Mr. Billings has four teenage children, a swimming pool, a big lawn, and a large garden. His water bills are very high, so he wants to learn how to reduce his bill.


Every month, he pays a base fee of $37.78, and then he gets billed for how much water he uses. His water bill states the following tiers for different levels of water usage. HCF stands for one hundred cubic feet, or about 748.05 gallons.


Mr. Billings has four teenage children, a swimming pool, a big lawn, and a large garden. His water bills are very high, so he wants to learn how to reduce his bill.


How much does the Billings family need to reduce their water usage to so that their water bill for August is less than $200? Less than $150?

The result of applying the power rule to [tex](A^{x} )^{y}[/tex] is [tex]A^{xy}[/tex].

The power rule of exponentiation states that when a base is raised to a power, and that power is then raised to another power, we can simply multiply the exponents. In other words, [tex](A^{m} )^{n}[/tex] = [tex]A^{mn}[/tex].

Therefore, when we apply the power rule to [tex](A^{x} )^{y}[/tex], we can simply multiply the exponents. This gives us the result of [tex](A^{x} )^{y}[/tex] = [tex]A^{xy}[/tex].

To understand this, let's take an example. Suppose A=2, x=3, and y=4. So we have [tex](2^{3} )^{4}[/tex]. By applying the power rule, we can simplify this as [tex](2^{3} )^{4}[/tex]=[tex]2^{12}[/tex].

In essence, what the power rule does is it allows us to simplify complex expressions involving exponents into simpler forms. This is particularly useful when dealing with algebraic expressions or mathematical formulas that involve multiple exponentiations.

In summary, the result of applying the power rule to [tex](A^{x} )^{y}[/tex] is[tex]A^{xy}[/tex], which represents the simplified form of the expression.

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1. The set of sophomores at your school who are not taking discrete mathematics: A ∩ Bᶜ.
2. The set of sophomores taking discrete mathematics in your school: A ∩ B.
3. The set of students at your school who either are sophomores or are taking discrete mathematics: A ∪ B.
4. The set of students at your school who either are not sophomores or are not taking discrete mathematics: Aᶜ ∪ Bᶜ.

1. The set of sophomores at your school who are not taking discrete mathematics can be represented symbolically as A - B. This means that we take all the elements in set A (sophomores) and subtract the elements in set B (students taking discrete mathematics) from it, which gives us the set of sophomores who are not taking discrete mathematics.

2. The set of sophomores taking discrete mathematics in your school can be represented symbolically as A ∩ B. This means that we take the intersection of sets A and B, which gives us the set of students who belong to both sets A and B. In this case, it gives us the set of sophomores taking discrete mathematics.

3. The set of students at your school who either are sophomores or are taking discrete mathematics can be represented symbolically as A ∪ B. This means that we take the union of sets A and B, which gives us the set of all students who belong to either set A or set B (or both). In this case, it gives us the set of all sophomores and all students taking discrete mathematics.

4. The set of students at your school who either are not sophomores or are not taking discrete mathematics can be represented symbolically as U - (A ∩ B). This means that we take the complement of the intersection of sets A and B from the universal set U. In other words, we take all the elements in the universal set U and subtract the elements that belong to both sets A and B, which gives us the set of all students who either are not sophomores or are not taking discrete mathematics.

1. The set of sophomores at your school who are not taking discrete mathematics: A ∩ Bᶜ. This represents the intersection of set A (sophomores) and the complement of set B (students not in discrete mathematics).

2. The set of sophomores taking discrete mathematics in your school: A ∩ B. This represents the intersection of set A (sophomores) and set B (students in discrete mathematics).

3. The set of students at your school who either are sophomores or are taking discrete mathematics: A ∪ B. This represents the union of set A (sophomores) and set B (students in discrete mathematics).

4. The set of students at your school who either are not sophomores or are not taking discrete mathematics: Aᶜ ∪ Bᶜ. This represents the union of the complement of set A (students not in the sophomore class) and the complement of set B (students not in discrete mathematics).

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a) The domain of the function is D : x < 7 or x > 7

b) The range of the function R : f ( x ) < 6

c) The vertical asymptote : x = 7

d) The horizontal asymptote : y = 6

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = [ -1/ ( 5x - 35 )² ] + 6

On simplifying , we get

when the denominator is simplified to 0 , the function is undefined

So , 5x - 35 = 0

Adding 35 on both sides , we get

5x = 35

x = 7

So , the domain cannot be 7

a) The domain of the function is D : x < 7 or x > 7

b) The range of the function R : f ( x ) < 6

c) The vertical asymptote : x = 7

d) The horizontal asymptote : y = 6

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Answer: 9/8 is the slope

The cli option on the model statement of an mlr analysis in proc glm is used to produce confidence intervals for the slope parameters.

These intervals provide an estimate of the range of values within which the true slope parameter is likely to lie, given the data and the model that has been fitted to it. Confidence intervals are a useful tool for assessing the uncertainty associated with estimates of model parameters and can be used to determine whether a particular predictor variable is statistically significant or not.

In contrast to prediction intervals, which are used to estimate the likely range of values for a future response variable given a set of predictor variables, confidence intervals are used to estimate the likely range of values for a model parameter, such as a slope coefficient. The cli option can be a valuable tool for interpreting the results of an mlr analysis, as it can help to identify which predictor variables are most strongly associated with the response variable and which may be less important.

Overall, the cli option provides a valuable tool for conducting a thorough and comprehensive analysis of the relationships between predictor and response variables in a given dataset.

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Answer: To find the volume of a shape, we multiply the length, width, and height.

Volume = length x width x height

Volume = 15cm x 28cm x 22cm

Volume = 9240 cubic centimeters (cm³)

Answer:

the answer is 9240 cm3

Step-by-step explanation:

V=length x width x height

V=15cm x 28cm x 22cm

[tex]v = 9,240cm {}^{3} [/tex]

Based on the given circle with secants HIJ and LKJ, the length of HI to the nearest tenth is equal to 46.3 units.

In Mathematics and Geometry, the Tangent Secant Theorem states that if a secant segment and a tangent segment are drawn to an external point outside a circle, then, the product of the length of the external segment and the secant segment's length would be equal to the square of the tangent segment's length.

By applying the Tangent Secant Theorem to this circle, we have the following:

LJ × KJ = IJ × HI

37 × 15 = 12HI

555 = 12HI

HI = 555/12

HI = 46.3 units.

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False. A truth table for p V ~q requires only two possible combinations of truth values.

False. A truth table for p V ~q requires a total of two possible combinations of truth values.

The statement "p V ~q" is a logical disjunction, meaning it is true if either p is true or ~q is true (or both). There are only two possible truth values for each of these propositions: true or false. Therefore, there are only two possible combinations of truth values for the statement "p V ~q," which are:

- p is true, ~q is false (i.e., q is true)
- p is true, ~q is true (i.e., q is false)

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We need 588.75 square inches of leather to create the travel case which is cylindrical.

The surface area of a cylinder is given by the formula:

A = 2πr² + 2πrh

where r is the radius of the circular base, h is the height of the cylinder, and π is the mathematical constant pi, which is approximately equal to 3.14.

In this case, we are given that the cylinder has a diameter of 15 inches, so the radius is 7.5 inches (half of the diameter).

We are also given that the height of the cylinder is 5 inches.

Using these values in the formula, we can calculate the surface area of the cylinder as:

A = 2π(7.5)² + 2π(7.5)(5)

= 2π(56.25) + 2π(37.5)

= 2(π)(93.75)

= 187.5π

=588.75

Therefore, we need 588.75 square inches of leather to create the travel case.

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To find the expected value of X, we need to first determine the probability of having a pair of consecutive zeroes in a given bit string of length n. Let P be the probability of having a pair of consecutive zeroes in any given position of the bit string.

We can calculate P by considering the possible pairs of consecutive zeroes that can occur in a bit string of length n. There are n-1 pairs of adjacent bits in the bit string, so the probability of a given pair being two zeroes is 1/4 (since there are four possible pairs: 00, 01, 10, 11). However, if the first bit is 0 or the last bit is 0, then there are only n-2 pairs, and the probability of a given pair being two zeroes is 1/2. Therefore, the probability of having a pair of consecutive zeroes in a bit string of length n is:

P = [(n-2)/n * 1/4] + [1/n * 1/2] + [1/n * 1/2] + [(n-2)/n * 1/4]
 = (n-3)/2n + 1/n

Now, let Xi be the random variable that counts the number of pairs of consecutive zeroes that start at position i in the bit string (where 1 <= i <= n-1). Then X = X1 + X2 + ... + Xn-1 is the total number of pairs of consecutive zeroes in the bit string.

To find the expected value of X, we use linearity of expectation:

E[X] = E[X1] + E[X2] + ... + E[Xn-1]

We can calculate E[Xi] for any i by considering the probability of having a pair of consecutive zeroes starting at position i. If the i-th and (i+1)-th bits are both 0, then there is one pair of consecutive zeroes starting at position i. The probability of this occurring is P. If the i-th bit is 0 and the (i+1)-th bit is 1, then there are no pairs of consecutive zeroes starting at position i. The probability of this occurring is 1-P. Therefore, we have:

E[Xi] = P * 1 + (1-P) * 0
      = P

Finally, we substitute our expression for P into the formula for E[X] to get:

E[X] = (n-3)/2n + 1/n * (n-1)
    = (n-3)/2n + 1

So the expected value of X for a random bit string of length n is (n-3)/2n + 1.
To find the expected value of a random function X that counts the number of pairs of consecutive zeroes in a random bit string of length n, we can follow these steps:

1. Calculate the total number of possible bit strings of length n. There are 2^n possible bit strings since each position can be either a 0 or a 1.

2. Find the probability of each pair of consecutive zeroes occurring in the bit string. Since there are 2 possible values for each bit (0 or 1), the probability of a specific pair of consecutive zeroes is 1/4 (0.25).

3. Determine the maximum number of pairs of consecutive zeroes in a bit string of length n. The maximum number is n - 1 since the first n - 1 bits can form pairs with the bits that follow them.

4. Calculate the expected value by multiplying the probability of each pair of consecutive zeroes by the number of pairs that can occur, and sum the results. The expected value E(X) can be calculated using the formula:

E(X) = Sum(P(i) * i) for i from 0 to n - 1, where P(i) is the probability of i pairs of consecutive zeroes occurring.

To simplify the calculation, consider that each position has a 1/4 chance of forming a consecutive zero pair with the following position, and there are n - 1 such positions:

E(X) = (1/4) * (n - 1)

So, the expected value of a random function X that counts the number of pairs of consecutive zeroes in a random bit string of length n is (1/4) * (n - 1).

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Answer: One way is video games. Video games help people escape from reality, which prevents people from going out and exercising. One way is treadmills, where you are able to increase your heart rate through cardio without straining the body.

Step-by-step explanation: a

The Equation of circle is (x+3)² + (y-5)² = (√20)².

We have,

Center = (-3, 5)

Point = (1, 7)

We know the standard form of Equation of circle

(x-h)² + (y-k)² = r²

where (x, y) is any point on the circle, (h, k) is the center

So, (x+3)² + (y-5)² = r²

Put the point (1, 7) in above equation we get

(1+3)² + (7-5)² = r²

(4)² + (2)² = r²

16 + 4= r²

r= √20

Thus, the Equation of circle is

(x+3)² + (y-5)² = (√20)²

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Step-by-step explanation:

The y intercept of a function is when the graph crosses the y axis(vertical line ).

The y intercepts occurs when x=0,

Basically to find the y intercept of a function find

f(0), where f is the given function.

Here the graph crosses the y axis at (0,2)

So the y intercept is 2.

A) A point C such that the distance from the origin can be plotted at (1, 0).

B) A point E which is at 4/5 closer to the origin than C can be plotted at (4/5, 0) = (0.8, 0)

A) Given a point O(0, 0).

A distance of 1 from the origin can be marked at 4 points :

(1, 0), (-1, 0), (0, 1) and (0, -1).

Using the distance formula, all the points from O is 1.

Let's take C as (1, 0).

B) Point E is at 4/5 closer to O than C.

Ratio of the distance between OE and EC is 4/5 : 1/5 = 4 : 1.

The section formula states that If a line with end points (x, y) and (x', y') is divided in the ratio m : n, then the divided point is,

P = [(mx' + nx)/(m + n) , (my' + ny)/ (m + n)]

Here (x, y) = (0, 0) and (x', y') = (1, 0)

m : n = 4 : 1

Using the section formula,

Coordinates of E = ((4 + 0)/ 5 , (0 + 0)/5) = (4/5, 0) = (0.8, 0).

If the distance between (0, 0) and (1, 0) is divided in to 5 segments, then the point E will be at 4th segment.

Hence the required coordinates are C(1, 0) and E(0.8, 0).

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Answer:  21/29

Step-by-step explanation:

sin B = opposite side/hypotenuse

=21/29

Answer:

21/29

Step-by-step explanation:

sin B= opposite/hypotenuse

sin B = 21/29

Asymptotic stability is a property of a dynamical system where the solutions of the system approach a particular equilibrium point as time goes to infinity, but they do not oscillate or move away from the equilibrium point. In other words, the solutions of the system converge to the equilibrium point as time goes to infinity.

Formally, a critical point x* of a dynamical system x' = f(x) is asymptotically stable if for any solution x(t) that starts sufficiently close to x*, there exists a positive constant ε such that ||x(t) - x*|| → 0 as t → ∞, where ||.|| denotes the Euclidean norm.

Intuitively, this means that if the initial condition of the system is perturbed slightly from the equilibrium point, then the solutions of the system will still converge to the equilibrium point as time goes to infinity. This is a desirable property for many systems, as it implies that the system will eventually settle down to a steady state.

The concept of asymptotic stability is often studied in the context of linear systems, where the stability of the equilibrium point is determined by the eigenvalues of the system matrix. For a linear system, the equilibrium point is asymptotically stable if all the eigenvalues have negative real part. In this case, the solutions of the system decay to zero exponentially as time goes to infinity.

Overall, asymptotic stability is an important concept in the study of dynamical systems, as it provides a way to analyze the long-term behavior of a system and predict its future state.

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The solution is, the measure of angle 7 is, ∠7 = 145°.

Here, we have,

∠4 and ∠8 are corresponding angles

∠8 and ∠7 are supplementary angles

so, we get,

Then, ∠4 and ∠7 are supplementary angles.

This means that

∠4 + ∠7 = 180°

we, have,

35° + ∠7 = 180°

so, we get,

∠7 = 180° - 35°

or, ∠7 = 145°

Hence, The solution is, the measure of angle 7 is, ∠7 = 145°.

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complete question:

Oak Street and Elm Street run parallel to each other. When Main Street interest them, it forms interior angle 4, and measuring 35 degrees. What is the measure of angle 7 ?

Answer:

(-4, 4)

Step-by-step explanation:

5x + y = -16

2x + y = -4

Eliminate the y variable.

5x + y = -16

-1 (2x + y = -4)

Solve:

5x + y = -16

-2x - y = 4

3x = -12

Divide both sides by 3.

x = -4

5(-4) + y = -16

-20 + y = -16

Add 20 to both sides.

y = 4

The relationship of the angles is ∠P = 1/2(ACB - AB) and the measure of angle P is (180 - x) degrees

Given that

Arc are intercepted by tangents and the exterior angle

The theorem of intersected tangents states that

The measure of the angle is the difference between the measures of the arc

So, the relationship of the angle is ∠P = 1/2(ACB - AB)

Here, we have

AB = x

This means that

ACB = 360 - x

So, we have

∠P = 1/2(360 - x - x)

When evaluated, we have

∠P = 180 - x

Hence, the measure of angle P is 180 - x degrees

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It should be noted that to ascertain the composite area of a trapezoid and two similar parallelograms, the following steps should be followed.

Find the area of the trapezoid:

First, compute the length of both parallel sides of this trapezoid and then measure its height.

Next, substitute these figures into formulae for computing its area.

Identify the area of one parallelogram:

Then use an instrument to determine the length of the base as well as the altitude of one of the congruent parallelograms and input these values in the given equation to calculate its area.

Multiply the area of the single parallelogram by 2:

For attaining the total area of both parallelograms, simply multiply the area of one parallelogram by two.

Add the areas of the trapezoid and both involved parallelograms to get the combined area:

Finally, combine the area of the trapezoid with the overall area of both parallelograms to determine the aggregate area.

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In triangle LMN, l = 6.9 cm, m = 8.1 cm and n=8.8 cm then the  measure of ∠N is 71.3 degrees

The equation to set up for this, following the pattern for the Law of Cosines, is as follows:

From triangle LMN

n² = m² + l² - 2 mlcos N

We have to find the measure of ∠N

8.82 = 8.12 + 6.92 - 2( 8.1)(6.9) cos N

77.44 = 113.22 - 111.78 cos N

Subtract 113.22 on both sides

-35.78 = -111.78 cos N.

Divide both sides by 111.78

cos N = 0.32

N=Cos⁻¹(0.32)

N=71.3 degrees

Hence, in triangle LMN, l = 6.9 cm, m = 8.1 cm and n=8.8 cm then the  measure of ∠N is 71.3 degrees

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The value of x will be; x = 1/8

Since equation is an expression that shows the relationship between two or more numbers and variables.

We are given that  the equation  (8x-1).

Here, we need to solve for x;

(8x-1).

combine the like terms;

(8x-1) = 0

8x = 1

x = 1/8

Therefore, the solution will be as x = 1/8

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The point (1, -4) does not make the equation y = x + 5 true.

Given information:

The equation is y = x + 5.

To check if the point (1, -4) makes the equation y = x + 5 true:

we need to substitute the x and y values of the point into the equation and see if the equation is true.

y = x + 5

-4 = 1 + 5

-4 = 6

The equation is not true when we substitute the values of x = 1 and y = -4 into it.

Therefore, the point (1, -4) does not make the equation y = x + 5 true.

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The requried distance between points P(1,6) and Q(5,8) in simplest radical form is 2√5.

We can use the distance formula to find the distance between the two points:

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

where (x₁, y₁) = (1, 6) and (x₂, y₂) = (5, 8).

Substituting the values, we get:

d = √[(5 - 1)² + (8 - 6)²]

= √[4² + 2²]

= √(16 + 4)

= √20

= 2√5

Therefore, the distance between points P(1,6) and Q(5,8) in simplest radical form is 2√5.

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The measure of angle D in is 19° which is option (A)

To measure D, recall that sum of the angles in a triangle is 180°. We have two angles in triangle BCD, so we can find the third angle as follows:

m∠BCD + m∠CBD + m∠DCB = 180°

46° + m∠CBD + 90° = 180° (since angle DCB is a right angle)

m∠CBD = 44°

Now, we can use the fact that the sum of the angles in triangle CDE is 180° to find the measure of angle D:

m∠CDE + m∠DCE + m∠ECD = 180°

m∠CDE + 71° + 90° = 180° (since angle ECD is a right angle)

m∠CDE = 19°

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The number of problems, Paige assigned as homework was 60.

We are given that Paige takes a break while working on her math homework to help herself stay focused.

Since solves 20 problems and takes a break then she solves 12 problems and takes a break. and finishes the last 20% of her math problems.

Let the value of which a thing is expressed in percentage is "a' and the percent that considered thing is of "a" is b%

Since percent shows per 100, thus we will first divide the whole part in 100 parts and then multiply it with b so that we collect b items per 100 items.

we have to find what 20% of a number is 12

20% of x =  12

x = 12/20%

x = 12/2 x 10

x = 60

The answer is 60

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The exact values of the trigonometric functions are listed below:

Case 9: sec θ = 5√2 / 7

Case 11: tan θ = 1 / 3

In this problem we must find the exact values of trigonometric functions, this can be done by means of definitions of trigonometric functions:

sin θ = y / √(x² + y²)

cos θ = x / √(x² + y²)

tan θ = y / x

cot θ = 1 / tan θ

sec θ = 1 / cos θ

csc θ = 1 / sin θ

Where:

Case 9

cos θ = √2 / 10

√(x² + y²) = 10

√(2 + y²) = 10

2 + y² = 100

y² = 98

y = 7√2

sin θ = 7√2 / 10

sec θ = 10 / 7√2

sec θ = 10√2 / 14

sec θ = 5√2 / 7

Case 11

csc θ = √10

sin θ = 1 / csc θ

sin θ = 1 / √10

sin θ = √10 / 10

y = √10

√(x² + y²) = 10

√(x² + 10) = 10

x² + 10 = 100

x² = 90

x = 3√10

tan θ = √10 / 3√10

tan θ = 1 / 3

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Answers are in bold:

Complete the Square: x^2+6x+(6/2)^2+y^2-4y+(4/2)^2=23+(6/2)^2+(4/2)^2

Simplify: x^2+6x+9+y^2-4y+4=23+9+4
              (x+3)^2+(y-2)^2=36

^That will be the standard equation^

The vertex is (-3,2) and the radius is 6 (sqr36).

To find the domain and range, note that their interval is on the vertical and horizontal diameter of the circle, fixed on a vertex point.

This means that the domain is the x value (-3) of the vertex + or - the radius (6): 3 and -9

Hence, domain is -9<=x<=3

Find the range using the same method: 8 and -4

Range is -4<=x<=8

Answer:

Standard equation =(x+3)²+(x-2)²=6²

Domain:     -9 ≤ x ≤ 3

Range:     -4 ≤ y ≤ 8  

Step-by-step explanation:

You need to put it in a format

(x-h)²+(y-k)²=r²  where (h,k) is your center

Equation:

x²+y²+6x-4y=23        rearrange the variables so x's and y's are together

x²+6x     +y²-4y      =23    complete the square for the quadratic by taking the middle term of each quadratic 6 and -4  

divide by 2 => [tex](\frac{6}{2} )^{2}[/tex] =9    and   [tex](\frac{-4}{2} )^{2} = 4[/tex]

add 9 and 4 to both sides

x² + 6x + 9 + y² - 4y + 4 = 23 +9+4     factor both of the quadratics

(x+3)(x+3) +(x-2)(x-2) = 36

(x+3)²+(x-2)²=36      now put it in form with radius

(x+3)²+(x-2)²=6²      (-3,2) center    and r=6

Standard equation =(x+3)²+(x-2)²=6²

Domain: we get that by where the circle starts and ends for x.  Since the radius is 6   and the center x point is -3

move left 6 from -3, that's your lower domain = -6-3=-9

move 6 right from center, that's your upper domain = -3+6 = 3

Domain:     -9 ≤ x ≤ 3  circle is between -9 and 3 in the x direction

Range: Now we do same for range but in y direction

Center y point is 2

move down 6 from 2 = -6+2 =-4, this is lower range

move up 6 from 2 = 2+6=8, this this is your upper range

Range:     -4 ≤ y ≤ 8   circle is between -4 and 8 for y direction

Haru can go on 12 rides for $10.25, assuming he rents a mat for each ride and the prices remain unchanged.

The amount charged by slide = $1.25

Amount to rent a mat per ride = $0.75

Total amount with Haru = $10.25

Calculating the total amount that Haru has -

= Total amount with Haru - The amount charged by slide

= $10.25 - $1.25

= $9.00

Dividing is a mathematical process that includes dividing a sum into groups of equal size. It includes a remainder and a quotient as well.

Determining the number of rides Haru can go on:

= $9.00/ $0.75

= 12

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Answer:

The answer is 0.7880

or 1 to the nearest whole number

Step-by-step explanation:

cos 38=0.7880

1 to the nearest whole number