In what form is an equation that relates two proportional quantities x and y?
Oy=k+x, where k is the constant of proportionality
O y = kx, where k is the constant of proportionality
k
where k is the constant of proportionality
O y
y=
k
where y is the constant of proportionality

Answer:

135

Step-by-step explanation:

subtract 180 by 45 since a line is 180, that is what you get for the angle that is adjacent to angle 2, there is a rule if it is adjacent, they equal each other. thus, angle 2 is 135

The probability of selecting a non-smoker is 6/62 or approximately 0.097 or 9.7%. The probability of selecting a non-smoker on the second draw is 5/61 or approximately 0.082 or 8.2%.

To find the probability of both events occurring (selecting a non-smoker, then another non-smoker), we multiply the probabilities together: 0.097 * 0.082 = 0.007954 or approximately 0.795%.

(a) The probability of a patient being a non-smoker can be calculated by dividing the number of non-smokers by the total number of patients. In this case, there are 62 patients, of which 56 are smokers. So, the number of non-smokers is 62 - 56 = 6. Therefore, the probability of selecting a non-smoker is 6/62.

(b) When drawing two patients' charts at random without replacement, the probability of selecting a non-smoker on the first draw is calculated by dividing the number of non-smokers by the total number of patients. After the first draw, there will be one less patient, so the number of remaining patients and non-smokers changes. To find the probability of selecting a non-smoker on the second draw, we divide the number of non-smokers remaining by the updated total number of patients.

To calculate the probability of both events occurring (selecting a non-smoker, then another non-smoker), we multiply the individual probabilities together. This multiplication gives us the joint probability of both events happening sequentially.

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Answer:

2x + 17

Step-by-step explanation:

5 * 2 = 10

5 + 2 = 7

2x + 17

Answer:

The time now is 7 pm

Step-by-step explanation:

Suppose that now is the time T.

We know that:

"if time is four hours from now, the time left till midnight would be a quarter that if it is one hour from now".

Then:

if we define midnight as 12, and we assume that T is in the pm range.

Then the "time left till midnigth, assuming that the time is four hours from now" will be written as (12 - (T + 4))

With this in mind, we can write the problem as:

12 - (T + 4) = (1/4)*( 12 - (T + 1))

Now we can solve this for T.

12 - T - 4 = (1/4)*(12 - T - 1)

8 - T = (1/4)*(11 - T)

4*(8 - T) = 11 - T

32 - 4*T = 11 - T

32 - 11  = -T + 4*T

21 = 3*T

21/3 = T

7 = T

Then T = 7 pm

The time now is 7 pm

Answer:

9836523 is the answer

Answer:

The correct answer should be 9,836,523

Answer:

3rd option

Step-by-step explanation:

The equation of a line in point slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

Given

y - 4 = \(\frac{1}{4}\) (x - 8)

with m = \(\frac{1}{4}\) and (a, b) = (8, 4 )

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept ) , then

y = \(\frac{1}{4}\) x + c ← is the partial equation

To find c substitute (8, 4) into the partial equation

4 = 2 + c ⇒ c = 4 - 2 = 2

y = \(\frac{1}{4}\) x + 2 ← equation in slope- intercept form

The sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse. The hypotenuse exists c = 50.

To determine the hypotenuse from the sides of a right triangle, use the Pythagorean theorem. Sum of squares is squared as c = √(a² + b²).

The longest side of a right-angled triangle, or the side opposite the right angle, exists comprehended as the hypotenuse in geometry. The Pythagorean theorem, which asserts that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.

a² + b² = c²

⇒ c = √(a² + b²)

Where, a = 30 and b = 40, then

substitute the  values in the above equation, we get

30² + 40² = c²

900 + 1600 = c²

2500 = c²

50 = c

Therefore, the hypotenuse exists c = 50.

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Changing a figure's location without spinning, reflecting, or changing its size is known as a translation in geometry.So g(x) = ln[1/8(x - 3)] + 1.

When you group "3" with the "right-left" variable, which is "x," you will have 3 units to the right.

However, "x" is the opposite of what it seems to be, therefore in order to shift right, you must subtract 3 from "x," making ln(x) into ln (x - 3).

Simply add 1 to the function to advance it up one unit, making ln(x-3) become ln(x-3) + 1.

In order to multiply the "horizontal variable" (also known as "x") by a factor of 8, you must divide by 8 (or multiply by 1/8), because "x" is the opposite of what it seems to be.

Ln(x - 3) + 1 so becomes Ln[1/8(x - 3)] + 1.

so that g(x) = ln[1/8(x - 3)]

+ 1.

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If she wanst to have an average of 71.5%, then she needs to score 69% on the last test.

Let's say that she scores X on test 4, if she wants to have an average of 71.5%, then we can write the equation:

(77 + 54 + 86 + X)/4 = 71.5

Now we need to solve that equation for X.

217 + X = 71.5*4

X = 71.5*4 - 217 = 69

She needs to score 69% in the last test.

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Answer: is it 0 -6

Step-by-step explanation:

The value of y will be 75°. The correct option is C.

Straight lines with little depth or width are present. You will learn about a number of lines, including transversal, intersecting, and perpendicular lines.

A figure called an angle is one in which two rays originate from the same point. In this area, you could also encounter contrasting and related viewpoints.

Given that the two parallel lines are DE and XY. The angle y will be calculated as,

y = 180 - 105

y = 75°

Hence, the measure of the angle y is 75°

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Answer:

its positive

Step-by-step explanation: the two positives cancel out the negative

Answer:

b

Step-by-step explanation:

Answer:

32.4

Step-by-step explanation:

The equation for area of a triangle is a=1/2bh. So all triangles on outside have area of a=1/2x4.5x3.5. Then you multiply what you get times 3 bc there are three triangles. Then you add that number to the area of the inside triangle. Which you find by doing a=4.5x3.9x1/2

Answer:

angle (3x-15)°=angle (2x+10)° (by vertically opposite angles)

3x-15=2x+10

3x-2x=10+15

x=25

by putting the value of x.

3x-15=3×25-15 = 60°

38°+ 60°+ <ebf= 180° (by sum of all sides is 180° )

98°+<ebf = 180°

<ebf = 180° - 98°

<ebf = 82°

94 cause 50- -60=110 then 110-16=94

Answer:

180

Step-by-step explanation:

The definition of angles that are supplementary is that their measures add to 180°.

The answer is b=18. To solve, multiply 6 by 3 to get 18. This is called doing the inverse operation. Since the equation is a division equation, we would have to multiply in order to find the missing variable.

Answer: A and C

Step-by-step explanation:

Abs. val is distance from 0, and 100 and -100 are both the same distance from 0, so x=100 and x=-100.

An equation of the tangent line to the curve \(x e^y+y e^x=4\) at the point (0, 4) is \(y=-(4+e^4) x+4\).

A tangent is described as a line that intersects a circle or an ellipse only at one point. If a line touches a curve at P, the point "P" is known as the point of tangency.

Now according to the question;

To obtain the tangent at a given point, we must first obtain the slope at that point by obtaining the differentiation value at that point  \(\left.y^{\prime}\right|_{x=0, y=4}\) as-

Consider the given equation;

\(x e^y+y e^x=4\)

Differentiate both side with respect to x;

\(\begin{aligned}&\frac{d}{d x}\left(x e^y+y e^x\right)=\frac{d}{d x} 4 \\&\frac{d}{d x} x e^y+\frac{d}{d x} y e^x=0\end{aligned}\)

Now apply product rule;

\(\begin{aligned}&e^y \frac{d}{d x} x+x \frac{d}{d x} e^y+e^x \frac{d}{d x} y+y \frac{d}{d x} e^x=0 \\&e^y \frac{d}{d x} x+x \frac{d}{d y} e^y \cdot y^{\prime}+e^x y^{\prime}+y \frac{d}{d x} e^x=0\end{aligned}\)

Applying exponential and power rule;

\(\begin{aligned}&e^y \cdot 1+x e^y \cdot y^{\prime}+e^x y^{\prime}+y e^x=0 \\&\left(x e^y+e^x\right) y^{\prime}=-y e^x-e^y\end{aligned}\)

Solve the value of y'

\(y^{\prime}=\frac{-y e^x-e^y}{x e^y+e^x}\)

Now, find the value of slope m.

\(m=\left.y^{\prime}\right|_{x=0, y=4}\)

\(\frac{-4 \cdot e^0-e^4}{0 e^4+e^0}=-4-e^4\)

Now, using the point-slope formula, obtain the line equation as follows.

\(\begin{aligned}&\left(y-y_1\right)=m\left(x-x_1\right) \\&(y-4)=-(4+e^4) \cdot(x-0) \\&y=-(4+e^4) x+4\end{aligned}\)

Therefore, an equation of the tangent line to the curve is   \(y=-(4+e^4) x+4\).

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The cost of each desk is $42.

The initial cost to make these new school desks is $635.

What is a solution of linear function?

The terms "linear function" in mathematics apply to two different but related ideas: A polynomial function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.

Assume that the cost of each desk be m.

The initial cost to make these new school desks be c.

Then the total cost will represent by the equation:

y = mx + c .....(i)

Putting x =21 and y = 1517 in the equation (i)

1517 = 21m + c ...(ii)

Putting x = 47 and y = 2609 in the equation (i)

2609 = 47m + c ...(iii)

Subtract equation (ii) from (iii)

47m + c =2609

21m + c = 1517

(-)     (-)     (-)

___________

26m = 1092

Divide both sides by 26

m = 42

Putting m = 42 in equation (ii)

1517 = 21 × 42 + c

1517 = 882 + c

c = 1517 - 882

c = 635

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The inverse function of the given function which gives the value of the number of days when the population of bacteria is known is:

f ⁻¹(x) = log₁.₆(1.6x - 32)

What is an inverse function?

A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function. The output of a function is returned by the inverse function, which also returns the initial value. A function that can reverse into another function is known as an inverse function or anti function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y.

The given function is:

\(f(x) = 1.6^{x-1} + 20\\\)

\(y = 1.6^{x-1} + 20\\\)

Now we are asked to find the inverse of this function.

That is, we have to write x in terms of y.

And then substitute the y back with x, to write as an inverse function

f ⁻¹(x).

\(y = 1.6^{x-1} + 20\\\)

y - 20 = \(1.6^{x-1}\)

y-20 = 1.6ˣ / 1.6

1.6y - 1.6 * 20 = 1.6ˣ

1.6y - 32 = 1.6ˣ

x = log₁.₆(1.6y - 32)

Therefore the inverse function of the given function which gives the value of the number of days when the population of bacteria is known is:

f ⁻¹(x) = log₁.₆(1.6x - 32)

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The points of solution that are obtained for the system of linear equations 3x + 2y = 11 and -8x - 4y = -20 are (-1,7).

2(3x + 2y = 11)

1(-8x - 4y = -20)

3x + 2y - 8x - 4y = 11 - 20 gives -5x - 2y = -9

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The system of linear equations are -

3x + 2y = 11....(1)

-8x - 4y = -20....(2)

When solved initially the value of equation is -

3x + 2y - 8x - 4y = 11 - 20

-5x - 2y = -9

Multiply equation (1) by 2 -

2(3x + 2y) = 2 × 11

6x + 4y = 22.....(3)

Simplify the equation (2) and (3) by adding -

-8x - 4y + 6x + 4y = -20 + 22

-2x = 2

x = -1

Substituting the value of x = -1 in equation (1) -

3x + 2y = 11

3(-1) + 2y = 11

Simplifying the equation -

-3 + 2y = 11

2y = 11 + 3

2y = 14

y = 7

Therefore, the final value is obtained as (-1,7).

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Answer:

13.50 per hour

Step-by-step explanation:

she makes 13.50 per hour, you know this ny dividing 27 by 2. If she makes 27 for 2 hours you just got to find half of 27 for 1 hour.

Answer:

13.50

Step-by-step explanation: i did an exam and got it correct

Answer:

.... thats alot there buddy ...

Step-by-step explanation:

The probability that a randomly selected point inside a triangle with side lengths 5, 12, and 13 has a distance from the nearest vertex of the triangle less than 2 is approximately 0.4286, or 42.86%.

To find the probability, we can consider the triangle with side lengths 5, 12, and 13 as a right triangle, where the side length 13 represents the hypotenuse. Let's assume the vertices of the triangle are A, B, and C, with AB = 5, AC = 12, and BC = 13.

First, we calculate the area of the triangle using Heron's formula, which gives us √(s(s-a)(s-b)(s-c)), where s is the semiperimeter of the triangle and a, b, and c are the side lengths. In this case, s = (5+12+13)/2 = 15.

Using the formula, the area of the triangle is \(\sqrt{15(15-5)(15-12)(15-13)} = \sqrt{15 \cdot 10 \cdot 3 \cdot 2} = \sqrt{900} = 30\).

Now, let's consider the smaller triangle formed by the original triangle's vertices and a point P inside it. To calculate the probability, we need to find the area of the region where the distance from P to the nearest vertex is less than 2.

If we draw circles centered at each of the vertices A, B, and C with radius 2, the area enclosed by these circles within the triangle represents the region we are interested in.

Calculating the areas of these circles, we find that each circle has an area of 4π. Since there are three circles, the total area of the enclosed region is 3 × 4π = 12π.

Therefore, the probability that a randomly selected point inside the triangle has a distance from the nearest vertex less than 2 is given by (12π / 30) = (2π / 5), which is approximately 0.4286 or 42.86%.

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The expected value of X (number of hearts drawn) is E(X) = 5, and the standard deviation is σ ≈ 0.9682.

To find the probability of drawing at least 8 hearts in the given experiment, we need to consider the number of hearts drawn in 20 cards. Let's calculate it step by step:

Calculate the probability of drawing exactly 8 hearts:

The probability of drawing a heart in one draw is 13/52 (as there are 13 hearts in a standard deck of 52 cards).

The probability of drawing a non-heart in one draw is 39/52.

Since there are 8 hearts, we need to calculate the probability of drawing exactly 8 hearts and exactly 12 non-hearts. This can be calculated using the binomial probability formula:

P(X = 8) = C(20, 8) * (13/52)^8 * (39/52)^12

Calculate the probability of drawing 9, 10, 11, 12, ..., 20 hearts:

We need to calculate the individual probabilities for each number of hearts greater than 8 using the same binomial probability formula.

For each number of hearts, we sum up the probabilities.

Calculate the probability of drawing at least 8 hearts:

To find the probability of drawing at least 8 hearts, we sum up the probabilities calculated in step 2.

P(X ≥ 8) = P(X = 8) + P(X = 9) + P(X = 10) + ... + P(X = 20)

Now, let's calculate the expected value and standard deviation for the random variable X, which represents the number of hearts drawn.

Expected Value (E(X)):

The expected value of a random variable is the average value we expect to obtain over multiple trials. For a binomial distribution, the expected value can be calculated using the formula: E(X) = n * p, where n is the number of trials and p is the probability of success.

In this case, n = 20 (number of draws) and p = 13/52 (probability of drawing a heart in one draw):

E(X) = 20 * (13/52) = 5

Standard Deviation (σ):

The standard deviation measures the dispersion or variability of a random variable. For a binomial distribution, the standard deviation can be calculated using the formula: σ = √(n * p * (1 - p)).

In this case, n = 20 and p = 13/52:

σ = √(20 * (13/52) * (1 - 13/52)) ≈ √(5 * 0.25 * 0.75) ≈ √0.9375 ≈ 0.9682

Therefore, the expected value of X (number of hearts drawn) is E(X) = 5, and the standard deviation is σ ≈ 0.9682.

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Answer:

-1/2

Step-by-step explanation:

slope is  \(\frac{y_{2}- y_{1}}{x_{2}-x_{1}}\)

so:

\(\frac{6-8}{12-8} = -\frac{2}{4} = -\frac{1}{2}\)

Step-by-step explanation:

if you would just maintain your natural curiosity and imaginative qualities, geometry would be the easiest of all math disciplines, because you can always "see" the things you are working with and on, almost "touch" them.

a few things you should burn into your brain though, and keep them there for the rest of your life :

Pythagoras in right-angled triangles : come on !

c² = a² + b²

c is the Hypotenuse (the baseline opposite of the 90° angle). a and b are the legs of the triangle enclosing the 90° angle.

AND : the sum of all angles in a triangle is always (ALWAYS !) 180°.

so,

in the first case

x² = 6² + 6² = 36 + 36 = 72

x = sqrt(72) = sqrt(9×4×2) = 3×2×sqrt(2) = 6×sqrt(2)

FYI this is 8.485281374...

in the second case we have to use also trigonometry, a little bit (not just geometry).

first the angle at the bottom right corner is

180 - 90 - 60 = 30° (again, because the sum of all angles is 180°).

so, 8×sqrt(3) = sin(30) × x

because the basic sine and cosine values are only for the standard circle with radius = 1. for any larger (or smaller) circle these values have to be scaled up by the actual radius, which is in our case here x.

sin(30) = 0.5

so, we get

8×sqrt(3) = x/2

16×sqrt(3) = x

FYI - that is 27.71281292...