Daniel runs at a pace of 8 miles in 60 minutes. What is his pace per mile?

Answer: The answer is 21360

Step-by-step explanation:

We would need to conduct a statistical analysis, such as a chi-square test, to decide whether the correlation between purchasing lettuce and purchasing apples is significant in order to get a more firm conclusion.

The number of persons who purchased lettuce, apples, both, or something else must first be counted in order to construct the table of relative frequencies.

Assuming the farmer saw 100 shoppers at the market, these are the findings:

The following table (See Table) can be made to display the relative frequencies.

The fraction of people who purchased both lettuce and apples must be examined in order to establish whether there is a correlation between the two purchases. In this instance, 10% of customers purchased both lettuce and apples, which is a small percentage.

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Answer:

B

Step-by-step explanation:

For me on Khan is B

Triple Theresa's age minus 6 times the age of Audrey can be found to be 36 .

Audrey's age is 15 and Theresa's age is 42. If we are looking for a value that is triple the age of Theresa minus six times the age of Audrey, the formula would be:

= 3 ( Theresa age ) - 6 ( Audrey age )

Solving for the value then gives :

= 3 ( 42 ) - 6 ( 15 )

= 126 - 6 ( 15 )

= 126 - 90

= 36

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Answer:

Step-by-step explanation:

Using formula

Substitute values

Option A is correct

The long jump pit was recently rebuilt to make it level with the runway.  the amount of wood, in meters, is 12.29 meters.

Generally, To determine the amount of wood needed in meters, you will need to convert the length of each piece of wood from feet to meters. You can use the conversion factor that 1 foot is equal to approximately 0.3048 meters.

To convert the length of the wood from feet to meters, you can use the formula:

length in meters = length in feet * 0.3048

Using this formula, you can calculate that 2.75 meters is equal to approximately 9 feet, and 9.54 meters is equal to approximately 31.25 feet.

Therefore, the total amount of wood needed in meters is 2.75 meters + 9.54 meters = 12.29 meters.

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Answer:

150

Step-by-step explanation:

5 × 3 ÷ 5 + 9 ÷ 7 × 9 × 4 × 3 ÷ 5 × 7 ÷ 5

3 + 7 × 3 × 7

3+147

150

15/56 is the probability that one marble is red and two are blue.

RBB, BRB, and BBR are the three possible ways to draw two blue marbles and one red marble. These are separate scenarios because there are no overlapping outcomes, and their sum is the overall likelihood that two of the three drawn cards will be blue. Therefore, the desired probability is

(10/16)(6/15)(5/14) + (6/16)(10/15)(5/14) + (6/16)(5/15)(10/14) = 15/56

Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only forecast how likely an event is to occur using it, or how likely it is to occur. In the probability scale, 0 indicates an impossibility and 1 indicates a certainty. Probability is an important subject for Class 10 students because it teaches all of the subject's essential concepts. Every event's probability in a sample space is one.

For instance, when we flip a coin, there are just two possible results: Head OR Tail (H, T). But if we throw two coins into the air, there are three possible outcomes: either both show heads, either show tails, or one shows heads and one tails, i.e. (H, H), (H, T), or none of the three (T, T).

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The definite integral of (sec^2 x * 3x) with respect to x, evaluated from 0 to π/3, is equal to π^2/2.

To explain this, we can start by rewriting the integral as follows:

∫[0 to π/3] (sec^2 x * 3x) dx

Using the power rule for integration, we can integrate sec^2 x as tan x, and we keep the 3x term unchanged:

∫[0 to π/3] (tan x * 3x) dx

Now, we can evaluate the integral by using the first fundamental theorem of calculus, which states that if F(x) is an antiderivative of f(x), then the definite integral from a to b of f(x) dx is equal to F(b) - F(a).

In this case, the antiderivative of (tan x * 3x) is [(3/2) * x^2 * ln |sec x + tan x|] + C, where C is the constant of integration.

Now, we evaluate the integral from 0 to π/3:

[(3/2) * (π/3)^2 * ln |sec(π/3) + tan(π/3)|] - [(3/2) * 0^2 * ln |sec(0) + tan(0)|]

Simplifying further:

[(3/2) * (π/9) * ln(2)] - [0]

Thus, the definite integral evaluates to (π^2/6) * ln(2), which is approximately equal to π^2/2.

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The linear approximation of the function f(x) = ln(π3x + sin x) at x = π/2 is L(x) = 2.50x - 0.33. The linear approximation of the function g(x) = e cos(4x) at x = 0 is L(x) = 1. The approximation of f(π/2) using L(π/2) is 2.50, and the approximation of g(0) using L(0) is 1.

The linear approximation of a function f(x) at x = a is the equation of the tangent line to the graph of f(x) at x = a. To find the linear approximation, we need to find the slope of the tangent line at x = a. The slope of the tangent line is given by f'(a). Once we have the slope, we can use the point-slope form of linear equations to find the equation of the tangent line.

In the case of f(x) = ln(π3x + sin x), we have a = π/2. The derivative of f(x) is f'(x) = π3/(π3x + sin x). Therefore, the slope of the tangent line at x = π/2 is π3/(2π). The equation of the tangent line is then L(x) = 2.50x - 0.33.

In the case of g(x) = e cos(4x), we have a = 0. The derivative of g(x) is g'(x) = -4e cos(4x). Therefore, the slope of the tangent line at x = 0 is 0. The equation of the tangent line is then L(x) = 1.

We can use Desmos to sketch the graphs of f(x) and L(x) for each case. In both cases, the linear approximation is a good approximation of the function near x = a. However, as x moves further away from a, the approximation becomes less accurate.

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Answer:

Because ΔABC ≅ ΔDEC, ∠B ≅ ∠E by CPCTC which means:

2x + 31 = 7x - 24

-5x = -55

x = 11°.

Answer:

-4

Step-by-step explanation:

-2x +4 < 12

-2x < 12 -4

-2x < 8

x > -8/2

x > -4

Answer:

x > - 4

Step-by-step explanation:

- 2x + 4 < 12 ( subtract 4 from both sides )

- 2x < 8

Divide both sides by - 2, reversing the symbol as a result of dividing by a negative quantity.

x > - 4

Answer:

\(3\frac{1}{3}\ ft^3\)

Step-by-step explanation:

A rectangular prism is a polyhedron with six rectangular faces. The volume of a prism is given by:

Volume = width * height * length

From the diagram, the rectangular prism is made up of cubes. Each cube is has a size of 1/3 ft by 1/3 ft.

The height of the prism is made up of 5 cubes. Height = 5 * 1/3 = 5/3 ft.

The length of the prism is made up of 3 cubes. length = 3 * 1/3 = 1 ft.

The width of the prism is made up of 2 cubes. Width = 2 * 1/3 = 2/3 ft.

The volume of the prism = width * height * length = 2/3 * 5/3 * 1 = 10/9 ft³ =  \(3\frac{1}{3}\ ft^3\)

Answer:

it is 3 1/3 good day

Step-by-step explanation:

Answer:

4x - 2y = 2

Step-by-step explanation:

Given that (1, 1 ) is a solution then it must satisfy the equation

Consider the equations given

2x + y = 2 → 2(1) + 1 = 2 + 1 = 3 ≠ 2 ← not True

4x - 2y = 2 → 4(1) - 2(1) = 4 - 2 = 2 ← True

2x - 2y = 2 → 2(1) - 2(1) = 2 - 2 = 0 ≠ 2 ← not True

x + y = 4 → 1 + 1 = 2 ≠ 4 ← not True

Thus

4x - 2y = 2 completes the system.

The work done by the force on the particle is approximately 12.96 N.m.

To find the work done by the force on the particle, we can use the formula:

Work (W) = Force (F) ⋅ Displacement (δr) ⋅ cos(θ)

where F is the force vector, δr is the displacement vector, and θ is the angle between the force and displacement vectors.

Given:

Force vector, F = 4 î - 3 ĵ N

Displacement vector, δr = 4 î + ĵ m

First, let's calculate the dot product of the force and displacement vectors:

F ⋅ δr = (4 î - 3 ĵ) ⋅ (4 î + ĵ)

= 4 * 4 + (-3) * 1

= 16 - 3

= 13

Next, we need to find the angle between the force and displacement vectors. The angle θ can be determined using the dot product and the magnitudes of the vectors:

θ = cos^(-1)((F ⋅ δr) / (|F| * |δr|))

|F| = √(4² + (-3)²)

= √(16 + 9)

= √25 = 5

|δr| = √(4² + 1²)

= √(16 + 1)

= √17

θ = cos^(-1)(13 / (5 * √17))

Now we can calculate the work done:

W = F ⋅ δr ⋅ cos(θ)

= 13 * cos(θ)

Substituting the value of θ:

W = 13 * cos(cos^(-1)(13 / (5 * √17)))

Simplifying:

W ≈ 13 * 0.997

W ≈ 12.96 N.m (rounded to two decimal places)

Therefore, the work done by the force on the particle is approximately 12.96 N.m.

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\( \frac{3}{16} \)

Answer:

3/16

Step-by-step explanation:

Total no.of beads = 16

No.of blue beads = 3

Probability of picking a blue bead = 3/16

I think this is the answer.

The rate of constant for the above-given first-order reaction is b.) 8.77 × 10–3 h–1.

The half-life of a first-order reaction can be calculated using the equation t1/2 = ln(2)/k, where t1/2 is the half-life and k is the rate constant.

In this case, we know that the reaction goes to half completion in 79 hours. Therefore, the half-life is also 79 hours.

Plugging this into the equation, we get:

79 = ln(2)/k

Solving for k, we get:

k = ln(2)/79

Using a calculator, we can evaluate this expression to get:

k = 8.77 × 10–3 h–1

Therefore, the correct answer is b) 8.77 × 10–3 h–1.

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The surface area of this locker is 432 square centimeters .

The right rectangular prism shown in the figure has dimensions 8 cm (length) x 6 cm (width) x 12 cm (height).

1. The top and bottom faces are both rectangles with dimensions 8 cm (length) x 6 cm (width). The area of each face is:

A = length x width = 8 x 6 = 48 cm²

Since there are two of these faces, the total area is:

2 x 48 = 96 cm²

2. The front and back faces are also rectangles with dimensions 8 cm (length) x 12 cm (height). The area of each face is:

A = length x height = 8 x 12 = 96 cm²

the total area is:

2 x 96 = 192 cm²

3. The left and right faces are rectangles with dimensions 6 cm (width) x 12 cm (height). The area of each face is:

A = width x height = 6 x 12 = 72 cm²

the total area is:

2 x 72 = 144 cm²

4. Therefore, the total surface area of the locker is the sum of all the faces:

Total surface area = 96 + 192 + 144 = 432 cm²

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Answer:

One way to find the least common multiple of two numbers is to first list the prime factors of each number. Then multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor the greatest number of times it occurs.

Step-by-step explanation:

Answer:

First convert numbers into prime numbers. find which number(s) is/are repeating. Multiply all numbers execpt for the number that repeat. Multiply those once.

Step-by-step explanation:

12 = 3*2*2

14 = 2*7

One 2 repeats

3*2*2*7 = 21*4 = 84

Lcm(12, 14) = 84

Answer:

6.0435*10²⁴

Step-by-step explanation:

Moon:  7.35*10²²

Earth: 5.97*10²⁴

7.35*10²² = 0.0735*10²⁴

then:

0.0735*10²⁴ + 5.97*10²⁴ = (0.0735 + 5.97)*10²⁴

=  6.0435 *10²⁴

Answer:

The equation of the line is;

Explanation:

Given that

the slope of a line is -2 and it passes through the point (4,-5).

Applying the slope-intercept form of equation;

Substituting the values of the slope and coordinates;

Therefore, the equation of the line is;

Answer:

2x + y = 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute (4, - 5 ) into the partial equation

- 5 = - 8 + c ⇒ c = - 5 + 8 = 3

y = - 2x + 3 ← in slope- intercept form

add 2x to both sides

2x + y = 3 ← equation in standard form

Answer: A trend line is a line on a scatter plot, drawn near points, that approximates the association between the data sets.

Step-by-step explanation:

2. The linear trend in precipitation is the dominant trend type. The nonlinear trends occur much less frequently and more widely scattered over the globe. However, the nonlinear trends are credible patterns of change in precipitation.

3. The trend is the component of a time series that represents variations of low frequency in a time series, the high and medium frequency fluctuations having been filtered out. This component can be viewed as those variations with a period longer than a chosen threshold

4. The trend component represents changes in time-series data that are unpredictable and cannot be associated with a seasonal, cyclical, or random component. OB. The trend component is the long-term increase or decrease in a variable being measured over time.

5. The trend is the component of a time series that represents variations of low frequency in a time series, the high and medium frequency fluctuations having been filtered out.

6. The trend component is the long-term increase or decrease in a variable being measured over time.

The expectation value of the position squared when the particle in the box is in its third excited state is equal to \(\frac{9l^2}{8}\), where l is the length of the box. This is equal to nine-eighths of the length of the box squared.

The expectation value of the position squared when the particle in the box is in its third excited state can be calculated using the formula\(\langle x^2 \rangle = \frac{l^2}{8} \left( 2n^2 + 6n + 3 \right)\),

where n is the quantum number of the state and l is the length of the box. Here, n is 3, so the expectation value is equal to

\(\frac{l^2}{8} \left( 2 \times 3^2 + 6 \times 3 + 3 \right) = \frac{9l^2}{8}\).

This can be written as nine-eighths of the length of the box squared.

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Answer:

Step-by-step explanation:

Answer:

10.) 469 R1

11.) 4358

12.) 1744 R2

13.) 4 R2

16.) 206 R2

17.) 148

Step-by-step explanation:

Answer:

(B) -8

Step-by-step explanation:

Given the 2-column table below:

\(\left|\begin{array}{c|c}x&y\\--&--\\-3&14\\-1&10\\1&6\\4&0\\8&?\\10&-12\end{array}\right|\)

Taking the pair (-3,14) and (-1,10)

\(Slope, m=\dfrac{10-14}{-1-(-3)} =\dfrac{-4}{2} =-2\)

Taking the pair (1,6) and (4,0)

Slope, \(m=\dfrac{0-6}{4-1} =\dfrac{-6}{3} =-2\)

Since the slope is constant, the table represents a linear function whose slope is -2. Therefore:

Taking the pair (8,y) and (4,0)

Slope, \(m=\dfrac{0-y}{4-8} =-2\)

\(\dfrac{-y}{-4} =-2\\y=-2*4=-8\)

Therefore, the value of ? on the y-column is -8.

Answer:

-8

Step-by-step explanation:

9514 1404 393

Answer:

  4) -438.75

  8) 539.68

  12) 22.54

Step-by-step explanation:

Put the values in place of the corresponding variables and do the arithmetic.

__

4) 6xy = 6(-7 1/2)(9 3/4) = -6(7.5)(9.75) = -438.75

__

8) I = prt = $2442 × 0.085 × 2.6 = $539.68

__

12) I = prt = ($578)(0.0325)(1.2) = $22.54

Since tan m = 1/2 and tan n = -6, the precise value of tan (m+n) will be 3.51.

The tangent of an angle in trigonometry is the ratio of the lengths of the adjacent side to the opposing side. In order for the value of the cosine function to not be 0, it is the ratio of the sine and cosine functions of an acute angle. The law of tangent is another name for tan. The ratio of a triangle's opposing side to its adjacent side is known as the tangent formula for a right-angled triangle. The angle's sine to cosine ratio can also be used to represent the angle.

Here,

tan m= 1/2

tan n= -6

m=tan inverse(1/2)

n=tan inverse(-6)

m=26.565 degrees

n= -80.537 degrees

n=360-80.537

n=279.463 degree

tan (m+n)=tan(26.565+279.463)

tan 306.028=3.51

The exact value of tan (m+n) will be 3.51 as the value of tan m= 1/2 and tan n= -6.

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