In a class of 120 students numbered 1 to 120, all even number students opt for physics, whose number are divisible by 5 opt for chemistry & those whose no are divisible by 7 opt for math. How many opt for none of these subjects?

When p equals 1/3, 9p^2 calculates to 1 after squaring p and multiplying by 9.

The question involves calculating the expression 9p^2 given that p = 1/3. First, we square the value of 'p' and then multiply it by 9. Following the process, we have:

[tex](\frac{1}{3} )^2 = \frac{1}{9} \\9 \times (\frac{1}{9} ) = 1[/tex]

Therefore, 9p^2 is equal to 1 when p is equal to 1/3.

Answer: The answer is ∠XWZ.

Step-by-step explanation:  Given that WXYZ is a parallelogram. We are to name an angle that is congruent to ∠XYZ.

Attached herewith, an image of parallelogram WXYZ.

We know that the opposite angles in a parallelogram are congruent to each other. So, in the parallelogram WXYZ, we must have

∠WXY ≅ ∠WZY and ∠XYZ ≅ ∠XWZ.

Therefore, angle congruent to ∠XYZ is ∠XWZ.

Thus, the answer is ∠XWZ.

Final answer:

Angle congruent to angle XYZ in parallelogram WXYZ would be angle W since opposite angles in a parallelogram are congruent.

Explanation:

If WXYZ is a parallelogram and you are asked to name an angle congruent to angle XYZ, you should look at the properties of a parallelogram. One key property is that opposite angles are congruent. Therefore, the angle congruent to angle XYZ would be angle W. If we consider the vertices in order around the parallelogram W, X, Y, Z, angle XYZ corresponds to angle WZY, so its opposite angle is angle WXZ (or simply angle W).

It's important to remember that in a parallelogram, consecutive angles are supplementary (their sum is 180 degrees). This supplementary property could help you in other problems related to angles in a parallelogram, but for this particular case—identifying a congruent angle—the opposite angles property directly gives us the answer.

Answer:

all real numbers less than or equal to 3

Step-by-step explanation:

The range of the function is set of all y value for which the function is defined

To find out the range we look at the maximum or minimum point on the graph

Maximum point on the graph that is vertex is (-1,3)

x=-1 and y=3

The graph of y is below 3 (vertex)

So the range of the function is set of all real numbers less than or equal to 3

Answer:

The value of x is 16 .

Step-by-step explanation:

Definition of vertically opposite angles

Two lines crosses angles opposite to each other are called vertically opposite angle .

Thus

(2x + 13)° = (3x-3)°

(Vertically opposite angles )

2x + 13 = 3x-3

2x - 3x = -3-13

-x = -16

x = 16

Therefore the value of x is 16 .

Correct Answer: maturity date

start off by finding 10% of $14. in order to find 10%, divide it by 70 which gives 2. you now need to make the 30% to add to the 70%, by timesing the 2 by 3to give 6. now all you need to do it add the 6 to 14 to make 20!

so your answer is $20

Answer:

The original price was $20.00

Step-by-step explanation:

Joe paid $14.00 for a board game.

This is the 70% of the original price.

Let the original price of a board game be x

70% of x = $14.00

0.70x = 14.00

x = [tex]\frac{14}{0.7}[/tex] = $20.00

The original price was $20.00

The pair of sets, {x | x < 0} and {x | x > 0}, has no solution because no number can be simultaneously less than zero and greater than zero. The other pairs do have solutions as they include the number zero.

The set of mathematical expressions provided in the question represent intervals along the number line. Understanding which intervals overlap and which intervals don't is the key to comprehending which of these options potentially has a solution. To consider when these sets will have no solution, you must find where no numbers exist that can satisfy both conditions simultaneously.

The first pair, {x | x < 0} and {x | x > 0}, means 'the set of all x such that x is less than 0' and 'the set of all x such that x is greater than 0'. Because no number can be both less than zero and greater than zero at the same time, this pair has no solution.

The other pairs, {x | x ≤ 0} and {x | x ≥ 0} and {x | x ≤ 0} or {x | x ≥ 0} do have solutions because they both include 0 itself, so there are numbers that can satisfy both conditions.

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Answer:

Option a. 0

Step-by-step explanation:

As we know if we draw two circles with same center but with the different radii, they neither touch each other nor intersect. This is true not only for two circles but for infinite number of the circles having the same center. They never have the common points to share. Set of points lying on each concentric circles are different.

Therefore Option a. 0 points is the correct answer.

The detailed answer provides the solutions to a series of questions involving finding specific values for y given x in various exponential equations, as well as recognizing the relationship between graphs of exponential functions and identifying which equations are not exponential.

1. If (-1, y) lies on the graph of y = 3ˣ+1, then y equals the value of the function when x is -1. Therefore, y = 3⁻¹ + 1 which simplifies to y = 1/3 + 1 = 4/3, which is not one of the provided options.

2. If (x, 1/100) lies on the graph of y = 10ˣ, then we need to find the value of x such that 10ˣ equals 1/100. 10ˣ = 1/100 is equivalent to 10ˣ = 10⁻², so x = -2.

3. If (-1, y) lies on the graph of y = 2²ˣ, we substitute x with -1. Then y = 2²*⁻¹ = 2⁻² = 1/4.

4. The relationship between the graphs of y = 2ˣ and y = 2⁻ˣ is that they are reflections over the y-axis. When x is replaced by -x in the function, the resulting graph is a reflection over the y-axis.

5. If (3, y) lies on the graph of y = -(2ˣ), then y is the negative value of 2 raised to the power of 3, which is -8. So, y = -8.

6. Among the given equations, y = -2ˣ is not exponential because it lacks the variable as an exponent. So, y = -2ˣ is not exponential.

7. If (-2, y) lies on the graph of y = 4ˣ, then y = 4⁻² = 1/16.

8. If (-3, y) lies on the graph of y = 3⁻ˣ, then y = 3⁻⁽⁻³⁾ = 3³ = 27.

9. If (-3, y) lies on the graph of y = 3ˣ, then y = 3⁻³ = 1/27.

10. If (-3, y) lies on the graph of y = (1/2)ˣ, then y = (1/2)⁻³ = 2³ = 8.

The equations of the tangent and normal to f(x) at x = 2 are -

Tangent → y = 5x - 7

Normal → y = -1/2 x + 3.4

A tangent is a line touching the curve at one distinct point, and this distinct point is called the point of contact.

The normal line to a curve at a particular point is the line through that point and perpendicular to the tangent.

Given is a function f(x) and f(2) = 3 and f'(2) = 5.

We can find the tangent to the curve at x = 2 by finding the value of the derivative of f(x) at x = 2. The slope of the tangent at x = 2 is -

m[T] = (dy/dx) [at x = 2] = f'(2) = 5

Now. the equation of tangent can be written as -

(y - y₁) = m [T] (x - x₁)

and

f(2) = 3

At x = 2, y =3 →

y - 3 = 5 (x - 2)

y - 3 = 5x - 10

y = 5x - 10 + 3

y = 5x - 7

This is the equation of the tangent.

In order to find the slope of Normal at x = 2, use the following formula -

m [T] x m [N] = -1

m [T] = 5

Then -

m [N] = - 1/5

The equation of the normal is given by -

(y -  y₁) = m [N] (x - x₁)

(y - 3) = -1/5 (x - 2)

y - 3 = -x/2 + 2/5

y = -x/2 + 2/5 + 3

y = -1/2 x + 3.4

This is the equation of Normal.

Therefore, the equations of the tangent and normal to f(x) at x = 2 are -

Tangent → y = 5x - 7

Normal → y = -1/2 x + 3.4

To solve more questions on Tangents and Normal, visit the link below-

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Answer:

D

Step-by-step explanation:

The horizontal axis of the graph is Salary.

Given there is a positive correlation between salary and education, means that as if education increase, salary increase OR if education decrease, salary decrease, and vice versa.

Out of the 4 choices, they wanted to know the one that requires LEAST education. So we will look at the bar that has LEAST salary.

Looking at the graph and bars, out of the 4 choices, Surveyor has the LEAST SALARY, so SURVEYOR would require LEAST EDUCATION. Answer choice D is right.

The career with the least education and having positive correlation between salary and education is [tex]\boxed{{\text{Surveyor}}}.[/tex] Option (d) is correct.

Further Explanation:

Given:

The options are as follows,

(a). Accountant

(b). Architect

(c). Pharmacist

(d). Surveyor

Explanation:

Correlation is a relationship between the two events. The change in one will affect the in change of another one.

There are two type correlations.

A positive correlation mean that if one increases the second event will also increase and if one decreases the second event will also decreases.

A negative correlation mean that if one increases the second event will also decrease and if one decreases the second event will also increase.

There is a positive correlation between salary and education.

The least salary in the given option is of surveyor and has least education.

The career with the least education and having positive correlation between salary and education is [tex]\boxed{{\text{Surveyor}}}[/tex]. Option (d) is correct.

Learn more:

Answer details:

Grade: High School

Subject: Statistics

Chapter: Correlation

Keywords: correlation, salary, education, positive correlation, based, careers, least education, accountant, architect, pharmacist, surveyor, negative correlation, average salaries, personal trainer,  

Answer:

and only if they have the same slope. Any two vertical lines are parallel. Therefore, the slope of AB is -8 if AB is parallel to CD.

Step-by-step explanation: