between 9 am and 6:36 am, the water in a swimming pool decreased by 8/25 in. assuming that the water level decreased at a constant rate, how much did the water level drop each hour

At the 5% significance level, we can reject the null hypothesis and conclude that there is sufficient evidence to suggest that the average weight of the vacuums from Nature Abhors is less than 19.64 pounds.

To answer this question, we can use a one-sample t-test, assuming that the population of weights is normally distributed. The null hypothesis is that the true mean weight of the vacuums from Nature Abhors is 19.64 pounds, while the alternative hypothesis is that it is less than 19.64 pounds.

We can calculate the t-statistic using the formula

t = (X - μ) / (s / sqrt(n))

where X is the sample mean (19.33), μ is the hypothesized population mean (19.64), s is the sample standard deviation, and n is the sample size (31).

Since we don't know the population standard deviation, we can estimate it using the sample standard deviation. We calculate the sample standard deviation as follows

s = sqrt(sum((xi - X)^2) / (n - 1))

where xi is the weight of the i-th vacuum in the sample. We assume that the weights are normally distributed, so we can use the t-distribution with (n-1) degrees of freedom to calculate the p-value.

Using a t-table or calculator, we can find the critical t-value for a one-tailed test at the 5% significance level with 30 degrees of freedom to be -1.699.

Plugging in the numbers, we get

t = (19.33 - 19.64) / (s / sqrt(31))

s = sqrt(sum((xi - X)^2) / (n - 1)) = 0.714

t = (-0.31) / (0.714 / sqrt(31)) = -1.84

Since the calculated t-value (-1.84) is less than the critical t-value (-1.699), we can reject the null hypothesis at the 5% significance level. Therefore, we can conclude that there is sufficient evidence to suggest that the average weight of the vacuums from Nature Abhors is less than 19.64 pounds.

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Answer:

384 square units

Step-by-step explanation:

Square prism = Cube

Formula for finding the surface area of a cube = L x L (6)

Surface area = 8 x 8 (6)

Surface area = 64(6)

Surface area = 384 square units

Answer:

384 units squared

Step-by-step explanation:

Square 8 and then multiply by 6.

The ethnicity of respondents in a political poll of randomly selected adults is an example of a categorical variable.

A categorical variable is a type of variable that represents data that can be categorized into distinct groups or categories. In this case, the ethnicity of the individual respondents in the political poll represents different categories such as Asian, African American, Hispanic, Caucasian, etc. Each respondent falls into one of these categories based on their ethnicity.

The variable is categorical because it does not have numerical values that can be quantified or measured. Instead, it represents qualitative data that can be described using labels or categories.

Therefore, the ethnicity of the individual respondents in a political poll of randomly selected adults is an example of a categorical variable.

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The provided expression is equivalent to the expression mentioned in option (C) is correct.

It is defined as the combination of constants and variables with mathematical operators.

The number expression is:

\(= \dfrac{\sqrt[4]{6} }{\sqrt[3]{2} }\)

After applying the integer exponent property:

\(= \dfrac{\sqrt[4]{6} }{\sqrt[3]{2} } \times\dfrac{\sqrt[3]{2^2} }{\sqrt[3]{2^2} }\)   (rationalization)

\(= \dfrac{\sqrt[4]{6} \times\sqrt[3]{2}}{2 }\)

= \(\rm \dfrac{\sqrt[12]{55296} }{2}\)

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

Thus, the provided expression is equivalent to the expression mentioned in option (C) is correct.

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Answer:

\(6(a - 2) = 6a - 12\)

Answer:

32 boxes of gummies

The average velocity from t = 2s to t = 4s would be - 48 ft/s.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that an object is thrown upward with initial velocity of 48 feet per second from a high of 120 feet. The height of the object t seconds after it is thrown is given by h(t) = - 16t² + 48t + 120.

Average rate of change of velocity with time is called average velocity. Mathematically -

v{avg.} = Δx/Δt                                                         .... Eq { 1 }

Δx = x(4) - x(2)

Δx = - 16(4)² + 48(4) + 120 - {- 16(2)² + 48(2) + 120}

Δx = - 96

Δt = 4 - 2 = 2

So -

v{avg.} = Δx/Δt = -96/2 = - 48 ft/s

Therefore, the average velocity from t = 2s to t = 4s would be - 48 ft/s.

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Answer:

1. 300%

2. 108

3. 60

Step-by-step explanation:

Hope this helps!

26. 33.33% is 37 percent of 11

27.  48%

28.  60 seeds

Answer:

Area of circle = 33.17 yd²

Explanation:

First, we need to convert the number 3 ¼ yd into a decimal number, so:

Then, the area of a circle can be calculated using the following equation:

Where π is approximately 3.14 and r is the radius of the circle. So, if we replace π by 3.14 and r by 3.25 yd, we get:

Therefore, the answer is 33.17 yd²

Answer:

39a^2 * b

Step-by-step explanation:

27a^2 * b + a^2 * 12b

39a^2 * b

Answer:

AHHHHH U TELL ME AT THE WORST TIMES HOMIE IMMA TRY THO

The general solution of the given differential equation expressed explicitly as a function of the independent variable, is:

w(x) = (1/16) * \(((3x + 2)^2 + 4Cx - 4x^2)^2\)

To obtain the solution, we can rewrite the given differential equation by separating the variables and integrating. First, we can divide both sides by √w and rearrange the terms:

√w dw = (3x + 2)/\(x^2\) dx

Then, with regard to the relevant variables, we integrate both sides. The integral of √w with respect to w can be computed using the power rule, while the integral of (3x + 2)/\(x^{2}\) with respect to x can be found using partial fractions. After integrating and simplifying, we obtain the general solution as:

w(x) = (1/16) * \(((3x + 2)^2 + 4Cx - 4x^2)^2\)

Here, C is the arbitrary constant that can take any real value.

This general solution represents a family of functions that satisfy the given differential equation. By choosing different values for the constant C, we can obtain specific solutions corresponding to different initial conditions or constraints imposed on the problem.

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The complete question is:

Find the general solution of the following equation. Express the solution explicitly as a function of the independent variable.

\(x^2\)(dw/dx) = √(w)(3x+2)

Answer:

The answer is -1

Answer:

-2-3--4

Step-by-step explanation:

-2-3 is -5

-5+4

-1

Hire purchase is a method of purchasing goods in which the retailer arranges for a lending firm to collect a down payment from you and you pay the remaining balance in monthly instalments.

A hire purchase, often referred to as an instalment plan, is a deal where a client accepts a contract to buy an item by making a down payment and paying the remaining amount of the asset's price plus interest over time.

Hire purchase is a method of purchasing goods in which the retailer arranges for a lending firm to collect a down payment from you and you pay the remaining balance in monthly instalments.

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The value of x, in the solution of the system of equations, is 6.

To find the value of x in the solution for the system of equations, we need to use the substitution method. First, we need to rearrange one of the equations to solve for one variable in terms of the other. Let's rearrange the second equation to solve for y:

18 - 2y = 2x

2y = 18 - 2x

y = 9 - x

Now, we can substitute the value of y from the second equation into the first equation:

6x - 3(9 - x) = 27

6x - 27 + 3x = 279

9x = 54

x = 6

Therefore, the value of x in the solution for the system of equations is 6.

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In the theater, that have 1,464 seats.

1426 seats are in "regular" sections

38 seats are  "premium" front-row section

The seat arrangement is solved by division. In this case the 62 equal spaced is the divisor while the number of seats is the in each row is the quotient

The division is as follows

1464 / 62

= 23 19/31

The number of seats in the regular section is 23 * 62 = 1426

The remainder will be arranged in premium front row

using equivalent fractions

19 / 31 = 38 / 62

the remainder is 38 and this is the seat for the premium front row section

OR 1464 - 1426 = 38 seats

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Answer:

66/65.

Step-by-step explanation:

22/5 / 13/3

Invert the divisor and multiply.

---> 22/5 * 3/13

= 66/ 65

Answer:

8,3 y=3x+4

Step-by-step explanation:

The y intercept of line AB is 56/5 and the equation of the line CD is y = -7/5 x + 12.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

Given A(8, 0) and B(3, 7).

Equation of line in slope intercept form is y = mx + c, where m is the slope and c is the y intercept.

Slope of AB = (7 - 0) / (3 - 8) = -7/5

Substituting in the equation,

y = -7/5 x + c

Substituting a point (8, 0) on the equation,

0 = (-7/5 × 8) + c

c = 56 / 5

Given AB parallel to CD.

Slope of parallel lines are equal.

Slope of CD is -7/5.

Equation of the line CD is y = -7/5 x + c.

Substituting (5, 5),

5 = (-7/5 × 5) + c

c = 12

Equation of CD is y = -7/5 x + 12

Hence the equation of line CD is y = -7/5 x + 12.

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Answer:

5(9y + 4).

Step-by-step explanation:

GCF of 45y and 20 is 5

Answer is 5(9y + 4).

Answer:

D is an arithmetic sequence

Therefore, The Taylor series for f(x)=sin(x) at x=π/2 is ∑n=0[infinity](-1)^n(x−π/2)^{2n+1}/(2n+1)! and can be found by evaluating the derivatives of sin(x) at x=π/2.

The Taylor series for f(x)=sin(x) at x=π/2 can be found by taking the derivative of sin(x) and evaluating it at x=π/2. We get f(π/2) = sin(π/2) = 1 and f'(x) = cos(x). Evaluating f'(π/2) gives us cos(π/2) = 0. We can then find the second derivative f''(x) = -sin(x) and evaluate it at x=π/2 to get f''(π/2) = -1. This pattern continues, with each derivative evaluated at x=π/2 giving us a coefficient for our Taylor series. Therefore, the Taylor series for f(x)=sin(x) at x=π/2 is ∑n=0[infinity](-1)^n(x−π/2)^{2n+1}/(2n+1)!.

Therefore, The Taylor series for f(x)=sin(x) at x=π/2 is ∑n=0[infinity](-1)^n(x−π/2)^{2n+1}/(2n+1)! and can be found by evaluating the derivatives of sin(x) at x=π/2.

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Answer:

-21i

Step-by-step explanation:

\(i^{2}\) = -1

7*3=21

21 x -1 = -21

Answer:

-21

Step-by-step explanation:

Answer:

area=length*width

32/width=length

The expression to find the side length of the fabric is,

⇒ Side length = √32

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The area of a square piece of fabric = 32 square feet

Now,

Since, We know that;

⇒ Area of square = Side²

Substitute the value of area of square piece of fabric in above equation, we get;

Side² = 32

Take square root both side, we get;

Side = √ 32

Thus, The expression to find the side length of the fabric is,

⇒ Side length = √32

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BD = AE + ED = CE + EC = CA (sum of congruent parts)

A , B , C,  D are diameters.

To prove:

B D = C A.

Proof:

In a circle, if two diameters intersect, the intersection point bisects each diameter.

As we know that AB and CD are diameters, they intersect at E as shown below:

Now, from triangle ABE and triangle CDE, we have:

∠BAE = ∠DCE (Angle formed by a diameter bisects the other diameter)

BE = DE (Opposite sides of rectangle ABCD)

AB = CD (Given diameters)

By angle-angle-side congruency, triangle ABE ≅ triangle CDE,

we have:

∠ABE = ∠CDE (angle-angle congruence)

BE = DE (side-side congruence)

AE = CE (hypotenuse congruence)

Hence, BD = CA as required.

Therefore, the proof is complete.

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The inverse and domain of the function are y = x²-9 and all real numbers.

A function's inverse is a function that reverses the action of a function, such as g(x). If and only if g(x) is bijective, then the inverse of g(x) exists, and if it exist.

If the function f(x)=√x + 9, find the inverse;

y = √x+9

x = √y+9

x² = y+9
y = x²-9

The domain of the inverse function will exist on all real numbers.
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Answer:

A.... -5

Step-by-step explanation:

-35 + 30 = -5

3(2x - 4) = 6(x + 2)

The equation that has no solution is the one that leads to a contradiction, where the left side of the equation does not equal the right side regardless of the value of x.

Let's analyze the given equations:

Ix - 3r-4=4

Zx - 3r+4=4

3(2x - 4) = 6(x^2)

3(2x - 4) = 6(x + 2)

Upon evaluating these equations, it is evident that equation 3 is not possible because it simplifies to 6x - 12 = 6x^2, which is a quadratic equation. However, there is no value of x that satisfies this equation, leading to a contradiction. Therefore, the equation 3(2x - 4) = 6(x^2) has no solution.

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In a cross-country race with 30 runners, there are 4,060 different groups that can finish in the top 3 positions.

Use the concept of combination defined as:

Combinations are made by choosing elements from a collection of options without regard to their sequence.

Contrary to permutations, which are concerned with putting those things/objects in a certain sequence.

Given that,

There are 30 runners in a cross-country race.

The objective is to determine the number of different groups of runners that can finish in the top 3 positions.

To determine the number of different groups of runners that can finish in the top 3 positions:

Use combinations instead of permutations.

In this case:

Calculate the number of different groups,

Use the combination formula:

\(^nC_r = \frac{n!} { (r!(n - r)!)}\)

Here

we have 30 runners and want to select 3 for the top 3 positions.

Put the values into this formula:

\(^{30}C_3 = \frac{30!}{ (3!(30 - 3)!)}\)

Simplifying this expression, we get:

\(^{30}C_3 = \frac{30!}{ (3! \times 27!)}\)

Calculate the value:

\(^{30}C_3 = 4060\)

Hence,

There are 4,060 different groups of runners that can finish in the top 3 positions.

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