Which set of three angles could represent the interior angles of a triangle? 26 degrees, 51 degrees, 103 degrees 29 degrees, 54 degrees, 107 degrees 35 degrees, 35 degrees, 20 degrees 10 degrees, 90 degrees, 90 degrees

Answer:

If all the 300 students were surveyed, 220 would have been in favor of the photo booth.

Step-by-step explanation:

Sample size = 15

People out of 15 in favor of photo booth = 11

Percentage of people in favor of school dance = [tex]\frac{11}{15} \times 100\% = 73\frac{1}{3} \%[/tex]

We have to find if all 300 students are surveyed how many will be in favor of photo booth. Remember that, the sample data is the best estimator of the population data. So, the sample data of 15 students will be the best estimator for the entire population of 300 students.

Since, in the sample of 15 students, [tex]73\frac{1}{3} \%[/tex] were in favor of photo booth, we would expect that if all the 300 students were surveyed, the same percentage will be in favor of photo booth. So we need to calculate [tex]73\frac{1}{3} \%[/tex] of 300.

[tex]73\frac{1}{3} \% \text{ of 300}\\\\ = 73\frac{1}{3} \% \times 300\\\\ =\frac{220}{3} \% \times 300\\\\ =\frac{220}{300} \times 300\\\\ = 220[/tex]

This means if all the 300 students were surveyed, 220 would have been in favor of the photo booth as per the sample data.

Approximately 220 out of 300 students are likely to be in favor of the photo booth.

To determine how many of the 300 students are likely to be in favor of the photo booth, we can use the proportion given by the sample.

1. Calculate the proportion of students in favor from the sample:

Proportion = Number in favor / Total surveyed = 11 / 15

Proportion = 0.7333 (rounded to four decimal places)

2. Apply this proportion to the entire school population:

Expected number in favor = Proportion × Total school population

Expected number in favor = 0.7333 × 300

Expected number in favor ≈ 220

Therefore, out of 300 students, approximately 220 students are likely to be in favor of the photo booth.

Answer:

$62.17

Step-by-step explanation:

Answer:

The answer is 62.17.Because you would add 18.62 + 43.55 to get your answer of 62.17

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Answer:

(a)The position of the particle after a time t is

[tex]S(t)=\frac{t^3}3+9t+c[/tex]

(b)The position of the particle after a time t is

[tex]S(t)=\frac{t^3}3+9t+3[/tex]

Step-by-step explanation:

We know that, the first order derivative of the position of an object is the velocity of the object.

(a)

Given that, the velocity of a particle moving in straight line is

[tex]V(t)=t^2+9[/tex]

[tex]\Rightarrow \frac{dS(t)}{dt}=t^2+9[/tex]

[tex]\Rightarrow {dS(t)}=t^2dt+9\ dt[/tex]

Integrating both sides

[tex]\int {dS(t)}=\int t^2dt+\int9\ dt[/tex]

[tex]\Rightarrow S(t)=\frac{t^3}3+9t+c[/tex]  [ c is an arbitrary]

The position of the particle after a time t is

[tex]S(t)=\frac{t^3}3+9t+c[/tex]

(b)

Given that S= 3 at time t=0

[tex]\therefore 3=S(t)=\frac{0^3}3+9.0+c[/tex]

[tex]\Rightarrow c=3[/tex]

The position of the particle after a time t is

[tex]S(t)=\frac{t^3}3+9t+3[/tex]

The position function is computed by integrating the given velocity function v(t) = t^2 + 9. The constant of integration C was found to be 3 using the given initial condition of s(0) = 3. Thus, the position function without any unknown constants is S(t) = (1/3)t^3 + 9t + 3.

The velocity function given for the particle moving in a straight line is v(t) = t2 + 9. This function can be used to find the position function using integral calculus.

hen t=0 the position function S(t) =  (1/3)*03 + 9*0 + C = C = 3.

Thus, using the constant of integration we found, we can write the position function without any unknown constants as S(t) = (1/3)t3 + 9t + 3.

(a) Finding the Position Function

To find an expression for the position, we integrate the velocity function. Here, the integral of the given velocity function v(t) = t2 + 9 is S(t) = ∫(t2 + 9)dt = (1/3)t3 + 9t + C, where C is the constant of integration.

(b) Finding the Constant of Integration

Given that s(0) = 3, w

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Answer:

178.85

Step-by-step explanation:

Answer:

153 !

Step-by-step explanation:

begin by multiplying 180 by .15 then you should get 27. next, subtract 27 from 180 and you're left with 153.

Answer:

The volume of the Perfume bottle is 128 cubic cm.

Step-by-step explanation:

We are given the following in the question:

Height of bottle, h = 6 cm

Base edge of perfume bottle, a = 8 cm

The perfume bottle in the shape of square pyramid.

Volume of perfume bottle = Volume of square pyramid.

[tex]V = a^2\times \dfrac{h}{3}[/tex]

Putting values, we get,

[tex]V = (8)^2\times \dfrac{6}{3}\\\\V = 128\text{ cubic cm}[/tex]

Thus, the volume of the Perfume bottle is 128 cubic cm.

Answer:

23.4 feet

Step-by-step explanation:

Please refer to the attached image for explanations

Using similar triangles and a proportion, the length of the tree's shadow that will allow it to be cut down needs to be 448 inches, or 37.3 feet to the nearest tenth of a foot.

To find the length of the tree's shadow that would allow for the tree to be tall enough (41 feet or more) to be cut down, we need to use similar triangles. The person cutting the tree is 5 feet 3 inches tall, which is 63 inches, and their shadow is 36 inches long. Using this information, we can set up a proportion since the tree and the person form similar triangles with their respective shadows. The proportion is 63 inches / 36 inches = 492 inches (41 feet) / length of tree's shadow. To find the tree's shadow length, we cross multiply and solve for the tree's shadow length as follows:

63 * length of tree's shadow = 36 * 492

Length of tree's shadow = (36 * 492) / 63

Length of tree's shadow = 28224 / 63

Length of tree's shadow = 448 inches

Therefore, the length of the tree's shadow needs to be 448 inches, or to the nearest tenth of a foot, 37.3 feet.

Answer:

450 $

Step-by-step explanation:

1). Bench = x

   Garden Table = x - 60

2). x + x - 60 = 840

    2x = 900

    x = 450 $ - the cost of the bench.

Hope this Helps)))

The cost of the bench is $450 if the garden table and a bench cost $840 combined. The garden table costs $60 less than the bench.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

A garden table and a bench cost $840 combined.

The garden table costs $60 less than the bench.

Let the cost of the bench is x

Cost of the Garden Table = x - 60

x + x - 60 = 840

2x = 900

x = 450 $ - the cost of the bench.

Thus, the cost of the bench is $450 if the garden table and a bench cost $840 combined. The garden table costs $60 less than the bench.

Learn more about the linear equation here:

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For a sphere of radius r the volume V is

V=(4/3)πr³

We have r=10 so

V = (4/3) π 10³ = 4000π/3

Answer: 4000π/3

The volume of a sphere can be calculated using the formula V = 4/3 * π * r³. Assuming the radius is 10 units, the calculated volume is 4186.67 cubic units.

The volume V of a sphere can be found using the formula V = 4/3 * π * r³, where π is a constant (approximately 3.14) and r is the radius of the sphere. In your question, it appears there may be missing information as the value for the radius is not provided. Assuming that 10 is the radius of the sphere, we can substitute this value into the formula. So, V = 4/3 * 3.14 * 10³ = 4186.67 cubic units. Therefore, the volume of a sphere with a radius of 10 units is approximately 4186.67 cubic units.

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The inequality that represents Max's situation with renting a bicycle is 5 + 3h <= 20. Max can rent the bicycle for up to 5 hours with his $20 budget, and renting for 4 hours would satisfy the inequality.

The inequality to represent Max's situation with renting a bicycle, considering his budget constraints, would be:

5 + 3h \<= 20

Where h represents the number of hours Max can rent the bike. To solve for h, you subtract 5 from both sides of the inequality (which represents the fixed insurance fee) and then divide by 3 (the hourly rate for renting the bike):

3h \<= 15

h \<= 5

Thus, Max can rent the bicycle for up to 5 hours to stay within his budget of $20. An example value that satisfies this inequality is 4 hours, which would cost Max $5 for insurance plus $12 for the rental time, totaling $17.

Answer:850

Step-by-step explanation:

To find this 2% of x= 17

2/100×x=17

2x/100=17

2x=1700

x=850

The total number of yards of metal fencing needed for the kennel at the dog park is 27 yards.

The fence segments are determined by the vertices A, B, C, D, E, and F. The distances between consecutive vertices can be calculated using the distance formula:

[tex]\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]

Let's calculate the lengths of the segments:

1. Length of AB: [tex]\(\sqrt{(-4 - 4)^2 + (-4 - (-4))^2} = \sqrt{64 + 0} = 8\) yards[/tex]

2. Length of BC: [tex]\(\sqrt{(-4 - (-4))^2 + (3 - (-4))^2} = \sqrt{0 + 49} = 7\) yards[/tex]

3. Length of CD: [tex]\(\sqrt{(1 - (-4))^2 + (3 - 3)^2} = \sqrt{25 + 0} = 5\) yards[/tex]

4. Length of DE:[tex]\(\sqrt{(1 - 1)^2 + (-1 - 3)^2} = \sqrt{0 + 16} = 4\) yards[/tex]

5. Length of EF: [tex]\(\sqrt{(4 - 1)^2 + (-1 - (-1))^2} = \sqrt{9 + 0} = 3\) yards[/tex]

Now, sum up these lengths:

[tex]\[ 8 + 7 + 5 + 4 + 3 = 27 \][/tex]

So, the total number of yards of metal fencing needed for the kennel at the dog park is 27 yards.

Answer:

Step-by-step explanation:

If two variables are directly proportional, it means that an increase in the value of one variable would cause a corresponding increase in the other variable. Also, a decrease in the value of one variable would cause a corresponding decrease in the other variable.

Given that x varies directly with y, if we introduce a constant of proportionality, k, the expression becomes

x = ky

If x = - 4 when y = 6, then

- 4 = 6k

k = - 4/6 = - 2/3

Therefore, the equation that relates x and y is

x = -2y/3

Answer:

3/2

Step-by-step explanation:

Answer:

10 yd

Step-by-step explanation:

The length of the top is

6+4 = 10 yd

The bottom must be the same length

To find the length of the bottom side, we can look around the shape to see if there are any similar sides. The sides 6ft and 4ft make up the same length as the bottom side, so, we can add.

6 + 4 = 10ft.

Best of Luck!

Answer:

The answer to your question is    Volume = 125 π in³

Step-by-step explanation:

Data

Volume = ?

Base area = 25π in²

height = radius

Process

1.- Find the radius

   Area of the base = πr²

-Equal

               πr² = 25π

-Solve for r

                r² = 25π/π

-Simplify

                r² = 25

-Result

                r = 5 in

2.- Find the volume of the cylinder

     Volume = πr²h

-Substitution

                   = (25π)(5)

-Simplification

     Volume = 125 π in³

The study investigates the connection between office habits and health outcomes. Key considerations include factors such as stress, job status, personal hygiene, and historical trends in workforce health. The goal is to improve policies to promote healthier workplaces.

The ministry of health study you're referring to is looking into how habits within the office workplace can impact employees' health. Various factors such as stress levels, personal hygiene habits, the status of the job, and societal impacts can influence the health outcomes of individuals in workplaces.

Stress is a critical factor, as studies have suggested those in high stress or low status jobs, such as the mentioned British civil servants, are more prone to health issues like heart disease. This emphasizes the necessity of stress management in the workplace.

Another element of consideration is personal hygiene, which relates to individuals' private habits in maintaining their physical appearance, not strictly health-related. Various habits could reflect differently on personal health outcomes.

Historical context also plays a role in understanding workforce health trends, such as the transformation during and after World War II. Anthropologists worked intensively on public and private health initiatives, focusing on improving health outcomes both in warfare and post-war times, which influenced the health perspectives in today's workplaces.

This is a multidimensional investigation that potentially will reveal valuable insights that could inform policies on how to better protect workers' health and productivity. Overall, a healthy workforce translates to a more robust and vibrant society.

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Answer:

8

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

arrange from the smallest to the largest or largest to the smallest and then carry out binary division

Answer:

The shop did not meet their goal of selling 65 per month. You can tell this because if you look at the graph you see that January, May, and June are all under the 65 mark.

Hope this helps ;)

Answer:

G, I, H

Step-by-step explanation:

6 and 4 force H to be the largest and G to be the smallest.

For any right triangle, the 90 degree angle is always the largest. The longest side of a triangle is always opposite the largest angle. Similarly, the shortest side of a triangle is always opposite the smallest angle.

Angle G is opposite side HI = 4 which is the smallest side, so angle G is the smallest angle.

Angle H is the middle angle as this is the longer leg, but it is not longer than the hypotenuse. The hypotenuse is always the longest side.

Answer:

The angular velocity is 6.72 π radians per second

Step-by-step explanation:

The formula of the angular velocity is ω = [tex]\frac{v}{r}[/tex] , where v is the linear velocity and r is the radius of the circle

The unit of the angular velocity is radians per second

∵ The diameter of the tire is 25 inches

∵ The linear velocity is 15 miles per hour

- We must change the mile to inch and the hour to seconds

∵ 1 mile = 63360 inches

∵ 1 hour = 3600 second

∴ 15 miles/hour = 15 ×  [tex]\frac{63360}{3600}[/tex]

∴ 15 miles/hour = 264 inches per second

Now let us find the angular velocity

∵ ω = [tex]\frac{v}{r}[/tex]

∵ v = 264 in./sec.

∵ d = 25 in.

- The radius is one-half the diameter

∴ r = [tex]\frac{1}{2}[/tex] × 25 = 12.5 in.

- Substitute the values of v and r in the formula above to find ω

∴ ω = [tex]\frac{264}{12.5}[/tex]

∴ ω =  21.12 rad./sec.

- Divide it by π to give the answer in terms of π

∴ ω = 6.72 π radians per second

The angular velocity is 6.72 π radians per second

The result is approximately 21.12 or  6.72 π radians per second.

The question asks for the angular velocity of a point on a bicycle tire with a diameter of 25 inches, traveling at 15 miles per hour.

Convert speed to inches per second:
15 miles per hour = 15 × 5280 feet per hour = 15 × 5280 × 12 inches per hour = 950400 inches per hour

Since there are 3600 seconds in an hour:
950400 inches per hour ÷ 3600 seconds per hour ≈ 264.00 inches per second

Convert diameter to radius in inches:
Diameter = 25 inches, so Radius = 25 ÷ 2 = 12.5 inches

Using the formula:
Linear speed (v) = Angular velocity (ω) × Radius (r)

264.00 = ω × 12.5
ω = 264.00 ÷ 12.5 ≈ 21.12 radians per second

Thus, the angular velocity of a point on the bicycle tire is approximately 21.12 or  6.72 π radians per second in terms of π.

Answer:

840

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: The percentage of hotels in the city have a nightly cost of more than $200 is 21%

Step-by-step explanation:

Since the nightly cost of hotels in a certain city is normally distributed,

we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = the nightly cost of hotels.

µ = mean cost

σ = standard deviation

From the information given,

µ = $180.45

σ = $24.02

The probability that a hotel in the city has a nightly cost of more than $200 is expressed as

P(x > 200) = 1 - P(x ≤ 200)

For x = 200,

z = (200 - 180.45)/24.02 = 0.81

Looking at the normal distribution table, the probability corresponding to the z score is 0.79

Therefore,

P(x > 200) = 1 - 0.79 = 0.21

The percentage of hotels in the city have a nightly cost of more than $200 is

0.21 × 100 = 21%

Answer: it is c. 10.7 cm

Rounded to the nearest tenth, the length of CD is approximately 5.8 cm.

To find the length of CD in a right triangle ABC where:

BA = 10 cm (the side adjacent to angle B)

angle B = 30 degrees

angle C = 90 degrees (a right angle)

angle D = 25 degrees

We can use the trigonometric ratio for tangent (tan) since we know the measure of angle B and the length of side BA. The tangent of an angle in a right triangle is the ratio of the length of the side opposite to the angle to the length of the side adjacent to the angle.

In this case, we want to find CD, which is the side opposite to angle B. So, we can use the following relationship:

tan(B) = CD / BA

First, find the tangent of angle B (30 degrees):

tan(30 degrees) ≈ 0.5774 (rounded to four decimal places)

Now, we can solve for CD:

CD = tan(B) * BA

CD ≈ 0.5774 * 10 cm

CD ≈ 5.774 cm

Rounded to the nearest tenth, the length of CD is approximately 5.8 cm.

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Answer:

34

Step-by-step explanation:

Answer:

All the people who have tried their beverages will be the representing population.

Step-by-step explanation:

If people in the United States like the new logo of a beverage company that the company wants to determine.

Now, we have to choose from the given options that represent the population.

From my point of view, option fourth option gives the correct answer.

Therefore, all the people who have tried their beverages will be the representing population.

Answer:

Every person in the united states

Answer:

The probability is 0.000000207176

Step-by-step explanation:

In this question, we are asked to calculate the probability that if 6 cards are selected from a deck of cards, we will be having 4 kings and 2 queens.

Before we answer, we should understand that in a deck of cards, there are 4 queens and 4 kings. The probability of selecting a king is the same as the probability of selecting a queen which is 4/52 = 1/13

Okay now we want to find the probability of the six cards being 4 kings and 2 queens. Since the probabilities are equal, we proceed to calculate at the same time.

That would be (1/13)^6 = 0.000000207176

The probability of selecting 4 kings and 2 queens is 0.000000207176

Final answer:

The probability of getting four queens and two kings out of six cards from a standard deck of 52 cards is calculated by dividing the product of the combinations of getting those particular cards by the total number of six-card combinations available from the deck.

Explanation:

To calculate the probability of getting four queens and two kings from a shuffled deck of 52 cards when dealt 6 cards, we can follow these steps:

Identify the total number of ways to choose 6 cards from 52: This can be calculated using combinations, as the order the cards are drawn doesn't matter. The formula for combinations is:

C(n, k) = n! / (k! × (n-k)!)

In this case, n = 52 (total cards) and k = 6 (cards chosen). Therefore, the total number of ways to choose 6 cards is:

C(52, 6) = 52! / (6! × (52-6)!) ≈ 270,735,576

Identify the number of ways to get four queens and two kings: We need to choose 4 queens out of 4 and 2 kings out of 4. Again, using combinations:

C(4, 4) × C(4, 2) = 1 × 6 = 6

There are only 6 ways to get this specific combination (4 queens and 2 kings) within the 6 cards chosen.

Calculate the probability: Finally, divide the number of successful outcomes (6) by the total number of possibilities (270,735,576) to get the probability:

Probability = 6 / 270,735,576 ≈ 0.000002217 ≈ 0.0002%

Therefore, the probability of getting four queens and two kings from a shuffled deck of 52 cards when dealt 6 cards is incredibly low, at approximately 0.0002%.

Answer:

Let play build royale together

Step-by-step explanation:

b. y = r cosa

Answer: A. y= r sin e

Step-by-step explanation: I just did it

Answer:

A

Step-by-step explanation:

A is the right answer

f has the greater slope, 3. The slope of g is 2.

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Answer:

( -[tex]\sqrt{3}[/tex]/2 , -1/2)

Step-by-step explanation:

-210 degrees in standard position corresponds to an angle in the 3rd quadrant  30 degrees below the negative x-axis

The hypotenuse of the triangle here is 1, and we want the coordinates.

_______________________(0,0)

|(x = -root(3)/2)

|

| (y = -1/2)

The coordinates of the point at which the terminal side intersects the unit circle are (-√3/2, -1/2).

The cartesian plane is a two-dimensional coordinate plane that is formed when two parallel lines meet. The X-axis is the horizontal line, and the Y-axis is the vertical line. On the Cartesian plane, the coordinate point (x, y) indicates that the point is on the right of the origin if the sign of x is positive; otherwise, the point is on the left of the origin.

Given  -210 degrees is in standard position,

-210° lies in the third quadrant,

which is 180° + 30° or π + 30°

the coordinate are x = cos(π + 30°)

and y = sin(π + 30°)

cos(π + Ф) = -cosФ and

sin(π + Ф)  = -sinФ

x = cos(π + 30°) = -cos30° = -√3/2

y = sin(π + 30°) = -sin30° = -1/2

Hence the coordinates of points are (-√3/2, -1/2).

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Answer:

1.68 km

Step-by-step explanation:

You want the horizontal distance (on the ground) from beneath the helicopter to the vertex of the 37 degree angle.  The hypotenuse is given and is 2.1 km.

We want to find the horizontal distance when we already know the angle and the hypotenuse.

That horizontal distance could be called 'x.'   Then:

x/r = adj/hyp = cos 37 degrees, which becomes adj = (2.1 km)cos 37 degrees, which is found using a calculator:  adj = (2.1 km)(0.7987)  =  1.68 km