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laila [671]
3 years ago
14

Determine whether the relationship between the circumfrance of a circle and its diameter is a direct variation. If so, identify

the constant of proportionality. Justify your response.
Mathematics
1 answer:
kipiarov [429]3 years ago
3 0

Answer:

The relationship between the circumference of a circle and its diameter represent  a direct variation and the constant of proportionality is equal to the constant \pi

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y=kx

where K is the constant of proportionality

In this problem we know that

The circumference of a circle is equal to

C=\pi D

therefore

the relationship between the circumference of a circle and its diameter is a direct variation and the constant of proportionality is equal to the constant \pi

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A tree is currently 8 feet tall and growing at a rate of 3 feet per year. How tall will the tree be in 12 years?
aleksandr82 [10.1K]

Answer:

44

Step-by-step explanation:

3 x 12 =36

36+8 =44

so the answer is 44 ft tall remember to include ft tall

4 0
3 years ago
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Could someone help me with this?
natulia [17]
Distributive property was the first property used in STEP 1, where -4 was distributed to -3x+ 2 resulting in the equation in STEP 1. Next in STEP 2, commutative property of addition no matter how 12x and 6x are arranged, when you add them together the result will be the same. 
*Take note that 12x and 6x are put together because they are like terms. 

For Steps 3 and 4, you will see that the addition property of equality was used in STEP 3. To keep the equation equal, you will add the same number on both sides.

STEP 4 uses Division property of Equality. Like Step 3, to keep both sides of the equation equal, you must divide both sides with the same number. It keeps the statement true by doing so. 

STEP 4 and 5 uses transitive property if you examine both as a whole. 
Transitive property assumes that if a = b and b = c, then a = c

If   18/18 (a) = 1 (b),  and x (c) = 18/18(a)  then, x (c) = 1 (b). 
5 0
3 years ago
Find the volume of the given prism. Round to the nearest tenth if necessary.
BigorU [14]

Answer: 616

Explanation:

When finding the volume of an object use: LxWxH

L=14

W=11

H=4

Now multiply 14x11x4=616


-LizzyIsTheQueen

4 0
3 years ago
Solve for x. mx2 + y e = b
m_a_m_a [10]
X=(b/2m)*y-e is the answer I believe.
7 0
3 years ago
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The information below is the number of daily emergency service calls made by the volunteer ambulance service of Walterboro, Sout
mafiozo [28]

Answer:

Step-by-step explanation:

Hello!

The variable of interest is

X: The number of emergency service calls made by the volunteer ambulance service of Walterboro, South Carolina for 50 days.

a)

In the first column, you have the possible number of emergency calls made, in the second column, you have the observed absolute frequency (fi) for each value of the variable.

To establish the probability distribution you have to calculate the relative frequency (hi) for each value of X.

The formula for the relative frequency is

hi= fi*n where i= 0, 1, 2, 3, 4

X₁= 0

f₁= 8

h₁= 8/50= 0.16

X₂= 1

f₂= 10

h₂= 0.20

X₃= 2

f₃= 22

h₃= 22/50= 0.44

X₄= 3

f₄= 9

h₄= 9/50= 0.18

X₅= 4

f₅= 1

h₅= 1/50= 0.02

(See attachment)

b)

The variable of interest is a cuantitative discrete variable, so this is an example of a driscrete distribution.

Discrete variables are numerical and take certain numbers within its range of definition, contrary to the continuous variables that can take any value within the range of definition of the variable.

Another example of a discrete variable is "the money", If the variable is "I have at most 10 dollars in my wallet", the range of definition goes from 0 dollars to 10 dollars.

c) To calculate the mean when the data is arranged in a frequency table you have to use the following formula:

X[bar]= ∑Xihi= (0*0.16)+(1*0.2)+(2*0.44)+(3*0.18)+(4*0.02)= 1.7

This means that they expect an average of 1.7 calls per day.

d) The formula for the standard deviation is:

S=\sqrt{\frac{1}{n-1}[sumX^2fi-\frac{(sumXfi)^2}{n} ] }

∑X²fi= (0²*8)+(1²*10)+(2²*22)+(3²*9)+(4²*1)=  195

∑Xfi= (0*8)+(1*10)+(2*22)+(3*9)+(4*1)= 85

S=\sqrt{\frac{1}{49}[195-\frac{(85)^2}{50} ] }= 1.015

I hope this helps!

3 0
3 years ago
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