which statement best explain the relationship between numbers divisable by 9 and 3

Answers

Answer 1

Answer/Step-by-step explanation:

All numbers that are divisible by 9 are also divisible by 3.

Since 3 goes into 9, if 9 is a factor, 3 is also a factor.

Example:

81 is divisible by 9.

So, 81 is also divisible by 3.



Another example:

1,273,050 is divisible by 9.

So 1,273,050 is also divisible by 3.

But the other way around is not necessarily true. If 3 goes into a number, 9 may or may not go into the number.

That is, if a number is divisible by 3, you cannot necessarily know that it is divisible by 9.

Example (seems like it works):

18 is divisible by 3. 18 is also divisible by 9.

But it doesn't work every single time so it cannot be a rule.

Example(sometimes it doesn't work):

24 is divisible by 3.

24 is not divisible by 9.


Related Questions

1) How much would you have to invest in an account earning 8% interest compounded continuously, for it to be worth one million dollars in 30 years?

Answers

The principal that would need to be invested to have an accrued amount of 1 million dollars after 30 years is $90,717.95.

What is the amount of principal to be invested?

The formula compound interest where interest is compounded continuously is expressed as;

A = P × e^(rt)

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given the data in the question;

Accrued amount A = $1,000,000Time t = 30 yearsInterest rate r = 8% = 8/100 = 0.08Compounded consciouslyPrincipal P = ?

Plug the given values into the above formula and solve for P.

A = P × e^(rt)

P = A / e^(rt)

P = $1,000,000 / e^( 0.08 × 30 )

P = $1,000,000 / e^( 2.4 )

P = $90,717.95

Therefore, the amount of principal is $90,717.95.

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question 8in all segments, how many orders were placed in one quarter of the year but shipped in the next quarter (for example, an order in which order date = qtr1 2009 and ship date = qtr2 2009)?

Answers

The number of orders placed in one quarter of the year and shipped in the next quarter will vary depending on the segment. To determine the exact number, you would need to analyze the data from each segment separately.

To determine the number of orders placed in one quarter of the year but shipped in the next quarter, you will need to analyze the data from each segment separately. Begin by extracting the data from the segment you are interested in and sorting it by order date and ship date. For example, if you are interested in orders placed in Q1 2009 and shipped in Q2 2009, you will need to identify all orders with an order date in Q1 2009 and a ship date in Q2 2009. Once you have identified these orders, you can count them up to determine the total number of orders in the segment that fit this criteria. You can then repeat this process for the other segments to determine the total number of orders placed in one quarter of the year but shipped in the next quarter across all segments.

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Solve the given system of equations
2y = 6y = -15

Answers

The system of equation has no solution

How to determine the solution to the system

From the question, we have the following parameters that can be used in our computation:

2y = 6

y = -15

Since these are two different equations with the same variable, y, we can use substitution to find a solution.

Starting with the second equation, y = -15, we can substitute this value into the first equation:

2y = 6

2(-15) = 6

-30 = 6

This equation is false, meaning there is no solution for y that satisfies both equations.

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find the number of revolutions taken by a road roller whose lsa is 32cm² to level a play ground of area 6400m²​

Answers

Answer:

the number of revolutions that are required to level the playground is 194 revolutions

Step-by-step explanation:

We know that LSA, that is lateral surface area of a cylinder is the area of a rectangular sheet, which when spread onto the ground, covers the area equal to the LSA of the cylinder.

Hence, area covered by the roller in one revolution = area of LSA of cylinder  = 32 cm².

Now, to cover the are of 6200 cm²,

the number of revolutions required  = Total area of the playground/ LSA of the cylinder = 6200/32 = 193.75 = 194

Hence the number of revolutions that are required to level the playground is 194.

Please help me its for my hw

Answers

Answer:

a) 144π cm²

b) 248π cm²

Step-by-step explanation:

Using the formula, curved surface area of a cone = πrl where r = radius and l = slant height,

Curved surface area of large cone = π (10) (12 + 3) = π (10)(15) = 150π

Curved surface area of small cone = π(2)(3) = 6π

a) Curved surface area of frustum = 150π - 6π = 144π cm²

b)
The frustum has a top surface which is a circle of radius 2 and a bottom surface which is also a circle of radius 10

The area of a circle is πr²

So Total area of both circles = π(2)² + π(10)² = 4π + 100π = 104π

Total surface area of frustrum = 144π + 104π = 248π cm²

To help determine the roots of x =tan(x), graph y = x and y = tan(x), and look at the intersection points of the two curves. (a) Find the smallest nonzero positive root of x = tan(x), with an accuracy of E=0.0001. Note: The desired root is greater than 1/2. (b) Solve x =tan(x) for the root that is closest to x = 100.

Answers

(a) the root of the equation is =4.4.(b) x=31pi for x=100 approx.

the root of an equation is said to be that value where the equation gets zero. And the intersection point of two equations is the same value of equations.

The roots of x =tan(x), graph y = x and y = tan(x), and look at the intersection points of the two curves.

a) Find the smallest nonzero positive root of x = tan(x),

after seeing the graph the root of the equation is =4.4.

(The desired root is greater than pi/2).

b) Solve x =tan(x) for the root that is closest to x = 100.

after examining the graph of the function we can see that 31pi for x=100 approximately.

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Karen owns a seafood restaurant. She orders trout from an online retailer. Each pound of trout costs $28, and the company charges a $4 fee for shipping the order. However, if Karen orders 10 or more pounds, the trout costs only $22 per pound, but the shipping fee is $8. Which piecewise function models the cost of x pounds of trout?

Answers

Answer: the answer is A), normal is 28 + 4fee, but if she buys LOTS its 22 +8

contact me through discord Acathia#0103, its easier to help, I can help with multiple questions aswell

Step-by-step explanation:

9 more than a number g equals 18

Answers

Answer: 9

Step-by-step explanation:

g + 9 = 18

g = 18-9

  =9

The answer should be 9

a cone-shaped pile of sawdust has a base diameter of 32 feet, and is 14 feet tall. find the volume of the sawdust pile.

Answers

The volume of the sawdust pile is 3754.667 cubic feet

A cone is a three-dimensional shape that has a circular base with tapers from the flat base into the vertex.

The formula for searching the volume of the cone can be described below :

V = [tex]\frac{1}{3}[/tex] π [tex]r^{2}[/tex] h

which

V = volume of the cone

r = radius of cone circular base

h = height of cone ( tall of the cone )

From the question, we have following information :\

1. Base diameter = 32 feet

  Base radius = Base diameter / 2 = 32 feet / 2 = 16 feet

2. Tall / Height of the cone = 14 feet

Since the known parameter is enough to be put into the formula, we can simply subtitute the formula with known parameter

V = [tex]\frac{1}{3}[/tex] π [tex]r^{2}[/tex] h

  = [tex]\frac{1}{3}[/tex] x π x [tex]16^{2}[/tex] x 14

  = 3754.667 cubic feet

Hence the volume of the cone is 3754.667 cubic feet

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bryant bought 24 hockey tickets for $83. adult tickets cost $5.50 and child tickets cost $2.00. how many child tickets did he buy?

Answers

There about 24 hockey tickets were bought by Bryant. Out of which 14 tickets were child tickets.

A mathematical claim containing two equal algebraic expressions is known as an algebraic equation.

Given that the cost of an adult ticket is $5.50, and a child ticket is $2.00. The total spent is $83, and the total number of tickets bought is 24.

Let us consider the number of adult tickets bought is x and the number of children tickets bought is y.

Then x+y=24. From this, x=24-y.

Also, the given situation is written in an expression as,

[tex]\begin{aligned}5.50x+2.00y&=83\\5.50(24-y)+2.00y&=83\\132-5.50y+2.00y&=83\\-3.5y&=-49\\y&=14\end{aligned}[/tex]

The required answer is 14.

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A certain inect can beat it wing 240 time per econd. Write an equation in lope-intercept form that how the relationhip between flying time in econd and the number of time the inect beat it wing

Answers

The equation is in slope-intercept form is y = 240t + 0

How to write an equation in slope-intercept form?

The equation of a line in slope-intercept form is given by:

y = mx + b

where m is the slope and b is y-intercept

Let's say the number of times the insect beats its wing in t seconds is represented by y. Then the relationship can be expressed as:

y = 240t

The slope (240) shows that for every 1 second increase in time, the number of wing beats increases by 240. The y-intercept (0) indicates that when t = 0, y=0, i.e. when the insect has not started flying, it has not beaten its wing yet.

Therefore, the equation is in slope-intercept form: y = 240t + 0

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A large university accepts 50​% of the students who apply. Of the students the university​ accepts, 40​% actually enroll. If 30,000 students​ apply, how many actually​ enroll?

Answers

The number of students actually enrolled is 6000.


What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a large university accepts 50​% of the students who apply. Of the students the university​ accepts, 40​% actually enroll. If 30,000.

The number of students will be calculated as:-

Number = ( 30000 x 0.5 x 0. 4 )

Number = 6000

Therefore, the number of students will be 6000.

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Please help me figure out what the last one is and how to get the answer
Tysm!

Answers

Answer:

see explanation

Step-by-step explanation:

for the given angles to form a triangle they must sum to 180°

given

31 [tex]\frac{3}{4}[/tex]°  , 53 [tex]\frac{1}{2}[/tex]° , 94 [tex]\frac{3}{4}[/tex] ° ( changing to decimal form and adding )

= 31.75° + 53.5° + 94.75°

= 180°

Thus the 3 given angle measures can form a triangle.

100 points

answer ?
( L to G )

Answers

Answer:

It's already in order

[tex]\frac{3}{4}[/tex] × [tex]\frac{4}{9}[/tex], [tex]\frac{7}{7}[/tex] × [tex]\frac{4}{9}[/tex]  , [tex]1\frac{2}{3}[/tex] × [tex]\frac{4}{9}[/tex], [tex]2[/tex] × [tex]\frac{4}{9}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4}[/tex] × [tex]\frac{4}{9}[/tex]

[tex]=\frac{1}{3}[/tex]

[tex]\frac{7}{7}[/tex] × [tex]\frac{4}{9}[/tex]

[tex]=\frac{4}{9}[/tex]

[tex]1\frac{2}{3}[/tex] × [tex]\frac{4}{9}[/tex]

[tex]=\frac{20}{27}[/tex]

[tex]2[/tex] × [tex]\frac{4}{9}[/tex]

[tex]=\frac{8}{9}[/tex]

Change them all to the same common denominator of 27

[tex]\frac{9}{27}, \frac{12}{27}, \frac{20}{27}, \frac{24}{27}[/tex]

pls help asap :(!!!!!!!

Answers

The midpoints of the segment is (4, -3.5).

What is Section Formula?

The coordinates of the point A(x, y) which divides the line segment joining the points P(a , b) and Q(c , d) internally in the ratio m : n are given by the formula: P ( x , y ) = ( a x n + c x m / (m+n)  , bn + dn / (m+n))

Given:

Points (-4, -7) and (12, -6).

So, the ratio is line is m:n = 1:1

let (x, y) be the midpoint.

Now, using section formula

x = (-4 x 1 + 12 x 1)/ (1+1)

x= (-4 +12) /2

x= 8/2

x= 4

and, y = (-7 x 1 -6 x 1)/ 2

y = -7-6/2

y = -13/2

y = -3.5

Hence, the midpoints are (4, -3.5).

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evaluate the integral using integration by parts with the indicated choices of u and dv. (use c for the constant of integration.) 5x2 ln(x) dx; u = ln(x), dv = 5x2 dx

Answers

The integral using integration by parts with the indicated choices of u and dv is equal to,   [tex]\int\limits 5x^{2} lnx dx[/tex] = [tex]\frac{5x^{3} }{3} (ln(x)-\frac{1}{3} )[/tex] + c

Basic Power Rule:

f(x) = cxⁿ

f’(x) = c· n xⁿ⁻¹

Integration

Integrals

[Indefinite Integrals] Integration Constant C

Integration Property [Multiplied Constant]:              

[tex]\int\limits cf(x)dx[/tex] = c [tex]\int\limitsf(x) dx[/tex]

Integration Rule [Reverse Power Rule]:

[tex]\int\limits x^{n} dx[/tex] = [tex]\frac{x^{n+1} }{n+1}[/tex] + c

Integration by Parts:  

[tex]\int\limits u dv[/tex] = uv - [tex]\int\limits v du[/tex]

Given that,

= [tex]\int\limits 5x^{2} lnx dx[/tex]

Rewrite [Integration Property - Multiplied Constant]:

[tex]\int\limits 5x^{2} lnx dx[/tex] = 5 [tex]\int\limits x^{2} lnx dx[/tex]

Set u:  

u = [tex]lnx[/tex]

[u] Logarithmic Differentiation:          

du = [tex]\frac{1}{x}[/tex] dx

Set dv:  

dv = [tex]x^{2}[/tex]                                                                                                        

[dv] Integration Rule [Reverse Power Rule]:  

v = [tex]\frac{x^{3} }{3}[/tex]

Integration by Parts:  

[tex]\int\limits 5x^{2} lnx dx[/tex] = 5 [tex]( \frac{x^{3}ln(x) }{3} - \int\limits \frac{x^{2} }{3} dx )[/tex]

Rewrite [Integration Property - Multiplied Constant]:  

[tex]\int\limits 5x^{2} lnx dx[/tex] = 5 [tex](\frac{x^{3}ln(x) }{3} -\frac{1}{3} \int\limits x^{2} dx )[/tex]

Factor:  

[tex]\int\limits 5x^{2} lnx dx[/tex] = [tex]\frac{5}{3} (x^{3} ln(x) - \int\limits x^{2} dx )[/tex]

Integration Rule [Reverse Power Rule]:  

[tex]\int\limits 5x^{2} lnx dx[/tex] = [tex]\frac{5}{3} (x^{3} ln(x) - \frac{x^{3} }{3} )[/tex] + c

Factor:

[tex]\int\limits 5x^{2} lnx dx[/tex] = [tex]\frac{5x^{3} }{3} (ln(x)-\frac{1}{3} )[/tex] + c

Therefore,

The integral using integration by parts with the indicated choices of u and dv is equal to,   [tex]\int\limits 5x^{2} lnx dx[/tex] = [tex]\frac{5x^{3} }{3} (ln(x)-\frac{1}{3} )[/tex] + c

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using the 68-95-99.7 empirical rule-of-thumb, answer the following questions. no partial credit will be given for using any other method. a given exam has a normal distribution with a mean of 70 and a standard deviation of 10. a sample of size 25 is selected. what percentage of the time would you expect the mean of this sample size to fall between 68 and 72? %

Answers

The mean of the sample size of 25 would fall between 68 and 72 68% of the time.

68% Expect Mean Interval

Using the 68-95-99.7 rule, if a variable is normally distributed with mean μ and standard deviation σ, then:

68% of the data falls within 1 standard deviation of the mean (μ - σ to μ + σ)95% of the data falls within 2 standard deviations of the mean (μ - 2σ to μ + 2σ)99.7% of the data falls within 3 standard deviations of the mean (μ - 3σ to μ + 3σ)Given that the mean of the exam scores is 70 and the standard deviation is 10, the range of 68% of the data falls between 60 and 80.So, 100% - 68% = 32% of the data falls outside this range.

Since the interval we are interested in (68 to 72) falls within the 68% of the data that falls within 1 standard deviation of the mean, it means that 100% - 32% = 68% of the data falls within this interval.

Thus, the mean of this sample size of 25 would fall between 68 and 72 68% of the time.

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The perimeter of a rectangle is 96 cm. if the ratio of the length to width is 7 : 5, find the dimensions of the rectangle

Answers

Salut/Hello!

Answer: w = 20 cm and l = 28 cm

Step-by-step explanation:
l - length
w - width
P - perimeter
/ - fraction line
=> - results

we know that P = 2 x (l + w)
we also know that our ratio is l/w = 7/5

l/w = 7/5 => l = 7/5 x w
so now we can go back to the perimeter and replace l

96 = 2 x (7/5 x w + w)
96 = 2 x (7/5 x w/1 + w)   Why w/1? - We can't multiply unless w is also in a fraction, so we put it as w/1
96 = 2 x (7w/5 + w)
96 = 2 x (7w/5 + w/1)  and we amplify w/1 with 5
96 = 2 x (7w/5 + 5w/5)
96 = 2 x 12w/5
48 = 12w/5
48/1 = 12w/5
48 x 5 = 12w
240 = 12w
w = 20 cm

with that we can find l
96 = 2 x (l + 20)
48 = l + 20
l = 48 - 20
l = 28 cm

I hope it was helpful! :]

A continuous random variable X has a PDF f(x) = ax + X^2 for 0<=x<=1. What is the probability that X is between 0.5 and 1?

A. 15/24

B.17/24

C. 19/24

D. 21/24

Answers

The probability that X is between 0.5 and 1 is (C) 19/24.

The probability that X is between 0.5 and 1 can be found by calculating the definite integral of the PDF f(x) over the interval [0.5, 1]:

P(0.5 <= X <= 1) = ∫f(x)dx from 0.5 to 1

Given the PDF f(x) = ax + X^2 for 0<=x<=1, we can evaluate this definite integral as:

P(0.5 <= X <= 1) = ∫(ax + X^2)dx from 0.5 to 1

= [ax^2/2 + x^3/3] from 0.5 to 1

= (1.5a + 1/3) - (0.5a + 0.125)

= (1 + 1/6) - (0.5 + 1/8)

= (2/3 - 3/8)

= 5/24

Since 5/24 is equal to 0.2083, the closest answer choice to this value is 19/24.

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Find the specified lengths and measures.
Given: △ABC ≅ △DEF
Find: AB and m∠F
A
B
C
4
6
30°
50°
D
E
F

Answers

Answer:

In the given triangle △ABC, AB is equal to 4 and m∠F is equal to 30°. In the triangle △DEF, AB is equal to 6 and m∠F is equal to 50°.

Which statement could be used to describe the functions?

Answers

A statement could be used to describe the functions include the following: D. the domain of f(x) is (−∞, 0] while the domain of g(x) is [0, ∞).

What is a domain?

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.

Additionally, the horizontal extent of any graph of a function represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

By using interval notation, the domain of this function shown in the graph above can be written as follows;

Domain of f(x) = {-∞, 0}

Domain of g(x) = {0, ∞}

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What is the value of the expression below when y=7?
y 2 + 4y +3

Answers

Insert 7 for y

7•2+4•7+3

Multiply #

14•28+3

Evaluate

Solution

45
7(2) = 14
4(7) = 28
14+28+3 = 45

Brenda plans to reduce her spending by $70 a month. What would be the future value of this reduced spending over the next 12 years? (Assume an annual deposit to her savings account and an annual interest rate of 6 percent.) Use Exhibit 1-B. (Round FVA factor to 3 decimal places and final answer to 2 decimal places.)

Please show me how to figure this out using a financial calculator and the inputs I would put into excel please.

Answers

If Brenda plans to reduce her spending by $70 a month, the future value of this reduced spending over the next 12 years is $14710.5.

We are given that Brenda will be saving $70 every month for a period of 12 years.

So, the future value of the annuity formula will be used for the calculation of future value.

Future value = R [( (1 + i)^n - 1 ) / i], where R is the regular payment, i is the interest rate and n is the number of payments

Here R = monthly amount to be saved = $70

i = interest rate = 6/12 = 0.5%

n = Number of payments = 12 x 12 = 144 months

Future value=70 [( (1+0.5%)^144 - 1) / 0.5%] = $14710.5

Hence, the future value of this reduced spending over the next 12 years is $14710.5.

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pretty please someone help me! Determine the slope of the line that passes through (-2, 7) and (-12, 9). Type a numerical answer in the space provided. If
necessary, use the / key for a fraction bar. Do not include spaces in your answer.

Answers

Answer:

-5

Step-by-step explanation:

Δy =9-7=2

Δx = -12-(-2) =-10

-10/2= -5

If ¯x represents the mean of n observations x1, x2, ……xn, then value of ∑ni−1(xi−¯x) is:A) -1B) 0C) 1D) n - 1

Answers

If [tex]\overline{x}$[/tex] represents the mean of n observations x₁, x₂, ……xₙ, then the value of [tex]$\sum_{i=0}^{n} (x_{i} - \overline{x})$[/tex] is 0.

Mean is the average value of the group of values. It shows the equal distribution of values for a given data set.

To calculate the arithmetic mean of a group of data, first, add up (sum) all of the data values (x) and then divide the result by the number of values (n). Since ∑ is the symbol used to indicate that values are to be summed, we obtain the following formula for the mean ([tex]\overline{x}[/tex]):

[tex]\overline{x}= $\sum {\frac{x}{n} $[/tex]

The formula of the mean ([tex]\overline{x}$[/tex]) is:

[tex]\overline{x} = $\sum_{i=0}^{n} {x_{i}$/n[/tex]

[tex]$\sum_{i=0}^{n} {x_{i} = \overline{x}n[/tex]           Eqn(1)

Here, n is total number of observations.

The value of [tex]$\sum_{i=0}^{n} (x_{i} - \overline{x})$[/tex] is calculated as follows:

[tex]$\sum_{i=0}^{n} (x_{i} - \overline{x}) = \sum_{i=0}^{n} x_{i} - \sum_{i=0}^{n}\overline{x}[/tex]

Now, from equation (1), we get

[tex]$\sum_{i=0}^{n} (x_{i} - \overline{x}) = n\overline{x} - \sum_{i=0}^{n}\overline{x}[/tex]

[tex]$\sum_{i=0}^{n} (x_{i} - \overline{x}) = n\overline{x} - \overline{x}\sum_{i=0}^{n}1[/tex]

[tex]$\sum_{i=0}^{n} (x_{i} - \overline{x}) = n\overline{x} - \overline{x}n[/tex]

[tex]$\sum_{i=0}^{n} (x_{i} - \overline{x}) = 0[/tex]

Hence, the correct answer is B.

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the bases of a trapezoid lie on the lines y=9x+8 and y=9x-2. write and equation of the line that contains the midsegment of the trapezoid

Answers

Answer:

y = 8x+3

Step-by-step explanation:

hoping its correct for you

Find the coordinates of point P along the directed line segment AB so that AP to PB is in the ratio 4 to 1. Round your answers to the nearest tenth. (i rlly need help)

Answers

The coordinate of the point P that lies on the line segment AB will be (6.6, 3.8).

What is the section of the line?

Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divides the line segment in the ratio of m:n. Then we have

x = (mx₂ + nx₁) / (m + n)

y = (my₂ + ny₁) / (m + n)

AP to PB is in the ratio of 4 to 1. Then the coordinate of the point P is given as,

x = (4 × 8 + 1 × 1) / (4 + 1)

x = (32 + 1) / 5

x = 33 / 5

x = 6.6

y = (4 × 4 + 1 × 3) / (4 + 1)

y = (16 + 3) / 5

y = 19 / 5

y = 3.8

The coordinate of the point P that lies on the line segment AB will be (6.6, 3.8).

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A gas company's delivery truck has a cylindrical tank that is 14 feet in diameter and 40 feet long.
Use the space in your supplement to draw the tank, if that would help. Use 3.14 as an approximation of
π
. Round to the nearest tenth if needed.

How much gas can fit in the tank?

Answers

Answer:

Hi, I'm Za'Riah! I will gladly assist you with your problem. (see explanation)

Step-by-step explanation:

Volume of Cylinders:

Cylinder volume: Considering that;

14 feet is the cylindrical tank's diameter.

The cylindrical tank is 40 feet long.

Find:

how much gas is in the tank.

Computation:

14 feet is the cylindrical tank's diameter.

Tank's cylinder's radius is 14/2, or 7 feet.

Volume of the tank: x amount of gas inside it

Volume of gas in the tank equals πr²h.

Portion of gas in the tank = (3.14)(7)²(40)

Fuel level in tank equals (3.14)(49) (40)

6154.4 feet³ of gas have been filled into the tank.

(Hope this helped!)

Bear Mountain Summer Camp opened last year and had 650 campers. After doing some advertising in the off-season, the camp has enrolled 676 campers for this year, and enrollment is expected to continue increasing each year. Write an exponential equation in the form y = a(b) that can model the number of campers, y, x years after the camp opened. Use whole numbers, decimals, or simplified fractions for the values of a and b.​

Answers

The number of campers is y = 650(676/650)^x

What is exponential equation ?

Exponential equations are equations in which variables occur as exponents.

An exponential equation in the form y = a(b)^x can be used to model the number of campers, y, x years after the camp opened. Let's use x = 0 for the first year the camp opened (last year) and x = 1 for this year.

Then, we have:

y = a(b)^0 = 650 (when x = 0)

y = a(b)^1 = 676 (when x = 1)

We can use these two points to solve for the values of a and b.

First, we'll use the first equation to solve for a:

a = 650

Next, we'll use the second equation to solve for b:

676 = 650(b)^1

676/650 = (b)^1

b = 676/650

So, the exponential equation in the form y = a(b)^x that can model the number of campers is:

y = 650(676/650)^x

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the radius of a circle increases at a rate of 12ms. find the rate, in m2s, at which the area of the circle is increasing when the radius is 7 m.

Answers

The rate at which the area of the circle is increasing when the radius is 7 m is 527.52 m^2.

We already know that the area of a circle can easily be calculated using the formula -

= A = π(r^2)

So, in order to find out the rate at which it increases, we have to -

= dA/dt = dπ(r^2)/dt

= dA/dt = dπ(r^2)/dr × dr/dt

= dA/dt = 2πr × dr/dt

It has been mentioned that the value of dr/dt is 12 m/s.

So, after using this value, we find that the rate of increase is -

= dA/dt = 2π × 7 × 12

= dA/dt = 527. 52 m^2

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