the measure of three interior angle of a triangle are in the ratio 2፡3፡4. what is the measure of the smallest and largest interior angles of triangle?​

The minimum number of feet in the length of the rope [tex]8\sqrt{(4\pi^2 + 36)}[/tex] feet.

To find the minimum number of feet in the length of the rope, we need to first calculate the height of the point on the circumference where the rope is attached. We can do this by using the formula for the circumference of a cylinder:

C = 2πr

where C is the circumference, r is the radius of the cylinder, and π is pi. Since we know that the circumference of the pole is 2 feet, we can solve for the radius:

2 = 2πr

r = 1/π

Next, we need to calculate the length of the rope that is wrapped around the pole. We know that the rope is wrapped around the pole four times, so the length of the rope is:

L = 4 × height of the pole

To find the height of the pole, we can use the Pythagorean theorem:

[tex]a^2 + b^2 = c^2[/tex]

where a is the radius of the pole, b is the height of the point where the rope is attached, and c is the length of the rope wrapped around the pole.

Solving for b, we get:

b = [tex]\sqrt{c^2 - a^2)}[/tex]

Substituting the values we know, we get:

b = [tex]\sqrt{((4\pi^2 + 12^2) - \pi^2)}[/tex]

b = [tex]\sqrt{sqrt(16\pi^2 + 144)}[/tex]

Finally, we can substitute this value into the formula for the length of the rope:

[tex]L = 4 * \sqrt{16\pi^2 + 144)}[/tex]

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By using pythagorean theorem, the length of the missing side is 12 feet.

What is the Pythagorean theorem?

Pythagoras' theorem is a fundamental principle in geometry that relates to the three sides of a right-angled triangle. It states that:

"In a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides."

In mathematical terms, if a, b, and c are the lengths of the sides of a right-angled triangle, where c is the hypotenuse, then the theorem can be written as:

[tex]c^2 = a^2 + b^2[/tex]

We can use the Pythagorean theorem to determine the length of the missing side if we know that the given sides form a right triangle.

In this case, we have two sides of the triangle given: 7.2 feet and 9.6 feet. Let's assume that c is the length of the hypotenuse.

If the triangle is a right triangle, then we can use the Pythagorean theorem to solve for c:

[tex]c^2 = 7.2^2 + 9.6^2[/tex]

[tex]c^2 = 51.84 + 92.16[/tex]

[tex]c^2 = 144[/tex]

[tex]c = \sqrt{144}[/tex]

c = 12 feet

Therefore, if the triangle is a right triangle, then the length of the missing side is 12 feet.

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Answer:

x=5/6

Step-by-step explanation:

lcm=6x

6xX1/2x+6xX1/3x=6xX1 (divide through)

3x1+2x1=6xX1

3+2=6x

5=6x

5/6=6x/6 (divide through)

x=5/6

Hope it help

The function f(x) = (x+4)/x is defined for all real numbers except x = 0, since division by zero is undefined. Therefore, the domain of the function is all real numbers except x = 0.

In interval notation, we can write the domain of the function as: (-∞, 0) U (0, ∞). This means that the function is defined for all values of x that are less than zero or greater than zero, but it is not defined at x = 0. The domain of a function is the set of all possible input values (also called independent variables) for which the function is defined. In other words, it is the set of values for which the function yields a valid output (also called dependent variable). In the case of the function f(x) = (x+4)/x, the domain is restricted by the fact that division by zero is undefined. Therefore, we cannot include x = 0 in the domain of the function. To find the domain of a function, we need to look for any values of the input variable that would make the function undefined or result in an error. These include situations such as division by zero, taking the square root of a negative number, or taking the logarithm of a non-positive number. In general, the domain of a function can be described using interval notation or set-builder notation, depending on the specific circumstances of the function. It is important to identify the domain.

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Answer:

-3, -1 and 1

Step-by-step explanation:

substitute what ever the x column says into 2x-3

2×0-3=-3

2×1-3=-1

2×2-3=1

the answers: -3, -1, 1

A5 has a value of -11. This can also be confirmed by looking at the words in order: 5, 1, -3, -7, and -11.

Using the given formula, we can find the value of the nth term by recursively applying the formula, starting from the first term:

a1 = 5

a2 = a1 - 4 = 1

a3 = a2 - 4 = -3

a4 = a3 - 4 = -7

a5 = a4 - 4 = -11

Therefore, the value of a5 is -11. We can also verify this by checking the sequence of terms: 5, 1, -3, -7, -11.

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Answer:

62

Step-by-step explanation:

Surface area of a prism = S = 2(lw + lh + wh)

where l = length

w = width

h = height

Given l = 3, w = 5 and h = 2

S = 2(3 x 5 + 3 x 2 + 5 x 2)

= 2(15 + 6 + 10)

= 2(31)

= 62

The quadrants in which the points A = (2,-3) B = (-4,1) as required to be determined are fourth and second quadrant respectively.

As evident from the task content; the quadrant in which the given points are located are to be determined.

On the Cartesian plane; given a pair of coordinates (x, y).

In the first quadrant; x is positive and y is positive.

In the second quadrant; x is negative and y is positive.

In the third quadrant; x is negative and y is negative.

In the fourth quadrant; x is positive and y is negative.

Ultimately, the point A = (2, -3) is located in the fourth quadrant and the point B = (-4, 1) is located in the second quadrant.

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Answer:

The answer is to this question is D. 41/10

Pete runs farther per carry, with a unit rate of 9.05 yards per carry compared to Branden's unit rate of 7.33 yards per carry.

A unit rate is a rate that has a denominator of 1. It is a ratio that compares a quantity to its unit of measurement.

To determine who runs farther per carry, we can use unit rates to compare the distance each player runs per carry.

For Branden:

Distance per carry is

= 550 yards ÷ 75 carries

Divide the numbers

= 7.33 yards per carry

For Pete:

Distance per carry is

= 380 yards ÷ 42 carries

Divide the numbers

= 9.05 yards per carry

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The mean of 5x3+8 is 23 and the standard deviation of 5x3+8 is 5.65, rounded down to 2 decimal places.

Consider the following experiment: Throw two fair dice sequentially and define a random variable X as the sum of the numbers of the two dice. We are to compute the mean and standard deviation of 5x3+8. Mean of 5x3+8 is 23 and standard deviation of 5x3+8 is 5.65. Thus, option 1 and option 2 are the correct answers.What is the expected value of a discrete random variable?In probability theory and statistics, the expected value of a random variable is the measure of the center of the probability distribution. It represents the long-run mean of occurrences, for example, the average value in a long sequence of trials.The standard deviation of a random variable is the measure of the spread or variability of a probability distribution, similar to variance. It is the square root of variance, denoted as σ.Here, the sum of the numbers of two dice follows a uniform distribution, where each event is equally likely, and the probability of each event is 1/36. Therefore, the random variable X is discrete with probability mass function:f(x) = 1/36, for x = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.Using this distribution, we can find the mean and standard deviation of the random variable X.Mean of 5x3+8=5(3)+8=23σ2=∑(x−μ)2P(X=x)where,μ = E(X) = ∑xf(x) = 7σ = √σ2=√ ∑(x−μ)2P(X=x)= √(2-7)2 (1/36)+ (3-7)2 (2/36)+ (4-7)2 (3/36)+ (5-7)2 (4/36)+ (6-7)2 (5/36)+ (7-7)2 (6/36)+ (8-7)2 (5/36)+ (9-7)2 (4/36)+ (10-7)2 (3/36)+ (11-7)2 (2/36)+ (12-7)2 (1/36)≈ 5.65Therefore, the mean of 5x3+8 is 23 and the standard deviation of 5x3+8 is 5.65, rounded down to 2 decimal places.

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Using the equation y = 7x , we can compute that when x = 2, y = 14 and when x = 4 , y = 28. So, correct option is B.

The equation y = 7x relates the variables y and x, where y is a function of x. To compute the value of y for a given value of x, we simply substitute that value of x into the equation and solve for y.

When x = 2, we can substitute this value into the equation:

y = 7(2) = 14

Therefore, when x = 2, y = 14.

Similarly, when x = 4, we can substitute this value into the equation:

y = 7(4) = 28

Therefore, when x = 4, y = 28.

So, the correct option is B: When x = 2, y = 14 and when x = 4, y = 28.

In summary, to compute the value of y for a given value of x using an equation, we substitute that value of x into the equation and solve for y. In this case, when x = 2, y = 14, and when x = 4, y = 28, according to the given equation y = 7x.

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We can conclude after answering the provided question that  If the data expression points are arranged in a curve, the function could be a quadratic, exponential, or other non-linear equation.

In mathematics, an expression is a grouping of representations, digits, and huge corporations that resemble a clear relationship or regimen. An expression can be a real number, a transitory, or a combination of the two. Addition, subtraction, pervasiveness, division, and exponentiation are examples of mathematical operators. Expressions are common in arithmetic, mathematics, and geometry. They are used in mathematical formula representation, equation solution, and mathematical relationship simplification.

This graph appears to be a scatter plot of data points based on the visual representation you provided. The values of an independent variable are represented by the horizontal axis (x-axis), while the values of a dependent variable are represented by the vertical axis (y-axis).

Without any additional information, determining the specific function represented by this graph is difficult. The shape and pattern of the scatter plot, on the other hand, can provide some insight into the relationship between the two variables. If the data points are arranged in a linear pattern, for example, the function could be a linear equation. If the data points are arranged in a curve, the function could be a quadratic, exponential, or other non-linear equation.

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Given data:

pH of lye = 12.13

Using the formula pH = -log[H+], we have to find the hydrogen ion concentration, [H+].

Now, putting the given values in the formula, we get:

pH = -log[H+]

12.13 = -log[H+]

log[H+] = -12.13

[H+] = 10^-12.13 = 5.01187 x 10^-13

So, the hydrogen ion concentration, [H+] is 5.01187 x 10^-13 moles/liter. Therefore, the answer is 5.01187 x 10^-13.

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Therefore, the annual interest rate is approximately 12%.

How to compute interest is as follows: P x R x T is the formula for calculating interest. Principal Amount is P. (the beginning balance). rates of interest (usually per year, expressed as a decimal). T stands for the value T. (generally one-year time periods).

Let r be the annual interest rate as a decimal. Then the balance after 2 years is given by:

Balance = 3500(1+r)²

Setting this equal to $4390.40 and solving for r, we have:

4390.40 = 3500(1+r)²

Dividing both sides by 3500 and taking the square root, we get:

(1+r)² = 4390.40/3500 = 1.2544

Taking the square root of both sides, we get:

1 + r = √(1.2544) ≈ 1.12

Subtracting 1 from both sides, we get:

r ≈ 0.12 or 12%

Therefore, the annual interest rate is approximately 12%.

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According to given equation Baxter’s Hardware had 27 followers on Sunday morning.

What is equation?

Equations can take many forms, including linear, quadratic, polynomial, trigonometric, and exponential, and can be used to model and solve a wide range of real-world problems.

The given equation is:

f + 18 - 20 = 25

Adding the numbers on the left side, we get:

f - 2 = 25

Adding 2 to both sides, we get:

f - 2 + 2 = 25 + 2

Simplifying, we get:

f = 27

Therefore, Baxter’s Hardware had 27 followers on Sunday morning.

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a) Note that the Angle of Elevation from R to T is 63.4°

b) The angle fact tells you that the answer to part a) is also the angle of depression from T to R is "the Alternate Angle Postulate"

The principle used in below is SOH CAH TOA.

a) Tanθ = Opp/Adjacent

Tanθ = 340/165
Tanθ = 2.0606060606
θ = Tan⁻¹ 2.0606060606
θ = 63.4349

θ [tex]\approx[/tex] 63.4

b) The principle of alternate angles is a theorem in geometry that states that when a straight line intersects two other lines, the angles formed on opposite sides of the intersection and on opposite sides of the transversal are equal. This principle is based on the fact that parallel lines cut by a transversal create corresponding angles that are congruent.

Thus the angle fact tells you that the answer to part a) is also the angle of depression from T to R is "the Alternate Angle Postulate"

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P(Z > -0.475) ≈ 0.68

(a) The probability of having at least 9 events can be calculated as follows:ppois(8, 10, lower.tail = FALSE)This gives the probability of having less than or equal to 8 events, so we subtract it from 1 to get the probability of having at least 9 events. Hence, the probability of having at least 9 events is:1 - ppois(8, 10, lower.tail = FALSE) = 0.3446(b) For a Poisson distribution with λ=10, the mean is μ=10 and the variance is σ²=10. Hence, the standard deviation is σ=√10 ≈ 3.162.To approximate this using a normal distribution, we need to standardize the Poisson random variable. That is,(X-μ)/σ ~ N(0,1)where X is a Poisson random variable with λ=10. We want to find P(X ≥ 9), which can be written as P(X > 8.5) using the continuity correction. Hence,P(X > 8.5) = P(Z > (8.5-10)/3.162) = P(Z > -0.475)Using a standard normal table or calculator, we find that P(Z > -0.475) ≈ 0.68. Therefore, the approximate probability of having at least 9 events is 0.68.

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The sampling distribution of the means has a mean of 172 pounds and a standard deviation of 4.83 pounds.

In the context of sampling distribution of the means, the standard deviation represents the degree of spread or variation of sample means around the true population mean.

To compute the standard deviation of the sampling distribution of the means, one typically divides the population standard deviation by the square root of the sample size.

Therefore, the standard deviation of the sampling distribution of the means is 29/√36 = 29/6 = 4.83 pounds.

So, the sampling distribution of the means has a mean of 172 pounds and a standard deviation of 4.83 pounds.

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The length of the rectangular prism with a volume of 1.512 m³​ is equal to 0.9 meters.

Mathematically, the volume of a rectangular prism can be calculated by using this formula:

Volume of a rectangular prism = L × W × H

Where:

By substituting the given parameters into the formula for the volume of a rectangular prism, we have;

Volume of a rectangular prism = L × W × H

1.512 = L × 2.4 × 0.7

Length, L = 1.512/1.68

Length, L = 0.9 meters.

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Complete Question:

Find the length of the rectangular prism shown below with a volume of 1.512 m³​, a width of 2.4 m and a height of 0.7 m.

Answer:

the number 228

Step-by-step explanation:

Let's call the smallest number in the consecutive sequence "x". Then, the 10 consecutive numbers are x, x+1, x+2, x+3, x+4, x+5, x+6, x+7, x+8, and x+9.

If we exclude one of these numbers, then the sum of the remaining 9 numbers would be:

(x) + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) + (x+7) + (x+8) or 9x + 36.

We know that the sum of the remaining 9 numbers is 2023, so we can set up the equation:

9x + 36 = 2023

Solving for x, we get:

9x = 1987

x = 221

Therefore, the smallest number in the consecutive sequence is 221, and the 10 numbers are 221, 222, 223, 224, 225, 226, 227, 228, 229, and 230.

If we exclude the number 228, then the sum of the remaining 9 numbers is 2023.

50%

The cran-orange juice contains 50% cranberry juice. The juice is 100% juice. Subtract 50% cranberry juice from 100% cran-orange juice and that leaves you with 50% orange juice.

Answer:

The answer is B

Step-by-step explanation:

e [0.1}

We know that P(X < 2.24) = 0.7257. Also, the mean is 2.Let us calculate the variance of the given normal distribution random variable. Given that P(X < 2.24) = 0.7257, we have to find variance. Let us solve this question as follows:We know that mean of normally distributed random variable is μ and standard deviation is σ. As the mean is 2, μ = 2.We have the z-score: z = (2.24 - 2) / σFrom the normal distribution table, we can find out that P(Z < 0.80) = 0.7881Now, we have the following equation:0.7881 = (2.24 - 2) / σσ = 0.3158Finally, we can find the variance (σ^2) = 0.3158^2 = 0.0995 ≈ 0.1Therefore, the correct answer is option e. 0.1.

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The value of sides a and b from the triangle. A = 50 degrees, B = 50 degrees, c = 12 meters is 9.341 metres and angle C is 80 dgree.

From the Law of Sines states that the follow proportions must be true which is

sin (A)/a = sin (B)/b= sin (C)/c

Where A = 50 degrees

B = 50 degrees

c = 12 meters

Angle C = (180-100=80   ( angle in the triangle is 180 degree)

sin (50)/a = sin (50)/b= sin (80)/12

0.766/a = 0.766/b= 0.985/12

0.766/a = 0.766/b=0.082

0.766/a =0.082

a =0.766/0.082 = 9.341

0.766/b=0.082

b=0.766/0.082= 9.341

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complete questions

Solve the given triangle. A = 50 degrees, B = 50 degrees, c = 12 meters

Round your answers to the nearest integer.

C = ? degrees

b = ? meters

c = ? meters

Answer:

Step-by-step explanation:

do it yourself

A person's cycling rate can be expressed mathematically in the equation that describes their cycling motion. Specifically, the cycling rate can be represented by the frequency or number of revolutions per unit time (usually in seconds) that the person completes while cycling.

The equation that describes a person's cycling motion is typically a kinematic equation that relates the person's position, velocity, and acceleration as a function of time. One commonly used equation is:

d = vit + 1/2at^2

where d is the distance traveled by the person, vi is the initial velocity (usually zero), a is the acceleration, and t is the time elapsed.

The cycling rate can be incorporated into this equation by expressing the velocity as a function of the frequency of revolutions (f) and the radius of the wheel (r). This gives:

v = 2πrf

where v is the velocity of the cyclist, r is the radius of the wheel, and π is the mathematical constant pi (approximately 3.14).

Substituting this expression for v into the kinematic equation gives:

d = (2πrf)t + 1/2at^2

This equation shows how the person's cycling rate, represented by the frequency f, affects their distance traveled as a function of time. If the person increases their cycling rate, their velocity increases, and they will travel a greater distance in the same amount of time.

The cost of water from the store and the cost from the tap will be the same when the number of liters

reaches 7.5 liters.

Let's assume that the cost of buying 'x' liters of water from the store is the same as the cost of buying 'x' liters of water from the tap.

For water from the store, the cost per liter is 3, so the cost of buying 'x' liters of water from the store would be 3x.

For water from the tap, there is a flat rate of 15 plus per liter. So, the cost of buying 'x' liters of water from the tap would be 15 + x.

Now we can set up an equation to find the value of 'x' when the costs are equal:

3x = 15 + x

Simplifying this equation, we get:

2x = 15

x = 7.5

Therefore, the cost from the store and the cost from the tap would be the same at 7.5 liters.

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