Let S={[8 -2 6+ ]: ab oed} a, (a) Prove that S is a subspace of Mus(R) by verifying that S is closed under addition and closed under scalar multiplication (b) Find a basis fo?

The probability of winning $600 or less if you play the game 10 times, assuming that each game is independent IS 0.5630.

A popular probability distribution known as the binomial distribution simulates the likelihood of getting one of two outcomes given a set of parameters. It totals the number of trials when each trial has an equal chance of producing a particular result. The probability of success raised to the power of the number of successes and the probability of failure raised to the power of the difference between the number of successes and the number of trials are multiplied to create the binomial distribution.

Given,

Cash prize = $100

Probability of winning the game = 0.7

Using binomial distribution,

P(4 ≤X≤ 6) = P( X = 4) + P( X = 5) + P( X = 6)

P( 4 ≤ X ≤ 6)

= 1/4(0.6)⁴(0.4)⁴ + 10/5 (0.6)⁵(0.4)⁵ + 10/6 (0.6)⁶(0.4)⁶

= 0.1115 + 0.2007 + 0.2508

= 0.5630

The probability of winning $600 or less if you play the game 10 times, assuming that each game is independent IS 0.5630.

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The expression for  d=rt in terms of the time is t = d/r; t = 5.

Therefore,

In the equation d=rt

                          t = d/r

when distance is 40 and the rate is 8

                          t = d/r

Replace d with 40 and rate with 8

                          t = 40/8

                          t = 5

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The value of the fraction -5/7 and -4/7 added and subtracted from the fraction -21/2 added to 1/22 is 64/77.

The sum of 1/2 and -21/22 can be found by finding a common denominator,

1/2 = 11/22 (since 11 x 2 = 22)

-21/22 = -21/22

Therefore, the sum of 1/2 and -21/22 is,

= 11/22 - 21/22

= -10/22 = -5/11

The sum of -4/7 and -5/7 is,

-4/7 - 5/7 = -9/7

Now, subtracting as asked in the question.

= (-5/11)-(-9/7)

= (-5/11)+(9/7)

Finding common denominator to add the fractions,

7 x 11 = 77

(-5x7)/(11x7)+(9x11)/(7x11)

= -35/77 + 99/77

Now, we can combine the numerators,

-35/77 + 99/77 = 64/77

Therefore, the final answer is 64/77.

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Answer:

9

Step-by-step explanation:

Because x = 2 we can re arrange this too 3x2^2 - 2x2 + 1

after doing this we can simplify it too 12-4+1 which when we do it is just 9.

Answer:

Step-by-step explanation:

y=10

The measure of the angle the minute hand traces in 20 minutes is 120 degrees.

In a clock, the minute hand completes a full revolution every 60 minutes, which is 360 degrees. Therefore, in 1 minute, the minute hand covers 360 degrees / 60 minutes = 6 degrees.

To find the measure of the angle the minute hand traces in 20 minutes, we can multiply the rate per minute (6 degrees) by the number of minutes:

Angle traced by minute hand = Rate per minute × Number of minutes

Angle traced by minute hand = 6 degrees/minute × 20 minutes

Angle traced by minute hand = 120 degrees

Therefore, the measure of the angle the minute hand traces in 20 minutes is 120 degrees.

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The angles m∠APE and m∠EPD are complementary angles and so the measure of angle m∠EPD is equal to 20° which makes option D correct.

In geometry, if two angles are said to be complementary, then the total of their sum is equal to 90°.

The angles m∠APE and m∠EPD are complementary angles so we evaluate for the angle m∠EPD as follows:

m∠APE + m∠EPD = 90°

70° + m∠EPD = 90°

m∠EPD = 90° - 70° {subtract 70° from both sides}

m∠EPD = 20°.

Therefore, the measure of angle m∠EPD is equal to 20°.

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Answer:

11.6 is right

Step-by-step explanation:

Answer:

  ∠ABD = 19.5°

  ∠ABE = 160.5°

Step-by-step explanation:

Given angle ABC = 39° and its bisector BD, you want the measures of angle ABD and ABE, its supplement.

An angle bisector divides an angle into two equal parts, each with half the measure of the whole.

  ∠ABD = 1/2∠ABC

  ∠ABD = 1/2(39°)

  ∠ABD = 19.5°

The angles of a linear pair are supplementary: they total 180°. Angles ABD and ABE form a linear pair.

  ∠ABE = 180° -∠ABD

  ∠ABE = 180° -19.5°

  ∠ABE = 160.5°

Answer:

It represents a linear function because there is a constant rate of change.

Step-by-step explanation:

A linear function is arranged in or extending along a straight or nearly straight line.

So if the numbers keeps increasing, which it is, it will be rising in an almost complete straight line on a graph.  That means it is a linear function because the numbers keep increasing.

Answer:

g(y) = 1/3y + 5/3

Step-by-step Explanation:

We know that f(x) is synonymous with y so we can rewrite f(x) as y = 3x -5

To find the inverse of the function, we can switch y with x and x with y:

x = 3y - 5

Now we can isolate y to find the inverse of f(x):

(x = 3y - 5) + 5

(x + 5 = 3y) / 3

x/3 + 5/3 = y

1/3x + 5/3 = y

Thus, the inverse of f(x) is f^-1(x) = 1/3x + 5/3.  Since we want to write the inverse in terms of y, we get g(y) = 1/3y + 5/3.

If this answer doesn't match your answer choices (some of the answer choices you provided are unclear), please attach a pic and I can help you figure out which answer choice is correct)

Based on the calculated test statistic and the degrees of freedom, you can find the p-value associated with the test statistic.

To determine if the average height of Kennesaw State University (KSU) students has changed since 2005, we can conduct a hypothesis test.

Here are the steps to perform the test:

1. Set up the null and alternative hypotheses:
  - Null hypothesis (H0): The average height of KSU students has not changed since 2005.
  - Alternative hypothesis (Ha): The average height of KSU students has changed since 2005.

2. Determine the test statistic:
  - We will use a t-test since we have a sample mean and standard deviation.

3. Calculate the test statistic:
  - Test statistic = (sample mean - population mean) / (sample standard deviation / √sample size)
  - In this case, the sample mean is 69.1 inches, the population mean (from 2005) is 68 inches, the sample standard deviation is 3.5 inches, and the sample size is 50.

4. Determine the p-value:
  - The p-value is the probability of obtaining a test statistic as extreme as the one calculated, assuming the null hypothesis is true.

  - Using the t-distribution and the degrees of freedom (n-1), we can calculate the p-value associated with the test statistic.

5. Compare the p-value to the significance level:
  - In this case, the significance level is 0.05 (or 5%).
  - If the p-value is less than 0.05, we reject the null hypothesis and conclude that the average height of KSU students has changed since 2005. Otherwise, we fail to reject the null hypothesis.

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Answer:

1 = 44° (Opposite angles>

2 = 77° (By Angle sum property of a triangle)

3 = 82° ('' '' ' '' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ''')

There are 275 different desserts at this ice cream shop.

If the ice cream shop made 22 different flavors of ice cream, you would have 22 choices for a single flavor in a cone or a cup. For a sundae, you could choose a combination of two or more flavors. Let's assume you choose two flavors for your sundae.

You would have 22 options for the first flavor and 21 options for the second flavor since you can't repeat the same flavor.

So, the total number of different desserts you could have is:
22 (single flavor in a cone) + 22 (single flavor in a cup) +\(22 (\frac{21}{2} )\) (two flavors in a sundae)
= 22 + 22 + 231
= 275

Therefore, you could have 275 different desserts at this ice cream shop.

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-0.05 is the average rate of change in median age per year from 1930 to 1960.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given,  a data set that gives the median age of an American man at the time of his first marriage.

Year                             Median age

1910                              25.1

1920                             24.6

1930                             24.3

1940                             24.3

1950                             22.8

1960                             22.8

1970                             23.2

1980                             24.7

1990                             26.1

2000                             26.8

The average rate of change from 1930 to 1960 = (-24.3 + 22.8) / (1960-1930)

The average rate of change from 1930 to 1960 = -0.05

Therefore, the average rate of change in median age per year from 1930 to 1960 is -0.05.

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Answer:

about 64.29%

Step-by-step explanation:

900/1400= 0.64285...

=about 64.29%

Hey there!

3(7n + 6) - 5n

= 3(7n) + 3(6) - 5n

= 21n + 18 - 5n

= 16n + 18

Therefore, your answer should be:

16n + 18

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

y/( 3b-7)=x

Step-by-step explanation:

y=3bx-7x

Factor out x

y=(3b-7)x

Divide each side by (3b-7)

y/( 3b-7)=(3b-7)x/ ( 3b-7)

y/( 3b-7)=x

Answer:

\(\huge \boxed{x= \frac{y}{3b-7} }\)

Step-by-step explanation:

\(\sf y=3bx-7x\)

Factor out x from the expression.

\(\sf y=x(3b-7)\)

Divide both sides by (3b - 7).

\(\sf \displaystyle \frac{y}{3b-7} =x\)

Answer:

x = 5

Step-by-step explanation:

9(x - 2) = 27

9x - 18 = 27

     +18    +18

9x = 45

/9    /9

x = 5

Answer:

x = 2

Step-by-step explanation:

note that 4096 = \(8^{4}\) , then

\(8^{2x}\) = \(8^{4}\)

Since bases on both sides are equal, both 8 , then equate the exponents

2x = 4 ( divide both sides by 2 )

x = 2

Answer:

x = 2

Step-by-step explanation:

\(8^{2x} = 4096\)

Step 1 :- Write 4096 in the exponential form with the base of 8.

\(8^{2x} = 8^4 \)

Step 2 :- Since the base of both equation is same , set the exponents equal.

2x = 4

Step 3 :- Divide both side by 2

\({2x}{2} = \frac{4 }{2}\)

x = 2

The solution is,  the value of the given expression is  equivalent to 25.

An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.

here, we have,

given that,

the given expression is

125^2/ 125^(4/3)

=125^2/ 5^4

=125*125/5*5*5*5

=25*5*25*5/5*5*5*5

=25*25/ 5*5

=5*5

=25

so, we get the value of the given expression is  equivalent to 25.

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Answer:

Step-by-step explanation:

The probability that it contains no 0's is 0.19%

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. The chances that an event will occur increases with its probability.

Total number of integer from 100 to 999 where both are included = 900

Now, from 100- 999 inclusive there are 19 numbers containing at least zero

(100,101,102,103,104,105,106,107,108,109,110,120,130,140,150,160,170,180,

190)

and we have the same number in each hundred from x00 to x99 where x ranges from 1 to 9

so, the total number of integer from 100 - 999 inclusive that have zero = 9 (19) = 171

Hence, the probability that  we select a digit that contain zero

= 171/900

= 19/100

=0.19%

The probability that it contains no 0's randomly is 0.19%

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The solution for the equation given would be x = 2 and x = -1.

To solve the equation 2[x² + 2x + 1] - x² - 4x + 4 = x² - 3x, we can simplify and rearrange the terms as follows:

2x² + 4x + 2 - x² - 4x + 4 = x² - 3x

x² - 3x + 6 = x² - 3x

2x² - 2x - 6 = 0

Dividing both sides by 2, we get:

x² - x - 3 = 0

We can then solve for x by factoring or using the quadratic formula. Factoring gives:

(x - 2)(x + 1) = 0

So, the solutions are x = 2 and x = -1.

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Answer:

\(G\) is not function. The reason is that it is not one-to-one.

Step-by-step explanation:

A function is a mapping that is also one-to-one.

\(G\) is indeed a mapping; it takes an input and relates it to one or more outputs.

A mapping is one-to-one if and only if each input is mapped to only one output. \(G\) is not one-to-one because it maps the input \(1\) to four different outputs. Hence, \(G\) isn't a function.

The probability that at least one of them is not wearing a seatbelt is 0.5021.

Potential is described by probability. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of events. Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true.

These concepts now have an axiomatic mathematical formalization thanks to probability theory, which is widely employed in disciplines including statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, and philosophy.

Let X be the proportion of drivers who do not use a seat belt. It has a binomial distribution, as shown by,

n=4, p=1-0.84

p=0.16

The likelihood that at least one of them is not wearing seatbelt is:

P(X≥1)=1-P(X<1)

=1-P(X=0)

=1-{(4₀)(0.16)⁰(1-0.16)⁴⁻⁰

=1-0.4979

=0.5021.

Therefore, the probability that at least one of them is not wearing a seatbelt is 0.5021.

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The next number in the series is 125.

The given series appears to follow a pattern of dividing each number by 2 and then subtracting 1 to obtain the next number. Let's analyze the pattern step by step:

Starting with 8, when we divide it by 2, we get 4. Then subtracting 1 from 4 gives us 3, which is not part of the given series. However, if we continue the pattern, dividing 4 by 2 gives us 2, and subtracting 1 from 2 gives us 1, which matches the next number in the series.

Moving forward, if we divide 2 by 2, we get 1, and subtracting 1 from 1 gives us 0. However, 0 is not part of the given series. If we continue the pattern, dividing 1 by 2 gives us 0.5, and subtracting 1 from 0.5 gives us -0.5. Again, -0.5 is not part of the series.

Therefore, it seems reasonable to consider that the pattern is only valid when the result of the division is a whole number. Following this pattern, if we divide 1 by 2, we obtain 0.5, and subtracting 1 from 0.5 gives us -0.5. However, if we divide 0.5 by 2, we get 0.25, and subtracting 1 from 0.25 gives us -0.75. Therefore, we conclude that the pattern breaks down after reaching 1.

Taking into account the valid results of the pattern, the next number in the series would be obtained by dividing 1 by 2, which gives us 0.5, and then subtracting 1 from 0.5, resulting in -0.5. However, since negative numbers are not part of the given series, we disregard this result.

Considering that the pattern breaks down after reaching 1, we cannot determine the next number based on the given pattern. Therefore, the given series does not follow a consistent pattern, making it impossible to identify the next number accurately.

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Answer:

Total framed print = 517

Step-by-step explanation:

Framed print:

Small = 23

Medium = 264

Large = 188

Extra large = 42

Total framed print = Small + Medium + Large + extra large

= 23 + 264 + 188 + 42

= 517

Total framed print = 517

Unframed print:

Small = 152

Medium = 544

Large = 496

Extra large = 81

Total unframed print= Small + Medium + Large + extra large

= 152 + 544 + 496 + 81

= 1,273

Answer:

C- 517

Step-by-step explanation: