a force of 15 lb is required to hold a spring stretched 6 in. beyond its natural length. how much work w is done in stretching it from its natural length to 10 in. beyond its natural length?

Answer:

1.07

friend me? anyone

Answer:

6.5 hours

Step-by-step explanation:

distance = rate times time

1.1 = .17t  t stands for time  Divide both side by .17

my calculator shows 6.47058823527  We need to round to one decimal place

time = 6.5 hours or 6 1/2 hours

Answer:

Slope= y=1/2x+6

Step-by-step explanation:

Hope it helps.

Answer: x + 1

Hope this helps :)

Answer:

x+1

Step-by-step explanation:

I hope you have a merry christmas!

Answer:

x=6/5

Step-by-step explanation:

The car's speed after the given amout of time is 19.8 m/s²

The rate at which an object's velocity with respect to time changes is referred to as acceleration in mechanics. They are vector quantities, accelerations. The direction of the net force acting on an object determines the direction of its acceleration. A point or object going straight ahead is accelerated when it accelerates or decelerates. Any alteration in an object's velocity could take the form of a change in direction of motion or a speed increase or reduction. The moon orbiting the earth, an apple falling to the ground, and a car stopped at a stop sign are a few instances of acceleration.

Average Acceleration =Change in Velocity/ Time Taken

So Change in Velocity is 10-x m/s

Time taken is 7.25 s

Given accelaration 4.11 m/s²

Putting the values we get,

4.11 = (10-x)/7.25

⇒29.8 = 10-x

⇒x=19.8 m/s²

​

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The equation of the line which is perpendicular to 5x - 4y = 16 is  \(y = -\frac{4}{5}x -4\).

The study of geometry using coordinate points is known as coordinate geometry (also known as analytical geometry). Finding the distance between two points, breaking lines into m:n segments, locating a line's midpoint, computing a triangle's area in the Cartesian plane, and other operations are all feasible using coordinate geometry.

Not all crossing lines are parallel ones. If the intersecting lines satisfy the following conditions, they are said to be perpendicular lines. Following are the two primary characteristics of perpendicular lines:

Let's say that lines AB and CD are parallel to one another. Line AB has a slope of m1, whereas line CD has a slope of m2.

If and only if the product of the slopes of the two lines equals negative of unity, two lines are perpendicular to one another.

As a result, the following is the formula for the perpendicular's slope:

m1.m2 = -1

The equation of the line be "y = mx + c".

Equation of the line Perpendicular to the line is 5x - 4y = 16

Therefore,  4y = 5x - 16

⇒ \(y = \frac{5}{4}x -4\)

Slope of the line Perpendicular to the required line is \(\frac{5}{4}\).

Slope of the required ine be m .

Therefore, m * \(\frac{5}{4} = -1\)

⇒ \(m = -\frac{4}{5}\).

Equation of the line is ,

\(y = -\frac{4}{5}x + c\)

The line passes through (5,-8)

Therefore,

\(-8 = \frac{-4}{5}*5 + c\)

⇒ c = -4

The equation of the line is \(y = -\frac{4}{5}x -4\).

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Answer:

J''(- 3, 3 )

Step-by-step explanation:

Under a counterclockwise rotation about the origin of 90°

a point (x, y ) → (- y, x )

Thus J(1, 1 ) → J'(- 1, 1 )

Under a dilatation with scale factor 3, multiply each of the coordinates of J' by 3, that is

J'' = (3(- 1), 3(1)) = (- 3, 3 )

Answer:

40 cows=16 days

= 10 days

Step-by-step explanation:

a field is grazed in 16 days by 40 cows so for the same field to be grazed in 10 days more cows are needed

so more/ less

16/10×40

64 cows it should be.

Yes, there are two possible shapes that fit this description.

Lilly is describing a parallelogram, which is a quadrilateral with two pairs of parallel opposite sides.

A parallelogram has opposite sides that are congruent and parallel, and opposite angles that are congruent. Therefore, it has two pairs of equal opposite sides.

There are two types of parallelograms: a rectangle and a rhombus. A rectangle is a parallelogram with four right angles, while a rhombus is a parallelogram with four congruent sides.

Both shapes have two pairs of equal opposite sides and opposite sides that are parallel.

Therefore, Robin is correct that there are two possible shapes. Depending on whether all four angles are right angles or all four sides are congruent, the shape could be a rectangle or a rhombus. It is also possible for a shape to be both a rectangle and a rhombus, in which case it would be called a square.

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The surface area of the rectangular prism is 88 square inches.

Given that:

Length, L = 6 inches

Width, W = 2 inches

Height, H = 4 inches

Let the prism with a length of L, a width of W, and a height of H. Then the surface area of the prism is given as

SA = 2(LW + WH + HL)

SA = 2(6 x 2 + 2 x 4 + 4 x 6)

SA = 2 (12 + 8 + 24)

SA = 2 x 44

SA = 88 square inches

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The growth rate of the bacterial colony after 3 hours is 32%, the population of a slowly growing bacterial colony after t hours is given by the function p(t) = 100 + 24t + 2t²

The growth rate of the colony is the rate of change of the population, which is given by the derivative of the function. The derivative of p(t) is p'(t) = 24 + 4t

The growth rate after 3 hours is p'(3) = 24 + 4 * 3 = 32. This means that the population of the colony is increasing by 32% after 3 hours.

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The total number of acres planted for the optimal solution is not provided in the given information.

The amount of fertilizer (in tons) required to produce only corn is not provided in the given information.

The peak number of acres of wheat planted as fertilizer availability varies from 200 tons to 2200 tons in 100-ton increments cannot be determined without additional information.

I can help explain the general approach to answering the questions you mentioned.

To determine the total number of acres planted for the optimal solution, you would need to refer to the problem's constraints and objective function. The optimal solution would be obtained by solving the problem using linear programming techniques such as the simplex method or graphical method. By solving the problem, you can identify the values of the decision variables (such as acres planted) that maximize or minimize the objective function while satisfying the given constraints. The total number of acres planted for the optimal solution would depend on the specific problem setup and the solution obtained.

Similarly, to find out how much fertilizer would be needed to produce only corn, you would need to refer to the constraints and objective function of the problem. The specific requirements and coefficients associated with the corn production and fertilizer usage would determine the amount of fertilizer needed. By solving the problem, you can obtain the value of the decision variable representing fertilizer usage, which would indicate the required amount of fertilizer in tons.

SolverTable is a tool in Excel that allows you to perform sensitivity analysis by varying certain input values and observing the impact on the output. By using SolverTable, you can analyze the relationship between fertilizer availability (input) and acres planted (output) in the given problem. By varying the fertilizer availability from 200 tons to 2200 tons in 100-ton increments, you can observe how the acres of wheat planted change accordingly. The peak number of acres of wheat planted would be the maximum value observed during this range of fertilizer availability.

Since I don't have access to the specific problem you mentioned, I cannot provide precise answers or calculations. Please refer to the problem in your textbook or reference material to obtain the exact values and final answers.

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The least positive integer we can get as the product is 2.

Here we have the following set of numbers:

{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}

And we want to take the product between 3 of them and find the least positive integer that we can get as the product.

So it makes sence to choose the smallest absolute value numbers (not zero) such that one is positive and two are negative (we want two negative ones so the signs cancell eachother)

Then we will get:

1*(-1)*(-2) = 2

That is the least positive integer we can get as the product.

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The outward flux of the vector field F across the boundary of the region D, which is the cube bounded by the planes x = ±1, y = ±1, and ±1, can be found using the divergence theorem.

The outward flux is the integral of the divergence of F over the volume enclosed by the boundary surface.The first step is to calculate the divergence of F. The divergence of a vector field F = P i + Q j + R k is given by div(F) = ∂P/∂x + ∂Q/∂y + ∂R/∂z. In this case, div(F) = ∂/∂x(5y - 4x) + ∂/∂y(-4z - 5y) + ∂/∂z(-3y - 2x). Simplifying these partial derivatives, we have div(F) = -4 - 2 - 3 = -9.

Applying the divergence theorem, we can relate the flux of F across the boundary surface to the triple integral of the divergence of F over the volume enclosed by the surface. Since D is a cube with sides of length 2, the volume enclosed by the surface is 2^3 = 8.

Therefore, the outward flux of F across the boundary of D is given by ∬S F · dS = ∭V div(F) dV = -9 * 8 = -72. The negative sign indicates that the flux is inward.

In summary, the outward flux of the vector field F across the boundary of the cube D, as described by the given vector components, is -72. This means that the vector field is predominantly flowing inward through the boundary of the cube.

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In a triangle one side that lies on an extended line segment,  statement about x is true, x = 62 because 147−85=62 and 85 + 62 = 147. So Option B is correct

In mathematics, the triangle is a type of polygon which has three sides and three vertices. the sum of all the interior angles of the triangle is 180°

Given that,

A triangle, which has one interior angle 85° and one exterior angle 147°

Another exterior angle x = ?

It is already known that,

Sum of complementary angles are 180

So,

⇒  Y + 147 = 180

⇒  Y  = 180 - 147

⇒  Y = 33

sum of all the interior angles of the triangle is 180°

X + Y + 85 = 180

X = 180 - 85 - 33

X = 62

Hence, the value of x is 62

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Answer:

C) 1

Step-by-step explanation:

The answer is C) 1

Answer:

He can only make 8 cheese pizzas

Step-by-step explanation:

4➗1/2=8

1/2+1/2+1/2+1.2+1.2+1.2+1.2+1.2=8

As calculated from the given data Jane's calorie intake is 1200 per day.

From the details given in the question we can say that Jane doesn't likes milk. Hence, she lacks dairy fat  in her food. As per the given case she likes vegetables and eats fruit a lot. Therefore, and the grams of total caloric intake for her should be 1200 calories per day.

She does, however, lack fats from dairy products like milk. A child of 8 years old is thought to need at least 2 cups of milk or its equivalent each day. Jane is getting enough carbohydrates because she consumes 225 gram per day as opposed to the recommended 130 gram.

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Answer:

8.373

Step-by-step explanation:

Cone

Find the volume of the cone

V = 1/3 pi r^2 h

r = d/2

r = 4/2

r = 2 inches

h = 6 inches

pi = 3.14

V = 1/3 * 3.14 * 2^2 *  6

V = 25.12

Half sphere

V = 1/2 (4/3) pi r^3

r = 2 from above calculation

pi = 3.14

V = 2/3 * 3.14 * 2^3

V = 2/3 * 3.14 * 8

V = 16.74

Nothing spills out so I scoop must be a whole sphere. The sphere is 2 times what I calculated it to be or

V = (4/3) * 3.14 * 2^3

V = 33.49 cubic inches

The difference in volume is 33.49 - 25.12 = 8.373

By introducing an additional association between an input value and multiple output values, such as assigning 4 to both 1 and 3, we can make the relation not represent a function.

In order for a relation to represent a function, each input value (x) must have a unique corresponding output value (y). If there is any input value that is associated with multiple output values, the relation does not represent a function.

Looking at the given table:

Input: 7 7 4 5

Output: 2 5 1 2

We can see that the input value of 7 is associated with two different output values, 2 and 5. This violates the requirement for a function because an input value should have only one corresponding output value.

To make the relation not represent a function, we need to choose a value that will introduce another instance where an input value is associated with multiple output values.

Let's choose an input value that already exists in the table, such as 4. Currently, the input value 4 is associated with an output value of 1. To make the relation not represent a function, we can associate 4 with another output value, let's say 3.

Updated relation:

Input: 7 7 4 4 5

Output: 2 5 1 3 2

Now, the input value of 4 is associated with two different output values, 1 and 3. Therefore, the relation does not represent a function.

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According to the image we can infer that both figures are similar. Their ratio is 11:4; their scale factor is 1:2 and their areas are: 40cm² and 14.54cm²

We know that the two figures are similar because they have the same angles. Therefore they are similar. In this case it can be inferred that they have a scale factor close to half because the small triangle represents more or less half of the large triangle.

The value of the ratio can be found taking as reference the measurements of the base of the triangles. Then it would be a ratio of 11:4, that is to say that for every 11cm of large triangle, the small one has a 4cm base.

Finally, if the area of the large triangle is 40cm², the area of the small triangle would be the following:

11cm base = 40cm²

4 cm base = cm²

4 * 40 / 11 = 14.54cm²

Yes they are similar because they have the same angle values.

According to the graph we can infer that the scale factor of the similarity transformation that takes ABC to CDE is 1:2.

According to the information, we can infer that the ratio of the area of both triangles is 11:4 because those values correspond to their base length.

if the area of the large triangle is 40cm², the area of the small triangle would be the following:

11cm base = 40cm²

4 cm base = cm²

4 * 40 / 11 = 14.54cm²

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Answer:

38 degrees

Step-by-step explanation:

Angle 38 and b are the same.

The distribution that t follows is the maximum of three independent exponential distributions with a mean of 5 minutes each.

Each block takes an exponential amount of time with a mean of 5 minutes, which means that the time it takes to compile each block follows an exponential distribution with a rate parameter of 1/5. Since the blocks are being compiled independently of each other, the time it takes to compile all three blocks is the maximum of the three independent exponential distributions.

This distribution is known as the maximum of exponential distributions or the generalized extreme value distribution with a shape parameter of 0 and scale parameter of 5 minutes. Therefore, t follows a generalized extreme value distribution with a shape parameter of 0 and scale parameter of 5 minutes.

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Answer:

7.5%

Step-by-step explanation:

a probability is always

desired cases / totally possible cases

the totally possible cases is everybody in the survey :

24+18+14+10+8+6 = 80

the desired cases are everybody having potatoes a favorite food : 6

the probability the picked person prefers potatoes is

6/80 = 3/40 = 0.075 = 7.5%

The set which represents the range of the function g(x) = 14 -2x if the domain is x = { 2,4,9} is; y = {10, 6, -4)

The set which represents the range of the function for the given domain can be gotten as follows;

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The area of the pyramid is 517.28 m²

To calculate the surface area of a triangular pyramid, we need to find the area of each face and sum them up.

The base of the pyramid is a triangle, so its area can be calculated using the formula: A = 1/2 x base area x height.

In this case, the base side is 12.2 m and the height is 10.6 m.

Therefore, the area of the base is:

Area = 1/2 x 10.6 x 12.2 = 64.66 m²

So, the area of the pyramid =

A = 1/2 x 64.66 x 16

A = 517.28 m²

Hence the area of the pyramid is 517.28 m²

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The measure that would most correctly answer this question is standard deviation.

What is standard deviation?

The standard deviation is measure of how spread out data from mean.

Step-by-step explanation:

Average age of respondents in a survey is \(49\) years. Researcher interested in finding out if most respondents are close to \(49\) years or not.

Hence here measures of dispersion fact will be used.

Measures of dispersion are range and standard deviation.

Range is nothing but the difference between maximum and minimum values of the data.

Standard deviation gives proper idea about how far the data values are scattered from the mean point \(49\) years.

Therefore the correct option is standard deviation.

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The number of books that Jessica read in the fifth year is 2⁵ m.

Given that,

Jessica joined a book club five years ago.

The club tries to increase the number of books you read by a factor of two each year.

Given that,

Number of books that Jessica read in the year she joined = m

Each year the number of books read will be increasing by the factor of 2.

So in the first year, she will read 2m.

The second year, she will read, 2² m

In this way, in the fifth year, she will read 2⁵ m number of books.

Hence the correct option is B.

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Answer:

-23°F

Step-by-step explanation:

Since it says "less", we are going to subtract.

-12 - 11 = -23

Best of Luck!