A bucket that has a mass of 20 kg when filled with sand needs to be lifted to the top of a 10 meter tall building. You have a rope that has a mass of 0.4 kg/m that must be secured to the bucket. It takes 1 meter of rope to secure the bucket. Once the bucket reaches the top of the building it only has mass 16 kg because there was a hole in the bottom and sand was leaking out at a constant rate while it was being lifted to the top of the building.

Find the work done lifting the bucket (sand and rope) to the top of the building.

At x=0

At x=5

At x=10

Answer:

25x-4

Step-by-step explanation:

3x+10x

+ 2x. -4

=5x+10x-4

=15x-4

Answer:

C 1/3

Step-by-step explanation:

out of the 6 possible moves you have the possibility of landing on question mark twice. 2/6 -> 1/3

The values of f⁻¹(f(6.022)) is 6.022 and f⁻¹(10) + f(-6) is 4

As  a general rule;

f⁻¹(f(x)) = x

This means that:

f⁻¹(f(6.022)) = 6.022

Also, we have:

f⁻¹(10) + f(-6)

From the table of values, we have:

f⁻¹(10) = -6 and f(-6) =10

So, we have:

f⁻¹(10) + f(-6) = -6 + 10

Evaluate

f⁻¹(10) + f(-6) = 4

Hence, the values of f⁻¹(f(6.022)) is 6.022 and f⁻¹(10) + f(-6) is 4

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The equation 9cos(sin¯¹(x)) = √(81 – 81x²) is true since L.H.S = R.H.S

To answer the question, we need to know what an equation is

An equation is a mathematical expression that show the relationship between two variables.

Given 9cos(sin¯¹(x)) = √(81 – 81x²), we need to show L.H.S = R.H.S

So, L.H.S = 9cos(sin¯¹(x))

= 9[√{1 - sin²(sin¯¹(x)}] (Since sin²y + cos²y = 1 ⇒ cosy = √[1 - sin²y])

9[√{1 - sin²(sin¯¹(x)}] = √9² × √{1 - sin²(sin¯¹(x)}]

= √[9² × {1 - sin²(sin¯¹(x)}]

= √[81 × {1 - sin²(sin¯¹(x)}]

= √[81 × {1 - x²}]   (since sin²(sin¯¹(x) = [sin(sin¯¹(x)]² = x²)

= √(81 – 81x²)

= R.H.S

So, the equation 9cos(sin¯¹(x)) = √(81 – 81x²) is true since L.H.S = R.H.S

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This is an exercise on Thermometric scales.

We have as data:

We apply the following formula:

[tex]\large\displaystyle\text{$\begin{gathered}\sf ^{\circ}F=\frac{9}{5}\ ^{\circ}C+32 \end{gathered}$}[/tex]

We substitute data in the formula:

[tex]\large\displaystyle\text{$\begin{gathered}\sf ^{\circ}F=\frac{9}{5}\times220+32 \end{gathered}$}[/tex]

First multiply 9 x 220, then the result of this division is divided by 5.

[tex]\large\displaystyle\text{$\begin{gathered}\sf =396+32 \ \ \to \ \ [Add] \end{gathered}$}[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf =428 \ ^{\circ}F \end{gathered}$}}[/tex]

Therefore the cake recipe that should be baked at 220 °C for 45 minutes, on the Fahrenteir scale is 428 °F. Which indicates that it will be very hot.

Answer:

Second option

Step-by-step explanation:

As its a solid line, it indicates the inequality contains equal to in it. As the line crosses the x - axis it must be an option whereby x > or x < . Now read the value which is 7 therefore x ≤ 7

Answer:

6

Step-by-step explanation:

The equation for this problem would be c = (20 + 8) / 2 - 8. Add 20 and 8 to get 28, divide 28 by 2 to get 14, then subtract 8 to get 6.

The monthly payments for each add-on interest loan is $29.7.

Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.

According to the question,

Principal (P) = $1150

Rate of Interest(R) = 6%

Time (T) = 4 years

The interest is calculated as follows:

SI = (P × R × T)/100

SI = (1150 × 6 × 4)/100

SI=$ 276

Amount (A) = P + SI

A = $(1150 +276)

A = $1426

Monthly payment with interest = A/(4×12)

= $ 1426/48

= $29.7

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Answer:

35 2/3

Step-by-step explanation:

49 1/3 - 13 2/3

First convert both into improper fractions, which is

148/3 - 41/3

Then subtract!

107/3

Next simplify the fraction.

35 2/3

The simplifications of all the given ratios are as detailed below.

The simplification of each of the given ratios are;

1) 56 : 49

The highest common multiple is 7 and so we divide by 7 to get;

56 : 49 = 8:7

2) 36:48

The highest common multiple is 12 and so we divide by 12 to get;

36 : 48 = 3:4

3) 48:42

The highest common multiple is 6 and so we divide by 6 to get;

48 : 42 = 8:7

4) 24:36

The highest common multiple is 12 and so we divide by 12 to get;

24 : 36 = 2:3

5) 20:30

The highest common multiple is 10 and so we divide by 12 to get;

20 : 30 = 2:3

6) 24:32

The highest common multiple is 8 and so we divide by 8 to get;

24 : 32 = 3:4

7) 18:27

The highest common multiple is 9 and so we divide by 9 to get;

18 : 27 = 2:3

8) 16:14

The highest common multiple is 2 and so we divide by 2 to get;

16 : 14 = 8:7

9) 9:12

The highest common multiple is 3 and so we divide by 3 to get;

9 : 12 = 3:4

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First, we need to understand that these two triangles are

similar.

we know this because their lines (the arrows) prove they are the same direction. A similar triangle does

NOT mean they are proportional,

they are just similar by ratio.

Lets call the triangle on the left ABC and the triangle on the right A'B'C'.

I will attach an image of the labels.

Because they are similar triangles, angle A is the same as angle A'. Angle B is the same as angle B', angle C is the same as angle C'.

Based on that information, we know xº is = 65º. We know that the interior angles add up to 180º. So for triangle A'B'C', we can do 180º-40º-65º which is 70º. This means angle C' is 70º.

Now the important part is getting yº. A line is 180º. That means that 180º-70º=yº which is 110º.

If you do not understand anything, please let me know and I will try to teach you.

The arc length of the partial circle is 7.5π

From the question, we are to determine the arc length of the partial circle

The length of an arc can be calculated by using the formula

[tex]l = \frac{\theta}{360^\circ} \times 2\pi r[/tex]

Where [tex]l[/tex] is the length of the arc

[tex]\theta[/tex] is the angle subtended

and r is the radius

From the diagram,

θ = 270°

r = 5

Putting the values into the equation, we get

[tex]l = \frac{270 ^\circ}{360^\circ} \times 2\pi \times 5[/tex]

[tex]l = \frac{3}{4} \times 2\pi \times 5[/tex]

[tex]l = \frac{30\pi}{4}[/tex]

[tex]l = \frac{15}{2}\pi[/tex] OR 7.5π

Hence, the arc length of the partial circle is 7.5π

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Answer:

Step-by-step explanation:

Given inequalities below and we are looking for a pair with no solution.

Let's verify:

A) x > 3 and x < 2,

B) x > - 3 and x < - 2,

C) x > - 3 and x < 2,

D) x > - 3 and x > - 2,

Answer:

0

Step-by-step explanation:

Since the x coordinate is -1, 2+t = -1, and thus t = -3.

So, y = 1+(3/(-3)) = 0.

The monthly payments for each add-on interest loan will be $29.71.

Given Information and Formula Used

Principal Amount, P = $1150

Rate of Interest, R = 6%

Duration of loan in years, T = 4

The formula for simple interest is given as,

I = (P × R × T)/100

Calculating the Add-On Interest For Each Month

Interest, I = (P × R × T)/100

Substituting the values of P, R, and T in the above formula, we get,

I = $ (1150 × 6 × 4)/100

I = $ 27600/100

I = $276

Calculating the Total Monthly Payment With Interest

Amount of add-on interest loan, A = P + I

A = $1150 + $276

A = $1,426

Monthly payment with interest = A/(4×12)

= $ 1426/48

= $29.71

Hence, the monthly payments for each add-on interest loan would be $29.71.

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Answer:

[tex](-\infty, -1) \cup (0, \infty)[/tex]

Step-by-step explanation:

The function is decreasing if, as x increases, the value of the function (y) gets smaller.  This means as you read the graph from left-to-right, the function is decreasing if the graph is falling.

From -infinity to -1, the graph is falling, then the graph rises (f is increasing) until x =0, then the graph falls again from x = 0 to infinity.

i. P(A) = 0. 4

ii. P(AB) = 0. 9

iii. P(A∩B) =0. 25

From the information given,

Universal set = 40% + 50% + 25% = 0.40 + 0. 50 + 0. 25

A = Mechanical defects = 40%

B = Electrical defects = 50%

A∩B =25%

i. Probability of A , P(A)

= [tex]\frac{40}{100}[/tex]

= [tex]0. 4[/tex]

ii. Probability of B, P(AB)

= [tex]\frac{40}{100} + \frac{50}{100}[/tex]

= [tex]0. 4 + 0. 5[/tex]

= [tex]0. 9[/tex]

iii. Probability of A∩B entails the common factor between A and B

P(A∩B)  = [tex]\frac{25}{100}[/tex] = [tex]0. 25[/tex]

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hi

f(x) = x² -2x

g(x) = 6x+4

(f+g) (x) = x²-2x +6x+4 =  x²+4x +4 =  (x+2)² =  (x+2) (x+2)

(f+g) (x) = 0  means  =  (x+2) (x+2) = 0  

so x+2 = 0

   x = -2

(f+g) (x) = 0  for x = -2

Step-by-step explanation:

Let take the first derivative

[tex] \frac{d}{dx} ln(x)) = x {}^{ - 1} [/tex]

The second derivative

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

The third derivative

[tex]2 {x}^{ - 3} [/tex]

The fourth derivative

[tex] - 6 {x}^{ - 4} [/tex]

The fifth derivative

[tex]24 {x}^{ - 5} [/tex]

Let create a pattern,

The values always have x in it so

our nth derivative will have x in it.

The nth derivative matches the negative nth power so the nth derivative so far is

[tex] {x}^{ - n} [/tex]

Next, lok at the constants. They follow a pattern of 1,2,6,24,120). This is a factorial pattern because

1!=1

2!=2

3!=6

4!=24

5!=120 and so on. Notice how the nth derivative has the constant of the factorial of the precessor

so our constant are

[tex](n - 1)[/tex]

So far, our nth derivative is

[tex](n - 1)!x {}^{ - n} [/tex]

Finally, notice for the odd derivatives we are Positve and for the even ones, we are negative, this means we are raised -1^(n-1)

[tex] - 1 {}^{n -1} (n - 1) ! {x}^{-n} [/tex]

That is our nth derivative

[tex]f(x) = 7x {}^{2} - 3x {}^{4} [/tex]

The 12th fastest time a goose took to join the gaggle is 49 seconds.

A Stem and Leaf Plot is a type of graph where the data is divided into a stem (the first digit or digits) and a leaf (usually the last digit).

The data in the stem plot arranged from the first fastest time it takes a goose to join the gaggle is: 13, 14, 15, 19, 19, 21, 27, 27, 28, 32, 45, 49, 49, 62, 62.

The 12th fastest time is 49

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Using the t-distribution, the 95% confidence interval within which the mean of the total population of such cases is expected lie is:

(112.5, 127.5).

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 18 - 1 = 17 df, is t = 2.1098.

The parameters for this problem are:

[tex]\overline{x} = 120, s = 15, n = 18[/tex].

Hence the bounds of the interval are:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 120 - 2.1098\frac{15}{\sqrt{18}} = 112.5[/tex]

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 120 + 2.1098\frac{15}{\sqrt{18}} = 127.5[/tex]

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Answer: The largest common factor of 28 and 32 is 4.

Step-by-step explanation:

The factors of 28 are 1, 2, 4, 7, 14, 28

The factors of 32 are 1, 2, 4, 8, 16, 32

Based on the Venn diagram with results from the travel agency and the popular cities to visit, the following are true:

The Venn diagram shows that the number of people who chose Orlando alone are 5 people namely: John, Michael, Angel, Andrew, and Sally.

Only one customer in the person of Jordan preferred New York and Los Angeles.

2 people liked Orlando and New York only and they were Luke and Robert.

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Answer:

India score 290 more than pakistan

Step-by-step explanation:

India score 20 more

Answer:

D

Step-by-step explanation:

substitute x = 4 , y = - 5 into the expression

[tex]\frac{8(4)(-5)+16(-5)}{5(4)}[/tex]

= [tex]\frac{-160-80}{20}[/tex]

= [tex]\frac{-240}{20}[/tex]

= - 12

Answer:

B

Step-by-step explanation:

1-cos2x=2sin²(x/2)

[tex]sin^2(\frac{x}{2} )=\frac{(1-cos(2x))}{2}\\(sin^2(\frac{x}{2} ))(1+cos(x))= \frac{(1-cos(2x))(1+cos(x))}{2}[/tex]

Answer:

C & D

Step-by-step explanation:

A. 4 is greater than 0, so use the third equation to find f(x). 4*4 - 1 = 15, so A is wrong.

B. -2 is less than 0, so use the first equation to find f(x). -(-2) + 1 = 3, so B is also wrong.

C. -1 is less than 0, so use the first equation to find f(x). -(-1) + 1 = 2, so C is correct.

D. 1 is greater than 0, so use the third equation to find f(x). 1*1 - 1 = 0, so D is also correct.

Answer:

y = -2x + 4

Step-by-step explanation:

The x-intercept would be the point (2,0) and the y intercept would have the point (0,4).  Once we know two points we can write the equation in the line intercept for of y = mx + b.  

We need to find the slope and the y intercept.  The slope is the steepness of the line and it is the change in y over the change in x.

The ordered pairs are written in  the form of (x, y).  From our two points, we will subtract the y's to find the top number of our fraction.

0 - 4 = -4 that is the numerator (top number) of our slope.  We do the same with the two x numbers that we have been given.

2 - 0 = 2  This is our numerator (or bottom number of our slope)

Our slope is -4 /2 to simplify, we divide the top and bottom number by 2 to get -2 / or just -2

Now that we have the slope we need to find the y-intercept.  We can use either of our original two points and our slope to determine the y-intercept.  It does not matter if you use the point (2,0) or (0,4).  I will use (2,0) and the slope of -2

y = mx + b

0 = -2(2) + b  

0 = -4 + b   add 4 to both sides of the equation

4 = b

Now that we have the slope and the y-intercept, we can write the equation

y = mx + b

y = -2x + 4