3. A prop for the theater club’s play is constructed as a cone topped with a half-sphere. What is the volume of the prop? Round your answer to the nearest tenth of a cubic inch. Use 3.14 to approximate pi.

The dimensions of the window that maximize the area of the window is x = 17/(π - 1)(2) and y = 17 - (17/(π - 1)(2)) (1 + π ).

An area is just a surface that is empty. The length and breadth of a form are used to compute its area. The units used to measure length are unidimensional and include feet (ft), yards (yd), inches (in), etc. Nevertheless, a shape's area can only be measured in two dimensions. As a result, it is expressed in square units such as square inches (in2), square feet (ft 2), square yards (yd2), etc. Most forms and things have edges and corners. When determining an object's area, the length and breadth of these edges are taken into account.

Let us suppose the width of the rectangle = x.

The length of the rectangle = y

Thus,

Perimeter = 2 (x + y) + πx

34 = 2x + 2y + πx

2y = 34 - 2x + πx

The area of the window is:

A = (1/2)πx²+ xy

Substitute y = 34 - 2x + πx / 2

To maximize the area we differentiate the area and equate it to 0:

A = (1/2)πx²+ x(34 - 2x + πx / 2)

A =  (1/2)πx²+ 17x - x² + π/2x²

dA/dx = πx + 17 - 2x + πx

2πx + 17 - 2x = 0

2x(π - 1) = - 17

x = 17/(π - 1)(2)

Substitute the value of x in equation:

2y = 34 - 2x + πx

2y = 34 - 2(17/(π - 1)(2)) + π( 17/(π - 1)(2))

y = 17 - (17/(π - 1)(2)) (1 + π )

Hence, the dimensions of the window that maximize the area of the window is x = 17/(π - 1)(2) and y = 17 - (17/(π - 1)(2)) (1 + π ).

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To cover one suitcase, we need to find the surface area of the suitcase that needs to be covered. The surface area of the suitcase can be calculated by finding the sum of the areas of its six sides.

Area of one side of the suitcase = length x height = 80cm x 48cm = 3840 sq.cm

Area of the opposite side of the suitcase = length x height = 80cm x 48cm = 3840 sq.cm

Area of the other four sides of the suitcase = width x height = 24cm x 80cm + 24cm x 80cm + 24cm x 48cm + 24cm x 48cm = 7296 sq.cm

Total surface area of one suitcase = 3840 sq.cm + 3840 sq.cm + 7296 sq.cm = 14976 sq.cm

To cover 100 such suitcases, we need to multiply the surface area of one suitcase by 100.

Total surface area of 100 suitcases = 14976 sq.cm x 100 = 1497600 sq.cm

To find the amount of tarapaulin required, we need to divide the total surface area of 100 suitcases by the width of the tarapaulin.

Amount of tarapaulin required = (1497600 sq.cm) / (96 cm) = 15600 sq.cm

We now need to convert the required area into meters.

1 sq.cm = 0.0001 sq.m

15600 sq.cm = 15600 x 0.0001 sq.m = 1.56 sq.m

Therefore, we need 1.56 sq.m of tarapaulin to cover 100 such suitcases, assuming that there is no overlap of the tarapaulin.

The population in this case is all adults in the United States, and the sample is the 1001 adults who were surveyed by Citrix Security.

The sample was selected in such a way as to be representative of the larger population of adults in the United States.

The value of 69% is a statistic, not a parameter. A statistic is a measure that describes a characteristic of a sample, while a parameter is a measure that describes a characteristic of a population. In this case, the 69% refers to the proportion of the 1001 adults surveyed who believe that having their personal information stolen is inevitable, which is a characteristic of the sample. It does not necessarily reflect the proportion of all adults in the United States who hold this belief, which would be a parameter.

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The value of cot A is √55/3

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

cot A = 1/tanA

AC = √ 8²-3²

AC = √64-9

AC = √ 55

tanA = 3/√55

cot A = 1/tanA

cot(A )= 1/(3/√55)

cot( A) = √55/3

therefore the value of cot(A) = √55/3

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PLEASE GIVE BRAINLIEST <3

Answer:

I'm pretty sure it's bumper cars ( B ).

Hope this helped! <3

Answer:[tex]m[/tex] = [tex]d[/tex]/[tex]25[/tex]

Step-by-step explanation:I don't know if this is correct but i think it is:

Solve D=25m

Evaluate powers D = 25m

Subtract D from both sides D= 25m[tex]1[/tex] - D

Add D to both sides D=25m1

Evaluate powers D=25m

Divide both sides by 25 D/25 =m

Solution m = D/25

The value of expression [tex]2F(6) + F(-5) - 3F(-1)[/tex] is 6 while considering the given piece wise function.

What is piece wise function ?

A piecewise function is a function that is defined by different mathematical expressions or formulas for different intervals or "pieces" of the domain. In other words, a piecewise function is a function that is defined by multiple sub-functions, each corresponding to a different part of the domain.

While considering piece wise function:

[tex]F(6) = 4[/tex]                                                                 [tex](x \geq 3)[/tex]

[tex]F(-5) = x + 3 = (-5) + 3 = -2[/tex]                            [tex](x\leq -3)[/tex]

[tex]F(-1) =[/tex] [tex]-x^2 + 1 = -(-1)^2 + 1 = -1 + 1 = 0[/tex]       [tex](-3 < x < 3)[/tex]

Now put the value of F(6), F(-5) and F(-1) in the expression :

[tex]2F(6) + F(-5) - 3F(-1)[/tex]

we get :

[tex]= 2F(6) + F(-5) - 3F(-1) \\= 2(4) + (-2) -3(0)\\= 8 -2\\= 6[/tex]

Therefore, the value of expression [tex]2F(6) + F(-5) - 3F(-1)[/tex] is 6 while considering the given piece wise function.

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Answer:

Equal to.

Step-by-step explanation:

multiply both numbers by 2

By answering the above question, we may state that As a result, there is standard deviation a roughly 0.9999 or 99.99% chance that the sample mean will be within 8 of the population mean.

A statistic known as standard deviation may be used to indicate the variation or variability of a set of statistics. A low standard deviation means that the values tend to be closer to the established mean whereas a large standard deviation shows that the values are widely spread. The standard deviation serves as a gauge for how far the data are from the mean (or ). The data tend to cluster around the mean when the standard deviation is low, and are more scattered when the standard deviation is high. Standard deviation is a measurement of the data set's average variability. It displays the standard deviation of each score with respect to the mean.

population + standard deviation departure from the mean / sqrt (sample size)

Standard deviation is 90/sqrt(100) and equals 9.

z is equal to (x - ) / ( / sqrt(n)).

where:

The sample mean is x. We are looking for the probability given the following conditions: where is the sample size, which is 100; is the population mean, which is 400; is the standard deviation of the distribution of sample means, which is 9;

When we change the values, we obtain:

[tex]Z = (9 / sqrt(100) / (x - 400)\\z = (x - 400) / 0.9\\P(392 < = x < = 408)\s= P[(392 - 400) / 0.9 < = z < = (408 - 400) / 0.9] .9]\\= P[-8.89 < = z < = 8.89] .89]\\[/tex]

To determine this probability, we can use a calculator or a conventional normal distribution table.

[tex]P[-8.89 < = z < = 8.89] = 0.9999[/tex]

As a result, there is a roughly 0.9999 or 99.99% chance that the sample mean will be within 8 of the population mean.

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it will take approximately 1.30 loads of trash from the garbage truck to fill the 40-foot by 9-foot by an 8-foot storage container. However, since you can't have a partial load, you would need to round up to 2 loads to completely fill the container.

what is an algebraic expression?

An algebraic expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that can be simplified and evaluated.

To determine the number of loads of trash from the garbage truck that will fill a 40-foot by 9-foot by 8-foot storage container, we need to compare the volume of the container to the volume of the garbage truck's back.

The volume of the garbage truck's back is:

V_garbage_truck = length x width x height

V_garbage_truck = 23 ft x 8 ft x 12 ft

V_garbage_truck = 2,208 cubic feet

The volume of the storage container is:

V_container = length x width x height

V_container = 40 ft x 9 ft x 8 ft

V_container = 2,880 cubic feet

To find out how many loads of trash from the garbage truck will fill the storage container, we need to divide the volume of the container by the volume of the garbage truck's back:

Number of loads = V_container / V_garbage_truck

Number of loads = 2,880 cubic feet / 2,208 cubic feet

Number of loads ≈ 1.30 loads

Therefore, it will take approximately 1.30 loads of trash from the garbage truck to fill the 40-foot by 9-foot by an 8-foot storage container. However, since you can't have a partial load, you would need to round up to 2 loads to completely fill the container.

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geometric series:

[tex]\dfrac{4}{-8} = - \dfrac{1}{2}[/tex]

[tex]\dfrac{-2}{4} = - \dfrac{1}{2}[/tex]

[tex]\implies r = - \dfrac{1}{2} \ \ and \ \ a_{1} = -8[/tex]

[tex]\boxed{S_{n} = \dfrac{a_{1}\cdot (1 - {r}^{n}) }{1 - r}}[/tex]

a. n = 3

[tex]S_{3} = - 8 + 4 - 2 = 4 - 10 = \bf -6\\[/tex]

b. n = 6

[tex]S_{6} = \dfrac{(-8)\cdot \Big(1 - { \Big(- \dfrac{1}{2}\Big)}^{6}\Big) }{1 - \Big( - \dfrac{1}{2}\Big)} = \dfrac{(-8)\cdot \Big(1 - \dfrac{1}{2^{6}}\Big)}{1 + \dfrac{1}{2}} = \dfrac{-8 + \dfrac{1}{2^{3}}}{\dfrac{3}{2}} =\\[/tex]

[tex]= \dfrac{-64+1}{2^{3}} \cdot \dfrac{2}{3} = -\dfrac{63}{2^{2}(3)} = \bf -\dfrac{21}{4}[/tex]

c, n = 25

[tex]S_{25} = \dfrac{(-8)\cdot \Big(1 - { \Big(- \dfrac{1}{2}\Big)}^{25}\Big) }{1 - \Big( - \dfrac{1}{2}\Big)} = \dfrac{(-8)\cdot \Big(1 + \dfrac{1}{2^{25}}\Big)}{1 + \dfrac{1}{2}} = - \dfrac{8 + \dfrac{1}{2^{22}}}{\dfrac{3}{2}} =\\[/tex]

[tex]= - \dfrac{8 + \dfrac{1}{2^{22}}}{\dfrac{3}{2}} = - \dfrac{1 + 2^{25}}{2^{22}} \cdot \dfrac{2}{3} = \bf - \dfrac{1 + 2^{25}}{(3)2^{21}}\\[/tex]

The volume generated by rotating the region bounded by curves x = √y, x= 0 and y = 6 about the x-axis is 24π cubic units.

To use the method of b, we will imagine taking thin slices parallel to the axis of rotation and adding up their volumes.

To use the method of cylindrical shells, we need to determine the height and radius of each cylindrical shell. We will take thin vertical slices parallel to the y-axis.

The height of each cylindrical shell will be dy. The radius of each cylindrical shell will be x, which is equal to √y.

The volume of each cylindrical shell will be:

[tex]dv = 2\pi x * dy[/tex]

Substituting x = √y, we get:

[tex]dV = 2\pi \sqrt{y} * dy[/tex]

To find the total volume, we need to integrate dV from y = 0 to y = 6:

V = ∫₀⁶ 2π√y dy

Using the power rule of integration, we get:

V = 2π [2/3 * y^(3/2)] from 0 to 6

[tex]V = 2\pi * [2/3 * (6)^\frac{3}{2} - 0][/tex]

[tex]v = 24\pi[/tex]

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After evaluating the given expression, d3a2−(c+b) equals -39 when a=-2, b=3, c=-12, and d = -4

An Algebraic expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that can be simplified and evaluated.t may contain one or more variables, which are symbols that represent unknown quantities or values that can vary.

Algebraic expressions can be written using letters, symbols, or a combination of both, and they can be used to model real-world situations, solve problems, and express mathematical relationships. For example, "3x + 5" is an algebraic expression that represents a linear equation with one variable "x".

The given expression is d3a2−(c+b), where a = -2, b = 3, c = -12, and d = -4. Substituting these values, we get:

d3a2−(c+b) = (-4)3(-2)² - (-12 + 3) = -434 - (-9) = -48 + 9 = -39

Therefore, d3a2−(c+b) equals -39 when a=-2, b=3, c=-12, and d=-4.

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The zeros of the following functions are

1. f(x)=2x(3−x)(x+1) , the zeros are x = 3 and -1

2.f(x)=2(x−3)(x+2)2(x−1), the zeros are x = 3 ,-2 and 1

3. f(x)=x3(x−2)(x+3), the zeros are x = 2 and -3

On a graph of the function, the zeroes will be the x-coordinate values at the points where the line intersects with the x-axis, or where the y-coordinate value is zero. Linear functions have one zero, but polynomial functions can have multiple zeroes. They can also have no zeroes at all.

1. 2x(3−x)(x+1) = 0

2x = 0

x = 0

3-x = 0

x = 3

x+1 = 0

x = -1

2. 2(x−3)(x+2)2(x−1) = 0

x-3 = 0

x = 3

x+2 = 0

x = -2

x -1 = 0

x = 1

3. f(x)=x³(x−2)(x+3) = 0

x³ = 0

x= 0

x-2 = 0

x = 2

x+3 = 0

x = -3

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Answer:

x^2 - 9 = 0

Step-by-step explanation:

its right one.......

According to the probability, the answer is option D: 1/98,000.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

The chance of Steve being selected is 1. This means that out of 1 individual, Steve is selected. The probability of Steve being selected is 1/1 or 1. Since the sample is a simple random sample, each individual in the population has an equal chance of being selected. If there are a total of 98,000 individuals in the population, then the probability of Silva being selected is 1 out of 98,000, or 1/98,000.

Therefore, the answer is option D: 1/98,000.

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Answer:

a. 480       Then 384

b. 845       Then 591.5
c. 1,189      Then 653.95
d. 153.75   Then 149.90625
e. 315        Then 299.25

f. 430.5     Then 419.7375

Answer:

150 %6=es igual 1% dividimis 150 ÷100 para tener 150, se calcula el porcwntaje

Answer:

25

Step-by-step explanation:

let the no of days food avl for eat be X .

according to question...

100/80=X/20

=X × 80 = 100×20

=80x =2000

= x =2000/80

x=25 days

Answer:

Step-by-step explanation:

SEE THE ATTACHMENT

Answer:

See below.

Step-by-step explanation:

Hello!

The topic we should review for this problem is Order of Operations.

Order of Operations is a rule that identifies which part of an equation should be simplified first.

You might've heard of PEMDAS, where;

P for Parentheses, always first unless there's an exponent inside.

E for Exponent, simplified after the Parentheses.

M or D - Multiplication or Division after the Exponent(s).

A or S - Addition or Subtraction after Multiplication or Division.

[tex](5+3^2)+18[/tex]

First we know that there's an Exponent inside the Parentheses, so we must evaluate that number first.

[tex](5+9)+18[/tex]

Next, evaluate what's in the Parentheses.

[tex]14+18\\32[/tex]

Our correct answer is 32.

We are asked what mistake did Raquel make, and what's the correct simplified version of the expression.

1a.) Raquel's mistake is combining unlike terms. It's impossible to combine together a natural number (5) and an exponential number. (3²)

1b.) The correct simplified version of the expression is represented here;

[tex](5+9)+18\\(First \ Step)[/tex]

Answer:

20cm³

Step-by-step explanation:

Volume = Base x Height

1/2 x 5 x 2 x 4

=20cm³

The best represent graph of the function is option a.

What is a function?

It is an expression which contains one independent variable and another is dependent variable.

The given function is

   f(x)= [tex]4^{x[/tex] - 4

As it is an exponential function so it must have a horizontal asymptote. Here the horizontal asymptote is f(x)= -4

For x intercept we need to take f(x)=0 and for y intercept substitute 0 for x and solve for y. [Here y can be treated as f(x).]

Here x intercept(s)= None

y intercept(s) = (0,-3)[ putting x=0 in   f(x) so 1-4= -3]

Hence the graph is given below.

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The equations where b = 11 are A, B, C, D, and E. All of these equations are true when b = 11.

To point an equation on a graph, first, determine the equation and its variables. Then, plot the points of the equation on the graph by substituting the variable values and plotting the corresponding points. To find the equation’s slope, calculate the rise and run of two points on the graph. The slope is used to draw a line of best fit. Finally, draw a line that intersects the points of the equation and the line of best fit. This will be the equation’s graph.

Choice A states that 2b = 2112, b, equals, 211, which means that 2 times 11 is equal to 21. Choice B states that b + 18 = 7b, plus, 18, equals, 7, which means that 11 plus 18 is equal to 7. Choice C states that 77 = 7b77, equals, 7, b, which means that 77 divided by 7 is equal to 11. Choice D states that 9 = b − 29, equals, b, minus, 2, which means that 11 minus 2 is equal to 9. Finally, Choice E states that 11 = 33 ÷ b11, equals, 33, divided by, b, which means that 33 divided by 11 is equal to 11. Therefore, all of these equations are true when b = 11.

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Answer:

x=6

Step-by-step explanation:

The price οf the ticket when the number οf stοps is 13, fοund using the given expressiοn, is $6.55.

Mathematical expressiοns cοnsist οf at least twο numbers οr variables, at least οne maths οperatiοn, and a statement. It's pοssible tο multiply, divide, add, οr subtract with this mathematical οperatiοn. A finite cοmbinatiοn οf symbοls that are well-fοrmed in accοrdance with cοntext-dependent principles is referred tο as an expressiοn οr mathematical expressiοn. There are twο sοrts οf expressiοns in mathematics: numerical expressiοns, which οnly cοntain numbers, and algebraic expressiοns, which alsο include variables. Expressiοns can be categοrised as arithmetic/numerical expressiοns, fractiοnal expressiοns, οr algebraic expressiοns depending οn the terms they cοntain.

Given the expressiοn as:

1.35 + 0.40(s)

This is used tο calculate the price οf a ticket οn the lοcal cοmmuter train.

s = number οf stοps

Nοw the cοmplete questiοn is tο calculate the price οf the ticket fοr 13 stοps.

Sο s = 13

Substitute in the expressiοn,

1.35 + 0.40(s) = 1.35 + 0.40 * 13 = 1.35 + 5.2 = $6.55

Therefοre the price οf the ticket when the number οf stοps is 13, fοund using the given expressiοn, is $6.55.

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The slope of a line parallel to the line whose equation is 5x - 3y = 18 is equal to 5/3.

In Mathematics, the slope-intercept form of an equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Making y the subject of formula, we have the following:

5x - 3y = 18

3y = 5x - 18

y = 5x/3 - 6

In Geometry and Mathematics, two (2) lines are said to be parallel under the following conditions:

m₁ = m₂ ⇒ 5/3 = 5/3

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The ordered pair representing the point where both companies would charge the same amount is (25, 136.25).

From the given table, we can form the following equation for monthly cost of each company.

Company 1, the function for the monthly cost is;

(5, $55.25 ) and (10, $75.5). Let the monthly cost = y₁

(y₁ - 55.25 )/(x - 5) = ( 75.5 - 55.25 )/ (10 - 5)

y₁ = 4.05x + 35

Company 2, the function for the monthly cost is;

(5, $31.25 ) and (10, $57.5). Let the monthly cost = y₂

(y₂- 31.25 )/(x - 5) = ( 57.5 - 31.25 )/ (10 - 5)

y₂ = 5.25x + 5

To find the point where both companies charge the same amount, we need to set their costs equal to each other and solve for the number of garments, x:

y₁ = y₂

4.05x + 35 = 5.25x + 5

Subtracting 4.05x and 5 from both sides:

30 = 1.2x

Dividing both sides by 1.2:

x = 25

So both companies would charge the same amount when 25 garments are laundered. T

To find the cost, we can plug x = 25 into either equation:

y₁ = 4.05(25) + 35 = 136.25

y₂ = 5.25(25) + 5 = 136.25

Ordered pair = (25, 136.25)

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The complete question is below:

Two dry cleaning companies offer a home pick-up and delivery service. The monthly cost depends on the number of garments laundered, and is shown in the following table.

Number of Garments      Company 1       Company 2

5                                         $55.25              $31.25

10                                        $75.50             $57.50

15                                        $95.75              $83.75

Determine when both companies would charge the same amount and what that cost would be. Write your answer as an ordered with x representing the number of garments and y representing the cost.

The line of reflection that produces X'(2, 4) is,

⇒ y - axis

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

We have to given that;

Triangle XYZ is drawn with vertices X(-2, 4), Y(-9, 3), Z(-10, 7).

Now, We know that;

The rule for a reflection over the y -axis is (x, y) → (- x, y)

Here, The line of reflection is produces X'(2, 4).

Hence, We get;

The rule for line of reflection that produces X'(2, 4) is,

⇒ y - axis

Thus, The line of reflection that produces X'(2, 4) is,

⇒ y - axis

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