Write the expression in terms of sine only. −√3 sin x + cos x

Answer:

the statement KS ≅ MS is true based on the congruence of the angles KST and MST.

Step-by-step explanation:

Based on the given information that TA is parallel to KM, we can apply the alternate interior angles theorem for parallel lines. According to the theorem, when a transversal intersects two parallel lines, the alternate interior angles are congruent.

In this case, the angles KST and MST are alternate interior angles formed by the transversal line KS and the parallel lines TA and KM. Since the lines TA and KM are parallel, we can conclude that:

KST ≅ MST

The person bought 4 pizzas.

Let's assume the number of pizzas the person bought is "p".

We are given that he pays $4 for parking and $12 for each pizza he buys. So, the total cost can be calculated as follows:

Total cost = $4 (for parking) + $12 × p (for pizzas)

According to the problem, the total cost is $52. We can write this as an equation:

$4 + $12p = $52

To find the value of "p," we need to solve this equation:

$12p = $52 - $4

$12p = $48

Now we divide both sides of the equation by $12 to solve for "p":

p = $48 / $12

p = 4

Therefore, the person bought 4 pizzas.

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Answer:

[tex]\huge\boxed{\sf 44\ units}[/tex]

Step-by-step explanation:

Solution:

So,

= 3 + 8 + 3 + 6 + 5 + 6 (again) + 4 + 5 + 4

[tex]\rule[225]{225}{2}[/tex]

Answer:

8-4=4

therefore 6+4=10

then perimeter =2(5)+10+6+2(3)+8+4=44units

Approximately 7 singers have joined the initial singer to increase the level from 74 dB to 83 dB.

To calculate the number of singers that have joined the initial singer, we can use the logarithmic nature of the decibel scale. The decibel scale is logarithmic, meaning that an increase of 10 dB represents a tenfold increase in sound intensity.

In this case, we have an increase from 74 dB to 83 dB, which is an increase of 9 dB. Since each singer is equally loud, we can assume that each additional singer adds the same amount of sound intensity.

To find out how many singers have joined, we need to determine how many times 9 dB represents a tenfold increase. We can use the formula:

[tex]10^{\\increase} ^{\\in dB/10)}\\[/tex] = number of singers

Let's calculate it:

[tex]10^{(9/10)[/tex] ≈ 7.94

Therefore, approximately 7 singers have joined the initial singer to increase the level from 74 dB to 83 dB.

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Using the given values, we can calculate the angle of diffraction (θ) and the distance between adjacent bright fringes (y).

To analyze the diffraction of light passing through a narrow slit, we can use the concept of the single-slit diffraction equation:

sin(θ) = (m * λ) / w

Where:

- θ is the angle of diffraction

- m is the order of the bright fringe

- λ is the wavelength of light

- w is the width of the slit

Given:

- Wavelength (λ) = 694 nm = 694 × 10^(-9) m

- Slit width (w) = 7.90 μm = 7.90 × 10^(-6) m

- Distance to the screen (D) = 1.95 mm = 1.95 × 10^(-3) m

First, let's calculate the angle of diffraction (θ):

θ = sin^(-1)((m * λ) / w)

Now, let's calculate the distance between adjacent bright fringes (y):

y = (m * λ * D) / w

Using the given values, we can calculate the angle of diffraction (θ) and the distance between adjacent bright fringes (y).

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The probability of an event and the probability of its complement always sum to 1.

The probability of an event and its complement refers to the likelihood of either the event occurring or its opposite (not occurring). In any probability space, the sum of these two probabilities must always equal 1.

This can be understood using the concept of the sample space, which represents all possible outcomes of an experiment. The event and its complement together cover the entire sample space, leaving no room for other outcomes. Therefore, the sum of their probabilities must account for the entire probability space, which is equal to 1.

In other words, if the probability of an event occurring is P(A), then the probability of its complement (not A) occurring is 1 - P(A). Adding these probabilities together yields 1:

P(A) + P(not A) = P(A) + (1 - P(A)) = 1

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The height of the trapezoid is 13cm.

A trapezoid is a convex quadrilateral with at least one pair of parallel sides.

Area of a trapezoid =   0.5 x (sum of the lengths of the parallel sides) x height

Height = area / (0.5 x sum of lengths)

Sum of lengths = 23 + 17 = 40 cm

= 260 / (0.5 x 40) = 13 cm

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In the given expression, the multiplication and division operations are performed first, followed by any addition and subtraction operations.

To evaluate the given expression, we need to break it down into individual operations and then apply the order of operations. Let's analyze each operation step by step:

Parentheses: In this expression, there are no parentheses, so we can skip this step.

Exponents: The exponentiation operation is denoted by the "^" symbol. However, in this expression, there are no exponents.

Multiplication and Division: The multiplication and division operations are performed from left to right. In the given expression, we have two multiplication operations: "[tex]3 * 2 ^ 2[/tex]" and "100 / 10 * 2." According to the order of operations, we need to evaluate these multiplications before moving on to other operations.

First, let's consider "[tex]3 * 2^2[/tex]" In this case, the exponentiation operation (^) takes precedence over multiplication. Therefore, we need to evaluate "[tex]2^2[/tex]" first. Since 2 raised to the power of 2 is 4, the expression becomes "3 * 4."

Next, we have "100 / 10 * 2." As there are no other operations to perform before division, we can proceed with evaluating this expression. The division of 100 by 10 results in 10, and then multiplying by 2 gives us 20.

Addition and Subtraction: The addition and subtraction operations are also performed from left to right. In the given expression, we have "16 5" and "15 - 3" as the remaining operations.

Let's consider "16 5" first. The expression "16 5" is ambiguous because there is no operator between the numbers. It is essential to have a proper operator like ">" or "<" to determine the relationship between the two numbers. Without it, the expression is invalid.

Finally, we have "15 - 3." Subtracting 3 from 15 gives us 12.

Now that we have evaluated each operation, we can rewrite the expression as "3 * 4 < 12 and also 20 > 12."

To summarize, the operations are performed in the following order:

Exponents (if any)

Multiplication and Division (from left to right)

Addition and Subtraction (from left to right)

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