Directions: Show all work. Round to the nearest tenth. 1. What is the volume of a cone with a diameter of 12 inches and a height of 16 inches?

​

Answer:

Θ ≈ 41.8103°

Step-by-step explanation:

using the sine ratio in the right triangle

sinΘ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{4}{6}[/tex] , then

Θ = [tex]sin^{-1}[/tex] ( [tex]\frac{4}{6}[/tex] ) ≈ 41.8103° ( to 4 decimal places )

Therefore, the smaller of the two acute angles is 8°.

Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. Here are some general steps to solve trigonometry problems:

Understand the problem: Read the problem carefully and identify what is being asked for.

Draw a diagram: Draw a diagram of the triangle and label the sides and angles.

Identify the known values: Identify what is given in the problem, such as the lengths of the sides or the measure of an angle.

Choose the appropriate formula: Choose the formula that relates the known values to the unknown value that you need to find.

Solve for the unknown value: Use algebraic manipulation and/or your calculator to solve for the unknown value.

Check your answer: Check your answer to make sure it makes sense and that it satisfies any given constraints.

Let's start by using the trigonometric identity cos(x) = sin(90° - x) for the left-hand side of the equation:

[tex]cos(4x) =[/tex][tex]sin(90^{0} - 4x)[/tex]

Now we can substitute this into the original equation and simplify:

[tex]sin(90^{0} - 4x) = sin(6x + 10)[/tex]

Using the identity sin(a) = sin(b) implies a = b + 2kπ or a = π - b + 2kπ for some integer k, we can set the angles inside the sine function equal to each other and solve for x:

90° - 4x = 6x + 10 + 2nπ or 90° - 4x = π - (6x + 10) + 2nπ

where n is an integer.

Solving for x in the first equation, we get:

10x = 80° + 2nπ

x = 8° + (2n/10)π

Solving for x in the second equation, we get:

10x = 80° + π + 2nπ

x = (8° + π/10) + (2n/10)π

Since we want the acute angle of the right triangle, which is less than 90°, we only need to consider the values of x that satisfy 0° < x < 22.5°. From the two equations above, we see that x can take on values between 8° and 9° or between 89° and 90°. Therefore, the smaller of the two acute angles is 8°.

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The standard form of rational number of -30/75 is -2/5.

The standard form, given is -30/75.

Both numerator and denominator are a multiple of 15,

Hence we divide them by 15,

The result is -2/5 which is its standard form.

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Forever Quilting's monthly profit is $10,250. We can caclculate it in the following manner.

To calculate the company's monthly profit, we need to subtract its total expenses from its total revenue.

Total Revenue = Number of kits sold x Price per kit

Total Revenue = 150 kits x $120 per kit

Total Revenue = $18,000

Total Costs = (Cost of materials per kit + Labor cost per kit) x Number of kits sold + Monthly expenses

Total Costs = ($45 + $5) x 150 kits + $1,000 + $200 + $500 + $4,500

Total Costs = $7,750

Monthly Profit = Total Revenue - Total Costs

Monthly Profit = $18,000 - $7,750

Monthly Profit = $10,250

Therefore, Forever Quilting's monthly profit is $10,250.

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Answer:

137 in binary is 10001001

Step-by-step explanation:

Conner's answer did not receive full credit because he did not convert the hexadecimal number #FF0000 to decimal and binary correctly.

While it is true that the letter F represents 1111 in binary, in hexadecimal, FF represents the decimal value 255, not 1111.

Therefore, Conner's answer is incorrect, and he needs to use the correct conversions to get the right answer.

To convert 255 to binary using divisions, we can use the following steps:

Start with the decimal number 255.

Divide 255 by 2, and write down the quotient and remainder. The quotient is 127, and the remainder is 1.

Divide the quotient (127) by 2, and write down the quotient and remainder. The quotient is 63, and the remainder is 1.

Repeat this process of dividing the quotient by 2 and writing down the quotient and remainder until the quotient becomes 0.

The binary equivalent of 255 is the sequence of remainders written in reverse order: 11111111.

Decimal Number      Quotient          Remainder

        255                   127                1

        127                           63                    1

        63                             31                    1

        31                              15                    1

        15                            7                    1

        7                            3                    1

        3                            1                      1

        1                                0                    1

Divide 137 by 2. The quotient is 68, and the remainder is 1.

Divide 68 by 2. The quotient is 34, and the remainder is 0.

Divide 34 by 2. The quotient is 17, and the remainder is 0.

Divide 17 by 2. The quotient is 8, and the remainder is 1.

Divide 8 by 2. The quotient is 4, and the remainder is 0.

Divide 4 by 2. The quotient is 2, and the remainder is 0.

Divide 2 by 2. The quotient is 1, and the remainder is 0.

Divide 1 by 2. The quotient is 0, and the remainder is 1.

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This allows you to visualize all of the possible solutions that meet the Constraint and determine the optimal solution for your problem.

To graph the feasible region for the constraint y≥0, you would start by using the polygon tool in a graphing program or software. This tool allows you to create and manipulate polygons on a coordinate plane.

To create the feasible region for the constraint y≥0, you would draw a horizontal line at y=0 on the coordinate plane. This line represents the boundary between the feasible and infeasible regions. Any point above the line is infeasible, while any point below the line is feasible.

Once you have drawn the horizontal line, you can use the polygon tool to create the feasible region by shading in the area below the line. This region represents all of the possible solutions that meet the constraint y≥0. Any point within this region would satisfy the constraint, while any point outside the region would violate the constraint.

Overall, using the polygon tool to graph the feasible region for the constraint y≥0 is a simple process that involves drawing a horizontal line at y=0 and shading in the area below it. This allows you to visualize all of the possible solutions that meet the constraint and determine the optimal solution for your problem.

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Answer: (-2,-3)

Step-by-step explanation:

I don't think anything is wrong with your values. Since it's an equation, you can see something different and get the right answer.

Answer:

o=3

Step-by-step explanation:

3+0+3=6

Answer:

1 ⅓

Step-by-step explanation:

there 4 glasses and you put ⅓ in each one therefore 4 x ⅓ = 1 ⅓

Answer:

Length ≥ 40

Width ≥ 5

Perimeter = 2 × (Length + Width)

2 × (Length + Width) ≤ 150

Step-by-step explanation:

To create a graph showing the possible dimensions of the garden, we need to plot the length and width of the rectangular area on the x and y axes, respectively. Since we want the length to be at least 40 feet and the width to be at least 5 feet, we can represent these constraints by the following inequalities:

Length ≥ 40

Width ≥ 5

We also know that the total length of fencing available is 150 feet, which means that the perimeter of the rectangular area must be less than or equal to 150 feet. The perimeter of a rectangle is given by:

Perimeter = 2 × (Length + Width)

So, we can write the inequality representing the perimeter as:

2 × (Length + Width) ≤ 150

To graph the possible dimensions of the garden, we can plot the points that satisfy all three inequalities on the x-y plane.

Regarding the vegetables, it is not clear what vegetables the user would like to plant in the garden. As such, we cannot provide a specific answer to this question.

In summary, we need to write three inequalities to represent the constraints in the problem, and we can graph the solution space using these inequalities.

By adding  the monthly finance charge to the unpaid balance, the new account balance is $4,056.91.

What is addition?

Addition is a mathematical operation that involves combining two or more numbers to produce a sum or total. It is commonly denoted by the plus sign (+) and is one of the four basic arithmetic operations.

To find the new account balance, we need to add the monthly finance charge to the unpaid balance.

First, we need to calculate the monthly finance charge:

Monthly finance charge = 1.75% of unpaid balance

= 0.0175 * $3,987.11

= $69.80

Next, we add the monthly finance charge to the unpaid balance:

New account balance = Unpaid balance + Monthly finance charge

= $3,987.11 + $69.80

= $4,056.91

Therefore, the new account balance is $4,056.91.

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Cheryl ran a total of 8 miles in five days.

1 + 1 + 1 + 2 + 3 = 8

Written as a decimal, this is 8.0 miles.

Answer:
8. A) 3.75

9. B) 5.00

Without the specific details or an image of the line segment on the coordinate grid, I'm unable to provide you with the specific numbers included in the range.

To help you generally, a line segment is a part of a line with two endpoints, and it is located on a coordinate grid, which is a two-dimensional plane formed by the intersection of horizontal and vertical lines (x and y axes).

To determine the range of the line segment, you need to identify the y-coordinates of the two endpoints.

The range includes all the y-coordinates between those two points, inclusive of the endpoints. To find the range, observe the line segment and note the y-coordinates of both endpoints. Then, list all the numbers (whole or fractional) between those values, including the endpoints themselves.

Once you have the necessary details or an image of the line segment, feel free to ask again, and I'll be happy to help you identify the numbers within the range.

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Answer:

what is 5+17894874298748

Answer:

Therefore, the total amount the Bells will pay for their house is $344,520.

Step-by-step explanation:

We can start by using the information about the monthly mortgage payment to calculate the total number of payments they will make over the 30-year term:

30 years × 12 months/year = 360 months

So the Bells will make 360 monthly payments of $957. To find the total amount they will pay for the house, we need to multiply the monthly payment by the number of payments:

$957/month × 360 months = $344,520

Therefore, the total amount the Bells will pay for their house is $344,520.

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Answer:

The number line that shows ï > 7 would be from 8 to 10, as the symbol > means greater than. So the correct answer is B. Submit B.

Answer:

 y = 7x + 10

Step-by-step explanation:

Use your point-slope form: y- y1 = m (x - x1) to substitute the given information.

    y - 6 = 7(x - (-4))

Then simplify.

     y - 6 = 7(x + 4)

Next, distribute the 7 into the parenthesis which will give you the point-slope form.

     y - 6 = 7x + 28

In order to write it in slope-intercept form, add 6 to both sides.

    y - 6 + 6 = 7x + 4 + 6

Then simplify to write the equation in slope-intercept form.

    y = 7x + 10

The formal statement of the Limit Comparison Test are discuss below with ∑bₙ converges, then ∑aₙ converges as well.

The Limit Comparison Test is a method used to determine the convergence or divergence of a series.

Suppose we have two series, aₙ and bₙ. If we can find a third series, cₙ, such that the limit of the ratio aₙ/cₙ and bₙ/cₙ both exist and are finite, and the limit of aₙ/cₙ divided by bₙ/cₙ is also finite and non-zero, then the two series aₙ and bₙ will converge or diverge together.

In other words, we can say that if the series aₙ diverges, then bₙ also diverges, and if the series bₙ converges, then aₙ also converges.

Here's the formal statement of the Limit Comparison Test:

Let aₙ and bₙ  be two positive series. If there exists a positive series cₙ such that  [tex]\lim_{n \to \infty} \frac{a_n}{c_n}[/tex]  and  [tex]\lim_{n \to \infty} \frac{b_n}{c_n}[/tex] both exist and are finite and positive, then:

(i) If ∑bₙ converges, then ∑aₙ converges as well.

(ii) If ∑aₙ diverges, then ∑bₙ diverges as well.

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We can use the method of integrating factors to solve the equation.

Y' + x = (x-1)y' + 1

The integrating factor method is a technique used to solve linear first-order ordinary differential equations.

Find the integrating factor:

The integrating factor is given by:

I(x) = e^(∫x dx) = e^(x^2/2)

Multiply both sides of the equation by the integrating factor I(x)

e^(x^2/2)Y' + xe^(x^2/2) = (x-1)e^(x^2/2)y' + e^(x^2/2)

Let's simplify the left-hand side using the product rule of differentiation

(d/dx)(e^(x^2/2)Y) = e^(x^2/2)Y' + xe^(x^2/2)

Rewrite the equation using the simplified left-hand side

(d/dx)(e^(x^2/2)Y) = (x-1)e^(x^2/2)y' + e^(x^2/2)

Then, Integrate both sides with respect to x

∫(d/dx)(e^(x^2/2)Y) dx = ∫((x-1)e^(x^2/2)y' + e^(x^2/2)) dx

e^(x^2/2)Y = ∫((x-1)e^(x^2/2)y' + e^(x^2/2)) dx

Using integration by substitution and integration by parts, we can evaluate the integral on the right-hand side and simplify the equation:

e^(x^2/2)Y = e^(x^2/2) + C - e^(x^2/2)y + D

where C and D are constants of integration.

We Solve for Y:

Y = 1 - y + Ce^(-x^2/2) + De^(x^2/2)

Therefore, the solution of the given differential equation is:

Y = 1 - y + Ce^(-x^2/2) + De^(x^2/2)

where C and D are constants of integration.

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(a) The right distributive law is proven for S.For S, this is expressed as (a,b)·(c,d)=(a,b)·(c,d)=(a·c,a·d+b·c).

(a,b)·(c,d)=(bd−ad−bc,ac−ad−bc)=(a·c,a·d+b·c).

(b) we can deduce that x=1 and y=0. Hence, the multiplicative identity element for S is (1,0).

(c) For S, this is expressed as (a,b)·(1,0)=(a,b). Let (a,b) be an arbitrary element in S. The multiplicative identity law is proven for S.

The right distributive law states that the product of a scalar and a vector is equal to the sum of the products of the scalar with each component of the vector.

(a) For S, this is expressed as (a,b)·(c,d)=(a,b)·(c,d)=(a·c,a·d+b·c).

To prove this, we need to show that (a,b)·(c,d)=(a·c,a·d+b·c).

Let (a,b) and (c,d) be two arbitrary elements in S. Then,

(a,b)·(c,d)=(bd−ad−bc,ac−ad−bc)

=(a·c,a·d+b·c).

Therefore, the right distributive law is proven for S.

(b) The multiplicative identity element for S is (1,0). To find this, we need to find a pair of elements (x,y) such that (a,b)·(x,y)=(a,b).

Let (x,y) be an arbitrary pair of elements in S. Then,

(a,b)·(x,y)=(ax−by,ay+bx)

=(a,b).

From this, we can deduce that x=1 and y=0. Hence, the multiplicative identity element for S is (1,0).

(c) The multiplicative identity law states that the product of a scalar and the multiplicative identity element is equal to the scalar itself. For S, this is expressed as (a,b)·(1,0)=(a,b).

To prove this, we need to show that (a,b)·(1,0)=(a,b).

Let (a,b) be an arbitrary element in S. Then,

(a,b)·(1,0)=(a·1−b·0,a·0+b·1)

=(a,b).

Therefore, the multiplicative identity law is proven for S.

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Answer:

To translate a shape, we need to move all its vertices by the same amount in the same direction. Here are the answers to the three parts of the question:

1. To translate parallelogram ABCD 2 units down, we need to subtract 2 from the y-coordinates of all its vertices. Let's say the original coordinates of the vertices are A(a,b), B(c,d), C(e,f), and D(g,h). Then the new coordinates of the vertices will be A'(a,b-2), B'(c,d-2), C'(e,f-2), and D'(g,h-2). Plot these new vertices to get the translated parallelogram.

2. To translate rhombus EFGH 2 units to the left and 4 units down, we need to subtract 2 from the x-coordinates and 4 from the y-coordinates of all its vertices. Let's say the original coordinates of the vertices are E(a,b), F(c,d), G(e,f), and H(g,h). Then the new coordinates of the vertices will be E'(a-2,b-4), F'(c-2,d-4), G'(e-2,f-4), and H'(g-2,h-4). Plot these new vertices to get the translated rhombus.

3. If the coordinates of the vertices of a square LMNO are L(-5,-5), M(-5,5), N(5,5), and O(5,-5), and we want to translate it 3 units to the right and 2 units up, we need to add 3 to the x-coordinates and subtract 2 from the y-coordinates of all its vertices. The new coordinates of the vertices will be L'(-2,-7), M'(-2,3), N'(8,3), and O'(8,-7). Plot these new vertices to get the translated square.

In conclusion, the integer solutions of the given system of equations are [tex]$(x, y, z) = (1, 2, 0)$ and $(x, y, z) = (-1, 4, 0)$.[/tex]

An integer is a positive, negative, or zero-valued whole number. It is a number without a fractional or decimal component.

To find all integer solutions of the given system of equations:

[tex]x + y &= 3 \[/tex]

[tex]3xy - z^2 &= 9[/tex]

We can start by solving the first equation for one of the variables. Let's solve for y in terms of x:

[tex]x + y &= 3 \[/tex]

[tex]y &= 3 - x[/tex]

Now we substitute this expression for y into the second equation:

[tex]3xy - z^2 &= 9 \[/tex]

[tex]3x(3-x) - z^2 &= 9 \quad \text{Substituting } y = 3-x \[/tex]

[tex]9x - 3x^2 - z^2 &= 9 \[/tex]

[tex]3x^2 + z^2 &= 9x - 9 \[/tex]

[tex]3x^2 - 9x + z^2 &= -9 \quad \text{(1)}[/tex]

Now we will examine equation (1) for integer solutions.

Case 1: [tex]z= 0[/tex]

If  then equation (1) becomes:

[tex]3x^2 - 9x &= -9 \quad \text{(1a)} \[/tex]

[tex]3x(x-3) &= -9[/tex]

Since we are looking for integer solutions, 3x and x-3 must have opposite signs. The possible pairs of factors of -9 with opposite signs are (3,-3) and (-3,3). So we have two possible sets of equations to solve:

The discriminant is negative, there are no integer solutions. Therefore, there are no integer solutions for the original system of equations when [tex]z \neq 0.[/tex]

In conclusion, the integer solutions of the given system of equations are [tex]$(x, y, z) = (1, 2, 0)$ and $(x, y, z) = (-1, 4, 0)$.[/tex]

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The correct answer is B. The spread of the data distribution for Lake Mockingbird is about 40% greater than the spread for Lake Warbler.

What is the data distribution?

The data distribution refers to the pattern of the data values in a dataset. It describes how the data is spread out, including the range of values, the shape of the distribution, and any clustering or gaps in the data. The data distribution can be described using various statistical measures, such as the mean, median, and standard deviation.

The correct answer to the first question is B: "The spread of the data distribution for Lake Mockingbird is about 40% greater than the spread for Lake Warbler."

For the second question, the statement that is NOT true about the data is B: "The distribution for Lake Mockingbird shows a center that is 3 inches greater than the center of the distribution for Lake Warbler."

hence, The correct answer is B. The spread of the data distribution for Lake Mockingbird is about 40% greater than the spread for Lake Warbler.

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The value of the equation are 1. (-2√3 + 2)(√3 - 5) = -16 + 8√3 2. (5 - 4√5)(-2 + √5) = -30 + 21√. 3. (-2 - 3√5)(5 - √5) = -5 - 17√5. 4. (√5 - √3)(√5 + √3) = 2.

An expression is a mathematical sentence without the equal sign that can include variables, operators, and integers. Although it can be appraised or simplified, there isn't a single perfect answer. An expression is, for instance, 3x + 2y.

A mathematical statement that has an equal sign and expresses the equivalence of two expressions is called an equation, on the other hand. To determine the values of variables that meet an equality, equations can be solved. One equation is 3x + 2y = 7, for instance.

1. Multiplying (-2√3 + 2)(√3 - 5), we get:

= -2√3 × √3 + (-2√3 × -5) + (2 × √3) + (2 × -5)

= -2√(3 × 3) + 10√3 - 2√3 - 10

= -2(3) + 8√3 - 10

= -16 + 8√3

Therefore, (-2√3 + 2)(√3 - 5) = -16 + 8√3.

2. Multiplying (5 - 4√5)(-2 + √5), we get:

= 5(-2) + 5√5 + (-4√5)(-2) + (-4√5)(√5)

= -10 + 13√5 + 8√5 - 4(5)

= -30 + 21√5

Therefore, (5 - 4√5)(-2 + √5) = -30 + 21√5.

3. Multiplying (-2 - 3√5)(5 - √5), we get:

= (-2 × 5) + (-2 × √5) + (-3√5 × 5) + (-3√5 × -√5)

= -10 - 2√5 - 15√5 + 3(5)

= -5 - 17√5

Therefore, (-2 - 3√5)(5 - √5) = -5 - 17√5.

4. Multiplying (√5 - √3)(√5 + √3), we get:

= (√5 × √5) - (√3 × √3)

= 5 - 3

= 2

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Answer:

k+5

Step-by-step explanation:

k= Elliot

Victoria is 5 years older than Elliot

=k+5

a) 40 seconds is hypothesized mean b) mean time to solve problem by UBC students = 40 sec is null hypothesis c) Alternative hypothesis is time taken is different from 40 sec d) t = -2.353 h) 2% sample mean

Part a) The following variables are significant to this hypothesis test:

B. The null hypothesis is based on the assumption that it will take healthy Canadian adults an average of 40 seconds to solve the logic puzzle.

D. The test statistic is calculated using the sample mean, which is the average time it took the 80 UBC students to solve the logic puzzle.

D. Based on our sample data, we wish to determine the mean time it takes for all UBC students to complete the logic problem.

Part b) The null hypothesis would be that it took UBC students an average of 40 seconds to solve the logic puzzle.

The alternate hypothesis (part c) is that students at UBC take longer than 40 seconds on average to answer the logic puzzle (two-sided alternative).

Part d) You can compute the test statistic as:

t = [tex]\sqrt{sample size} / (sample standard deviation / hypothesised mean) / (sample mean - hypothesised mean)[/tex]

[tex]t = (36 - 40) / (17 / \sqrt{80} )[/tex]

t = -2.353

Part e) The normal distribution can be used to approximate the sampling distribution of the test statistic because the sample size is high (n = 80).

Part f) If we reject the null hypothesis, we can draw the conclusion that there is enough evidence to support the idea that UBC students took longer on average than healthy adult Canadians to solve the logic puzzle.

Part g) It's feasible that we are committing a Type I error if we determine that UBC students perform on average better than healthy adult Canadians (rejecting the null hypothesis when it is actually true).

Part h) If the null hypothesis is correct, a p-value of 0.02 indicates that there is a 0.02 chance of receiving a sample mean that is as severe as the one we observed (or more extreme). In other words, there is only a 2% probability of observing a sample mean that is as different from 40 seconds (or more different) as the one we obtained, if the true mean time taken to solve the logic problem by all UBC students is 40 seconds. Hence, at a significance level of 0.05 but not at a significance level of 0.01 we would reject the null hypothesis.

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