The dot plot shows the number of goals that the Springlane High School soccer team scored per game last season. How many games did the team play?

Answer:

Option D.

Step-by-step explanation:

To find the answer we will analyse each options.

Option A.

If we rotate a semicircle by a vertical axis then an sphere will be formed. Therefore this option is not correct.

Option B.

In this rotation we will get a hollow sphere, so this option is also not correct.

Option C.

By rotation of a strip we will find the shape similar to the given object but there will not be a hole at the center. Therefore, the option is not correct.

Option D.

When we rotate this strip with a distance from vertical axis, we will find the same shape as given in the picture.

Option D is the correct option.

The mean or the average of a number is calculated by adding the frequencies of the given data and then dividing by the total frequency. It is represented by the formula mentioned under -

Mean = [tex] \frac{Sum of all the frequencies}{Number of frequencies} [/tex]

Similarly, here, we need to find the mean of their time spent in brushing.

It will be calculated as -

For Fiona

Mean of time spent in brushing = [tex] \frac{Sum of the total time spent in 10 days}{10 days} [/tex]

Similarly, for Gary

Mean of time spent in brushing = [tex] \frac{Sum of the total time spent in 10 days}{10 days} [/tex]

Answer:

Step-by-step explanation:

Alright, lets get started.

The most precise measurement is,  the one which has most numbers after the decimal.

The number round off to hundred decimal place is more precise than the number round off to tenth decimal place.

There are 4 different numbers in which two numbers are complete number 7 and 19.

20.1 is rounded off to nearest tenth.

15.98 is rounded off to nearest hundred.

So, 15.98 yards is the most precise.   :   Option C

Hope it will help :)

Answer:

15.98 yards

Step-by-step explanation:

Final answer:

The base of the triangle is 25 meters, and the height is 17 meters. This was calculated using the area formula for a triangle and by solving the resulting quadratic equation by using the quadratic formula.

Explanation:

The area of a triangle is given by the formula 1/2 × base × height. Given that the area is 212.5 square meters and the height is 8 meters less than the base, let's call the base 'b' and the height will then be 'b - 8'. Using the area formula:

Area = 1/2 × base × height

212.5 = 1/2 × b × (b - 8)

Multiplying both sides by 2 to get rid of the 1/2 gives:

425 = b × (b - 8)

Now we have a quadratic equation in the form of:

b² - 8b - 425 = 0

We can solve this equation by factoring or using the quadratic formula. In this case, the equation doesn't factor neatly, so we use the quadratic formula:

b = (-(-8) ± √((-8)² - 4 × 1 × (-425)))/(2 × 1)

b = (8 ± √(64 + 1700))/2

b = (8 ± √(1764))/2

b = (8 ± 42)/2

Since the base cannot be negative, we take the positive root:

b = (8 + 42)/2

b = 25 meters

Therefore, the base of the triangle is 25 meters and the height is b - 8 = 25 - 8 = 17 meters.

If you use a large enough statistical sample size, you can apply the Central Limit Theorem (CLT) to a sample proportion for categorical data to find its sampling distribution. The population proportion, p, is the proportion of individuals in the population who have a certain characteristic of interest (for example, the proportion of all Americans who are registered voters, or the proportion of all teenagers who own cellphones). The sample proportion, denoted

Answer:

Whatever the lowest value answer choice is will be the correct answer.

Step-by-step explanation:

Say your answer choices are

A.  56

B.  42

C.  70

D.  84

The correct answer would be 42

The area of the surface is  [tex]\rm \dfrac{1}{54}(53\sqrt{53} -17\sqrt{17} )[/tex] and this can be determined by doing the integration.

Given :

The part of the surface [tex]\rm z = 9+5x+2y^2[/tex] that lies above the triangle with vertices (0, 0), (0, 1), (2, 1).

The formula of the surface area is given by:

[tex]\rm A(S) = \int \int_D\sqrt{1+\left(\dfrac{\delta z}{\delta x}\right)^2 +\left(\dfrac{\delta z}{\delta y}\right)^2 }[/tex]

Now, the values of D varies from:

D = {(x,y): 0 [tex]\leq[/tex] y [tex]\leq[/tex] 1 , 0 [tex]\leq[/tex] x [tex]\leq[/tex] 2y}

Now, the area of the surface is given by:

[tex]\rm A(S) = \int \int_D\sqrt{1+4^2+(6y)^2 }\;dA[/tex]

[tex]\rm A(S) = \int^1_0 \int^{2y}_0\sqrt{17+36y^2 }\;dx\;dy[/tex]

[tex]\rm A(S) = \int^1_02y\sqrt{17+36y^2 }\;dy[/tex]

Now, let [tex]u=17+36y^2[/tex]

[tex]du = 72y dy[/tex]

[tex]\rm \dfrac{du}{36}=2ydy[/tex]

Now, the integral becomes:

[tex]\rm A(S)= \dfrac{1}{36}\sqrt{u} \; du[/tex]

[tex]\rm A(S) = \dfrac{1}{54}\times u^{3/2}+C[/tex]

Now, substitute the value of u in the above expression.

[tex]\rm A(S) = \dfrac{1}{54}\times \left[\left[\sqrt{17+36y^2} \right]^{3/2}\right]^1_0[/tex]

Now, simplify the above expression.

[tex]\rm A(S) = \dfrac{1}{54}(53\sqrt{53} -17\sqrt{17} )[/tex]

For more information, refer to the link given below:

https://brainly.com/question/18125359

To calculate the surface area of the part of the surface z = 9 + 5x + 2y² lying over a triangle, the limits of the variables are determined by triangle vertices. Then, the double integral of the surface area formula, which integrates the square root of 1 plus the squares of the partial derivatives of the function over these limits, is computed.

The problem presented is leading us to calculate the surface area of a part of z = 9 + 5x + 2y² that lies above a right triangle whose vertices are (0, 0), (0, 1), (2, 1). The first step in resolving this is to recognize the given formula of the surface, it is a quadratic surface in three-dimensional space, also known as a paraboloid.

The vertices of the triangle give as a hint to define the limits of the variables. Given that this triangle is defined in the xy plane, owing to the vertices of the triangle provided, the limits for x would range from 0 to 2, the limits of y would range from 0 to 1 (since for x = 0, y = 1 and for x = 2, y = 1).

Finally, the area S of a part of the surface z = f(x, y) that lies above the region D in the xy plane is defined by the double integral: S = ∫∫D √(1 + (fx)² + (fy)²) dA where fx and fy are partial derivatives of the function f(x, y) with respect to x and y respectively. The integral needs to be computed over the region D which is defined by triangle vertices.

https://brainly.com/question/33042040

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To eliminate the parameter t in the parametric equations x = 6 cos t and y = 3 sin t, we can use the trigonometric identity

cos⁡²t + sin⁡²t = 1cos²t + sin²t = 1.

Starting with x=6 cos t, we can rewrite it as cos t=x6​ and from y=3 sin t, we can rewrite it as sin t = (y/3)​.

Now, we square both equations:

(cos t)² = (x/6​)²

(sin t)² = (y/3​)²

As soon as we multiply both sides by 36, we arrive at:

x² + 4y² = 36

Therefore, the equation x² + 4y² = 36 is the Cartesian equation that eliminates the parameter t from the given parametric equations.

To eliminate the parameter t in the parametric equations x=6 cos t and y=3 sin t, we use trigonometric identities.

From x=6 cost, we get cos t = x//6​, and from y = 3 sin t, we get sin t = (y/3).

Squaring both equations and using the identity cos2t+sin2t=1 we obtain (x/6​)² + (y/3​)² = 1. Simplifying, we get (x²/36) + (y²/9) = 1 which, after multiplying by 36, becomes x² + 4y² = 36. Thus x² + 4y² = 36 is the Cartesian equation eliminating the parameter t.

Complete Question:

Eliminate the parameter, t, in the parametric equation, x=6 cos t, and y =3 sin t.

Answer:

The correct answer is False

Step-by-step explanation:

I already took this test. I got it right.

Hope this helps! ;)

Answer:

[tex]x=41^o[/tex]

Step-by-step explanation:

We have been given an equation [tex]sin(49^o)=cos(x)[/tex] and we are asked to find the value of x.

Since we know that trigonometric ratios are applied to right triangles and we also know that [tex]sin(a)=cos(b)[/tex], where a and b are the angles other than 90 degree angle.

As one angle of our triangle is given 49 degrees, so to find the value of angle x we need to subtract 49 degrees from 90 degree angle as 49 degree angle and x will be equal to 90 degrees.

[tex]x=90^o-49^o[/tex]

[tex]x=41^o[/tex]

Therefore, the value of x is 41 degrees.

1/7-3(3/7n-2/7) in simplest form

[tex]\frac{1}{7} -3(\frac{3}{7}n-\frac{2}{7}) \\\\ Using \;Distributive \;property \\\\ =\frac{1}{7} -(3)\frac{3}{7}n-(-3)\frac{2}{7} \\\\ Multiplication \\\\ =\frac{1}{7} -\frac{3*3}{7}n+\frac{3*2}{7} \\\\ =\frac{1}{7} -\frac{9}{7}n+\frac{6}{7} \\\\ Combining \;terms \;with \;common \;denominator \\\\ =\frac{1-9n+6}{7} \\\\ Combining \;like \;terms \\\\ =\frac{7-9n}{7} \\\\ Simplification \\\\ =\frac{7}{7} -\frac{9n}{7} \\\\ =1 -\frac{9n}{7}[/tex]

Hence, final answer is [tex]\frac{7-9n}{7}[/tex] or [tex]1 -\frac{9n}{7}[/tex].