Determine whether the graph represents a proportional relationship.

yes, it is a proportional relationship because the graph goes through the origin

No, it is not a proportional relationship because the graph does not go through the origin

Yes, it is a proportional relationship because the graph is a straight line

No, it is not a proportional relationship because the graph is not a straight line

Answer:

79 ft

Step-by-step explanation:

The formula for the circumference of a circle is

C = 2πr.  If it's the diameter that is known, then C = πd.  We will use the latter formula to find the circumference of this pool:

C = π(25 ft) = 78.54 ft, approx., which, to the nearest foot, is 79 ft

Step-by-step explanation:

hi I have answered ur question

Step-by-step explanation:

given that u=<-3,7>

-1/2u=<-1/2(-3),-1/2(7)>

-1/2u=<3/2,-7/2>

Answer:

66.7% is the answer.

Step-by-step explanation:

A country has 50 million people, 30 million of whom are adults.

Of the adults, 5 million are not interested in working.

5 million are interested in working but have given up looking for work.

5 million are still looking for work.

Of those who do have jobs, 5 million are working part time but would like to work full time, and the remaining 10 million are working full time.

Total labor force = Employed people + Unemployed  people

=> 15 million+ 5 million = 20 million

The labor force participation rate is [tex]\frac{20million}{30million} \times100[/tex]

= 66.66% ≈ 66.7%.

The labor force participation rate of the country is 66.7%, calculated by dividing the number of employed and actively seeking employment individuals (20 million) by the total adult population (30 million) and multiplying by 100.

To calculate the labor force participation rate, we include only those adults who are either employed or actively seeking employment. In the given scenario, the country has 30 million adults. Out of these, 5 million are not interested in working, 5 million have given up looking for work, and there are 15 million employed (10 million full-time and 5 million part-time). Therefore, the labor force includes those employed full-time, employed part-time, and those actively looking for work, adding up to 20 million.

The labor force participation rate is calculated by dividing the number of people in the labor force (20 million) by the total adult population (30 million) and multiplying the result by 100 to convert it into a percentage:

Labor Force Participation Rate = (Number in labor force ÷ Total adult population) x 100

Labor Force Participation Rate = (20 million ÷ 30 million) x 100

Labor Force Participation Rate = (2÷3) x 100

Labor Force Participation Rate = 66.7%

Answer:

  A, D, E (probably preferred)

  B, C, F (also true)

Step-by-step explanation:

"This situation" problems are almost always ambiguous. The first problem is to figure out what it is about "this situation" that you want to model.

__

If we want to model concession stand revenue in a general way, then statements B, C, and F could represent "this situation." No specific values can be determined from this model.

__

More likely, we want to model the details of sales and revenue, so we want to know the exact numbers of water bottles and hamburgers that were sold. For "this situation," we can assign variables to the numbers of items of each type, and write equations for the total number of items and for the revenue their sales generates. Appropriate statements about this interpretation of the problem are those of A, D, and E:

  A: x could represent bottles sold

  D: y could represent hamburgers sold

  E: The system of equations could be 2.50x +5.50y = 1325; x +y = 350.

_____

The solution to the last model is 200 bottles were sold for revenue of $500, and 150 hamburgers were sold for revenue of $825.

Answer:

A-The variable x could represent the number of bottles of water sold.

D-The variable y could represent the number of hamburgers sold.

E-The system of equations that could represent the concession sales is

2.50x + 5.50y = 1,325

x+y=350

Step-by-step explanation:

When doing a system of equations you need variables and constants, in this case it´s easy to know what are the constants, since they are given directly to you by the problem, the constan 1 is the cost of the bottled water, the cost of each hamburger, the number of items sold and the total sum of the sells.

The only variables that we have are the number of items sold, we are going to express them with X and Y, the cost of the number of bottles of water sold will be expressed with the letter X and the number of hamburgers sold will be expressed by the letter Y.

Answer:

The most common source of income is business ownership. A. True.

Step-by-step explanation:

The most common source of income is employment. Other sources of income may include investments, business profits, or government assistance.

The statement "The most common source of income is employment" is true.

Employment is the main source of income for the majority of people worldwide. It refers to a person's work for which they receive financial compensation in the form of wages or salary. Other sources of income may include investments, business profits, or government assistance, but employment is the most common and reliable.

Examples of employment include working in various sectors such as healthcare, technology, education, manufacturing, and services.

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Answer:

ABC ~ FED

Step-by-step explanation:

A ~ F

B~E

C~D

If you're still confused, look at the angles. No lines match to A and F, 1 line matches to B and E, and 2 lines match to C and D.

The correct answer is ΔABC ~ ΔDEF, where the corresponding congruent angles are matched to affirm triangle similarity, making option A correct.

To determine which triangles are similar, we need to match the angles from ΔCBA to ΔFDE. Since angle D is congruent to angle B and angle E is congruent to angle A, we need to ensure that the order of the vertices corresponds to the congruent angles in the similar triangles. Therefore, the correct order that names the similar triangles is ΔABC ~ ΔDEF, which makes option A correct. In ΔABC, angle A corresponds to angle E in ΔDEF, and angle B corresponds to angle D. This order maintains the sequence of corresponding congruent angles in both triangles.

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Approximately 26 out of 320 students like sports. Therefore, about 294 students do not like sports.

To draw a diagram for the given statement, we begin with understanding that the total of 320 students represents 100%. Therefore, if 8% of the students like sports, we would multiply 320 by 0.08 (or 8%).

The calculation would be:
320 * 0.08 = 25.6

However, because we cannot have a fractional student, we round this figure to 26. This implies that about 26 students like sports.

To calculate the number of students who do not like sports, subtract the number that do from the total, which is 320. That calculation would be:
320 - 26 = 294

Therefore, approximately 294 students do not like sports.

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Answer:

  a. 3093

Step-by-step explanation:

The missing two terms in the 5-term sequence are ... 300 + 750.

You can add up these 5 terms directly, or you can recognize that the sum will be more than the last term (not C), but cannot be more than double the last term (not B or D). The sum must be 3093, choice A.

_____

If you use the formula for the general term of the series, you can find the number of terms.

The common ratio is 120/48 = 2.5

The general term is ...

  an = a1·r^(n -1)

Solving for n, we get ...

  n = log(an/a1)/log(r) +1 = log(1875/48)/log(2.5) +1 = 5 . . . . the number of terms

Then the sum is given by ...

  Sn = a1(r^n -1)/(r -1) . . . . . using a1=48, r=2.5, n=5

  S5 = 48(2.5^5 -1)/(2.5 -1) = 48(96.65625/1.5)

  S5 = 3093

_____

The sum of a geometric sequence with a common ratio of 2 is double the last term, less the first term. When the common ratio gets larger, the sum gets smaller than double the last term.

  Sn = a1(r^n -1)/(r -1) = (a1·r^n -a1)/(r -1) = (r·an -a1)/(r -1)

  Sn = (r/(r -1))an -a1/(r -1) . . . . . . verifies the above comment

In our case, this evaluates to ...

  S5 = (2.5/1.5)(1875) -48/1.5 = (5/3)(1875) -(2/3)(48)

  = 3125 -32 = 3093

Using the first and last terms this way, we only need the common ratio and don't need to know the number of terms.

Answer:

  no

Step-by-step explanation:

Opposite numbers are the same distance from 0 on the number line, but in opposite directions. Steps I would follow:

  3 is not the opposite of -6

__

  6 is the opposite of -6

Answer:

Sample Response: Although 6 and 3 are on opposite sides of sea level, or 0, they are not opposites because they are unequal distances from 0.

Step-by-step explanation:

I got the answer correct

The sum of the mixed fraction numbers - 6 ⁴/₅ and 6 ⁴/₅ will be 0. Then the correct option is C.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

- 6 ⁴/₅ and 6 ⁴/₅

Convert the mixed fraction number into a fraction number. Then we have

- 6 ⁴/₅ = -34/5

6 ⁴/₅ = 34/5

Then the sum of the expressions will be given as,

⇒ - 34/5 + 34/5

⇒ 0

The sum of the mixed fraction numbers - 6 ⁴/₅ and 6 ⁴/₅ will be 0. Then the correct option is C.

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Answer:

A) A statement of “no effect” or “no difference.

Answer: 28/125

Step-by-step explanation: To divide two fractions, flip the second fraction and multiply. The equation will be:

4/25 x 7/5

Multiply the numerators by the numerators and the denominators by the denominators.

4 x 7 = 28 (numerator)

25 x 5 = 125 (denominator)

Put into a fraction.

28/125

Answer:

diagonal is 20.68 ft; shorter base is 17.21 ft

Step-by-step explanation:

If base angles add up to 140, then each is 70 since this is an isosceles trapezoid.  We can use the Law of Cosines now to find the length of the diagonal which I will call d:

[tex]d^2=7^2+22^2-2(7)(22)cos(70)[/tex] and

[tex]d^2=533-308cos(70)[/tex] and

[tex]d^2=533-105.3422041[/tex],

[tex]d^2=427.6577959[/tex]

so the length of the diagonal is

d = 20.68 ft

The length of the shorter base is a little more tedious.  First drop an altitude from each of the upper vertices to the base measuring 22 ft.  We have 2 smaller right triangles now, each with unknown height (we need to find this), each with unknown base measures (we need to find this, too!), each with a base angle of 70 degrees, and each with a hypotenuse of 7.  We need only work with one of these since they are both the same.  

We will first find h, the height of each of these right triangles.  Using the sin ratio:

[tex]sin(70)=\frac{h}{7}[/tex] and

[tex]7 sin(70)=h[/tex] so

h = 6.577848

Now we can use that along with the hypotenuse measure to find the base measure, b:

[tex]7^2-6.577848^2=b^2[/tex],

[tex]b^2=5.731911137[/tex] so

b = 2.394141002

Because we have 2 identical small right triangles with base measures of 2.394141002 each, we can subtract 2(2.394141002) from 22 to get the measure of the shorter base, which I will call x:

22 - 2(2.394141002) = x so

x = 17.21 ft

Answer:

65

Step-by-step explanation:

The outlier made the mean bigger/greater. Rounded to the nearest tenth it would be 40.8.

Answer:

  33π square units

Step-by-step explanation:

The area of a sector is given by this formula. The larger sector angle is 2π-π/6 = 11π/6 radians.

  A = (1/2)r²θ = (1/2)6²(11π/6) = 33π . . . . square units

Answer:

Area of larger sector = 33π units²

Step-by-step explanation:

Points to remember

Area of circle = πr²

Where 'r' is the radius of circle

To find the area of circle

Here r = 6 units

Area =  πr²

 = π * 6²

 =  36π units²

To find area of large sector

The central angle of larger sector = 360 - 30 = 330

Area of larger circle = (330/360) * area of circle

 =  (330/360) * 36π

 = 33π units²

Answer:  ΔABC ~ ΔBDC ~ ΔADB

Step-by-step explanation:

Match the degrees of each angle:

In ΔABC:  ∠A = 60° , ∠B = 90° , ∠C = 30°

In ΔBDC:  ∠B = 60° , ∠D = 90° , ∠C = 30°

In ΔADB:  ∠A = 60° , ∠D = 90° , ∠B = 30°

Answer:

See below.

Step-by-step explanation:

Triangle ABC is similar to triangle ADB is similar to triangle BDC.

To solve the problem of the airplane needing to head due north while compensating for the wind blowing from the northeast, we'll need to use vector addition to determine the angle at which the pilot needs to fly.

First, we'll represent the airplane's velocity and the wind's velocity as vectors. Since the wind is blowing from the northeast, it has both a southward component and a westward component relative to due north.

Let's define our axes such that the north direction is positive y, and east is positive x. The airplane needs to end up flying due north, which is along the positive y-axis.

We'll denote:
- \( V_p \) = Velocity of the plane with respect to the air (airspeed) = 700 km/hr (directed at an angle we need to find, east of north),
- \( V_w \) = Velocity of the wind = 50 km/hr (from the northeast, so it has equal components to the south and west, at a -45-degree angle to the axes),
- \( V_r \) = Resultant velocity of the plane with respect to the ground (due north).

To cancel out the wind's effect and ensure that the plane ends up flying due north, the eastward (x) component of the plane's velocity must be equal in magnitude and opposite in direction to the eastward component of the wind's velocity.

Given that the wind velocity \( V_w \) is at a -45-degree angle, its components can be found using trigonometry:

\[ V_{wx} = V_w \cos(-45^\circ) \]
\[ V_{wy} = V_w \sin(-45^\circ) \]

Since \( \cos(-45^\circ) = \sin(-45^\circ) = \frac{\sqrt{2}}{2} \), and we're looking for the eastward component, \( V_{wx} \) will be positive and \( V_{wy} \) negative because it's to the south:

\[ V_{wx} = 50 \cdot \frac{\sqrt{2}}{2} \]
\[ V_{wx} = 25\sqrt{2} \]

Similarly, \( V_{wy} = -25\sqrt{2} \) but this component doesn't factor into our calculation for the required angle, since it affects only the north/south direction.

Now, to counteract this eastward wind component, the eastward component of the plane's velocity \( V_{px} \) must be equal to \( -V_{wx} \):

\[ V_{px} = -V_{wx} \]
\[ V_{px} = -25\sqrt{2} \] km/hr

The plane's airspeed is \( V_p = 700 \) km/hr, so using trigonometry with \( V_{px} \) and \( V_p \), we can find the angle \( \theta \) east of north that the plane should head:

\[ \sin(\theta) = \frac{V_{px}}{V_p} \]
\[ \sin(\theta) = \frac{-25\sqrt{2}}{700} \]
\[ \sin(\theta) = \frac{-25\sqrt{2}}{700} \approx -0.05071 \]

Taking the inverse sine (arcsin) to solve for \( \theta \):

\[ \theta = \arcsin(-0.05071) \]

The value of \( \theta \) obtained will be negative, indicating the angle west of north, but we want the angle east of north, so we take the absolute value:

\[ |\theta| \approx \arcsin(0.05071) \]

Using a calculator to find \( \theta \) in degrees:

\[ |\theta| \approx 2.905 \] degrees

Therefore, the pilot will have to fly approximately 2.905 degrees east of north to compensate for the northeast wind and ensure the resultant path is due north.

The pilot needs to fly approximately 4.28 degrees east of north to compensate for the wind and reach due north.

To calculate the angle the plane needs to fly east of north to compensate for the wind, we can use trigonometry. Here are the steps:

Step 1:

Determine the components of the wind.

The wind blowing from the northeast forms a right triangle with its northward and eastward components. The eastward component can be found using the sine function:

[tex]\( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \).[/tex]

[tex]\[ \sin(\theta) = \frac{50}{700} \][/tex]

Step 2:

Solve for the angle [tex]\( \theta \).[/tex]

[tex]\[ \theta = \arcsin\left(\frac{50}{700}\right) \][/tex]

Step 3:

Calculate the angle in degrees.

[tex]\[ \theta \approx 4.28^\circ \][/tex]

So, the pilot needs to fly approximately [tex]\( 4.28^\circ \)[/tex] east of north to compensate for the wind and end up due north.

Answer:

All your steps are correct.  Well done!

For this case we have that by definition, the surface area of a cylinder is given by:[tex]SA = LA + 2B[/tex]

Where:

LA: It is the lateral area of the cylinder

B: It is the area of the base

We have as data that:

[tex]LA = 75.36 \ cm ^ 2\\B = 28.26 \ cm ^ 2[/tex]

Substituting:

[tex]SA = 75.36 + 2 (28.26)\\SA = 75.36 + 56.52\\SA = 131.88[/tex]

Finally, the surface area is:

[tex]131.88 \ cm ^ 2[/tex]

Answer:

Option D

Answer:

The solid formed is a cylinder

The total surface area is [tex]131.88cm^2[/tex]

Step-by-step explanation:

The given net is made up of a rectangle and two circles.

The total surface area is the area of the rectangle plus the area of the two circles.

This implies that:

[tex]S.A=75.36+2(28.26)[/tex]  

[tex]\implies S.A=75.36+56.52[/tex]  

[tex]\implies S.A=131.88cm^2[/tex]

The rectangular surface can be folded into the curved surface of a cylinder with the two circles becoming the lid.

Answer:

  the mean age is greater

Step-by-step explanation:

The mean age is ...

  (1/2)14 + (1/3)15 + (1/6)13 = 14 1/6

The median age is 14. (half the students are 14 or younger)

The mean age is greater.

_____

1 -1/2 -1/3 = 6/6 -3/6 -2/6 = 1/6 . . . . . 1/6 of the students are 13.

Answer:

Step-by-step explanation:

Given that half of the students in a freshman class are 14 years old one third are 15 and the rest are 13

If no of students are n, then we have

n/2 have ages as 14, n/3 as 15 and remaining n/6 as 13.

Average would be total/n

= [tex]\frac{\frac{14n}{2}+\frac{15n}{3} +\frac{13n}{6}  }{n} \\=7+5+\frac{13}{6} =14.67[/tex]

Median would be middle entry when arranged in ascending order hence = 14

Mean > median

Answer:

The answer is 126 seconds.

Step-by-step explanation:

Volume of the cone is given as:

[tex]\frac{1}{3} \pi r^{2} h[/tex]

Volume of cylinder is given as:

[tex]\pi r^{2} h[/tex]

We can find the total volume of the sand by adding volume of cone and volume of cylinder.

Height for cylinder is 30 mm (as we will subtract the cone height from 45mm that is 45-15=30)

Total volume of sand = [tex]\pi /3*(6^{2})*(15)[/tex] + [tex]\pi *(6)^{2}*(30)[/tex] = 1260π mm³

Given is - Sand drips from the top of the hourglass to the bottom at a rate of 10π cubic millimeters per second.

So, for all the sand to drip down, it will take [tex]\frac{1260\pi }{10\pi }[/tex]= 126 seconds.

Answer:

40 = x

Step-by-step explanation:

They reflect each other like a mirror, so set 120 equal to 3x, then simply divide by 3 to get your answer.

Answer:

the pitcure isnt clear.

Answer:

y=2.5x+7

Step-by-step explanation:

You are basically being asked to use slope-intercept form for linear equations. It says y=mx+b where m is the slope and b is the y-intercept.

Plug in 2.5 for m and 7 for b giving you y=2.5x+7.

The equation is: y = mx + b

y = 2.5x + 7

so it's option D.

Answer:

2

Step-by-step explanation:

The range of class A is 5-0 = 5

The range of class B is 3-0 = 3

the difference between 3 and 5 is 2.

The mean can be calculated by adding all of the values and dividing that sum by the number of values you added.  To take advantage of the way data is being collected, I am grouping the addends as, for example, 5(1), instead of writing out 1 + 1 + 1 + 1 + 1.

\A CLASS mean is:

B CLASS  mean is:

Based on these findings, we can conclude that the mean for Mrs. Ramos' class is about 2 more than the mean for Mr. McIntyre's class.

Answer:

D

Step-by-step explanation:

If the lines are parallel, the slope of both of them are going to be the same. So if one line is 3, the other one will be too.

The answer is:

If the red line has a slope of 3, the slope of the red line will also be 3.

So, the correct option is, D. 3

We need to remember that if two or more lines are parallel, they will share the same slope, no matter where are located their x-intercepts and y-intercepts, the only condition needed for them to be parallel, is to have the same slope.

So, if two lines are parallel, and one of them (the red line) has a slope of 3, the slope of the other line (the green line) will also be 3.

Have a nice day!

an isosceles triangle has always two twin sides, so if one side is 3 and another is 6, there's another twin that's either 3 or 6.

now, let's take a peek at a caveat, if the twin angle missing is say 3, then the triangle has sides 3, 3 and 6, but but but, if the two slanted sides are 3 each, and the base or bottom is 6, the only way the bottom can be 6 is if the other sides lie flat on top of it, in which case we no longer have a triangle, since it'll be just 3 pancaked flat-lines, so it can't be 3, it must be 6.

The length of the third side is 6.

Therefore, the correct answer is option B) 6.

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Answer:

My estimate would be D, if you view 0, -23 as the vertex and compare the other values, the values on D show the most similarities.

Definitely not B since it's exponential.

Answer:

The correct option is A.

Step-by-step explanation:

According to statement a1 = 4 and r = 3. This shows that r is greater than 1.

If r is greater than 1 than it includes integers greater than 1 or equal to 1. It does not include all the real numbers because real numbers include negative numbers also.

If starting value is 4,if we put n=0, then we get 4, but if we put a negative value than we would get a number which is not a part of our sequence. Thus the correct option is All integers where n ≥ 1....

Answer:

The answer is A. All integers where n > 1

Step-by-step explanation:

The domian for n is restricted and cannot be less than 1 and the domain is the x value while 4 would be a y value.