A pile of coins, consisting of quarters and half dollars, it worth $11.75. If there are 2 more quarters than half dollars, how many of each are there?

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:

The statements that are true about the information given will be:

It should be noted that Euclidian geometry is simply about understanding the geometry of flat, two-dimensional spaces while non-Euclidian geometry is about curved surfaces.

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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.

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:

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

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........

Answer: the answer is -2192

Compound inequality is the combination of more than one inequality.

The compound inequality from [tex]|3x - 5| > 10[/tex] is:

(c) [tex]3x - 5 < -10[/tex] or [tex]3x - 5 > 10[/tex]

Given that:

[tex]|3x - 5| > 10[/tex]

When the above inequality is split, we have the following inequalities:

So, the result of the split is:

[tex]3x - 5 < -10[/tex] or [tex]3x - 5 > 10[/tex]

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S/cos 55• the answer D

This is a true statement!

The set of counting numbers {1, 2, 3, 4, 5, ...} is called the set of natural numbers. The natural numbers begin at 1 and go on indefinitely.

When we include 0 in the natural numbers, we then have a new set of numbers called the whole numbers. All the natural numbers are contained within the set of whole numbers.

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).

The standard deviation is the square root of the variance, which is about 1.897 grams when the variance is 3.6 grams.

If the variance of a probability was computed to be 3.6 grams, the standard deviation is the square root of the variance. To calculate the standard deviation, you perform the following steps:

By using a calculator, we find that the standard deviation is approximately 1.897 grams.

Final answer:

To determine the number of grains of sand in a 10kg bag with each grain weighing 10 to the negative third gram, convert the weight to grams and then divide by the weight of one grain. The answer is 10 million grains.

Explanation:

Grains of sand in a 10kg bag can be calculated by converting the weight to grams first: 10kg = 10,000g. Then, since each grain weighs 10-3g, we divide the total weight by the weight of one grain: 10,000g / 10-3g = 10,000,000 grains. So, there are 10 million grains of sand in a 10kg bag.

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.

Sketch the graph of Y=7^X.

Reflect the graph across the y-axis to show the function y=7^-x.

Stretch the graph vertically by a factor of 3 to show the function y=3 x 7^-x.

Shift the graph up 2 units to show the function y= 3 x 7^-x +2