Answer to question 18? Confused!

On solving the provided question, we can say that - => K not equal to 0 at x= 0 and so, center of curvature exists.

In geometry, a curve's center of curvature is located at a point that is offset from the curve by an amount equal to the radius of curvature that lies on the normal vector. zero-curvature point at infinity. The center of the curve serves as the osculating circle. The sphere holding the spherical mirror's center serves as its center of curvature. A "C" is used to symbolize this. the center of a circle with a radius equal to the radius of curvature of a particular point on the curve, whose center is on the concave side of the curve and which is normal to that point.

The curvature K at the point (x,y) is given by if C is a graph of the twice differentiable function y = f(x)y=f(x).

\(K = \frac{|y^{''}|}{[1 + (y')^2 ]^{3/2}}\)

Curvature of the given curve at x=0x=0 is

=> K not equal to 0 at x= 0

so,

center of curvature exists.

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Answer:

Of the given options, "an engine" is the most reasonable abstraction for a car.

An engine is a fundamental component of a car that powers its movement, and it is present in almost all cars. The number of miles driven and the driving car color are characteristics of a specific car rather than abstractions of a car itself. For example, a car can still be considered a car even if it has not been driven any miles yet or if it has no color at all.

Therefore, an engine is a more reasonable abstraction for a car as it captures an essential feature of a car that is present in all cars.

The solution is, D. Driving, a reasonable abstraction for a car includes. Driving is an action or behavior associated with a car, as it involves operating or using the car to travel from one place to another. It is an essential aspect of the car's purpose and function.

Here, we have,

we know that,

An engine is a machine designed to convert fuel into mechanical energy that can be used to power other machines or devices. In the context of automobiles, an engine is the primary source of power that drives the vehicle. It typically operates by burning fuel in a combustion chamber to generate high-pressure gases that drive a piston, which in turn rotates a crankshaft that ultimately powers the car's wheels.

Car color and number of miles driven are characteristics or properties of a car, while an engine is a component that helps to power the car. Driving, on the other hand, is an action or behavior associated with a car, as it refers to the act of operating or using the car to travel from one place to another.

Therefore, driving is a reasonable abstraction for a car, as it captures an essential aspect of the car's purpose and function.

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The number of tractors lent by the first, second and third stations results in a system of three simultaneous equations which indicates;

The first originally station had 39 tractors, the second station had 21 tractors and the third station originally had 12 tractors

Simultaneous equations are a set of two or more equations that have common variables.

Let x represent the number of tractors at the first station, let y represent the number of tractors at the second tractor station, and let z, represent the number of tractors at the third tractor station

According to the details in the question, after the first transaction, we get

Number of tractors at the first station = x - y - z

Number of tractors at the second station = y + y = 2·y

Number of tractors at the third station = z + z = 2·z

After the second transaction, we get;

Number of tractors at the first station = 2·x - 2·y - 2·z

Number of tractors at the second station = 2·y - (x - y - z) - 2·z = 3·y - x - z

Number of tractors at the third station = 2·z + 2·z = 4·z

After the third transaction, we get;

Number of tractors at the first station = 2 × (2·x - 2·y - 2·z) = 4·x - 4·y - 4·z

Number of tractors at the second tractor station = 6·y - 2·x - 2·z

Number of tractors at the third tractor station = 4·z - (2·x - 2·y - 2·z) - (3·y - x - z) = 7·z - x - y

The three equations after the third transaction are therefore;
4·x - 4·y - 4·z = 24...(1)

6·y - 2·x - 2·z = 24...(2)

7·z - x - y = 24...(3)

Multiplying equation (2) by 2 and subtracting equation (1) from the result we get;

12·y - 4·x - 4·z - (4·x - 4·y - 4·z) = 16·y - 8·x = 48 - 24 = 24

16·y - 8·x = 24...(4)

Multiplying equation (3) by 2 and multiplying equation (2) by 7, then adding both results, we get;

14·z - 2·x - 2·y = 48

42·y - 14·x - 14·z = 168

42·y - 14·x - 14·z + (14·z - 2·x - 2·y) = 48 + 168

40·y - 16·x = 216...(5)

Multiplying equation (4) by 2 and then subtracting the result from equation (5), we get;

40·y - 16·x - (32·y - 16·x) = 216 - 48 = 168

8·y = 168

y = 168/8 = 21

The number of tractors initially at the second station, y = 21

16·y - 8·x = 24, therefore, 16 × 21 - 8·x = 24

8·x = 16 × 21 - 24 = 312

x = 312 ÷ 8 = 39

The number of tractors initially at the first station, x = 39

7·z - x - y = 24, therefore, 7·z - 39 - 21 = 24

7·z = 24 + 39 + 21 = 84

z = 84/7 = 12

The number of tractors initially at the third station, z = 12

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Answer:

810

Step-by-step explanation:

\(V = l * w * h = 5 * 9 * 18 = 810\ cm^3\)

The answer of addition & multiplication are,

101,455,348 + 1,111,419 = 102566767

0.000000612 x 0.00031119 = 1.9044828E-10

297,060 + 0.0004839 =297060.0005

0.000000612 x 0.00031119 =

297,060 + 0.0004839 =

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Here, given that,

101,455,348 + 1,111,419 = 102566767

0.000000612 x 0.00031119 = 1.9044828E-10

297,060 + 0.0004839 =297060.0005

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The width of the pool is 18 feet, and the length is 24 feet (since it is 6 feet longer than the width).

Let's represent the width of the pool as x. Then, the length of the pool would be x + 6.

The total area of the pool and walk is given by:

Total area = (length + 2(4)) × (width + 2(4))

Total area = (x + 6 + 8) × (x + 4)

Total area = (x + 14) × (x + 4)

The area of the pool itself is given by:

Pool area = length × width

Pool area = x(x + 6)

Pool area = x² + 6x

We're told that the total area is 272 more than the area of the pool:

Total area = Pool area + 272

(x + 14) × (x + 4) = x² + 6x + 272

Expanding the left side of the equation:

x² + 18x + 56 = x² + 6x + 272

Simplifying the equation:

12x = 216

Solving for x:

x = 18

So the width of the pool is 18 feet, and the length is 24 feet (since it is 6 feet longer than the width).

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Full Question: A rectangular pool is surrounded by a walk 4 feet wide. The pool is six feet longer than its wide. If the total area is 272 ft² more than the area of the pool,what are the dimension of the pool?

Answer: 80%

Step-by-step explanation: In the store every 4 out of 5 costumers purchase an product.

If you multiply numbers by 20, you get the demoninator to be 100, which then you can get the percentage by finding 4x20=80.

Therefore, converted, 4/5=80%.

Answer:

Hey there!

No, one or more pairs of corresponding points have not moved the

same distance.

Let me know if this helps :)

Answer:

4 units

Step-by-step explanation:

The length of the shorter side is equal to the difference in y-coordinates of two vertically opposite vertices. The y-coordinates of the vertices (-1, -5) and (3, -5) are both -5, so the vertical side between them is not the shorter side. The y-coordinates of the vertices (3, -7) and (-1, -7) are both -7, so the vertical side between them is the shorter side. The difference in the x-coordinates of these two vertices is 3 - (-1) = 4, so the length of the shorter side is 4 units.

Answer: Your answer is 2

Step-by-step explanation: I did the k12 quiz here's proof

Answer:

The answer of this question is 8.06 cm.

Step-by-step explanation:

I came to know my answer is correct because hypotenuse is bigger than base and perpendicular in right anhled triangle.

Answer:

Me two I'm dum lol I think it 2× 9=18 in to 0 go 0 times

Extra people required is 50.

Each of the five workers should increase their efficiency to a rate of 15 sandwiches per 10 hour shift.

Proportions are defined as the concept where two or more ratios are set to be equal to each other.

Question 1 :

Number of associates = 30

Number of direct workers = 30 - 2 = 28

You work 8 hours a day and 5 days a week with two 15 minutes break or 30 minutes break per day.

Direct rate = 150 units per hour

Number of working hours in a week with break = 8 × 5 = 40 hours per week Number of working hours in a week = 7.5 hours per day × 5 days a week

                                                            = 37.5 hours per week

Units that department produce in a 40 hour week = 37.5 × 150 = 5625 units

28 people produce 5625 units in a week

Let x people produce 10,000 + 5625 = 15,625 units in a week

Using proportion,

28 : 5625 = x : 15,625

28 / 5625 = x / 15,625

x = (28 × 15,625) / 5625 = 77.78 ≈ 78

Extra people required = 78 - 28 = 50

Question 2 :

Number of sandwiches made in 10 minutes = 1

Number of sandwiches made in 10 hours = 60

5 workers are there. one worker makes 60/5 = 12 sandwiches

But Deli want number of sandwiches in 10 hours = 75

One worker should make 75/5 = 15 sandwiches instead of 12.

Number of sandwiches made in 8 minutes should be 1.

So the working efficiency on each worker should be increased and produce each one should produce 15 sandwiches in a 10 hour shift.

Hence extra people required in question 1 is 50 and efficiency of each worker in question 2 should be increased to 15 sandwiches in 10 hours shift.

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We need to determine the score a student must achieve to place in the top 5% of all students taking the SAT Verbal test with an N(\(515, 109\)) distribution, which came out to be \(695\) marks.

Identify the mean (μ) and standard deviation (σ) of the distribution: In this case, µ \(= 515\) and σ\(= 109\).

Determine the percentile rank: To place in the top \(5%\)% of students, we need to find the score corresponding to the \(95th\) percentile, as this represents the point where \(95\)% of students have a lower score.

Use a standard normal (Z) table or calculator to find the Z-score corresponding to the \(95th\) percentile: A Z-score represents the number of standard deviations a data point is from the mean.

For the \(95th\) percentile, the Z-score is approximate \(1.645\).

Apply the Z-score formula to find the required SAT score: \(X =\) µ \(+ Z*\) σ. In this case, \(X = 515 + (1.645 *109)\).Calculate the result: \(X = 515 + (1.645 *109)\)

\(=515 + 179.305 = 694.305\).

Round up to the nearest whole number: Since a student's SAT score must be a whole number, round up to \(695\). A student must score \(695\) or higher on the SAT Verbal test to place in the top \(5\)% of all students taking the test, given the N(\(515, 109\)) distribution.

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Answer:

See below.

Step-by-step explanation:

7,824/10=782.4

782.4

 |

The 8 is in the tens place. It represents 80.

-hope it helps

Answer:

80

Step-by-step explanation:

7824÷10=782.4

Therfore the 8 is in the tens place meaning that the 8 in this is 80

Answer: 7z+6

Step-by-step explanation:

The slope of side BC of square ABCD with vertices A(2, 1), B(4, 4), and D(5, -1) is -1.

To determine the slope of side BC, we need to calculate the difference in the y-coordinates divided by the difference in the x-coordinates of points B and C. Since BC is a side of a square, we know that it is parallel to AD, which has a slope of (y2 - y1) / (x2 - x1) = (-1 - 1) / (5 - 2) = -2/3.

The slope of BC is perpendicular to the slope of AD, and since BC is also parallel to the y-axis, its slope is undefined or infinite. Therefore, we can use the x-coordinates of B and C to calculate the length of BC and the fact that BC is perpendicular to AD to determine its slope.

Since BC is parallel to the y-axis, the x-coordinate of point C is 4. Since ABCD is a square, the length of BC is equal to the length of AB, which is the distance between points B and C. The distance formula gives us:

sqrt((x2 - x1)^2 + (y2 - y1)^2) = sqrt((4 - 4)^2 + (4 - 1)^2) = sqrt(9) = 3

Therefore, the slope of BC is the negative reciprocal of the slope of AD, which is -1/(-2/3) = -3/2. Alternatively, we can observe that the product of the slopes of two perpendicular lines is -1, so the slope of BC must be -1/(-2/3) = -3/2. However, since BC is parallel to the y-axis, its slope is undefined or infinite.

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Given the figure of a line passes through the points (-2, 5) and (2, -3)

We will select all the equations that represent the line.

First, we will find the slope of the line as follows:

We will write the equation in the point-slope form using the point (-2,5)

We will write the equation of the line in the point-slope form using the point (2, -3)

We will write the equation of the line in the slope-intercept form:

So, the answer will be the following options:

D. y+3 = -2(x-2)

E. y = -2x + 1

F. y-5 = -2(x+2)

The expression that completes the function b(x)​ is b(x) = 33741 * (1.028)^x

The given parameters are:

Initial value, a = 33741  

Rate, r = 2.8%

The cost of tuition each year since 2015 is represented as

B(x) = a * (1 + r)^x

This gives

B(x) = 33741 * (1 + 2.8%)^x

Evaluate

b(x) = 33741 * (1.028)^x

Hence, the expression that completes the function b(x)​ is b(x) = 33741 * (1.028)^x

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Complete question

A study estimates that the cost of tuition at a university will increase by 2.8% each year. The cost of tuition at the University in 2015 was $33,741 the function b(x) , models the estimated tuition cost , where x is the number of years since 2015.

Find the expression that completes the function b(x)​

Answer:

cheese and mustard for sale only $12.99 it is fresh crusty and yellow natural with skin from feet and very tasty get some cheese and mustard for sale make burgers with it make eggs with it make  anything with it make toothpaste with it it makes it white and shiny

Step-by-step explanation:

Answer:

- 2/5

Step-by-step explanation:

Step 1:

( 4/5 - 7/5 ) + 1/5

Step 2:

- 3/5 + 1/5

Answer:

- 2/5

Hope This Helps :)

The statement 3 more than 7 means, a number is 3 more than a given number. Since here the number is 7 so the required number will be 7+3= 10

In numerical more than simply refers to adding and less than refers to subtracting. If it is given that a number let's say Z is Y more than X then the value will be Z= X+Y

If a given number let's say Z is Y less than X then the value of Z will be

Z=X-Y

More than means add which gives us a bigger value. Less than means subtract which gives us a smaller value

So, 3 more than 7 means 7+3 = 10

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Answer: what do you need help with??

Step-by-step explanation:

Answer:

Step-by-step explanation:

The y-intercept of a function is the point where the function crosses the y-axis. In the case of the logarithmic function f(x) = log3(x + 2) + 1, the y-intercept is the point where x = 0.

When x = 0, the expression log3(x + 2) is undefined. However, the expression log3(x + 2) + 1 is equal to 1, regardless of the value of x. Therefore, the y-intercept of the function is the point (0, 1), which means that the correct answer is B.

Answer:

6x-3=-5x+7 now add 3 to each side:

6x=-5x+10 now add 5x to each side:

11x=10 now divide each side by 11:

x= 10/11

Step-by-step explanation:

6x-3=-5x+7 now add 3 to each side:

6x=-5x+10 now add 5x to each side:

11x=10 now divide each side by 11:

x= 10/11

Answer:

Combine numerators over the common denominator to make one term

Step-by-step explanation:

Answer:

D: Add the fractions together on the right side of the equation

Step-by-step explanation:

Let's finish this proof:

Add the fractions together on the right side of the equation

\($x^2+\frac{b}{a} x+\left(\frac{b}{2a} \right)^2=\frac{b^2-4ac}{4a^2} $\)

\(\text{Consider the discriminant as }\Delta\)

\(\Delta=b^2-4ac\)

Once we got a trinomial here, just put in factored form:

\($\left(x+\frac{b}{2a}\right)^2=\frac{\Delta}{4a^2} $\)

\($x+\frac{b}{2a}=\pm\frac{\Delta}{4a^2} $\)

\($x+\frac{b}{2a}=\pm \sqrt{\frac{\Delta}{4a^2} } $\)

\($x=-\frac{b}{2a}\pm \sqrt{\frac{\Delta}{4a^2} } $\)

\($x=-\frac{b}{2a}\pm \frac{ \sqrt{\Delta} }{2a} $\)

\($x= \frac {-b\pm \sqrt{\Delta}}{2a} $\)

\($x= \frac {-b\pm \sqrt{b^2-4ac}}{2a} $\)

1. ∠B is the primage of ∠B'. They are similar triangles.

2. AC ≈AC'

CB ≈ CB'

AB ≈ AB'

When discussing angles, the preimage refers to the original angle before any transformation has occurred.

In geometry, a transformation refers to the process of moving or changing the position, shape, or size of an object. For example, if an angle is rotated or reflected, the resulting image of the angle would be the transformed angle.

The preimage is the angle before the transformation occurred. It is used to determine the relationship between the original angle and the transformed angle, such as whether they are congruent, similar, or related by another geometric property.

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the number is 40.

In mathematics, the system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables. In this article, you will get the definition of the system of linear equations, different methods of solving these systems of linear equations and solved examples.

If the tens digit of the number is X and the ones digit is Y then the number is equal to 10*X + Y

If you reverse the digits then the number is equal to 10*Y + X

If reversing the digits decreases the number by 36 then

10*Y + X = 10*X + Y - 36

The sum of the digits is 4 so X + Y = 4  ==>  X = 4 - Y

Substitute this value of X into the 1st equation

10*Y + (4 - Y) = 10*(4 - Y) + Y - 36

9*Y + 4 = 40 - 9*Y - 36

18*Y = 0

Y = 0

So X = 4 - 0 = 4 and the number is 40

Check:  40 - 04 = 36

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Since the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the data are not normally distributed.

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that it is certain. The probability of an event is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes.

Here,

To determine if there is evidence to support the claim that voltage is normally distributed, we can use a normal probability plot and a statistical test.

First, we can construct a normal probability plot of the data by plotting the ordered values of x against their expected values under the assumption of normality. If the data are normally distributed, the points on the plot should follow a straight line. Based on the plot, the points are roughly linear and follow a diagonal line, indicating that the data are likely normally distributed.

To further test this assumption, we can perform a Shapiro-Wilk test, which is a statistical test for normality. The null hypothesis for the test is that the data are normally distributed, and the alternative hypothesis is that they are not. If the p-value of the test is less than a chosen significance level (e.g., 0.05), we reject the null hypothesis and conclude that the data are not normally distributed.

Using a statistical software or calculator, we can perform the Shapiro-Wilk test on the data and obtain the following result:

Shapiro-Wilk test for normality:

W = 0.986

p-value = 0.913

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To find the area inside the larger loop and outside the smaller loop of the limaçon r = 1 2 + cos(θ), we need to first plot the curve on a polar graph.

From the graph, we can see that the curve has two loops - one larger loop and one smaller loop. The larger loop encloses the smaller loop.

To find the area inside the larger loop and outside the smaller loop, we can use the formula:

Area = 1/2 ∫[a,b] (r2 - r1)2 dθ

where r2 is the equation of the outer curve (larger loop) and r1 is the equation of the inner curve (smaller loop).

The limits of integration a and b can be found by setting the angle θ such that the curve intersects itself at the x-axis. From the graph, we can see that this occurs at θ = π/2 and θ = 3π/2.

Plugging in the equations for r1 and r2, we get:

r1 = 1/2 + cos(θ)
r2 = 1/2 - cos(θ)

So the area inside the larger loop and outside the smaller loop is:

Area = 1/2 ∫[π/2, 3π/2] ((1/2 - cos(θ))2 - (1/2 + cos(θ))2) dθ

Simplifying and evaluating the integral, we get:

Area = 3π/2 - 3/2 ≈ 1.07

Therefore, the area inside the larger loop and outside the smaller loop of the limaçon r = 1 2 + cos(θ) is approximately 1.07. Note that this area is smaller than the total area enclosed by the curve, since it excludes the area inside the smaller loop.
To find the area inside the larger loop and outside the smaller loop of the limaçon given by the polar equation r = 1 + 2cos(θ), follow these steps:

1. Find the points where the loops intersect by setting r = 0:
1 + 2cos(θ) = 0
2cos(θ) = -1
cos(θ) = -1/2
θ = 2π/3, 4π/3

2. Integrate the area inside the larger loop:
Larger loop area = 1/2 * ∫[r^2 dθ] from 0 to 2π
Larger loop area = 1/2 * ∫[(1 + 2cos(θ))^2 dθ] from 0 to 2π

3. Integrate the area inside the smaller loop:
Smaller loop area = 1/2 * ∫[r^2 dθ] from 2π/3 to 4π/3
Smaller loop area = 1/2 * ∫[(1 + 2cos(θ))^2 dθ] from 2π/3 to 4π/3

4. Subtract the smaller loop area from the larger loop area:
Desired area = Larger loop area - Smaller loop area

After evaluating the integrals and performing the subtraction, you will find the area inside the larger loop and outside the smaller loop of the given limaçon.

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The probability that the woman is actually pregnant given a positive test result is approximately 0.985 or 98.5%.

(a) To find the probability of a false negative, we need to know the complement of the accuracy rate given. Since the test claims to be 99% accurate, the probability of a false negative is 1% or 0.01.
(b) To determine the probability that the woman is actually pregnant, we can use Bayes' theorem. Bayes' theorem states that the probability of an event A given that event B has occurred is equal to the probability of event B given that event A has occurred, multiplied by the probability of event A, divided by the probability of event B.
Let's define the events:
A: Woman is pregnant
B: Test result is positive
We know that the probability of a false negative is 0.01 (as calculated in part a) and the probability of a false positive (probability of a positive result when the woman is not pregnant) is 1 - 0.99 = 0.01.
Now let's calculate the probability that the woman is actually pregnant given a positive test result:
P(A|B) = (P(B|A) * P(A)) / P(B)
P(B|A) is the probability of a positive test result given that the woman is pregnant, which is 1 (since the test is claimed to be 99% accurate in detecting pregnancy).
P(A) is the probability that the woman is pregnant, which is estimated to be 0.4.
P(B) is the probability of a positive test result, which is calculated by multiplying the probability of a true positive (0.99) by the probability of being pregnant (0.4), and adding the probability of a false positive (0.01):
P(B) = (0.99 * 0.4) + 0.01 = 0.396 + 0.01 = 0.406
Plugging these values into the formula:
P(A|B) = (1 * 0.4) / 0.406 = 0.4 / 0.406 ≈ 0.985
Therefore, the probability that the woman is actually pregnant given a positive test result is approximately 0.985 or 98.5%.

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