From an aeroplane vertically above a straight horizontal road, the angles of depression of two consecutive mile stones on opposite sides of the aeroplane are observed to be α and β. Show that the height in miles of aeroplane above the road is given by tan α + tan β
tan α tan β
​

Answer: $2,275.94

Step-by-step explanation: First, we need to find how much he pays for the stocks alone. So, we would use this equation:

41.09(55)

41.09 x 55

That would get us to $2,259.95. Now, we have to add the $15.99, bc he had to pay a fee. So $2,259.95 + 15.99 = $2,275.94. I hope this helped!

option D

Given;

larger cube edge length  -  3x+2 units

smaller cube edge length -  2x-1 units

We know that  volume of a cube  = (Edge of the cube)3

volume of larger cube = (3x+2 )³

                                     =27x³+8 +54x²+36x

volume of smaller cube=(2x-1)³

                                        =8x³-1 -12x²+6x

Volume difference = volume of larger cube -volume of smaller cube

volume difference =( 27x³+8+54x²+36x)-(8x³- 1 - 12x²+6x)

                                = 19x³+9+66x²+30x

                                 =19x³+66x²+30x+9

Hence volume of larger cube is greater by (19x³+66x²+30x+9)

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The balloon's vertical distance above the ground is 358.9 feet.

An angle is said to be that of depression when it is measured downwards with respect to the horizontal plane.

So that applying the appropriate trigonometric function to solve the question, we have;

Tan θ = Opposite side/ Adjacent side

But,

θ = 90 - 24

  = 66

θ = [tex]66^{o}[/tex]

Let the vertical distance of the balloon be represented by x.

Tan 66 = 806/ x

x = 806/ Tan 66

  = 806/ 2.246

  = 358.86

x = 358.9 feet

The balloon's vertical distance above the ground is 358.9 feet.

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As per the random sampling, the marginal relative frequency for action movies is 44%.

The term sampling refers the process of selecting the group that you will actually collect data from in your research.

Here we have given that  a relative frequency table that shows the percentage of comedy lovers that prefer each location and the percentage of drama lovers that prefer each location.

And we need to find the marginal relative frequency of action movies.

While we looking into the given question, we have identified that the joint relative frequency for 8th graders who like comedy movies is 16%. And the half of the 7th graders prefer action movies.

Based on these facts the resulting frequency is 44%.

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The equation to model on this situation is :

                   0.6 = (0.75x + 0.9)/(x + 3)

Noemi makes bracelets averaging $0.60 per bead, so we need to write an equation that models this average bead cost. This can be found by dividing the total bead cost by the number of beads used.

1. The total cost of a bead can be found by multiplying the price of each type of bead by the number used and adding these values ​​together.

So:

Total Cost = 0.75x + 3*0.3

                  = 0.75x + 0.9

2. Total number of beads = x + 3

3. Thus, the average cost is:

        (0.75x + 0.9)/(x + 3)

4. Using the value of the average cost per bead given to us ($0.60), we can now write up the full equation:

                      0.6 = (0.75x + 0.9)/(x + 3)

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The function f(t) = 2cos (∏/4 t) lowest at (4,-2), (12,-2),(20,-2). The points are pl0ted in the graph.

What is a function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Given function is  f(t) = 2cos (∏/4 t).

f(t) will be lowest when cos (∏/4 t) is lowest.

The value of cosine lies between -1 to 1.

When cos (∏/4 t) = -1, f(t) has lowest value.

Solve the equation cos (∏/4 t) = -1

cos (∏/4 t) = -1

∏/4 t =cos ⁻¹ (-1)

∏/4 t = (2n + 1)∏

t = (2n + 1)4  where n is a whole number.

The value of the function is lowest at t = 4, 12, 20.

The lowest points are (4,-2), (12,-2),(20,-2) etc.

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Answer: (4, -2) (12,-2)

Step-by-step explanation:

Answer:

≈20.35°

Step-by-step explanation:

height = 8

hypotenuse =23

angle is x

sin(x) =8/23

[tex]sin^{-1} (\frac{8}{23} )[/tex] ≈20.35°

x is about ≈20.35°

The ramp makes an angle of approximately 20.86 degrees with the ground.

Given that there is a truck with a ramp at a height of 8 feet the size of the ramp is 23 feet,

we need to find the angle ramp make with the ground.

To find the angle that the ramp makes with the ground, we can use the sine function.

The sine of an angle is equal to the opposite side divided by the hypotenuse in a right triangle.

In this case, the opposite side is the height of the ramp (8 feet), and the hypotenuse is the length of the inclined portion of the ramp (23 feet).

Let's calculate the angle:

sin(angle) = opposite/hypotenuse

sin(angle) = 8/23

To find the angle, we need to take the inverse sine (or arcsine) of both sides of the equation:

angle = arcsin(8/23)

We can find the approximate value of the angle:

angle ≈ 20.86 degrees

Therefore, the ramp makes an angle of approximately 20.86 degrees with the ground.

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The value of x in the problem is 0

Given that PQR is a straight line

In this problem PQ+QR=PR

The value of PQ is 9

The value of QR is not given but given an equation 2x+3

And QR is x+12

So PQ+QR=PR

9+2x+3=x+12

12+2x=x+12

2x-x=12-12

x=0

Therefore, the value of x in the problem is 0

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Based on the provided proportional relationship, 14 skeins of yarn can make 7 scarves.

The data provided shows a proportional relationship between the number of skeins of yarn and the number of scarves made from the yarn. Proportional relationships refer to relationships between two variables where their ratios are equivalent. In order words, in a proportional relationship, one variable is always a constant value times the other. That constant is called the constant of proportionality (k). It is calculated as: k = y/x where y is the variable that changes due to change in x. Based on the information, k = 2/4 = 4/8 = 0.5.

Hence, the number of scarves made using 14 skeins of yarn is given by y = 0.5x. When x = 14, y = 0.5*14 = 7

Note: The question is incomplete. The complete question is attached.

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Answer: It's not possible for a positive, even integer to have a specific shape, such as the shape of a 4. This is because integers are abstract mathematical concepts that represent whole numbers and do not have any physical properties, such as shape. Additionally, even integers are simply integers that are divisible by 2, and do not have any specific shape associated with them.

If you're asking about a specific number that has the shape of a 4, such as the number "4" written in a specific way, it's important to note that the value of a number does not depend on its physical appearance. For example, the number 4 written as "4" and the number 4 written as "IV" (the Roman numeral for 4) are both the same number, and have the same value.

The percent of increase Maria walked if found as the 50%.

The formula for the percentage increase is given as;

Percent increase = Increase / original number x 100

original number = 20 miles

Increase = 30 miles - 20 miles

Increase = 10 miles

So,

Percent increase = 10 / 20 x 100

Percent increase = 50%

Thus, the percent of increase Maria walked if found as the 50%.

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The correct question is-

9) Maria walked 20 miles yesterday. Today she walked 30 miles. What was the percent of increase Maria walked?

To create a  finite-state machine that models an old fashioned soda machine which can perform the stated work we can follow the given steps.

The machine accepts nickels (5 cents), dimes (10 cents) and quarters (25 cents).

Let the states be s , s1 ,s2 ,s3 ,s4 etc.

If we add a nickel to the machine, then the the input is 5 to the current state s , we move them to state s+1 ans so on , and similarly for dime and quarter.

On taking x a the input button for soda pop , we can create the required  finite-state machine that models an old fashioned soda machine that accepts nickels, dimes, and quarters.

A finite-state machine (FSM), sometimes known as a finite automaton  or simply a state machine, is a mathematical model of computation.

It is an abstract machine that can only be in one of a finite set of states at any one moment. In response to some inputs, the FSM can transition from one state to another; this transition is referred to as a transition. An FSM is defined by a set of states, an initial state, and the inputs that cause each transition.

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Answer:

x = 2

Step-by-step explanation:

Simplify both sides of the equation.

[tex]x(2)+4x-9=x+1\\2x+4x+-9=x+1\\(2x+4x)+(-9)=x+1[/tex] (combine like terms)

[tex]6x+-9=x+1\\6x-9=x+1\\[/tex]

subtract x from both sides.

[tex]6x-9-x=x+1-x\\5x-9=1[/tex]

add 9 to both sides.

[tex]5x-9+9=1+9\\5x=10[/tex]

divide both sides by 5

[tex]\frac{5x}{5} =\frac{10}{5} \\x=2[/tex]

Two triangles are similar if they have the same ratio of corresponding sides and equal pairs of corresponding angles.

If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures. Consider a hula hoop and the wheel of a cycle, the shapes of both these objects are similar to each other as their shapes are the same.

Triangle is a three-sided polygon. The condition for the similarity of triangles is;

i) Corresponding angles of both the triangles are equal, and

ii) Corresponding sides of both the triangles are in proportion to each other.

Properties of the triangle:

1-Both have the same shape but sizes may be different

2-Each pair of corresponding angles are equal

3-The ratio of corresponding sides is the same

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Answer:

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

Since AB and QS are parallel, the segment AB divides QR and SR proportionally.

As QR = QA + AR we get:

Answer:

864

Step-by-step explanation:

The six trigonometric functions at 11π/3 are as follows-

sin (11π/3) = -[tex]\sqrt{3}[/tex]/2

cos (11π/3) = 1/2

tan (11π/3) = -[tex]\sqrt{3}[/tex]

cot (11π/3) = -1/[tex]\sqrt{3}[/tex]

sec (11π/3) = 2

cosec (11π/3) = -2/ [tex]\sqrt{3}[/tex]

Let us evaluate the six trigonometric functions at 11π/3 as follows -

11π/3 can be written as (6π+5π)/3 = 2π + 5π/3.

a. sin (11π/3) = sin (2π + 5π/3)

this angle is greater than or equal to 0 and less than 2π.

= sin (5π/3)

Finding the angle with equivalent trigonometric values in the first quadrant. Also, sin is negative in the 4th quadrant.

= -sin (π/3)

= -[tex]\sqrt{3}[/tex]/2

Hence, sin (11π/3) = -[tex]\sqrt{3}[/tex]/2

b. cos (11π/3) = cos (2π + 5π/3)

this angle is greater than or equal to 0 and less than 2π.

= cos (5π/3)

Finding the angle with equivalent trigonometric values in the first quadrant. Also, cos is positive in the 4th quadrant.

= cos (π/3)

= 1/2

Hence, cos (11π/3) = 1/2

c. tan (11π/3) = tan (2π + 5π/3)

this angle is greater than or equal to 0 and less than 2π.

= tan (5π/3)

Finding the angle with equivalent trigonometric values in the first quadrant. Also, tan is negative in the 4th quadrant.

= -tan (π/3)

= -[tex]\sqrt{3}[/tex]

Hence, tan (11π/3) = -[tex]\sqrt{3}[/tex]

d. cot (11π/3) = 1/ tan (11π/3)

Hence, cot (11π/3) = - 1/ [tex]\sqrt{3}[/tex]

e. sec (11π/3) = 1/ cos (11π/3)

Hence, sec (11π/3) = 2

f. cosec (11π/3) = 1/ sin (11π/3)

Hence, cosec (11π/3) = -2/ [tex]\sqrt{3}[/tex]

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The solution of the algebraic equation is n = (3-4c)/p

An algebraic equation or expression is any equation that contains unknown values, usually represented with alphabets or letter

Given: -np-5=4(c-2)​

-np-5 = 4(c-2)​

Expand the bracket:

-np-5 = 4c-8

Collect like terms:

-np = 4c-8+5

-np = 4c-3

Divide both sides by -p:

n = -(4c-3)/p

n = (-4c+3)/p = (3-4c)/p

Thus, the solution is n = (3-4c)/p

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The time taken to drain 23 liter at the rate of 2.5 liters per minute=9 minutes.

A cistern is a tank used to hold liquids, usually water, and it contains inlet and outlet pipes so it can fill up or empty itself. A pipe is a segment of a hollow cylindrical object used to transport water from one location to another. The cistern or tank typically has pipes attached to it so that they may be filled and emptied. Part of the tank evacuated in an hour is equal to 1/y if it takes y hours to completely empty it. If a pipe can completely fill and drain a tank in x and y hours, respectively. The net portion of the tank will be filled in one hour when both pipes are opened simultaneously, assuming y>x, by the formula (xy) = (xy) / (y-x).

70 liters of water were initially present in a water tank.

2.5 liters of water were drained every minute.

The tank holds 47 liters before water is added, thus 70-47 =23 liters.

Therefore,23/2.5=9.2 is the time it takes to drain 23 liters at the rate of 2.5 liters per minute.

Taking 2.5 liters per minute to fill a 23liter container takes 9.2minutes.

Water filled in a certain amount of time is equal to the water filling rate in minutes.

Taking 2.5 liters per minute to drain a 23liter container will take 9 minutes.

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Answer:

Angular Displacement: 180° or π radians

Angular Velocity: 3°/sec or 0.0524 radians/sec

Angular Acceleration: 0°/sec^2 or 0 radians/sec^2

Step-by-step explanation:

P-Value for the hypothesis test will be of z = 1.9065

The P-value for conducting the right-tailed test H0 : μ = 3 versus HA : μ > 3 is the probability that we would observe a test statistic greater than t* = 2.5 if the population mean

μ really were 3. Recall that probability equals the area under the probability curve. The P-value is therefore the area under a tn - 1 = t14 curve and to the right of the test statistic t* = 2.5. It can be shown using statistical software that the P-value is 0.0127

The P-value, 0.0127, tells us it is "unlikely" that we would observe such an extreme test statistic t* in the direction of HA if the null hypothesis were true. Therefore, our initial assumption that the null hypothesis is true must be incorrect. That is, since the P-value, 0.0127, is less than

α

= 0.05, we reject the null hypothesis H0 : μ = 3 in favor of the alternative hypothesis HA : μ > 3.

Note that we would not reject H0 : μ = 3 in favor of HA : μ ≠ 3 if we lowered our willingness to make a Type I error to α = 0.01 instead, as the P-value, 0.0254, is then greater than

α= 1.9065.

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A bi-weekly visit to your favorite restaurant. Say on average you spend $25 each visit.

You will spend an average of $50 a week at this restaurant.

Answer:

Step-by-step explanation:

Angle E = W =119 degree

Angle V = 360-105-59-119

Angle V = 77

As DEFG = VWXY

There for D = V

So angle D = 77

Angle G = 360 -77-59-119

Angle = 105

Answer:

119 degree

Step-by-step explanation:

Any similar polygons have:

1- congruent corresponding angles

2- proportional corresponding sides

Here the question asking about measure of angle E.

The easiest way to find the corresponding angles by comparing the polygons names DEFG and VWXY, the 1st letter in both are D and V, that means these two angles are corresponding and congruent. Same for the 2nd letter in both are E and W, that means angle E is congruent to angle W which is 119 degree.

Done

Answer: [tex]14\sqrt 2[/tex]

Step-by-step explanation:

The combination of streamers and balloons at the Party Palace will be 21 and 34, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Marisol necessities to buy Somewhere around 55 party enrichments. The Party Castle charges $0.50 per beautiful decoration and $0.25 per expansion, including the charge.

Let 'x' be the number of decorative streamers and 'y' be the number of balloons. Then the equations are given as,

0.50x + 0.25y = 19           ...1

x + y = 55                         ...2

From equations 1 and 2, then we have

0.50x + 0.25(55 - x) = 19

0.25x = 5.25

x = 21

The value of y is given as,

21 + y = 55

y = 34

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Answer:

Graph A

Step-by-step explanation:

Given piecewise function:

[tex]f(x)=\begin{cases}9+x, \;\;\:\:x\leq3\\x^2+3,\;\;x > 3\end{cases}[/tex]

To graph the given piecewise function:

The line  y = 9 + x  is a straight line with a positive gradient.  

It crosses the x-axis at (-9, 0) and crosses the y-axis at (0, 9).

Therefore, the only graph that shows the line  y = 9 + x  is the first graph.

The Error checking button provides an automatic means of checking for mathematical errors within formulas of a worksheet.

The modeling process begins with the framing of a conceptual model that shows the relationships between the various parts of the problem being modeled.

Arrows pointing from the selected cell to cells that depend on the selected cell are generated by using the Trace dependents button of the Formula Auditing group.

nodes in an influence diagram represent part of the model

The Trace Precedents button, located in the Formula Auditing group, creates arrows pointing to the selected cell from cells that are part of the formula in that cell

The Error checking button provides an automatic means of checking for mathematical errors within formulas of a worksheet.

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Answer:

Below

Step-by-step explanation:

If you turn it sideways and use the y-axis portion as the base (4)  , you can see height = 5

Area = 1/2 * b * h =    1/2 *  4 *5 = 10 units^2

Step-by-step explanation:

-5 is greater than or equal to k-16

-5 ≥ k - 16

add 16 to both sides:

-5 + 16 ≥ k - 16 + 16

11 ≥ k

Answer:

Step-by-step explanation:

k-16 is greater then -5.