vector v has components of 9,6 determine the angle, Ф, in degrees , that vector v makes with the x-axis

The period of the trigonometric function in this problem is given as follows:

A) 540º.

The standard definition of the sine function is given as follows:

y = Asin(B(x - C)) + D.

For the tangent function, we have that it is similar to the sine function, that we use tan() instead of sin().

For which the parameters are given as follows:

The coefficient B for the equation is given as follows:

B = 2/3.

Hence the period of the function is given as follows:

2π/(2/3) = 3π = 540º.

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The equation of the circle with center (-4, 4) and passing through (-2, 4) is [tex](x + 4)^2 + (y - 4)^2 = 4.[/tex]

We have,

To determine the equation of a circle, we need the center coordinates and the radius. The center coordinates are given as (-4, 4), and we have a point on the circle as (-2, 4).

The distance between the center (-4, 4) and the point on the circle (-2, 4) represents the radius of the circle.

Using the distance formula.

[tex]radius = √[(x_2 - x_1)^2 + (y_2 - y_1)^2]\\= \sqrt{(-2 - (-4))^2 + (4 - 4)^2}\\= \sqrt{2^2 + 0^2}\\= \sqrt{4}\\= 2[/tex]

Now that we have the center coordinates (-4, 4) and the radius 2, we can write the equation of the circle in standard form:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

Substituting the values:

[tex](x - (-4))^2 + (y - 4)^2 = 2^2\\(x + 4)^2 + (y - 4)^2 = 4[/tex]

Therefore,

The equation of the circle with center (-4, 4) and passing through (-2, 4) is [tex](x + 4)^2 + (y - 4)^2 = 4.[/tex]

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The area of the logo 1 in square feet is  38.465 ft²

Remember that the area of a circle of radius R is given by the formula:

A = 3.14*R²

Here we can see that the radius of the circle is (1/2 in), but we wat the are in square feet, so let's write that in feets.

1 in = 7ft, then:

(1/2 in) = (7/2 ft) = 3.5 ft.

Replace that in the formula for the area:

A = 3.14*(3.5 ft)²

A = 38.465 ft²

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Answer:

Kendra's Tea Shop served 87 caffeinated teas and 13 decaffeinated teas. This means that 87 out of 100 teas served were caffeinated. Therefore, 87% of the teas served were caffeinated.

The probability that this song will be played on exactly 0 days out of 7 days, if The probability that a particular song is played is 0.23 is 0.008.

We have,

A combination is a choice of items from a group of different items, where the order of the choices is irrelevant.

Given:

The probability that a particular song is played is 0.23,

As can be seen that the problem is of combination, so we have to choose 5 out of 7,

Calculate the combination as shown below,

⁷C₅ = 7! / (5! × 2!) = 7 × 6 / 2

⁷C₅ = 7 × 6 / 2

⁷C₅ = 21

Calculate the probability as shown below,

P = ⁷C₅  × (0.23)⁵ × (0.77)²

P = 0.008

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complete question;

During a single day at radio station WMZH, the probability that a particular song is played is 0.23. What is the probability that this song will be played on exactly 0 days out of 7 days? Round your answer to the nearest thousandth.

The variables in this problem are classified as follows:

In the context of this problem, the number of siblings is the only discrete variable, as is the only variable that cannot assume decimal values.

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To determine the optimal number of matted and unmatted pictures to maximize the company's profit, we can set up a linear programming problem.

Let's denote:

- x: the number of matted pictures

- y: the number of unmatted pictures

The objective is to maximize the profit, which can be expressed as:

Profit = 40x + 35y

We need to consider the following constraints:

1) The number of pictures completed each day cannot exceed 36:

x + y ≤ 36

2) The total man-hours of labor cannot exceed 80:

4x + 2y ≤ 80

3) The number of pictures cannot be negative:

x, y ≥ 0

Now we can solve this linear programming problem to find the optimal values for x and y.

First, let's graph the feasible region defined by the constraints:

```

x + y ≤ 36

4x + 2y ≤ 80

x, y ≥ 0

```

The feasible region is the area of the graph that satisfies all the constraints.

Next, we need to evaluate the objective function (Profit = 40x + 35y) at the vertices of the feasible region to find the maximum profit.

We can use different methods such as the corner-point method or the simplex method to determine the vertices and evaluate the profit at each vertex.

Thus, once we find the vertex that yields the maximum profit, we will have the optimal values for x and y.

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Candidate A would win the election using the plurality method.

According to the given preference schedule, the number of votes and the corresponding preferences are as follows:

Candidate A: 15 (1st preference: A, 2nd preference: D, 3rd preference: B)

Candidate B: 11 (1st preference: D, 2nd preference: C, 3rd preference: A)

Candidate C: 9 (1st preference: B, 2nd preference: C, 3rd preference: A)

Candidate D: 6 (1st preference: C, 2nd preference: D, 3rd preference: A)

Candidate E: 2 (1st preference: C, 2nd preference: D)

To determine the winner using the plurality method, we look at the candidate with the highest number of first preference votes.

In this case, Candidate A has 15 first preference votes, which is the highest.

Therefore, Candidate A would win the election using the plurality method.

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The volume of the two prisms compares that the volume of prism B will double.

We are given that side length of the cube measured 18 inches in length. She built another prism (Prism B) with the same dimensions as the cube, except she doubled its height.

When the prism is such that if we slice it horizontally at any height smaller or equal to its original height, the cross-section is same as its base, then its volume is:

V = B x h

So, the volume of the two prism A= V = B x h

V = 18 x h = 18h

the volume of the two prism B= V = B x h

V = 18 x 2h = 36h

So, the volume of prism B will double thus the correct option is B.

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The complete question is;

Anna built a prism (Prism A) out of a cube of wood. The side length of the cube measured 18 inches in length. Anna built another prism (Prism B) with the same dimensions as the cube, except she doubled its height.

How does the volume of the two prisms compare?

The volume of prism B will triple.

The volume of prism B will double.

The volume of prism B will decrease.

The volume of prism B will be cut in half.

Answer:

∠CDF = 48°

Step-by-step explanation:

∠CDE = ∠EDF + ∠CDF

Given that,

∠CDE = 114°

∠EDF = 66°

So, to find the value of ∠CDF, you have to subtract the value of ∠EDF from ∠CDE.

∠CDF = ∠CDE - ∠EDF

∠CDF = 114 - 66

∠CDF = 48°

The output of the exponential function when x = 5 is given as follows:

f(5) = 96.

An exponential function has the definition presented as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

The parameter values for this problem are given as follows:

Hence the function is given as follows:

[tex]f(x) = 3(2)^x[/tex]

The numeric value at x = 5 is given as follows:

[tex]f(5) = 3(5)^x = 96[/tex]

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The rocket's maximum height is 800 feet. It reached its maximum height at 5 seconds after launch.

To solve this problem, we need to find the vertex of the parabola represented by the equation Y= -16t^2+160t. The vertex of a parabola is the point where the parabola changes direction, from increasing to decreasing or vice versa.

The vertex of the parabola is given by the following formula:

(-b/2a, c - b^2/4a)

In this case, the value of b is 160 and the value of a is -16. Plugging these values into the formula, we get the following:

(-160/2(-16), 800 - 160^2/4(-16))

(5, 800)

Therefore, the rocket reached its maximum height at 5 seconds after launch. The maximum height is 800 feet.

Answer:

Step-by-step explanation:express the 15% as a fraction divided by 100.Multiply the result by $9000.

The result is $ 1350

Subtract the result from new price of the car.$9000-$1350

=$7650

2/5 of the frogs in that portion of the South American rainforest are not poisonous.

On the off chance that 3/5 of the frogs in a rainforest in South America are poisonous, at that point, the remaining division speaks to the frogs that are not poisonous.

To discover this division, we subtract the division of poisonous frogs from 1 (which speaks to the complete):

1 - 3/5 = 5/5 - 3/5 = 2/5

Hence, 2/5 of the frogs in that portion of the rainforest are not poisonous. This fraction represents the parcel of frogs that don't have poisonous characteristics.

It is important to note that this calculation expects that all frogs within the rainforest are either poisonous or notpoisonous, and there are no other conceivable outcomes or middle states.

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Answer:

B. 11

Step-by-step explanation:

√380.13/pi = 10.99, Round: 11

Does the relation represent a function: C. Yes, because for each input there is exactly one output.

In Mathematics and Geometry, a function can be defined as any mathematical equation which is typically used to define and represent a relationship that exists between two or more variables such as an ordered pair, points on a graph or table.

Based on the mapping diagram, we can reasonably infer and logically deduce that the relation represent a function because the input values (domain, x-value, or independent values) are uniquely mapped to the output values (range, y-value or dependent values).

In this context, we can reasonably infer and logically deduce that the relation represent a function because for each input (independent value) there is exactly one output (dependent variable).

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The rigid transformations that can take AEFD to CFEB are translation, rotation, and reflection.

To describe the rigid transformations that take polygon AEFD to CFEB, we need to identify the transformations that preserve the shape and size of the polygon. Here are some possibilities:

Translation: A translation involves moving the entire polygon without changing its orientation or shape. If we shift polygon AEFD to the right, it will align with polygon CFEB. Therefore, translation is one way to achieve this transformation.

Rotation: If we rotate polygon AEFD around a fixed point, such as the center of the polygon or a vertex, by a certain angle, it can align with polygon CFEB. A rotation preserves the shape and size of the polygon.

Reflection: A reflection involves flipping the polygon across a line, resulting in a mirror image. If we reflect polygon AEFD across a line of reflection, it can match polygon CFEB.

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Answer:

d

Step-by-step explanation:

To calculate the average budget across the four quarters, we need to add the budget for each quarter and divide by 4:

Average budget = (5623 + 5892 + 6382 + 5325) / 4 = 5805.5

Next year's estimated budget is £6,032 per quarter.

To calculate the percentage difference, we can use the following formula:

Percentage difference = (new value - old value) / old value x 100%

Percentage difference = (6032 - 5805.5) / 5805.5 x 100% = 3.9%

Therefore, the answer is (d) 3.9%.

Answer:

360

Step-by-step explanation:

80*5=400 and .25*400=100 so it costs 300 for five nights without tax, and adding on the tax raises the cost to 60 (300+(.2*300)=360)

The measure of each missing indicated side of the triangle would be given as follows;

1.) X = 2.7

2.) X = 15.2

For question 1.)

Using the sine formula such as given below;

a/sinA = b/sin B

where ;

a = X

A = 27°

b = 6

B = 90°

That is;

X/sin27° = 6/sin90°

X = 6×0.453990499/1

= 2.7

For question 2.)

a/sinA = b/sin B

where ;

a = X

A = 47.4°

b = 14

B = 180-(47.4+90)

= 180-137.4

= 42.6

That is;

X/sin47.4° = 14/sin42.6°

X = 14×0.736097087/0.676875969

= 10.305359218/0.676875969

= 15.2

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The correct solution is,

D. Mean = 50.4,

Variance = 27.2,

Standard deviation = 5.2.

Now, Formula for the mean, variance, and standard deviation of the given values,

Mean (μ) = (Σx) / n

Variance (σ) = (Σ(x-μ)) / n

Standard deviation (σ) = sqrt(σ)

where: Σx = sum of the values

Σ(x-μ)² = sum of the squared differences between each value and the mean

n = number of values

Substituting the given values into these formulas, we get:

Mean (μ) = (50 + 46 + 53 + 51 + 52) / 5

Mean (μ) ≈ 50.4

Variance (σ) = [(14 - 50.4)² + (50 - 50.4)² + (-0.4 - 50.4)² + ... + (2.6 - 50.4)] / 13

Variance (σ) ≈ 27.2

Standard deviation (σ) = √(27.2)

Standard deviation (σ) ≈ 5.2

Therefore, the correct answer is,

D. Mean = 50.4,

Variance = 27.2,

Standard deviation = 5.2.

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Answer:

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

Given:

Convert the interest rate to a decimal:

Convert the time from months to years:

Now, we can calculate the simple interest using the formula:

Finally, add the interest to the principal to find the amount due:

Susan's amount due for the loan is $1047.50.

The simple interest amount of Susan for time of 8 months is A = $ 1047.50

Given data ,

To calculate the amount due, we need to consider the principal amount borrowed, the interest rate, and the time period.

Principal (P) = $1000

Time (t) = 8 months

Interest rate (r) = 7 1/8% per annum

First, we need to convert the interest rate from a percentage to a decimal. To do this, we divide the given rate by 100:

r = 7 1/8% = 7.125% = 7.125/100 = 0.07125 (decimal)

Next, we can calculate the simple interest using the formula:

Simple Interest (I) = Prt

I = $1000 x 0.07125 x (8/12)

I = $1000 x 0.07125 x (2/3)

I = $47.50

Finally, to find the amount due, we add the principal amount to the simple interest:

Amount Due = Principal + Simple Interest

Amount Due = $1000 + $47.50

Amount Due = $ 1047.50

Hence , the amount is A = $ 1047.50

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Answer:

  125/384 ≈ 0.32552

Step-by-step explanation:

You want the area between the curves y = 5x and y = 8x².

The difference between the curves is ...

  f(x) = 5x -8x² = x(5 -8x)

This difference is zero when ...

  x = 0

  5 -8x = 0   ⇒   x = 5/8

The area will be the integral of f(x) with the limits 0 and 5/8:

  [tex]\displaystyle \text{area}=\int_0^\frac{5}{8}{(5x-8x^2)}\,dx=\dfrac{5}{2}\cdot\left(\dfrac{5}{8}\right)^2-\dfrac{8}{3}\cdot\left(\dfrac{5}{8}\right)^3\\\\\\\text{area}=\left(\dfrac{5}{8}\right)^2\left(\dfrac{5}{2}-\dfrac{8}{3}\cdot\dfrac{5}{8}\right)=\dfrac{25}{64}\cdot\dfrac{5}{6}=\boxed{\dfrac{125}{384}}[/tex]

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Answer:

The answer is the third option

Step-by-step explanation:

When an exponent is raised to the power of another exponent, both exponents are multiplied.
Recall that a number without an exponent is thought to be raised to the power of 1.

So after multiplying the exponents of all of the variables by 4, we are left with a solution identical to the third option.

Answer: [tex]\sf\$6.48[/tex]

Step-by-step explanation:

If a six-pack of cola is sold for $1.50, then the price per can is:

[tex]\sf\implies\$1.50 \div 6 = \$0.25[/tex]

A 24 pack of cola contains 24 cans, so the total cost of the 24 pack is:

[tex]\sf\implies 24 \times \$0.25 = \$6.00[/tex]

The sales tax is 8%, so the tax on the purchase is:

[tex]\sf\implies \dfrac{8}{100} \times \$6.00 = \$0.48[/tex]

Therefore, the total charge including sales tax is:

[tex]\sf\implies\$6.00 + \$0.48 = \$6.48[/tex]

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Answer:

Step-by-step explanation:

Ok so, as given in the table, the cost of the 3rd tank is 800$, we can thus determine the cost of 1 cubic inch for a tank and use that to determine the cost of the other tanks.

[tex]volume =L\times W\times H\\=24\times 24\times 24\\=13824 in^3[/tex]

thus, to compute the cost of one cubic inch, we can divide the cost by the volume of the 3rd tank (in cubic inches)

[tex]\frac{800}{13824}=0.0579[/tex] [tex]usd/in^3[/tex]

now, we can determine the dimensions of the second tank that will make it cost 150$

[tex]0.0579\times 18\times W\times 24=150[/tex]

[tex]W=\frac{150}{0.0579\times 18\times 24} =6 in.[/tex]

Now to determine the cost of the first tank, we can multiply its volume by the cost per cubic inch:

[tex]cost=0.0579\times36\times 36\times 36=2700[/tex]$

As of question B, the cost will increase as the width increases.

For Question C, we can find the volume of the sphere by the formula:

[tex]volume=\frac{4}{3}\pi r^3 =\frac{4}{3}\pi \times 24^3=57905 in^3[/tex]

To find the cost of that tank, we just multiply its volume by the cost per unit volume:

[tex]cost=57905\times 0.0579=3352[/tex]$ (roughly)

Answer:

Step-by-step explanation: