relationship between ω and angular speed. We have just come to accept that the symbol, ω, stands for angular speed.

Analogical representation hold some of the actual characteristics of what they represent. One can tell much about what is being represented just by looking at the analogical representation.

Pictures, graphs, Maps etc., are great examples of analogical representations.

Answer:

The medical doctor prescribed 0.35 ml of insulin per day.

Step-by-step explanation:

To find out how many millimiters of insulin was prescribed we need to find out how many units we have to took. The doctor prescribed two does of 15 units and 20 units, so the total of units for the day is the sum of the two in this cas 15 + 20 = 35 units. Now we can use a proportion rule, if we have 100 units for 1 ml in 35 units we will have an x amount of ml:

x = 35/100 = 0.35 ml

The medical doctor prescribed 0.35 ml of insulin per day.

Step-by-step explanation:

Below is an attachment containing the solution

Answer:

x = 7, y = 27

Step-by-step explanation:

The triangles are equilateral triangles.  So all sides are equal, and all angles are equal (60°).

Setting sides equal:

x + 4 = 2x − 3

7 = x

Setting the angle to 60°:

2y + 6 = 60

2y = 54

y = 27

Answer:

7

Step-by-step explanation:

24/1/3 -8/5/6- 8/1/2 (accorin to fractions la)

improper fraction make it into proper fraction

73/3- 53/6- 17/2 (change the base of 3 and 2 into 6)

146/6-53/6-51/6= (146-53-51)/6

= 7

Answer:

Step-by-step explanation:

you got to try your hardest

Answer:

The answer to the question is

If Boston is at D and C is 90 km away from Boston, then the two cars will meet at 30 km from Boston.

Step-by-step explanation:

Let the speed of the car that start from C = V₁

Let the speed of the car that start from D = V₂

Therefore where V₁ = 2·V₂

We have at time t when the cars meet the distance covered by the car that start from C will be V₁×t = 2·V₂×t, while the distance of the other car will be

V₂×t

Which means that the distance covered by the car that start from C is twice that of the car that start from D

Hence if Boston is located at D which is 90 km from C then both cars will meet at

90 km /3 = 30 km from Boston as the car originating from Boston would only have covered 30 km when the two cars meet.

Answer:

Identity; conditional

Explanation:

Identity functions are functions that returns the SAME value which was used in its argument. In this case, f(x) = g(x). Therefore f(x) = g(x) = x.

Conditional functions are conditions that evaluates the condition and returns DIFFERENT values all depending on the condition value. That is, in this case, f(x) is not equal to g(x) for every x domain.

So, while identity functions returns the same value, conditional functions returns different functions.

Final answer:

An equation where f(x) equals g(x) for every x in the domain is an identity equation; otherwise, it's a conditional equation. For f(x) = x² and g(s) = s², they are the same function. Function f can be expressed in terms of y if g is invertible.

Explanation:

If f(x) equals g(x) for every x in the domain, the equation is called an identity. Otherwise, it is called a conditional equation.

For the given functions f(x) = x² and g(s) = s², we can see that they are indeed the same function, as they both satisfy the vertical-line test and map every x in the domain to a unique y in the range.

In the context of variable transformations, if y = g(x) defines a transformation from x to y, we could describe function f(x) in terms of the variable y only if there is a way to express x in terms of y. If g is invertible, then we can write f as a function of y by finding g⁻¹(y) and then applying f to it, yielding f(g⁻¹(y)).

Answer:

y = 7 csc(½ x) − 2

Step-by-step explanation:

General form of a cosecant function is:

y = A csc(2π/T x + B) + C

where A is the amplitude, T is the period, B is the horizontal offset ("phase shift"), and C is the vertical offset ("midline").

The range is (-∞, -9] [5, ∞), so the midline is halfway between -9 and 5.

C = (-9 + 5) / 2

C = -2

The amplitude is half the difference between -9 and 5.

A = |-9 − 5| / 2

A = 7

The period is twice the distance between consecutive asymptotes.

T = 2 (2π − 0)

T = 4π

So far, we have:

y = 7 csc(½ x + B) − 2

We know there is an asymptote at x = 0.  Cosecant is undefined at multiples of π, so:

½ (0) + B = kπ

B = kπ

B is any multiple of π.  The simplest choice is B = 0.

y = 7 csc(½ x) − 2

Answer:

  see below

Step-by-step explanation:

When a line goes through the origin, it expresses a proportional relationship such that for every point on the line ...

  y/x = constant

The graph shows points (-5, 4) and (5, -4) as being on the line. So, we can determine the constant to be ...

  constant = (y-value)/(x-value) = -4/5 . . . . . using point K

Then the proportion can be written as ...

  y/x = -4/5

Multiplying both sides of this equation by -1 lets us also write the same relation as ...

  -y/x = 4/5 . . . . matches the 2nd answer choice

The mode is 1. 1 shows up the most in the given data.

Answer: 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

given that in a round robin tennis tournament, each player plays every other player exactly once.

Suppose there are two players i.e. n=2, we have only one match satisfies

[tex]\frac{2(2-1)}{2} =1[/tex]

Hence P(2) is true

Assume P(k) is true.  For k players no of matches played

= [tex]\frac{k(k-1)}{2}[/tex]

To prove true for n = k+1

If to k players one new player is introduced, then the new player should play all the k players to have the condition satisfied

i.e. no of matches = no for k players + k

= [tex]\frac{k(k-1)}{2} +k\\= \frac{k^2-k+2k}{2} \\= \frac{(k+1)k}{2}[/tex]

So if true for n =k, then true for n =k+1

Already true for n =2

By induction true for all natural numbers starting from 2.