Mr. Rell runs 14 miles every 2 hours. How far
can he run in 7 hours?

Answer:

826

Step-by-step explanation:

82.6 x 10 to the power of 2 :

8.26 * 10^2

8.26 * (10 * 10)

8.26 * (100)

= 826

The volume of the pencil cup is given as follows:

d) 27 in³.

The volume of a rectangular prism, with dimensions defined as length, width and height, is given by the multiplication of these three defined dimensions, according to the equation presented as follows:

Volume = length x width x height.

Considering that the base is a rectangle, we have that length x width = Base Area, hence:

Volume = Base Area x Height.

The parameters for this problem are given as follows:

Hence the volume is given as follows:

V = 9 x 3 = 27 in³.

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The guideline for establishing causality is look for cases where correlation exists between the variables of a scatterplot. i.e., The correct option is (b)

Causality is defined as the relationship that exists between the cause and the effect of an outcome.

The guidelines or the principles that can be use for establish a causality include the following:

There are 3 guidelines for establishing “causality”:

Variables should are “associated”.

The “Independent” variable should precede the “Dependent” variable.

All the possible “alternative explanations” for the relationships “accounted” for and “dismissed”.

It should be “controlled” and “randomized”.

The correct option is (b)

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Answer:

Option B is the correct option.

Step-by-step explanation:

\( \sf{ \frac{3}{5} = \frac{x - 1}{8} }\)

Apply cross product property

⇒\( \sf{ 5(x - 1) = 3 \times 8}\)

Distribute 5 through the parentheses

⇒\( \sf{5x - 5 = 3 \times 8}\)

Multiply the numbers

⇒\( \sf{5x - 5 = 24}\)

Move 5 to right hand side and change it's sign

⇒\( \sf{5x = 24 + 5}\)

Add the numbers

⇒\( \sf{5x = 29}\)

Divide both sides of the equation by 5

⇒\( \sf{ \frac{5x}{5} = \frac{29}{5} }\)

⇒\( \sf{x = \frac{29}{5} }\)

Hope I helped!

Best regards!!

A qualitative problem statement is one that identifies and defines an issue or challenge using qualitative research techniques. A good qualitative problem statement should define both the independent and dependent variables while conveying a sense of emerging design and specifying a specific hypothesis to be tested.

Additionally, it should specify a relationship between the independent and dependent variables. The problem statement must be clear and concise, providing enough context for the reader to understand the research problem.In a qualitative research study, the researcher may not have a hypothesis and instead may use the problem statement to frame the research questions. In this case, the problem statement should still identify the independent and dependent variables and convey a sense of emerging design.

For example, a qualitative problem statement for a study on the experience of low-income students in higher education might read as follows: The purpose of this study is to explore the relationship between socioeconomic status and academic success among low-income college students. In this example, the independent variable is socioeconomic status, and the dependent variable is academic success.

The problem statement conveys a sense of emerging design by indicating that the study will explore the relationship between these two variables, rather than testing a specific hypothesis.

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A) Let the side length of the square base be x, and the height of the box be h. Then, the volume of the box is given by:

V = \(x^2\) * h = 8500

Solving for h, we get:

h = 8500 / \(x^2\)

The surface area of the box can be expressed as:

S = 2x^2 + 4xh

Substituting the value of h obtained above, we get:

S = \(2x^2\) + 4x(8500 / \(x^2\)) = 2\(x^2\)+ 34000 / x

Thus, the surface area of the box can be expressed as a function of x.

B) To graph the function, plot the surface area (S) on the y-axis and the side length of the square base (x) on the x-axis. Since x cannot be negative, the domain of the function is (0, infinity). As x gets very large or very small, the surface area approaches infinity, so we should only graph the function for values of x that make sense in the context of the problem.

C) The minimum amount of cardboard required to construct the box is equal to the surface area of the box. To find the minimum surface area, we need to find the minimum of the function S(x) obtained in part A.

D) To find the dimensions of the box that minimize the surface area, we need to find the value of x that minimizes the function S(x). We can do this by taking the derivative of S(x) with respect to x, setting it equal to zero, and solving for x. This gives us:

dS/dx = 4x - 34000/\(x^2\) = 0

Multiplying both sides by \(x^2\) and solving for x, we get:

x = (8500/2\()^(1/3)\) ≈ 18.3

Therefore, the dimensions of the box that minimize the surface area are a square base with side length of approximately 18.3 inches, and a height of:

h = 8500 / \(x^2\) ≈ 26.2 inches

E) UPS might be interested in designing a box that minimizes the surface area because it can reduce the amount of cardboard used in each box, resulting in cost savings and a reduced environmental impact. Additionally, minimizing the surface area of a box can make it more efficient to stack and transport, reducing shipping costs and making the overall process more sustainable.

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A) The Surface Area = \(X^2 + 34000/X\)

B) The y-axis and the side length X on the x-axis.

C) The minimum amount of cardboard required to construct the box is approximately 1649.39 square inches.

D) The dimensions of the box that minimize the surface area are X = 20.5 inches and Y = 16.87 inches.

E)  Smaller boxes take up less space in delivery trucks and planes, allowing more packages to be shipped at once and reducing transportation costs.

A) Express the surface area of the box as a function of X:

Let the side length of the square base be X and the height of the box be Y. Then, we know that the volume of the box is 8500 cubic inches, so:

\(X^{2Y} = 8500\)

To find the surface area of the box, we need to add up the area of each face. There are 5 faces in total (the bottom square and 4 identical rectangular sides), so:

Surface Area = \(X^2 + 4XY\)

We can substitute the value of Y from the equation for volume, giving:

Surface Area = \(X^2 + 4X(8500/X^2)\)

Surface Area = \(X^2 + 34000/X\)

B) Graph the function found in part a:

To graph this function, we can plot the surface area on the y-axis and the side length X on the x-axis. The graph will have a minimum value, which we can find using calculus or by using a graphing calculator.

C) What is the minimum amount of cardboard that can be used to construct the box:

The minimum amount of cardboard required to construct the box is the surface area of the box. To find this minimum value, we need to find the minimum point on the graph in part b. From the graph or by using calculus, we can see that the minimum occurs at X = sqrt(8500/5) = 20.5 inches. Substituting this value into the equation for surface area, we get:

Surface Area = \(20.5^2 + 4(20.5)(8500/20.5^2)\)= 1649.39 square inches

D) What are the dimensions of the box that minimize the surface area:

From part c, we know that the minimum occurs at X = sqrt(8500/5) = 20.5 inches. To find the height of the box, we can substitute this value of X into the equation for volume:

\(X^2Y = 8500\)

\((20.5)^2 Y = 8500\)

\(Y = 8500/(20.5)^2 = 16.87\) inches

E) Why might UPS be interested in designing a box that minimizes the surface area:

UPS and other parcel delivery services are always looking for ways to reduce their costs and increase efficiency. By designing a box that minimizes the surface area while still containing the same volume of goods, they can reduce the amount of cardboard used for each shipment. This would save them money on materials and shipping costs, while also reducing their environmental impact. Additionally, smaller boxes take up less space in delivery trucks and planes, allowing more packages to be shipped at once and reducing transportation costs.

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Answer:

\(763 ft^3\) or 763 cubic feet.

Step-by-step explanation:

The tank is cylindrical and the volume of a cylinder is given as:

\(V = \pi r^2h\)

where r = radius and h = height

The radius, r, of the tank is 4.5 ft and the height, h, of the tank is 12 ft.

Therefore, the volume of the cylindrical water tank is:

\(V = \pi * 4.5^2 * 12\\V = 763.407 ft^3\)

Approximating to whole number, the volume of the tank is \(763 ft^3\) or 763 cubic feet.

The ratio of 2 meters to 76 centimetres is 50: 19.

In mathematics, a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other.

In simpler terms, a ratio compares values.

Let's find the ratio of 2 meters to 76 centimetres as follows:

We have to first convert the units so they will be same.

Hence,

1 cm = 0.01 m

76 cm = ?

cross multiply

length in metres = 76 × 0.01

length in metres = 0.76 metres

Therefore, let's multiply the 2 units by 100.

0.76 × 100 = 76 metres

2 × 100 = 200 metres

In ratio, 200 : 76 will be simplified as 50 : 19

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Answer:

29

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Any number multiplying to a variable will be a term, but not a constant.

A constant is a term, just one without variables.

We are given 6y + 29. 6y would be a term and 29 would be another term. Since 29 has no variables, it will be the constant.

Answer:

width = 35 m

Step-by-step explanation:

w is the width, then l = w + 5

Perimeter P = 2(l + w)

=> 150 =2(w + 5 + w)

75 = 2w + 5

2w = 70

w = 35

Answer:

Not exactly

Step-by-step explanation:

Total payment:

Total amount is a little different:

The best way to solve this problem is to imagine the situation as follows: Suppose that each position (first, second and third) is a numbered box. (first is box number one, and so on).

Now, imagine that each student is a ball that is numbered from 1 up to 11.

The situation translates to calculate in how many different ways we can put a ball in each box, without putting 2 balls in each box. We have the following

To solve this, we will use the multiplication principle. This principle relays on multiplying the number of possibilites for each box. Consider the case in which we will fill the box number 1. We can choose any of the numbers, so we have 11 posibilites. Now, suppose that we chose one number for box 1, and now we want to fill box 2. Then, we will have 10 possibilites only, since we already picked one. In the same manner, to fill the third box we have 9 possibilities. So the total number of possibilites is the product of this three numbers. That is

Answer:

6b + 5n = 101

Step-by-step explanation:

I hope this helps!

Answer:

6b+5n = 101 because if you look at each equation and back at the question you’ll understand that it’s asking for 6 bracelets plus 5 necklaces for a total of 101 dollars... hope this helped...and I need brainliest thx

Step-by-step explanation:

The volume of the solid is approximately 807.08 cubic units.

To determine the volume of the solid, we can use the method of cylindrical shells.

Imagine taking a slice of the solid parallel to the base, with the cross-sectional area being a square of side length x (where x is a function of the height). The volume of this slice is the product of the square area and the height. The height of the slice is equal to the difference in the radii of two consecutive circular cross sections.

The radius of the larger circular cross-section can be found using the Pythagorean theorem, which states that the square of the hypotenuse (the radius) is equal to the sum of the squares of the other two sides (the height and half the side length of the square). Thus, we have:

r² = x² + (15-x)²

Solving for x, we get:

x = 15 * √(1 - (r/15)²)

The volume of the slice is then given by:

V = x² * (15 - x)

To find the total volume of the solid, we integrate this expression with respect to r from 0 to 15. The result is approximately 807.08 cubic units.

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Answer:

ASA

Step-by-step explanation:

there are two congruent angles with an included side in between

Answer: Triangle RHS and NKW are congruent through the Congruence Theorem Angle-Side-Angle.

Step-by-step explanation:

The side HS is congruent to the side KW.

The angle H is congruent to angle K.

The angle S is congruent to angle S.

Answer:

here I am again

60 gallons

Step-by-step explanation:

Katie deleted my answer and I got warned

The work required to pump all the water over the edge of the tank is approximately 271,433.64 foot-pounds.

To calculate the work required to pump all the water over the edge of the tank, we need to consider the weight of the water in the tank and the height it is lifted.

First, let's find the volume of the water in the tank. The volume of a cone is given by the formula V = (1/3)πr²h, where r is the radius and h is the height. Plugging in the values, we have:

V = (1/3)π(3²)(12)

= (1/3)π(9)(12)

= 36π

Next, we need to find the weight of the water. The weight of an object is given by the formula W = mg, where m is the mass and g is the acceleration due to gravity. The mass of the water can be found by multiplying its volume by the density of water, which is approximately 62.4 pounds per cubic foot:

m = (36π)(62.4)

≈ 22619.47 pounds

Now, we can calculate the work done by multiplying the weight of the water by the height it is lifted. In this case, the height is 12 feet:

W = (22619.47)(12)

≈ 271433.64 foot-pounds

Therefore, the work required to pump all the water over the edge of the tank is approximately 271,433.64 foot-pounds.

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The work required to pump water out of an inverted conical tank involves calculating the pressure-volume work at infinitesimally small volumes within the tank and integrating this over the entire volume of the tank. This provides an interesting application of integral calculus in Physics.

The question requires the concept of work in Physics applied to a fluid, in this case, water lying within an inverted conical tank. Work is done when force is applied over a distance, as stated by work = force x distance. In the fluid analogy, the 'force' link is the pressure exerted on the water and the distance is the change in volume of the fluid. Therefore, work done (W) = Pressure x Change in Volume (ΔV).

In this scenario, you are required to pump out water from an inverted conical tank, hence, the work you do is against the gravitational force pulling the water downwards. To calculate the total work done, you have to consider the work done at each infinitesimally small (hence, constant pressure) strip of volume and integrate over the entire volume of the tank.

The detail of calculation would require the knowledge of integral calculus and the formula for volume of a cone. I recommend considering this as an interesting application of integrals in Physics. Also remember that the volume of a cone = 1/3πr²h, where 'r' is the radius of base and 'h' is the height of cone.

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The ladder can reach 21.17 feet high up of Denise's house.

Given,

The length of ladder Denise used to clean the outside of her second story windows = 24 feet

The distance between the base of the ladder and house = 13 feet

We have to find the height of the house which the ladder can reach:

For that we can use Pythagorean Theorem.

That is,

Hypotenuse² = Altitude² + Base²

Here,

Hypotenuse is the length of the ladder = 24 feet

Altitude is the height of the house ladder can reach = x

Base is the distance between base of the ladder and house = 13 feet

Therefore,

24² = x² + 13²

576 = x² + 169

x² = 576 - 169

x² = 407

x = \(\sqrt{407}\)

x = 21.17

That is, the ladder can reach 21.17 feet high up of Denise's house

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Answer:

Correct option: third one -> x > 2

Step-by-step explanation:

Writing the inequation from the sentence in the question, we have:

\((5/6)x - 1/3 > 1\ 1/3\)

To solve this inequation we can do the following steps:

\((5/6)x > 1\ 2/3\)

\((5/6)x > 5/3\)

\(x > (5/3) / (5/6)\)

\(x > (5/3) * (6/5)\)

\(x > 2\)

So the correct option is the third one: x > 2

Answer:

The answer is C.

x>2

Step-by-step explanation:

on edge

Answer:

he walked 7 block's

Jay walks 3 blocks north and then 4 blocks east from his home if he walks straight back home, 5 blocks  does Jay walk-in all

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given,

Jay walks 3 blocks north and then 4 blocks east from his home if he walks straight back home.

We have to use pythagorean theorem in finding distance

As given in the attachment, Let AB= 3

BC=4

AC=x

To find AC we use pythagorean theorem

AC²=AB²+BC²

AC²=3²+4²

AC²=9+16

AC²=25

Take square root on both sides.

AC=5

Hence 5 blocks he walks straight back home how far does Jay walk-in all

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The equation of the tangent plane to the surface f(x,y) at the point (a) x=1,y=-1 is z = -12x + 4y + 2, and at the point (b) x=2,y=2 is z = 128x + 80y - 384.

To find the equation of the tangent plane to the surface defined by z=f(x,y), where f(x,y)=2(x^2+y^2)x^2y, at the given points, we need to find the partial derivatives with respect to x and y.

Step 1: Find the partial derivative with respect to x:
f_x = d(f(x,y))/dx = 4xy(x^2+y^2) + 4x^3y

Step 2: Find the partial derivative with respect to y:
f_y = d(f(x,y))/dy = 4xy(x^2+y^2) + 2x^2y^2

Step 3: Substitute the given point (a) x=1, y=-1 into the partial derivatives to find the slope of the tangent plane at this point:
f_x(1,-1) = 4(-1)(1^2+(-1)^2)(1^2+(-1)^2) + 4(1)^3(-1) = -12
f_y(1,-1) = 4(-1)(1^2+(-1)^2)(1^2+(-1)^2) + 2(1)^2(-1)^2 = -4

Step 4: Use the point-slope form of the equation of a plane, z = f(a,b) + f_x(a,b)(x-a) + f_y(a,b)(y-b), to find the equation of the tangent plane:
z = f(1,-1) + f_x(1,-1)(x-1) + f_y(1,-1)(y-(-1))
  = 2(1^2+(-1)^2)(1^2)(-1) + (-12)(x-1) + (-4)(y+1)
  = -2 - 12x + 12 + 4y + 4
  = -12x + 4y + 2

Step 5: Substitute the given point (b) x=2, y=2 into the partial derivatives to find the slope of the tangent plane at this point:
f_x(2,2) = 4(2)(2^2+2^2)(2^2+2^2) + 4(2)^3(2) = 128
f_y(2,2) = 4(2)(2^2+2^2)(2^2+2^2) + 2(2)^2(2)^2 = 80

Step 6: Use the point-slope form of the equation of a plane to find the equation of the tangent plane:
z = f(2,2) + f_x(2,2)(x-2) + f_y(2,2)(y-2)
  = 2(2^2+2^2)(2^2)(2) + 128(x-2) + 80(y-2)
  = 32 + 128x - 256 + 80y - 160
  = 128x + 80y - 384

Therefore, the equation of the tangent plane to the surface f(x,y) at the point (a) x=1,y=-1 is z = -12x + 4y + 2, and at the point (b) x=2,y=2 is z = 128x + 80y - 384.

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False, sample evidence cannot prove that a null hypothesis is true.

Sample evidence can be used to infer whether a null hypothesis is true or not, but it cannot prove it to be true. The null hypothesis is a statement of no effect or no difference, and it is typically used as a starting point for statistical hypothesis testing. When sample data is collected, it is used to calculate a test statistic, which is then used to make a decision about the null hypothesis.

If the test statistic falls within the acceptance region, meaning that it is not unlikely to occur if the null hypothesis is true, then the null hypothesis is not rejected. However, if the test statistic falls in the rejection region, meaning that it is unlikely to occur if the null hypothesis is true, then the null hypothesis is rejected. The conclusion is that the sample evidence provides a probability that the null hypothesis is true or not, but it cannot prove it to be true.

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Based on the property of the consecutive angles of a parallelogram, the value of x is calculated as: E. 37.

In a parallelogram, the angles that are opposite to each other are congruent while consecutive angles are supplementary.

Angles F and G are consecutive angles and are therefore supplementary (have a sum of 180 degrees.)

Angle F + angle G = 180

4x - 2 + 34 = 180

4x + 32 = 180

4x = 180 - 32

4x = 148

x = 148/4

x = 37

Value of x is: E. 37.

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The function that has a well-defined inverse is b. : → (x) = 2x - 5.

To explain why this function has a well-defined inverse, we need to consider the conditions for a function to have an inverse.

For a function to have an inverse, each input value (x) must have a unique output value (y), and each output value must have a unique corresponding input value. In other words, the function must be one-to-one, with no two different input values producing the same output value.

In the case of function b. : → (x) = 2x - 5, it is a linear function with a constant slope of 2. This means that for every different input value (x), we get a unique output value (y) through the formula 2x - 5.

Moreover, the fact that the coefficient of x is non-zero (2 in this case) ensures that no two different input values can produce the same output value. This guarantees the one-to-one nature of the function.

To find the inverse of b(x), we can follow these steps:

1. Replace the function notation with the variable y: x = 2y - 5.

2. Solve for y: x + 5 = 2y, y = (x + 5)/2.

3. Replace y with the inverse function notation: b^(-1)(x) = (x + 5)/2.

Therefore, the function b(x) = 2x - 5 has a well-defined inverse given by b^(-1)(x) = (x + 5)/2, satisfying the conditions for a function to have an inverse.

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The pair of lines 4x - 3y = 6 and 3x - 4y = 2 are neither parallel nor perpendicular.

To find if the pair of lines is parallel, perpendicular, or neither, follow these steps:

Therefore, the pair of lines 4x - 3y = 6 and 3x - 4y = 2 are neither parallel nor perpendicular.

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Answer:

it is just 64-18=48

Step-by-step explanation:

you have to just keep 64 the same and do the 9*2. And sum those outcomes.