Solve the word problem below

Answer:

[tex]\dfrac{3}{2}\; \sf cm/s[/tex]

Step-by-step explanation:

To determine the unit rate corresponding to the proportional relationship shown in the given graph, we need to calculate the slope of the line.

The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) can be found using the slope formula:

[tex]\boxed{\textsf{slope} =\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

Substituting the defined points (0, 0) and (6, 9) into the formula, we can calculate the slope:

[tex]\textsf{slope} =\dfrac{9-0}{6-0}=\dfrac{9}{6}=\dfrac{3}{2}[/tex]

Therefore, the slope of the line is 3/2.

The slope represents the rate of change between the two variables.

Therefore, the unit rate corresponding to this proportional relationship is 3/2 cm/s. This means that for every increase of 2 seconds, there is a corresponding increase of 3 cm.

Answer: -1/2

Step-by-step explanation:

1. We know that -2 1/3 is also equal to -7/3, because we can multiply the denominator by the main number, and add the numerator.

2. We can do the same with 4 2/3, which would be 14/3.

3. Now, we are left with -7/3 divided by 14/3.

4. To make this easier, we can flip flop the 14/3 so we can multiply instead of divide, which leaves us with -7/3 x 3/14.

5. -7/3 x 3/14 = -21/42

6. We can simplify this to -1/2.

Answer:

234

Step-by-step explanation:

Answer:

209.58mm(Rounded)

Step-by-step explanation:

V=[tex]\pi[/tex]r^2h

=[tex]\pi[/tex](6.5)^2(60)

=7963.94/38

=209.58mm

The legs of similar triangles are used to set a proportion of heights and shadows of the tall objects in order to find the value of unknown measure.

Answer:

  (a) C: $36 per hour; B: $38 per hour

  (b) C: c = 36(h -1) +52; B: c = 38(h -1) +42

  (c) C: $196; B: $194

  (d) 270 = 38(h -1) +42; h = 7

  (e) Brian charges $270 for working 7 hours

Step-by-step explanation:

Given a table of costs and hours for hiring DJs Celinda and Brian, you want to know their hourly costs, equations for their costs, cost for 5 hours, and hours for a cost of $270.

The cost of an additional hour can be found by subtracting the cost for 1 hour from the cost for 2 hours:

  Celinda: $88 -52 = $36 . . . . . cost increase per hour

  Brian: $80 -42 = $38 . . . . . . . cost increase per hour

We can use the "point-slope form" equation of a line to write the equations for the costs.

  y -k = m(x -h) . . . . . . . line with slope m through point (h, k)

Rearranging, this is ...

  y = m(x -h) +k

Here, the slope is the cost per hour. A suitable point is the first one in the table. The variables 'c' and 'h' are defined for us.

  Celinda: c = 36(h -1) +52

  Brian: c = 38(h -1) +42

Using h=5 in each of these equations, we have ...

  Celinda: c = 36(5 -1) +52 = 196 . . . . cost for 5 hours

  Brian: c = 38(5 -1) +42 = 194 . . . . cost for 5 hours

Using the equation for Brian's cost, we simply need to set c=270 to have the equation we need:

  270 = 38(h -1) +42 . . . . equation to find hours

The solution to that equation is ...

  270 -42 = 38(h -1) . . . . . subtract 42

  228/38 = h -1 . . . . . . . . . divide by 38

  6 +1 = h = 7 . . . . . . . . . . . add 1. This is the solution.

It would cost $270 to hire Brian for 7 hours.

The solution to the equation for c=270 is h=7. Since h represents the number of hours the DJ is working, this solution tells us Brian will charge $270 for working 7 hours.

__

Additional comment

The two equations can be simplified by eliminating parentheses and combining like terms:

  Celinda: c = 36h +16

  Brian: c = 38h +4

Parts (d) and (e) work together. The "solution" h=7 doesn't mean anything except in the context of the question it is answering. The question is "how many hours for a charge of $270." The value h=7 means the answer is Brian charges $270 for 7 hours' work.

Answer:

Step-by-step explanation:

The surface area of a cylinder can be calculated using the formula:

SA = 2πr^2 + 2πrh

where r is the radius of the base of the cylinder, h is the height of the cylinder, and π is approximately equal to 3.14.

Looking at the given diagram, we can see that the height of the cylinder is 10 cm and the radius of the base is 6 cm.

So, substituting these values into the formula:

SA = 2π(6)^2 + 2π(6)(10)

SA = 2π(36) + 2π(60)

SA = 72π + 120π

SA = 192π

Using a calculator, we can approximate this value to:

SA ≈ 602.88 cm^2

Therefore, the surface area of the cylinder is approximately 602.88 cm^2.

Answer:

(-4,11)

Step-by-step explanation:

This will complete the rectangle have a great day and please like it helps!

Answer:    the fourth vertex needed to create a rectangle with vertices located at (−29, 11), (−4, −2), and (−29, −2) is (-4, 11).

Step-by-step explanation:

Answer:

1. Class A/Range=7

2.Class A/Median=6

3.Class A/Mean=6

4.Class B

Step-by-step explanation:

1. Class A/Range=7

2.Class A/Median=6

3.Class A/Mean=6

4.Class B

Answer: question 1) 12

question 2) 3.3 (repeating)

Step-by-step explanation:

question 1) count x axis (goes from 3 to 5 so 2) the count y axis (36 to 60 so  24) so do y/x or 24/2 which equals 12

question 2)  x axis = 6-1.5 aka 4.5 y axis= 20-5 aka 15 y/x aka 15/4.5 which gives you 3.333333333333

Answer:

Population: All Americans eligible to vote in the local election

Sample: 4,000 Americans who were surveyed

Population: All members of the basketball team

Sample: Every third member of the basketball team

Population: All college graduates

Sample: The group of college graduates studied in the study

Population: All readers of the Washington Post

Sample: The group of readers who responded to the poll

Answer: Population: All Americans eligible to vote in the local election

Sample: 4,000 Americans who were surveyed

Population: All members of the basketball team

Sample: Every third member of the basketball team

Population: All college graduates

Sample: The group of college graduates studied in the study

Population: All readers of the Washington Post

Sample: The group of readers who responded to the poll

Step-by-step explanation: That's gotta be it

Answer:

First, we need to arrange the numbers in order:

0.5, 0.8, 1.3, 1.5, 1.9, 2.0, 2.4, 2.7, 3.2, 3.6

There are 10 numbers in the list, so the median is the middle value. In this case, the middle values are 1.9 and 2.0. To find the median, we take the average of these two numbers:

(1.9 + 2.0) / 2 = 1.95

Therefore, the median drying time is 1.95 hours, option B.

Answer:

MRO’s orbit is near enough to circular

that the formulas for circles can be used.ep-by-step explanation:

The MRO completes one orbit around Mars in about 2.3 hours, and travels a distance of 40,727 km in that time.

The Mars Reconnaissance Orbiter (MRO) is an orbiting spacecraft that was launched in 2005 by NASA. The objective of MRO is to study the climate, geology, and geography of Mars. MRO is currently in a nearly circular polar orbit around Mars, which allows it to observe the entire planet in high resolution. MRO has an orbital altitude of 255 km, and its orbital period is about 2.3 hours.

The circumference is 2πr, where r is the radius of the orbit. The radius of the orbit of MRO is the difference between the polar diameter of Mars and the closest approach of MRO to the planet, which is 6752 km - 255 km = 6507 km.

Thus, the circumference of the orbit of MRO is 2πr = 2π x 6507 km = 40,727 km. Therefore, the MRO travels 40,727 km in one orbit.

For more questions related to circumference

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1 Each person can have ordered a medium drink if they bought drinks at the stadium on Friday. Therefore, 160 people can be expected to have ordered a medium drink.

Answer:

D

Step-by-step explanation:

The two legs ( shorter sides) have the right angle between them in a right triangle and

5^2 + 9^2   DOES equal 13^2

Answer: 420

Step-by-step explanation:

Answer:

   The original length of the board is 8 feet.

   The length that was cut off is 2 feet.

   One possible equation we can use is: x = 8 - 2, where x represents the length of the board that is left. Solving for x, we get x = 6 feet.

   The length of the board that is left is 6 feet.

Step-by-step explanation:

We are given that the board was originally 8 feet long. Bryce cuts off 2 feet from the board to use for a project. Therefore, the length of the board that is left is 8 - 2 = 6 feet.

To solve this problem algebraically, we can set up an equation where x represents the length of the board that is left. We know that the original length of the board is 8 feet, and 2 feet was cut off, so we can write:

x = 8 - 2

Simplifying this equation gives us:

x = 6

Therefore, the length of the board that is left is 6 feet.

Answer:

1017 cm³

Step-by-step explanation:

To find the volume of this figure we will first need to divide it into 2 sections. First, we will find the volume of the semicircle on top then the cone at the bottom!

1) Semicircle

The simplest way of doing this is to find the volume as if it was a circle and then divide that result by 2! ([tex]\frac{4}{3}[/tex]πr³)

2) Cone

To find the volume of the cone we need to apply the equation πr²[tex]\frac{h}{3}[/tex] (where h = height)

3) Add

Hope this helps, have a lovely day! :)

Answer:  

[tex](24\pi x^2-10\pi x-4\pi)[/tex] square centimeters

Explanation:

Let

[tex]r=\text{radius of the cylinder}=3x-2 < br/ >[/tex]

[tex]h=\text{height of the cylinder}=x+3[/tex]

Then the surface area of the cylinder is given by

[tex]A=2\pi r^2+2\pi rh[/tex]

[tex]=2\pi r(r+h)[/tex]

[tex]=2\pi (3x-2)((3x-2)+(x+3))[/tex]

[tex]=2\pi (3x-2)(4x+1)[/tex]

[tex]=2\pi(12x^2-5x-2)[/tex]

[tex]\boxed{A=(24\pi x^2-10\pi x-4\pi )cm^2}[/tex]

Answer:

60% of the students have dogs

10% of the students have birds

Bryan interviewed 200 students

Step-by-step explanation:

a.3/5 = 60%

b.60% + 30% = 90%

100% - 90% = 10%

c. 20 x 10 = 200

Answer: 60%, 10%, 200 students.

Step-by-step explanation:

Let's start with turning all of the values into percentages.

3/5 of the students said dogs. As a percentage, 3/5 is equal to 60%.

We now have two percentages, the amount of cats and the amount of dogs. 30%+60%=90%. So that leaves 10%, and that 10 percent is the 20 students who had birds.

If 20=10%, all we have to do is multiply 20 ten times to get to 100%. 20x10=200.

There were 200 students interviewed.

Answer:

Step-by-step explanation:

9t + 3

3(3t + 1)

(3 * 3t) + (3 * 1)

4t + 3 + 5t

9(t + 3)  

(9 * t) + (9 * 3)

9t + 27

Neither

(9 + t) + (9 + 3)

Answer: hope this helps ♡

9t + 3:

3(3t + 1)       &       (3 × 3t) + (3 × 1)       &        4t + 3 + 5t

9(t + 3):

(9 × t) + (9×  3)       &       9t + 27


Neither:

(9 + t) + (9 + 3)

Answer: the small number shows how many numbers their should be so small number 7 then big number 5 would mean 5 5 5 5 5 5 5

Step-by-step explanation:

★ hope this helps you !

step 1 ⋆ multiply 4 by 5 and multiply 4  by 3x

step 2 ⋆ subtract the products

( i ' m not 100 % sure this is correct bc i don ' t know the equation : ( because you didn ' t show it . . . so it may be wrong , sorry ! )

Answer:

X = 8

Explanation:

First you have to multiply 4 · 5 and also multiply 4 · 3x

Then you subtract the products

Hope this helps :)

It is the 3rd option

Solved each one and 3rd option was equivalent with a solution of 16.

Answer:

Step-by-step explanation:

(i) Number of people who are into classical music =10%

10% of pie chart =20 people.

1% ⇒ 10/20 ×100

and 100% ⇒ 10/20 ×100 × 100/ 100

​⇒200 people.

(ii) Light chart represent maximum number as it is 40% of total. ∴ Light music is liked by maximum people.

(iii)

Number of CD's of classical music ⇒ 100/10 × 1000(10%) =100

umber of CD's of semi classical music = 100/20 × 1000(20%) =200

just like that 30% is 300, 40% is 400.

Hope this helped :)

Answer:

Step-by-step explanation:

Assuming angles are numbered clockwise at each intersection before moving to the next intersection, corresponding angles will differ in their numbers by a factor of 4.

Among the offered choices, the differences of angle numbers are ...

2, 12, 5, 4, 1, 7

Of those pairs listed, angles 2 and 14, and angles 3 and 7 are corresponding angles.

Answer:

Step-by-step explanation:

You would do base times height so 11x11=121 then you divide it by 2 which equals 60.5.