Please help me respond these two questions!!

To find the value of sin theta, we are given that theta is in the first quadrant and tan theta = 15/4. We will use the Pythagorean identity to find the value of sin theta. the value of sin theta is:sin θ = 15/17Answer: sin θ = 15/17

Pythagorean identity: sin²θ + cos²θ = 1We know that tan theta = 15/4, which means that: tan θ = sin θ / cos θ15/4 = sin θ / cos θRearranging the above equation, we get: sin θ = (15/4) cos θ ... (1)Now, we will use the Pythagorean identity to find the value of cos θ.cos²θ + sin²θ = 1Using the above identity, we can write: cos θ = √[1 - sin²θ]Substituting the value of cos θ in equation (1), we get:sin θ = (15/4) √[1 - sin²θ]Squaring both sides, we get: sin²θ = (225/16)(1 - sin²θ)Solving for sin²θ, we get: sin²θ + (225/16) sin²θ = 225/16(1 - sin²θ)sin²θ + (225/16) sin²θ = (225/16) - (225/16) sin²θ(289/16) sin²θ = 225/16sin²θ = (225/16) / (289/16)sin²θ = 225/289Taking the square root of both sides, we get:sin θ = ± 15/17Since theta is in the first quadrant, sin θ is positive. Therefore, the value of sin theta is:sin θ = 15/17Answer: sin θ = 15/17

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Answer:

35) x = 3 1/3

Step-by-step explanation:

for each of these parallelograms, the diagonals are congruent

in #35, DT = RT so you can set their expressions equal to each other

22 = 6x + 2

20 = 6x

20/6 = x

10/3 = x (simplified)

Answer:  c or d

Step-by-step explanation:

We can see from the table and the graph that the relationship is proportional. Also, the line passes through the origin

A relationship between two variables is said to be proportionate if it causes both of the variables' values to rise or fall by the same amount.

To know if the relationship is proportional we have to look at the table so that we can be able to see the movement of the values and thus know whether or not we can classify what we see as a proportional relationship.

If the relationship is proportional, then the increase would be by fixed amounts as shown in the graph.

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Answer:

$63 is the answer to this problem

The missing alphabet using logic in the puzzle is X.

To unlock the logic behind a puzzle, it is important to evaluate the given relationships in other to be sure of arriving at the right conclusion.

The reasoning behind the puzzle is that a given alphabet is followed by the fifth alphabet after it.

fifth alphabet after A is F

fifth alphabet after F is K

To solve for the missing alphabet after S, the fifth alphabet after S is X .

Hence, the missing alphabet is X .

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The Laplace Transform of f(t) isL{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                            = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...= (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

Given function is,f(t) ={ t, 0 < t < π π < t < 2π}

where f(t + 2 π) = f(t)

Let's take Laplace Transform of f(t)

                     L{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...f(t + 2π) = f(t)

∴ L{f(t + 2 π)} = L{f(t)}⇒ e^{2πs}L{f(t)} = L{f(t)}

     ⇒ [e^{2πs} − 1]L{f(t)} = 0L{f(t)} = 0

when e^{2πs} ≠ 1 ⇒ s ≠ 0

∴ The Laplace Transform of f(t) is

                       L{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                               = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...

                              = (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

The Laplace Transform of f(t) isL{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                            = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...= (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

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The two numbers are 7 and 8. The greater number of the two missing variables is 8.

To solve this problem, we will use the given information to create a system of equations. Let's define the two numbers as x and y. We are given:
1. x + y = 15
2. 4x - 3y = 4

We can solve this system of equations using substitution or elimination method. Here, we will use the substitution method. From equation 1, we can express y as:
y = 15 - x
Now, substitute this expression for y in equation 2:
4x - 3(15 - x) = 4
Distribute the -3:
4x - 45 + 3x = 4
Combine like terms:
7x = 49
Now, divide by 7:
x = 7
Now that we have found the value of x, we can find the value of y by substituting x back into the equation for y:
y = 15 - 7
y = 8

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The researcher makes decisions based on the results of the hypothesis test : d. The null hypothesis should not be rejected because 0.04 is greater than 0.01.

The correct decision for the researcher to make based on the results of the hypothesis test is d. The null hypothesis should not be rejected because 0.04 is greater than 0.01. The researcher's sample provides evidence that the proportion of left-handed professional golfers is less than the claimed value of 0.06, which supports rejecting the null hypothesis.

The p-value of 0.04 is greater than the significance level of 0.01, but this does not impact the decision as the decision is based on the comparison between the sample proportion and the claimed value.

The researcher should make the decision based on the comparison of the p-value with the significance level (alpha).
In this case, the significance level (alpha) is 0.01 and the p-value is 0.04.
Since the p-value (0.04) is greater than the significance level (0.01), the researcher should not reject the null hypothesis.
Therefore, the correct answer is:
d. The null hypothesis should not be rejected because 0.04 is greater than 0.01.

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Answer:

yes

Step-by-step explanation:

if i did the math right marcy should have enough

Answer:

C

Step-by-step explanation:

yards and feet would take to long, miles would be the most efficient

Answer:

You'll need to find the area first.

18ft x 25ft= 450ft

Area is 450ft.

Area divided by $6.00 = 75

The total cost is $75 dollar for the whole room flooring.

The total amount Julio spent on a salad and a container of yogurt in the form of note and coin is equal to $6.38.

To determine how much Julio spent while buying  a salad and a container of yogurt, we have to multiply the value of each notes into their quantity then add all of them.

Number of 25 cents coins = 4

⇒ 4×0.25 = 1.00

Number of 5 dollar note = 1

⇒ 1×5 = 5.00

Number of 10 cents coins = 3

⇒ 3×0.10=0.30

Number of 1 cents = 3

⇒ 3×0.01=0.03

Number of 5 cents = 1

⇒ 1×0.05=0.05

Julio spent = 1.00 + 5.00 + 0.30 + 0.03 + 0.05

                  = $6.38

Therefore, the total amount Julio spent on a salad and a container of yogurt in the form of note and coin is equal to $6.38.

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The complete question is :

Julio buys a salad and a container of yogurt. These bills and coins shown in attached image represent the cost of each item. How much did Julio spend in all?

The value of function, f(t) for L⁻¹ ( e−s /(s²+ 1)) is equals to sin( t - π ) u(t-π) .

The Laplace transform is the essential term of the given derivative function. Moreover, it comes with a real variable (t) for converting into complex function with variable (s). For ‘t’ ≥ 0, let ‘f(t)’ be given, the Laplace transform of ‘f(t)’, denoted by 'L{f(t)}' or ‘F(s)’ is definable with the equation:

\( L(f(t)) = F(s) = ₀∫^{ \infty } e⁻ˢᵗ f(t)dt\)

we have L⁻¹ ( e−s /(s²+ 1))

Now, L⁻¹ (1 /(s²+ 1)) = sin(t)

so, L⁻¹ ( e−s /(s²+ 1)) = sin( t - π ) u(t-π)

where u(t-π) is unit of step function.

so, required function f(t) is sin( t - π ) u(t-π).

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Complete question:

Find f(t) ℒ−1 (e−s /(s²+ 1))

f(t)=? + (?) (t - ?)

Answer:

More people ordered processed than produce

Step-by-step explanation:

They are comparing \(\frac{1}{5} and \frac{19}{91}\)

First we have to find the least common multiple (lcm)

The lcm is 455

\(\frac{1}{5} x \frac{91}{91} = \frac{91}{455}\) (produce)

\(\frac{19}{91} x \frac{5}{5} =\frac{95}{455}\) (processed)

\(\frac{91}{455} < \frac{95}{455}\)

More people ordered processed than produce.

(a) The simplest interest is $12.

(b) The simplest interest is 5 cents.

(c) The simplest interest is $360.

(d) The simplest interest is $15.

What is the interest rate?

In relation to the amount lent, deposited, or borrowed, the amount of interest due each period is expressed as an interest rate. The total interest on a sum lent or borrowed is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time over which it is lent deposited, or borrowed.

The formula of simple interest is I = P × R × T

(a) Given that P = $500, R = 8% = 0.08, T = 3 months = (3/12) years = 1/4 years

The simple interest is

500 × 0.08 × (1/4)

= $12

(b) Given that P = $50, R = 12% = 0.12, T = 1 months = (1/12) years

The simple interest is

50 × 0.12 × (1/12)

=$0.5

= 5 cents

(c) Given that P = $1,000, R = 18% = 0.18, T = 24 months = (24/12) years = 2 years

The simple interest is

1000 × 0.18 × 2

=$360

(d) Given that P = $600, R = 15% = 0.15, T = 60 days = (60/360) years

The simple interest is

600 × 0.15 × (60/360)

=$15

P is principal, R is known as rate of interest.

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Step-by-step explanation:

To find the first four terms of the sequence given by the formula Tn = 2n² - 3, we substitute values of n from 1 to 4 into the formula.

For n = 1:

T1 = 2(1²) - 3

T1 = 2 - 3

T1 = -1

For n = 2:

T2 = 2(2²) - 3

T2 = 8 - 3

T2 = 5

For n = 3:

T3 = 2(3²) - 3

T3 = 18 - 3

T3 = 15

For n = 4:

T4 = 2(4²) - 3

T4 = 32 - 3

T4 = 29

Therefore, the first four terms of the sequence are: -1, 5, 15, 29.

Let the event that a tree has disease be D and the event that tree is being damaged by insects be I.

Therefore,

Recall that:

The required probability is given by:

Hence, the required probability is 20%=0.2

Answer:

x = 126°

x - 30 = 96°

Step-by-step explanation:

The sum of angles in a 5 sided polygon is 540°.

Hence all these angles would = 540

x + x + (x - 30) + (x - 30) + (x - 30) = 540

Collect like terms

5x - 90 = 540

Rearrange

5x = 540 + 90

5x = 630

x = 126

x - 30 = 96

The composition R2(R1(x)) is a rotation about the center C with angle of rotation given by the angle between the vectors P-Q and R2(R1(P))-C.

Lemma 10.3.3 states that any rigid motion of the plane is either a translation a rotation about a fixed point or a reflection across a line.

To prove that the composition of two rotations with the same center is a rotation can use the following argument:

Let R1 and R2 be two rotations with the same center C and let theta1 and theta2 be their respective angles of rotation.

Without loss of generality can assume that R1 is applied before R2.

By Lemma 10.3.3 know that any rotation about a fixed point is a rigid motion of the plane.

R1 and R2 are both rigid motions of the plane and their composition R2(R1(x)) is also a rigid motion of the plane.

The effect of R1 followed by R2 on a point P in the plane. Let P' be the image of P under R1 and let P'' be the image of P' under R2.

Then, we have:

P'' = R2(R1(P))

= R2(P')

Let theta be the angle of rotation of the composition R2(R1(x)).

We want to show that theta is also a rotation about the center C.

To find a point Q in the plane that is fixed by the composition R2(R1(x)).

The angle of rotation theta must be the angle between the line segment CQ and its image under the composition R2(R1(x)).

Let Q be the image of C under R1, i.e., Q = R1(C).

Then, we have:

R2(Q) = R2(R1(C)) = C

This means that the center C is fixed by the composition R2(R1(x)). Moreover, for any point P in the plane, we have:

R2(R1(P)) - C = R2(R1(P) - Q)

The right-hand side of this equation is the image of the vector P-Q under the composition R2(R1(x)).

The composition R2(R1(x)) is a rotation about the center C angle of rotation given by the angle between the vectors P-Q and R2(R1(P))-C.

The composition of two rotations with the same center is a rotation about that center.

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Approximately 34% of American adults have a mobile phone but not a landline, based on the given proportions from the study conducted by the Centers for Disease Control.

The proportion of American adults who have a mobile phone but not a landline, we need to subtract the proportion of those who have both a mobile phone and a landline from the proportion of those who have a mobile phone.

Let's denote the proportion of American adults who have a mobile phone as P(M), the proportion who have a landline as P(L), and the proportion who have neither as P(N).

Given information:

P(M) = 89% (proportion with a mobile phone)

P(L) = 57% (proportion with a landline)

P(N) = 2% (proportion with neither)

We can now calculate the proportion of adults who have a mobile phone but not a landline using the following equation:

P(M and not L) = P(M) - P(M and L)

To find P(M and L), we can subtract P(N) from P(L) since those who have neither are not included in the group with a landline:

P(M and L) = P(L) - P(N)

P(M and L) = 57% - 2%

P(M and L) = 55%

Now we can substitute the values back into the equation to find P(M and not L):

P(M and not L) = P(M) - P(M and L)

P(M and not L) = 89% - 55%

P(M and not L) = 34%

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The probability that the coin is fair given that it lands heads is 0.3571.

Given that a coin is picked from the box and flipped, the probability of the coin being fair is 1/3.

The probability of the coin being biased towards heads and the coin being biased towards tails is 1/3.

Therefore, the probability that the coin is fair and lands heads is (1/3) x 0.5

= 0.1667.

The probability that the coin is biased towards heads and lands heads is (1/3) x 0.8

= 0.2667.

The probability that the coin is biased towards tails and lands heads is (1/3) x 0.1

= 0.0333.

Therefore, the total probability that the coin lands heads is 0.1667 + 0.2667 + 0.0333

= 0.4667.

Using Bayes' Theorem, the probability of the coin being fair given that it lands heads is:

P(fair|heads)

= P(heads|fair) * P(fair) / P(heads)

= 0.5 * 1/3 / 0.4667

= 0.3571.

Thus, the probability that the coin is fair given that it lands heads is 0.3571.

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Answer:

C (-4, 2)

Step-by-step explanation:

When rotating a point 90 degrees counterclockwise about the origin our point P(x,y) becomes P'(-y,x).

(-4, 2) is  the coordinates of M’, the image of M(2,4), after a counterclockwise rotation of 90° about the origin.

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given, The coordinates of M(2,4)

Coordinates of the image after counterclockwise rotation.

Since,

When a point with coordinate ( x , y ) is rotated 90° counterclockwise then the new coordinates of the point are given by ( -y , x ).

thus,

Coordinates of image(M') = (-4, 2)

Therefore, the coordinates of M’, the image of M(2,4), after a counterclockwise rotation of 90° about the origin is (-4, 2).

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Answer:

2.08 × \(10^{7}\)

Step-by-step explanation:

Multiply 4 × 5.4 to get 20.8. Then multiply \(10^{-2}\) × \(10^{8}\) = \(10^{6}\)

However, that is not an answer. So, you can divide 20.8 by 10 and multiply \(10^{6}\) × 10.

Then you get 2.08 × \(10^{7}\)

Answer:5/5x-15/x

Step-by-step explanation:

Answer: your answer should be 3x^2 + 10x -75 / 5x.

Step-by-step explanation:

1. Combine multiplied terms into a single fraction

2. Find common denominator

3. Combine fractions with common denominator

4.  Multiply the numbers

5. Re-order terms so constants are on the left

6. Combine exponents

7. Multiply the numbers

8. Rearrange terms

therefore hopefully giving you the answer of 3x^2 + 10x -75 / 5x.

Your viewing angle α is approximately 46.34 degrees when sitting in the classroom next to the wall and looking at the blackboard.

To show that your viewing angle α is determined by the length of the blackboard and its distance from the wall, we can use geometry and trigonometry.

Let's consider a right triangle formed by your line of sight, the distance from the wall to the blackboard, and the length of the blackboard.

The adjacent side of the triangle is the distance from the wall to the blackboard, which is 5 ft. The opposite side is half the length of the blackboard since you are looking at the midpoint of the blackboard. Therefore, the opposite side is (11 ft)/2 = 5.5 ft.

We can use the tangent function to calculate the viewing angle α:

tan(α) = opposite/adjacent

tan(α) = (5.5 ft)/(5 ft)

tan(α) = 1.1

To find α, take the arctan (inverse tangent) of both sides:

α = arctan(1.1)

Using a calculator, we find that α ≈ 46.34 degrees.

Therefore, your viewing angle α is approximately 46.34 degrees when sitting in the classroom next to the wall and looking at the blackboard.

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Answer:

(C)Stefano should have divided by 6 when finding the mean absolute deviation.

Step-by-step explanation:

Step 1: Find the mean.

\(Mean = \dfrac{32 + 4 + 12 + 40 + 20 + 24}{6}=22\)

Step 2: Find each absolute deviation.

10, 18, 10, 18, 2, 2

Step 3: Find the mean absolute deviation.

\(M A D = \dfrac{10 + 18 + 10 + 18 + 2 + 2}{4} =\dfrac{60}{4}=15\)

However, there are 6 values in the data. Stefano should have divided by 6 when finding the mean absolute deviation.

The correct mean absolute deviation is therefore:

\(M A D = \dfrac{10 + 18 + 10 + 18 + 2 + 2}{6} =\dfrac{60}{6}=10\)

Answer:

c: Stefano should have divided by 6 when finding the mean absolute deviation.

Step-by-step explanation:

edg2020

The general solution form for the recurrence tn = 120,-2 - 166n-3 + 2.

Given a recurrence relation tn = 120,-2 - 166n-3 + 2 we have to derive the general solution form for the recurrence sequence.

We have the recurrence relation tn = 120,-2 - 166n-3 + 2

We need to find the solution for the recurrence relation.

Associated Homogeneous Equation: First, we need to find the associated homogeneous equation.

                                     tn = -166n-3 …..(i)

The characteristic equation is given by the following:tn = arn. Where ‘a’ is a constant.

We have tn = -166n-3..... (from equation i)ar^n = -166n-3

                                Let's assume r³ = t.

Then equation i becomes ar^3 = -166(r³) - 3ar^3 + 166 = 0ar³ = 166

Hence r = ±31.10.3587Complex roots: α + iβ, α - iβ

Characteristics Polynomial:

                   So, the characteristic polynomial becomes(r - 31)(r + 31)(r - 10.3587 - 1.7503i)(r - 10.3587 + 1.7503i) = 0

The general solution of the Homogeneous equation:

Now we have to find the general solution of the homogeneous equation.

                  tn = C1(-31)n + C2(31)n + C3 (10.3587 + 1.7503i)n + C4(10.3587 - 1.7503i)

                        nWhere C1, C2, C3, C4 are constants.

Computing a Particular Solution:

                Now we have to compute the particular solution.

                                  tn = 120-2 - 166n-3 + 2

Here the constant term is (120-2) + 2 = 122.

The solution of the recurrence relation is:tn = A122Where A is the constant.

The General Solution of Non-Homogeneous Equation:

        The general solution of the non-homogeneous equation is given bytn = C1(-31)n + C2(31)n + C3 (10.3587 + 1.7503i)n + C4(10.3587 - 1.7503i)n + A122

Hence, we have derived the general solution form for the recurrence tn = 120,-2 - 166n-3 + 2.

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