Rewrite 6x2 + 2xy + 9x + 3y in factored form. (2x + 3)(3x + y) (2x + y)(3x + 3) (3x + 2)(3x + y) (3x + y)(2x + 1)

Answer:

fraction form: 1/20

decimal form:0.05

The statements that are always true regarding the given diagram of the triangle are m∠2 + m∠3 = m∠6, m∠3 + m∠4 + m∠5 = 180°, m∠5 + m∠6 = 180°. Therefore, options (4) and (5) are not always true.

An exterior angle of a polygon is an angle that forms a linear pair with an interior angle of the polygon. In other words, it is an angle formed by extending one of the sides of the polygon. For any given vertex of the polygon, the exterior angle is the angle between a line containing the side of the polygon next to the vertex and a line that is an extension of the adjacent side. The measure of an exterior angle is equal to the sum of the measures of its corresponding remote interior angles (interior angles that are not adjacent to the exterior angle). The sum of the exterior angles of any polygon, including a triangle, is always equal to 360 degrees. Exterior angles are used in a variety of geometric proofs and constructions.

We know that the sum of all the interior angles of any triangle is 180 degrees. Therefore, we can use this fact to determine which statements are always true regarding the given diagram.

Now, we can use the following relationships between the interior and exterior angles of a triangle:

Exterior angle = Sum of interior angles adjacent to it

Interior angle = 180  - Exterior angle

Using these relationships, we can determine which statements are always true:

m∠5 + m∠3 = m∠4: This is true because the exterior angle at angle 3 is equal to the sum of angles 3 and 4, and the exterior angle at angle 5 is equal to the sum of angles 5 and 6. Therefore, m∠5 + m∠3 + m∠6 = m∠4 + m∠3, which simplifies to m∠5 + m∠3 = m∠4.

Given m∠3 + m∠4 + m∠5 = 180°: This is true because the sum of all the interior angles of a triangle is 180 degrees.

m∠5 + m∠6 = 180°: This is not always true because sum of all the angles should be 180. It is true in this specific case because angle 1 is a straight angle, which means that m∠5 + m∠6 = 180°. However, in general, this statement is not always true.

m∠2 + m∠3 = m∠6: This is true because the exterior angle at angle 2 is equal to the sum of angles 2 and 6. Therefore, m∠2 + m∠3 = m∠6.

Given m∠2 + m∠3 + m∠5 = 180°: This is may not always true. It is true in this specific case because angle 1 is a straight angle, which means that m∠2 + m∠3 + m∠5 = 180°. However, in general, this statement is not always true.

Therefore, the three statements that are always true from the diagram are:

m∠5 + m∠3 = m∠4

m∠3 + m∠4 + m∠5 = 180°

m∠2 + m∠3 = m∠6

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Angle A equals 41.81°

c:

Answer: The actual difference between the numbers is:

87.71 - 5.8 = 81.91

Therefore, Yasmine's estimate was 81, and the actual difference between the numbers is 81.91. Brainliest?

Step-by-step explanation:

To round 87.71 to the nearest whole number, we look at the digit in the ones place, which is 1. Since 1 is less than 5, we round down to 87. To round 5.8 to the nearest whole number, we look at the digit in the ones place, which is 8. Since 8 is greater than or equal to 5, we round up to 6.

Using these rounded values, Yasmine estimated the difference between the numbers to be 87 - 6 = 81.

The actual difference between the numbers is:

87.71 - 5.8 = 81.91

Therefore, Yasmine's estimate was 81, and the actual difference between the numbers is 81.91.

Answer:

Yasmine estimated the difference to be 82. The actual difference is 81.91.

Step-by-step explanation:

The rounded whole number of 87.71 is 88 and the rounded whole number of 5.8 is 6.

So, the difference between the numbers 87.71 and 5.8 by rounding each number to the nearest whole numbers will be

(88 - 6) = 82.

The actual difference between the numbers 87.71 and 5.8 is (87.71 - 5.8) = 81.91.

Therefore, Yasmine estimated the difference to be 82. The actual difference is 81.91.

Therefore, the correct response From these integral is option D   is.  

``` 10 + ∫₅¹  R(t) dt

An integral is a mathematical construct in mathematics that can be used to represent an area or a generalization of an area. It computes volumes, areas, and their generalizations. Computing an integral is the process of integration.

Integration can be used, for instance, to determine the area under a curve connecting two points on a graph. The integral of the rate function R(t) with respect to time t can be used to describe how much water is present in a tank.

The following equation can be used to determine how much water is in the tank at time t = 5 if there are 10 gallons of water in the tank at time t = 1.

``` 10 + ∫₅¹  R(t) dt

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Answer:

Step-by-step explanation:

I think its 42 because 7/20ths of 120 is 42

7/20 x 120 =42

Step-by-step explanation:

6^2 / 6^1   x    6^12 / 6^8   =

6^(2-1)      x    6^(12-8)   =

6^1          x    6^4   =

6^(1+4)  =   6^5     or  = 7776

The type of the relation are

A linear expression is an algebraic expression in which each term has a degree of 1 (or 0), and the variables are raised only to the first power.

In the given expressions:

Therefore, the linear expressions are "5x", "6x + 1", and "17". The nonlinear expressions are "10xy" and "4x^2".

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The equation of p(x) in vertex form is;

p(x) = 9.67(x + 1.04)² - 10.25

The closest answer choice is:

p(x) = 3(x - 1)²  - 2, which is not correct.

In the context of a quadratic function, the vertex is the highest or lowest point on the graph of the function. It is the point where the parabola changes direction. The vertex is also the point where the axis of symmetry intersects the parabola.

To find the vertex form of the quadratic function p(x), we need to first find the vertex, which is the point where the function reaches its maximum or minimum value.

To find the vertex, we can use the formula:

x = -b/2a, where a is the coefficient of the x²  term, b is the coefficient of the x term, and c is the constant term.

Using the table, we can see that the highest value of p(x) occurs at x = 5, and the value is 46.

We can then use the formula to find the vertex:

x = -b/2a = -5/2a

Using the values from the table, we can set up two equations:

46 = a(5)² + b(5) + c

1 = a(0)²  + b(0) + c

Simplifying the second equation, we get:

1 = c

Substituting c = 1 into the first equation and solving for a and b, we get:

46 = 25a + 5b + 1

-20 = 5a + b

Solving for b, we get:

b = -20 - 5a

Substituting b = -20 - 5a into the first equation and solving for a, we get:

46 = 25a + 5(-20 - 5a) + 1

46 = 15a - 99

145 = 15a

a = 9.67

Substituting a = 9.67 and c = 1 into b = -20 - 5a, we get:

b = -20 - 5(9.67) = -71.35

Therefore, the equation of p(x) in vertex form is:

p(x) = 9.67(x - 5)²  + 1

Simplifying, we get:

p(x) = 9.67(x²  - 10x + 25) + 1

p(x) = 9.67x²  - 96.7x + 250.85 + 1

p(x) = 9.67x²  - 96.7x + 251.85

Rounding to the nearest hundredth, we get:

p(x) = 9.67(x - 5²  + 1 = 9.67(x + 1.04)²  - 10.25

Therefore, the answer is:

p(x) = 9.67(x + 1.04)² - 10.25

The closest answer choice is:

p(x) = 3(x - 1)²  - 2, which is not correct.

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The answers to each question are:

(a)  0.351.

(b)  0.317.

(c)  20.24 years.

(d)  16.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

(a) What is the probability that a randomly selected male has growth plates that fuse between the ages of 18 and 20 years?

To answer this question, we need to standardize the values of 18 and 20 using the mean and standard deviation provided. Let X be the age at which growth plates fuse for males. Then,

Z = (X - mean) / standard deviation

Z for X = 18 is (18 - 18.8) / (15.1/12) = -0.53

Z for X = 20 is (20 - 18.8) / (15.1/12) = 0.53

Using a standard normal distribution table or a calculator, we can find the probability of Z being between -0.53 and 0.53, which is approximately 0.351.

Therefore, the probability that a randomly selected male has growth plates that fuse between the ages of 18 and 20 years is 0.351.

(b) What is the probability that a randomly selected male has growth plates that fuse between the ages of 16 and 18 years?

We need to standardize the values of 16 and 18 using the mean and standard deviation provided.

Z for X = 16 is (16 - 18.8) / (15.1/12) = -2.03

Z for X = 18 is (18 - 18.8) / (15.1/12) = -0.53

Using a standard normal distribution table or a calculator, we can find the probability of Z being between -2.03 and -0.53, which is approximately 0.317.

Therefore, the probability that a randomly selected male has growth plates that fuse between the ages of 16 and 18 years is 0.317.

(c) What is the age at which growth plates fuse for the top 5% of males?

We need to find the age X such that the probability of a male having growth plates fuse at an age less than X is 0.95 (since 5% is the complement of 95%).

Using a standard normal distribution table or a calculator, we can find the Z-score corresponding to the 95th percentile, which is approximately 1.645.

Then, we can solve for X using the formula:

Z = (X - mean) / standard deviation

1.645 = (X - 18.8) / (15.1/12)

Simplifying the equation, we get:

X = 18.8 + (1.645)(15.1/12) = 20.24

Therefore, the age at which growth plates fuse for the top 5% of males is approximately 20.24 years.

(d) What percentage of males have growth plates that fuse before the age of 16?

We need to find the probability of a male having growth plates fuse before the age of 16, which is equivalent to finding the probability of Z being less than -2.03 (calculated in part (b)).

Using a standard normal distribution table or a calculator, we can find the probability of Z being less than -2.03, which is approximately 0.0228.

Therefore, approximately 2.28% of males have growth plates that fuse before the age of 16.

hence, the answers to each question are:

(a)  0.351.

(b)  0.317.

(c)  20.24 years.

(d)  16.

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Answer: 46 ft by 92 ft

Step-by-step explanation:

The largest area is enclosed when half the fence is used parallel to the wall and the other half is used for the two ends of the fenced area perpendicular to the wall. Half the fence is 184 ft/2 = 92 ft. Half that is used for each end of the enclosure.

The function has a vertical asymptote at x = 1, x-intercepts are x = 1 and x = 5, hole at x = 5 and horizontal asymptote is y = 0.

A rational function is a function that can be expressed as the ratio of two polynomial functions. In other words, it is a function of the form f(x) = p(x)/q(x), where p(x) and q(x) are polynomial functions and q(x) is not equal to zero for any value of x.

To plot the rational function f(x) = (x² - 6x + 5)/(-x + 1)

Vertical asymptote: The denominator of the function (-x + 1) is equal to zero when x = 1.

Therefore, there is a vertical asymptote at x = 1.

x-intercept: To find the x-intercept, we set the numerator equal to zero and solve for x:

x² - 6x + 5 = 0

This quadratic equation can be factored as:

(x - 5)(x - 1) = 0

Therefore, the x-intercepts are x = 1 and x = 5.

y-intercept: To find the y-intercept, we set x equal to zero:

f(0) = (0² - 6(0) + 5)/(-0 + 1) = 5

Therefore, the y-intercept is (0, 5).

Hole: The function has a hole at x = 5 because both the numerator and the denominator become zero at x = 5.

Horizontal asymptote: To find the horizontal asymptote, we need to compare the degrees of the numerator and the denominator. The degree of the numerator is 2 and the degree of the denominator is 1, so the horizontal asymptote is y = 0.

Now, we can plot the function by choosing some values of x and calculating the corresponding values of y:

x y = f(x)

-1 4

0 5

0.5 3.25

1 undefined

2 -1

Image is attached below.

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The option that is true about the equations for these two lines iis that they represent the same lines.

The trick to questions like this is to get both equations into the slope-intercept form.  That is done for our first equation (y = 3x + 5).  However, for the second, some rearranging must be done:

5y – 25 = 15x; 5y = 15x + 25; y = 3x + 5

Note: Not only do these equations have the same slope (3), they are totally the same; therefore, they represent the same equation.

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Two lines are described by the equations:

y = 3x + 5 and 5y – 25 = 15x

Which of the following is true about the equations for these two lines?They represent perpendicular lines.

None of the other answers

They represent non-perpendicular, intersecting lines.

They represent the same lines.

They represent parallel lines.

The total number of employees is 112.

Explain numbers

Numbers are symbols or representations used to quantify or count objects, quantities, or measurements. They form the basis of mathematical operations, such as addition, subtraction, multiplication, and division, and are used in various fields such as science, finance, and engineering. Numbers can be positive, negative, whole, or fractional, and are essential for communication and calculation in our daily lives.

According to the given information

Let's use x to represent the total number of employees.

According to the problem, the ratio of union members to nonunion members is 4 to 5. This means that out of every 4 + 5 = 9 employee, 4 are union members and 5 are nonunion members.

So, we can set up the following proportion:

4/9 = x/(x - 140)

To solve for x, we can cross-multiply and simplify:

4(x - 140) = 9x

4x - 560 = 9x

560 = 5x

x = 112

Therefore, the total number of employees is 112.

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Based on the information given, we can use the Pythagorean theorem to determine the distance traveled by the northbound car.

Let's denote the distance traveled by the northbound car as 'x' kilometers.

According to the Pythagorean theorem, in a right triangle, the square of the hypotenuse (the straight-line distance between the two cars) is equal to the sum of the squares of the other two sides (the distances traveled by each car).

In this case, the northbound car's distance is 'x' kilometers and the eastbound car's distance is 5 kilometers.

So we have the equation:

x^2 + 5^2 = 13^2

Simplifying, we get:

x^2 + 25 = 169

Subtracting 25 from both sides, we get:

x^2 = 144

Taking the square root of both sides, we get:

x = 12

So the northbound car has traveled 12 kilometers.

Answer: 12 km

Step-by-step explanation:

As seen in the figure the distance that the northbound car traveled equals to the distance from point N to the parking lot.

pythagorean: [tex]\sqrt{13^{2}-5^{2} }=12km[/tex]

The equation of the function g(x) is g(x) = 1/2x²

If we want to stretch or compress the function f(x) = x^2, we can multiply or divide the input variable x by a constant value a.

Specifically, if we use g(x) = f(ax), then g(x) is a stretched or compressed version of f(x).

To find the value of a that will make g(x) pass through the point (2,2), we can substitute these values into the equation g(x) = f(ax):

[tex]g(2)=f(a*2)=f(2a)=(2a)^2 =4a^2 =2[/tex]

So, we have

a = 1/2

Recall that

g(x) = f(ax)

So, we have

g(x) = f(1/2x)

This means that

g(x) = 1/2x²

Hence. the function is g(x) = 1/2x²

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Answer: 76 pages

Step-by-step explanation:

700 photo spaces = 100%

-The total

168 photo spaces = 24%

-The number of empty spaces in the album.

- Find 24% of 700:

70(10%) x 2 = 140

7(1%) x 4 = 28

140 + 28 = 168

532 photo spaces = 76%

- The number of photos in the album

700 - 168 = 532

Finding the number of pages.

-As we know 1 page holds 7 photos, if we had 532 photos we'd have to divide it by 7 to see how many pages all the photos would be held in.

532 ÷ 7 = 76.

Thus, the correct equation for the given parabolic graph is found as: f(b) = (b – 8)² + 4.

A parabola has a lowest point if it opens upward. A parabola has a highest point if it opens downward.

The vertex of the parabola is located at this lowest or highest point.

Vertex form of a quadratic function:

f(x) = a(x – h)² + k, where a, h, and k are constants.

The vertex of the parabola is at because it is translated h horizontal units and k vertical units from the origin (h, k).

(h,k) are the vertex of parabola.

From the given graph:

f(b) is the given function:

Vertex (h,k) = (8, 4)

Thus, h= 8 and k = a = 1, x = b.

Put the values in quadratic function:

f(b) = 1(b – 8)² + 4

f(b) = (b – 8)² + 4

Thus, the correct equation for the given parabolic graph is found as: f(b) = (b – 8)² + 4.

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The value or measure of following are :-

x = 17.18°

∠JK = 143.78°

∠MJ = 116.48°

∠LMK = 47.17°

A segment of a circle called an arc is made up of two endpoints on the circle and the curve that connects them.

Since the two lines JL and MK intersect at the center of the circle at point N, the angles formed by them are inscribed angles of the circle. Moreover, the angles formed by an inscribed angle and its corresponding arc are equal. Therefore, we can write:

∠JNK = ½ arc JNK = ½(5x+23)° = 2.5x + 11.5°

∠KNL = ½ arc KNL = ½(17x-41)° = 8.5x - 20.5°

We are also given that arc MNJ and LNK are similar, so their corresponding angles are equal. Similarly, arc MNL and JNK are similar, so their corresponding angles are equal. Let's use these facts to find x:

∠MNJ = ∠LNK

The arc MNJ is equal to the sum of arcs MNL and LNK. Therefore, we have:

½(5x+23)° + ½(17x-41)° = ∠MNJ + ∠LNK

2.5x + 11.5° + 8.5x - 20.5° = 2∠MNJ

11x - 9° = 2∠MNJ

∠MNL = ∠JNK

The arc MNL is equal to the sum of arcs MNJ and JNK. Therefore, we have:

½(5x+23)° + ½(8.5x-20.5°) = ∠MNL + ∠JNK

2.75x + 1.5° = 2∠JNK

1.375x + 0.75° = ∠JNK

Since ∠MNJ = ∠LNK and ∠MNL = ∠JNK, we can write:

2∠MNJ + 2∠JNK = 360°

Substituting the expressions we found for ∠MNJ and ∠JNK, we get:

22x - 18° = 360°

22x = 378°

x = 17.18° (rounded to two decimal places)

Now that we know x, we can find the values of the other angles of arc-

∠JNK = 1.375x + 0.75° = 24.43°

∠KNL = 8.5x - 20.5° = 119.35°

∠MNJ = (11x - 9°)/2 = 92.05°

∠LNK = ∠MNJ = 92.05°

∠MNL = 360° - ∠MNJ - ∠JNK = 243.52°

∠JK = ∠JNK + ∠KNL = 143.78°

∠MJ = ∠MNJ + ∠JNK = 116.48°

∠LMK = 360° - ∠MNJ - ∠JNK - ∠KNL = 47.17°

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Answer:

A = 50.24 m²

Step-by-step explanation:

A = π r²

d = 8 m

r = d/2

r = 8/2

r = 4 m

A = 3.14 × (4)² m

A = 3.14 × 16 m

A = 50.24 m²

Answer:

50.24 m²

Step-by-step explanation:

Diameter = 8 m

Formula

Radius ( r ) = Diameter/2

r = 8/2

r = 4 m

Formula

Area of circle = π r²

Note

The value of π is 3.14 ( approximately )

Area of circle

= 3.14 × 4²

= 3.14 × 4 × 4

= 3.14 × 16

= 50.24 m²

Hence,

The area of circle is 50.24 m².

63% of people Surveyed shop at a local grocery store.

A number can be expressed as a fraction of 100 using a percentage. The word "%" stands for percentage.

For instance, 50% represents 50 out of 100, or 0.5 in decimal form. Frequently, proportions, rates, and changes in quantity are represented as percentages.

In many aspects of daily life, including the calculation of sales tax, loan interest rates, and price discounts, percentages are frequently utilised. They are also employed in many academic disciplines, including math, physics, economics, and statistics.

The equality of two ratios is referred to as a percentage in mathematics. A ratio is a comparison of two amounts or values;

it is frequently stated as a fraction.

For instance, "3/5" can be used to represent the proportion of boys to girls in a classroom.

An assertion of equality between two ratios is a proportion.

For instance, the ratio of males to girls is the same as the ratio of boys to all pupils,

hence the sentence "3/5 = 6/10" is a proportion.

Analysis: -

people surveyed at store = 45

total no. of people = 72

the

Percent of peopla = 45/72  x100

= 0.625 × 100

= 62.5 %

= 63 %

63% of people Surveyed shop at a local grocery store.

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Answer:

21.8 - 0.1 = 21.7

21.7 is 0.1 less than 21.8

Answer:

The answer is 21.7

Step explanation

21.8 - 0.1 = 21.7

I hope it helped you.

Please Mark me brainliest

Answer: 104%

Step-by-step explanation: 26% times 4 years

Step-by-step explanation:

the answer is 115 remainder 1

The probability that a person who tests positive actually has the disease is ≈0.0158.

        Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty. 1 is the probability of every event in a sample space.

    For instance, when we flip a coin, there are just two possible results: Head OR Tail. (H, T). However, if two coins are tossed, there are four possible results: (H, H), (H, T), (T, H), and (T, T).

we solve the given question using BAYE's theorem:

Bayes' Theorem states that the conditional probability of an event, based on the occurrence of another event, is equal to the likelihood of the second event given the first event multiplied by the probability of the first event.

P(disease/positive)= [tex]\frac{P(disease)P(positive/disease)}{P(disease)P(positive/disease)+P(no disease)P(positive/disease)}[/tex]

P(disease/positive)= [tex]\frac{(0.008)(0.04)}{(0.008)(0.04)+(0.992)(0.02)}[/tex]  ≈ 0.0158

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Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).

The origin is the location where the two axes meet. On both the x- and y-axes, the origin is at 0. The coordinate plane is divided into four portions by the intersection of the x- and y-axes. The term "quadrant" refers to these four divisions.

We can use the slope formula to get the slopes of the lines f(x) and g(x):

slope of f(x) = (change in y)/(change in x) = (1 - (-2))/(1 - 0) = 3/1 = 3

slope of g(x) = (change in y)/(change in x) = (2 - 0)/(0 - (-4)) = 2/4 = 1/2

The slope of g(x) is 1/2, which is less than the slope of f(x), which is 3.

Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).

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Answer:

B

Step-by-step explanation:

The fraction of Earth that is not made up of ocean = 1/4.

The numbers we are familiar with are whole numbers, such as 1, 2, and so on.

Numbers expressed as fractions have a numerator and a denominator, separated by a line known as a vinculum.

In essence, a fraction explains how a portion of a group interacts with the entire group.

Given that-

The fraction of Earth that is not made up of ocean = 1 - fraction of Earth made up of water

The fraction of Earth that is not made up of ocean = 1 - 3/4

The fraction of Earth that is not made up of ocean = (4 - 3)/4

The fraction of Earth that is not made up of ocean = 1/4

Thus, the fraction of Earth that is not made up of ocean = 1/4.

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Complete question:

Approximately 3/4 of the Earth's surface is made up of the oceans. What fraction of the surface is not made up of oceans?​

It is estimated that 0.861 percent of the population is faulty. The sample proportion's standard error is 0.022. A 98% confidence level has an upper bound of 0.910 and a lower bound of 0.812.

The comparative relationship between two or more things in terms of their size, amount, or number is referred to as a "proportion." Either a ratio or a fraction can be used to express it. The term "proportion" in statistics refers to the division of the total number of events by the frequency of each event.

The formula p = x/n, where p is the estimated proportion of defectives in the population, x is the number of defectives in the sample, and n is the sample size, can be used to determine the estimated proportion of defectives in the population.

When we substitute values, we obtain:

p = 353/410 = 0.861

As a result, the population's estimated defectiveness rate is 0.861.

The formula SE = √(p(1-p)/n), where SE is the standard error and n is the sample size, can be used to get the standard error of the sample percentage.

When we substitute values, we obtain:

SE is equal to√(0.861(1.0.861)/410) = 0.022.

As a result, the sample proportion's standard error is 0.022.

Using the following formula, the upper and lower bounds for a 98% confidence level can be determined:

Lower bound = z*SE - p

Upper bound = z*SE + p

where z is the z-score for a 98% degree of confidence.

We discover that the z-score corresponding to a 98% confidence level is roughly 2.33 using a z-table or calculator.

When we substitute values, we obtain:

Lower bound is equal to 0.861 - 2.33*0.022, or 0.812.

Upper bound is equal to 0.861 + 2.33 * 0.022 = 0.910.

Consequently, the range of a 98% confidence level is as follows:

Maximum: 0.910

Upper limit: 0.812

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It is estimated that 0.861 percent of the population is faulty. The sample proportion's standard error is 0.022. A 98% confidence level has an upper bound of 0.910 and a lower bound of 0.812.

What is a proportion?

The comparative relationship between two or more things in terms of their size, amount, or number is referred to as a "proportion." Either a ratio or a fraction can be used to express it. The term "proportion" in statistics refers to the division of the total number of events by the frequency of each event.

The formula p = x/n, where p is the estimated proportion of defectives in the population, x is the number of defectives in the sample, and n is the sample size, can be used to determine the estimated proportion of defectives in the population.

When we substitute values, we obtain:

p = 353/410 = 0.861

As a result, the population's estimated defectiveness rate is 0.861.

The formula SE = √(p(1-p)/n), where SE is the standard error and n is the sample size, can be used to get the standard error of the sample percentage.

When we substitute values, we obtain:

SE is equal to[tex]\sqrt{\frac{0.861(1.0.861)}{410)}[/tex]= 0.022.

As a result, the sample proportion's standard error is 0.022.

Using the following formula, the upper and lower bounds for a 98% confidence level can be determined:

Lower bound = z*SE - p

Upper bound = z*SE + p

where z is the z-score for a 98% degree of confidence.

We discover that the z-score corresponding to a 98% confidence level is roughly 2.33 using a z-table or calculator.

When we substitute values, we obtain:

Lower bound is equal to 0.861 - 2.33*0.022, or 0.812.

Upper bound is equal to 0.861 + 2.33 * 0.022 = 0.910.

Consequently, the range of a 98% confidence level is as follows:

Maximum: 0.910

Upper limit: 0.812

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Answer:

k = 10

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ MYZ is an exterior angle of the triangle , then

4k + 5 + 6k + 10 = 115

10k + 15 = 115 ( subtract 15 from both sides )

10k = 100 ( divide both sides by 10 )

k = 10

Answer:

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Exterior angle of a triangle is equal to the sum of remote interior angles.

In the given picture, the exterior angle is 115°, and remote interior angles are (4k + 5)° and (6k + 10)°.

Set up equation and solve for k:

Therefore the value of k is 10.