Find the theoretical probability of randomly selecting a face card​ (J, Q, or​ K) from a standard deck of playing cards.

If g(x) is not equivalent to 0 for every x and f and g are constant functions, then f/g is additionally constant.

To prove that the function f/g is continuous, we need to show that it satisfies the epsilon-delta definition of continuity.

Let x0 be a point in the domain of f/g, and let ε be a positive real number. We must locate a real number that is positive so that

\(|(f/g)(x) - (f/g)(x0)| < ε |(f/g)(x) - (f/g)(x0)| < ε\) whenever \(|x - x0| < δ\).

\((f/g)(x0) = f(x0)/g(x0).\)

f(x) →  f(x0) and g(x) →  g(x0) as x →  x0 are known since f and g were continuous at x0. Therefore, we can assume that f(x) and g(x) are arbitrarily close to f(x0) and g(x0) respectively, provided x is sufficiently close to x0. Specifically, there exists a positive real number δ1 such that

\(|f(x) - f(x0)| < ε|g(x0)|/2\)  and \(|g(x) - g(x0)| < ε|g(x0)|/2\)  whenever

\(|x - x0| < δ1\).

These disparities allow us to estimate|(f/g)(x) - (f/g)(x0)| as follows:

\(|(f/g)(x) - (f/g)(x0)| = |(f(x)g(x0) - f(x0)g(x))/[g(x)g(x0)]|\)

\(≤ |f(x) - f(x0)|/|g(x)g(x0)| + |g(x) - g(x0)|/|g(x)g(x0)|\)

\(< (ε|g(x0)|/2)/|g(x)g(x0)| + (ε|g(x0)|/2)/|g(x)g(x0)|\)

\(= ε/2 + ε/2\) equals to ε,

provided we choose We have therefore demonstrated that f/g is constant at \(x0\). Since \(x0\) was arbitrary, we conclude that f/g is continuous on its entire domain.

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Answer:

8

Step-by-step explanation:

Let the number be n

6*n = 16 + 4*n

6n = 16 + 4n

6n - 4n = 16

2n = 16

2n/2 = 16/2

n = 8

Answer:

thx sa points

Step-by-step explanation:

Answer:

(-1, 2)

Step-by-step explanation:

1.) The way to use elimination is to add or subtract both of the equations together to eliminate a variable. If we add the two equations together, the -6x and 6x cancel out. Since we added the equations together, -12y and 10y would add up to -2y, and -18 and 14 would add up to -4

2.) Now, we have the equation -2y = -4. By dividing by -2 on both sides, we get y=2.

3.) Next, we need to substitute y back in to get the x value. If you use the first equation, we get -6x - 12 * 2 = -18.

4.) By simplifying, you get that -6x - 24 = -18. If you add 24 on both sides, you get -6x = 6, and by dividing by -6 on both sides, you get x = -1.

5.) Finally, you have to put the answer in form of a point. -1 would be the x-coordinate and 2 would be the y-coordinate. Therefore, the point is (-1, 2)

\((\stackrel{x_1}{-1}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{8}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{2}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{(-1)}}} \implies \cfrac{6}{4 +1} \implies \cfrac{ 6 }{ 5 }\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{ \cfrac{6}{5}}(x-\stackrel{x_1}{(-1)}) \implies y -2 = \cfrac{6}{5} ( x +1) \\\\\\ y-2=\cfrac{6}{5}x+\cfrac{6}{5}\implies y=\cfrac{6}{5}x+\cfrac{6}{5}+2\implies {\Large \begin{array}{llll} y=\cfrac{6}{5}x+\cfrac{16}{5} \end{array}}\)

Thus, the probability of getting at least 5 questions correct by guessing randomly on a 20-question multiple-choice test with 4 possible answers for each question is approximately 0.074 or 7.4%.

To calculate the probability of getting at least 5 questions correct, we need to use the binomial distribution formula. This formula calculates the probability of getting a specific number of successes in a fixed number of trials, given a specific probability of success.

The formula for the probability of getting at least 5 successes in 20 trials with a probability of success of 1/4 is:

P(X ≥ 5) = 1 - P(X < 5)

where X is the number of correct answers.

Using the binomial distribution formula, we can calculate the probability of getting less than 5 correct answers as:

P(X < 5) = ΣP(X = k) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

= (0.75)^20 + 20(0.25)(0.75)^19 + (20*19/2)(0.25)^2(0.75)^18 + (20*19*18/6)(0.25)^3(0.75)^17 + (20*19*18*17/24)(0.25)^4(0.75)^16

= 0.926

Therefore, the probability of getting at least 5 questions correct is:

P(X ≥ 5) = 1 - P(X < 5)

= 1 - 0.926

= 0.074

So the probability of getting at least 5 questions correct by guessing randomly on a 20-question multiple-choice test with 4 possible answers for each question is approximately 0.074 or 7.4%.

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Answer:

\(m = 2017\)  and \(m = -1000\)

Step-by-step explanation:

Given equations are (I am hoping it is 1017 as written by you)

From the first equation we get

\(mx-1000=1017 \\\\\rightarrow mx = 1017 + 1000\\\\\rightarrow mx = 2017\\\\\rightarrow m = 2017/x\dots [1]\)

From the second equation we get
\(1017=m-1000x\\\\m-1000x = 1017\\\\m = 1000x + 1017 \dots[2]\)

Equating [1] and [2] we get

\(\dfrac{2017}{x} = 1000x + 1017\\\\\)

Multiply above equation throughout by x to get

\(2017 = 1000x^2+ 1017x\\\)

Subtract 2017 from both sides:
0 = 1000x^2 + 1017x - 2017\\\\

Switching sides:

\(1000x^2 + 1017x - 2017 = 0\\\\\)

This is a quadratic equation in x which can be solved by the quadratic formula, completing the square or factorization

Let's choosing factoring to solve
\(1000x^2 + 1017x - 2017 = 0\) can be factored as

\(\left(1000x^2-1000x\right)+\left(2017x-2017\right) = 0\)\\\\

Factor out 1000x from the first term and 2017 from the second term:

\(\rightarrow 1000x(x - 1) + 2017(x -1) = 0\)\\\\

Factor out common term x - 1:
\(\left(x-1\right)\left(1000x+2017\right)\\\\\)

This means either \(x - 1 = 0 \;or\; 1000x + 2017 = 0\)

giving two possible solutions

\(x - 1 = 0 \rightarrow \boxed{x = 1}\)

and

\(1000x + 2017 = 0 \rightarrow 1000x = - 2017 \rightarrow \boxed{ x = -\dfrac{2017}{1000}}\)

Use these two values of x in equation 1 to solve for possible values of m

At x = 1
\(m = \dfrac{2017}{1} = 2017\)

At
\(x = -\dfrac{2017}{1000}\)

\(m = \dfrac{2017}{-\dfrac{2017}{1000}}\)

When dividing by a fraction, just multiply the numerator by the reciprocal of the denominator
\(\dfrac{a}{\dfrac{b}{c}}=\dfrac{a\cdot \:c}{b}\)

\(m =\dfrac{2017}{-\dfrac{2017}{1000}}\\\\\\= -\dfrac{2017\cdot \:1000}{2017}\\\\\\= - 1000\)

So the possible values of m are
\(\text{m = 2017 \;and\; m = -1000}\)

Answer:

x= 21

y= 3

z= 21

Step-by-step explanation:

Let the center be O,

=> Triangle AOD is an Isosceles triangle so AO≅DO, "21 = x"

=> Line AC is divided in two equal parts by the center so if AO= 21 then

    7y = 21, and thus "y = 3"

=> BOC is also an Isosceles triangle so CO ≅ BO, if CO = 21 (7y → 7*3) then so will be BO. Therefore "z = 21"

Answer:

2) The negative reciprocal of 4 is -1/4.

Using the point-slope form of a line (y - y1 = m(x - x1)), where (x1, y1) is the given point (-16, 2) and m is the slope:

y - 2 = -1/4(x - (-16))

y - 2 = -1/4(x + 16)

y - 2 = -1/4x - 4

y = -1/4x - 2

Therefore, the equation of the line perpendicular to y = 4x - 10 that passes through the point (-16, 2) is y = -1/4x - 2. So, the correct answer is A.

3) The given equation is y - 3x = -8. To find the equation of a line perpendicular to this, we need to determine the negative reciprocal of the slope of the given line, which is 3. The negative reciprocal of 3 is -1/3.

Using the point-slope form with the point (3, 2) and the slope -1/3:

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

y - 2 = -1/3x + 1

y = -1/3x + 3

Therefore, the equation of the line perpendicular to y - 3x = -8 that passes through the point (3, 2) is y = -1/3x + 3. So, the correct answer is D.

4) The given line passes through the point (-5, 2) and the origin (0, 0). The slope of a line passing through two points can be found using the formula (y2 - y1) / (x2 - x1).

slope = (0 - 2) / (0 - (-5))

slope = -2 / 5

slope = -2/5

The negative reciprocal of -2/5 is 5/2. Therefore, the slope of a line perpendicular to the line passing through (-5, 2) and the origin is 5/2. So, the correct answer is D.

Answer:

\(w=\frac92\)

Step-by-step explanation:

Let's remember that the slope of a line measures the ratio of the variation in y over the variation in x. Let's plug the numbers we have and see what we get

\(m= \frac {\Delta y}{\Delta x}; \frac18 = \frac{w-4}{-6-(-10)}\rightarrow\\\frac18 = \frac{w-4}{4}\rightarrow 2w-8=1 \rightarrow w=\frac92\)

Answer:

C. \(\frac{9}{2}\)

Step-by-step explanation:

Hi there!

We are given the points (-6, w) and (-10,4), and that the slope that passes between these two lines is 1/8

We want to find the value of w

We can do that by plugging in our given values into the equation \(\frac{y_2-y_1}{x_2-x_1}=m\), where \((x_1, y_1)\) and \((x_2, y_2)\) are points, and m is the slope

We have everything we need to solve the equation, let's just label their values to avoid any confusion.

\(x_1=-6\\y_1=w\\x_2=-10\\y_2=4\\m=\frac{1}{8}\)

Now plug all of these values into the formula (remember: we have NEGATIVE values, and the formula contains SUBTRACTION)

\(\frac{y_2-y_1}{x_2-x_1}=m\)

\(\frac{4-w}{-10--6}=\frac{1}{8}\)

Simplify:

\(\frac{4-w}{-10+6}=\frac{1}{8}\)

Add the values together

\(\frac{4-w}{-4}=\frac{1}{8}\)

Now we can cross multiply; multiply -4 by 1 and (4-w) by 8

-4=32-8w

Subtract 32 from both sides

-36=-8w

Divide both sides by 8

w=\(\frac{9}{2}\)

The answer is C

Hope this helps!

Answer:

no

Step-by-step explanation:

yes

The linear independence of vector sets forms the basis of the space of polynomials of third degree.

In vector space theory, a collection of matrices is said to be heavily dependent if there is a nontrivial concatenation of the vectors that equal the zero vector. If no such linear combination exists, the vectors are said to be linearly independent. These concepts are crucial to the concept of dimension.

The maximum number of nonzero vectors determines whether the dimensions of a vector space are finite or infinite. The capacity to recognize whether a subset of columns in a vector space is dependent, as well as the concept of linear dependence, are crucial for determining a vector space's dimensionality.

If the same vector appears twice in a vector sequence, it must be dependent. The linear dependency of a vector series is independent of the order of the terms. A restricted collection of vectors can have linear independence if the sequence obtained by sorting a finite number of lines is linearly independent. In other words, the following outcome is frequently useful.

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Given: Mount Everest is the tallest mountain in the set of data

Required:

Question 1: Use the scatter plot to estimate the height of Mount Everest

From the plot,

Question 2: Year of the first recorded ascent of mount Everest

From the plot,

By using multiplication and division, it can be calculated that-

The multiple according to the number 3 = 162

The submultiple according to the number 7 = 7

What is multiplication and division?

Repeated addition is called multiplication. Multiplication is used to find the product of two or more numbers.

Division is the process in which a value of single unit can be calculated from the value of multiple unit.

The number to be divided is called dividend. The  number by which dividend is divided is the divisor. The result obtained is called quotient and the remaining part is the remainder.

This is a problem of multiplication and division.

One segment measures 161 cm

So, to find the multiple according to the number 3, we have to divide 161 by 3

161 \(\div\) 3 = 53.67

Nearest integer of 53.67 is 54

The multiple according to the number 3 = 54 \(\times\) 3 = 162

To find the submultiple according to the number 7, we have to divide 161 by 7

161 \(\div\) 7 = 23

Nearest integer of 23 is 23

The submultiple according to the number 7 = 161 \(\div\) 23 = 7

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Answer:

12

Step-by-step explanation:

Answer:

1) 12 boxes

2) 3, 6, 12

3) 12

4) 110 degrees

Step-by-step explanation:

1) Count the rectangles. Multiply the length of the rectangle in boxes to the width of rectangle in boxes.

Length: 4 boxes

Width: 3 boxes

4 x 3 = 12

12 boxes

2)

10% of 30 is 0.1 times 30.

0.1 x 30 = 30/10 = 3

20% of 30 is 0.2 times 20.

0.2 x 30 = 30/5 = 6

40% of 30 is 0.4 times 20.

0.4 x 30 = 30/2.5 = 12

3) Count the cubes. Reminder there are 2 boxes you cannot see.

Top Layer: 2

Middle Layer: 4

Back Bottom Layer: 4

Front Bottom Layer: 2

2 + 4 + 4 + 2 = 12

4) I cannot see the semicircle clearly, but I do know that a circle is 360 degrees. A semicircle, half of a circle, is 180 degrees.

180/18 (The angle of each section)

10

11 Sections

10 x 11 = 110

Questions that require responses at fixed intervals along a scale of answers are called scale questions.

Closed-ended questions, such as the Likert Scale, are one of the most popular methods for gauging public opinion. To gauge people's opinions, attitudes, and beliefs, they employ psychometric testing. Statements are used in the questions, and respondents are asked how much they agree or disagree with each assertion. Likert Scale questions typically have a scale from 0 to 10, while shorter scales are also conceivable.

Every sort of research has benefits and drawbacks, and this particular question type has both in spades. The fundamental benefit of Likert Scale questions is that they follow a standard way of data collection, making them simple to comprehend.

Hence, according to the definition questions that require responses at fixed intervals along a scale of answers are called scale questions.

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The standard normal distribution has a mean of 0 and a standard deviation of 1. M ≈ 30.935. The median of the distribution is also 25.

(a) To find M, we first need to convert the given values of mean and standard deviation to the standard normal distribution. This can be done by using the formula Z = (X - μ) / σ, where Z is the Z-score, X is the value of interest, μ is the mean, and σ is the standard deviation. In this case, we have X ~ N(25, 9). Substituting the values into the formula, we get Z = (X - 25) / 3. Now we need to find the Z-score that corresponds to the desired probability of 0.95. Using a standard normal distribution table or a calculator, we find that the Z-score corresponding to a cumulative probability of 0.95 is approximately 1.645. Setting Z equal to 1.645, we can solve for X: (X - 25) / 3 = 1.645. Solving for X, we get X ≈ 30.935. Therefore, M ≈ 30.935.

(b) The median is the value that divides the distribution into two equal halves. In a normal distribution, the median is equal to the mean. In this case, the mean is given as 25. Therefore, the median of the distribution is also 25.

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Answer:

128

Step-by-step explanation:

PEMDAS:

P = PARENTHESES

E = EXPONENTS

M = MULTIPLICATION

D = DIVISION

A = ADDITION

S = SUBTRACTION

STEPS:

1. Simplify 10 * 12 to 120.

120 - 14/2 + 15

2. Simplify 14/2 to 7.

120 - 7 + 15

3. Simplify 120 - 7 to 113.

113+ 15

4. Simplify.

128

The evaluated expression using pemdas is 128

From the question, we have the following parameters that can be used in our computation:

10 x 12 - 14/2 + 15

Using PEMDAS, we start by evaluating the products

10 x 12 - 14/2 + 15 = 120 - 14/2 + 15

Using PEMDAS, we evaluate the quotient next

10 x 12 - 14/2 + 15 = 120 - 7 + 15

Lastly, we have

10 x 12 - 14/2 + 15 = 128

Hence, the solution is 128

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Answer:

D) 504,414

Step-by-step explanation:

Hope it helps!

Answer:

Formula: divide the value in centimeters per second by 100 because 1 meter per second equals 100 centimeters per second. So, 9000 centimeters per second = 9000100 = 90 meters per second.

Step-by-step explanation:

x + 7y + 3z

Explanation:

The expression: 4x + 2y + 6z - 3x + 5y - 3z​

collect like terms by bringing same letters together:

= 4x - 3x + 2y + 5y + 6z - 3z

= x + 7y + 3z

Since the letters are different, we can't simplify any further

The simplified form: x + 7y + 3z

Answer:

6 male wolves

Step-by-step explanation:

Step 1

Find the total number of students

A biologist was observing a pack of wolves. There were 8 female wolves and the ratio of female wolves to male wolves was 4 : 5.

Ratio of Female to make

= 4:5

Sum of Proportion = 4 + 5 = 9

Let the total number of wolves = x

Hence

4/9 × x = 8

4x/9 = 8

Cross Multiply

4x = 9 × 8

4x = 72

x = 72/4

x = 18 wolves

The current number of male wolves = 5/9 × 18

= 10 wolves

Step 2

A little later some more male wolves arrived and the ratio was now 1 : 2.

The current ratio = 4:5

The new ratio = 1:2

For 4:5 = 1:2

We Multiply the number of females by 2 = 8 × 2

= 16 females

Hence,

16 - current number male of wolves

16 - 10

= 6 male wolves

Therefore, 6 more male wolves arrived.

The probability that of those 45 people sampled, between 33 and 36 of them own a cell phone is 0.2413

We have to solve for the  probability that of those 45 people sampled, between 33 and 36 of them own a cell phone

The standard deviation is given as

\(s = \sqrt{} \frac{P(1-p)}{n}\)

where we have p = proportion = 70% = 0.7

q = 1 - p

= 1 - 0.7

= 30 % = 0.3

s = \(\sqrt{\frac{0.7(1-0.7}{45} }\)

= 0.07

we are to find the interval of

P(33 ≤ x ≤ 36)

this would be written as

(33 / 45 - 0.70) / 0.07 < z < (36 / 45 - 0.70) / 0.07)

p(0.49 < z < 1.46)

we have to find the critical values of p(z < 0.49) and p(z < 1.46)

= 0.9284 - 0.68721

= 0.2413

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The bug changes direction at t = 4. This can be answered by the concept of velocity.

To determine when the bug changes direction, we need to find when its velocity changes sign from positive to negative. From the graph, we see that the bug's velocity is positive for t < 4 and negative for t > 4. Therefore, the bug changes direction at t = 4.

To verify this, we can look at the behavior of the bug's velocity as it approaches t = 4. From the graph, we see that the bug's velocity is increasing as it approaches t = 4 from the left, and decreasing as it approaches t = 4 from the right. This indicates that the bug is reaching a maximum velocity at t = 4, which is when it changes direction.

Therefore, the bug changes direction at t = 4.

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Answer:

31.5576

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

oof

Answer: (x,y) -> (1.4x,1.4y)

Step-by-step explanation:

I got it right

The volume of a stack of 9 books is 1368.75 cubic inches.

To find the volume of a stack of 9 books, we first need to find the height of the stack. Since each book is 3/4 inch thick, the height of the stack is 9 times 3/4 inch, which is 6 3/4 inches.

Now we need to find the area of the base of the rectangular prism formed by the stack of books. Since each book has an area of 22 1/2 square inches, the total area of the base of the stack is 9 times 22 1/2 square inches, which is 202 1/2 square inches.

Therefore, the volume of the stack of 9 books is:

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