2. Determine the product of the first 100 Whole Numbers.​

Answer:

49

Step-by-step explanation:

Jen bought 5 CDs for $57.50. What was the unit rate?

The given price for five CD's is $57.50. You're being asked to find the unit rate, also known as unit price, which is the cost of one CD.

To find the unit rate of an item, you need to divide the price by the quantity.

\(\text{Unit Rate} = \frac{price}{quantity}\)

The first step is to substitute the given amounts into the above formula.

\(\text{Unit Rate} = \frac{\$57.50}{5}\)

Now, all you need to do is divide.

\(\text{Unit Rate} = \frac{\$57.50}{5} \rightarrow \$11.50\)

The unit rate is $11.50 per CD.

Answer:

The unit rate is $11.50 per CD.

Step-by-step explanation:

Answer:

A dilation is a type of transformation that changes the size of the image. The scale factor, sometimes called the scalar factor, measures how much larger or smaller the image is. Below is a picture of each type of dilation (one that gets larger and one that gest smaller).

Step-by-step explanation:

Dilations can also reduce the size of shape. The picture below demonstrations a dilation of 12 Any time that the scale factor is a fraction, the image will get smaller.

It's always easier to understand a concept by looking at specific examples with pictures, so I suggest looking at the dilation examples below first...before you try to internalize the steps listed below and that explain the general formula for dilating a point with coordinates of (2, 4) by a scale factor of 12.

We have shown that for every ε > 0 and e>0, there exists a measurable subset A⊆E and N∈N such that (a) If n > N then |fn(x) - f(x)| < ε for all x∈A. (b) m(E - A) < ε/.

Given E is a measurable set with finite measure and {fn} be a sequence of measurable functions on E that converges point wise to f:

E → R.

We need to prove that for every e>0 and ε > 0, there exists a measurable subset A⊆E and N∈N such that:

(a) If n > N then |fn(x) - f(x)| < ε for all x∈A.

(b) m(E - A) < ε.

Let {< € E: |f(x) - f(x)| < ε}  be measurable, where ε > 0.

Therefore, {Em} = {x ∈ E: |f(x) - f(x)| < ε} is an increasing sequence of measurable sets since {fn} converges pointwise to f, {Em} is a sequence of measurable functions on E.

Since E is a measurable set with finite measure, there exists a measurable set A⊆E such that m(A - Em) < ε/\(2^n\).

Then we have m(A - E) < ε using continuity of measure.

Since Em is increasing, there exists an n∈N such that Em ⊆ A, whenever m(E - A) < ε/\(2^n\)

Now, if n > N, we have |fn(x) - f(x)| < ε for all x∈A.

Also, m(E - A) < ε/\(2^n\) < ε.

Thus, we have shown that for every ε > 0 and e>0, there exists a measurable subset A⊆E and N∈N such that

(a) If n > N then |fn(x) - f(x)| < ε for all x∈A.

(b) m(E - A) < ε

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The given pair of events are independent when your first coin flip results in heads. and your second coin flip results in heads.

Events that occur independently of any other events are referred to as independent events. if we flip a coin in the air and get the head, we will then flip the coin again, but this time we will get the tail. The occurrence of both events is unrelated in either instance. Tossing the coin the first time does not affect the outcome of the second toss.

Note that the events are not mutually exclusive as it is possible that both the first and the second toss are headed.

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Answer:

4/-2 (-2)

Step-by-step explanation:

bascically the slope is rise over run, so you rise 4 times and you go 2 to the left. Since its going to the left, it makes the slope negative (also by looking at the graph you can see that the slope is going down)

Answer:

The solution is 1

Step-by-step explanation:

(a^2)+b

(-2^2)+5

-4+5

1

The radius of the circle is r = 3.78 cm for the given circle.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the circle in a two-dimensional plane is called the area of the circle.

Given that the angle of the sector of the circle is 1.2 radians the area of the sector is 54 cm².

The radius of the circle will be calculated as:-

Area = Angle x πr²

54 = 1.2 x πr²

r² = ( 54 ) / ( 1.2 x π )

r² = 14.32

r = √14.32

r = 3.78 cm

Therefore, the radius of the circle is 3.78 cm.

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The vertex of the Quadratic function with a y-intercept of (5, 0) and an x-intercept of (0, 80) is located at the point (0, 0).

The vertex of a quadratic function given the y-intercept and x-intercept, we need to determine the axis of symmetry, which is the line that passes through the vertex. The x-coordinate of the vertex will be the midpoint between the x-intercepts, while the y-coordinate will be the same as the y-intercept.

Given that the y-intercept is (5, 0) and the x-intercept is (0, 80), we can determine the x-coordinate of the vertex by finding the midpoint of the x-intercepts. The x-coordinate of the midpoint is simply the average of the x-values:

x-coordinate of vertex = (0 + 0) / 2 = 0 / 2 = 0

Since the y-coordinate of the vertex is the same as the y-intercept, the vertex will have the coordinates (0, 0).

Therefore, the vertex of the quadratic function is (0, 0).

In conclusion, the vertex of the quadratic function with a y-intercept of (5, 0) and an x-intercept of (0, 80) is located at the point (0, 0).

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Answer:

16

Step-by-step explanation:

2x+ y -z = 2*10+5-9

             = 16

Answer:

2x + y - z = 16

Step-by-step explanation:

Given expression,

→ 2x + y - z

Now we have to use,

→ x = 10

→ y = 5

→ z = 9

→ w = 12

Let's evaluate the expression,

→ 2x + y - z

→ 2(10) + 5 - 9

→ 20 + 5 - 9

→ 20 - 4

→ 16 => {answer}

Therefore, the answer is 16.

The number of combinations of 6 boys and 20 girls that can exist among 26 children born in a hospital on a given day is 230,230.

]To calculate the number of combinations, we can use the concept of binomial coefficients. The formula for calculating the number of combinations is C(n, k) = n! / (k!(n-k)!), where n is the total number of objects and k is the number of objects we want to select.

In this case, we have 26 children in total, and we want to select 6 boys and 20 girls. Plugging these values into the formula, we get C(26, 6) = 26! / (6!(26-6)!) = 230,230. Therefore, there are 230,230 different combinations of 6 boys and 20 girls that can exist among the 26 children born in the hospital on that given day.

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Answer:

2

Step-by-step explanation:

\( \sqrt[3]{8} \\ \\ = \sqrt[3]{ {2}^{3} } \\ \\ = 2\)

5

+

8

+

3

+

4

=

−

4

0

+

4

5x+8+3x+4=-40+4

5x+8+3x+4=−40+4

Solve

1

Add the numbers

5

+

8

+

3

+

4

=

−

4

0

+

4

5x+{\color{#c92786}{8}}+3x+{\color{#c92786}{4}}=-40+4

5x+8+3x+4=−40+4

5

+

1

2

+

3

=

−

4

0

+

4

5x+{\color{#c92786}{12}}+3x=-40+4

5x+12+3x=−40+4

2

Combine like terms

3

Add the numbers

4 more steps

Solution

=

−

6

x=-6

x=−6

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Answer:

9.4

Step-by-step explanation:

a2+b2=c2

8^2 + 5^2 = c2

64 + 25 = 89

square root of 89 = 9.4

Atmospheric pressure is an indicator of weather. When a low-pressure system moves into an area, it usually leads to cloudiness, wind, and precipitation. High-pressure systems usually lead to fair, calm weather. A barometer measures atmospheric pressure, which is also called barometric pressure.

Here's how air pressure impacts weather as:

High and Low Pressure Systems: Air pressure is the weight of the atmosphere above a specific area. High-pressure systems (anticyclones) are associated with descending air, leading to clear skies and stable weather conditions. On the other hand, low-pressure systems (cyclones) are characterized by ascending air, which often brings clouds, precipitation, and unsettled weather.

Wind: Wind influences weather patterns, such as moving clouds, precipitation, and temperature changes.

Fronts: When two air masses with different temperatures and pressures meet, it forms a weather front. Fronts are responsible for significant weather changes, such as storms, rain, and temperature fluctuations.

Precipitation: Air pressure affects the formation of clouds and precipitation. When air rises due to low pressure, it cools, and the moisture in the air condenses into clouds and eventually falls as rain, snow, sleet, or hail.

Air Stability: High-pressure systems typically create stable atmospheric conditions, inhibiting the formation of clouds and precipitation. Conversely, low-pressure systems tend to bring unstable weather conditions and are associated with stormy weather.

Barometric Pressure: Monitoring changes in barometric pressure is an essential tool in predicting short-term weather changes. A rapid drop in pressure often indicates the approach of a storm, while a rise in pressure usually signals improving weather.

Hence, air pressure is a key factor in the formation and movement of weather systems. Meteorologists use air pressure measurements to make weather forecasts and understand the atmospheric conditions that lead to various weather phenomena.

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The probability that the length of a component lies between 19 and 21 centimeters is 0.0376.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given:

Population mean, µ = 14

Population standard deviation, σ = 3

Probability that the length of a component lies between 19 and 21 centimeters

= P(19 <  X  < 21)

= P( (19 - 14) / 3 < (X - µ) / σ < (21 - 14) / 3)

= P(1.67 < z < 2.33)

= P(z < 2.33) - P(z < 1.67)

Using excel function:

= NORM.S.DIST(2.33,1) - NORM.S.DIST(1.67,1)

= 0.9901 - 0.9525

= 0.0376

Hence, the probability that the length of a component lies between 19 and 21 centimeters is 0.0376.

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Answer:

\(P(Not\ 2019) = \frac{2}{7}\)

Step-by-step explanation:

Given

\(n(2019)= 3\)

\(n(2001)= 2\\\)

\(n(2008)= 2\)

\(n = 7\) --- total

Required

\(P(Not\ 2019)\)

When two quarters not minted in 2019 are selected, the sample space is:

\(S = \{(2001,2001),(2001,2008),(2008,2001),(2008,2008)\}\)

So, the probability is:

\(P(Not\ 2019) = P(2001,2001)\ or\ P(2001,2008)\ or\ P(2008,2001)\ or\ P(2008,2008)\)

\(P(Not\ 2019) = P(2001,2001) + P(2001,2008) + P(2008,2001) + P(2008,2008)\)

\(P(2001,2001) = P(2001) * P(2001)\)

Since it is a selection without replacement, we have:

\(P(2001,2001) = \frac{n(2001)}{n} * \frac{n(2001)-1}{n - 1}\)

\(P(2001,2001) = \frac{2}{7} * \frac{2-1}{7 - 1}\)

\(P(2001,2001) = \frac{2}{7} * \frac{1}{6}\)

\(P(2001,2001) = \frac{1}{7} * \frac{1}{3}\)

\(P(2001,2001) = \frac{1}{21}\)

\(P(2001,2008) = P(2001) * P(2008)\)

Since it is a selection without replacement, we have:

\(P(2001,2008) = \frac{n(2001)}{n} * \frac{n(2008)}{n - 1}\)

\(P(2001,2008) = \frac{2}{7} * \frac{2}{7 - 1}\)

\(P(2001,2008) = \frac{2}{7} * \frac{2}{6}\)

\(P(2001,2008) = \frac{2}{7} * \frac{1}{3}\)

\(P(2001,2008) = \frac{2}{21}\)

\(P(2008,2001) = P(2008) * P(2001)\)

Since it is a selection without replacement, we have:

\(P(2008,2001) = \frac{n(2008)}{n} * \frac{n(2001)}{n - 1}\)

\(P(2008,2001) = \frac{2}{7} * \frac{2}{7 - 1}\)

\(P(2008,2001) = \frac{2}{7} * \frac{2}{6}\)

\(P(2008,2001) = \frac{2}{7} * \frac{1}{3}\)

\(P(2008,2001) = \frac{2}{21}\)

\(P(2008,2008) = P(2008) * P(2008)\)

Since it is a selection without replacement, we have:

\(P(2008,2008) = \frac{n(2008)}{n} * \frac{n(2008)-1}{n - 1}\)

\(P(2008,2008) = \frac{2}{7} * \frac{2-1}{7 - 1}\)

\(P(2008,2008) = \frac{2}{7} * \frac{1}{6}\)

\(P(2008,2008) = \frac{1}{7} * \frac{1}{3}\)

\(P(2008,2008) = \frac{1}{21}\)

So:

\(P(Not\ 2019) = P(2001,2001) + P(2001,2008) + P(2008,2001) + P(2008,2008)\)

\(P(Not\ 2019) = \frac{1}{21} + \frac{2}{21} +\frac{2}{21} +\frac{1}{21}\)

Take LCM

\(P(Not\ 2019) = \frac{1+2+2+1}{21}\)

\(P(Not\ 2019) = \frac{6}{21}\)

Simplify

\(P(Not\ 2019) = \frac{2}{7}\)

The branch of mathematics that analyses the strategic behavior of decision-makers is known as game theory.

The branch of mathematics that analyzes the strategic behavior of decision-makers is known as Game Theory.

Game theory is the study of the mathematical modeling of social interactions between agents. [1] It has applications in all areas of the social sciences, including logic, systems science, and computer science. It was originally focused on a two-player zero-sum game where each player's win or loss equals the other player's win or loss. In the 21st century, game theory applies to many social relationships; is now the subject of research on decision-making in humans, animals, and computers. The modern theory begins with the idea of ​​a combination of competition in a two-player zero-sum game and its proof by John von Neumann.

Von Neumann's original proof of continuity in a linear system using Brouwer's fixed point theorem has become a standard in game theory and business mathematics. His research was based on the 1944 book Game Theory and Economic Behavior by Oskar Morgenstern, which deals with multiplayer cooperative games. The second edition of this book presents an axiomatic theory of expected utility that enables mathematical statisticians and economists to solve decisions in uncertainty.

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It would be (4, -5)

Hope this helps!

Answer:

the actual length is 15 yards

Answer:

2x-5y

Step-by-step explanation:

9x-7x= 2x

3y-8y= -5y

Answer:

....................

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

Answer:

the correct answer is 0

Step-by-step explanation:

The correct formula to simulate a variable uniformly distributed between 100 and 200 using x is c. 100 + 100x.

To simulate a variable uniformly distributed between 100 and 200 using a random number x between 0 and 1, you can use the formula:

Variable = 100 + (200 - 100) * x

Let's break down the formula:

a. 100 + x: This will give a variable that ranges from 100 to 101, not between 100 and 200.

b. 200 - x: This will give a variable that ranges from 199 to 200, not between 100 and 200.

c. 100 + 100x: This formula is correct and will give a variable that ranges from 100 to 200, with x ranging from 0 to 1.

d. 200x: This formula will give a variable that ranges from 0 to 200, not between 100 and 200.

Therefore, the correct formula to simulate a variable uniformly distributed between 100 and 200 using x is c. 100 + 100x.

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Answer:

substituting  & graphing

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

\(\frac{1}{5}x-5\)

-5/5

-1

Hopes this helps please mark brainliest

Answer:  The answer is -1 or 1

Answer:

equivalent is the aswer

Hence the given statement if p is an invertible m x m matrix, then rank PA = rank A is proved.

what is invertible matrix?

An invertible matrix is a matrix for which matrix inversion operation exists, given that it satisfies the requisite conditions.

proof:

Let A be an m × m matrix and P be an invertible m × m matrix.

We know that Rank(A) is the number of non-zero rows in A based on the definition of matrix rank.

Therefore,

Rank(PA) = Number of non-zero rows in PA

Therefore,

Rank(PA) = Number of non-zero rows in PA

               = Number of non-zero rows in A

               = Rank(A)

Hence, we can conclude that if P is an invertible m × m matrix, then Rank(PA) = Rank(A).

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