The empty gas tank of a truck needs to be completely filled. The tank is shaped like a cylinder that is 3 ft long with a diameter of 2.4 ft . Suppose gas is poured into the tank at a rate of 2.5 ft 3 per minute. How many minutes does it take to fill the empty tank? Use the value 3.14 for π , and round your answer to the nearest minute. Do not round any intermediate computations.

Answers

Answer 1

Find out the volume of the cylinder using the formula for the volume of a cylinder. When you do that, you get that the volume of the tank, when it's full, is 4.5216 ft^3. If the tank is being filled at a rate of 2.5 ft^3 per minute, just divide the total volume by 2.5 to get that, after rounding, it takes 2 minutes to fill the tank. 1.80864 before rounding.

Answer 2

the diameter of the gas tank is 2.4, that means the radius is half that, or 1.2, check the picture below.

now, the tank is filling up at 2.5 ft³/min

how many times is 2.5 into V?

[tex]\bf V=\pi ft \cdot 1.2^2 ft\cdot 3 ft\implies 4.32\pi\ ft^3 \\\\\\ \textit{the rate is filling up is }2.5\frac{ft^3}{min} \\\\\\ \cfrac{4.32\pi \ ft^3}{\frac{2.5\ ft^3}{min}}\implies \cfrac{\frac{4.32\pi \ ft^3}{1}}{\frac{2.5\ ft^3}{min}}\implies \cfrac{4.32\pi \ ft^3}{1}\cdot \cfrac{min}{2.5\ ft^3}\implies \cfrac{4.32\pi }{2.5}min[/tex]

that many minutes, round it away.

The Empty Gas Tank Of A Truck Needs To Be Completely Filled. The Tank Is Shaped Like A Cylinder That

Related Questions

just need to check these answers

Answers

Great Job! they are all correct. :)

Good luck in your next tests.

Please help!! Will give medal!!
Compare the following functions:
(see attachment)
Which function has the smallest minimum?
A. All three functions have the same minimum
B. f(x)
C. g(x)
D. h(x)

Answers

The minimum value for f(x) is pretty straight-forward. -5+2=-3

We can tell by looking at the graph of g(x) that its minimum is -2

By symmetry the table shows a minimum of 3

So f(x) has the smallest minimum.

Answer:

Step-by-step explanation:

We are given three functions and we have to find which one has the smallest minimum.

I function is

[tex]f(x) = -5sin(2x-\pi) +2[/tex]

Since sine varies from -1 to 1, we get this function has a minimum when sine takes value 1.

Minimum of f(x) =1(-5)+2 =-3

II function is

a graph of parabola with minimum at x=3 and y =-2

III function is shown in tabular form.

From the table we find that minimum is x=1 y=3

Tabulating we have

f(x) (3pi/4, -3)

g(x) (3,-2)

h(x) (1,3)

Smallest is for f(x) with least value of -3

The length of the shadow of a flagpole was found to be 72 feet. the shadow of a 3 foot picket fence in line with the flagpole was 4 feet. what is the height of the flagpole?

Answers

We can solve this problem by simply using ratio and proportion. Let us call the height of the flagpole to be X. Therefore the ratio and proportion would be:

3 ft is to 4 ft and X ft is to 72 ft

3 / 4 = X / 72

X = (3 / 4) * 72

X = 54 ft

The height of the flagpole is 54 ft.

What type of transformation can be defined as turning a figure about a fixed point with no change to the size or shape of the figure?

Answers

The type of transformation that turns a figure without changing the size or the shape of the figure is called a ROTATION. An example is given in the diagram below. The triangle has been rotated 90° about the origin

The domain of the function is given. Find the range.

f(x) = 2x - 1

Domain: {-2, 0, 2, 4}

Answers

The range is found by plugging in the values of the domain into 2x - 1
So for x = -2, f(x) = 2(-2) - 1 = -5

The range will consist of -5 and the other 3 values of f(x) found for x = 0, x=2 and x=4.

What are the exact solutions of x2 − 3x − 1 = 0?
Select one:

a. x = the quantity of 3 plus or minus the square root of 5 all over 2 Incorrect

b. x = the quantity of negative 3 plus or minus the square root of 5 all over 2

c. x = the quantity of 3 plus or minus the square root of 13 all over 2

d. x = the quantity of negative 3 plus or minus the square root of 13 all over 2

Answers

Option C is the answer!

Hi, the quadratic formula is: [tex]\boxed{X= \dfrac{-b \pm \sqrt{b ^{2}-4ac } }{2a}}[/tex]

Values: a = 1; b = - 3; c = -1
Solving:

[tex]X ^{2}-3X-1=0[/tex]

[tex]X= \dfrac{-(-3) \pm \sqrt{(-3) ^{2}-4(1)(-1) } }{2(1)}[/tex]

[tex]X= \dfrac{3 \pm \sqrt{9+4} }{2}[/tex]

[tex]X= \dfrac{3 \pm \sqrt{13} }{2}\ ===\ \textgreater \ \ Answer:\ \boxed{ \textbf{Option\ {C.}}}[/tex]

GOOD LUCK...!!!

Explain how the GCF helps with the distributive property. Why is it so important to use the GCF when factoring a sum of two numbers?

Answers

GCF is the greatest common factor, that divides two number and the distributive property is that when a number multiplied with each number in the bracket and then perform addition or subtraction etc.

GCF help with distributive property and it is important to use when factoring a sum of two numbers. For example we have to add fractions 2/3 and 4/9, now the GCF is 9

2/3 + 4/9

= 2(3) + 4 (1) / 9

Now 2 is the common factor, so it allow us to use the distributive property.

= 2 (3 + 2) / 9

= 2(5) /9

=10 / 9 is the answer.

Answers for 1.2.1 how can I describe a graph

Answers

I don't know if this is quite what you're looking for but I think it is a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.
Hope this helps!

12.38 in expanded form

Answers

12.38 in expanded form is write like:-

10 + 2 + .3 + .08 = 12.38

To write a number in expanded form just means to write the number in a layout and when you add it up it will become the number you needed to write in expanded form.

So, 12.38 written in expanded form is:- 10 + 2 + .3 + 0.8

Hope this helps. Please make me brainliest

10+2+0.3+0.08 because you split each number into tens, ones, tenths, and hundredths.

Mary, who is sixteen years old, is four times as old as her brother. how old will mary be when she is twice as old as her brother? explained

Answers

First, you find the brother's age by dividing mary's age by 4.
16 ÷ 4 = 4
Now that you have two ages, you can just make a list to find the answer.
16 and 4
18 and 6
20 and 8
22 and 10
24 and 12

Use basic identities to simplify the expression. sin2θ + tan2θ + cos2θ

Answers

I think the correct expression for the problem would be as follows:

sin^2 (θ) + tan^2 (θ) + cos^2 (θ)

To be able to simplify this, we need to have knowledge on the different trigonometric identities. These identities are expressions which would relate the different trigonometric functions. For this case, we use two known basic identities. These are

sin^2 (θ) + cos^2 (θ) = 1
1 + tan^2 (θ) = sec^2 (θ)

We simplify as follows:
sin^2 (θ) + tan^2 (θ) + cos^2 (θ) = sin^2(θ) + tan^2 (θ) + cos^2 (θ)
= 1 + tan^2 (θ)
= sec^2

Therefore, the expression sin^2 (θ) + tan^2 (θ) + cos^2 (θ) is equal to sec^2 (θ). Other form that would also be equivalent to the same expression would be sin^2 (θ) + sin^2 (θ) / cos^2 (θ) + cos^2 (θ).

PLEASE HELP!! Use the following image↓

Answers

I assume it is negative three fourths (c) because when you graph that line, it is the closest line that meets the needs of the points.

A doorway is 8 feet high and 4 feet wide. A square piece of plywood needs to be moved through the doorway. The plywood is 10 feet long and 10 feet wide. The door is a rectangle with a height of 8 feet, and a width of 4 feet. A dotted line shows the diagonal.

Will the piece of plywood fit through the door if it is tilted diagonally?

A. No, because the length of the diagonal is close to 9 feet.
B. No, because the height of the door is less than 10 feet.
C. Yes, because the length of the diagonal is close to 11 feet.
D. Yes, because the sum of the height and width of the door is greater than 10 feet.

Answers

By the Pythagorean Theorem:

d^2=x^2+y^2

d^2=8^2+4^2

d^2=64+16

d^2=80

d=√80

d=4√5 ft

d≈8.944

So

A. No because the diagonal is close to 9 feet.

After calculating the diagonal of the doorway to be approximately 8.944 feet using the Pythagorean theorem, it's clear that the 10-foot square piece of plywood will not fit diagonally through the door. Thus, the correct answer is option (A).

The question is whether a 10-foot square piece of plywood can fit through an 8-foot by 4-foot doorway when tilted diagonally. To determine if the plywood can fit, we need to calculate the diagonal of the doorway using the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as c² = a² + b² where c is the hypotenuse, and a and b are the other two sides.

Let's apply the theorem to our doorway:

Height (a) = 8 feet

Width (b) = 4 feet

Diagonal (c) = ?

We calculate the diagonal:

c² = a² + b²
c² = 8² + 4²
c² = 64 + 16
c² = 80
c = sqrt(80)
c = 8.944 feet (approx)

The diagonal of the doorway is approximately 8.944 feet, which is less than the 10 feet length of the plywood. Therefore, the correct answer is:

No, because the length of the diagonal is close to 9 feet.

The option (A) is correct.

Greg is trying to solve a puzzle where he has to figure out two numbers, x and y. Three less than two-third of x is greater than or equal to y. Also, the sum of y and two-third of x is less than 4. Which graph represents the possible solutions?

Answers

The first inequality is
(2/3)x - 3 ≥ y
or
y ≤ (2/3)x - 3 (1)

The second inequality is
y + (2/3)x < 4
or
y < 4 - (2/3)x (2)

A graph of the two inequalities indicates the solution as a shaded region in the figure below.

Can anyone please help ASAP, will give thanks and all that fun stuff

Answers

We can begin by taking each part of the table and writing it out as a term of the geometric sequence. For example, for n=4, we have ar^3=6, and for n=9 we have ar^8=-192. Then, we can divide these two terms to get r^5=-32. Taking the fifth root on both sides, we get that r=-2. We can then just plug this in, getting -8a=6, or that a=-3/4, giving us B.

(every time i use a in this, i mean a1)

Answer:

The answer is B!!!!

Stanfing in your tree house 50ft off the ground you look down at a 60 degree angle how many feet from the base of the tree is the frisbee

Answers

multiply 50 x tan(60) = 86.6 feet.

round your answer as needed

What is the length of CF? look at image attached

Answers

If two chords intersect each other inside a circle, the products of their segments are equal.

СF * DF = BF * EF
СF * 14 = 7 * 17
14СF = 119
СF = 119/14
СF = 8.5

Which of the following is true when probability answer is written in the form of a fraction

Answers

The subject area of probability is actually expressed as a fraction or percentage because it represents a part of a whole. In lay man's term, probability is the scientific study of chance, likeliness and odds of an event happening. For example, you want to find the odds of getting a heads in a toss of the coin. You know that there are 2 possible results: head and tails. So, the probability of getting a head is 1/2 or 50%. Since it is a part of a whole, the probability in fraction should never be an improper fraction. This is the type of fraction in which the numerator is greater than the denominator. This is impossible as a probability because it will never exceed 1.

In probability, a fraction does not need to be simplified but converting to a percentage or decimal can aid in interpretation, with percentages being fractions with a denominator of 100. (First option)

When a probability answer is written in the form of a fraction, it is important to know how to handle the result. Simplifying the fraction is not generally required, especially in Probability Topics, where the focus is on understanding the probability itself rather than the arithmetic of fractions.

However, converting the probability to a percentage is a common practice that can help with interpretation. This is done by writing the value of the percent as a fraction with a denominator of 100 and then simplifying it if possible.

Converting a fraction to a decimal is another common step, which involves dividing the numerator by the denominator. It's also important to note that for rounding answers to probability problems, the convention is to round to four decimal places.

JL is a common tangent to circles M and K at point J. If angle MLK measures 61ᵒ, what is the length of radius MJ? Round to the nearest hundredth. (Hint: Show that triangles LMJ and LKJ are right triangles, and then use right triangle trigonometry to solving for missing sides of the right triangles.)

Answers

Final answer:

To find the length of radius MJ, we can use right triangle trigonometry. Firstly, we can show that triangles LMJ and LKJ are right triangles. Then, we can use the given angle MLK of 61ᵒ to find the length of radius MJ, using the sine function. The equation to find MJ is MJ = rM * sin(29ᵒ).

Explanation:

To find the length of radius MJ, we can use right triangle trigonometry. Firstly, we can show that triangles LMJ and LKJ are right triangles. Since JL is a common tangent, it is perpendicular to the radii of the circles at points J. Therefore, angle LMJ and angle LKJ are right angles. Now, we can use the given angle MLK of 61ᵒ to find the length of radius MJ.

Let's call the radius of circle M rM and the radius of circle K rK. In triangle LMJ, we have the following relationships:

angle LMJ = 90ᵒ (since it is a right triangle)angle MLJ = angle MLK - angle JLK = 61ᵒ - 90ᵒ = -29ᵒ (since angle JLK is a right angle)angle MJL = angle JML = 90ᵒ - angle MLJ = 90ᵒ - (61ᵒ - 90ᵒ) = 119ᵒ

Using the sine function, we can find the length of side MJ:

sin(angle MLJ) = length of side MJ / length of side LJ

sin(-29ᵒ) = MJ / rM

Since sin(angle MLJ) = -sin(angle MJL), we can rewrite the equation as:

sin(29ᵒ) = MJ / rM

Now, we can rearrange the equation to solve for MJ:

MJ = rM * sin(29ᵒ)

Since we are not given the values of rM or rK, we cannot find the specific value of MJ. However, we can use this equation to find the length of radius MJ if we are given the values of the radii of the circles and the given angle MLK.

Remember to round the answer to the nearest hundredth as specified in the question.

Find the area of a regular hexagon whose side length is 16 in. and the apothem is 8 square root of 3 in

Answers

polygon area = (# of sides) * (side length) * (apothem) / 2
polygon area = 6 * 16 * 13.8564064606 / 2
polygon area = 665.1075101088 square inches

Suppose a study estimated that 85% of the residents of a town (with an error range of ±12 percentage points at 95% confidence) favor building a new community center. Which of the following percentages of the town's residents may favor building a new community center?
A. 69%
B. 79%
C. 59%
D. 99%

Answers

The confidence interval for a given sample value can be calculated using the following formula:

Confidence interval = Average value ± Margin of error

Which in this case the values are:

Average value = 85%

Margin of error = 12%

Therefore substituting the given values into the equation will give us:

Confidence interval = 85 ± 12

Confidence interval = 73, 97

Therefore the percentage of the residents of the town who are favour of building a new community center ranges from 73% to 97%.

Based from the given choices, only letter B 79% is within this range:

Answer:

B. 79%

Answer:

B. 79%

Step-by-step explanation:

yes

A phone company offers two monthly plans. Plan A costs $30 plus an additional $0.15 for each minute of calls. Plan B costs $16 plus an additional $0.20 for each minute of calls.
For what amount of calling do the two plans cost the same?
What is the cost when the two plans cost the same?

Answers

Plan A = 30 +0.15x

Plan B = 16 +0.20x

30+0.15x = 16+0.20x

subtract 16 from each side

14 +0.15x = 0.20x

subtract 0.15x from each side

14=0.05x

x = 14/0.05 = 280 minutes

280*0.15 = 42 +30 = $72

280 * 0.20 = 56 +16 = 72

280 minutes and cost $72 each

Lets m = number of minutes calls

Plan A : 30 + 0.15 m
Plan B: 16 + 0.20 m

For what amount of calling do the two plans cost the same?

30 + 0.15m = 16 + 0.20m
0.05m = 14
m = 280

280 minutes of calling, the two plans cost the same

What is the cost when the two plans cost the same?

Plan A: 30 + 0.15 m = 30 + 0.15 (280) = 72

Plan B: 16 + 0.20 m = 16 + 0.20 (280) = 72

answer

It's cost $72 when the two plans cost the same

in the system shown below, what are the coordinates of the solution that lies in quadrant I? x^2-y^2=25, x+y=25

Answers

The given equations in this item are,
x² - y² =25
and
x + y = 25

It can be deduced that the first equation is a difference of two squares and can be factored out as that one shown below.
(x - y)(x + y) = 25

From the second equation, x+y = 25. Substituting this to the equation above,
(x-y)(25) = 25
Hence, x - y = 1

The system of linear equations is,
x + y = 25
x - y = 1
Adding the equations together,
2x = 26
x = 13

The value of y is 12.

Since both x and y are positive values then, this solution lies in the first quadrant.

ANSWER: (13,12)

The course for the frog hopping race is 59 inches long. Max's frog has jumped 2 feet and 3 inches. How much further does Max's frog need to jump in order to reach the finish line?

Answers

2ft is equal to 24 inches+3 is equal to 27 inches travelled total.
To find what is left subtract 59-27=32 inches left, which is equivalent to 2 ft 8 inches

To find the remaining distance Max's frog needs to jump in the race, convert the initial jump to inches, and subtract it from the total race length.

The frog hopping race's course is 59 inches long. Max's frog has jumped 2 feet and 3 inches. To find out how much further Max's frog needs to jump to reach the finish line, convert 2 feet and 3 inches to inches and subtract it from 59 inches.

The conversion is: 2 feet x 12 inches = 24 inches. Adding 24 + 3 inches gives 27 inches. Subtract 27 inches from 59 inches to find the remaining distance Max's frog needs to jump.

The distance Max's frog still needs to jump is 32 inches.

Find the measure of each interior angle and each exterior angle of the following regular polygons. Show your work

Answers

[tex]\bf \textit{sum of all interior angles of a regular polygon}\\\\ n\theta =180(n-2)\qquad \begin{cases} n=\textit{number of sides}\\ \theta =\textit{interior angle} \end{cases}\\\\ -------------------------------\\\\ \textit{sum of all exterior angles of a regular polygon}\\\\ n\theta =360\qquad \begin{cases} n=\textit{number of sides}\\ \theta =\textit{interior angle} \end{cases}[/tex]

now, with that in mind... let's take a peek at .. hmmm say c) dodecagon
now, a Dodecagon has 12 sides.... let's check the angles then

[tex]\bf n\theta =180(n-2)\qquad n=12\implies 12\theta =180(12-2) \\\\\\ 12\theta =180\cdot 10\implies 12\theta =180\implies \theta =\cfrac{1800}{12} \\\\\\ \theta =150^o\impliedby \textit{interior angle of a Dodecagon}\\\\ -------------------------------\\\\ n\theta =360\qquad n=12\implies 12\theta =360\implies \theta =\cfrac{360}{12} \\\\\\ \theta =30^o\impliedby \textit{exterior angle of a Dodecagon}[/tex]

so... hmm now for a) a decagon is 10 sides, b) pentagon is 5 sides, d) and e) pretty much you can tell how many sides on those already.

Answer:

Step-by-step explanation:

As we know for a regular polygon sum of all interior angles is represented by n A = 180 (n-2)

and sum of all exterior angles is represented by n A' = 360°

Here n represents number of sides of the polygon.

Now we will go for each options given.

(A) Decagon : (Having 10 sides)

(1) 8A = 180 ( 8-2 )

8A = 180 × 6

A = [tex]\frac{1080}{8}[/tex] = 160° ( interior angle )

(2) n A' = 360°

8 A' = 360°

A = 45° ( exterior angle )

(B) Pentagon ( having 5 sides )

(1) 5A = 180 ( 5-2 )

5A = 180 × 3 = 540

A = 108° ( interior angle )

(2) 5A' = 360

A' = 72° (exterior angle )

(C) Dodecagon : ( having 12 sides )

(1) 12A = 180 (12-2)

12 A = 180 × 10 = 1800

A = 150° ( interior angle )

(2) 12 A' = 360

A' = 30° ( exterior angle )

(D) 16-gon ( having 16 sides )

(1) 16 A = 180 ( 16 - 2 )

16A = 180 × 14

16 A = 1520

A = 157.5° ( interior angle )

(2) 16 A' = 360

A' = 22.5°

(E) 25-gon ( having 25 sides )

(1) 25 A = 180 ( 25-2)

25A = 180 (23)

A = 165.6° ( interior angle )

(2) 25A' = 360

A = 14.4° ( exterior angle)

2 Questions~
Evaluate the expression.

38+16⋅12÷2−(30⋅2)

Simplify this expression.

5 + 10 ÷ 5

3

7

10

15

Answers

answer is 3 hope this helps

Your answer would be a.

Answer: 3

hope this helps! :)

~Izzie

(04.01 LC)

Which of the sets of ordered pairs represents a function?

A = {(2, −2), (5, −5), (−2, 2), (−5, 5)}
B = {(4, 2), (4, −2), (9, 3), (9, −3)}

Only A
Only B
Both A and B
Neither A nor B

Answers

Answer:

Only A

Step-by-step explanation:

Let's remember the definition of a function:

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

In A, each input has exactly one output so it's a function.

But in B, the inputs 4 and 9 have two different outputs, it can't represent a function.

The answer is only A.

1,226 days late to answer this question but that will not stop me!

The answer is... drumroll please ... Only A :]

The point (–3, –5) is on the graph of a function. Which equation must be true regarding the function?
f(–3) = –5
f(–3, –5) = –8
f(–5) = –3
f(–5, –3) = –2

Answers

[tex]f(-3) = -5[/tex]

Answer:

Option 1st is correct

[tex]f(-3) = -5[/tex]

Step-by-step explanation:

If any point [tex](x, y)[/tex] is on the graph then we can write the function as:

[tex]y= f(x)[/tex]

where

x is the independent variable and

y is the dependent variable.

As per the statement:

The point (–3, –5) is on the graph of a function.

⇒x = -3 and y = -5

By above definition we have;

[tex]f(-3) = -5[/tex]

Therefore, the equation must be true regarding the function is, [tex]f(-3) = -5[/tex]

helpppppppppppppppppppppppppppp

Answers

Finding the area of one triangle:

h^2 + 3^2 = 6^2
x^2 = 27
x=sqrt(27)
x=3*sqrt(3)

0.5*x*6=9*sqrt(3)

Then multiplying by 7 for all 7 sides,

9*sqrt(3)*7

63*sqrt(3)

Final simplification: 109.12, D

Hope this helps.

8% of x is equal to 48

Answers

48 / 0.08 = 600

answer

8% of 600 is equal to 48

divide 48 by 8%

48/0.08 = 600

check

600*0.08 = 48

x=600

Other Questions