What is the value of x when y=31

The exact length of the curve x = 1/3 √y (y − 3), 16 ≤ y ≤ 25 is 64/3.

Given,

x = 1/3 √y (y − 3), 16 ≤ y ≤ 25

Length of the curve y = f(x) from x =a to x = b is given by:  ∫√1 + [f′(x)]2 dx.

x = 1/3 √y (y − 3)

x = 1/3 . y3/2 - y1/2

Let's find the first derivative of x.

dx/dy = 1/3. 3/2. y1/2- 1/2 . y1/2

dx/ dy = 1/2 ( y1/2 -y-1/2)

(dx/dy)2 = 1/4 ( y1/2 -y-1/2)2

= 1/4(y + y-1 -2)

1 + {f′(x)}2 = 1 + 1/4(y + y-1 -2)

= 1/4 y + 1/4y + 1/2

1 + {f′(x)}2= 1/4 (y + y-1 + 2)

√[1 + {f′(x)}2] = 1/2 ( y1/2 + y-1/2)

Length of curve =   \(\int\limits^a_b {\sqrt{ [1 + {f'(x)}2]} \, dx\)

where a = 25 and b = 16

= [(y)3/2 /3 + √y]

= [(25)3/2 /3 + √25] - [(16)3/2 /3 + √16]

= [125/3 + 5] - [64/3 + 4]

= 140/3 - 76/3

= (140 - 76)/3

= 64/3

Hence, the exact length of the curve x = 1/3 √y (y − 3), 16 ≤ y ≤ 25 is 64/3.

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Answer:

y = 1/2x + 2

Comparison: The black and blue line haver the same y-intercept, however they have different slopes. The slope of the black line is 2/3 and the slope of the blue line is 1/2.

Step-by-step explanation:

PLEASE MARK BRAINLIEST

Answer:

-7 × 10

Step-by-step explanation:

Explanation:

6.3

×

10

5

is the same value as

63

×

10

4

So we have:

63

×

10

4

9

×

10

3

ddd

→

ddd

63

9

×

10

4

10

3

ddddddddd.d

→

ddd

63

9

×

10

If the sum of the digits is exactly divisible by 3 then the actual number is also exactly divisible by 3

→

6

+

3

=

9

so we will divide both top and bottom by 3 to simplify the fraction.

ddddddddd.d

→

ddd

63

÷

3

9

÷

3

×

10

Note that:

63

÷

3

9

÷

3

=

21

÷

3

3

÷

3

=

7

1

=

7

so we have:

(

6.3

×

10

5

)

÷

(

9

×

10

3

)

=

7.0

×

10

Negative version works the same exact way but with a negative sign

The scientific notation of (6.3 × 10⁻⁵) / (9 × 10⁻³) on simplifying is 7 × 10⁻³.

Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using scientific notation. It is also known as the standard form in the UK and scientific form, standard index form, and standard form.

Given:

The expression is (6.3 × 10⁻⁵) / (9 × 10⁻³),

The values in the negative power in the numerator go to the denominator and vice versa,

(6.3 × 10⁻⁵) / (9 × 10⁻³) = (6.3 × 10³) / (9 × 10⁵)

Divide the 6.3 by 9 as shown below,

(6.3 × 10⁻⁵) / (9 × 10⁻³) = 0.7 / 10²

(6.3 × 10⁻⁵) / (9 × 10⁻³) = 0.7 × 10⁻²

(6.3 × 10⁻⁵) / (9 × 10⁻³) = 7 × 10⁻³

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According to the combination, The value of the Two blue pebbles is a 3 red pebbles and 1 yellow pebbles.

According to the statement

We have to find that the value of the combination.

So, For this purpose, we know that the

A combination could be a mathematical technique that determines the quantity of possible arrangements in an exceedingly collection of things where the order of the choice doesn't matter.

From the given information:

A red pebble is capable 3 yellow pebbles. A blue pebble is adequate a red pebble and a couple of yellow pebbles. Therefore, the blue pebbles will be:

= 3 yellow pebble + 2 yellow pebbles

= 5 yellow pebbles or 15 red pebbles

And

Two blue pebbles will be:

= 10 yellow pebbles

= 3 red pebbles and 1 yellow pebbles.

So, According to the combination, The value of the Two blue pebbles is a 3 red pebbles and 1 yellow pebbles.

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Disclaimer: This question was incomplete. Please find the content below.

Question:

A red pebble is equal to 3 yellow pebbles A blue pebble is equal to a red pebble and 2 yellow pebbles. A green pebble is equal to 3 red pebbles

Using the smallest number of pebbles possible and without using blue pebbles, what is the value in pebbles of 2 blue pebbles?

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The present value of the cash flows is approximately $11,754.04.

To calculate the present value of the cash flows, we need to discount each cash flow to its present value using the appropriate discount rate. The present value (PV) can be calculated using the formula:

PV = CF1 / (1 + r)^1 + CF2 / (1 + r)^2 + CF3 / (1 + r)^3 + ... + CFn / (1 + r)^n

where CF is the cash flow and r is the discount rate.

Using the given discount rate of 9.89 percent per year, we can calculate the present value as follows:

PV = 2,200 / (1 + 0.0989)^1 + 2,600 / (1 + 0.0989)^2 + 4,800 / (1 + 0.0989)^3 + 5,400 / (1 + 0.0989)^4

Calculating each term and summing them up:

PV = 2,200 / 1.0989 + 2,600 / 1.0989^2 + 4,800 / 1.0989^3 + 5,400 / 1.0989^4

PV ≈ 1,999.64 + 2,271.89 + 3,622.82 + 3,860.69

PV ≈ 11,754.04

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Answer:

~~~~~~~~~~~~24 inches

Answer:

The answer is 13.25 I'm so sorry if its incorrect please let me know so I can fix it

Answer:

64percents

Step-by-step explanation:

25-9=16 grams - weight of copper

(16/25)*100=64 percents

Answer:

To calculate the interior angles of a triangle, we need to understand some basic principles of geometry.

1. Principle 1: The sum of the interior angles of a triangle is always 180°. This is a fundamental rule in Euclidean geometry, which is the study of flat space. It's based on the definition of a triangle as a three-sided polygon.

2. Principle 2: Each angle in a triangle is measured in degrees (°). Degrees are a unit of measurement for angles, just like meters or feet are units of measurement for distance. There are 360° in a full circle, so an angle that measures 180° is half of a full circle.

Now, let's apply these principles to calculate the third angle in a triangle with angles measuring 30° and 60°.

3. Step 1: Add the two known angles together. If one angle measures 30° and another measures 60°, their sum is 30° + 60° = 90°.

4. Step 2: Subtract the sum from 180° to find the third angle. Since the sum of all three angles must be 180°, we can find the third angle by subtracting the sum of the known angles from 180°. So, 180° - 90° = 90°.

Therefore, the third angle in a triangle with angles measuring 30° and 60° is 90°.

Answer:

(7,4)

Step-by-step explanation:

The midpoint formula is expressed as:

M(X, Y) = {(x2+x1)/2, (y2+y1)/2

Given the coordinates of the midpoint

M(2.5, -1.5)

Endpoint A(-2, -7)

Required

Endpoint B

From the formula;

X = x2+x1/2

Given

X = 2.5, x1 = -2

Get x2

2.5 = -2+x2/2

5 = -2+x2

x2 = 5+2

x2 = 7

Also

Y = y2+y1/2

-1.5 = -7+y2/2

-3 =-7+y2

y2 = -3+7

y2 = 4

Hence the coordinate of the endpoint B (x2,y2) is (7,4)

Answer:

(0,0.5)

Step-by-step explanation:

Trust me, it's from Khan Academy

The sampling technique used in this scenario is Random sampling

The correct answer is an option (a)

We know that the random sampling is nothing but a method of choosing a sample of observations from a population to make assumptions about the population. It is also called as a porbability sampling.

It  allows for the randomization of sample selection.

There are four random sampling methods –

simple random sampling,

systematic sampling,

stratified sampling,

and cluster sampling.

In random sampling, the randomized selection of a small segment of individuals or members from a whole population.

Here, the soda bottle company  have equipment that can pull every tenth bottle from the assembly line without causing a backup on the line.

Therefore,  the sampling technique used: Random

The correct answer is an option (a)

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The complete question is:

Select the sampling technique used:

A soda bottling company needs to test the quality of the bottles they produce. They have equipment that can pull every tenth bottle from the assembly line without causing a backup on the line.

a) Random

b) Stratified

c) Cluster

d) Systematic

e) Convenience

The new variance is 0.0625 / n

We can use the following formula to calculate the variance of a data set

variance = (sum of (x - mean)^2) / (number of data points)

where x is a data point and mean is the mean of the data set.

If the mean cost of a box of Cheerios Oat Crunch is $4.00 and the variance is 0.35, we can find the standard deviation as follows

standard deviation = square root of variance = sqrt(0.35) = 0.59

Now, if the price increases by 25 cents a box, the new mean cost will be

new mean = $4.00 + $0.25 = $4.25

To find the new variance, we need to calculate the sum of (x - mean)^2 for the new data set and divide by the number of data points. Let's assume we are still considering the same number of boxes.

sum of (x - mean)^2 = [(4.25 - 4)^2 × n] = 0.0625 × n

where n is the number of data points.

Therefore, the new variance can be calculated as

new variance = (sum of (x - mean)^2) / (number of data points) = 0.0625 / n

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Answer:

A 45degrees

Step-by-step explanation:

Answer:

Step-by-step explanation:

the curve described by the equation r^2 = 5 represents a circle with a radius of √5 centered at the origin in the Cartesian coordinate system.

To find the Cartesian equation for the curve r^2 = 5, we can rewrite it in terms of x and y coordinates. The polar coordinates (r, θ) can be converted to Cartesian coordinates (x, y) using the formulas x = r * cos(θ) and y = r * sin(θ).

Substituting the equation r^2 = 5 into these formulas, we have x = √5 * cos(θ) and y = √5 * sin(θ). Simplifying further, we get x^2 + y^2 = 5, which is the Cartesian equation of a circle with a radius of √5 centered at the origin (0, 0).

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Answer:

of course ,the refree or the umpire

Answer:

Step-by-step explanation:

The original image is the the black one.  The dilated image is blue.  It got bigger.  So it is an enlargment.

Each side got bigger by times 2

So the dilation is 2

Answer:

100ml bottle is cheapest per ml

Step-by-step explanation:

The 80 ml bottle sells for 55 so that makes 80 ml for 5500 p which calculates to 68.75p per ml.

the 2 50 ml bottles will cost 45+22.50  = 67.50 which makes 100 ml for 6750p

this makes it 67.5p per ml which is cheaper than the 80 ml bottle

The presence of a statistically significant difference tells you that there is a large effect size is false.

Statistical significance: When conducting a statistical analysis, researchers aim to determine if the results they observe are statistically significant. Statistical significance is a measure that helps determine whether the observed difference between groups (or the relationship between variables) is unlikely to have occurred due to random chance. It is typically assessed using statistical tests such as t-tests, chi-square tests, or analysis of variance (ANOVA).

Effect size: Effect size, on the other hand, provides a measure of the magnitude or strength of the relationship or difference being studied. It quantifies the practical significance or importance of the effect observed in the data. Effect size is independent of sample size and helps researchers understand the extent to which the independent variable (or intervention) influences the dependent variable.

The misconception in the statement you mentioned is that a statistically significant difference does not necessarily imply a large effect size. Statistical significance focuses on the likelihood that the observed difference is due to more than just chance, while effect size focuses on the magnitude or practical importance of that difference.

In some cases, a study may find a statistically significant difference with a small effect size, indicating that although the groups being compared are different, the practical significance of that difference may be minimal. Conversely, a study may find a statistically nonsignificant difference with a large effect size, suggesting that although the difference observed may not be statistically significant, it still has practical importance.

To gain a comprehensive understanding of the results, it is important to consider both statistical significance and effect size together. This helps researchers interpret the practical implications of their findings accurately.

Therefore, The presence of a statistically significant difference tells you that there is a large effect size is false.

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Answer:

=5x2+7x+11

Step-by-step explanation:

In a fast-food management program, there are 15 qualified applicants for 8 trainee positions. We are supposed to calculate the number of different groups of trainees that can be selected. For this, we can use the formula for combination. In mathematics, a combination is a way of selecting items from a collection, such that the order of selection doesn't matter.

It is represented as n Cr, where n is the total number of items and r is the number of items to be selected. In this problem, we have to select 8 trainees from a total of 15 qualified applicants. Hence, the solution is as follows: Now, we can use the formula for combination, which is as follows:

n Cr = n!/(r!(n-r)!)  where n is the total number of items, and r is the number of items to be selected. In this case, we have 15 items to choose from, and we want to select 8 of them. Hence, we get:  15C8 = 15!/(8!(15-8)!) 15C8 = (15 × 14 × 13 × 12 × 11 × 10 × 9 × 8!)/(8! × 7 × 6 × 5 × 4 × 3 × 2 × 1)15C8 = 6435  Therefore, there are 6,435 different groups of trainees that can be selected from the 15 qualified applicants for 8 trainee positions in a fast-food management program.

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Answer:

option H.

Line A increase more rapidly than B

hope it helps

Answer:

50, 90, 65, 25

Step-by-step explanation:

I dont know how to get to it that is why I searched it up :/

Answer:

its B

Step-by-step explanation:

Answer:

2n(8n + 5)

Step-by-step explanation:

you need to see what you can take out of both the numbers.

ex they both have an 'n' and they both are divisible by 2

The solution to the differential equation is:

\(y = e^{(2\sqrt{y} - 0.6137)}\)

To solve this differential equation, we can use the method of separation

of variables. This involves isolating the variables x and y on different

sides of the equation and then integrating both sides with respect to

their respective variables.

Starting with the given equation:

\(dy/dx = e^{(\sqrt{(x/y)} )}\)

We can begin by multiplying both sides by dx:

\(dy = e^{(\sqrt{(x/y)} ) dx}\)

Now we can separate the variables and integrate both sides:

\(\int(1/y)dy = ∫e^{(\sqrt{(x/y))dx} }\)

ln|y| = 2√y + C1 ...where C1 is a constant of integration

To solve for y, we can exponentiate both sides:

\(|y| = e^{(2\sqrt{y} + C1)}\)

Since y(1) = 4, we can use this initial condition to determine the sign of y and the value of C1:

\(4 = e^{(2\sqrt{4} + C1)} \\4 = e^{(4 + C1)}\)

ln(4) = 4 + C1

C1 = ln(4) - 4 = -0.6137

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The value of m<1 based on the given diagram is 53°

Let

m<1 = y

So,

(20x + 7) + y = 180°

Angles on a straight line

20x + 7 + y = 180

20x + y = 180 - 7

20x + y = 173

79° + 8x + y = 180° (sum of angles in a triangle)

8x + y = 180 - 79.

8x + y = 101

20x + y = 173

8x + y = 101

Subtract

12x = 72

x = 72/12

x = 6

Substitute into (1)

(20x + 7) + y = 180°

20(6) + 7 + y = 180

120 + 7 + y = 180

127 + y = 180

y = 180 - 127

y = 53°

Therefore, m<1 is 52° and x is 6

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(a) There are 48620 different routes you can take to work.  (b) The number of routes to the donut shop is 118800. (c) There are 330671 routes that avoid the pothole.

The Principle of Inclusion-Exclusion is a counting technique used to find the number of elements in a set that satisfies at least one of several conditions.

(a) Since you need to travel 18 blocks, and each block can either be a street or an avenue, you have a total of 18 intersections to go through. You need to choose 9 of these intersections to be streets, and the other 9 will be avenues. The number of ways to choose 9 intersections out of 18 is given by the binomial coefficient C(18, 9), which is equal to 48620. Therefore, there are 48620 different routes you can take to work.

(b) To get to the donut shop on the way to work, you must pass through the intersection of 8th st and 10th ave. There are several ways to get to this intersection from your starting point, but once you get there, there is only one way to get to your workplace. Therefore, the problem reduces to finding the number of ways to get to the intersection of 8th st and 10th ave. You need to travel 7 blocks east (from 3rd st to 10th st) and 5 blocks north (from 3rd ave to 8th ave) to get to the donut shop. You can choose any 7 of the 12 intersections along 3rd st to be streets, and any 5 of the 10 intersections along 3rd ave to be avenues. Therefore, the number of routes to the donut shop is given by the binomial coefficient C(12, 7) * C(10, 5), which is equal to 118800.

(c) There are several ways to approach this problem, but one possible method is to use the principle of inclusion-exclusion. Let A be the set of all routes that pass through the pothole, B be the set of all routes that pass through the intersection of 5th st and 4th ave, and C be the set of all routes that pass through the intersection of 6th st and 4th ave. We want to find the number of routes that avoid the pothole, which is equal to the size of the set A complement. By the principle of inclusion-exclusion, we have:

|A complement| = |universe| - |A|

= C(18, 9) - [|B| + |C| - |B intersection C|]

To compute the size of each set, note that:

|B| = C(10, 4) * C(8, 5) (choose 4 out of 10 intersections along 4th ave to be streets, and 5 out of 8 intersections along 5th st to be avenues)

|C| = C(10, 4) * C(8, 4) (choose 4 out of 10 intersections along 4th ave to be streets, and 4 out of 8 intersections along 6th st to be avenues)

|B intersection C| = C(10, 4) * C(6, 3) (choose 4 out of 10 intersections along 4th ave to be streets, and 3 out of 6 intersections between 5th st and 6th st to be avenues)

Substituting these values, we get:

|A complement| = C(18, 9) - [C(10, 4) * C(8, 5) + C(10, 4) * C(8, 4) - C(10, 4) * C(6, 3)]

= 330671

Therefore, there are 330671 routes that avoid the pothole.

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