Hello can you help meee

The rate at which the gas powered pump deliver water is 160.9 litres per seconds

The gas powered water pump delivers 42.50 gallons of water per minute.

Therefore,

1 gallon = 3.78541 litres

42.50 gallons = ?

cross multiply

volume = 42.50 × 3.78541 = 160.879925 litres

Hence,

60 seconds = 1 minutes

1 second = ?

time = 1 / 60 = 0.01666666666 seconds

Hence,

rate = 160.9 litres per second

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Answer:

4.8

Step-by-step explanation:

Answer:

4.8 miles

Step-by-step explanation:

Let's make a proportion using this setup:

miles/minutes=miles/minutes

We know that Nicole runs 6 miles in 55 minutes. We don't know how many miles she runs in 44 minutes, so we can say she runs x miles in 44 minutes.

6 miles/55 minutes=x miles/44 minutes

6/55=x/44

Now, we have to find x. To do this, we need to get x by itself. x is being divided by 44. To undo this, multiply both sides by 44, since multiplication is the opposite of division.

44*(6/55)=(x/44)*44

The 44s on the right cancel, so we are left with:

44*6/55=x

4.8=x

Nicole can run 4.8 miles in 44 minutes

Angle-Angle-Side (AAS) Theorem has two sides and a non-included angle.

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Since this time is faster than the qualifying time of 1 minute and 30 seconds, Tyler will qualify for the state swim competition.

The domain for this model would be as follows:

Current Race Time: Any positive value representing minutes and seconds (e.g., 1:42 would be 1 minute and 42 seconds).

Reduction Percentage: 1.5% (0.015) per month.

Number of Months: Any positive integer value between 0 and 12.

Current Race Time: 1 minute 42 seconds (1:42).

Qualifying Time: 1 minute 30 seconds (1:30).

Estimated Race Time = 1:42 * (1 - 0.015)¹²

= 1:42 * (0.985)¹²

= 1:42 * 0.832677567

≈ 1:25.1

The estimated race time after 12 months of practice is approximately 1 minute and 25.1 seconds. Since this time is faster than the qualifying time of 1 minute and 30 seconds, Tyler will qualify for the state swim competition.

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The extreme values of f(x, y) = xy occur at the points (2, 1) and (-2, -1) on the ellipse \(3x^{2} +2y^{2} =1\).

To find the extreme values of f(x, y) = xy on the ellipse \(3x^{2} +2y^{2} =1\), we can use the method of Lagrange multipliers.

Define the function g(x, y) = \(3x^{2} +2y^{2} -1\). We need to find points (x, y) where the gradient of f is proportional to the gradient of g:

∇f = λ∇g

The gradient of f is ∇f = (y, x), and the gradient of g is ∇g = (6x, 4y). Therefore, we have the following system of equations:

y = 6λx
x = 4λy

Substitute the second equation into the first:

y = 6λ(4λy)
y = \(24λ^{2y}\)

If y ≠ 0, then 1 = \(24λ^{2}\), and λ = ±1/2. Plugging this value into the second equation gives x = ±2. Thus, we have two potential extreme points: (2, 1) and (-2, -1).

Now consider the case when y = 0. The constraint equation becomes \(3x^{2} =1\), and x = ±1/√3. However, these points correspond to f(x, y) = 0, which is not an extreme value.

Therefore, the extreme values of f(x, y) = xy occur at the points (2, 1) and (-2, -1) on the ellipse \(3x^{2} +2y^{2} =1\).

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Using separation of variables, it is found that the solution to the initial value problem is of y(x) = x² + 2.

In separation of variables, we place all the factors of y on one side of the equation with dy, all the factors of x on the other side with dx, and integrate both sides.

In this problem, the differential equation is given by:

\(\frac{dy}{dx} = 2x\)

Then, applying separation of variables:

\(dy = 2x dx\)

\(\int dy = \int 2x dx\)

\(y = x^2 + K\)

Since y(0) = 2, we have that the constant of integration is K = 2, and the solution is:

y(x) = x² + 2.

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The differential equation is y(x) = x² + 2.

Differential Equations In Mathematics, a differential equation is an equation that contains one or more functions with their derivatives.

The given equation is;

\(\rm \dfrac{dy}{dx}=2x\)

Applying the variable separation method;

\(\rm \dfrac{dy}{dx}=2x\\\\\int\limits \, dy=\int\limits\, 2x. dx\\\\y = 2 \times \dfrac{x^{1+1}}{1+1} +c\\\\y = 2 \times \dfrac{x^{2}}{2} +c\\\\y = x^2+c\)

The value of c when y( 0 ) = 2 is c =2.

Hence, the required differential equation is y(x) = x² + 2.

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Answer:

12

Step-by-step explanation:

7x4=28

40-28=12

To find the matrix A, we need to use the definition of eigenvectors and eigenvalues

Let's denote the eigenvectors as v₁ and v₂, and the corresponding eigenvalues as λ₁ and λ₂:

v₁ = [-3]

[-2]

v₂ = [-5]

[-5]

λ₁ = 3

λ₂ = -2

According to the definition, for an eigenvector v and eigenvalue λ, the matrix A satisfies the equation Av = λv.

So, we can set up two equations using the given information:

Av₁ = λ₁v₁

Av₂ = λ₂v₂

Substituting the values:

A[-3] = 3[-3]

[-2] [-2]

and

A[-5] = -2[-5]

[-5] [-5]

Simplifying these equations, we have:

[-3a₁ - 2a₂] = [-9]

[-2a₁ - 2a₂] [-6]

and

[-5a₁ - 5a₂] = [10]

[-5a₁ - 5a₂] [10]

We can rewrite these equations as a system of linear equations:

-3a₁ - 2a₂ = -9 (Equation 1)

-2a₁ - 2a₂ = -6 (Equation 2)

-5a₁ - 5a₂ = 10 (Equation 3)

-5a₁ - 5a₂ = 10 (Equation 4)

To solve this system of equations, we can use any method such as substitution or matrix operations. However, we can observe that Equations 3 and 4 are the same, which means they provide redundant information. We can eliminate one of them:

From Equation 1: -3a₁ - 2a₂ = -9

Multiplying Equation 2 by 3, we get:

-6a₁ - 6a₂ = -18 (Equation 5)

Adding Equation 1 and Equation 5, we have:

-3a₁ - 2a₂ + (-6a₁ - 6a₂) = -9 + (-18)

Simplifying, we obtain:

-9a₁ - 8a₂ = -27 (Equation 6)

Now we have a system of two linear equations:

-3a₁ - 2a₂ = -9 (Equation 1)

-9a₁ - 8a₂ = -27 (Equation 6)

Solving this system, we find the values of a₁ and a₂. Once we have these values, we can construct the matrix A:

A = [a₁ a₂]

[a₁ a₂]

Substituting the calculated values of a₁ and a₂ will give us the final matrix A.

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The equation of the parabola is y = -3(x + 2)^2 + 6

From the graph, we have:

A parabola is represented as:

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

Substitute (h,k) = (-2,6)

y = a(x + 2)^2 + 6

Substitute (x,y) = (-1,3)

3 = a(-1 + 2)^2 + 6

Evaluate

3 = a + 6

Subtract 6 from both sides

a = -3

Substitute a = -3 in y = a(x + 2)^2 + 6

y = -3(x + 2)^2 + 6

Hence, the equation of the parabola is y = -3(x + 2)^2 + 6

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Since we want to find the number of trips to the park for which paying daily admission is more expensive than purchasing a season pass​, we can express an inequality, like this:

total daily admission cost > season pass cost

The total daily admission cost, can be expressed as the number of days that this pass is purchased (n) times the daily admission cost ($39), and the season pass cost equlas $117, then we get:

$39*n > $117

From this expression we can solve for n, then we get:

Then, more than 3 daily passes would be more expensive than the season pass. Since it must be more than 3, the answer is 4 trips

Answer:

Step-by-step explanation:

 This problem is borers on elasticity of materials.

according to Hooke's law, "provided the elastic limit of an elastic material is not exceeded the the extension e is directly proportional to the applied force."

\(F= ke\)

where F is the applied force in N

          k is the spring constant N/m

          e is the extension in meters

Given data

mass m= 24kg

extensnion=15cm in meters= \(\frac{15}{100}\)= \(0.15m\)

we can solve for the spring constant k

we also know that the force F = mg

assuming \(g=9.81m/s^{2}\)

therefore

\(24*9.81=k*0.15\\235.44=k*0.15\\k=\frac{235.44}{0.15} \\k=1569.6N/m\\\)

We can use this value of k to solve for the mass that will cause an extension of  \(10cm= 0.1m\)

\(x*9.81=1569.6*0.1\\\\x= \frac{156.96}{9.81} \\\x= 16kg\)

The coordinate matrix of x in the basis b' is calculated to be,

[-2    1      6]

[ 1     0     4]

[ 0   10    6]

To find the coordinate matrix of x in the basis b', we need to express x as a linear combination of the basis vectors in b', and then use the coefficients of the linear combination as the entries of the coordinate matrix.

So we want to find scalars a, b, and c such that:

(4, 30, -8) = a(8, 11, 0) + b(7, 0, 10) + c(1, 4, 6)

Expanding this equation, we get a system of linear equations,

8a + 7b + c = 4

11a + 4c = 30

10b + 6c = -8

Solving the above  system of equations, we will get:

a = -2, b = 1, and c = 6

Hence , the required coordinate matrix of x in the basis b' is found to be :

[-2  1  6]

[ 1  0  4]

[ 0 10  6]

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Answer:

707

Step-by-step explanation:

If 5/8 of the pupils are boys if there are 15 girls in that class then the number of boys are 25.

A fraction represents a part of a whole.

If 5/8 are boys then

1 - 5/8 = girls

3/8 = girls

3/8 of the total are girls

Let x = total

3/8 ( x) = 15

8/3 * 3/8 * x = 15 * 8/3

x = 40

There are 40 total students

5/8 are boys

5/8 × 40

25 are boys

Hence, if 5/8 of the pupils are boys if there are 15 girls in that class then the number of boys are 25.

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In order to summarize qualitative data, a useful tool is a frequency distribution.

Frequency distribution is a table or graph that shows the number of occurrences of each unique value or range of values in a dataset. It is a way of summarizing and organizing a set of data by grouping them into mutually exclusive classes or bins and counting the number of observations in each class. The resulting table or graph is called a frequency table or frequency distribution. The classes or bins are often defined based on the scale of measurement of the variable, such as intervals for continuous variables or categories for categorical variables. Frequency distribution is a useful tool for understanding the distribution of a variable and identifying patterns or outliers in the data.

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The product of three numbers 2 , 4, 9 will be 72 .

Given,

Absolute values: 2 , 4 , 9

Here 2 can be generated both from 2 and - 2, 4 from 4 and - 4 and 9 from 9 and - 9.

Then, the product of the three numbers is presented below:

|x₁| · |x₂| · |x₃| = 2 · 4 · 9 = 72

The product of the three absolute values is equal to 72.

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Answer:

a  

Step-by-step explanation:

hope this help u  and  hope u get a good grasde :}

Answer:

A) x < 9

Step-by-step explanation:

Here we have an open circle. Open circles are used for greater than signs (>) and less than signs (<).

Since we have an open circle, we can eliminate option C and option D.

Now, we look at the number line.

The point is at 9, and the line from the point is going towards the left (where the smaller numbers are.)

9 is greater than every number is going toward.

**Let x represent every number is going toward.**

Therefore, x < 9.

The probability that a randomly selected woman is taller than 5 ft 10 in (70 inches) is approximately 0.0143 or 1.43%.

To find the probability that a randomly selected woman is taller than 5 ft 10 in, we need to convert the height to inches and then calculate the probability using the Normal distribution.

5 ft 10 in is equivalent to 5(12) + 10 = 70 inches.

Let's calculate the z-score corresponding to a height of 70 inches using the formula: z = (x - μ) / σ

where x is the observed value, μ is the mean, and σ is the standard deviation. In this case, x = 70 inches, μ = 63.8 inches, and σ = 2.8 inches.

\(z=\frac{70-63.8}{2.8} = 2.214\)

Using a standard Normal distribution table or calculator, we can find the probability associated with this z-score.The probability of a randomly selected woman being taller than 5 ft 10 in (70 inches) can be found by calculating the area under the Normal distribution curve to the right of z = 2.214.

P(Z > 2.214) = 1 - P(Z ≤ 2.214)

By looking up the corresponding probability in the standard Normal distribution table or using a calculator, we find that P(Z ≤ 2.214) ≈ 0.9857.

Therefore, P(Z > 2.214) = 1 - 0.9857 =0.0143.

Thus, the probability that a randomly selected woman is taller than 5 ft 10 in (70 inches) is approximately 0.0143 or 1.43%.

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Answer:

p/m^8

Step-by-step explanation: because the 0 in p^0 would be erelivant so you would divide those to letters together getting that awser

Answer:

On time: 0.67

Late: 0.33

Step-by-step explanation:

Probabilities

One approach to estimating the probability of occurrence of an event is to record the number of times that event happens (e) and compare it with the total number of trials (n).

The probability can be estimated with the formula:

\(\displaystyle P=\frac{e}{n}\)

And the probability that the event doesn't occur is

Q = 1 - P

Paulo arrives on time to school e=53 times out of n=79 times. The probability that he arrives on time is:

\(\displaystyle P=\frac{53}{79}\)

P = 0.67

And the probability he arrives late is:

Q = 1 - 0.67 = 0.33

4b + 6 = 2 - b + 4

Combine like terms on the right side:

4b + 6 = -b + 6

Subtract 6 from both sides:

4b = -b

Add 1b to both sides:

5b = 0

Divide both sides by 5:

B = 0

Answer:

0

Step-by-step explanation:

4b +6 =2-b +4

4b +b =2+4 - 6

5b =6 - 6

5b =0

b=0

Therefore, the correct option is (b) 46 that is the number of students who like Twix and Reese's peanut butter cups only (region D) by principle of inclusion-exclusion, we need to subtract the number of students who like Snickers, as well as the number of students who like all three kinds of candy, from the number of students who like Twix and Reese's peanut butter cups along with one or both of the other kinds of candy.

We can start by using the principle of inclusion-exclusion, which tells us that:

|A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|

where |X| denotes the number of elements in set X.

Using the numbers given in the problem, we have:

|A| = 129

|B| = 118

|C| = 145

|A ∩ B| = 22

|B ∩ C| = 54

|A ∩ C| = 55

|A ∩ B ∩ C| = 8

Substituting these values into the formula, we get:

|A ∪ B ∪ C| = 129 + 118 + 145 - 22 - 55 - 54 + 8 = 269

This tells us that 269 students like at least one of the three kinds of chocolate candy.

To find the number of students who like Twix and Reese's peanut butter cups only (region D), we need to subtract the number of students who like Snickers, as well as the number of students who like all three kinds of candy, from the number of students who like Twix and Reese's peanut butter cups along with one or both of the other kinds of candy:

|D| = |B ∩ C| - |A ∩ B ∩ C|

= 54 - 8

= 46

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To find f(g(x)), substitute g(x) into f(x). Simplifying gives f(g(x)) = log6(36g(x)). For range of y in f(x) + g(x), Take possible values . Since log6(36x) is defined for x > 0, and 6 is positive, the range of y is (0, ∞).

a) To find f(g(x)), we substitute g(x) into f(x):

f(g(x)) = f(6x) = log6(36(6x)) = log6(216x) = log6(6^3x) = 3log6(6x) = 3(log6(6) + log6(x)) = 3(1 + log6(x)) = 3 + 3log6(x).

Thus, f(g(x)) simplifies to 3 + 3log6(x).

(b) To find the range of y in f(x) + g(x), we need to consider the possible values of f(x) and g(x). Since log6(36x) is defined for x > 0, and 6* is always positive, the range of f(x) is (0, ∞). Similarly, g(x) = 6* is always positive, so the range of g(x) is also (0, ∞).When we add f(x) and g(x), we are adding two positive functions, resulting in values greater than 0. Therefore, the range of y in f(x) + g(x) is (0, ∞).

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Answer:

(-4,5)

Step-by-step explanation:

(-4,5) is the solution.

Answer:

(a) y = (p - 3x) cm

(b) p = 35 cm

Step-by-step explanation:

Total length of the ribbon = p cm

The length of the first part = x cm

The length of the second part = 2x cm

Let the length of the third part be represented by y.

(a) Thus,

x + 2x + y = p

3x + y = p

y = p - 3x

An expression for the length of the third part is (p - 3x) cm

(b) If x = 10 cm, then;

length of first part = 10 cm

length of the second part = 2x

                                           = 2(10)

                                           = 20 cm

But,

length of the second part = 4y

i.e 20 = 4y

y = 5 cm

The value of p = 10 + 20 + 5

                        = 35 cm

p = 35 cm

Angle ABC is greater than angle C, as required. Given triangle ABC with AC greater than AB, and BD drawn such that AD is congruent to AB, we need to prove that angle ABC is greater than angle C.

To begin with, we can draw a diagram to visualize the situation. In the diagram, we see that BD is an altitude of triangle ABC, as well as a median since it divides the base AC into two equal parts. We also see that triangles ABD and ABC are congruent by the side-side-side (SSS) criterion, which means that angle ABD is equal to angle ABC.

Now, we can use this information to prove our statement. Since triangle ABD and triangle ABC are congruent, their corresponding angles are also equal. Therefore, we know that angle ABD is equal to angle ABC.

Next, we observe that angle ABD is a right angle, since BD is an altitude of triangle ABC. This means that angle ABC is the sum of angles ABD and CBD.

Since AD is congruent to AB, we also know that angles ABD and ADB are congruent. Therefore, angle CBD is greater than angle ADB.

Putting all of this together, we can conclude that angle ABC is greater than angle C, as required.

In summary, we have shown that given triangle ABC with AC greater than AB and BD drawn such that AD is congruent to AB, angle ABC is greater than angle C. This is because angles ABD and CBD add up to angle ABC, and angle CBD is greater than angle ADB.

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Answer:

Number is 20.

Step-by-step explanation:

Let's call the number we're trying to find "x".

We can translate the problem into an equation:

1/8x + 1.5 = 4

To solve for x, we'll first subtract 1.5 from both sides:

1/8x = 2.5

Then, we'll multiply both sides by 8:

x = 20

So the number we're looking for is 20.

The Laplace transform of the given function is,

L{f(t)} = (8/s) - 4e^{-3s/2}/s - 6e^{-2s}/s

Given function is f(t) = {8 12 1 Jo, 0 ≤ t < 3/2, 3/2 ≤ t < 2, 2 ≤ t < ∞ respectively.

We have to find Laplace transform of the given function.

For first interval 0 ≤ t < 3/2,

f(t) = 8u(t) - 8u(t-3/2)

For second interval 3/2 ≤ t < 2,

f(t) = 12u(t-3/2) - 12u(t-2)

For third interval 2 ≤ t < ∞,

f(t) = Jo(u(t-2))

Hence, we can write the Laplace transform of the given function as,

L{f(t)} = L{8u(t) - 8u(t-3/2)} + L{12u(t-3/2) - 12u(t-2)} + L{Jo(u(t-2))}

Where, L is Laplace transform.

Let's calculate each Laplace transform stepwise,

1. L{8u(t) - 8u(t-3/2)}L{8u(t)} = 8/L{u(t)}L{u(t)}

= 1/sL{u(t-3/2)}

= e^{-3s/2}/s

Therefore,

L{8u(t) - 8u(t-3/2)} = 8[1/s - e^{-3s/2}/s]

2. L{12u(t-3/2) - 12u(t-2)}L{12u(t-3/2)}

= 12e^{-3s/2}/sL{12u(t-2)}

= 12e^{-2s}/s

Therefore,

L{12u(t-3/2) - 12u(t-2)} = 12[e^{-3s/2}/s - e^{-2s}/s]

3. L{Jo(u(t-2))}L{Jo(u(t-2))} = ∫_{0}^{∞}δ(t-2)e^{-st}dtL{Jo(u(t-2))}

= e^{-2s}

Hence, the Laplace transform of the given function is,

L{f(t)} = 8[1/s - e^{-3s/2}/s] + 12[e^{-3s/2}/s - e^{-2s}/s] + e^{-2s}

= (8/s) - 4e^{-3s/2}/s - 6e^{-2s}/s

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