If f(x) is differentiable for the closed interval [-1, 4] such that f(-1) = -3 and f(4) = 12, then there exists a value c, -1 < c < 4 such that: A) f'(c) = 3 B) f'(c) = 0 C) f(c) = -15 D) f(c) = 3

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.

Step-by-step explanation:

Answer: the monthly​ payment is $192

Step-by-step explanation:

The cost of the new home entertainment system is $14230.

If the down payment is ​$2300, then the balance to be paid would be

14230 - 2300 = $11930

We would apply the periodic interest rate formula which is expressed as

P = a/[{(1+r)^n]-1}/{r(1+r)^n}]

Where

P represents the monthly payments.

a represents the amount of the balance

r represents the annual rate.

n represents number of monthly payments. Therefore

a = $11930

r = 0.05/12 = 0.0042

n = 72 months

Therefore,

P = 11930/[{(1+0.0042)^72]-1}/{0.0042(1 + 0.0042)^72}]

11930/[{(1.0042)^72]-1}/{0.0042(1.0042)^72}]

P = 11930/{1.352 -1}/[0.0042(1.352)]

P = 11930/(0.353/0.0056784)

P = 11930/62.125

P = $192

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:

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:

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.

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: 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:

12 ??

Step-by-step explanation:

Answer:

12 cubic units

Step-by-step explanation:

1. Multiply 4 and 3

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:

Hello There!

~~~~~~~~~~~

(2x + y) (2x - y) =

[tex]4x^{2} - y^{2}[/tex]

Step-by-step explanation: Simplify the expression.

Hope this helped you. Brainliest would be nice!

☆_____________❤︎______________☆

Answer:

Step-by-step explanation:

there is  formula (a+b)(a-b)=a^2-b^2

(2x+y)(2x-y)=(2x)^2-y^2=4x^2-y^2

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:

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]

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:

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:

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:

The correct options are;

1) Continue walking 5 dogs per week, but increase his rate to $5 per dog

4) Double the amount of dogs walked per week but  keep the same rate of $3 per dog

Step-by-step explanation:

The parameters given are;

Jonah is hoping to earn $200 from 8 weeks of dog walking

Therefore, Jonah has to make $200/8 per week or $25 per week

1) Continue walking 5 dogs per week, but increase his rate to $5 per dog

With the above strategy, Jonah will make $5 × 5 = $25 per week which will amount to $25 × 8 = $200 in 8 weeks total

2) Walking 5 dogs per week at $4 per dog = $20 per week and 8 × $20 = $160 in 8 weeks

3) Walking 8 dogs per week at $3 per dog = $24 per week and 8×$24 = $192 in 8 weeks

4) Double the amount of dogs walked per week to 5×2 or 10 dogs per week but keep the same rate of $3 per dog would give him 10 × $3 = $30 per week and 8 × $30 = $240 in 8 weeks

5) Double the amount of dogs walked per week to 5×2 or 10 dogs per week and cut his rate to $2 per dog would give him 10 × $2 = $20 per week and 8 × $20 = $160 in 8 weeks

Therefore, the strategies that would allow Jonah to reach his $200 goal in 8 weeks are;

1) Continue walking 5 dogs per week, but increase his rate to $5 per dog

4) Double the amount of dogs walked per week but  keep the same rate of $3 per dog.

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:

Exponential growth

Step-by-step explanation:

This is not a negative so it is growing.

Hope this helps!

Answer:

6,8

Step-by-step explanation:

Answer:

17 nickels

Step-by-step explanation:

To be able to find the answer, you can say that the sum of the value of each coin multiply for its quantity is equal to 10.08, which you can express as follows:

quarters= 0.25

dimes= 0.10

nickels= 0.05

pennies= 0.01

(0.25*19)+(0.10*39)+(0.05*x)+(0.01*58)=10.08, where

x= the quantity of nickels

Now, you can solve for x:

4.75+3.9+0.05x+0.58=10.08

0.05x=10.08-4.75-3.9-0.58

0.05x=0.85

x=0.85/0.05

x=17

According to this, the answer is that there are 17 nickels in the cup holder.

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:

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.

Learn more about probability here;

https://brainly.com/question/9326835

#SPJ2

Answer: greaterright

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:

The slope is -3/4

Step-by-step explanation:

We need two points to find the slope

We have one point at (0,5) and we have one point at (4,2)

We can use the slope formula

m = (y2-y2)/(x2-x1)

   = (2-5)/( 4-0)

   = -3/4

The slope is -3/4

Answer:

-3/4

Step-by-step explanation:

Get the coordinates of 2 points on the line:

Use formula to find the slope:

So the slope is -3/4

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:

131°.

Step-by-step explanation:

its equal to that other angle i forgot how but i learned this 1 week ago