What is the rate of change of the function y = \frac{5}{4}x+1y=
4
5

x+1?

Answers

Answer 1

Rate of change of y = [tex]\frac{5}{4}x+1[/tex] is 5/4.

What is rate of change?

The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time.

Given that the expression, y = [tex]\frac{5}{4}x+1[/tex].

To find the rate of change,

first we make the equation in standard form.

Slope intercept form ;

(y₂ - y₁) =m (x₂ -x₁) + c

Comparing the expression to the standard form;

Here, x intercepts: ( -4/5 , 0) and y intercepts: (0,1)

Rate of change = (y₂ - y₁) / (x₂ -x₁)

Rate of change = 5/4

Therefore, rate of change of y = [tex]\frac{5}{4}x+1[/tex] is 5/4.

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Related Questions

The heights (in cm) of 17 students are, 106,110,123,125,117,120,112, 115,110,120,115, 102, 115,115,109,115 and 101. Find the mean and median of the above data.
brainiest marked

Answers

Answer:To find the mean of the heights of the 17 students, we need to add up all of the heights and divide the sum by the number of students. The sum of the heights is 1777 cm, and when we divide this by 17, we get a mean height of 104 cm.

To find the median of the heights of the 17 students, we first need to put the heights in order from least to greatest. The heights in order are 101,102,106,109,110,110,112,115,115,115,115,115,117,120,120,123,125. There are 17 students, so the median is the height of the 9th student, which is 115 cm.

Step-by-step explanation:

What’s the answer please help

Answers

Can I see a phot of the entire page

The Washington Wheat Farmers Club is studying the impact of rising grain prices on their members' planting habits. The club members produce an average of 150 million bushels of wheat per year, with a standard deviation of 18 million bushels. The club takes a random sample of 35 years to create a statistical study. Identify each of the following, rounding to the nearest hundredth when necessary:
Provide your answer below: u= million bushels
a= million bushels n= 0 - million bushels
0 = LA million bushels

Answers

Sampling distribution of mean, Sampling distribution of proportion and T-distribution.

How does sampling distribution work?

An example of a sampling distribution is a probability distribution of a statistic that is derived by repeated sampling of a particular population. It describes a variety of potential possibilities for a statistic, such the mean or mode of some variable in a population.

Give an example of sampling distribution.

When you repeat your survey or poll for all potential samples of the population, you get the sampling distribution of a proportion. For instance, you may conduct many polls rather than asking 1000 cat owners which cat food they prefer.

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Answer:

μ = 150

σ = 18

n = 35

μx¯ = 150

σx¯ = 3.04

Step-by-step explanation:

We are given population mean μ=150 and population standard deviation σ=18, and want to find the mean and standard error of the sampling distribution, μx¯ and σx¯ for samples of size n=36.

By the Central Limit Theorem, the means of the two distributions are the same:

μx¯=μ=150

To find the Standard Deviation of the sampling distribution, we divide the population standard deviation by the square root of the sample size:

σx¯=σn−−√=1835−−√≈3.04

help meeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeeeeeee

Answers

Answer:

Step-by-step explanation:

[tex]3^{2} +3[2^{3}(\sqrt{49} -2^{2}) (3^{2} -2^{3}) - 2^{2} ][/tex]

Answers

[tex]\stackrel{\textit{\LARGE P~E~M~D~A~S}}{3^2 + 3[ ~~ 2^3 (\sqrt{49}-2^2)(3^2-2^3) -2^2 ~~ ]}\implies 3^2 + 3[ ~~ 2^3 (\sqrt{49}-4)(9-8) -2^2 ~~ ] \\\\\\ 3^2 + 3[ ~~ 2^3 (7-4)(9-8) -2^2 ~~ ]\implies 3^2 + 3[ ~~ 2^3 (3)(1) -2^2 ~~ ] \\\\\\ 3^2 + 3[ ~~ 8 (3)(1) -4 ~~ ]\implies 3^2 + 3[ ~~ 24 -4 ~~ ]\implies 3^2 + 3[ ~~ 20 ~~ ] \\\\\\ 9+3[20]\implies 9+60\implies \text{\LARGE 69}[/tex]

Estimate the product.
0.99 X 45​

Answers

Answer: 44.55

Step-by-step explanation:

Which set of points includes all of the solutions for y = negative four fifths times x plus two?line going through 0 comma 2 and 5 comma negative 2 a (15, 10), (0, 2), and (−10, 10) b (−10, 10), (−5, 6), (0, 2), (5, −2), (10, −6) c (x, y) for all real numbers d (x, negative four fifths times x plus two) for all real numbers

Answers

The set of points includes all of the solutions is (x, - 4/5 x + 2).

What is the solution of an equation?

An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.

Given equation is

y = - 4/5 x + 2

The value of x can be any real number.

The value of y is - 4/5 x + 2.

The solution of the equation is (x, - 4/5 x + 2).

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Write the equation in standard form.

2y+3=−1/3(x−2)

Answers

The given equation can be written in standard form as x + 6y + 11 = 0.

How to solve a linear equation?

A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.

The given equation is 2y + 3 = −1/3 (x − 2).

It can be written in the standard form of ax + by + c = 0 as follows,

2y + 3 = −1/3 (x − 2)

=> 3(2y + 3) = -1(x − 2)

=> 6y + 9 = 2 - x

=> 6y + x + 9 + 2 = 0

=> x + 6y + 11 = 0

Hence, the standard form of the given equation is x + 6y + 11 = 0.

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Can anyone help me graph this out. its the last question for my homework and im stuck on it

Answers

The required graph of the given function has been shown.

Given that,
To draw the graph of the composite function,

What are functions?

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

here,
Illustrating the function on the graph for the respective domain
f(x) = 0 for x ≤ -1
f(x) = -x -1 for -1 < x ≤ 2
f(x) = -1 for x > 2

Thus, the required graph of the given function has been shown.

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ANSWER QUICK!!
question and answer choices in the picture below

Answers

Answer: B

Step-by-step explanation:

Find the sixth number in this sequence. (a.) The fourth number is equal to 3x10. (b.) The second number is equal to 10+6. (c.) The Third number is halfway between the second and fourth numbers. (d.) The fifth number is 7 more than the fourth number.

Answers

The sixth term of the sequence 9, 16,23,30,37 is 44

What is arithmetic sequence?

An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 2, 4, 6, 8, 10, 12.. . is an arithmetic progression with a common difference of 2.

The nth term of an arithmetic sequence is given as a+(n-1)d. Where d is the common difference and a is the first term.

fourth term = 30

second term = 16

third term = (30+16)/2 = 46/2 = 23

therefore d= 30-23 = 7

a = 16-7 = 9

therefore the sixth term = 9+(6-1)7= 9+5×7 = 9+35= 44.

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A bank put $50 into a savings account when you opened the account. 12 weeks later, you have a total of $275. a. If y is the total amount of money in the savings account and x represents the number of weeks, write an equation in the form of y=mx+b that describes the situation. Be sure to show or explain how you got your answer.

Answers

Answer:

In this problem, we are looking for an equation in the form of y = mx + b that describes the situation where a bank puts $50 into a savings account when it is opened and 12 weeks later, the account has a total of $275.

To find the equation, we need to find the slope (m) and the y-intercept (b). The y-intercept is the point at which the line crosses the y-axis, which in this case is the initial amount of money in the account ($50). The slope is the rate at which the amount of money in the account is changing over time.

To find the slope, we can use the following formula:

slope = (y2 - y1) / (x2 - x1)

In this case, y2 is the total amount of money in the account after 12 weeks ($275), y1 is the initial amount of money in the account ($50), x2 is the number of weeks after the account is opened (12 weeks), and x1 is the number of weeks before the account is opened (0 weeks).

Plugging these values into the formula, we get:

slope = (275 - 50) / (12 - 0) = 225 / 12 = 18.75

Now that we have the slope, we can plug it into the equation y = mx + b, along with the y-intercept (b = 50), to get the final equation:

y = 18.75x + 50

This equation represents the situation described in the problem, where the bank puts $50 into a savings account when it is opened and 12 weeks later, the account has a total of $275.

A car moving at a constant speed passes the timing device at T equals 0 after 8 seconds the car has traveled 840 ft what linear function in the form y equals mx + b represents the distance in feet d, the car has traveled any number of seconds, t, after passing the timing device

Answers

Answer:

Answer

d = 840t + 0

T/F problem 1e. given rosebud lane's cost structure, which reimbursement method is less risky for the hospital? group of answer choices

Answers

The less risky reimbursement method for the hospital is fee for service.

Given,

Rosebud lane's cost structure;-

We have to find the lass risky reimbursement method for the hospital;

Reimbursement method;-

A system of reimbursement that pays for each time a service is rendered. A system of payment that bases compensation on the volume of services delivered rather than the number of lives covered. A fee-for-service reimbursement system that takes service costs into account

Therefore,

The best reimbursement method that suits for the hospital is fee for service which is less risky also.

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What is the AREA of this composite figure?


A. 134 square units

B. 72 square units

C. 234 square units

D. 102 square units

E. 132 square units

Answers

Answer:

102

Step-by-step explanation:

As we know that the area of triangle is 1/2 × base × height so A.TQ

1) finding the triangle area = 1/2 × base × height

= 6 × 5.

= 30

2) finding the area of rectangle = l×b

= 12 × 6

= 72

Now to find total area is 72 + 30 which will be 102

so the answer is = 102

Julie is considering enrolling in two courses: physics and chemistry. There is a 10% chance she will enroll in physics and a 45% chance she will not enroll in physics but enroll in chemistry. Given that her decision of enrolling in a course is independent of enrolling in other courses, find the probability she will not enroll in chemistry? Assume Event A: she enrolls in physics; Event B: she enrolls in chemistry.

Answers

If the decision of enrolling in the course in independent events, the probability of not enroll in chemistry is 0.55

The chances of enroll in physics = 10%

The chances of the not enroll in physics but enroll in chemistry = 45%

The probability is the ratio of the number of favorable outcomes to the total number of outcomes

The probability = Number of favorable outcomes / Total number of outcomes

Given that her decision of enrolling in a course is independent of enrolling in other courses

The probability of not enroll in chemistry = 1 - The probability of enroll in chemistry

Substitute the value in the equation

The probability of not enroll in chemistry = 1 - 0.45

= 0.55

Therefore, the probability of not enroll in chemistry is 0.55

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the speed (or rate) josiah travels to work is inversely proportion to time it takes to get there. if he travels 35 miles per hour it will take him 2.5 hours to get to work.

Answers

Josiah will take 1.5 hours to travel to work at the speed of 55 miles per hour.

As the speed and time are inversely proportional to each other, we can represent it as -

speed(i)/speed(f) = time(f)/time(i), where I represents initial and f represents final. Now, keep the values in formula to find the time (final).

35/55 = time(f)/2.5

Rewriting the equation according to variable time(f).

time(f) = (35×2.5)/55

Performing multiplication on Right Hand Side of the equation

time(f) = 87.5/55

Performing division on Right Hand Side of the equation

time(f) = 1.59 hours

Hence, it will take 1.59 hours.

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The complete question is -

The speed (or rate) Josiah travels to work is inversely proportional to time it

takes to get there. If he travels 35 miles per hour it will take him 2.5 hours to get to work. How long will it take him if he travels 55 miles per hour?

On January 1, Year 1, the Platte Corporation issues a 5-year note payable for $5,000. The interest rate is 5% and the annual payment of $1,156, due each December 31, includes both interest and principal. Which of the following correctly shows the effect of the issuance of the note on Platte's financial statements?

Answers

The correct effect of the note issuance on Platte's financial statements is A. Cash and Notes Payable increased by $5,000 on the balance sheet and an increase in Financing Activity on the Cash Flows Statement.

What is the journal entry to record the issuance?

The journal entry to record the issuance of the 5-year note payable for $5,000 by Platte Corporation on January 1, Year 1 includes:

Debit to Cash

Credit to Notes Payable.

This entry increases the Cash account, an asset that appears on the balance sheet.

It also increases the Notes Payable, a liability on the balance sheet.

On the Cash Flow Statement, the issuance is a financing activity as cash inflow is increased by the amount.

January 1, Year 1:

Note payable = $5,000

Note period = 5 years

Interest rate = 5%

Annual payment = $1,156

Thus, the note issuance does not affect the Income Statement and will not have an effect on the Equity, but Option A is correct.

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Question Completion:

Answer Options are attached.

Find Θ in radians:

(Use \large \pi=3.14 when necessary and round your final answer to the tenths.)






Θ =

Answers

Angle θ in radians is 12/5 or 2.4 radians.

Define Arc Length

Arc length is more accurately described as the length along the perimeter of any circle or curve (arc). The arc length is the measurement of any distance along the curved path that forms the arc. Arc refers to a segment of a curve or the circumference of a circle. Each of them is shaped like a curve. An arc's length is more than the distance in a straight line between its endpoints (a chord).

Given,

radius = 5 cm

length of arc = 12 cm

We know that,

θ = length of arc / radius

Now, plug in the values

θ = 12 / 5 or 2.4 radians

Hence,angle θ in radians is 12/5 or 2.4 radians.

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Answer: 2.4

Step-by-step explanation:

radius = 5 cm

length of arc = 12 cm

θ = length of arc / radius

θ = 12 / 5 or 2.4 radians

2.4 radians

Compare the graph to the graph of f(x) = | x |. Describe the shift of g(x).
g(x) = |x+4| - 2

Answers

g(x) is shifted 4 units left and -8 units down from f(x).

How would you define a graph's shift?Shifts. A shift is similar to a stiff translation in that it does not alter the size or shape of the function's graph. The graph's placement will only change as a result of a shift. A vertical shift maintains the x-coordinate while adding or subtracting a constant from each y-coordinate.In other words, we multiply the y-coordinate of each point on the graph of f by 2 to generate the graph of g. Geometrically, a point is moved 2 units above its former location by adding 2 to its y-coordinate. It is common to refer to "moving the graph up 2 units" when adding 2 to all of the y-coordinates on a graph at once.

when y=f(x)

When y = f (x + a), the function is either shifted to the right by a units (a 0) or to the left by a units (a > 0).

g(x)=(x+4)-2⇒f(x−8)

This causes f (x) to be moved by 8 units to the right.

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with double-digit annual percentage increases in the cost of health insurance, more and more workers are likely to lack health insurance coverage (usa today, january 23, 2004). the following sample data provide a comparison of workers with and without health insurance coverage for small, medium, and large companies. for the purposes of this study, small companies are companies that have fewer than 100 employees. medium companies have 100 to 999 employees, and large companies have 1000 or more employees. sample data are reported for 50 employees of small companies, 75 employees of medium companies, and 100 employees of large companies. health insurance size of company yes no total small 37 13 50 medium 64 11 75 large 88 12 100 Conduct a test of independence to determine whether employee health insurance coverage is independent of the size of the company. Use = .05.
Compute the value of the 2 test statistic (to 2 decimals).
The p value is Selectless than .005between .005 and .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 2
What is your conclusion?
SelectConclude health insurance coverage is not independent of the size of the companyCannot reject the assumption that health insurance coverage and size of the company are independentItem 3
The USA Today article indicated employees of small companies are more likely to lack health insurance coverage. Calculate the percentages of employees without health insurance based on company size (to the nearest whole number).
Small %
Medium %
Large %
Based on the percentages calculated above, what can you conclude?
SelectLarge companies have a higher percentage of no coverage than medium and small companiesMedium companies have a higher percentage of no coverage than large and small companiesSmall companies have a higher percentage of no coverage than large and medium companiesSmall, medium, and large companies all have roughly the same percentage of no coverage

Answers

The value of the test statistics is , χ² = 15.3902

The value of P is less than 0.005 and the conclusion which we can draw from this is that  the health insurance coverage is depending on the size of the business in point a.

The percentages of employees without health insurance based on company size for small , medium and large companies is ,

Small%= 33/50= 0.66Medium%=68/75 =0.91Large%= 88/100= 0.88

We established our null hypothesis and alternate hypothesis as

H0: The availability of health insurance for employees is unrelated to the size of the business

H1 :The availability of employee health insurance is depending on the size of the business.

2) The alpha level for significance is set at 0.05.

3) The H0 test statistic is

O is the measured frequency, and E is the anticipated frequency, so that 2 = (O - E)2/E

This has a chi-square distribution that is around (3-1) (2-1)= 2 d.f.

We reject the null hypothesis that employee health insurance coverage is NOT independent of the size of the company because the calculated 2 = 15.3902 falls in the critical area 2 5.99.

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et p be prime. determine the number of polynomials of the form x2 ax b which are [15 pts] irreducible over zp.

Answers

We observe that there are p² polynomials of the form x² + ax + b in Zp.

Since there are p choices for each of a and b.

Now a polynomial which is reducible over Zp may be rewritten in the form

(x - c)(x - d)

where c and d are roots.  

So there are p choices if c = d

and if c ≠ d then there are [tex]\frac{p(p-1)}{2}[/tex] choices, the division of 2 eliminates repeated pairs.

Therefore there are p² - ( p + [tex]\frac{p(p-1)}{2}[/tex]) polynomials irreducible over Zp.

A polynomial is said to be irreducible if it cannot be factored into nontrivial polynomials over the same field. The property of irreducibly depends on the field or ring to which the coefficients are considered to belong. Irreducible polynomials appear naturally in polynomial factorization and algebraic field extension.

A polynomial expressible as the product of two or more polynomials of lower degree is known as Reducible polynomial.

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Rob says all numbers have an even number of factors. Enrique says some numbers have an odd number of factors. Who is correct?

Answers

Answer:

Enrique

Step-by-step explanation:

9 has the factors 1, 3 and 9.  That is an odd number of factors (3).

Which statement best describe a parallelogram a parallelogram? A.a quadrilateral with one pair of parallel sides
B.A quadrilateral with two pairs of parallel sides
C.A quadrillateral with two pairs of congruent sides. D.any four sided figure with opposites sides congruent

Answers

B.A quadrilateral with two pairs of parallel sides

How do you identify a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side. 360 degrees is the sum of all interior angles.

What is an example of a parallelogram?

Few examples of a parallelogram are rhombus, rectangle, and square.

A quadrilateral with both pairs of opposite sides parallel is known as a parallelogram.

Additionally, a parallelogram has the following qualities:

Congruent opposite angles;

The opposing factions are in agreement;

Additional angles can be found nearby;

The diagonals cut each other in half.

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Sofia and her children went into a grocery store that sells bananas for $0.80 each and mangos for $2 each. Sofia has $20 to spend and must buy a minimum of 12 bananas and mangos altogether. If xx represents the number of bananas purchased and yy represents the number of mangos purchased, write and solve a system of inequalities graphically and determine one possible solution.

Answers

Using graphical method to solve the system of inequality, the number of banana is 2 and mango is 10

System of Linear Inequality

A system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.

In this question, we can set the unknown variables as;

x = Number of bananay = Number of Mango

0.2x + 2y = 20 ...eq(i)

x + y ≥ 12 ..eq(i)

Solving x and y

This can be done graphically;

The number of banana and mango is approximately 2 and 10 respectively

Kindly find the attached graph below

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Which piece of information listed below does the central limit theorem allow us to disregard when working with the sampling distribution of the sample mean?A) all can be disregardedB) the mean of the populationC) the standard deviation of the populationD) the shape of the population

Answers

The shape of the population can be disregarded when working with sampling distribution of sample mean.

The correct option is Option D)

What is central limit theorem?

The central limit theorem in probability theory proves that, even if independent random variables are not normally distributed in themselves, in many cases, when they are added together, their correctly normalized sum tends toward a normal distribution.

As in the central limit theorem mean and standard deviation is given but there is not mention of shape of the distribution.

Hence shape of the distribution is not taken into considerations.

Therefore, The shape of the population can be disregarded when working with sampling distribution of sample mean.

The correct option is Option D)

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Winnie, a waitress, holds a 5.0-N tray stacked with twelve 3.5-N dishes in one hand. The
length of her arm from her hand to her elbow is 30.0 cm and her bicepts exert a force 5.0 cm
from her elbow, which acts as a fulcrum. How much force must her biceps exert to allow her to
hold the tray?

Answers

The force exerted by her biceps to allow her hold the tray is 282 N.

What is force?

Force is the product of mass and acceleration.

To calculate the force the biceps must exert to allow her hold the tray, we use the formula below.

Formula:

Fd = F'd'....................... Equation 1

Where:

F = Weight of the tray and the platesd = Distance of her hand to her elbowF' = Force exerted by the biceptsd' = Distance of her biceps to the elbow.

From the question,

Given:

F = 5+12(3.5) = 47 Nd = 30 cmd' = 5 cm

Substitute these values into equation 1 and solve for F'

47×30 = F'×5F' = 47×30/5F' = 282 N

Hence, the force exerted by her biceps is 282 N.

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according to a recent pew research center report, many american adults have made money by selling something online. in a random sample of 4579 american adults, 914 reported that they earned money by selling something online in the previous year. assume the conditions for inference are met. construct a 98% confidence interval for the proportion of all american adults who would report having earned money by selling something online in the previous year.

Answers

As per the 98% confidence interval for the proportion of all American adults who would report having earned money by selling something online in the previous year is (0.1859,0.2133).

Confidence interval:

In statistics, confidence interval is an estimate of an interval in statistics that may contain a population parameter.

Given,

According to a recent pew research center report, many American adults have made money by selling something online. in a random sample of 4579 American adults, 914 reported that they earned money by selling something online in the previous year. assume the conditions for inference are met.

Here we need to construct a 98% confidence interval for the proportion of all American adults who would report having earned money by selling something online in the previous year.

As per the given question, the value of

Confidence interval = 98%

Number of samples = 4579

Reported numbers = 914

Therefore, the number of failure is calculated as,

=> 4579 - 914

=> 3665

Here the sample proportion is the number of successes divided by the sample size:

=> 941/4579

=> 0.1996

Here for confidence level 1 − α = 0.98,

We have to determine zα / 2 ​= z0.01​ using the normal probability table in the appendix, we get

zα/2 ​= 2.33

Then the margin of error is calculated as,

E = 2.33 x √[0.1996 x (1 - 0.1996)]/4579

E = 0.0137

Then the boundaries of the confidence interval are then:

p⁻ˣ = 0.1996−0.0137 = 0.1859

p⁺ˣ = 0.1996+0.0137 = 0.2133

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select all of the factors of x3 5x2 2x 8 x 5 x3 x 4 x 1 x3 x 2

Answers

The all the factors of x³ + 5x² + 2x – 8 are (x+4)(x-1) and (x+2) , the correct options are (c) , (d) and (f) .

In the question ,

it is given that the equation is f(x) = x³ + 5x² + 2x – 8 ,

we have to find the factors of f(x) = x³ + 5x² + 2x – 8 .

We know that ,The Factor Theorem states if (x-t) is a factor of f(x) if and only if f(t)=0 .

So , Option(a)  Let g(x) = x + 5 be a factor

that means for  x = -5 , f(-5) = (-5)³ + 5(-5)² + 2(-5) – 8 = 2 ≠ 0 ,

hence it is not a factor .

In option (b) Let g(x) = x - 5 be a factor

that means For  x = 3 , f(3) = (3)³ + 5(3)² + 2(3) – 8 = 70 ≠ 0 ,

hence it is not a factor .

In option (c) Let g(x) = x + 4 be a factor

that means For  x = -4 , the equation is f(-4) = (-4)³ + 5(-4)² + 2(-4) – 8 = 0 ,

hence it is a factor .

In option (d) Let g(x) = x - 1 be a factor

that means For  x = 1 , f(1) = (1)³ + 5(1)² + 2(1) – 8 = 0 ,

hence it is a factor .

In option (e) Let g(x) = x + 3 be a factor

that means For  x = -3 , it becomes f(-3) = (-3)³ + 5(-3)² + 2(-3) - 8 = 4 ≠ 0 ,

hence it is not a factor .

In option (f) Let g(x) = x + 2 be a factor

that means For  x = -2 ,the equation f(-2) = (-2)³ + 5(-2)² + 2(-2) - 8 [tex]=[/tex] 0 ,

hence it is a factor .

Therefore , the factors are (x+2) , (x - 1) and (x + 4) .

The given question is incomplete , the complete question is

Select all of the factors of x³ + 5x² + 2x – 8.

(a) x + 5

(b) x – 3

(c) x + 4

(d) x – 1

(e) x + 3

(f) x + 2

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In a genetics class, 7 students have GREEN eyes, 4 students have BLUE eyes, and 10 have HAZEL eyes. If a single student is picked at random, what is the probability that their eyes are BLUE or HAZEL?

Provide the final answer as a simplified fraction.

Answers

Answer:

1/14

Step-by-step explanation:

all together the probability would be 1/21 because we're adding all the color eyes together. After that, it narrows to only blue and hazel which is 14 so the new probability is 1/14, so the answer is 1/14.

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