Find the value of x explain how you got your answer ​

In Activity 1, you are asked to draw dental floss through a model at an angle parallel to an imaginary line on the side of the cone through the cone's base. The resulting shape will be an ellipse.

Here is a step-by-step explanation:

1. Start by imagining a cone with a circular base.
2. Draw an imaginary line on the side of the cone that is parallel to the base.
3. Take the dental floss and draw it through the model along this imaginary line, making sure to keep the angle parallel.
4. As you draw the dental floss, you will notice that it forms a curved shape that is symmetrical on both sides.
5. This curved shape is known as an ellipse.

An ellipse is a closed curve that resembles a stretched circle. It has two main axes: the major axis and the minor axis. The major axis is the longest diameter of the ellipse, while the minor axis is the shortest diameter. The point where the major and minor axes intersect is called the center of the ellipse. The resulting ellipse will have a shape that is elongated or flattened depending on the angle at which the dental floss is drawn through the model. If the angle is close to perpendicular to the base, the resulting ellipse will be more circular. If the angle is more parallel to the base, the resulting ellipse will be more elongated.
It's important to note that an ellipse is a common shape that can be found in various fields of study, such as mathematics, physics, and astronomy. Understanding its properties and characteristics can help in solving problems and analyzing real-world situations.

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The half life period is the time in which only half of the given population remains. It can be represented through this equation:

\(f(t)=a\times(1/2)^{\frac{t}{h}}\)

We're given:

For most questions like this, we would have to plug these values into the equation mentioned above. However, this question asks for the time elapsed after 3 half-lives.

This can be calculated simply by multiplying the given half-life by 3:

28 million years x 3

= 84 million years

84 million years

Answer:

length-14cm width-7cm

Step-by-step explanation:

To work out the sides, you can use 2l+2w=42. Since the length is twice the width, this becomes 2(2w)+2w=42.

This can be expanded to 4w+2w=42 or 6w=42.

From there, we can divide both sides by 6 to isolate w, meaning w=7.

Since the length is twice the width, it is given by l=2×7 or l=14.

**This question involves writing and solving algebraic equations from worded questions, which you may wish to revise. I'm always happy to help!

The Pythagorean theorem rounding of 16 and 18 would be = 24 (approximately)

Pythagorean theorem is defined as the theorem that expresses the relationship that exists between the three side of a right angle triangle.

The relationship states that the square of the longest side is equal to the sum of the square of the other two sides.

That is, c² = a² + b²

Where, a = 16

b = 18

c² = 16²+18²

c² = 256 + 324

c² = 580

C =√580

C = 24.1

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Answer:

Step-by-step explanation:

ok equation are like fraction but let me put it like this lets say x+y=7;x+2y=11 thats how you do eqution done.

Answer:22

Step-by-step explanation:

By answering the presented question, we may conclude that As a result, the linear equation describing the link between the number of scoops and the cost is as follows: y = (-5/12)x + (16/3)

The slope of a line indicates how steep it is. The term "gradient overflow" refers to a mathematical equation for the gradient (the change in y divided by the change in x). The slope is defined as the ratio of the vertical change (rise) between two places to the horizontal change (run). The slope-intercept form of an equation is used to express a straight line's equation, which is written as y = mx + b. The y-intercept is found where the slope of the line is m, b is b, and (0, b). For example, the slope and y-intercept of the equation y = 3x - 7 (0, 7). The slope of the line is m. b is b at the y-intercept, and (0, b).

To get the linear equation describing the link between the number of scoops and the price,

slope = (Anusha's scoops minus Caroline's scoops) / (Anusha's scoops minus Caroline's scoops)

slope = ((4/3) - (7/4)) / (3 - 4)

slope = (-5/12)

y - y1 = m(x - x1) (x - x1)

where m is the slope and (x1, y1) is a line point. At a point on the line, we can utilise either Anusha's or Caroline's data. Let's look at Caroline's data:

y - 7 = (-5/12)(4) (4)

y - 7 = (-5/3)

y = (-5/3) + 7 = (16/3)

As a result, the linear equation describing the link between the number of scoops and the cost is as follows:

y = (-5/12)x + (16/3)

where y is the price and x denotes the number of scoops.

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Answer:

x = 5

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

21x + 5 is an exterior angle of the triangle , then

21x + 5 = 5 + 13x + 40

21x + 5 = 13x + 45 ( subtract 13x from both sides )

8x + 5 = 45 ( subtract 5 from both sides )

8x = 40 ( divide both sides by 8 )

x = 5

Answer:

x=5

Step-by-step explanation:

Angles Q and R are supplementary

13x  + 21x +5 = 180

10+34x =180

34x=170

x = 5

Answer:

j.35 times

Step-by-step explanation:

Answer:

Step-by-step explanation:

4 z ^3 √ y / x ^2 y

Answer:

-4.4

Step-by-step explanation:

2.8 + 7.2 = -4.4

Answer:

x/5

Step-by-step explanation:

y=5x

interchange the variables x and y

x=5y

Solve x=5y for y

y=x/5

Answer:

Step-by-step explanation:

Answer:

145.9 cubic inches

Step-by-step explanation:

The volume of a triangular prism is:

1/2 x length x width x height

Use the formula with the given dimensions:

1/2 x 5.27 x 8.13 x 6.81 = 145.8875655

Round it up to the nearest tenths:

145.8875655 —> 145.9

I hope this helps!

Answer:

145.9 cubic inches

Step-by-step explanation:

Scaling transformation onto the x co ordinate by a factor of 5.

A co-ordinate system represents two points one for x axis and another for y axis in a ordered pair (x,y)

According the given question Point (w, z) is transformed by the rule (w5, z).

Here w represents x co-ordinate points and z represents y co-ordinate points.

We can observe that the x co-ordinate point have been scaled by a factor of 5.We can think of that after this transformation the line has become less steeper from origin.

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Answer:

Step-by-step explanation:

We know that

Considering the above we have:

Substitute the given values and solve for x:

Answer:

35.26m

Step-by-step explanation:

6.7/ 2 = 3.35

Radius = 3.35^2

Circle = pie x 3.35^2

pie x 11.2225 = 35.25652355

35.25652355 estimated = 35.26

P/Q is in the lowest form as the when the HCF is 1 and if we divide it by 1 P/Q remains same so it is the lowest form ,if P and Q have no common factor other than 1.

It is possible to express rational numbers in the form p/q, where p and q are integers and q≠0.

If there is just one other common factor between the denominator and numerator of a rational number, that number is said to be in its lowest form. In other words, if the HCF of a and b is 1 and a and b are relatively prime, then we can state that a rational number a/b is considered to be in its simplest form.

as described in the above contion in order to reduce any rational number to its lowest form we need to divide both numerator and denominator by the HCF of p,q . suppose if the HCF of p,q is 1 then divide p and q 1 won't change the value of the rational number.

so, now it is shown that the given rational number can't be further deduced and hence we conclude that a rational number is in lowest form when HCF of its numerator and denominatior is equal to 1.

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Complete question:

Write the reason why a rational number written in the form of p/q is said to be in lowest form if P and Q have no common factor other than 1.

The area of the surface generated by revolving the curve about the axis y = 9-x² is 12π

Surfaces of revolution are graphs of functions f(x,y) that rely exclusively on the distance from the origin of the point (x,y).

Polar coordinates (r,) are one approach to discuss such surfaces. A "surface of revolution" is formed by rotating a curve around an axis.

Consider a curve with coordinates x and z in the "x0" half of the Euclidean plane.

y = √(9-x²)

⇒ dy = (-2x)/2√9-x²)

= -x/√(9-x²)

Note that surface area (s) is given as:

\(\int\limits^b_a {2\pi y}\) √1 + (dy/dx)² dx

= 2\(\pi\) \(\int_{1}^{-1}\) √9-x² * √[1 + (-x)/√9-x²)]dx

= 2π \(\int_{1}^{-1}\)3dx
= 6π [x]₋¹₁

= 6π (1-(-1)

= 6π (2)

= 12π

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Answer:

its easy figure it out lol good luck

Step-by-step explanation:

Answer: 1

The full term is (6,1)

Answer:

1

Step-by-step explanation:

Trust me on this, also can I have brainiest please?

Hope you do well! :D

(a-1) The value of the population mean is unknown.

(a-2) The best estimate of the population mean is the sample mean, which is 20 eggs.

(c) The value of t for a 95% confidence interval with 17 degrees of freedom is approximately 2.110.

(d) the 95% confidence interval for the population mean is approximately (17.902, 22.098).

(e-1) It would not be reasonable to conclude that the population mean is 17 eggs.

(e-2) It would be reasonable to conclude that the population mean is 18 eggs.

(a-1) The given information provides the sample mean (20 eggs) and the sample standard deviation (5 eggs), but it does not directly provide the population mean.

(a-2) In the absence of other information, the sample mean is a reasonable estimate of the population mean.

(c) For a 95% confidence interval, the value of t can be determined using the t-distribution with n-1 degrees of freedom, where n is the sample size. In this case, the sample size is 18, so the degrees of freedom is 18 - 1 = 17.

Using a t-distribution table or a statistical software, the value of t for a 95% confidence interval with 17 degrees of freedom is approximately 2.110.

(d) To determine the 95% confidence interval for the population mean, we can use the formula: Confidence interval = sample mean ± (t * standard error), where the standard error is the sample standard deviation divided by the square root of the sample size.

In this case, the sample mean is 20, the standard deviation is 5, the sample size is 18, and the value of t is 2.110. Plugging in these values, the confidence interval is 20 ± (2.110 * (5 / √18)), which evaluates to approximately 20 ± 2.098.

(e-1) The 95% confidence interval calculated in part (d) does not include 17 eggs, indicating that it is unlikely for the population mean to be 17 eggs.

(e-2) The 95% confidence interval calculated in part (d) includes 18 eggs, suggesting that it is plausible for the population mean to be 18 eggs.

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There is a theorem that says:

If two angles are supplementar to two other congruent angles, then they're congruent.

For example:

So,

The value for the new mean, after removing a score with a value of X = 4 from the population, is c. 66/7.

To calculate the new mean, we need to subtract the score that is removed from the original sum of scores and then divide by the new number of scores.

Given that the population originally has N = 7 scores with a mean of μ = 10, the sum of the scores is N * μ = 7 * 10 = 70.

When the score of 4 is removed, the sum of the remaining scores becomes 70 - 4 = 66. The new number of scores is N - 1 = 7 - 1 = 6.

Therefore, the new mean is 66/6 = 11.

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The correct option is (c). If the coefficient of correlation is -.4, then the slope of the regression line must be negative.

The coefficient of correlation tells us about the direction and strength of the linear association between two variables. It is used to determine how strong or weak a relationship is between two variables. The coefficient of correlation ranges between -1 to 1.

If the correlation coefficient is negative, then it tells us that as the value of one variable increases, the value of the other variable decreases. That is, the variables move in the opposite direction. When the slope of the regression line is negative, it indicates that as the value of the independent variable increases, the value of the dependent variable decreases. Therefore, the correct answer is option (c).

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The minimum value of the objective function subject to the given constraints is 48 and it occurs at (6,0).

The given problem is:

min 8x₁ + 6x₂ subject to4x₁ + 2x₂ ≥ 20−6x₁ + 4x₂ ≤ 12x₁ + x₂ ≥ 6x₁ + x₂ ≥ 0

The feasible region is as follows:

Firstly, plot the following lines:4x₁ + 2x₂ = 20-6x₁ + 4x₂ = 12x₁ + x₂ = 6x₁ + x₂ = 0On plotting, the following graph is obtained:

Now, let's check each option one by one:

a. 4x₁ + 2x₂ ≥ 20

The feasible region is the region above the line 4x₁ + 2x₂ = 20.

b. −6x₁ + 4x₂ ≤ 12

The feasible region is the region below the line −6x₁ + 4x₂ = 12.c. x₁ + x₂ ≥ 6

The feasible region is the region above the line x₁ + x₂ = 6.d. x₁ + x₂ ≥ 0

The feasible region is the region above the x-axis.

Now, check the point of intersection of the lines.

They are:(10,0),(2,4),(6,0)The point (2,4) is not in the feasible region as it lies outside it.

Therefore, we reject this point.

The other two points, (10,0) and (6,0) are in the feasible region.

Now, check the values of the objective function at these two points.

Objective function value at (10,0): 80

Objective function value at (6,0): 48

Therefore, the minimum value of the objective function subject to the given constraints is 48 and it occurs at (6,0).

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Answer:

Figure ABCD was formed by first translating figure ABCD \(\boxed{5}\)  units left and \(\boxed{4}\) units down, and then reflecting across the \(\boxed{\textrm{x}}\) -axis

Step-by-step explanation:

To determine the translated units take any point in the pre-image ABCD and see the relative position of the corresponding point in the translated image A'B'C'D'

All other points and hence the entire pre-image will be translated by the same amount

So the answer is 5 units left, 4 units down and reflected across the x-axis