Find the volume of the composite solid (STEP BY STEP PLEASE) 25 POINTS

The cone would fit into the beachball two times, and has a volume of 134 in^3. Answers required are:

Blank 1 - two

Blank 2 - 134 in^3.

A beachball has the shape of a sphere, so that its volume can be determined by;

volume of a sphere = 4/3 [tex]\pi r^{3}[/tex]

where r is the radius of the sphere.

Given that the diameter of the beachball is 8 inches, then;

its radius = 8/ 2

               = 4 inches

volume of beachball = 4/3 x 22/7 x 4^3

                          = 268.19 cubic in.

The volume of a cone can be determined by;

volume of a cone = 1/3 [tex]\pi r^{2} h[/tex]

where r is its radius, and h is its height.

Given a cone of radius 4 inches and height 8 inches, then;

its volume = 1/3 x 22/7 x 4^2 x 8

                 = 134.1cubic inches

Thus,

268.19/ 134.10  = 1.999993

                     ≅ 2.0

Thus the cone would fit into the beachball twice, and its volume is 134.10 in^3.

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The slope of the line is 3.

The slope or gradient of a line is a number that describes both the direction and the steepness of the line.

Given that, are points of a line,

The slope of a line passing through two points is = (y₂-y₁)/(x₂-x₁)

Considering the points (0, 3) and (1, 6)

Therefore, slope = (6-3)/(1-0) = 3

Hence, the slope of the line passing through the given points is 3.

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Answer:<I=78

Step-by-step explanation:

<1 and 102 are supplementary angles so they add to 180 degrees

<1 + 102 = 180

Subtract 102 from each side

<1 + 102 -102 = 180-102

<1 = 78

Answer:

72y

Step-by-step explanation:

Perfect square monomials are in the form:

[tex]x^2+bx+\left(\dfrac{b}{2}\right)^2[/tex]

They factor as:

[tex]\left(x + \dfrac{b}{2}\right)^2[/tex]

To find the middle term of this polynomial, first factor 16 out of the expression.

[tex]16(y^2 \: + \: ?+5.0625)[/tex]

We know that the middle term will be in the form [tex]by[/tex], and the last term will be in the form [tex]\left(\dfrac{b}{2}\right)^2[/tex]. Using this information, we can solve for b.

[tex]5.0625 = \left(\dfrac{b}{2}\right)^2[/tex]

[tex]\sqrt{5.0625} = \dfrac{b}{2}\right[/tex]

[tex]4.5 = b[/tex]

Then, we can substitute that into the term [tex]by[/tex].

[tex]16(y^2 + 4.5y+5.0625)[/tex]

Finally, distribute the 16 and then take the middle term as the answer.

[tex]16y^2 + 72y+81[/tex]

72y

Answer:

-----------------------------

We are given a binomial and need to add a monomial to make it a perfect square.

Recall the identities for a square of a sum or difference of two numbers:

Analyze the given and compare with the identity above:

To complete the square we need to add ± 2ab, which is:

By adding this we get:

or

The cone will fit in 4 times and the volume of the cone is 535.89 in³

To solve this problem, we have to find the volume of the cone and the volume of the sphere.

The formula of volume of a cone is given as;

V = 1/3πr²h

We need to calculate the volume of the sphere which is given as

V = 4/3 πr³

The volume of the ball = 4/3 * 3.14 * 8³ = 2143.57in³

The volume of the cone = 1/3 * 3.14 * 8² * 8 = 535.89 in³

The number of times it will fit into will be 2143.57 / 535.89 = 4

It will fit in 4 times

b)

The volume of the cone is 535.89in³

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The required equation that following the pattern is n = 4s+1. So the option c is correct.

In the given question, we have to choose which equation below relates the number of squares, n, in a picture to the size number, s.

The given options are:

a) n = s+4

b) n = 4s

c) n = 4s+1

d) s = 4n

We find the pattern we firstly observe the given diagram closely.

As we can see that in first diagram have 5 blocks.

In second diagram have 9 blocks.

In third diagram have 13 blocks.

So, if the number of squares, represent by n, in a picture and the size number, represented by s, so the required equation that following the pattern is n = 4s+1. So the option c is correct.

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The graph of cubic equations, a to d and the associated cubic equations are as follows;

Equation (B) ⇒ Graph a

Equation (C)  ⇒ Graph b

Equation (D) ⇒ Graph c

Equation (A) ⇒ Graph d

A cubic equation that has only one variable is an equation of the form a·x³ + b·x² + c·x + d, where a ≠ 0.

The evaluation of the graphs are as follows;

Graph a

The y-intercept of the graph a, is 1, and the x-intercept, which is a solution of the equation is x = -1,

Therefore, when x = 0, y = 1, and when y = 0, x = -1

The function in graph a represents the translation of the parent function, y = x³, one unit, upwards, which corresponds with the function;

y = x³ + 1

Therefore, graph a corresponds to cubic equation (B) y = x³ + 1

Graph b

The y-intercept is one (1), and the turning point is at the point x = -1, which represents a shift of one unit to the left, and which can be obtained by the equation; y = (x + 1)³

Therefore, graph b corresponds with the cubic equation (C) y = (x + 1)³

Graph c

The turning point of the graph and the y-intercept is shifted one unit down, which corresponds with the equation; (D) y = x³ - 1

Graph d

The turning point is shifted 1 unit to the right and is located on the x-axis, The y-intercept is located at the point y = 1, therefore, the graph corresponds with the equation y = (x - 1)³

Graph d corresponds to equation (A), y = (x - 1)³

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Answer:

m = -1/3

Step-by-step explanation:

(-1, 2) and (-4, 3)

m = 3-2/-4+1

m = 1/-3

m = -1/3

The reciprocal of 2/43 of the difference between 3 2/15 and 2 5/12 is 30.

Here, we have to subtract 2 mixed fractions i.e

=> (3 2/15) - (2 5/12)

which when converted to a proper fraction is equal to,

=> (47/15) - (29/12)

= 43/60

∵ (3 2/15) - (2 5/12) = 43/60

now, 2/43 of the difference of 3 2/15 and 2 5/12,

=> (2/43) × (43/60) = 1/30............(i)

taking the reciprocal of the value obtained above,

∴ reciprocal of 1/30 = 30.

Thus, The reciprocal of 2/43 of the difference between 3 2/15 and 2 5/12 is 30.

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The reason for data variation is that the researchers are studying different samples, so there will be some variation in the data.

In mathematics, data is a collection of facts and figures that can take any shape, whether it be numerical or not. You can calculate numerical data, which is always gathered in number form and includes things like student test results, employee salaries, football team member heights, etc.

Qualitative, quantitative, discrete, continuous, primary and secondary are the types of data.

Since researches choose same school but group of 150 people is randomly chosen and different therefore, the reason for data variation is that the researchers are studying different samples, so there will be some variation in the data.

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Answer:

D= [-4,-1) U (2,4)

R = [-3,5)

In the case of regression analysis, the dependent variable must be metric; in multiple discriminant analysis, the dependent variable is nominal in nature. (Option B)

Regression analysis refers to a collection of statistical methods which are used for the estimation of relationships between a dependent variable and one or more independent variables. It can used to assess the strength of the relationship between variables and for modeling their future relationship. In regression analysis the dependent variable is metrically scaled (where distance between values can be calculated). Multiple discriminant analysis is a regression technique used in statistics to group objects into categories for analysis. In multiple discriminant analysis the dependent variable is nominally scaled (where characteristics can be distinguished).

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Answer:

She will have a balance of more than $18 for up to 6 days

Step-by-step explanation:

Start with $30.

Each day, x, subtract $1.99 from $30.

30 - 1.99x

The amount must be greater than $18.

30 - 1.99x > 18

Subtract 30 from both sides.

-1.99x > -12

Divide both sides by -1.99. Remember than when you multiply or divide both sides of an inequality by a negative number, the inequality sign changes direction.

-1.99x/(-1.99) < -12/(-1.99)

x < 6.03

The number of days must be less than 6.03. Since we deal with whole days, she will have a balance of more than $18 for up to 6 days.

The time it takes a freshman to choose their major is thought to have a standard deviation of one year by an undeclared major. A t-distribution table can be used to determine the crucial value.

The confidence interval for the average time it takes for freshmen to pick a major can be found by taking the sample mean of the 10 freshmen surveyed and adding and subtracting

The margin of error is calculated by multiplying the sample standard deviation by the critical value from a t-distribution with degrees of freedom equal to (n-1), where n is the sample size.

The sample size in this instance is 10. A t-distribution table can be used to determine the crucial value.

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The solution to the system, as an ordered triple is: (3, -4, 6).

To solve the following given system of equations:

2x + y + 3z = 20 --> eqn. 1

x + 2y - z = -11 --> eqn. 2

3x - 2z = -3 --> eqn. 3

Multiply equation 1 by 2 to get eqn. 4:

4x + 2y + 6z = 40 --> eqn. 4

Subtract eqn. 4 from eqn. 2:

x + 2y - z = -11 --> eqn. 2

4x + 2y + 6z = 40 --> eqn. 4

-3x - 7z = -51 --> eqn. 5

Add equations 3 and 5 together:

3x - 2z = -3 --> eqn. 3

-3x - 7z = -51 --> eqn. 5

-9z = -54

z = -54/-9

z = 6

Substitute the value of z into equation 5:

-3x - 7(6) = -51 --> eqn. 5

-3x - 42 = -51

-3x = -51 + 42

-3x = -9

-3x/-3 = -9/-3

x = 3

Find the value of y by substituting the values of x and z into equation 1:

2(3) + y + 3(6) = 20 --> eqn. 1

6 + y + 18 = 20

24 + y = 20

y = 20 - 24

y = -4

The solution as an ordered triple is: (3, -4, 6).

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When each independent variable is changed by one unit, use linear regression to get the mean change in the dependent variable. Polynomials can be used to simulate curvature as well as to add interaction effects.

An entire second order model is what?

The x1 and x2 linear terms, the x12 and x22 second-degree terms, and the x1x2 interaction term make up the entire second degree polynomial model. As could be used to represent the estimated model.

Which kind of model would you apply to discover the relationship between the dependent and independent variables?

Considering a one-unit change in each independent variable, use linear regression to determine the mean change in a dependent variable. To represent curvature and take interaction effects into account, you may also employ polynomials.

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The complete question is "Consider a regression analysis with three independent variables x1,x2, and x3. Give the equation for the following regression models: a. The model that includes as predictors all independent variables but no quadratic or interaction terms. b. The model that includes as predictors all independent variables and all quadratic terms. c. All models that include as predictors all independent variables, no quadratic terms, and exactly one interaction term. d. The model that includes as predictors all independent variables, all quadratic terms, and all interaction terms (the full quadratic model)."

Equation of parabola: y =ax² and receiver should be placed 18 feet above vertex.

Explanation:

Considering satellite dish as parabola we can have vertex as origin and concave upward.

So, equation of parabola will be justifying structure of satellite dish i.e

y = ax² -------(1)

Two points other than (0,0) are (-12,2) and (12,2), unit being feet.

This points will satisfy equation of parabola, substituting them in equation 1, we will calculate the value of constant 'a'.

a = [tex]\frac{2}{12^{2} }[/tex]

[tex]\frac{2}{2*6*12}\\ =\frac{1}{72}[/tex]

Substituting value of a = 1/72 in equation 1 we get

72y = x²

As receiver need to be located at focus, so it will be places at a distance of 'p' above the vertex

4p = 72

Dividing both sides by 4, we get

p = 18 feet

So, receiver will be placed at a distance of 18 feet above vertex.

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Answer:

2,700

Step-by-step explanation:

10,000x2=20,000+7,000=27,000÷10=2,700

The p-value for the test is 0.9821.

What is hypothesis?

A statistical hypothesis test is a technique for determining if the available data are sufficient to support a specific hypothesis. We can make probabilistic claims regarding population parameters through hypothesis testing.

What is z-score?

You can plot a z-score on a normal distribution curve. The range of Z-scores ranges from -3 standard deviations (which would be on the far left of the normal distribution curve) to +3 standard deviations (which would fall to the far right of the normal distribution curve). You must be aware of the mean and population standard deviation in order to use a z-score.

Given that the test statistic Z based on the sample information is z = 2.10.

z = 2.1 + 0.00

From the z-score table the value of p is 0.9821.

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Answer:

Step-by-step explanation:

I also need help.

The distance that Ian can drive is 198 miles.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

Here, Ian's car can go 165 miles on 5 gallons of gas. The mile per gallon will be:

= 165 / 5

= 33 miles per gallon.

Therefore, the miles in 6 gallons will be:

= 33 × 6

= 198 miles.

The distance is 198 miles.

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Answer:

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

To find the derivative of f(x) = 3x² + 2x at x = 3, we can use the power rule:

f'(x) = 2*3x + 2

When x = 3, the derivative of f(x) is:

f'(3) = 2*3(3) + 2

f'(3) = 18 + 2

f'(3) = 20

Therefore, the derivative of f(x) = 3x² + 2x at x = 3 is f'(3) = 20.

Answer:

No

Step-by-step explanation:

No, this is not correct. When you divide both sides of an inequality by a negative number, the inequality symbol must be reversed. So in this case, dividing both sides of the inequality -3x > 9 by -3 would give us x < -3, which is not what Diego claimed.

Answer:

19 small room and 25 big room

Step-by-step explanation:

Answer:

d= 120

Step-by-step explanation:

c+d = 180 degree

d = 180-60 =120 degree