inverse function of f(x)=x-7/x+4

Answers

Answer 1

Final Answer: The inverse of f (x)=7x-4 is f^-1 (x)= (x+4)/7


Related Questions

The base of the right pyramid is a rectangle with an area of 1326 square cm. If the volume of the pyramid is 21,452 cubic cm, find its approximate height.

Answers

The height of the right pyramid is 48.53 cm.

What is the height of the pyramid?

A rectangle pyramid is a 3-dimensional shape that is made up of a rectangular base and 4 triangular faces.

Height = ( 3 x Volume of a pyramid) /( area)

Height = (3 x 21452) / 1326 = 48.53 cm

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find x and the length of each segment
s
13
T
6
U
2x-18
y
4x-29

Answers

Answer:

x = 15, UV = 12, SV = 31

Step-by-step explanation:

13 + 6 + (2x - 18) = 4x - 29

2x + 1 = 4x - 29

2x = 30

x = 15

UV = 2x - 18 = 2*15 - 18 = 30 - 18 = 12

SV = 4x - 29 = 4*15 - 29 = 60 - 29 = 31

Can you guys show me what process you would use for this? I mostly need the process

Answers

The value of the expression for the given values of the variables is 1/9

Evaluating an Expression

From the question, we are to determine the value of the expression for the given values of the variables

The given expression is

[tex](\frac{4x^{3} -2y-2z^{3} }{4y^{2}-16x^{2} }) ^{2}[/tex]

From the given information,

x = 2

y = -5

z = 3

Putting the values of the variables into the expression

[tex](\frac{4(2)^{3} -2(-5)-2(3)^{3} }{4(-5)^{2}-16(2)^{2} }) ^{2}[/tex]

[tex](\frac{4(8) +10-2(27) }{4(25)-16(4) }) ^{2}[/tex]

[tex](\frac{32 +10-54 }{100-64 }) ^{2}[/tex]

[tex](\frac{-12 }{36 }) ^{2}[/tex]

[tex](\frac{-1 }{3 }) ^{2}[/tex]

[tex]= \frac{1}{9}[/tex]

Hence, the value of the expression for the given values of the variables is 1/9

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On Monday, Cinthia studied for 3 1/2 hours. On Tuesday, she studies 2/3 of her study time on Monday. How many hours did Cinthia study on Tuesday?

Answers

Monday = 3 1/2 hour
Tuesday = 3 1/2 hour • 2/3
Tuesday = 7/2 • 2/3 = 14/6
14/6 = 2 2/6 = 2 1/3
Answer = 2 1/3 hours

Answer:

Cinthia studied 2/3 of her time on Tuesday

Andy is preparing the company's income statement. His first line item is the company's service revenue. What will he deduct from this line item to obtain the net income?
Andy needs to subtract _______ from the service revenue.

Fill in the blank

Answers

Andy needs to subtract cost from the service revenue.

What does Andy need to subtract?

Revenue is the total income earned before any deductions are made. Net income is the total revenue less total expenses or cost.

Net income = total revenue - cost

For example, if a company sold 100 loaves of bread for $100 dollars. The cost of making the bread is $50. The revenue is $100 and the net income is $50 (100 - 50).

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The following data show the height, in inches, of 11 different plants in a garden:


9

4

10

9

5

2

22

10

3

3

5



After removing the outlier, what does the mean absolute deviation of this data set represent?
On average, the height of a plant varies 2.8 inches from the mean of 6 inches.
On average, the height of a plant varies 3.2 inches from the mean of 5 inches.
On average, the height of a plant varies 2.8 inches from the mean of 5 inches.
On average, the height of a plant varies 3.2 inches from the mean of 6 inches.

Answers

On average, the height of a plant varies 3.2 inches from the mean of 6 inches.

What does the mean absolute deviation represent?

An outlier is a number that is way smaller or way larger than that of other numbers in a data set. The outlier is 22.

Mean absolute deviation =  (1/n) x ∑ l x - m(x) l

Mean without the outlier : (9 + 4 +  10 + 9 + 5+  2 +  10 + 3 + 3+  5) / 10 = 6

(1/10) x ∑ l (9 - 6) + (4 - 6) +  (10 - 6)  + (9 - 6)  + (5 - 6) +  (2 - 6) +  (10 - 6)  + (3 - 6)  + (3 - 6) + ( 5 - 6) = 3.2

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For f(x) = 4x+1 and g(x)=x²-5, find (f-g)(x).

Answers

Answer: -x² + 4x + 6

Given:

f(x) = 4x + 1

g(x) = x² - 5

Solve:

= (f - g)(x)

= f(x) - g(x)

= 4x + 1 - (x² - 5)

= 4x + 1 - x² + 5

= -x² + 4x + 6

Answer:

(f-g) (x) = 4x+1 - x² + 5 = -x² + 4x + 6

Step-by-step explanation:

Explanation can be given if needed in the comments (ㅅ´ ˘ `)

Find all pairs of prime numbers (a,b) such that a^b✖️b^a+1 is prime

Answers

The pairs of prime numbers (a,b) between 1 and 10 inclusive such that a^b * b^a+1 is prime are

How to determine the pairs of numbers?

The expression that is a prime number is given as:

a^b * b^a + 1

The boundary or range of numbers of a and b is not given.

So, we make use of numbers between 1 and 10

i.e. 1 ≤ a ≤ 10 and 1 ≤ b ≤ 10

Using the above range, we have the following program to determine the pairs of prime numbers (a, b).

for a in range(1,11):

   for b in range(1,11):

       num = (a* *b) * (b* *a) + 1

       flg = False

       if num > 1:

           for i in ra nge(2, num):

               if (num % i) == 0:

                   flg = True

                   break

       if not flg:

           print(str(a)+","+str(b))

The output of the above program is:

(1,1), (1,2), (1,4), (1,6), (1,10), (2,1), (2,2), (2,3), (2,4), (3,2), (4,1), (4,2), (4,4) and (4,6)

The above represent all pairs of prime numbers (a,b) such that a^b * b^a+1 is prime

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en una fiesta hay 16 personas de las cuales el 25% son mujeres, luego llegan mas mujeres a la fiesta, de tal manera que ahora los hombres son el 60% ¿cuantas mujeres llegan a la fiesta?

Answers

Answer:

English (Ingles):
10 Women come to the party.

Spanish (Espanol):

10 Las mujeres vienen a la fiesta.

Step-by-step explanation:

English (Ingles):

We know that there are 16 people there at the start. 25% of those people are women. We can work out by subtracting 100 by 25 that 75% of the p-eople there are men. We need to do 25% of 16 so we can work out how many men and women there are there.

So we find 10% of 16 which is 1.6 then we take off 5% of 1.6 which is 0.08. We then double 1.6 to get 20% which gives us 3.2. We now add on the 5% to make it 25% which gives us 4.

This means 25% of 16 is 4.

This tells us that there are 4 women at the party and 12 men as 16 - 4 = 12.

It now says that more women arrive which makes the percentage for men go down to 60%. We now need to add 5% on to the 25% of women there are which will tell us how many more women there are now and it will let us work out how many women and men there are in total now.

As we can't do this without it giving us 4.8, we know that 25% of people is 4 women which means 50% of people would be 8 women and we make an estimate of how many women have joined which gives us 6 people which means the total amount of women at the party is 10.

Spanish (Espanol):

Sabemos que hay 16 personas allí al principio. El 25% de esas personas son mujeres. Podemos calcular restando 100 por 25 que el 75% de las personas son hombres. Necesitamos hacer el 25% de 16 para poder calcular cuántos hombres y mujeres hay allí.

Así que encontramos el 10 % de 16, que es 1,6, luego quitamos el 5 % de 1,6, que es 0,08. Luego duplicamos 1,6 para obtener el 20%, lo que nos da 3,2. Ahora sumamos el 5% para convertirlo en 25%, lo que nos da 4.

Esto significa que el 25% de 16 es 4.

Esto nos dice que hay 4 mujeres en la fiesta y 12 hombres como 16 - 4 = 12.

Ahora dice que llegan más mujeres lo que hace que el porcentaje de hombres baje al 60%. Ahora necesitamos agregar un 5% al ​​25% de mujeres que hay, lo que nos dirá cuántas mujeres más hay ahora y nos permitirá calcular cuántas mujeres y hombres hay en total ahora.

Como no podemos hacer esto sin que nos dé 4.8, sabemos que el 25% de las personas son 4 mujeres, lo que significa que el 50% de las personas serían 8 mujeres y hacemos una estimación de cuántas mujeres se han unido, lo que nos da 6 personas que significa que la cantidad total de mujeres en la fiesta es 10.

20 x (-5) + 10x (-3) + (-5) × (-6)-(3x5)​

Answers

20 x (-5) + 10x (-3) + (-5) × (-6)-(3x5) = -115

Answer:

The simplified form of the above expressions solution is -115.

Step-by-step explanation:

Hello!20 x (-5) + 10x (-3) + (-5) × (-6)-(3x5).. given expression [tex] - 100 + 10( - 3) + ( - 5)( - 6) - 15 \\ - 100 - 30 + ( - 5)( - 6) - 15 \\ - 100 - 30 + 30 - 15 \\ - 130 + 30 - 15 \\ - 100 - 15 \\ - 115[/tex]

Please answer fast!
Ted practices two types of swimming styles for a total of 50 minutes every day. He practices the breaststroke for 20 minutes longer than he practices the butterfly stroke.

Write a pair of linear equations to show the relationship between the number of minutes Ted practices the butterfly stroke every day (x) and the number of minutes he practices the breaststroke every day (y). (5 points)

Answers

Answer:

x = 15 & y = 35

Step-by-step explanation:

[tex]y = x + 20[/tex]

[tex]x + y = 50 \\ x + (x + 20) = 50 \\ 2x + 20 = 50 \\ 2x = 50 - 20 \\ 2x = 30 \\ x = \frac{30}{2} = 15[/tex]

[tex]y = x + 20 = (15) + 20 = 35[/tex]

90°
Find mZR.
A. 30°
B. 60°
C. 120°
D. 180°
(2x)
to
P
90°
S

Answers

Answer:

120°

Step-by-step explanation:

Angles in a quadrilateral add to 360°, so

90+90+x+2x=360

180+3x=360

3x=180

x=60

So, angle R measures 120°.

the correct would be 120°

find the slope of this line

Answers

Answer:

0

Step-by-step explanation:

On a graph, any line that is horizontal has a slope of zero. Try any points and and plug them into the slope formula equation

(Y2-Y1/X2-X1).

The answer will always be zero.

Construct a 96% confidence interval if a sampling distribution has a mean of 20, a standard deviation of 5, and a size of 100.

Answers

Using the t-distribution, the 96% confidence interval is given as follows:

(18.96, 21.04).

What is a t-distribution confidence interval?

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.

The critical value, using a t-distribution calculator, for a two-tailed 96% confidence interval, with 100 - 1 = 99 df, is t = 2.0812.

The parameters are given as follows:

[tex]\overline{x} = 20, s = 5, n = 100[/tex]

Hence the bounds of the interval are:

[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 20 - 2.0812\frac{5}{\sqrt{100}} = 18.96[/tex]

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 20 + 2.0812\frac{5}{\sqrt{100}} = 21.04[/tex]

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A preimage can never be congruent to Which of the following is the notation for a translation that moves a figure 2 units right and 2 units up?

(x, y) → (2x, 2x)

(x, y) → (x − 2, y − 2)

(x, y) →

(x, y) → (x + 2, y + 2)its image.

Answers

The notation for the translation is (x, y) → (x + 2, y + 2)

How to determine the translation?

The translations are given as:

2 units right2 units up

The above implies that we add 2 to the x coordinate and 2 to the y coordinate.

So, we have:

(x, y) → (x + 2, y + 2)

Hence, the notation for the translation is (x, y) → (x + 2, y + 2)

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Craig decides to purchase a property that has been valued at $475,000. He has $80,000 available as a deposit and will require a mortgage for the remaining amount. The bank offers him a 25 year mortgage at 2% interest. Calculate the total interest he will pay over the life of the loan, assuming he makes monthly payments. Give your answer in dollars to the nearest ten dollars. Do not include commas or the dollar sign in your answer.

THE REAL ANSWER IS $107, 270


First, we note that Craig requires a mortgage on $475,000−$80,000=$395,000. To calculate the monthly repayments we must apply the formula for P0 and solve for d, that is,
P0=d(1−(1+rk)−Nk)(rk).
We have P0=$395,000,r=0.02,k=12,N=25, so substituting in the numbers into the formula gives
$395,000=d(1−(1+0.0212)−25⋅12)(0.0212),
that is,
$395,000=235.9301d⟹d=$1,674.22.
Therefore the total interest payable is
I=$1,674.22×25×12−$395,000=$107,266
which is $107,270 to the nearest $1

Answers

The total interest is $107,270

What is monthly payment formula?

The formula for monthly payment is:

[tex]M = \frac{P(\frac{r}{12})( 1+\frac{r}{12})}{( 1+\frac{r}{12})^n-1}[/tex]

We can find total interest as shown below:

Value of property = $475,000

Money available as a deposit = $80,000

P = 475,000-80,000

= 395000

t = 25 year

r = 2% = 0.02

n = 25*12 = 300

[tex]M = \frac{P(\frac{r}{12})( 1+\frac{r}{12})}{( 1+\frac{r}{12})^n-1}[/tex]

Putting the value of P, t, r, and n in the above formula

[tex]=\frac{395000(\frac{0.02}{12} )(1+\frac{0.02}{12}) }{(1+\frac{0.02}{12})^{300}-1}[/tex]

after solving the above expression

M = $1674.22

Interest = M*n-P

Putting the value of P, n and M

= 1674.22*300-395000

= 502266-395000

= 107,266

Rounding to nearest ten dollar

= $107,270

Hence, the total interest is $107,270.

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Answer:

Step-by-step explanation:


Intelligence test.
If you get it right ,you are a critical thinker.
You were in the garden, there are 34 people in the yard. You killed 30 .How many people are in the garden.

I

Answers

Answer: 5

Step-by-step explanation:

Because there are 35 when you add yourself so u subtract 30 to get 5

There would be 4 people left in the garden.

34 - 30 = 4.

Subtraction of Numbers

Subtraction is a mathematical operation that involves taking away one number from another to find the difference between them. For the question, At first, there were 34 people in the garden and later 30 people were no longer alive in the garden, so the difference between 30 people and 34 people is 4.

Subtraction is the opposite of addition, and it is used to measure the distance between two values on the number line.

Subtraction is represented by minus Sign (-). For example, subtracting 5 from 10 gives you a difference of 5 (10 - 5 = 5).

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A cellular network transmits its signals in a circular pattern. The tower is considered the origin, (0,0), of the signal and there is a house located on the edge of the circle at (2, 4). Which of the following coordinates could represent the location of another house that is also on the edge of the circle?
A.(1.3)
B.(-2,-4)
C.(3,3)
D.(4,4)​

Answers

Answer:

B

Step-by-step explanation:

because at origin they are both positive and when it rotates about 270 both will change to negative

Using traditional methods, it takes 103 hours to receive a basic driving license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique with 60 students and observed that they had a mean of 102 hours. Assume the variance is known to be 9. A level of significance of 0.01 will be used to determine if the technique performs differently than the traditional method. Find the value of the test statistic. Round your answer to 2 decimal places. Enter the value of the test statistic.

Answers

The test statistic based on the probability illustrated is -2.57.

How to calculate the probability?

The basic training is given as 103 hours. The variance is also given as 9.

The test statistic will be:

= (102 - 104/3/✓60)

= -1/(3/7.7)

= -2.57.

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what is the pattern 324,256,196,144

Answers

The pattern of 324, 256, 196, 144 is the square of the even numbers in a descending order starting from 18.

What is a sequence?

A sequence is a set of things next to each other in a set order. It is also referred to as a series.

According to this question, the following sequence is given: 324, 256, 196, 144. A careful observation of these numbers shows that each is the square of even numbers.

18² = 324

16² = 256

14² = 196

12² = 144

Therefore, the pattern of 324, 256, 196, 144 is the square of the even numbers in a descending order starting from 18.

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Question 1 of 10
What is the slope of the line that contains the points (-2, 5) and (6,-3)?
OA. 8
OB. 1
O C. -1
OD. -8

Answers

Answer:

slope is -1

Step-by-step explanation:

Slope of the line is changes in y over changes in x. It can also be referred as rise over run.

We can express mathematically as:

[tex]\displaystyle{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

where m is slope.

Let (-2,5) be [tex]\displaystyle{(x_2,y_2)}[/tex] and (6,-3) be [tex]\displaystyle{(x_1,y_1)}[/tex]. Hence, apply the slope formula:

[tex]\displaystyle{m=\dfrac{5-(-3)}{-2-6}}\\\\\displaystyle{m=\dfrac{5+3}{-8}}\\\\\displaystyle{m=\dfrac{8}{-8}}\\\\\displaystyle{m=-1}[/tex]

Therefore, the slope is -1

in ΔWXY, m∠W = (2x - 12)°, m∠X = (2x +17)°, and m∠Y = (9x - 7)°. Find m∠X.​

Answers

Answer:

45°

Step-by-step explanation:

Angles in a triangle add to 180 degrees, so

2x - 12 + 2x + 17 + 9x - 7 = 18013x - 2 = 18013x = 182x = 14

So, the measure of angle X is 2(14)+17=45°

solve this equation -1/2 ( -3y + 10)

Answers

Answer:

3/2y-5

Step-by-step explanation:

The person above me’s answer is correct

Points A, B and C make the triangle triangle ABC and are at the coordinates A(- 4, 3) , B(- 48, 17) and C(22, - 53) . Point D is the midpoint of BC and AD is a median of triangle ABC . What is the equation of the median in standard form?

PLEASE HELP ASAP

Answers

The equation of the median in standard form is; 9y - 38x = 179.

What is the equation of the media in standard form?

It follows from the task content that the point D is the midpoint of segment BC; Hence, the coordinates of point D given the coordinates of B and C above are given as; D(-13, -35).

The equation of the median which is the line joining points A and D is therefore determined as follows;

Slope = (-35-3)/(-13-(-4)) = 38/9

38/9 = (y-3)/(x+4)

9y -27 = 38x + 152

9y - 38x = 179.

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Find the axis of symmetry:
Picture is below.

Answers

Answer:

x = -3

Step-by-step explanation:

Axis of symmetry:

Axis of symmetry is the vertical line that divides the parabola into two equal halves and it passes through the vertex of the parabola.

From the graph, Vertex (-3, 4)

Axis of symmetry:  x = -3

Lindsay is checking out books at the library, and she is primarily interested in mysteries and nonfiction. She has narrowed her selections down to six mysteries and nine nonfiction books. If she randomly chooses three books from her selections, what’s the probability that they will all be nonfiction? Enter a fraction or round your answer to 4 decimal places, if necessary.
Please explain in detail

Answers

The probability that all 3 books would be nonfiction is 0.1846.

What is the probability?

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that all 3 books would be nonfiction = (number of non fiction books / total number of books) x (number of non fiction books - 1 / total number of books - 1) x (number of non fiction books - 2 / total number of books - 2)

9 /15 x 8/14 x 7/13 = 0.1846

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4/3*(1/2-6)=(4/3*1/2)-(4/3-6)

Answers

Answer:

The product would be: -22/3 = 16/3, if true or false: false the left side -7.3 does not equal to the right side 5.3 which means the given statement is false, if it is evaluated -22/3 = 16/3, if multiplied it would still be -22/3 = 16/3 (you never said how to solve it so here are ways)

At an Ice cream parlor, ice cream cones cost x dollars each and sundaes cost y dollars each. The total cost of 4 cones and 3 sundaes is more than $20. The total cost of 5 cones and 1 sundae is less than $16. Which system of inequalities models this situation?

Answers

4x+3y “more than” 20
5x+y “less than” 16

This are the two system of inequalities.

Results from a survey conducted in a certain grocery store showed that 3 out of 5 people preferred crispy-flakes cereal to crunchy-flakes cereal. Based on this survey, if a total of 2,500 customers bought one of these two cereals, how many most likely purchased crunchy-flakes cereal?

Answers

The number of people who how many most likely purchased crunchy-flakes cereal is 1000 customers.

How many most likely purchased crunchy-flakes cereal?

Ratio expresses the relationship between two or more numbers. It shows the number of times that one value is contained within other value(s).

The first step is to determine the ratio of people who preferred crunchy-flakes cereal:

Ratio of people who preferred crunchy-flakes cereal : 5 - 3 = 2

Now, multiply the ratio of those who prefer crunchy-flakes cereal by the total number of customers: (2/5) x 2500 = 1000  customers.

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A company is reviewing a batch of 28 products to determine if any are defective. On average,3.2 of products are defective.


What is the probability that the company will find 2 or fewer defective products in this batch?


What is the probability that 4 or more defective products are found in this batch?


If the company finds 5 defective products in this batch, should the company stop production?

Answers

Using the Poisson distribution, it is found that:

There is a 0.3799 = 37.99% probability that the company will find 2 or fewer defective products in this batch.There is a 0.3975 = 39.75% probability that 4 or more defective products are found in this batch.Since [tex]P(X \geq 5) > 0.05[/tex], the company should not stop production it there are 5 defectives in a batch.

What is the Poisson distribution?

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

x is the number of successese = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval.

In this problem, the mean is:

[tex]\mu = 3.2[/tex]

The probability that the company will find 2 or fewer defective products in this batch is:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

In which:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3.2}3.2^{0}}{(0)!} = 0.0408[/tex]

[tex]P(X = 1) = \frac{e^{-3.2}3.2^{1}}{(1)!} = 0.1304[/tex]

[tex]P(X = 2) = \frac{e^{-3.2}3.2^{2}}{(2)!} = 0.2087[/tex]

Then:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0408 + 0.1304 + 0.2087 = 0.3799[/tex]

There is a 0.3799 = 37.99% probability that the company will find 2 or fewer defective products in this batch.

The probability that 4 or more defective products are found in this batch is:

[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]

In which:

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3).

Then:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3.2}3.2^{0}}{(0)!} = 0.0408[/tex]

[tex]P(X = 1) = \frac{e^{-3.2}3.2^{1}}{(1)!} = 0.1304[/tex]

[tex]P(X = 2) = \frac{e^{-3.2}3.2^{2}}{(2)!} = 0.2087[/tex]

[tex]P(X = 3) = \frac{e^{-3.2}3.2^{3}}{(3)!} = 0.2226[/tex]

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0408 + 0.1304 + 0.2087 + 0.2226 = 0.6025

[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.6025 = 0.3975[/tex]

There is a 0.3975 = 39.75% probability that 4 or more defective products are found in this batch.

For 5 or more, the probability is:

[tex]P(X \geq 5) = 1 - P(X < 5)[/tex]

In which:

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4).

Then:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3.2}3.2^{0}}{(0)!} = 0.0408[/tex]

[tex]P(X = 1) = \frac{e^{-3.2}3.2^{1}}{(1)!} = 0.1304[/tex]

[tex]P(X = 2) = \frac{e^{-3.2}3.2^{2}}{(2)!} = 0.2087[/tex]

[tex]P(X = 3) = \frac{e^{-3.2}3.2^{3}}{(3)!} = 0.2226[/tex]

[tex]P(X = 4) = \frac{e^{-3.2}3.2^{4}}{(4)!} = 0.1781[/tex]

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0408 + 0.1304 + 0.2087 + 0.2226 + 0.1781 = 0.7806

[tex]P(X \geq 5) = 1 - P(X < 5) = 1 - 0.7806 = 0.2194[/tex]

Since [tex]P(X \geq 5) > 0.05[/tex], the company should not stop production it there are 5 defectives in a batch.

More can be learned about the Poisson distribution at https://brainly.com/question/13971530

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