If the test for a disease is accurate 65% of the time, how often will it come back positive if a patient doesn't have the disease?

The solution of expression is, x = 6

We have to give that,

An expression to simplify as,

⇒ 45 + 5/6x = 50

Now, Simplify the expression by combining like terms,

⇒ 45 + 5/6x = 50

Subtract 45 on both sides,

⇒ 45 + 5/6x - 45 = 50 - 45

⇒ 5/6x = 5

Multiply by 6 on both sides,

⇒ 5x = 5 × 6

⇒ 5x = 30

Divide by 5 on both sides,

⇒ x = 30/5

⇒ x = 6

So, The solution is, x = 6

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The dot product of vectors a⃗ =3i^−8j^ and b⃗ =−2i^−6j^ is calculated by multiplying the corresponding components of the vectors and summing the results, giving a final dot product of 42.

The dot product of two vectors a and b is calculated by multiplying the corresponding components of the vectors and summing the results. So, given the vectors a⃗ =3i^−8j^ and b⃗ =−2i^−6j^, the dot product can be found as follows:

a⃗ ⋅b⃗ = (a_x * b_x) + (a_y * b_y)

Therefore, substituting the known values: a⃗ ⋅b⃗ = (3 * -2) + (-8 * -6) = -6 + 48 = 42

So, the dot product a⃗ ⋅b⃗ for vectors a⃗ =3i^−8j^ and b⃗ =−2i^−6j^ is equal to 42.

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The fraction of apple juice shared by 6 people is A = 4/9 of the apple juice

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given data ,

Let the fraction of apple juice shared by 6 people be A

Let the total number of people be represented as n = 6 people

Now , the fraction of total amount of apple juice = 2 2/3

The fraction of total amount of apple juice T = ( 8/3 ) of apple juice

And , the equation is

A = fraction of total amount of apple juice T / total number of people n

On simplifying , we get

A = ( 8/3 ) / 6

A = ( 8/18 )

Divide by 2 on both numerator and denominator of the fraction , we get

A = 4/9 of the apple juice

Therefore , the value of A is 4/9

Hence , the fraction of apple juice is ( 4/9 ) equally

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The reference angle is simply the acute angle between the terminal side and the x-axis

The terminal angles in the four quadrants are

The given parameters are:

[tex]\theta \to[/tex] reference angle

[tex]\bar \theta \to[/tex] terminal angle

(a) If the reference angle is in the first quadrant

In the first quadrant, the x-axis is at [tex]0\ rad[/tex]

So, the terminal angle is:

[tex]\bar \theta = \theta - 0[/tex]

[tex]\bar \theta = \theta[/tex]

(b) If the reference angle is in the second quadrant

In the second quadrant, the x-axis is at [tex]\pi \ rad[/tex],

While the reference angle is between [tex]\frac{\pi}{2}[/tex] and [tex]\pi \ rad[/tex]

It means that, we have to subtract the reference angle from the x-axis

So, the terminal angle is:

[tex]\bar \theta = \pi - \theta[/tex]

(c) If the reference angle is in the third quadrant

Here, the x-axis is still at [tex]\pi \ rad[/tex],

But the reference angle is between [tex]\pi \ rad[/tex] and [tex]\frac{3}{2}\pi[/tex]

It means that, we have to subtract the x-axis from the reference angle.

So, the terminal angle is:

[tex]\bar \theta = \theta - \pi[/tex]

(d) If the reference angle is in the fourth quadrant

Here, the x-axis is at [tex]2\pi \ rad[/tex]

And the reference angle is between  [tex]\frac{3}{2}\pi[/tex] and [tex]2\pi \ rad[/tex]

It means that, we have to subtract the reference angle from the x-axis.

So, the terminal angle is:

[tex]\bar \theta = 2\pi - \theta[/tex]

See attachment for illustration of terminal angles

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Final answer:

When dealing with angles in radians and their reference angles, each quadrant has a specific relationship for determining the reference angle based on the given angle θ.

Explanation:

Radian Measure with Reference Angles:

If θ is in QI, then θ hat = θ

If θ is in QII, then θ hat = π - θ

If θ is in QIII, then θ hat = θ - π

If θ is in QIV, then θ hat = 2π - θ

The temperature in Seattle was 19 degrees lower than in the Hudson.

we subtract the temperature of Seattle from the temperature of the Hudson:

18°C - (-1°C) = 19°C

Therefore, the temperature in Seattle was 19 degrees lower than the temperature in the Hudson.

To solve the formula F=J+Jrt for 't', first, subtract 'J' from both sides to get F-J=Jrt. Then, divide both sides by 'Jr', for the final equation for 't' = (F-J)/Jr.

This physics-related mathematics question is asking you to solve the given formula F=J+Jrt for 't'. To isolate 't', we first want to eliminate 'J' from the right side. We do this by subtracting 'J' from both sides of the equation. This gives us F-J=Jrt.

Then, we divide both sides by 'Jr'. When we do this, we are left with t=(F-J)/Jr as the rearranged formula with 't' as the subject. This results in 't' being isolated in the equation, which answers the student's question.

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1. at a discount

2. add all the items together at their sales cost then add salves tax

3. $26.75

4. $66.23