In the triangle above, a = 45. What is the value of b ?

Rounding to the nearest whole number, the distance from Mike's eyesight to the top of the statue is approximately 27 ft.

To find the distance from Mike's line of sight to the top of the statue, we can use trigonometry and the concept of similar triangles. Let's assume the distance from Mike's eyesight to the top of the statue is represented by 'd'. We have two right triangles:

Triangle 1: Mike's triangle

Angle of elevation: 11°

Opposite side: Mike's height = 5 ft

Adjacent side: Distance from Mike's eyesight to the statue = d ft

Triangle 2: Statue triangle

Angle of elevation: 90°

Opposite side: Statue height = 420 ft

Adjacent side: Distance from Mike's eyesight to the statue = d ft

We can use the tangent function to set up the equation:

tan(11°) = (Mike's height) / (Distance from Mike's eyesight to the statue)

tan(11°) = 5 / d

To find d, we can rearrange the equation:

d = 5 / tan(11°)

Using a calculator, the value of d is approximately 27.48 ft.

To know more about distance,

https://brainly.com/question/10276808

#SPJ11

A.  Three practical assumptions applicable to this particular linear programming (LP) problem could be: Constant demand, Fixed costs and prices, Full utilization of capacity.

B. LP Model: Decision Variables, Objective Function, Constraints.

C. set up the LP model in Excel and run Solver to obtain the answer and sensitivity reports.

D. it would not be feasible to deploy buses to Malacca.

E. The revenue would decrease due to the lower number of passengers, while the cost may remain relatively fixed (assuming the breakdowns do not incur additional repair costs).

(a) Three practical assumptions applicable to this particular linear programming (LP) problem could be: Constant demand, Fixed costs and prices, Full utilization of capacity.

Constant demand: The LP model assumes that the demand for Merlion's point-to-point coach services remains constant throughout the planning period. This means that the number of passengers traveling between Singapore and Malaysia is assumed to be consistent.

Fixed costs and prices: The LP model assumes that the costs associated with operating the buses, such as fuel, maintenance, and driver salaries, remain fixed. It also assumes that the ticket prices charged to passengers are constant and do not change based on factors like demand or competition.

Full utilization of capacity: The LP model assumes that all available seats on each bus will be filled by passengers. It does not account for scenarios where there might be empty seats due to insufficient demand or other factors.

(b) LP Model: Decision Variables, Objective Function, Constraints.

Decision Variables:

Let X i represent the number of buses deployed to city i, where i can take values 1 to n (n being the total number of cities in Malaysia).

Objective Function:

Maximize daily profit:

Maximize Profit = ∑(Revenue - Cost)

Constraints:

Capacity constraint for each city:

∑(X i * Seats per Bus) ≤ Total Available Seats

Demand constraint for each city:

X i ≥ Minimum Demand i

Non-negativity constraint:

X i ≥ 0 for all i

(c) Solution using Excel Solver:

Please provide the following information:

Total available seats

Seats per bus

Minimum demand for each city

Revenue and cost data

With the given input, I can help you set up the LP model in Excel and run Solver to obtain the answer and sensitivity reports.

(d) To determine the profit per passenger required for buses to be deployed to Malacca, we need to consider the revenue and cost associated with each passenger. Let's assume the revenue per passenger is R and the cost per passenger is C.

The profit per passenger can be calculated as follows:

Profit per Passenger = Revenue per Passenger - Cost per Passenger

To deploy buses to Malacca, the profit per passenger should be at least equal to zero or positive. If the profit per passenger is negative, it means that the cost per passenger is higher than the revenue per passenger, resulting in a loss for each passenger. In such a case, it would not be feasible to deploy buses to Malacca.

(e) If two buses were to break down on a given day, it would impact Merlion's profit because there would be a reduction in the number of available buses to transport passengers. This could result in a lower revenue as fewer passengers can be accommodated.

To analyze the impact on profit, you would need to consider the revenue and cost implications of operating with reduced capacity. The revenue would decrease due to the lower number of passengers, while the cost may remain relatively fixed (assuming the breakdowns do not incur additional repair costs).

By estimating the revenue and cost changes based on the reduced capacity, you can compare the new profit with the original profit to determine the impact.

Learn more about  function  from

https://brainly.com/question/11624077

#SPJ11

Answer:

Associative Property of Addition

Step-by-step explanation:

The centre of dilation of second circle is same as of first circle and the scale factor is found to be r.

By evaluating the length about one side of such pre-image to the relate to the overall of the post-image, one can establish the scale factor of the dilation. The pre-image must always be multiplied by the scaling factor in order to equal its post-image.

Here, the radius of the inner circle : r1.

Radius of the outer circle : r2

As both are the concentric circles,the centre of dilation will be same for second circle as of first circle.

Difference of radius r = r2 - r1

By the scale factor of r the second circle is dilated to given the radius of r2.

Thus, centre of dilation of second circle is same as of first circle and the scale factor is found to be r.

Know more about the centre of dilation

https://brainly.com/question/9659751

#SPJ1

The distance between the observer and the hot air balloon is increasing at a rate of \(25\times \sqrt{5}\) feet/minute when the balloon is rising at a rate of 50 feet/minute and is 150 feet above the ground.

point A and the hot air balloon is at point B, 200 feet away horizontally and 150 feet above the ground vertically. We want to find how fast the distance AB is increasing at the moment when the balloon is rising at a rate of 50 feet/minute.

Let's call the distance AB "d" and the time "t". We are given that:

\(d = \sqrt{(200^2 + (200 - 150)^2)} = \sqrt{(50000)} = 100\times \sqrt{5}\) feet (using the Pythagorean theorem)

h = 150 feet (the height of the balloon above the ground)

dh/dt = 50 feet/minute (the rate at which the height of the balloon is increasing)

To find dd/dt, we can use the chain rule of differentiation:

dd/dt = (dd/dh) × (dh/dt)

We can find dd/dh by taking the derivative of the distance formula with respect to h:

\(dd/dh = 1/\sqrt{(200^2 + (200 - h)^2)} \times d/dh(\sqrt{(200^2 + (200 - h)^2)} )= (200 - h) \sqrt{(200^2 + (200 - h)^2)}\)

Plugging in h = 150, we get:

\(dd/dh = (200 - 150) / \sqrt{(200^2 + (200 - 150)^2) } = 50 / \sqrt{(50000) } = \sqrt{(5)/2}\) feet/foot

Now we can find dd/dt:

\(dd/dt = (dd/dh) \times (dh/dt) = (\sqrt{(5)/2) } \times 50 = 25\times \sqrt{5}\) feet/minute

for such more question on distance

https://brainly.com/question/12356021

#SPJ11

Answer: rational

Step-by-step explanation: If a number is terminating number or repeating decimal, then it is rational.

Answer:

Rational

Step-by-step explanation:

If a number has a finite number of digits or could be written in a fraction that consists of numbers with a finite number of digits(-51 and 5 have a finite number of digits), then it is a rational number. Hence, -51/5 is a rational number.

Answer:

the answer is B

Step-by-step explanation:

1. convert the mixed number choices to improper fractions

2. type each improper fraction into a calculator

3. see which one comes out as 2.111111111

4. find out that it's B and you'll B happy (see what I did there, it's a pun)

Answer:

9

Step-by-step explanation:

i can not really tell what letters are on the picture but i think it is 9

To use a centimeter ruler to measure a matchstick, place the ruler parallel to the matchstick, aligning the zero mark with one end. Identify the nearest centimeter mark and estimate the millimeter measurement by looking at the divisions between centimeters and smaller increments for more precision.

To begin, ensure the centimeter ruler is in good condition and properly calibrated. Lay the matchstick on a flat surface, making sure it is straight. Position the ruler next to the matchstick, aligning the zero mark with one end while keeping it parallel to the matchstick. Observe the other end of the matchstick and identify the nearest centimeter mark on the ruler to the left of the end point. This represents the whole centimeter measurement. Next, look at the lines or ticks between the whole centimeter marks. Each centimeter is divided into 10 millimeter intervals. Estimate the length of the matchstick by identifying the millimeter line that aligns with the end of the matchstick. For more precise measurements, use the smaller divisions on the ruler. Each millimeter is further divided into smaller increments called tenths of a millimeter. Estimate the length by identifying the smallest increment that aligns with the end of the matchstick. Record the measurement by noting the number of centimeters, followed by the number of millimeters (and tenths of millimeters, if necessary). Handle the matchstick carefully to avoid any damage or inaccuracies in the measurement..

Learn more about centimeter ruler here:

https://brainly.com/question/30667952

#SPJ11

Answer:

13.

We already have two angles, so we will just need another side to be equal to prove they are congruent. Any side will do (JK and MO lets say, which is the ASA congruency identity)

14.

The sides JL and DF differ in length (JL is longer than DF), so that proves why SSA identity (c'mon you know why i didn't write A... nvm) does not exist, as there can be two possible lengths for the last side.

Answer:

The slope of the line would be 3/4

Step-by-step explanation:

When you put the coordinates in the point-slope formula, it would be 4 - (-2) over 7 - (-1). The answer would then be 6/8 but if simplified, the answer would then be 3/4.

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The greatest common factor (divisor) is found in the GCD column of the attached spreadsheet. The GCD is calculated using the spreadsheet function. The least common multiple (LCM) is the product of the numbers, divided by their GCD.

Other multiples shown are 2 times, 3 times, and 4 times the least common multiple.

The area of a regular tetrahedron with the edge α is √3α².

A regular tetrahedron is a tetrahedron in which all four faces are equilateral triangles. It is one of the five regular Platonic solids, which have been known since antiquity. In a regular tetrahedron, all faces are the same size and shape (congruent) and all edges are the same length.

Given that, an edge of a regular tetrahedron ABCD is α.

We know that, area of a regular tetrahedron is √3a².

Here, the area is √3α²

As we know that, the perimeter of regular tetrahedron is P=6a.

Now, the perimeter is P=6α

Therefore, the area of a regular tetrahedron with the edge α is √3α².

Learn more about the regular tetrahedron here:

https://brainly.com/question/30504218.

#SPJ9

Answer:

  yes

Step-by-step explanation:

You want a graph of P = 125 +50W.

The given equation is in slope-intercept form. The independent variable is W, and the dependent variable is P.

Usually, the independent variable is graphed on the horizontal axis, which you have done.

The dependent variable is graphed on the vertical axis, which you have done.

The axes are correctly labeled and graduated.

The "y-intercept" (P value) when the independent variable is zero is the constant in the equation, 125. You have correctly shown that on the graph.

The slope of the line is the coefficient of the independent variable (W) in the equation. You have correctly shown that P increases by 50 when W increases by 1.

Yes, you properly graphed the equation.

<95141404393>

Answer:
Slope is 3/2
y-intercept is (0,-45)

The values of b for the function f(x) = x² + bx + 1  has

(a) two real roots is |b| > 2 .

(b) has only one real roots is b = ±2  .

(c) has no real roots is  b < -2 or b > 2.

A Quadratic Function of the form f(x) = x² + bx + 1 has two real roots if and only if its discriminant (b² - 4ac) is positive, where a = 1, c = 1 .

So ,the discriminant can be written as ⇒ b² - 4 × 1 × 1

⇒ b² - 4.

Part (a) ; the two roots are real if and only if b² - 4 > 0,

⇒ b² > 4.

⇒ |b| > 2 .

Part (b) : function has only one real root if and only if its discriminant =0 .

⇒ b² - 4 = 0  ;

⇒ b² = 4  ;

which implies ⇒ b = ±2  .

Part (c) : function has no real root if and only if its discriminant < 0 .

⇒ b² - 4 < 0  ;

⇒ b² < 4  ;

which implies ⇒  b < -2 or b > 2.

Learn more about Functions here

https://brainly.com/question/23888866

#SPJ4

The smallest integer solution to the inequality 6x+2>2x+23 is 6.

What is an inequality?

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations, including:

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

Given, the inequality is 6x+2>2x+23

⇒ 6x-2x > 23-2

⇒ 4x > 21

⇒ x >21/4

⇒ x > 5.25

Hence, the smallest integer satisfying the inequality would be 6.

To know more about inequality visit:

brainly.com/question/28823603

#SPJ1

The equation that describes the relationship between the number of cans of paint used, and the number of square feet that are covered is y = 375x  .

In the question ,

a table representing relationship between the number of cans of paint used, and the number of square feet that are covered is given ,

we have to find the equation that represents it ,

the slope is = (750 - 375)/(2 - 1)

= 375/1

= 375

which means 1 can will cover 375 square feet of area

So , the equation for the point (2 , 750) and slope 375 ,

y - 750 = 375(x - 2)

y - 750 = 375x - 750

y = 375x - 750 + 750

y = 375x

Therefore , The equation that describes the relationship between the number of cans of paint used, and the number of square feet that are covered is y = 375x  .

The given question is incomplete , the complete question is

Employees of a painting service paint the interior walls of homes and office buildings. The following table shows the number of cans of paint the employees use, and the number of square feet they cover ,

Cans of paint      Area painted (square feet)

1                                   375

2                                  750

3                                  1125

4                                  1500

Write an equation describes the relationship between the number of cans of paint used, and the number of square feet that are covered ?

Learn more about Equations here

https://brainly.com/question/15169364

#SPJ4

Answer:JEROME

Step-by-step explanation:

Answer:

AB= 12                      AB=18

Step-by-step explanation:

sin(30)=AB/AC

=> AB=Sin(30)*AC

sin(30)=0.5

=>AB=0.5*24=15

sin(30)=AB/AC

=> AB=Sin(30)*AC

sin(30)=0.5

=>AB=0.5*36=18

Answer:

part a: AB = 12cm

part b: AB = 18cm

Step-by-step explanation:

sin(angle)=OPP/HYP

sine of an angle is a ratio of two sides of a right triangle. For sine, the ratio is the opposite side over the hypotenuse. In part a the marked angle is 30° and AB is the opposite side. The hypotenuse is given, 24cm.

So the sin 30°

= opp/hyp

= AB / 24

also given is the fact that sin30°=.5

Substitute that into our equation also.

sin30° = AB/24

.5 = AB/24

multiply both sides by 24.

.5×24 = AB

12 = AB

AB is 12 cm.

Part b is an identical calculation except the hypotenuse is 36cm.

sin30° = AB/36

.5 = AB/36

.5×36 = AB

18 = AB

AB is 18cm.

They may be trying to lead you to discover some shortcut patterns in a 30°-60°-90° triangle. That is that the short leg is HALF the hypotenuse OR the hypotenuse is double the short leg.

Answer:

the customer pays 4500 for the gas cooker

We will investigate how to use ratios to determine the actual distance between cities as per defined scale.

We are given a scale conversion ( ratio ) at which distances are scaled down:

We will use the given scale ratio to determine the actual distance between two citites. The scale distance between Hawthorne and Doyelstown can be read.

Now utilize the scale conversion ratio to determine the actual distance:

Therefore, the distance between Hawthorne and Doylestown is:

Answer:

Step-by-step explanation:

explain what ? what is the question here ?

to find the intersecting point of both lines ?

if that is the case, then please consider that an intersection point is a point, where both equations deliver the same coordinates. it is the same point for both of them.

in other words, the question is for what pair of (x, y) are both equations true (their left and right sides are equal).

we do this by finding a way to express one variable by an expression in the other variable, and then use that identity in one of the equations to solve for the remaining variable. and then we use that in the other equation to solve for the first variable.

line b gives us such an identity right away.

y = (-1/2)x + 6

we can use that in the line a equation :

2x - ((-1/2)x + 6) = 7

2x + (1/2)x - 6 = 7

2x + (1/2)x = 13

(4/2 + 1/2)x = 13

(5/2)x = 13

5x = 26

x = 26/5 = 5.2

y = (-1/2)×5.2 + 6 = -2.6 + 6 = 3.4

The greatest length that Liz can make using the strings is 6 cm.

Given,

In the question:

Liz has two piece of string one 18cm other 24cm long.

and, He want to cut them up to produce smaller piece of string that are all of the same length with no string leftover.

To find the greatest length, in cm.

Now, According to the question:

Let's know:

Greatest Common Factor (GCF):-

The GCF of a set of values (typically two) is the greatest factor that applies to every number.

We must find the GCF of 18 and 24:

List the factors of both values:

18: 1, 2, 3, 6, 9, 18

24: 1, 2, 3, 4, 6, 8, 12, 24

Let's identify the common factors between 18 and 24:

18: 1, 2, 3, 6, 9, 18

24: 1, 2, 3, 4, 6, 8, 12, 24

Hence, the GCF is 6.

The greatest length that Liz can make using the strings is 6 cm.

Learn more about Greatest Common factor at:

https://brainly.com/question/11221202

#SPJ4

Triangles can be inscribed in and circumscribed around circles, and circles can be inscribed in and circumscribed around triangles.

There are several relationships between triangles and circles, including:

Incenter: The incenter of a triangle is the center of the circle that is tangent to all three sides of the triangle.

Circumcenter: The circumcenter of a triangle is the center of the circle that passes through all three vertices of the triangle.

Orthocenter: The orthocenter of a triangle is the point where the altitudes of the triangle intersect. The circumcircle of a triangle passes through the orthocenter.

Inscribed angle: An inscribed angle of a circle is an angle whose vertex lies on the circle, and whose sides are chords of the circle. The measure of an inscribed angle is half the measure of the intercepted arc.

Tangent: A tangent to a circle is a line that intersects the circle at exactly one point. If a line is tangent to a circle at a point, then it is perpendicular to the radius at that point.

Similarity: If two triangles are inscribed in the same circle and share a common chord as a side, then they are similar.

These relationships have important applications in geometry and trigonometry, and can be used to solve problems involving triangles and circles.

Learn more about triangles

brainly.com/question/2773823

#SPJ11

mark me brainlist

Step-by-sThe corresponding parts are:

<A = <A' = <A"

<B = <B' = <B"

<C = <C' = <C"

AB = A'B' = A"B"

AC = A'C' = A"C"

BC = B'C' = B"C"

How to compare the sides

The statement is given as:

△ABC was transformed using two rigid transformations.

The rigid transformations imply that:

The images of the triangle after the transformation would be equal

So, the corresponding parts are:

<A = <A' = <A"

<B = <B' = <B"

<C = <C' = <C"

AB = A'B' = A"B"

AC = A'C' = A"C"

BC = B'C' = B"C"

Why the results are true?

The results are true because rigid transformations do not change the side lengths and the angle measures of a shape

How to prove that two triangles are congruent without using rigid transformations?

To do this, we simply make use any of the following congruent theorems:

SSS: Side Side Side

SAS: Side Angle Side

AAS: Angle Angle Side

How to respond to this classmate?

The classmate's claim is that

Only two pairs of corresponding parts are enough to prove the congruent triangle

The above is true because of the following congruent theorems:

SSS: Side Side Side

SAS: Side Angle Side

Based on the information provided, we have a random sample of 60 measurements taken from a population with a mean (µ) of 25 and a variance (σ²) of 200.

The mean of the sample (X) will be equal to the population mean, so X = 25.

To calculate the standard error (SE) of the sample, we use the formula SE = σ / √n, where σ is the population standard deviation and n is the sample size. Since the variance is given as 200, the standard deviation (σ) is the square root of 200, which is approximately 14.14.

Now, we can calculate the standard error: SE = 14.14 / √60 ≈ 1.82.

So, the pair for the mean and standard error of x is (25, 1.82).

To learn more about mean visit;

brainly.com/question/31101410

#SPJ11

Answer:

30.8 cm³

Step-by-step explanation:

slant height of small cone =l

using; l²= h²+r²

l²=5²+3²=25+9=34

l=√34=5.8cm

volume of small cone =1/3πrl

=1/3(π×3×5.8)

=1/3(54.67)= 18.2 cm³

slant height of big cone =l

using; l²= h²+r²

l²=5²+6²=25+36=61

l=√61=7.8cm

volume of big cone =1/3πrl

=1/3(π×6×7.8)

=1/3(147.02)= 49.0 cm³

49.0-18.2= 30.8 cm³

Answer:

29.5 years

Step-by-step explanation:

Answer:

The keyword is than, which means you are subtracting Saturn to Jupiter.

You can fact check you answer by adding the lowest number to your answer.

Answer: 2.5

Step-by-step explanation:

A negative of a negative is a positive.

Answer:

2.5

Step-by-step explanation:

Just make everything inside the parentheses opposite of what it is

-2.5 becomes 2.5 because double negative