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Find the unknown side length. Simplify radicals to simplest radical form.

Thus, the height of flagpole from the ground is found as 23.34 feet.

The measurement of the angle between a person's eyes' line of sight to anything above and the horizontal line is known as the angle of elevation.

The movement of the observer's eyes determines the elevation angle. The angle of elevation is the angle formed by the line of sight and the horizontal line when a viewer is looking up at an object.

Given data:

Using the trigonometric ratios in the right triangle ABE.

tan 35 = h / 30

h = 30* tan(35)

h = 18.34

Height of flagpole = 18.34 + 5 = 23.34 feet

Thus, the height of the flagpole from the ground is found as 23.34 feet.

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Step-by-step explanation:

5 cos (307)  = 3

5 sin (307) = -4  

just plot the point   ( 3, -4 )     Done.

Answer:

The point is (3, -4) because 5 cos [307] = 3 and 5 sin [307] = -4

Step-by-step explanation:

From 1860 to 2018 is  158 years

 Use compounding formula

$ 28.95    =   $ 1   ( 1 +i) ^158       where i is decimal inflation rate %

[tex]\sqrt[158]{28.95}[/tex]  = 1 + i

i = .0215       = 2.15 %

Fraction: 0/4

Percent: 0%

Likelihood: Impossible

Answer:

1.fraction 1/4

percentage 25%

unlikely

2.same as number one

Since all the students in the class are more than 10 years old, we can write the inequality: greater than

x > 10

what is greater than ?

The symbol ">" is commonly used in mathematics to represent "greater than." It is used to indicate that one quantity or value is larger than another. For example, if we say that 5 > 3, we mean that 5 is greater than 3. Similarly, if we say that x > y, we mean that x is greater than y.

In the given question,

The symbol ">" is commonly used in mathematics to represent "greater than." It is used to indicate that one quantity or value is larger than another.

Let "x" be the age of a student in the class.

Since all the students in the class are more than 10 years old, we can write the inequality:

x > 10

This inequality means that the age "x" of any student in the class must be greater than 10 years.

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Answer:

Step-by-step explanation:

We get triangle PQR by plotting the point P (1, 4), Q (3, 1), R (2, -1) on the graph paper when rotated through 180° about the origin. The new position of the point is: P (1, 4) → P' (-1, -4) Q (3, 1) → Q' (-3, -1) R (2, -1) → R' (-2, 1) Thus, the new position of ∆PQR is ∆P’Q’R’.

The plane degrees off course is 6.79 degrees off at a speed of 541. 92 km / hr relative to the ground.

To find the airplane's course deviation and its ground speed, we need to first determine the velocity vectors of the airplane and the wind.

W x = W x cos(225) = 90 x cos(225) = -63.64 km/hr

Wy = W x sin(225) = 90 x sin(225) = -63.64 km/hr

Magnitude: |R| = sqrt(Rx^2 + Ry^2) = √(536.36^2 + (-63.64)^2) = 541.92 km/hr

Direction: θ = arctan(Ry / Rx) ≈ arctan (-63.64 / 536.36) = -6.79 degrees

So, the airplane is 6.79 degrees off course, and its ground speed is 541.92 km/hr.

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Answer:

Step-by-step explanation:

Okay so when a smaller number is divided by a larger number, the quotient is less than 1.  Hope this helps Bye sisters slay.

The answer of the given question based on the variance is , 92% confidence that the true population mean lies between 69.11 and 74.89.

In statistics, the mean is a measure of central tendency that represents the average of a set of numerical data. It is also known as the arithmetic mean or simply the average. The mean is calculated by adding up all the values in the dataset and then dividing the sum by the number of values.

To construct a random interval with a 0.92 confidence level, we need to find the corresponding z-score for the level of confidence. Since the interval is not two-sided, we will use a one-tailed z-score.

Using a standard normal distribution table or calculator, we find that the z-score corresponding to a 0.92 confidence level is approximately 1.41.

To find the 92% confidence interval for the population mean, we can use the following formula:

CI = ₓ⁻ ± zα/2 * σ/√n

where ₓ⁻ is the sample mean, σ is the population standard deviation (unknown in this case), n is the sample size, and zα/2 is  critical value of  standard normal distribution corresponding to desired level of confidence.

Substituting the given values, we get:

CI = 72 ± 1.41 * (4 / √20)

CI = (69.11, 74.89)

Therefore, we can say with 92% confidence that the true population mean lies between 69.11 and 74.89.

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When the car travels east on 4th Street and turns onto King Avenue heading northeast, the angle created by the car's turning is a 45-degree angle.

When the car travels southwest on King Avenue and turns left onto 3rd Street, the angle created by the car's turning is a 135-degree angle.

When the car travels northeast on King Avenue and turns right onto 3rd Street, the angle created by the car's turning is a 45-degree angle.

(a) When the car travels east on 4th Street and turns onto King Avenue heading northeast, the angle created by the car's turning is a 45-degree angle. This is because the intersection of 4th Street and King Avenue creates a right angle, and the car turns northeast, creating another 45-degree angle with the horizontal 4th Street.

(b) When the car travels southwest on King Avenue and turns left onto 3rd Street, the angle created by the car's turning is a 135-degree angle. This is because the intersection of King Avenue and 3rd Street creates a right angle, and the car turns left, creating an additional 90-degree angle. Therefore, the total angle is 90 degrees + 45 degrees = 135 degrees.

(c) When the car travels northeast on King Avenue and turns right onto 3rd Street, the angle created by the car's turning is a 45-degree angle. This is because the intersection of King Avenue and 3rd Street creates a right angle, and the car turns right, creating another 45-degree angle with the horizontal 3rd Street.

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Answer:

The speed of the boat in still water is 15 mi/hr while the speed of the current is 10 mi/hr.

Step-by-step explanation:

Given: d = 350 miles

[tex]t_{ds}[/tex] = 14 hours

[tex]t_{us}[/tex] = 70 hours

Asked: Speed of the boat [tex]V_b[/tex] in still water and speed of the current [tex]V_c[/tex]

Solve:

Note that when the boat is going downstream, the current is helping the boat to speed up and when the boat is going upstream, the current is slowing it down.

Get the speed downstream

[tex]V_{ds} = V_b + V_c[/tex]

350mi/14hrs = [tex]V_b + V_c[/tex]

25 mi/hr =    [tex]V_b + V_c[/tex]  

Transpose to get the value of Vb

25 mi/hr - Vc = Vb   ---equation 1

Get the speed upstream

[tex]V_{us} = V_b - V_c[/tex]

350mi/70hrs = Vb - Vc

5 mi/hr = Vb - Vc

Transpose to get the value of Vb

5 mi/hr + Vc = Vb   ----equation 2

Equate equations 1 and 2

25 mi/hr - Vc = 5 mi/hr + Vc

Transpose

25 mi/hr - 5 mi/hr = Vc + Vc

20 mi/hr = 2 Vc

Divide both sides of the equation by 2

10 mi/hr = Vc

Vc = 10 mi/hr

From 25 mi/hr =    [tex]V_b + V_c[/tex]  we then solve the speed of the boat

25 mi/hr = Vb + 10 mi/hr

25 mi/hr - 10 mi/hr = Vb

15 mi/hr = Vb

Vb = 15 mi/hr

Answer:

Step-by-step explanation:

Given:-

•α=

•β=

To Find:-

♦The Quadratic Equation using the Given details?

AnsWer:-

↓Quadratic Formula↓

→k[x²-(α+β)x+αβ]

→α+β=+

•Take LCM•

→α+β=+

→α+β=

→αβ=×

→αβ=

↑Using these Values in The Formula↑

→k[x²-(x)+() ]

★Let k=8★

→8[x²-(x)+() ]

→8x²-(-2x)+(-3)

→8x²+2x-3=quadratic Equation

To create points for the graph of f(x) = (2/3)x - 1, we can choose values of x and calculate the corresponding values of f(x). See explanation below and attached graph.

To create points for the graph of f(x) = (2/3)x - 1, we can choose values of x and calculate the corresponding values of f(x). For example:

So, we have the following points for the graph: (-3, -4), (-2, -2 1/3), (-1, -1 2/3), (0, -1), (1, -1/3), (2, 1/3), (3, 1).

We can now plot these points on a graph, with x-values on the horizontal axis and f(x) values on the vertical axis. We can label the horizontal axis as "x" and the vertical axis as "f(x)" or "y".

Note that the graph of f(x) = (2/3)x - 1 is a straight line with slope 2/3 and y-intercept -1.

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Answer:

40 cm²

Step-by-step explanation:

you have to multiply the top of the triangle by the base(40) which is 80 then you divide by two since it's a triangle then you get 40 again since your finding the area you have to put the 2 above the cm

To the nearest block, Landon's house is at distance of 12 blocks away from Maria's house if Maria could walk in a straight line.

A basic mathematical theorem relating to the sides of a right-angled triangle is known as Pythagoras' theorem. The square of the length of the hypotenuse, the side that faces the right angle, is said to be equal to the sum of the squares of the lengths of the other two sides, known as the legs, in a right triangle.

This can be written in mathematical notation as:

c² = a² + b²

where c is the length of the hypotenuse, and a and b are the lengths of the legs of the right triangle.

In this case, we can consider the straight line between Maria's house and Landon's house as the hypotenuse of a right triangle, with the distances they walked as the other two sides. We can use the distance formula to find the lengths of those sides:

Distance walked by Maria = √(9² + 3²) = √90 ≈ 9.49 blocks

Distance walked by Landon = √(5² + 7²) = √74 ≈ 8.60 blocks

Now we can use the Pythagorean theorem to find the distance between their houses:

Distance between houses = √(9.49² + 8.60²) ≈ 12.46 blocks

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Answer:

good luck

Step-by-step explanation:

Answer:

We can use the Pythagorean theorem to solve this problem. Let's call the distance Brenda is away from the fish "x". Then, we have a right triangle with legs of length 12 and x, and a hypotenuse of length 16. So:

x^2 + 12^2 = 16^2

Simplifying:

x^2 + 144 = 256

x^2 = 112

Taking the square root of both sides:

x ≈ 10.6 feet

Therefore, Brenda is approximately 10.6 feet away from the fish.

Answer:

y=9 (3x/9-2) + 18=3x

Step-by-step explanation:

This null hypothesis prompt is actually straight forward. Note that where the above conditions exist, we must NOT reject the null hypothesis due to the values of the z-statistics and the significance level.

The idea that there is no influence on the population is known as the null hypothesis. We can reject the null hypothesis if the sample contains sufficient data to refute the assertion that there is no impact in the population (p≤α ).

So to determine whether or not to accept or reject the null hypothesis, we must determine dthe z-score.

To find the the critial value for a left-tailoed test, where the signifiance level is 0.01, note that we must find the z-score that leaves 1% of the area in the left tail.

Using the standard distribution table, the z-score for 0.01 left tail is about -2.33.

Since

z-satistics which  is equal to -1.95 (as given) is greater than the z-score, we must NOT reject the null hypothesis.

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2298 divided by 24 using long division shows what is the quotient and remainder while 2298 divided by 24 and the complete steps for how to find it.

Question:

2298/24 = (?)

what is 2298 divided by 24?

the quotient is 95 and the remainder is 18 when 2298 is divided by 24.

Answer: x=14

Step-by-step explanation:

cb=10.

ac=14

The value of X will be 14.

This is a simple mathematics problem that can be solved by using ratios.

Given, AC : BC : AB = 7 : 5 : 8

AC = X ; BC = 10 ; AB = X + 2

AC/ BC = X/ 10 = 7/5  (Ratios can also be represented as fractions)

X/10 = 7/5

On Transposing,

5X = 70

X = 70/5

X = 14

Alternatively,

BC/AB = 5/8 = 10/ (X + 2)

5/8 = 10/ (X + 2)

On Transposing,

80 = 5X + 10

5X = 70

X = 14

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Answer:1111

Step-by-step explanation:

To cover a 2000 sq ft wall, we will need 5 gallons of paint.

what is area?

Area is the measure of the size of a two-dimensional surface or region, expressed in square units. It is a fundamental concept in geometry and is used to quantify the amount of space inside a shape, such as a square, rectangle, triangle, or circle. The unit of measurement for area varies depending on the system used, but in the International System of Units (SI), the standard unit of area is the square meter (m²). In everyday life, we often use other units of area such as square feet, square inches, or square centimeters.

To find the conversion factor, we need to divide the number of square feet by the number of square feet covered by one gallon of paint:

Conversion factor = 1 gallon / (400 sq ft/gallon)

So, for a wall that is 2000 sq ft, we can use this conversion factor to find the number of gallons of paint needed:

Number of gallons = (2000 sq ft) / (400 sq ft/gallon) = 5 gallons

Therefore, to cover a 2000 sq ft wall, we will need 5 gallons of paint.

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1 kg = 1000 G

so 1000/4g = 250g

I hope it’s helpful

The percent of the box that will remain unwrapped by the 60 square feet of paper is about 20.70%

A percentage is a proportion of a number expressed as fraction of a 100

The dimensions in mixed fractions can be expressed as follows;

Height of the box = 1 2/3 feet = 5/3 feet

Width of the box = 4 feet

Length of the box = 5 1/2 feet = 11/2 feet

Surface area of the box, A = 2 × (5/3) × 4 + 2 × 4 × 11/2 + 2 × (5/3) × 11/2 = 227/3 = 75 2/3 square inches

The percent of the box that will remain unwrapped is therefore;

Percentage = 60/(227/3) × 100 ≈ 79.3%

The percentage of the box that will remain unwrapped is about (100 - 79.3)% = 20.70%

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Required algebraic expression is (t+30).

What is algebraic expression?

An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. It may also contain brackets or parentheses to indicate the order of operations.

Algebraic expressions can be written using letters or symbols to represent variables, and they are used to represent mathematical relationships or formulas. For example, the expression "3x + 4" represents the sum of three times a variable x and the constant 4.

Let's represent the amount of time that Jill spends watching television as the variable j. We know that she watches 30 minutes more than Bill, so we can write:

j = t + 30

This algebraic expression says that Jill's time j is equal to Bill's time t, plus 30 additional minutes.

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The expression 10m‾‾√ is an expanded form of the mathematical term ln10.

I hope this helps you.

you can check your ans. by sub. in the value of x and y into both the equation which must give you the same answer.

Answer:

167.6190 approximately 167.62 inches

Step-by-step explanation:

formula for surface area of a cone is 1/3πr×r×slant height. How this helps.