Solve
7 1/2 ÷ (4 1/2 - 5 1/8)

Answer:

no it is not a proportional relationship

It will take the town 21 years 4 months to reach 4600 in population

a rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

initial population = 3000

population increase every year = 2.5% of 3000

which is 2.5/100 x 3000 = 75

let the time taken to reach 4600 be d

increment for d number of years = 75d

Total population after d years is 75d + 3000

so 75d + 3000 = 4600

75d = 4600  - 3000

75d = 1600

d = 1600/75

d = 21.33 years which is 21 years 4 months

In conclusion 21 years 4 months is the time taken for the ton tto get tto 4600

Learn more about rate: https://brainly.com/question/24304697

#SPJ1

The interval where the derivative function f'(x) has a relative maximum is -2.478 and 1.732 (B) only.

To find the relative maximum of a function, we need to find the critical points of the derivative function. Critical points are where the derivative function is equal to zero or undefined. In this case, the derivative function is f'(x) = sin(x^2 − 3).

To find the critical points, we need to set the derivative function equal to zero and solve for x:
sin(x² − 3) = 0

x² − 3 = nπ, where n is an integer

x² = nπ + 3

x = ±√(nπ + 3)

We need to find the values of x that are in the interval −3 < x < 3. By plugging in different values of n, we can find the critical points in this interval:

n = 0: x = ±√3 ≈ ±1.732

n = 1: x = ±√(π + 3) ≈ ±2.478

n = 2: x = ±√(2π + 3) ≈ ±2.915 (not in the interval)

So the critical points in the interval are -2.478, -1.732, 1.732, and 2.478.

To determine which of these are relative maximums, we need to look at the sign of the derivative function on either side of the critical points. If the derivative function changes from positive to negative at a critical point, then that point is a relative maximum.

At x = -2.478, the derivative function changes from positive to negative, so this is a relative maximum.

At x = -1.732, the derivative function changes from negative to positive, so this is not a relative maximum.

At x = 1.732, the derivative function changes from positive to negative, so this is a relative maximum.

At x = 2.478, the derivative function changes from negative to positive, so this is not a relative maximum.

Therefore, the values of x in the interval −3 < x < 3 where f has a relative maximum are -2.478 and 1.732.

Learn more about Derivative Function here: brainly.com/question/25752367

#SPJ11

Answer:

Step-by-step explanation:

How to Solve for l: s=l+w

if s = l + w

l = s - w

Answer:

The answer is n⊥m I think.

Answer: 89

the 18th term is 4 + (18 - 1).5 = 4 + 17.5 = 89

Step-by-step explanation:

Answer:

89

Step-by-step explanation:

formula: Tn= a+(n-1)d

T89= 4+(18-1)*5

T89= 4+(17*5)

4+85

=89

hoped this helped:)

Answer: k= -10x+12

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Convert any mixed numbers to fractions.

Then your initial equation becomes:

463/3÷23/6(fraction)

Applying the fractions formula for division,

=46×63×23(fraction)

=27669(fraction)

Simplifying 276/69(fraction), the answer is

=4

Answer:

\(\displaystyle 4\)

Step-by-step explanation:

Transform the mixed numbers into improper fractions:

\(\displaystyle 15\frac{1}{3} \div 3\frac{5}{6} \hookrightarrow \frac{46}{3} \div \frac{23}{6} \rightarrow \frac{2}{\frac{1}{2}} \\ \\ \boxed{4}\)

I am joyous to assist you at any time.

Answer:

6560

Step-by-step explanation:

add them all up that's what sum means

The set can be described as {-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

{x €R[x² = 3} can be described by listing its elements as: {√3, -√3}. Thus, the set can be described as {√3, -√3}.2. {m € Zm² = 3} can be described by listing its elements as:

This set has no elements as there are no integers whose square is equal to 3. Thus, the set can be described as {} or the null set.3.

{m Zmn = 60 for some n € Z} can be described by listing its elements as: This set has an infinite number of elements.

Some of them are:

{1,60}, {2,30}, {3,20}, {4,15}, {5,12}, {6,10}, {-1,-60}, {-2,-30}, {-3,-20}, {-4,-15}, {-5,-12}, and so on.

The set can be described as

{(-n, -60/n), (n, 60/n)| n € Z - {0}}.4. {m € Z m² m < 115}

can be described by listing its elements as:

{-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

To learn more about set, visit:

https://brainly.com/question/30096477

#SPJ11

Answer:

£200

Step-by-step explanation:

Let the original price of the camera be x.

The 10% discounted price of the camera is £180. This means that 10% of x was deducted from x to give £180:

x - (10/100 * x) = 180

x - 0.1x = 180

0.9x = 180

x = 180 / 0.9 = £200

The pre-sale price was £200.

Answer:

The perimeter of parallelogram WXYZ is 2√5 + 2√17 units or also known as about 12.72 units.

Step-by-step explanation:

In the diagram, we have a parallelogram. A parallelogram is a shape with two pairs of congruent sides. So, this means that we only need to find the measurement of two sides. From there, we are going to multiply those individual measurements by 2 because both has another side that is congruent  to them. Lastly, we will add up all of the measurements to find the perimeter.

We can find the lengths by using the distance formula.

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_2)^2}\)

Let's find the length of WX.

\(WX=\sqrt{(4-0)^2+(0-(-1))^2}\)

\(WX=\sqrt{((4)^2+(1)^2)}\)

\(WX=\sqrt{16+1}\)

\(WX=\sqrt{17}\)

Now, we multiply this number by 2 because ZY is congruent to this side.

√17 × 2 = 2√17

Now, let's find the length of WZ.

\(WZ=\sqrt{(0-(-1))^2+(-1-(-3))^2}\)

\(WZ=\sqrt{(1)^2+(2)^2}\)

\(WZ=\sqrt{1+4}\)

\(WZ=\sqrt{5}\)

Now, we multiply this number by 2 because XY is congruent to this side.

√5 × 2 = 2√5

Now, we add these numbers together to get the perimeter.

2√5 + 2√17 = 12.72

The required perimeter of parallelogram WXYZ is \(2\times \sqrt5 + 2\times \sqrt17 \ units\).

We have to determine, The perimeter of parallelogram WXYZ.

According to the question,

A parallelogram is a shape with two pairs of congruent sides. So, this means need to find the measurement of two sides.

From there, multiply those individual measurements by 2 because both has another side that is congruent  to them. Lastly, add up all of the measurements to find the perimeter.

To find the lengths by using the distance formula,

\(d = \sqrt{(x_2-x_1)^{2}+ (y_2-y_1)^{2}} \\\\WX = \sqrt{(4-0)^{2}+ (0-(-1))^{2}} \\\\WX = \sqrt{16+1} \\\\WX = \sqrt{17}\)

Then, multiply this number by 2 because ZY is congruent to this side.

\(\sqrt{17} \times 2= 2 \sqrt{17}\)

Now, let's find the length of WZ by using distance formula,

\(d = \sqrt{(x_2-x_1)^{2}+ (y_2-y_1)^{2}} \\\\WZ = \sqrt{((-1)-(-3))^{2}+ (0-(-1))^{2}} \\\\WX = \sqrt{4+1} \\\\WX = \sqrt{5}\)

Now, multiply this number by 2 because XY is congruent to this side.

\(=\sqrt{5} \times 2= 2\sqrt{5}\)

Therefore, adding these numbers together to get the perimeter of parallelogram WXYZ,

Perimeter of parallelogram WXYZ  \(=2\times \sqrt5 + 2\times \sqrt17 \ units\)

Hence, The required perimeter of parallelogram WXYZ is \(2\times \sqrt5 + 2\times \sqrt17 \ units\).

To know more about Parallelogram click the link given below.

https://brainly.com/question/14592910

"An arithmetic sequence is a linear function whose domain is restricted to the set of non-negative integers."  

The general form an arithmetic sequence is:

       \(a_{n} = a_{1} + (n- 1) d\)

So, the statement provided is True.

Learn more about arithmetic sequence

brainly.com/question/10396151

#SPJ4

The polynomial function has zeros when x=-2,3/4,5 is option D  f(x)=(x+2)(4x-3)(x-5), according to the question.

What do you mean by function?

A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

According to the given question,

We have the given options are:

A f(x)=(x-2)(3x+4)(x+5)

B f(x)=(x-2)(4x+3)(x+5)

C f(x)=(x+2)(3x-4)(x+5)

D f(x)=(x+2)(4x-3)(x-5)

We will putting given x=-2,3/4,5 in the given functions one by one,

Option A,B and C are not the required polynomial function.

Now, we will show that the option D is the required polynomial function.

Putting x=-2,

f(x)=(x+2)(4x-3)(x-5)

f(-2)=(-2+2)(4(-2)-3)(-2-5)

= (0)(-8-3)(-7)

= 0

Then, putting x=3/4,

f(x)=(x+2)(4x-3)(x-5)

f(3/4)=((3/4)+2)(4(3/4)-3)((3/4)-5)

\(=(\frac{3+8}{4} )(\frac{12-12}{4} )(\frac{3-20}{4} )\\\\=(\frac{3+8}{4} )(0 )(\frac{3-20}{4} )\\=0\)

Then, putting x=5,

f(x)=(x+2)(4x-3)(x-5)

f(5)=(5+2)(4(5)-3)(5-5)

= (5+2)(4(5)-3)(0)

= 0

Therefore, the polynomial function has zeros when x=-2,3/4,5 is option D  f(x)=(x+2)(4x-3)(x-5).

To learn more about function, visit:

brainly.com/question/5975436?referrer=searchResults

#SPJ1

x = 2

Answer:

x = 2

Step-by-step explanation:

Each triangle is made up of 2 radii (each of 5 units in length) and an included 30° angle.  

Therefore, the triangles are congruent.

So, DC = AB ⇒ x = 2

Answer:

1 - 3090

2 - 12

3 - 2.16

Step-by-step explanation:

hope you find this helpful...

The maximum possible number of handshakes that can happen at the party with 23 people with at most 22 other people is 253. This is calculated by combination.

Twenty-three people attend a party. each person shakes hands with at most 22 other people.

To find the maximum possible number of handshakes, assuming that any two people can shake hands at most once, we need to use Combination by finding the number of unique pairs of people in the party.

nCr (combination) to find the number of unique pairs of people.

Therefore,\(^nC_r = \frac{n!}{(n-r)!  r!}\)

where n is the total number of people and r is the number of people in a handshake at a time.

Therefore, the number of unique pairs of people that can shake hands at most once is:

\(^{23}C_2 = \frac{23!}{(23-2)!  (2!)}\) \(=\frac{23 X22}{2} = 253\)

Hence, the maximum possible number of handshakes that can happen at the party is 253.

Learn more about Combination here:

https://brainly.com/question/13387529

#SPJ11

Answer:

\(343\)

Step-by-step explanation:

\(1^{3} =1\\2^{3} =8\\3^{3} =27\\4^{3} =64\\5^{3} =125\\6^{3} =216\\7^{3} =343\\8^{3} =512\)

\(\sqrt[3]{x } >500\)

\(\sqrt[3]{343} >500\)

Answer:

time = 70 minutes

Step 1

Given;

Required; Solve the following exponential equation. Express your answer as both an exact expression and a decimal approximation rounded to two decimal places.

Step 2

Solve the equation

Answer;

Answer:

4. rise

match the following definition with the correct term:

the vertical distance between two points on a line

1. run

2. rate of run

3. slope

4. rise

Regarding the exponential function y = 3(2)^x, we have that:

An exponential function is defined as follows:

y = ab^(x/n).

In which the parameters are defined as follows:

The function for this problem is given as follows:

y = 3(2)^x.

Hence the parameters are given as follows:

At x = 3, the numeric value of the function is obtained as follows:

y = 3 x 2^3

y = 3 x 8

y = 24.

More can be learned about exponential functions at https://brainly.com/question/30113628

#SPJ1

Answer:

It is a linear.

Step-by-step explanation:

Because after factor the function you will get f(x)= 5x, and the linear function is y=ax.

The dimensions of the garden are 12.5 feet by 30.5 feet.

To model this situation, we can use two equations. Let the width of the rectangular garden be w feet and the length be l feet.

Then:We know that the perimeter of the garden is 90 feet because the amount of fencing used was 90 feet.Perimeter = sum of all sides2(l + w) = 90Divide both sides by 22(l + w)/2 = 45l + w = 45Now,

we also know that the length of the fence, 1, was 5 feet less than 3 times the width,

w.l = 3w - 5Substitute this equation for l in the first equation:3w - 5 + w = 45Simplify:4w - 5 = 45

Add 5 to both sides :4w = 50Divide both sides by 4:w = 12.5

Now that we know the width of the garden is 12.5 feet, we can use the equation for l to find the length:l = 3w - 5l = 3(12.5) - 5l = 30.5

To learn more about : dimensions

https://brainly.com/question/28107004

#SPJ8

Answer:

11

Step-by-step explanation:

11*11 = 121

Answer:

answer is 3.75 step-by-step explanation:

750÷2= 375 ..3.75

Answer:

3.5N

Step-by-step explanation:

140g=0.14kg

F=ma

F=0.14×25

F=3.5N

Answer:

45 sandwiches

Step-by-step explanation:

create a proportion from sandwiches to people equals sandwiches to people

21/14 = s/30

21/14 can be reduced to 3/2

let 's' = # of sandwiches

3/2 = s/30

cross-multiply to get:

2s = 90

s = 45