heeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeelp

Answer:

B =  38.57052934902012

C =  55.42947065097988

c =  13.20702502008021

Step-by-step explanation:

A =  86

B =  38.57052934902012

C =  55.42947065097988

a =  16

b =  10

c =  13.20702502008021

The integral is equal to 1/2 [ln|1 + v| - ln|1 - v|] + C.

The integral in this exercise converges, which means that it has a finite value.

To evaluate the integral without using a table, start by breaking the fraction into partial fractions.

Use the identity 2 cot-1v = ln(v²+1) - ln(v²-1) and partial fractions to rewrite the integral as follows:

∫ dv/[(1 + v)(1 - v)]

= ∫ [1/2(1 + v) - 1/2(1 - v)] dv

= 1/2 ∫ [1/(1 + v) - 1/(1 - v)] dv

= 1/2 [ln|1 + v| - ln|1 - v|] + C, where C is the constant of integration.

Therefore, the integral is equal to 1/2 [ln|1 + v| - ln|1 - v|] + C.

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Answer: The length of AC to one decimal place in the trapezium is 18.1 cm

Step-by-step explanation: Using Pythagoras theorem, we can find the length AC

Pythagoras theorem

c² = a² + b²

Therefore, draw a line from the point B to the line AD and call it line BX.

BX ║ CD

Therefore,

16² - 7² = BX²

256  - 49 = BX²

BX² = 207

BX = √207

BX = 14.3874945699

BX = 14.4 cm

Therefore,

11² + 14.4² = AC²

121 + 207.36 = AC²

AC = √328.36

AC = 18.120706388

AC = 18.1 cm

Hoped This Helped!

Answer:

Ship one is closer to the coast guard

Using mathematical operations, we know that the drop in temperature in each hour is 2°C, and the operations which represent this is 10/5 = 2°C.

Calculating a value using operands and a math operator is referred to as performing a mathematical "operation."

The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers.

In mathematics, addition, subtraction, multiplication, division, and modular forms are the five basic operations.

So, the operation that represents the change in temperature:

Time taken is 5 hours.

The temperature drop is 10°C.

The same amount of temperature in each hour.

Then, the operation will be:

10/5 = 2°C

Therefore, using mathematical operations, we know that the drop in temperature in each hour is 2°C, and the operation which represents this is 10/5 = 2°C.

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Answer:

0.59

Step-by-step explanation:

15+14+13 are the possibilities,

0.30 + 0.28 +0.01 = 0.59!

Sorry for the late answer pls mark as brainliest.

The probability that the age of a student chosen at random will be 15 or younger is 0.59 or 59%.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

To find the probability that the age of a student chosen at random will be 15 or younger,

We need to add up the probabilities of the ages 13, 14, and 15 since those are the ages that are 15 or younger.

The probability of an age of 13 is given as 0.01, the probability of an age of 14 is given as 0.28, and the probability of an age of 15 is given as 0.30.

The probability of an age of 15 or younger is:

0.01 + 0.28 + 0.30 = 0.59

Thus,

The probability that the age of a student chosen at random will be 15 or younger is 0.59 or 59%.

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Answer: 4 i think

Step-by-step explanation:

Answer:

it does have a solution x=0

Step-by-step explanation:

9x+15=3x+15

6x+15=15

6x=0

x=0

Answer:

I agree.

Step-by-step explanation:

Here is my explantion:

\(9x+15=3x+15\\\\Simplify:\\9x=3x\\\\Subtract 3x from both sides\\9x-3x=3x-3x\\\\\\Simplify:\\6x=0\\\\Divide both sides by 6\\\frac{6x}{6} =\frac{0}{6}\\\)

Answer:

in order to find the least number of plums that can be shared, we have to find the greatest common factor of 6 ,9 and 12. the greatest common factor of 6 , 9 and 12 is 3. so if we have three plums. for 6 children , we have 3 plums.

Step-by-step explanation:

:)

Answer:

C, The measure of the angle is 30 degree, hence it is acute, you can easily figure out the angle by looking at the smaller portion on top.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Because it starts from 0° and ends at 30

The cone should have its maximum volume. V=1/*3r2h is the formula for calculating the volume V of a cone with height h and radius r.

The cone has a volume of

V=πr2h/3

Therefore, we must calculate the values of r and h in terms of R. R is the diameter of the cone's top-circular circle, and h is the cone's height.

R is the cone's slant height, and it serves as the hypotenuse of a right triangle.

R2 = h2 + r2, or r2 = R2-h2.

So V = (1/3)π

[R2-h2]

h = (π/3)[R2h-h3]

You must take the derivative of the cone's volume, set it to zero, then solve for h to determine the cone's maximum volume.

dV/dh=(π/3)[R2-3h2]

R2-3h2=0 --> h2=R2/3 -> h = R/√3

Now we can determine r:

r2=R2-R2/3 = (2/3)R2

The volume formula with r and h substituted:

V = (π/3)

r2h = (π/3)(2R2/3)

(R/√3)

V(R)=2πR3/(9√3)

The complete question is:

A cone-shaped drinking cup is made from a circular piece of paper of radius R by cutting out a sector and joining the edges CA and CB. Find the maximum capacity of such a cup (Your answer may depend on R).

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Answer:

3.1 in

Step-by-step explanation:

a² + b² =c²

12=c

11.6=b

c²- b² = a²

12²-11.6²= 9.44

√9.44 = 3.07 Rounded = 3.1 in

The x-coordinate of the x-intercept of line k is -5/2.

Since this point lies on the x-axis, its y-coordinate is 0.

Given that the line has a y-intercept at the point (0, p), where p is a positive constant. This means that when x = 0, y = p.

As we know that the equation of the line can be written as y = mx + b, where m is the slope and b is the y-intercept.

Here, the slope is the negative of the fraction 2p/5, so the equation of line k is y = -2p/5 x + p.

Substitute y = 0 into the equation and solve for x:

0 = -2p/5 x + p

Subtract p from both sides and then multiply by 5/(-2p):

-2p/5 x = -p

x = (-p)(5/2p)

x = -5/2

Therefore, the x-coordinate of the x-intercept of line k is -5/2.

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Answer:

52 Degrees

Step-by-step explanation:

Subtract 29 (lower number) from 81 (higher number). This will often give you the difference (52) between the two measurements.

Answer:

-46438023156

Step-by-step explanation:

C = 300000

a = -0.07

The correct interpretation of x is OD. The variable x represents the number of years after 2000.

Answer:

Step-by-step explanation:

The exponential decay formula for this situation is

\(y=300,000(.93)^x\)

where 300,000 is the initial value, .93 is decay rate (100% - 7% = 93% which is .93 as a decimal), and x represents the number of years after the year 2000. B is your answer.

The optimal consumption bundle (x1*, x2*) can be determined by solving the consumer's utility maximization problem subject to the budget constraint. Given the utility function u(x1, x2) = ax1 + bx2, where a > 0 and b > 0, and the budget constraint p1x1 + x2 = w, we need to find the values of x1* and x2* that maximize the utility function while satisfying the budget constraint.

To analyze the problem graphically, we can plot the budget constraint on a two-dimensional graph with x1 on the horizontal axis and x2 on the vertical axis. The slope of the budget constraint is -p1, indicating the rate at which the consumer can trade x1 for x2. The budget constraint represents all the possible combinations of x1 and x2 that the consumer can afford given their wealth (w) and the price of good 1 (p1).

By drawing indifference curves for different levels of utility, which are downward-sloping straight lines in this case due to the linear utility function, we can identify the optimal consumption bundle. In this particular case, since the utility function represents perfect substitutes, the indifference curves are parallel straight lines with a slope of -a/b. The consumer maximizes utility by choosing the consumption bundle that lies on the highest possible indifference curve and is tangent to the budget constraint.

Now, let's consider three different cases:

Case 1: When w/p1 < a/b, the consumer's wealth is not sufficient to reach the highest indifference curve. In this case, the consumer's optimal consumption bundle will be at the corner point of the budget constraint where x1 = w/p1 and x2 = 0.

Case 2: When w/p1 > a/b, the consumer's wealth is more than enough to reach the highest indifference curve. In this case, the consumer's optimal consumption bundle will be at the point where the budget constraint is tangent to the highest indifference curve, which will be at x1 > 0 and x2 > 0.

Case 3: When w/p1 = a/b, the consumer's wealth is exactly enough to reach the highest indifference curve. In this case, the consumer can choose any consumption bundle along the budget constraint.

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Answer:

∠WXY = 107°

Step-by-step explanation:

In a trapezoid, adjacent angles are supplementary, meaning they add up to 180°. ∠W and ∠WXY are adjacent, so they are supplementary. 180° - 73° = 107°.

Another way to do this is to know that there are 360° in a trapezoid. This is a right trapezoid, so two of the angles are 90°. One angle is 73°. 90° + 90° + 73° = 253°. 360° - 253° = 107°.

I hope this helps :))

The measure of angle WXY is,

= 107°

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

Sides XY and WZ are parallel.

And, Angle W is 73 degrees and angles Y and Z are right angles.

Now, In a trapezoid, adjacent angles are supplementary, meaning they add up to 180°.

Here, ∠W and ∠WXY are adjacent, so they are supplementary.

Hence, We get;

The measure of angle WXY is,

= 180° - 73°

= 107°.

Thus, The measure of angle WXY is,

= 107°

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Yes, x + 1 is a factor of the polynomial x³ + 4x² + x - 6.

To determine if x + 1 is a factor of the given polynomial x³ + 4x² + x - 6, we can use the factor theorem. According to the factor theorem, if a polynomial f(x) has a factor of the form (x - a), then f(a) = 0.

In this case, we substitute -1 (opposite of the constant term of x + 1) into the polynomial x³ + 4x² + x - 6:

(-1)³ + 4(-1)² + (-1) - 6 = -1 + 4 + (-1) - 6 = 0.

Since the result is 0, it confirms that x + 1 is indeed a factor of the polynomial x³ + 4x² + x - 6.

This means that if we perform polynomial long division or synthetic division of x³ + 4x² + x - 6 by x + 1, the quotient will be a polynomial without any remainder.

In summary, x + 1 is a factor of the polynomial x³ + 4x² + x - 6. This can be confirmed by substituting -1 into the polynomial and obtaining a result of 0.

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Answer:

7.5 cm.

Step-by-step explanation:

The height of a rectangle can be calculated using the rectangle's base and area using the following formula:

height = area / base

This formula can be derived from the formula for the area of a rectangle:

area = base x height

By rearranging this formula, we get:

height = area / base

Therefore, if we know the area and base of a rectangle, we can use this formula to calculate its height.

1) rewrite

Height = are / base

2) plug in

h = 30 cm / 4 cm

3) solve (divide)

height = 7.5 cm

Therefore, the height of the rectangle is 7.5 cm.

Answer:

free points thanks

Step-by-step explanation:

Answer: y = (1/2)*x - 1

Step-by-step explanation:

a linear relationship is something like:

y = a*x  + b, lets find the values of a and b.

We have that the output (y) must be 1 less than half of the imput (x), then our relation is:

y = (1/2)*x - 1

Answer:

C.

Step-by-step explanation:

You are looking for an equation that, when you input 0 for x, you get 4 for y, and when you input -5 for x, you get -1 for y.

That only works for Option C.

Hope this [sorta] helps!

Answer:

C

Step-by-step explanation:

C

The test to use when there's an independent group design and ordinal data is the Kruskal Wallis test

Given: Independent group and ordinal data. To find which test to use.

What's the Kruskal Wallis test?

The Kruskal Wallis test is used when you have one independent variable with two or further situations and an ordinal dependent variable. In other words, it's thenon-parametric interpretation of ANOVA and a generalized form of the Mann- Whitney test system since it permits two or further groups.

The Kruskal Wallis test is used when you have one independent variable with two or further situations and an ordinal dependent variable. In other words, it's thenon-parametric interpretation of ANOVA and a generalized form of the Mann- Whitney test system since it permits two or further groups.

The null thesis for the Kruskal- Wallis test simply states that there are no methodical or harmonious differences among the treatments being compared.

How to calculate the Kruskal Wallis test?

The computation of the Kruskal- Wallis statistic requires

Hence as is mentioned for an independent group design and ordinal data so we use the Kruskal Wallis test.

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We can use the Kruskal Wallis test when we have an independent group design and ordinal data.

We are given an independent group design and ordinate data.

We need to tell which test to use on them.

The Kruskal Wallis test is used when you have one independent variable with two or more situations and one ordinal dependent variable. In other words, it is an interpretation of ANOVA table and a generalized form of the Mann- Whitney test system.

The null hypothesis for the Kruskal- Wallis test tells us that:

There are no methodical or harmonious differences among the treatments being compared.

Therefore, we can use the Kruskal Wallis test when we have an independent group design and ordinal data.

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The slope of the line passing through the points (0, 30) and (8, 18) is -1.5.

Given is a graph of a line passing through the points (0, 30) and (8, 18).

To find the slope of the line passing through two points, you can use the formula:

slope = (y2 - y1) / (x2 - x1)

Let's use the points (0, 30) and (8, 18) to calculate the slope:

x1 = 0

y1 = 30

x2 = 8

y2 = 18

slope = (18 - 30) / (8 - 0)

= -12 / 8

= -1.5

Therefore, the slope of the line passing through the points (0, 30) and (8, 18) is -1.5.

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The value of y in the given triangle is 5√3. Therefore, option A is the correct answer.

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

In the given triangle, one of the leg of right tringle is 5 units.

We know that, tanθ= Opposite/Adjacent

tan60° =y/5

√3 =y/5

y=5√3

Therefore, option A is the correct answer.

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Answer:   Let the length and breadth of a rectangle are x and y units , its area is x.y units^2

Step-by-step explanation: sorry no explanation