A water delivery truck is filling the water tank at Morgan's house. The truck arrived with 2400 L of water. The number of liters, L, remaining in the truck at time t minutes decreases at a rate of 110 L/min. Write an equation to represent this situation and then find how long it takes for the truck to have 1100 L left.

Z-score of given data comes to be -5.30.

It is given that

Population mean μ= 310

Standard deviation σ= 20

Mean of sample data X= 295

Sample size n= 50

A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.

For a hypothesis test

Z-score = (X-μ)/(σ/√n)

Where, X = observed value

μ= mean

σ = standard deviation

n =sample size

Z-score of above data = (295-310)/(20/√50)

Z-score = -5.30

Therefore, Z-score of given data comes to be -5.30.

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3475.699

°°°°°°°°°°°°°°°

Am I correct?

Considering the two dimensional autonomous system:

Hence, x′=−x+x

y=0⇒ x(1-y)=0

y′=98y−y2−12xy=0⇒ y(9-y-12x)=0

Therefore, the critical points of the system are given by(x, y) = (0,0), (0,9), and (2,6). The critical points are of the formx0 = [0 0], x1 = [0 y1], and x2 = [x2 y2].
The critical points of the system above have the form:

x0 = [0, 0],
x1 = [0, y1],
x2 = [x2, y2].

A two-dimensional autonomous system is a system of differential equations that describes the behavior of two variables over time, where the equations do not depend explicitly on time. These systems are also known as planar autonomous systems, since they can be graphically represented in a two-dimensional plane.

A general two-dimensional autonomous system can be written in the following form:

dx/dt = f(x,y)

dy/dt = g(x,y)

where x and y are the two variables, t is time, and f(x,y) and g(x,y) are the functions that describe how the variables change over time. The system is autonomous because it does not explicitly depend on time t.

To analyze the behavior of a two-dimensional autonomous system, one can use techniques such as phase plane analysis, which involves plotting the direction field (a grid of arrows indicating the direction of motion at each point in the plane) and the trajectories (curves that represent the solutions to the differential equations). The behavior of the system can be characterized by the equilibrium points (points where the trajectories do not move) and their stability (whether the trajectories move towards or away from the equilibrium points).

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The measure of angle ABO is 60 degrees. As O is the incenter of an isosceles triangle, the angle bisectors from O to AB and to the equal sides of the triangle are congruent.

Let the isosceles triangle be ABC with AB = AC and angle C = 100 degrees. Then, angle A is also 40 degrees. Since angle ABO is the exterior angle to triangle BOO100, it is equal to the sum of angles BOO100 and O100B.

Since triangle BOO100 is isosceles with BO = OO100, angle BOO100 = angle BOO = 40/2 = 20 degrees.

Similarly, triangle BO100 is isosceles with BO = O100, so angle BO100 = angle BCO = (180 - 100)/2 = 40 degrees. Thus, angle ABO is 20 + 40 = 60 degrees.

Therefore, the answer is (A) 40.

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Answer:

4n^2

Step-by-step explanation:

n to the power of 2 (squared), multiplied by 4

\(4n^{2}\)

An algebraic expression is one that is constructed using integer constants, variables, and algebraic operations.

Any of the common arithmetic operations, such as addition, subtraction, multiplication, division, raising to a whole number power, and taking roots, is a basic algebraic operation.

Square of \(n=n^{2}\)

Four times the square of \(n^{2}\) is equal to \(4n^{2}\)

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Answer:

1:25 or 1/25

Step-by-step explanation:

Rate=16/400

1/25 or 1:25

Answer: 16 to 400. This will be the answer I believe.

There were 9 zebra mussels in 2018.

We are given that in 2018, there were z zebra mussels in a section of the river.

In 2019, there were \(z^3\) zebra mussels in the same section.

And it is mentioned that there were 729 zebra mussels in 2019.

To find the value of z, we can set up an equation using the given information.

We know that \(z^3\) represents the number of zebra mussels in 2019.

And we are given that \(z^3\) = 729

To find the value of z, we need to find the cube root of 729.

∛(729) = 9

So, z = 9.

Therefore, in 2018, there were 9 zebra mussels in the section of the river.

You can verify this by substituting z = 9 into the equation:

\(z^3 = 9^3 = 729.\)

Hence, there were 9 zebra mussels in 2018.

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14. Constant of variation, k = 3/2

15. The graph does not represent a direct variation.

16. Constant of variation, k = 1/4

17. Constant of variation, k = 1

A direct variation is a proportional relationship where variable x varies directly with variable y. The equation of a direct variation is modelled by the equation below:

y = kx.

k is the constant of proportionality of the relationship between x and y. It is also referred as the unit rate. On a proportional or direct variation graph, it can be determined by using any point on the graph (x, y) to find k.

k = y/x.

All graphs that represent direct variations passes through the origin (0, 0). The coordinate of the constant of proportionality of a direct variation graph is (1, k), where the constant of variation = k, and x = 1.

14. The graph passes through the origin (0, 0), so it represents a direct variation.

Constant of variation, k = 3/2

15. The graph does not pass through the origin (0, 0), so it does  represent a direct variation.

16. The graph passes through the origin (0, 0), so it represents a direct variation.

Constant of variation, k = 1/4

17. The graph passes through the origin (0, 0), so it represents a direct variation.

Constant of variation, k = 1

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We want to complete the steps to convert the given quadratic equation into vertex form.

Eventually we will get:

y = (x + 1)^2 - 2

For a quadratic equation with the vertex (h, k), the vertex form is:

y = a*(x - h)^2 + k

Here we start with:

y = x^2 + 2x - 1

1) First, we complete the perfect-square trinomial, we need to add and subtract 1 to get that:

y = x^2 + 2x - 1 + 1 - 1

2) Now we rewrite the equation to be able of completing squares:

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

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

3) Now we complete squares

y = (x + 1)^2 - 2

And this is the equation in vertex form, where you can see that the vertex is the point (-1, - 2)

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Answer:

Q = 35

Step-by-step explanation:

1. You add both (m)x values and y values making them equal to 180 creating a 2 step-equation: (7x+2) + (10x-31) making that 17x-33= 180

2. Now you have a 2 step-equation to solve: 17x-33 = 180-33=147

                                                                                  +-33  +-33

                                                                                 __________

                                                                              17x = 147/17=21

                                                                               /17     /17

3. From here with 21, knowing the kite must equal to 180, you add 21 to the other angle 124: 124+21=145

4. Seeing that you don't have a total of 180, you now subtract 145 from 180 in order to get the value of Q: 180-145= 35

Q= 35

Step-by-step explanation:

7x + 2 = 10x - 31

33 = 3x

x = 11

so, 7x + 2 = 7( 11 ) +2 = 79°

10x - 31 = 10( 11 ) - 31 = 79°

ΔP + ΔQ + ΔR + ΔS = 360°

79° + ΔQ + 79° + 124° = 360°

ΔQ + 282° = 360°

ΔQ = 360° - 282°

ΔQ = 78°

The response variable in this experiment is the length of shots played by the golfers in a subsequent round after wearing the wrist bracelet. So, correct option is C.

This variable is of interest because it measures the potential impact of the wrist bracelet on the golfer's performance.

In this experiment, the independent variable is the type of wrist bracelet worn by the golfer - one with magnets and the other without magnets. The dependent variable, or response variable, is the length of the shots played by the golfer in a subsequent round.

To conduct the experiment, the golfers are randomly assigned to either wear a bracelet with magnets or without magnets. This is done to ensure that there is no bias in the sample and that each group has similar characteristics. The golfers then play normally for a month, and their shots are recorded in a subsequent round.

By comparing the lengths of shots played by the two groups, the golfer can determine if wearing a wrist bracelet with magnets has an impact on their performance. If there is a significant difference between the two groups, it may suggest that the magnets in the wrist bracelet improve balance and the length of shots played off the tee.

So, correct option is C.

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Complete question is:

Many golfers wear wrist bracelets containing magnets because they claim the magnets improve balance and the length of shots played off the tee. A golfer would like to determine if the claim has merit and finds 200 volunteers who play golf to participate in an experiment. Half of the golfers are randomly assigned to wear a bracelet with magnets, while the other half wear a bracelet without magnets. Each golfer plays normally for a month, after which the length of their shots in a subsequent round is recorded.

What is the response variable in this experiment?

a. the age of each golfer

b. the 200 volunteers

c. the length of shots played by the golfers

d. whether the golfers wear or do not wear the bracelet

Answer:

1 lb of chips cost $3.50

1 lb of walnuts cost $2.75

Step-by-step explanation:

c = $ chips

w = $ walnuts

System of Equations:

2w + 3c = 16

6w + 5c = 34

I multiplied the first equation by -3 to eliminate the 'w' terms to get

c = 3.5

I substituted 3.5 for 'c' to get 2.75 for 'w'

Answer:

$80,425

Step-by-step explanation:

total salary = base salary + commission

commission = commission rate * total sales

total salary = base salary + commission rate * total sales

total salary = $54,300 + 2.75% * $950,000

total salary = $54,300 + 0.0275 * $950,000

total salary = $80,425

Right triangles are said to be congruent if both the hypotenuse and one leg are the same length. These triangles are congruent by HL, or hypotenuse-leg.

When a triangle has precisely the same three sides and precisely the same three angles, it is said to be congruent. If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.

When the hypotenuse and one of the right triangle's sides equals the hypotenuse and the corresponding side of the other right-angled triangle, two right-angled triangles are said to be congruent to one another.

There are four theorems that demonstrate congruence with respect to right triangles. They are the hypotenuse-angle, leg-angle, hypotenuse-leg, and hypotenuse-angle-angle theorems.

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Complete question

Explain congruence in right angles.

Answer:

Step-by-step explanation:

We have to use PEMDAS

P is parentheses so we turn it to 6 + 2 divided by 15(7600)

E is for exponents but we don't have any

M is for multiplication and we have that so its 6 + 2 divided by 114000

D is for division so now its 6 + 1.754

A is for addition so 7.75400

Answer:

4,053.3 repeating

Answer: number 3 is the answer!!!

Step-by-step explanation:

number 3!!!

1) To find the missing ordered pair of a rectangle, we can use the fact that opposite sides of a rectangle are parallel and equal in length. This means that the x-coordinate of D must be equal to the x-coordinate of A, and the y-coordinate of D must be equal to the y-coordinate of C. Therefore, D(-3, -3).

2) Similarly, we can use the fact that opposite sides of a rectangle are parallel and equal in length. This means that the x-coordinate of H must be equal to the x-coordinate of E, and the y-coordinate of H must be equal to the y-coordinate of F. Therefore, H(0, 0).

3) To find the missing ordered pair of a square, we can use the fact that all sides of a square are equal in length and all angles are right angles. This means that the distance between J and K must be equal to the distance between K and L, which is 4 units. Therefore, the distance between L and M must also be 4 units. Since L has an x-coordinate of 2, M must have an x-coordinate of 2 + 4 = 6. Similarly, since L has a y-coordinate of -2, M must have a y-coordinate of -2 + 4 = 2. Therefore, M(6, 2).

4) To find the missing ordered pair of an isosceles right triangle, we can use the fact that two sides of an isosceles triangle are equal in length and two angles are equal in measure. This means that the distance between P and Q must be equal to the distance between Q and R, which is 6 units. Therefore, R must be 6 units away from Q along the x-axis. Since Q has an x-coordinate of 0, R must have an x-coordinate of 0 + 6 = 6. Similarly, since Q has a y-coordinate of 6, R must have a y-coordinate of 6 - 6 = 0. Therefore, R(6, 0).

Answer:

620

Explanation:

When the sample is given, the number of elk are likely to be infected is to be considered as the 620.

Calculation of the number of elk:

Since the population is 7,750.

The random sample is 50.

So here be like

= 620

hence, When the sample is given, the number of elk are likely to be infected is to be considered as the 620.

When booking a show for a future date, it is normal practice for the booking agent to collect a 50% advance fee when the advances are not given for shows. This is to ensure that the performer is fully committed to performing at the event and to cover any expenses that may be incurred in the process.

The advance fee is usually non-refundable and is paid by the promoter or venue operator to the booking agent. This is to show their commitment to the performer and to demonstrate that they are serious about booking them for the event. The remaining balance is then usually paid on the day of the performance or shortly after.

The booking agent should also ensure that all parties involved in the booking are aware of the terms and conditions and have signed a contract or agreement to confirm their agreement.

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Answer:

x = 15

Step-by-step explanation:

Interior angles and their exterior angles make a supplementary angle meaning they have a sum of 180°. Knowing this, we can make an equation to solve for x.

x + 165 = 180

x = 15

Answer:

C 4cm

Step-by-step explanation:

times 1.3 by 4 then divide 16 by 4

a) X'Y' + X'Y + XY simplifies to X' + Y.

b) A'BC' + ABC' + BC'D simplifies to BC'.

Complement of the functions:

a) Complement is W' + X' + YZ.

b) Complement is (A' + B + C)(A'B' + C' + A'B).

a) To prove X'Y' + X'Y + XY = X' + Y, we can use Boolean algebra identities:

X'Y' + X'Y + XY

= Y'(X' + X) + XY(Distributive Law)

= Y' + XY(X + X' = 1)

= X' + Y(Commutative Law)

Therefore, X'Y' + X'Y + XY simplifies to X' + Y.

b) To prove A'BC' + ABC' + BC'D = BC', we can simplify the expression using Boolean algebra:

A'BC' + ABC' + BC'D

= BC'(A' + A) + BC'D   (Distributive Law)

= BC' + BC'D(A + A' = 1)

= BC'(BC' + BC'D = BC' + BC'(1) = BC')

Hence, A'BC' + ABC' + BC'D simplifies to BC'.

Complement of the given functions:

a) The complement of WX(Y'Z + YZ') + W'X'(Y' + Z)(Y + Z') is W' + X' + YZ.

b) The complement of (A + B' + C')(A'B' + C)(A + B'C') is (A' + B + C)(A'B' + C' + A'B).

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Using DeMorgan's Law, an expression for the complement of F if F(x,y,z) = (x′ + y)(x + z)(y′ + z)′ is F'(x,y,z) = x'y'z' + xy'z' + x'y'z + xyz' + xyz.

To find the complement of F, we first need to apply DeMorgan's Law, which states that the complement of a product is the sum of the complements of the terms. So, we can rewrite F(x,y,z) as:
F(x,y,z) = (x' + y)(x + z)(y' + z)'
Using DeMorgan's Law, we can take the complement of each term inside the parentheses, and then switch the operation from multiplication to addition:
F'(x,y,z) = (x' * y')(x' * z') + (x * y')(x' * z') + (x' * y)(y' * z') + (x * y)(y' * z') + (x * z)(y' * z')
Simplifying this expression, we get:
F'(x,y,z) = x'y'z' + xy'z' + x'y'z + xyz' + xyz
Therefore, the complement of F(x,y,z) is F'(x,y,z) = x'y'z' + xy'z' + x'y'z + xyz' + xyz.

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To determine the total amount of soap needed, we can multiply the number of cars by the amount of soap required per car.

Let's denote the number of cups of soap needed as "x".

We know that it takes 8 2/3 cups of soap to wash each car, which can also be expressed as 26/3 cups of soap per car.

Therefore, the equation representing the situation is:

                                          x = (26/3) * 45

To solve this equation, we multiply the amount of soap required per car (26/3 cups) by the number of cars (45).

Multiplying these values gives us:

                           x = (26/3) * 45 = 390/3 ≈ 130 cups

Hence, the team needs approximately 130 cups of soap in total for washing 45 cars.

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Answer:

The range of possible values of x are;

x > 6

Step-by-step explanation:

To form a triangle, the length of two sides must be greater than the third side

Thus;

6x + 3 + 4x-17 > x + 40

6x + 4x-14 > x + 40

10x-14 > x + 40

10x-x > 40 + 14

9x > 54

x > 54/9

x > 6

Answer:

2 hours

Step-by-step explanation:

(MPH) = Miles an hour, So if you're going 50 Miles an hour it would take you 1 hour to travel 50 miles and 2 hours to drive 100 miles

Answer:

Multiply instead of divide

Step-by-step explanation

39/40=0.975  (Correct)

0.975x100=97.5%

If it were me I would just move the decimal point in 0.975 right twice, but since they're asking for a formula you would multiply instead of divide.

Hope this helps :)