Yolanda is buying supplies for school. she buys n packages of pencils at 1.40 per package and m pads of paper at 1.20 each. what does each term in the expression 1.4 1.2 represent?

The relationship between the squares formed by the sides of a right triangle is defined by Pythagorean Theorem, which states that the square on the hypotenuse side is the sum of the squares on the other two sides.

According to Pythagorean Theorem, the square formed by the side length of the hypotenuse side of right triangle is equivalent to the sum of the squares formed by the lengths of the other two sides

Let a, b, and c represent the lengths of the sides of the right triangle, where;

a = The length of the hypotenuse side

b = The length of a leg of the right triangle

c = The length of the other leg of the right triangle

The area of each squares are therefore;

Area of the square formed by the hypotenuse side = a²

Area of the square formed by the legs = b² and c²

Therefore; a² = b² + c²

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Answer:

6x

Step-by-step explanation:

2x × 2= 4x

x +x = 2x

4x+ 2x = 6x

We need to find the probability that no students arrive during the professor's one-hour nap using the Poisson distribution. In this case, the average arrival rate (λ) is 3 students per hour (60 minutes / 20 minutes per student).

The probability mass function (PMF) for the Poisson distribution is given by:

P(X=k) = (e^(-λ) * λ^k) / k!

For k=0 (no student arrivals):

P(X=0) = (e^(-3) * 3^0) / 0!
P(X=0) = (e^(-3) * 1) / 1
P(X=0) ≈ 0.05

So the probability that the professor's nap will not be disrupted by any student arrivals is 0.05, which corresponds to option B.

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Answer:

n = 2

Step-by-step explanation:

16 = 8n

divide by 2 on both sides

2 = n

n equals 2

Answer: n = 2

Step-by-step explanation:

Switch sides:

8n =16

Divide both sides by 8:

8n/8 = 16/8

Simplify:

n =2

Answer:

40 students

Step-by-step explanation:

Answer:

y=1

Step-by-step explanation:

Original Equation:

6y+11=17(Group like terms)

6y=17-11(You will subtract 11 from 17)

6y=6(You will then Divide Both Sides by 6)

Y=1( Leaving y with 1 because 6 will cancel each other out, and 6 divided by 6 is 1)

The mean of a dataset is the average of the dataset.

The given parameters are:

\(\mathbf{x = 0, 0, 0, 1, 1, 1, 2, 2, 3, 5}\)

(a) Mean and Standard deviation

The mean of the dataset is calculated using:

\(\mathbf{\bar x = \frac{\sum x}{n}}\)

So, we have:

\(\mathbf{\bar x = \frac{0+ 0+ 0+ 1+ 1+ 1+ 2+ 2+ 3+ 5}{10}}\)

\(\mathbf{\bar x = \frac{15}{10}}\)

\(\mathbf{\bar x = 1.5}\)

Hence, the mean is 1.5

The standard deviation is calculated using:

\(\mathbf{\sigma_x = \sqrt{\frac{\sum(x - \bar x)^2}{n - 1}}}}\)

So, we have:

\(\mathbf{\sigma_x = \sqrt{\frac{(0 - 1.5)^2 + (0- 1.5)^2 + (0- 1.5)^2 + (1- 1.5)^2 + (1- 1.5)^2 + (1- 1.5)^2 + (2- 1.5)^2 + (2- 1.5)^2 + (3- 1.5)^2 + (5- 1.5)^2}{10 - 1}}}\)

\(\mathbf{\sigma_x = \sqrt{\frac{22.5}{9}}}\)

\(\mathbf{\sigma_x = \sqrt{2.5}}\)

\(\mathbf{\sigma_x = 1.58}\)

Hence, the standard deviation is 1.58

(b) When 5 is increased to a larger value

When 5 is increased:

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True. Probability of an uncertain outcome is a number between 0 and +1, exclusively.

The probability of an uncertain outcome is a measure of the likelihood that the outcome will occur, and it is always a number between 0 and 1, inclusive. A probability of 0 means that the event is impossible, while a probability of 1 means that the event is certain. Probabilities between 0 and 1 indicate the degree of uncertainty about whether the event will occur or not.

Probabilities cannot be negative or greater than 1, as they represent a proportion of the total possible outcomes. If the probability of an event were negative or greater than 1, it would imply that the event is impossible or certain to occur, respectively, and violate the fundamental laws of probability theory.

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volume= 16/3, A coordinate plane is a graphing and description system for points and lines. A vertical (y) axis and a horizontal (x) axis make up the coordinate plane. There are four quadrants in the coordinate plane. The point where these lines connect is called the origin (0, 0).

limits

z= 0 to z = 4-y-2x

y= 0 to y = 4- 2x

x= 0 to x= 2

volume

v= \(\int\limits^2_0 \int\limits^4_0 \int\limits^4_0 dzdydx\)

v= \(\int\limits^2_0 \int\limits^4_0 (4-y-2x) dydx\)

v= \(\int\limits^2_0 ( 4y- y^{2} / 2 - 2xy) ^4^-^2^x _0\)

dx= \(\int\limits^2_0 [ 16-8x - 16+ 4x^2 - 16x / 2 - 8x+ 4x^2 ] dx\)

v= \(\int\limits^2_0 [ 8+ 2x^2- 8x] dx\\\)

= [ 8x + 2x^3 / 3 - 8x^2 / 2 ] ^2_0

= [16+ 16/3- 16]

v= 16/3

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Complete Question

Question: Sketch The Tetrahedron Enclosed By The Coordinate Planes And The Plane 2x+Y+Z=4. Use A Triple Integral To Find The Volume Of The tetrahedron

Answer:

17.5

Step-by-step explanation:

don't know why 17.5 isn't one of the answer choices but it's right

The simplified form of the trigonometric expression 1 - cos²θ is sin²θ.

To simplify the trigonometric expression 1 - cos²θ, we can use the trigonometric identity:
sin²θ + cos²θ = 1

Rearranging this identity, we get:
cos²θ = 1 - sin²θ

Now, substituting this into the original expression, we have:
1 - cos²θ = 1 - (1 - sin²θ)

Simplifying further:
1 - cos²θ = 1 - 1 + sin²θ

Combining like terms:
1 - cos²θ = sin²θ

So, the simplified form of the trigonometric expression 1 - cos²θ is sin²θ.

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Answer:

Explanation:

1.) 3.2 - 5.7 = -2.5

2.) 4.25 - (-2.3) = *double negative = positive* = +6.55

3.) -0.18-2 = -2.18 *2 negatives will add numbers, but the sign remains negative*

4.) -9 + 2.5 = -6.5 *since 9 is greater, we will use its sign, then subtract the two*

5.) (-9 + 5) +4 = -4 +4 = 0

3.2-5.7=C

4.25-(-2.3)=C

-0.18-2=C

-9+2.5=C

-9+5=4=B

Answer: \(60^{\circ}\)

Step-by-step explanation:

Given

Andy wants to turn \(180^{\circ}\) on his skateboard

Currently, he can make a turn of \(120^{\circ}\)

The difference between the required and current turn degree meets his goal i.e.

\(\Rightarrow 180^{\circ}-120^{\circ}\\\Rightarrow 60^{\circ}\)

Thus, he needs to turn by \(60^{\circ}\) to meet his goal

Answer:

  d = e

Step-by-step explanation:

An inscribed sphere in a cube will have a diameter equal to the edge length of the cube:

  d = e

__

The distance between the faces of the cube is the same as the edge length.

Answer:

Graphed verison:

See screenshot below! :^)

Solution version:

\(x > \frac{5}{4}y+5\)

Step-by-step explanation:

For graphed verison:

See screenshot below.

For solution version:

\(4x-5y > 20\)

Step 1: Add 5y on each side:

\(4x-5y+5y > 20+5y\)

\(= 4x > 5y+20\)

Step 2: Divide both sides by 4:

\(\frac{4x}{4} > \frac{5y+20}{4}\)

\(= x > \frac{5}{4}y + 5\)

Therefore, your answer is \(x > \frac{5}{4}y + 5.\)

Hope this helped! :^)

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Submitted on 4/15/2022 at 10:43 PM

(To avoid plagarism, by users whom decide to copy.)

There are no free variables or parameters, and the number of parameters in the general solution of Ax=0 is at most 0.

(a) If A is a 2×6 matrix, then the number of leading 1's in the reduced row echelon form of A is at most 2.

In the reduced row echelon form (RREF), the leading 1's are the first non-zero entry in each row. Since A is a 2×6 matrix, it can have at most two rows. In the RREF, each row can have at most one leading 1. Therefore, the maximum number of leading 1's in the RREF of A is 2.

(b) If A is a 2×6 matrix, then the number of parameters in the general solution of Ax=0 is at most 4.

The general solution of Ax=0 represents the solutions to the homogeneous equation when A is multiplied by a vector x resulting in the zero vector. The number of parameters in the general solution corresponds to the number of free variables or unknowns that can take any value.

In this case, since A is a 2×6 matrix, we have 6 variables but only 2 equations. This means that there will be 6 - 2 = 4 free variables or parameters. Therefore, the number of parameters in the general solution of Ax=0 is at most 4.

(c) If A is a 6×2 matrix, then the number of leading 1's in the reduced row echelon form of A is at most 2.

In the reduced row echelon form (RREF), the leading 1's are the first non-zero entry in each row. Since A is a 6×2 matrix, it can have at most two columns. In the RREF, each column can have at most one leading 1. Therefore, the maximum number of leading 1's in the RREF of A is 2.

(d) If A is a 6×2 matrix, then the number of parameters in the general solution of Ax=0 is at most 0.

Since A is a 6×2 matrix, we have more rows (6) than columns (2). This implies that the system of equations represented by Ax=0 is overdetermined. In an overdetermined system, it is possible for there to be no non-trivial solutions, meaning the only solution is x = 0.

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Answer:

Yes ! After 3.5 hours, it will be over half full !

Step-by-step explanation:

In the photo :)

Let \(\(a\)\) and \(\(b\)\) be integers such that \(\(ab = 4\)\). We want to prove that \(\((a - b)^3 - 9(a - b) = 0\).\)

Starting with the left side of the equation, we have:

\(\((a - b)^3 - 9(a - b)\)\)

Using the identity \(\((x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3\)\), we can expand the cube of the binomial \((a - b)\):

\(\(a^3 - 3a^2b + 3ab^2 - b^3 - 9(a - b)\)\)

Rearranging the terms, we have:

\(\(a^3 - b^3 - 3a^2b + 3ab^2 - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\(a^3 - b^3 - 3a^2(4) + 3a(4^2) - 9a + 9b\)\)

Simplifying further, we get:

\(\(a^3 - b^3 - 12a^2 + 48a - 9a + 9b\)\)

Now, notice that \(\(a^3 - b^3\)\) can be factored as \(\((a - b)(a^2 + ab + b^2)\):\)

\(\((a - b)(a^2 + ab + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Simplifying further, we get:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\)

Now, we can observe that \(\(a^2 + 4 + b^2\)\) is always greater than or equal to \(\(0\)\) since it involves the sum of squares, which is non-negative.

Therefore, \(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\) will be equal to \(\(0\)\) if and only if \(\(a - b = 0\)\) since the expression \(\((a - b)(a^2 + 4 + b^2)\)\) will be equal to \(\(0\)\) only when \(\(a - b = 0\).\)

Hence, we have proved that if \(\(ab = 4\)\), then \(\((a - b)^3 - 9(a - b) = 0\).\)

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When three standard six-faced dice are rolled, the probability that the sum of the three numbers rolled is 9 is equal to 10/216 or 5/108.

Total number of ways three dice can be rolled = 6 × 6 × 6 = 216.

Each dice can have any number from 1 to 6. The probability of rolling a particular number on a dice = 1/6.

The probability of rolling a particular number on three dice = (1/6) × (1/6) × (1/6) = 1/216.

In order to get a sum of 9, there are four combinations that can be rolled:

3 + 3 + 3 = 9

3 + 4 + 2 = 9

3 + 5 + 1 = 9

4 + 3 + 2 = 9

The probability of rolling any of these combinations = probability of rolling 3-3-3 + probability of rolling 3-4-2 + probability of rolling 3-5-1 + probability of rolling 4-3-2

= (1/216) + (3/216) + (3/216) + (3/216)

= 10/216 or 5/108.

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Answer:

y = -8x-5/4: -8

y = 1/8x + 4/5: 1/8

Step-by-step explanation:

The slope is the first number after the y =

Answer:

  (a)  3

Step-by-step explanation:

The fundamental theorem of algebra tells you a polynomial has a number of roots equal to its degree.

The degree of a polynomial is the largest exponent of the variable. Here, the degree is 3. That means there are three roots.

In general, the roots of a polynomial with real coefficients will be real or pairs of complex roots. The attached graph shows the roots of this cubic function are all real (and irrational).

Answer:

30

Step-by-step explanation:

That means that there are 6 pie pieces in each pie so just multiply by 5

another thing we can do is get rid of 1/6 by multiplying by 6 which means we also have to multiply 5 by 6

Answer:

\((d)\) \(H_o: p = 0.35\) \(H_a: p > 0.35\)

Step-by-step explanation:

Given

\(\mu = 35\%\)

Required

The hypothesis statements

First claim: 35% will support a strike.

This represents the null hypothesis

\(H_o: p = 0.35\)

Second claim: A greater percentage will support the strike.

This represents the alternate hypothesis

\(H_a: p > 0.35\)

Answer: 112.5

Step-by-step explanation: When line AB and CD intersect at point E, angle AEC equals BED so you set them equal to each other and find what x is. 5x -20 = x + 50, solving for x, which gives you 17.5. Finding x will tell you what AEC and BED by plugging it in which is 67.5. Angle BED and BEC are supplementary angles which adds up to 180 degrees. So to find angle CEB, subtract 67.5 from 180 and you get 112.5 degrees.

Answer: The reflection is across x = 6.

Step-by-step explanation:

As you look at the reflection, you can see there is a shadowing with the two points on this graph. Point X1 is on (6, -1) and Point X is on (6, -7)

When looking at the graph, you can easily eliminate the x-axis and y-axis for an answer is because neither Point X1 nor Point X has a relationship to the axis.

Since the coordinates are precisely 6 units from each other, there is a reflection across x = 6.

Therefore, the reflection is across x = 6. Hope this helps!

-From a 5th Grade Honors Student

Temperature of refrigerators - Cannot determine. Horsepower of race car engines - Ratio. Marital status of school board members - Nominal. Ratings of television programs - Ordinal. Ages of children enrolled in a daycare - Interval

The level of measurement for the temperature of refrigerators cannot be determined based on the given information. The temperature could potentially be measured on a nominal scale if the refrigerators were categorized into different temperature ranges. However, without further context, it is not possible to determine the specific level of measurement.

The horsepower of race car engines can be measured on a ratio scale. Ratio scales have a meaningful zero point and allow for meaningful comparisons of values, such as determining that one engine has twice the horsepower of another.

The marital status of school board members can be measured on a nominal scale. Nominal scales are used for categorical data without any inherent order or ranking. Marital status categories, such as "married," "single," "divorced," etc., can be assigned to school board members.

The ratings of television programs, such as "poor," "fair," "good," and "excellent," can be measured on an ordinal scale. Ordinal scales represent data with ordered categories or ranks, but the differences between categories may not be equal or measurable.

The ages of children enrolled in a daycare can be measured on an interval scale. Interval scales have equal intervals between values, allowing for meaningful differences and comparisons. Age, measured in years or months, can be represented on an interval scale.

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The sentence "After Tiara's lawn had been mowed, she cooled off in the swimming pool." contains a remote reference because the pronoun "she" is ambiguous and could refer to either Tiara or someone else. The sentence "After her lawn had been mowed, Tiara cooled off in the swimming pool." would avoid the remote reference by explicitly stating who cooled off in the pool.