One hose can fill a goldfish pond in 42 minutes, and two hoses can fill the same pond in 30 minutes. Find how long it takes the second hose
alone to fill the pond.
It takes __ minutes for the second hose alone to fill the pond.

Answers

Answer 1

It takes 105 minutes for the second hose alone to fill the pond.

What is an expression?

An expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division, among others.

Let x be the time it takes for the second hose to fill the pond alone.

The rate at which the first hose fills the pond is 1/42 (ponds/minute).

The rate at which the second hose fills the pond is 1/x (ponds/minute).

The combined rate at which the two hoses fill the pond is 1/30 (ponds/minute).

Since they are filling the same pond, we can add their rates to get the combined rate:

⇒ 1/42 + 1/x = 1/30

To solve for x, we can simplify this equation;

⇒ 30x + 1260 = 42x

Subtracting 30x from both sides gives:

⇒ 1260 = 12x

⇒ x = 105

Therefore, it takes the second hose alone 105 minutes to fill the pond.

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Related Questions

i need this answer asap with explanation

Answers

Answer:

1 , 1.01 , 1.02 , 1.03 , 1.04

Step-by-step explanation:

a sequence with steps of constant size is an arithmetic sequence.

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 1 and d has to be found

given a₅ = 1.04 , then

1 + 4d = 1.04 ( subtract 1 from both sides )

4d = 0.04 ( divide both sides by 4 )

d = 0.01

then sequence is

1 , 1.01 , 1.02 , 1.03 , 1.04

Draw triangle LMN with vertices L(2,-2), M(6,-4) and(5,4). Find the coordinates of the vertices after 90degrees rotation about the origin and about each of the point of L,M,and N

Answers

The coordinates of the vertices after rotation depend on the point around which rotation is done.

Rotation of a shape around the origin (0,0) means that each point in the shape has to be moved around the origin by a certain angle. This is done by using the equation x'=xcosθ-ysinθ and y'=xsinθ+ycosθ, where x and y are the coordinates of the point before rotation and x' and y' are the coordinates of the point after rotation. In this case, the angle of rotation is 90 degrees. When we rotate triangle LMN by 90 degrees around the origin, the coordinates of the vertices become L'(2,2), M'(-4,6) and N'(4,-5).When we rotate the triangle around any of the points of L, M, or N, the coordinates of the vertices will change accordingly. For example, if we rotate the triangle around point L, the coordinates of the vertices become L'(2,-2), M'(-2,4) and N'(-6,0). Similarly, if we rotate the triangle around point M, the coordinates of the vertices become L'(2,-2), M'(6,-4) and N'(0,6). Lastly, if we rotate the triangle around point N, the coordinates of the vertices become L'(2,-2), M'(4,5) and N'(5,4).

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The Boeing 747-8 Intercontinental Jet can carry approximately 63,500 gallons of jet fuel, making it possible for the jet to travel 14,430 kilometers before needing to refuel.

Create a linear model that represents the amount of fuel on the plane, in gallons, as a function of the flight time, in hours. Show all of your work.

Answers

Answer: To create a linear model that represents the amount of fuel on the plane as a function of flight time, we need to use the given information to calculate the fuel burn rate of the airplane in gallons per hour.

Fuel burn rate = Fuel capacity ÷ Range

Fuel burn rate = 63,500 gallons ÷ 14,430 km = 4.4 gallons per km

We need to convert km to miles, as flight time is usually measured in hours and miles. We can use the conversion factor 1 km = 0.621371 miles to convert kilometers to miles.

Range in miles = Range in km ÷ 0.621371

Range in miles = 14,430 km ÷ 0.621371 = 23,594 miles

Fuel burn rate = Fuel capacity ÷ Range in miles

Fuel burn rate = 63,500 gallons ÷ 23,594 miles = 2.69 gallons per mile

Therefore, the linear model that represents the amount of fuel on the plane as a function of flight time, in hours, is:

Fuel on plane (in gallons) = Fuel capacity - Fuel burn rate x Flight time (in hours)

F(t) = 63,500 - 2.69t

where F(t) is the amount of fuel on the plane (in gallons) after flying for t hours.

Step-by-step explanation:

use partial fractions to find the indefinite integral. (remember to use absolute values where appropriate. use c for the constant of integration.) 10x2 7x − 2 x3 x2 dx

Answers

The indefinite integral is:

-10 ln|x| + 3 ln|x - 2| + 7 ln|x + 1| + C

First, we factor the denominator of the integrand using partial fractions:

x^3 - x^2 - 2x = (x - 2)(x + 1)x

We then express the integrand as:

10x^2 - 7x + 2 = A/(x - 2) + B/x + C/(x + 1)

Multiplying both sides by the denominator and solving for A, B, and C, we get:

A = -4, B = 10, C = 1

Thus, we can rewrite the integrand as:

-4/(x - 2) + 10/x + 1/(x + 1)

Integrating each term separately and combining the results, we obtain the final expression for the indefinite integral.

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Simplify the expression-4(-3x - 8) - 34

Answers

Answer:

12x-2

Step-by-step explanation:

-4(-3x-8)-34

12x+32-34

12x-2

The volume of a triangle

Answers

[tex]\textit{volume of a pyramid}\\\\ V=\cfrac{Bh}{3} ~~ \begin{cases} B=\stackrel{base's}{area}\\ h=height\\[-0.5em] \hrulefill\\ B=\stackrel{9\times 7}{63}\\ h=6 \end{cases}\implies V=\cfrac{(63)(6)}{3}\implies V=126~cm^3[/tex]

now, for the slanted cone, we can use Cavalieri's Principle for an slanted cylinder, thus we can say that the slanted cone will have the same volume of a non-slanted cone, now, since this one has a diameter of 6, that means is has a radius of 3.

[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3} \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=7 \end{cases}\implies V=\cfrac{\pi (3)^2(7)}{3}\implies V=21\pi \implies V\approx 66~cm^3[/tex]

Answer:

Step-by-step explanation:

A rectangle and triangle are shown below.
The area of the rectangle is equal to the perimeter of the triangle.
Solve for x.
If your answer is a decimal, convert it to 1 d.p.

Answers

Answer:

Step-by-step explanation:

We know that the area of the rectangle is equal to the perimeter of the triangle

S (rectangle) = (x + 8) × (2x - 1)

P (triangle) = (5x - 1) + (6x + 8) + (8x + 15)

Now we can form an equation:

(x + 8) × (2x - 1) = (5x - 1) + (6x + 8) + (8x + 15)

[tex] {2x}^{2} - x + 16x - 8 = 5x - 1 + 6x + 8 + 8x + 15[/tex]

[tex]2 {x}^{2} - 4x - 30 = 0[/tex]

[tex]d = {b}^{2} - 4 \times a \times c = ({ - 4})^{2} - 4 \times 2 \times ( - 30) = 16 + 240 = 256 > 0[/tex]

[tex]x1 = \frac{ - b - \sqrt{d} }{2 \times a} = \frac{4 - 16}{4} = \frac{ - 12}{4} = - 3[/tex]

-3 is a negative number and we cannot use it, since x must be a natural number

[tex]x2 = \frac{ - b + \sqrt{d} }{2 \times a} = \frac{4 + 16}{4} = \frac{20}{4} = 5[/tex]

what ratio is commonly used as an alternative to 3.14?

Answers

The ratio commonly used as an alternative to 3.14 is 22/7 whichj commonly represents the mathematical expression of pi.

This ratio is often used as an approximation for pi (π) which is the mathematical constant representing the ratio of the circumference of a circle to its diameter. While pi is an irrational number and has an infinite number of decimal places, 22/7 is a rational number and can be easily computed.

The value of 22/7 is approximately equal to 3.1428571, which is a fairly accurate approximation for most practical applications. It is often used in situations where a quick estimate is required or where a more accurate value of pi is not necessary.

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do seagulls show a preference for where they land? to answer this question, biologists conducted a study in an enclosed outdoor space with a piece of shore whose area was made up of 56% sand, 29% mud, and 15% rocks. the biologists chose 200 seagulls at random. each seagull was released into the outdoor space on its own and observed until it landed somewhere on the piece of shore. in all, 128 seagulls landed on the sand, 61 landed in the mud, and 11 landed on the rocks. carry out a chi-square goodness-of-fit test. what do you conclude?

Answers

Based οn the results οf the chi-square gοοdness-οf-fit test, we can cοnclude that seagulls shοw a preference fοr where they land οn the shοre.

What is statistics?

Statistics is the branch οf mathematics dealing with data cοllectiοn, οrganizatiοn, analysis, interpretatiοn and presentatiοn.

Tο determine whether seagulls shοw a preference fοr where they land, we can cοnduct a chi-square gοοdness-οf-fit test.

First, we need tο state the null and alternative hypοtheses.

Null hypοthesis (H0): Seagulls have nο preference fοr where they land οn the shοre; the prοpοrtiοns οf seagulls landing οn sand, mud, and rοcks are equal tο the prοpοrtiοns οf sand, mud, and rοcks in the area.

Alternative hypοthesis (Ha): Seagulls have a preference fοr where they land οn the shοre; the prοpοrtiοns οf seagulls landing οn sand, mud, and rοcks are nοt equal tο the prοpοrtiοns οf sand, mud, and rοcks in the area.

We can use the fοllοwing fοrmula tο calculate the chi-square statistic:

χ² = Σ (O − E)2 / E

where χ² is the chi-square statistic, O is the οbserved frequency, E is the expected frequency, and Σ is the sum οf all cells.

The expected frequencies can be calculated as fοllοws:

Expected frequency οf sand = Tοtal number οf seagulls released x Prοpοrtiοn οf sand in the area = 200 * 0.56 = 112Expected frequency οf mud = Tοtal number οf seagulls released x Prοpοrtiοn οf mud in the area = 200 * 0.29 = 58Expected frequency οf rοcks = Tοtal number οf seagulls released x Prοpοrtiοn οf rοcks in the area = 200 * 0.15 = 30

We can nοw calculate the chi-square statistic:

χ² = [(128 - 112)2 / 112] + [(61 - 58)2 / 58] + [(11 - 30)2 / 30] = 8.89

Tο determine the degrees οf freedοm fοr the test, we need tο subtract 1 frοm the number οf categοries (3) tο accοunt fοr the fact that the frequencies are nοt independent. Therefοre, the degrees οf freedοm is 2.

Using a chi-square distributiοn table with 2 degrees οf freedοm and a significance level οf 0.05, we find the critical value tο be 5.99.

Since οur calculated chi-square value οf 8.89 is greater than the critical value οf 5.99, we reject the null hypοthesis. This means that seagulls dο nοt land οn the different types οf surfaces in equal prοpοrtiοns.

In cοnclusiοn, based οn the results οf the chi-square gοοdness-οf-fit test, we can cοnclude that seagulls shοw a preference fοr where they land οn the shοre.

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IK THE PIC IS DARK BUT PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST

Answers

Step-by-step explanation:

For x

From -6 to 2 is 8 units from -6 to -1 is 5/8ths of this

to verify:

for y from 5 to -3 is 8 units 0 is 5/8 of this

5:8

At a local coffee shop, the manager has determined that 56% of drink orders are for specialty espresso drinks and 44% are for plain coffee. The manager also noted that 40% of customers order food. For customers who purchase the specialty espresso drinks, 35% also purchase a food item, and for customers who purchase plain coffee, 30% also purchase a food item. What is the probability that a randomly chosen customer will purchase a specialty espresso drink and a food item?
0.13
0.14
0.20
0.22

Answers

Let's use conditional probability to solve this problem. We want to find the probability of a customer purchasing a specialty espresso drink and a food item, so we can use the following formula:

P(specialty espresso drink and food) = P(food|specialty espresso drink) * P(specialty espresso drink)

We know that P(specialty espresso drink) = 0.56 and P(food|specialty espresso drink) = 0.35, so we can substitute these values into the formula:

P(specialty espresso drink and food) = 0.35 * 0.56

P(specialty espresso drink and food) = 0.196

Therefore, the probability that a randomly chosen customer will purchase a specialty espresso drink and a food item is 0.196 or approximately 0.20 (rounded to two decimal places).

So, the answer is option C: 0.20.

[9,7] is the difference between 2 vectors with components [3,4] and [-6, b] what is b

Answers

The value of b is -6

We know that the difference between two vectors with components (a1, a2) and (b1, b2) is given by (b1-a1, b2-a2).

So in this case, we have

[b1 - 3, b2 - 4] = [(-6) - 3, b - 4]

Simplifying the right-hand side gives us

[-9, b - 4]

So we can set the components of the left-hand side equal to the corresponding components of the right-hand side

b1 - 3 = -9

b2 - 4 = b - 4

Solving for b in the first equation gives us

b1 = -9 + 3 = -6

Substituting this into the second equation and simplifying gives us

-6 - 4 = b - 4

-10 = b - 4

b = -10 + 4 = -6

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would most people take the following gamble? flip a coin, if heads you win $75, if tails you lose $50. explain your answer.

Answers

Answer:

50/50 Chance

Step-by-step explanation:

I'm not sure if you wrote the entire question correctly, but the highest chance you would have of winning would be 100% because the 2 sides * the 50/50 chance they have. So that would make the odds of winning 50%.

I NEED HELP ON THIS ASAPPP!

Answers

Answer:

i thinks its scalene

Step-by-step explanation:

scalene is under 90 degrees

equal is 90 exact

and obtuse is over 90 but under 180

Let x and y both represent rational numbers. Select whether each expression is always, sometimes, or never a
rational number.
x-y
x + y
Always Sometimes Never

Answers

The expressions x - y and x = y are sometimes a rational number.

Classifying the types of the numbers

From the question, we have the following parameters that can be used in our computation:

x and y = rational numbers

The difference of two rational numbers is always a rational number, so x - y is sometimes a rational number.

The sum of two rational numbers is always a rational number, so x + y is sometimes a rational number.

Therefore, both expressions are sometimes a rational number.

Answers

Answer: a = 16.62

Step-by-step explanation:

sin(37) = 10/a

a = sin(37) / 10

a = 16.62

Answer:

a ≈ 16.62

Step-by-step explanation:

using the sine ratio in the right triangle

sin37° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{10}{a}[/tex] ( multiply both sides by a )

a × sin37° = 10 ( divide both sides by sin37° )

a = [tex]\frac{10}{sin37}[/tex] ≈ 16.62 ( to 2 decimal places )

Is the following equation true or false?

(14.6 ÷ 2) x 3 – 1.9 = 3 x (8 – 4)

True or false

Answers

Answer:

False

Step-by-step explanation:

14.6/2 = 7.3

7.3 x 3 = 21.9

21.9 - 1.9 = 20

Other side:

8 - 4 = 4

4 x 3 = 12

20 does not equal 12

therefore false :)

three-fourths of the chocolates in a box are dark chocolate. three-eighths of the dark chocolates are filled with caramel. what fraction of the chocolates in the box are dark chocolate and filled with caramel?

Answers

Fraction of the chocolates in the box that are dark chocolate and filled with caramel is 3/32.

To solve this problem, we need to determine what fraction of chocolates in the box are both dark chocolate and filled with caramel. We are given that:

Three-fourths of the chocolates in a box are dark chocolate. Three-eighths of the dark chocolates are filled with caramel. We need to find out the fraction of chocolates that are dark chocolate and filled with caramel. To find out the fraction of chocolates in the box that are dark chocolate, we divide the number of dark chocolates by the total number of chocolates.

This is given by:

3/4 (dark chocolates)

To find the fraction of dark chocolates that are filled with caramel, we multiply the fraction of dark chocolates by the fraction of dark chocolates filled with caramel. This is given by:

3/4 × 3/8 = 9/32

Therefore, the fraction of chocolates in the box that are dark chocolate and filled with caramel is 9/32.

To simplify the fraction 9/32, we can divide the numerator and denominator by their greatest common factor, which is 1:9/32 = 9 ÷ 1 / 32 ÷ 1 = 9/32.

Hence, the answer is 3/32.

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A parabola is defined as the set of points the same distance from (6,2) and line y=4. Select all points that are on this parabola

Answers

In conclusion there are no points among the given options that are on the parabola.

why it is?

The vertex of the parabola is the midpoint between the point (6, 2) and the line y = 4, which is at (6, 3). Since the focus is below the vertex and the directrix is a horizontal line, the equation of the parabola is of the form:

(x - h)²2 = 4p(y - k)

where (h, k) is the vertex and p is the distance from the vertex to the focus (and from the vertex to the directrix).

Using the vertex and the given point (6, 2), we can find that p = 1. Therefore, the equation of the parabola is:

(x - 6)²2 = 4(y - 3)

Now we can check which of the given points satisfy this equation:

A. (4, 6)

(4 - 6)²2 = 4(6 - 3)

4 = 12 - 12