The names eben , evelyn , eunice, frieda and frank are to be randomly chosen, and each has the same probability of being selected. Use events E,F,G and H to determine the probabilities in part A to E .
A: Find P(e) in simple fraction form
B: find p(f) In simplest fraction form
C : find p(g) In simplest fraction form
D: find p ( E U F) simplest fraction form

Answer:

Step-by-step explanation:

You want the domain and range of the function ...

  f(x) = 5·|x|

The domain of the function is the set of values of x for which it is defined. Here, the absolute value function is defined for all values of x.

The domain is all real numbers.

The range is the set of output values the function can produce. The absolute value function can produce any non-negative number.

The range is all real numbers greater than or equal to zero.

<95141404393>

To find out what percentage 25 is of 500, you can use the following formula:

percentage = (part / whole) x 100

In this case, 25 is the part and 500 is the whole. So, we can substitute these values into the formula:

percentage = (25 / 500) x 100

Simplifying the equation:

percentage = 0.05 x 100

percentage = 5%

Therefore, 25 is 5% of 500.

I hope it helps!

Answer:

5 % of 500 is 25

Step-by-step explanation:

500 * x% = 25

Divide each side by 500

x% = 25/500

x% = .05

Change to percent

x = 5

5 % of 500 is 25

The ordered pairs on the graph with the given equation will be of the form (x, 2).

Given a linear equation,

-4y = -8

We have to find the ordered pairs on the given graph.

Dividing both sides of the equation by -4,

y = 2

So for any point on the line, the y coordinate will be 2.

So any general point on the graph will be of the form, (x, 2).

Graph is a line parallel to the X axis.

Hence the orderd pairs are of the form (x, 2).

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2x² - 6x = -7 equation has  imaginary solutions

To determine if an equation has imaginary solutions, we can examine the discriminant of the quadratic equation

x² + 3x - 5 = 0

a = 1, b = 3, c = -5

Discriminant = (3)² - 4(1)(-5) = 9 + 20 = 29

The equation has two real solutions

x⁴ - 5x ^ 2 + 3 = 0

This equation is a quartic equation, not a quadratic equation. Quartic equations can have both real and imaginary solutions

2x² - 6x = -7

2x^2 - 6x + 7 = 0

a = 2, b = -6, c = 7

Discriminant = (-6)²- 4(2)(7) = 36 - 56 = -20

Since the discriminant (-20) is negative, the equation has two complex (imaginary) solutions.

-3x² = -5

Dividing both sides by -3, we get:

x²= 5

a = 1, b = 0, c = -5

Discriminant = 0² - 4(1)(-5) = 20

The equation has two real solutions.

Hence, 2x² - 6x = -7 equation has imaginary solutions

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Answer:

The given function f(x) = alxl is not a valid absolute value function because the absolute value symbol is represented by two vertical bars (|) and not the letter "l". Additionally, the point (3,-4) cannot be on the graph of an absolute value function because the output of an absolute value function is always non-negative.

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so we have a point at -2-i or -2 - 1i, that means that both "x" and "y" are negative, the only occurs in the III Quadrant, so hmmm let's find the modulus and angle θ

[tex]\stackrel{a}{-2}\stackrel{b}{-1i}\hspace{5em} \begin{cases} r=\sqrt{(-2)^2 + (-1)^2}\\ \qquad \sqrt{5}\\ \theta =tan^{-1}\left( \frac{-1}{-2} \right)\\[1em] \qquad \approx 206.57^o \end{cases} \\\\\\ \stackrel{\textit{let's keep in mind that}}{\sqrt[3]{\sqrt{5}}\implies \left( 5^{\frac{1}{2}} \right)^{\frac{1}{3}}}\implies 5^{\frac{1}{6}}\implies \sqrt[6]{5} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\sqrt[n]{z}=\sqrt[n]{r}\left[ \cos\left( \cfrac{\theta+2\pi k}{n} \right) +i\sin\left( \cfrac{\theta+2\pi k}{n} \right)\right]\quad \begin{array}{llll} k\ roots\\ 0,1,2,3,... \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\boxed{k=0}\hspace{5em} \sqrt[ 3 ]{\sqrt{5}} \left[ \cos\left( \cfrac{ 206.57^o + 360^o( 0 )}{3} \right) +i \sin\left( \cfrac{ 206.57^o + 360^o( 0 )}{3} \right)\right] \\\\\\ \sqrt[ 6 ]{5} \left[ \cos\left( \cfrac{ 206.57^o }{3} \right) +i \sin\left( \cfrac{ 206.57^o }{3} \right)\right] \\\\\\ \sqrt[6]{5}\left[ \cos(68.86^o) +i \sin(68.86^o)\right] ~~ \approx ~~ 0.47~~ + ~~1.22i \\\\[-0.35em] ~\dotfill[/tex]

[tex]\boxed{k=1}\hspace{5em} \sqrt[ 6 ]{5} \left[ \cos\left( \cfrac{ 206.57^o + 360^o( 1 )}{3} \right) +i \sin\left( \cfrac{ 206.57^o + 360^o( 1 )}{3} \right)\right] \\\\\\ \sqrt[ 6 ]{5} \left[ \cos\left( \cfrac{ 566.57^o }{3} \right) +i \sin\left( \cfrac{ 566.57^o }{3} \right)\right] \\\\\\ \sqrt[ 6 ]{5} \left[ \cos(188.86^o) +i \sin(188.86^o)\right] ~~ \approx ~~ -1.29~~ - ~~0.20i \\\\[-0.35em] ~\dotfill[/tex]

[tex]\boxed{k=2}\hspace{5em} \sqrt[ 6 ]{5} \left[ \cos\left( \cfrac{ 206.57^o + 360^o( 2 )}{3} \right) +i \sin\left( \cfrac{ 206.57^o + 360^o( 2 )}{3} \right)\right] \\\\\\ \sqrt[ 6 ]{5} \left[ \cos\left( \cfrac{ 926.57^o }{3} \right) +i \sin\left( \cfrac{ 926.57^o }{3} \right)\right] \\\\\\ \sqrt[ 6 ]{5} \left[ \cos(308.86^o) +i \sin(308.86^o)\right] ~~ \approx ~~ 0.82~~ - ~~1.02i[/tex]

just a quick clarification, notice that if we get the inverse tangent of (-1 / -2) the angle we get will be in the range of ±π/2, that's because that is the range inverse tangent is restricted to, however, our terminal point on the complex plane is on the III Quadrant, not the 1st one, so we use the reference angle on the III Quadrant, and that is about 206.57°.

The percent of the original price you end up paying is 42%.

Let's assume that the original price of an item is $100

The first discount of 25% off would reduce the price by:

25% of $100 = $25

So the sale price after the first discount is:

$100 - $25 = $75

Then, the store is offering an additional discount of 45% off on the clearance items.

The discount is removed from the sale price after the first discount:

45% of $75 = $33

So the final sale price after both discounts is:

$75 - $33 = $42

Therefore, you end up paying $42 for an item that originally cost $100. This is equivalent to paying:

($42 / $100) x 100% = 42% of the original price.

Hence, the percent of the original price you end up paying is 42%.

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hello

the answer to the question is:

length A = 5 ft

length B = 4 ft

total volume = (8 × 3 × 2) + (4 × 5 × 2) = 88 ft³

The proposition X^2 > 0 for every real number x is true.

We are given that;

The equation x^2 > 0

Now,

The square of any real number is always greater than or equal to zero.

An example of a mathematical proposition is “For all real numbers x, x + 1 = 2.” This is a proposition because it makes a claim about all real numbers x.

Therefore, by the given function X^2 > 0 the answer will be true.

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The meaning of the number 30,500 is given as follows:

The maximum altitude of the airplane.

The coordinates of the vertex are (h,k), meaning that:

Considering a leading coefficient a, the quadratic function is given as follows:

y = a(x - h)² + k.

In which a is the leading coefficient.

The function for this problem is given as follows:

y = -16(t - 12)² + 30500.

The coordinates of the vertex are given as follows:

(12, 30500).

The leading coefficient is negative, hence the meaning of the vertex is given as follows:

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The given algebraic expression is written as:

4b/n³ > 7b/4

Algebraic expressions are defined as the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra makes us to know how to express an unknown value with the aid of letters such as x, y, z, etc. These letters are referred to as variables. An algebraic expression can even be a combination of both variables as well as constants. Any value that is placed before and multiplied by a variable is a coefficient.

4b divided by n cubed more than 7b divided by 4, cubed can be expressed as:

4b/n³ > 7b/4

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Answer:

Shorter leg is 6

Step-by-step explanation:

In a 30°-60°-90° triangle, the hypotenuse is twice the length of the shorter leg. Therefore, if the hypotenuse is 12, then the shorter leg is 6.

Answer:

Step-by-step explanation:

You want to identify the graphs that go with each of these functions, along with a particular point on the curve.

The equations are written here in standard form, factored form, and vertex form. (The "factored form" is sometimes called "intercept form.") Each of these forms can be analyzed for characteristics relevant to identifying the corresponding graph.

In general, we can readily identify the opening direction, based on the sign of the leading coefficient. Depending on the form, we can also identify zeros, the vertex, and the y-intercept.

The line of symmetry (x-coordinate of the vertex) of the equation in the form ax² +bx +c is x = -b/(2a). That is, it will be left of the y-axis when the coefficients 'a' and 'b' have the same sign.

The graph of equation A will be graph 4, the only one with its vertex left of the y-axis. The y-intercept is the constant: point S = (0, 9).

Equation B has a positive leading coefficient, so opens upward. The zeros of the factors are -3 and +9, so identify the places where the graph crosses the x-axis. Graph 3 is the only one that opens upward and has x-intercepts. Point R is (9, 0).

The vertex form of a quadratic is ...

  y = a(x -h)² +k . . . . . . . vertex (h, k); leading coefficient 'a'

Equation C has its vertex at (h, k) = (3, 9) and opens upward (a>0). Graph 1 is the only one matching those characteristics. Point P is the vertex, so point P is (3, 9).

Equation D is the same as equation B, but with a negative leading coefficient. That is, it opens downward and crosses the x-axis in two places, at x = -3 and x = 9. Graph 2 is matches this description. The left zero is point Q, (-3, 0).

<95141404393>

The cosine of the angle θ in the circle s -12/13

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

The unit circle

Where we have

(x, y) = (-12/13, -5/13)

In a unit circle, we have

(cos θ, sin θ) = (x, y)

Using the above as a guide, we have the following:

cos θ = -12/13

Hence, the cosine of the angle θ is -12/13

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The cardinal number for the given set. A {20, 22, 24, 26, 34} sees; The given set has a cardinal number of 5.

This is further explained below.

Generally, cardinal numbers are an extension of the natural numbers that are used to assess the cardinality of sets. Cardinals are often referred to by their shorter form, cardinals. A finite set has a cardinality that is equal to a natural number, which is the number of items that are included inside the set.

A set of counting numbers is called its cardinal number. There is speculation that they are cardinals as well. Cardinal numbers are whole, non-fractional numerals, beginning with 1 and continuing in numerical order. Cardinal numbers include 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20.

To conclude it, The provided set A equals {20, 22, 24, 26, 34}

The number of unique components that make up a set is referred to as the cardinal number.

The given set has a cardinal number of 5, which is denoted by the notation n(A).

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Answer: The cardinal number for the given set is 5

Step-by-step explanation:

The cardinal number for a set is the quantity, or how many numbers are in the set. Since Set A has these numbers {20, 22, 24, 26, 34}, you can easily indicate how many numbers are in there. The n(a) quantity in the set would be the number five.

Since there is five numbers in this set, therefore, the cardinal number for the given set would be simply 5.

It will cost approximately $16 per person if 95 people rent the bus.

The price per person of renting a bus varies inversely with the number of people renting the bus. This means that as the number of people increases, the price per person decreases, and vice versa.

Given that it costs $20 per person when 76 people rent the bus, we can use this information to find the constant of variation (k) in the inverse variation equation. Let's denote the number of people as "n" and the cost per person as "c":

c = k/n

We can substitute the values into the equation to solve for k:

20 = k/76

Multiplying both sides by 76 gives:

k = 20 × 76 = 1520

Now, we can determine the cost per person when 95 people rent the bus by plugging the values into the equation:

c = 1520/95 ≈ 16.00

Therefore, it will cost approximately $16 per person if 95 people rent the bus.

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The sequence of transformations includes translation, rotation, and reflection. The resulting image is congruent to the original if the transformations maintain the size, shape, and orientation of the object.

I need to know the specific transformations that you're referring to. However, I can provide you with a general explanation using the common types of transformations.

The sequence of transformations typically includes translation, rotation, and reflection. A translation involves moving an object from one location to another without changing its size or orientation. Rotation is the turning of an object around a fixed point, while reflection is flipping an object over a line, like a mirror image.

The resulting image is congruent to the original if the transformations preserve the size, shape, and orientation of the object. In the case of translation and rotation, the resulting image is always congruent to the original because the size and shape of the object do not change.

However, for reflection, the image remains congruent only if the reflection line is aligned with the symmetry axis of the object, preserving the shape and size.
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Step-by-step explanation:

14 out of 20 were full in the experiment   14/20 = 7/10 chance that the next one will be full too.

Answer:

  x = 1, 12

Step-by-step explanation:

You want the solutions to y = x² -13x +12 when y = 0, using the quadratic formula.

The quadratic formula gives the solutions to ...

  ax² +bx +c = 0

as ...

  [tex]x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Your equation has a = 1, b = -13, c = 12, so the solutions are ...

  [tex]x = \dfrac{-(-13)\pm\sqrt{(-13)^2-4(1)(12)}}{2(1)}=\dfrac{13\pm\sqrt{169-48}}{2}\\\\\\x=\dfrac{13\pm11}{2}\\\\\boxed{x=\{12,1\}}[/tex]

This answer is correct because we used and evaluated the formula correctly. There are several ways to check the answer is correct.

A graph of the equation is attached. It shows the x-intercepts (zeros) to be x = 1 and x = 12.

When the equation is factored, it looks like ...

  y = (x -12)(x -1)

The zeros are the values of x that make the factors zero: 12 and 1.

The equation can be rewritten to simplify evaluating it:

  y = (x -13)x +12

For x = 1, y = (1 -13)(1) +12 = -12 +12 = 0.

For x = 12, y = (12 -13)(12) +12 = -12 +12 = 0.

The values x = 1 and x = 12 are zeros of the function.

<95141404393>

A Normal distribution has skewness and kurtosis values close to zero.

There are several methods that can be used to assess whether a variable follows a normal distribution.

1. Histogram: Creating a histogram of the variable's data can provide a visual representation of its distribution. If the histogram displays a bell-shaped curve with a symmetric pattern, it suggests the variable may follow a normal distribution. However, this method is subjective and depends on the chosen bin width.

2. Normal probability plot: Also known as a Q-Q plot (quantile-quantile plot), this graphical tool compares the quantiles of the variable's data against the expected quantiles of a normal distribution. If the points on the plot roughly fall along a straight line, it suggests that the variable approximates a normal distribution.

3. Shapiro-Wilk test: The Shapiro-Wilk test is a statistical test that assesses the normality of a variable. It produces a test statistic and a p-value. If the p-value is greater than the chosen significance level (e.g., 0.05), it indicates that there is not enough evidence to reject the null hypothesis of normality.

4. Kolmogorov-Smirnov test: The Kolmogorov-Smirnov test compares the cumulative distribution function (CDF) of the variable's data with the expected CDF of a normal distribution. The test produces a test statistic and a p-value. Similarly, if the p-value is above the chosen significance level, it suggests the variable follows a normal distribution.

5. Skewness and kurtosis: Skewness measures the symmetry of a distribution, while kurtosis quantifies the shape of the distribution's tails. A normal distribution has skewness and kurtosis values close to zero. Assessing these measures can provide insights into the departure from normality.

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Hello !

2(5 - 2 * 3 - 4)​

= 2(5 - 6 - 4)

= 2 * (-5)

= -10

Answer:

average=9 hours

Step-by-step explanation:

10hours on Friday

12 hours on Saturday

300 mins to hours= 300÷60=5

5 hours on Sunday

average=10+12+5

average=27

average=27÷3

average=9 hours

Answer:

My friend you have to send a picture, we can't see through the screen

Answer:

I hope this helps.

Step-by-step explanation:

In an isosceles trapezoid, the two non-parallel sides (legs) are congruent, and the base angles opposite each other are also congruent. Let's denote the measures of the angles as follows:

Angle A: The top left angle.

Angle B: The top right angle.

Angle C: The bottom left angle.

Angle D: The bottom right angle.

In an isosceles trapezoid, angles A and B are congruent, and angles C and D are congruent. The sum of the interior angles of any quadrilateral is 360 degrees. Therefore, we can set up the following equation:

Angle A + Angle B + Angle C + Angle D = 360 degrees

Since angles A and B are congruent, and angles C and D are congruent, we can rewrite the equation as:

2(A) + 2(C) = 360 degrees

Simplifying further:

2A + 2C = 360 degrees

Dividing both sides of the equation by 2:

A + C = 180 degrees

In an isosceles trapezoid, the base angles (C and D) are supplementary angles, meaning they add up to 180 degrees. Therefore, the measure of each base angle (C and D) is 180 degrees divided by 2:

Each base angle (C and D) = 90 degrees.

Since the sum of the interior angles in a quadrilateral is 360 degrees, and angles C and D (the base angles) each have a measure of 90 degrees, the sum of angles A and B (the top angles) must be:

Angle A + Angle B = 360 degrees - (Angle C + Angle D)

Angle A + Angle B = 360 degrees - (90 degrees + 90 degrees)

Angle A + Angle B = 360 degrees - 180 degrees

Angle A + Angle B = 180 degrees

Therefore, in an isosceles trapezoid, each top angle (A and B) has a measure of 180 degrees divided by 2:

Each top angle (A and B) = 90 degrees.

To summarize:

Each top angle (Angle A and Angle B) measures 90 degrees.

Each base angle (Angle C and Angle D) measures 90 degrees.

Answer:

Step-by-step explanation:

sin 325=sin (360-35)=-sin 35=-t

cos 325=cos (360-35)=cos  35=√(1-sin²35)=√(1-t²)

tan 215=tan (180+35)=tan 35

[tex]=\frac{sin~35}{cos~35} \\=\frac{-t}{\sqrt{1-t^2} }[/tex]

The standard deviation is around 1.06, and there are on average 2 frogs having the feature.

Given that the trait is usually found in 1 out of every 8 frogs, the probability of a frog having the trait is p = 1/8. Therefore, the probability of a frog not having the trait is q = 1 - p = 7/8.

(a) To find the probability of not finding any frogs with the trait, we calculate the probability of a frog not having the trait and raise it to the power of the number of trials:

P(X = 0) = (7/8)¹⁶ ≈ 0.0747

(b) To find the probability of finding at least 1 frog with the trait, we subtract the probability of finding none from 1:

P(X ≥ 1) = 1 - P(X = 0) ≈ 1 - 0.0747 ≈ 0.9253

(c) The mean (μ) and standard deviation (σ) of the number of frogs with the trait can be calculated using the formulas:

μ = np

σ = √(npq)

For this case, n = 16, p = 1/8, and q = 7/8:

μ = 16 * (1/8) = 2

σ = √(16 * (1/8) * (7/8)) ≈ 1.06

Therefore, the mean number of frogs with the trait is 2, and the standard deviation is approximately 1.06.

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140

Step-by-step explanation:

Area of parallelogram=bxh

=14x10

=140

Answer:

140 square units

Step-by-step explanation:

The area of a parallelogram can be found by multiplying the length of its base by its height.

[tex]\boxed{\sf Area = base \times height}[/tex]

From inspection of the given parallelogram, its height is 10 units.

Since the lengths of opposite sides in a parallelogram are equal, the base of the given parallelogram is 14 units.

Therefore, the area of the parallelogram is:

[tex]\begin{aligned}\sf Area&=14 \times 10\\&=140\; \sf square\;units\end{aligned}[/tex]

The distance from the point (-2, 4) to the line y = 2x - 2 is approximately 4.47 units (rounded to the nearest hundredth).

Step 1: To find the equation of the line perpendicular to y = 2x - 2 that goes through (-2, 4), we need to determine the negative reciprocal of the slope of the given line. The slope of the given line is 2, so the negative reciprocal of 2 is -1/2.

We can use the point-slope form of a linear equation to find the equation of the line. Using the point (-2, 4) and the slope -1/2, the equation of the line can be written as:

y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.

Substituting the values, we have:

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

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

y - 4 = -1/2x - 1

y = -1/2x + 3

Therefore, the equation of the line perpendicular to y = 2x - 2 that goes through (-2, 4) is y = -1/2x + 3.

Step 2: Now we need to solve the system of equations formed by y = 2x - 2 and y = -1/2x + 3. We can do this by setting the two equations equal to each other and solving for x:

2x - 2 = -1/2x + 3

Multiplying both sides by 2 to eliminate the fraction:

4x - 4 = -x + 6

Bringing like terms to one side:

4x + x = 6 + 4

5x = 10

Dividing both sides by 5:

x = 10/5

x = 2

Substituting the value of x back into one of the equations (let's use y = 2x - 2), we can find the value of y:

y = 2(2) - 2

y = 4 - 2

y = 2

Therefore, the coordinates of the point of intersection are (2, 2).

Step 3: To find the distance between (-2, 4) and the point (2, 2), we can use the distance formula:

d = √([tex](x2 - x1)^2 + (y2 - y1)^2)[/tex]

Substituting the coordinates, we have:

d = √((2 - [tex](-2))^2 + (2 - 4)^2)[/tex]

d = √([tex](4)^2 + (-2)^2)[/tex]

d = √(16 + 4)

d = √20

d ≈ 4.47

Therefore, the distance from the point (-2, 4) to the line y = 2x - 2 is approximately 4.47 units (rounded to the nearest hundredth).

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Answer:

Step-by-step explanation:

The Axiom of Pairing in mathematics states that for any two sets, there exists a set that contains exactly those two sets as its only elements. In other words, given sets A and B, there exists a set {A, B} whose only elements are A and B.

For example, consider the sets A = {1, 2} and B = {3, 4}. According to the Axiom of Pairing, there exists a set that contains exactly these two sets as its only elements. We can form such a set as {A, B} = {{1, 2}, {3, 4}}, where A and B are the elements of the set. Thus, {A, B} is a set that satisfies the Axiom of Pairing.

Answer:

28.2 cm

Step-by-step explanation:

Circumference of circle = 2π r

Value of π = 3.14

Putting the required values,

Circumference = 2 × 3.14 × 4.5

= 6.28 × 4.5

= 28.2

Hence the circumference of the circle is 28.2 cm