Solve for x. 2000=500e^4x

Answer:

Solution,

Circumference of circular tank = 44m

Radius = ?

Diameter= ?

Now,

Circumference of a circle = 44

[tex]or \: 2\pi \: r \: = 44[/tex]

[tex]or \: 2 \times 3.14 \times r = 44[/tex]

[tex]or \: 6.28r = 44[/tex]

[tex]or \: r = \frac{44}{6.28} [/tex]

[tex]r = 7.0 \: m[/tex]

Again,

Diameter = 2 radius

= 2 * 7.0

= 14 m

Hope this helps..

Good luck on your assignment..

Answer:

2×3.14×r=44

6.28r=44

r=44/6.28

r=7.0

d=r

2×7.0

14

Answer: 4:3.

Step-by-step explanation:

Given: Point P is [tex]\dfrac{4}{7}[/tex] of the distance from M to N.

To find: The ratio in which the point P partition the directed line segment from M to N.

If Point P is between points M and N, then the ratio can be written as

[tex]\dfrac{MP}{MN}=\dfrac{MP}{MP+PN}[/tex]

As per given,

[tex]\dfrac{MP}{MP+PN}=\dfrac{4}{7}\\\\\Rightarrow\ \dfrac{MP+PN}{MP}=\dfrac{7}{4}\\\\\Rightarrow\ \dfrac{MP}{MP}+\dfrac{PN}{MP}=\dfrac{7}{4}\\\\\Rightarrow\ -1+\dfrac{PN}{MP}=\dfrac{7}{4}\\\\\Rightarrow\ \dfrac{PN}{MP}=\dfrac{7}{4}-1=\dfrac{7-4}{4}=\dfrac{3}{4}\\\\\Rightarrow\ \dfrac{PN}{MP}=\dfrac{3}{4}\ \ \or\ \dfrac{MP}{PN}=\dfrac{4}{3}[/tex]

Hence, P partition the directed line segment from M to N in 4:3.

Answer:

1/16

Step-by-step explanation:

Total = 32 footballers

25 stretch regularly.

3 injure last year

now, 22 stretch regularly.

out of 32, 8 are injured. Therefore, 32-8=24 should stretch regularly but only

22 stretch regularly. Therefore, 24-22 =2 are not stretching regularly.

fraction of players are not stretching regularly = 2/32 =1/16

Answer:

Both expressions equal 5 when substituting 2 for x because both expressions are equivalent

Step-by-step explanation:

Given

[tex]\frac{1}{2}x + 4[/tex] - Expression 1

[tex]x + 6 - \frac{1}{2}x - 2[/tex] -- - Expression 2

Required

Find the result of both expressions when [tex]x = 2[/tex]

Expression 1

[tex]\frac{1}{2}x + 4[/tex]

Substitute [tex]x = 2[/tex]

[tex]\frac{1}{2} * 2 + 4[/tex]

[tex]1 + 4[/tex]

[tex]Result = 5[/tex]

Expression 2

[tex]x + 6 - \frac{1}{2}x - 2[/tex]

Substitute [tex]x = 2[/tex]

[tex]2 + 6 - \frac{1}{2} * 2 - 2[/tex]

[tex]2 + 6 -1 -2[/tex]

[tex]Result = 5[/tex]

Answer:

Putting it short: Both expressions equal 5 when substituting 2 for x because both expressions are equivalent

Step-by-step explanation:

Answer:

∠A ≅ ∠E

Step-by-step explanation:

The AAS (Angle-Angle -Side) congruence theorem implies that triangles ABC and EDC are congruent if both have equal two angles and a non included side.

In the given figures,

<ACB ≅ <ECD (vertical opposite angles)

BC ≅ DC (congruence property)

<ABC ≅ <EDC (alternate angles property)

∠A ≅ ∠E (alternate angle property)

With respect to AAS congruence theorem, ∠A ≅ ∠E is the correct option.

Answer:

-2x⁴+4x³+10x²+8x-4

Step-by-step explanation:

Standard form for a polynomial is from highest power to lowest power

4x³-2x⁴+8x+10x²-4

-2x⁴+4x³+10x²+8x-4

Answer:

[tex] \frac{97pi}{18} m [/tex]

Step-by-step Explanation:

==>Given:

radius (r) = 10 m

m<VCW = 97°

==>Required:

Length of arc VW

==>Solution:

Formula for length VW is given as 2πr(θ/360)

Using the formula, Arc length = 2πr(θ/360), find the arc length VW in the given circle

Where,

θ = 97°

r = radius of the circle = 10 m

Thus,

Arc length VW = 2*π*10(97/360)

Arc length VW = 20π(97/360)

Arc length VW = π(97/18)

Arc length VW = 97π/18 m

Our answer is,

[tex] \frac{97pi}{18} m [/tex]

Answer: greaterright

Step-by-step explanation:

Question

An octagon has a side length of 15 feet and an area of 1089.6 ft²

Find the area of a smaller octagon that has a side length of 7 feet.

Answer:

237.3ft²

Step-by-step explanation:

We are given two octagons in the above question.

Side length of larger octagon = 15 ft

Area of larger octagon = 1089.6 ft²

The area of a smaller octagon = X

Side length of smaller octagon = 7 ft.

We solve for this using scale factor

Scale factor(k) = ratio of the side length of the octagon = smaller side length/ larger side length

k = 7/15

It is important to note that

The square of the scale factor k = ratio of the areas of the octagon

Hence,

k² = X/1089.6 ft²

(7/15)² = X/1089.6 ft²

7²/15² = X/1089.6 ft²

Cross Multiply

15² × X = 7² × 1089.6ft²

X = 7² × 1089.6ft²/15²

X = 237.29066667ft²

Approximately, the area of the smaller octagon = 237.3ft²

The answer is the second image from left to right (B). Examples of direct and inverse variations are showed in the image below. :)

Answer:

Exponential growth

Step-by-step explanation:

This is not a negative so it is growing.

Hope this helps!

Step-by-step explanation:

Answer:

See Attached Image, Explanation in order to understand how to calculate is below.

Step-by-step explanation:

The Jar Contains 20 Coins.

The probability that it is a 1p coin is 1/5

The probability that it is a 2p coin is 1/2

The total value of the coins in the jar is 59 pence.

The Section in bold is vitally important in this question.

We know we have 4 combinations of 1p, 2p , 5p & 10p in order to make 59p, and only have 20 coins to make it.

--------------------------------------------------------------------------------------------------------------

Calculate 1p:

1/5 of 20 = 4

We know the answer is 4 as we have 20 coins, you find 1/5 of 20.

Calculate 2p:

1/2 of 20 = 10

We know the answer is 10 as we have 20 coins, you find 1/2 of 20.

10 (2p Coins) + 4 (1p coins) = 14

20 coins - 14 (2p & 1p coins) = 6.

Now we only have 6 remaining coins for both 5p and 10p.

Calculate 5p:

We know we currently have a total of 24p if we subtract that from 59 we are left with 35.

So we can work establish here that we are not going to need many 10p's. As we only have 6 coins left!.  

5x5 = 25p.

Therefore you need 5, 5p's

Calculate 10p:

With 1 pence left out of the 20, we need 1 10p.

--------------------------------------------------------------------------------------------------------------

Hope this helps, mark as brainilest if found useful.

There are 1 10p coin of each type in the jar.

Given that ;

The Jar Contains 20 Coins.

Probability that it is a 1p coin is 1/5

Probability that it is a 2p coin is 1/2

The total value of the coins in the jar is 59 pence.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

We know we have 4 combinations of 1p, 2p , 5p & 10p. so to make 59p, and only have 20 coins to make it.

Calculate 1p:

1/5 of 20 = 4

The answer is 4 as we have 20 coins, find 1/5 of 20.

Calculate 2p:

1/2 of 20 = 10

The answer is 10 as we have 20 coins, you find 1/2 of 20.

10 (2p Coins) + 4 (1p coins) = 14

20 coins - 14 (2p & 1p coins) = 6.

Now we only have 6 remaining coins for both 5p and 10p.

Now Calculate 5p:

We know that we have a total of 24p if we subtract that from 59 we are left with 35

5x5 = 25p.

Therefore we need 5, 5p's

Now Calculate 10p:

With 1 pence left out of the 20, we need 1 10p.

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Answer:

Hey there!

Eight years ago, Manuel's age was 36/2, or 18.

Now, his age is 18+8, or 26 years old.

So, he is 26 years old now.

Hope this helps :)

Answer:

B. The amount spent on grapes compared with the weight of the purchase.

Step-by-step explanation:

A: The shoe size of a young girl compared with her age in years. For the first few years of a girl's life, her shoe size is relatively the same. When she goes through a growth spurt, her shoe size increases exponentially. So, that is not a constant rate of change.

B: The amount spent on grapes compared with the weight of the purchase. In most grocery stores, grapes are sold based on their weight, like $2.50 per pound. With each increase in 1 pound, the cost increases by $2.50. That is a constant rate of change.

C: The number of people on a city bus compared with the time of day. This value widely changes throughout the day. For example, during rush hour, there will be many people. But during times at, say, 2 to 3 AM, there will not be many people. So, this is not a constant rate of change.

D: The number of slices in a pizza compared with the time it takes to deliver it. The number of slices in a pizza never changes, so it does not depend on the time it takes to deliver. There is no rate of change.

So, B is your answer.

Hope this helps!

Answer:

B

Step-by-step explanation:

i just did it

Answer:

a. [tex] 4*10^{-5} [/tex]

b. [tex] 5*10^{-5} [/tex]

c. [tex] 6*10^{-6} [/tex]

d. [tex] 8*10^{-10} [/tex]

Step-by-step explanation:

To write the above given numbers in standard form, all you need to do is count how many places you have to move the decimal point till you get to a non-zero digit. The number of places you move the decimal point to the right would determine the value of the negative power you would raise to 10.

a. 0.00004:

To place our decimal point after the first non-zero digit in this number given, we would have to move the decimal point to 5 places. The digit 4, would now be multiples by 10 raised to the negative power of 4.

The standard form would be: [tex] 4*10^{-5} [/tex].

Now let's check if we're correct.

[tex] 4*10^{-1} = 4*\frac{1}{10^5} = 4*\frac{1}{100,000} = 4*0.00001 = 0.00004 [/tex]

Follow same procedure as shown above to  write the rest numbers in standard form.

You should have the following as their standard form:

b. [tex] 0.00005 = 5*10^{-5} [/tex]

c. [tex] 0.000006 = 6*10^{-6} [/tex]

d. [tex] 0.0000000006 = 8*10^{-10} [/tex]

Answer: 3 < t < 4

Step-by-step explanation:

Given the following information :

Initial Velocity of projectile = 112 ft/s

Height (h) above the ground after t seconds :

h = –16t2 + 112t

To calculate the time when h exceeds 192 Feets (h >192)

That is ;

-16t^2 + 112t = > 192

-16t^2 + 112t - 192 = 0

Divide through by - 16

t^2 - 7t + 12 = 0

Factorizing

t^2 - 3t - 4t + 12 =0

t(t - 3) - 4(t - 3) = 0

(t-3) = 0 or (t-4) =0

t = 3 or t=4

Therefore, t exist between 3 and 4 for height in excess of 192ft

–16(3)^2 + 112(3) = 192 feets

–16(4)^2 + 112(4) = 192 feets

3 < t < 4

Answer:

120.00

Step-by-step explanation:

Let x be the original price

The price is 10% off, or we pay 90% of the original price

.9 x

Then we have to pay 7% sales tax

.9x * 7%

.9x * .07

.063x is the tax

Add this to the .9x we have to pay for the jacket

.9x + .063x = .963x

This is the cost of the jacket

.963x = 115.56

Divide each side by.963

.963x/.963 = 115.56/.963

x =120.00

The cost of the jacket before discount and tax is 120.00

Answer: The tank which has 3 m side.

Step-by-step explanation: A cube is a form that has equal sides. To calculate the volume of it, multiply all three sides:

V = length*width*height

Since they are all the same, volume will be:

V = s³

One tank has a 3 m side, so its volume is:

V = 3³

V = 27 m³

The other has half of the first one side, then s = [tex]\frac{3}{2}[/tex] and volume will be:

V = [tex](\frac{3}{2})^{3}[/tex]

V = [tex]\frac{27}{8}[/tex] m³

As you can see, the volume of the second tank is [tex]\frac{1}{8}[/tex] smaller than the first one. Therefore, the tank which has 3 m side can store more water than the  tank with side measuring half of the first.

Answer:

7.87?

Step-by-step explanation:

Answer:

a) DE is 12 cm

b) CE is 2 cm

Step-by-step explanation:

In the two triangles [tex]\triangle ABC[/tex] and [tex]\triangle ADE[/tex].

[tex]\angle A[/tex] is common.

BC || DE

[tex]\Rightarrow \angle B = \angle D\ and \\ \Rightarrow \angle C = \angle E[/tex]

[tex]\because[/tex] two parallel lines BC and DE are cut by BD and CE respectively and the angles are corresponding angles.

All three angles are equal hence, the triangles:

[tex]\triangle ABC[/tex] [tex]\sim[/tex] [tex]\triangle ADE[/tex].

Ratio of corresponding sides of two similar triangles are always equal.

[tex]\dfrac{AB}{AD} = \dfrac{BC}{DE}\\\Rightarrow \dfrac{9}{9+3} = \dfrac{9}{DE}\\\Rightarrow \dfrac{9}{12} = \dfrac{9}{DE}\\\Rightarrow DE = 12\ cm[/tex]

[tex]\dfrac{AB}{AD} = \dfrac{AC}{AE}\\\Rightarrow \dfrac{9}{9+3} = \dfrac{6}{AC+CE}\\\Rightarrow \dfrac{9}{12} = \dfrac{6}{6+CE}\\\Rightarrow 6+CE = \dfrac{4\times 6}{3}\\\Rightarrow 6+CE = 8\\\Rightarrow CE = 2\ cm[/tex]

So, the answers are:

a) DE is 12 cm

b) CE is 2 cm

Answer:

Perimeter = 22

Step-by-step explanation:

To find the perimeter, we will follow the steps below:

A = (-1,-1), B = (2,3), C = (5,3), D = (8,-1).

First, we will find the distance AB

A = (-1,-1), B = (2,3)

|AB| = √(x₂-x₁)²+(y₂-y₁)²

x₁ = -1    y₁=-1     x₂=2     y₂=3

we can now proceed to insert the values into the formula

|AB| = √(x₂-x₁)²+(y₂-y₁)²

      = √(2+1)²+(3+1)²

      = √(3)²+(4)²

      = √9 + 16

      =√25

      = 5

|AB| = 5

Next, we will find the distance BC

B = (2,3), C = (5,3),

|BC| = √(x₂-x₁)²+(y₂-y₁)²

x₁ = 2    y₁=3    x₂=5     y₂=3

we can now proceed to insert the values into the formula

|BC| = √(x₂-x₁)²+(y₂-y₁)²

      = √(5-2)²+(3-3)²

      = √(3)²+(0)²

      = √9 + 0

      =√9

      = 3

|BC|=3

Next, we will find the distance CD

C = (5,3), D = (8,-1).

|CD| = √(x₂-x₁)²+(y₂-y₁)²

x₁ = 5    y₁=3    x₂=8    y₂=-1

we can now proceed to insert the values into the formula

|CD| = √(x₂-x₁)²+(y₂-y₁)²

      = √(8-5)²+(-1-3)²

      = √(3)²+(-4)²

      = √9 + 16

      =√25

      = 5

|CD|=5

Next, we will find the distance DA

D = (8,-1)      A = (-1,-1)

|DA| = √(x₂-x₁)²+(y₂-y₁)²

x₁ = 8    y₁=-1   x₂=-1    y₂=-1

we can now proceed to insert the values into the formula

|DA| = √(x₂-x₁)²+(y₂-y₁)²

      = √(-1-8)²+(-1+1)²

      = √(-9)²+(0)²

      = √81 + 0

      =√81    

      = 9

|DA|=9

PERIMETER = |AB|+|BC|+|CD|+|DA|

                     =5 + 3+5 +9

                     =22

Perimeter = 22

Answer:

Infinite solutions

Step-by-step explanation:

Both lines have the same slope and y-intercept, therefore they are the same line and intersect at all points, resulting in infinite solutions.

Answer

y= 12.5x + 210,000

Step-by-step explanation:

This is a linear function because it is increasing constantly by 12.5 percent so it will me written as y=mx+b

The value of function that represents the situation is,

⇒ P = 210,000 (1.125)ⁿ

Where, n is number of years.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The situation is,

⇒ A population of 210,000 increases by 12.5% each year​.

Now, Let number of years = n

Hence, The value of function that represents the situation is,

⇒ P = 210,000 (1 + 12.5%)ⁿ

⇒ P = 210,000 (1 + 0.125)ⁿ

⇒ P = 210,000 (1.125)ⁿ

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Answer:

  8 pounds

Step-by-step explanation:

Let a, b, c represent the number of pounds of nuts in the first, second, and third boxes, respectively. We can write the equations ...

  a = b +c -6 . . . . . first box has 6# fewer than the total of the others

  b = a +c -10 . . . . second box has 10# fewer than the total of the others

Substituting the second equation into the first, we find ...

  a = (a +c -10) +c -6

  0 = 2c -16 . . . . subtract a

  0 = c -8 . . . . . . divide by 2

  8 = c . . . . . . . . . add 8

There are 8 pounds of nuts in the third box.

Answer:

6,8

Step-by-step explanation:

Answer:

Measure of angle T = 25 degrees and TU = 12

Step-by-step explanation:

Tamar is measuring the sides and angles of Triangle T U V to determine whether it is congruent to the triangle below. For triangle K L M, side K M is 27 millimeters, side L M is 20 millimeters, and side K L is 12 millimeters. Angle K is 45 degrees, angle M is 25 degrees, angle L is 110 degrees. Which pair of measurements would eliminate the possibility that the triangles are congruent? Measure of angle T = 25 degrees and Measure of angle U = 45 degrees Measure of angle T = 110 degrees and Measure of angle V = 25 degrees Measure of angle T = 25 degrees and TU = 12 Measure of angle T = 110 degrees and UV = 27

Answer:  Two triangles are congruent to each other if they have the same shape and size (i.e the same sides and angles).

The ways used to find congruence are:

1) Angle-side-angle: If two angles and an included side of a triangle is equal to the two angles and corresponding side of another triangle, then they are equal.

2) Side-side-side: If all three sides of a triangle is equal to the three sides of another triangle, then the two triangles are congruent.

3) Side angle side: If two sides and an included angle of a triangle is equal to the two sides and corresponding angle of another triangle, then they are equal.

4) Hypotenuse - leg: If the hypotenuse and one leg of a triangle is equal to the hypotenuse and leg of another triangle then they are equal.

5) Angle angle side: If two angles and an non included side of a triangle is equal to the two angles and corresponding side of another triangle, then they are equal.

Measure of angle T = 25 degrees and TU = 12 would eliminate the possibility that the triangles are congruent because if T = 25°, then the side opposite angle T (UV) is suppose to be 12

Answer:

the answer is C

Step-by-step explanation:

I got it right on my final exam on edge

Answer:

12 ??

Step-by-step explanation:

Answer:

12 cubic units

Step-by-step explanation:

1. Multiply 4 and 3

Answer:

a. Domain = All real numbers

Range = y ≥ 2

b. Domain = -4 < x ≤ 4

Range = 0 ≤ y < 4

Answer:

Y= 8*x

Step-by-step explanation:

You can notice that the graph is a straight line that crosses the origin so it's a graph that has an equation written this way : y= a*x

a is the slope

You can easily find it by notice that the image of 1 is 8

So a = 8

Then y= 8*x

Answer:

[tex]y=8x[/tex]

Step-by-step explanation:

Well drawing the line further then we can tell the y intercept is 0.

So we have to find the SLOPE using the following formula

[tex]\frac{y^2-y^1}{x^2-x^1}[/tex]

So we need two points on the line, we can use the following

(1,8) and (2,16)

So 16 is y2 and 8 is y1 so 16-8 is 8.

2-1 is 1.

So the slope is 8x.

Do the equation is [tex]y=8x[/tex]

We don’t have to put the y intercept because it is 0.