An average swimming pool contains 19200 gallons of water. The pool needs drained at the end of the summer. Water drains from the pool at the rate of 12 gallons per

Which equation can be used to find the volume, V, of the water in the pool t minutes after draining begins?


A- V = 12t - 19200
B- V= 19200- 12/60t
C- V= 12/60t- 19200
D= V= 19200- 12t

PLEASE HELP ASAP
PLEASE EXPLAIN HOW YOU GOT THE ANSWER

Answer:

Ans.=250 21/50

Step-by-step explanation:

54.2%=542/100

=271/50

=250 21/50

to get any percent value to a decimal or fraction format, we simply divide it by 100, first off let's make 54.2 to a fraction and then divide by 100.

\(54.\underline{2}\implies \cfrac{542}{1\underline{0}}~\hspace{10em}\cfrac{542}{10}\div 100\implies \cfrac{542}{10}\cdot \cfrac{1}{100}\implies \cfrac{271}{500}\)

The value of the union of sets A and B is, P(A ∪ B) is 0.64.

The union of two sets means the total elements in both the sets combined.

Given: sets P(A) = 0.38, P(B) = 0.83, and  intersection P(A ∩ B) = 0.57

We need to find the union of P(A ∪ B).

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Let us substitute the given values in the formula.

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

=0.38+0.83-0.57

=1.21-0.57

=0.64

Therefore, the value of union of sets P(A ∪ B) is 0.64.

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Answer: y = 45x + 345

Step-by-step explanation:

Hope this helps!!! :)

Answer:

2

Step-by-step explanation:

The number of traditional viewing theater is 14 , number of 3D movie viewing theaters is 2 , and number of luxury movie viewing theater is 5 .

In the question ,

it is given that

The 21-screen movie complex has  three types of movie theaters,

let the number of traditional movie viewing theater be  "a" ,

let the number of 3D movie viewing theater be  "b" ,

let the number of luxury movie viewing theater be  "c" ,

So , a+b+c=21      ...(i)

given that ,

Traditional viewing theaters are twice of the combined number of 3D and luxury theaters ,

So the equation is

a=2(b+c)         ...(ii)

also , the number of luxury theaters exceeds the number of 3D theaters by 3 ,

So , the equation is

c=b+3     ....(iii)

Substituting value of c from (iii) in (ii) and (i) we get ,

a-4b=6 and a+2b=18

Solving , we get a=14 and b=2 .

Substituting a=14 and b=2 in (iii) , we get

c=5 ,

So , a =14 , b=2 and c=5

Therefore , the number of traditional viewing theater is 14 , number of 3D movie viewing theaters is 2 , and number of luxury movie viewing theater is 5.

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Answer:

N=13

Step-by-step explanation:

For a pentagon, it's (5-2)180=(3)180=540 degrees. So plug in n=13 to see the sum of the angle measures for a 13-sided polygon.

There are 7920 different ways to pick four objects at a time.

If the order of objects is of importance, then we need to use the permutation formula to calculate the number of ways 11 objects can be selected 4 at a time. The permutation formula is:

P(n,r) = n! / (n-r)!

where P(n, r) is the number of permutations of n objects taken r at a time.

Substituting n = 11 and r = 4, we have:

P(11,4) = 11! / (11-4)!

P(11,4) = 11! / 7!

P(11,4) = (11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (7 x 6 x 5 x 4 x 3 x 2 x 1)

P(11,4) = 11 x 10 x 9 x 8

P(11,4) = 7920

Therefore, there are 7920 ways to select 11 objects 4 at a time if the order of objects is of importance.

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There are 1663200 different ways to pick four objects at a time.

Permutation is the process of rearrangement of elements of an ordered set.02 It is a bijection from S to itself, in which every element occurs exactly once as an image value

The statement reads that

If the order of objects is of importance, how many ways can eleven objects be selected four at a time

That is 11 permutation 4

\(11p_{4}\)

= 11!/(11-4)!

= 11*10*9*8*7*6*5

= 1663200

Therefore, there are 1663200 different ways to pick four objects at a time.

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The value of the function, f(1) is 3. Note that the answer is already in its simplest form and cannot be expressed as a fraction.

First, let's start by understanding what the function f(x) represents. The function f(x) takes an input value x and returns an output value based on a specific rule. In this case, the rule is defined by the equation f(x) = 4(1/4)^x+2.

To find f(1), we need to substitute 1 in place of x in the equation for f(x). So, we get:

f(1) = 4(1/4)^1 + 2

Now, we need to simplify this expression. Recall that any number raised to the power of 1 is just that number itself. So, (1/4)^1 is just 1/4.

Therefore, we can simplify the expression as follows:

f(1) = 4(1/4) + 2

= 1 + 2

= 3

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To get the ball to Craig, Natalie needs to throw it a distance of 10 feet.

The Pythagorean Theorem is named after the Greek mathematician Pythagoras. It is a theorem that relates the side lengths of a right triangle. It can be represented as a² + b² = c², where a, b, and c are the sides of the triangle. To solve the problem, we can use the Pythagorean Theorem. We can see that Shawn, Natalie, and Craig form a right-angled triangle. Hence, we can use the Pythagorean Theorem to calculate the distance between Natalie and Craig.

Using the Pythagorean Theorem, we can find that: Natalie and Craig are the two sides of the triangle that form the right angle. Let's label them as a and b. The hypotenuse, which is the distance between them, will be the side opposite to the right angle. Let's label it as c. We can see that a = 6 ft and b = 8 ft. The distance that Natalie needs to throw the ball to get it to Craig is equal to c.

Thus, substituting the values of a and b into the Pythagorean Theorem, we get: c² = a² + b²c² = 6² + 8²c² = 36 + 64c² = 100c = √100c = 10

Therefore, to get the ball to Craig, Natalie needs to throw it at a distance of 10 feet.

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The unit price for the apples is $1.5 per pound. The statement is true.

Now, According to the question:

How to calculate the Unit rate of the cost per pound?

8 pounds of Apple costs $12

The unit rate is

8= 12

1= x

We can write, by cross - multiply

8x = 12

x= 12/8

x= 1.5

Hence, the unit rate of the cost per pound is $1.5

And,  5 pounds of apples cost $7.50

cross multiply,

5× 12/8

60/8 = 7.50

5 pounds of apples = 7.50

Hence, The unit price for the apples is $1.5 per pound. The statement is true.

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Answer:

12/6=2

Step-by-step explanation:

If you set n=∞ it approaches zero

Therefore \(7^0+5=12\)

The total electric force on the 7.00−μC charge is 0.872 N at an angle of 330°.

The force exerted on the 7.00−μC charge by the 2.00−μC charge is

F₁​ ​= \(k_{e}\)q₁q₂​​/r₂ r^

= [(8.99×10⁹N.m²/C²)(7.00×10^−6C)(2.00×10^−6C) ×(cos60°i^+sin60°j^​)]/ (0.500m)²

F₁ ​= (0.252i^+0.436j^​)N

Similarly, the force on the 7.00μC charge by the −4.00−μC charge is

F₂​ ​= \(k_{e}\)q₁​q₃/​r² ​​r^

= [(8.99×10⁹N.m²/C²)(7.00×10^−6C)(−4.00×10^−6C)​×(cos60°i^−sin60°j^​)]/(0.500m)²

F₂​ ​=(0.503i^−0.872j^​)N

Hence, the total force on the charge 7.00−μC  is

F = F₁​​+F₂​

​=(0.755i^−0.436j^​)N

We can also note the total force as:

F = (0.755N)i^−(0.436N)j^​ = 0.872N

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--This question is incomplete; the complete question is

"Three charged particles are located at the corners of an equilateral triangle, as shown in Figure. Calculate the total electric force on the 7.00−μC charge."--

The number of periods over which interest is calculated on the loan.

We have to determine

The following formula is used to calculate the monthly payment on a personal loan.

The formula used to calculate monthly payments are as follows;

\(\rm P = PV \times \dfrac{i}{1-(i+1)^{-n}}\)

Where,

1. PV is the present value or the amount of the loan.

2. i is the interest rate per period and is calculated by dividing the yearly percent rate by 100 and by the number of periods in a year.

3. n is the total number of periods and is calculated as the product of the number of periods in a year times the number of years.

Hence, the number of periods over which interest is calculated on the loan.

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Answer: B.

Step-by-step explanation:

edge 2023

The null hypothesis (H0) is that the average time spent studying is 2 hours or less, while the alternative hypothesis (H1 or Ha) is that the average time spent studying is more than 2 hours.

The null hypothesis (H0) is a statement of no effect or no difference, while the alternative hypothesis (H1 or Ha) is a statement of the opposite, suggesting that there is an effect or a difference.

In this case, the professor does not believe that his students spend 2 hours on average studying for the final exam and thinks they spend more time than that.

The null hypothesis (H0) would be that the average time spent studying for the final exam is indeed 2 hours or less:

H0: μ ≤ 2

The alternative hypothesis (H1 or Ha) would be that the average time spent studying for the final exam is more than 2 hours:

Ha: μ > 2

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Answer:

8

Step-by-step explanation:

the volume of a box is L x W x H

so if you take the length x height, you can divide the volume by that to get your width.

hope this helps!! :)

The width of the rectangular box will be; 8cm

Given that the formula for calculating the volume of a rectangular box is expressed as:

V= w l h

Where L is the length

w is the width

h is the height

Given the following parameters;

Length l = 3 cm

Volume V = 120cm³

Height = 5cm

Find the width of the box as :

V= w l h

120 = w x 3 x 5

w = 120/ 15

w = 8

Hence, the width of the rectangular box will be 8 cm.

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The values of a and b that make the piecewise defined function f(x) = 3x + 4, for x < -3, and f(x) = 2x^2 + ax + b, for x > -3, both continuous and differentiable everywhere are a = 6 and b = 9.

To ensure that the piecewise defined function is continuous at the point where x = -3, we need the left-hand limit and right-hand limit to be equal. The left-hand limit is given by the expression 3x + 4 as x approaches -3, which evaluates to 3(-3) + 4 = -5.

On the right-hand side of the function, when x > -3, we have the expression 2x^2 + ax + b. To find the value of a, we need the derivative of this expression to be continuous at x = -3. Taking the derivative, we get 4x + a. Evaluating it at x = -3, we have 4(-3) + a = -12 + a. To make this expression continuous, a must be equal to 6.

Next, we find the value of b by considering the right-hand limit of the piecewise function as x approaches -3. Substituting x = -3 into the expression 2x^2 + ax + b, we get 2(-3)^2 + 6(-3) + b = 18 - 18 + b = b. To make the function continuous, b must equal 9.

Therefore, the values of a and b that make the piecewise defined function both continuous and differentiable everywhere are a = 6 and b = 9.

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Answer:

i don't know

Step-by-step explanation:

i don't know

Answer:

The answer would be 45 cups/ 75 people

Answer:

-8xy^5-6xy^4

Step-by-step explanation:

-10xy^5+(2x^3)(y^2)-(6x^2)(y^2)

-10xy^5+2xy^5 -6xy^4

-8xy^5-6xy^4

This should be good but if your teacher requires it just put 0 with the exponent in descending order

Answer:

Answering on an Alt account to give brainliest :p

Step-by-step explanation:

Personal car would be the best option to manage both tasks efficiently. While the train is a reliable mode of transportation, it may have fixed schedules that might not align perfectly with Patrick's needs.

On the other hand, using his personal car provides more flexibility and allows him to tailor the departure time according to his daughter's coding class schedule.

If Patrick decides to take the train, he would need to check the train schedule to see if there are convenient departure and arrival times for both the soccer game and the coding class. This option would require planning and coordination to ensure he arrives at the game on time and can pick up his daughter afterward.

Using his personal car gives Patrick the freedom to leave at a time that accommodates both the soccer game and the coding class. He can drop off his daughter at her coding class, attend the soccer game, and then pick her up afterward without being restricted by train schedules.

Considering the circumstances, Patrick might find it more convenient to use his personal car to manage both tasks effectively and ensure he can attend his son's soccer game while also ensuring his daughter arrives at her coding class on time.

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The length of the rectangle would be equal to the square root of 2 times "n/a".


To find the length (l) of a rectangle when you know the width (w) and the diagonal (d), you can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (d) is equal to the sum of the squares of the other two sides (l and w). In this case, we're looking for the length (l), so we can rearrange the formula to solve for it:

d^2 = l^2 + w^2
l^2 = d^2 - w^2
l = sqrt(d^2 - w^2)

However, in your question, you say that the width (w) and the diagonal (d) are both equal to "n/a". This means that we don't actually know their specific values - we only know that they are the same.

So if we substitute "n/a" for both "w" and "d" in the Pythagorean theorem, we get:

(n/a)^2 = l^2 + (n/a)^2
2(n/a)^2 = l^2
l = sqrt(2)*n/a

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The new pair of basketball shoes become a "desire" because Frankie already owns a pair that he can use for the tryout. Frankie's new basketball shoes would be viewed as a "need" if he didn't already have a pair for the tryout.

When referring to possessing or acquiring specific commodities, people frequently use the terms "want" and "need" interchangeably. In terms of economics, a need is what a person needs in order to survive. If a certain need is not met, a person may get sick or perhaps pass away. On the other hand, a desire is something that a person hopes to achieve in the near or distant future. In the first instance, Frankie is able to attend the tryout in a pair of basketball shoes that he already has. He could wear the shoes he already owns, thus the new pair of shoes would be his desire. In contrast, Frankie needs a new pair of sneakers in the second scenario because he doesn't have any basketball shoes for the tryout.

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Step-by-step explanation:

Point slope-form of a line passing through the point \((x_0, y_0)\) and having m is \(y-y_0=m(x-x_0)\cdots(i)\)

The slope-intercept form of a line having slope m and y-intercept c is

\(y=mx+c\cdots(ii)\)

(1). The line is passing through \((x_0, y_0)=(-5,6)\) and having the slope m=3.

So, by using equation (i), the point-slope form of the line is

\(y-6=3(x-(-5))\)

\(\Rightarrow y-6=3(x+5)\)

By using equation (ii), the slope-intercept form of the line is

\(y=3x+c\cdots(iii)\)

as the line is passing through the point (-5,6), so pout this point in the equation (iii) to get the value of c.

\(6=3\times(-5)+c\)

\(\Rightarrow 6=-15+c\)

\(\Rightarrow c=6+15=21\)

From equation (iii), the slope-intercept form of the line is \(y=3x+21\).

(2). The line is passing through the points (–5, 9) and (1, 3).

As two points are given, so the slope of the line is

\(m=\frac{3-9}{1-(-5)}=-1.\)

Now, proceeding in the same way as in part (1),

By using equation (i), the point-slope form of the line is

\(y-3=-1(x-1)\) [taking point (1,3) and m=-1]

By using equation (ii), the slope-intercept form of the line is

\(y=(-1)x+c\cdots(iv)\)

as the line is passing through the point (1,3), so pout this point in the equation (iv) to get the value of c.

\(3=-1\times1+c\)

\(\Rightarrow 3=-1+c\)

\(\Rightarrow c=3+1=4\)

From equation (iv), the slope-intercept form of the line is y=-x+4.

Answer:

f(x + 8) = x² + 23x + 121

Step-by-step explanation:

f(x + 8) = (x + 8)² + 7(x + 8) + 1

f(x + 8) = x² + 16x + 64 + 7x + 56 + 1

f(x + 8) = x² + 23x + 121

Answer

f(x + 8) = x^2 + 23x + 121

Answer:

No

Step-by-step explanation:

No, because 8 - 1 ≠ 27 - 8. So, there is no common difference which is needed in order for the sequence to be arithmetic

Answer:

35 miles per gallon.

Step-by-step explanation:

We need to simplify 175/5 into 35/1 to make it into a unit rate. So, 35 miles per gallon is the answer.

The z-score for a GPA of 3.29 that are normally distributed with a mean of 2.47 is 1.41.

A z-score can be defined as a measure of the distance between a raw score and the mean, when standard deviation units are used.

In a normal distribution, the z-score of a given sample score can be calculated by using this formula:

Z = (x - μ)/σ

Where:

Substituting the given parameters into the formula, we have;

Z-score, z = (3.29 - 2.47)/(0.58)

Z-score, z = 0.82/0.58

Z-score, z = 1.41

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Answer:

60x$70=$4100

Step-by-step explanation:

ekdjnsjs

Answer:

60 x 70= 4200$

Step-by-step explanation:

60

70   x

_____

(jk no need to do this just multiply them this way,because there are zeros just multiply 6 and 7 which equals 42 then add the zeros which are equal to= 4200$

Given the following expression:

The similar terms must have the same variable with the same exponents

So, note the following:

So, the given expression will be: