Assume that the salaries of elementary school teachers in the united states are normally distributed with a mean of $32,000 and a standard deviation of $3000. if 100 teachers are randomly selected, find the probability that their mean salary is less than $32,500.

Answer: the answer is -2192

The correct interpretation of -2 + (-7) is that "the number 7 is to the left of -2 on the number line".

The correct interpretation of the expression -2 + (-7) which is results in -9.

Let's break this down:

When we move 7 units left from -2, we land on -9.

Thus, -2 + (-7) results in -9, which confirms that we have moved 7 to the left of -2 on the number line.

Complete question:

Which of the following is a correct interpretation of the expression -2 + (-7)?

Choose 1 answer:

In a 30-60-90 triangle, the side opposite the 30-degree angle (s) has a length of "s," and the hypotenuse has a length of "2s."

The side opposite the 60-degree angle is "s√3."

We have,

In a 30-60-90 triangle, the sides are in a specific ratio:

x, x√3, and 2x,

where x is the length of the shortest side (opposite the 30-degree angle).

Step 1:

Identify the shortest side (opposite the 30-degree angle).

Let's assume the length of the shortest side (opposite the 30-degree angle) is "s."

Step 2:

Find the other side lengths.

The side opposite the 60-degree angle is s√3.

The hypotenuse is twice the length of the shortest side, so it is 2s.

Thus,

In a 30-60-90 triangle, the side opposite the 30-degree angle (s) has a length of "s," and the hypotenuse has a length of "2s."

The side opposite the 60-degree angle is "s√3."

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The distance between charges of +2.35 and −1.96,  should be approximately 1.566 picometers (pm).

Coulomb's law states that the force (F) between two point charges is given by:

F =[tex]\dfrac{(k \times q1 \times q2)}{r^2}[/tex]

Where:

The electrostatic force between the charges is F

k is Coulomb's constant, approximately equal to 8.99 × 10^9 N m²/C².

The magnitudes of the two charges are [tex]q_1[/tex] and [tex]q_2[/tex].

The distance between the charges is r.

Given that the charges are +2.35 and −1.96, we'll call the distance between them x (in pm). Similarly, for charges +4.06 and −2.11, the distance is given as 2.26 pm.

Setting up the equation:

For the first pair of charges (q1 = +2.35 C and q2 = −1.96 C):

F1 =[tex]\dfrac{(k \times |2.35 \times (-1.96)|)}{x^2}[/tex]

For the second pair of charges (q1 = +4.06 C and q2 = −2.11 C):

F2 =[tex]\dfrac{(k \times |4.06 \times (-2.11)|)}{(2.26)^2}[/tex]

Since the forces are said to be equal, we have:

F1 = F2

The solution of the expression for x is given by:

[tex]\dfrac{(k \times |2.35 \times (-1.96)|}{x^2}[/tex] =[tex]\dfrac{(k \times |4.06 \times (-2.11)|)}{(2.26)^2}[/tex]

|[tex]\dfrac{(2.35 \times (-1.96)}{x^2}[/tex]| =[tex]\dfrac{|4.06 \times (-2.11)|}{ (2.26)^2}[/tex]

[tex]{(2.35 \times 1.96)} {x^2}[/tex] = [tex]\dfrac{(4.06 \times 2.11)} { (2.26)^2}[/tex]

[tex]x^2[/tex] =[tex]\dfrac{(2.35 \times 1.96 \times (2.26)^2} {(4.06 \times 2.11)}[/tex]

[tex]x^2[/tex] = 2.450206485

x ≈ [tex]\sqrt{2.450206485[/tex]

x ≈ 1.566 pm

Therefore, the distance between charges of +2.35 and −1.96,  should be approximately 1.566 picometers (pm).

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To find the distance between charges of +2.35 and -1.96 for the attractive force to be the same, use Coulomb's Law to calculate the force between charges of +4.06 and -2.11 separated by a distance of 2.26 pm. Then solve for the distance using the same formula and the calculated force value.

To find the distance between charges of +2.35 and -1.96 for the attractive force to be the same as between charges of +4.06 and -2.11, we can use Coulomb's Law. The formula for calculating the force between two charges is F = k * (|q1 * q2| / (d^2)) where k is the proportionality constant and d is the distance between the charges.

First, we calculate the force between charges of +4.06 and -2.11. Let q1 = +4.06, q2 = -2.11, and d = 2.26 pm. Plugging these values into the formula, we get:

F = (1/47e) * (|4.06 * -2.11| / (2.26^2))

Next, we can find the distance between charges of +2.35 and -1.96 such that the attractive force is the same. Let q1 = +2.35, q2 = -1.96, and F = the value we calculated earlier. Rearranging the formula to solve for d, we get:

d = sqrt((|q1 * q2| / (F * k)))

Answer:

The answer is actually 5.17 centimeters

Step-by-step explanation:

The question is asking you to calculate the minimum thickness so you have to find the lowest bounds.

The covers are 0.9 mm to 1 d.p so the minimum thickness is 0.85 because that is the lowest bound.

The pages are 0.13 mm to 2 d.p so the minimum thickness is 0.125 as that is the lowest bound.

0.85  x 2 = 1.7 and 0.125 x 400 = 50

50 + 1.7 = 51.7 which is the minimum length.

Final answer:

The minimum thickness of a book with 400 pages, each 0.13mm thick, and two covers, each 0.9mm thick, is calculated to be 53.8mm.

Explanation:

The minimum thickness of a book can be calculated by summing the thickness of the covers and all the pages. We are given that each cover is 0.9mm thick and each page is 0.13mm thick. To find the minimum thickness of the book, we multiply the thickness of each page by the total number of pages and then add the thicknesses of the front and back covers.

To calculate:

Thickness of all pages: 400 pages × 0.13 mm/page = 52 mm

Thickness of both covers: 2 covers × 0.9 mm/cover = 1.8 mm

Total minimum thickness: 52 mm + 1.8 mm = 53.8 mm

The minimum thickness of the book is therefore 53.8 mm.

The way to calculate the sum of the forces in the y direction of an elevator; has been outlined below

If you are in an elevator by itself, then the combined system of you and the elevator could have 3 possible situations which are;

Now, in the vertical y direction, there are three forces namely;

Thus, the sum of forces in the y-direction with the normal force acting on you from the elevator are any of the following;

N = mg;  provided that the elevator is at rest or moving at constant velocity.

N = mg + ma; Provided that the elevator has an upward acceleration.

N = mg - ma; Provided that the elevator has a downward acceleration.

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In an elevator at rest, the sum of the forces in the y direction is equal to the weight of the person.

If the elevator is at rest, the sum of the forces in the y direction is equal to zero. This means that the upward force exerted by the scale, Fs, must be equal to the downward force exerted by the weight of the person, w. According to Newton's third law, Fs and Fp (the force exerted by the person on the scale) are equal in magnitude and opposite in direction.

To find the value of Fs, we can apply Newton's second law, which states that the net force in the y direction is equal to the mass of the object times its acceleration. In this case, the net force is Fs - w and the acceleration is zero. Therefore, Fs = w.

So, the sum of the forces in the y direction of the elevator is equal to the weight of the person.

Answer:

B) 15

Step-by-step explanation:

In order to solve this we have to create a system of equations, where the easy puzzles are represented by x, and the hard puzzles are y, so you just have to multiply that for the points to get the total points in all:

30x+60y=1950

If the player did 50 in total:

x+y=50

Now we just solve for x in the second equation and then insert that into the first equation:

x=50-y

30(50-y)+60y=1950

1500-30y+60y=1950

30y=450

y=450/30

y=15

So we know that Tina solved 15 hard puzzles.

Answer:

A. 5/8 = h/20

Step-by-step explanation:

Topic: Triangle Similarity

As you can see in the image you can paint the problem that way, it means that each side of the triangle is a multiplier from the other one same side, so you can build a relation as follows:

[tex]\frac{5}{h} = \frac{8}{20} \\[/tex]

you can re arrange the equality as

[tex]\frac{5}{8} = \frac{h}{20}[/tex]

as you can ssee you just reached the option A. 5/8 = h/20

30240 are 5-digit numbers (including leading 0s) are there with no digit appearing exactly two times

A number system is defined as a system of writing to express numbers.

By means of Permutation we solve this

The term permutation refers to a mathematical calculation of the number of ways a particular set can be arranged.

The formula for permutation is [tex]^{n}P_{r} =\frac{n!}{(n-r)!}[/tex]

n is total number of objects

r is number of objects selected

We need to find 5-digit numbers (including leading 0s) are there with no digit appearing exactly two times

¹⁰P₅=10!/(10-5)!

=10!/5!

=10×9×8×7×6×5!/5!

=30240

Hence, 30240 are 5-digit numbers (including leading 0s) are there with no digit appearing exactly two times

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S/cos 55• the answer D

Final answer:

To find dwdt using the chain rule, differentiate w=xy+yz, where x=e^2t, y=2+sin(4t), and z=2+cos(7t), as functions of t, apply partial derivatives and multiply by dx/dt, dy/dt, and dz/dt.

Explanation:

The student asked how to use the chain rule to find dwdt as a function of x, y, z, and t, without rewriting x, y, and z in terms of t, and keeping e2t as x. Given w=xy+yz, where x=e2t, y=2+sin(4t), and z=2+cos(7t), we apply the chain rule to differentiate w for t, remembering that x, y, and z are all functions of t. To find debt, we derive each component individually and sum their contributions. The calculation involves taking partial derivatives of w to x, y, z, multiplied by their respective derivatives to t (dx/dt, dy/dt, dz/dt).

a. Let x  represent the number of questions finished.
b. The equation is  x + 37 = 78 , and solving yields  x = 41 .
c. The student finished 41 questions.

a. Define a variable for the unknown value. Let  x  represent the number of questions the student has finished.

b. Write and solve the equation. The total number of questions is the sum of the questions finished and the questions left:  x + 37 = 78 . Now solve for  x :

x = 78 - 37 = 41

So, the student has finished 41 questions.

c. Answer the question with the correct units. The student has finished 41 questions out of the total 78. Therefore, the student has [tex]\( \frac{41}{78} \)[/tex] of the test complete. To express this as a percentage, multiply by 100:

[tex]\[ \frac{41}{78} \times 100 \approx 52.56\% \][/tex]

The student has finished approximately 52.56% of the test.

Que. A student is taking a test. He has 37 questions left. If the test has 78 questions, how many questions has he finished? a. Define a variable for the unknown value. Let ...........represent............
b. Write and solve the equation.
c. Answer the question with the correct units........

To subtract the fractions 7 8/9 and 5 3/5, first convert them into improper fractions. Then, adjust them to the common denominator (45 in this case) and subtract to get the answer of 2 13/45.

To begin, we need to convert these mixed fractions (7 8/9 and 5 3/5) into improper fractions. 7 8/9 equals 71/9 (since 7*9 + 8 = 71) and 5 3/5 equals 28/5 (since 5*5 + 3 = 28). Now, we can subtract these fractions by finding a common denominator or a number that 9 and 5 mutually divide into. This number is 45. Therefore, we adjust these fractions to have the denominator of 45, getting 355/45 and 252/45. The subtraction of these adjusted fractions equals 103/45. That can be simplified into 2 13/45.

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