On any given day, the probability that it is raining when Randy goes to class is 0.2. If it is raining, the probability that Randy is on time to class is 0.7. If it is not raining, the probability that Randy is on time to class is 0.90. What is the probability that it is raining given that Randy is late to class

1.7a+0.3a=0.8

2a=0.8

a=0.4

The proportion of households that own mutual funds but not individual stocks or individual stocks but not mutual funds is in option (b) 60%.

Proportion: Two ratios are said to be proportional if they express the same relationship.

Given that:

P (households owning mutual funds) = 60% = 0.6

P (households owning individual stocks) = 40% = 0.4

P (households owning both mutual funds and individual stocks) = 20% = 0.2

P (households that own mutual funds but not individual stocks or individual stocks but not mutual funds)

= P(A) only + P(B) only = [P(A) - P(A∩B)] + [P(B) - P(A∩B)]

= 0.4 + 0.2 = 0.6 = 60%.

Please refer to this complete question:

In a certain town, 60% of the households own mutual funds, 40% own individual stocks, and 20% own both mutual funds and individual stocks. The proportion of households that own mutual funds but not individual stocks or individual stocks but not mutual funds is

a. 40%.

b. 60%.

c. 80%.

d. 100%

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The data set is approximately periodic with a period of 3 and an amplitude of about 7.5.

The period is the length of time it takes for the data to repeat itself. In this case, the data repeats itself every 3 hours. The amplitude is the distance between the highest and lowest values in the data set. In this case, the amplitude is about 7.5 cars.

Hour | Number of cars

------- | --------

1     | 90

2     | 52

3     | 76

4     | 75

5     | 91

6     | 104

7     | 89

8     | 105

9     | 119

10    | 103

11    | 121

12    | 135

As you can see, the data repeats itself every 3 hours. The highest value in the data set is 135 cars, and the lowest value is 52 cars. The difference between these two values is 83 cars, which is about 7.5 times the average number of cars (90 cars). Therefore, the amplitude of the data set is about 7.5 cars.

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Well let's take the equation and try to clear y:

Let's put every term with the variable y on the left side of the equation and the rest of the terms in the right side:

Then:

And finally:

Every time you try to solve an equation and end in a situation like this (two numbers that are not the same being equalized) it's said you reached an absurd. Ending in an absurd means that the equation has no solution, that is to say, there's no possible value for the variable y.

An astronaut is a person who has been prepared, outfitted, and sent into space as part of a human spaceflight program to serve as a commander or crew member.

How much more time does it take an astronaut to install a light than a cable?

The time an astronaut is a person who has been prepared, outfitted, and sent into space as part of a human spaceflight program to serve as a commander or crew member.

How much more time does it take an astronaut to install a light than a cable?

The time it takes to put on the unique undergarments that keep astronauts cool is included in the 45-minute period it takes to put on a spacesuit.

it takes to put on the unique undergarments that keep astronauts cool is included in the 45-minute period it takes to put on a spacesuit.

In the near future, pilot astronauts may pilot and command space shuttles as well as command missions to Mars or the moon. Astronauts with a focus on missions collaborate with pilots to launch satellites, conduct experiments, and repair spacecraft and equipment. Engineers, scientists, and doctors are all examples of mission experts.

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The length of LN in units is 64 units

The complete question is added as an attachment

From the question, we have the following parameters

LM = 10x + 8

MN = 5x - 4

LN = 12x + 6

The above means that

LN = LM + MN

So, we have

10x + 8 + 5x -4 = 12x + 16

Evaluate the like terms

So, we have

15x +4 = 12x + 16

Collect the like terms

So, we have

15x - 12x = 16 - 4

Evaluate the like terms

So, we have

3x = 12

Divide both sides by 3

x = 4

Next, we substitute x into LN = 12x + 16

So, we have

LN = 12(4) + 16

Evaluate

LN = 64

Hence, the length of LN in units is 64 units

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The values of ab, b - c, and c/d are 6, -1, and 4 respectively when a = 2, b = 3, c = 4 and d = 1.Using BODMAS rule, we can simplify the given expression.ab - c/d = 24

Given ab-c/d has a value of 24.Now, we have to find the value ofab, b - c, and c/d.Multiplying d on both sides, we getd(ab - c/d) = 24dab - c = 24d...(1)Now, we can find the value of ab, b - c, and c/d by substituting different values of a, b, c and d.Value of ab when a = 2, b = 3, c = 4 and d = 1ab = a * b = 2 * 3 = 6.

Value of b - c when a = 2, b = 3, c = 4 and d = 1b - c = 3 - 4 = -1Value of c/d when a = 2, b = 3, c = 4 and d = 1c/d = 4/1 = 4Putting these values in equation (1), we get6d - 4 = 24dSimplifying, we get-18d = -4d = 2/9

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The current population of Algeria is 38 million

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

P = 38(1 + r)^t

In the initial year, we have

t = 0

Substitute the known values in the above equation, so, we have the following representation

P = 38(1 + r)^0

Evaluate

P = 38

Hence, the population is 38 million

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Answer:

24:
6 of 4
or

8 of 3

Step-by-step explanation:

6x4=24
8x3=24

Same-sized rectangles are possible. However, because their sides might differ in length, they are not congruent.

Congruent refers to two rectangles having the same dimensions and shape. So, two rectangles are said to be congruent if their length and width are equivalent in size. The length and width of two rectangles must match for them to be congruent.

Also having the same area are congruent shapes, such as rectangles. However, congruent rectangles with the same area are not always the case. There are differences among rectangles. Figures that have the exact same shape but differ in size are referred to as similar figures.

These two polygons are incongruent because while their matching sides are equal, their corresponding angles are not. Despite the sides being the same size, they have different forms.

The complete question is:

Draw two rectangles that have the same area but are not congruent.

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Answer:

2.3

Step-by-step explanation:

Answer:

66.66 repeating, or 66.7

Step-by-step explanation:

3rds only go to 99 if your looking for fractions, and to get from 3-99, you would multiply the fraction times 33.3 repeating. to keep the fraction even, you would also multiply the numerator (top number) by 33.3 repeating, getting 66.66 repeating

Based on the definition of the formula unit, the only one that is an example of this concept is NaCl.

In chemistry, this concept refers to the representation of an ionic compound. This formula differs from others because it displays the lowest possible ratio in which the ions have the same charges and therefore the compound is neutral.

A classical example of this concept is NaCl because this includes a cation (positively charged) and an anion (negatively charged). Moreover, in this formula, the compound shows the lowest possible ratio between the two elements.

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Answer:

A.  The probability of event B​ occurring, given that event A has occurred

Step-by-step explanation:

Conditional probability

A probability is conditional if is depends on what has already happened.

The probability that event B happens, given that event A has already happened is "B given A" or P(B | A)

Therefore, P(B | A) means "The probability of event B​ occurring, given that event A has occurred"

Additional information:

P(A | B) means "A given B", i.e. the probability of event A​ occurring, given that event B has occurred

P(A ∩ B) means the probability of event A and event B both happening.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Answer: It is a reflection of Reflections of You (second location) in the x-axis.

Step-by-step explanation: Based on the given information, the relationship between the new location (The Gridiron) and the previous locations can be determined.

The correct answer is:

   It is a reflection of Reflections of You (second location) in the x-axis.

The coordinates of the first three checkpoints of The Gridiron (A''(0,−5), B''(9,−5), and C''(4,−5)) indicate that they have the same y-coordinate (-5) as the corresponding checkpoints in the second location, Reflections of You. However, there is no indication of a reflection in the y-axis or any transformation related to the first location, Transformation Fitness Studios. Therefore, the correct answer is that The Gridiron is a reflection of Reflections of You in the x-axis.

Answer:

-5/-2, 10/4, -10/-4, 5/2

Step-by-step explanation:

The Surface Area of cylinders are: 100 yd² , 264 m², 226  mm²

The Surface Area of Can is 219 cm².

We know the formula for Surface Area of Cylinder

= 2πrh

1. Radius = 2 yd

Height = 8 yd

So, Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 2 x 8

= 100 yd²

2. Radius = 7 m

Height = 6 m

So, Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 6 x 7

= 264 m²

3. Radius = 3 mm

Height = 12 mm

So,  Surface Area of Cylinder

= 2πrh

= 2 x 3.14 x 3 x 12

= 226  mm²

4. Radius = 3.5 cm

Height = 10 cm

So, Surface Area of Can

= 2πrh

= 2 x 3.14 x 3.5 x 10

= 219 cm²

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Answer:

\((-\frac{1}{3},\frac{1}{2} )\) , \((-\frac{3}{2} ,3)\)

Step-by-step explanation:

2y = 3x + 1

y = 2x + 3

Graph 2y = 3x + 1.

Divide each term by 2 and simplify.

      \(y=\frac{3x}{2}+\frac{1}{2}\)

Rewrite in slope-intercept form.

      \(y=\frac{3}{2}x+\frac{1}{2}\)

Use the slope-intercept form to find the slope and y-intercept.

Find the values of m and b using the form y = mx + b.

       \(m=\frac{3}{2}\)

        \(b=\frac{1}{2}\)

The slope of the line is the value of m, and the y-intercept is the value of b.

Slope: \(\frac{3}{2}\)

y-intercept: \((0,\frac{1}{2} )\)

Any line can be graphed using two points. Select two x values, and plug them into the  equation to find the corresponding y values.

Find the x-intercept.

x-intercept(s):  \((-\frac{3}{2},0 )\)

y-intercept(s): (0, 3)

Create a table of the x and y values.

  _x_|_y_

  \(-\frac{3}{2}\)  |   \(0\)

     \(0\)  |   \(3\)

Graph the line using the slope and the y-intercept, or the points.

Slope: 2

intercept: (0, 3)

  _x_|_y_

  \(-\frac{3}{2}\)  |   \(0\)

     \(0\)  |   \(3\)

Graph y = 2x + 3

Use the slope-intercept form to find the slope and y-intercept.

Slope: 2

intercept: (0, 3)

x-intercept(s): \((-\frac{3}{2},0)\)

y-intercept(s): (0, 3)

Plot each graph on the same coordinate system.

Answer:

3. (x | x > 5)

Step-by-step explanation:

To solve this inequality, we need to isolate the variable on one side and the constant on the other side. To do this, we need to use the properties of inequalities and the order of operations to manipulate the given inequality into a form we can solve.

First, we need to distribute the coefficients in front of the parentheses on the left-hand side of the inequality. This gives us:

4x - 12 - 2x + 2 > 0

Next, we can combine like terms on the left-hand side of the inequality by adding the terms with the variable and subtracting the constant terms. This gives us:

2x - 10 > 0

Now, we have isolated the variable on one side of the inequality and the constant on the other side. To solve the inequality, we need to determine the values of x that make the inequality true.

To do this, we can divide both sides of the inequality by the coefficient of the variable, which gives us:

x - 5 > 0

This inequality is satisfied when x is greater than 5. Therefore, the solution to the original inequality is x > 5.

Answer:

Mayor will lose a large percentage

Step-by-step explanation:

Answer:

The mayor will lose by a large perecentage

Step-by-step explanation:

Answer: Lateral area = 750 square inches

Lateral area of a prism is given as

Perimeter = a + b + c

Firstly, we need to find the base using pythagoras theorem

Lateral area = Perimeter x height

Perimeter = a + b + c

Perimeter = 17 + 17 + 16

Perimeter = 50 inches

Lateral area = 50 x 15

Lateral area = 750 square inches

Therefore, the lateral area of the prism is 750 square inches

The area of the park is 12 square units.

To find the area of the park, we can use the Shoelace Formula (also known as Gauss's area formula). This formula allows us to calculate the area of any polygon given the coordinates of its vertices.

The Shoelace Formula states that if we have the coordinates of the vertices of a polygon in counterclockwise order (x₁, y₁), (x₂, y₂), ..., (xn, yn), then the area (A) of the polygon is given by:

A = 1/2 × |(x₁y₂ + x₂y₃ + ... + xn-1yn + xny₁) - (y₁x₂ + y₂x₃ + ... + yn-1xn + ynx₁)|

In our case, the coordinates of the park's vertices are (-9, -9), (-3, -9), and (-6, -5). Let's calculate the area using the Shoelace Formula:

A = 1/2 × |(-9 × -9 + -3 × -5 + -6 * -9) - (-9 × -3 + -9 × -6 + -5 × -9)|

Simplifying further:

A = 1/2 × |(81 + 15 + 54) - (27 + 54 + 45)|

A = 1/2 × |150 - 126|

A = 1/2 × |24|

A = 12

Therefore, the area of the park is 12 square units.

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Answer:

---------------------

Plot the given vertices and connect.

See attached.

Then add the height CD.

The base is AB, with the length:

The height is CD, with length:

Find the area using equation:

The x-intercept of the function is (-1/3, 0) and (5, 0)

Given is a graph of a parabola having equation y = -3x²+14x+5, we need to find the x-intercept of the graph,

So to find the x-intercept put y = 0,

Therefore,

-3x²+14x+5 = 0

-3x²+15x-x+5 = 0

-3x(x-5)-1(x-5) = 0

(-3x-1)(x-5) = 0

Therefore,

x = -1/3 and x = 5

Hence the x-intercept of the function is (-1/3, 0) and (5, 0)

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Answer:

\( \large \rm \frac{3}{4} + \frac{5}{6} + \frac{7}{8} \)

\( \large \rm \frac{3}{4} = \frac{3 \times 6}{4 \times 6} = \frac{18}{24} \)

\( \large\frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24} \)

\(\large \frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24} =\frac{59}{24}=2\frac{11}{24}\)

\( \dashrightarrow\dfrac{3}{4} + \dfrac{5}{6} + \dfrac{7}{8} \\ \\ \)

\( \\ \\ \)

\( \sf \dashrightarrow \dfrac{\frac{3 \times 24}{4} + \frac{5 \times 24}{6} + \frac{7 \times24}{8}} {24} \\ \\ \)

\( \\ \\ \)

\( \sf \dashrightarrow \dfrac{3 \times 6 +5 \times 4+ 7 \times 3} {24} \\ \\ \)

\( \\ \\ \)

\( \sf \dashrightarrow \dfrac{18 +20+ 21} {24} \\ \\ \)

\( \\ \\ \)

\( \sf \dashrightarrow \dfrac{18 +41} {24} \\ \\ \)

\( \\ \\ \)

\( \sf \dashrightarrow \dfrac{59} {24} \\ \\ \)

\( \\ \\ \)

\( \sf \dashrightarrow 2.4 \\ \\ \)

\( \\ \\ \)

Answer:

\(sec(-\theta)=-3.1\)

\(sin(-\theta)=-0.62\)

Step-by-step explanation:

Part a.

\(sec(\theta)\) is related to \(cos(\theta)\) through a reciprocal relationship \(sec(\theta)=\frac{1}{cos(\theta)}\).

Since \(cos(\theta)\) is an even function (reflecting left-right across the y-axis doesn't change the graph), then \(sec(\theta)\) is also an even function.

For any input in the domain, even functions produce the same output if the opposite of the input is used.  In other words, if "f" is an even function, for all x in the domain of f, \(f(x)=f(-x)\).

Thus, for the secant function, if a mystery value "x" is used as an input, and -3.1 is obtained as an output, then if the opposite of x, or -x, is input into the secant function, the output will also be -3.1.

\(sec(-\theta)=-3.1\)

Part b.

The \(sin(\theta)\) function does not reflect left-right across the y-axis to produce the same graph, so the sine function is not even.

However, the sine function can be rotated 180 degree about the origin, sometimes thought of as reflecting through the origin, to produce the same graph.  Visually, this is an "odd" function.

For any input in the domain, if the opposite of the input is used, odd functions produce the opposite of the original output.  In other words, if "g" is an odd function, for all x in the domain of g, \(-g(x)=g(-x)\).

Thus, for the sine function, if a mystery value "x" is used as an input, and 0.62 is obtained as an output, then if the opposite of x, or -x, is input into the sine function, the output will be the opposite of 0.62, meaning -0.62.

\(sin(-\theta)=-0.62\)

INFORMATION:

We know that:

- you flip a coin and use a random number generator to generate a number from 1 to 10

And we must find the probability that the coin shows heads and the generated number is two

STEP BY STEP EXPLANATION:

To find the probability, we need to use that we have two independent events. First, flip a coin and second, generate a number from 1 to 10. They are independent events because their occurrence is not dependent on any other event.

So, to calculate the probability, we need to use the formula for compound probability of independent events

In this case:

- A represents the event of flip a coin

- B represents the event of generate a number from 1 to 10

Now, we must calculate P(A) and P(B)

Then, knowing that P(A) = 0.5 and P(B) = 0.1 we need to replace their values in the initial formula

ANSWER:

The probability that the coin shows heads and the number is two is 0.05

Answer:

  (a)  83°

Step-by-step explanation:

You want the measure of angle 5, given that the adjacent angle 6 has a measure of 97° where the lines cross.

The two angles, 5 and 6, are a linear pair, so are supplementary.

  ∠5 = 180° -∠6

  ∠5 = 180° -97°

  ∠5 = 83°

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Answer:

\(6x^4y^8\sqrt{5x}\)

Step-by-step explanation:

\(\textsf{When $x > 0$ and $y > 0$, we want to find the expression that is equivalent to}\) \(\sqrt{180x^9y^{16}}.\)

\(\textsf{First, apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}\)

\(\sqrt{180}\sqrt{x^9}\sqrt{y^{16}}\)

\(\textsf{Rewrite $x^9$ as $x^{8+1}$:}\)

\(\sqrt{180}\sqrt{x^{(8+1)}}\sqrt{y^{16}}\)

\(\textsf{Apply the exponent rule:} \quad a^{b+c}=a^b \cdot a^c\)

\(\sqrt{180}\sqrt{x^{8}\cdot x^1}\sqrt{y^{16}}\)

\(\sqrt{180}\sqrt{x^{8}}\sqrt{x}\sqrt{y^{16}}\)

\(\textsf{Apply\:the\:radical\:rule:\:}\sqrt[n]{a^m}=a^{\frac{m}{n}},\:\quad a\geq 0\)

\(\sqrt{180}\;x^{\frac{8}{2}}\sqrt{x}\;y^{\frac{16}{2}}\)

\(\sqrt{180}\;x^4\sqrt{x}\;y^8\)

\(\sqrt{180}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Rewrite $180$ as $(6^2 \cdot 5)$:}\)

\(\sqrt{6^2 \cdot 5}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}\)

\(\sqrt{6^2} \sqrt{5}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Apply the radical rule:} \quad \sqrt{a^2}=a, \quad a \geq 0\)

\(6 \sqrt{5}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Apply the radical rule:} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}\)

\(6 \sqrt{5x}\;x^4\;y^8\)

\(\textsf{Rearrange:}\)

\(6x^4y^8\sqrt{5x}\)

\(\textsf{Therefore, when $x > 0$ and $y > 0$, the expression that is equivalent to}\)

\(\sqrt{180x^9y^{16}}\;\textsf{is}\;\;\boxed{6x^4y^8\sqrt{5x}}\:.\)