A newspaper article indicated that 43 percent of cars with black seats are white, 46 percent of cars with black seats are blue, 7 percent of cars with black seats are red, and 4 percent of cars with black seats are black. A test was conducted to investigate whether the color of cars with black seats was consistent with the newspaper article. A random sample of cars of these colors was selected, and the value of the chi-square test statistic was x = 8.2. Which of the following represents the p-value for the test?
A) P(x2 ≥ 8.2) = 0.08
B) P(x2 ≥ 8.2) = 0.04
C) P(x2 ≤ 8.2) = 0.96
D) P (x2 = 8.2) = 0.00
E) The p-value cannot be calculated because the sample size is not given.

Answers

Answer 1

Answer:

C) P (X2 ≤ 8.2) = 0.96

Step-by-step explanation:

P value for the test is the probability of obtaining results that have been observed in the null hypothesis statement. A very small value of p indicates that there is unlikely chance of null hypothesis being true which means that we cannot accept null hypothesis based on the small p value.

Answer 2

Answer:

P(χ2≥8.2)=0.04

Step-by-step explanation:

Just took the test. This was correct


Related Questions

A train traveled 300 miles. How long did the trip take if the train was traveling at a rate of: Note * Use the d=rt formula (distance = rate * time). NOTE: You may not be able to solve for the variable. If you do not have enough information to solve for the variable then write the equation. 1) 50 mph 2) 70 mph 3) x mph 4) (x+10)mph 5) (x-5)mph

Answers

If a train traveled 300 miles. The time is, 6 hours, 4.29 hours, 300/x hours, 300/(x+10) hours,300/(x+5) hours.

How to find the time?

Distance = Rate × Time

Time =Distance/Rate

1. 50 mph

Time = 300/50

Time = 6 hours

2. 70 mph

Time = 300/70

Time = 4.29 hours

3. x mph

Time = 300/x

Time = 300/x hours

4. (x+10)mph

300/(x+10) hours

5. (x-5)mph

300/(x-5) hours

Therefore the  time is, 6 hours, 4.29 hours, 300/x hours, 300/(x+10) hours,300/(x+5) hours.

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it takes Carly 39 minutes to walk 3 miles at that rate how long will it take Carly to walk 7 miles

Answers

The time it takes Carly to walk 7 miles is 91 minutes

How to determine how long will it take Carly to walk 7 miles

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

Time = 39 minutes

Distance = 3 miles

The speed can be calculated as

Speed = Distance/Time

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

Speed = 3 miles/39 minutes

So, we have

Speed = 1/13 miles per minute

From the question, we have

Distance = 7 miles

Recall that

Speed = Distance/Time

Make time the subject

Time = Distance/Speed

So, we have

Time = 7/(1/13)

Evaluate

Time = 91 minutes

Hence, the time is 91 minutes

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Use the figure to complete each sentence. The base of this rectangle is cm. The height of this rectangle is cm. The area of this rectangle is cm2.

Answers

Answer:

Step-by-step explanation:

Use the figure to complete each sentence. The base of this rectangle is cm. The height of this rectangle is cm. The area of this rectangle is cm2.

you have the base and the height in the drawing, the area of ​​the rectangle is found by multiplying the base by the height, 6 x 4 = 24 cm²

The base of this rectangle is 4 cm.The height of this rectangle is 6 cmThe Area of this rectangle is 24cm²

Answer:

24 cm²

Step-by-step explanation:

Solution Given:

The base of this rectangle is 4 cm. The height of this rectangle is 6 cm

height =6 cm

base = 4cm

Since

Area of Rectangle= base*height

=6*4

=24 cm²

Therefore, the area of this rectangle is 24 cm².

A food truck did a daily survey of customers to find their food preferences. The data is partially entered in the frequency table. Complete the table to analyze the data and answer the questions:


Likes hamburgers Does not like hamburgers Total
Likes burritos 29 41
Does not like burritos 54 135
Total 110 205

Part A: What percentage of the survey respondents liked neither hamburgers nor burritos? Show all work. (3 points)

Part B: What is the marginal relative frequency of all customers who like hamburgers? Show all work. (3 points)

Part C: Which category has the lowest joint relative frequency? Show all work. (4 points)

Answers

A: 16.09 %  of the survey respondents liked neither hamburgers nor burritos

B) 0.65  is the marginal relative frequency.

C) The lowest joint relative frequency of those who like Hamburgers but not burritos.

What is Marginal Frequency?

The ratio of a row total's or column total's frequency to the overall frequency of the data is known as marginal relative frequency. It is frequently used to examine broad trends in a single type of data.

   

Given:

                          Like Hamburgers    Does Not Like Hamburgers    Total

Likes burritos                  39                           38                                   77

Does not like burritos     95                           33                                 128

Total                                 134                           71                                 205

A) There are 33 such respondents.  

So, percentage is

= 33/205 x 100

= 16.095

B) It will be the ratio of the sum of the customers that like hamburgers to the total number of respondents

So, the ratio is

= 134/205

= 0.65 :1

Part C:  For this, we need to find the ratio of all the four data with the total.

Those who like Hamburgers and burritos

= 39/134

Those who like Hamburgers but not burritos

= 95/134

Those who like burritos but not Hamburgers

=38/71

Those who do not like burritos or Hamburgers = 33/71

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Lakeside amusement park charges an entry fee plus $1.25 per ticket used to go on the rides. The entry fee is the same amount for everyone.

Louisa spent a total of $43.75 on the entry fee plus 25 ride tickets. Click “show your work” below and show calculations to determine how much Louisa paid for the entry fee.

Answers

Using mathematical operations, the amount that Louisa paid for the entry fee is $12.5.

What are mathematical operations?

The basic mathematical operations include addition, subtraction, division, and multiplication.

These mathematical operations combine values, numbers, and variables with mathematical operands to solve mathematical problems.

For instance, the variable cost per ride ticket is given as $1.25.  There are a total of 25 ride tickets spent by Louisa.

Mathematically, the total variable cost is the product of per unit cost and total ride tickets.

The total variable cost is subtracted from the total amount spent to determine the fixed entry fee.

Fee per ticket = $1.25

Total amount spent by Louisa = $43.75

The number of ride tickets = 25

The fixed entry fee per person = $12.50 ($43.75 - $1.25 x 25)

Thus, whereas, Louisa spent $1.25 per ride ticket, she spent $12.50 as the fixed entry fee.

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Factors 3x^4-5x^3+6x^2-15x completely over the set of integers

Answers

The Factors of 3x^4-5x^3+6x^2-15x completely over the set of integers will give 5(1-3x).

How can this be calculated?

In mathematics, factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller

The expression can be broken down after the other as

[2x4 = 8] + [5x3=15] + [6x2=12]

= [8-15+12-15x]

=5-15x

then we can factorize as

5(1-3x)

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What tastes juicier?

Mixture A: 2 cups of concentrate and 3 cups of water
Mixture B: 6 cups of concentrate and 8 cups of water


Group of answer choices

Mixture B

Mixture A

They taste the same

Answers

Answer:

Mixture B

Step-by-step explanation:

A) the concentrate per cup is 2/3

B) the concentrate per cup is 6/8 = 3/4

The concentration of B is higher, so it will taste juicier.

Caleb is a fashion designer. He designed a jacket with 2 types of fabric. Now Caleb has to make samples. He buys 68 yards of nylon and 94 yards of wool. The nylon is $3 a yard, and a yard of wool is 3 times more expensive. How much did Caleb spend?​

Answers

To find out how much the wool costs, we need to multiply the price of a yard of nylon by 3, since the wool is 3 times more expensive. So a yard of wool costs $3 * 3 = $<<3*3=9>>9.

To find out how many yards of wool Caleb bought, we need to divide the total number of yards by the number of fabrics, since he bought the same amount of each fabric. So Caleb bought 68 / 2 = <<68/2=34>>34 yards of wool.

To find out how much Caleb spent on wool, we need to multiply the number of yards of wool by the price of a yard of wool. So Caleb spent 34 * $9 = $<<34*9=306>>306 on wool.

To find out how much Caleb spent on nylon, we need to multiply the number of yards of nylon by the price of a yard of nylon. So Caleb spent 68 * $3 = $<<68*3=204>>204 on nylon.

To find out how much Caleb spent in total, we need to add the amount he spent on wool and the amount he spent on nylon. So Caleb spent $306 + $204 = $<<306+204=510>>510 in total. Answer: \boxed{510}.

Michael pays $34.65 for eleven 18-count boxes of granola bars. How much does 1 box of granola bars cost?
One box of granola bars costs $

Answers

Answer:−cnotu+53.65

Step-by-step explanation: I don't really know how I got it. But it was quite easy.

(x+1)=(7x-5) how do i solve this

Answers

Step-by-step explanation:

You start with x+1=7x-5

Basically you want all the x's on one side and all the constants on the other

(x+1)+5=(7x-5)+5, to get rid of the 5 on the right side

(x+6)-x=7x-x, to get rid of the x on the left side

We are now left with 6x=6

No we simplify, 6x/6=6/6

Now we have x=1, which is the answer

I hope this made sense.

Answer:

x= 1.

Step-by-step explanation:

1. Write the expression.

[tex](x+1)=(7x-5)\\ \\x+1=7x-5[/tex]

2. Subtract "1" from both sides of the equation.

[tex]x+1-1=7x-5-1\\ \\x=7x-6[/tex]

3. Subtract "7x" from both sides of the equation.

[tex]x-7x=7x-6-7x\\ \\-6x=-6[/tex]

4. Divide both sides by "-6".

[tex]\frac{-6x}{-6} =\frac{-6}{-6} \\ \\x=1[/tex]

5. Verify.

[tex](1)+1=7(1)-5\\ \\2=7-5\\ \\2=2[/tex]

That's correct!

6. Conclude.

x= 1.

The diagram shows the lengths of corresponding sides of similar triangles A'B'C' and ABC. Which expression gives the perimeter of A'B'C'?

Answers

The expression that gives the perimeter of the A'B'C is 2 (a + b + c).

Option B is the correct answer.

What is a triangle?

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

The side length of triangle A'B'C' is twice the length of the corresponding side length of triangle ABC.  

The perimeter of a triangle.

= Sum of all the three sides

Now,

The perimeter of the triangle ABC.

= a + b + c

Thus,

The perimeter of the triangle A'B'C'.

= 2 (a + b + c)

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Marta conducts emissions inspections on cars. She finds that 8 % 8%8, percent of the cars fail the inspection. Let X XX be the number of cars Marta inspects until a car fails an inspection. Assume that the results of each inspection are independent. Find the mean and standard deviation of X XX. Round your answers to one decimal place.

Answers

There are X automobiles, with a mean of 12.5 cars. The standard deviation for X is also SD = 12.0.

What connection exists between the mean and the standard deviation?

First, a data set's mean and standard deviation convey distinct information. The average (center) of a data collection is provided by mean (it is a measure of central tendency). You may learn about the range (dispersion) of data around the mean by looking at the standard deviation. We may investigate a data set's characteristics and characterize it using both the mean and standard deviation. To provide confidence intervals for data that has a normal distribution, they are frequently combined. If two or more data sets need to be compared:

The mean reveals whether data set is, on average, greater or lower (or better or worse). We can determine whether data set has a wider dispersion using the standard deviation (higher standard deviation means data is more spread out from the mean). Second, there are variations in how each metric is calculated. In particular, we utilize squaring to get the standard deviation but not the mean. We completely avoid using squaring when determining the mean of a data collection. Simply multiplying the total number of data points in the set by the sum of all the values in the data set yields the answer.

What is the standard deviation and mean formula?

The mean is calculated as follows:

Mean = (all data values added together) / (number of data values)

However, when calculating standard deviation, we do employ squaring. We take the square of the deviation between each data point and the mean in particular.

The standard deviation equation is as follows:

Finally, when we add the identical value to each data point in the data set, the mean and standard deviation "respond" differently. If we multiply every value in a data collection by the constant "K":

No of the size of the data collection, the mean rises by precisely K.

No matter how many observations are in the data collection, the standard deviation does not vary. The identical value is then added.

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The sum of two consecutive mile markers on the interstate is 365. Find the numbers on the markers.

Answers

Answer:

x is the first mile marker

then, x+%2B+1 the second mile marker

given:

x%2Bx+%2B+1=655

2x+=655-1

2x+=654

x+=654%2F2

x+=327->the first mile marker

and

x+%2B+1=328 the second mile marker

24 divided by 4•2 - 2

Answers

Answer:

the answer is 10

Step-by-step explanation:

The value of the numerical expression 24 / (4 × 2 - 2) will be 4.

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ 24 / (4 × 2 - 2)

Simplify the expression, then we have

⇒ 24 / (4 × 2 - 2)

⇒ 24 / (8 - 2)

⇒ 24 / 6

⇒ 4

The value of the numerical expression 24 / (4 × 2 - 2) will be 4.

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Solve the equation for x.

−0.28x − 8.4 = 8.26

x = 59.5
x = −59.5
x = 50.5
x = −50.5

Answers

The value of x after solving −0.28x − 8.4 = 8.26  is   x = −59.5 .

What is linear equation in one variable ?

The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution. For example, 2x+3=8 is a linear equation having a single variable in it.

To solve linear equation in one variable:

Step 1: Simplify each side, if needed.

Step 2: Use Add./Sub. Properties to move the variable term to one side and all other terms to the other side.

Step 3: Use Mult./Div. Properties to remove any values that are in front of the variable.

Given :

-0.28x - 8.4 = 8.26

Adding 8.4 both the sides , we get

-0.28x + (-8.4 + 8.4) = 8.26 + 8.4

-0.28x = 16.66

x = - (16.66/0.28)

x = -59.5

Hence , the value of x after solving −0.28x − 8.4 = 8.26  is   x = −59.5 .

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26
Select the correct answer.
The height (cm) of an object oscillating up and down at the end of a spring is s(t) = 100 + cos t. Find the eceleration at time t.
O A.
100-cos t
OB.
-sin t
O C.
-cos t
O D. 100-sin t
Reset
Next

Answers

-sint is the acceleration at time t.

What is Acceleration?

Acceleration is the rate of change of the velocity of an object with respect to time.

Given, the height (cm) of an object oscillating up and down at the end of a spring is s(t) = 100 + cos t.

We need to find the  acceleration at time t.

s(t) = 100 + cos t.

To find the acceleration we have to differentiate the above equation.

d/dt=d/dt(100+cost)

=d/dt(100)+d/dt(cost)

=0+(-sint)

s'(t) = -sint.

Hence, the acceleration at time t is -sint.

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Two parallel lines are cut by transverse as shown suppose

Answers

This might be the answer because you didn’t include a picture of your problem

b) If the marginal revenue function for output x is given by MR = C, where a, b, c, m and n are constant. mn (ax+b)² Prove that the demand function is p mn b(ax+b) C.

Answers

The demand function is given by the expression -

D{x} = mn(a²x + 2b + b²)

What is a mathematical function, equation and expression?                function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.

Given is the revenue function as follows -

f(x) = mn (ax + b)²

The revenue function is simply [x] multiplied by the demand function.

R{x} = x (D{x})

The revenue function is -

f(x) = mn (ax + b)²

So, the demand function can be written as -

mn(ax + b)² = x (D{x})

D{x} = {mn(ax + b)²}/x

D{x} = {mn(a²x² + b² + 2abx)}/x

D{x} = {a²x²mn + mnb² + 2bmnx}/x

D{x} = a²xmn + 2bmn + mnb²

D{x} = mn(a²x + 2b + b²)

Therefore, the demand function is given by the expression -

D{x} = mn(a²x + 2b + b²).

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Find the y-intercept from the line of best fit y = 6 + 2x.

Answers

Answer:

y - intercept = 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 6 + 2x , that is

y = 2x + 6 ← is in slope- intercept form

with y- intercept c = 6

1-9 Enrichment Worksheet
Geometry Crossword Puzzle
12
NAME
16
13
19
3
18
10
ACROSS
3. Points on the same line
are -
4. A point on a line and all
points of the line to one
side of it.
9. An angle whose measure
is greater than 90.
10. Two endpoints and all
points between them.
16. A flat figure with no
thickness that extends
indefinitely in all
directions.
1
17. Segments of equal length
segments.
are -
18. Two noncollinear rays
with a common endpoint.
19. If m ZA+ m ZB = 180,
then ZA and ZB are -
angles.
17
2
15
9
4
8
14
18
DATE
DOWN
1. The set of all points collinear to two points
is a.
Glencoe Division, Macmillan/McGraw-Hill
7
2. The point where the x- and y-axis meet.
5. An angle whose measure is less than 90.
6. If m ZA+ m ZD = 90, then ZA and ZB are
angles.
7. Lines that meet at a 90° angle are
8. Two angles with a common side but no
common interior points are
10. An "angle" formed by opposite rays is a
_________ angle.
11. The middle point of a line.segment.
12. Points that lie in the same plane are -
13. The four parts of a coordinate plane.
14. Two nonadjacent angles formed by two
intersecting lines are - angles.
15. In angle ABC, point B is the

Answers

Answer:

Look at the image I attached to this answer for the answers.

Final answer:

This is a crossword puzzle on geometry terms and concepts, including lines, angles, and planes.

Explanation:Geometry Crossword Puzzle



ACROSS

Points on the same line are collinear.A point on a line and all points on one side of it is called a ray.An angle whose measure is greater than 90 degrees is obtuse.A line segment with two endpoints and all points between them is a line.A flat figure with no thickness that extends indefinitely in all directions is called a plane.Segments of equal length are called congruent segments.Two noncollinear rays with a common endpoint form an angle.If the sum of two angles is 180 degrees, then they are supplementary angles.



DOWN

The set of all points collinear to two points is called a line.The point where the x- and y-axis meet is called the origin.An angle whose measure is less than 90 degrees is acute.If the sum of two angles is 90 degrees, then they are complementary angles.Lines that meet at a 90° angle are perpendicular lines.Two angles with a common side but no common interior points are called adjacent angles.An angle formed by opposite rays is a straight angle.The middle point of a line segment is called the midpoint.Points that lie in the same plane are coplanar.The four parts of a coordinate plane are quadrants.Two nonadjacent angles formed by two intersecting lines are vertical angles.In angle ABC, point B is the vertex.

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Write and equation of a circle that has a diameter that passes through the points (3,0) and (7,6)

Answers

The equation of a circle that has a diameter that passes through the points (3,0) and (7,6) is x² + y² - 10*x  - 6*y +21 =0

Given that, the points (3,0) and (7,6)

(x1, y1) = (3,0) and (x2, y2) = (7,6)

We know that the formula for the equation of circle whose points of diameter are given is equal to :

(x - x1) * (x - x2) + (y - y1) * (y - y2)

So now,

(x - 3) * (x - 7) + (y - 0) * (y - 6) = x² + y² - 10*x  - 6*y +21 =0

so the equation of a circle that has a diameter that passes through the points (3,0) and (7,6) is x² + y² - 10*x  - 6*y +21 =0

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The total weight of a giraffe and her calf is 904 kilograms. How much does the calf weigh? Use a tape
diagram to model your thinking.

Answers

The Calf weigh about 75 kg.

How is weight calculated ?The force of gravity acting on an item is known as its weight, and it can be determined using the formula w = mg, which equals the mass times the acceleration of gravity. The newton is the SI unit for weight since it is a force.The gravitational force that pulls a body toward the earth or another celestial body; it is equal to the mass times the acceleration due to local gravity.We treat our weight as mass and use the unit kg to measure weight by presuming that the gravitational field is the same everywhere.The fundamental mass unit in the metric system is the kilogramme (kg). The mass of 1,000 cubic centimeters of water is extremely close to (and was originally meant to be exactly) one kilogram. The actual weight of a pound is 0.45359237 kg.

Given data :

The total weight of a giraffe and her calf is 904 kilograms.

Weight of the giraffe is 829 kg

So the weight of the calf = Total weight - weight of giraffe

                                         =  904 - 829 = 75

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Chau sells beaded necklaces.Each large necklace sells for $6.30 and each small necklace sells for $4.80.How much will he earn from selling 4 large necklaces and 5 small necklaces?

Answers

4 times 6.30 is 25.20 and 5 times 4.80 is 24 so 49.20 is the answer

write the equation in slope intercept form and graph using a table

X = 5

Answers

Answer:

y=5x+0

Step-by-step explanation:

wouldn't the equation be something like y=5x+0?  If x=5 then x would be the slope. So then if the slope is 5 you'd start off your equation y=5x but there might not be a y-int for this equation because the equation only has an x and there is no y.

(Not sure if you understand it, but if it were to me I'd do something like this because there is only one number in the equation, hope this helps in some way....)

Joseph is 3 times as old as his son now, if 10 years ago the sum of their ages was 44 ,how old was Joseph when his son was born ?​

Answers

Answer:

Step-by-step explanation:

j = 3s

(j-10 + s-10) =44

3s-20 + s =44

4s = 64

s = 16

j=3*16

j=48

currently Joseph is 48,  the son is 16,  so

16 years ago,  when the son was born,  Joseph was 32

Answer:

Joseph was 34 years old when his son was born.

A basketball player makes 70 % of her free throws. When fouled, she gets to take 2 free throws. Let X represent the number of free throws made in two tries. The probability distribution for the number of free throws she makes in two attempts is summarized in the following table:Number of free throws made 0 1 2Probability 0.09 0.42 0.49The probability that she makes at least one free throw isa.0.67b.0.91c.0.95d.1.00

Answers

The probability that she makes at least one free throw is b. 0.91. Probability theory is a branch of mathematics that is used to model and analyze random events.

Probability can be used to predict the likelihood of different outcomes in a wide range of situations, from games of chance to scientific experiments to everyday events. Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.

To find the probability that the player makes at least one free throw in two attempts, you can subtract the probability that she misses both free throws from 1. The probability that she misses both free throws is 0.09, so the probability that she makes at least one free throw is:

1 - 0.09 = 0.91.

Therefore, the correct answer is 0.91, or choice (b).

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which fraction is equivalent to -4/8

Answers

Answer:

-2/4

Step-by-step explanation:

The most simplified fraction of -4/8 is -1/2.

tia equally shares 8 cookies among herself and 4 friends which fraction shows how many cookies each person gets?
answers:
8/4
8/5
5/8
4/8

Answers

Answer: The answer is 8/5

Answer:

Each person gets 8/5 part of cookie

determine the area (in units2) of the region between the two curves by integrating over the y-axis. x

Answers

The area of the region between the two curves by integrating over the y-axis, x = y² and x = 9 is 18 square units.

Total Area inclosed between line and Curve:

The area where the "area under the curve" is common to both the straight line and the given curve is called the bounding area. Therefore, the area common to both can be found by subtracting the area under line T from the area under curve C. The x constraint for computing the area under the curve can be found by solving the system of equations for the coordinates of the intersection of the line and the curve.

We have given the curve , x = y² and line x = 9 and bounded region is A in above graph of x = y² and line x = 9.

Now, we determine the intersection points of curve and line,

put x = 9 in curve equation we get,

y² = 9 => y = +-√9

= + 3 or -3

Total area bounded by curve and line, A = integration of curve over y from y = -3 to y= 3

= ₋₃∫³x dy = ₋₃∫³y² dy = ₋₃[ y³/3]³

= [ (3)³/3 - (-3)³/3]

= 9 + 9 = 18

Hence, the required area is 18 square unit.

Complete question:

determine the area (in units2) of the region between the two curves by integrating over the y-axis. x = y² , x = 9

a coin is flipped, and a number cube is rolled. what is the probability of getting heads on the coin and a number less than 3 on the number cube

Answers

The required probability for the given case is obtained as 1/6.

What is probability?

Probability is the measurement of the chance for a random event.

It is the ratio of the favorable outcome to the total possible outcome.

It always lies in the interval [0, 1].

The sample space for the given case can be written as follow,

The total number of sample space elements are,

Possible outcomes for coin × Possible outcomes for cube

= 2 × 6 = 12

Now, the number of favorable outcomes for the given event is as below,

Number of head × Number of numbers less than 3

= 1 × 2 = 2

Now, the probability is given as,

P(Head on coin and less than 3 on cube) = 2/12 = 1/6

Hence, the probability of getting heads on the coin and a number less than 3 on the number cube is given as 1/6.

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