The amount of time needed to complete a job, t, varies inversely with the number of workers, w. If 10 workers can complete a job in 20 minutes, how many minutes would it take 5 workers?

Step-by-step explanation:

Given that,

A motor boat travels 60 miles down a river in 3 hours but takes 5 hours to return upstream,

We know that,

Speed = distance/time

The rate while moving downstream[tex]=\dfrac{60}{3}=20\ mph[/tex]

The rate while moving upstream [tex]=\dfrac{60}{5}=12\ mph[/tex]

The rate of the boat in still water is the average of these:

[tex]v_s=\dfrac{20+12}{2}=16\ mph[/tex]

The rate of the current is the difference between the boat speed and actual speed = 16 mph - 12 mph = 4 mph

Hence, this is the required solution.

Answer:

E) π/9

Step-by-step explanation:

The angles are complementary meaning they add up to 90°.

Convert radians to degrees:

7π/18 · 180/π = 70°

Now we know that we need the radian equivalent of 20°.

Convert degrees to radians:

70 · π/180 = π/9

Therefore, the measure of the missing degree is π/9.

Answer:

[tex](a)\ G(t) = 100 *e^{0.1823t}[/tex]

[tex](b)\ t = 6[/tex]

[tex](c)\ t = 1.7[/tex]

Step-by-step explanation:

Given

[tex]G_0 = 100[/tex] --- initial

[tex]G(1) = 120[/tex] --- after 1 year

[tex]r \to rate[/tex]

Solving (a): The expression for g

Since the rate is constant, the distribution of G follows:

[tex]G(t) = G_0 * e^{rt}[/tex]

[tex]G(1) = 120[/tex] implies that:

[tex]G(t) = G_0 * e^{rt}[/tex]

[tex]120 = G_0 * e^{r*1}[/tex]

Substitute [tex]G_0 = 100[/tex]

[tex]120 = 100 * e^{r[/tex]

Divide both sides by 100

[tex]1.2 = e^{r[/tex]

Take natural logarithm of both sides

[tex]\ln(1.2) = \ln(e^r)[/tex]

[tex]0.1823 = r[/tex]

[tex]r = 0.1823[/tex]

So, the expression for G is:

[tex]G(t) = G_0 * e^{rt}[/tex]

[tex]G(t) = 100 *e^{0.1823t}[/tex]

Solving (b): t when G(t) = 300

We have:

[tex]G(t) = 100 *e^{0.1823t}[/tex]

[tex]300 = 100 *e^{0.1823t}[/tex]

Divide both sides by 100

[tex]3 = e^{0.1823t}[/tex]

Take natural logarithm

[tex]\ln(3) = \ln(e^{0.1823t})[/tex]

[tex]1.099 = 0.1823t[/tex]

Solve for t

[tex]t = \frac{1.099}{0.1823}[/tex]

[tex]t = 6[/tex] --- approximated

Solving (c): When there will be no grass

Reduction at a rate of 80 tons per year implies that:

[tex]G(t) = 100 *e^{0.1823t}- 80t[/tex]

To solve for t, we set G(t) = 0

[tex]0 = 100 *e^{0.1823t}- 80t\\[/tex]

Rewrite as

[tex]80t = 100 *e^{0.1823t}[/tex]

Divide both sides by 100

[tex]0.8t = e^{0.1823t}[/tex]

Take natural logarithm of both sides

[tex]\ln( 0.8t) = \ln(e^{0.1823t})[/tex]

[tex]\ln( 0.8t) = 0.1823t[/tex]

Plot the graph of: [tex]\ln( 0.8t) = 0.1823t[/tex]

[tex]t = 1.7[/tex]

Answer:

width = 9 inches

length= 20 inches

perimeter of the rectangle=2(9+20)

2w +2L= 2×29

=58 inches

area of the rectangle=w×L

=9×20=180 inch²

Answer:

25/30

5/8

Step-by-step explanation:

Which fraction is it out of all of these 6/14,5/8,25/30,or 3/6?

to determine which fractions are greater than 1/2, convert the fractions to decimals

to convert to decimals, divide the numerator by the denominator

1/2 = 0.5  less than half

6/14 = 0.43 less than half

5/8 = 0.625 greater than half

25 / 30 = 0.83 greater than half

3 / 6 = 0.5 equal to half

Answer: 1547 bricks are required to build the staircase.

Step-by-step explanation:

We are given:

Number of bricks in the first step, [tex]a_1[/tex] = 131

Number of bricks in the second step, [tex]a_2[/tex] = 131 - 5 = 126

Number of bricks in the third step, [tex]a_3[/tex] = 126 - 5 = 121

Sequence become:

131, 126, 121, .....

These are in arithmetic progression where a = 131 and d (common difference) = -5

To calculate the sum of an AP, we use the formula:

[tex]S_n=\frac{n}{2}[2a+(n-1)d][/tex]

where,

n = number of terms = 17

Putting values in above equation, we get:

[tex]S_n=\frac{17}{2}[2(131)+(17-1)(-5)]\\\\S_n=\frac{17\times 182}{2}=1547[/tex]

Hence, 1547 bricks are required to build the staircase.

Answer:

2/9

Step-by-step explanation:

the question didnt say replaced it with another colour

Answer:

the answer to this is D "an external threat to Denmark"

Step-by-step explanation: just did the assignment :)

Answer:

[tex]x = \frac{35}{8} [/tex]

Step-by-step explanation:

Divide both sides by 8:

[tex] \frac{8x}{8} = \frac{35}{8} \\x= \frac{35}{8} [/tex]

Answer:

The area of a rugby pitch is more as compared to the area of the tennis court.

Step-by-step explanation:

Given that,

The area of a tennis court is 2000 m².

The length and width of a rugby pitch are 45 m and 45 m.

The area of a rugby pitch is given by :

A = lb

So,

A = 45×45

A = 2025 m²

So, it is clear that the area of a rugby pitch is more as compared to the area of the tennis court.

9514 1404 393

Answer:

  The triangle is not acute because 2² + 4² < 5²

Step-by-step explanation:

The square of the hypotenuse of a right triangle with the given short sides would be 2² +4² = 20. So, that hypotenuse would be √20, about 4.47. The long side of this triangle is longer than that, so the angle opposite is larger than 90°. The triangle with sides 2, 4, 5 is an obtuse triangle.

  The triangle is not acute because 2² + 4² < 5²

The triangle is not acute because 22 + 42 < 52.

Option C is the correct answer.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

To determine if a triangle is acute, we need to check whether all three angles of the triangle are acute angles (less than 90 degrees).

Pythagorean theorem,

- If the square of the length of the hypotenuse is greater than the sum of the squares of the other two sides, then the triangle is acute.

- If the square of the length of the hypotenuse is less than the sum of the squares of the other two sides, then the triangle is obtuse.

Now,

The triangle with side lengths 2 in., 5 in., and 4 in. is not a right triangle.

So we can't use the Pythagorean theorem directly.

Now,

We can check if the sum of the squares of the two shorter sides is greater than the square of the longest side.

2² + 4² = 4 + 16 = 20

5² = 25

Since 20 < 25, we know that the triangle is not acute.

Therefore,

The triangle is not acute because 22 + 42 < 52.

Learn more about triangles here:

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Hector is the one who discovered

Answer:

.60 + .40 + 3.00 = 4.00

Step-by-step explanation:

Answer:

$ 4

Step-by-step explanation:

six dimes (.10 each) = .60

8 nickels (.05 each)= .40

3 dollars (1.00 each) = 3.

Add together

Answer:10.2 inches

Step-by-step explanation:

we know that

In this problem we have two cases

First case

The given lengths are two legs of the right triangle

so

Applying the Pythagoras Theorem

Find the length of the hypotenuse

substitute

Second case

The given lengths are one leg and the hypotenuse

so

Applying the Pythagoras Theorem

Find the length of the other leg

substitute

Find the difference between the two possible lengths of the third side of the triangle

so

Answer:

The difference between the two possible lengths for the third side of the triangle is about 10.21 inches.

Step-by-step explanation:

We are given that the lengths of two sides of a right triangle is 12 inches and 15 inches.

And we want to find the difference between the two possible lengths of the third side.

In the first case, assume that neither 12 nor 15 is the hypotenuse of the triangle. Then our third side c must follow the Pythagorean Theorem:

[tex]a^2+b^2=c^2[/tex]

Substitute in known values:

[tex](12)^2+(15)^2=c^2[/tex]

Solve for c:

[tex]c=\sqrt{12^2+15^2}=\sqrt{369}=\sqrt{9\cdot 41}=3\sqrt{41}[/tex]

In the second case, we will assume that one of the given lengths is the hypotenuse. Since the hypotenuse is always the longest side, the hypotenuse will be 15. Again, by the Pythagorean Theorem:

[tex]a^2+b^2=c^2[/tex]

Substitute in known values:

[tex](12)^2+b^2=(15)^2[/tex]

Solve for b:

[tex]b=\sqrt{15^2-12^2}=\sqrt{81}=9[/tex]

Therefore, the difference between the two possible lengths for the third side is:

[tex]\displaystyle \text{Difference}=(3\sqrt{41})-(9)\approx 10.21\text{ inches}[/tex]

Answer:

Y= -x^2+12x-36

Step-by-step explanation:

Answer:

14.0833333333 feet | 13 feet

Step-by-step explanation:

169 Inches is 14.0833333333 feet on calculator compared to 13 feet

and 1.08333333333 is 14.0833333333 divided by 13

if is not it, then 13/14.0833333333 is 0.92307692307

i guess that is the lowest terms in ratio

This Is What I Got!

Hope This Helps! :)

Have A Good Day!!

And If You Can I Wouldn't Mind A Brainliest! :))

Answer:

Divide 1/6 miles to 1/12hour since u wanna find our miles per hour

So it’ll be : 1/6 / 1/12

= 1/6 x 12/1

= 2 miles

Answer:

Baguette. :)

Step-by-step explanation:

Answer:

I don't know you lollollollll

Hi there!  

»»————-　★　————-««

I believe your answer is:  

m = (7/4)

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{The slope formula is rise over run.}}\\\\m=\frac{\text{Rise}}{\text{Run}}\\\\m=\frac{y_2-y_1}{x_2-x_1}\\-------------\\(x_1,y_1) \text{ and } (x_2,y_2) \text{ are two points that are on the line.}[/tex]

⸻⸻⸻⸻

The line passes through the points (3,4) and (-1, -3).

⸻⸻⸻⸻

[tex]\boxed{\text{Calculating the Slope:}}\\\\\rightarrow m = \frac{-3-4}{-1-3}\\\\\rightarrow m=\frac{-7}{-4}\\\\\rightarrow m=\boxed{\frac{7}{4}}[/tex]

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

See below.

Step-by-step explanation:

Problem 1.

1. QU

2. QW

3. UW

Given

4. QUW

Problem 2.

1. CB

2. <1, <2

Given

3. BD, BE

Given

4. ABD, CBE

SAS

Answer:

1 : 12

Step-by-step explanation:

P(4) = 4 cards out of 52 = 1/13

P(4') = 48 cards out of 52 = 12/13

Odds in favour of selecting a four

Probability "for" : Probability "against" = P(4) : P(4') = 1/13 : 12/13 = 1 : 12

Simplify ratio to the simplest integers.

A Plane does not have one dimensions.

A plane is a doubly ruled surface in two dimensions that is spanned by two linearly independent vectors. A hyperplane is a generalisation of the plane to higher dimensions. The dihedral angle is the angle formed by two intersecting planes.

A plane doesn't only have one dimension, though. The two dimensions of a plane.

A plane is a flat, infinitesimally long two-dimensional surface.

The plane can occasionally be extended into three dimensions.

Consequently, a plane has more than one dimension.

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Answer:

πr of length

»» 3.14 x (5)²

»» 3.14 x 30 = 94.2cm²

πr of base

»» 3.14 x (4)²

»» 3.14 x 16 = 50.24cm²

Length x base

»» 94.2cm² x 50.25cm²

A= 4733.55cm²

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15 + 36 not-equals 41, so those lengths will not form a triangle.

15 squared + 36 squared = 1,521

41 squared = 1,681

Since a squared + b squared not-equals c squared, it will not be a right triangle.

15 squared + 36 squared = 297

41 squared = 82

Step-by-step explanation; did it on the website euphoria

The translation of the parent function is f ( x ) = | x + 6 | which is shifted 6 units to the left

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the transformation of the function be a translation , where

The parent function is f ( x ) = | x |

And , the translated function is f ( x ) = | x + 6 |

So , original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

And , the function is translated 6 units to the left

Hence , the translated function is f ( x ) = | x + 6 |

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Answer:

3

Step-by-step explanation:

Numbers between 21 and 30 divisible by 3 are 24 and 27. so you get the HCF of the two.

Answer:

Option A:

x^2 + (y - 2)^2 = 9

Step-by-step explanation:

We know that the equation for a circle centered in the point (a, b) and of radius R is given by:

(x - a)^2 + (y - b)^2 = R^2

So the first thing we need to find is the center of the circle.

We can see that the center is at:

x = 0

y = 2

Then the center is at the point (0, 2)

Now we want our circle to pass through point 2, located at a distance of 2 units from the radius of the first circle.

So the distance between the center and point 2 is 2 units plus the radius of the smaller circle:

And the radius of the smaller circle is one unit.

Then, the radius of a circle centered at (0, 2) that passes through point 2 is:

R = 1 + 2 = 3

Then we have a circle centered at (0, 2) and of radius R = 3

Replacing these in the equation for a circle we get:

(x - 0)^2 + (y - 2)^2 = 3^2

x^2 + (y - 2)^2 = 9

The correct option is A

Answer:

around 90 cm because that measure is equal to 180 you divide into 2 so the answer is 90

Answer:

6536 cubic in

Step-by-step explanation:

1. Split both the prisms apart- In doing so, you can simplify the problem.

2. Put in the #'s for the formula which in this case is V=L*W*H, we will start with the formula for the front one, V=7*8*1 or V=7*8

3. answer for the front is 56 cubic in, now we solve for the other half.

4. V=9*1*90 or V=9*90 which is 6480 cubic in.

5. add 6480 and 56 and your answer is 6536 cubic in as your answer.

Hope this helped ;D

Answer:

Amount of water pumped out by the motor = 1117.46 liters

Step-by-step explanation:

Amount of water pumped out by the motor pump = 6704.76 liters

Time taken by the motor to pump the water = 6 hours

Rate at which the motor pumps out the water = [tex]\frac{\text{Amount of water pumped out}}{\text{Time taken to pump the water}}[/tex]

                                                                             = [tex]\frac{6704.76}{6}[/tex]

                                                                             = 1117.46 liters per hour

Therefore, amount of water pumped out by the motor = 1117.46 liters