Connor filled his 150 gallon pool with water in 6.25 hours. How many gallons per hour did he use?

Answer:

TR is the smallest side.

RS is in the middle.

ST is the largest side.

Step-by-step explanation:

Angle R is the biggest angle, so it is opposite from the biggest side (not R) side ST.

Angle S is the smallest angle so it is opposite from the smallest side (not S) side TR.

The third angle is in between, so the opposite side is in between.

The speed at which the bottom of the ladder is being pulled away from the wall is equal to the rate at which the top is sliding down, which is 1 ft/second.

The bottom of the ladder is being pulled away from the wall at the same rate at which the top of the ladder is sliding down the wall. As the top of the ladder slides down at a rate of 1 ft/second, the bottom of the ladder is also being pulled away at a rate of 1 ft/second.

The bottom of the ladder is being pulled away from the wall at a rate of 100 ft/second if the top of the ladder is sliding down at a rate of 100 ft/second.

The speed at which the bottom of the ladder is being pulled away from the wall is equal to the rate at which the top is sliding down, which is 1 ft/second.

Learn more about rate here

https://brainly.com/question/13481529

#SPJ4

Points C and D are elements of the same direct variation as Points A and B. When we say that Point A is an element of a direct variation, it means that there is a relationship between Point A and another point.

Let's call it Point B, such that when one value changes, the other changes in a specific way. Specifically, in a direct variation, when one value increases, the other value increases proportionally.

To select two other points that are also elements of this direct variation, we need to find two other points that have this same proportional relationship. One way to do this is to find points that have the same ratio of their values as Point A and Point B. For example, if Point A has values (2,4) and Point B has values (4,8), we can find two other points that have the same ratio of y-values to x-values.

Let's say we choose Point C to have x-value 3. Then its y-value would be 6, since 6/3 = 2/1 (the same ratio as Point A and Point B). Similarly, if we choose Point D to have x-value 5, then its y-value would be 10, since 10/5 = 2/1. Thus, Points C and D are elements of the same direct variation as Points A and B.

Learn more about variation here:

brainly.com/question/26537808

#SPJ11

By applying permutation concepts, there are 2730 possible sets of officers.

Permutation calculates the number of ways to choose a sample of r elements from a set of n distinct objects where order does matter and replacements are not allowed.

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

where n is the number of objects and r is the number of samples

In such an election, each person can only occupy one office. Therefore, the permutation concept is precisely used to calculate the number of ways to set these people.

P(15,3) = 15! / (15 - 3)!

           = (15 x 14 x 13 x 12!) / 12!

           = 15 x 14 x 13

           = 2730 ways

Thus, there are 2730 possible sets of officers.

To learn more about permutation, click here: https://brainly.com/question/28065038

#SPJ4

Step-by-step explanation:

Answer is in above picture

Answer:

Perimeter of the triangle is 58

Step-by-step explanation:

create an equation

(x+3)2+(2x-1)2=(x-7)+(4x-8)+(3x+1)

2x+6+4x-2=x-7+4x-8+3x+1

combine like terms

6x+4=8x-14

18=2x

x=9

now we substitute in the expression to find the perimeter

9-7=2

36-8=28

27+1=28

2+28+28=30+28=58

Step-by-step explanation:

Rules:

\( \sqrt[n]{a} = a^{\frac{1}{n}} \)

\( \sqrt[n]{a^m} = a^{\frac{m}{n}} \)

1.

\(\sqrt[3]{2} = 2^{\frac{1}{2}}\)

2.

\( \sqrt[3]{2x^2} = \sqrt[3]{2} \sqrt[3]{x^2} = 2^{\frac{1}{3}}x^{\frac{2}{3}} \)

3.

\(\sqrt[3]{(2x)^2} = \sqrt[3]{4x^2} = \sqrt[3]{4} \sqrt[3]{x^2} = 4^{\frac{1}{3}}x^{\frac{2}{3}}\)

Answer:

A Reflection

Step-by-step explanation:

In geometry, a reflections would be referred to as a flip. A reflection is a representation of a shape. An picture will mirror thru the line of reflection. If a figure is said to be a mirror of another figure, then every point in that figure is equal to every corresponding point in another figure.

Answer:

3 does not belong because its not long enough

Answer:

It should be red or green 125 times

Step-by-step explanation:

The first thing to do here is to calculate the probability of selecting a red or a green marble

Total number of marbles = 7 + 3 + 2 + 8 = 20

Probability of selecting a red marble is 7/20

Probability of selecting a green marble is 3/20

The probability of selecting a red or a green marble = Probability of selecting a red marble + Probability of selecting a green marble = 7/20 + 3/20 = 10/20 = 1/2

Now our selection spans 250 times, the number of times it should have been a green or a red marble = The probability of selecting a green or a red marble * number of selection times = 1/2 * 250 = 125 times

The solution to the given system is:

x(t) = (-2c₂/9) * exp(3t) * [3; -6] + c₂ * exp(-6t) * [-6; 2]

y(t) = (-2c₂/9) * exp(3t) * [3; -6] + c₂ * exp(-6t) * [-6; 2]

What is the system of equations?

A system of equations is a collection of one or more equations that are considered together. The system can consist of linear or nonlinear equations and may have one or more variables. The solution to a system of equations is the set of values that satisfy all of the equations in the system simultaneously.

To find the solution to the constant coefficient linear system, we can use the eigenvectors and eigenvalues provided.

Given:

X₁ = -4, eigenvalue λ₁ = 3, eigenvector v₁ = [3; -6]

X₂ = 0, eigenvalue λ₂ = -6, eigenvector v₂ = [-6; 2]

The general solution of the system is given by:

x(t) = c₁ * exp(λ₁ * t) * v₁ + c₂ * exp(λ₂ * t) * v₂

y(t) = c₁ * exp(λ₁ * t) * v₁ + c₂ * exp(λ₂ * t) * v₂

Plugging in the values:

x(t) = c₁ * exp(3t) * [3; -6] + c₂ * exp(-6t) * [-6; 2]

y(t) = c₁ * exp(3t) * [3; -6] + c₂ * exp(-6t) * [-6; 2]

To find the particular solution, we need to determine the values of c₁ and c₂ using the initial conditions:

x(0) = 0, y(0) = 0

Substituting t = 0:

x(0) = c₁ * exp(0) * [3; -6] + c₂ * exp(0) * [-6; 2] = c₁ * [3; -6] + c₂ * [-6; 2] = [0; 0]

y(0) = c₁ * exp(0) * [3; -6] + c₂ * exp(0) * [-6; 2] = c₁ * [3; -6] + c₂ * [-6; 2] = [0; 0]

This gives us the following system of equations:

3c₁ - 6c₂ = 0

-6c₁ + 2c₂ = 0

Solving this system of equations, we can find the values of c₁ and c₂. Adding twice the second equation to the first equation:

3c₁ - 6c₂ + 2(-6c₁ + 2c₂) = 0

3c₁ - 6c₂ - 12c₁ + 4c₂ = 0

-9c₁ - 2c₂ = 0

Simplifying:

9c₁ + 2c₂ = 0

We can solve this equation to find the values of c₁ and c₂:

c₁ = -2c₂/9

Therefore, the solution to the given system is:

x(t) = (-2c₂/9) * exp(3t) * [3; -6] + c₂ * exp(-6t) * [-6; 2]

y(t) = (-2c₂/9) * exp(3t) * [3; -6] + c₂ * exp(-6t) * [-6; 2]

To learn more about the system of equations visit:

brainly.com/question/25976025

#SPJ4

Proportions

All of the ingredients are given in amounts enough to make 3 dozen cookies. But we want to know how much of them are required to make 4 dozen cookies.

Following the proportions rules, if we want 4 and have 3, the adjustment must be 4 / 3, or four thirds.

For example, if you use 6 eggs for 3 dozen cookies, you now need 6*4/3=8 eggs.

This proportion will be applied to all of the ingredients as follows.

We needed 1 and 3/4 cups of vegetable oil. Expressing that as a single fraction:

The new amount of vegetable oil will be:

We now need 2 and 1/3 cups of vegetable oil.

It's required to use 2 and 1/4 teaspoons of almond extract. Expressing as a single fraction:

The new amount of almond extract is:

Now we need exactly 3 teaspoons of almond extract.

Finally, the recipe required 2 and 1/2 teaspoons of cinnamon. The equivalent fraction is:

This means the new amount of cinnamon is:

We now need 3 and 1/3 teaspoons of cinnamon.

Summarizing, for 4 dozen cookies we need:

2 and 1/3 cups of vegetable oil

3 teaspoons of almond extract

3 and 1/3 teaspoons of cinnamon

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{30\% of 25}}{\left( \cfrac{30}{100} \right)25}\implies 7.5\hspace{5em}\underset{ \textit{marked up price} }{\stackrel{25~~ + ~~7.5 }{\text{\LARGE 32.5}}}\)

Therefore, the state government should consider investing in new affordable housing initiatives.

a) To compute the 90% confidence interval, we can use the formula:

CI = p ± z*(√(p(1-p))/n)

where p is the sample proportion, z is the z-score corresponding to a 90% confidence level (which is 1.645), and n is the sample size.

Plugging in the values, we get:

CI = 0.517 ± 1.645*(√((0.517)(1-0.517))/4527)

CI = 0.505 to 0.529 (rounded to three decimal places)

b) The 90% confidence interval tells us that we are 90% confident that the true proportion of Californians who considered moving out of the state is between 0.505 and 0.529.

c) Since the confidence interval does not include the value of 0.5, which is the null hypothesis value, we can conclude that there is evidence to suggest that more than 50% of Californians would consider moving out of state due to high cost of housing.

To know more about confidence interval,

https://brainly.com/question/27375978

#SPJ11

"Why did you choose the outfit you wore today?" is an example of a open-ended question question.

An illustration of an open-ended question is "why did you choose the outfit you wore today?" An open-ended question is one that invites a range of responses and motivates the reply to give more specific information.

In this situation, a question is open-ended and is meant to inspire a unique response based on the person's preferences, views, or situation. In research, interviews, counseling, and other situations where gathering in-depth and varied information is desired, open-ended questions are frequently employed.

They can help researchers and practitioners better understand people's experiences and perspectives by offering insightful information about their thoughts, feelings, and behaviors.

To know more about open-ended question

https://brainly.com/question/20294009

#SPJ11

Answer:

92.4°

Step-by-step explanation:

Answer:

D. 16, 9, 8

Step-by-step explanation:

sum of any two sides of triangles must be greater than the third side

only the fourth option follows this rule

The number of different ways to select all of the items without replacement from a sample space with 48 elements is approximately 1.241391 × 10^61, which can be expressed in factorial notation as 48!.

When selecting items without replacement from a sample space, the number of different ways to select all of the items can be calculated using factorial notation.

In this case, the sample space has 48 elements. To find the number of ways to select all of the items without replacement, we need to calculate the factorial of 48, denoted as 48!.

Factorial notation represents the product of all positive integers less than or equal to a given number. So, 48! represents the product of all positive integers from 1 to 48.

Mathematically, we can calculate 48! as:

48! = 48 × 47 × 46 × ... × 3 × 2 × 1

This calculation can be time-consuming and challenging to do manually. However, using mathematical software or calculators with factorial capabilities, we can find the value of 48!.

By evaluating the expression, we find that 48! is an extremely large number:

48! ≈ 1.241391 × 10^61

Therefore, there are approximately 1.241391 × 10^61 different ways to select all of the items from the sample space without replacement.

Learn more about expression here:

https://brainly.com/question/29583350

#SPJ11

The level in the pot is rising at a rate of approximately 0.795 in./min. and the level in the cone is falling at a rate of 0.125 in./min.

To solve this problem, we can use related rates. Let's denote the radius and height of the cone by r and h, respectively, and the height of the coffee in the cone by x. We are given that dx/dt = -10 in^3/min, since the coffee is draining from the cone into the pot.

Using the formula for the volume of a cone, V = (1/3)πr^2h, we can express the rate of change of the volume of coffee in the cone as dV/dt = (1/3)πr^2 dh/dt.

To find dh/dt, we can use similar triangles, since the radius and height of the cone are changing as the coffee drains. Specifically, we have r/x = (r+h)/h, which implies r = (hx)/(x+h). Taking the derivative of both sides with respect to time, we get dr/dt = (hdx - xdh)/(x+h)^2.

Now, we can substitute our expressions for dV/dt and dr/dt into the formula for the chain rule: dV/dt = dV/dr * dr/dt = (1/3)πr^2 dh/dt. Solving for dh/dt, we get:

dh/dt = (-3x/x^2) * (πr^2/3) * dx/dt - (2r/3) * (πr^2/3) * dh/dt

Simplifying and solving for dh/dt, we get:

dh/dt = (-10πx^2r)/(3x^2 + 3hx + h^2)

Plugging in x = 5 in., r = (5/6) in. (since the radius of the cone is half the height), and h = 10 in. (since the cone is full), we find that dh/dt ≈ -0.125 in./min. This means that the level in the cone is falling at a rate of 0.125 in./min.

We know that dh/dt = -10 in^3/min, so we can express the rate of change of the volume of coffee in the pot as dV/dt = π(r₁)^2 dh₁/dt.

Solving for dh₁/dt, we get:

dh₁/dt = (1/π(r₁)^2) dV/dt = (10π(5/6)^2)/(π(6/2)^2) ≈ 0.795 in./min.

To learn more about cone click on,

https://brainly.com/question/30271642

#SPJ4

The linear equation which can be derived from this proportion is 2x - 6 = 5x - 45

The correct answer choice is option D.

(x - 9) / (x - 3) = 2/5

cross product

(x - 9)5 = (x - 3)2

5x - 45 = 2x - 6

combine like terms

5x - 2x = - 6 + 45

3x = 39

divide both sides by 3

x = 39/3

x = 13

Ultimately, 2x - 6 = 5x - 45 is the linear equation that can be derived from the proportion.

Read more on linear equations:

https://brainly.com/question/2030026

#SPJ1

roots = {-2, -6}

Factors: (x + 6) and (x + 2)

Answer: 63.114

Step-by-step explanation:

Multiply like normal but don’t bring your decimal down count how many number are behind the decimal. You have 2 on the first number and 1 on the second so count 3 places

Answer:

63.114

Step-by-step explanation:

See the picture I attached, I hope this helps!

Answer:

8

Step-by-step explanation:

2 : 1/4

2 x 4/1

2 x 4

8

Answer:

x = 135

Step-by-step explanation:

The angles are vertical angles and vertical angles are equal

125 = x-10

Add 10 to each side

125+10 = x

135 =x

Answer:

B

Step-by-step explanation:

use y=mx+c

follow the flow

Answer:

Well no solution equations meaning it doesn't equal anything but

Infinite solutions means it can be any number according to the question

Step-by-step explanation:

Answer:

See the attached worksheet

Step-by-step explanation:

The function is transformed by subtracting 3 from both the x and y values. I'm uncertain how this is expressed in a functional form.

Answer:

3;  y=4

Step-by-step explanation:

2 should be distributed as 2y + 8; y = 4

2(y +4) = 4y

2y + 8 = 4y

8 = 2y

y = 4