Consider the following refinery-type problem: 10x1 5x2 5x3 = 300 5x 1 10x2 8.,t3 = 300

We will need to add 85 grams of mass to the mass hanger in order to get a total single mass hanger system equal to 90 grams.

To get a total single mass hanger system equal to 90 grams, you will need to add 85 grams of mass to the mass hanger. This is because the mass hanger is already 5 grams, and you need to add enough mass to get to 90 grams.

Here's the step-by-step explanation:

1. Start with the mass of the mass hanger: 5 grams
2. Subtract this from the desired total mass: 90 grams - 5 grams = 85 grams
3. The result is the amount of mass you need to add to the mass hanger: 85 grams

The combination of slotted masses and mass hanger allows a student to quickly create any desired amount of mass.

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Answer:

x=7

Step-by-step explanation:

2x-0.4=1+1.8x

Subtract 1.8x from both sides

0.2x-0.4=1

Add 0.4 to both sides of the equation

0.2x=1.4

Divide both sides by 0.2

x=7

The original price of the laptop is calculated as $545

We are given;

Sales Price of Laptop = $299.75

Now, the laptop is on sale for 45% off regular price.

If original price is x, then we can express that;

(100% - 45%) * x = 299.75

Thus;

55%x = 299.75

0.55x = 299.75

x = 299.75/0.55

x = $545

Thus, the original price of the laptop is calculated as $545

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Answer:

B) 5p

Step-by-step explanation:

If you substitute 7 in for each equation you will see that the answers are either 7, 38, or 32, which are not 35. But when you substitute 7 in for B, 5(7), and multiply it out you get 35. I hope this helps :)

Answer:

\(\frac{18348}{1000}\)

Step-by-step explanation:

The 8 in the decimal part 0.348 is in the thousandths position, thus

18.348

= 18 \(\frac{348}{1000}\)

= \(\frac{18(1000)+348}{1000}\)

= \(\frac{18348}{1000}\)

Answer: A

Step-by-step explanation:

The coefficient of each x of each equation is the slope of that equation. So, you can find the slope of the lines.

For the red line, you see the line passes the (0, 2) point. It also passes (-4, -1). Since you have two points, you can find the slope. The slope is (y2-y1)/(x2-x1). Plugging these in, you get (-1-2)/(-4-0), which results in a slope of 3/4.

Now for this line, you can find the y-intercept to find the equation, which is where the line touches the y axis. This point is (0, 2). So, the equation for the red line is y = 3x/4 + 2, which is option A.

You don't need to find the equation for the blue line since all the other answers are incorrect.

None of the expressions is an identity

The expressions are given as:

I. y=x

II. 4 = 3x^2 + 2

III. x=x

In algebra, there are three identities; and they are

None of the given expression take the above forms

Hence, none of the expressions is an identity

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Answer:

Similarity is it is beautiful like your mom

Step-by-step explanation:

All 3 angles of the triangle added up will be equal to 180 degrees.

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with 100 flips, the outcome is very likely to be 45 heads or even less.

just because you have a 50% chance of getting heads, does not necessarily mean that you will get heads at exactly 50%.

100 coin flips will not always produce a 50-50 outcome of heads or tails. This is due to the fact that random events, while predictable in the long run, are not 100% predictable in small cases. For example, if we flipped a fair coin a quadrillion times, the variability in the outcomes caused by the coin's randomness would amount to a fractional value so small that calculators might even round the percentage of heads to 50%. However, with 100 flips, the outcome is very likely to be 45 heads or even less.

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The correct answer is: B. The function has no local maximums and has local minimums at approximately x = 5.8 and x = 28.8 (rounded to the nearest tenth).

To determine the location of the local extrema (maxima and minima) of the function f(x) = -0.697x^3 + 16642x^2 - 102407x + 650015, we need to find the critical points where the derivative of the function is equal to zero or does not exist. First, let's find the derivative of f(x) with respect to x: f'(x) = -2.091x^2 + 33284x - 102407. To find the critical points, we set f'(x) = 0 and solve for x: -2.091x^2 + 33284x - 102407 = 0. Using the quadratic formula, we can solve for x: x = (-b ± √(b^2 - 4ac)) / (2a). Plugging in the values a = -2.091, b = 33284, and c = -102407, we can calculate the values of x: x ≈ 5.779 or x ≈ 28.755. These are the potential locations of the local extrema.

To determine whether these points are maxima or minima, we can analyze the concavity of the function. Taking the second derivative, we have: f''(x) = -4.182x + 33284. Setting f''(x) = 0 and solving for x: -4.182x + 33284 = 0; x ≈ 7963.28. Since the second derivative is negative for x < 7963.28, we can conclude that x ≈ 5.779 corresponds to a local maximum, and x ≈ 28.755 corresponds to a local minimum. Therefore, the correct answer is: B. The function has no local maximums and has local minimums at approximately x = 5.8 and x = 28.8 (rounded to the nearest tenth).

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Answer:

AB=CD=10,AD=BC=29

Step-by-step explanation:

11111111111

Answer:

------------------------

AD and AB are adjacent sides hence their sum is half the perimeter:

And we are given that AD is 9 more than twice AB:

Substitute this into first equation:

Find AD by substituting the value of AB:

So the side lengths are:

Jay's error is that he misinterpreted the concept of the mean of the data set. The mean, also known as the average, is the sum of all numbers in a data set divided by the total number of data points. In this case, we do not know the context of the data set, so we cannot assume it refers to weight or the weight of a couch.

Jay's interpretation of the mean as "half the couch weight less than 7.76 pounds and half weighed more" is incorrect because it assumes that the data follows a symmetrical distribution, which may not be the case. The mean can be influenced by the values on either side of it, and it does not necessarily divide the data set in half.

If we assume that the data set refers to the weight of couches, then Jay's interpretation is incorrect because it is impossible for half the weight of a couch to be less than its weight. Rather, weight is always a positive value, so it would be more appropriate to describe the data in terms of a range or distribution rather than in terms of half and half.

In conclusion, Jay's error was in misinterpreting the meaning of the mean, assuming a symmetrical distribution, and making assumptions about the data set without the necessary context. It is important to understand the context and statistical properties of data before making any conclusions or interpretations.

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531,441

solution:

Multiply.

(9²)³

Multiply 9².

9 x 9

9² the 2 means multiply to itself.

so 9x9 is equal to (81)³

Now multiply it again

81 x 81 x 81

= 531,441

The students could use what they know of triangle rectangles, in the image below you can see the diagram that the students could use to estimate the height of the tower.

First, the students could use the measuring tape to find the distance between the base of the tower and them, this distance is represented with the variable S in the image below.

Now, using the clinometer, they could find the elevation angle between their viewpoint and the tip of the tower. This would be the angle θ in the image (notice that they should do this from the ground).

So at this point, we know one angle and the adjacent cathetus to that angle.

And we want to find the height of the tower, which is the opposite cathetus to the known angle.

Then we can remember the trigonometric relation:

tan(a) = (opposite cathetus)/(adjacent cathetus)

Replacing these by the things we know:

tan(θ) = H/S

tan(θ)*S = H

Then, by measuring θ and S, we can find the height.

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Answer:

x=9

Step-by-step explanation:

Answer:

x = 9

Step-by-step explanation:

According to the Product of a Power Property, when you multiply the power with the same base, you just have to add the exponents.

Answer:

10

Step-by-step explanation:

PEMDAS

Answer:

a homogeneous mixture of two or more substances in relative amounts that can be varied continuously up to what is called the limit of solubility

The greatest common factor (GCF) of the expression 12x^3y, 6x^2y^2, and -9xy^3 is 3xy, and factoring out this GCF yields 3xy(4x^2 - 2xy - 3y^2).

To factor the GCF, we need to identify the common factors present in all the terms. In this case, the common factors among the terms are 3, x, and y. By factoring out the GCF, we can rewrite the expression as 3xy multiplied by the remaining factors.

The GCF, 3xy, is then distributed to each term within the parentheses. This process leaves us with the expression (4x^2 - 2xy - 3y^2) within the parentheses. By factoring out the GCF, we have effectively extracted the common factors, leaving behind the remaining factors that differ from term to term.

Thus, the correct factorization of the GCF is 3xy(4x^2 - 2xy - 3y^2), where the GCF 3xy has been factored out, and the remaining factors are contained within the parentheses.

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Answer:

Step-by-step explanation:

If the parabola is 72 m wide, then if we were to plot this parabola on a piece of (very large, lol) graph paper, we could plot one point at (72, 0) and the other one at (0, 0) since that would ensure that the arch is 72 m wide (72 - 0 = 72). The thing to remember now is that the vertex is exactly halfway between those 2 points with regards to the x-intercepts. In other words, if the width of the arch is 72 meters and the x values run from 0 to 72, then the x coordinate (or h, actually) of the vertex is 36 since 36 is halfway between 0 and 72 on the x-axis. Since the vertex goes up to 27 m, the k coordinate of the vertex is 27.

So here's what we have:

Coordinate points: (0, 0) and (72, 0)

Vertex: (36, 27)

We will use one of those coordinates along with the vertex in

\(y=a(x-h)^2+k\) and solve for a. Pro tip: since this is an upside down parabola, a better be negative when we solve for it!

Filling in x, y, h, and k:

\(0=a(72-36)^2+27\) and

\(o=a(36)^2+27\) and

\(0=1296a+27\) and

\(-27=1296a\) so

\(a=-\frac{27}{1296}\) which simplifies to

\(a=-\frac{1}{48}\)

Writing the equation now looks like this:

\(y=-\frac{1}{48}(x-36)^2+27\)

Not sure what form you need that expressed in, but that's the vertex form so it should work, considering you were given a vertex to work with.

Answer:

yes

Step-by-step explanation: i agree its 3

Answer:

30.2%

Step-by-step explanation:

Use the percent error formula:

| (experimental - actual) / actual | x 100

Plug in the experimental and actual values:

| (experimental - actual) / actual | x 100

| (56 - 43 ) / 43 | x 100

(13 / 43) x 100

= 30.2

So, the percent error is 30.2%

9514 1404 393

Answer:

  ∠QPS = 101°

  ∠PSR = 79°

Step-by-step explanation:

The marked angles are called "same-side interior angles" or "consecutive interior angles". By either name, they are supplementary.

  (2k +89) +(3k +61) = 180

  5k +150 = 180 . . . . . . . . . collect terms

  5k = 30 . . . . . . . . . subtract 150

  k = 6 . . . . . . . divide by 5

Then the angles are ...

  ∠QPS = (2·6 +89)° = 101°

  ∠PSR = (3·6 +61)° = 79°

Answer:

∠QPS = 2 x 6 + 89 =101°

∠PSR = 3 x 6 + 61 =79°

Step-by-step explanation:

∠QPS and ∠PSR are consecutive interior angles, they are supplementary

(2k+89) + (3k+61) = 180

5k + 150 = 180

5k = 180-150 = 30

k = 6

∠QPS = 2 x 6 + 89 =101

∠PSR = 3 x 6 + 61 =79

There are 18.384 pounds in 16.6 in³ of gold weighs.

To determine the weight of 16.6 in³ of gold, we can use the given density of gold and conversion factors for inches, centimeters, grams, and pounds.

Density of gold = 19.3 g/cm³

1 inch = 2.54 cm

454 g = 1 lb

Convert the volume from cubic inches to cubic centimeters:

16.6 in³ × (2.54 cm/in)³ = 432.08888 cm³ (rounded to five decimal places)

Calculate the mass of gold using the density and volume:

Mass = Density × Volume

Mass = 19.3 g/cm³ × 432.08888 cm³ = 8352.992 g (rounded to three decimal places)

Convert the mass from grams to pounds:

Mass in pounds = 8352.992 g × (1 lb/454 g) ≈ 18.384 lb (rounded to three decimal places)

Therefore, 16.6 in³ of gold weighs approximately 18.384 pounds.

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The mom delivered a total of 283 ounces of baby.

The lucky mom gave birth to three babies, each with different weights. Baby A weighed 4 lbs and 9 oz, which is equivalent to 73 oz. Baby B weighed 7 lbs and 8 oz, which is equivalent to 120 oz.

Finally, baby C weighed 5 lbs and 10 oz, which is equivalent to 90 oz. To find the total weight of the babies, we need to add the weight of each baby together. So, 73 oz + 120 oz + 90 oz equals 283 oz. Therefore, the mom delivered a total of 283 ounces of baby.

It is important to note that delivering triplets can be challenging for the mother and the medical team. It requires careful monitoring and attention to ensure that all three babies are healthy and developing normally.  

Additionally, the mom may need additional support to manage the demands of caring for three newborns. However, despite the challenges, triplets are a special and unique blessing for families.

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The expression rewrites the total 32 + 80 using the largest common factor and the distributive property, and the expression can be expressed as 16(2 + 5).

Option (c) is correct.

The least common multiple of two integers is defined as the lowest number that is a multiple of two or more numbers. The abbreviation LCM stands for least common multiple.

It is assumed that:

The mathematical formula is:

= 32 + 80

To identify the most prevalent factor:

GCF( 32, 80) ( 32, 80) ( 32, 80)

We can use Euclid's division lemma to find the GCF:

GCF(32,80)= 16

The phrase 32 + 80 can be expressed as follows:

= 32 + 80\s= 16(2 + 5)

As a result, the equation rewrites the total 32 + 80 using the largest common component and the distributive condition, and the expression can be expressed as 16(2 + 5).

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Answer:

Transformations can affect a function in a number of ways. Some common types of transformations include translations, reflections, rotations, and dilations.

A translation shifts a function horizontally or vertically without changing its shape. A reflection flips a function over a line of symmetry. A rotation rotates a function around a point. A dilation stretches or shrinks a function along one or both axes.

Each type of transformation changes the graph of the function in a specific way and can affect the domain, range, symmetry, and asymptotes of the function.

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Transformations affect functions by changing their position, shape, or size on the coordinate plane. The following are the common types of transformations and their effects on functions:

These are explained below:

Translation: A translation moves a function horizontally or vertically without changing its shape. This changes the position of the function on the coordinate plane, but not its slope or intercepts.

Reflection: A reflection flips a function over either the x-axis or y-axis. This changes the signs of the function's y-coordinates, but not its slope or x-intercepts.

Dilation: A dilation changes the size of a function, but not its shape. The scale factor determines how much the function expands or contracts.

Rotation: A rotation rotates a function around a fixed point, changing its orientation. The angle of rotation and the direction (clockwise or counterclockwise) determine the effect on the function's shape.

In general, transformations preserve the basic characteristics of a function, such as its slope and intercepts, while changing its position or shape on the coordinate plane.

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