6 water pumps fill a water tank in 15 hours if they work together. a) If one of these pumps is not working, how long will the 5 water pumps take to fill the tank? b) If we want the tank filled in 9 hours, how many water pumps do we need?​

Answer: 2/90 = 1/45

Step-by-step explanation:

The number of minutes that the players spend running bases during each hour of practice is the constant of proportionality of the proportional relationship.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

In the context of this problem, the variables x and y are given as follows:

The equation for the constant is given as follows:

k = y/x.

Representing the hourly time spent running times, you can calculate it taking any point (x,y) on the graph of the function.

More can be learned about proportional relationships at https://brainly.com/question/10424180

#SPJ1

The future value of the loan is $5807.65.

It is expressed as a percentage of the amount borrowed and is paid over a specific period of time. The interest rate represents the cost of borrowing money and is one of the key factors in determining the overall cost of a loan. Interest is usually calculated on a yearly basis and can be compounded, meaning that the interest earned on a loan is added to the original principal and the interest rate is then applied to the new, higher amount. This process continues over time, leading to the growth of the original loan amount. The purpose of charging interest is to compensate the lender for the risk they are taking in lending the money and for the opportunity cost of not being able to invest the money elsewhere.

The future value of a loan is equal to the present value plus the interest earned over a specified time period. The formula to calculate the future value of a loan with simple interest is:

FV = PV (1 + rt)

where:

PV is the present value of the loan, which is $5250

r is the interest rate as a decimal, which is 5.3% ÷ 100 = 0.053

t is the time period in years, which is 24 months ÷ 12 months/year = 2 years

Substituting the values into the formula, we get:

FV = $5250 (1 + 0.053 * 2)

FV = $5250 (1.106)

FV = $5807.65

So, the future value of the loan is $5807.65. This is the amount Lynne will have to repay to her grandmother after 24 months, including the interest earned.

To know more about amount visit:

https://brainly.com/question/8082054

#SPJ1

The value of m equals 65.

The correct option is C: 65.

The given equation m - 14 = 51 represents an algebraic equation where m is an unknown variable.

To find the value of m, we need to isolate it on one side of the equation by performing operations that keep the equation balanced.

In this case, we add 14 to both sides of the equation to isolate the variable m. By doing this, we are essentially undoing the subtraction of 14 that was initially done to m, which allows us to obtain the value of m.

The equation m - 14 = 51 can be interpreted as follows: a number (m) decreased by 14 results in 51.

To find the original number (m), we need to undo the subtraction by adding 14 to the result.

This leads to the value of m being equal to 65.

To learn more about the equation;

https://brainly.com/question/12788590

#SPJ1

Answer:

B(6, 5), C(1, -7)

Step-by-step explanation:

A(2, 5)

From A to B, there is translation x, (4, 0).

Add 4 to A's x-coordinate, and add 0 to A's y-coordinate.

B(2 + 4, 5 + 0) = B(6, 5)

From C to B there is the translation y, (5, 12).

Since we are going from B to C, we undo translation y.

The translation from B to C is (-5, -12).

C(6 - 5, 5 - 12) = C(1, -7)

Answer:

i = 2

Step-by-step explanation:

-8(i - 6) = 32

-8i + 48 = 32

-8i = -16

i = 2

While an absolute value may be any number, the output from an absolute value expression is always greater than or equal to zero

The absolute value | x | of a real number x is defined as the non-negative value of x without regard to its sign. For example, the absolute value of 3 is 3, and the absolute value of −3 is also 3. The absolute value of a number may be thought of as its distance from zero along real number line.

The absolute value of any number is seen to be always greater than or equal to zero. Both a number and its opposite are the same distance from zero on the number line. Since they have the same distance from zero, they have the same absolute value.

Read more about Absolute Value Function at: https://brainly.com/question/3381225

#SPJ1

Answer:

The gain percent is 33.3 %

Step-by-step explanation:

Let the selling price of 1 m cloth is p.

Cost of 33 m = 33 p

gain = cost of 11 m = 11 p  

The gain percentage is given by

\(\frac{11 p}{33 p}\times 100\\\\= 33.3 %\)

The gain percent is 33.3 %.

Answer:

A) 75

Step-by-step explanation:

All 3 angles of any triangle add up to 180° so we can subtract all known angles from 180° to get the missing angle.

40°+65°=105°

180°-105°

75°

Answer: 59.98

Step-by-step explanation: :)

The distance between them is 59.92 ft

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle.

Given that, a scenario that is making an arrangement of a right-angled triangle, we need to find the base, [refer to the figure attached]

So, here we will use the Pythagoras theorem

75²+base² = 96²

base² = 96²-75²

base = √3591

base = 59.92

Hence, the distance between them is 59.92 ft

Learn more about Pythagoras theorem click;

https://brainly.com/question/343682

#SPJ3

Answer:  \(x = \frac{7\sqrt{6}}{2}\\\\\)

==============================================================

Explanation:

Focus on the upper triangle. This is a 30-60-90 triangle. The short leg is 7 and the long leg is \(7\sqrt{3}\). The long leg is always sqrt(3) times that of the short leg (and this only works for 30-60-90 triangles).

In short, the horizontal length is \(7\sqrt{3}\) units long.

Now move to the lower triangle. This is a 45-45-90 triangle with congruent legs (each are x units long). We just found the hypotenuse is \(7\sqrt{3}\)

We can use the pythagorean theorem to say the following:

\(a^2 + b^2 = c^2\\\\x^2 + x^2 = (7*\sqrt{3})^2\\\\2x^2 = 147\\\\x^2 = \frac{147}{2}\\\\x = \sqrt{\frac{147}{2}}\\\\x = \frac{\sqrt{147}}{\sqrt{2}}\\\\x = \frac{\sqrt{147}*\sqrt{2}}{\sqrt{2}*\sqrt{2}}\\\\x = \frac{\sqrt{147}*\sqrt{2}}{2}\\\\x = \frac{\sqrt{147*2}}{2}\\\\x = \frac{\sqrt{294}}{2}\\\\x = \frac{\sqrt{49*6}}{2}\\\\x = \frac{\sqrt{49}*\sqrt{6}}{2}\\\\x = \frac{7\sqrt{6}}{2}\\\\\)

Answer:

Step-by-step explanation:

17.5

Answer:

a = 8 m.

Step-by-step explanation:

This is a right triangle, so the Pythagorean Theorem applies.

The Pythagorean Theorem states that the legs of a triangle, squared, equals the hypotenuse, squared.

The legs of a triangle are the sides that make the right angle.

The hypotenuse is the longest side of a right triangle.

Here, I am solving for one of the legs.

\(formula=a^2+b^2=c^2\)

\(a, b = legs\)

\(c=hypotenuse\)

\(a^2+15^2=17^2\)

\(a^2+225=289\)

\(289 - 225 = 64\)

\(a^2=64\)

\(a=8\)

The exponential form of the given sequence is - \(t_n\) = \(t_(n-1)\) + \(2^x\) where x is a set of whole numbers and n is a set of natural numbers.

The given sequence is -  4, 5, 7, 11, 19, 35, 67, ...

the first term - \(t_1\) is 4

Hence, we can write the sequence as follows-

4 + \(2^0\) = 5

5+\((2)^1\)=7

7+\((2)^2\)=11

11+\((2)^3\)=19

and so on.

Here, we are adding the previous term with the exponential form of 2.

thus, we can conclude that -

\(t_n\) = \(t_(n-1)\) + \(2^x\)

where,  x is a set of whole numbers, and n is a set of natural numbers.

Read more about Sequences:

brainly.com/question/28417178

#SPJ4

Answer: 5 inspections in 4 hours, because if its 8 hours it would be 10 inspections

Step-by-step explanation:

Answer:

1.25

Step-by-step explanation:

10 ÷ 8 = 1.25

Answer:

The answer is b

Step-by-step explanation:

Answer:

4/15

Step-by-step explanation:

2/5 drive

1/3 bus

and rest walk

fraction of those who walk is 1-(2/5+1/3)

2/5+1/3=(6+5)/15=11/15

15/15-11/15=4/15

Answer:

=54

Step-by-step explanation:

- Combine multiplied terms into a single fraction

0.5(-9)=22.51(−9)2=22.52

- Multiply by 1

- Multiply all terms by the same value to eliminate fraction denominators

- Cancel multiplied terms that are in the denominator

- Multiply the numbers

- Add 999

- to both sides of the equation

- Simplify

The required length of the other piece of the board is  12.3 meters.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,

To find out the length of the other piece we need to subtract the length of one piece from the original length of the board,
So,
Length of the other piece = 19.5 - 7.2 meters
                                        = 12.3 meters

Thus, the required length of the other piece of the board is  12.3 meters.

Learn more about simplification here:

https://brainly.com/question/12501526

#SPJ1

The values of the expressions are;

z³³

d⁻¹⁶

Note that index forms are described as forms used in the representation of numbers or variables too large or small.

Some rules of index forms are;

Then, from the information given, we have that;

(z⁻⁴/z⁶  × z⁵/z⁻⁶)⁻¹¹

Subtract the exponents, we have;

(z⁻² × z⁻¹)⁻¹¹

expand the bracket

z²² ⁺ ¹¹

z³³

(d⁴)⁻³/(d⁶)⁻²  ÷  (d⁴/d⁶)⁻⁸

expand the brackets

d⁻¹²/d¹²  ÷    (d⁻²)⁻⁸

subtract the exponents

d⁰  ÷  d¹⁶

d⁻¹⁶

Learn more about index forms at: https://brainly.com/question/15361818

#SPJ1

minimum value: 1

lower quartile: 3

median of the data: 6

upper quartile: 8

maximum value: 14

Sorry for the late answer, i hope this will help you in the future and everyone else who reads this.

Answer:

Step-by-step explanation:

    A,  use  three_digite  rounding  arithmetic  to compute  13- 6 and determine  the absolute,relative ,and percentage errors.

tepeat part (b) using  three – digit chopping arithmetic.

Answer: x=3√14

Step-by-step explanation:

Answer:

A Type II error happens when the null hypothesis failed to be rejected, although it is false and the alternative hypothesis is true.

In this context, would be that the test does not give enough evidence to support the claim that the new procedure reduces the average cost, although it really does reduces it.

The new procedure is effective, but the sample does not give enough evidence.

Step-by-step explanation:

Answer:

x = -3

Step-by-step explanation:

7 + 2x/3 = 5

7*3 + 2x = 5*3 ( we multiply by 3 to remove the denominator )

21 + 2x = 15

2x = 15 - 21

2x = -6

x = -6/2

x = -3

Answer:

X=4

Step-by-step explanation:

Times both side by 3

then you get 7+2x=15

then minus 7 from both sides

2x=8

divide by 2

x=4

Answer:

20.68976

Step-by-step explanation:

Convert the percentage into decimal :

58% = 0.58

0.58 × x = 12

Divide both sides by 0.58 :

x = 12÷0.58

x = 20.689655...

x = 20.68976

So the method to these types of question is to make the question into an equation by converting the percentage into a decimal, rearrange to make the unknown number the subject and solve .

Hope you understood and have a good day

The general form of the equation of the hyperbola with the given information is \(9x^2 - 16y^2 - 36x + 160y - 508 = 0\). The equation can be determined by first finding the center of the hyperbola, which is (2, 5), and the distance between the foci, which is 4.

The general form of the equation of a hyperbola can be determined from the given information. The vertices of the hyperbola are given as (-2, 5) and (6, 5). The foci of the hyperbola are given as (-3, 5) and (7, 5). The first step in finding the equation of the hyperbola is to determine the center of the hyperbola. The center of the hyperbola can be calculated by taking the average of the x-coordinates of the vertices and then the average of the y-coordinates of the vertices. The center of the hyperbola is then (2, 5). The distance between the foci of the hyperbola is 4. This distance can be calculated by subtracting the x-coordinates of the foci and then subtracting the y-coordinates of the foci. The standard equation for a hyperbola can then be formed by substituting the center coordinates and the distance between the foci into the equation. The resulting equation is \(9x^2 - 16y^2 - 36x + 160y - 508 = 0\). This equation is the general form of the equation of the hyperbola with the given

Learn more about equation here

https://brainly.com/question/29657992

#SPJ4

Answer:

3.14159265358979

Step-by-step explanation:

The simplified form of -20/2(7 2/3) is -230/3.

To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

First, let's convert the mixed number 7 2/3 to an improper fraction.

7 2/3 = (7 * 3 + 2) / 3 = 23/3

Now, let's substitute the value back into the expression:

-20/2 * (23/3)

Next, we simplify the multiplication:

-10 * (23/3)

To multiply a fraction by a whole number, we multiply the numerator by the whole number:

-10 * 23 / 3

Now, we perform the multiplication:

-230 / 3

Therefore, the simplified form of -20/2(7 2/3) is -230/3.

​for such more question on simplified form

https://brainly.com/question/11680269

#SPJ8

Answer:

C) The amount of money in his lunch account

Step-by-step explanation: