A company buys a machine for $225,000 that depreciates at a rate of 30% per year. Find a formula for the value of the machine after n years. V(n) =

Answer:

The rate of the heat flow = 1260 π

Step-by-step explanation:

From the information given :

k = 4.5

u(x,y,z) = 5y² + 5z²

Surface cylinder:

y² +z² = 5,     0 ≤ x ≤ 2

[tex]\mathtt{\overline F = \bigtriangledown u = -k(0,10y, 10z )}[/tex]

[tex]\mathtt{\overline F = -4.5(0,10y, 10z )}[/tex]

[tex]\mathtt{\overline F = (0,-45y, -45z ) \ --- (1)}[/tex]

Now parameterizing the surface by :

x = u  , y = [tex]\mathtt{\sqrt{7} \ cos \ t}[/tex]  , z = [tex]\mathtt{\sqrt{7} \ sin \ t}[/tex]

0 ≤ x ≤ 2        ,        0 ≤ t ≤ 2π

[tex]\mathtt{{ \left. \begin{array}{1} \overline{r_y} = (1,0,0) } \\ \\ \overline{r_t} = (0, \ - \sqrt{7}\ sin \ t, \sqrt{7} \ cos \ t) \end{array} \right\} = r_u \times r_t}[/tex]

[tex]\mathtt{\overline r_u \times \overline r_t = ( -0, - \sqrt{7} \ cos \ t , - \sqrt{7} \ sin \ t) --- (2)}[/tex]

Taking integral of both equations; we have:

[tex]\mathtt{= \int ^{2}_0 \int ^{2 \pi}_{0} (0, -45y, -45 z) (0, - \sqrt{7} \ cos \ t, - \sqrt{7} \ sin \ t) \ dtdu}[/tex]

[tex]\mathtt{= \int ^{2}_0 \int ^{2 \pi}_{0} ( 45\sqrt{7} \ y\ cos \ t+ 45 \sqrt{7} \ z \ sin \ t) \ dtdu}[/tex]

[tex]\mathtt{= 45\sqrt{7}\ \int ^{2}_0 \int ^{2 \pi}_{0} (( \sqrt{7} \ cos \ t)cos \ t + (\sqrt{7} \ \ sin \ t) sin \ t) \ dtdu}[/tex]

[tex]\mathtt{= 45\times {7}\ \int ^{2}_0 \int ^{2 \pi}_{0} (1) \ dtdu}[/tex]

= 315 × (2) × (2π)

= 1260 π

Answer:

Yes

Step-by-step explanation:

Yes.  They did exponents and grouping symbols first, then multiplication and division left to right.  Addition came before multiplication and division because it was inside a grouping symbol.

Answer:

£837.5

Step-by-step explanation:

Cost of slabs =  £16.75 / m²

Ordered amount = 50 m²

Total cost:

Total cost of slabs is  £837.5

Answer:

Accept the null hypothesis if it is two tailed test.

Step-by-step explanation:

The null hypotheses can only be accepted if it is a two tailed test and calculated chi square must be less than the critical value of chi square.

Then the difference between the  the observed and expected frequencies will be zero.

where

H0 : σ²-σ²= 0             Ha: σ²-σ²≠0

For this the critical region would be greater than the calculated value of chi square. If so we will accept the null hypothesis and reject the alternative hypothesis.

Answer:

Y= 7.9 lb

X= 10.1 lb

Step-by-step explanation:

The chef orders 2.2 lb more carrots than celery. The two orders weigh 10.8 lb combined.

Let carrot= x

Let celery= y

X+y = 18...... equation one

X= 2.2 +y.... equation two

Substituting the value of x into equation one

2.2 +y +y =18

2y= 18-2.2

2y= 15.8

Y= 7.9 lb

Substituting the value of yinto equation 2

X= 2.2 +y

X= 2.2 + 7.9

X= 10.1 lb

Answer:

Hey there!

In this expression, 5k and -6 are terms, not factors.

In this expression, 5 and k are factors, so the last option is correct.

Let me know if this helps :)

Answer:

5 and k are factors.

Step-by-step explanation:

A factor would be a value or variable which is multiplied by something else. It is 'a part' of the product.

In [tex]5k-6[/tex], 5 and k are being multiplied by each other. This would mean that 5 and k are factors.

Option E should be the correct answer.

Answer:

the rate of change of the water depth when the water depth is 10 ft is;  [tex]\mathbf{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}[/tex]

Step-by-step explanation:

Given that:

the inverted conical water tank with a height of 20 ft and a radius of 8 ft  is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec.

We are meant to find the  rate of change of the water depth when the water depth is 10 ft.

The diagrammatic expression below clearly interprets the question.

From the image below, assuming h = the depth of the tank at  a time t and r = radius of the cone shaped at a time t

Then the similar triangles  ΔOCD and ΔOAB is as follows:

[tex]\dfrac{h}{r}= \dfrac{20}{8}[/tex]    ( similar triangle property)

[tex]\dfrac{h}{r}= \dfrac{5}{2}[/tex]

[tex]\dfrac{h}{r}= 2.5[/tex]

h = 2.5r

[tex]r = \dfrac{h}{2.5}[/tex]

The volume of the water in the tank is represented by the equation:

[tex]V = \dfrac{1}{3} \pi r^2 h[/tex]

[tex]V = \dfrac{1}{3} \pi (\dfrac{h^2}{6.25}) h[/tex]

[tex]V = \dfrac{1}{18.75} \pi \ h^3[/tex]

The rate of change of the water depth  is :

[tex]\dfrac{dv}{dt}= \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}[/tex]

Since the water is drained  through a hole in the vertex (bottom) at a rate of 4 ft^3/sec

Then,

[tex]\dfrac{dv}{dt}= - 4 \ ft^3/sec[/tex]

Therefore,

[tex]-4 = \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}[/tex]

the rate of change of the water at depth h = 10 ft is:

[tex]-4 = \dfrac{ 100 \ \pi }{6.25}\ \dfrac{dh}{dt}[/tex]

[tex]100 \pi \dfrac{dh}{dt} = -4 \times 6.25[/tex]

[tex]100 \pi \dfrac{dh}{dt} = -25[/tex]

[tex]\dfrac{dh}{dt} = \dfrac{-25}{100 \pi}[/tex]

Thus, the rate of change of the water depth when the water depth is 10 ft is;  [tex]\mathtt{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}[/tex]

Answer:

the rate of change of the water depth when the water depth is 10 ft is;  

Step-by-step explanation:

Given that:

the inverted conical water tank with a height of 20 ft and a radius of 8 ft  is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec.

We are meant to find the  rate of change of the water depth when the water depth is 10 ft.

The diagrammatic expression below clearly interprets the question.

From the image below, assuming h = the depth of the tank at  a time t and r = radius of the cone shaped at a time t

Then the similar triangles  ΔOCD and ΔOAB is as follows:

   ( similar triangle property)

h = 2.5r

The volume of the water in the tank is represented by the equation:

The rate of change of the water depth  is :

Since the water is drained  through a hole in the vertex (bottom) at a rate of 4 ft^3/sec

Then,

Therefore,

the rate of change of the water at depth h = 10 ft is:

Thus, the rate of change of the water depth when the water depth is 10 ft is;  

Step-by-step explanation:

Answer:

A. H: mu1< mu2

Step-by-step explanation:

Given that :

Mean amount of time per domestic cars = mu1

Mean amount of time per foreign cars = mu2

Automobile technicians claim :

The mean amount of time (in hours) per domestic car repair is more than that of foreign cars. This will be the Null hypothesis.

Null hypothesis : mu1 > mu2

The alternative hypothesis will negate the Null hypothesis and will hence be the opposite. This can this be expressed as :

Alternative hypothesis : mu1 < mu2

Answer:

B

Step-by-step explanation:

Hello!

A function is a equation that every input has one output

To find if an equation is a function we put in a number for one variable and solve

I'll use 0

y^2 = 0^2 + 5(0) + 4

Simplify

y^2 = 0 + 0 + 4

Combine like terms

y^2 = 4

To remove the square from y you put 4 in the square root in both negative and positive

[tex]y=\sqrt{4}[/tex] [tex]y=-\sqrt{4}[/tex]

Simplify

y = 2, y = -2

For one input (0) we get two outputs (2 and -2) this means it is not a function. So the answer is B

Hope this Helps!

Answer:

the absolute value of -5 is 5, and the absolute value of 5 is also 5. ∣ a + b i ∣ = a 2 + b 2 . |a+bi| = \sqrt{a^2 +b^2}

please give me heart

Answer:

Debbie would need to purchase 2 1-gallon bottles of juice.

Step-by-step explanation:

So we have 20 cups and each cup holds 10 fluid ounces. 20 times 10 equals 200 fluid ounces. We need to see how many fluid ounces are in 1 gallon. There are 128 fluid ounces in 1 gallon. 200 divided by 128 equals to 1.56 gallons. Debbie needs more than 1 gallon. Since we have a decimal and 1 is on the left of the decimal, Debbie would need to purchase 2 1-gallon bottles of juice.

Answer:

B

Step-by-step explanation:

∠ U = ∠ F = 76° thus are congruent

Consider the ratios of corresponding sides

[tex]\frac{UW}{FH}[/tex] = [tex]\frac{9}{21}[/tex] = [tex]\frac{3}{7}[/tex]

[tex]\frac{UV}{FG}[/tex] = [tex]\frac{18}{42}[/tex] = [tex]\frac{3}{7}[/tex]

Thus Δ UVW ~ Δ FGH by the SAS postulate

Yes the given two triangles are similar.

The similarity statement is B) ΔUVW ∼ ΔFGH

The triangles that have similar shape but the sizes of the triangles may be different, are called similar triangles.

Here, in the given triangles,

∠U = ∠F = 76°

Therefore they are congruent.

The ratio of corresponding sides, [tex]\frac{UW}{FH} =\frac{9}{21} = \frac{3}{7}[/tex]

Again the ratio of corresponding sides, [tex]\frac{UV}{FG}=\frac{18}{42}=\frac{3}{7}[/tex]

Thus, ΔUVW ∼ ΔFGH by SAS rule of similarity.

Learn more about Similarity of triangle here :

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Answer:

d) r = -65.

Step-by-step explanation:

The absolute value of r represents the relationship strength and the sign represents the relationship direction

Also if the relationship is nearest to 1 then it would be termed as positive correlated and if the relationship is nearest to -1 then it would be termed as negative correlated

Therefore based on the given options, the last option is correct

Answer:

You have 1/60 of the original hair color left

Step-by-step explanation:

Add up the fractions

1/3 + 1/4 + 2/5

Get a common denominator of 60

1/3 * 20/20    + 1/4 * 15/15    + 2/5 * 12/12

20/60 + 15/60 + 24/60

59/60

The total is 1 or 60/60

60/60 - 59/60

1/60

You have 1/60 of the original hair color left

Answer:

The Commutative property is represented by 5 + (-8) = -8 + 5.

Step-by-step explanation:

We are the following the following expression below;

5 + (-8) = -8 + 5

This property says that is any number is added to 0, then the result is the number itself, i.e.;

2 + 0 = 2 or (-7) + 0 = -7.

Suppose there are three numbers; a, b and c.

So, this property hold the condition that; a + (b + c) = (a + b) + c

If we add the second and third numbers and then add the first number to it or if we add the first and second numbers and then add the third number to it, the result will be the same.

Suppose there are two numbers 6 and 8.

This property states that if we add 6 + 8 or 8 + 6, both are equal, i,e;

6 + 8 = 8 + 6

14 = 14.

This property states the following condition;

a [tex]\times[/tex] (b + c) = (a [tex]\times[/tex] b) + (a [tex]\times[/tex] c)

So, 5 + (-8) = -8 + 5 is represented by the commutative property.

Answer:

It will be 1:50

Step-by-step explanation:

Answer:

11:50 + 2 hr. = 1:50 or 13:50 Military/European time

Step-by-step explanation:

Answer: Hi!

The place value of 6 in 37651 is equal to 600, as it is in the hundreds place.

All we need to do is multiply 600 by 11:

600 * 11 = 6600

Hope this helps!

━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━  

So in 37,651, the 6 is in the hundreds place since it's the third digit (from right to left).

6 in the hundreds place is 600.

600 times 11 equals 6600.

━━━━━━━━━━━━━━━ ♡ ━━━━━━━━━━━━━━━  

♡ Hope this helps! ♡

❀ 0ranges ❀

Answer:

14

Step-by-step explanation:

you clean 2 a hour so 7*2=14

Answer:

14 houses

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

:)

Answer: 45 45 90

Step-by-step explanation:

Answer:

the answer is -7

Step-by-step explanation:

m+9=2-9

-9

m=. -7

Answer:

(C) Maria's elevation increased between 9:00 and 12:00

Step-by-step explanation:

Looking at the graph, we can test each statement.

For A, it says Maria's elevation remained constant for 2 hours. Looking at the graph, we can see that it remained constant for just one hour, so this is eliminated.

For B, Maria's elevation decreased between 1:00 and 3:00, we can see that while x is between 1:00 and 3:00, the y is decreasing, meaning this statement is false - this is eliminated.

For C, Maria's elevation increased between 9:00 and 12:00, we can see that while x is between 9:00 and 12:00, the graph is increasing - which means this is correct.

For D, Maria spent more time decreasing her elevation than increasing, we can count how many hours were spent doing each. Comparing the x-axis, we can see that Maria spent 5 hours increasing and 3 hours decreasing, meaning that Maria spent more time INCREASING than decreasing, making this statement false.

Hope this helped!

Answer: C A B C D

Step-by-step explanation: I HAVE NONE IM JUST SMART

I THINK?

Answer:

See below for answers to both questions.

Step-by-step explanation:

Question 13)

We know that the perimeter is the sum of all of the side lengths of the square, and we know that a square has 4 sides that are all the same length.  This lets us set up the following equation:

4(10x + 6) = 74

To solve this equation, we should first distribute the 4 through the parentheses using the distributive property.

40x + 24 = 74

Next, we should subtract 24 from both sides of the equation.

40x = 50

Finally, we should divide both sides by 40.

x = 50/40 = 1.25

Therefore, the answer to question 13 is x = 1.25.

Question 14)

If we know the rectangle and triangle have the same perimeter, we can set up the following equation:

2(4x-1) + 2(x-1) = (4x + 1) + (3x + 5) + (x + 1)

We should begin by simplifying the left side of the equation using the distributive property, as we did above.

8x - 2 + 2x -2 = 4x + 1 + 3x + 5 + x + 1

Next, we can combine like terms on both sides of the equation.  This means adding together the constant terms (numbers) and also combining the variable terms (x's).  This is modeled below:

(8x + 2x) + (-2 + -2) = (4x + 3x + x) + (1 + 5 + 1)

10x - 4 = 8x + 7

Next, we should subtract 8x from both sides.

10x - 8x - 4 = 8x - 8x + 7

2x - 4 = 7

Next, we should add 4 to both sides.

2x - 4 + 4 = 7 +4

2x = 11

Finally, we should divide both sides by 2.

x = 11/2 = 5.5

The question asks us to find the perimeter, so we can use the perimeter of the rectangle:

10x - 4 = 10(5.5) - 4 = 51

Therefore, the answer is 51 units.

Hope this helps!

Answer:

A) It fulfills the condition of binomial experiment

B) P (x=12) =0.1678

C)P ( x ≥16)= 0.1011

d) P (x>17) =0.0096 < 0.5

Step-by-step explanation:

A. The binomial probability distribution has the following four properties

1. the outcomes of each trial maybe classified into success and failure.

2) the probability of success p remains constant for all trials.

3) the successive trials are all independent.

4) the experiment is repeated a fixed number of times ,n.

These all conditions are fulfilled by the given question so it is a  binomial experiment.

B) P (x=12) = 20C12 (0.64)^12 * (1-0.64)^8= 0.1678

C) P ( x ≥16) = P (x=16) + P (x=17) + P (x=18) + P (x=19)+ P (x=20)

where

P (x=16)= 20C16 (0.64)^16 * (1-0.64)^4= 0.0645

P (x=17)= 20C17 (0.64)^17 * (1-0.64)^3= 0.0270

P (x=18)= 20C18 (0.64)^18 * (1-0.64)^2= 0.0080

P (x=19)=20C19 (0.64)^10 * (1-0.64)^1= 0.0015

P (x=20)= 20C20 (0.64)^20 * (1-0.64)^0= 0.0001

so

P ( x ≥16)= 0.0645+ 0.0270 +0.0080+ 0.0015+0.0001= 0.1011

d) P (x>17)= P (x=17) + P (x=18) + P (x=19)+ P (x=20)

                    =0.0270 +0.0080+ 0.0015+0.0001

                         =0.0096

From this we see that the probability of  more than 17  people who flush public toilets with their foot is unusual because it is far away from the mean which is supposed to be somewhere 0.5 in a given distribution.

Answer Choice 1

Take it step by step!

First find what sqrt(x-7) is like. Compare it to sqrt(x).

You can see that in sqrt(x), when x = 0, y = 0. However, in sqrt(x-7), when x = 7, y = 0. When y = 0, sqrt(x-7) is 7 more, which means it is shifted 7 units to the right.

Similarly, +8 means that whatever sqrt(x-7) is, you add 8 more to y. Adding on extra for y is just moving it up by 8 units.

Hope that helped,

-sirswagger21

Answer:

8+7=15 therefore 8

                          5

Step-by-step explanation:

The numerator from the fraction of apple fruits to total fruits is 8

How to find fraction of apples to total fruits?

Total fruits = apples + oranges

= 8 + 7

= 15

Fraction of apple fruits to total fruits = Number of apples / Total fruits

= 8/15

Therefore, the numerator from the fraction of apple fruits to total fruits is 8

Learn more about fraction:

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Answer:

a. 1120 is the area b. max # of ppl is 80

Step-by-step explanation:

a. Area= Length* width = 28 * 40 = 1120

(8,10) and (8,38) have 28 units between them

(8,10) and (48,10) have 40 units between them

b. Since the area is 1120 and they say that only one person is allowed per 14 square feet, you would divide 1120 by 14 to get 80 people

If each coordinate equals 1 foot then:

(8,10) to (48,10) is 40 feet (48-8)

(8,10) to (8,38) is 28 feet (38-10)

so now you got length 40 and width 28

40 x 28 = 1120

a. 1120ft^2

b. 1120 / 14 = 80

Answer:

The remainder is 87.

Step-by-step explanation:

By definition of remainder theorem, whenever a polynomial f(x) is divided by (x-b) the remainder will be: f(b)

Following the Remainder Theorem, in this question the remainder will be f(5).

In this case we were given f(x) as

f(x) = x^2 + 14x − 8

We're are to find the remainder when it is divided by (x-5)

Then(x-5)= 0

X=5

If we substitute x=5 into equation of f(x), we will have the remainder of

f(x) = x^2 + 14x − 8

f(4)= (5)^2 +14(5)-8

f(4)=25+70-8

f(4)=87

Hence, The remainder is 87.

Answer:

87

Step-by-step explanation:

Answer:

$233.39

Step-by-step explanation:

Pants = $82, 2 Shirts = $53 * 2, Shoes = $120

Add all these values up to find the total cost of your order excluding tax.

82 + 53(2) + 120 = 308

Next find the price w/ tax. Multiply 308 by 8.25%, or 0.0825.

308 * 0.0825 = 25.41

Now you add the tax to the total value.

308 + 25.41 = 333.41

The total value including tax is $333.41. The online retailer is offering a 30% savings (discount), so multiply the total price including tax by 30% (0.30).

333.41 * 0.30 = 100.023

Now you subtract the discount from the total price.

333.41 - 100.023 = 233.38700

The question say the answer rounded to the nearest cent or hundredths, so your final answer is 233.39.

The final price of the clothing including all discounts and taxes is $233.39.

Answer:

B

Step-by-step explanation:

If the figure is regular, then everyone of the central angles are equal. They add up to 360 degrees.

x + x + x + x + x + x + x = 360          Combine

7x = 360                                           Divide by 7

x = 360/7

x = 51.43