Dmitry suspects that his friend is using a weighted die for board games. To test his theory, he wants to see whether the proportion of odd numbers is different from 50%. He rolled the die 40 times and got an odd number 14 times.
Dmitry conducts a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of odds is different from 50%
(a) H0:p=0.5H0:p=0.5; Ha:p≠0.5Ha:p≠0.5, which is a two-tailed test.
(b) Use Excel to test whether the true proportion of odds is different from 50% Identify the test statistic, z, and p-value from the Excel output, rounding to three decimal places.

As proportional relationship, the amount decreasing at a rate milligrams per hour expression P(t) = 500 + e⁻⁰²ˣ

Proportional relationship:

In math, the relationships between two variables where their ratios are equivalent is known as proportional relationship.

Given,

Here we have the rate at which the= drug leaves the bloodstream proportional to the amount of the drug bloodstream: The amount of the drug in the bloodstream can be modeled by K; where constant and- time; hours At time 500 milligrams of the drug was administered. At the moment when the amount of the drug in the bloodstream 50 milligrams, the amount decreasing at a rate milligrams per hour.

Here we need to find the expression.

While we looking into the given question, we have identified the following details,

=> Bloodstream = 500 milligrams

Here they state that the bloodstream 50 milligrams, the amount decreasing at a rate milligrams per hour.

So, the expression for this proportional relationship is written as,

=> P(t) = 500 + e⁻⁰²ˣ

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Answer: 27.5 gallons in a full tank

Step-by-step explanation:

Let's call "x" the entire tank.

After adding 11 gallons, in the end, he has 2/5 tanks full

so the equations would be

11=2/5x

solve for x

x=55/2

x=27.5

27.5 gallons

The integer minus four to vector input integers:

# Python program to count positive and negative numbers in a List
# list of numbers
list1 = [10, -21, 4, -45, 66, -93, 1]
pos_count, neg_count = 0, 0
# iterating each number in list
for num in list1:
  # checking condition
  if num >= 0:
      pos_count += 1
  else:
      neg_count += 1
print("Positive numbers in the list: ", pos_count)
print("Negative numbers in the list: ", neg_count)

What is loop in python?

A for loop is used for iterating over a sequence (that is either a list, a tuple, a dictionary, a set, or a string). This is less like the for keyword in other programming languages, and works more like an iterator method as found in other object-orientated programming languages.
Using a for loop, count both positive and negative numbers from a specified list. Use a for loop to iterate each member in the list, then check to see if the positive number test is true by seeing if num >= 0.
Increase the positive count if the condition is true; else, increase the negative count.

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The equation that can be used to model the total time y for number of chimes is y = 2x.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

From the information, it takes Ernest's grandfather clock 2 seconds to chime.

Therefore, the equation that can be used to model the total time y for number of chimes x will be:

y = 2 × x

y = 2x.

The equation is y = 2x.

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The solution is

a) ∠1 ≅ ∠5 by Corresponding Angles

b) m∠4 + m∠5 = 180° by Co-Interior Angles or same side Interior angles

c) ∠6 ≅ ∠4 by Alternate Interior Angles

d) ∠2 ≅ ∠8 by Alternate Exterior Angles

What are Parallel Lines Cut by Transversal?

Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.

Corresponding angles

When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position

Alternate Interior Angles

Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.

Alternate Exterior Angles

The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.

Consecutive Interior Angles

When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.

Given data ,

From the figure , we can see that

The Corresponding angles are

Angle 1 and Angle 5

Angle 2 and Angle 6

Angle 4 and Angle 8

Angle 3 and Angle 7

The Alternate Interior angles are

Angle 4 and Angle 6

Angle 3 and Angle 5

The Co-Interior angles are

Angle 4 and Angle 5

Angle 3 and Angle 6

The Alternate exterior angles are

Angle 1 and Angle 7

Angle 2 and Angle 8

Hence , the angles from the figure that are true are

a) ∠1 ≅ ∠5 by Corresponding Angles

b) m∠4 + m∠5 = 180° by Co-Interior Angles or same side Interior angles

c) ∠6 ≅ ∠4 by Alternate Interior Angles

d) ∠2 ≅ ∠8 by Alternate Exterior Angles

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Martin served 24 orders, Ahmad served 15, and Ryan served 48 orders.

To find an unknown quantity in a problem we use the algebraic expression. These are combinations of variables and constant terms. Here variables are used to represent the Unknown Numbers.

Here we have

Martina, Ahmad, and Ryan served a total of 87 orders

Since we don't how many orders served each one

Let's assume that each of them with different variables

Martina served 'm' orders

Ahmad served 'a' orders

Ryan served 'r'

Given that

Ahmad served 9 fewer orders than Martina  

=> a = m - 9 ---- (1)

Ryan served 2 times as many orders as Martina.

=> r = 2m --- (1)    

Given that total served orders = 87

=> m + a + r = 87

=> m + m - 9  + 2m = 87        [ from (1) and (2) ]

=> 4m = 87 + 9

=> 4m = 96

=> m = 24

Number of orders served by Ahmad, a = 24 - 9 = 15  

Number of orders served by Ryan, r = 2(24) = 48

Therefore,

Martin served 24 orders, Ahmad served 15, and Ryan served 48 orders.

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Answer:

Rosemary worked 12 hours at the bookstore and 16 hours driving around for pizza delivery.

Step-by-step explanation:

Let x be the number of hours spent working at the bookstore where she makes 8.25 an hour. Her pay from the bookstore is in total, 8.25x.

Likewise, let's let y = the number of hours working at the pizza place. Her total pay there would be 9.25y.

Her all together over all pay would be:

bookstore$ + pizza$

8.25x + 9.25y

= 247

8.25x + 9.25y = 247

here is one equation. It tells us her total pay from both jobs is 247.

Also, her hours totaled 28. So,

x + y = 28

Solve the system of equations:

8.25x + 9.25y = 247

x + y = 28

You could use substitution or elimination. If you are learning matrices or a graphing program you could use that.

Here is the substitution work.

x + y = 28

y = 28 - x

8.25x + 9.25y = 247

substitute. y = 28-x

8.25x+9.25(28-x)=247

use distributive property.

8.25x+259 - 9.25x=247

combine like terms.

259 - x = 247

subtract 247, add x

12 = x

This means that Rosemary worked 12 hours at the bookstore. And since 28 - 12 = 16.

She works 16 hours at the pizza delivery

12 + 16 is 28, the number of hours she worked.

Also, 8.25(12)+9.25(16)

= 99 + 148

= 247

So these number check out.

The Spearman correlation coefficient is used to calculate a significance test, whereas the Pearson correlation coefficient is not.

The Spearman correlation coefficient is a non-parametric measure of correlation that uses ranks rather than raw data to assess the strength of the relationship between two variables. This makes it more robust than the Pearson correlation coefficient, which relies on the assumption that the two variables have a normal distribution. Additionally, Spearman correlation coefficients are used to measure the degree of monotonicity between two variables, while Pearson correlation coefficients are not. Finally, the Spearman correlation coefficient is used to calculate a significance test, whereas the Pearson correlation coefficient is not.

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Answer:

One plus one is equal to two

Step-by-step explanation:

1. Identify the numbers being added: In this case, the numbers being added are "one" and "one."

2. Write the equation using the proper mathematical notation: The equation would be written as "1 + 1."

3. Perform the addition: To solve the equation, you would add the numbers together. In this case, 1 + 1 = 2.

4. Write the final answer: The final answer to the equation "one plus one" is "two."

I hope this helps! Let me know if you have any other questions.

Answer:

9

Step-by-step explanation:

2|-9| - |-2|

=2+9-2 the negative number becomes positve when it come out of absolute value

=11-2

=9

Answer:

Below

Step-by-step explanation:

See image below

The error in computing the area of triangle is 10.75 and the percentage error in computing the area of triangle is 1.194%.

Given that, base of the triangle is 36 cm (a)

Altitude of the triangle is 50 cm (b)

Error in each measurement is 0.25 cm

We know that, area of the triangle (s) = 1/2 * base * altitude

Let us consider base as ' a ' and altitude as ' b '

So, the maximum error of ' s ' can be calculated as

⇒ ds/da * da + ds/db * db

⇒ 1/2* b * da + 1/2 *a * db

⇒ 1/2* 36 * 0.25 + 1/2* 50* 0.25

⇒ 4.5 + 6.25 = 10.75

Now, let us calculate the percentage error in computing the area of the triangle.

dA/A * 100 = [(1/2* b* da + 1/2* a * db)/ 1/2* b *h] * 100

⇒ [(1/2* 36 * 0.25 + 1/2* 50 * 0.25)/ 1/2* 36 * 50] * 100

⇒ [ 21.5/ 1800 ] * 100

⇒ 1.194%

Thus, the error in computing the area of the triangle is 10.75 and the percentage error in computing the area of the triangle is 1.194%.

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the given statement if a is an n x n diagonalizable matrix then each vector in R^n can be written as a linear combination of eigenvectors of a is false.

What is Diagonalizable matrix?

If there is an invertible matrix P and a diagonal matrix D such that

P^-1AP=D, or alternatively A=PDP^-1, then the square matrix A is said to be diagonalizable or non-defective in linear algebra.

If and only if the algebraic multiplicity of each of A's eigenvalues is equal to the geometric multiplicity of each eigenvalue, then A is diagonalizable. The fact that the geometric sum of the eigenvalues of A is n is an equivalent description.

The given statement is false.

If A is diagonalizable, then A had n distinct eigenvalues. It could have repeated eigenvalues as long as the basis of each eigenspace is equal to the multiplicity of that eigenvalue.

Hence, the given statement is false.

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Graph of ​y+6=45(x+3)​ using the point and slope is given.

The slope of a line in mathematics, usually referred to as its gradient, is a numerical representation of the steepness and direction of the line.

Standard form of the slope-intercept form;

y = mx + b,

where m is the slope and b is the y-intercept.

We have the equation,

​y+6=45(x+3)​

Simplifying,

y = 45x + 135 - 6

y = 45x + 129.

Now, comparing the equation to the slop-intercept form;

we get,

m = 45,

and b = 129

And point slope form is the slope-intercept form.

And the graph is given in the image.

Therefore, y = 45x + 129 is the required equation.

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The value of g(t) is 18 when x is 2.

Proportionality is defined as, the fact or quality of being in proper balance or relation as to size or quantity, degree, severity, etc

Given that, g(t) varies inversely with t and g(t)=9 when t=4.

According to question,

g(t) ∝ 1/t

Let k be constant of proportionality, then,

g(t) = k/t

Solving for k, we get,

9 = k/4

k = 36

When, t = 2, then

g(t) = 36/2

g(t) = 18

Hence, The value of g(t) is 18 when x is 2.

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[tex]2^{x}[/tex] + [tex]\frac{2}{3}[/tex],  [tex]2^{x}[/tex], [tex]2^{x}+2[/tex], [tex]2^{x}-3[/tex] are examples of exponential parent function.So all of the given options are true.

Parent function:  The most basic function in a family of functions is the parent function. A family of functions is a collection of functions that have similar graph shapes because they all have the same greatest degree.

Four graphs that illustrate the U-shaped graph, or parabola, are displayed in the graph above. We can classify them as belonging to the same family of functions since they all have the same highest degree of two and the same form.

Exponential parent function: Algebraic expressions appear in the exponent of exponential functions. The formula for its parent function is y = [tex]b^{x}[/tex], where b can be any non-zero constant.

For above definitions we can conclude that all options given to us are exponential parent function.

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Answer:

θ = 2 π n_1 + π/3 for n_1 element Z

or θ = 2 π n_2 + (5 π)/3 for n_2 element Z

or θ = π n_3 for n_3 element Z

θ = π n_3 for θ element Z and cos(θ)!=0 and n_3 element Z

Step-by-step explanation:

Solve for θ:

tan(θ) - 2 sin(θ) = 0

Factor sin(θ) from the left hand side:

sin(θ) (sec(θ) - 2) = 0

Split sin(θ) (sec(θ) - 2) into separate parts with additional assumptions.

Assume cos(θ)!=0 from sec(θ):

sec(θ) - 2 = 0 or sin(θ) = 0 for cos(θ)!=0

Add 2 to both sides:

sec(θ) = 2 or sin(θ) = 0 for cos(θ)!=0

Take the reciprocal of both sides:

cos(θ) = 1/2 or sin(θ) = 0 for cos(θ)!=0

Take the inverse cosine of both sides:

θ = 2 π n_1 + π/3 for n_1 element Z or θ = 2 π n_2 + (5 π)/3 for n_2 element Z

or sin(θ) = 0 for cos(θ)!=0

Take the inverse sine of both sides:

θ = 2 π n_1 + π/3 for n_1 element Z

or θ = 2 π n_2 + (5 π)/3 for n_2 element Z

or θ = π n_3 for cos(θ)!=0 and n_3 element Z

The roots θ = π n_3 never violate cos(θ)!=0, which means this assumption can be omitted:

Answer: θ = 2 π n_1 + π/3 for n_1 element Z

or θ = 2 π n_2 + (5 π)/3 for n_2 element Z

or θ = π n_3 for n_3 element Z

Solve for θ over the integers:

tan(θ) - 2 sin(θ) = 0

Factor sin(θ) from the left-hand side:

sin(θ) (sec(θ) - 2) = 0

Split sin(θ) (sec(θ) - 2) into separate parts with additional assumptions.

Assume cos(θ)!=0 from sec(θ):

sec(θ) - 2 = 0 or sin(θ) = 0 for cos(θ)!=0

Add 2 to both sides:

sec(θ) = 2 or sin(θ) = 0 for cos(θ)!=0

Take the reciprocal of both sides:

cos(θ) = 1/2 or sin(θ) = 0 for cos(θ)!=0

Take the inverse cosine of both sides:

θ = 2 π n_1 + π/3 for θ element Z and n_1 element Z or θ = 2 π n_2 + (5 π)/3 for θ element Z and n_2 element Z

or sin(θ) = 0 for cos(θ)!=0

The roots θ = 2 π n_1 + π/3 violate θ element Z for all n_1 element Z:

θ = 2 π n_2 + (5 π)/3 for θ element Z and n_2 element Z

or sin(θ) = 0 for cos(θ)!=0

The roots θ = 2 π n_2 + (5 π)/3 violate θ element Z for all n_2 element Z:

sin(θ) = 0 for cos(θ)!=0

Take the inverse sine of both sides:

Answer: θ = π n_3 for θ element Z and cos(θ)!=0 and n_3 element Z

The value of e⁻ᴿᵗ is 0.8886 for the given the standard deviation of returns averages 28 percent with the options mature in 5 years and the risk-free rate is 2.36 percent.

So, the correct option is option ( C).

Exponential function is characterized by rapid increase (as in size or extent) and an exponential growth rate.

We have given that,

standard deviation of returns averages = 28%

options mature, t = 5 years and

Risk-free rate , R = 2.36 percent.

we have to calculate the value of e−Rt.

Exp(-Rt) = e⁻⁽²·³⁶⁾⁵

use exp(value) function to find the value :

=exp(-5 × 2.36%)

= exp(- 0.118 )

=0.8886

Hence, the the value of e⁻ᴿᵗ is 0.8886.

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Complete question:

I. M. Greedy has been granted options on 500,000 shares. The stock is currently trading at $48 a share and the options are at the money. The standard deviation of returns averages 28 percent. The options mature in 5 years and the risk-free rate is 2.36 percent. What is the value of e-rt?

a) .7087

b) .8476

c) .8886

d) .6087

e) .7952

The value of (p+q+r+s) / (a+b+c) is 3.66 if the basketball player has probability 0.4 to make a perfect shot.

We know that if probability is given for r distribution and if question is asking distribution for n terms, we need to use binomial probability distribution which is given by [tex]^nC_r[/tex][tex]p^r[/tex][tex]q^r[/tex] where p is defined as the success probability and q is called as failure probability.

We have success probability =0.4

Failure probability(q) = 1-p=1-0.4=0.6

From 9 terms, we need to choose single term having success probability =0.4 and failure probability=0.6

So, this can be given by =[tex]^9C_1[/tex] × (0.4)¹ ×(0.6)⁹⁻¹

which is equivalent to =9 × (0.4) × (0.6)⁸

On comparing with the given equation =([tex]p^a[/tex] × [tex]q^b[/tex]×[tex]r^d[/tex]) / [tex]s^c[/tex] ,we get

p=9,a=1,q=0.4,b=1,r=0.6,d=8,s=1,c=1.

So,value of p+q+r+s = 9+0.4+0.6+1=11

and value of a + b + c = 1+1+1=3

So, value of (p + q + r + s) / (a + b + c)= 11 / 3=3.66

Hence, required value is 3.66

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Answer:

c

Step-by-step explanation:

Therefore by making a line through following points we can make graph which is parabola in shape

Two things are equal, according to an equation. Like this: 9 + 2 = 11 . It will have an equivalent sign "=". According to that equation, "this equals that" is expressed as "what is on the left (9 + 2) is equal to what is on the right (11).

Here,

Given Equation : x² = 8y

Given Equation agrees with conventional equation of parabola on positive y-axis

x² = 4ay

Comparison of the two equations yields,

4a = 8 ⇒ a = 2

Focus of parabola = ( 0 , 2 ) ( 0 , 2 )

Parabola vertex equals ( 0 , 0 )

Axis of Symmetry = y-axis

To sketch its, we find some points

with x = 4 or -4 we get

4² = 8y ⇒ 16 = 8y ⇒ y = 2

So, points are ( 4 , 2 ) and ( -4 , 2 ) ( -4 , 2 )

we obtain when x = 8 or -8.

(-8)² = 8y ⇒ 64 = 8y ⇒ y = 8

So, points are ( 8 , 8 ) and ( -8 , 8 ) ( -8 , 8 )

Therefore by making a line through following points we can make graph which is parabola in shape

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The correct question is :-

Which graph represents the equation x2 = 8y?

By analytic geometry, the resulting expression for the value t in the geometric system formed by two parallel lines is t = b + n.

In this question we find the case of two parallel lines, in which we are asked to derive an equation to replace the value t seen in the figure. By analytic geometry, two lines are parallel when they have the same slope. Slope is defined by the following formula:

m = Δy / Δx

Where:

The slope of each line is described below:

Line j

m = (t - a - n) / (x₂ - x₁)

Line k

m' = (b - a) / (x₂ - x₁)

Then, we eliminate m, m' and (x₂ - x₁) by assumption of parallelism:

t - a - n = b - a

t - n = b

t = b + n

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Yes Rhombuses are special parallelograms is true statement. Yes square is also a special rhombus. True square is a specific type of parallelogram.

What is parallelograms?

A parallelogram is a geometric shape with sides that are parallel to one another in two dimensions. It is a type of polygon with four sides (also known as a quadrilateral) in which each parallel pair of sides is the same length.

A parallelogram has adjacent angles that add up to 180 degrees.

rhombuses is a quadrilateral with all the four sides having equal lengths.

In a rhombus, the opposite sides are parallel and equal. Hence, it is a parallelogram.

So  rhombuses are special parallelograms this statement is true.

A square is a special rhombus Yes that is true

The sides of a square and a rhombus are both the same length. A rhombus only has its opposite angles equal, whereas a square has all of its angles at 90 degrees.

why is a parallelogram not the same type of quadrilateral is a trapezoid?

Since they both have four sides, it is obvious that a trapezoid and a parallelogram are quadrilaterals. There are at least one set of parallel sides in a trapezoid. Two sets of parallel sides make up a parallelogram. Therefore, a trapezoid is not a parallelogram if it has only one pair of parallel sides.

a square is a specific type of parallelogram this statement is true.

A square is a quadrilateral in two dimensions that has four equal sides and four equal angles. It is a unique parallelogram with equal angles and sides.

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Q falls to 251,400 to 201,400 which means a fall of 50,000 which should be counteracted by advertising. If advertising expenditure becomes 30,000 it will raise the Q again to 251,400.

Given that,

One of a travel company's main products, a guided tour to a specific country, was the subject of a demand analysis by a management consulting firm for 26 regional markets. The consultant estimates the following equation using data:

Q=1500−4P+5A+10I+3PY

Q is the quantity of the product that is demanded;

P represents the item's monetary price;

A represents advertising costs in thousands of dollars;

I represents income expressed in dollars;

PY is the cost of a different travel product provided by a rival travel agency.

We have to find

(a) Utilizing the information below, determine the amount demanded for this product:

P = $400

A = $20,000

I = $15,000

PY=$500

Q = 1,500 - 4 × 400 + 5 × 20,000 + 10 × 15,000 + 3 × 500

= 1,500 - 1,600 + 100,000 + 150,000 + 1,500

= 251,400

(b)  In Income falls to 10,000

Q = 1,500 - 4 × 400 + 5 × 20,000 + 10 × 10,000 + 3 × 500

= 1,500 - 1,600 + 100,000 + 100,000 + 1,500

= 201,400

Q falls to 251,400 to 201,400 which means a fall of 50,000 which should be counteracted by advertising. If advertising expenditure becomes 30,000 it will raise the Q again to 251,400.

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The value of x + y +z is 15.

A whole number is what?

a variety of numbers that contains both zero and the natural number.

Fractions and decimals are excluded.

Real numbers that are not divisible by two are referred to be odd numbers.

X, Y, and Z are all full numbers in the equation.

x, y, and z all have values larger than 2.

xyz² = 735

A value for x + y + z must be found.

Assuming x = 3, the preceding statement results in y = 5 and z = 7

These are odd numbers with a difference of 2 and are greater than 2.

They must satisfy the condition that xyz2 = 735.

= 3 * 5 * 7²

= 735

These are the variables' values and as a result,

The sum of x, y, and z equals.

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The solution is 194, rounded to the closest whole number. Thus, x2≈194. In light of this, the weight ranges for raisin bags that require new packaging are less than 157 grams and also more than 194 grams.

A statistic called the standard deviation describes how much variation or dispersion there is in a set of statistics .In contrast to a high standard deviation, which shows that the values are spread out, a low standard deviation suggests that the values tend to be close to the mean of the collection. out over a wider range.

Here,

In this instance, the standard deviation is 11 and the mean is 175. Assume that x1 is the heaviest weight at which the bags fall into the lower 5% and x2 is the lightest weight at which they fall into the upper 4.5%. 5% of the time, and 4.5% of the time, the likelihood is below x1 and above x2. The raisin bags should fall below x1 and above x2 if they need to be repackaged. The points x1 and x2 are illustrated in the image below.

1 x 0.045 x 0.05 = 0.905 is the probability between x1 and x2. Below is a picture of the normal distribution curve for raisins bag weights.

To calculate x1 and x2, locate x1 first. To the left of x1, there is a 0.05 probability. To find x1, use Excel. 1. Start Excel. Toggle a cell that is empty. Press ENTER after typing =NORM.INV(0.05,175,11).

The answer is 157, rounded to the nearest whole number. Thus, x1≈157. To compute x2, use the formula 0.05+0.905=0.955 for the probability to the left of x2. To determine x2, use Excel. Start Excel. Toggle a cell that is empty. Enter the command =NORM.INV(0.955,175,11).

The solution is 194, rounded to the closest whole number. Thus, x2≈194. In light of this, the weight ranges for raisin bags that require new packaging are less than 157 grams and also more than 194 grams.

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Answer:

Below

Step-by-step explanation:

231469.335329 to the nearest thousand.     '1' is the thousand position

the '4' next to it says leave the '1' alone to get

231000      rounded to nearest thousand.

The ASA (angle-side-angle) congruence rule states that two triangles are congruent if two angles and the side between them are equal in both triangles.

The ASA congruence rule is a fundamental rule of geometry that states that two triangles are congruent when two angles and the side between them are equal in both triangles. This rule is especially important when solving geometry problems, as it can help determine the size and shape of a triangle.

The ASA congruence rule is applicable to all triangles, regardless of their size or shape, and can be used to find the missing angles or sides of a triangle. By applying the ASA congruence rule, students can gain a better understanding of the properties of triangles and other geometric shapes.

Learn more about the ASA congruence: https://brainly.com/question/3168048

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