How many envelopes can be made from a sheet of paper measuring 324 cm by 172 cm, if
each envelope requires a piece of paper of size 18 cm by 12 cm?

Answer:

Number is -10

Step-by-step explanation:

Let Number be x

so, 5x= 30+8x

Take 30 other side and 5x other side

so, 8x-5x=-30

3x=-30

x=-10

HOPE THIS HELPS... THANK YOU

Answer:

Step-by-step explanation:

3400/170 = 20 minutes.

Answer:

20 minutes

Step-by-step explanation:

3400 words / 170 wpm

20 minutes

The statements are A. ∠x and ∠y are supplementary angles, B. ∠w and ∠z are a linear pair.

Angle is the void between two surfaces or lines that meet. The angle is also expressed in degrees. The angle is 360 degrees for a full rotation.

Supplementary angle: When two angles add up to 180 degrees, they are considered to be supplementary angles.

Corresponding angle: The third line if two lines are parallel. Equal angles are formed by the matching angles.

Angles that are vertically opposed to one another are equal when two lines intersect.

Alternate angle: When two lines are parallel, a third line forms a z-angle, which is an equal angle to the parallel lines.

Complementary angle - When two angles add up to 90 degrees, they are considered to be complementary angles.

Angle x and angle y are supplementary angles. True.

Angle w and angle z are a linear pair. True.

Angle w and angle y are adjacent angles. False.

Angle x and Angle z are vertical angles. False.

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Answer: 96

The sum of the interior angles of a regular heptagon is equal to (n-2)180 degrees, where n is the number of sides of the polygon.

Since a regular heptagon has 7 sides, the sum of its interior angles is (7-2)180 = 720 degrees.

Therefore, the measure of each interior angle is 720 degrees / 7 = 104 degrees.

If the measure of an interior angle is (w + 8) degrees, then w + 8 = 104.

Solving for w, we get w = 96.

Answer: To find the father's and son's ages, we can set up two simultaneous equations:

Let's say the son's age is "x"

Then, the father's age would be x + 25

And the sum of their ages is x + (x + 25) = 53

So, 2x + 25 = 53

Solving for x, we get:

2x = 28

x = 14

Therefore, the son is 14 years old, and the father is 14 + 25 = 39 years old.

To use the elimination method, we can add the two equations:

x + (x + 25) = 53

2x + 25 = 53

Simplifying, we get:

2x = 28

x = 14

And the father's age would be x + 25 = 14 + 25 = 39 years old.

Step-by-step explanation:

On solving the provided question, we can say that the linear equation 100(p + s) + 100(p + s)

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

salad costs s dollars per serving. he needs to order 100 lunches for seventh graders and 100 lunches for eighth graders

the linear equation

100(p + s) + 100(p + s)

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The true statements are ∠X and ∠Y are supplementary angles, ∠W and ∠Z are a linear pair and ∠Y and ∠Z are complementary angles. The solution has been obtained by using angles and line.

What are angles and line?

Lines having little depth or width are said to be straight. Lines can be perpendicular, intersecting, transversal, and many more various forms. A figure in which two rays emanate from the same point is referred to be an angle.

We know that angles on a straight line add up to 180° and such angles are called supplementary angles.

Therefore, ∠X and ∠Y are supplementary angles.

Similarly, we know that angles on a straight line form a linear pair.

Therefore, ∠W and ∠Z are a linear pair.

Also, we know that two angles are complementary when their sum is 90°.

We can see from the figure that ∠Z and ∠Y add up to 90°.

Therefore, ∠Y and ∠Z are complementary angles.

Hence, the above provided statements are true about the angles.

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The figure of the question is attached below

Answer:

Step-by-step explanation:

To find the length of JL in the right triangle JKL, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides equals the square of the length of the hypotenuse (the longest side). In this case, JL is the hypotenuse and JK and KL are the two shorter sides.

Since K is a right angle in triangle JKL, we can find the lengths of JK and KL using the given information. We have KM = 6 and JM = 8, so we can use those values to find JK and KL:

JK = √(JM^2 - KM^2) = √(8^2 - 6^2) = √(64 - 36) = √(28) = 2√(7)

KL = KM = 6

Finally, to find JL, we can use the Pythagorean theorem:

JL = √(JK^2 + KL^2) = √( (2√(7))^2 + 6^2) = √(4 * 7 + 36) = √(52) = 2√(13)

So, JL = 2√(13).

Answer:

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The equivalent expression by combining like terms is 0.57b

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we substitute the same value(s) for the variable(s).

In order to write an equivalent expression by combining like terms, subtract 0.43b from b (Note: b = 1b). That is:

b-0.43b = 0.57b

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The algebra word problem method shows that Richard is 22 years old and Teo is 6 years old.

Algebra is used in our daily lives without us even recognizing it. Students can relate to and comprehend the significance of mathematics in the real world by solving algebraic word problems in worksheets.

Algebraic word problems usually comprise interpreting words into numbers, variables, their coefficients, and the use of appropriate arithmetic operations.

From the information given, we can the following system of equations as follows:

r + t = 28     --- (1)

r =  2t + 10   --- (2)

(2t + 10) + t = 28

3t + 10 = 28

3t = 28 - 10

3t = 18

t = 18/3

t = 6

From (1),  r + t = 28

r + 6 = 28

r = 28 - 6

r = 22

Therefore, we can conclude that Richard is 22 years old and Teo is 6 years old.

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Answer:

length = 12 feet , area = 72 ft²

Step-by-step explanation:

the perimeter (P) is the sum of the 4 sides of the rectangle.

let w be width then length is 2w

opposite sides of a rectangle are congruent , so

P = 2(2w) + 2w = 4w + 2w = 6w

given P = 36 , then

6w = 36 ( divide both sides by 6 )

w = 6

then

length = 2w = 2 × 6 = 12 feet

the area (A) of a rectangle is calculated as

A = length × width = 12 × 6 = 72 ft²

The level of measurements that the data we collect is weights in pounds is Ratio level.

The Ratio level of measurement: At this level of measurement, observations can have a value of zero as well as equal intervals. Although the characteristics are similar to those of interval level measurement, the zero in the scale distinguishes this sort of measurement from others. In the ratio level of measurement, the divisions between the points on the scale have an equivalent distance between them. We may confidently assert that 20 pounds are twice as heavy as 10 pounds. Ratio variables also have a meaningful zero-point.

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The mean absolute deviation, mad, of the given data, 21, 25, 16, 8, 16, 10, is 4.83

From the question, we are to calculate the mean absolute deviation, mad, of the given data

First, we will calculate the mean of the data

21, 25, 16, 8, 16, 10

Mean = (21 + 25 + 16 + 8 + 16 + 10)/6

Mean = 96/6

Mean = 16

Now, we will determine the positive differences of each number from the mean

         Positive differences

21        5

25       10

16        0

8         8

16        0

10        6

Now, we will find the mean of the positive differences

Mean absolute deviation =(5 + 10 + 0 + 8 + 0 + 6)/6

Mean absolute deviation = 29/6

Mean absolute deviation = 4.83

Hence, the mad is 4.83

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It is important to note that this calculation provides the value of tan(x) in terms of the cosine of the angle x, which is dependent on the specific triangle that is being considered.

Given the triangle with sides ZY = 48, ZX = 50, and XY = 14, we can use trigonometry to find the value of tan(x).

First, we can use the Pythagorean theorem to find the value of YX, the length of the side opposite angle x:

[tex]YX = \sqrt{(ZY^2 + ZX^2 - 2 * ZY * ZX * cos(x))[/tex]

We know that ZY = 48 and ZX = 50, so we can substitute these values into the equation:

[tex]YX = \sqrt{(48^2 + 50^2 - 2 * 48 * 50 * cos(x))[/tex]

[tex]YX = \sqrt{(2304 + 2500 - 2400 * cos(x))[/tex]

Next, we can use the definition of tangent to find the value of tan(x):

[tex]tan(x) = YX/ZX = \sqrt{(2304 + 2500 - 2400 * cos(x)) / 50[/tex]

It is important to note that this calculation provides the value of tan(x) in terms of the cosine of the angle x, which is dependent on the specific triangle that is being considered. The exact value of tan(x) will depend on the specific angle x in the triangle.

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The hare can afford to nap for approximately 3686.33 seconds if he does not want to lose the race.

We can use the time it takes the hare to run 100 m to determine how long he can afford to nap.

First, let's find the time it takes the hare to run the 100 m:

t = d / v

Where t is the time, d is the distance, and v is the velocity (speed) of the hare.

t = 100 m / 15 m/s

t = 6.67 s

Next, let's find the time it takes the tortoise to run 1 km (1000 m):

t = d / v

Where t is the time, d is the distance, and v is the velocity (speed) of the tortoise.

t = 1000 m / 0.27 m/s

t = 3700 s

So, the time it takes the tortoise to run the race is 3700 s. The time it takes the hare to run the first 900 m is 7 s. Therefore, the time the hare has left to nap is:

3700 s - 7 s = 3693 s

And the time it takes the hare to run the last 100 m is 6.67 s. Therefore, the hare can afford to nap for:

3693 s - 6.67 s = 3686.33 s

So, the hare can afford to nap for approximately 3686.33 seconds if he does not want to lose the race.

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The function represented by the graph is:

f(x) = |x – 1| + 3

This function takes the absolute value of the difference between x and 1, and then adds 3 to the result. The graph of this function will have a "V" shape centered at x = 1 with the vertex at (1, 3). The left side of the vertex will have a slope of -1, and the right side of the vertex will have a slope of +1. The y-intercept will be 3 units above the x-axis.

Answer:  B

Step-by-step explanation: YES

The probability that a 34 square foot metal sheet has at least 9 defects is 0.4308, rounded to four decimals.

Given that the sheet metal has an average of 7 defects per 20 square feet, we can find the rate parameter (λ) of the Poisson distribution as follows:

λ = (7 defects / 20 sq ft) = 0.35 defects per square foot

Let X be the number of defects in a 34 square foot metal sheet. Since X follows a Poisson distribution with rate parameter λ, we can find the probability that X is at least 9 defects using the cumulative distribution function (CDF) of the Poisson distribution:

P(X ≥ 9) = 1 - P(X < 9) = 1 - F(8)

where F(k) is the CDF of the Poisson distribution with rate parameter λ evaluated at k.

Using the Poisson distribution formula for F(k), we have:

F(k) = P(X ≤ k) = ∑(i=0 to k) [(λ^i * e^(-λ)) / i!]

Using a calculator or software, we can find that:

F(8) = P(X ≤ 8) = 0.5692

Therefore, we have:

P(X ≥ 9) = 1 - F(8) = 1 - 0.5692 = 0.4308

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Answer:

Step-by-step explanation:

Since they are congruent, you know that 8=x-3. 11-3=8. and 14=x+6=8. x is 8

We can fit 33 books on a 42-inch shelf if each book is 1 1/4 inches wide.

Using a unitary method, we can easily solve problems that involve proportional relationships between different units. In this problem, we used the unitary method to determine how many books can fit on a shelf based on its length and the width of one book.

To find out how many books can fit on a 42-inch shelf, we need to divide the length of the shelf by the width of one book. In this case, each book is 1 1/4 inches wide. However, it's important to convert this fraction to a decimal so we can do the math more easily. To do this, we can divide 1 by 4 and add it to 1 1/4:

1/4 = 0.25

1 1/4 = 1 + 0.25 = 1.25

Now that we know each book is 1.25 inches wide, we can use the unitary method to find how many books can fit on the shelf:

1 book = 1.25 inches

x books = 42 inches

To solve for x, we can cross-multiply:

1 book * 42 inches = 1.25 inches * x books

42 = 1.25x

Finally, we can divide both sides by 1.25 to isolate x:

42 / 1.25 = x

33.6 = x

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25 random students are asked how much they spent on books  is an example of a statistic.

The primary areas of study in statistics include data collection, organization, organization, analysis, interpretation, and presentation. It is customary to begin with a statistical population or a statistical model that will be examined when applying statistics to a scientific, industrial, or social problem. There are many different groups of people or things that can be referred to as populations, such as "each person living in a country" or "each atom making up a crystal." Every aspect of data is covered by statistics, including the planning of data collection in terms of survey and experiment design. Statisticians gather data using custom experiment designs and survey samples in the absence of census data.

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On solving the provided question we can say that the slope intercept of line is y = (3/2)x + 8

In mathematics, the intersectiοn point is the place on the y-axis where the slοpe of the line crosses. a place where the y-axis crosses οn a line or curve. Y = mx+c, where m stands fοr the slope and c for the y-intercept, is used as the equatiοn for the straight line to shοw this. The slope (m) οf the line and its y-intercept (b) are emphasised in the equatiοn's intercept form.

When an equation has the intercept fοrm (y=mx+b), the slope is m and the y-intercept is b. Sοme equations can alsο be rewritten such that they seem to be slοpe intercepts. If y = x is rewritten as y=1x+0, for instance, the slοpe and y-intercept are bοth changed to 1.

the line is y = -2/3x+1

so the slope, m = -2/3

since it parallel , new slope = 3/2

the slope intercept of line is

y +1 = 3/2(x+6)

y + 1= (3/2)x + 9

y = (3/2)x + 9 - 1

y = (3/2)x + 8

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There are a few general reasons why Marcus's results might differ from Zara and Arun's:

In terms of Solubility: Different solutes have different solubilities, which means they will dissolve to different extents in water. It's possible that the solutes Marcus is using have lower solubilities than the solutes used by Zara and Arun, which could lead to differences in the amount of solute that dissolves.

   Amount of solute added: Even if all three individuals add the same amount of solute to their test tubes, the amount of solute that actually dissolves may differ due to differences in solubility. If Marcus is using solutes with lower solubilities, he may be adding the same amount of solute as Zara and Arun, but a smaller proportion of it is dissolving.

  Spatula size: Marcus has the same number of spatulas for all three solutes, but it's possible that the size of his spatulas differs from those used by Zara and Arun. If Marcus's spatulas are smaller, he may be adding less solute to his test tubes, which could explain the differences in his results.

 Lastly, in terms of Experimental error: Finally, it's possible that there is some experimental error that is affecting Marcus's results. For example, he may not be measuring the amount of solute accurately, or he may be adding it to the test tube in a way that doesn't allow it to dissolve as well.

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Samantha drove 217 miles during the second day.

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Let D be the distance Samantha traveled during the second day. Then the total distance she drove is 468 miles. The equation will be:

D + 251 = 468

Solving for D:

D = 468 - 251

D = 217

Therefore, Samantha drove 217 miles during the second day.

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Answer:

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