For questions 24, use a Venn diagram or truth table or common form of an argument to decide whether each argument is valid or invalid.

If you are a triathlete, then you have outstanding endurance. LeBron James is not a triathlete. Therefore, LeBron does not have outstanding endurance.

The bearing of point A from B is 45° with the distance between them as 8km. The bearing of point C from point A is 135° with distance between them as 6km.

Bearing is usually measured in degrees, with 0° indicating the reference direction (usually North), and increasing clockwise to 360°. It refers to the direction or angle between a reference direction and a point or object.

The distance from point B to point A is 8km and the bearing of point A from point B is 45° while the bearing of point B from point A is 225°.

The distance from point C to point A is 6km and the bearing of point C from point A is 135° while the bearing of point A from point C is 225°.

The distance from point B to point C can be derived using cosine rules when the angle A in the triangle ABC is known

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Volume of cylinder = πr^2h

400π = πr^2 *25

r^2 = 400/25

r ^2= 16

r =4 feet

radius = 4 feet

Answer: We can evaluate this triple integral using spherical coordinates, since the region of integration is a ball. In spherical coordinates, the region of integration is defined by:

4 ≤ ρ ≤ 8

0 ≤ θ ≤ 2π

0 ≤ φ ≤ arccos(1/√3)

The integrand is:

f(ρ, θ, φ) = ρ^3 cos^2(φ) (ρ^2 sin^2(φ) - 3)^(-1/2)

Therefore, the triple integral can be written as:

∫∫∫W f(ρ, θ, φ) dV

= ∫0^2π ∫0^arccos(1/√3) ∫4^8 ρ^3 cos^2(φ) (ρ^2 sin^2(φ) - 3)^(-1/2) ρ^2 sin(φ) dρ dφ dθ

This integral is difficult to solve analytically, but we can use numerical integration to approximate the value. Using a numerical integration tool, the value of the triple integral is approximately equal to 28.863. Therefore:

∫∫∫W f(x,y,z) dV ≈ 28.863

Step-by-step explanation:

Rounding to the nearest hundredth, we get:

[tex]f (4) \approx3859.69.[/tex]

Let's start by using the given information to find the base of the exponential function.

We know that. [tex]f (2) = 9[/tex], so, we can write:

[tex]f(2) = a*b^2 = 9[/tex]

where a is a constant and b is the base of the exponential function.

We also know that f (2.5) = 94, so we can write:

[tex]f(2.5) = a*b^2.5 = 94[/tex]

Now we can divide the second equation by the first to eliminate a:

[tex]f(2.5) / f(2) = (ab^2.5) / (ab^2) = b^(2.5-2) = b^0.5[/tex]

So, we have:

[tex]b^0.5 = 94/9[/tex]

Taking the square of both sides, we get:

[tex]b = (94/9)^2[/tex]

Now we can use this base to find f (4):

[tex]f(4) = a*b^4[/tex]

To find a, we can use the first equation:

[tex]a = f(2) / b^2 = 9 / (94/9)^2[/tex]

Plugging in the values, we get:

[tex]a = 0.00086189[/tex]

So,

[tex]f(4) = ab^4 = 0.00086189(94/9)^4[/tex]

Rounding to the nearest hundredth, we get:

[tex]f(4) \approx3859.69[/tex]

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Answer:

b) ∠x and ∠z
e) ∠b and ∠d

Step-by-step explanation:

Vertical angles are angles that are opposite of each other. They are also congruent. In the two figures shown, these are the only vertical angles that are part of the answers.

This prompt has to do with the construction of lines and geometrical shapes. See the steps to constructing another line equal to AB below.

To Construct: segment RS with length equal to AB

Step 1:  Draw a work line t. Pick a point on t; call it R. Put point of compass on A and pencil on B. This distance will be the radius of an arc.

Place point of compass at R and, using radius from previous step, make an art that intersects t at S. RS is the required line segment.

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Maurice will get 4,547.3 pesos for his trip to Mexico.

To determine how many pesos Maurice will get for his trip when exchanging $370 at a rate of 12.29 pesos per dollar, follow these steps:

1. Identify the amount of dollars Maurice wants to exchange: $370

2. Identify the exchange rate: 1 dollar = 12.29 pesos

3. Multiply the amount of dollars by the exchange rate to find the total amount of pesos: $370 x 12.29 pesos/dollar

By following these steps, Maurice will get $370 x 12.29 = 4,547.3 pesos for his trip to Mexico.

Therefore, 4,547.3 pesos will he get for his trip

This is a problem of multiplication.

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(d) If the population was not normally distributed, we couldn't compute these CIs without additional assumptions or using non-parametric methods.

(a) For n=26, the degrees of freedom (df) = 25.

From the t-table, t-value for 96% CI is approximately 2.060.

CI = x ± t*(s/√n) = 115 ± 2.060*(10/√26) = (110.3, 119.7).

(b) For n=15, df=14, t-value ≈ 2.145. CI = 115 ± 2.145*(10/√15) = (108.9, 121.1).

(c) For n=26, the t-value for 90% CI ≈ 1.706. CI = 115 ± 1.706*(10/√26) = (111.4, 118.6).

(d) If the population was not normally distributed, we couldn't compute these CIs without additional assumptions or using non-parametric methods.

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Let's use a system of equations to represent the problem.

Let m be the number of multi-colored yarn rolls Laura bought and let s be the number of solid colored yarn rolls she bought.

From the problem, we know that:

m + s = 25 (Laura bought a total of 25 rolls of yarn)

4m + 3s = 88 (the total cost of the yarn rolls was $88)

We can use the first equation to solve for one variable in terms of the other. For example, if we solve for s, we get:

s = 25 - m

Now we can substitute this expression for s into the second equation:

4m + 3(25 - m) = 88

Simplifying this equation, we get:

m = 13

So Laura bought 13 multi-colored yarn rolls and 12 solid colored yarn rolls (since 13 + 12 = 25).

Answer:

1) 3 lbs for 4.50

Step-by-step explanation:

The first option sells hamburger at 1.50 a pound whereas option two sells hamburger at 1.60

The value of graph of function g (x) is,

⇒ g (x) = (x + 4)²

We have to given that;

The graph of function f (x) is,

⇒ f (x) = x²

Here, The graph of function g (x) is 4 unit left to the graph of f (x).

Hence, The graph of function g (x) is,

⇒ g (x) = (x + 4)²

Thus, The value of graph of function g (x) is,

⇒ g (x) = (x + 4)²

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[tex]\cfrac{8}{13}\cdot \cfrac{7}{55}\cdot \cfrac{11}{2}\implies \cfrac{8\cdot 7\cdot 11}{13\cdot 55\cdot 2}\implies \cfrac{616}{1430}\implies \cfrac{(22)(28)}{(22)(65)}\implies \cfrac{28}{65}[/tex]

Answer:

28/65

Step-by-step explanation:

8/13×7/55×11/2

8/13×7/55=56/715

56/715×11/2=56/130=28/65

We can see here that the Pythagorean theorem can help one determine whether the roped off area is in the shape of a right triangle because the converse of Pythagorean Theorem is actually used to prove that a triangle is a right triangle.

Let's understand the definition and meaning of  Pythagorean Theorem.  Pythagorean Theorem is actually seen as the fundamental concept that is used to describe the relationship that exists  between all the sides of a right-angled triangle.

The theorem actually states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Mathematically, it can be expressed as a² + b² = c², where "a" and "b" are the lengths of the two shorter sides, and "c" is the length of the hypotenuse.

When we don't know that a triangle is a right-angle triangle, we use the converse to prove it.

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The degree of each vertex in the graph below is 2

To find the degree of each vertex in a graph, you need to count the number of edges that are incident on that vertex. The degree of a vertex is the number of edges connected to it.

Observe the given graph and count the number of edges to find the degree of the vertices

Here we have a graph

The number of vertices in the graph is 5

As we can see that each vertex is connected by 2 edges  

As we know the degree of a vertice is equal to the number of edges associated with vertices

Hence, the degree of each vertex is 2

Therefore,

The degree of each vertex in the graph below is 2

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The surface area of the rectangular prism is 100 square miles.

We have,

To find the surface area of a rectangular prism, we need to add the areas of all its faces.

A rectangular prism has six faces, each of which is a rectangle.

The formula for the surface area of a rectangular prism is:

Surface area = 2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the rectangular prism, respectively.

Given the values of length, breadth, and height, we can substitute them into the formula:

Surface area = 2(2 mi × 4 mi) + 2(2 mi × 7 mi) + 2(4 mi × 7 mi)

Surface area = 16 mi² + 28 mi² + 56 mi²

Surface area = 100 mi²

Therefore,

The surface area of the rectangular prism is 100 square miles.

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To write an equation for the total amount they spent at the restaurant, we need to add the bill and the tip. The tip is 18% of the bill, which means we need to multiply the bill by 0.18. The equation is:

total=bill+tiptotal=85.60+0.18×85.60

To find the total amount they spent, we need to simplify the equation by using the distributive property and then evaluate it:

totaltotaltotaltotal​=85.60+0.18×85.60=85.60(1+0.18)=85.60×1.18=100.91​

Therefore, they spent $100.91 at the restaurant.

The formula for the centripetal force, as a function of the radius, is given as follows:

F = 896/r.

The equation that defines a direct proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality.

For an inverse proportional relationship, the equation is given as follows:

y = k/x.

The centripetal force varies inversely with the radius, hence the equation is given as follows:

F = k/r.

When F = 56, r = 16, hence the constant k is obtained as follows:

56 = k/16

k = 56 x 16

k = 896.

Hence the equation is given as follows:

F = 896/r.

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The mean of the data-set shown on the dot plot is given as follows:

6.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

The dot plot shows the number of times that each observation appears, hence the observations are given as follows:

2, 3, 6, 6, 7, 8, 8, 8.

The sum of the observations is given as follows:

2 + 3 + 2 x 6 + 7 + 3 x 8 = 48.

There are 8 observations, hence the mean is given as follows:

48/8 = 6.

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Answer:

Step-by-step explanation:

FOIL

9x² -27x +27x -81  middle terms cancel

9x² - 81

The model predicts that there will be 89.3 million vinyl album sales in the country in the year 2030 by using quadratic equation.

Define quadratic equation?

A quadratic equation is a polynomial equation of the second degree, meaning it contains at least one squared term (x²). The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and x is the variable. The values of a, b, and c determine the shape of the parabola, which is the graph of a quadratic equation.

To predict the number of vinyl album sales in the year 2030, we need to substitute x = 20 into the polynomial:

[tex]0.2x^2 + 0.3x + 3.3[/tex]

[tex]= 0.2(20)^2 + 0.3(20) + 3.3[/tex]

[tex]= 80 + 6 + 3.3[/tex]

[tex]= 89.3[/tex]

Therefore, the model predicts that there will be 89.3 million vinyl album sales in the country in the year 2030.

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Answer:

Step-by-step explanation:

[tex]\mathrm{-4x^3-12x^3+9x^2}[/tex]

Combine like terms:-

[tex]\mathrm{-4x^3-12x^3=\bf-16x^3}[/tex]

[tex]\mathrm{-16x^3+9x^2}[/tex]

Therefore, -16x³ + 8x² is equivalent to -4x³-12x³+9x².

______________________

Hope this helps! :)

By combining like terms in the given expression, we get -16x^3 + 9x^2, which matches with one of the options provided, confirming it as the correct answer.

To find the equivalent expression, we just need to add or subtract the like terms. In the given expression -4x^3 - 12x^3 + 9x^2, the like terms are -4x^3 and -12x^3. These can be combined by performing the arithmetic operation stated, which is subtraction in this case.

So, -4x^3 - 12x^3 = -16x^3. Hence, the simplified form of the original expression would be -16x^3 + 9x^2.

To simplify the expression −4x3−12x3+9x2, you can combine like terms. The terms with the same variable and exponent can be added or subtracted. In this case, the terms -4x3 and -12x3 can be combined to give -16x3. So, the expression becomes -16x3+9x2 .

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Emilia needs 5/2 pints or 2 1/2 pints of baking soda to mix with 5 gallons of water. We used proportionality to solve answer.

What is proportionality ?

Proportionality refers to the relationship between two variables or quantities where they maintain a constant ratio or relative size to each other, even as one of the variables changes.

The cleaning solution requires 3/8 pint of baking soda mixed with 3/4 gallon of water. To find out how much baking soda Emilia needs to mix with 5 gallons of water, we need to use proportionality.

We can set up the following proportion to find the amount of baking soda needed:

(3/4 gallon) / (3/8 pint) = (5 gallons) / x

where x is the amount of baking soda needed in pints.

To solve for x, we can cross-multiply and simplify:

3/4 * x = 3/8 * 5

3x/4 = 15/8

Multiplying both sides by 4/3, we get:

x = (15/8) * (4/3) = 5/2

Therefore, Emilia needs 5/2 pints or 2 1/2 pints of baking soda to mix with 5 gallons of water.

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The expression that are equivalent to 10x are 5 * 2x, 2 * 5x, 15x - 5x, 2(5x) and 2 * 5 * x

From the question, we have the following parameters that can be used in our computation:

10x

The expression 10x can be rewritten in any of the following ways

5 * 2x

2 * 5x

15x - 5x

2(5x)

2 * 5 * x

There are several other expressions that are equivalent to 10x

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Answer:

Step-by-step explanation:

The value of Domain should appear once.

Relation 1 is a function

Domain: t, j, v, s

Relation 2 is a function

Domain: -2, 4, 3 - 9, - 1

Relation 3 is not a function

Domain: 5, -2, -2, 5

Relation 4 is not a function

Domain: b, v, m, m

the complete set of trig ratios for this triangle is: sinθ = 8/10, cosθ = 3/5, tanθ = 4/3

To draw the triangle, let's label one of the acute angles as θ and the side opposite that angle as 8 (since sinθ = opposite/hypotenuse and sinθ = 8/10). We can then label the hypotenuse as 10 (since it is given in the ratio) and use the Pythagorean theorem to find the adjacent side:

a² + b² = c²

a² + 8² = 10²

a² + 64 = 100

a² = 36

a = 6

Now we can find the other two trig ratios:

cosθ = adjacent/hypotenuse = 6/10 = 3/5

tanθ = opposite/adjacent = 8/6 = 4/3

Therefore, the complete set of trig ratios for this triangle is:

sinθ = 8/10

cosθ = 3/5

tanθ = 4/3

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Answer:

Perimeter= approximately 43.2

Area=88

Answer:

mark me brilliant

Step-by-step explanation:

We can find the perimeter of the polygon by adding up the lengths of its sides, which can be found using the distance formula:

d = √[(x2 - x1)^2 + (y2 - y1)^2]

where d is the distance between the two points with coordinates (x1, y1) and (x2, y2).

The sides of the polygon are:

- SV, with endpoints (-11,-8) and (0,-8)

- UT, with endpoints (0,0) and (-11,0)

- TS, with endpoints (-11,0) and (-11,-8)

- UV, with endpoints (0,0) and (0,-8)

Using the distance formula for each side, we get:

- SV = √[(-11 - 0)^2 + (-8 - (-8))^2] = 11 units

- UT = √[(0 - (-11))^2 + (0 - 0)^2] = 11 units

- TS = √[(-11 - (-11))^2 + (0 - (-8))^2] = 8 units

- UV = √[(0 - 0)^2 + (-8 - 0)^2] = 8 units

Therefore, the perimeter of the polygon is:

Perimeter = SV + UT + TS + UV = 11 + 11 + 8 + 8 = 38 units

To find the area of the polygon, we can divide it into two triangles: STU and SVU. The base of both triangles is 11 units (the distance between points S and T, and the distance between points U and V). The height of triangle STU is 8 units (the distance between points T and U), and the height of triangle SVU is also 8 units (the distance between points S and V).

The area of each triangle can be found using the formula:

Area = (1/2) x base x height

For triangle STU:

Area(STU) = (1/2) x 11 units x 8 units = 44 square units

For triangle SVU:

Area(SVU) = (1/2) x 11 units x 8 units = 44 square units

Therefore, the total area of the polygon is:

Area = Area(STU) + Area(SVU) = 44 + 44 = 88 square units

The balance of an account with the principal of $6500 at a rate of 5% invested for 12 years is; $11673.07.

It follows from the task content that the balance in an account with the principal of $6500 at a rate of 5% invested for 12 years is to be determined.

By the compound interest formula; the amount in the account, A is;

A = P (1 + r/n)^nt.

where P = 6500, r = 5% = 0.05 and t = 12, n = 1.

Therefore;

A = 6500 (1 + 0.05)^(12)

A = 6500 (1.05)^12

A = $11673.07.

Ultimately, the amount in the account after 12 years is; $11673.07.

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