john and jane are married. the probability that john watches a certain television show is .5. the probability that jane watches the show is .3. the probability that john watches the show, given that jane does, is .5. (a) find the probability that both john and jane watch the show. (round your answer to 2 decimal places.) (b) find the probability that jane watches the show, given that john does. (round your answer to 3 decimal places.) (c) do john and jane watch the show independently of each other? multiple choice yes no

The probability that a chosen point, in the figure lies in the shaded region is 3.18.

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%

The probability of the point chosen in the shaded region is calculated by the formulae

Probability = [tex]\frac{Area of shaded region}{Total area}[/tex]

To find the total area we need to find the area of a triangle and the area of a semicircle.

Area of triangle = 1/2 * Base * Height

                          = 1/2 * 15 * 6

                          = 45

Area of semicircle =  [tex]\frac{\pi r^{2} }{2}[/tex]

                              = [tex]\frac{\pi (3)^{2} }{2}[/tex]

                              =14.13

Therefore the probability that chosen point = [tex]\frac{45}{14.13}[/tex] = 3.18

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The linear equation that passes through the given points is:

y + 9 = -10*(x - 1)

A general linear equation that passes through two points (x₁, y₁) and (x₂, y₂) has a slope given by:

a = (y₂ - y₁)/(x₂ - x₁)

Then using any of these points we can write the line as:

y -  y₁ = a*(x - x₁)

Here the points are (1, -9) and (-10, 101), then the slope is:

a = (101 + 9)/(10 - 1) = 110/-11 = -10

And using the point (1, -9) we can write the line as:

y + 9 = -10*(x - 1)

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Answer: 4

Step-by-step explanation:

2x6 = 3xd

12=3d

d=4

You can trust this answer because I answered it right now and it was correct. <3

The value of length of segment d is,

⇒ d = 4

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

A circle is shown in figure.

Now, We can formulate;

⇒ 6 × 2 = d × 3

Solve for d;

⇒ 12 = 3d

⇒ 3d = 12

⇒ d = 12/3

⇒ d = 4

Thus, The value of length of segment d is,

⇒ d = 4

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If the amount of time is exponentially distributed with mean 20 minutes, then the standard deviation of the time a student would spend at a terminal is also 20 minutes.

The amount of time which the student spends at a terminal in ISEN computer-room is said to be exponentially distributed, and

The mean-time spent at computer room is = 20 minutes,

We know that, for an exponentially-distributed random variable, the standard deviation is equal to the mean.

So, the standard deviation of the time a student spends at a terminal is also 20 minutes, since the mean is given as 20 minutes.

Therefore, the standard deviation is 20 minutes.

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The arc for the following circle is arc YZ that is option D.

In geometry, an arc is a part of a circle's circumference. It is defined as the portion of the circle that is contained between any two points on the circle. The length of an arc is proportional to the measure of its central angle, which is the angle formed by the two radii drawn to the endpoints of the arc. The measure of an arc is typically expressed in degrees, and it can be calculated using the formula:

arc length = (central angle measure / 360 degrees) x (circumference of the circle)

In addition to being a fundamental concept in geometry, arcs are commonly used in fields such as engineering, architecture, and physics to describe the shape and motion of objects that move along curved paths.

Here,

In the given options, we have four letters X, W, Y, and Z, which represent the points on the circle. The arcs are defined by the pairs of these points as follows:

Arc YZ is the arc of the circle that starts at point Y and ends at point Z.

Therefore, the answer is that the arcs of the circle mentioned in the options are O arc YZ.

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Using the equations we know that the square should be finished by adding 9 to both sides.

An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.

As in 3x + 5 = 15, for example.

There are many different types of equations, including linear, quadratic, cubic, and others.

The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.

So, write the equation so that the terms with x are on the left and the constants are on the right:

x² – 6x = 5

Ensure that the x2 term's coefficient is 1:

x² – 6x = 5

Including a phrase on both sides will complete the left side's square. The x term's coefficient is multiplied by two and squared to achieve this.

To make the equation equal on both sides, add the same amount to the right side.

x² – 6x + 9 = 5 + 9

(x-3)² = 14

Therefore, using the equations we know that the square should be finished by adding 9 to both sides.

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Correct question:

What number should be added to both sides of the equation to complete the square?

x2 – 6x = 5

Answer:

here are the factors

Cost of living data includes the expenses incurred for food, shelter, transportation, energy, clothing, education, healthcare, childcare, and entertainment. A cost of living index tracks how much basic expenses rise over time and among different regions.

here

How To Calculate Cost Of Living

Subtract the index of your current city from the index of the city you want to move to: 115.1 - 90.9 = 24.2.

Divide the resulting difference by the index of your current city: 24.2 ÷ 90.9 = 0.266.

Multiply the resulting quotient by 100 to get the percentage: 0.266 x 100 = 26.6%

Answer:

Frequency is high hope this help you

r offers to pay $1,000 over the dealer' cost for a luxury coupe. The base price is $62.685 and options total $5,209. There is no destination charge. If the dealer' costs are 87 percent of the base price and 89 percent of the options, what is Huster's offer?The dealer's cost for the base price would be 87% of $62,685, which is $54,508.95. The dealer's cost for the options would be 89% of $5,209, which is $4,638.01. Therefore, the total dealer's cost would be $54,508.95 + $4,638.01 = $59,146.96. Brad Huxter's offer is $1,000 over the dealer's cost, so his offer would be $59,146.96 + $1,000 = $60,146.96.

Answer:

1 over 36

Step-by-step explanation:

The slope intercept form of the given line whose coordinate of point is (- 5,9) and slope is - 5 would be y = -5x - 16.

Equation of a straight line: y = mx + b ------(i)

Given that

y = 9, x = -5

and slope, m = - 5

By putting above values in equation (i)

9 = -5 (-5) + b

9 = 25 + b

-16 = b

b = -16

y = -5x - 16

The slope of a line is the measure of the steepness and the direction of the line. Finding the slope of lines in a coordinate plane can help in predicting whether the lines are parallel, perpendicular, or none without actually using a compass.

The slope of any line can be calculated using any two distinct points lying on the line. The slope of a line formula calculates the ratio of the "vertical change" to the "horizontal change" between two distinct points on a line. In this article, we will understand the method to find the slope and its applications.

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The correct equation to isolate principal, P, is:

Simple interest refers to the interest that is earned on an initial amount of money, known as the principal, over a fixed period of time. It is called "simple" because it is calculated based only on the initial principal amount and does not take into account any interest earned on the interest itself, which is known as compound interest.

To isolate principal, P, we need to rearrange the given formula as follows:

[tex]A - P(1 + rt) =[/tex] Interest earned on principal (I)

The interest earned on the principal (I) is given by:

[tex]I = Prt[/tex]

Now, we can rewrite the above formula as:

[tex]A = P + I[/tex]

Substituting the value of I, we get:

[tex]A = P + Prt[/tex]

Now, we can isolate P by subtracting Prt from both sides:

[tex]A - Prt = P[/tex]

Therefore, the correct equation to isolate principal, P, is:

[tex]P = (A - Prt)[/tex]

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The correct equation to isolate P is c. P = A/(1 + rt)

Simple interest is the term used to describe the interest that is accrued over a predetermined amount of time on an initial sum of money, known as the principal. It is known as "simple" interest because it is computed just using the initial principal sum and ignores any interest that has been earned on top of the interest itself, a concept known as compound interest.

The formula for the final amount earned using simple interest is A = P(1 + rt), where A is the total amount at the end of t years, P is the principal amount, r is the interest rate, and t is the time in years.

To isolate P, we can rearrange the formula as:

A = P(1 + rt)

Divide both sides by (1 + rt):

A/(1 + rt) = P

Therefore, the correct equation to isolate P is:

c. P = A/(1 + rt)

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Answer to Whats the answer for that question?:

A correct response to a question asked to test one's knowledge.

Step-by-step explanation:

The way you answer a question depends on how you view it. This could entail thought process, method, and calculations. So overall it depends on perspective.

The scale factor of the given triangle is 3/2.

What is triangle?

Triangles are a particular form of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional image shown here. An example of a 3-sided shape is a triangle. The total of a triangle's three angles is 180 degrees.

In triangle ABC and triangle DEF;

AB= 15, BC=18, AC=12 and DE=10, EF=12, DF=8

NOW, we know that scale factors are the REDUCED FORM of corresponding sides of two similar triangles, then;

HERE;

scale factors will be....

AB/DE=15/10=3/2

BC/EF=18/12=3/2

AC/DF=12/8=3/2

Hence, scale factor is 3/2.

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The correct question is:

Verify that △ABC∼△DEF. Find the scale factor of △ABC to △DEF. If △ABC: BC = 18, AB = 15, AC = 12 △DEF: EF = 12, DE = 10, DF = 8.

Answer:

Step-by-step explanation:

x + 5 < 7

x + 5 - 5 < 7 - 5

x < 2

The number line will have a open circle at 2 and be shaded to the left

completely.  The solution is all numbers less than positive 2.

Based on the amount predicted to be spent, the hypotheses Null Hypothesis = $1,007.24 and Alternate Hypothesis ≠ $1,007.24

The null hypothesis, or H0, in statistics science is the exact reverse of what the researcher wants to investigate. Generally, unless there is compelling proof to the contrary, the null hypothesis is taken to be correct. Another theory that will demonstrate the area one wants to investigate and be reflected by H1 must be developed.

The forecast is confirmed by the null hypothesis, which in this instance is that the typical consumer will indeed spend $1,007.24. According to the Alternate Hypothesis, the predicted occurrence won't occur, so in this instance, the shopper wouldn't spend $1,007.24. In conclusion, the variant contradicts the null hypothesis and supports it.

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Answer: 4, -7

Step-by-step explanation:

Plug the numbers into the variables and solve;

(6)(12) / 6+12

Multiply the values in the numerator and add the values in the denominator.

72/18

Then divide and the answer will be 4.

For the second one:

4+3 / 3-4

Add the values in the numerator and subtract the values in the denominator.

7/-1

Dividing this will make 7 a negative, so the answer is -7.

Hope that helped ^^;;

Henry is predicted to receive 360 votes, Christy is predicted to receive 420 votes, and Celina is predicted to receive 220 votes for the president’s position.

What is probability?

Probability is a measure of the likelihood of an event occurring.

Part A:

To predict how many votes each candidate for president will get in the election, we can set up a proportion between the sample and the population

Let x be the number of votes each candidate will receive in the election.

For Henry:

36/150 = x/1500

x = (36/150) * 1500

x = 360

For Christy:

42/150 = x/1500

x = (42/150) * 1500

x = 420

For Celina:

22/150 = x/1500

x = (22/150) * 1500

x = 220

Therefore, Henry is predicted to receive 360 votes, Christy is predicted to receive 420 votes, and Celina is predicted to receive 220 votes for the president’s position.

Part B:

Based on the survey results, Christy is most likely to get the highest percentage of votes for the president’s position with 42/100 votes, which is approximately 42%.

Part C:

To predict how many votes each candidate for vice president will get in the election, we can set up a proportion between the sample and the population.

Let x be the number of votes each candidate will receive in the election.

For Tristan:

14/150 = x/1500

x = (14/150) * 1500

x = 140

For Kenny:

46/150 = x/1500

x = (46/150) * 1500

x = 460

For Madison:

40/150 = x/1500

x = (40/150) * 1500

x = 400

Therefore, Tristan is predicted to receive 140 votes, Kenny is predicted to receive 460 votes, and Madison is predicted to receive 400 votes for the vice president’s position.

Part D:

Based on the survey results, Kenny is most likely to get the highest percentage of votes for the vice president’s position with 46/100 votes, which is approximately 46%.

Part E:

To predict how many votes each candidate for treasurer will get in the election, we can set up a proportion between the sample and the population.

Let x be the number of votes each candidate will receive in the election.

For Priscilla:

53/150 = x/1500

x = (53/150) * 1500

x = 530

For Reuben:

24/150 = x/1500

x = (24/150) * 1500

x = 240

For Erica:

23/150 = x/1500

x = (23/150) * 1500

x = 230

Therefore, Priscilla is predicted to receive 530 votes, Reuben is predicted to receive 240 votes, and Erica is predicted to receive 230 votes for the treasurer’s position.

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The value of imports is $304,533,333.33 and the value of exports is $311,633,333.33. So, option B is correct.

Let's denote the value of exports as E and the value of imports as I. We can then use the following system of equations to solve for E and I:

E - I = 7,100,000 (balance of trade equation)

0.12E + 0.21I = 9,148,200 (tariff revenue equation)

Multiplying the first equation by 0.12 and adding it to the second equation, we get:

0.12E - 0.12I + 0.21I = 9,148,200 + 0.12(7,100,000)

0.12E + 0.09I = 9,988,000

Multiplying both sides by 100, we can eliminate decimals:

12E + 9I = 998,800,000

We can now use this equation with the balance of trade equation to solve for E and I:

E - I = 7,100,000

12E + 9I = 998,800,000

Multiplying the first equation by 9 and subtracting it from the second equation, we get:

12E + 9I - 9E + 9I = 998,800,000 - 63,900,000

3E = 934,900,000

E = 311,633,333.33

Substituting this value into the balance of trade equation, we get:

311,633,333.33 - I = 7,100,000

I = 304,533,333.33

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A 0.025kg golf ball is hit off a tee with a force of 450N. If the golf club was in contact with the ball for 0.012 s, the velocity of the golf ball will increase by 216 m/s.

what is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.

To solve this problem, we can use the equation:

F = m*a

where F is the force applied, m is the mass of the object, and a is the acceleration.

We can rearrange this equation to solve for acceleration:

a = F/m

Using this equation, we can find the acceleration of the golf ball:

a = 450N / 0.025kg = 18000 m/s²

Next, we can use the equation:

v = v0 + a*t

where v is the final velocity, v0 is the initial velocity (which we'll assume is 0 m/s), a is the acceleration, and t is the time.

We know the acceleration and the time, so we can solve for the final velocity:

v = 0 + (18000 m/s²) * 0.012 s

v = 216 m/s

Therefore, the velocity of the golf ball will increase by 216 m/s.

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The total area of the pool and the walkway will be 210 square feet, the walkway should be 1.8 feet wide.

In mathematics, area is a measure of the size or extent of a two-dimensional shape or surface. It is typically measured in square units, such as square meters, square feet, or square inches. The area of a shape is calculated by multiplying its length by its width or by using a formula specific to that shape.

The concept of area is fundamental to many areas of mathematics, science, and engineering. It is used to calculate the size of land and buildings in real estate, the amount of material needed for construction, the amount of paint needed to cover a surface, and many other practical applications. In addition, the study of area is important in geometry, calculus, and other areas of mathematics.

Let's start by finding the area of the pool, which is 9 feet by 8 feet:

Area of pool = 9 feet * 8 feet = 72 square feet

Next, we need to add the width of the walkway to each dimension of the pool to find the dimensions of the entire area:

Width of area = 9 feet + 2(width of walkway)

Length of area = 8 feet + 2(width of walkway)

The total area of the pool and walkway is given as 210 square feet, so we can set up the equation:

Area of pool + Area of walkway = 210 square feet

Substituting the formulas for the area of the pool and area of the walkway, we get:

72 + (9 + 2x)(8 + 2x) = 210

Expanding the right side and simplifying, we get:

4x² + 34x - 33 = 0

We can solve for x using the quadratic formula:

x = (-34 ± √(34² - 44(-33))) / (2*4)

x = (-34 ± √(1660)) / 8

x = (-34 ± 40.74) / 8

x = 1.8 or x = -5.075

Since the width of the walkway cannot be negative, the width of the walkway should be 1.8 feet.

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Using the area formula,

Area of the prism = 40mm².

Define area?

The word "area" designates a vacant region. The length and width of a form are used to calculate its area. The units of unidimensional length are feet (ft), yards (yd), inches (in), etc. Yet, the area of a shape is a two-dimensional quantity. Measurements like square inches (in²), square feet (ft²), square yards (yd²), etc. are used to measure anything in a square.

In the figure,

We have 2 equal rectangles and 2 equal triangles.

Now dimensions of the rectangles, l = 4mm and b = 3mm.

Area of 2 rectangles = 2 × 4 × 3

= 24mm².

Height of triangle, h = 4mm and base, b = 4mm.

Area of 2 triangles = 2 × 1/2 × b × h

= 4 × 4

= 16mm².

Therefore, total area of the prism = 24 + 16 = 40mm².

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In the above mentioned similar triangles the length of DE is 5.25 cm.

A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed.

Since triangles ABC and ADE are similar, their corresponding sides are proportional. We can use this fact to set up a proportion:

AB / AD = BC / DE

Substituting the given values, we get:

8 / AD = 6 / DE

Multiplying both sides by DE, we get:

8DE / AD = 6

Dividing both sides by 8/AD, we get:

DE = (6/8)AD

We need to find AD to solve for DE. To do this, we can use the fact that BD is an altitude of triangle ABC and triangle ADE is similar to triangle ABC. Therefore, triangle ABD is also similar to triangle ABC, and we can set up another proportion:

BD / AB = AD / AC

Substituting the given values, we get:

4 / 8 = AD / (8 + 6)

Simplifying, we get:

1/2 = AD / 14

Multiplying both sides by 14, we get:

AD = 7

Substituting this value back into the first equation, we get:

DE = (6/8)AD = (6/8)7 = 21/4 = 5.25

Therefore, the length of DE is 5.25 cm.

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Answer: D Mario owes the bank a little less than $50

Answer:45 & 90

Step-by-step explanation:

Answer:

∠x = 159° and ∠y = 149°

Step-by-step explanation:

∠a = 31°

∠b = 52°

∠x = ?

∠y = ?

∠a and ∠y are supplementary angles so:

∠a + ∠y = 180

31 + ∠y = 180

∠y = 180 - 31

∠y = 149°

∠b also has a supplementary angle which is not labeled in the question so let's label that ∠c.

∠b + ∠c = 180

52 + ∠c = 180

∠c = 180 - 52

∠c = 128°

∠a and ∠c  are both inside a triangle formed by all the lines crossing with each other. Since the sum of angles inside a triangle is 180°, find the third angle in this triangle (∠d) using all the values we were given and solved for:

∠a + ∠c + ∠d = 180

31 + 128 + ∠d = 180

∠d = 180 - 31 - 128

∠d = 21°

∠d and ∠x are supplementary angles so:

∠d + ∠x = 180

21 + ∠x = 180

∠x = 180 - 21

∠x = 159°

∠x = 159° and ∠y = 149°

The fact that PC is less than 50% indicates a higher probability of underage.

However, without additional information on the costs associated with overage and underage, we cannot determine which cost is higher.

From the information given in the student question, it is clear that the probability of underage (PC) is less than 50%, as indicated by the shaded area under the graph.

To determine whether the cost of overage or the cost of underage is higher, follow these steps:
1. Identify the costs associated with overage and underage in the given context. Overage cost refers to the cost incurred when the inventory is higher than demand, while underage cost refers to the cost incurred when the inventory is lower than demand.
2. Analyze the graph or data provided to compare the costs of overage and underage. Since the student question does not provide any specific data or graph, we cannot accurately determine which cost is higher based on the given information.
3. Interpret the results. If the cost of overage is higher than the cost of underage, this means that having excess inventory is more expensive than having insufficient inventory.

Conversely, if the cost of underage is higher than the cost of overage, this means that not having enough inventory is more expensive than having excess inventory.

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When two numbers appear side by side, the number and number should be written together for clarity. The statement is true.

The term numeric expression consists of two words, number for a number and expression for a sentence. Therefore, it is a word containing numbers. Teaching mathematics is the combination of numbers and mixed numbers using mathematical operations such as addition, subtraction, division, or division. There are many number expressions such as word form and number form. Numerical expressions are mathematical expressions that contain only numbers and one or more operators.

Examples of symbol operations are addition, subtraction, multiplication, and division. It can be represented by a radical symbol (square root symbol) or a real value.

Equations consist of numbers and contain multiple digits. There is no limit to the number of operators a shared account can have. Some numbers use only one operator of the two numbers, while others may have more than one operator. The only requirement for a numeric expression is that it only contains a number and an operator. Some numbers have only one operator code others have two or more.

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