One worker takes 20 hours to do a job. A second worker can do the same job in 15 hours. When a third worker is added, it takes the three of them 6 hours to do the job. How long would it take the third worker to do the job

Kate can see across the horizon by 3.33 times further than Paul.

The assumed shape of the horizon shows that it forms a cone shape. The volume of the cone can be used to determine how far they can see.

The volume of the cone [tex]\mathbf{ V=\pi r \dfrac{h }{3}}[/tex]

For Kate:

[tex]\mathbf{ V=\pi r \dfrac{h }{3}}[/tex]

[tex]\mathbf{ V=\pi \times (6371000)^2 \times \dfrac{50 }{3}}[/tex]

V = 2.12526863 × 10¹⁵ m³

For Paul

[tex]\mathbf{ V=\pi r \dfrac{h }{3}}[/tex]

[tex]\mathbf{ V=\pi \times (6371000)^2 \times \dfrac{15 }{3}}[/tex]

V = 6.3758059 × 10¹⁴ m³

To determine how much further can kate see across the horizon than Paul, we have:

= Volume of Kate/Volume of Paul

= 2.12526863 × 10¹⁵ m³/6.3758059 × 10¹⁴ m³

= 3.33 times further.

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Answer:

3x -7y = -7y+3x

Step-by-step explanation:

3x is positive and   7y is negative

We can reverse the order

3x -7y = -7y+3x

Answer:

Down below

Step-by-step explanation:

If I am correct, it would be 6x + 6x + 3x - 5 + 3x - 5.  I am almost positive this is what they are asking for.  If I am incorrect, I will answer three questions for free, on any topic of your choosing.  In advance, sorry if I'm incorrect.

Answer:

$288

Step-by-step explanation:

We first need to find what 0.8% of 300 makes and to do that we multiply 300 with 0.8 and divide that by 100

300*(0.8)/100 = 2.4 this is the monthly interest

Now we need to find how much it'd be after 10 years

There are 10*12 = 120 months in 10 years

120*(2.4) = 288 is the interest Bob will earn after 10 years

Answer:

0.3456 = 34.56%

Step-by-step explanation:

Binomial distribution

[tex]\displaystyle P(X=x)=\binom{n}{x} \cdot p^x \cdot (1-p)^{n-x}[/tex]

where:

Given:

Substitute the given values into the formula:

[tex]\begin{aligned}\implies \displaystyle P(X=3) & =\binom{5}{3} \cdot 0.6^3 \cdot (1-0.6)^{5-3}\\ & = \dfrac{5!}{3!(5-3)!}\cdot 0.6^3 \cdot 0.4^2\\ & = 10 \cdot 0.216 \cdot 0.16\\ & =0.3456\end{aligned}[/tex]

Therefore, the probability of exactly 3 successes is 0.3456 = 34.56%

Answer:

x + y = 12

40 x + 120 y = 640

Step-by-step explanation:

Answer:

d = 306 m

Step-by-step explanation:

calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (10, 20) and (x₂, y₂ ) = (280, 164) ← house and beach coordinates

d = [tex]\sqrt{(280-10)^2+(164-20)^2}[/tex]

   = [tex]\sqrt{270^2+144^2}[/tex]

   = [tex]\sqrt{72900+20736}[/tex]

   = [tex]\sqrt{93636}[/tex]

   = 306 m

Answer:

The distance from Francesca's house to the beach is 306 meters.

Step-by-step explanation:

Use the Pythagorean Theorem to find the straight-line distance from Francesca's house to the beach.

Step 1 Find the length of the horizontal leg.

The length of the horizontal leg is the absolute value of the difference between the x- coordinates of the points (280,20) and (10,20).

|280 - 10| = 270

The length of the horizontal leg is 270 meters

Step 2 Find the length of the vertical leg.

The length of the vertical leg is the absolute value of the difference between the y- coordinates of the points (280,164) and (280,20)

|164 - 20| = 144

The length of the vertical leg is 144 meters.

Step 3 Let a = 270 and b = 144. Let c represent the length of the hypotenuse. Use the Pythagorean Theorem to find c.

a² + b² = c²

270² + 144² = c² Substitute into the formula.

72900 + 20736 = c² Simplify.

93636 = c² Add.

√93636 = c Take the square root of both sides.

306 = c Simplify.

The distance from Francesca's house to the beach is 306 meters.

Answer:

D. 3x² - x - 6

Step-by-step explanation:

(f - g)(x) = f(x) - g(x)

Answer:

y= 129

x= 39

Step-by-step explanation:

First Sequence:

0 + 4 = 4 + 4 = 8 + 4 = 12 + 4 = 16 + 4 = 20

Second Sequence:
0 + 8 = 8 + 8 = 16 + 8 = 24 + 8 = 32 + 8 = 40

Identify correct option:

Each term in the second sequence is double the corresponding term in the first sequence.

[tex]\cfrac{2}{x+4}~~ + ~~\cfrac{x}{x-3}\implies \cfrac{(x-3)2~~ + ~~(x+4)x}{\underset{\textit{using this LCD}}{(x+4)(x-3)}} \\\\\\ \cfrac{2x-6+x^2+4x}{(x+4)(x-3)} \implies \cfrac{x^2+6x-6}{(x+4)(x-3)}\qquad x\ne -4,3[/tex]

why can't it be -4 or 3? for if it ever does become -4 or 3, the denominator will turn to 0, giving an undefined fraction.

Answer:

the exact same as the pre image

Answer:

the second one

Step-by-step explanation:

Answer: The area of the photo that fits the frame is 192 square inches.

Step-by-step explanation:

Hi, to answer this question we have to apply the next formula:

Area of a rectangle (A) = Length x width

Replacing with the values given and solving for A (area):

A = 16 x 12 = 192 in2

The area of the photo that fits the frame is 192 square inches.

Feel free to ask for more if needed or if you did not understand something.

Answer:

48 degrees.

Step-by-step explanation:

Adjacent angles add up to 180 degrees. 132 degrees and angle 1 should add up to 180 when added together.

132+angle 1 =180

angle 1=180-132

angle 1=48 degrees

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

[tex] \textsf{According to given question, lines k and l are parallel to each other } [/tex]~

[tex] \textsf{and we can clearly observe that} [/tex][tex] \sf{ \angle 1} [/tex][tex] \textsf{forms Co- interior angle pair with 132° } [/tex]

[tex] \textsf{[ sum of co - interior angle pair = 180° ] } [/tex]

[tex]\qquad \sf  \dashrightarrow \: \angle1 + 132 = 180[/tex]

[tex]\qquad \sf  \dashrightarrow \: \angle1 = 180 - 132[/tex]

[tex]\qquad \sf  \dashrightarrow \: \angle1 =48 \degree[/tex]

[tex] \texttt{So, the correct choice is C} [/tex]

Answer:

25% decrease

Step-by-step explanation:

Percentage Decrease = [(Start Value - Final Value) / |Start Value|]×100

80 - 60 = 20

20 / 80 = 0.25

0.25(100)= 25%

Answer:

There are many ways we can write [tex]5^{11}[/tex] one of them being that we just write 11 fives being multiplied against each other like the following:

[tex]5*5*5*5*5*5*5*5*5*5*5[/tex]

This can seem very repetitive which is why powers are a lot more helpful.  We can also rewrite [tex]5^{11}[/tex] using the power in the bottom of a fraction.  The way that we do this is put [tex]5^{-11}[/tex] on the bottom which can then be flipped to the top with a positive power and will be the same.

[tex]\frac{1}{5^{-11}}[/tex]

The final way that we can rewrite [tex]5^{11}[/tex] is by using several different powers.  We can do [tex]5^6*5^5[/tex] which will equal the same thing as [tex]5^{11}[/tex] because the base is the same and what we basically do is just add up the powers together to get back to 11.

[tex]5^6*5^5[/tex]

Answer:the answer above is correct

Step-by-step explanation:

Answer:

Actual volume = 40 cm^3.

Step-by-step explanation:

15% = 0.15 as a decimal fraction.

Let the actual volume be x cm^3, then we have the equation:

x + 0.15x = 46

1.15x = 46

x   = 46 / 1.15  

    = 40 cm^3.

[tex]∠BAD≈65.22°[/tex]

Note:

The following formula is tan formula:

[tex]tan(\theta)=\dfrac{opposite}{adjacent}[/tex]

1) Finding the tan of ∠BAC

[tex]tan(\theta)=\dfrac{4}{5}[/tex]

[tex]\theta=tan^-1(\dfrac{4}{5})[/tex]

2) Finding the tan of ∠CAD

[tex]tan(\theta)=\dfrac{3}{6}[/tex]

[tex]\theta=tan^-1(\dfrac{3}{6})[/tex]

3) Add the value of ∠BAC to the value of ∠CAD

[tex]tan^-1(\dfrac{4}{5})+tan^-1(\dfrac{3}{6})≈65.22°[/tex]

4) The sum of interior angles in quadrilateral is 360°

Then

[tex]tan(∠BAC)+tan(∠ACB)+tan(∠CAD)+tan(∠ACD)=360°[/tex]

[tex]tan^-1(\dfrac{4}{5})+tan^-1(\dfrac{5}{4})+tan^-1(\dfrac{3}{6})+tan^-1(\dfrac{6}{3})=180°[/tex]

[tex]180°+∠CDA+∠CBA=^?360[/tex]

[tex]180°+90°+90°=^?360°[/tex]

[tex]360°=360°[/tex]

Answer:

1.5 x 10 ^4

Step-by-step explanation:

Answer:

1.5 x 10 ^4

Step-by-step explanation:

hello hope this helps

Answer:

Kendra pours 500 milliliters of the mixture into each jar.

Step-by-step explanation:

Answer:

500

Step-by-step explanation:

Kendra poured

500

milliliters into each jar.

Answer: C. 30:1

Step-by-step explanation:

A ratio of x:y is created by taking the number of x and the number of y, plugging them in, and reducing if necessary. In this problem, x is orange trees and y is cherry trees. There are 30 orange trees and only 1 cherry tree, so the ratio is 30:1. It cannot be reduced.

Answer:

(a) C = $9250

(b) n = 21 tons

Step-by-step explanation:

(a)   11 tons being transported, so n = 11.

                ∴ C = 250 (11) + 650

                        C = $9250

(b)   C = $11,750

       ∴ 11750 = 250n + 6500

                250n = 5250

                   n = 21 tons

Hope this helps!

Answer:

Answer. = 2/2.

Step-by-step explanation:

Answer:

252 in^3

Step-by-step explanation:

Multiply all 12 x 7 x 3 = 84 x 3 = 252 in^3.

Hope this helps!

Answer:

x = -3/2

Step-by-step explanation:

x + 3 + d  = 2x + 1              First term plus common difference = 2nd term

x -2 = d

x + 3 + 2d = 5x+2              First term + 2 d = third term    re-arrange:

4x-1 = 2d                            sub in the definition of d from above

4x -1 = 2 (x-2)

4x-1 = 2x-4

2x = -3

x = -3/2

If x+3, 2x+1, and 5x+2 are consecutive terms of an arithmetic sequence then x is -3/2.

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

The sequence in which consecutive terms will have common difference is called as Arithmetic sequence.

x+3, 2x+1, and 5x+2

The common difference between first term and second term

d=2x+1-x-3

d=x-2

The common difference between second term and third term

5x+2-2x-1=d

3x+1=d

Now plug in d value

3x+1=x-2

Subtract x from both sides

3x-x=-3

2x=-3

Divide both sides by 2

x=-3/2

Hence, if x+3, 2x+1, and 5x+2 are consecutive terms of an arithmetic sequence then x is -3/2.

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Answer:

I hope this helps 40 divided by 4 is 10 10 per person 10-2=8 8 coins in each players bag and the total amount of coins in bags is 8 times 4 which is 32