Kate has 10 stickers. One half of them are purple. How many of Kate’s stickers are purple?

Answers

Answer 1

Answer:

5

Step-by-step explanation:

Half of ten is five  so Kate’s has five purple stickers


Related Questions

14
4(x + 6)
+
2(3x – 5) =
A) 4x + 14
B) 10x + 34
C) 10x + 14
D) 10x – 24
E) NOTA

Answers

Answer:

D) 10x - 24

Step-by-step explanation:

Bc I know maths a lot

Answer this .i will make you brainliest

Answer this .i will make you brainliest

Answers

\(\huge{\underline{\underline{\boxed{\sf{\purple{ǫᴜᴇsᴛɪᴏɴ}}}}}}\)

(8) An aeroplane takes off from Dubai located in the +4 time zone at 13:00. It arrives in Manila in Philippines, located in the +8 time zone at 20:00.

(1) Find the time in Manila when the aeroplane departsfrom Dubai.

(ii) Find the time duration of the flight.

(iii) What is the time in Dubai when the aeroplane arrives in Manila?

\(\huge{\underline{\underline{\boxed{\sf{\ref{Answer}}}}}}\)

(i)17.00(ii)3 hours(iii) 16.00

\(\large\huge\green{\sf{♥ Explanation♥}}\)

Dubai located +4 zone, takes off at 13.00,

∴Hence, at standard it is 13.00-4 =99.00 STD talk

off reached at Manila +8 Zone at 20.00

∴Hence at standard & 2000 -8

reached.⇒ 12.00 STD

Hence time of flight was = 3 hours.

(i) Time at Manila, whicle Plane de parts

12-3+8 ⇒9+8 → 17.00

(ii) duration = 3 hours.

(iii) in dubai 13.00 + 3 = 16,00

_____________________

Ans

i)17.0.0 (ii) 3 hours (iii) 16.00

________________________

♕ hence we done:) xD

When calculating a chi square, the _____ frequencies are based on the information from our sample data.

Answers

When calculating a chi-square, the observed frequencies are based on the information from our sample data.

When calculating a chi-square, the observed frequencies are based on the information from our sample data. The observed frequency (f_obs) is the frequency that a certain event or category actually appears in our data.

We use observed frequencies to test if there is any significant difference between the observed and expected frequencies.

Chi-square is a test used to examine the association between two variables. It compares the observed frequencies to the expected frequencies to test the null hypothesis that there is no association between the variables.

The formula for calculating chi-square is:χ2=Σ(f_obs−f_exp)2f_exp , where χ2 is the chi-square statistic, f_obs is the observed frequency, f_exp is the expected frequency, and Σ is the sum of all categories or events.

The chi-square test is used in many fields, including biology, psychology, sociology, and marketing. The test helps to determine if two categorical variables are independent or not.

The chi-square test can also be used to compare observed frequencies to expected frequencies in a contingency table. It can be used to determine if there is a significant difference between the expected and observed frequencies.

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I have no idea what the problem was with

I have no idea what the problem was with

Answers

Answer:

,,,,,,,,,,,,,,,,,,,,

I have no idea what the problem was with

Answer:

120in

Step-by-step explanation:

Okay, this is going to be a long one so hang onto your hats let's go

So, we first have to find the length that each of the frogs jumped so:

We're going to start with froggy #1, the 2-inch frog:

2 x 20 = 40

So froggy #1 can jump up to 40 inches so we're going to assume that each time our froggies jump, they jump to their full extent:

40 x 3 = 120

So froggy #1 jumped 120 inches

Now, we do the same with froggy #2, the 4-inch frog:

4 x 20 = 80

80 x 3 = 240

So froggy #2 jumped 240 inches

Now, we have to figure out how far ahead froggy #2 is from froggy #1:

240 - 120 = 120

So, the two froggies will end up 120 inches apart

hope this helps:)

Food Fair Fundraiser Food Samples Tasted 3 4 7 10 Money Spent ($) 7.50 10.00 17.50 25.00​

Answers

According to the solution we have come to find that, With the help of given ratios, the amount of money spent for 5 food samples would be $12.50.

What is ratio?

A ratio is a comparison of two quantities that expresses how many times one quantity is contained in the other.

From the given data, we can observe that there is a relationship between the number of food samples tasted and the amount of money spent. To find this relationship, we can calculate the ratio of money spent to the number of food samples tasted:

For the first sample, the ratio is 7.50/3 = 2.50.

For the second sample, the ratio is 10.00/4 = 2.50.

For the third sample, the ratio is 17.50/7 = 2.50.

For the fourth sample, the ratio is 25.00/10 = 2.50.

We can see that the ratio is constant at 2.50 for all the samples. This means that the relationship between the number of food samples tasted and the amount of money spent is linear, with a slope of 2.50.

Using this relationship, we can find the amount of money spent for any number of food samples tasted. For example, if someone tasted 5 food samples, we can find the amount of money spent as follows:

money spent = slope * number of food samples tasted + y-intercept

= 2.50 * 5 + 0

= 12.50

Therefore, the amount of money spent for 5 food samples would be $12.50.

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what is the probability of that she draws a green ball a d a tile with 4

Answers

Let:

A = Probability of draw a green ball

B = Probability of draw a numbered 4

P(A) = 4/8 = 1/2

P(B) = 1/5

So:

P(A ∩ B) = P(A) * P(B) = 1/2 * 1/5 =0.1 = 10%

p is inversely proportional to t complete the table of values

Answers

The requried table of values for P inversely proportional to t  has been shown below.

To complete the table of values for P inversely proportional to t, we need to use the formula for inverse proportion:

P = k/t

where k is the constant of proportionality. To find k, we can use any one of the given values of P and t. Let's use the first row of the table where P = 8 and t = 2:

8 = k/2

k = 16

Now we can use this value of k to find the corresponding values of P for the other values of t in the table:

t P

2 8

4 4

6 2.67

8 2

10 1.6

We can see that as t increases, P decreases, which is consistent with the behavior of inverse proportion.

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A group of students went on a field trip. There were 3 boys for every 4 girls inthe group. If there were 20 girls, how many students in all went on the field trip? 10 points

Answers

Answer:

15 boys

Step-by-step explanation:

start by dividing 20 by 4

you get 5

5 times 3 next

now you have 15

Answer:

25 girls and boys

Step-by-step explanation:

There are 3 boys for every 4 girls

To find the rate we must

Divide 20 by 4 then multiply that by 3

20 divided by 4 is 5

5 times 3 is 15

15 boys went on the field trip

20 girls went on the field trip

The total number of students is 25 girls and boys

Solve for X Please show your work.
(x+3)/(x^2-9)=(2x+7)/(x^2+2x-15)

Thank you

Answers

The answer is X=-2, explanation in the picture.

Solve for X Please show your work.(x+3)/(x^2-9)=(2x+7)/(x^2+2x-15)Thank you

(4x^2-6x+1)-(5x^2+8x+6)

Answers

I wasn’t sure if the question was asking for a simplified expression or if it was asking for the x-value, so I solved for both (use whichever one you need.)

To simplify the expression, make sure to distribute the minus sign to the second part (so 5x^2 turns into -5x^2, 8x turns into -8x, and so on.) When you have that new expression, simply combine like terms.

To find X, just use the quadratic formula.

Hope this was helpful & accurate - let me know if you spot any errors or have any questions.
(4x^2-6x+1)-(5x^2+8x+6)

An association of Realtors reports state-by-state median existing home prices for each quarter. Why do you suppose they use the median instead of the mean? What might be the disadvantage of reporting the mean? Choose the correct answer below. A. Home prices probably have a symmetric distribution which makes the median a better representation of the center than the mean. Reporting the mean would give the impression that the "typical" home price is much lower or higher than it actually is B. Home prices are discrete data, and the median should always be reported instead of the mean for discrete data. Reporting the mean would have the disadvantage of being more difficult to interpret c. Home prices are probably skewed to the left and not symmetric. This means the median a better representation of the center than the mean which would be influenced by the extremely low priced homes. Reporting the mean would give the impression that the "typical" home price is lower than it is D. Home prices are probably skewed to the right and not symmetric This makes the median a better representation of the center than the mean which would be influenced by the extremely high priced homes Reporting the mean would give the impression that the "typical" home price is higher than it is.

Answers

Home prices are probably skewed to the right and not symmetric. So the correct option would be A.

This makes the median a better representation of the center than the mean which would be influenced by the extremely high-priced homes.

Reporting the mean would give the impression that the​ "typical" home price is higher than it is.

they substitute the median for the mean. The median is unaffected by severe outliers or asymmetric score distributions because it only takes one or two values. In contrast, skewed distributions might have different mean and mode values.

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Enter values to write the function that matches the graph shown.

Enter values to write the function that matches the graph shown.

Answers

Answer:

\(k(x) = (x + 1) (4x + 16)\\\)

Step-by-step explanation:

The equation of a parabola given roots \(x_1\) and \(x_2\) is
\(y = a( x - x_1)(x - x_2)\)

where a is a constant

The x-intercepts of a parabola will be the roots of the quadratic equation to the parabola since k(x) = 0 at these points

The x-intercepts are (-1, 0) and (-4, 0)

Therefore the equation of the parabola is of the form
\(k(x) = a ( x - (-1) ) ( x - (-4) )\)

\(= a( x+ 1) (x + 4)\)

To find a, find a point (x, y) through which the parabola passes and plug this value into the above equation to solve for a

We see that the parabola passes through (-5, 16) and (0, 16). The latter point is also the y-intercept of the parabola

This means k(x) = 16 at x = 0

Plugging (0, 16) into the equation gives

\(k(x) = a(x + 1) ( x + 4)\)

\(a(x + 1) ( x+ 4) = k(x)\)

\(a(0 + 1) (0 + 4) = 16\)

\(a \cdot 1 \cdot 4 = 16\)

\(4a = 16\)

\(a = 16/4 = 4\)

Equation of the parabola is

\(k(x) = 4 (x + 1) (x + 4)\)


which can be rewritten as

does anyone know the answer to this question? i’ve been stuck on it for a bit now.

does anyone know the answer to this question? ive been stuck on it for a bit now.

Answers

Random quick vid
Ex: N/A<
does anyone know the answer to this question? ive been stuck on it for a bit now.

Triangle ABC is a right triangle. Point D is the midpoint of side AB and point E is the midpoint of side AC. The measure of angle ADD is 36°.?The proof, with a missing reason, proves that the measure of angle ECV is 54°. Which theorem can be used to fill in the missing reason?

Triangle ABC is a right triangle. Point D is the midpoint of side AB and point E is the midpoint of side

Answers

Answer: D is the correct answer

Step-by-step explanation:

Just took the test

A bakery's production is modeled by function f(x), where f(x) is the number of donuts made in a day and x is the number of bags of flour needed. Choose the ordered pair that represents a possible domain and range of the function.

(−1, 15)
(5, 92.75)
(10, 100)
(−5, 110.5)

Answers

it can't be A or D because they have negatives. you can't have negative donuts. you can't have 92.75 donuts therefore it's C

Question 2 of 30
Which among the following is the correct range of value for the included angle of a V-belt?
O 10° to 200°
O 30° to 40°
O 70° to 80°
O 100° to 1200°

Answers

The correct range of value for the included angle of a V-belt is 30° to 40°. The V-belt provides power to the drive pulley. In the mechanical power transmission, V-belts are used in a large number of industrial and farm applications.

The V-belt is used for a smooth transition of power, and it is made from rubber and polymer materials with cords in the inside. It is commonly used in industrial machines, and it is easy to install and maintain. It is also used in power transmission with a high level of flexibility.

The correct range of value for the included angle of a V-belt is 30° to 40°.This angle is produced by joining the planes of the faces of the belt in the V section. It is the angle between the V-belt sides. The recommended value for the included angle of the V-belt is 36.5 degrees.

When the value is within this range, the V-belt functions optimally. A low included angle would result in a loose belt, whereas a high angle would result in a tight belt. In power transmission, V-belts are commonly used in a wide range of industrial and farm applications. The V-belt is used to provide power to the drive pulley. It is an essential mechanical component that ensures a smooth transition of power.

It is made of rubber and polymer materials, which make it durable and flexible. The V-belt's flexibility allows it to transmit power between pulleys located at different angles.The included angle is the angle between the sides of the V-belt. This angle is produced by joining the planes of the faces of the belt in the V section. The range of value for the included angle of a V-belt is 30° to 40°. The recommended value for the included angle of the V-belt is 36.5 degrees. When the included angle value is within this range, the V-belt functions optimally.

A low included angle would result in a loose belt, whereas a high angle would result in a tight belt.The V-belt's flexibility allows it to transmit power between pulleys located at different angles. The V-belt's grip on the pulley is an essential factor that affects the transmission of power. A low included angle would reduce the grip of the belt, resulting in slippage and reduced power transmission. In contrast, a high included angle would increase the grip of the belt, resulting in a higher level of power transmission.

The correct value of the included angle is critical to the V-belt's performance and longevity.

The correct range of value for the included angle of a V-belt is 30° to 40°. The recommended value for the included angle of the V-belt is 36.5 degrees. When the included angle value is within this range, the V-belt functions optimally. A low included angle would result in a loose belt, whereas a high angle would result in a tight belt. The V-belt's flexibility allows it to transmit power between pulleys located at different angles. The V-belt's grip on the pulley is an essential factor that affects the transmission of power.

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HELP WILL MARK BRAINLIST AND 5 STARS

HELP WILL MARK BRAINLIST AND 5 STARS

Answers

Answer:

10 ft

Step-by-step explanation:

5 1/6 + 4 5/6 = 10

5 + 4 = 9

1/6 + 5/6 = 6/6 = 1

9 + 1 = 10

Answer:

10 feet

Step-by-step explanation:

We are trying to find Madison's height plus Jade's height...

Turn the fractions into improper fractions

So,

5 1/6 = 31/6

4 5/6 = 29/6

31/6 + 29/6 = 10 feet

or

5+4= 10 and 1/6+5/6 = 1

so the answer is 10 feet

PLEASE RATE!! I hope this helps!!!

If you have any questions comment below

Determine the slope of a line that passes through the following points.
(3,4), (5,7)

Determine the slope of a line that passes through the following points.(3,4), (5,7)

Answers

3.4 bc t itciyc txutxutxytxutciyxitxutcutcutcutx tx txt it

Answer:

6/4 and can be simplified as 3/2

Step-by-step explanation:

what makes the value n of the equation true -2n+1.8=3.2A.-3.4B.-0.7C. 0.7D.-2.5

Answers

the initial expression is:

\(undefined\)

Please help! Thx so much!

Please help! Thx so much!
Please help! Thx so much!
Please help! Thx so much!

Answers

Answer:

A) 143

B) 13.79

C) 14

Step-by-step explanation:

Frances can complete 91 oil changes in 7 days.

In 1 day, Frances can complete 91/7 = 13 oil changes.

In 11 days, Frances can complete 13 × 11 = 143 oil changes.

At the market, 5 light bulbs cost $9.85.

1 light bulb costs 9.85/5 =  $1.97.

7 light bulbs cost 1.97 × 7 = $13.79.

Henry can read 5.25 pages in 3 hours.

Henry can read 5.25/3 = 1.75 pages in 1 hour.

In 8 hours, Henry can read 1.75 × 8 = 14 pages.

A hospital has a nursing staff of 250 nurses, working four shifts: A (7:00 AM to 1:00 PM); B (1:00 PM to 7:00 PM); C (7:00 PM to 1:00 AM); D (1:00 AM to 7:00 AM)
The number of nurses apportioned to each shift is based on the average number of patients, per shift, given the following table:

Answers

In conclusion, the hospital needs to consider their staffing needs on a shift-by-shift basis, taking into account the number of patients and nurses' preferences.

What is number?

Number  mathematical entity used to represent a quantity or magnitude it can be symbol or a combination of symbol used to denoted a quantity such as 2573 or 8 1 number are used in a variety of context including counting measuring and computing they are also used to denote the size or amount of something such as a number of people in a room or the number of apples in a basket number play an important role in mathematics including algebra geometry and calculus.

Based on the above figures, the hospital would require a staffing of approximately 62 nurses on Shift A, 93 nurses on Shift B, 68 nurses on Shift C, and 27 nurses on Shift D. This would equate to a total of 250 nurses, which is the number of nurses the hospital has on its staff.

The hospital can adjust the staffing needs by taking into account the amount of nurses needed to provide the necessary patient care. If the shift with the highest number of patients (Shift B) requires additional nurses, the hospital could move nurses from the shift with the lowest number of patients (Shift D). This would result in fewer nurses on Shift D, but would allow for more nurses on Shift B.

In order to ensure that nurses are working in a safe and comfortable environment, the hospital should also take into account the nurses' own preferences. If nurses prefer to work certain shifts, the hospital can adjust the staffing levels accordingly. This can help create a better work-life balance for the nurses, which can, in turn, improve their job satisfaction and performance.

In conclusion, the hospital needs to consider their staffing needs on a shift-by-shift basis, taking into account the number of patients and nurses' preferences. This way, they can maintain a safe and comfortable environment for their nursing staff, while also ensuring that they have enough nurses to provide the necessary care to their patient.

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The image below represents a 12 x 16 room with an 8 x 10 piece of linoleum centered in the room. The yellow and blue rectangles extend the length of their respective sides. Where these two rectangles overlap, there is a green rectangle. In the paragraph box, explain why the total colored area is 62 square feet.

The image below represents a 12 x 16 room with an 8 x 10 piece of linoleum centered in the room. The

Answers

The total area of the colored rectangles is 62 square feet

How to explain why the total colored area is 62 square feet?

Given that: the room is  12 x 16 with an 8 x 10 piece of linoleum centered in the room

The shape will be treated as a composite rectangle. Thus, the room can be divided into smaller rectangles as shown in the image attached.

For the Yellow part:

Length(L) = 8 + 2 = 10 feet

width(W) = 3 feet

Area(A) = L × W

A = 10 × 3 = 30 square feet

For the Blue part:

Length(L) = 2 feet

Width(W) = 3 + 10 = 13feet

Area(A) = L × W

A = 13 × 2 = 26 square feet

For the Green part:

Length(L) = 2 feet

width(W) = 3 feet

Area(A) = L × W

A =  2 × 3 = 6 square feet

Total colored area = Area of Yellow +  Area of Blue +  Area of Green

Total colored area = 30 + 26 + 6 = 62 square feet

Therefore, the total colored area is 62 square feet

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The image below represents a 12 x 16 room with an 8 x 10 piece of linoleum centered in the room. The

which set of sides will NOT make a triangle?

12cm, 7cm, 5cm

2cm, 3c, 4cm

11cm, 13cm, 3cm

19cm, 14cm, 7cm

which set of sides will NOT make a triangle?12cm, 7cm, 5cm2cm, 3c, 4cm11cm, 13cm, 3cm19cm, 14cm, 7cm

Answers

12,7&5.
This is because the sum of any 2 sides must be longer than the third side. Here 5+7 = 12 and is not larger than 12.

solve it please, (√9 + √9) ASAP​

Answers

Answer:

6

Step-by-step explanation:

(sqrt(9)+sqrt(9))

3+3

6

Answer:

6 is the answer.

Step-by-step explanation:

(√9 + √9) = ?

→ √9 + √9

→ 3 + 3 = 6

the partition where the bundle branches are located is called the

Answers

The partition where the bundle branches are located is called the interventricular septum. The interventricular septum is a wall of tissue that separates the ventricles of the heart. It plays a crucial role in electrical conduction within the heart.

Within the interventricular septum, there are specialized bundles of cardiac muscle fibers known as the bundle branches. These bundle branches are responsible for transmitting electrical signals from the atrioventricular (AV) node to the ventricles, coordinating the contraction and pumping of blood.

The bundle branches consist of the left bundle branch and the right bundle branch. The left bundle branch further divides into the anterior and posterior fascicles, while the right bundle branch extends towards the right ventricle. These branches distribute electrical impulses to specific regions of the ventricles, ensuring synchronized and efficient contraction.

In summary, the partition where the bundle branches are located is known as the interventricular septum. It serves as a pathway for electrical signals to reach the ventricles, facilitating coordinated contraction and efficient pumping of blood.

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hi, timed text please help! ​

hi, timed text please help!

Answers

i’m literally bad at rounding but uh for the total volume of both shapes added together its 37.68

A cylindrical metal pipe, 1m long, has inner and outer radii of 3. 7cm and 2. 3cm respectively. Use the value 22/7 for pi to find the volume of metal in the pipe?

Answers

Answer:

\(2640 \:cm^3\)

Step-by-step explanation:

The given solid is a hollow cylinder and we are asked to calculate the volume of the solid part

The volume of the solid part is given by
V = π (R² - r²) h

where
R = outer radius

r = inner radius

h = height of the hollow cylinder

Since R² - r² = (R + r)(R - r) we can rewrite the volume equation as
V = π(R + r)(R - r)h    (I am only doing this for easier computation manually)


We are given
R = 3.7cm, r = 2.3cm and h = 1m

Note that height is in meters so convert to cm
1 m = 100 cm
So h = 100 cm

Plugging in known values
\(V = \dfrac{22}{7}(3.7 + 2.3)(3.7-2.3)100\\\\= \dfrac{22} {7}(6.0) (1.4) 100\\\\= 22 \times 6 \times 0.2 \times 100 \quad\quad(1.4/7 = 0.2)\\\\= 2640 \:cm^3\)

Harriet and Maya share £300 in the ratio of 7:5. Wirk out how much money harriet gets

Answers

Answer:

$175

Step-by-step explanation:

you need to specify if harriet got the 7 portion or the 5 portion. I'll answer as if she got the 7 portion.

They split it into 12 portions because the ratio is 7:5 and 7+5=12. So do $300/12=25

Assuming Maya got the 5 portion, do $25 x 5 = $125, so Maya got $125.

Assuming Harriet got the 7 portion, do $25 x 7 = $175, so Harriet got $175.

GIVING 35$ TO WHOEVER DOES THIS!

GIVING 35$ TO WHOEVER DOES THIS!

Answers

Answer:

A = 2(7) + (1/2)(4)(4 + 9) = 14 + 26 = 40 m²

in a particular county of our state, it was revealed that 5% of all automobiles did not pass inspection. of the next ten automobiles entering the inspection station, a. what is the probability that none will pass inspection? b. what is the probability that all will pass inspection? c. what is the probability that exactly two will not pass inspection? d. what is the probability that more than three will not pass inspection? e. what is the probability that fewer than two will not pass inspection?

Answers

According to the question, it was revealed that 5% of all automobiles did not pass inspection. Of the next ten automobiles entering the inspection station

a. The probability that none will pass inspection is

P(x = 0) = \(^{10}C_{0}(0.05)^{0}(0.95)^{10}\)

P(x = 0) = 0.5987

b. The probability that all will pass inspection is

P(x = 10) = \(^{10}C_{0}(0.05)^{10}(0.95)^{0}\)

P(x = 10) = 0.5987

c. The probability that exactly two will not pass inspection is

P(x = 2) = \(^{10}C_{2}(0.05)^{2}(0.95)^{8}\)

P(x = 2) = 0.0746

a. The probability that none will pass inspection is 0.001%.

b. The probability that all will pass inspection is 59.87%.

c. The probability that exactly two will not pass inspection is 0.27%.

d. The probability that more than three will not pass inspection is 0.0102.

e. The probability that fewer than two will not pass inspection is 6.48%.

In statistics, probability is the measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means that the event is impossible, and 1 means that the event is certain.

In a particular county of our state, it was revealed that 5% of all automobiles did not pass inspection. This means that the probability of an automobile not passing inspection is 0.05, and the probability of an automobile passing inspection is 0.95.

To find the probability of none of the ten automobiles passing inspection, we need to multiply the probability of an automobile not passing inspection by itself ten times since the events are independent. Therefore, the probability of none of the ten automobiles passing inspection is 0.05¹⁰, which is approximately 0.00001 or 0.001%.

To find the probability of all ten automobiles passing inspection, we need to multiply the probability of an automobile passing inspection by itself ten times since the events are independent. Therefore, the probability of all ten automobiles passing inspection is 0.95¹⁰, which is approximately 0.5987 or 59.87%.

To find the probability of exactly two of the ten automobiles not passing inspection, we need to use the binomial distribution formula. The formula is P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, p is the probability of success, and (n choose k) is the binomial coefficient. Therefore, the probability of exactly two of the ten automobiles not passing inspection is P(X=2) = (10 choose 2) * 0.05² * 0.95⁸, which is approximately 0.0027 or 0.27%.

The complement rule states that the probability of an event occurring is equal to one minus the probability of the event not occurring. Therefore, the probability of more than three of the ten automobiles not passing inspection is 1 - P(X<=3), where P(X<=3) is the probability of three or fewer automobiles not passing inspection.

To find P(X<=3), we can use the binomial distribution formula with k=0,1,2, and 3. Therefore,

P(X<=3) = P(X=0) + P(X=1) + P(X=2) + P(X=3)

=> (10 choose 0) * 0.05⁰ * 0.95¹⁰ + (10 choose 1) * 0.05¹ * 0.95⁹ + (10 choose 2) * 0.05² * 0.95⁸ + (10 choose 3) * 0.05³ * 0.95⁷, which is approximately 0.9898 or 98.98%.

Therefore, the probability of more than three of the ten automobiles not passing inspection is 1 - 0.9898, which is approximately 0.0102.

To find the probability of fewer than two of the ten automobiles not passing inspection, we need to use the complement rule again. The probability of fewer than two automobiles not passing inspection is the same as the probability of one or zero automobiles not passing inspection.

To find the probability of more than two automobiles not passing inspection, we can use the complement rule again:

=> P(X>2) = 1 - P(X<=2) = 1 - (P(X=0) + P(X=1) + P(X=2)) = 1 - [((10 choose 0) * 0.05⁰ * 0.95¹⁰ + (10 choose 1) * 0.05¹ * 0.95⁹ + (10 choose 2) * 0.05² * 0.95⁸]

which is approximately 0.0648 or 6.48%.

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