An engineer determines that the angle of elevation from her position to the top of a tower is 52°. She measures the angle of elevation again from a point 47 meters farther away from the tower and
finds it to be 31°. Both positions are due east of the town. Find the height of the tower

pls help

It is simply the largest of the common factors.

We have:

12x³- 18x² + 6x

We find GCF of 12, 18 and 6:

GCF(12, 18, 6) = 6

12 = 2 · 6

18 = 3 · 6

6 = 1 · 6

and GCF of x³, x² and x:

GCF(x³, x², x) = x

x³ = x² · x

x² = x · x

x = 1 · x

Therefore:

The approximate solution using the three-point formula with step size h = 1/2 is y(t) = 0 for all t.

The boundary value problem given is y′′ − y = 0 with boundary conditions y(0) = 0 and y(2) = e2 − e−2.

(a) To find the exact solution y(t), we can use the characteristic equation r^2 - 1 = 0. This gives us r = 1 and r = -1. The general solution is therefore y(t) = c1e^t + c2e^-t.

Using the boundary conditions, we can find the constants c1 and c2.

For y(0) = 0, we have 0 = c1 + c2, which gives us c2 = -c1.

For y(2) = e2 − e−2, we have e2 − e−2 = c1e^2 + c2e^-2. Substituting c2 = -c1, we get e2 − e−2 = c1e^2 - c1e^-2.

Solving for c1, we get c1 = (e2 − e−2)/(e^2 - e^-2) = 1/2. Therefore, c2 = -1/2.

The exact solution is y(t) = (1/2)e^t - (1/2)e^-t.

(b) To use the three-point formula with step size h = 1/2, we can set up a table with tn and yn values.

tn | yn
---|---
0  | 0
1/2| y1
1  | y2
3/2| y3
2  | e2 - e-2

The three-point formula is yn+1 = yn-1 + 2h(y′n). We can use this formula to find the values of y1, y2, and y3.

For y1, we have y1 = 0 + 2(1/2)(y′0) = y′0. Since y′0 = y′(0) = (1/2)e^0 - (1/2)e^0 = 0, we have y1 = 0.

For y2, we have y2 = y0 + 2(1/2)(y′1) = 0 + 2(1/2)(0) = 0.

For y3, we have y3 = y1 + 2(1/2)(y′2) = 0 + 2(1/2)(0) = 0.

Therefore, the approximate solution using the three-point formula with step size h = 1/2 is y(t) = 0 for all t.

It is important to note that the three-point formula is not accurate for this particular boundary value problem due to the size of the step and the nature of the differential equation. A smaller step size or a different numerical method may yield a more accurate approximation.

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None of the given options represents an amount of money equivalent to fife tenths of a dollar.

What is Money?

In mathematics, money is a unit of measure used to represent the value of goods or services. It is typically denoted in a currency unit, such as dollars, euros, or yen, and is often used to express prices, wages, or financial transactions. Money is a form of quantitative data and can be manipulated using various mathematical operations, such as addition, subtraction, multiplication, and division.

Fife tenths of a dollar is equivalent to $0.50, since there are 10 tenths in a dollar.

The amount of money that the digit 5 represents $0.50.

Looking at the given options, the only option that contains a total value of $0.50 is option B:

1 dollar bill = $1.00

quarter = $0.25

dime = $0.10

nickel = $0.05

5 Pennies = $0.05

Adding these values together, we get a total of $1.45, which is more than $0.50. Therefore, option B is incorrect.

Option D contains a total value of:

10 dollar bill = $10.00

quarter = $0.25

5 nickels = $0.25

2 Pennies = $0.02

Adding these values together, we get a total of $10.52, which is more than $0.50. Therefore, option D is incorrect.

Option A contains a total value of:

5 dollar bill = $5.00

quarter = $0.25

dime = $0.10

2 nickels = $0.10

4 Pennies = $0.04

Adding these values together, we get a total of $5.49, which is more than $0.50. Therefore, option A is incorrect.

The only remaining option is option C, which contains a total value of:

Two 20 dollar bills = $40.00

10 dollar bill = $10.00

quarter = $0.25

dime = $0.10

2 Pennies = $0.02

Adding these values together, we get a total of $50.37, which is more than $0.50. Therefore, option C is also incorrect.

Thus, none of the given options represents an amount of money equivalent to fife tenths of a dollar.

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Answer:

8290

Step-by-step explanation:

Explanation is on the pic

The solution for c in the equation is 35/3

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

\(c = 5\frac{5}{6} \times 2 \)

Express the equation properly

So, we have the following representation

c = 5 5/6 * 2

Convert the fraction to improper​ fraction

So, we have the following representation

c = 35/6 * 2

Evaluate the products

c = 35/3

Hence, the solution is 35/3

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a. If 1,200 students are in the district, 165 students can be expected to oppose school uniforms.

b. From the sample, the most likely outcome is in favor, as it got the most responses, hence we should disagree with Bernice.

A proportion is a fraction of the total amount.

Out of 80, 11 opposed, hence, out of 1200, we apply the proportion and find that the amount will be of:

1200 x 11/80 = 165.

Hence, a - 165 students can be expected to oppose school uniforms.

b - We should disagree with Bernice because the sample indicates that the outcome in favor is the most likely because it received the most answers.

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By answering the supplied question, we may infer that the response is percentage Thus, pizza was chosen as the celebratory food by 75% of the pupils in Karen's class.

A ratio or value stated as a percentage of 100 is referred to as a percentage in mathematics. The abbreviations "pct.," "pct," and "pc" are also sporadically used. Nonetheless, the percentage symbol "%" is frequently used to denote it. The percentage amount is dimensionally empty. When the denominator is 100, percentages are essentially fractions. To show that a number is a percentage, a percent symbol (%) should be used next to it. For instance, you receive a 75% grade if you correctly answer 75 out of 25 questions (75/100) on a test. For percentage calculations, multiply the outcome by 100 after dividing the amount by the total. The percentage is calculated by multiplying (value/total) by 100%.

We must divide the number of students who chose pizza (15) by the total number of students (20) and multiply the result by 100 to determine the percentage of students who chose pizza:

(15/20) x 100 = 75%

Thus, pizza was chosen as the celebratory food by 75% of the pupils in Karen's class.

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Answer: The ones you have selected are correct

Step-by-step explanation:

Answer:

the ones you selected are all correct

Step-by-step explanation:

Answer

the answer is b

The family uses 68.7 gallons of water every day for all purposes

If 22.9% of the water is used for cleaning, then the remaining 100% - 22.9% = 77.1% of the water is used for other purposes such as drinking and cooking.

To find out how much water the family uses every day, we need to add the amount of water used for cleaning to the amount of water used for other purposes.

Quantity of water used for cleaning = 22.9 percentage of the total amount of water used every day = 0.229 x 68.7 gallons = 15.71 gallons

Quantity of water used for other purposes = 77.1% of the total amount of water used every day = 0.771 x 68.7 gallons = 52.99 gallons

Total quantity of water used every day = amount of water used for cleaning + amount of water used for other purposes = 15.71 gallons + 52.99 gallons = 68.7 gallons

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The zeros of the polynomial p(x)=x²+16 are x = 4i and x = -4i. The zeros of the polynomial can be found using the Quadratic Formula: x = (-b ± √(b²-4ac))/(2a), where a, b, and c are the coefficients of the polynomial. In this case, a = 1, b = 0, and c = 16.

Plugging in these values into the Quadratic Formula, we get:

x = (-0 ± √(0²-4(1)(16)))/(2(1))

Simplifying the expression, we get:

x = (0 ± √(-64))/(2)

Since the square root of a negative number is a nonreal number, we can write this as:

x = (0 ± 8i)/(2)

Simplifying further, we get:

x = 0 ± 4i

So the zeros of the polynomial are x = 4i and x = -4i, both of which are nonreal numbers.

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The answer as a single polynomial is x^(3) + 9x^(2) - 15.

To subtract the two polynomials as indicated, we need to distribute the constants in front of each polynomial and then combine like terms.

First, we distribute the 5 and -2 to each term in the respective polynomials:
5(x^(3)) + 5(x^(2)) - 5(3) - 2(2x^(3)) - 2(-2x^(2))

Simplifying each term gives us:
5x^(3) + 5x^(2) - 15 - 4x^(3) + 4x^(2)

Next, we combine like terms by adding the coefficients of each term with the same exponent:
(5x^(3) - 4x^(3)) + (5x^(2) + 4x^(2)) - 15

Simplifying the coefficients gives us:
x^(3) + 9x^(2) - 15

Therefore, the answer as a single polynomial is x^(3) + 9x^(2) - 15.

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The probability of selecting either lunch is 50%, as both lunches are equally likely to be chosen. This is because both lunches have the same ingredients, with the only difference being the dessert item.

Probability is a measure of the likelihood of a certain event or outcome occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event or outcome is impossible and 1 indicates that the event or outcome is certain to occur. Probability is an important concept in mathematics and statistics, and it is widely used in fields such as finance, science, engineering, and gaming.

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Answer is SAS, we can solve this question by SAS theorem of triangle, for that we have to know more about triangle.

A triangle in geometry is a three-sided polygon or object with three edges and three vertices.

If two triangles satisfy one of the following conditions, they are congruent:

a. Each of the three sets of corresponding sides is equal. (SSS)

b. The comparable angles between two pairs of corresponding sides are equal.(SAS)

c. The corresponding sides between two pairs of corresponding angles are equal. (ASA)

d. One pair of corresponding sides (not between the angles) and two pairs of corresponding angles are equal. (AAS)

e. In two right triangles, the Hypotenuses pair and another pair of comparable sides are equal. (HL)

So, △MNP≅△OPN and NO II MP and NO ≅ MP

then, ∠ ONP = ∠ MPN and Side NP is common.

Therefore we can solve it by SAS Theorem.

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The time taken to empty one tank is 1000 seconds or 16.67 minutes. Therefore, the total time required to empty all three tanks one after another is 50 minutes (16.67 minutes x 3).

The volume of water that can be emptied through the hole at the bottom of each tank per second is 0.2 liters. Therefore, the time taken to empty 200 liters of water from one tank is:

200 liters ÷ 0.2 liters per second = 1000 seconds

Converting the time to minutes:

1000 seconds ÷ 60 seconds per minute = 16.67 minutes

So, it takes 16.67 minutes to empty one tank. Multiplying this by three gives us the total time required to empty all three tanks:

16.67 minutes x 3 = 50 minutes

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Emily can read 5 words per minute.

Minutes are often used to measure the duration of activities such as meetings, phone calls, or workouts. They are also used to express the duration of processes or events that occur over a short period of time.

To find out how many words Emily can read per minute, we need to divide the total number of words she can read by the amount of time it takes her to read them.

75 words in 15 minutes can be written as a ratio:

75 words / 15 minutes

To simplify this ratio, we can divide both the numerator and the denominator by 15:

(75 words / 15 minutes) ÷ (15 minutes / 15 minutes)

This gives us:

5 words / 1 minute

Therefore, Emily can read 5 words per minute.

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Answer:

25%

Step-by-step explanation:

Number of favorable outcomes 4

Total number of outcomes=4+5+2+3+2=16

4/16=0.25

0.25x100=25

25%

​

Answer:

We do not have enough information to find the exact value of f(2.5) without additional assumptions about the nature of the exponential function. However, we can make an estimate using the given data and the properties of exponential functions.

First, we can write the general form of an exponential function as:

f(x) = a * b^x

where a is the initial value or y-intercept, and b is the base or growth factor. We can use the two given data points to set up a system of equations and solve for a and b:

f(-1) = a * b^(-1) = 18

f(5) = a * b^5 = 75

Dividing the second equation by the first equation, we get:

f(5) / f(-1) = (a * b^5) / (a * b^(-1)) = b^6 = 75 / 18 = 25 / 6

Taking the sixth root of both sides, we get:

b = (25 / 6)^(1/6) ≈ 1.472

Substituting this value of b into the first equation, we get:

a = f(-1) / b^(-1) = 18 / 1.472 ≈ 12.223

Therefore, we have the exponential function:

f(x) ≈ 12.223 * 1.472^x

Using this function, we can estimate the value of f(2.5) as:

f(2.5) ≈ 12.223 * 1.472^(2.5) ≈ 34.311

Note that this is only an estimate, and the exact value of f(2.5) may be different depending on the specific nature of the exponential function.

Wok out the probability of rolling one 6 from 2 throws on a biased dice rolling 6 1/5 of the time is 8/25

The given data is as follows:

Number of throws = 2

probability of rolling number = 6

The probability of getting dice one 6 from 2 throws can happen in two different ways.

1. Rolling a number 6 on the first throw and not getting a number 6 on the second throw.

2. Not rolling a number 6 on the first throw and getting a number 6 on the second throw.

Here, the multiplication rule of probability is used to find the probability of the above two different events.

1.

The probability of getting a 6 on the first throw = is 1/5

The Probability of not getting a 6 on the second throw = (4/5)

The Probability of both happening: (1/5) x (4/5) = 4/25

2.

The Probability of not getting a 6 on the first throw = (4/5)

The Probability of getting a 6 on the second throw = (1/5)

The Probability of both happening: (4/5) x (1/5) = 4/25

The probability of both events is = 4/25 + 4/25 = 8/25

Therefore we can conclude that the probability of getting one 6 from 2 throws on a  dice rolling 6 1/5 of the time is 8/25.

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$$x \frac{dy}{dx}\sin \left(\frac{y}{x}\right)=y \sin \left(\frac{y}{x}\right)-x$$

QUESTION 1:

Using the substitution $u = xy$, we have the following equation:

$$(x^2u+xu-u)dx + (x^2u-2x^2)dy = 0$$

Multiplying both sides by $\frac{dy}{dx}$, we get:

$$(x^2u+xu-u)\frac{dy}{dx}dx + (x^2u-2x^2)\frac{dy}{dx}dy = 0$$

Simplifying, we have:

$$(x^2u+xu-u)\frac{dy}{dx} + (x^2u-2x^2)dy = 0$$

Rearranging, we get:

$$x\frac{dy}{dx}(u \sin \left(\frac{y}{x}\right)) + y\sin \left(\frac{y}{x}\right) - x = 0$$

Which simplifies to:

$$x \frac{dy}{dx}\sin \left(\frac{y}{x}\right)=y \sin \left(\frac{y}{x}\right)-x$$

QUESTION 2:

The solution to the given differential equation is:

$$x \frac{dy}{dx}\sin \left(\frac{y}{x}\right)=y \sin \left(\frac{y}{x}\right)-x$$

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Answer:

To eliminate y, we can add the two equations.

5x + y + 3x - y = 48 + 16

Simplifying the left side, we get:

8x = 64

Dividing both sides by 8, we get:

x = 8

Now we can substitute x = 8 into either of the original equations and solve for y:

5x + y = 48

5(8) + y = 48

40 + y = 48

y = 8

So the solution is (x,y) = (8,8).

We can conclude that the square pyramid has a volume of 111.5 in³.

A square pyramid in geometry is a pyramid with a square base.

It is a right square pyramid with C4v symmetry if the apex is perpendicular to and above the square's center.

It is an equilateral square pyramid, the Johnson solid J1 if all edge lengths are equal.

A polyhedron with seven faces is called a heptahedron.

One "normal" heptahedron exists, and it is formed up of a surface with one side made up of four triangles and three quadrilaterals.

So, 6.6 inches wide is the square pyramid's base.

The square pyramid's height is 7.7 inches or h.

V = a²(h/3) is the formula for the square pyramid's volume.

By changing the values given:
V = 6.6²(7.7/3)

V = 43.56(2.56)

V = 111.51 ≈ 111.5

Therefore, we can say that the square pyramid has a volume of 111.5 in³.

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Answer:

4x+3y

Step-by-step explanation:

Combining like terms, we get:

5x - x + 4y - y = 4x + 3y

Therefore, 5x+4y-x-y simplifies to 4x+3y.

The solution is, distance from the point to the line is 22√10 feet.

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

The distance from point (x, y) to the line ax+by+c=0 is given by ...

 d = |ax +by +c|/√(a²+b²)

In general for, the equation of the line is ...

y = x/3 - 4

i.e. x -3y -12 = 0

so the distance formula is ...

 d = |x -y -12|/√(1² +(-3)²) = |x -y - 12|/√10

For the given point, the distance is ...

 d = |-6 -4 -12|/√10

   = 22/√10

 d = 22/√10 . . . .

distance from the point to the line = 22/√10

now, distance = 22/√10 * 10

                       =22√10 feet.

Hence, The solution is, distance from the point to the line is 22√10 feet.

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The required measure of y in the given triangle is 14 cm.

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

Here,
Following the property of proportionality of sides in similar triangles,
8 + 3.2 / 8 = y / 10
11.2/8 = y / 10
112 = 8y
y = 14

Thus, the required measure of y in the given triangle is 14 cm.

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If the selection is made randomly, there are 30045015 ways to select a committee of size 10 from a group of 10 men and 20 women. The probability that the committee consists of 5 men and 5 women is 0.129. The probability that there is no woman in the committee is  0.000000033.

1. The total number of ways to select a committee of size 10 from a group of 10 men and 20 women is given by the combination formula:
C(n,k) = n! / (k! * (n-k)!)
Where n is the total number of people (10 men + 20 women = 30) and k is the size of the committee (10).
C(30,10) = 30! / (10! * (30-10)!)
C(30,10) = 30! / (10! * 20!)
C(30,10) = 30045015
Therefore, there are 30045015 ways to select a committee of size 10 from a group of 10 men and 20 women.

2. The probability that the committee consists of 5 men and 5 women is given by:
P(5 men and 5 women) = C(10,5) * C(20,5) / C(30,10)
P(5 men and 5 women) = (10! / (5! * 5!)) * (20! / (5! * 15!)) / (30! / (10! * 20!))
P(5 men and 5 women) = (252 * 15504) / 30045015
P(5 men and 5 women) = 0.129

3. The probability that there is no woman in the committee is given by:
P(no woman) = C(10,10) * C(20,0) / C(30,10)
P(no woman) = (10! / (10! * 0!)) * (20! / (0! * 20!)) / (30! / (10! * 20!))
P(no woman) = (1 * 1) / 30045015
P(no woman) = 0.000000033
Therefore, the probability that there is no woman in the committee is 0.000000033.

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Yes, the fraction 4/9 will make each equation true.

Fraction is an element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

To see why, we can simplify the fraction 4/9 as follows:

4/9 = (4 x 7)/(9 x 7) = 28/63

Now, we can substitute 4/9 with 28/63 in each equation to see that they are all true:

63 x 28/63 = 28

18 x 28/63 = 8

96 x 28/63 = 42

36 x 28/63 = 16

We can also write it as:

63 × (4/9) = 28

18 × (4/9) = 8

96 × (4/9) = 42

36 × (4/9) = 16

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Answer:

The answer is 2/15

Step-by-step explanation:

2/5 × 1/3

Answer:

C

Step-by-step explanation:

Answer choice A implies that less than received an 80 or better, while according to the boxplot, at least 18 students did.

Answer choice B suggests that most students scored at least 90%, but that is false.

Answer choice C implies that the same number of students scored in the 70-80% range as in the 80-90% range, which is true according to the box plot.

Answer D says that more people scored 65-70% than 90-100%, but the opposite is true.