To calculate the height of a mountain, the following method was used. From a point A on a level plain, the angle of elevation of the top of the mountain was found to be 32°. At a point B nearer the mountain, where |AB| = 400m, the angle of elevation was found to be 58°. Calculate the height of the mountain to 2 s.f​

Answer:

y = -x - 10

Step-by-step explanation:

set y as the total money owed

set x as how many days passed

if 0 days are passed, they owed $10, which is "-10" the y-intercept

and owed $1 more everyday which is -1x. We can write it as -x.

Answer: they are ripped

Step-by-step explanation:

i guessed

Answer:

3 mi / hr

Step-by-step explanation:

It takes the cyclist 2 hours to go 6 miles further ( 30 -24 mi)

  6 mi / 2 hr = 3 m/hr    

Answer:

125 = (15x) + 45
(Sorry if I'm wrong!)

The two sequences of transformations that would show that triangles ABC and AED are similar are:

Dilating ΔABC by scale factor 1/2 and reflect A'B'C' over AD.

Reflect AED over line AB and Dilate A'E'D' by scale factor 2.

Two triangles are said to be comparable if their two sides are in the same ratio as the two sides of another triangle and their two sides' angles inscribed in both triangles are equal.

Given:

as, From the Figure we have to dilate the sides of ΔABC by scale factor 1/2.

Then, sides of Δ will be Similar with equal side ratio.

Then we can have,

Dilating ΔABC by scale factor 1/2 and reflect A'B'C' over AD.

or, Reflect AED over line AB and Dilate A'E'D' by scale factor 2.

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Using a system of equations, the unit cost of a charcoal pencil is $3.16.

A system of equations involves two or more equations, also known as simultaneous equations, which are solved concurrently or simultaneously.

The cost of one charcoal pencil is the quotient of the total cost of a charcoal pencil divided by the number.

In this situation, after eliminating brushes, we can determine that the total cost of 5.5 charcoal pencils is $17.39.  After the division operation, the unit cost is computed to be $3.16.

                               Allison     Aubrey

Charcoal pencils       3               2

Brushes                     2               5

Total costs          $17.18          $26.56

Let charcoal pencils = c and brushes = b

3c + 2b = 17.18 ... Equation 1

2c + 5b = 25.56 ... Equation 2

Multiply Equation 1 by 2.5:

7.5c + 5b = 42.95 ... Equation 3

Subtract Equation 2 from Equation 3:

7.5c + 5b = 42.95

-

2c + 5b = 25.56

= 5.5c = 17.39

c = 3.16

Thus, after solving the simultaneous equations, we can determine that the cost of one charcoal pencil is $3.16.

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The probability of randomly selecting a can that is not a cola is:

P = 0.8

We know that there are 30 cans of soda on a refrigerator, such that 6 of these are of cola.

We want to find the probability of randomly selecting a can that is not of cola, to get that probability, we need to take the quotient between the number of cans that are not of cola and the total number of cans.

There are:

30 - 6 = 24 cans that are not of cola.

30 cans in total.

Then the probability is:

P = 24/30  = 0.8

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Answer:

[tex]$\boxed{(c) : 11}$[/tex]

Step-by-step explanation:

We can think of this problem as placing $7$ dividers (representing the boys) in $20$ slots (representing the people). Thus, the number of ways to arrange the boys and girls is the number of ways to place the dividers, which is $\binom{20}{7}$.

To find the average value of $S$, we need to find the total number of arrangements where $S = k$ for each possible value of $k$, then divide by the total number of arrangements.

Let's first consider the case where $k=0$. There is only $1$ way to arrange the boys and girls such that there are no boys and girls standing next to each other: BBBBBBBBBBBBBBBBBBBBB.

Next, let's consider the case where $k=1$. There are $\binom{7}{1}\binom{13}{6}$ ways to arrange the boys and girls such that there is exactly $1$ pair of boys and girls standing next to each other. To see this, consider that there are $\binom{7}{1}$ ways to choose the position of the divider that separates a boy and a girl, and $\binom{13}{6}$ ways to arrange the remaining dividers and slots.

We can continue this process to find the total number of arrangements for each possible value of $k$. When we add up all of these arrangements and divide by the total number of arrangements, we get the average value of $S$.

More specifically, the average value of $S$ is equal to

[\frac{1\cdot1+\binom{7}{1}\binom{13}{6}\cdot1+\binom{7}{2}\binom{13}{5}\cdot2+\binom{7}{3}\binom{13}{4}\cdot3+\binom{7}{4}\binom{13}{3}\cdot4+\binom{7}{5}\binom{13}{2}\cdot5+\binom{7}{6}\binom{13}{1}\cdot6+\binom{7}{7}\binom{13}{0}\cdot7}{\binom{20}{7}}.]

Simplifying this expression gives us $\boxed{(c) : 11}$.

a) The list with all the possible outcomes is given as follows:

b) The probabilities are given as follows:

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

Of the 2³ = 8 outcomes, only one result in three heads, hence the probability is given as follows:

p = 1/8.

At least one tail is complementary to three heads, hence it's probability is given as follows:

p = 1 - 1/8 = 8/8 - 1/8 = 7/8.

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Note that the percentage of the students in the survey, to the nearest whole number, that prefer outdoor activities given they prefer non-fiction is: 11%.

To get the percentage of those who love outdoor activities as well as non-fiction, we must complete the table.

Given:

Total number of those who love Fiction and Non Fiction but who love indoors = 50

From that list those who love fiction = 24, thus, those who love indoor and non-fiction =

50 - 24 = 26

Total number of those who were served are = 90

If the total number of those who love Fiction and Non-Fiction but who love indoors = 50

Then the total number of those who love Fiction and Non Fiction but who love Outdoors = 90 - 50 = 40

If the total number of those who love outdoor (Fiction and non-fiction) = 40 and those who prefer fiction only from this category is = 30;

Then the total number of those who love Non Fiction but who love Outdoors =

40 -30

= 10

Thus, the percentage of this number against the total number of those surveyed is:

10/90

= 0.1111111111 or 11%

Therefore, the percentage of students in the survey, to the nearest whole number, prefer outdoor activities given they prefer non-fiction is given as 11%. See the full table attached.

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Answer:

no

Step-by-step explanation:

The scale factor of dilation from WY to W'Y' is 2.75

From the question, we have the following parameters that can be used in our computation:

The length of WY is 1.5

The length of W'Y' is 4.125

From the complete question, we understand that:

Dilation changes the size of the shape that is being dilated.

This means that

Scale factor = The length of W'Y'/The length of WY

Substitute the known values in the above equation, so, we have the following representation

Scale factor = 4.125/1.5

Evaluate the quotient

Scale factor = 2.75

Hence, the scale factor is 2.75

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Complete question

Line WY is dilated to create line W'Y' using point Q as the center of dilation.

What is the scale factor?

Given that The length of WY is 1.5 and the length of W'Y' is 4.125

On solving the provided question we can say that - here in trigonometry [tex]v^2x - 2u - 3 = 0[/tex] = (u-3)(u+1)

The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.

[tex]sin^2x - 2 sinx - 3 = 0\\u= sinx\\u^2 = sin^2x\\v^2x - 2u - 3 = 0\\\\[/tex]

factors are = -3 and 1

(u-3)(u+1)

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After 31 years the population will be the same. Their populations will be 2072 when they are the same.

Growth rates are calculated by dividing the difference between the ending and beginning values for the period under consideration by the starting value. The most common time periods for growth rates are annually, quarterly, monthly, and weekly.

The formula for the growth of the population is:

A = P(1+r)^n

A is the total number population after n years.

P is the initial number of population

r is rate of interest.

For town A,

The initial population is 700. The growth rate is 3.5% = 0.035.

The population of town A after t year is y = 700(1+0.035)^t

For town B,

The initial population is 1400. The growth rate is 1.25% = 0.0125.

The population of town A after t year is y = 1400(1+ 0.0125)^t

The system of equations is:

y = 700(1+0.035)^t

y = 1400(1+ 0.0125)^t

The intersection point is (31.537,2071.432).

After 31 years the populations will be the same.

their populations will be 2072 when they are the same

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Answer:

B

Step-by-step explanation:

$7 for a child X and $13 for a adult Y

Answer:

  a) 125 different numbers

  b) 60 numbers with different digits

Step-by-step explanation:

You want to know the number of different combinations you can have with three dials, each having numbers 1–5, and you want to know the number of combinations with three different digits.

Any of the three dials may be set to any of the five digits, so there are ...

  5 × 5 × 5 = 125

possible three digit combinations.

The number of different 3-digit numbers is 125.

If the digits are to be different, there can be 5 different first digits, 4 different second digits, and 3 different 3rd digits, for a total of ...

  5 × 4 × 3 = 60

possible combinations with different digits.

The number of 3-digit numbers with different digits is 60.

<95141404393>

Step-by-step explanation:

I attached the image of answer

Therefore , As a result 5, 10, and 15 make up the reasonable domain for the function 2 (l + w) = 64..

A connection between a group of sources and one output for each input is referred to as a function. A function is, to put it simply, a collection of equation  connected to a single, unique output. In mathematics, a function is a statement, rule, or law that describes the connection between two variables (the dependent variable). One input leads to one output when a rule of this type is used. by Alex Federspiel, the photographer. This statement gives an example of y=x2. There is just one output for y from any input for x. According to our definition, y is a function of x since x is the input value.

We must determine the length and breadth values necessary to make the rectangle's perimeter 64.

l + w = 32

The possible widths are 5, 10, 15, 20, and 25.

Now,

[tex]l + 5 = 32\\l = 27\\l + 10 = 32\\l = 22\\l + 15 = 32\\l = 17\\l + 20 = 32\\l = 12\\l + 25 = 32\\l = 7[/tex]

The domain has widths of 5, 10, 15, 20, and 25.

The range for length is: 27, 22, 17, 12, and 7.

The following is the reasonable domain for the aforementioned situation:

5, 10, 15, 20, and 25

Below is a graph of the function 2 (l + w) = 64.

Therefore , As a result, 5, 10, and 15 make up the reasonable domain for the function 2 (l + w) = 64.

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Answer:

Rs.2700

Step-by-step explanation:

14% profit means 100% +14% more=114% profit

then to make into decimal 114% divided by 100 to give 1.14

then divide 2850 by 1.14 to find original selling price of bicycle

which will be Rs.2,500

next, a 8% profit means 100%+8% which equals 108% and then make into decimal which is 1.08

then multiply the original selling price (Rs.2,500) by 1.08 to give your final selling price after the 8% profit of ...

Rs.2,700

The y-intercept of the graph is (0, 10)

This is the point where the graph crosses the y-axis

So, the y-intercept is (0, 10)

To do this, we check the values of x in relation to the values of y

From the graph, we can see that the values of y reduces as the values of x increases to 20

This means that the end behaviour is

As x ⇒ +20, y ⇒ 0 and As x ⇒ -∝, y ⇒ +∝

To do this, we again check the values of x in relation to the values of y

From the graph, we can see that the values of y when x = 0 is 10 and also, we have x = -50 and y = 15

So, the possible values are (0, 10) and (-50, 15)

Here, we make use of the end behaviours

So, we have

The function has no maximum, but it has a minimum at (20, 0)

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Answer:

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

Sum of interior angles of a 6-sided polygon is:

Both angles ∠X and ∠Y marked as same, let them be x and ∠W is marked as right angle.

The sum is:

m∠X = m∠Y = 100.5°.

Answer:

m∠X = 100.5°

m∠Y = 100.5°

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.3cm}\underline{Sum of the interior angles of a polygon}\\\\$S=(n-2) \times 180^{\circ}$\\\\where:\\ \phantom{ww}$\bullet$ $n$ is the number of sides. \\ \end{minipage}}[/tex]

The given polygon has 6 sides.

Therefore, the sum of its interior angles is:

[tex]\implies S = (6 - 2) \times 180^{\circ} = 720^{\circ}[/tex]

From inspection of the given polygon:

Therefore:

[tex]\implies m \angle U + m \angle V + m \angle W + m \angle X + m \angle Y + m \angle Z = 720^{\circ}[/tex]

[tex]\implies 159^{\circ} + 99^{\circ} + 90^{\circ} + m \angle X + m∠ \angle Y + 171^{\circ} = 720^{\circ}[/tex]

[tex]\implies m \angle X + m \angle Y + 519^{\circ} = 720^{\circ}[/tex]

[tex]\implies m \angle X + m \angle Y = 201^{\circ}[/tex]

As m∠X is equal to m∠Y:

[tex]\implies m \angle X = m \angle Y = 201^{\circ} \div 2 = 100.5^{\circ}[/tex]

Answer: 14

Step-by-step explanation:

f(-2) means x is -2, so we can solve for when x = -2 by plugging -2 into the equation.

[tex]f(-2) = 3(-2^{2}) - (-2)\\=3(4) + 2\\=12+2\\=14[/tex]

Answer:

Step-by-step explanation:

So what you start with is the variable "x" in 3 different places. When you are changing the x variable, you need to plug it into every variable in the equation. Start by doing that and the problem will look like: f (-2) = 3 (-2)^2 - (-2) Now you can start with either the 3 (-2)^2 or the - (-2), but it is better to go from left to right.

Your Best

Elina

Answer:

B

Step-by-step explanation:

personally it feels like the best fit

Answer:

13 years old.

Step-by-step explanation:

Let x be the age of Jada

Given from the question:

Bobby's Age: 7x + 3 years old

Jada's Age: x years old

7x + 3 = 94

7x = 94 - 3

7x = 91

x = [tex]\frac{91}{7}[/tex]

x = 13

Therefore Jada is 13 years old.

Answer:

  6.08 fluid ounces

Step-by-step explanation:

You want the amount of stain required to cover the surface area of the ends and three sides of a beam 6" square and 6 ft long. 128 floz of stain will cover 200 square feet.

The two ends of the beam are 1/2 ft square, so the area of each is ...

  A = s² = (1/2 ft)² = 1/4 ft²

The two ends have a total area of ...

  2 × (1/4 ft²) = 1/2 ft² . . . . end area

Three of the four sides of the beam are to be stained, so their total area is the area of 3 rectangles, each of which is 1/2 ft by 6 ft.

The area of each rectangle is ...

  A = LW

So, the area of the three rectangles is ...

  total side area = 3 × (1/2 ft)(6 ft) = 9 ft²

Then the area to be stained is the sum of the end area and the side area:

  stained area = (1/2 ft²) +(9 ft²) = 9.5 ft²

The amount of stain required is proportional to the area, so we can write the proportion ...

  q/(9.5 ft²) = (128 floz)/(200 ft²)

Multiplying by 9.5 ft² gives ...

  q = (128 floz)(9.5/200) = 6.08 floz

The homeowner needs 6.08 fluid ounces of stain to stain the beam.

Line {m} is the line of reflection for the given geometry.

Given is a pair of heart shaped geometrical figures as shown.

It can be seen clearly that the line {m} forms the line of reflection for the given figure.

Therefore, line {m} is the line of reflection for the given geometry.

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The smallest of the consecutive numbers is 495

From the question, we have the following parameters that can be used in our computation:

Mathematical statement

The mathematical statement is given as

The sum of four consecutive multiples of 11 is 2046

The smallest mulitple of 11 is represented by 11x

Where x is an integer greater than 0

This means that the other numbers are 11(x + 1), 11(x + 2) and 11(x + 3)

When represented as an equation, we have

11x + 11(x + 1) + 11(x + 2) + 11(x + 3) = 2046

Evaluate the like terms

44x = 2046 - 66

So, we have

44x = 1980

Divide through by 44

x = 45

The smallest is then calculated as

Smallest = 11 * 45

Evaluate

Smallest = 485

Hence, the smallest of the numbers is 495

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Answer:

x = 128

Step-by-step explanation: