f ''(x) = x−2, x > 0, f(1) = 0, f(8) = 0

Answer:

x = - 8, 4

Step-by-step explanation:

x² + 4x - 32 = 0

to factorise , consider the factors of the constant term (- 32) which sum to give the coefficient of the x- term (+ 4)

the factors are + 8 and - 4 , since

+ 8 × - 4 = - 32 and + 8 - 4 = + 4 , then

(x + 8)(x - 4) = 0 ← in factored form

equate each factor to zero and solve for x

x + 8 = 0 ⇒ x = - 8

x - 4 = 0 ⇒ x = 4

zeros are x = - 8 , 4

Answer:

Rylee

Step-by-step explanation:

Carina ran 7.18

and Rylee 7.16

7 4/25

4÷25= 0.16 7+0.16=7.16

The chance of the event B is 0.4 when using the probability for the two independent two event formula.

In the given question, if a and b are independent events with p(a) = 0.65 and p(a ∩ b) = 0.26, then we have to find the value of p(b).

Events classified as independent do not depend on other events for their occurrence.

Event A's likelihood of happening is P(A)=0.65.

The likelihood of the two events A and B intersecting is P(A∩B)=0.26.

Given that the likelihood of the two independent events is:

P(A∩B) = P(A)⋅P(B)

Then the probability of the event B will be,

P(B) = P(A)/P(A∩B)

P(B) = 0.65/0.26

P(B) =0.4

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The observed chi square score rounded to the nearest hundredth is 31.32. So, the option D is correct.

In the given question;

Of the 47 men polled, 25 agreed and 10 were neutral.

Of the 50 women polled 14 agreed and 5 were neutral.

Of the 41 transgendered people polled 18 agreed and 4 were neutral.

Of the 50 non-binary people, 6 agreed and 12 were neutral.

The rest disagreed with such a platform being allowed to exist in our society.

We have to find how many transgendered people would be expected to disagree with such a platform being allowed to exist in our society under the null hypothesis.

We can determine the anticipated frequencies for each cell in the contingency table using the following formula:

Expected Frequencies

                         Agree                       Disagree                        Neutral

Men                    15.5                            31.5                                 10

Women              8.5                              41.5                                 5

Transgender     12.5                             28.5                                4

Non-binary        3.5                               46.5                               12

The formula for Pearson's chi square test to calculate the chi square score:

Χ² = ∑(Observed - Expected)² / Expected

Χ² = [(25 - 15.5)² / 15.5] + [(14 - 8.5)² / 8.5] + [(18 - 12.5)² / 12.5] + [(6 - 3.5)² / 3.5] + [(22 - 31.5)² / 31.5] + [(36 - 41.5)² / 41.5] + [(23 - 28.5)² / 28.5] + [(44 - 46.5)² / 46.5] + [(10 - 10)² / 10] + [(5 - 5)² / 5] + [(4 - 4)² / 4] + [(12 - 12)² / 12]

Χ² = 31.32

Hence, the option D is correct.

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The right question is:

A university student wishes to explore whether GENDER (man, woman, A university student wishes to explore whether GENDER (man, woman, trans, non-binary) is associated with AGREEMENT (agree, disagree, neutral) to the existence of a social media platform that allows almost all forms of non-violent free speech, with minimal content moderation to censure only the most egregious of posts, Of the 47 men polled, 25 agreed and 10 were neutral. Of the 50 women polled 14 agreed and 5 were neutral. Of the 41 transgendered people polled 18 agreed and 4 were neutral, Of the 50 nonbinary people, 6 agreed and 12 were neutral. The rest disagreed with such a platform being allowed to exist in our society. The student wishes to test the hypothesis of independence using Pearson's chi square test. Determine the observed chi square score rounded to the nearest hundredth.

A. 0.25

B. 0.53

C. 0.54

D. 31.32

E. None of the above

The mean, median, mode and the mean of the extra ten rolls are  

 2.96,2.5,1 and 2.9 respectively  

The mean represents the average of the dataset, the median represents the middle value of the data set, and the mode represents the repeated value in the dataset.

Using the given information we construct the following table

Score     frequency           Cumulative Frequency  (frequency*score)

1                 15                          15                                      15

2                10                          25                                     20

3                7                            32                                      21

4                 5                           37                                      20

5                 6                           43                                      30

6                 7                           50                                      42

thus N= 50 (even) The Median is the average of the 25th and 26th observations. The 25th and 26th observations corresponds to the value 3.

The Median is = 2.5

The modal score = 1

Mode = 3×(median) – 2×(mean)

mean = 2.96

The mean score for the 60 roles is 2.95×60 = 148+sum of the extra ten

                                       sum of the extra ten =29

               Thus mean of the extra ten roles is        

                                                                       = 29/10

                                                                       = 2.9

Hence the mean, median, mode and the mean of the extra ten rolls are  

 2.96,2.5,1 and 2.9 respectively

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Answer: 26, 28, 30

Explanation:

Let's define a variable x to represent the least of the three consecutive even integers. This means that the three integers are x, x + 2, and x + 4.

We can write the given information as an equation:

3 * (x + 4) = 2 * x + 38

We can solve for x by moving all the terms with x to one side of the equation and all the other terms to the other side:

3 * (x + 4) - 2 * x = 38

Then we can distribute the 3 and the -2 to get:

3 * x + 12 - 2 * x = 38

And then we can combine like terms on each side of the equation:

x + 12 = 38

Finally, we can subtract 12 from both sides to solve for x:

x = 26

Therefore, the three consecutive even integers are 26, 28, and 30.

We can check our solution by substituting these values back into the original equation and verifying that it holds true:

3 * (26 + 4) = 2 * 26 + 38

3 * 30 = 52 + 38

90 = 90

The equation holds true, so our solution is correct.

To find the amount of red and white that Peter needs to add to the large batch, we can set up the following proportion:

(3/5 qt red) : (1 qt blue) : (2/5 qt white) = (x qt red) : (15 qt blue) : (y qt white)

The proportion states that the ratio of red to blue to white in the test batch is equal to the ratio of red to blue to white in the large batch.

Cross-multiplying and solving for x and y gives us:

(3/5)x = 15y

(2/5)y = 15x

Solving the first equation for y and substituting it into the second equation gives us:

(2/5)y = 15x

(2/5)(15x/3) = 15x

x = 9 qt

Substituting this value for x back into the first equation gives us:

(3/5)x = 15y

(3/5)(9 qt) = 15y

y = 6 qt

Therefore, Peter needs to add 9 qt of red and 6 qt of white to the large batch to make it the same color as the test batch.

Answer:

f.[157]

Step-by-step explanation:

set A consists of odd numbers and choise F also consists of odd numbers

we are not going for choise A because 2and4are even numbers choise E is a repetition

The options D. { } and F. {1, 5, 7} are the proper subsets of set A={1, 3, 5, 7, 9}.

To determine which sets are proper subsets of set A={1, 3, 5, 7, 9}, we need to understand the definition of a proper subset. A proper subset of a set A is a subset that contains fewer elements than A but is not equal to A.

Let's evaluate each option:

A. {1, 2, 3, 4}

This set is not a proper subset of A because it contains the element 2, which is not in A.

B. {9}

This set is not a proper subset of A because it is equal to A. A proper subset should have fewer elements than the original set.

C. {2, 4, 6, 8}

This set is not a proper subset of A because it does not have any elements in common with A.

D. { }

This set is a proper subset of A since it contains no elements, and it is always a subset of any set, including A.

E. {1, 3, 5, 7, 9}

This set is not a proper subset of A because it is equal to A, and we are looking for subsets with fewer elements.

F. {1, 5, 7}

This set is a proper subset of A since it contains fewer elements than A but is not equal to A.

Correct answers:

D. { }

F. {1, 5, 7}

So, options D and F are the proper subsets of set A={1, 3, 5, 7, 9}.

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Option - B : Decision support system is a flexible tool for data analysis, since its reports do not have a fixed format.

  Decision support systems, a subset of business intelligence, are created to help organisations make sensible business decisions based on vast volumes of analysed data. Huge volumes of data are analysed using an interactive information system called a decision support system (DSS) to aid in the direction of business choices. A DSS aids management, operations, and planning levels of an organisation in making better decisions by assessing the importance of uncertainties and the tradeoffs involved in selecting one option over another. A DSS uses a variety of raw data, papers, personal knowledge, and/or business models to aid users in making decisions. A DSS may make use of relational data sources, cubes, data warehouses, electronic health records (EHRs), income projections, sales projections, and other sources.

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Answer:

Let x be the shorter side of the rectangular house. Since the length of the house is two-and-a-half times its width, we can write this as 2.5x. The area of a rectangle is given by the formula length * width, so the area of the rectangular house in terms of x is 2.5x * x = 2.5x^2. This is the expression for the area of the rectangular house in terms of the shorter side x.

Answer:

[tex]2.5x^2[/tex]

Step-by-step explanation:

Let x be the shorter side of the rectangle, which is also its width (w), so:

[tex]w=x[/tex]

Given that the length of the rectangle is two-and-a-half times its width, this means the length (l) can be expressed as:

[tex]l=2.5x[/tex]

The area of a rectangle (A) is the product of its length (l) and width (w):

[tex]A =l \cdot w[/tex]

Substitute the expressions for length and width into the formula for area:

[tex]A=2.5x \cdot x[/tex]

Simplify this expression:

[tex]A=2.5x^2[/tex]

Therefore, the expression for the area of the rectangle in terms of x is:

[tex]\Large\boxed{\boxed{2.5x^2}}[/tex]

Answer:

15997.787145 cm³

Step-by-step explanation:

Answer: 13

Step-by-step explanation: First you have to subtract the remaining amount of people from the total. 162-6=156. Then you have to divide the remaking amount, (people who went on) by the amount of people that can fit in a car to get how many cars are left. 156/12=13.

Answer:

I believe the answer is the first one.

Step-by-step explanation:

The domain of a function is the lowest X value to the highest X value. The range of a function is the lowest Y value to the highest Y value. Since this question is asking about the domain, we can narrow down the answers to either 1, or 2 because 3 and 4 are for the range, with Y in them.

Next, we look at the points. The differences between them is that 1 has greater OR EQUAL and less than OR EQUAL, whereas 2 has just greater or less then. The circles are filled in on the graph, meaning they are closed. this means it could be equal. Since we know the equation must contain equals in it, we can eliminate 2 and 4 because they only have greater and less than signs.

This leaves the only correct answer for the domain of the graph to be 1.

The domain is the interval of x thus {x | −4 ≤ x ≤ 3} will be the domain so option (A) is correct.

A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.

The domain is for the independent variable while the range is for the dependent variable.

As per the given linear function,

The domain is the set of x that the function defines.

Since (-4,9) is a closed circle so -4 will be included and (3,-5) is also a closed circle thus 3 will also be included.

So the interval will be as {x | −4 ≤ x ≤ 3}.

Hence "The domain is the interval of x thus {x | −4 ≤ x ≤ 3} will be the domain".

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Answer:

0.1% of honor roll students

Step-by-step explanation:

to get the total percentage, find the boy's and girl's percentage numbers first.

15% out of 80: 0.05

25% out of 88: 0.04

0.05+0.04=0.09

the total number of honor students increased: 0.09,

round to the nearest tenth: 0.1

and the total number of honor students are: 80+88=168

0.1 is=0.06% out of 168

0.1% of honor roll students increased this year.

The probabilities are 1. 27/50, 2. 3/4, 3. 31/100, 4. 25/46, 5. 25/48

What is probability ?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

A probability is the number of desired outcomes divided by the number of total outcomes.

Item 1:

54 out of 100 people prefer bacon, hence:

P = 54/100

  = 27/50

Item 2:

Out of 100 people, 54 prefer bacon, 21 prefer sausage but pancakes, hence 54 + 21 = 75 desired outcomes, hence:

P = 75/100

  = 3/4

Item 3:

31 out of 100 people prefer bacon and pancakes, hence:

P = 31/100

Item 4:

Out of 46 people that prefer sausage, 25 prefer french toast, hence:

P = 46 / 25

Item 5:

Out of 48 people that prefer french toast, 25 prefer sausage, hence:

P = 48 / 25

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Answer:

C. Paying a cell phone bill

It will cost $225 to pour 25 yd3 of concrete with 3 workers working at a rate of $15 per hour.

To determine the cost to pour 25 yd3 of concrete, you can use the following formula:

cost = (number of workers * worker rate per hour * number of hours)

In this case, the number of workers is 3, the worker rate per hour is $15, and the number of hours can be calculated by dividing the volume of concrete to be poured (25 yd3) by the rate at which the workers can pour concrete (5 yd3 per hour). Therefore, the number of hours it will take to pour 25 yd3 of concrete is 25/5=5 hours.

Plugging these values into the formula gives:

cost = (3 workers * $15/hour * 5 hours) = $<<3155=225>>225

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In calculation, the precise bisector is a line section that separates a point into two equivalent points and parts.

The measure of P Q R is equal to the sum of ∠PQT and ∠TQR if line segment QT is the angular bisector of an angle ∠PQR.

∠PQR is equal to ∠PQT + ∠TQR.

There are three angular bisectors that can be made in a triangle, and all of them meet at the incenter of the triangle because line Q T is the angular bisector of P Q R. As a result, P Q T = T Q R.

BD divides ABC into two angles, ABD and DBC, given that line.

Additionally, given that DBC = 20 x + 16

ABD = 12 x + 24

Therefore, A B C = ABD + DBC (1) and ABD = DBC (2) respectively.

According to the second equation, 12 x + 24 = 20 x + 16 24  16 = 20 x 12 x 8 x = 8 x = 8 8 = 1

As a result, A B D = 12 (1) + 24; A B D = 36;

D B C = 20 (1) + 16; A B C = 36.

As a result of the equation (1), A B C = A B D + D B C;

A B C = 36; A B C = 72.

Therefore, ∠ABC measure 72.

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Full Question = Suppose line BD bisects ∠ABC. If m ∠ABD = 12 x + 24 and m ∠DBC = 20 x + 16, what is m ∠ABC?

The largest area possible is when the length and width of the chicken pen are both 100 feet. In that case, the area of the chicken pen would be 10,000 square feet.

We are given that the farmer has 200 feet of fencing to build a rectangular chicken pen along the side of a barn. We need to find the largest possible area the chicken pen can have.

To do this, we need to find the length and width of the chicken pen such that the total amount of fencing used is 200 feet.

Since the total amount of fencing needed is 200 feet, the length and width of the chicken pen must both be 100 feet. In this case, the area of the chicken pen would be 10,000 square feet.

Therefore, the largest area possible is 10,000 square feet when the length and width of the chicken pen are both 100 feet.

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The commutative property of addition justifies step 1 and the substraction of the property of equality justifies step 3.

What is the Substitution Property of Equality?

The substitution property of equality is applied by replacing a variable with a number or quantity. For example, if we have:

5x + 3 = 18, if x = 3, we can substitute x = 3 into the equation by applying the substitution property of equality as shown below:

5(3) + 3 = 18

15 + 3 = 18

18 = 18.

We have,

0.4x + 5 + 0.2x = 17

Step 1 : 0.4x + 0.2x + 5 = 17

commutative property of addition

Step 2: 0.6x + 5 = 17

Step 3: 0.6x = 12

substraction of property of equality

so, step 1  :  commutative property of addition

Step 3 : substraction of property of equality

Hence, the commutative property of addition justify for step 1 and the substraction of the property of equality justify for step 3.

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In this case, the amount of population of fruit flies doubled in 18 days, meaning the doubling time is 9.5 days.

The doubling time of a population is the amount of time it takes for a population to double in size. In this case, the population of fruit flies started at 182 individuals and grew to 340 in 18 days. To calculate the doubling time, we used the equation (182 x 2^(18/9.5)) = 340, where the 2^(18/9.5) is the exponentiation of the number of days divided by the doubling time. This equation can be rearranged to solve for the doubling time, yielding a result of 9.5 days. This means that the population of fruit flies doubled in size every 9.5 days, which is the doubling time of the population.

182 x 2^(18/9.5) = 340

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Answer: The answer is 6x^2y(9 - 2y)

Step-by-step explanation: I am not completely sure sorry if its wrong

For a function h such that h(4) = -3 and h'(x) = (x² - 2)/ x for all x∈R-{0}, the function has two local minima at x = -2 and x = 2. The local maxima is not determined implying it would be at the critical value x = 0.

A graph has a horizontal tangent at a local minimum or local maximum and the slope is zero at that point. That is at points which has horizontal tangent. h'(x) = 0.

(x² - 2)/ x = 0

Thus x = 2 or x = -2

At the local minimum or local maximum, the slope is zero or tangent is horizontal as the graph change from decreasing to increasing or increasing to decreasing.

h''(x) = 1 + 2/x²

h"(2) = 1 + 2/ 4 > 0

h''(-2) = 1 + 2/ 4 > 0

Therefore at x = 2 and x = -2 we have local minimum.

The graph of h will be concave up between two local minimum. So graph is concave up in the interval -2<x<2.

Let us assume the tangent line is y = mx + c.

m = h'(4) = (4² - 2)/ 4

m = 3.5

we know h(4) = -3, that is

-3 = m×(4) + c

c = -3 - 4×3.5 = -17

Therefore the tangent line is y = 3.5x - 17.

The line tangent to the graph of h at x = 4 lie below the graph of h at x = 4 as x = 2 is a minimum and thus the slope is increasing for x>2.

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Answer:

in Right triangles you can use this formula to find altitude by using two parts which altitude has made on the base

H² = b¹ × b²

So using this formula (which can be proven by triangle similarity) can help us to find x

10² = 4x × x ===>> x =5

The closest allowable distance that a randomly chosen datum falls within the required 2 standard deviations of the mean is 0.95.

The likelihood that a data is within two standard deviations of the mean

By observation, the distribution depicted in the task content above is a normal distribution.

One can tell the difference between the following .

In the case of a standard normal distribution, 68% of the observations (datum) are within one standard deviation of the mean, 95% are within two standard deviations of the mean, and 99.9% are within three standard deviations of the mean.

On this note, when expressed as a percentage; the probability that the randomly selected datum falls with 2 standard deviations is; 95/100 = 0.95.

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Answer:

undefined

Step-by-step explanation:

The slope of a vertical line is undefined since its calculation involves division by zero which is undefined.

Answer: undefined

Answer:2.4

Step-by-step explanation:

The quotient of 3.12 × 10⁸ and 2.6 × 10⁵ is 1.2 × 10².

What is quotient?

A quotient in mathematics is the amount created by dividing two numbers. The term "quotient" is used frequently in mathematics and is sometimes known as the integer portion of a division, a fraction, or a ratio.

Given numbers are 3.12 × 10⁸ and 2.6 × 10⁵.

Now divides 3.12 × 10⁸  by 2.6 × 10⁵:

(3.12 × 10⁸)/(2.6 × 10⁵)

Break the number into two fractions:

= (3.12/2.6) × (10⁸/10⁵)

Applying formula a^m/a^n = a^(m-n):

= (3.12/2.6) × (10⁸⁻⁵)

= 1.2 × 10³

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If Kurt milked 21 goats, then it will take 7/2 hours.

What is arithmetic?

Mathematical arithmetic is the study of the properties of the standard operations on numbers, such as addition, subtraction, multiplication, division, exponentiation, and root extraction.

Here, we have

Given

The proportional relationship between the number of hours milking, x, and the number of goats milked by Kurt, y, can be modeled by the equation y = 6x.

We have to find out if Kurt milked 21 goats, and how many hours did it take.

y = 6x

if Kurt milked 21 goats, then

21 = 6x

x = 21/6

x = 7/2

Hence, if Kurt milked 21 goats, then it will take 7/2 hours.

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The probability of choosing sausage and onion by Rosa's mom from the given 8 different toppings as per given condition is equal to

(1/ ⁸C₂).

As given in the question,

Total number of different toppings = 8

Number of different toppings choose by Rosa's mom randomly = 2

Possibility of choosing sausage and onion (any one) = 1

Total number of outcomes = ⁸C₂

Number of favorable outcomes = 1

Probability of choosing sausage and onion ( exactly ) one topping

= ( Number of favorable outcomes ) / ( Total number of outcomes )

= ( 1/⁸C₂ )

Therefore, the probability when Rosa's mom chooses sausage and onion out of 8 toppings is equal to ( 1/⁸C₂ ).

The above question is incomplete, the complete question is:

A pizza restaurant is offering a special price on pizzas with 2 toppings. They offer the toppings

below:

Pepperoni ,Sausage, Chicken ,  Green pepper , Mushroom ,Pineapple, Ham, Onion

Suppose that Rosa's favorite is sausage and onion, but her mom can't remember that, and she is going to randomly choose 2 different toppings.

What is the probability that Rosa's mom chooses sausage and onion?

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Answer:

1/8c^2

Step-by-step explanation:

Khan Acadmey